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2012 36 Juan Miguel Lujano Rojas Análisis y gestión óptima de la demanda en sistemas eléctricos conectados a la red y en sistemas aislados basados en fuentes renovables Departamento Director/es Ingeniería Eléctrica Bernal Agustín, José Luis Dufo López, Rodolfo Director/es Tesis Doctoral Autor Repositorio de la Universidad de Zaragoza – Zaguan http://zaguan.unizar.es UNIVERSIDAD DE ZARAGOZA Departamento Director/es Juan Miguel Lujano Rojas ANÁLISIS Y GESTIÓN ÓPTIMA DE LA DEMANDA EN SISTEMAS ELÉCTRICOS CONECTADOS A LA RED Y EN SISTEMAS AISLADOS BASADOS EN FUENTES RENOVABLES Director/es Ingeniería Eléctrica Bernal Agustín, José Luis Dufo López, Rodolfo Tesis Doctoral Autor 2012 Repositorio de la Universidad de Zaragoza – Zaguan http://zaguan.unizar.es UNIVERSIDAD DE ZARAGOZA Departamento Director/es Director/es Tesis Doctoral Autor Repositorio de la Universidad de Zaragoza – Zaguan http://zaguan.unizar.es UNIVERSIDAD DE ZARAGOZA Tesis Doctoral Análisis y Gestión Óptima de la Demanda en Sistemas Eléctricos Conectados a la Red y en Sistemas Aislados Basados en Fuentes Renovables Autor Juan Miguel Lujano Rojas Directores José Luis Bernal Agustín Rodolfo Dufo López Departamento de Ingeniería Eléctrica 2012 Esta tesis se presenta en la modalidad de compendio de publicaciones. Artículos en revistas con índice de impacto SCI: 1. Lujano-Rojas JM, Dufo-López R, Bernal-Agustín JL. Optimal sizing of small wind/battery systems considering the DC bus voltage stability effect on energy capture, wind speed variability, and load uncertainty. Applied Energy 2012;93:404-412. 2. Lujano-Rojas JM, Monteiro C, Dufo-López R, Bernal-Agustín JL. Optimum load management strategy for wind/diesel/battery hybrid power systems. Renewable Energy 2012;44:288-295. 3. Lujano-Rojas JM, Monteiro C, Dufo-López R, Bernal-Agustín JL. Optimum residential load management strategy for real time pricing (RTP) demand response programs. Energy Policy 2012;45:671-679. Artículos en congresos internacionales: 4. Lujano-Rojas JM, Dufo-López R, Bernal-Agustín JL. Optimal design of PV/Wind/Battery systems by genetic algorithms considering the effect of charge regulation. International Conference on Mechanical and Electronic Engineering (ICMEE 2012). Se publicará en Lecture Notes in Electrical Engineering. 5. Lujano-Rojas JM, Dufo-López R, Bernal-Agustín JL. A qualitative evaluation of operational conditions in PV/Wind/Battery systems. AsiaPacific Power and Energy Engineering Conference (APPEEC 2012). Disponible en IEEEXplore. 6. Lujano-Rojas JM, Bernal-Agustín JL, Dufo-López R, Domínguez-Navarro JA. Forecast of hourly average wind speed using ARMA model with discrete probability transformation. Lecture Notes in Electrical Engineering 98. Springer-Verlag; 2011. p. 1003-1010. Los directores de la tesis, el Dr. José Luis Bernal Agustín y el Dr. Rodolfo Dufo López, Profesores del Departamento de Ingeniería Eléctrica de la Universidad de Zaragoza, Hacen constar: Que D. Juan Miguel Lujano Rojas, Ingeniero Electricista por la Universidad Simón Bolívar de Venezuela, ha realizado bajo su dirección y supervisión la presente tesis Doctoral que lleva por título: “Análisis y gestión óptima de la demanda en sistemas eléctricos conectados a la red y en sistemas aislados basados en fuentes renovables”, y autorizamos su presentación en la modalidad de compendio de publicaciones. Y para que así conste a los efectos oportunos, firmamos la presente autorización. Zaragoza, 28 de mayo de 2012 ____________________________ _________________________ Fdo.: Dr. José Luis Bernal Agustín Fdo.: Dr. Rodolfo Dufo López Introducción 1 1. Introducción La energía es un instrumento fundamental en el desarrollo social y productivo de cualquier región del mundo. Durante mucho tiempo el consumo de energía a nivel mundial se ha mantenido en constante crecimiento. Según la Administración de Información Energética de Estados Unidos (EIA, U.S. Energy Information Administration) [1], se espera que el consumo mundial de energía alcance 770 cuatrillones de BTU en el año 2035, lo cual representa un aumento del 53% desde el año 2008. Este aumento se debe al robusto crecimiento económico y expansión poblacional de algunos países en vías de desarrollo, mientras que en aquellos países con economías más avanzadas, como por ejemplo los pertenecientes a la Organización para la Cooperación y Desarrollo Económicos (OCDE), la recesión económica mundial ha dado lugar a un crecimiento más lento en el consumo energético. Como puede observarse en la Figura 1, se estima que la demanda de energía en países pertenecientes a la OCDE puede crecer según una tasa promedio del 0,6% anual, mientras que el crecimiento en el consumo de energía en los países que no pertenecen a la OCDE se estima que puede ser de un 2,3% anual [1]. Figura 1. Consumo de energía mundial entre 1990 y 2035 [1] En la situación actual, de recesión económica mundial, China e India mantienen un crecimiento económico acompañado de un aumento significativo en sus consumos de energía. En 2008 el consumo de energía conjunto de ambos países representó el 21% del consumo energético mundial, mientras que para 2035 se estima que ambas naciones consumirán el 31%. Por otra parte, en 2009 Estados Unidos no lograba superar la recesión económica, mientras que China e India alcanzaban crecimientos económicos 0 100 200 300 400 500 600 700 800 900 1990 2000 2008 2015 2020 2025 2030 2035 Consumo energía (cuatrillón BTU) OCDE No-OCDE Total 2 Introducción del 12,4% y 6,9%, respectivamente. Como puede observarse en la Figura 2, esto trajo como consecuencia que, por primera vez, el consumo energético de China fuera superior al consumo energético de los Estados Unidos. Se estima que para 2035 el consumo de energía en China será un 68% mayor que el consumo energético de los Estados Unidos [1]. Figura 2. Consumo de energía en Estados Unidos, China e India [1] De acuerdo a las futuras tendencias (Figura 3), se estima que el consumo de combustibles líquidos se incremente, en promedio, un 1% anual, debido a que probablemente los precios del petróleo y otros combustibles líquidos se mantengan relativamente altos. Figura 3. Consumo de energía mundial por tipo de combustible [1] El consumo mundial de gas natural se espera que aumente, en promedio, un 1,6% anual a causa de su uso en procesos industriales y en la generación de energía eléctrica. El consumo de carbón se espera que aumente, en promedio, un 1,5% anual a causa del 0 50 100 150 200 250 1985 1990 1995 2000 2005 2010 2015 2020 2025 2030 2035 2040 Consumo energía (cuatrillón BTU) China India Estados Unidos 0 50 100 150 200 250 1980 1990 2000 2010 2020 2030 2040 Consumo energía (cuatrillón BTU) Combustibles líquidos Gas natural Carbón Nuclear Renovables Introducción 3 acelerado ritmo en el crecimiento de las economías de los países ubicados en Asia y que no pertenecen a la OCDE. En cuanto al crecimiento de la energía nuclear, todavía existe una elevada incertidumbre, relacionada con la seguridad de las plantas y el tratamiento de los residuos radiactivos, que podría dificultar la instalación de nuevas centrales. Las energías renovables son las fuentes de energía con mayor crecimiento, estimándose que la energía que proporcionan aumentará un 2,8% anual. Esta previsión de aumento se basa en considerar que los precios de los combustibles fósiles se van a mantener relativamente altos, en el impacto medioambiental producido por el uso de combustibles fósiles y en los incentivos ofrecidos por algunos países [1]. Dentro del conjunto de las energías renovables, la energía eólica ha experimentado, durante los últimos años, un importante desarrollo. En la Figura 4 se muestra la evolución de la potencia eólica instalada a nivel mundial, estimándose que puede alcanzar 425 GW para el año 2015 [2]. Figura 4. Capacidad instalada mundial de energía eólica [3] Los cinco países con mayor potencia instalada son China, Estados Unidos, Alemania, España e India. China es el mercado de energía eólica más grande del mundo, con una potencia instalada de 42,3 GW en 2010. Debido a su gran potencial eólico, se espera que para 2015 alcance los 90 GW, y para 2020 los 200 GW de potencia instalada. En 2011 Estados Unidos alcanzó los 40,2 GW, suministrando alrededor del 2% de su consumo de energía eléctrica, y se espera que para el año 2030 la potencia instalada aumente y sea capaz de suministrar el 20% de la demanda. Alemania y España son los principales productores de energía eólica de Europa. En 2010 Alemania alcanzó los 27,2 GW de potencia instalada, suministrando el 6,2% de la demanda eléctrica nacional, 0 50 100 150 200 250 300 350 400 450 1985 1990 1995 2000 2005 2010 2015 2020 Capacidad instalda (GW) 4 Introducción y se espera que para 2020 la potencia instalada de parques eólicos en tierra ascienda a 45GW, mientras que la potencia instalada de parques eólicos en el mar se espera que ascienda a 10 GW. En 2010 España alcanzó 20,7 GW de potencia instalada, suministrando el 16,6% de la demanda eléctrica nacional. Para 2020 se espera que la potencia instalada de parques eólicos en tierra alcance 40 GW, mientras que en el mar se estima que puede llegar a 5 GW. En 2010 la India alcanzó 13,1 GW de potencia instalada [2]. Como puede observarse en la Figura 5, la energía solar fotovoltaica ha crecido significativamente en los últimos años. Este crecimiento se ha debido a la reducción de sus costes y a los incentivos gubernamentales ofrecidos en algunos países con el fin de fomentar su uso y desarrollo, alcanzando 40 GW de potencia instalada en 2010, de los que el 85% corresponde a sistemas conectados a la red [4]. Figura 5. Potencia instalada mundial de energía solar fotovoltaica [4] En la Figura 6 se muestran los principales productores de energía solar fotovoltaica. Figura 6. Potencia instalada de energía solar fotovoltaica por país [5] Alemania (44%) Resto del mundo (6%) Korea del sur (2%) Otros UE (2%) Bélgica (2%) China (2%) Francia (3%) España (10%) Japón (9%) Italia (9%) Estados Unidos (6%) República Checa (5%) 0 5 10 15 20 25 30 35 40 45 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 Capacidad instalada (GW) Introducción 5 La República Checa ha elevado su potencia instalada desde casi un valor nulo en 2008 hasta 2 GW en 2010, mientras que la India ha acumulado 102 MW, y China 893 MW. Los países con mayor potencia instalada de energía solar fotovoltaica son Alemania, Italia, España y Estados Unidos. Muchos de los sistemas fotovoltaicos conectados a la red se encuentran ubicados en países pertenecientes a la OCDE, mientras que algunos de los países en vías de desarrollo, liderados por China e India, presentan un mayor desarrollo de sistemas aislados de la red, a causa de sus extensas zonas rurales [5]. De acuerdo con lo expuesto anteriormente, la situación energética actual se caracteriza por un constante aumento de la demanda de energía como consecuencia del crecimiento económico de algunos de los países en vías de desarrollo, lo que a su vez trae como consecuencia un incremento significativo en la capacidad de generación, siendo así posible satisfacer de forma segura y fiable esta creciente necesidad de energía. En este aumento de la capacidad de generación de electricidad intervienen diferentes fuentes de energía, como el gas natural, el carbón, la energía nuclear, los derivados del petróleo y las energías renovables. Respecto a estas últimas, se espera que tengan un acelerado desarrollo, impulsado principalmente por aspectos medioambientales, el agotamiento de las reservas de petróleo y gas, y los avances tecnológicos que han permitido una reducción significativa en sus costes. Tal y como se ha indicado anteriormente, la energía eólica y la energía solar fotovoltaica tienen un gran interés en todo el mundo. En el caso específico de la energía eólica, que de acuerdo a las Figuras 4 y 5 supera en potencia instalada a la energía solar a nivel mundial, tiene un efecto importante sobre el sistema eléctrico por dos motivos: el nivel de penetración y el grado de flexibilidad del sistema [6]. Por un lado, si se incrementa el nivel de penetración, el impacto sobre el sistema eléctrico será mayor, es decir, el uso de la energía eólica trae consigo un grado de incertidumbre, relacionado con su naturaleza aleatoria, que puede incrementar de manera significativa los costes de producción cuando el nivel de penetración es elevado. Las fluctuaciones de la potencia generada por los parques eólicos afectan a otras unidades del sistema de potencia que pueden ser despachadas y controladas. Esta intermitencia de la potencia proveniente de los parques eólicos puede obligar a las centrales de generación convencional a operar en un punto subóptimo. Por otro lado, cuanta mayor flexibilidad tenga el sistema, se puede alcanzar un mayor grado de integración de energía eólica, ya que durante los periodos de baja demanda y abundante 6 Introducción recurso eólico es posible reducir la potencia proveniente de los parques eólicos para que el sistema eléctrico funcione de forma estable y fiable. La decisión de reducir la potencia proveniente de los parques eólicos depende del nivel de penetración de la energía eólica en el sistema y del grado de flexibilidad que ofrezca el mismo [6]. Además, los problemas derivados de las restricciones impuestas a los precios de la energía, tales como el uso de tarifas fijas y la imposición de límites superiores a los precios de la energía, han dado lugar a una significativa diferencia entre los costes de generación y el precio que deben abonar los consumidores. Esta diferencia ha provocado que en muchos países la tasa de crecimiento de la demanda sea mayor a la tasa a la cual crece la potencia instalada de generación de electricidad, es decir, el crecimiento en la capacidad de generación se ve afectado por el hecho de que las tarifas de electricidad no reflejan el verdadero coste de generación. Mientras que el desarrollo de la población y el crecimiento económico requieren del consumo de grandes cantidades de energía, la liberalización del sector de la energía es vista como una política arriesgada que podría dar lugar a la pérdida del beneficio por parte de los consumidores a corto plazo, lo que a su vez pone en peligro la continuidad del desarrollo debido a que los procesos de reestructuración se ven inhibidos [7]. Como solución a los problemas derivados de la creciente penetración de la energía eólica en la red y del aumento constante de la demanda, algunos autores han propuesto el uso de almacenamiento masivo de energía como una opción que permitiría convertir a las fuentes de energía con naturaleza aleatoria en centrales de generación controlables. Anagnostopoulos et al. [8] y Varkani et al. [9] han propuesto un sistema basado en energía eólica e hidráulica que está diseñado para recuperar y aprovechar la energía eléctrica excedente que proviene de los parques eólicos. Con esta idea se pretende incrementar la potencia instalada de energía eólica y los beneficios económicos provenientes de la misma. Recientemente, Fertig et al. [10] han planteado utilizar un sistema de almacenamiento de energía mediante aire comprimido. Bernal-Agustín et al. [11] proponen almacenar la energía que excede de los parques eólicos en un tanque de hidrógeno y utilizarla para satisfacer la demanda máxima. Dufo-López et al. [12] han propuesto una idea similar pero utilizando diferentes tipos de baterías. Por otro lado, el grado de flexibilidad del sistema puede aumentarse mediante la Gestión de la Demanda (DSM, Demand Side Management) o mediante la implementación de programas que Introducción 7 incentiven a los usuarios a utilizar la energía eléctrica durante los momentos en los cuales esta es abundante [6], lo que permitiría utilizar la energía excedente proveniente de centrales eólicas. Este tipo de programas se conocen como Programas de Adaptación de la Demanda (Demand Response Programs). En esta tesis doctoral se propone un análisis profundo del funcionamiento de los sistemas eléctricos residenciales aislados y conectados a la red eléctrica basados en fuentes renovables, así como el desarrollo de estrategias de gestión de la demanda que ayuden al usuario a encontrar la manera óptima en la que sus electrodomésticos podrían ser utilizados. Los principales resultados y aportaciones obtenidos en este trabajo se presentan de forma clara y concisa en los artículos científicos que se encuentran a continuación. Publicaciones 9 Publicaciones que forman el compendio Página 1. Lujano-Rojas JM, Dufo-López R, Bernal-Agustín JL. Optimal sizing of small wind/battery systems considering the DC bus voltage stability effect on energy capture, wind speed variability, and load uncertainty. Applied Energy 2012;93:404-412. 2. Lujano-Rojas JM, Dufo-López R, Bernal-Agustín JL. Optimal design of PV/Wind/Battery systems by genetic algorithms considering the effect of charge regulation. International Conference on Mechanical and Electronic Engineering (ICMEE 2012). Se publicará en Lecture Notes in Electrical Engineering. 3. Lujano-Rojas JM, Dufo-López R, Bernal-Agustín JL. A qualitative evaluation of operational conditions in PV/Wind/Battery systems. Asia-Pacific Power and Energy Engineering Conference (APPEEC 2012). Disponible en IEEEXplore. 4. Lujano-Rojas JM, Dufo-López R, Bernal-Agustín JL. Probabilistic modeling and analysis of PV/Wind/Diesel/Battery systems. Applied Energy (En revisión). 5. Lujano-Rojas JM, Bernal-Agustín JL, Dufo-López R, Domínguez-Navarro JA. Forecast of hourly average wind speed using ARMA model with discrete probability transformation. Lecture Notes in Electrical Engineering 98. Springer-Verlag; 2011. p. 1003-1010. 6. Lujano-Rojas JM, Monteiro C, Dufo-López R, Bernal-Agustín JL. Optimum load management strategy for wind/diesel/battery hybrid power systems. Renewable Energy 2012;44:288-295. 7. Lujano-Rojas JM, Monteiro C, Dufo-López R, Bernal-Agustín JL. Optimum residential load management strategy for real time pricing (RTP) demand response programs. Energy Policy 2012;45:671-679. 11 21 29 33 49 57 65 (8), the reduction of the battery lifetime due to changes in the temperature is only about 2.2%. This result suggests that in some cases, the influence of ambient temperature on battery lifetime could be neglected. To illustrate the methodology for the stochastic optimization using the wind/battery model presented in this paper, another case study is analyzed. The wind turbines have a power between 100 W and 600 W, 12 V, a lifetime of 20 years, and are installed at 10 m. The cost of this type of wind turbine (including the charge controller) is between 720 €and 3045 €. The replacement is assumed to be 70% of capital cost. The battery bank capacities are between C 10 = 100 A h and C 10 = 1000 A h, with 300 cycles at 70% depth of discharge, floating lifetime of 9 years, 12 V, and cost of 250 €/ kW h. The operation and maintenance costs for the wind turbines and lead acid batteries were negligible. The economic analysis included an inflation rate of 3% and a nominal interest rate of 4.5% for a project lifetime of 35 years. The variability of the wind speed and load uncertainty were considered using the Monte Carlo simulation method. The hourly temperature time series of 2005 was used, but the ambient temperature variability was not considered. The wind speed simulation model explained in Section 3 was used to generate 100 wind speed time series synthetically (i.e., 100 years). Similarly, 100 load time series with 10% error on the load profile of Fig. 6 was used. As mentioned in Section 2.2, 17.5% of error in the Ah throughput model was considered. Table 2 ARMA model parameters. Season u 1 u 2 u 3 u 4 u 5 u 6 u 7 u 8 u 9 r Winter 0.6563 0.0786 0.1581 0.0501 0.0105 0.031 0.0275 0.0215 0.0655 0.4184 Spring 0.6422 0.1336 0.0818 0.011 0.0109 0.0187 0.0168 0.0326 0.0562 0.5312 Summer 0.7049 0.1039 0.0907 0.0055 0.0405 0.0893 0.0305 – – 0.509 Autumn 0.6429 0.1435 0.0567 0.0249 0.0368 0.0156 0.0133 0.0428 – 0.5171 Table 3 Comparison of observed and simulated values. Season Average wind speed Standard deviation kc Observed Simulated Observed Simulated Observed Simulated Observed Simulated Winter 4.9067 4.9159 4.0393 4.05 1.3408 1.3391 5.8463 5.8531 Spring 4.5329 4.5412 3.0464 3.0569 1.6321 1.6286 5.1951 5.2015 Summer 5.133 5.14 2.8309 2.8374 1.9503 1.9462 5.8613 5.8664 Autumn 4.0838 4.0917 3.0805 3.0915 1.4985 1.4955 4.8064 4.8123 100 150 200 250 300 350 400 450 500 550 600 0 500 1000 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 x 10 4 Wind turbine capacit y (W) Batter bank capacity (Ah) Net present cost ( ) Fig. 11. Expected value of net present cost. 0 5 10 15 20 25 30 123456789101112 Month Temperature (ºC) Fig. 10. Monthly average temperature in Zaragoza. Table 1 Characteristics and diagnostic checking of the ARMA model. Season pqL–p–q v 2 ( a = 0.05) Sm Winter 9 0 207 241.5657 239.1245 0.3724 Spring 9 0 212 246.968 212.4908 0.4533 Summer 7 0 214 249.1275 242.3096 0.542 Autumn 8 0 211 245.8879 208.6985 0.4597 410 J.M. Lujano-Rojas et al. / Applied Energy 93 (2012) 404–412 17 P ublicaciones The ARMA model was fitted to a wind speed time series of 2005 for each season of the year. Table 1 shows the order of the ARMA model, the selected power of transformation, and diagnostic checking of results for each season. A value of D x= 0.0001 was used. Table 2 shows the values of the parameters of the ARMA model. Table 3 shows the comparison between observed and simulated values for each season. The results obtained by stochastic analysis of different system configurations are shown in Figs. 11 and 12, which present the relationship between the expected value of net present cost and energy index of unreliability with a confidence level of 1%. Both figures represent the expected values, the upper limit and the lower limit. These results show that an uncertainty of 17.5% in the battery bank lifetime calculated using the Ah throughput model implies about 12% uncertainty in the net present cost. The uncertainty in the system reliability is directly related to the battery bank size and the wind turbine size. For example, in the case of very low battery bank capacity and wind turbine power, there is a high probability that the annual energy demand cannot be satisfied (the system reliability has a very low uncertainty), while if the system storage capacity and wind power generation are increased, under the weather conditions presented in the location of study, the uncertainty presents a higher value. 6. Conclusions A mathematical model for the stochastic simulation and sizing of small wind energy systems has been presented. The model considers the loss of energy due to voltage stability, coulombic efficiency in charge and discharge process, temperature effects on the battery bank capacity, wind speed variability, and load uncertainty. No other previous work has considered all the aspects included in this paper. As a study case, a small wind energy system installed in Zaragoza, Spain, was analyzed. The wind/battery system model presented in this paper was compared with the simulation and optimization tool HOMER, which does not consider the charge controller operation nor the influence of temperature on battery bank capacity, and it considers the square root of the battery roundtrip efficiency instead of the coulombic efficiency. The results have shown that if the analysis is carried out without considering the charge controller operation nor the influence of temperature on the battery bank nor the coulombic efficiency, the reliability level obtained in the operation of the physical system could be lower than that obtained in the analysis. In the case of study, an increment of 25% in the capacity of the battery bank would be required to reach a reliability level of 90%. Different system configurations with wind turbine capacities between 100 W and 600 W and battery bank capacities between 100 A h and 1000 A h were analyzed using Monte Carlo Simulation approach. The wind speed variability was considered using an ARMA model; the uncertainties in the load profile and battery bank lifetime have been considered using random numbers. The results show that an uncertainty of 17.5% in the battery bank lifetime calculated using the Ah throughput model implies about 12% uncertainty in the net present cost. According to the monthly temperature behavior of Zaragoza, it does not represent an important factor in the reduction of the battery bank lifetime. Acknowledgment This work was supported by the ‘‘Ministerio de Ciencia e Innovación’’ of the Spanish Government under Project ENE2009-14582C02-01. References [1] Independent Evaluation Group. The welfare impact of rural electrification: a reassessment of the costs and benefits. The World Bank; 2008. [2] Urban F, Benders RMJ, Moll HC. Energy for rural India. Appl Energy 2009;86(1):S47–57. [3] Fleck B, Huot M. Comparative life-cycle assessment of a small wind turbine for residential off-grid use. 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Appl Energy 2009;86(2):163–9. [39] Stevens JW, Corey GP. A study of lead–acid battery efficiency near top-ofcharge and the impact on PV system design. IEEE Photovoltaic Spec Conf 1996. [40] Sexton ED, Olson JB. Coulombic efficiency of a sealed, thin plate, spiral lead– acid battery. In: IEEE battery conference on applications and advances; 1998. 412 J.M. Lujano-Rojas et al. / Applied Energy 93 (2012) 404–412 19 P ublicaciones Optimal Design of PV/Wind/Battery Systems by Genetic Algorithms Considering the Effect of Charge Regulation Juan M. Lujano Rojas, Rodolfo Dufo-López, José L. Bernal-Agustín Department of Electrical Engineering, University of Zaragoza, Calle María de Luna 3, 50018, Spain [email protected] {rdufo, jlbernal}@unizar.es Abstract. Hybrid power systems (HPS) play an important role in the social development of areas located far from the electric grid. The optimal sizing of these systems is difficult to determine due to the variable nature of renewable energy resources and the complex behavior of their components. An important device of HPS is the charge controller as it protects the battery bank against extreme operational conditions, directly affecting the acceptance of charge from the battery bank and consequently the ability of the system to store energy. This paper presents a study about optimization of stand-alone PV/wind/battery hybrid power systems based in a genetic algorithm that considers the effect of charge regulation in the energy capture of the battery bank. Keywords: Genetic Algorithms, Hybrid power systems. 1 Introduction Autonomous renewable energy systems are an important option for rural electrification in many places around the world. Designing these types of systems is difficult due to the variability of renewable resource and the complex behavior of some components. Many algorithms have been proposed to find the optimal combination of power sources to meet energy demands. The following possible combinations were tested: [1] direct algorithm [2], design space methodology [3], particle swarm optimization [4], linear programming [5], simulated annealing [6], genetic algorithm [7], and hybrid genetic-simulated annealing [8]. The charge controller protects the battery bank against excessive charge or discharge conditions using voltage set points. For example, when the battery bank voltage reaches a high voltage set point, the charge controller disconnects the renewable generator, and when low voltage set point is reached, the charge controller disconnects the load. In systems with high power from a renewable source, high charge currents produce a premature disconnection of renewable generators; consequently, the state of charge of the battery bank results in low values [9]. In this paper, a study about optimization of hybrid power systems with photovoltaic panels, wind turbines, an inverter, and a lead acid battery bank using a genetic algorithm, which considers the influence of charge controller in the performance of the system, is carried out. The paper is organized as 21 P ublicaciones follows: Section 2 describes the mathematical model of a PV/wind/battery system, and the implementation of the genetic algorithm is explained in Section 3. A case of study is analyzed in Section 4, and conclusions are presented in Section 5. 2 PV/Wind/Battery System Model The next sections describe mathematical models for each components of a typical hybrid system with several photovoltaic panels, wind turbines, a lead acid battery bank, an inverter, and a load coupled in AC. 2.1 Wind Turbine Wind turbines are commonly modeled based on their power curve. Fig. 1 shows several wind turbines with small capacities. Fig. 1. Typical wind turbines power curves. 2.2 Photovoltaic Panel The power of the photovoltaic generator is calculated using equations (1) and (2) [10]. >@ ¿ ¾ ½ ¯ ®  )25(1 c STC STCPV T G G PP D (1) 0 1 2 3 4 5 6 7 8 9 05 10 15 20 25 30 Wind speed (m/s) Power (kW) 22 P ublicaciones G NOCT TT ac ¸ ¹ · ¨ © §  800 20 (2) where G is the incident solar radiation in W/m2, GSTC is the solar radiation at standard test conditions, Tc is cell temperature ºC, Ta is ambient temperature in ºC, Į is the temperature coefficient in %/ºC, and NOCT is the nominal operation cell temperature in ºC. 2.3 Lead Acid Battery Bank In this paper, a simplification of the general lead acid battery model proposed in [11] and [12] is used. The capacity of the battery is calculated using equations (3) and (4). )005.01(67.1 10 aT TCC ' (3) 9.0 10 67.01 ¸ ¸ ¹ · ¨ ¨ © §  I I C CT (4) where C is the capacity at constant current I, CT is the maximum capacity, C10, and I10 are the capacity and discharge current after 10 hours, respectively. The efficiency (Șb) during charge (I>0) and discharge (I<0) is calculated using Equation (5) [12].  ° ¯ ° ®   ! » ¼ º « ¬ ª ¸ ¸ ¹ · ¨ ¨ © §   01 01 55.0/ 73.20 exp1 10 I ISOC II b K (5) where SOC is the state of charge calculated according to Equation (6) [12]. ° ¯ ° ®   ! 01 0 I C Q I C Q SOC b b K K (6) where Q=|I|t is the charge supplied or subtracted during the charge or discharge processes, respectively. The charge regulator disconnects the renewable generators when the battery bank voltage reaches a specific value. Equation (7) [11] allows us to estimate the SOC in this moment and then represents the effect of charge regulation in the acceptance of the battery bank charge. )025.01)(036.0 )/1( 48.0 1 6 ()16.02( 2.16.0 10 a T T CQIC I C Q V'     (7) where V is battery voltage per cell during the charge process and ¨Ta=Ta-25. 23 P ublicaciones 2.4 Inverter The efficiency (Șp) of the inverter could be described using Equation (8). linv l pPP P )1( ]H K  (8) where Pl is the alternant current load, Pinv is the rated power of the inverter, İ and ȗ are parameters determined using experimental data. 3 Mono-Objective Optimization The problem of finding a combination of photovoltaic panels, wind turbines, and lead acid batteries that minimize the costs of the system, thus guaranteeing a determined level of reliability, is solved using the genetic algorithm described below. 3.1 Optimization Criteria The variables considered are net present cost (NPC) and energy index of unreliability (EIU). NPC have been defined according to equations (9) and (10) [1]. ),( )( jiCRF AMCARCACC NPC  (9) 1)1( )1( ),(   j j i ii jiCRF (10) where ACC is the annualized capital cost, ARC is the annualized replacement cost, AMC is the annualized maintenance cost, CRF(i,j) is the capital recovery factor, i is the real interest rate, and j is the project lifetime. EIU have been defined according to Equation (11). 0 E ENS EIU (11) where ENS is the energy not supplied and E0 is the total energy demanded. 3.2 Genetic Algorithm Implementation To find the combination of renewable energy sources and lead acid batteries that minimize the NPC during the j years, the genetic algorithm could be implemented in the following ways [13]: 1. Adjust the number of individuals in the population (Ȍ), number of generations (Ȥ), crossing rate (ø), mutation rate (Ȧ), and EIU required (EIU0). 24 P ublicaciones 2. An individual is represented as an integer vector |ij|ȕ|Ȝ|ȝ|į|Ȗ| that contains a representation of solar generator manufacturer (ij), number of PV panels in parallel (ȕ), battery manufacturer (Ȝ), number of batteries in parallel (ȝ), wind generator manufacturer (į), and number of wind turbines in parallel (Ȗ). The initial population with Ȍ individuals is randomly obtained. 3. For each individual in the population, the NPC and EIU are evaluated, and then an arbitrarily high value of NPC is assigned for those individuals with an EIU higher than EIU0. 4. With k=1,2,..,Ȍ, the aptitude (ĭk) of individual k is obtained according to its rank in the population, rank 1 for the best individual and rank Ȍ for the worst individual. Fitness function is shown in (12). ¦   Ȍ k k kȌ kȌ ĭ 1 )1( )1( (12) 5. Reproduction, crossing, and mutation are carried out to obtain the next generation. Reproduction is done using the roulette-wheel methods, crossing is done using the one crossing point method, and mutation is done by randomly changing the components of some individuals. 6. The steps described from 3 to 5 are repeated until Ȥ generation is reached. The best solution obtained is that which has a lower NPC and an EIU at least lower than the required EIU0. 4 Case Study A PV/wind/battery system installed in the Netherlands in 2009 was analyzed. The installation site is the K13 meteorological station. Wind speed time series are provided by the Royal Netherlands Meteorological Institute [14]. The hourly solar radiation time series was generated synthetically according to Graham and Hollands’ methodology [15] using information provided by NASA [16] for this location. The load is assumed to require 900W over 24 hours. The genetic algorithm explained in Section 3 was implemented in MATLAB to find the combination of PV panels, wind turbines, and battery bank capacity that guarantee at least EIU=0.1. The wind turbines considered are showed in Figure 1. For the PV generator, capacities between 0.175kW and 4.375kW were considered, and for the lead acid battery bank, capacities between 200Ah and 3,000Ah and strings between 1 and 10 were considered. The rated capacity of the inverter is 900W with İ=0.0064 and ȗ=0.0942. The economic analysis was carried out considering 35 years of project lifetime, a 5% interest rate, and a 3% inflation rate. For wind turbines, we considered 15 years of lifetime and capital cost between 1700€ and 30000€, and operation and maintenance cost between 50€ and 140€, respectively. The lifetime of the inverter is estimated at 20 years and its acquisition cost is estimated at 700€; the operation and maintenance cost is considered negligible. The lifetime of considered batteries is between 8 years and 20 years, and its capital cost is considered 250€/kWh. For a PV panel, its lifetime is considered 20 years, a capital cost of 4€/W is used, and operation and maintenance costs are considered negligible. Fig. 2 shows the evolution of net 25 P ublicaciones present cost in the optimization for 100 individuals in the population, 10 generations, crossing rate of 0.9, and a mutation rate of 0.01. After 10 generations, a hybrid system with 11 PV panels of 175W each, a wind turbine of 1kW, a battery bank of 1,000Ah, and a floating lifetime of 20 years is suggested. The EIU value obtained is 0.0675. Fig. 2. Evolution of Net Present Cost in the optimization. 5 Conclusions In this paper, a genetic algorithm was used to find the optimal combinations of photovoltaic panels, wind turbine, and battery bank capacity in a typical hybrid power system to guarantee a determined level of reliability. The model presented in this paper is able to consider the coulombic efficiency, the charge controller operation, and many different types of photovoltaic panels, wind turbines, and battery bank capacities in the mono-objective optimization problem. These characteristics allow us to obtain fast and realistic results from the sizing process. Acknowledgments This work was supported by the “Ministerio de Ciencia e Innovación” of the Spanish government under Project ENE2009-14582-C02-01. Furthermore, the authors would like to thank the Royal Netherlands Meteorological Institute and NASA for providing the wind speed and solar radiation data for the case of study presented in this paper. 1 2 3 4 5 6 7 8 9 10 3 3.2 3.4 3.6 3.8 4x 10 Net Present Cost (€) 4 Generations 26 P ublicaciones Probabilistic Modeling and Analysis of PV/Wind/Diesel/Battery Systems Juan M. Lujano-Rojas, Rodolfo Dufo-López, José L. Bernal-Agustín1 Department of Electrical Engineering - University of Zaragoza Calle María de Luna, 3. 50018 Zaragoza (Spain) [email protected]; [email protected], [email protected] Abstract This paper presents a probabilistic model for hybrid power systems considering photovoltaic panels, wind turbine, conventional diesel or gasoline generator, and a battery bank (PV/Wind/Diesel/Battery system). The model can consider the main sources of uncertainty related to renewable resources, fuel cost, the battery bank's lifetime, energy demand, charge controller operation and coulombic efficiency. As a case study, a hybrid system installed in Zaragoza (Spain) is analyzed. First, the impact of charge controller operation and coulombic efficiency are studied through comparative analysis of the presented model and HOMER model, which is a less accurate model because it does not consider the charge controller operation or the dependence between the coulombic efficiency and state of charge. The results show a difference between both models of approximately 33% in the number of hours of operation of a conventional generator, 31% in fuel consumption, and 31% in net present cost for hybrid power system configurations with low storage capacity. However, these differences are lower when the capacity of the battery bank is incremented because the charge currents are reduced, the acceptance of charge by the battery bank is improved, and the effect of the charge controller is minimized. Furthermore, a probabilistic analysis has been carried out for different sizes of battery banks, obtaining the uncertainty in the net present cost, which depends on fuel cost and the battery bank's lifetime. Keywords: hybrid power systems, coulombic efficiency, charge controller, probabilistic modeling. 1. Introduction Stand-alone hybrid power systems are useful for satisfying energy demands in remote areas where there is not access to electricity. In this context, several models and optimization techniques have been carried out to sizing hybrid power systems. HOMER [1] is a very frequently used computational tool for hybrid power system design. This software evaluates all possible combinations of components, of the hybrid system, to determine the system configuration that minimizes the net present cost. Furthermore, this tool can consider hybrid power systems, including photovoltaic (PV) panels, wind turbines, small hydro, biomass power, lead-acid batteries, a diesel generator, fuel cells, and hydrogen storage. Another tool, HOGA [2], is a computer program for optimal sizing of hybrid power systems, which includes wind turbines, PV panels, small hydro, lead-acid batteries, a diesel generator, fuel cells, and hydrogen storage. This computational tool uses genetic algorithms to obtain the optimal system, taking much less computational time than evaluating all possible combinations. HOGA can consider the net present cost, energy not supplied, and CO2 emissions as objectives in the monoor multi-objective optimization. 1Corresponding author. Tel.: +34 976761921; fax: +34 976762226. E-mail address: jlb[email protected] (J.L. Bernal-Agustín). 33 P ublicaciones In addition to the two mentioned tools, several researchers have applied other techniques for the design of hybrid systems. This way, Boonbumroong et al. [3] presented an application of the Particle Swarm Optimization (PSO) and the constriction coefficient algorithm to design a typical hybrid power system. This methodology was applied to size a hybrid system that includes PV arrays, wind turbines, a battery bank, and an inverter. Reached results were compared with the one obtained using the rule-ofthumb method and HOMER software, concluding that the PSO algorithm substantially reduces the required time to find the optimal configuration. Belfkira et al. [4], using the DIviding RECTangles (DIRECT) algorithm, developed an optimization model for hybrid wind/PV/diesel systems to minimize the total cost while the energy required is covered. This methodology was implemented to design a hybrid system installed in Senegal, and the results showed the influence of the load profile and renewable resources in the optimal configuration of the hybrid system. Furthermore, the authors conclude that the size of the battery bank is a relevant parameter, because it can significantly reduce the number of operating hours of the diesel generator and the total cost. Recently, Kaldellis et al. [5] presented a study about electrification for remote consumers, in a Greek island region of medium-high solar potential, using PV-diesel hybrid systems and storage. The applied methodology evaluated the possible combinations of PV panels, battery bank size, and diesel generator capacity, calculating the long-term electricity generation cost for 10 and 20 years of operation, respectively. Results showed different optimal configurations when these operation time periods were considered. These results reveal the importance of using long-term data about the renewable resources and probabilistic assessment in the design process. In this sense, Kaplani and Kaplanis [6] developed a simulation model for stand-alone PV systems that could also be adapted to system with diesel generators. The proposed methodology was applied to design some PV systems installed in various European cities. The stochastic PV sizing methodology suggests a 37% reduction in pick power of PV generator and battery storage capacity compared to the results reached using a conventional methodology. Similar results can be found were founded by Távora et al. [7], who presented a comparative study of deterministic and probabilistic approaches to design PV systems. The results showed that the deterministic method could oversize the system. Karaki et al. [8] applied a probabilistic methodology to estimate the production costs of a wind-diesel system. A wind farm model was built using the joint probability distribution function of the total available wind power, while the diesel generator model was obtained using convolution methods. The production costs associated with the diesel system were estimated using the expected energy that is not supplied and a deconvolution process in reverse economic order. Giannakoudis et al. [9] presented a model for optimization and power management of hybrid systems with hydrogen storage adapting the simulated annealing algorithm to consider uncertainty (stochastic annealing). The variables under uncertainty included the solar radiation, the wind speed, and the efficiencies of the electrolyzer and fuel cell. The objective function considered was the net present value of investment over the lifetime of the system. Tan et al. [10] developed a methodology for stochastic sizing of a battery bank in an uninterruptible power system with a PV generator using a Monte Carlo simulation approach. In this methodology, first a random event of load profile, weather conditions, and failure was generated, and the required energy capacity was calculated. This process was repeated a number of times. Then the results were statistically analyzed using the cumulative distribution function and, finally, the battery capacity was economically evaluated considering a determined confidence level. Another technique, applying Monte Carlo 34 P ublicaciones simulation and a reliability analysis methodology, including battery storage for PV systems with diesel generators, was developed by Moharil and Kulkarni [11]. Other authors have published studies that have shown the importance of battery storage in the reduction of operating hours of diesel generators and total net present cost [4,12,13]. This is a relevant topic because the charge controller operation and the coulombic efficiency have an important influence on the acceptance of the battery bank’s charge, and consequently on the ability of the system to meet the energy demand. However, these factors are not considered in many studies and simulation models [1,2]. Otherwise, the use of long-term data and the consideration of uncertainty of the potential of renewable resources in the simulation and optimization process are determinant factors in the optimal sizing of hybrid systems [6,7]. In this paper, a probabilistic model based in a Monte Carlo simulation approach of a PV/Wind/Diesel/Battery system is developed and the influence of charge controller and coulombic efficiency in its performance is analyzed. This research work is a continuation of our previous one presented in [14]. This work is presented as follows: xThe PV/Wind/Diesel/Battery system model xStochastic modeling of the renewable resources xThe case study xConclusions. 2. PV/Wind/Diesel/Battery system model The hybrid power system being analyzed is shown in Fig. 1. The lead acid battery bank, the wind turbine, and the photovoltaic generator are connected to the AC bus through the inverter. The model of this system will be carefully described in the following sections. Fig. 1. Hybrid power system G DC Wind Turbine Battery Bank DC/AC LOAD P W P gd AC Conventional Diesel Generator PV Panels 35 P ublicaciones 2.1 Photovoltaic panel model The output power of the photovoltaic panel (PPV) could be estimated using Eq. (1) and its efficiency can be estimated by means of Eq. (2) [15]. PVPV AGP K (1) >@ )25(1  cSTCPV T DK K (2) where A is the area of the photovoltaic panel in m2,G is the incident solar radiation in W/m2,ηPV is the efficiency in a determined operating condition, ηSTC is the efficiency at standard test conditions, Tc is the cell temperature in degrees C, and α is the temperature coefficient in %/degrees C. Combining Eqs. (1) and (2), the production of photovoltaic panel could be expressed in terms of power obtained under standard test conditions (PSTC). >@ ¿ ¾ ½ ¯ ®  )25(1 1000 cSTCPV T G PP D (3) G NOCT TT ac ¸ ¹ · ¨ © §  800 20 (4) where Ta is the ambient temperature in degrees C and NOCT is the nominal operation cell temperature in degrees C. 2.2 Wind turbine model Frequently, the wind generator is represented using the power curve provided by the manufacturer; Fig. 2 shows a normalized power curve of a typical wind turbine of low rated power and horizontal axes. The start-up wind speed is between 3 to 4 m/s, and the rated wind speed is between 14 to 15 m/s. Generally, if the wind speed is higher than 14 or 18 m/s, the output power is between 30% and 70% of the rated power [13]. Fig. 2. Typical power curve of wind turbine 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 5 10 15 20 25 Wind speed (m/s) P/Pn Start-up wind speed [3m/s-4 m/s] Rated wind speed [14m/s15m/s] 36 P ublicaciones 2.3 Diesel or gasoline generator model The fuel consumption of a conventional generator is an important variable in the hybrid system performance analysis. The fuel consumption (Fl) is calculated using Eq. (5). gdgdnlPmPmF 21  (5) where Pgdn is the rated power, Pgd is the output power, and the constants m1 and m2 could be determined using data provided by the manufacturer. For a diesel generator, typical values for these constants are m1=0.085 l/kWh and m2=0.246 l/kWh [16], while for a gasoline generator, typical values are m1=0.2 l/kWh and m2=0.5 l/kWh [17]. 2.4 The inverter model The inverter is modeled calculating its efficiency (ηi) for the power transmission from the DC bus to AC bus. The efficiency is variable with the AC load and can be represented by means of Eq. (6). linv l iPmPm P )1( 43  K (6) where Pl is the load in the AC bus, Pinv is the rated power of the inverter, m3 and m4 are parameters fitted using data provided by the manufacturer. Fig. 3 shows a typical efficiency curve for m3=0.0119 and m4=0.0155. Fig. 3. Typical efficiency curve for an inverter 2.5 Lead acid battery and charge controller model The lead acid battery model used in this paper is a simplified version of Copetti’s model [18,19]. An extended discussion of other lead acid battery models and lifetime estimation methods can be found in reference [14], in which this simplified version was used for probabilistic modeling of small capacity wind energy systems using a Monte Carlo simulation approach. 0.40 0.50 0.60 0.70 0.80 0.90 1.00 0 20 40 60 80 100 120 Pl/Pinv (%) Efficiency Manufacturer Model 37 P ublicaciones The battery capacity (C) is calculated using Eqs. (7) and (8) [18,19]. )005.01(67.1 10 aT TCC ' (7) 9.0 10 67.01 ¸ ¸ ¹ · ¨ ¨ © §  I I C CT (8) where CT is the maximum capacity of the battery, I is the charge or discharge current, ∆Ta=Ta-25 is the change in the temperature from the reference of 25º C, and C10 and I10 are the capacity and current in 10 hours at 25º C, respectively. The state of charge (SOC) is estimated by means of Eq. (9) [19]. ° ¯ ° ®   ! 01 0 I C Q I C Q SOC b b K K (9) where Q=|I|t represents the charge supplied to the battery (charge process) or supplied by the battery (discharge process) during the time of interest t, while ηb is the coulombic efficiency calculated according to Eq. (10) [19] for the charge (I>0) and discharge (I<0) processes.  ° ¯ ° ®   ! » ¼ º « ¬ ª ¸ ¸ ¹ · ¨ ¨ © §   01 01 55.0/ 73.20 exp1 10 I ISOC II b K (10) The charge controller protects the battery bank against overcharging or overdischarging by disconnecting the renewable generators or the load, respectively. During the charge process, the charge controller operation can affect the energy capture of the battery as it prematurely disconnects the renewable generators when the voltage increases suddenly, producing a low state of charge in the battery bank [20]. The charge controller is an important component of the hybrid system that is not considered by several simulation and optimization tools available nowadays. The battery voltage during the charge process can be estimated using Eq. (11) [18]. For a determined charge controller setpoint (the set-point at which the charge controller protects the battery from overcharging by disconnecting the renewable generators), the Q value and the state of charge in the moment at which the charge controller disconnects the renewable generators can be calculated using Eq. (11). For example, if the charge controller set-point is 2.50 V per cell, by using Eq. (11), the upper limit of the state of charge due to operation of the charge controller could be determined calculating the Qvalue with V=2.50 V. )025.01)(036.0 )/1( 48.0 1 6 ()16.02( 2.16.0 10 a T T CQIC I C Q V'     (11) This simplification in the lead acid battery model presented in [18,19] allows us to estimate the effects of the voltage stability on the DC bus and the coulombic efficiency in the state of charge without calculating the battery voltage in detail, thus reducing the computational effort, which is desirable in a probabilistic model based on Monte Carlo simulations. The lower limit of the state of charge is the minimum value recommended by the manufacturer; the charge controller disconnects the load when this value is reached. 38 P ublicaciones Similar to the model presented in [14], in this paper, the Ah throughput model is implemented considering 17.5% error [21]. In this battery, a lifetime model assumes that the amount of energy that can be cycled through the battery is fixed. Using the depth of discharge versus the cycles to failure curve frequently provided by the manufacturer, the estimated throughput energy (Qt) can be calculated using Eq. (12) [21]. ¦ p N i ii p tCFDODC N Q 1 10 ))(( 1 (12) where DODi and CFi are points of the depth of discharge versus the cycles to failure curve and Np is the total number of points considered. Calculating the total amperehours cycled by the battery bank from the simulation of the hybrid system and comparing this value with the expected throughput determines the battery lifetime. 3. Model of the renewable resources The stochastic analysis of a PV/Wind/Diesel/Battery system based in a Monte Carlo simulation approach requires that a model be able to consider the main sources of uncertainty in the power obtained from the photovoltaic panels and wind turbine. 3.1 Stochastic modeling of photovoltaic generator. The output power of the photovoltaic generator can be estimated by means of the model described in section 2.1. The hourly solar radiation could be synthetically generated using the stochastic procedure proposed by Graham and Hollands [22]. However, if hourly global radiation data are available, the methodology to fit an autoregressive moving average (ARMA) model described by Kamal and Jafri [23] is suggested. The uncertainty related to the production of the photovoltaic generator could be modeled using a Gaussian distribution with mean and standard deviation of -15% and 9.45%, respectively. This probability distribution models the uncertainty related to climate variability, solar radiation, transposition model, power rating of modules, dirt and soiling, snow, and other errors [24]. 3.2 Stochastic modeling of wind power generation. If the wind speed time series is known, the wind turbine output power is calculated using the model described in section 2.2. Some studies [25,26] have shown the ability of the ARMA model to represent the mean characteristics of the hourly average wind speed time series such as the diurnal non-stationarity, non-Gaussian shape of its probability distribution function (PDF), and the autocorrelation between successive wind speeds. The mathematical formulation of ARMA model is presented in Eq. (13). )()1(1)()()1(1)( ... ˆ ... ˆˆ qtqttptptt WWW   HTHTHMM (13) where Ŵ(t) is the transformed and standardized wind speed of hour t, M 1,…, M pare the autoregressive (AR) parameters, T 1,…, T qare the moving average (MA) parameters, and H (t), H (t-1),…, H (t-q) are random variables with mean zero and standard deviation of σ. The estimation of autoregressive and moving average parameters require carrying out the processes of transformation and standardization, estimation, and diagnostic checking. 39 P ublicaciones The transformation and standardization processes are necessary because the PDF of the wind speed time series is frequently a Weibull distribution, which make it necessary to transform the measured wind speed time series to another with Gaussian PDF. This transformation is carried out using a power min Eq. (14) [27]. m t t TUU )( )( with nt ,...,1 (14) where U(t) is the measured wind speed time series with n observations, and UT(t) is the transformed time series. The transformed time series become a stationary one (W(t)) by means of the standardization process of Eq. (15) [27]. )( )()( )( th thtT t U W V P  with nt ,...,1 (15) where μh(h) and σh(h) with h=1,2,....24 are the hourly mean and standard deviation of the transformed wind speed time series (UT(t)). It is assumed that these variables have a periodical behavior, that is to say, μh(h=25)= μh(h=1) and σh(h=25)= σh(h=1) [27]. During the estimation process, the autoregressive and moving average parameters are calculated, and these are finally validated during the diagnostic checking process. Details about all these processes can be found in [14]. To simulate a wind speed time series, first Eq. (13) is evaluated. Then, the transformed values of the simulated wind speed time series (ÛT(t)) are calculated using Eq. (16). )()()()( ˆˆ tththtT WU VP  (16) Finally, the simulated wind speed time series (Û(t)) is obtained applying the probability transformation described in Fig. 4 [29], where the curve of the left-hand side is the cumulative distribution function (CDF) of the time series ÛT(t) and the curve of the right-hand side is the CDF of the measured wind speed time series under uncertainty βU(t). The factor β represents the uncertainty due to long-term variations in the average wind speed. This idea is expressed in Eq. (17). Z \ E (17) where ψ is a random variable normally distributed with mean and standard deviation equal to that obtained from the historical data, and ω is the average of the wind speed time series measured U(t). The algorithm used to calculate the inverse of the CDF in discrete form presented in our previous work [14] could be used, but taking into consideration the time series βU(t) instead the measured time series U(t). Fig. 4. Probability transformation 0 1 2 3 4 5 6 7 -1 0 5 10 15 20 25 30 35 40 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 )( ˆ t U )(t u nt ,...,2,1m )( ˆtT U 40 P ublicaciones 4. The case study The probabilistic model presented in the previous section was used to analyze a PV/Wind/Diesel/Battery system installed in Zaragoza, Spain. The hourly wind speed and ambient temperature time series of 2005 and monthly averages between 1953 and 2010 provided by AEMET [29] were considered. Fig. 5 shows the histogram of seasonal average wind speed, while its total average and standard deviation are shown in Table 1. Fig. 6 shows the global horizontal radiation and clearness index provided by NASA [30], and Fig. 7 shows the monthly average ambient temperature. Fig. 5. Histogram of seasonal average wind speed between 1953 and 2010 Table 1 Seasonal characteristics from 1953 to 2010 in Zaragoza Season Average wind speed Standard deviation Winter 5.3322 1.5329 Spring 5.4598 1.2853 Summer 4.6920 1.0417 Autumn 4.6546 1.3004 Fig. 6. Monthly average global horizontal radiation and clearness index in Zaragoza 0 1 2 3 4 5 6 7 1 2 3 4 5 6 7 8 9 10 11 12 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Clearness index Daily radiation Clearness index Daily radiation (kWh/m2/d) Month 3 4 5 6 7 8 9 10 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Probability Winter Spring Summer Autumn 41 P ublicaciones Fig. 7. Monthly average temperature in Zaragoza The typical load profile considered is shown in Fig. 8, which is composed of three household appliances of 150W, 100W, and 100W, respectively. However, there is uncertainty in the possible hour at which each appliance could be used. For example, the first appliance typically operates between 17h and 22h, but it could be used between 1h and 24h. In a similar way, the second appliance typically operates between 19h and 21h, but it could be used between 17h and 24h. The third appliance typically operates during all hours of the day. Fig. 8. Typical load profile The photovoltaic generator is conformed by a panel with output power under standard test conditions (PSTC) of 175W, temperature coefficient (α) of -0.485%/ºC, nominal operation cell temperature (NOCT) of 47.5ºC, 60º tilt angle, and open circuit voltage of 44.4V. The rated power of the wind turbine is 1,000W; it is installed at 20 m height. The renewable generators and battery bank of 24V are coupled to the AC bus through 0 50 100 150 200 250 300 350 400 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Time (h) Power demand (W) 0 5 10 15 20 25 30 1 2 3 4 5 6 7 8 9 10 11 12 Month Temperature (ºC) 42 P ublicaciones M. Zhu (Ed.): Electrical Engineering and Control, LNEE 98, pp. 1003–1010. springerlink.com © Springer-Verlag Berlin Heidelberg 2011 Forecast of Hourly Average Wind Speed Using ARMA Model with Discrete Probability Transformation Juan M. Lujano-Rojas, José L. Bernal-Agustín, Rodolfo Dufo-López, and José A. Domínguez-Navarro Department of Electrical Engineering, University of Zaragoza, Calle María de Luna 3, 50018, Spain [email protected], {jlbernal,rdufo,jadona}@unizar.es Abstract. In this paper the methodology for wind speed forecasting with ARMA model is revised. The transformation, standardization, estimation and diagnostic checking processes are analyzed and a discrete probability transformation is introduced. Using time series historical data of three weather stations of the Royal Netherlands Meteorological Institute, the forecasting accuracy is evaluated for prediction intervals between 1 and 10 hours ahead and compared with artificial neural network training by back-propagation algorithm (BP-ANN). The results show that for the wind speed time series under study, in certain cases the ARMA model with discrete probability transformation can improve the BP-ANN at least 17.71%. Keywords: Wind Speed Forecasting, Autoregressive Moving Average Model (ARMA), Artificial Neural Network. 1 Introduction Wind speed and power predictions are important aspects for the wholesale energy market, wind farm owners and power system operators [1]. The autoregressive moving average model (ARMA) is a conventional statistical method for wind speed prediction that is based on analyzing historical data. This model frequently achieves accurate results in short-term prediction [2]. Brown [3] proposed a general model that considers the non-Gaussian shape of the probability distribution function (PDF), the diurnal non-stationarity and the autocorrelation of wind speed. This model is used by Daniel and Chen [4] for evaluating the forecasting accuracy of wind speed in Jamaica. Torres et al. [5] compared the forecasting accuracy between the ARMA and persistence models using time series data of five weather stations in Spain for prediction intervals between 1 and 10 hours ahead. The results show that for an interval prediction of 1 hour in advance the ARMA model improved the persistence model from 2–5% and, for an interval of 10 hours, 12–20%. In [6-8], comparative studies between ARMA and artificial neural network (ANN) models are shown. However, the ARMA models used in these studies do not consider the non-Gaussian shape of the PDF. This must be considered because the PDF of wind speed time series follows 49 P ublicaciones 1004 J.M. Lujano-Rojas et al. a Weibull distribution, making the direct application of stochastic models difficult for its analysis [9]. Reference [10] presents a comparative analysis of three types of ANN for forecasts 1 hour ahead, concluding that the most suitable ANN depends on the time series under study and the index error used to evaluate the forecasting accuracy. In this paper, the methodology for wind speed forecasting with the ARMA model is revised. The transformation, standardization, estimation and diagnostic checking processes are analyzed and a Discrete Probability Transformation (DPT) is introduced. The forecasting error is evaluated for prediction intervals between 1 and 10 hours ahead using hourly average wind speed data of three weather stations in Netherlands. The ARMA model with discrete probability transformation (ARMA+DPT) is compared with an ANN training with back-propagation algorithm (BP-ANN). 2 Materials and Methods The hourly average wind speed time series of weather stations Volkel (January 2007, 2008 and 2009), K13 (February 2007, 2008 and 2009) and Valkenburg (March 2007, 2008 and 2009) are used to fit the ARMA model (2007 and 2008 for each station) and evaluate the forecasting error (2009 for each station). These time series are provided by the Royal Netherlands Meteorological Institute [11]. 2.1 ARMA Model The mathematical formulation of the autoregressive moving average (ARMA) model is: )()1(1)()()1(1)( ... ˆ ... ˆˆ qtqttptptt aWWW −−−− −−−+++= εθεθϕϕ (1) Where Ǒ(t) is the transformed and standardized wind speed of hour t, ϕ 1,…, ϕ p are the autoregressive parameters, θ 1,…, θ q are the moving average parameters, ε (t), ε (t-1),…, ε (-qt) are random variables with an average value of zero and a standard deviation of ı. The fit of the ARMA model to the wind speed time series of interest requires the transformation, standardization, estimation and diagnostic checking processes. 2.1.1 Transformation and Standardization The Weibull PDF is frequently used in the time series analysis. In order to analyze a determined wind speed time series it is necessary to transform the series to another one that has a Gaussian PDF. This transformation is [3]: m t t TUU )( )( = with nt ,...,1= (2) Where U(t) is the wind speed time series of interest, UT(t) is the transformed wind speed time series with Gaussian PDF, m is the power transformation and n is the number of hourly wind speed observations. The power transformation m is calculated from Weibull shape k. Dubey (1967) [12] showed that for shape factors between 3.26 and 3.60, the Weibull PDF is similar to the Gaussian PDF, thus the power 50 P ublicaciones Forecast of Hourly Average Wind Speed Using ARMA Model 1005 transformation of equation (2) with m between k/3.60 and k/3.26 adequately describes the Gaussian PDF. The selected value of this range is m value, for which the coefficient of skewness (SK) is closest to zero. The coefficient of skewness is calculated by equation (3) [13]. 13 213 2 QQ QQQ SK − −+ = (3) Where Q1=C-1(0.25), Q2=C-1(0.5) and Q3=C-1(0.75) are the first, second and third quartiles, respectively. C-1(.) is the inverse of the Cumulative Distribution Function (CDF) calculated by the algorithm of the Fig. 3 (Section 2.1.4). The transformed wind speed time series is not stationary. In order to be stationary it is necessary to subtract the hourly average and divide per the hourly standard deviations. If μ h(h) and σ h(h) with h=1,2,…, 24 are the hourly average and standard deviation of transformed wind speed series, respectively, it is assumed that these functions are periodic: μ h(t=25)= μ h(h=1) and σ h(t=25)= σ h(h=1) [3]. The transformed and standardized series (W(t)) is: )( )( )( )( t h t h t T t U W σ μ − = (4) 2.1.2 Estimation The plots of autocorrelation function (ACF) and partial autocorrelation function (PACF) of the series of Equation (4) have useful information to determine the value of order p and q of the ARMA model [14]. Others approach for selecting the p and q values are Bayesian Information Criterion (BIC) [15] and Akaike Information Criterion (AIC) [16]. The optimal value of p and q are selected minimizing the respective criterion BIC or AIC of the equations (5) and (6), respectively. )log()()log(),( 2 ),( nqpnqpBIC qp ++= σ (5) )(2)log(),( 2 ),( qpnqpAIC qp ++= σ (6) )( ) ˆ (2 )( 1 )( 2 ),( qpn WW t n t t qp +− − = ¦ = σ (7) Where σ (p,q) 2 is the variance of the residual, Ǒ(t) is the value calculated by the ARMA model. The autoregressive and moving average parameters are calculated by minimization of the quadratic prediction error criterion [17]. 51 P ublicaciones 1006 J.M. Lujano-Rojas et al. 2.1.3 Diagnostic Checking The statistical checking is made by the Ljung-Box test [18]. In this test the statistical S is compared with the chi-square distribution χ α 2 with L-p-q degrees of freedom. If χ α 2>S then the model is adequate for the significance level α . The statistical S is calculated by Equation (8). ¦ =Ω Ω Ω− += L n r nnS 1 2 )( )2( (8) Where L is a number of lags considered and rΩ is the correlation coefficient of the residuals corresponding to lag Ω. 2.1.4 Forecasting with ARMA Model The forecasting process starts by evaluating expressions (9) and (10). )()1(1)()()1(1)( ...... ˆlqtqltltlptpltlt WWW +−+−++−+−+ −−−+++= εθεθεϕϕ (9) )()()( )( ˆˆ ltlthlth lt TWU +++ ++= σμ (10) Where l=1,…,hrp, hrp are the hours ahead of forecasting. An important fact is that the values of equation (10) can be negative, so depending of the m value, undoing the transformation process using the power 1/m is difficult. For this reason, in this paper the undoing of the transformation process is made with the probability transformation in the discrete form. Using this transformation process, the PDF of the equation (10) will be the PDF of the original wind speed time series. This probability trans-formation is based in Equation (11) [19] and the forecasting values Û(t+l) are calcula-ted by Equation (12). ) ˆ ( ˆ ) ˆ ()()()( ltTTltlt UCuUC +++ == (11) )) ˆ ( ˆ ( ˆ)( 1 )( ltTTlt UCCU + − += (12) Where C is the CDF in discrete form of the original wind speed time series U(t), ƘT is the CDF of Equation (10), assuming a Gaussian CDF with average and standard deviation equal to the transformed time series and u(t+l) is a variable with uniform density function in [0,1]. Once u(t+l) is calculated with Equation (11), it is necessary to calculate the value of Û(t+l)=C-1(u(t+l)). The first step is to build the vector x, whose elements are zero until ceil(max(U(t))) with t=1,2,…,n in step Δx. The next step is to build the vector C, whose elements are the cumulative probabilities of each element of vector x. Finally, the forecasted value of wind speed Û(t+l) is calculated by the algorithm of Figure 1. The function size(C) calculates the number of rows of vector C. 52 P ublicaciones Forecast of Hourly Average Wind Speed Using ARMA Model 1007 Sta r t u (t+l) ← 1,2,..,hrp l ← 1 l  hrp i ← 1 i  size(C) u ( t+l )  C(1) u (t+l) == 1 Û ( t+l ) ← max(U ( 1 ) ,..,U ( n ) ) l ← l+1 End Û ( t+l ) ← x(i) Û (t+l) ← min(U (1) ,..,U (n) ) i ←i+1 1> u ( t+l ) C ( i ) No No No No No Y es Yes Ye s Ye s Y es Fig. 1. Algorithm to calculate the inverse of the CDF in discrete form. 2.1.5 BP-ANN Model The artificial neural network training by back-propagation algorithm (BP-ANN) used for hourly average wind speed forecasting is shown in Fig. 2. U (t+l-1) U ( t+l-2 ) U (t+l-3) U (t+l-p) Û (t+l) Fig. 2. Artificial neural network for wind speed forecasting. The data used for training the artificial neural network is scaled between 0.1 and 0.9 to avoid the saturation regions of the sigmoid function. 53 P ublicaciones 1008 J.M. Lujano-Rojas et al. 3 Results A program in MATLAB has been developed to fit the ARMA model with discrete probability transformation (ARMA+DPT) and BP-ANN to the wind speed time series of January, February and March of 2007 and 2008 for the Volkel, K13 and Valkenburg stations, respectively. The 2009 data for each station and month combination were used to evaluate the forecasting error. The results of transformation, standardization, estimation and diagnostic checking processes are summarized in Table 1. In tables 2, 3 and 4, the comparison among forecasting errors indices is shown: mean bias error (MBE), root mean square error (RMSE), mean absolute bias error (MABE) and correlation coefficient (R). 4 Conclusion In this paper, the methodology for wind speed prediction with the ARMA model is carefully reviewed. The transformation, standardization, estimation and diagnostic checking processes are analyzed and a discrete probability transformation is introduced for undoing the transformation process necessary to calculate the autoregressive and moving average parameters of the ARMA model. This model was used as a prediction tool and has been compared with the artificial neural network training by the back-propagation algorithm. According to the results shown in the Tables 2, 3 and 4, the ARMA+DPT model present in average RMSE errors between 0.90 and 1.89 m/s and MABE errors between 0.63 and 1.39 m/s, while the BP-ANN model present higher average RMSE errors, between 0.95 and 2.05 m/s and higher average MABE errors, between 0.72 and 1.56 m/s for intervals prediction between 1 and 10 hours ahead, respectively. Figures 17, 18 and 19 show that the ARMA+DPT in certain cases can improve the BP-ANN by as much as 17.71%; however, in other cases the BP-ANN error can be 0.9% smaller than the ARMA+DPT model. Table 1. Parameters of ARMA+DPT model for each station. Parameter/Station Volkel K13 Valkenburg (p,q) (2,0) (5,0) (7,0) L-p-q 147 132 142 χ 0.05 2 176.2938 159.8135 170.8092 S 143.1374 137.8389 154.9721 m 0.7162 0.6899 0.6269 ϕ 1 0.9014 1.0225 0.9210 ϕ 2 0.0487 0.0150 0.0173 ϕ 3 ----- 0.0024 0.0359 ϕ 4 ----- -0.0480 -0.0210 ϕ 5 ----- -0.0211 -0.0295 ϕ 6 ----- ----- 0.0438 ϕ 7 ----- ----- -0.0174 k 2.3353 2.25 2.0436 Criterion AIC AIC AIC Δx 0.0001 54 P ublicaciones Forecast of Hourly Average Wind Speed Using ARMA Model 1009 Table 2. Forecasting errors (Volkel). Volkel BP-ANN ARMA+DPT l(h) RMSE MABE R RMSE MABE R 1 0.9750 0.7123 0.9142 0.8691 0.5714 0.9241 2 1.1982 0.8692 0.8656 1.0547 0.7097 0.8879 3 1.3531 0.9805 0.8243 1.1596 0.7828 0.8632 4 1.4959 1.0858 0.7825 1.2793 0.8751 0.8326 5 1.6316 1.1950 0.7364 1.3899 0.9382 0.8024 6 1.7451 1.2642 0.6930 1.4960 1.0168 0.7698 7 1.8598 1.3561 0.6431 1.5865 1.0750 0.7419 8 1.9457 1.4107 0.6137 1.6018 1.1096 0.7431 9 2.0668 1.5201 0.5407 1.7507 1.2042 0.6842 10 2.1068 1.5652 0.4943 1.8121 1.2774 0.6492 Table 3. Forecasting errors (K13). K13 BP-ANN ARMA+DPT l(h) RMSE MABE R RMSE MABE R 1 0.8802 0.6747 0.9671 0.8789 0.5989 0.9674 2 1.0489 0.7972 0.9528 1.0705 0.7533 0.9515 3 1.2238 0.9270 0.9353 1.2795 0.9069 0.9313 4 1.3589 1.0109 0.9195 1.4179 1.0146 0.9146 5 1.4839 1.1252 0.9044 1.5478 1.1445 0.8999 6 1.6193 1.2432 0.8838 1.6471 1.2304 0.8823 7 1.8601 1.3519 0.8483 1.9063 1.3775 0.8457 8 1.8986 1.4056 0.8421 1.9441 1.4217 0.8420 9 2.0141 1.5466 0.8232 1.9005 1.4359 0.8458 10 1.9873 1.4650 0.8234 2.0244 1.5064 0.8214 Table 4. Forecasting errors (Valkenburg). Valkenburg BP-ANN ARMA+DPT l(h) RMSE MABE R RMSE MABE R 1 1.0081 0.7779 0.9380 0.9521 0.7048 0.9449 2 1.1910 0.9330 0.9128 1.0935 0.8157 0.9256 3 1.3945 1.0750 0.8765 1.2158 0.9056 0.9086 4 1.5402 1.2119 0.8467 1.3302 1.0016 0.8877 5 1.6996 1.3384 0.8080 1.4590 1.1203 0.8639 6 1.8082 1.4060 0.7793 1.5904 1.1965 0.8389 7 1.9382 1.5316 0.7404 1.6971 1.2914 0.8112 8 2.0466 1.6378 0.7042 1.7202 1.3218 0.8067 9 2.0129 1.6190 0.7154 1.7490 1.3378 0.7979 10 2.0649 1.6530 0.6967 1.8301 1.3936 0.7748 55 P ublicaciones 1010 J.M. Lujano-Rojas et al. Acknowledgments This work was supported by the “Ministerio de Ciencia e Innovación” of the Spanish Government under Project ENE2009-14582-C02-01. References 1. Barthelmie, R.J., Murray, F., Pryor, S.C.: The economic benefit of short-term forecasting for wind energy in the UK electricity market. Energy Policy 36, 1687–1696 (2008) 2. Lei, M., Shiyan, L., Chuanwen, J., Hongling, L., Yan, Z.: A review on the forecasting of wind speed and generated power. 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Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19, 716–723 (1974) 17. Ljung, L.: System Identification. Theory for the user. PTRInformation and System Sciences Series. Prentice-Hall, Englewood Cliffs (1999) 18. Ljung, G.M., Box, G.E.P.: On a measure of lack of fit in time series models. Biometrika 65, 297–303 (1978) 19. Rosenblatt, M.: Remarks on a multivariate transformation. Annals of Mathematical Statistics 23, 470–472 (1952) 20. Rojas, R.: Neural Networks. Springer, Berlin (1996) 56 P ublicaciones Optimum load management strategy for wind/diesel/battery hybrid power systems Juan M. Lujano-Rojas a , Cláudio Monteiro b , c , Rodolfo Dufo-López a , José L. Bernal-Agustín a , * a Department of Electrical Engineering, University of Zaragoza, 50018 Zaragoza, Spain b FEUP, Fac. Engenharia Univ. Porto, Portugal c INESC eInstituto de Engenharia de Sistemas e Computadores do Porto, Porto, Portugal article info Article history: Received 4 August 2011 Accepted 25 January 2012 Available online 8 February 2012 Keywords: Load management strategy Hybrid system Controllable loads abstract This paper discusses a novel load management strategy for the optimal use of renewable energy in systems with wind turbines, a battery bank, and a diesel generator. Using predictions concerning wind speed and power, controllable loads are used to minimize the energy supplied by the diesel generator and battery bank, subject to constraints imposed by the user’s behavior and duty cycle of the appliances. We analyzed a small hybrid power system in Zaragoza, Spain, and the results showed load management strategy allowed improvement in the wind power use by shifting controllable loads to wind power peaks, increasing the state of the charge in the battery bank, and reducing the diesel generator operating time, when compared to a case without load management. Ó2012 Elsevier Ltd. All rights reserved. 1. Introduction Management of hybrid power systems has two important components: a strategy for controlling energy sources and load management. In an important study, Barley and Winn [1] proposed the following general control strategies for systems with renewable energy sources, a diesel generator and a battery bank: the frugal dispatch strategy, the load following strategy, the state of charge (SOC) setpoint strategy, and the full power/minimum run time (FPMRT) strategy. In the frugal dispatch strategy, the intersection of the diesel energy cost curve with the battery wear cost line determines a critical load. If the net load (the difference between load and power from renewable sources) is higher than the critical load, the diesel generator is used; otherwise, the batteries are discharged. In the load following strategy, the diesel generator runs to match the instantaneous net load and never charges the batteries. In the state of charge (SOC) setpoint strategy, the diesel generator operates at full power until the SOC reaches the setpoint previously arranged. In the FPMRT strategy, the diesel generator operates for a predetermined length of time, charging the batteries with the excess energy, and then is disconnected. The authors used the predictive dispatch strategy as a benchmark for evaluating these strategies and found the actual use of the diesel generator and the battery bank depended on the critical load value in the future. Ashari and Nayar [2] developed a control strategy for systems with renewable energy sources, diesel generators, and battery banks that uses power demand, battery bank voltage, and minimum power of a diesel generator to decide when to charge or discharge the battery bank and start or stop the diesel generator, i.e., the optimal strategy operation is searched, determining the load setpoint to start and stop the diesel generator and the SOC setpoint to charge the battery bank. More recently, Dufo-López and Bernal-Agustín [3] analyzed combining the load following strategy and the state of charge setpoint strategy proposed, by Barley and Winn [1], in photovoltaic systems combined with other sources of energy. They found that if the net load is lower than the critical load, the state of charge setpoint strategy should be applied; otherwise, the load following strategy should be applied. Yamamoto et al. [4] proposed a predictive control method for systems with photovoltaic panels, diesel generators, and battery bank. Their strategy used the forecast of photovoltaic production and an hourly load profile to decide on the diesel generator output power. If the SOC of the battery bank was between 0.5 and 0.7, the diesel generator started and, when the SOC was higher than 0.7, the diesel generator stopped. Concerning load management, Groumpos et al. [5] did the first work in stand-alone photovoltaic systems with a system located in the village of Schuchuli, Arizona (USA). In this system, four load *Corresponding author. Tel.: þ34 976761921; fax: þ34 762226. E-mail address: [email protected] (J.L. Bernal-Agustín). Contents lists available at SciVerse ScienceDirect Renewable Energy journal homepage: www.elsevier.com/locate/renene 0960-1481/$ esee front matter Ó2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.renene.2012.01.097 Renewable Energy 44 (2012) 288e295 57 P ublicaciones priorities and four SOC setpoints (0.5, 0.4, 0.3 and 0.2) were established. For example, if the battery bank was discharging and the SOC setpoints values were sequentially reached, the loads were disconnected beginning with the lowest priority. Otherwise, if the battery bank was charging and the SOC setpoints values were sequentially reached, the loads were reconnected. The same authors, Groumps and Papegeorgiou, proposed in [6] an optimal load management technique for a stand-alone photovoltaic system based on three major categories of load classifications: an operational classification (DC and AC loads), a system classification (uncontrollable, controllable, and semi-controllable loads), and a priority classification (useful, essential, critical, and emergency loads). In this method, using the controllable load, the general load curve is manipulated to minimize the integral of the square of the net load over a 24-h period in order to reduce the required battery bank capacity and total life cycle costs. Khouzam and Khouzam [7] developed a methodology for load management in stand-alone photovoltaic systems wherein the loads were classified into four general categories according to their priorities: convenient, essential, critical, and emergency; the priority of the battery bank was variable and dependent on the SOC. The optimal management was based on the maximization of an objective function that depended on the load priorities and was subject to the availability of an energy supply. In another study, Moreno et al. [8] implemented a fuzzy controller to be applied to load management in stand-alone photovoltaic systems. The variable considered was supply expectancy predicted 1 h ahead in order to decide in real time whether to connect or disconnect the load according to its priority. Salah et al. [9] proposed a load management method for a domestic gridconnected photovoltaic system without batteries. In this approach, the photovoltaic generator was considered a complementary source of energy. This technique uses the fuzzy logic controller to decide in real time which appliance must be connected, the photovoltaic panel or the electric grid. The decision is made after considering photovoltaic and operating power, the priority of the appliances, and the maximum time the appliances are connected to the photovoltaic generator. This approach allows continuous energy savings. Ammar et al. [10] proposed a methodology for daily optimum management of a household photovoltaic system connected to the electrical grid without a battery bank. This approach uses predictions concerning photovoltaic generator production the next day to plan the connection times of appliances to the photovoltaic generator. The decision is made considering the duty cycle for each appliance. Similar criteria were used by Salah et al. in [9]. Finally, Thiaux et al. [11] analyzed the influence of the load profile shape on the energy cost of the life cycle of stand-alone photovoltaic systems. Their results showed the gross energy requirements are minimized when the load and photovoltaic production profiles are similar. According to these papers, renewable power sources forecasting, control strategies for power sources, and load management are important in reducing the life cycle cost of a determined standalone hybrid power system. In this paper, we describe a novel load management strategy developed for the optimal use of renewable energy in systems with wind turbines, a battery bank, and a diesel generator. This paper is organized as follows. In section 2, we provide a description of the wind/diesel/battery hybrid power system model. In section 3, we explain the prediction of the hourly average wind speed with the ARMA model. In section 4,we carefully detail the proposed load management strategy. We illustrate the load management strategy with a case study described in section 5, and we draw conclusions in the final section of the paper. 2. Wind/diesel/battery hybrid power system model The system under study is the AC coupled hybrid power system [12] shown in Fig. 1. In this system, the small capacity wind turbine and the battery bank are coupled through a power inverter to an AC bus. The next sections describe the mathematical models for each component of the system. 2.1. Small capacity wind turbine model The typical power curve of a small capacity wind turbine with horizontal axes is shown in Fig. 2; this curve can be obtained using data in discrete form frequently provided by the manufacturer. In this type of wind turbine, the start-up wind speed is between 3 and 4 m/s, and the rated power is reached for wind speeds between 14 and 15 m/s. When the wind speed is higher than 14 or 18 m/s, the power production falls to between 30 and 70% of the rated power [13]. 2.2. Lead acid battery bank and charge controller model Coppeti and Chenlo [14] proposed that a lead acid battery model is able to adequately represent the complex behavior of the charge and discharge processes in the battery [15]; however, their mathematical formulation was very complex because it needed to solve a nonlinear equations system for each hour of simulation. Therefore, for the purposes of this paper, we simplified this model, which is normalized with respect to the total ampere-hours that may be charged or discharged in 10 h at 25  C(C 10 capacity), and it considers the low current operation and temperature effects of the battery capacity. Equations (1) and (2) show the capacity equation [14]. G DC Wind Turbine Battery Bank DC/AC Load PW Pgd AC Conventional Diesel Generator Pl Fig. 1. AC coupled hybrid power system. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 5 10 15 20 25 Wind speed (m/s) P/Pn Fig. 2. Typical power curve of small wind turbine. J.M. Lujano-Rojas et al. / Renewable Energy 44 (2012) 288e295 289 58 P ublicaciones Optimum residential load management strategy for real time pricing (RTP) demand response programs Juan M. Lujano-Rojas a , Cla ´udio Monteiro b,c , Rodolfo Dufo-Lo ´pez a , Jose ´L. Bernal-Agustı ´n a,n a Department of Electrical Engineering, University of Zaragoza, Spain b FEUP, Faculty of Engenharia University of Porto, Portugal c INESC-Instituto de Engenharia de Sistemas e Computadores do Porto, Porto, Portugal article info Article history: Received 3 November 2011 Accepted 8 March 2012 Available online 28 March 2012 Keywords: Smart grid Demand response Electric vehicle abstract This paper presents an optimal load management strategy for residential consumers that utilizes the communication infrastructure of the future smart grid. The strategy considers predictions of electricity prices, energy demand, renewable power production, and power-purchase of energy of the consumer in determining the optimal relationship between hourly electricity prices and the use of different household appliances and electric vehicles in a typical smart house. The proposed strategy is illustrated using two study cases corresponding to a house located in Zaragoza (Spain) for a typical day in summer. Results show that the proposed model allows users to control their diary energy consumption and adapt their electricity bills to their actual economical situation. &2012 Elsevier Ltd. All rights reserved. 1. Introduction Energy demand is increasing in many countries as a result of economic and industrial developments; consequently, many governments are working to provide reliable electrical energy. However, problems related with restrictions in electricity prices by means of a price ceiling and flat rates have produced a difference between marginal electricity generation costs and energy consumption cost of electricity. This increases the growth of demand faster than the growth of generation capacity. In addition, the volatility of wholesale electricity prices affects the retailer’s ability to generate profit and increase the investment uncertainty (Kim and Shcherbakova, 2011). The demand response (DR) is defined as changes in the electricity consumption patterns of end consumers to reduce the instantaneous demand in times of high electricity prices. A change in consumption patterns could be made by means of a change in the price of electricity (Price-Based Programs) or incentive payments (Incentive-Based Programs Albadi and El-Saadany, 2008). Time-of-Use (TOU) is a particular type of Price-Based Program whereby peak periods have higher prices than prices during off-peak periods; consequently, the users change their use of electricity. This type of DR program is particularly convenient for residential users (Eissa, 2011). Recently, many studies have been carried out to determine how end-users can adjust their load level according to a determined DR program. Molderink et al. (2010) developed an algorithm for the control of energy streams on a single house and a large group of houses. It is assumed that every house has microgenerators, heat and electricity buffers, appliances, and a local controller. In this approach, global and local controllers are used in three steps. First, a prediction is made for production and consumption for one day ahead, and then the local controller determines the aggregated profile and sends it to the global controller. Second, the plan for each house is made for the next day. Third, the algorithm decides how the demand is matched. Two examples were analyzed, and the results showed that it is possible to plan for a fleet of houses based on a one-day prediction; however, any forecasting error affects the outcomes of this approach. Houwing et al. (2011) analyzed the importance of the microCombined Heat and Power systems (micro-CHP) as a special type of distributed generation (DG) technology. The model-predictive control (MPC) proposed to make a demand response, minimizing the cost of the domestic energy use, subject to operational constraints and assuming the perfect prediction of energy demand and electricity prices. The results showed that the costs are between 1% and 14% lower than the standard control strategies. Mohsenian-Rad and Leon-Garcia (2010) developed a residential load control for real-time pricing (RTP) environments where the electricity payment and the waiting time for the operation of each appliance are minimized in response to the variable realtime prices. First, a price prediction is made for a determined scheduling horizon. Next, an objective function that considers the total electricity payment and the total cost of waiting (cost of using appliances at later hours) into the scheduling horizon is minimized. Mohsenian-Rad et al. (2010) presented a demand side Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/enpol Energy Policy 0301-4215/$ - see front matter &2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.enpol.2012.03.019 n Corresponding author. Tel.: þ34 976761921; fax: þ34 976762226. E-mail address: [email protected] (J.L. Bernal-Agustı ´n). Energy Policy 45 (2012) 671–679 65 P ublicaciones management model where, for a fleet of residential consumers, the optimal energy consumption schedule for each consumer is determined by minimizing the energy cost in the system based on game theory. Conejo et al. (2010) presented a demand response model that minimizes the cost of energy consumption considering the load-variation limits, hourly load, and price prediction uncertainty. This model assumes that prices and decisions in the prior t1 h are known; in the actual moment (hour t), the price and power demand are known, and the prices in the next 24th are estimated using an autoregressive integrated moving average (ARIMA)-based model with a confidence interval. Using this information, the optimization model establishes a floor for daily consumption, and ramping down/up limits are solved, obtaining the energy consumption in the current hour tand the demand at the beginning of hour tþ1. Finally, this procedure is repeated each hour on a scheduling horizon of 1 day. Sianaki et al. (2010) proposed a methodology for demand response that considers the customers’ preferences for the use of certain appliances during peak hours by means of the Analytic Hierarchy Process. This quantification of customer preferences is used to decide what appliances must be used during the peak hours, solving the Knapsack Problem, wherein the numerical priority obtained by the Analytic Hierarchy Process for a certain appliance is considered as a measure of the profit obtained by its use. The authors conclude that this method allows improvement both in customers’ budgets and the global energy consumption on the electrical grid. Tanaka et al. (2011) presented a methodology to minimize the power flow fluctuation in the smart grid with a fleet of houses using optimally a battery bank and a heat pump, concluding that this methodology allows for the reduction of the electric power consumption and the cost of electricity. An important aspect is that the success of a determined DR program depends widely on awareness, attitude, and behavioral adaptation of consumers (Bartusch et al., 2011). However, according to results obtained by Gyamfi and Krumdieck (2011), customers are very sensitive to the energy prices. In scientific articles previously mentioned, the motivation and intention of consumers to participate in the DR program is represented in different ways. For example, Mohsenian-Rad and Leon-Garcia (2010) use a factor that is equal to 1 when a strict cost reduction is required, slightly higher than 1 when a medium cost reduction is required, and much higher than 1 when a cost reduction is not required. However, this type of representation might be a simplistic way to effectively reflect the relationship between the reduction in the electricity bill and the economic situation of the consumers. Based on this reasoning, this paper proposes a load management strategy that considers the power-purchase of energy of the consumers in a real-time pricing DR program optimizing the negotiation between the consumer and retailer. The paper is organized as follows. Section 2 explains the smart grid infrastructure required for the real-time pricing demand response program implementation, and the mathematical modeling of household appliances and electric vehicles. Section 3 describes in detail the load management strategy proposed. Section 4 analyzes two study cases of a residential consumer in a real-time pricing demand response in the Iberian Peninsula. Finally, Section 5 gives conclusions. 2. Mathematical model of system The load management based on the real-time prices requires an electricity grid that allows for active participation of consumers in demand response programs to supply electricity economically and efficiently. This electricity grid is known as the ‘‘smart grid.’’ Future smart grids will be provided with a communication infrastructure that can be categorized into three classes: wide area network (WAN), field area network (FAN), and home area network (HAN). A WAN is used to exchange real-time measurements between the control center and electric devices located in power plants, substations, and distributed storage. A FAN allows communication between distribution substations, distribution feeders, transformers, and customers’ homes. A HAN allows communication between loads, sensors, and appliances in homes. An Energy Services Interface (ESI) is a secure two-way communication interface between the utility and the customers. An ESI can receive hourly prices from the utility and inform the customers; using a web-based Energy Management System (EMS) or In-Home Display (IHD) connected to the ESI, customers can respond to the pricing signal (Wang et al., 2011). For a typical house provided with a smart meter, wind turbine, photovoltaic (PV) panels, several household appliances, and an electric vehicle (EV), the technique proposed in this paper consists of using information about wholesale energy prices, the power of renewable sources and temperature, energy demand, and user behavior to determine optimal demand response for the following day, considering the power-purchase of energy of the consumers. Fig. 1 describes the load management strategy proposed, where, using ESI, the user is informed about the actual and forecasted values of energy prices, energy consumption, and renewable power. Then, using a diary planner for the next day—expressed by means of the user’s power-purchase of energy and predictions of wholesale energy prices, renewable power productions, and energy demand—the EMS can determine the optimal use of household appliances for the next dayandthebesttimetousetheelectricvehicle,subjecttothe conditions imposed by a specific trip. The next section describes a mathematical model of household appliances and electric vehicles of a typical residential consumer. 2.1. Energy demand modeling 2.1.1. Household appliances Let n¼1,2,3,y,Nbe the household appliances. In this paper, it is assumed that a typical household appliance ncan be modeled by means of an idealized load profile, as shown in Fig. 2. Here, h n is the possible hour at which the appliance will start its operation, P n is its power required, and d n is the duration of its operation. The matrix of all possible load profiles for this appliance PDCA n (Possible Demand Curve of the Appliance n) can be obtained using the algorithm shown in Fig. 3. The matrix PDCA n will have 24 columns, and its number of rows will be a variable value called R n , while the variables rand lare counters used by the algorithm. Additionally, a row with zeros must be added to the matrix PDCA n to consider the option of shutting down the appliance n. 2.1.2. Electric vehicle Environmental factors related to greenhouse gas emissions, petroleum-based transportation, and air pollution are promoting Smart Meter Forecasting 24 hours ahead Real-Time Prices Wind Power Photovoltaic Power Power Demand FAN HAN DR Activities Scheduling b y the User Power Line EMS Fig. 1. Smart house and load management strategy. J.M. Lujano-Rojas et al. / Energy Policy 45 (2012) 671–679672 66 P ublicaciones the development of EVs. For these reasons, it is expected that EVs will be an important electric load in the urban environments; therefore, this is considered in our analysis. Recently, there are plug-in hybrid electric vehicles that use nickel-metal hydride and lithium ion batteries (Bradley and Frank, 2009); however, for simplicity and illustrative purposes, in our optimal load management strategy, a lead acid battery model will be considered. Copetti and Chenlo (1994) developed a general lead acid battery model to represent the complex battery behavior; however, its mathematical formulation is complex because we need to solve a nonlinear equations system for each hour of simulation; for this reason, a simplification is used. The following Equations represent the capacity model normalized with respect to the total ampere-hours that might be charged or discharged in 10 h at 25 1C(C 10 capacity): C T ¼1:67C 10 ð1þ0:005 D T a Þð1Þ C¼C T 1þ0:67ð9I9=I 10 Þ 0:9 ð2Þ where D T a ¼T a 25 is the temperature variation from the reference of 25 1C, T a is the ambient temperature in 1C, C T is the maximum capacity of the battery and Cis the ampere-hours capacity at the charge or discharge constant current I. The Coulombic efficiency ( Z b ) during the discharge (Io0) and charge (I40) processes is calculated using the following equation (Copetti et al., 1993): Z b ¼1exp 20:73 I=I10 þ0:55  ðSOC1Þ hi ,I40 1,Io0 8 < :ð3Þ where I 10 is the charge or discharge current in 10 h at 25 1C. The state of charge (SOC) of the battery is calculated by SOC ¼ Q C Z b ,I40 1 Q C Z b ,Io0 8 < :ð4Þ where Q¼9I9tis the charge supplied by the battery (discharge) or to the battery (charge) during time t. During the charge process, the battery voltage at which the charge controller disconnects the power source is assumed to be 2.5 V/cell; during this process, the battery voltage per cell might be approximated by (Copetti and Chenlo, 1994) V¼2þ0:16 Q C  þI C 10 6 1þI 0:6 þ0:48 ð1Q=C T Þ 1:2 þ0:036 ! ð10:025 D T a Þ ð5Þ Eq. (5) allows us to estimate the Qvalue at which the battery voltage is 2.5 V per cell and, therefore, the state of charge in the moment at which the charge controller disconnects the power sources. During the discharge process, when the state of charge is equal to the minimum value specified by the battery manufacturer, the charge controller disconnects the traction system to prevent over-discharge. Let k¼1,2,3,y,Kbe the number of electric vehicles in the house. A matrix PDCEV k (Possible Demand Curve of the Electric Vehicle k) can be made similar to the one used to represent all possible load profiles of household appliances (PDCA n ) but using the lead acid battery model presented above to estimate power required from the electric grid to charge the battery bank of EV considering a determined level of autonomy. The matrix PDCEV k will have 24 columns, and its number of rows will be a variable value called F k . 3. Optimum load management strategy As explained in Section 2, the optimum load management strategy requires forecasting of renewable power production, load, and electricity prices for the next day. Then, using the activity scheduling by the user—expressed as the power-purchase of energy—the negotiation between utility and user is optimized. The next sections present a survey about predictions of interest, show users how to express the activities scheduling, and describe the optimization problem and its solution methodology to determine the optimal demand response of the user for the next day. 3.1. Ensemble forecasting Several models have been developed to forecast wind speed and power using different types of information. Lei et al. (2009) divided the forecasting methods into four categories: physical model, conventional statistical model, spatial correlation model, and artificial intelligence model. The physical model uses information about terrain, obstacles, pressure, and temperature to predict wind speed. The result obtained with this model can be used as the n d n P n h P(kW) t(h) Fig. 2. Idealized load profile of household appliances. hdP ,, dl −≤ 25 )( hlr +< PrlPDCA =),( 0),( =rlPDCA Fig. 3. Algorithm to find PDCA n . J.M. Lujano-Rojas et al. / Energy Policy 45 (2012) 671–679 673 67 P ublicaciones auxiliary input of a statistical model, which is based on analyzing historical data. Spatial correlation models consider the spatial relationship between the wind speeds at different places. The models based on artificial intelligence use an artificial neural network (ANN), fuzzy logic, or a support vector machine to make predictions of wind speed and wind power. The photovoltaic power prediction can be made using models based on artificial intelligence and statistical analysis such as ANNs, autoregressive moving average (ARMA) process, Bayesian inference, and Markov chains (Paoli et al., 2010). However, other approaches based on analyses of satellite data and numerical weather predictions present greater accuracy for horizons of more than 5 h (Kleissl, 2010). Aggarwal et al. (2009) divided the electricity price forecasting methodologies in three main categories: game theory-based models, simulation-based models, and time series analysis-based models. Game theory models consider the strategies of the market participants to maximize their benefits. Simulation models consider system operational conditions by means of optimal power flow. Time series classification includes statistical techniques such as ARMA models, ANNs, and data mining. Artificial intelligence models have been applied to analyze the relationship between energy consumption patterns and temperature behavior. Some examples of this type of approach have been proposed by Abdel-Aal (2004a, 2004b) and Fan et al. (2009). Electric vehicles will be an important load whose patterns of use must be known. In the load management strategy proposed in this paper, the home-arrival time of the EV must be predicted. Wang et al. (2011) have developed a probability distribution of this variable to analyze the impact of plug-in hybrid electric vehicles on power systems; however, statistical analysis could also be considered. 3.2. Activity scheduling by user Anexampleofthepower-purchaseofenergyoftheuserisshown in Table 1. For the household appliance n,thecolumnVUA n (Value to User of the household Appliance n) contains the hourly values assigned by the consumer to use this appliance during a determined hour of the following day. According to Table 1, the consumer could pay h0.05 per kWh to use the household appliance nfrom 16:00 to 18:00 h. Similarly, the column VUEV k (Value to User of the Electric Vehicle k) contains the hourly values assigned by the consumer to use the electric vehicle kduring a determined hour of the next day. According to Table 1, the consumer would pay 7 cents of euro per kWhtotravelwiththeEVkfrom 11:00 to 15:00 h. It is assumed that the energy required for an EV kto travel from 11:00 to 15:00 h is bought previously between the 1:00 and 10:00 h; when the consumer comes back home (16:00 h), the EV is reconnected, and consequently, the consumer must negotiate with the utility again. Other possibilities of use of EVs can be included in the model simply by changing the value to use the EV in determined hours of the following day. Additionally the user must express the required level of autonomy for future travel with the EV. This methodology allows us to express the diary planning consumption for one day ahead in terms of the interest shown in using a determined household appliance or EV at a determined time—this interest is conveniently expressed in h/kWh. Table 1 shows the input information to EMS, which optimizes the negotiation between retailer and consumer. 3.3. Optimization problem The optimal demand response for the next day, considering the power-purchase of energy of the user, could be determined by maximizing the difference between the amount of money the user can pay and the cost of obtaining the required energy from the grid, which is related to the energy market prices. Let n¼1,2,3,y,Nbe the number of household appliances and k¼1,2,3,y,Kthe number of electric vehicles in the house. The matrix PDCA n with R n rows and 24 columns, and the matrix PDCEV k with F k rows and 24 columns, are determined according to the Sections 2.1.1 and 2.1.2, respectively. Let a n be an integer number contained in the interval [1,R n ]and b k an integer number contained in the interval [1,F k ]. For a specific combination of load profiles for different household appliances indicated by the row a n in the matrix PDCA n , and the different charge profiles for the electric vehicles indicated by the row b k in the matrix PDCEV k , the objective function described above could be represented mathematically using f¼X i¼24 i¼1 X n¼N n¼1 VUA n ðiÞPDCA n ð a n ,iÞþ X k¼K k¼1 VUEV k ðiÞPDCEV k ð b k ,iÞ ! EPðiÞX n¼N n¼1 PDCA n ð a n ,iÞþ X k¼K k¼1 PDCEV k ð b k ,iÞ ! þEPðiÞðWPðiÞþPVPðiÞÞ 2 6 6 6 6 6 6 6 6 4 3 7 7 7 7 7 7 7 7 5 ð6Þ where fis the difference between the amount of money that the user can pay and the cost of obtaining the required energy from the grid, VUA n (i) is the user value of household appliance nin the hour i, PDCA n ( a n ,i) is the power demanded by household appliance nin the hour i,VUEV k (i) is the user value to travel in electric vehicle kin the hour i,PDCEV k ( b k ,i) is the power demanded by electric vehicle k during charge process in the hour i,EP(i) is the forecasted electricity prices in the hour iand WP(i)andPVP(i) are the forecasted wind power and photovoltaic power in the hour i, respectively. In Eq. (6), the first term represents the power-purchase of energy of the consumer, while the second term represents the cost of the required energy, and the third term represents the benefits obtained due to selling wind and photovoltaic energy back to the grid. The number of possible combinations (N c ) in the optimization problem to maximize the objective function of Eq. (6) depends on the operation time of the different appliances (d n ) and on the number of appliances according to N c ¼ð26d 1 Þð26d 2 Þð26d n Þð26d N Þð7Þ Fig. 4 shows in a semi-logarithmic graph the behavior of the number of possible combinations when the number of appliances is between 1 and 20, and their operation time (d 1 ,d 2 ,y,d n ,y,d N )is Table 1 Activities scheduling by the user for the next day. t(h)VUA 1 (h/kWh) VUA n (h/kWh) VUEV 1 (h/kWh) VUEV k (h/kWh) 1 0 0 0.15 0.07 2 0 0 0.15 0.07 3 0 0 0.15 0.07 4 0 0 0.15 0.07 5 0 0 0.15 0.07 6 0 0 0.15 0.07 7 0 0 0.15 0.07 8 0 0 0 0.07 9 0 0 0 0.07 10 0 0 0 0.07 11 0 0 0.15 0 12 0.1 0 0.15 0 13 0.1 0 0.15 0 14 0.1 0 0.15 0 15 0.1 0 0.15 0 16 0.1 0.05 0.15 0.07 17 0.1 0.05 0.15 0.07 18 0 0.05 0.15 0.07 19 0 0 0.15 0.07 20 0 0 0.15 0.07 21 0 0 0.15 0.07 22 0 0 0.15 0.07 23 0 0 0.15 0.07 24 0 0 0.15 0.07 J.M. Lujano-Rojas et al. / Energy Policy 45 (2012) 671–679674 68 P ublicaciones represented as a integer random variable between 1 and 24. According to these results, the number of possible combinations grows exponentially (N c ¼0.5566e 2.4809n ,R 2 ¼0.9765) with the number of appliances considered. Considering the nonlinear nature of the optimization problem and the number of possible combinations, we concluded that heuristic optimization techniques should be applied. Heuristic optimization techniques do not ensure finding a global optimal solution, but they can find very good solutions while consuming a low computational time. The proposed methodology requires solving the optimization problem at the end of the present day in order to reduce uncertainty in the ensemble of forecasting. Thus, the problem of finding the combination of household appliances’ load profiles and EV trips that maximize the objective function of Eq. (6) can be solved using a heuristic optimization technique. In this case, we used a genetic algorithm (Goldberg, 1989) that, for a determined number of individuals in the population (P o ), number of generations (G o ), crossing rate (C o ) and mutation rate (M o ), can be implemented in the following way: 1. The initial population is obtained randomly, where an individual is an integer vector such as this: 9 a 1 9 a 2 9y9 a n 9y9 a N 9 b 1 9 b 2 9y9 b k 9y9 b K 9with n¼1,2,3,y,N;k¼1,2,3,y,Kand a 1 , a 2 ,y, a n ,y, a N A[1,R n ]; b 1 , b 2 ,y, b k ,y, b K A[1,F k ]. 2. For each individual in the population, the objective function (f) of Eq. (6) is evaluated. 3. The fitness function (F it ) of individual pis determined according to its rank in the population (rank 1 is assigned to the best individual, which maximizes fdefined by Eq. (6), and rank P o to the worst individual, which minimizes f). The fitness function is shown as F it ¼ðP o þ1Þp P Po p¼1 ðP o þ1pÞwith p¼1,2,...,Pð8Þ 4. Reproduction, crossing, and mutation are carried out on the obtained solutions, defining the next generation. Reproduction is made using the roulette-wheel method, where the selection probability of a determined individual is proportional to its fitness. The crossing between two individuals is made by the ‘‘one crossing point’’ method with a crossing rate C o (0oC o o1), which defines how many descendants will be produced in each generation. The mutation is made by randomly changing the components of some individuals, whose quantity is defined by the mutation rate M o (0oM o o1), which determines the number of individuals which will be mutated in each generation. 5. The process in steps 2–4 is repeated until G o generations are reached. The best solution obtained is the one that has the highest value of f, and then the optimal load profile of each household appliance and travel with the EV fitted to the power-purchase of energy of the consumer is determined. 4. Study cases To illustrate the load management strategy proposed in this paper, a residential house located in Zaragoza (Spain) is analyzed. The house has a television of 0.12 kW (n¼1), air conditioner of 1kW(n¼2), computer of 0.1 kW (n¼3), 15 bulbs of 10 W (n¼4), other household appliances with total consumption of 0.15 kW (n¼5), a wind turbine of 3 kW, and an EV with a battery bank of C 1 ¼53 Ah and 312 V (k¼1). Two cases have been considered, as presented in the next sections. 4.1. Case study determining the best time to use EV During the previous day of our analysis, the user specified his plan to EMS using Table 1 linked to ESI. Specifically for this day, the user, according to his power-purchase, could pay 1 ch/kWh to watch television between 14 h and 23 h, 10 ch/kWh to use the air conditioner for 5 h between 13 h and 22 h, 10 ch/kWh to use the computer between 9 h and 20 h, 10 ch/kWh to use the lights between 21 h and 23 h, 10 ch/kWh to use the other household appliances during the 24 h period, and 5 ch/kWh to use the EV for 5 h at any time of the day. According to Section 3, predictions 24 h ahead of electricity prices, ambient temperature, and wind power are simulated. Analyzing information published by Foley et al. (2012),Aggarwal et al. (2009),Hahn et al. (2009), and Abdel-Aal (2004a), wind power forecasting error of 20%, energy prices forecasting error of 10%, ambient temperature forecasting error of 10% and load forecasting error of 2% have been considered. The household appliances and EV were modeled according to Section 2. For example, for the air conditioner (n¼2, P 2 ¼1 kW, and d 2 ¼5 h), the matrix of all possible load profiles derived from all possible uses (PDCA 2 ) is built using the algorithm presented in Fig. 3. The transpose matrix of PDCA 2 is shown in Table 2. Note that a row with zeros in PDCA 2 has been included to consider the option of shutting down the air conditioner (R 2 ¼21). Initially, the battery bank of the EV has an SOC of 35%, and then the user connects the EV to the grid to increment the SOC to 60% or higher. It is estimated that 11.7% of energy stored in the battery bank is spent during travel, and when the user returns with the EV, he will reconnect it to the grid to recharge its battery bank. The transpose matrix of the load for each possible travel with the EV (PDCEV 1 ) under these autonomy requirements is shown in Table 3, assuming that the EV is charged optimally, maintaining 1.E+00 1.E+10 1.E+20 1.E+30 0 5 10 15 20 25 Number of Appliances (n) Number of combinations (Nc) Fig. 4. Relationship between number of combinations (N c ) and number of appliances (N). J.M. Lujano-Rojas et al. / Energy Policy 45 (2012) 671–679 675 69 P ublicaciones the voltage at a constant value. Note that a row with zeros in PDCEV 1 has been included to consider the option of no travel with the EV (F 1 ¼13). Tables similar to Table 2 were built for other household appliances, and then the optimum load management strategy, explained in Section 3, was implemented in MATLAB considering P o ¼1000, G o ¼30, C o ¼95%, and M o ¼1%. The evolution of the genetic algorithm is shown in Fig. 5. The total number of possible combinations is 2,812,992, and the implemented program evaluates about 28 combinations per second. Fig. 6 shows forecasted and actual values of electricity prices and ambient temperature 24 h ahead of a typical summer day based on information provided by the Spanish electrical market operator OMEL (http://www.omel.es) and the Spanish meteorological agency AEMET (http://www.aemet.es). Typically, the residents of this house use their air conditioner between 18 h and 22 h—assuming that this house has a good thermal insulation— so the air conditioner could be used in the daytime hours, during which electricity prices are low. In this sense, Fig. 7 shows the load shifting recommended by load management strategy regarding the use of the air conditioner for this day. The user of the EV typically travels between 8:00 h and 13:00 h. However, in the plan, the user has expressed flexibility to use the EV on this day. Under the travel conditions explained above, Fig. 8 shows the results obtained by the load management strategy about the use of the EV; note that if the user travels with the EV at 8:00 h (SOC¼61.7%) and returns at 13:00 h (SOC¼50%), electricity to recharge the battery bank will be bought when electricity prices will be high. However, if the user travels with the EV at 19:00 h (SOC¼77.7%) and returns at 23:00 h, the autonomy of EV is incremented and its battery bank is charged when energy prices are low. The user has specified a value of 1 ch/kWh to watch television between 14 h and 23 h, which, according to the hourly prices shown previously in Fig. 6, is a very low value, and the load management strategy recommends shutting down the television. Fig. 9 shows a comparison between typical and optimal load profiles, which allows the reduction of the electricity bill of 21.7%. These results could be shown by EMS through ESI to give the users an incentive to change their energy consumption pattern. Note that according to Fig. 9, the load management strategy allows users to reach an important reduction of energy consumption in hours of high electricity prices. 4.2. Case study selecting time to use EV In a typical situation, we can consider that the consumer needs to use EV from 8:00 to 13:00 h and can pay 5 ch/kWh for the Table 2 Transpose matrix PDCA 2 . Possible load curves 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 100000000000000000000 110000000000000000000 111000000000000000000 111100000000000000000 111110000000000000000 011111000000000000000 001111100000000000000 000111110000000000000 000011111000000000000 0000011111 00000000000 0000001111 1 0000000000 0000000111 1 1 000000000 000000001111100000000 000000000111110000000 0000000000 11111000000 0000000000 0 1111100000 0000000000 0 0 111110000 0000000000 0 0 0 11111000 000000000000001111100 000000000000000111110 000000000000000011110 000000000000000001110 000000000000000000110 000000000000000000010 Table 3 Transpose matrix PDCEV 1 . Possible travel 12345678910111213 3.42 3.42 3.42 3.42 3.42 3.42 3.42 3.42 3.42 3.42 3.42 3.42 0.00 3.36 3.36 3.36 3.36 3.36 3.36 3.36 3.36 3.36 3.36 3.36 3.36 0.00 3.02 3.02 3.02 3.02 3.02 3.02 3.02 3.02 3.02 3.02 3.02 3.02 0.00 2.24 2.24 2.24 2.24 2.24 2.24 2.24 2.24 2.24 2.24 2.24 2.24 0.00 1.99 1.99 1.99 1.99 1.99 1.99 1.99 1.99 1.99 1.99 1.99 1.99 0.00 1.68 1.68 1.68 1.68 1.68 1.68 1.68 1.68 1.68 1.68 1.68 1.68 0.00 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 0.00 0.00 1.51 1.51 1.51 1.51 1.51 1.51 1.51 1.51 1.51 1.51 1.51 0.00 0.00 0.00 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 0.00 0.00 0.00 0.00 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 0.00 0.00 0.00 0.00 0.00 1.12 1.12 1.12 1.12 1.12 1.12 1.12 1.12 0.00 0.00 0.00 0.00 0.00 0.00 1.07 1.07 1.07 1.07 1.07 1.07 1.07 0.00 2.45 0.00 0.00 0.00 0.00 0.00 0.81 0.81 0.81 0.81 0.81 0.81 0.00 2.07 2.45 0.00 0.00 0.00 0.00 0.00 0.82 0.82 0.82 0.82 0.82 0.00 1.76 2.07 2.45 0.00 0.00 0.00 0.00 0.00 0.84 0.84 0.84 0.84 0.00 1.35 1.76 2.07 2.45 0.00 0.00 0.00 0.00 0.00 0.78 0.78 0.78 0.00 1.29 1.35 1.76 2.07 2.45 0.00 0.00 0.00 0.00 0.00 0.56 0.56 0.00 1.10 1.29 1.35 1.76 2.07 2.45 0.00 0.00 0.00 0.00 0.00 0.48 0.00 1.13 1.10 1.29 1.35 1.76 2.07 2.45 0.00 0.00 0.00 0.00 0.00 0.00 1.10 1.13 1.10 1.29 1.35 1.76 2.07 2.45 0.00 0.00 0.00 0.00 0.00 0.95 1.10 1.13 1.10 1.29 1.35 1.76 2.07 2.45 0.00 0.00 0.00 0.00 0.82 0.95 1.10 1.13 1.10 1.29 1.35 1.76 2.07 2.45 0.00 0.00 0.00 0.85 0.82 0.95 1.10 1.13 1.10 1.29 1.35 1.76 2.07 2.45 0.00 0.00 0.83 0.85 0.82 0.95 1.10 1.13 1.10 1.29 1.35 1.76 2.07 2.45 0.00 J.M. Lujano-Rojas et al. / Energy Policy 45 (2012) 671–679676 70 P ublicaciones 2.73 2.74 2.75 2.76 2.77 2.78 2.79 2.8 2.81 2.82 0 5 10 15 20 25 30 35 Generations Objective function ( ) Fig. 5. Evolution of genetic algorithm optimization. 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 8 9 14 15 16 19 20 211234567 10111213 1718 222324 Time (h) 0 5 10 15 20 25 30 35 40 Tem p erature (°C) Forecasted price Actual price Actual temperature Forecasted temperature Price (c /kWh) Fig. 6. Energy prices and temperature for a typical day of summer. 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 123456789101112131415161718 2220 21 23 24 Time (h) 0 0.2 0.4 0.6 0.8 1 1.2 Power (kW) Forecasted price Actual price Optimal Typical 19 Price (c /kWh) Fig. 7. Comparison of typical and optimal use of air conditioner. 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 123456789101112131415161718192021222324 Time (h) 0 0.5 1 1.5 2 2.5 3 3.5 4 Power (kW) Forecasted price Actual price Optimal Typical SOC=35% SOC=61.7% SOC=50% SOC=77.7% SOC=66% SOC=74.18% Price (c /kWh) Fig. 8. Illustration of optimal use of EV for 5 h. J.M. Lujano-Rojas et al. / Energy Policy 45 (2012) 671–679 677 71 P ublicaciones energy required from the grid to charge its battery bank. It is expected that the user comes home and reconnects the EV at 13:00 h. The conditions for the other appliances are the same as previously analyzed in Section 4.1.Fig. 10 shows the results obtained from the optimization process, where the use of EV is required by the consumer. Fig. 11 shows a comparison between the typical and optimal load profiles. Under these conditions, the reduction of the electricity bill is 8%, mainly due to air conditioner use. An important aspect to consider is that a forecasting error of electricity prices could affect the ability of the load management strategy to determine optimal scheduling for different appliance usages and traveling with EVs, while a forecasting error of renewable power could affect the estimation of benefits obtained from selling renewable energy to grid. 5. Conclusions In this paper, an optimal load management strategy for residential consumers is shown that utilizes the communication infrastructure of the future smart grid, predictions of electricity prices, energy demand, renewable power production, and powerpurchase of energy of the consumer to determine—through the negotiation between retailer and consumer—the optimal utilization of different appliances and EVs. Two study cases, of a residential 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 178111223456 910 131415161718192021222324 Time (h) 0 0.5 1 1.5 2 2.5 3 3.5 4 Power (kW) Forecasted price Actual price Optimal Typical Price (c /kWh) Fig. 9. Comparison between typical and optimal load profiles. 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 123456789101112131415161718192021222324 Time (h) 0 0.5 1 1.5 2 2.5 3 3.5 4 Power (kW) Forecasted price Actual price Optimal Typical Price (c /kWh) Fig. 10. Illustration of the required use of EV during 5 h. 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 123456789101112131415161718192021222324 Time (h) 0 0.5 1 1.5 2 2.5 3 3.5 4 Power (kW) Forecasted price Actual price Optimal Typical Price (c /kWh) Fig. 11. Comparison between typical and optimal load profiles under typical use of EV. J.M. Lujano-Rojas et al. / Energy Policy 45 (2012) 671–679678 72 P ublicaciones consumer in Zaragoza (Spain), have been analyzed. Results show that the proposed model allowed users to reduce their electricity bill between 8% and 22% for the typical summer day analyzed and adapt the electricity bill to their actual economical situation. Acknowledgments This work was supported by the Ministerio de Ciencia e Innovacio ´n of the Spanish Government, under Project ENE200914582-C02-01. References Abdel-Aal, R.E., 2004a. Hourly temperature forecasting using abductive networks. Engineering Applications of Artificial Intelligence 17, 543–556. Abdel-Aal, R.E., 2004b. Short-term hourly load forecasting using abductive networks. IEEE Transactions on Power Systems 19, 164–173. Aggarwal, S.K., Saini, L.M., Kumar, A., 2009. Electricity price forecasting in deregulated markets: a review and evaluation. Electrical Power and Energy Systems 31, 13–22. Albadi, M.H., El-Saadany, E.F., 2008. A summary of demand response in electricity markets. Electric Power Systems Research 78, 1989–1996. 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Lujano-Rojas et al. / Energy Policy 45 (2012) 671–679 679 73 P ublicaciones Resumen 81 operación requerido por cada uno de ellos. Se obtuvo la conclusión de que esta técnica permitía obtener un ahorro de energía continuo. Ammar et al. [39] propusieron una metodología para la gestión óptima de la demanda en consumidores residenciales conectados a la red eléctrica sin baterías, utilizando predicciones diarias de la potencia proveniente del generador fotovoltaico para decidir el tiempo que un determinado electrodoméstico estará conectado al generador fotovoltaico. Esta decisión se tomaba considerando la energía que cada electrodoméstico requiere para su funcionamiento. Un criterio similar fue utilizado por Salah et al. [38]. Thiaux et al. [40] analizaron la influencia de la forma del perfil de consumo en el coste de la energía durante el ciclo de vida de un sistema fotovoltaico autónomo. Los resultados de este estudio mostraron que las necesidades de energía se reducen cuando el perfil de carga y la producción fotovoltaica son similares. La Adaptación de la Demanda (DR, Demand Response), se define como el cambio en el modelo de consumo de la electricidad, por parte de los consumidores, para reducir la demanda en horas en las que los precios de la electricidad son altos, o cuando la fiabilidad del sistema está en peligro. Los cambios en el modelo de consumo se pueden conseguir a través de cambios en el precio de la electricidad o a través de incentivos [41]. Así, la Adaptación de la Demanda modificando el modelo de consumo puede reducir la incertidumbre y los problemas relacionados con las diferencias entre los costes de generación y el precio de venta de la energía eléctrica [7], y también puede mejorar la eficiencia y la fiabilidad de la infraestructura disponible, además de reducir la volatilidad en los precios de la energía [41]. La implementación de estrategias para la Adaptación de la Demanda requiere de una red eléctrica equipada con una tecnología que facilite la fluida comunicación entre el distribuidor de la energía y todos los usuarios beneficiarios de la misma. Hoy en día este concepto de red eléctrica se denomina Red Eléctrica Inteligente (Smart Grid). Los programas de Adaptación de la Demanda pueden clasificarse en dos categorías: Programas Basados en Incentivos (IBP, Incentive-Based Programs) y Programas Basados en Precios (PBP, Price-Based Programs). Los IBP están basados en pagos o descuentos por participar en el programa, mientras que los PBP están basados en precios que cambian dinámicamente en cada hora. Los programas IBP están clasificados en Programas Clásicos (Classical Programs) y Programas Basados en el Mercado (Market-Based Programs). Los programas clásicos son los Programas de 82 Resumen Control Directo de Carga (Direct Load Control Programs) y los Programas de Carga Interrumpible (Interruptible/Curtaible Load Programs); mientras que los Programas Basados en el Mercado son los Programas de Adaptación de la Demanda durante Emergencia (Emergency DR Programs), Licitación de Demanda (Demand Bidding), Capacidad del Mercado (Capacity Market) y Mercado de Servicios Auxiliares (Ancillary Services Market). En los Programas Clásicos IBP los consumidores reciben un pago semejante a un vale de descuento. En los Programas de Control Directo de Carga la empresa de distribución puede desconectar cargas del consumidor participante después de una breve notificación, mientras que en los Programas de Carga Interrumpible los participantes son convocados para reducir su consumo a un valor predefinido. En los PBP el cambio en los precios se define de diferentes formas: de acuerdo a la hora a la cual se utiliza la energía eléctrica (TOU, Time of Use), si la energía eléctrica se utiliza durante situaciones de emergencia o de alto precio (CPP, Critical Peak Pricing), estableciendo altos precios durante los días de demanda extrema (ED-CPP, Extreme Day CPP), y programas que reflejan directamente al usuario los costes de generación de la electricidad en cada hora (RTP, Real Time Pricing) [41]. Los programas TOU son los que habitualmente utilizan los consumidores residenciales [42]. Los programas de Adaptación de la Demanda se han implementados en varios países. En los Estados Unidos existen varios programas de Adaptación de la Demanda, administrados por el Operador Independiente del Sistema (ISO, Independent System Operator) o por el Operador Regional del Sistema de Transmisión (RTO, Regional Transmission Operator). Ejemplos de estos tipos de operadores son el Operador Independiente del Sistema de Nueva York y el Operador de la Interconexión PJM. Existen diferentes programas de Adaptación de la Demanda, en los que el consumidor puede participar usando estrategias de control de la demanda para reducir su consumo de acuerdo a un determinado precio o señal de emergencia [43]. En el Reino Unido los sectores industrial y comercial pueden acordar programas TOU y/o Programas de Carga Interrumpible con la empresa de distribución eléctrica. Muchos usuarios participan en programas con la opción de obtener descuentos en el precio de la energía durante la noche. En Italia los Programas de Carga Interrumpible son aplicados a las grandes industrias, reduciendo su consumo a un valor de carga predefinido. En España se han desarrollado dos programas de Adaptación de la Demanda para los grandes consumidores, uno está dirigido por el sistema y otro está dirigido por el precio. En el Resumen 83 programa dirigido por el sistema los consumidores pueden participar voluntariamente en el programa, de forma que el operador del sistema de transmisión (TSO, Transmission System Operator) puede solicitar a estas industrias que limiten su demanda durante periodos que van desde 45 minutos hasta 12 horas. En el programa dirigido por el precio el TSO puede aplicar el TOU en siete periodos del año [44]. En China los programas de Adaptación de la Demanda han sido implementados para mejorar la fiabilidad y el factor de carga. En Pekín se ha incrementado la diferencia de precios entre las horas que se encuentran dentro y fuera del pico de demanda. Así, los consumidores industriales han acordado Programas de Carga Interrumpible, utilizando equipos de almacenamiento de energía y cargas controladas. En Jiangsu se han aplicado Programas de Carga Interrumpible a consumidores industriales, se ha promovido el uso de equipos de almacenamiento de energía, se han aplicado tarifas TOU y se ha implementado el control de máquinas industriales [45]. Se han desarrollado diversos estudios sobre cómo el usuario final puede ajustar su demanda de acuerdo a un determinado programa de Adaptación de la Demanda. Molderink et al. [46] desarrollaron un algoritmo para el control de los flujos de energía en una casa o en un gran conjunto de casas. En el algoritmo propuesto se asumía que cada casa poseía micro-generadores, cogeneración, electrodomésticos y un controlador local. En este enfoque existen tres etapas. En la primera se realizaba la predicción de las producciones de generación renovable y de los consumos en un día, y con esta información el controlador local determinaba el perfil agregado y lo enviaba al controlador global. En la segunda etapa se realizaba la planificación para cada una de las casas y, finalmente, en la tercera etapa el algoritmo decidía cómo satisfacer la demanda. Mohsenian-Rad y Leon-Garcia [47] desarrollaron un control de carga residencial para consumidores acogidos a programas RTP en el que el pago por la electricidad y el tiempo de espera para utilizar un determinado electrodoméstico se minimizaba teniendo en cuenta los precios que cambian dinámicamente. En primer lugar, para un determinado horizonte de tiempo, se realizaba la predicción de los precios de la electricidad, y a continuación se minimizaba una función objetivo que consideraba el pago total por la electricidad y el coste total por utilizar un determinado electrodoméstico después de la hora requerida. Mohsenian-Rad et al. [48] presentaron un modelo para la gestión de la demanda en programas IBP en el que, para un conjunto de consumidores residenciales, la planificación óptima del consumo de cada 84 Resumen consumidor se obtenía minimizando el coste de la energía mediante teoría de juegos. Conejo et al. [49] presentaron un modelo de respuesta de la demanda que minimizaba el coste de la energía consumida considerando los límites de variación de la carga, demanda horaria e incertidumbre en la predicción de los precios. Sianaki et al. [50] propusieron una metodología que analizaba la preferencia de los consumidores por utilizar un cierto electrodoméstico durante la hora de máximo consumo mediante un proceso Analítico Jerárquico (Analytic Hierarchy Process), utilizándose esta información para decidir qué electrodoméstico debe ser usado durante la hora de máximo consumo. 2.3.1 Influencia de la temperatura, el regulador de carga y la eficiencia culómbica del banco de baterías en el funcionamiento de los pequeños sistemas eólicos. La Figura 7 muestra un sistema híbrido típico compuesto por una turbina eólica y un banco de baterías de plomo ácido, que satisface una determinada demanda de energía. Figura 7. Sistema eólico con almacenamiento Un componente de gran importancia en este tipo de sistemas es el controlador de carga, que tiene como principal objetivo proteger al banco de baterías contra condiciones de operación extremas como la sobrecarga y la sobredescarga, utilizando como indicador la tensión entre sus terminales. Cuando la tensión del banco de baterías alcanza el ajuste de nivel alto del regulador de carga, este asume que el banco de baterías está completamente cargado y desconecta el generador de energía (turbina eólica y/o paneles fotovoltaicos), mientras que cuando la tensión del banco de baterías alcanza el ajuste de nivel bajo del regulador, este asume que el banco de baterías está descargado y desconecta la carga. Basándose en resultados experimentales, Baring-Gould et al. [58] y Corbus et al. [59] demostraron que el regulador de carga puede tener un efecto importante sobre la habilidad del banco de baterías para almacenar energía. Corbus et al [59] analizando diferentes sistemas compuestos por una turbina eólica y un banco de baterías, y concluyeron que en sistemas con gran capacidad de generación eólica y poca capacidad de almacenamiento, la tensión del banco de baterías alcanza prematuramente Turbina Eólica Banco de Baterías Demanda de Energía Resumen 85 el ajuste de nivel alto del regulador de carga, y como consecuencia el aerogenerador se desconecta y el estado de carga del banco de baterías no alcanza el nivel adecuado. Este hecho se ilustra en la Figura 8, donde se observa que para un ajuste de nivel alto del regulador de carga de 2,25 V/celda, si el banco de baterías se carga con la corriente de carga en 5 horas (C/5), cuando la tensión alcanza 2,25 V el estado de carga del banco de baterías es del 45%. Se aprecia que a medida que se reduce la corriente de carga, se tarda más tiempo en alcanzar el ajuste del nivel alto del regulador, y por lo tanto el banco de baterías es capaz de aceptar más energía. Si el banco de baterías se carga con la corriente de carga en 8 horas (C/8), entonces el estado de carga será del 61%. Si la corriente de carga se reduce a la necesaria para cargar el banco en 10 horas (C/10), el estado de carga conseguido será del 65%; y finalmente, si el banco de baterías se carga con la corriente de carga en 20 horas (C/20), el estado de carga será del 78%. Figura 8. Tensión vs. Estado de carga en una batería de plomo ácido [59] Por otro lado, la eficiencia culómbica del banco de baterías es otro factor que afecta significativamente a su capacidad para aceptar carga. La eficiencia culómbica varía considerablemente de acuerdo con el estado de carga, mostrando valores muy bajos para estados de carga altos. Esta pérdida de eficiencia está relacionada con las reacciones de gaseo que se producen en el banco de baterías durante la carga [60]. Stevens y Corey [61] analizaron varios sistemas fotovoltaicos, y concluyeron que la baja eficiencia culómbica en altos estados de carga podría dar lugar a una reducción substancial en la energía almacenada. Esta situación se produce porque un porcentaje elevado de la energía disponible se utiliza para satisfacer pérdidas en lugar de utilizarse para cargar el banco de baterías. En [51] se muestra uno de los trabajos de investigación desarrollados durante la realización de esta tesis doctoral, en el que se utilizó una simplificación del modelo 1.95 2.05 2.15 2.25 2.35 2.45 2.55 2.65 0 20 40 60 80 100 120 Estado de carga (%) C/10 C/20 C/8 C/5 Tensión por celda (V) 78% 65% 61% 45% 86 Resumen general de la batería de plomo ácido propuesto por Copetti et al. [62,63], se presentó un modelo de un sistema híbrido compuesto por una turbina eólica y un banco de baterías capaz de considerar el efecto, en el funcionamiento general del sistema, del ajuste del nivel alto de tensión del regulador de carga, la eficiencia culómbica del banco de baterías y la temperatura ambiente. El efecto de estas variables se analizó mediante la simulación de un sistema instalado en Zaragoza, y los resultados de esta simulación se compararon con los obtenidos utilizando HOMER, que no considera el efecto del regulador de carga, la eficiencia culómbica ni la temperatura ambiente sobre la operación del sistema híbrido. En la Figura 9 se muestra la comparación entre las distribuciones de probabilidad del estado de carga en un sistema con 100Ah de capacidad en 10 horas, obtenidas utilizando HOMER y con el modelo presentado en [51]. Estos resultados muestran cómo el efecto conjunto de la pérdida de eficiencia culómbica y la operación del regulador de carga puede dificultar que el estado de carga del banco de baterías alcance valores altos. Sin embargo, los resultados obtenidos mediante HOMER sugieren una mayor probabilidad de obtener estados de carga elevados debido a que no considera la relación existente entre la eficiencia culómbica y el estado de carga, y tampoco tiene en cuenta la operación del regulador de carga ni el efecto de la temperatura. Figura 9. Comparación entre distribuciones de probabilidad del estado de carga (C10=100Ah) En la Figura 10 se muestra el comportamiento de la falta de fiabilidad (Unreliability) del sistema cuando se consideran capacidades del banco de baterías comprendidas entre 100Ah y 1000Ah. Considerando estos resultados, si se requiere un nivel de fiabilidad 0.4 0.5 0.6 0.7 0.8 0.9 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Estado de carga Probabilidad Modelo presentado en [51] HOMER Resumen 87 del 90%, y no se consideran en la simulación factores como la operación del controlador de carga, ni la eficiencia culómbica y la temperatura ambiente, un banco de baterías con capacidad de 800Ah sería el adecuado. Sin embargo, si se consideran estos factores, el banco de baterías debería ser de 1000Ah. Esto podría dar lugar a que el nivel de fiabilidad del sistema, tras ser instalado, fuese menor que el calculado al utilizar HOMER. Es decir, si se instala un sistema analizado con HOMER, el nivel de fiabilidad real será menor que el esperado, por lo que será necesario incrementar la capacidad del banco de baterías. En el ejemplo que se ha mostrado el aumento debería ser del 25%. Figura 10. Falta de confiabilidad para diferentes capacidades del banco de baterías El modelo matemático de un sistema típico, presentado en [51], compuesto por una turbina eólica y un banco de baterías, se amplió incorporando el modelo de un generador fotovoltaico compuesto por uno o más paneles fotovoltaicos, y el modelo de un inversor en el que se considera la eficiencia variable en función de la potencia de salida. En [52] este modelo se utilizó para desarrollar una metodología, basada en un algoritmo genético, para el dimensionado óptimo de este tipo de sistemas. Con esta metodología es posible encontrar la combinación óptima de componentes que garantice un determinado nivel de fiabilidad, considerando factores de gran importancia, como son la eficiencia culómbica, la operación del regulador de carga y la temperatura ambiente. La metodología presentada en este trabajo se ilustró mediante el diseño de un sistema localizado en los Países Bajos. Se consideraron, como posibles elementos para el diseño, las turbinas eólicas cuya curva de potencia se muestra en la Figura 11, un generador fotovoltaico con capacidad comprendida entre 175W y 4.375kW, un banco de baterías cuyas celdas podían tener una capacidad comprendida entre 200Ah y 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 100 200 300 400 500 600 700 800 900 1000 Capacidad del banco de baterías (Ah) Falta de confiabilidad Modelo presentado en [51] HOMER 0.13 0.1 0.07 88 Resumen 3000Ah (con un máximo de 10 celdas conectadas en paralelo), y un inversor de 900W. Teniendo en cuenta otras variables relacionadas con aspectos económicos, como los costes de capital y las tasas de interés e inflación, se obtuvo la configuración de componentes que minimizaba el coste neto considerando 35 años de vida útil del sistema, y garantizando un nivel de fiabilidad del 90%. Una vez transcurridas 10 generaciones del algoritmo genético, la configuración óptima encontrada constaba de 11 paneles fotovoltaicos de 175W de potencia cada uno, una turbina eólica de 1kW y un banco de baterías de 1000Ah. En la Figura 12 se muestra la evolución del coste neto actualizado durante cada generación del proceso de optimización. Figura 11. Curvas de potencia de diferentes turbinas eólicas Figura 12. Evolución del coste neto actualizado durante la optimización Como se ha podido observar, el banco de baterías es uno de los componentes más importantes de un sistema híbrido. El banco de baterías no solo afecta de forma importante al balance energético del sistema sino que también afecta de forma determinante a la rentabilidad del mismo. Esto se debe a que el banco de baterías es uno 1 2 3 4 5 6 7 8 9 10 3 3.2 3.4 3.6 3.8 4 x 10 4 Generaciones Coste neto actualizado (€) 0 1 2 3 4 5 6 7 8 9 0 5 10 15 20 25 30 Velocidad del viento (m/s) Potencia (kW) Resumen 89 de los componentes más costosos del sistema y a que su tiempo de vida operativa es una variable difícil de determinar, ya que depende en gran medida de las condiciones meteorológicas a las que el sistema híbrido está sometido. Por lo tanto, si no se tiene certeza del número de veces que será necesario reemplazar el banco de baterías, podrían obtenerse costes no previstos muy elevados al final de la vida útil del sistema, viéndose afectada su rentabilidad. 2.3.2 Análisis y efecto de la incertidumbre en la vida útil del banco de baterías, la variabilidad del viento y la demanda en pequeños sistemas eólicos. Existen varios trabajos en los que se han desarrollado modelos con el fin de determinar el tiempo de vida del banco de baterías. Los tres tipos de modelos que se han desarrollado son: x Los modelos físico-químicos (Physico-chemical ageing models). Los modelos físico-químicos se basan en un conocimiento detallado de los factores físicos y químicos relacionados con el proceso de envejecimiento. x Los modelos Ah (Ampere-hora) ponderados (Weighted Ah ageing models). Los modelos Ah ponderados asumen que la vida de la batería depende proporcionalmente de los Ah descargados del banco de baterías. Los Ah que han sido descargados del banco de baterías se multiplican por un factor de ponderación que se ajusta de acuerdo con las condiciones operativas. Se dice que el banco de baterías ha alcanzado su vida útil cuando los Ah ponderados totales han excedido un determinado valor que se ha obtenido a partir de las condiciones de operación nominales. x Los modelos orientados por eventos (Event-oriented ageing models). Los modelos orientados por eventos estiman el tiempo de vida de la batería identificando condiciones de operación extremas [64]. Utilizando la experiencia e información proveniente de expertos, Svoboda et al. [65] desarrollaron diferentes categorías de operación típicas, para el banco de baterías, basadas en la determinación de factores de estrés relacionados con la magnitud de la corriente de descarga, el tiempo transcurrido entre recargas sucesivas, la cantidad de Ah descargados en condiciones de bajo estado de carga, y el tiempo durante el cual el banco de baterías permanece en esta condición. En [53] se han utilizado estas 90 Resumen categorías de operación para evaluar cualitativamente el desempeño del banco de baterías de un sistema híbrido situado en Zaragoza, siendo este trabajo parte de esta tesis doctoral. En la Figura 13 se muestra la serie temporal del estado de carga que se utilizó para determinar la magnitud de los diferentes factores de estrés necesarios con el fin de determinar la categoría de operación del banco de baterías, que en este caso se caracterizaba por mantener un alto estado de carga durante la mayor parte del tiempo. Con esa serie temporal del estado de carga en ocasiones se producían descargas a altas corrientes y recargas frecuentes, lo que daba lugar a un elevado riesgo de corrosión de la rejilla positiva, un elevado riesgo de pérdida de agua y un alto riesgo de pérdida de masa activa, sin embargo existía un muy bajo riesgo de sulfatación irreversible o degradación de la masa activa, así como de la polarización inversa de la célula, y de la estratificación o congelación del electrolito [65]. Figura 13. Serie temporal del estado de carga El modelo Ah, sin considerar los factores de ponderación, ha sido implementado en muchas herramientas de simulación y optimización de sistemas híbridos. En [66] se validó experimentalmente este modelo de envejecimiento considerando baterías de plomo ácido con placas planas OGi y con placas tubulares OPzS bajo perfiles de generación eólica y fotovoltaica. Bajo condiciones de generación eólica, los resultados mostraron un 16,7% de error en la estimación de la vida de la batería de placas planas OGi y un 17,5% de error en la estimación de la vida de la batería de placas tubulares OPzS. Utilizando estos resultados, en [51] el modelo de envejecimiento Ah, sin considerar los factores de ponderación, se incorporó al modelo probabilístico, basado en la técnica de simulación por Monte Carlo, de un sistema híbrido similar al que se muestra en la Figura 7. Este modelo incorpora la variabilidad del recurso eólico 30 40 50 60 70 80 90 100 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 Tiempo (h) Estado de carga (%) Resumen 97 de gestión de la demanda que utiliza la predicción de velocidades promedio horarias de viento en un horizonte de 24 horas [56]. Usando esta predicción es posible determinar la hora a la que cada electrodoméstico debe ser utilizado con el objetivo de minimizar la energía suplida por las fuentes controlables de energía, que en este caso son el generador convencional y el banco de baterías. Esta idea se analizó utilizando como ejemplo un sistema localizado en Zaragoza con el perfil de carga que se muestra en la Figura 21. Figura 21. Perfil de carga típico para el caso de estudio En el caso que se estudió se consideró que el usuario disponía de dos cargas controlables que frecuentemente se utilizan entre las 7:00 y las 18:00 horas, y entre la 1:00 y las 24:00 horas, consumiendo 400W durante 4 horas y 100W durante 6 horas, respectivamente. El sistema disponía de una turbina eólica de 3500W, un generador diesel de 1kW, un inversor de 1kW y un banco de baterías de 1000Ah. A modo de ejemplo del funcionamiento del sistema al aplicar la estrategia de gestión de la demanda propuesta, las Figuras 22 y 23 muestran, para los días 5 y 6 de agosto de 2005, que la curva de carga se desplaza hacia las horas en las que la potencia eólica alcanza valores elevados, y en consecuencia la energía suplida por el generador convencional y el banco de baterías se minimiza. Las Figuras 24 y 25 muestran el efecto del desplazamiento de la carga en el estado de carga del banco de baterías y en el número de horas de operación del generador diesel. En general la estrategia de gestión de la demanda propuesta permite mejorar, en comparación con el caso en el que el perfil de carga se mantuviese rígido, el uso de la potencia disponible del viento, aumentando el estado de carga del banco de baterías y reduciendo el número de horas de operación del generador diesel. 0 5 10 15 20 25 0 100 200 300 400 500 600 700 800 900 1000 Potencia (W) Tiempo (h) 98 Resumen Figura 22. Potencia eólica y perfiles de carga para los días 5 y 6 de agosto de 2005 Figura 23. Gestión de la carga controlable para los días 5 y 6 de agosto de 2005 Figura 24. Estado de carga del banco de baterías para los días 5 y 6 de Agosto de 2005 Estado de carga Con gestión de demanda Sin gestión de demanda 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 0 100 200 300 400 500 600 700 800 900 1000 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 Potencia (W) Perfil de carga típico Perfil de carga óptimo Uso típico de la carga controlable Uso óptimo de la carga controlable Tiempo (h) 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 Tiempo (h) Potencia (W) Potencia Eólica Con gestión de demanda Sin gestión de demanda Pico Potencia Eólica Movimiento carga Pico Potencia Eólica Movimiento carga Tiempo (h) Resumen 99 Figura 25. Potencia suministrada por el generador diesel los días 5 y 6 de Agosto de 2005. 2.3.6. Optimización de la gestión de la demanda en sistemas residenciales conectados a la red eléctrica. Teniendo en cuenta el auge que tiene hoy en día el concepto de la nueva Red Eléctrica Inteligente (Smart Grid), es posible que en un futuro los usuarios residenciales compren la energía eléctrica a precios que varíen dinámicamente a lo largo del día, en función de los costes de generación. La implementación de la Red Eléctrica Inteligente puede permitir que los costes de generación se vean reflejados directamente en el precio al que los usuarios residenciales adquieren la energía eléctrica. Para el logro de este objetivo es necesario que la futura Red Eléctrica Inteligente permita la comunicación directa entre las empresas de distribución de energía eléctrica y los consumidores. Este tipo de comunicación puede llevarse a cabo mediante el uso de redes de ordenadores y mediante la Interfaz de Servicios de Energía (ISE), que es la interfaz que establece la comunicación entre el distribuidor de energía eléctrica y los consumidores. Esta interfaz puede recibir los precios horarios de la energía provenientes de la empresa distribuidora e informar al consumidor. Utilizando un Sistema de Gestión de la Energía (SGE) conectado a la Interfaz de Servicios de Energía, los consumidores pueden decidir cómo utilizar sus electrodomésticos en respuesta a las señales de precios que reciban. A partir del planteamiento descrito, en [57] se desarrolló una técnica de Adaptación de la Demanda que, usando predicciones de los precios de la energía, la producción de potencia de las fuentes renovables y la demanda, además del poder adquisitivo de los consumidores, determinaba la manera óptima en la que estos deben utilizar sus electrodomésticos. Para ello se consideró una casa equipada con un Medidor de Energía 0 100 200 300 400 500 600 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 Potencia (W) Con gestión de demanda Sin gestión de demanda Tiempo (h) 100 Resumen Inteligente (Smart Meter), una turbina eólica, un generador fotovoltaico, varios electrodomésticos y un vehículo eléctrico. En la Figura 26 se muestra la estrategia de gestión de la demanda propuesta, donde a través de la Interfaz de Servicios de Energía (conectada a una pantalla), se le informa al usuario del valor actual y de la predicción para las próximas 24 horas de los precios de la electricidad, del consumo de energía y de la potencia de los generadores renovables. Posteriormente, utilizando la planificación del usuario para el día siguiente, expresada mediante su poder adquisitivo y por el conjunto de predicciones indicadas anteriormente, el Sistema de Gestión de la Energía (SGE) puede determinar, estableciendo la óptima negociación entre la empresa distribuidora y el usuario, el uso que este debe hacer de sus electrodomésticos durante el día siguiente. Una vez realizado este proceso de optimización, mediante la Interfaz de Servicios de Energía, el Sistema de Gestión de la Energía informa al usuario acerca de cuánto podría reducir su factura de electricidad si se lleva a cabo el uso sugerido de los electrodomésticos. De esta manera se incentiva al usuario a hacer uso de sus electrodomésticos de forma racional teniendo en cuenta su poder adquisitivo. Figure 26. Casa inteligente y su estrategia para la gestión de la demanda. El análisis de esta estrategia de gestión de la demanda se realizó considerando un consumidor residencial durante un día típico de verano en la ciudad de Zaragoza, en una casa inteligente equipada con un televisor, un sistema de aire acondicionado, un ordenador, varias lámparas, otros electrodomésticos de uso cotidiano y un vehículo eléctrico. En nuestro análisis se han considerado dos posibles situaciones. En la primera situación el usuario, de acuerdo a su poder adquisitivo, indica en el día previo a nuestro análisis que podría pagar 1 c€/kWh por ver la televisión entre las 14:00 y las 23:00 Medidor Inteligente Predicción Precios de la energía en tiempo real Potencia eólica Potencia fotovoltaica Demanda de energía SGE Actividades planificadas por el usuario Resumen 101 horas, 10 c€/kWh por usar el aire acondicionado entre las 13:00 y las 22:00 horas durante 5 horas, 10 c€/kWh por usar el ordenador entre las 9:00 y las 20:00 horas, 10 c€/kWh por usar las lámparas entre las 21:00 y las 23:00 horas, 10 c€/kWh por usar los otros electrodomésticos durante las próximas 24 horas, y 5 c€/kWh por usar el vehículo eléctrico durante 5 horas en cualquier momento del día siguiente. En la Figura 27 se muestran los valores predichos y actuales de los precios de la energía y la temperatura ambiente para el día típico de verano bajo estudio. Figura 27. Precios de la energía eléctrica y temperatura ambiente. Habitualmente los residentes de esta casa utilizan el aire acondicionado entre las 18:00 y las 22:00 horas, ya que, asumiendo que esta casa tiene un buen aislamiento térmico, el aire acondicionado podría utilizarse durante las horas del día en las que los precios de la electricidad son bajos. En este sentido, en la Figura 28 se muestra el uso recomendado para este electrodoméstico. Figura 28. Comparación entre el uso típico y óptimo del aire acondicionado. 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Tiempo (h) Precio (c€/kWh) 0 0.2 0.4 0.6 0.8 1 1.2 Potencia (kW) Precios predichos Precios actuales Óptimo Típico 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Tiempo (h) Precio de la electricidad (c€/kWh) 0 5 10 15 20 25 30 35 40 Temperatura (ºC) Precios predichos Precios actuales Temperatura actual Temperatura predicha 102 Resumen El usuario del vehículo habitualmente viaja entre las 8:00 y las 13:00 horas. Sin embargo, en su planificación para este día específico el usuario ha expresado flexibilidad en su uso, siendo necesario un grado de autonomía correspondiente a un estado de carga (EC) del banco de baterías del vehículo de, al menos, el 60%. La Figura 29 muestra los resultados al aplicar la estrategia de gestión de la demanda al uso del vehículo eléctrico. Nótese que si el usuario comienza su viaje a las 8:00 (EC=61,7%) y regresa a las 13:00 horas (EC=50%), la electricidad necesaria para recargar el banco de baterías se adquirirá cuando su precio es elevado, mientras que si el usuario comienza su viaje a las 19:00 (EC=77.7%) y regresa a las 23:00 horas, la autonomía del vehículo es mayor y el banco de baterías se recarga cuando los precios de la energía son más bajos. Figura 29. Ilustración del uso óptimo del vehículo eléctrico en la primera situación. Considerando los precios horarios mostrados previamente en la Figura 27, el usuario ha especificado que puede pagar 1 c€/kWh por utilizar el televisor entre las 14:00 y las 23:00 horas, siendo este un valor muy bajo para el coste de la electricidad, por lo que la estrategia de gestión de la demanda recomienda no utilizar el televisor. La Figura 30 muestra la comparación entre las curvas de demanda típica y óptima para esta situación, observándose que es posible obtener una reducción en la factura de electricidad de, aproximadamente, un 22%. En otra situación que se estudió, el usuario comunica en su planificación la necesidad de utilizar el vehículo entre las 8:00 y las 13:00 horas pagando 5 c€/kWh por la energía eléctrica requerida. En esta situación no se expresa flexibilidad alguna en el uso del 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Tiempo (h) Precio (c€/kWh) 0 0.5 1 1.5 2 2.5 3 3.5 4 Potencia (kW) Precios predichos Precios actuales Óptimo Típico EC=66% EC=74.18% EC=61.7% EC=35% EC=50% EC=77.7% Resumen 103 vehículo eléctrico. Las especificaciones de uso para los otros electrodomésticos permanecen iguales a las de la situación anterior. La Figura 31 muestra el uso sugerido por la estrategia de gestión de la demanda bajo estas condiciones, que coincide con los requerimientos del usuario debido a que este puede pagar la suficiente cantidad de dinero por la energía necesaria para realizar el viaje en el momento solicitado y recargar el banco de baterías del mismo posteriormente. Figura 30. Comparación entre las curvas de demanda típica y óptima en la primera situación. Figura 31. Ilustración del uso óptimo del vehículo eléctrico en la segunda situación. La Figura 32 muestra la comparación entre las curvas de demanda típica y óptima para esta situación, observándose que es posible obtener una reducción en la factura de la electricidad de, aproximadamente, un 8%. 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Tiempo (h) Precio (c€/kWh) 0 0.5 1 1.5 2 2.5 3 3.5 4 Potencia (kW) Precios predichos Precios actuales Óptimo Típico 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Tiempo (h) Precio (c€/kWh) 0 0.5 1 1.5 2 2.5 3 3.5 4 Potencia (kW) Precios predichos Precios actuales Óptimo Típico 104 Resumen Figura 32. Comparación entre las curvas de demanda típica y óptima en la segunda situación. 2.4 Conclusiones En esta tesis doctoral se han analizado, de forma detallada, los principales aspectos relacionados con el funcionamiento de los sistemas eléctricos aislados y conectados a la red eléctrica basados en fuentes de energía renovable. En lo referente al análisis de los sistemas aislados de la red eléctrica, se ha analizado el efecto de la eficiencia culómbica y del regulador de carga en la fiabilidad de los sistemas eólicos con baterías. También se ha tratado la estimación de las horas de operación, consumo de combustible y coste neto actualizado de los sistemas que utilizan como respaldo un generador convencional. Por otra lado, se ha desarrollado un modelo probabilístico que permite considerar la incertidumbre existente en la estimación de la vida del banco de baterías, la incertidumbre asociada a los precios del combustible, la producción del generador fotovoltaico, el perfil típico de carga, así como la variabilidad de los recursos eólico y solar. Además, teniendo en cuenta la importancia que tiene el uso racional de la energía eléctrica, en esta tesis se ha desarrollado una novedosa técnica para la gestión de la demanda de sistemas aislados de la red eléctrica que sugiere al usuario del mismo el mejor momento para hacer uso de sus electrodomésticos, reduciendo el consumo de combustible y mejorando el uso de la energía almacenada en el banco de baterías. Finalmente, considerando sistemas conectados a la red eléctrica, se ha desarrollado una estrategia de Adaptación de la Demanda para consumidores residenciales que, haciendo uso de las capacidades de comunicación de la futura Red Eléctrica Inteligente, determina mediante la optimización de la negociación entre el usuario y la empresa de distribución de energía eléctrica, la forma en que el consumidor debe utilizar sus electrodomésticos considerando sus preferencias y su poder adquisitivo. 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Time (h) Price (c€/kWh) 0 0.5 1 1.5 2 2.5 3 3.5 4 Power (kW) Forecasted price Actual price Optimal Typical Resumen 105 Los resultados obtenidos sugieren importantes mejoras en los modelos que se utilizan habitualmente en la simulación y optimización de sistemas híbridos, específicamente en la consideración del regulador de carga como un importante elemento del sistema, y en la estimación de la vida útil del banco de baterías. Además, las estrategias para la gestión de la demanda, presentadas en este trabajo de investigación, pueden ayudar a que los usuarios de sistemas aislados o conectados a la red eléctrica realicen un uso eficiente de las fuentes de energía locales, y adapten sus patrones de consumo de electricidad a su condición económica actual. Introduction 113 are installed in countries that belong to the OECD, while many isolated systems are installed in developing countries such as China and India, due mainly to their large rural populations [5]. As explained previously, the actual energy situation is characterized by the growth of world energy consumption as a consequence of the robust economic development of countries with emerging economies, in addition to a considerable increase in the electricity generation capacity installed to satisfy the energy demand. In this expansion of the capacity installed of power generation are included different sources such as natural gas, coal, nuclear energy, fossil fuels, and renewable energies. Renewable energies have been quickly growing in recent years, driven by problems related to environmental factors, the depletion of oil and natural gas reserves, and technological advances that have allowed a considerable reduction in manufacturing costs. Wind energy and solar energy have garnered big interest around the world. In the specific case of wind energy (which, according to Figures 4 and 5, has greater capacity installed than solar photovoltaic energy), its impact in the power system is mainly related to its penetration level and the flexibility of the system [6]. On the one hand, if the penetration level is increased, the impact of wind energy in the power system will be higher; i.e., the uncertainty related to wind power could considerably increase the production costs when the penetration level is high. The fluctuations of wind power could affect the operation of other dispatchable generation units because the intermittence of wind power could drive other generation units to operate far from the optimal point. On the other hand, if the flexibility level of the system is increased, more wind energy can be integrated into the system; i.e., during periods of low demand and high production of wind power, a reduction in the power production from wind farms is necessary to maintain the energy balance of the system; this decision depends on the penetration level of wind power and the flexibility of the system [6]. Another important aspect is that problems related to restrictions imposed on electricity prices, such as price ceilings, flat rates, and other regulatory restrictions, have produced a significant difference between the marginal cost of power generation and the price at which consumers obtain the energy. As a consequence of this difference, in many countries, the growth of demand for energy is higher than the growth of the capacity installed; i.e., the growth in the capacity of power generation has been affected by the fact that the electricity prices do not reflect the real marginal cost. While the development of the population and economic growth require the consumption of large quantities of energy, 114 Introduction the liberalization of the electric energy sector is perceived as a risky policy that could drive the loss of welfare for consumers in the short term; this situation makes growth and development difficult due to the inhibition of the restructuring process [7]. As a solution to the problems related to the growth of energy demand and the growth in the penetration level of wind energy, several authors have proposed using massive storage of electric energy as an option that could convert random sources of energy in dispatchable power plants. Anagnostopoulos et al. [8] and Varkani et al. [9] proposed using a reversible hydraulic system to recover excess electric energy from wind farms due to the limitations required for the balanced operation of the electric grid. This idea could help the growth of the wind energy capacity installed and increase the economic benefits derived from it. Recently, Fertig et al. [10] proposed using a combination of a compressed air energy storage system and a wind farm to provide dispatchable power. Bernal-Agustín et al. [11], analyzing the shape of the demand curve, proposed using the excess energy produced during off-peak hours to generate hydrogen and store it in a hydrogen tank; this energy could then be sold to the electric grid during peak hours. Dufo-López et al. [12] proposed a similar idea but using different types of batteries. On the other hand, the flexibility of the power system can be increased using demand side management to incentivize consumers to use electric energy during hours of high wind power production [6]. In this doctoral thesis is carried out a deep analysis of the operation and modeling of electrical systems isolated and connected to an electric grid that uses renewable energies, along with the development of strategies to manage the energy demand to help residential consumers find the optimal use for their household appliances. The main results and novelties found in this research work are presented in the following group of scientific articles: 1. Lujano-Rojas JM, Dufo-López R, Bernal-Agustín JL. Optimal sizing of small wind/battery systems considering the DC bus voltage stability effect on energy capture, wind speed variability, and load uncertainty. Applied Energy 2012;93:404-412. 2. Lujano-Rojas JM, Monteiro C, Dufo-López R, Bernal-Agustín JL. Optimum load management strategy for wind/diesel/battery hybrid power systems. Renewable Energy 2012;44:288-295. Introduction 115 3. Lujano-Rojas JM, Monteiro C, Dufo-López R, Bernal-Agustín JL. Optimum residential load management strategy for real time pricing (RTP) demand response programs. Energy Policy 2012;45:671-679. 4. Lujano-Rojas JM, Dufo-López R, Bernal-Agustín JL. Optimal design of PV/Wind/Battery systems by genetic algorithms considering the effect of charge regulation. International Conference on Mechanical and Electronic Engineering (ICMEE 2012). This paper will be published in Lecture Notes in Electrical Engineering. 5. Lujano-Rojas JM, Dufo-López R, Bernal-Agustín JL. A qualitative evaluation of operational conditions in PV/Wind/Battery systems. Asia-Pacific Power and Energy Engineering Conference (APPEEC 2012). Available at IEEEXplore. 6. Lujano-Rojas JM, Bernal-Agustín JL, Dufo-López R, Domínguez-Navarro JA. Forecast of hourly average wind speed using ARMA model with discrete probability transformation. Lecture Notes in Electrical Engineering 98. Springer-Verlag; 2011. p. 1003-1010. Summary 117 Summary This research work presents an extensive analysis and the development of optimal demand response strategies for hybrid power systems and residential grid-connected systems that use uses renewable energies. The development of these tasks requires the carrying out of several objectives by means of a determined methodology. Objectives The main objectives of this doctoral thesis are: 1. To analyze the modeling of the different components of a typical hybrid power system that has a wind turbine, several photovoltaic panels, conventional generation, and a lead acid battery bank. 2. To analyze the simulation and optimization techniques of a typical hybrid power system that has a wind turbine, several photovoltaic panels, conventional generation, and a lead acid battery bank. 3. To develop strategies for optimal load management using hourly forecasting of wind speed, solar radiation, and ambient temperature to improve the performance of hybrid power systems that have a wind turbine, several photovoltaic panels, conventional generation, and a lead acid battery bank. 4. To analyze the main characteristics of a future smart grid, specifically a technological infrastructure that allows bidirectional communication between the retailer and the consumers. 5. To analyze the modeling of the different components of a typical residential electric system connected to a smart grid that has a wind turbine, several photovoltaic panels, and household appliances in a real-time pricing environment. 6. To analyze strategies for the optimal load management for a typical residential consumer in a real-time pricing environment. 118 Summary Methodology The methodology carried out in this thesis is presented next: 1. Carry out a literature review on the different mathematical models of wind turbines, photovoltaic panels, lead acid batteries, inverters, and conventional generation. 2. Carry out a literature review on the deterministic modeling and optimization of hybrid power systems. 3. Carry out a literature review on the probabilistic modeling and optimization of hybrid power system. 4. Carry out a literature review on forecasting techniques of hourly wind speed, solar radiation, and ambient temperature. 5. Develop and implement a strategy for load management that allows optimization of the performance of the battery bank and conventional generation in a typical hybrid power system. 6. Carry out a literature review on the infrastructure of smart grids. 7. Carry out a literature review on the main techniques to forecast wholesale energy market prices. 8. Develop a demand response strategy for a typical residential consumer connected to a smart grid considering a wind turbine, several photovoltaic panels, several household appliances, and an electric vehicle. Literature review and the main contributions of this doctoral thesis The management of power systems can be carried out by means of controlling the sources of power, managing demand, or both. These strategies can be applied to gridconnected systems or isolated systems. In this research work, the isolated and gridconnected systems are analyzed, and strategies to manage the energy demand of residential consumers of these types of systems are developed. Summary 119 Many studies have shown the importance of hybrid power systems in rural electrification [13,14,15] and reduction of the emission of greenhouse gases [16]. The sizing and control of hybrid systems is an important factor that has been studied by many authors. The Hybrid Optimization Model for Electric Renewables (HOMER) [17] is a computational tool developed by the U.S. National Renewable Energy Laboratory that is used frequently for the simulation and optimization of hybrid systems in testing all possible combinations. Belfkira et al. [18] implemented the Dividing Rectangles (DIRECT) algorithm for the optimal sizing of a system that has several photovoltaic panels, a wind turbine, and a diesel generator, minimizing the total cost. Boonbumroong et al. [19] used particle swarm with a constriction coefficient for the optimal sizing of a typical hybrid system with several photovoltaic panels, a wind turbine, a battery bank, and a bidirectional inverter. The results obtained were compared with HOMER, and it was concluded that the proposed methodology considerably reduced the time required to find the optimal configuration. Hakimi and Moghaddas-Tafreshi [20] used particle swarm optimization to size a system with a wind turbine, fuel cells, an electrolyzer, a hydrogen tank, a reformer, and an inverter, obtaining high reliability due to the fact that the fuel cells are a backup for the wind turbine. Hybrid Optimization by Genetic Algorithms (HOGA) [21] is a computational tool developed by the University of Zaragoza for the simulation and optimization of a hybrid system using genetic algorithms. Ekren and Ekren [22] used simulated annealing for the optimal sizing of a hybrid system comprising several photovoltaic panels, a wind turbine, and batteries installed in Turkey. Considering the variability of renewable resources in the optimization of a hybrid system is an important factor that has been studied by several authors. Bagul et al. [23] proposed a methodology that consists of estimating the probability density function of the energy that flows by means of the battery bank’s using information about the renewable resources and technical data provided by the manufacturers, obtaining the optimal configuration of components considering a determined confidence level. Karaki et al. [24,25] developed a sizing technique based on finding the expected value of the energy available to recharge the battery bank using the joint probability distribution function of the renewable resource and the duration curve of the energy demand, determining the optimal configuration considering the capital cost and the reliability of the system. Roy et al. [26] implemented a methodology that consists of identifying the 120 Summary set of all possible configurations of a hybrid system, and then the optimal configuration is determined using the probability distribution function of the renewable resources. Távora et al. [27] compared the deterministic and probabilistic approaches and concluded that the deterministic approach could suggest a configuration for a hybrid system with over-estimated generation capacity for a determined level of reliability. Giannakoudis et al. [28] presented an optimization methodology using simulated annealing adapted to consider uncertainty (stochastic annealing). Tan et al. [29] developed a methodology for the optimal sizing of a battery bank in an uninterruptible power system that has a photovoltaic generator using a Monte Carlo simulation approach. The first step of this methodology consists of generating a random event for a load profile, weather conditions, and failure. Then, under these operating conditions, in the second step, the required storage capacity is calculated. This process is repeated a specified number of times. Finally, the results are statistically analyzed using the cumulative distribution function, and the storage capacity is economically selected considering a determined confidence level. The control of hybrid power systems has two important components: the strategies to control the energy sources and energy demand management. In an important paper, Barley and Winn [30] proposed the following general strategies to control hybrid systems: the frugal discharge strategy, load following strategy, state of charge setpoint strategy, and full power/minimum run time strategy. In the frugal discharge strategy, the intersection of the cost curve of the diesel generator and the cost curve of the use of the battery bank determines the critical load. In this strategy, if the net load (the difference between the load and the renewable power) is higher than the critical load, the diesel generator is used; in other cases, the battery bank is discharged. In the load following strategy, the diesel generator is used only to meet the net load. In the state of charge setpoint strategy, the diesel generator is used to charge the battery bank up to a predefined value. In the full power/minimum run time strategy, the diesel generator operates during a predefined interval of time, charging the battery bank with the excess energy. Ashari and Nayar [31] developed a strategy that uses the load demand, the voltage of the battery bank, and the minimum operating power of the diesel generator to decide when to charge or discharge the battery bank and when the diesel generator must be started or stopped. The optimal strategy is obtained, determining the critical load at which the diesel generator must be started or stopped and the setpoint of state of charge Summary 121 at which the battery bank must be discharged. Dufo-López and Bernal-Agustín [32] proposed a control strategy that combines the load following strategy and the state of charge setpoint strategy proposed previously by Barley and Winn [30]. In this combined strategy, if the net load is lower than the critical load, the state of charge setpoint strategy is applied; in other cases, the load following strategy is used. Yamamoto et al. [33] proposed a strategy that uses predictions of the hourly power production of the renewable energy sources and the load demand to determine the operating power of the diesel generator. If the state of charge of the battery bank is between 0.5 and 0.7, the diesel generator starts to charge the battery bank, and when the state of charge is higher than 0.7, the diesel generator is shut off. Several authors have analyzed the load management in hybrid power systems. Groumps et al. [34] carried out the first research work about a standalone photovoltaic system, analyzing a system installed in the Village of Schuchuli, Arizona (USA). In the operative strategy of this system, four categories of priority and four settings of state of charge (0.5, 0.4, 0.3, and 0.2) were considered. For example, if the battery bank is discharged and the settings of state of charge are reached sequentially, the loads are sequentially disconnected starting with the load with the lowest priority level. Otherwise, if the battery bank is charged and the settings of state of charge are reached sequentially, the loads are sequentially reconnected. In another paper, Groumps and Papegeorgiou [35] proposed a technique for load management in standalone photovoltaic systems based on three main categories of load classification: a classification according to load operation (DC and AC loads), a classification according to the system operation (uncontrollable, controllable, and semi-controllable loads), and a classification according to the priority (useful, essential, critical, and emergency loads). In this strategy, using controllable loads, the load curve is manipulated to minimize the integral of the square of the net load over a 24-hour period to reduce the required capacity of the battery bank. Khouzam and Khouzam [36] developed a methodology to manage the load in a standalone photovoltaic system classifying the loads into four categories according to their priority level: convenient, essential, critical, and emergency. The priority of the battery bank is a variable that depends on its state of charge. The optimal load management is based on the maximization of an objective function that depends on the priority level of the load subject to constraints of the availability to supply the energy demand. Moreno et al. [37] implemented a fuzzy logic 122 Summary controller for the load management in standalone photovoltaic systems. This controller considers the expected supply forecasted one hour ahead to decide whether to connect or disconnect a determined load according to the priority level. The load management in residential grid-connected systems has been analyzed by many authors. Salah et al. [38] developed a methodology in which the photovoltaic generator is considered a complementary power source and then, using a fuzzy logic controller, it is decided which household appliance must be connected to the photovoltaic generator and the electrical grid. The decision is made considering the power production of the photovoltaic generator, the energy required by each appliance, and its priority level. According to the results obtained, this methodology allows continuous energy savings to be obtained. Ammar et al. [39] proposed a strategy for load management for residential consumers using daily predictions of the power production of the photovoltaic generator to decide the time at which a determined appliance will be connected to the photovoltaic generator. This decision is made considering the energy required by each appliance. A similar criterion was proposed by Salah et al. [38]. Thiaux et al. [40] analyzed the influence of the load profile shape in the cost of energy during the lifetime of a typical standalone photovoltaic system. The results have shown that the energy required is reduced when the load profile and the photovoltaic power production are similar. Demand response (DR) is defined as the changes in the electricity consumption patterns of the end consumers to reduce their energy demand in times of high electricity prices. The changes in the behavior and the consumption pattern of the consumers could be carried out through changes in electricity prices (price-based programs) or incentive payments (incentive-based programs) [41]. In this way, demand response’s changing the electricity consumption pattern of the end consumers can reduce problems related to the difference between the marginal generation costs and the price at which the end consumers obtain the energy [7]; additionally, demand response can improve the efficiency and the reliability of the available infrastructure and reduce the volatility of electricity prices [41]. The implementation of demand response programs requires an electrical grid that has the technology to allow communication between the consumers and the retailer; this concept of the electrical grid is known as a smart grid. DR programs have been divided Summary 129 Figure 11. Power curves of different wind turbines Figure 12. Evolution of the net present cost during the optimization It has been shown that the battery bank is one of the most important components in a hybrid system. The battery bank affects not only the performance of the system but also its profitability due to the fact that this is one of the most expensive components in the system and that its lifetime is difficult to determine. The problem is that, if the uncertainty regarding the battery bank lifetime is large, the net present cost could be too high at the end of the lifetime of the system, and, consequently, the system could not be profitable. Effect of uncertainty related to the battery bank lifetime, wind speed variability, and load profile uncertainty in small-capacity wind energy systems. Many studies have been carried out to determine the battery bank lifetime; as a result of these studies, three types of ageing models have been developed: physico-chemical ageing models, weighted Ah ageing models, and event-oriented ageing models. Physico-chemical ageing models are based on a detailed knowledge of physical and 1 2 3 4 5 6 7 8 9 10 3 3.2 3.4 3.6 3.8 4 x 10 4 Generations Net present cost (€) 0 1 2 3 4 5 6 7 8 9 0 5 10 15 20 25 30 Wind speed (m/s) Power (kW) 130 Summary chemical factors related to the ageing process, while weighted Ah ageing models are based on the assumption that the lifetime of the battery bank is proportionally related to the total Ah throughput. In the implementation of this ageing model, the actual Ah throughput is multiplied by a weight factor fitted according to the actual operating conditions. Finally, the battery bank lifetime is reached when the total Ah throughput exceeds a limit value calculated from nominal conditions. The event-oriented aging model determines the reduction in the battery bank lifetime by identifying extreme operating conditions by means of the pattern recognition approach [64]. Using information provided by experts, Svoboda et al. [65] developed different operating categories for the battery bank based on the calculation of stress factors related to the discharge current, time between successive recharge, and Ah throughput during low state of charge conditions. In [53], these operating categories were used for the qualitative evaluation of the operating conditions of the battery bank of a hybrid system installed in Zaragoza. Figure 13 shows the time series of state of charge, which was used to calculate the stress factors required to determine the operating categories of the battery bank. The study case analyzed was characterized by a high state of charge during many hours of the year, in some hours of high discharge currents, and frequent recharges, which produce a high risk of corrosion of the positive grid, a very high risk of water loss, and high risk of active mass shedding. However, there is a low risk of irreversible sulphation or active mass degradation, reverse polarization of cells, and stratification or freezing of the electrolyte [65]. Figure 13. Time series of state of charge The Ah ageing model (i.e. the weighted Ah ageing models without considering the weight factors) has been implemented in many computational tools for the simulation 30 40 50 60 70 80 90 100 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 Time (h) State of charge (%) Summary 131 and optimization of hybrid systems. In [66], the researchers carried out an experimental validation considering lead acid batteries of flat-plate OGi and tubular OPzS operating under wind and photovoltaic generation profiles. Specifically, in wind generation conditions, the results obtained showed an error of 16.7% in the estimation of the lifetime of the flat-plate OGi battery and an error of 17.5% in the estimation of the lifetime of the tubular OPzS battery. Based on these results, in [51], the Ah ageing model (without considering the weight factors) was incorporated in the probabilistic model of the small wind energy system shown in Figure 7 using the Monte Carlo simulation approach. This model can consider the variability of wind resources by means of the auto regressive moving average (ARMA) model, which considers the main features of wind speed time series: no-Gaussian shape of its probability distribution function, no stationarity, and a high-order autocorrelation. Additionally, this model can consider the uncertainty related to the load profile. Using this stochastic model, [51] analyzed the effect of uncertainty regarding the battery lifetime on the net present cost. The results showed that 17.5% uncertainty in the battery bank lifetime produces about 12% uncertainty in the net present cost. Figure 14 shows the net present cost and its uncertainty interval for different battery bank capacities and the rated power of the wind turbines considering a confidence level of 1%. Figure 14. Expected value of the net present cost 100 150 200 250 300 350 400 450 500 550 600 0 500 1000 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 x 10 4 Wind turbine capacity (W) Battery bank capacity (Ah) Net present cost (€) 132 Summary The system shown in Figure 7 was used to analyze the effect of uncertainty regarding the reliability of the system. In these systems, reliability is related to the battery bank capacity, the rated power of the wind turbine, and the weather conditions of the place of installation. Figure 15 shows the results obtained from the reliability analysis for different battery bank capacities and rated power of the wind turbines considering a confidence level of 1%. Figure 15. Expected value of the energy index of unreliability Frequently, hybrid power systems need to meet large energy demands or require high reliability levels; in these situations, the systems commonly incorporate a conventional generator, which provides dispatchable power, but due to the relatively high prices of the fuel, the use of conventional generation increases the net present cost considerably. However, the battery bank has an important role due to the fact that it can reduce the number of operating hours of the conventional generator, storing the excess energy from the renewable generators. The probabilistic model of a typical wind energy system presented in [51] was improved in [54], incorporating a photovoltaic generator, a conventional generator, and an inverter. Additionally, this probabilistic model was improved, incorporating the long-term uncertainty related to the wind resource, the uncertainty related to the photovoltaic generator, and the uncertainty related to the fuel prices. 100 150 200 250 300 350 400 450 500 550 600 0 500 1000 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Wind turbine capacity (W) Battery bank capacity (Ah) Energy index of unreliability Summary 133 Influence of the temperature, charge regulation, and coulombic efficiency of the battery bank in the performance of hybrid systems with conventional generation. The effect of the coulombic efficiency and operation of the charge controller of the battery bank in a typical hybrid system that has a photovoltaic generator, a wind turbine, and a conventional generator was analyzed in a system located in Zaragoza. The results obtained were compared with those obtained using HOMER, which does not consider these factors. The results obtained from the comparative analysis between the hours of operation of the conventional generator, its fuel consumption, and the net present cost of the system are shown in Figures 16, 17, and 18, respectively. According to this analysis, there are important differences between the simulations of the two models when the system has low storage capacity. Systems with low storage capacity have high charge currents, so the high voltage setpoint of the charge controller is reached prematurely and renewable generators are disconnected, producing a low state of charge for the battery bank, an increase in the number of hours of operation of the conventional generator and its fuel consumption, and, consequently, a considerable increase in the net present cost compared with the results obtained using the HOMER model. The highest difference between both models was obtained with a battery bank of 100Ah. For this configuration, the difference between the hours of operation of the conventional generator, its fuel consumption, and the net present cost of the system were about 33%, 31%, and 31%, respectively. When the battery bank capacity is increased, the results obtained from the comparative analysis are very similar due to the fact that, in these cases, the charge currents are reduced, the high voltage setpoint is not reached prematurely, and the battery bank can accept more energy. Figure 16. Comparison of the hours of operation 0 1000 2000 3000 4000 5000 6000 0 1000 2000 3000 4000 5000 6000 Capacity of the battery bank (Ah) Hours of operation (hr/yr) Model presented in [53] HOMER 33% 134 Summary Figure 17. Comparison of fuel consumption Figure 18. Comparison of the net present costs Effect of uncertainty related to the battery bank lifetime and fuel prices in the performance of hybrid systems with conventional generation In another case study, using the stochastic model developed previously, the effect of the long-term uncertainty related to the wind resource, the uncertainty in the power production of the photovoltaic generator, the uncertainty in the fuel prices, and the uncertainty in the load profile was analyzed in a hybrid system installed in Zaragoza and sized previously. Figure 19 shows the expected value of the net present cost and its uncertainty interval calculated considering a 10% confidence level. When the configuration of the hybrid system has low storage capacity (100Ah), the uncertainty in the net present cost is about 7%, influenced by the uncertainty in the fuel prices. If the capacity of the battery bank is increased, the uncertainty in the net present cost is jointly influenced by the uncertainty in the fuel prices and the uncertainty in the lifetime of the 0 10000 20000 30000 40000 50000 60000 70000 80000 90000 100000 0 1000 2000 3000 4000 5000 6000 Capacity of the battery bank (Ah) Net present cost (€) HOMER Model presented in [53] 31% 0 100 200 300 400 500 600 700 800 900 0 1000 2000 3000 4000 5000 6000 Capacity of the battery bank (Ah) Fuel consumption (l) Model presented in [53] HOMER 31% Summary 135 battery bank, reaching about 28% for a hybrid system with a capacity of 1000Ah. Finally, the uncertainty in the net present cost of systems with high storage capacity is influenced mainly by the uncertainty in the battery bank lifetime, reaching about 20% for a hybrid system with a capacity of 5000Ah. Figure 19. Expected value of the net present cost Forecasting of hourly wind speed and its application in the development of load management strategies in hybrid systems The concept of forecasting has long been a useful tool in the management of power systems with high penetration of renewable energy. In addition, this concept is useful in the residential load management. Residential consumers, using information provided by forecasting process, could use their household appliances in a convenient way to save money. The implementation of this idea in a hybrid system that has a wind turbine requires using a forecasting technique to predict the future values of wind power or wind speed. The auto regressive moving average (ARMA) model is a stochastic method frequently used in the literature as a forecasting technique for hourly wind speeds in the short term. In [55], a methodology to predict hourly average wind speeds using the ARMA model is described. The transformation, standardization, estimation, and diagnostic checking processes are carefully analyzed, and a discrete probability transformation has been incorporated to consider the shape of the probability density function of the original wind speed time series under study. Using data from three meteorological stations located in the Netherlands, a comparative analysis of forecasting errors obtained using the ARMA model with discrete probability transformation and an artificial neural network trained by back-propagation was carried out considering 0 20000 40000 60000 80000 100000 120000 140000 0 1000 2000 3000 4000 5000 6000 Capacity of the battery bank (Ah) Net present cost (€) 7% 28% 20% 136 Summary forecasting intervals between 1 and 10 hours. The results obtained showed that, in some cases, the ARMA model with discrete probability transformation could improve the artificial neural network by at least 17.71%. The methodology described in [55] to forecast hourly average wind speeds could be used in an illustrative form to develop a strategy for the load management in the typical standalone hybrid power system shown in Figure 20. Figure 20. Typical hybrid system The energy demand of the hybrid system under study could be managed to reduce the daily energy consumption of the conventional generator. This is possible using the controllable loads of the system when the wind speed is high. The load management strategy presented in [56] uses the prediction of the hourly average wind speed 24 hours ahead to determine when each household appliance must be used, minimizing the energy supplied by the controllable loads of the system (conventional generator and battery bank). This idea was analyzed using as an example a hybrid system installed in Zaragoza with the load profile presented in Figure 21. Figure 21. Typical load profile for the study case 0 5 10 15 20 25 0 100 200 300 400 500 600 700 800 900 1000 Power (W) Time (h) G Wind Turbine Battery Bank DC/AC Energy Demand Conventional Generator Summary 137 In our example, the user has two controllable loads that it uses frequently between 7:00 and 18:00 hours and between 1:00 and 24:00 hours, consuming 400W during 4 hours and 100W during 6 hours, respectively. The system is composed of a wind turbine of 3500W, a diesel generator of 1kW, an inverter of 1kW, and a battery bank of 1000Ah. Figures 22 and 23 show that, in applying the proposed idea, the load shifts to the wind power peak, reducing the requirements of the diesel generator and the battery bank. Figure 22. Wind power and load profiles for the 5th and 6th of August 2005 Figure 23. Controllable load management for the 5th and 6th of August 2005 Figures 24 and 25 show the effect of the load shifting in the state of charge of the battery bank and the reduction in the operating hours of the diesel generator. This strategy allows the improvement of the performance of the system, increasing the state of charge of the battery bank and reducing the number of operating hours of the diesel generator compared with a situation in which the load management is not implemented. 0 100 200 300 400 500 600 700 800 900 1000 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 Power (W) Typical load profile Optimal load profile Typical use of controllable loads Optimal use of controllable loads 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 Time (h) Power (W) Wind power With load management Without load management Wind power peak Load shifting Wind power peak Load shifting Time (h) 138 Summary Figure 24. State of charge for the 5th and 6th of August 2005 Figure 25. Diesel generator output power for the 5th and 6th of August 2005 Optimum load management strategies for grid-connected residential consumers Recently, the concept of the smart grid has been discussed by many authors in the specialized literature. Possibly, in the near future, residential consumers will buy electricity according to hourly dynamic prices; i.e., the implementation of the smart grid will allow the marginal cost of power generation to be reflected in the price at which residential consumers buy the energy. To meet this objective, the smart grid requires a communication infrastructure between the retailer and the consumers. This communication could be carried out using computer networks. An energy services interface (ESI) is a secure, two-way communication interface between the utility and the consumers. Using this interface, consumers could receive information about the hourly prices from the utility, and then, using a Web-based energy management system (EMS) connected to the energy services interface, the consumers can respond to the pricing signal previously received. For a typical house that had a smart meter, wind turbine, Time (h) State of charge With load management Without load management 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 0 100 200 300 400 500 600 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 Time (h) Power (W) With load management Without load management