A new tool to analysing photovoltaic self-consumption systems with batteries

Iso Self-consumption and Iso Self-sufficiency Curves. A New tool to Analyse Photovoltaic SelfConsumption Systems with Batteries. Abstract: Photovoltaic self-consumption systems with storage are an interesting option for residential consumption, especially due to the descending price of photovoltaics modules and batteries. However, the analysis of this type of systems can be complex since two independent variables must be considered: the array power and the rated capacity. In this sense, a new approach to analyse this type of systems is provided where not only the global Self-sufficiency and Self-consumption indices may be considered, but also direct and battery ones are defined. The latter represent the direct photovoltaic self-consumed energy and the one provided by the battery, respectively. Apart from these new indices, two new concepts are defined regarding Zero Energy Buildings (ZEB): ZEBdirect and ZEBbattery points. Furthermore, a new and intuitive tool to analyse this type of systems is provided: the iso self-consumption curves which may translate 3D self-consumption curves to 2D plots. This new method may help not only to determine the role of each element in the self-consumption system but it may be used by energy planners and designers to properly size the array power and the rated capacity. Moreover, it may assess the potential of this type of systems from either an energetic or profitability approaches. Keywords: Photovoltaic, self-consumption, batteries, analysis; iso self-consumption curves. Nomenclature: List of symbols EL Load consumption (kWh) EPV,con Photovoltaic energy self-consumed (kWh) EPV,generated Photovoltaic energy generated (kWh) EPV,direct Direct Photovoltaic energy self-consumed (kWh) ETPac Photovoltaic energy given to the bidirectional inverter to charge the battery (kWh) EFPac Energy given by the bidirectional inverter from the batteries to the loads (kWh) EPV-BAT Energy given by the array and the battery to the loads (kWh) isoSC Iso self-consumption isoSS Iso Self-sufficiency ZEBdirect point Direct Zero Energy Building point ZEBbattery point Battery Zero Energy Building point τ Reporting period τr Recording interval φsc Global self-consumption index φss Global self-sufficiency index φsc,direct Direct self-consumption index φss,direct Direct self-sufficiency index φsc,bat Battery self-consumption index φss,bat Battery self-sufficiency index Bidirectional inverter efficiency charge, storage and discharge efficiency Acronyms BDI Bidirectional inverter MPPT Maximum Power Point Tracker PV Photovoltaics PR Performance Ratio SC Self-consumption SS Self-sufficiency ZEB Nearly zero energy building 1. Introduction Climate change is a fact and it is necessary that CO2 emissions should be considerably reduced to mitigate the effect of global warming. In the European Union, commercial and residential consumption represents 40% of total energy consumption and 55% of total electricity consumption [1,2]. Policies that encourage to increase energy efficiency as well as the use of renewable energies in order to promote nearly Zero Energy Buildings (nZEBs) should be improved. In this way, a European Union directive requires that all buildings should fall into this category by 2021[3]. In this type of buildings, photovoltaics solar energy together with thermal solar energy can play an important role. Photovoltaic solar energy, due to its maturity and its modularity, is a real option to address residential consumption. It should be also noted that the cost of residential photovoltaic systems has been considerably reduced by 48% from 2007 to 2018 [4]. Moreover, it has been shown not only the costcompetitiveness but the profitability of this type of systems [5,6]. As there is not a complete matching between the generation and consumption profiles (i.e. there is energy consumption outside the generation profile), net zero energy buildings (ZEB) cannot be managed only considering direct photovoltaic self-consumption (i.e. without batteries). However, the matching between the aforementioned profiles in this type of systems can be improved through load shifting or Demand side management (DSM) and the use of energy storage systems [7]. The use of batteries may increase the selfconsumption rates in a range of 13-24% for photovoltaic self-consumption systems with batteries between 0.5-1.0 kWh / kWp [8]. Besides, the use of batteries has a prominent role in peak shaving potential [9]. On certain occasions, the injection of excess energy into the network is allowed considering net metering (US) and feed-in tariff policies (Europe, Australia, Asia) providing an economic alternative to this surplus energy. However, grid export rates are decreasing considerably in the PV markets [10,11]. So, it may be the case that the remuneration received is clearly lower than the price of the energy consumed from the grid. Therefore, energy storage is presented as an attractive solution to take advantage of energy that is not directly self-consumed and which may be later used when the generated energy is lower than the consumed one. Likewise, the increase in self-sufficiency and self-consumption rates while not only prevent energy from being lost or wasted but also limit the delivery of photovoltaic energy to the grid, reducing its stress [12,13]. The topology of a self-consumption photovoltaic system with storage system may have two variants depending on whether a DC or an AC-Bus is used, figure 1. The topology used in this paper will be the one with an AC-Bus [12,14,15]. Figure 1. Photovoltaic self-consumption system (a) DC Bus (b) AC Bus. If batteries are taken into account self-sufficiency (SS) and self-consumption (SC) indices may be defined as: (1) (2) L(t) and P(t) corresponds to the instantaneous building power consumption and the onsite photovoltaic generated power, respectively. M(t) represents the instantaneous photovoltaic self-consumed power (directly or to storage) while MB(t) defines the PV power directly self-consumed by the loads together with the power given from the battery to the loads. Figure 2 shows the two types of self-consumption to be considered: direct or with battery, respectively. If batteries are used, EPV,con should consider not only the overlapping part of the generation and load profiles (EPV,direct), but the one corresponding to the PV energy given to the charger-inverter or bidirectional inverter (BDI) in order to charge the battery (ETPac) [16]. Moreover, EPV-BAT should take into account EPV,direct and the energy given by the BDI from the batteries to the loads (EFPac). The reporting period, τ, as stated by the IEC61724, is provided by t2 and t1 and may be daily, weekly, monthly or annual. Generally, it may be considered an annual basis so as to take into account seasonal variations and to minimize the influence of short-term random fluctuations. The recording interval, τr , provides the time resolution. A proper recording interval that balances matching error, which leads to self-consumption indices overestimation [17,18], and monitoring resources should be considered [19]. (a) (b) Figure 2. Daily photovoltaic generation and load profiles. Direct photovoltaic self-consumption without Battery (a) and with battery (b). PV generator=5 kWp and CS= 3 kWh. SS and SC indices reported in the literature when analysing photovoltaic self-consumption systems with storage correspond to global indices where the self-consumption due to the array and the battery are gathered together. Moreover, they are generally provided for a given array power and a rated capacity. In [20] indices for different households in different countries as a function of the rated capacity are reported. SS and SC indices range from 27 to 87% and from 31 to 91%, respectively. Storage is a good choice when increasing self-sufficiency indices and leaving-off the grid. Moreover, battery prices have been considerably reduced in recent years [21,22]. However, it must be noted that, generally, the analysed photovoltaic self-consumed systems with storage do not differentiate array and battery self-consumption as the monitored data only considers global self-consumed energy. Moreover, photovoltaic selfconsumption systems have two independent variables (i.e. array power and rated capacity). In this sense, it may be quite interesting to differentiate self-consumption parameters related with the array power and battery as they may help not only to properly analyze this type of systems but to improve the sizing methods. Moreover, it may better assess the potential of storage when increasing self-sufficiency index. 2. Objectives Most of the studies regarding photovoltaic self-consumption with batteries focus on global SS and SC indices as indicated in Eq. (1) and (2) and they do not discriminate direct self-consumption (i.e the selfconsumed photovoltaic array energy given directly/instantaneously to loads) from self-consumption due to the battery (the self-consumed photovoltaic array energy delivered at first to the battery and then, when necessary, to the loads). This approach may highlight the differentiated role of each one in the selfconsumption system in order to make not only a comparison between them but to provide either a proper energetic or a profitability analysis of this type of systems. Moreover, a joint analysis where the direct and battery analysis are considered together may be complex as it is based on 3D plots (there are two independent variables to be considered: the array power and the rated capacity). The main objective of the manuscript is to provide a new approach to analyze photovoltaic selfconsumption systems with batteries. Therefore, indices of direct and battery self-consumption will be defined (i.e. self-sufficiency and self-consumption ones). Likewise, a separate study of the aforementioned indices will be developed based on the photovoltaic array power and the rated capacity. Apart from the new indices, new interesting points to be taken into account for the analysis of these types of systems will be defined: ZEBdirect and ZEBbattery obtained as the intersection of the corresponding selfsufficiency and self-consumption curves. The role of each of one will be studied separately. Furthermore, the ZEB curve (i.e the intersection between the two surfaces associated to the SS and SC indices) can be obtained. Finally, a new and interesting tool to analyze this type of systems will be provided: the iso selfconsumption and iso self-sufficiency curves (isoSC and isoSS curves). These curves allow a 2D representation of the aforementioned 3D plots and it may also provide, in a simple way, the different SS and SC indices: global, direct and battery ones together with the aforementioned ZEB points and the ZEB curve. This tool may not only manage an analysis of this type of systems but it may make easier and more intuitive the sizing methods based either on energetic and profitability criteria. This new approach will allow to select for a given consumption profile of a home, the necessary array power and rated capacity to get a given self-sufficiency index or to select the array power and rated capacity in a photovoltaic self- consumption system to manage cost-competitiveness. In this sense, it may be provided a tool that simplifies the analysis of photovoltaic self-consumption systems with batteries and which may be used not only by designers but energy planners to assess the potential of self-consumption systems with storage. The paper will be structured as follows: in next section load consumption data of three households together with irradiance data to illustrate the new method will be provided. In section 4 the new SS and SC indices together with the ZEB direct and battery points and ZEB curve will be presented. The new approach will be applied to three households escribed in section 3 considering array power and rated capacities ranging between 0-10 kWp and 0-10 kWh, respectively. In section 5 the isoSC and isoSS curves will be presented. Finally, in section 6, conclusions will be drawn. 3. Data 3.1 Household power consumption data Three dwellings, which are located in Jaen, Spain, have been used in order to illustrate either the new approach and the new tool to analyse photovoltaic self-consumption systems with storage. These dwellings have a contracted power rating of 4.4 kW (#H01), 5.75 kW (#H02) and 8.6 kW(#H03) and their annual household power consumption are 2636.7, 4651.8 and 14283.3 kWh/year, respectively. The lower annual household power consumption corresponds to household #01, which is inhabited by two adults and one teenager, meanwhile the largest annual household power consumption corresponds tohousehold #03 with two adults. The occupancy of household #02 is two adults and two children. The considerable high electricity consumption of householod#3 is due to electricity heating which takes place specially at night. Their household power consumption was measured from March 2017 to April 2018 by commercial smart-meters which have an accuracy lower than 2%. Missing data were filled by linear interpolation. Further details about the dwellings can be found in [6]. 3.2 Irradiance data Photovoltaic energy generation, EPV,gen, is estimated through in-plane irradiance on a flat surface. The measured data were obtained from two meteorological stations, which are placed in Jaén. Both meteorological stations have Eppley Piranometers with “Secundary standards” classification per ISO 9060. The irradiance measurement campaign was launched in March 2017 until April 2018. A recording interval of one minute has been considered in order to obtain the irradiance data which have been processed in order to avoid missing and invalid data according the recommendations of IEC 61724-1 [16], IEC 61724-2 [23] and IEC 61724-3 [24]. EPV,gen will be calculated using the method based on the performance ratio (PR) which has been used in other studies regarding self-consumption [5,6,25]. The value of PR for conventional PV systems is typically in the range between 0.70 and 0.80 in Spain [26]. In this paper, PR values of 0.75 will be considered, based on the reported values [27–31]. Regarding the battery charge and discharge, different energy management strategies may be implemented according to the parameters to be optimized [12,15]. Here, the one which maximize the self-consumption index is implemented. Therefore, and considering the state of charge, the battery is charged when PV generation exceeds the household power consumption and it is discharged if the household power consumption is higher than PV generation. It should be noted that the methods to estimate the photovoltaic generation and the battery management are not the main objectives of the paper but the new SS and SC indices (i.e. direct and battery ones) together with the new tool. SS and SC indices will be estimated as a function of both the photovoltaic array power, P0 , and rated battery capacity, Cs. The array power will vary from 0.01kWp to 10 kWp with a step of 0.05kWp while battery capacity will vary from 0.01 to 10 kWh with a step of 0.25 kWh. 4. Direct and battery SS and SC indices As can be observed in Eq. (1) and (2) φsc can be defined as the ratio between the photovoltaic energy consumed, EPV,con, that is, the absolute self-consumed energy (the direct self-consumed energy by the loads and the energy provided to the battery) and the photovoltaic generated energy, EPV,gen. Moreover, Figure 6. Intersection of SS and SC curves. ZEB points and ZEB curve. (a) global (b) direct and (c) battery. The array power and the battery range from 0 to 10 kWp and from 0 to 10 kWh, respectively. Data corresponding to household#2. The analysis of these 3D curves may be also achieved combining different 2D curves. In this sense, the different aforementioned indices can be plotted on an annual basis as a function of the PV array for a given capacity, Figure 7(a). Moreover, they can be also plotted as a function of the rated capacity for a given array power, Figure 7(b). As can be seen in Figure 7(a), φsc,direct and φss,direct corresponds to a negative exponential curve and a logarithmic curve, respectively. A deeper analysis for direct selfconsumption in provided in [5]. Regarding battery self-consumption it must be noted that although φss,bat may have a similar shape than φss,direct, φsc,battery evolves in a particular way: initially it increases with a considerably slope as the PV array power does, it reaches a maximum, and from this point, it decreases following a negative exponential trend. This is due to the considered capacity, in this case 3 kWh. As the array power becomes higher, there is more surplus power that can be used to charge de the battery, so the energy used to charge the battery, ETPac, increases, making higher the battery self-consumption index. However, there is a limit in the energy that the battery can store given a fixed capacity. Once this limit is exceeded, although the array power continues to grow, the surplus cannot be stored. Moreover, EPV,gen continues growing as the array power increases, which will make the battery self-consumption index decrease. On the other hand, φss,bat presents a similar shape than φss,direct. However, in this case, there are no asymptotes. Once the maximum is reached, self-sufficiency index slightly decreases with a marginal slope regardless the increase of the array power. As EPTac will be limited by the given capacity so will EPFac. However, in this case, EL is a fixed value so self-sufficiency index will remain almost constant. If now the array power is kept fixed and the rated capacity is varied, figure 7(b), direct SS and SC indices do not change regardless the rated capacity. On the other hand, battery self-sufficiency and selfconsumption curves do have similar shapes and follow a logarithmic trend. Moreover, global indices also follow this logarithmic trend with a given offset provided by the direct indices. (a) (b) Figure 7. (a) Annual direct and battery SS and SC indices. ZEB, ZEBdirect and ZEBbattery points. The array power ranges from 0 to 10 kWp. CS= 3 kWh. (b) Annual direct and battery SS and SC indices. The rated capacity ranges from 0 to 10 kWh. P0=3kWp. Data corresponding to household#2. The intersection between global φsc and φss provides the ZEB point where φss = φsc. Furthermore, in figure 7(a) it may be defined two more ZEB points: one for direct self-consumption, ZEBdirect, and the other for the battery, ZEBbattery. Direct indices curves intersect in the direct ZEB point. On the other hand, battery indices intersect in the battery ZEB point. Due to the BID and the battery efficiencies, ZEBbattery will be shifted to the right in relation to ZEBdirect. The more efficient device, the less displacement. If the BID and the battery were ideal devices, the three ZEB points will be aligned. It must be highlighted how, for the curves shown in figure 7(b) there is no intersection between them, either for direct or battery curves. In the direct ZEB point: (8) In the battery ZEB point: (9) Considering Eq. (5): (10) Regarding ZEB point (11) In this way, the use of a battery not only provides higher SS and SC indices but causes a shift to the right of the global ZEB point in relation to direct ZEB point. Furthermore, the battery ZEB point, in the same way as the direct ZEB point will be placed in the same abscissa regardless of the array power and the rated capacity (i.e. and for direct and battery self-consumption, respectively), Figure 8. On the other hand, and taking into account Equation 11, global ZEB point depends on the array power and the rated capacity, the higher array and capacity the higher ETPac which will provide a higher EPVgen/EL and a more displacement to the right of the global ZEB point, Figure 9. Regarding battery self-sufficiency index, and for the considered household, it ranges from 0,025 to 0,4 for storage capacities ranging from 0,025 to 10 kWh, Figure 8 (a). As aforementioned, given a rated capacity, self-sufficiency indices tend to increase linearly and then follows a cuadratic curve reaching a maximum. Once reached, the index is kept almost constant decreasing with a marginal slope as the array power increases. In this sense, and provided a determined rated capacity, it may be no use increasing the PV array beyond a given point. Furthermore, the maximum battery self-sufficiency indices do not increase in a proportional way as the rated capacity does. In fact, the higher capacity the lower increase in the maximum self-sufficiency index. Moreover, for high capacities, the increase in maximum self-sufficiency index may be marginal. For the considered household, and for the array power and rated capacities considered, battery self-sufficiency index may not exceed 0,4. If now the array power is kept constant and the rated capacity is varied, Figure 8 (b), the battery self-sufficiency index for a given array power increases as the rated capacity does, reaching a maximum. This can be clearly seen, for the capacity range considered, for 1 kWp and 2 kWp curves. Moreover, it must be highlighted how battery self-sufficiency curves for different array powers higher than 3 kWp almost match for capacities lower than 5 kWh. Beyond this capacity it may be marginal the increase in battery self-sufficiency when considering either higher array power or rated capacities. The global curves for φsc and φss are the sum of the direct and the battery indices curves. As can be seen, the global self-sufficiency index that considers the joint work of the photovoltaic generator and the battery becomes higher as the rated capacity increases. For the household considered it may even exceed 90% for rated capacities beyond 8 kWh. High array powers and rated capacities provides such a high index. However, as it can be seen, the associated self-consumption indices are quite low, wasting much of the energy generated. As can be seen, it is very important, for a given load profile, to find the most suitable array power and capacity that balances size with self-sufficiency. Achieving this task using either the 3D curves given in Figures 3, 4, 5 and 6 or using 2D plots such as the provided by Figures 8 and 9 may be quite complex and confusing. (a) (b) Figure 8. (a) Annual battery SS and SC indices as a function of the array power for a given rated capacity. (b) Annual battery SS and SC indices as a function of the rated capacity for a given array power. The array power and the battery range from 0 to 10 kWp and from 0 to 10 kWh, respectively. Data corresponding to household#2. (a) (b) Figure 9. (a) Annual global self-consumption indices as a function of the array power for a given rated capacity. (b) Annual global self-consumption indices as a function of the rated capacity for a given array power. The array power and the battery range from 0 to 10 kWp and from 0 to 10 kWh, respectively. Data corresponding to household#2. 5. IsoSC and IsoSS curves As aforementioned, although the analysis and sizing of a photovoltaic self-consumption system with battery may be achieved using 3D figures or 2D figures which considers together SS and SC indices either as a function of the array power depending on the considered capacity or as a function of the rated capacity depending on the array power, it may be a complex task. In this sense, an useful a tool that simplify not only the analysis but make even more simple and intuitive the sizing of this type of systems is provided: iso self-consumption (isoSC) and iso self-sufficiency (isoSS) curves. Iso curves are contour plots containing the iso-lines of SS and SC indices as a function of the array power and the rated capacity. The iso-lines represents the self-sufficiency and self-consumption values on the x-y plane, where ‘x’ is the array power and ‘y’ constitutes the rated capacity. The inputs for elaborating iso-curves are SS and SC indices as function of the array power and the rated capacity. The first step to plot them is to search the maximum and minimum values of both indices. Starting for the maximum value, the next steps manage to find the range of iso-lines from the maximum value to the minimum value with steps of 0.05. The final step is to graph the iso-lines in two dimensions plots, Figure 10. In figure 11 are shown the isoSS curves given by the dotted curves and isoSC curves for household#1: global, direct and battery ones. They are obtained from the 3D self-consumption curves through the intersection with iso self-sufficiency and self-consumption planes which are parallel to the plane defined by the array and the rated capacity axis. These curves give the different combinations of array power and rated capacity that provide a given self-sufficiency or a self-consumption index. The ZEB points (where the iso self-sufficiency and self-consumption curves with the same value intersect) can be easily obtained. Moreover, if the ZEB points are joined together the ZEB curve which is the intersection curve between the self-sufficiency and self-consumption 3D surfaces may be achieved. As can be seen, global isoSC curves resembles exponential curves, Figure 11 (a). Their slope increases as the self-consumption index gets higher and they tend to be straight and vertical lines as they approach unity. As expected, the lower array power, the higher self-consumption index. Regarding global isoSS curves, their shape resembles a decreasing exponential curve. Moreover, for each isoSS curve there is an interval where for a given array power the self-sufficiency index keeps almost constant regardless the rated capacity (e.g. in 0,6 global isoSS curve and for an array power of 3 kWp there may be no use increasing the rated capacity beyond 4,5 kWh). Moreover, for array powers lower than 2,5 kWp the global self-sufficiency index does only depend on the array power as the increase in the global self-sufficiency index may be marginal when increasing the rated capacity. Figure 10. Flowchart to plot IsoSC and isoSS curves. All the information contained in the 3D representation for the considered household is moved to this 2D figure which provides a complete sight of the performance of this type of systems considering different Input parameters Фsc (P0,Cs) and Фss (P0,Cs) Фsc,i= max(Фsc (P0,Cs) ) Фsc,min= min(Фsc (P0,Cs) ) Find (Фsc (P0,Cs) = Фsc,i) Фsc,i = Фsc,i -0.05 Фsc,i >Фsc,min? Yes Start END No Фss,i= max(Фss (P0,Cs) ) Фss,min= min(Фss (P0,Cs) ) Find ( Фss (P0,Cs) = Фss,i ) Фss,i= Фss,i-0.05 Фsc,i >Фsc,min? Yes No array powers and rated capacities given an annual load profile. This graph may be used either to analyse or to size in a simple and intuitive way the array power and the rated capacity of the photovoltaic selfconsumption system if determined SS and SC indices must be achieved. For example, if a global selfsufficiency index of 50% is to be reached, the corresponding global isoSS curve must be considered. This curve represents all the different solutions (i.e array power and rated capacity) to be considered in order to provide the aforementioned global self-sufficiency index, Figure 11 (a). If other self-sufficiency indices should be considered the corresponding curve should be taken into account. Now, either energetic or profitability criteria can be applied in order to choose the more suitable combination of array power and rated capacity. To get a global self-sufficiency index of 0,50 and if it is required to take advantage of a great part of the photovoltaic energy generated (i.e self-consumption index higher than 75%) it may be chosen, for the considered household, an array power of 2,5 kWp and a rated capacity of 2,5 kWh. Moreover, as can be seen for the 0,5 global isoSS curve, and given a 2,5 kWp array power there is no use considering higher rated capacities as the curve tends to be vertical. As can be seen in this global isoSS curve, the self-sufficiency index is kept almost constant although the rated capacity is increased. On the other hand, if cost-competiveness should be achieved, it may be considered a higher array power and a lower rated capacity in the aforementioned self-sufficiency curve (actually the cost of one kWp of array power is considerably lower than one kWh of rated capacity). In this case, an array power of 3.5 kWp and a rated capacity of 1 kWh may be chosen to get a 0,5 self-sufficiency index. Moreover, the global isoSC curve which intersect at this point provides a self-consumption index of 0,65. Anyway, once the global isoSC and isoSS curves have been plotted for a given household, it is only a question of applying the chosen criteria (grid autonomy, cost competitiveness or profitability) when using the aforementioned tool. Furthermore, these global isoSC curves may be complemented with the associated curves corresponding to the new indices defined in section 4 (i.e direct and battery indices). In this sense, the direct and battery isoSC and isoSS curves for the considered household are shown in figures 11(b) and 11(c), respectively. figures or a set of 2D plots. Anyway, they may make more easy and more intuitive comparisons of these systems when analysing different households. It has been shown either the global, direct and battery isoSC and isoSS curves. Regarding direct curves it must be noted that they do not depend on the rated capacity, so only two curves may be considered: one for the self-consumption index and one for the selfsufficiency index depending only on the array power. In this sense, only a direct ZEB point may be considered for a given household. On the other hand, when battery and global indices are considered a set of isoSC and isoSS curves are obtained. Different battery and, therefore, global ZEB points are obtained providing battery and global ZEB curves. The latter are the intersection curves between the selfsufficiency and self-consumption 3D surfaces. As has been seen, if a determined isoSS battery curve is considered for a household, for a given array power there is no use increasing the rated capacity as there is no increase in the battery self-sufficiency index and, therefore, in the global index. On the other hand, for a given rated capacity for the aforementioned curve there is also no use considering higher array powers as it is provided a marginal increase in the self-sufficiency. The only increase in the global self-sufficiency index, will be provided by the direct self-sufficiency index. The Battery isoSS and isoSC curves may provide very important information about the role of storage together with the array power in this type of systems. In this way, for each isoSS curve it may be easily defined a battery sizing window. This battery sizing window may be obtained with every isoSS battery curves and the obtained sizing area may be used in order to narrow the area to consider when sizing the rated capacity. The area outside this sizing area can be also considered, although increasing either the rated capacity or array power may play a negligible role in increasing the global self-sufficiency indices. Now, either energetic or profitability criteria can be applied to this area in order to choose the more suitable combination of array power and rated capacity. These isoSC and isoSS curves have been used to analyse the role of the array power and the rated capacity in 3 different households located in Jaén (Spain). Array powers and rated capacities up to 10 kWp and 10 kWh, respectively, have been considered. It has been shown how two of them may achieve, for the given array power and capacity ranges, a high degree of autonomy from grid (i.e self-sufficiency indices higher than 85%). Another household, due to its load profile may not suit photovoltaic selfconsumption systems as considerably high values of either array power and rated capacities are needed. It has been proved that isoSC and isoSS curves may help not only to determine the role of each element in the self-consumption system but it may be used by energy planners and designers to properly size the array power and the rated capacity. Moreover, it may assess the potential of this type of systems from either an energetic or profitability approaches. Further research should be done in order to use this isoSC and isoSS curves when sizing the array power and rated capacity using the aforementioned criteria. Acknowledgements This research was funded by the Agencia Estatal de Investigación (AEI) and the Fondo Europeo de Desarrollo Regional (FEDER) aimed at the Challenges of Society (Grant No. ENE 2017-83860-R "Nuevos servicios de red para microredes renovables inteligentes. Contribución a la generación distribuida residencial"). The authors would also like to thank the University of Jaén for the programme: “Plan de Apoyo a la I+D+I 2014-2015. Prorrogado hasta 2016”. References [1] F. Nemry, A. Uihlein, JRC Scientific and technical Reports. Environmental Improvement Potentials of Residential Buildings (IMPRO-Building), 2008. doi:10.2791/38942. [2] Bosseboeuf et al., Energy Efficiency Trends and Policies in the Household and Tertiary Sectors, 2015. [3] E. Commission, Directive 2010/31/EU of the European Parliament and of the Council of 19 May 2010 on the energy performance of buildings, 2010. [4] I. Renewable Energy Agency, Renewable Power Generation Costs in 2017, 2018. doi:10.1007/SpringerReference_7300. [5] D.L. Talavera, F.J. Muñoz-Rodriguez, G. Jimenez-Castillo, C. Rus-Casas, A new approach to sizing the photovoltaic generator in self-consumption systems based on cost–competitiveness, maximizing direct self-consumption, Renew. Energy. 130 (2019) 1021–1035. doi:10.1016/j.renene.2018.06.088. [6] G. Jiménez-Castillo, F.J. Muñoz-Rodriguez, C. Rus-Casas, D.L. Talavera, A new approach based on economic profitability to sizing the photovoltaic generator in self-consumption systems without storage, Renew. Energy. 148 (2020) 1017–1033. doi:10.1016/J.RENENE.2019.10.086. [7] A. Aoun, H. Ibrahim, M. Ghandour, A. Ilinca, Supply Side Management vs. Demand Side Management of a Residential Microgrid Equipped with an Electric Vehicle in a Dual Tariff Scheme, Energies. 12 (2019) 4351. doi:10.3390/en12224351. [8] R. Luthander, J. Widén, D. Nilsson, J. Palm, Photovoltaic self-consumption in buildings: A review, Appl. Energy. 142 (2015) 80–94. doi:10.1016/j.apenergy.2014.12.028. [9] W.L. Schram, I. Lampropoulos, W.G.J.H.M. van Sark, Photovoltaic systems coupled with batteries that are optimally sized for household self-consumption: Assessment of peak shaving potential, Appl. Energy. 223 (2018) 69–81. doi:10.1016/j.apenergy.2018.04.023. [10] A. Jäger-Waldau, PV status report 2013, 2013. [11] A. Dehamma, A. Eller, P. Asmus, Energy storage for renewables integration, 2015. [12] J. Li, M.A. Danzer, Optimal charge control strategies for stationary photovoltaic battery systems, J. Power Sources. 258 (2014) 365–373. doi:10.1016/j.jpowsour.2014.02.066. [13] J. Moshövel, K.P. Kairies, D. Magnor, M. Leuthold, M. Bost, S. Gährs, E. Szczechowicz, M. Cramer, D.U. Sauer, Analysis of the maximal possible grid relief from PV-peak-power impacts by using storage systems for increased self-consumption, Appl. Energy. 137 (2015) 567–575. doi:10.1016/j.apenergy.2014.07.021. [14] J. Weniger, T. Tjaden, V. Quaschning, Sizing of Residential PV Battery Systems, Energy Procedia. 46 (2014) 78–87. doi:10.1016/J.EGYPRO.2014.01.160. [15] Y. Riesen, C. Ballif, N. Wyrsch, Control algorithm for a residential photovoltaic system with storage, Appl. Energy. 202 (2017) 78–87. doi:10.1016/j.apenergy.2017.05.016. [16] IEC, IEC 61724-1 Edition 1.0 2017-03 Photovoltaic system performance – Part 1: Monitoring IEC, Edition 1., IEC publications, Geneva, 2017. [17] S. Cao, K. Sirén, Impact of simulation time-resolution on the matching of PV production and household electric demand, Appl. Energy. 128 (2014) 192–208. doi:https://doi.org/10.1016/j.apenergy.2014.04.075. [18] P. Wolf, J. Včelák, Simulation of a simple PV system for local energy usage considering the time resolution of input data, J. Energy Storage. 15 (2018) 1–7. doi:10.1016/j.est.2017.10.009. [19] G. Jiménez-Castillo, G.-M. Tina, F.-J. Muñoz-Rodríguez, C. Rus-Casas, Smart meters for the evaluation of self-consumption in zero energy buildings, in: 2019 10th Int. Renew. Energy Congr., IEEE, Sousse, 2019: pp. 1–6. doi:10.1109/IREC.2019.8754609. [20] R. Luthander, A.M. Nilsson, J. Widén, M. Åberg, Graphical analysis of photovoltaic generation and load matching in buildings: A novel way of studying self-sufficiency and self-consumption, Appl. Energy. 250 (2019) 748–759. https://www.sciencedirect.com/science/article/pii/S0306261919309110 (accessed April 11, 2020). [21] J. Figgener, P. Stenzel, K.P. Kairies, J. Linßen, D. Haberschusz, O. Wessels, G. Angenendt, M. Robinius, D. Stolten, D.U. Sauer, The development of stationary battery storage systems in Germany – A market review, J. Energy Storage. 29 (2020) 101153. doi:10.1016/j.est.2019.101153. [22] K.-P. Kairies, J. Figgener, D. Haberschusz, O. Wessels, B. Tepe, D.U. Sauer, Market and technology development of PV home storage systems in Germany, J. Energy Storage. 23 (2019) 416–424. doi:10.1016/J.EST.2019.02.023. [23] IEC, IEC TS 61724-2 Edition 1.0 2016-10 Photovoltaic system performance – Part 2: Capacity evaluation method, Edition 1., IEC publications, Geneva, 2016. [24] IEC, IEC TS 61724-3 Edition 1.0 2016-07. Photovoltaic system performance – Part 3: Energy evaluation method colour, Edition 1., IEC publications, Geneva, 2016. [25] G. Jiménez-Castillo, F.J. Muñoz-Rodríguez, A.J. Martinez-Calahorro, G.M. Tina, C. Rus-Casas, Impacts of Array Orientation and Tilt Angles for Photovoltaic SS and SC indices in Olive Mills in Spain, Electronics. 9 (2020) 348. doi:10.3390/electronics9020348. [26] T.A. Guerra, J.A. Guerra, B.O. Tabernero, G. De La Cruz García, Comparative energy performance analysis of six primary photovoltaic technologies in Madrid (Spain), Energies. 10 (2017) 1–23. doi:10.3390/en10060772. [27] J.D. Mondol, Y.G. Yohanis, M. Smyth, B. Norton, Performance analysis of a grid-connected building integrated photovoltaic system, in: ISES 2003 ISES Sol. World Congr. 2003 Sol. Energy a Sustain. Futur., teborg, 2003: pp. 14–19. [28] M. Šúri, T.A. Huld, E.D. Dunlop, H.A. Ossenbrink, Potential of solar electricity generation in the European Union member states and candidate countries, Sol. Energy. 81 (2007) 1295–1305. doi:https://doi.org/10.1016/j.solener.2006.12.007. [29] S.J. Ransome, J.H. Wohlgemuth, kWh/kWp dependency on PV technology and balance of systems performance, in: Conf. Rec. Twenty-Ninth IEEE Photovolt. Spec. Conf., IEEE, New Orleans, 2002: pp. 1420–1423. doi:10.1109/PVSC.2002.1190875. [30] J.A. Ruiz-Arias, J. Terrados, P. Pérez-Higueras, D. Pozo-Vázquez, G. Almonacid, Assessment of the renewable energies potential for intensive electricity production in the province of Jaén, southern Spain, Renew. Sustain. Energy Rev. 16 (2012) 2994–3001. doi:10.1016/j.rser.2012.02.006. [31] F. Almonacid, C. Rus, L. Hontoria, F.J. Muñoz, M. Fuentes, G. Nofuentes, Characterisation of Sicrystalline PV modules by artificial neural networks, Renew. Energy. 34 (2009) 941–949. doi:10.1016/j.renene.2009.11.018. [32] O. Palizban, K. Kauhaniemi, Energy storage systems in modern grids—Matrix of technologies and applications, J. Energy Storage. 6 (2016) 248–259. doi:10.1016/J.EST.2016.02.001.