Título: Co pa iso of Fou MPPT Algo ith s Applied I Bate ies Cha gi g With Photovoltaic Pa els Autores:

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1 GESEP Gercia de Especialistas e Sisteas Eltricos de Potcia Título: Copaiso of Fou MPPT Algoiths Applied I Bateies Chagig With Photovoltaic Paels Autores: João Heiue de Oliveia ; MALTA, A. L. ; Alla F. Cupeio ; PEREIRA, H. A. Puliado em: Sipósio Basileio e Sisteas Eléticos - SBSE Data da puliação: 4 Citação para a versão puliada: João Heiue de Oliveia ; MALTA, A. L. ; Alla F. Cupeio ; PEREIRA, H. A.. Copaiso of Fou MPPT Algoiths Applied I Bateies Chagig With Photovoltaic Paels. I: Sipósio Basileio e Sisteas Eléticos - SBSE, 4, Foz do Iguaçu. Aais do SBSE 4, 4.

2 Comparison of Four MPPT Algorithms Applied in Batteries Charging with Photovoltaic Panels Amaury L. Malta, João H. de Oliveira, Allan F. Cupertino,2 and Heverton A. Pereira,2 Gerência de Especialistas em Sistemas Elétricos de Potência Universidade Federal de Viçosa Av. P. H. Rolfs s/nº, 367- Viçosa, MG, Brazil Abstract In order to extract the maximum power of the panel for a given set of climatic conditions, it is used Maximum Power Point Tracker (MPPT). The MPPT consists in a power converter which controls the solar panel voltage. The maximum power point voltage is calculated by MPPT algorithms. Besides, this algorithm can be used by a feedback control or can calculate directly the duty cycle of the converter. In fact, the performance of these algorithms impacts directly in the generated power. In this context, this work compares four MPPT algorithms propose in literature: Perturb and Observe, Incremental Conductance, Constant Voltage and Ripple Correlation Control. Furthermore, it is analyzed the differences when it is used a feedback control spite of the direct calculus of the duty cycle. In the simulations, a battery charger of 48 W based on a buck converter was used. Index Terms MPPT algorithm, Buck converter, Battery, PI. I. INTRODUCTION The demand of electricity has been increasing in the last years. In this context, solar photovoltaic (PV) systems have growth considerably due to low environmental impact, quiet operation and easy aggregation structures. According to a survey released recently by European Photovoltaic Industry Association (EPIA), in 22 the installed capacity of PV modules reached a value around 2 GW. Despite its favorable characteristics, the generation of solar energy is seasonal and is strongly dependent on climatic conditions (solar radiation, temperature, wind speed, etc.). Thus, it is necessary to extract as power as possible of a solar panel. Figure shows a typical P x V curve of a solar panel. For a given value of radiation and temperature there is a point which the maximum power is obtained. For this reason, in PV systems there is a maximum power point tracker (MPPT) which controls the panel voltage to the maximum power point value. The MPPT consists in a power converter which changes the duty cycle and maintains the solar panel voltage at the maximum power point value. The maximum power point 2 Graduate Program in Electrical Engineering Federal University of Minas Gerais Av. Antônio Carlos 6627, Belo Horizonte, MG, Brazil allan.cupertino@yahoo.com.br, hevertonaugusto@yahoo.com.br voltage is obtained through maximum power point tracking algorithms (MPPT). The MPPT algorithm can work two different forms: the first one calculates directly the duty cycle of the power converter, similarly to an open loop control. The second one calculates the maximum power point voltage which is reference for a voltage closed loop control. The second method is preferable because it reduces losses and the stress of the converter by limiting the bandwidth of the duty cycle control [] Curve Power vs Voltage 2 2 Voltage(V) Figure - Typical curve of a solar panel. Several MPPT algorithms have been proposed in the literature. This work studied four strategies: constant voltage method [2], perturbation and observation (P&O) [3], incremental conductance [] and ripple correlation control (RCC) [4]. The performance of each algorithm during changes in solar radiation is compared. After, it is shown the effect of the voltage closed loop control in the response of the maximum power point tracker. This work is supported by the Brazilian agencies CAPES, FAPEMIG and CNPQ.

3 II. MPPT ALGORITHMS The MPPT algorithms studied in this work are detailed described in this section. A. Constant Voltage-CV Constant Voltage algorithm calculates the maximum power point voltage ( ) using a fractional value of the open circuit voltage ( ). According to [4], the relation between and is given by: = () Where is a constant of proportionality. This value usually varies between.7 and.76 [4], [] and needs to be obtained empirically. This fact results in a low generality. This algorithm considers that the maximum power point voltage presents small changes. This fact is valid only considering small variations in the solar panel temperature, like is shown in Figure 2. Besides, this method is few attractive because it is necessary disconnect the panel to the load in order to determine the value of [6]. This technique uses the derivative of the power curve with respect to the voltage (/). This fact guarantees smaller perturbations in steady state than P&O method [6]. In fact, at the MPP, / =. This derivative can be written in terms of the PV array current and voltage, like shown in (4). ( ) = = + + The algorithm compares periodically the conductance with the incremental conductance []. It is presented in Figure 4. Note that: = (2) If, the algorithm find the maximum power point; If >, it is necessary to increment the voltage to find the maximum power point; If >, it is necessary to decrement the voltage to find the maximum power point; Figure 2 - curves of a solar panel for various levels of radiation and a constant temperature. B. Perturbation and Observe P&O The Perturbation and Observation (P&O) algorithm is presented in Figure 3. This method is widely used due to its low complexity and origins many other algorithms as Modified P&O, Hill Climbing and Modified Hill Climbing []. The algorithm periodically increments or decrements the solar array voltage and compares the output power with the previous value. If the delivered power increased, the perturbation will continue in the same direction in the next cycle, otherwise the perturbation direction changes. This means the array terminal voltage will be perturbed every cycle. When the MPP is reached, P&O algorithm will oscillate around it [7]. C. Incremental Conductance IC The IC algorithm is frequently considered the best technique based on the Perturbation and observation method. This method presents a good behavior in steady state and a fast response during changes in the incident solar radiation [8]. Figure 3 - P&O algorithm. Figure 4 - IC algorithm.

4 D. Ripple Correlation Control(RCC) The RCC method was firstly presented as an analogic technique with a fast response [9]. Although, there is in literature some proposes of digital implementation [], []. This method uses the instantaneous PV power ripple p and the instantaneous PV voltage ripple v to find out the power derivative dp/dv [2]. It is used a first order highpass filter to obtain the instantaneous voltage and power ripples. Then, it is used a first order lowpass filter to calculate the average values of the power derivative (3). This method is shown in Figure. If the voltage increases ( > ) and the power increases ( > ), the operating point is below the MPP. On the other hand, if v increases and p decreases, then the operating point is above the MPP. So, if is positive the operation point is on the left of the MPP (dp/dv > ); If is negative the operation point is on the right of the MPP (dp/dv < ). (3) source and a resistance [7], [2]. The parameters of the solar panel are presented in Table. Figure 8 presents the IxV curve of this panel and the linearization round the MPP. In this case, it was obtained V = 37. V and R = 7. Ω TABLE - Parameters of the SM48KSM. Parameter Maximum Power Maximum Power Voltage Maximum Power Current Open Vircuit Voltage Short Circuit Current Temperature Coefficient of Temperature Coefficient of Value /.66 /.. Figure - Block diagram of the RCC method. III. BUCK CONVERTER Figure 6 shows a PV system connected to a DC/DC converter, which is used to charge a battery. The output power of the PV array is controlled by the converter [7]. In this work it is used a buck converter, as shown in Figure 7. Figure 6- Scheme of a battery charger. In photovoltaic applications, the voltage control is preferable because the maximum power voltage of the panel is approximately constant over a wide range of solar radiation changes []. The capacitor at the input of the converter reduces the input voltage ripple and filters the discontinuity in the input current. Figure 7- Topology of buck converter. In the buck converter modeling the photovoltaic panel is linearized around the MPP and is represented by a voltage = 2 2 Figure 8- curve of the panel and its linearization around the MPP. The state space equations of the converter are: Where: = +. ( ) ( ).. ; = ;. = ; = ; =.. = ; = ; < * > represents the average value of the variable *. represents the average value of the duty cycle. Equation (4) is nonlinear because it involves multiplication of time-varying variables. Therefore, it is necessary to linearize the model. Reference [3] proposes a methodology based on small-signal model. The first step of this method is generating a small disturbance in steady state and verifying what happens to the system. Then, ; (4)

5 = + = + = + Substituting () and (4) manipulations, the result is: () and doing some algebraic Magnitude (db) Bode Diagram Open Loop Compensated is: = (6) The transfer function relating the input voltage to the duty () = () = () (), The buck converter control strategy used in this work is shown in Figure 9. The parameters of the system are presented in Table 2. It is used a PI controller given by: () = 3 + The complete structure of the battery charger is presented in Figure 9. The MPPT algorithm calculates the reference to the voltage compensator. This last will change the duty cycle of the converter. (7) (8) Phase (deg) Figure - Bode diagram of the open loop and compensated transfer functions..4.2 Frequency (Hz) Step Response Amplitude Figure 9- Battery charger with MPPT. The bode diagram of the open loop and compensated transfer functions are shown in Figure. The closed loop step response is presented in Figure. It can be observed that the compensated transfer function presents a good phase margin and a high gain in low frequencies. TABLE 2 - Parameters of the buck converter. Parameter Inductor Capacitor in Panel Output Voltage Frequency Switching Inductor Resistance IV. SIMULATIONS Value Ω It was simulated in Matlab/Simulink the performance of a battery charger of 48 W. Firstly, it is compared the performance of the MPPT algorithms during variations in the incident solar radiation. It is used the profile presented in Figure. The parameters of the battery are shown in Table 3. The irradiation profile used changes fast and, for this reason, it was considered that the temperature of the panel is constant Time (sec) x -3 Figure - Step response of the closed loop. In a second moment, it is studied the influence of the close loop control in the performance of the system. In this case, it is simulated a situation which the MPPT algorithm calculates directly the duty cycle of the converter. The CV algorithm works with a sampling frequency of and =.76. The IC and P&O algorithms work with a sampling frequency of and Δ = 3. For the method RCC were used high-pass and low-pass first order filters, all with cutoff frequency of 3 Hz. The sign function in Figure returns if the derivative is positive, zero if the derivative is zero and - if is negative.

6 Solar radiation (W/m 2 ) Figure 2- Irradiation profile used in the simulations. TABLE 3 - Parameters of the battery. Battery (Nickel-Metal-Hydride) Nominal Voltage 2 Nominal Capacity 6 h Initial Stage of Charge 2 % Maximum Capacity 7 h Fully Charged Voltage 4.4 Nominal Discharge Current 6.2 Internal Resistance.8 Ω V. RESULTS A. Comparison of MPPT s agorithms Figure 3 show that the methods P&O, Incremental Conductance and RCC extracted the maximum power of the panel, while the method Constant Voltage cannot properly track the MPP. It is also observed that every.2 second the PV array power by the CV method goes to zero. In fact, this method disconnects the panel from the converter to obtain a measure of the open-circuit voltage of the panel, to calculate the MPP. The battery current of the four methods is shown in Figure 4. The current in CV method is smaller than the others three methods, mainly for radiation near the nominal. This occurs because the CV method did not increment or decrement the estimated voltage like happens in the other techniques. The RCC method presents the fast response in variation of solar radiation, as can be observed in Figure. P&O e Incremental Conductance showed a response 33% slower than RCC when the radiation increases and 63% slower, when the radiation decreases. CV presents the fastest response, however the PV array voltage is smaller than the maximum power voltage. PV Array Power Figure 3 - PV array power, varying solar irradiation on panel. Figure 4 - Current in battery, varying solar irradiation on panel. P&O IC CV RCC Current in the Battery P&O IC CV RCC

7 Voltage(V) Voltage(V) Voltage(V) 2 2 PV Array Voltage P&O IC CV RCC Power(W) Figure 6 - PV array power, using the MPPT algorithm RCC in different ways PV Array Power Time(s) PV Array Current Without PI With PI Without PI With PI Figure - PV array voltage, varying solar irradiation on panel. 3 2 B. Influence of the close loop control in the performance of the system. This section shows a comparison of the MPPT algorithm Ripple Correlations Control operating in two ways: calculating a reference voltage, using a PI controller to control the duty, and a situation which the MPPT algorithm calculates directly the duty cycle of the converter. The RCC method was chosen because it provides the best results analyzing the response time. Figure 6 shows the extracted power. It can be observed that the system using the PI controller presents lower ripple that direct duty cycle calculation. In Figure 7 and Figure 8 it is possible to see that the method using the PI controller showed better results. The direct duty method presents large ripple in the PV array power, voltage and current. The close loop control also acts avoiding abrupt variation of the duty, which reduces the stress of the converter Time(s) Figure 7 - Current in the Battery, using the MPPT algorithm RCC in different ways. Voltage(V) PV Array Voltage Without PI With PI Figure 8 - PV array voltage, using the MPPT algorithm RCC in different ways.

8 VI. CONCLUSION This paper presents a comparison of four MPPT algorithms. RCC method presents quick response to extract the maximum power of the panel in variations in solar radiation, but the use of filters in this method also brings a greater complexity in the construction of the MPPT algorithm. P&O and Incremental Conductance are easy to implement and have good results. Constant Voltage cannot extract the maximum power and it is necessary to disconnect the panel from the load. Besides, the results show that the use of a voltage closed loop control improves the operation of the buck converter, avoiding the stress of it. REFERENCES [] VILLALVA, M. G. Conversor Eletrônico de Potência Trifásico para Sistema Fotovoltaico Conectado à Rede Elétrica. Unicamp. Campinas, p (PHD Thesis). [2] HUSSEIN, K. H. et al. Maximum photovoltaic power tracking : an algorithm for rapidly changing atmospheric conditions. IEE Proceedings- Generation, Transmission and Distribution, 42, n., [3] MIDYA, P. et al. Dynamic Maximum Power Point Tracker for Photovoltaic Applications. Power Electronics Specialists Conference, PESC, 996. [4] CAVALCANTI, M. C. et al. Comparative study of maximum power point tracking techniques for photovoltaic systems. Eletrônica de Potência, p. 63-7, 27. [] ESRAM, T.; CHAPMAN, P. L. Comparison of photovoltaic array maximum power point tracking techniques. IEEE Transactions on Energy Conversion, p , 27. [6] BEKKER, B.; BEUKES, H. J. Finding an optimal pv panel maximum power point tracking method. 7th AFRICON Conference in Africa, p. 2-29, 24. [7] VILLALVA, M. G.; GAZOLI, J. R.; FILHO, E. R. Analysis and simulation of the P&O MPPT algorithm using a linearized photovoltaic array model. th Brazilian Power Electronics Conference, COBEP. :. 29. p.. [8] IMHOFF, J. et al. A stand-alone photovoltaic system based on dc-dc converters in a multi string configuration. Proc. European Conference on PowerElectronics and Applications, p. -, 27. [9] SPIAZZI, G.; BUSO, S.; MATTAVELLI, P. Analysis of mppt algorithms for photovoltaic panels based on ripple correlation techniques in presence of parasitic components. Brazilian Power Electronics Conference - COBEP, p. 88-9, 29. [] KIMBALL, J. W.; KREIN, P. T. Digital ripple correlation control for photovoltaic applications. Power Electronics Specialists Conference - PESC, p , 27. [] KIMBALL, J. W.; KREIN, P. T. Discrete-time ripple correlation control for maximum power point tracking. IEEE Transactions on Power Electronics, p , 28. [2] CUPERTINO, A. F. et al. A Grid-Connected Photovoltaic System with a Maximum Power Point Tracker using Passivity- Based Control applied in a Boost Converter. IEEE/IAS International Conference on Industrial Applications - INDUSCON, Fortaleza, November 22. [3] ERICKSON, R. W.; MAKSIMOVIC', D. Fundamentals of Power Eletronics. New York: Klumer Academic Publishers, 24. [4] CASADEI, D.; GRANDI, G.; ROSSI, C. Single-Phase Single- Stage Photovoltaic Generation System Based on a Ripple Correlation Control Maximum Power Point Tracking. IEEE Transactions on Energy Conversion, v. 2, p , 26. BIOGRAPHIES Amaury Leite Malta was born in Senhora dos Remédios, Brazil. He is student of Electrical Engineering at Federal University of Viçosa, Viçosa, Brazil. Currently is integrant of GESEP, where develop works about renewable energy system. His research interests include power electronics and solar energy. João Henrique de Oliveira was born in Timóteo- MG, Brazil. He is student in electrical engineering from the Federal University of Viçosa (UFV), Viçosa, Brazil. He is integrant of GESEP, where developed works about power electronics applied on renewable energy systems. His research interests include power electronics and solar energy. Allan Fagner Cupertino received the B.S. degree in electrical engineering from the Federal University of Viçosa (UFV), Viçosa, Brazil, in 23. He is integrant of GESEP, where developed works about power electronics applied in renewable energy systems. Currently he is Master student from Federal University of Minas Gerais (UFMG), Belo Horizonte, Brazil. His research interests include solar photovoltaic, wind energy, control applied in power electronics and grid integration of dispersed generation systems. Heverton Augusto Pereira received the B.S. degree in electrical engineering from the Federal University of Viçosa (UFV), Viçosa, Brazil, in 27, the M.S. degree in electrical engineering from the State University of Campinas (UNICAMP), Campinas, Brazil, in 29. Currently he is Ph.D. student from the Federal University of Minas Gerais (UFMG), Belo Horizonte, Brazil. Since 29 he has been with the Department of Electric Engineering, UFV, Brazil. His research interests are wind power, solar energy and power quality.