Solar Cell MPPT Technique Based on PI Controller Feri - CiteSeerX

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Advanced Materials Research ISSN: 1662-8985, Vols. 608-609, pp 89-96 doi:10.4028/www.scientific.net/AMR.608-609.89 © 2013 Trans Tech Publications, Switzerland

Online: 2012-12-13

Solar Cell MPPT Technique Based on PI Controller Feri Yusivar 1, a and Beng Tito2,b 1, 2

Real Time Measurement and Control Research Group, Electrical Engineering Department, Universitas Indonesia, Depok, Indonesia a

[email protected], [email protected]

Keywords: MPPT, ICM, P&O, PI Controller.

Abstract. The MPPT techniques of Incremental Conduction Method (ICM) and Perturbation and Observation (P&O) cannot track the maximum power point (MPP) of solar cell quickly without oscillation around MPP. This is happens because of the working point’s movement given by MPPT always has a same distance. This paper proposes a MPPT technique based on PI controller which able to reach the MPP quickly and the oscillation is near to zero. PI controller with error feedback is the gradient of solar cell’s power characteristic curve, is used as power optimizer replacing the step-size optimizer. Performance of the proposed technique is compared against the ICM one through simulations. The results show the proposed technique has much faster tracking time than the ICM has and the oscillation can be set to near zero. Introduction One of parameter to determine solar cell material’s quality is fill factor, defined by Eq. 1. Where, VMP and IMP is maximum power point (MPP) of solar cell’s power production [1].

FF 

VMP I MP . VOC I SC

(1)

Solar cell will not automatically work at the MPP unless be controlled. MPP changes over the changes of sun’s radiation and cell’s temperature. Maximum Power Point Tracking (MPPT) is used to track the MPP and makes solar cell work at the MPP all the time. V-I characteristic of solar cell is defined by Eq. 2 [2].  q V  IR S   V  IR S  I  I Ph  I S  e NKT  1  . R Sh  

(a)

(2)

(b)

Fig. 1. Solar cell characteristic. (a) different sun’s radiation. (b) different cell’s temperature

All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech Publications, www.ttp.net. (#69809423, Pennsylvania State University, University Park, USA-18/09/16,06:22:29)

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Fig. 1(a) shows P-V characteristic plot on different sun’s radiation, whereas Fig. 1(b) shows P-V characteristic plot on different cell’s temperature. It shows that, optimum power location is different for different environmental condition. Several approaches of MPPT methods have been studied and reported in literatures. In [3], basic principles of some MPPT methods have been discussed. Based on [3], there are at least 19 MPPT methods have different principles. Some robust methods, such as Incremental Conduction (ICM), Perturbation & Observation (P&O), and Hill Climbing have weakness on tracking time and oscillation around MPP. Refined method by fuzzy logic can shows a better performance. ICM works based on the gradient of solar cell’s P-V characteristic curve [3]. MPP have different location for different environmental condition, called VMPP. MPPT gives Vref to make solar cell’s working point on the MPP. The step size of Vref’s change given by the MPPT is constant for all iteration. The step size of Vref‘s change is consider from tracking time to the optimum working point and its oscillation. Both parameters have an up-side down relationship; there is always a compensation for every refined parameter. Therefore, one makes the step size of Vref varies [4]. The method uses gradient value’s changes (dP/dV). The method also has considered the different gradient’s threshold for each environmental condition to maintain the quality of MPPT. P&O consist of two steps, perturb which changes Vref and observation which calculating the power’s change after the last perturb. If the change of power is positive, then the next perturb will remain in the same direction, whereas, if the change of power is negative, then the next perturb will be reversed [3]. Same as ICM, the size of perturb given by the MPPT is constant. To achieve faster tracking time and less oscillation, the step size is varied [5]. The size changes in Vref can also be varied by using conventional controller. MPP can be achieved if the value of dP/dV zero, then the controller is designed to make the value zero. Error’s controller calculation method will determine the quality of tracking time and oscillation around MPP. Proposed Algorithm Solar cell’s characteristic is non-linear and time-variant as shown in Fig. 1. That makes the value of dP/dV which will be controlled also has a time-variant characteristic as shown in Fig. 2(a). In the design of the linear controller, the controlled system should be linear. A linearization in the V-I curve has performed in [6], whereas in this paper, linearization will be performed in V-m as shown in Fig. 2(b). As the result of linearization, the working region is divided into three parts. The region which contains MPP on it, is called control region. Each region will have different controller parameter’s values. In the proposed algorithm, the Proportional Integrator (PI) controller is used to search or track the MPP, instead to vary the size changes in Vref only.

(a)

(b)

Fig. 2. (a) dP/dV characteristic. (b) dP/dV characteristic linearization

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The proposed PI MPPT algorithm needed a method to separate the control region, the current source region, and the voltage source region, so that a given control action can be adjusted. One way of separating them is given in [4] through the Eq. 3. Here, P is solar cell’s produced power, n is the order, dP is the power’s change, and dI is the current’s change. The larger n, then the control region will be even narrower. C  Pn

dP . dV

(3)

Line C in Fig. 3 is obtained from Eq. 3. Line C on the left and right of the MPP has a maximum point for each. If the line C on the left part is defined as C1 and line C on the right part is defined as C2, then the three regions can be defined as follows.  ΔC1  ΔV  0  ΔC1  0  ΔV  ΔC2  0  ΔV  ΔC2  ΔV  0

, current source region , control region , control region

(4)

, voltage source region

The above method is not simple enough to be used in the proposed algorithm. The method to be used in the proposed PI MPPT algorithm is just using the gradient value. As shown in Fig. 1 and Fig. 2, the control region has a gradient value around zero. When the value of dP/dV getting close to zero, the magnitude of Vref’s change given by the MPPT should be getting smaller, and when the value of dP/dV is zero, the magnitude of Vref’s change given by the MPPT should be zero. That is what PI controller will be done. Eq. 5 defines transfer function of PI controller to be used [7].

G C (s)  k C 

kC . τis

(5)

Fig. 3. Normalized Power charactristic, dP/dV of Power charactristic, and Control region C. Input error of the PI controllers which is used in this paper is derived in Eqs. 6-8. Calculation of errors that would become an input for PI controller is performed alternately with the actual calculation of Vref. This is due to varies of changes of actual Vref output from the controller. In the other hand, to calculate the gradient of non-linear curve, the change should be near to zero.

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dP , dV

(6)

dV.I  dI.V , dV

(7)

dI.V . dV

(8)

error  0  error 

error  I 

Proposed PI MPPT System VPV in a solar cell system must be controlled so that the solar cells can release optimum power. A dc-dc converter can be used to provide a reference voltage which has been controlled to the solar cell. The boost type dc-dc converter is used whose output is connected to the power storage (batteries) as shown in Fig. 4 [6]. Panel Sel Surya

RL L + Vo -

IGBT C2

C1

VPV IPV

ICM Vref Algorith MPPT m

+

D

PI

PWM

Fig. 4. MPPT System Design Fig. 5(a) shows the conventional MPPT methods that use the ICM algorithm, while Fig. 5(b) shows the proposed PI MPPT. VPV IPV

ICM Algorithm

+

Vref

PI

D

(a)

VPV IPV

Error

e

PI

Calculation

+

Vref

PI -

(b)

Fig. 5. MPPT Design: (a) ICM, (b) Proposed PI

D

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Simulation Result and Analysis To verify the performance of the proposed algorithm, a simulation was built using Matlab/ Simulink. 15 solar cell modules of KC50T type from Kyocera arranged in series are simulated to match the number of solar cell modules there are in the engineering faculty of the Universitas Indonesia. Table 1 shows the specifications of KC50T solar cell module. Table 1. KC50T Module Spesification Electrical Performances under Standard Test Condition (*STC) Open Circuit Voltage 21.7 [Volt] Short Circuit Voltage 3.31 [Ampere] Temp. coefficient of ISC 1.33×10-3 [A/°C] Number Cell per Module 36 Boost converter parameters used in MPPT system will greatly affect the actual Vref. The selection of capacitors and inductors in the circuit affects the transient and ripple on the Vref respond. To view the ideal performance of the proposed algorithm, first MPPT system is not connected to the boost converter. It was suggested in [8, 9] that the systems should reach a steady state condition for each sampling period; therefore the sampling time used in the proposed PI MPPT is 0.01 second (sampling frequency of 100 Hertz). The output voltage of solar cells in these simulations are ranged from 200-250 Volts. In this range, the input capacitance of the capacitor must be large enough to reduce the ripple. The values of boost converter’s variables which are used here are shown in Table 2.

Variables Input Capacitance Inductance Switching Frequency Inductor Resistance Output Voltage

Table 2. Variables of Boost Converter Value 100 [µH] 3.2 [mF] 5 [kHz] 0.15 [Ω] 400 [Volt]

Controller parameter values which are used in the proposed PI MPPT along with the gradient used to separate the three regions are shown in Table 3. Table 3. Region Definition and Controller Parameters Controller Parameters Region Definition kC τi Current Source Region error > 2 0.8 0.7×10-3 Control Region -4 ≤ error ≤ 2 0.3 0.6×10-3 Voltage Source Region error < -4 0.5 0.7×10-3 Fig. 6 shows the result of the MPPT system to sun’s radiation changes when not connected to boost converter. Fig. 6(a) is the result of the ICM algorithm, Fig. 6(b) is PI MPPT without the controller’s parameter adjustment in each region, and Fig. 6(c) is PI MPPT with different controller parameters in each region. By using PI MPPT, clearly the tracking time is faster and the oscillations become smaller. Fig. 7 shows the result when the system is connected to boost converter. Fig. 8 shows the result of the MPPT system to cell’s temperature changes when not connected to boost converter. At the time of tracking (beginning from the high voltage over low temperature, such as shown in Fig. 8(b)), when a change in temperature from 293 K to 303 K, PI MPPT without the controller’s parameter adjustment in each region, passes through the MPP to the other side of curve. This is does not happen if the controller’s parameter be adjusted for each region as shown in Fig. 8(c).

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(a)

(a)

(b)

(b)

(c) Fig. 6. Simulation Result to Changes in Solar Radiation Without Boost Converter. (a) ICM, (b) PI with fixed parameter, (c) PI with different parameter for each region

Method ICM PI1 PI3

(c) Fig. 7. Simulation Result to Changes in Solar Radiation With Boost Converter. (a) ICM, (b) PI with fixed parameter, (c) PI with different parameter for each region

Table 4. Performace of MPPT System to Sun’s Radiation Change Produced Energy Tracking Time 2 (Wattsecond) 0 to 1000 W/m 1000 to 200 W/m2 200 to 1200 W/m2 2005.6 110 cycles 12 cycles 9 cycles 2311.8 27 cycles 19 cycles 5 cycles 2339.5 19 cycles 19 cycles 5 cycles

PI MPPT has shown a better performace compared to ICM MPPT as shown in Table 4. The quality of oscillation can be seen from the energy produced by the algorithm; more energy produced by the algorithm means that the oscillation is smaller.

Advanced Materials Research Vols. 608-609

(a)

(a)

(b)

(b)

(c)

(c)

Fig. 9. Simulation Result to Changes in Cell’s Temperature Without Boost Converter. (a) ICM, (b) PI with fixed parameter, (c) PI with different parameter for each region

Method ICM PI1 PI3

95

Fig. 8. Simulation Result to Changes in Cell’s Temperature Without Boost Converter. (a) ICM, (b) PI with fixed parameter, (c) PI with different parameter for each region

Table 5. Performace of MPPT System to Cell’s Temperature Change Produced Energy Tracking Time (Wattsecond) 0 to 298 K 298 to 293 K 293 to 303 K 2432.9 110 cycles 5 cycles 10 cycles 2723.5 27 cycles 3 cycles 10 cycles 2766.1 19 cycles 3 cycles 6 cycles

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Summary PI controller can be used for the MPPT with error feedback is the gradient of solar cell’s power characteristic curve. MPPT system based on PI controller can vary the magnitude of Vref’s changes to improve the quality of tracking time and oscillation MPP. The separations of linearization regions can improve the tracking time of the MPPT. Acknowledgment The authors express their gratitude to the General Directorate of Higher Education, Ministry of National Education and Culture for supporting the research. References [1] [2]

[3]

[4]

[5] [6] [7] [8]

[9]

M. A. Green: Solar Cells Operating Principles, Technology and System Applications, Prentice-Hall, New Jersey (1982). S. Nema, R. K. Nema and G. Agnihotri: Matlab Simulink Based Study of Photovoltaic Cells Modules Array and Their Experimental Verification. International Journal of Energy and Environment, vol. 1, no. 3 (2010), pp. 487-500. T. Esram and P. L. Chapman: Comparison of Photovoltaic Array Maximum Power Point Tracking Techniques. IEEE Transactions on Energy Conversion, vol. 22, no. 2 (june 2007), p. 11. Q. Mei, M. Shan, L. Liu and J. M. Guerrero: A Novel Improved Variable Step-Size Incremental-Resistance MPPT Method for PV Systems. Industrial Electronics, IEEE Transactions on, vol. 58, no. 6 (2011), pp. 2427 - 2434. L. Piegari and R. Rizzo: Adaptive perturb and observe algorithm for photovoltaic maximum power point tracking. Renewable Power Generation, IET, vol. 4, no. 4 (2010), pp. 317 - 328. W. Xiao, W. G. Dunford, P. R. Palmer and A. Capel: Regulation of Photovoltaic Voltage. Industrial Electronics, IEEE Transactions on, vol. 54, no. 3 (2007), pp. 1365 - 1374. S. W. Sung, J. Lee and I.-B. Lee: Process Identification and PID Control. Wiley-IEEE Press, Singapore (2009). 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, no. 4 (2005), pp. 963-973. F. Liu, S. Duan, F. Liu, B. Liu and Y. Kang: A Variable Step Size INC MPPT Method for PV Systems. Industrial Electronics, IEEE Transactions on, vol. 55, no. 7 (2008), pp. 2622 - 2628.

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Solar Cell MPPT Technique Based on PI Controller Feri - CiteSeerX

Advanced Materials Research ISSN: 1662-8985, Vols. 608-609, pp 89-96 doi:10.4028/www.scientific.net/AMR.608-609.89 © 2013 Trans Tech Publications, Swi...

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