Identification and Maximum Power Point Tracking of Photovoltaic Generation by a Local Neuro-Fuzzy Model

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1 Identification and Maximum Power Point Tracking of Photovoltaic Generation by a Local Neuro-Fuzzy Model Kumars Rouzbehi Arash Miranian2, Alvaro Lunai, Pedro Rodriguezi ielectrical Engineering Department (SEER Group) 2School of Electrical and Computer engineering Technical University of Catalonia University of Tehran Barcelona, Spain Tehran, Iran q.rouzbehi@gmail.com, luna@ee.upc.edu, ar.miranian@gmail.com prodriguez@ee.upc.edu Abstract-With the rapid proliferation of the DC distribution systems, special attentions are paid to the photovoltaic (PV) generations. This paper addresses the problem of maximum power point tracking (MPPT) for PV systems using a local neuro fuzzy (LNF) network and steepest descent (SD) optimization algorithm. The proposed approach, termed LNF + SD, first identifies a valid an accurate model for the PV system using the LNF network and through measurement data. Then the identified PV model is used for MPPT by SD optimization algorithm. The salient modeling abilities of the proposed LNF network results in a reliable and dependable PV model which takes voltage, temperature and insolation variations into account. The proposed approach is evaluated using several identification and MPPT simulations. The simulation results showed the accuracy of the LNF network in modeling of PV systems. Furthermore, simulations carried out for assessment of the MPPT performance during insolation transients demonstrated the high efficiency of the proposed LNF + approach for MPPT applications. Performance of the proposed method MPPT, while the PV array was supplying loads through DC-DC converters was also analyzed. Comparisons to the perturb-and-observe (P&O) and fuzzy logic methods revealed the superiority of the proposed approach. Keywords- PV system; LNF; steepest descent; DC distribution system; SER I. INTRODUCTION Utilization of photovoltaic (PV) generation has been on a growing path during the past decade. For instance, according to the published reports by international energy agency (lea) the cumulative PV power capacity installed in Australia from about 5 MW in 2 has reached to 5 MW in 21, exhibiting a dramatic tenfold increase [1]. In addition, by rapid growth of the DC distribution systems, PV generations, as sustainable energy resources (SERs), have drawn more attention, since they are DC-preferred and can be connected to DC grid with DC-DC converters [2]. Fig. 1 illustrates the general schematic of a DC distribution system which is supplied by SERs such as PV panels and fuel cells. In general, the output power of photovoltaic panels depends on the illumination of solar and environmental temperature. In order to deliver the maximum power, producible by a PV SD I PV cells HDC-DC DC bus Fig. 1. A DC bus with PV generation resources I DC-AC HAC loadsl panel under specific climate conditions, to the load, a maximum power tracking (MPPT) algorithm is necessary. The maximum power point tracking is the automatic control algorithm to adjust the power interfaces and achieve the greatest possible power harvest, during moment to moment variations of solar irradiation, shading, temperature, and photovoltaic module characteristics [3]. In recent year, many approaches have been proposed for MPPT in PV panels. Heuristic search algorithms, such as perturb and observe (P&O) [4], extreme seeking control [5] and direct search algorithm [6] are among the approaches developed during the past decade for MPPT in PV panels. However, most of the proposed approaches for MPPT require a pre-defined model of the PV panel, which is not perfectly exact. This may also lead to unsatisfactory results in case of variations photovoltaic module characteristics. To deal with this difficulty, we propose an identification method based on a local neuro-fuzzy (LNF) approach, to construct a valid model for the PV panel using measurement data. The proposed LNF approach has noteworthy capabilities in modeling high nonlinear and time varying system. If an online learning algorithm is adopted, the LNF model can easily take into account the variations and changes in the characteristics of the PV panel /12/$ IEEE 119

2 This paper is organized as follow. In sections II and III the LNF model and its learning algorithm are introduced, respectively. Then, in section IV the identification strategy and MPPT algorithm are presented. Section V presents the results of several case studies. Finally, the concluding remarks are summarized in section VI. II. LOCAL NEURO-Fuzzy MODEL Neuro-fuzzy (NF) models are fuzzy models that are not solely designed by expert knowledge, but are at least partly learned from data [7]. In fact an NF model is a fuzzy system drawn in a neural network structure and thus learning methods already developed for neural networks can be applied to the NF model. Therefore, the neuro-fuzzy systems inherit the learning capability of the neural networks as well as the logicality and transparency in the fuzzy systems [7]. Local neuro-fuzzy models are an appealing class of neuro-fuzzy systems and work based on the interpolation of the local models [8]. In the LNF approach, the whole input space is partitioned into a set of sub-regions, each is determined by its corresponding validity function and local model (LM). Interestingly, the procedure of input space partitioning allows describing a complex nonlinear process by creating a number of simpler local models, whose parameters are easily identifiable. The general mathematical expression for an LNF with p dimensional input, = U [Ul'U2,...,up f, and M local models is given by Y = M >i (! )<Pi (! ) () i=! where, hi (-) is a nonlinear function describing ith local model (LM;), <Pi is the corresponding validity function of the LMj and y is the LNF model's output. In order to have a smooth transition between local models, the validity functions are smooth and take their values between and 1. Furthermore, the validity functions must form a partition of unity to have reasonable interpretation of local models M = L i=! <Pi (! ) 1 (2) The architecture of the LNF model, described by (1), is illustrated in Fig. 2. As depicted in Fig. 2 the total output of the LNF model can be represented based on the output of each local model Y = M Lyi<Pi (! ) (3) 1=1 where Y i is the output of LMj and is equal to hi (! ). It is worth noting that the arbitrary nonlinear functions hi (.), and as a result arbitrary local models, can be utilized in the LNF model structure. This outstanding feature allows choosing complex local models in order to better model and describe complex and highly nonlinear processes and systems. In this paper the focus is on polynomial functions and Fig. 2. Structure of LNF with p inputs and M local models developing local polynomial models with arbitrary degree. The polynomial functions are powerful in describing nonlinear processes since polynomials with arbitrary degrees can be seen as Taylor series expansion of any unknown function. The next sub-sections describe the procedure of identification local models and validity functions. A. Identification of Local Models Considering a local polynomial model with degree n, the LNF model in (1) can be restated as, = [Oi'O +Oi,lUj +Oi.2Uj 2 +B;.3U2 +",]<p (u) Y L.. i=j 2 i.4uju2 + i.5u i.iup 11 ' - where ; = [O;,o,O;,I '...,O;. I J is the parameter vector of the local polynomial model i. For an n order polynomial function and with p dimensional input space, the number of parameters of each local polynomial model will be 1= (p + n )! p!n! For an efficient estimation of local model parameters, weighted least square algorithm is employed. In addition, it was assumed that the validity functions are known and predetermined. The weighted least square estimation was carried out based on the minimization of local error of each local polynomial model for target output samples. :n{i; = <P; y (4) (5) ( (J))e(J)} (6) where, = e (J) Y (J) -Y (J) and = [Y (1),.. " Y (N) J are N target outputs. The parameters in (4) can be estimated by a least square algorithm using (6) [7]. B. Identification o/validity Functions Multivariate Gaussian functions are normally chosen as validity functions in the LNF model. The multivariate p dimensional Gaussian function for the /" local model can be expressed as 12

3 [ () _ [ _ (Ul-C;I) 2 (U p-c;ptl] f.1; -exp (J,l p _ [ 1 (UI _ C;I) 2 j.. [_1 (UI-Cil) 2 : (7) -exp 2... exp 2 ' 2 l 2 l i=i,...,m where ; =[C;I'.. 'C;p] and =[(J;I,..,(J;p] represent center coordinates and standard deviations of the Gaussian function. The Gaussian functions in (7) need to be normalized to form a partition of unity. <P; ( ) = :; ( ),i = 1,..., M Lf.1j ( ) The sand Q:; are the parameters of the Gaussian validity functions which should be estimated from the observation data. These consequent parameters are estimated using polynomial model tree (POL YMOT) algorithm, described in the next section. In the POL YMPT learning algorithm, the first step is to determine the parameters of the validity functions using a heuristic approach. Having known the validity functions, parameters of the local models are estimated using weighted least square algorithm, presented in sub-section 2.1. The POL YMOT learning algorithm increases the complexity of the model until desired performance is achieved. TTT. LEARNING ALGORITHM The POL YMOT learning algorithm belongs to the category of incremental tree construction algorithms [9]. The POL YMOT algorithm is, in fact, the modified version of the local linear model tree (LOLTMOT) algorithm, which partitions the input space by axis-orthogonal splits into hyperrectangles [8]. In the POL YMOT algorithm, in each iteration, a new local model is added to the LNF network or the number of parameters of the worst local model is increased (i.e. the degree of the worst local polynomial model is incremented). Then he validity functions which correspond to the actual partitioning of the input space are computed and the parameters of the corresponding local polynomial models are optimized by the weighted least square technique. The POL YMOT algorithm can be summarized in the five steps, as stated below. - Step - Start from an initial model: Set M = 1 and start with a single first-order local model whose validity function ( <PI ( ) ) covers the whole input space. 1- Step 1- Find the worst performing local model: Calculate the loss function Ji defined in (6), for all local models and find the worst performing LM. 2- Step 2- Fit a higher degree polynomial: If increasing the polynomial order of the worst performing LM results in lower global model error, then increase the local model order and proceed to step 4, otherwise go to step 3. (8) 3- Step 3- Split the input space: If increasing of the order of worst local model does not lower global model error, then, a-division of the worst LM into two equal halves must be tried in all p dimensions. For each of p divisions, a multidimensional validity function must be constructed for both newly generated hyper-rectangles. Gaussian membership functions are placed at the centers of the hyper-rectangles and standard deviations are selected proportional to the extension of hyper-rectangles (usually 113 of hyper-rectangle's extension). Then the rule consequent parameters of both new LMs must be estimated using weighted least square approach and finally the loss function for the current overall model must be computed. b- The best LM related to the lowest loss function value, must be selected and the number of local models is incremented: M ---> M Step 4- Check termination criterion: If the termination criterion, e.g., a desired level of model's performance or complexity, is met then stop, otherwise go to step 1. The POL YMOT learning algorithm yields maximum generalization and noteworthy forecasting performance of the identified LNF model. It should be noted that in this paper the maximum order of polynomial functions was limited to 2 (i.e. implementing quadratic local models) in order to maintain the number of parameters of the local models to a reasonable level. IV. PV IDENTIFICA TlON AND MPPT BY LNF MODEL In this section it's shown how the proposed LNF model and the steepest descent method can be used for accurate identification and MPPT of the PV arrays. A. identification In the proposed approach, first the PV array is identified by the LNF model and through proper data set. In the identification stage, the input variables including solar insolation (S), temperature (T) and PV voltage (V) are used to describe the output variable, i.e. PV output power (P). Therefore, the following mathematical discretion is derived by the proposed LNF model. P =f (S,T,v ) (9) where f is the describing function of PV array's output power, constructed by the LNF model. In the MPPT stage, the objective is to find the MPP, and in particular the voltage ofmpp (VMPP) of the PV array using the identified PV model and during moment to moment variations of light level, shading, temperature, and photovoltaic module characteristics. In the MPPT stage, the insolation (S) and temperature (T) are assumed known and a search for voltage of the optimal operating point is carried out [6]. Therefore, description in (9) is modified to the expression below. (1) 121

4 Insolation ----M Temperature r--+I Voltage '- J TABLE I SPECIFICATIONS OF THE PV PANEL USED FOR SIMULATION Parameter Max. power Maximum Power point voltage Maximum Power point current Value 19 W 17 V IIA.45.4 Fig. 3. Identification procedure of a PV cell using LNF model where, S opng and T opng are the insolation and temperature at the operating point of the PV array. B. Maximum Power Point Tracking The expression in (1) is a single-variable function. Hence, a single-variable optimization is required to find the optimal voltage (VMPP) corresponding to the maximum output power of the PV array. A gradient-based optimization algorithm, i.e. steepest descent (SD) algorithm, is adopted in this paper. A brief description of the steepest descent optimization algorithm is presented in this sub-section. Steepest descent is an iterative nonlinear optimization technique which tries to find the local minimum (maximum) of an objective function by changing the function's parameters proportional to the negative (positive) of its gradient. For maximization of an arbitrary function F, the parameter updating equation at iteration k is given by ()k = ()k-l + rk-sf (()k-l) (II) where () is the vector parameters of function F and r is the step size [7]. Interested readers can refer to [7] for further information about steepest descent algorithm and its implementation. For maximization of PV output power, the describing function of PV array, constructed by the LNF model, is used. Hence (1) is modified to (9), and the following is resulted Vk =Vk_1 + rk_1vj (Vk_1) (12) The (12) can be iteratively used to find the optimal voltage corresponding to the maximum output power of the PV array. The combination of the LNF model and SD algorithm, designated as LNF + SD, will be used in the next section for identification an MPPT of the PV arrays. V. SIMULATION RESULTS AND DISCUSSION Several different simulation scenarios are considered in order to assess modeling and MPPT performance of the proposed LLNF + SD approach. First, simulations are carried out to show how accurate the LNF model can identify a PV array system. Then using the identified model of the PV array, other simulations are implemented to measure the MPPT performance of the proposed approach under different climate conditions. Finally, the proposed algorithm is used for MPPT in a PV array, connected to a DC bus through a DC-DC converter. The DC bus supplies a fixed resistive load. All simulations are implemented in MATLAB/SIMULlNK environment based on the block diagram shown in Fig. 3. The.35 w.25, (f),, ::2:,.2, a:, ".15 ' " ".1 " ".5 ' " Neurons Fig. 4. Training and test RMSE for different number of neurons general specifications of the PV panel used in simulations are presented in Table 1. A. Identification Results For identification of a PV array by the LNF model, 15 data points were randomly generated using a standard model of [6]. The results of identification will be compared with the { }ISO standard model. The input-output pairs of data Xi' Y j ; l were used for training and testing of the LNF model, where x = (S. T. v ) and y = P. The first 1 data points were employed for training and the remaining 5 data points were applied to the LNF model as the test data. The root mean square of error (RMSE) for training and test data are shown in Fig. 4. As seen from this Fig. the LNF model with nine neurons yields best performance. This model is selected for representing the PV system in other simulations. Now, the voltage and insolation profiles, as shown in Fig. 5 with constant temperature of 45 C are applied to the identified model. It must be noted that the voltage and insolation profiles in Fig. 5 are independent from each other. This is done to test model accuracy in case of simultaneous insolation and voltage variations. In fact, it's assumed there is a highly variable load at the output terminals of the PV panel which results in a voltage profile, shown in Fig. 5-(a). Besides, a voltage profile ranging from to 3 V is applied to the identified model to assess model's performance for whole operating range of the voltage of the PV panel, too. The target and identified output powers, and the absolute identification error during the simulation time are depicted in Fig. 6. Note that during the transition of solar insolation, the LNF model has followed the output of the standard PV array with remarkable accuracy. 122

5 OJ OJ $ (5 > 21 S Qj 2.. >< co LLNF+SD --- Max theoritical 2 3 Fig. 5. (a) Voltage profile and (b) insolation profile ==== --,----,----, [ Target Identified -- Error Fig. 8. MPPT results during transition of solar irradiation Period TABLE II COMPARISON OF MPPT EFFICIENCY (%) P&O Method LNF + SO Improvement Transient Transient Whole simulation period O o Fig. 6. Target and identified power curve for the voltage and insolation shown in Fig e! :::J 35 " OJ.. E OJ 3 I Fig. 7. Temperature profile during MPPT B. Maximum Power Point Tracking Results Now, the MPPT perfonnance of the proposed approach under transient climate conditions is evaluated. For this purpose, the insolation profile, shown in Fig. 5-(b) and the temperature profile, shown in Fig. 7, are applied to the identified LNF model of PV array. Obviously, the insolation has two transition periods, i.e. from 2.32 t3.6 seconds and from 4.4 to 5. seconds. The result of the maximum power point tracking is shown in Fig. 8. It's seen that the proposed LNF + SD approach has successfully tracked the maximum power point of the PV array even during the transients of both insolation level and temperature. For a numerical analysis and comparison, the efficiency of the MPPT (T/Ml' PT ) will be computed, as expressed below, T/ MPPT= f Pa ctual (t ) dt Pmax ( t ) dt (13) where, Pactual and Pmax are the actual and theoretical maximum power of the PV array, respectively. The T/ MPPT during the first and second transient and the whole simulation period for the proposed LNF + SD and the P&O [4] approaches are presented in Table IT. C. MP PTfor a Converter-Connected P V array Tn the last case study, application of the proposed MPPT algorithm for a PV array, which is supplying a 2 n load through a DC-DC boost converter, is investigated. Tn this simulation, it's intended to extract the maximum power of the PV arrays during variations of the solar illumination. The block diagram of the control strategy, which employs voltage regulation of the PV array, is shown in Fig. 9. Tn PV array voltage regulation scheme, the output voltage of PV array is regulated to the maximum power point (MPP) voltage in order to maximize its output power. Tn the control strategy shown in Fig. 9, first the MPP voltage is determined by the LNF + SD algorithm. Then this voltage is set as the reference voltage. The error between the reference voltage and the current 123

6 power obtained by the proposed strategy shown in ripple and fluctuation in contrast to the output power obtained by the FLC. Fig. 9. Identification procedure of a PV cell using LNF model 11, N E 95 c '@ 9 en c Time (second) Fig. 1. MPPT results during transition of solar irradiation 1-- Fuzzy controller Proposed method Q; $: D Time (second) Fig. 11. MPPT results during transition of solar irradiation voltage of PV array (Vpv) is fed into a PI controller which finally determines the duty cycle of a PWM generator. Fig. 1 shows solar irradiation profile during the simulation time. This profile is applied to the PV array to evaluate performance of the proposed MPPT algorithm. In this case study, a fuzzy logic controller (FLC), developed in [1], is also simulated and its results are compared to the proposed approach. Fig. 11 shows the output power of PV array obtained by the proposed approach and the FLC. The proposed approach exhibits several advantages over the FLC in [1]. First it has a faster response time. Furthermore, the output I I I. 8 8 VI. CONCLUSION This paper proposed a local neuro-fuzzy approach for identification and maximum power point tracking of PV systems. The proposed LNF approach requires no pre-defined model and constructs a valid and accurate model for the PV arrays using the measurement data. Local modeling capability of the LNF model was an advantageous feature for modeling the highly-nonlinear power curve of the PV systems. The constructed model was then employed by a steepest descent algorithm for MPPT. The conducted simulations demonstrated remarkable performance of the proposed LLNF + SD approach for identification and MMPT of PV systems. Based on the simulation results, the LNF model successfully followed the power curve of the PV array during transients of the solar irradiations and voltage changes. Furthermore, MPPT performance of the proposed approach was noticeable during variations of solar irradiation. ACKNOWLEDGEMENT This work has been supported by the project ENE C2-11 AL T funded by of Spanish Ministry of Science and Innovation. REFERENCES [1] International energy agency photovoltaic power systems program: Annual report 21. [Online.] Available: [2] M. Saeedifard, M. Graovac, R. F. Dias, and R. Iravani, "DC power systems: Challenges and opportunities," In 21 IEEE Power and Energy Society General Meeting, 21, pp [3] W. Xiao, A. Elnosh, V. Khadkikar, and H. Zeineldin, "Overview of maximum power point tracking technologies for photovoltaic power systems," in Proc. 37th Ann. Conf. on IEEE Ind. Electron. Society, 211, pp [4] S. Jain and V. Agarwal, "Comparison of the performance of maximum power point tracking schemes applied to single-stage grid-connected photovoltaic systems," Electric Power Applications, let, vol. I, pp ,27. [5] K. B. Ariyur and M. Krstic, Real-time optimization by extremumseeking control. Hoboken, N.J.: Wiley-Interscience, 23. [6] N. Tat Luat and L. Kay-Soon, "A Global Maximum Power Point Tracking Scheme Employing DIRECT Search Algorithm for Photovoltaic Systems," Industrial Electronics, IEEE Transactions on, vol. 57, pp ,21. [7] O. Neils, Nonlinear System Identification, Springer, Berlin, Germany, 21. [8] H. Iranmanesh and A. Miranian, "Split ratio optimized local linear neuro fuzzy model for prediction: application to oil consumption prediction," presented at 3rd IEEE Int. Conf. Intelligent Computing and Intelligent Systems, Guangzhou, China, Nov [9] O. Banfer, M. Franke, and O. Nelles, "Adaptive Local Model Networks with Higher Degree Polynomials," Int. Conf. Control. Autom. Syst., 21, Korea, pp [1] A.M. Alabedin, E.F. EI-Saadany, and M.M.A. Salama, "Maximum power point tracking for Photovoltaic systems using fuzzy logic and artificial neural networks," 211 I EEE Power and Energy Society General Meeting, pp