Digital twin of an absorption chiller for solar cooling

This is a repository copy of “Digital twin of an absorption chiller for solar cooling” in the Depósito de Investigación de la Universidad de Sevilla. Version: Author Accepted Version Citation: Diogo Ortiz Machado, William David Chicaiza, Juan Manuel Escaño, Antonio J. Gallego, Gustavo A. de Andrade, Julio E. Normey-Rico & Carlos Bordons “Digital twin of an absorption chiller for solar cooling”. Renewable Energy. Vol. 208, pp. 36-51. ISSN 0960-1481 https://doi.org/10.1016/j.renene.2023.03.048 To cite this publication, please use the final published version (if applicable). Please check the document version above. Copyright: Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons. Takedown policy: Please contact us ([email protected]) and provide details if you believe this document breaches copyrights. We will remove access to the work immediately and investigate your claim. Digital twin ofan absorption chiller for solar cooling Diogo Ortiz Machadoa,b,c,William David Chicaizac,Juan Manuel Escañoc, Antonio J. Gallegoc,Gustavo A. de Andradeb,Julio E. Normey-Ricob, Carlos Bordonsc,d aIFRS -Instituto Federal de Educação, Ciencia eTecnolgia do Rio Grande do Sul Rua Alfredo Huch, 475, Rio Grande, 96201 460, Rio Grande do Sul, Brasil. bUFSC -Universidade Federal de Santa Catarina. Departamento de Automação e Sistemas, R. Eng. Agronômico Andrei Cristian Ferreira, Florianópolis, 88040 900, Santa Catarina, Brasil. cUS -Universidad de Sevilla. Departamento de Ingeniería de Sistemas y Automática, Camino de los Descubrimientos, Sevilla, 41092, Andalucía, España. dENGREEN -Laboratory of Engineering for Energy and Environmental Sustainability. Universidad de Sevilla., Abstract This work develops a digital twin of a commercial absorption chiller installed in a solar plant. The objective is to use the model for further control and optimization applications. This work uses dynamic neuro-fuzzy modeling to describe the absorption chiller under transients and part-load events to overcome the problems of phenomenological complexity, solar intermittency, and non-linearities. Four sub-models divide the whole chiller where Adaptive Neuro-fuzzy Inference System (ANFIS) describe each one. Then, training, checking, and validation procedures run considering data sets of 36404, 15601, and 13001 samples, respectively, totaling 15 days of available data with a sampling time of 20s. The ANFIS models have generalized learning and predict the measured data with a worst-case Mean Absolute Percentage Error of MAPE = 3.30% . Furthermore, a comparison between the developed models and similar scientific publications shows superior precision, accuracy, and fast execution speed of the resulting digital twin. Therefore the resulting model has control and optimization applicability. Email address: Corresponding author - [email protected] (Diogo Ortiz Machado) Preprint June 21, 2022 Keywords: Dynamic modeling, ANFIS, PCA, HVAC PACS: 0000, 1111 2000 MSC: 0000, 1111 1. Introduction Knowledge is power and time is money. In an even faster and more connected society, making the best decisions just-in-time, planning on a broader horizon with accuracy, and controlling assets give technological and economic advantages. This work develops a double-effect absorption chiller dynamic model in the framework of digital twins using adaptive neuro-fuzzy networks. The intention is to use the resulting smart energy system to plan, integrate, and control the ETSI absorption plant installed in Seville, Spain. The building energy sector is responsible for 40% of the world’s energy use [1]. In this context, solar heating and cooling systems have the potential to reduce fossil fuel use and alleviate CO2 emissions [2]. Solar absorption chilling produces cold from a solar-heated source through an absorption thermodynamic cycle [3]. An advantageous feature of the solar absorption system is that the chilling demand follows the primary energy availability - solar irradiance. Absorption chillers are considered the most desirable method to harness solar thermal energy for cooling due to their relative maturity, reliability, and higher efficiency. However, Shirazi et al. [4] show that currently available absorption chillers cannot economically compete with conventional cooling. Therefore, improving the economic performance of these systems with control and optimization through digitalization tools [5] and artificial intelligence is highly desirable [6]. A Digital Twin is a "virtual representation of a physical asset enabled through data and simulators for real-time prediction, optimization, monitoring, controlling, and improved decision making" [7]. The first DT started in 2015 to be used in the entire life cycle of an asset, from concept to operation [8]. Since then, the concept has gained popularity due to key enabler development and DT advantages, such as remote monitoring and control in real time, greater efficiency and safety, accurate prediction, what-if analysis, integration of disparate systems, among others [7, 9]. This paper develops a Digital Twin of the solar absorption chiller of Escuela Técnica Superior de Ingeniería de Seville (ETSI), Spain, for control and optimization. The plant is located on the roof of the ETSI building and 2 has the objective of supplementing the air conditioning system with chilled water to reduce electric consumption, CO2 emissions and operating costs [10]. The plant is a multi-energy system once it transforms solar irradiance into thermal internal energy, hot water into chilled water (thermal to thermal), and gas chemical energy into thermal internal energy. This system is also evident as highly non-linear and dynamic, switching between electric, gas, and solar resources according to meteorology and demand profiles. The dynamic simulation of absorption chillers is critical to describe the system performance and aid control during activation or part-load operation [11]. Thus, dynamic simulation is even more essential if it is driven by an intermittent solar resource. This paper focuses on the dynamic modeling of the absorption chiller of the ETSI solar plant to compose the whole DT. The plant exists as a physical entity, has computers and servers that work as the virtual space, and is equipped with an industrial network capable of connecting the physical and virtual spaces [12]. Therefore, the only asset missing for the absorption chiller DT consolidation is its adaptive virtual entity representation - its adaptive dynamic model. Based on previous contributions to the ETSI plant absorption chiller modeling and control [10, 13, 14, 15], the following model specifications for this paper are set: 1. To have sufficient accuracy and precision accordingly to the last scientific publications. 2. To run fast enough to be used in Model Predictive Control (MPC) techniques. 3. To describe the chiller operation under transients, part-load, during the day and night for further operation decisions. 4. To describe the gas boiler for forthcoming economic analysis. 5. To cope with the aging of the plant for long-term and life-cycle assessment. 6. To incorporate the embedded, inaccessible, proprietary chillers‘ controls that regulate the process, avoiding dangerous operation and the crystallization of the Lithium Bromide (Li-Br) solution. The problem is that dynamic modeling of absorption chillers is not trivial, nor is the creation of its DT. Research on energy integration and dynamic control of absorption chillers has been mainly overlooked in favor of performance studies. Most modeling and simulations works consider steady-state thermodynamic models, and just a few are dynamic and control-oriented 3 [16]. The few dynamic models, in their turn, are phenomenological or objectoriented, complex, and computationally expensive [4]. In addition, for the specific case of this work, the authors have an incomplete and noisy set of variables. Therefore, soft computing modeling techniques are preferred because they use incomplete available data, describe a system with imperfect information, and are capable of updating the model online [17]. Adaptive neural networks (ANN) are successfully applied to solve complex, non-linear, dynamic, and multivariable problems because they also tolerate errors, imprecision, and missing data [18]. However, the application of ANN for dynamic modeling of absorption chillers is scarce [19], and the main contributions refer to steady-state performance prediction [11]. The authors found the following scientific contribution to the dynamic modeling of absorption chillers: •Lazrak et al. [11] obtain an ANN dynamic model of a single-effect absorption chiller of 15kW operating with H2O–LiBr considering two days of experimental data with no information on sampling time. Three ANNs describe the outlet temperatures of the absorption chiller subsystems: the generator with relative mean errors (RME) of 4.4 and 9.3%, the evaporator with RME of 4.9 and 5.0%, and the absorber+condenser with RME of 1.2 and 1.6% for two separated evaluation data sets, The results show good performance of the dynamic models, although the final ANN model is a black-box representation of the system because the mathematical equations are not explicit. In addition, the work did not inform the sampling times. Adaptive Neuro-Fuzzy Inference Systems (ANFIS) is a hybrid concept that implements a fuzzy inference system using ANN. The ANFIS constructs a set of if-then rules with adequate membership functions to find the desired input-output pairs. The advantage of ANFIS is that it can model non-linear functions and identify non-linear components online in a control system with good performance [20]. Furthermore, unlike neural networks, ANFIS allows the subsequent inclusion of rules or phenomenological modeling, and the resulting model has explicit functions that can be used in a wide range of optimization solvers that require the evaluation of model equations [21]. Because of this gray-box feature, this work employs ANFIS modeling. Further scientific research on the topic of dynamic absorption chiller modeling using ANFIS finds the following works: 4 •Tamiru et al. [22] develop an ANFIS to dynamically model a double effect LiBr/H2O steam absorption chiller for fault detection purposes. The work uses a day of experimental data with a sampling time of 20 s. The model output is the absorber + condenser and evaporator outlet temperatures with good performance with respect to model vs. actual temperature plots, although, without any error analysis. •Abdalla et al. [23] develop a dynamic subtractive clustering SC-ANFIS model of two steam absorption chillers with 4400kW of cooling load. The model predicts energy consumption, cooling load, coefficient of performance (COP) and cooling water return temperature (absorber+ condenser), the latter with a mean standard error and standard deviation of 1.724oCand 0.132, respectively. The work considers 20 days of experimental data with a sampling time of Ts= 1 h. Considering the scarce works on the theme, this paper proposes dynamic modeling using Adaptive Neuro-Fuzzy Inference Systems (ANFIS) [20] to generate a transparent model with explicit equations, using 15 days of operation data with a sampling time of Ts= 20 s. This work contributes to developing a dynamic neuro-fuzzy model of all outlet temperatures of a commercial absorption chiller. Note that simulating these temperatures enables further study of performance indexes. The ANFIS is trained, checked, and validated considering 15 days of measured data sampled every 20 seconds. This large amount of data results in another scientific contribution, such as a generalized dynamic model capable of representing the behavior of the absorption chiller across a broad operational range. The model is helpful for describing operations between day and night, during part-load operations, or in standby loosing heat, whether or not its boiler is used. The last scientific contribution is that the resulting dynamic model is computationally fast with explicit equations and therefore suitable for use with MPC and dynamic optimization techniques. The organization of the rest of paper is as follows. Section 2 defines the absorption chiller process and presents the data preparation. Section 3 describes input dimension reduction techniques to increase the model’s computational speed, such as correlation coefficient analysis and Principal Component Analysis (PCA). Section 4 describes the architecture of the dynamic ETSI absorption chiller model and defines training and checking parameters. Section 5.2 presents the validation results and Section 6 closes this work with the conclusions. 5 2. Absorption Chiller Process Figure 1 shows the schematic of the ETSI plant that started its operation in 2008. The objective of the plant is to complement the energy for the air conditioning system of the ETSI building. The building has an automatic heat, ventilation and air conditioning (HVAC) system that manages electric chillers and the use of the absorption plant. The absorption chiller has three primary external hydraulic connections. One connects the chiller to the Fresnel solar collector that receives heat Qsolar, the other connects the chiller to the ETSI building that delivers the chilled stream Qevap, and another connects the chiller to the Guadalquivir River to reject heat Qabs+cond. The Fresnel Solar collector has a mirror’s aperture surface of 354 m2operating with nominal pressurized water at 13 bar, outlet nominal temperature of 180oC. Furthermore, the absorption chiller is a multi-energy BROAD BZH15 model with 174kWh cooling capacity, 1.34 nominal Coefficient of Performance (COP), using Fresnel heated water or direct-fire gas heat [24]. Table 1 compiles the nominal operation points of the BROAD BZH15 absorption chiller, where Rated A refers to the manufacturer’s recommended operation and Rated B refers to the available operation range without affecting cooling capacity or COP. Table 1: Rated operation points of BROAD BZH15 absorption chiller [24, p.42-43] Var. Rated A Rated B Chilled water flowa(m3/h)V130 21.4 Chilled water inlet temperature (oC)T112 14 Chilled water outlet temperature (oC)T27 7 Cooling water flowb(m3/h)V236.6 46.6 Cooling water inlet temperature (oC)T330 32 Cooling water outlet temperature (oC)T437 37.5 Heat source water flow (m3/h)V67.6 7.6 Heat source water inlet temperature (oC)T6A180 180 Heat source water outlet temperature (oC)T6B165 165 aRated A adjustable chiller water flow rate: 50 ∼120% (15 ∼36 m3/h) bRated A adjustable cooling water flow rate: 30 ∼140% (11 ∼51 m3/h) The ETSI plant is a unique process pairing a double-effect absorption chiller, with a direct-fire gas boiler and concentrating solar collectors. Bermejo et al. analyze the operation of the plant showing that it has a solar heat frac6 Figure 1: General schematic of the absorption plant in the Escuela Técnica Superior de Ingeniería (ETSI) in Seville University. Modified from [10]. 7 tion of 0.75, a cooling ratio of 0.44, a COP of 1.1-1.4, and an average cooling power of 135kwh (77% nominal). The performance of the ETSI solar absorption plant is a step forward in solar absorption technology [10]. Still, it offers improvement possibilities [13]. The BROAD BZH15 operates with internal solutions of water + lithium bromide (LiBr), where water is the refrigerant and the bromide is the absorbent. Double-effect means using LiBr streams with different concentrations by employing cascade heat exchangers to increase the overall COP of the system through higher inlet temperatures thresholds. For further information about absorption chillers multi-effects refers to [25]. The manufacturer’s design manual [24, pg.40] depicts in detail the BROAD BZH process flow diagram (PFD) and the nomenclature used in this work. For simplicity and because the measurements of the internal variables are not available for model validation, this work considers the Figure 2 PFD. See that internal streams of LiBr (gray arrows in Figure 2) only exchange heat with external solutions (black arrows in Figure 2), not exchange mass or mixing. Besides, there is no available data from these internal streams; hence, they are suppressed. The main difference between the manufacturer’s and this work PFD is that the latter embeds the HTG, the LTG, the LTHE, and the HTHE processes, shown in [24, pg.40], in one process called HighTemperature Generator (HTG) in Figure 2. Note in Figure 2 that HTG (red color in Figure 2) can receive heat from two heat sources: the solar Fresnel collector (Qsolar) or the gas boiler (Qgas). If the plant is operating with solar heat, valve F38 opens and water from the Fresnel collector enters the High Temperature Generator (HTG) at temperature T6A and flow V6. The flow of heat source water, V6, with a given temperature T6A, exchanges Qsolar with a concentrated LiBr solution within the HTG at temperature T5. After exchanging heat, affecting T5, the solar collector stream exits HTG and goes to the Fresnel collector again; therefore, the solar hydraulic system is a closed loop. Note that the temperature T6B is an important variable for the operation of the whole plant. If the HTG operates with gas, the process receives Qgas from direct gas burning, increasing T5, according to the gas flow V3, affecting the temperature of the exhaust gas T6. Temperature T5 is a critical variable for the absorption chiller and the entire plant because it connects the Fresnel solar collector and the chiller, affecting the plant dynamics, cooling capacity, and COP. The absorption cycle must reject heat to the environment to operate. This heat rejection occurs in the condenser and absorber (blue in Figure 2). The 8 πj=λj Pp j=1 λj×100%.(8) 4. Neuro-fuzzy Modeling The following section presents the background of the ANFIS architecture, its parameterization, the training and checking procedures, and, lastly, the validation concept of the ANFIS model. Layer 4 Layer 5Layer 3Layer 2Layer 1 N N x y x y x y Figure 4: Adaptive Neuro-fuzzy Inference System (ANFIS) architecture [20]. The nodes and directional links compose the ANFIS as depicted in Figure 4, where the nodes have fixed (circle) or adaptive (square) parameters, and the links represent the direction of the signal flow. Thus, the node output depends on the input and its parameters. The ANFIS architecture has five layers. In the first layer, fuzzification occurs, which transforms the inputs x, y into linguistic labels with a degree of membership. The second layer is a product stratum composed of nodes that multiply each input. The output represents the firing strength of the node rule that flows to the next layer. The third layer normalizes each node output considering the total number of nodes. In the fourth layer, there occurs the defuzzification with a weighted output of the if-then rules. The mathematical representation of each fuzzy set (Fij) is a Gaussian membership function (MF) with {ai, bi, ci}as the parameter set that defines the mean, height, and width of the Gaussian. As the values of the parameters change, the MFs also change, representing various forms and combinations of membership functions. Lastly, the fifth layer has a unique node that sums up all the heightened rules outputs. 15 This work uses type-3 fuzzy reasoning. Thus, the ANFIS uses TakagiSugeno type rules [30]. The output of each rule is a linear combination of input variables summed to a constant term, and the final output of the inference system is the weighted average of each output of the rule. For a detailed description of ANFIS, refer to [20, 21]. After defining the ANFIS architecture, the problem becomes deciding the number of rules and MF in the nodes. This work uses the subtractive clustering method to estimate the number and initial centers of the premises of the fuzzy rule, avoiding the necessity of previous knowledge or the designer’s experience [31, 21]. Once the rules and MF are defined, the ANFIS is ready for training. The ANFIS training objective is to choose the MF parameters, minimizing the error between the training data and the ANFIS output by varying these parameters. The training procedure runs epochs or sweeps, where one epoch is both the direct information pass and the backward pass along the ANFIS layers. ANFIS uses a hybrid technique. First, a gradient descent to optimize the antecedent parameters, then a least-squares estimate to select the consequent linear parameters at each epoch or sweep. Therefore, the ANFIS learning procedure combines the gradient method and least squares to update the MF parameters, reducing the training time. The next question is, how many epochs are sufficient for training? The ideal number of epochs is the one that produces the stable and minimum error. The practice is to select a given supersized number of epochs and infer when the error does not decrease and stabilizes in error versus epoch graphic. The checking procedure evaluates the error between the checking data set; a new data set not used in training. The checking runs after each epoch during the training, and it has the objective of evaluating if the ANFIS training results in generalized learning. If the ANFIS output has low errors with unknown inputs, then it is said that the ANFIS model had general learning. Typically, the checking considers the root mean squared error (RMSE) given by Equation (9) RMSE =sPN i=1(xi,j −ˆxi,j)2 N,(9) where xi,j is a given actual variable j with N samples, and ˆxi,j is the output of the predicted variable. This work considers normalized outputs for training and checking. Therefore, the normalized RMSE, given by Equation (10), is used. 16 nRMSE =sPN i=1(zi,j −ˆzi,j ) N.(10) Lastly, the model validation compares the ANFIS outputs with the validation data set, a new, unused data set. The validation objective is to evaluate the final model’s ability to predict outputs. Validation tests the accuracy of the model with respect to different actual data that are not used in training or checking. Two indexes evaluate the accuracy and precision of the models based on their errors. The arithmetic error means to evaluate the accuracy, or the distance between the error points and their true center value; it is given by Equation (11). ,¯ E=PN i=1(xi,j −ˆxi,j) N(11) and standard deviation, given by Equation (12), provide information about precision, therefore, how much the error is dispersed, σE=sPN i=1(Ei,j −¯ E)2 N.(12) In addition to mean and standard deviation, this work calculates the validation metrics of each scientific publication cited in the Introduction for comparison purposes. Abdalla et al. [23] employ Equation (12) and standard mean error (SE), another measure of precision, given by Equation (13), SE =σE √N,(13) where SE measures how the number of samples Naffects the dispersion of different datasets, as the size of the data increases, the SE decreases; hence, the SE estimates the true mean of the population with greater precision. Lazrak et al.[11] do not explicitly defines its validation index, called the relative mean error (RME). It happens to be the Mean Absolute Percentage Error (MAPE), which Equation (14) describes, MAPE =PN i=1 |(xi,j −ˆxi,j )| xi,j N×100%.(14) where it is a measure of the precision of a predictive system considering absolute prediction errors, |(xi,j −ˆxi,j )|, relative to the actual measured data, xi,j. 17 5. Absorption Chiller Digital Twin The Absorption chiller modeling considers four models: (1) internal HTG LiBr temperature, (2) outlet HTG temperature, (3) absorber + condenser, and (4) evaporator. The modeling consists of training, checking, and validation procedures using the total input data from the model. Each model input choice considers only prepared data variables sorted using the correlation coefficient |ρ| ≥ 0.5and decomposed using PCA analysis. The result is the total inputs from Model 1, G1, given by (15): G1= [G11 G12 G13 G14],(15a) G11 = [T6BT6AT6T5(k−2) T5(k−1) T5],(15b) G12 = [V4P3F1Tamb INV6V6T4V3],(15c) G13 = [V2V1T3],(15d) G14 = [Tabs T1T2],(15e) where G1is the total prepared inputs for model 1, G11 is the group input 1 of model 1, etc., and each total vector has 65006 samples representing the measured data for 15 days of operation. Note that Model 1 uses three previous samples of T5; therefore, it is of the third order. The modeling procedure divides the total prepared inputs, G1, into three subsets. Equation (16) defines the training inputs, Gtrain 1= [Gtrain 11 Gtrain 12 Gtrain 13 Gtrain 14 ],(16) which uses 56% (8.5 days - 36404 samples) of the total prepared data G1. Equation (17) defines the checking inputs, Gcheck 1= [Gcheck 11 Gcheck 12 Gcheck 13 Gcheck 14 ],(17) which uses 24% (3.5 days - 15601 samples) of total prepared data G1. Equation (18) defines the validation input, using 20% (3 days - 13001) of the total prepared data, Gvalid 1= [Gvalid 11 Gvalid 12 Gvalid 13 Gvalid 14 ].(18) Equation (19) describes the training score matrix using the training data set; 18 the same idea extends to the checking and validation data sets. Ttrain 11 =Gtrain 11 ×PG11 ,(19a) Ttrain 12 =Gtrain 12 ×PG12 ,(19b) Ttrain 13 =Gtrain 13 ×PG13 ,(19c) Ttrain 14 =Gtrain 14 ×PG14 ,(19d) where the loading matrix PG1,g contains the coefficients of the first principal components of each input group (g = 1,2,...,4) that have a variability greater than 80%. The ANFIS learning process uses consolidated training, check, and validation data sets. These sets are composed of projections of the grouped inputs and the actual output to be modeled, Equations (20) to (22) describe these sets. TrnG1= [Ttrain 11 Ttrain 12 Ttrain 13 Ttrain 14 Ttrain 5(k+ 1)],(20) ChkG1= [Tcheck 11 Tcheck 12 Tcheck 13 Tcheck 14 Tcheck 5(k+ 1)],(21) ValG1= [Tvalid 11 Tvalid 12 Tvalid 13 Tvalid 14 Tvalid 5(k+ 1)].(22) Once the learning process is completed, it results in a third-order recursive NF model of the absorption machine. Figure 5 depicts model 1. Note that the respective inputs are multiplied by a constant loading matrix PG1g, truncated in the first two columns, and then fed into the FIS. For example, let us take the training procedure of Model 1, the FIS input results in Gtrain 11 (1 ×6) × P11(6 ×2) = Ttrain 11 (1 ×2), where Ttrain is the score matrix that feeds the FIS for training. Figure 5 depicts the model 1 schematic that predicts the internal temperature of the HTG LiBr, T5(k+ 1). Note that several loading matrices, P, make up the model, reducing the FIS inputs from 20 to 8. The blue lines in Figure 5 are the previous samples of the outlet variable that are fed back and form G11. The same methodology applies to the other models, from 2 to 4, in which the schematics are suppressed to avoid repetition, but are available in Appendix A. The final ANFIS uses Gaussian MF functions with a hybrid learning method, having a linear MF function output. Table 2 presents the resume of each ANFIS parameter for each chiller subsystem. The number of MFs and rules was chosen based on the subtractive clustering method that empirically varied the influence range. The following subsection describes the selection of epoch numbers. 19 P8x2 G12 P3x2 G13 P3x2 G14 z-n T5(k+1) P6x2 G11 G11 G12 G13 G14 FIS Model 1 HTG T 1x2 11 T 1x2 12 T 1x2 13 T 1x2 14 Figure 5: Model 1 - HTG internal LiBr temperature ANFIS model. Table 2: ANFIS parameters for each Absorption Chiller subsystem. Subsystem 1 2 3 4 FIS output T5 T6B T4 T2 Number MFs: 3 2 3 3 Number rules: 3 2 3 3 Influence range 0.7 0.8 0.7 0.7 Epoch number: 1250 1250 1250 200 5.1. Training and Checking Figure 6 shows the training errors (gray) and check errors (red) of each absorption chiller model versus the epoch number considering the training Gtrain, and checking Gcheck, data set. The number of epochs for Models 1 to 3 was chosen based on the decrease and stabilization of normalized RMSE (nRMSE) at epoch 1250. The learning and checking of model 4 are faster and more stable than the others. Thus, model 4 has 200 epochs. After selecting epochs, each model ran its training and check, varying its influence range, which affects the number of MF and fuzzy rules. Table 3 compiles the minimum normalized root mean square error of the best training and checking tests. 20 Normalized RMSE (nRMSE) 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 0.02 0.025 0.03 -3 -2 -1 0 1 nRMSE 10-4 a. Subsystem 1 - HTG Outlet Temperature Training Checking 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0.015 0.02 -10 -5 0 nRMSE 10-5 b. Subsystem 2 - HTG LiBr Temperature 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0.12 0.14 0.16 -6 -4 -2 0 nRMSE 10-4 c. Subsystem 3 - Absorber + Condenser Outlet Temperature 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Epoch 0.028 0.03 0.032 -2 0 2 nRMSE 10-3 d. Subsystem 4 - Evaporator Outlet Temperature Figure 6: Normalized Root Mean Squared Error (nRMSE) vs. epoch. Table 3: nRMSE index obtained of learning process (training and checking) for each ANFIS. Subsystem 1 2 3 4 FIS output T5 T6B T4 T2 nRMSEtrain(×10−3) 18.08 18.35 120.32 26.24 nRMSEcheck(×10−3) 17.85 19.14 120.23 26.59 21 5.2. Validation and Discussion Figure 7 depicts the validation procedure, which consists of comparing the output of the models (black) and the actual validation data set Gvalid (red). Figure 7: Validation results of model 1 (a) and model 2 (b). The gray shaded area depicts the standard deviation with 95% confidence interval (T(t)±2σ). The right figure depicts a detailed comparison between model output and actual data during operation. It can be seen in Figure 7 that the temperatures are intermittent, where the peaks indicate the operation of the chiller and the valleys represent the decrease in overnight temperature due to heat losses with the plant off. The chiller’s start-up typically occurs at noon. The delay between sunrise (07:00) and start-up occurs because the Fresnel solar collector takes all morning to heat tubes and water masses to reach the minimum temperature of operation of the chiller heat source of T6Amin = 140oC. After reaching the minimum temperature, the F38 inlet valve opens and the chiller runs from 12:00 to 20:00 in a hybrid way, using the solar resource and the gas boiler when solar power is not sufficient. Figure 7.a describes the internal temperature of LiBr T5during operation. It oscillates between 110 and 140 oCdue to the controller’s action on the F38 inlet chiller valve. Figure 7.a has a zoomed region on the right that depicts this oscillatory behavior from 15:00 to 20:00 on October 16th. Finally, the chiller shutdown occurs at 20:00 with the valve F38 closed, and T5decreasing 22 due to ambient heat losses. The shut-down happens at 20:00 because there is no more sufficient solar irradiance, the Fresnel cannot feed the chiller, and running only with the gas boiler is economically unfavorable. Figure 7.b shows the temperature of the outlet of the water from the heat source, T6B, which has a profile similar to the internal temperature of LiBr T5. This similar profile makes sense since T6Bis the outlet temperature of the HTG heat exchanger tube. Thus, T6Bresults from heat transfer between the inlet temperature of the chiller, T6Aand the internal temperature of LiBr, T5, along the length of the heat exchanger. The figure on the right 7.b shows the details of T6Bduring operation. Note that the T6Bmodel follows the trend of peaks and valleys due to the control of the incoming heat source valve F38. By inference, it can be said that the right-hand-zoom section of Figure 7 indicates that model 1 and model 2 describe the HTG temperatures T5and T6Bwithin the rated operation range. Both models maintain the measured data (red dashed) within two standard deviation intervals (gray area in Figure 7). Therefore, the resulting models describe the chiller at night, when the plant is idle and losing thermal energy to the ambient, and during the day, when the control system modulates the inlet water valves or gas valves operating the chiller. These models can describe the plant in its operating range, considering daily events and practical limitations that strongly affect or constrain plant performance. Therefore, the neuro-fuzzy approach embeds the control laws of each model. It is worth saying that the chiller control laws are proprietary and inaccessible. Considering the manufacturer’s internal control laws is an essential feature of the model once it is ready to optimize start-up and shut-down times, temperatures, gas boiler use, and prompts to evaluate new control approaches while considering the internal controls. Figure 8. a shows the absorber + condenser, Model 3, outlet temperature. Note, on the y-axis of Figure 8.a, that T4has a narrow operating range oscillating between 27 and 38oC. In inspection, it can be seen that the standard deviation (gray) of T4is proportionally higher because the temperature amplitude is approximately 10oC. The temperature amplitude is narrow because Model 3 is responsible for rejecting the absorption chiller heat from the Guadalquivir river. Therefore, the river temperature drops T4, fluctuating around the river temperature. Absorber + condenser has a strong oscillatory behavior during operation that seems to be caused by the HTG on-off temperature control and the T4control that modulates the Guadalquivir river flow. Despite the standard deviation and oscillations, ANFIS model 3 23 Figure 8: Validation results of model 3 (a) and model 4(b). The gray shaded area depicts the standard deviation with 95% confidence interval (T(t)±2σ). The right figure depicts a detailed comparison between model output and real data during operation. is capable of following the actual T4at night and during operation, as can be seen in the zoomed right graph of Figure 8.a. Figure 8.b presents the evaporator, model 4, outlet temperature. The temperature T2represents the temperature of the chilled water. Note that T2in Figure 8.b oscillates between 10 and 27oCand has an inverse correlation with T5and T6Bin Figure 8.a and Figure 8.b. This inverse correlation connects the performance of the Fresnel solar collector in supplying the HTG heat source to the absorption chiller production that the ETSI building HVAC system will ultimately use. Table 4 compiles the validation metrics. The greater mean error ( ¯ E) is 0.33oCof model 4 - evaporator, followed by 0.23oC, of the absorber + condenser model 3. Therefore, models 3 and 4 have their output mean slightly super-estimated, while models 1 and 2 have practically centered output mean errors. Furthermore, the greater standard deviation, with 95% of the confidence interval (2σE), is 3.46oCof model 1, followed in sequence by models 2, 3, and 4, the latter having 2σE= 1.42. The absorber plus condenser ANFIS and SC-ANFIS models in the literature [23] present σE= 1.72. Table 4 shows that the proposed model 3 has σE= 0.85, half of the error dispersion that was presented early. 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