Comparison between Maximum Power Point Tracking ...

IEEE CHILECON2017 - ISSN 0719-6806, Pág. Xxxx.xxx. Pucón, Chile, 18 al 20 de Octubre 2017

Comparison between Maximum Power Point Tracking Algorithms for dc/dc Power Converters Matias N. Garbarino, Rodrigo H. Morales, Pablo Henríquez, Sául Cuevas, Jaime Rohten, Eugenio Wernekinck, Angel Rubio, and Pedro Melín Abstract—During last period, the energy harvested from solar power cells have arisen exponentially, being every day more important, because it is a clean energy presented in almost all over the globe. However, in order to track the maximum power point to maximize the drained energy, different algorithms are implemented to impose certain current and voltage at the solar module output. The maximum power point depends upon the solar irradiance, the temperature and the angle between the solar irradiation and the solar modules normal vector. This paper presents an analysis of three different methods to track the maximum point variations: (1) the Perturbation and Observation (P&O) algorithm; (2) and improvement of the P&O with variable step; (3) the Incremental Conductance method. To corroborate the results of this work, simulations are performed on PSim® 9.0.3 under variations on the irradiance, temperature to show the feasibility of every algorithm. Index Terms—— MPPT Algorithms, dc/dc converters, Solar energy.

I. INTRODUCTION

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decades, the renewable energy, as the solar ones, has grown up exponentially, pretending to be one of the most popular clean energy together with wind generators based, due to the inexhaustible presence of sun irradiance and wind [1], [2]. Regards the point aforementioned, the study of control techniques to improve the maximum power point tracking, and the efficient use of energy has gained relevance and interest among researchers [3]. One way to maximize the power extraction from solar modules are the employment of Maximum Power Point Tracking (MPPT) algorithms [1], [4]. Theses algorithms track the Maximum Power Point (MPP) independently of the disturbances presented in the environment as change on irradiance and/or temperature. The MPPT algorithms, [5], are based on the solar cell module, which is nonlinear and difficult to run online in digital boards because the heavy equations that compose its modules as a function of the resistance, solar AST

This work was supported in part by the projects of internal initiation DIUBB 168310 4/l, the MacroFacultad 10804010-215 and Department of Electrical and Electronics Engineering at Universidad del Bío-Bío. The authors M. Garbarino Rodrigo H. Morales, Pablo Henríquez, Sául Cuevas, Jaime Rohten, Ernesto Rubio, Eugenio Wernekinck and Pedro Melín are with Department of Electrical and Electronics Engineering, University of Bío-Bío. Authors can be connected through [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], and [email protected], [email protected] respectively.

irradiance and temperature. In addition, new modules can be stacked or removed changing the MPP and therefore the algorithm should be adapted to the new conditions. The curves of interest are the I-V and P-V curves which describe the solar behavior under current, voltage, irradiation and temperature changes [2]. Currently, there are other works which presents different MPPT control algorithms, however, this paper studies, analyze and simulate three MPPT algorithms, with the aim to compare them and determine which present a better performance and reduced computational cost, considering a solar array under change on the external disturbances [1] – [5]. At the end of this work, simulations and tables are included to determinate the best algorithm including the computational time, the dynamic response and the noise rejection. This paper is organized in section as follow: Section II Introduces the solar cell model, which gives the curves to base the MPPT algorithms and improve the system efficiency. Section III: It is introduced the dc/dc static power converter, used to impose the desired voltage at the solar cell output. Section IV: It is detailed and given brief results of the proposed algorithms: a) Perturb & Observe (P&O), b) Perturb and Observe with variable step, and c) Incremental Conductance (ConInc). Section V: The three proposed algorithms are compared by simulations tests, comparing the computational cost, and studying the square error with respect the supplied power. Finally, Section VI shows the conclusions of the proposal.

II. SOLAR CELL MODEL A solar module can be model through its equivalent circuit shown in Fig. 1. This is built with a current source which synthetized the solar irradiance; one diode representing the p-n semiconductor junction; two resistance one in parallel and other in series with load, which represents the solar module internal losses [6]. This model represents the static behavior of the solar module before changes on the parameters and disturbances.


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Fig. 1. Equivalent circuit of a solar cell.

The equation that represents the circuit of Fig. 1 are obtained by sensing the system under open circuit and short-circuit connection at the cell output. When the cell output is in shortcircuit condition the currents ISC is obtained, on the other hand, when the cell is sensed in open circuit where Iph = Isc [8]. Applying the Kirchhoff laws, it is obtained that: I =I SC − I d , (1) where Id represents the diode intrinsic current, follow the Shockley mathematic model   qV   I d = I 0  exp  d  − 1 , (2)  nKT    where: I0 : The diode saturation inverse current. q : An electron electric charge (1.602x10-19[C]). Vd : Diode Voltage. K : Boltzman constant (1.381x10-21[J/K]). T : Absolute temperature in Kelvin [°K]. n : Diode ideality factor. Replacing (2) in (1), it is obtained the following:   qV   I = I SC − I 0  exp  d  − 1 . (3)  nKT    Considering the output current of the cell as zero, i.e. I = 0, and it is included on (3), the following is gotten:   qV   (4) 0 = I SC − I 0  exp  d  − 1 ,  nKT      qV   I SC = I 0  exp  d  − 1  . (5)  nKT    Furthermore, analyzing the circuit of Fig. 1, it is possible to conclude that: Vd = V + I ⋅ Rs . (6) Finally, the equation for the current that represents the behavior of it, is synthetized as:   qV   V + I ⋅ Rs I = I ph − I 0  exp  d  − 1 + , (7) Rsh  nKT    The model given in (7) is used for the current software to simulate the solar module behavior. Particularly, this works employed PSim® 9.0.3 where the model is given on the software help support, which is also represented by the defined equation. In addition, this work will work with a solar module constituted by 36 cells, where the parameters of the solar module are displayed on TABLE I.

0

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10 15 20 25 Voltage PV (V) (a)

30

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30

Fig. 2 Characteristic curves under irradiance and temperature variation, (a) current-voltage, (b) power-voltage TABLE I PV MODULE ELECTRIC PARAMETERS parameters Valor 58,1[kW] Maximum power ( á ) Voltage at MPP ( ) 16,6 [V] Current at MPP ( ) 3,5 [A] 3.8 [A] Short-circuit current ( ) 20 [V] Open circuito voltage ( )

Depending upon the particularities of the solar module, the curves I-V and P-V can be found by the equations listed before with irradiance and temperature change. Under the use of parameters listed in TABLE I, the curves graphic on Fig. 2 can be attained for different external conditions. To get the simulation of Fig. 2, it was considered a couples changes that the system may meet on real implementation [9], where more details of this conditions are registered on the data of TABLE II. TABLE II SIMULATION CONDITIONS Parameters Irradiation Temperature 500 [W/m2] 60°C 1000 [W/m2] 60°C 1000 [W/m2] 30°C 1000 [W/m2] 60°C 500 [W/m2] 60°C

Time Initial 0 [s] 0.05 [s] 0.15 [s] 0.20 [s] 0.30 [s]

III. DC/DC CONVERTER In order to impose a desired voltage at the solar module output and reach the MPP, a controlled power converter is proposed to boost the voltage and reject the variations imposed by the environment conditions. Between the numerous dc/dc power converters, the most common are: The Buck, BuckBoost, Cuk, Boost, among others. This paper employs a Boost Converter which is capable to boost the voltage to be used on residential higher voltage, where the converter configuration is presented on Fig. 3. The parameters of the power converter are defined on TABLE III, including a desired voltage at the load of 40V, i.e., a higher voltage with respect the solar module.

IEEE CHILECON2017 - ISSN 0719-6806, Pág. Xxxx.xxx. Pucón, Chile, 18 al 20 de Octubre 2017 L

diode

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No

v(k+1) = v(k) + δv

TABLE III POWER CONVERTER PARAMETERS Parameter Value L (Inductance) 500 μH fsw (commutation frequency) 10 kHz v (Voltage at capacitor C) 50 V

v(k+1) = v(k) - δv

v(k+1) = v(k) + δv

For the P&O algorithm, a simulation is performed, considering the parameters of TABLE II, giving as a result the graphics of Fig. 5. It is possible to mention that due to the nature behavior of this algorithm, this technique will never get the MPP, but only will be close to the desired point, and also will be affected by the noise due the converter and the measuring noise. B. P&O with variable step. The next algorithm will be the P&O with variable step, this algorithm is the same presented before, but the voltage variation step δv is changed as a function of the proximity with respect the optimum power. Despite there may be included many conditions, this paper uses only two (i) work with small step change δv when the power variation between the actual and the past time is small, which means that we are close to the MPP; and (ii) work with higher step change δv when the difference between the actual and the past power is higher, which in turn means that the algorithm is working far from the optimum operating point. Thus this algorithm allows to work with variable solar and temperature condition including a fast dynamic response, but minimizing the oscillation when the MPP is reached. The diagram of the proposed algorithm is shown in Fig. 6. To test the algorithm, there will be employed the parameters of Table II, resulting in the simulation shown on Fig. 7. 70 60 50 40 30 20 10 0

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A. Perturbation and Observation (P&O) This algorithm is based on manipulate periodically the solar module output voltage and as a function of the increase or decrease power decide the path to reach the MPP. If the path indicates to increase the voltage, because increasing the voltage the power increase, the P&O algorithm will continue to do so until the power starts to decrease, where the algorithm take the other path reducing the imposed voltage at the solar cell output [12]–[14]. The increasing and decreasing voltage is obtained by the manipulation of the power converter duty cycle which manipulate the relation between the solar panel voltage vPV and the load voltage v, where in steady state this relation is given by: 1 (8) v= vPV , 1− d being d the duty cycle. It is important to highlight that this algorithm will never converge to the MPP, but it will be oscillating around the MPP. As a consequence, the more fast dynamic is imposed the more oscillation will be attained around the MPP. Therefore, the main issue on this algorithm is to decide the value amount step of change to reduce the oscillation but at the same time reach the MPP as soon as possible. A graph interpretation of the P&O algorithm is presented on Fig. 4, where: V(k) : Voltage at time k, I(k) : Current at time k, P(k) : Power at time k, δv : Voltage step variation.

v(k+1) = v(k) - δv

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Fig. 4. P&O algorithm representation.

Power (W)

The main target of the designed MPPT algorithms is to keep the system working in the efficient point extracting all the possible power from the solar irradiation [10], [11], despite the possible fluctuations, natural of sun irradiance. The three algorithms, hereby presented, have their own advantages and disadvantages one respect the other, which are part of the present work discussion.

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Fig. 5. Simulation algorithm P&O. (a) time from 0 [s] to 0.35 [s]. (b) zoom, time from 0.149 [s] to 0.157 [s]. (c) zoom, time from 0.149 [s] to 0.152 [s].

IEEE CHILECON2017 - ISSN 0719-6806, Pág. Xxxx.xxx. Pucón, Chile, 18 al 20 de Octubre 2017 Start

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Fig. 8. Flowcharts algorithm incremental behavior.

Fig. 6. Flowcharts algorithm P&O Step Variable.

and therefore:

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Fig. 7. Simulation algorithm P&O. (a) time from 0 [s] to 0.35 [s]. (b) zoom, time from 0.149 [s] to 0.157 [s]. (c) zoom, time from 0.149 [s] to 0.152 [s].

(13)

 Δi i  dpPV < 0 (move left) . (14) if  PV < − PV  , then vPV  dvPV  ΔvPV When the MPP is at the left side, (13), the voltage should be increased; as well as if the point is on the MPP right side, (14), then the voltage should be decreased. To test the aforementioned algorithm, this algorithm is simulated where the results shown in Fig. 9 are obtained.

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ΔiPV i = − PV . (11) ΔvPV vPV When the equality of (11) is achieved, it is necessary to analyze the actual point, as it is shown on Fig. 8. The diagram shows the following equations:  Δi i  dpPV = 0 (on the MPP) . (12) if  PV = − PV  , then Δ v v dvPV  PV PV 

Power (W)

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Power (W)

Power (W)

C. Incremental Conductance (CondInc) The main disadvantage of P&O algorithms based are the oscillation near of the MPP, therefore, the Incremental Conductance is developed in order to reduce as much as possible this oscillation. The algorithm is strongly based on the solar cell curves (I-V y P-V), by the analysis of the curve slope [1], [3], [6], [13]. To know the slope sign, this algorithm make a comparison between the actual conductance –iPV/vPV with the incremental conductance diPV/dvPV, equations describe bellow. Considering dp/dvPV = 0 as the MPP, it can be found the following: d ( vPV iPV ) dp = = dvPV dvPV , (9) d ( iPV ) d ( vPV ) ΔiPV vPV + iPV ≈ vPV + iPV vPV vPV ΔvPV on the MPP, it can be noted that: Δi 0 = vPV PV + iPV , (10) ΔvPV

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Fig. 9. Simulation algorithm CondInc. (a) time from 0 [s] to 0.35 [s]. (b) zoom, time from 0.149 [s] to 0.157 [s]. (c) zoom, time from 0.149. [s] to 0.152 [s].

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variable and finally the CondInc To include the error between the delivered power and the maximum possible delivered power, Fig. 10, it is analyzed the square error between the power supplied by the converter to the load and the solar maximum power supplied by the module. The results are expressed in TABLE V. TABLE V SQUARE ERROR COMPARISON

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Total average error in the change step Total trapezoidal error in the change step Total average error in the all curve Error in stationary state

Fig. 10. Simulation comparison algorithms, P&O, P&O with step variable and CondInc. (a) time from 0 [s] to 0.35 [s]. (b) zoom, time from 0.149 [s] to 0.157 [s]. (c) zoom, time from 0.149. [s] to 0.152 [s].

V. COMPARISON Under the consideration of previous mathematical development and the simulated results, it is presented fare comparison between the three algorithms. As shown on Fig. 5, the P&O algorithm can track the maximum power point, oscillating around it. On Fig. 7, the P&O algorithm with variable step can reach the MPP faster since it accelerates the response when the system is far from the operating point. Finally, the results of Fig. 9 shows that the CondInc algorithm also has a proper response and the oscillation around the operating point is only due to the noise of commutation and the introduced sense noise. As shown in Fig. 10, the fastest algorithm is the P&O with variable step, followed by CondInc, and at last, the P&O algorithm. However, the dynamic behavior is not the only point of comparison, but the computational cost to implement this algorithm is also considered. TABLE IV shows the instructions needed to compute the proposed algorithms. As this comparison is based on the instructions it can be applied to any digital board by knowing every instruction computational cost. The instructions enumerated are summations, subtraction, multiplications and division, also a ‘one cycle instructions’ are included which represents the ‘if’, ‘else’, comparison between to values, etc. TABLE IV COMPUTATIONAL COMPARISON Type of instructions Summations Subtracts Divisions Multiplications One cycle Instructions

CondInc

3 2 0 1

P&O with Variable Step 4 5 0 1

25

27

39

P&O

6 6 6 5

P&O witch variable step

CondInc

0,9175

0,3519

1,1351

0,9189

0,3519

1,1365

1,2862

0,7245

1,5045

0,3687

0,3726

0,3695

The results of TABLE V shows that the best performance is obtained the P&O with variable step algorithm with the minor squared error in [W2], therefore this algorithm shows to be more efficient with a reduce computational effort.

VI. CONCLUSIONS As final conclusion, it can be mentioned, that the use of control techniques to track the MPP has help to exploit the energy in more efficient way. Comparing the results of this paper, the MPPT algorithm base on P&O is capable to reach the MPP, but it is shown that the oscillations are part of the normal operation of this technique. Just like the previous one, the P&O algorithm with variable step also has oscillations around the MPP, but the improvement comes from the faster dynamic results because when the solar irradiance or temperature changes, this algorithm quickly take the system to the new operating point by varying δv. Lastly, the CondInc algorithm is performed in order to avoid the oscillations, but due to the noise presented (introduced noise in the sensed variable, to make the simulations more real) and the noise due the power converter commutation, the oscillation is also presented. From the results of this paper, the best algorithm to be implemented is the P&O with variable step, which has a fast dynamic response and also requires a low computational effort. All investigation is performed with variable solar irradiance and change on the temperature which are the most common variation that a solar module is exposed.

REFERENCES [1]

From TABLE IV it important to highlight that the CondInc has 5 division which make this algorithm heavier than the others, because division are difficult to compute for microprocessors. On the other hand, the P&O algorithm is the simpler one, requiring only basic instructions. Therefore, if the computational cost is important, the most recommended algorithm is the P&O, then the P&O with step

P&O

[2] [3]

B. Gutiérrez and V. Salas, "Analisis del seguimiento del punto de maxima potencia de los inversores fotovoltaicos de conexion a red", Madrid, 2009. H. Zheng, S. Li, K. Bao, and D. Zhang, "Comparative Study of Maximum Power Point Tracking Control Strategies for Solar PV Systems", 2012. D. Armando, I. Torres, and J. Luis, "Comparacion de algoritmos MPPT aplicados a un conversor SEPIC en sistemas fotovoltaicos", Colombia, 2014.

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Y. Wang and X. Yu, "Comparison Study of MPPT Control Strategies for Double-stage PV Grid-connected Inverter", 39th Annual conf. IEEE, Industrial Electronics Society, IECON, Austria, 2013. S. Cuestas and L. Lebus, "Diseño de un seguidor de punto de máxima potencia", Laboratorios de Energias Alternativas, Universidad Tecnológica Nacional, Facultad Regional Paraná, Argentina, 2012. G. Molina, E. Mercado, and E. Wiernes, "Análisis y Simulación de Algoritmos de Control para el Seguimiento del Punto de Máxima Potencia de Sistemas Solares Fotovoltaicos Conectados a la Red Eléctrica", Avances en Energías Renovables y Medio Ambiente, vol 11 ASADES, Argentina, 2007. J. Silva, J. Espinoza, J. Rohten, and M. Torres, "Grid Connected PV System with Maximun Power Point Estimation based on Reference Cells", Chile, 2015. A. Salman, A. Williams, and H. Amjad, "Simplified Modeling of a PV Panel by using PSIM and its Comparison with Laboratory Test Results", Global Humanitarian Technology Conference, Seattle, USA, 2015. H. Romero, "Irradiación Solar en territorios de la República de Chile", CNE, PNUD, UTFSM, Santiago de Chile, 2008. J. F. Jiménez and D. Biel, "Estudio y simulacion de sistemas de conversión fotovoltaica-eléctrica mediante Matlab/Simulink", Departamento de Ingeniería Electrónica, Vilanova i la Geltrú, España, Chile, 2009. H. Desai and H. Patel, "Maximun Power Point Algorithm in PV Generation: An Overview", 7th Int. Conf. Power Electronics and Drive Systems, PEDS '07, Bangkok, Thailand, 2007. J. Vera and M. Ferreira, "Maximum Power Point Tracker Shaded Condition", Facultad de Ingeniría, Pontificia Universidad Javeriana, Bogota, Colombia, 2013. R. Faranda, S. Leva, y V. Maugeri, "MPPT techniques for PV Systems: Energetic and cost comparison", Power and Energy Society Gral. Meeting- Conversion and Delivery of Electrical Energy in the 21st Century, IEEE, Pittsburh, PA, USA, 2008. N. Femia, G. Petrone, G. Spagnuolo, and M. Vitelli, "Optimization of Perturb and Observe Maximum Power Point Tracking Method", IEEE Transactions on Power Electronics, vol 20, 2005. T. Esram and P. Chapman, "Comparison of Photovoltaic Array Maximum Power Point Tracking Techniques", IEEE Transactions on Energy Conversion, vol 22, 2007. Matías N. Garbarino was born in Concepcion, Chile in 1993. He received B.S degree from University of Bío-Bío in 2016. His areas of interest are, renewable energy sources, power electronics and nonlinear control. He is currently working in investigation of energy conversion and photovoltaics technology.

Rodrigo H. Morales was born in Laja, Chile in 1994. He received B.S degree form University of Bío-Bío in 2016. Some of my areas of interest are renewable energy sources, linear and nonlinear control. He is currently working in investigation of energy conversion and photovoltaics technology.

Pablo Henriquez, received the B.S. degree and the Automation Engineer from the Universidad del BíoBío in 2015 and 2016 respectively. His areas of interest are, renewable energy sources, industrial electronics, and nonlinear control. He is currently working in WoodTech.

Saúl Cuevas was born in Concepcion, Chile in 1991. He received the B.S degree and the Automation Engineer from the Universidad del Bío-Bío in 2015 and 2016 respectively. His areas of interest are, renewable energy sources, industrial electronics, and nonlinear control, image digital processing, communication networks, between others.

Jaime A. Rohten (S'15 – M'16) received the Engineering degree in Electronic Engineering (with first-class honors), the M.Sc. and D.Sc. degrees in Electrical Engineering from the University of Concepcion, Concepcion, Chile, in 2010, 2012, and 2017 respectively. His research interests include renewable energies, digital nonlinear, resonant and predictive control for voltage or current source converters. Since 2015, he has been teaching in the areas of power electronic and control systems analysis with the Department of Electrical and Electronic Engineering, Universidad del Bío-Bío, Concepción, Chile. Eugenio Wernekinck was born in Concepcion, Chile on October 8, 1947. He received the B.S. in electronics from the Universidad de Concepcion in 1962, and the M.S. and Ph.D. degrees from the University of Missouri, Columbia in 1980 and 1987, respectively. From 1981 to the present he has been with the Universidad del Bío-Bío, Concepcion, Chile where he currently is an Associate Professor. He has taught power electronics courses in the industry and his research interests include Dower conversion, control theory, and microcomputer control. Ernesto Rubio received his Bachelor Degree in Automatic Control Engineer from the Universidad Central “Marta Abreu” de Las Villas (UCLV) in 1997 and his PhD in Automation in 2009 at the same university. He is currently Assistant Professor in the Electrical and Electronic Engineering Department at University of Bío-Bío (UBB) and member of Sensor and Actuator Networks Research Group. His main interests are remote laboratories and robotics. Pedro E. Melín (S'10 – M'14) received the M.Sc., and the D.Sc. degrees in Electrical Engineering from the University of Concepción, Concepción, in 2010 and 2014 respectively. Since 2013, Dr. Melín has been with the Department of Electrical and Electronic Engineering, University of Bío-Bío, Concepción, Chile, where he is assistant professor teaching in the areas of industrial electronics and digital systems. His research interest include voltage-source and currentsource converters and their extension to multilevel topologies, including their design, digital control and the application of this kind of topologies to AC drives, active power filters and energy conversion.