[IEEE 2011 IEEE Colloquium on Humanities, Science and Engineering (CHUSER) - Penang, Malaysia...

Optimization of Partially Shaded PV Array using Fuzzy MPPT

C.S. Chin, M.K. Tan, P. Neelakantan, B.L. Chua and K.T.K. Teo Modelling, Simulation and Computing Laboratory

School of Engineering and Information Technology Universiti Malaysia Sabah

[email protected], [email protected]

Abstract — Solar photovoltaic (PV) array shows non-linear P-V characteristic when the array is illuminated under uniform solar irradiance. In this circumstance, the P-V characteristic consists only one maximum power point (MPP) along the functional operating voltage. However, the P-V characteristic has changed and become more complex with multiple MPP when the array is exposed under partially shaded conditions. This circumstance has caused maximum power point tracking (MPPT) algorithm faces difficulty to allocate the exact optimal operating voltage for PV array to generate maximum power. In this paper, initial voltage tracking function (IVTF) has been introduced to assign new initial voltage for tracking the absolute MPP when the PV array is at shaded conditions. Nevertheless, MPPT approach deals with the challenge of tracking the MPP in the faster mode while maintaining the power stability of the PV array toward the MPP. Therefore, fuzzy logic is embedded in the conventional MPPT to adapt the size of the perturbed voltage. The obtained results show that fuzzy logic based MPPT with IVTF is able to track the absolute MPP faster while minimizing power lost due to the power fluctuations.

Keywords – partially shaded condition; photovoltaic; fuzzy logic; MPPT

I. INTRODUCTION Solar energy can be converted into electrical energy via

solar cell and this phenomenon is generally called as photovoltaic effect [1]. The conversion of solar energy into electrical energy is static, quite and free of moving object. Since solar energy is an abundant resource and the conversion of energy does not have any negative impact to the environment, this promising renewable energy has high potential to be explored and investigated for continuous human development. Due to this reason, solar energy has gained high interest among researchers and the statistic shows that PV industry has been growth annually of average 30% during the past decade [2].

Solar cell is the basic element which converts the solar energy into electrical energy. The electricity generation via the solar cell is mainly affected by the received level of the solar illumination where the amount of the incident light determines the total charge carrier to be generated from the solar cell [3, 4]. Solar cells can be arranged to form PV module and several PV modules can be configured to form PV array.

PV array presents non-linear characteristics when it is exposed to uniform solar irradiance. In this environmental circumstance, the P-V characteristic shows there is only one maximum power point (MPP). If the PV array operated at that particular optimum voltage, the array will generate maximum power. This particular point is generally called as MPP. Although the array’s characteristics are also influenced by the cell temperature and tilt angle of the PV array facing the sunlight, this study will be focusing on the effects of the solar irradiance and the partially shaded PV array.

Maximum power point tracking (MPPT) algorithm is a common control approach used to track the MPP of the PV array. Perturb and observe (P&O) method has been chosen as MPPT controller in the PV array. However, when the PV array experiences partial shaded condition (PSC), MPPT halted its ability to track the exact absolute MPP. Under PSC, the PV array presents more complex characteristics where multiple peaks have occurred in the P-V characteristic. Conventional MPPT will cause the PV array to be trapped at the local MPP and consequently limit the power generated via the solar cells [5, 6]. Thus, initial voltage tracking function (IVTF) has been established to provide the resettable initial operating voltage to assist the tracking process. With this function, MPPT is able to track the array’s MPP beyond the trapped local MPP.

Fuzzy logic control has been proposed and implemented in the conventional MPPT to vary the size of the perturbed voltage. The characteristics of PV array will be changed when the array is under various partially shaded conditions. However, fuzzy logic based MPPT (FMPPT) can control the PV array to have faster transient response thus reaching the MPP immediately after IVTF is initialized. In addition, FMPPT is capable to select small perturbed voltage size when the PV array has reached the steady state MPP. This action ensures the power stability of the PV array is accomplished.

II. REVIEW OF PV ARRAY AND FUZZY MPPT

A. Modelling of PV Array The schematic model of a basic PV cell can be illustrated

by the equivalent circuit as shown in Fig. 1, namely one-diode model. The practical PV cell consists of a photo current source, Ipv, a diode, Dm, equivalent parallel resistor, Rp, and equivalent series resistor, Rs. The existence of Rp in the solar cell is caused

2011 IEEE Colloquium on Humanities, Science and Engineering Research (CHUSER 2011), Dec 5-6 2011, Penang

978-1-4673-0020-9/11/$26.00 ©2011 IEEE 481

by the p-n junction leakage current in the cell; however the occurrence of Rs is mainly because of the contact resistance of the metal base within the semiconductor layer [7].

The I-V characteristic of diode Dm is described by the Schockley diode equation. The mathematical modelling of I-V characteristic of the solar PV cell is derived as in (1),

⎟⎟⎠

⎞⎜⎜⎝

⎛ +−⎥⎥⎦

⎤

⎢⎢⎣

⎡−⎟⎟

⎠

⎞⎜⎜⎝

⎛ +−=p

s

T

spv R

IRVnV

IRVIII 1exp0 (1)

where I is the terminal current of the solar cell, Ipv is the light-generated current of solar cell, I0 is the diode Dm reverse biased saturation current, V is the solar cell terminal voltage, n is the ideality factor of the diode Dm, VT is the thermal voltage, Rs and Rp are the equivalent series and parallel resistance respectively.

The commercial PV module is usually formed by several identical solar cells connected in series so that the PV module can provide larger operating voltage to the load [8]. The further series or parallel connection of several PV modules can form PV array which provide larger operating voltage range and output power to the load. Fig. 2 shows the basic configuration of three identical PV modules connected in series to form a PV array.

The by-pass diode is externally coupled to each PV module as shown in Fig. 2. Under uniform solar irradiance, all the PV modules will generate same amount of current but the condition is differed during the PSC. The shaded PV module will generate less current since the module has received less amount of solar irradiance. As the consequence, the current generated by the entire PV array might be limited due to the shaded PV module. However, due to the availability of the by-pass diode, the excess current produced by the un-shaded PV module is allowed to flow through and the entire PV array is prevented from being limited by the shaded PV module.

By-pass diode can prevent hot spot formation in the PV array. When the solar cells become reverse biased due to the PSC, solar cell will dissipate power in the form of heat and

Figure 1. One-diode model.

Figure 2. PV array consists of three identical PV modules.

cause the formation of the hot spots. If the hot spots have exceeded the maximum power that can be sustained by the PV cells, the hot spots will cause permanent damage to the PV module and the array will be open circuited [9]. This will bring negative impact to the PV system where the interruption of the power supply might cause the appliances not working accordingly.

Blocking diode is the external connected diode to the string of series connected PV modules. It has the function of preventing the reverse flow of current from the secondary power sources such as the lead-acid battery if there is no sun light available.

B. MPPT Algorithm The Perturb and observe (P&O) method has been chosen to

perform maximum power point tracking for PV array due to its simplicity. The principle of P&O is initiated by applying perturbed voltage to change the operating voltage of the PV array and observe the change of output power at the present and the previous sampling interval. Based on the comparison of present and previous state of operating voltage and output power, the MPPT control system can make decision either to regulate the PV array to shift for larger or lower operating voltage. Eventually, the PV system will be operated at a particular optimum power operating voltage where maximum generated power from PV array can be obtained.

There are total of four cases under discussion for the operation of P&O. The tracking process of P&O can be shown in the flowchart as in Fig. 3 where initially the parameters of operating voltage and output power are measured at present and previous sampling interval. The four cases to be discussed are shown as below:

Case I: If the Pk>Pk – 1 and Vk>Vk – 1, then the module operating voltage should be increased by perturbed voltage.

Case II: If the Pk>Pk – 1 and Vk<Vk – 1, then the module operating voltage should be decreased by perturbed voltage.

Case III: If the Pk<Pk – 1 and Vk>Vk – 1, then the module operating voltage should be decreased by perturbed voltage.

Case IV: If the Pk<Pk – 1 and Vk<Vk – 1, then the module operating voltage should be increased by perturbed voltage.

P&O will continue to track MPP even it has successfully identify the optimal voltage point. The continuous tracking of MPP is vital to identify the next MPP for maximum power gaining from the PV array. However, the increment and decrement of perturbed voltage will lead to oscillation of the PV array operating voltage and caused the power fluctuation problem which lead to the power losses in the PV system. Therefore, fuzzy logic is suggested to be adopted into the existing P&O to minimize the oscillation of the PV operating voltage and subsequently reduced the unnecessary power losses in the PV system. Besides, FMPPT produces faster response in tracking the MPP where the time needed for FMPPT to track the MPP of PV array is shorter.

FMPPT can have good performance in tracking the MPP of PV array when the array is under uniform solar irradiance. However, when the PV array experiences PSC, the tracking

2

Conn2

1

Conn1

Rs

RpI pv

Dm

I ID

+

-

V


482

function of FMPPT has been halted due to the P-V characteristic of the array becomes more complex with the occurrence of multiple MPP. FMPPT may control the PV array to operate at the trapped MPP. Thus, the potential of PV array to generate more electrical energy will be limited. Therefore, initial operating voltage tracking function (IVTF) is introduced to the system to facilitate the FMPPT algorithm to track the absolute MPP which is located beyond the trapped local MPP.

C. Fuzzy Logic Fuzzy logic is relatively easy to use as it does not require

accurate mathematic model. Besides, fuzzy is able to function properly even without the precise inputs. Fuzzy is more robust compared to the conventional non-linear controller [10].

The operation of fuzzy logic control can be classified into four basic elements, namely fuzzification, rule base, inference engine and defuzzification. The operation of fuzzy logic control is shown in Fig. 4.

Figure 3. Flowchart of P&O operation.

Figure 4. Operation of fuzzy logic control.

Fuzzification is the progression of converting the PV system actual signal λ and δ into linguistic fuzzy sets through fuzzy membership function. Fuzzy membership function can be described as the curvature that presents each and every point of the membership value. Fuzzy rule base is a compilation of if-then rules which judging all the possible outcomes for the controlled parameters. The rules are determined according to the professional experience and also depending to the operation of the system control. Fuzzy inference engine has the ability of making decision based on the fuzzy rules which have been set accordingly. The inference engine will then transform the fuzzy rule base into fuzzy linguistic output. Finally, the defuzzifier converts the linguistic fuzzy sets back into the actual value of γ.

Fuzzy logic is adapted in the MPPT to vary the size of the perturbed voltage, ∆V in the P&O algorithm. Small size of ∆V may perform slow tracking of MPP but large size of ∆V will lead to large oscillation of operating voltage and subsequently causing the power fluctuation problem in the system. FMPPT is able to vary the size of ∆V depending on the instantaneous circumstances. It can control the PV array to reach the MPP faster meanwhile maintain the power stability when MPP has been identified. FMPPT is relatively important especially when the PV array is under PSC where the rapid changes of shading condition affects the quick changing of the P-V characteristic.

D. Initial Voltage Tracking Function When the PV array is under PSC, the PV array shows

multiple MPP in the P-V characteristic. FMPPT can track the MPP of the PV array but FMPPT might lead the PV array to operate at the trapped local MPP. When the PV array operated at local MPP, the array will generate less power to the load compared to the absolute MPP. In other words, PV array operated at the trapped local MPP obtains lower efficiency compared the absolute MPP.

The initial voltage tracking function (IVTF) can be used to compute the new and resettable initial voltage. When the PV array is detected under PSC, IVTF will instruct the PV array to operate at the computed initial voltage for new cycle of MPP tracking. Hence, FMPPT will perform and track the absolute MPP which is located beyond the local MPP [5]. Equation (2) is used for initial operating voltage computation when PV array is under PSC.

IIV

Vmp

mpinitial ×= (2)

In (2), Vmp is the maximum power voltage of PV array, Imp is the maximum power current of PV array and I is the PV array instantaneous generated current under uniform solar irradiance. The parameters Vmp and Imp can be determined from the I-V and P-V characteristics of the PV array operated at Standard Test Condition (STC). In this study, STC refers to 1000W/m2 solar irradiance and 25⁰C cell temperature.

Start

Measure Vk, Ik, Vk – 1, Ik – 1

Pk = Vk×Ik Pk – 1 = Vk – 1×Ik – 1

MPP continue track?

End

Pk>Pk – 1?

Vk>Vk – 1? Vk>Vk – 1?

Vk + 1 = Vk + ∆V Vk + 1 = Vk – ∆V

Y

Y

N

Y

Y

N

N Y = Yes N = No

N

λ

δ

Fuzzification Inference Engine

Defuzzification

Rule Base

γ


483

III. MODDELLING AND SIMULATION SHARP NE-80E2EA multi-crystalline silicon PV module

with 80W is used as the reference model of the PV array modelling in MATLAB-SIMULINK. The PV module has 36 series connected solar cell with 21.3V open circuited voltage and 5.16A short circuit current. Fig. 5 shows the I-V and P-V characteristics of three identical series connected SHARP NE-80E2EA under STC. It can be noticed from the result in Fig. 5 that the array can generate maximum power of 240W which is equivalent to three times of rated power of each PV module. The rated power of the simulated PV array is matched with the theoretical calculation. The parameters of Vmp and Imp are extracted as 49V and 4.9A for the computational of IVTF.

The generating current of PV array is depending to the amount of solar irradiance illuminated on the surface of the PV array. Larger solar irradiance will lead to the generation of greater current since higher solar energy can release more electrons from the covalent bond in the solar cell. Under uniform solar irradiance, the PV array shows only one MPP in the P-V characteristic. However when the PV array is experiencing partially shaded condition, the characteristic become more complex and multiple MPP might be occurred in the P-V characteristic. Fig. 6 shows the simulation result of the I-V and P-V characteristics of the PV array when one of the PV modules is shaded at 70%. It can be noticed that the generated current of the PV array is maintained at about 5A in the operating voltage range of 0V to 35V but the generated current is limited to 1.5A as the operating voltage of the PV array is further increased. PV array under the stated shading pattern shows two MPP in the P-V characteristic, where one of the MPP occurred at operating voltage approximately 35V and another MPP occurred at approximately 48V. The MPP at 48V is considered as the local MPP where PV array operated at this point will be limited to the power generation of 70W. If PV array operated at the absolute maxima of 35V, the MPP is able to generate output power of 170W, 142% larger than the trapped local MPP.

Figure 5. I-V and P-V characteristics of PV array under STC.

Figure 6. I-V and P-V characteristics of PV array under PSC.

When the PV array is exposed at various shaded conditions, the characteristics of PV array will be changed. Fig. 7 shows the simulation result of the I-V and P-V characteristics of PV array when three of the PV module is exposed to different level of solar irradiances. One of the PV modules is under STC whereas the other two modules are shaded at 40% and 70% respectively. It is noted that there are total of three MPP occurred in the P-V characteristic. Under this shading pattern, the MPP occurred at the operating voltage of 18V, 34V and 48V respectively. PV array operated at 34V will generate maximum output power.

Fuzzy logic is implemented to assist the P&O for faster response in tracking the MPP while controlling the PV array to have less oscillation around the MPP. Fuzzy logic can make decision to decide the size of the perturbed voltage, ∆V based on the information of the change of power, dp and change of power with respect to change of voltage, dp/dv. Fig. 8 shows the arrangement of membership function in the fuzzy output variable, ∆V.

Figure 7. I-V and P-V characteristics of PV array under STC, 40% and 70%

PSC.

I (A)

V (V)

P (W)

I (A)

V (V)

P (W)

I (A)

V (V)

P (W)


484

Figure 8. Membership function of the fuzzy output variable ∆V.

The configuration of membership function is not set to be distributed evenly along the universe of discourse particularly at the output variable ∆V. Referring to Fig. 8, the output variable has four membership functions at the range of [0 1] whereas there are only two membership functions at the range of [0.9 2]. This is because fuzzy logic has been set to be responded more sensitive at the range of [0 1], where fuzzy logic will determine smaller and more precise perturbed voltage when the PV array is closed to the MPP.

By matching the membership functions of the input variables with the membership functions of the output variable, fuzzy rule base system can be created. The rules can be further validated through fuzzy viewer by adjusting the index line and comparing the fuzzy computed ∆V with the desired value [1].

A. Results Fig. 9 shows the simulation results of the FMPPT

controlled PV array without IVTF whereas Fig. 10 is the simulation results of the FMPPT controlled PV array with IVTF.

B. Discussion The performances of FMPPT with and without IVTF have

been examined when the PV array at initial STC is suddenly changed to PSC at t = 30s. At PSC, one of the PV modules is shaded at 70%.

FMPPT is able to track the MPP when the PV array is under STC. It can be observed that in Fig. 9 and Fig. 10, FMPPT can control the PV array to have increment of perturbed voltage from the initial 40V until the PV array operated at the MPP. Although the FMPPT has overshot the operating voltage of PV array at simulation time of 3s and caused a sudden drop of output power, the FMPPT is capable to correct the overshooting and maintain the PV array at the corresponding MPP. Thus, PV array with the FMPPT manage to generate maximum power of 240W.

When the PV array is exposed to PSC at time of 30s, the generation power of PV array has been limited. Fig. 9 shows that the FMPPT without IVTF is trapped at the local MPP, where the PV array is operated at 48V. At this situation, the PV array is only able to generate output power of 70W.

FMPPT with IVTF is able to track the MPP beyond the trapped local MPP. IVTF computed new initial operating voltage for FMPPT to begin the tracking process. Referring to Fig. 10, it can be observed that when PSC being sensed at 30s, the PV array is instructed to be operated at the IVTF computed initial voltage of 15V. Subsequently, FMPPT start the tracking process from 15V and finally successfully tracked the absolute

MPP at operating voltage of 35V. At this particular point, PV array is able to generate more output power. Comparing Fig. 9 and Fig. 10, PV array controlled by FMPPT with IVTF can generate approximately 142% larger output power than the FMPPT without IVTF.

Figure 9. Simulation results of the FMPPT without IVTF.

Figure 10. Simulation results of the FMPPT with IVTF.

I (A)

V (V)

P (W)

t (s)

I (A)

V (V)

P (W)

t (s)


485

FMPPT can decide various size of ∆V according to the instantaneous environmental circumstances. Referring to Fig. 10, when the PSC being detected at 30s, FMPPT has selected larger ∆V for the PV array voltage regulation. At this stage, FMPPT aims to track and approach the MPP faster where FMPPT has taken 8s to reach the absolute MPP. On the other hand, when the PV array has reached the MPP, FMPPT is able to select small ∆V to maintain the power stability. It can be observed from Fig. 10 that FMPPT employ smaller ∆V at time interval between 4s to 30s and 38s onwards, where the PV array has reached the MPP. PV array is controlled to have minimum ∆V to minimize the power losses due to the voltage fluctuation.

IV. CONCLUSION PV array can be formed by series connected PV modules to

provide larger operating voltage to the load. Under partially shaded conditions, the array has more complex characteristics which will halt the ability of the FMPPT for power optimization control. This is mainly due to the FMPPT will be trapped at the local MPP. With the initial voltage tracking function, FMPPT is able to continuously search and track the absolute MPP beyond the trapped local MPP. FMPPT can control the PV array to have faster response in tracking MPP while minimizing the power fluctuation when the MPP has been successfully identified. Thus, the efficiency of the PV array is improved.

NOMENCLATURE Rs Equivalent series resistor

Rp Equivalent parallel resistor

Dm Diode

Ipv Light-generated current of solar cell I Terminal current of the solar cell

Ik Present state current

Ik – 1 Previous state current I0 Diode reverse biased saturation current Imp Maximum power current of PV array

n Ideality factor of the diode

VT Thermal voltage

Vmp Maximum power voltage of PV array

Vinital Initial voltage computed by initial voltage tracking function

Pk Present state power

Pk – 1 Previous state power

Vk Present state voltage

Vk – 1 Previous state voltage

∆V Fuzzy perturbed voltage

dp Change of power

dp/dv Change of power with respect to change of voltage

ACKNOWLEDGMENT The authors would like to acknowledge the financial

assistance of University Postgraduate Research Scholarship Scheme (PGD) by Ministry of Science, Technology and Innovation Malaysia (MOSTI).

REFERENCES [1] C.S. Chin, P. Neelakantan, H.P. Yoong, and K.T.K. Teo, “Fuzzy logic

based MPPT for photovotaic modules influenced by solar irradiance and cell temperature,” Proceedings of 13th International Conference on Computer Modelling and Simulation, Cambridge, United Kingdom, pp. 376-381, 2011.

[2] Syafaruddin, E. Karatepe, and T. Hiyama, “Polar coordinate fuzzy controller based real-time maximum-power point control of photovoltaic system,” Renewable Energy, vol. 34, issue 12, pp. 2597-2606, 2009.

[3] H. Patel, and V. Agarwal, “MATLAB-based modeling to study the effects of partial shading on PV array characteristics,” IEEE Transaction on Energy Conversion, vol. 23, no. 1, pp. 302-310, 2008.

[4] M.G. Villalva, J.R. Gazoli, and E.R. Filho, “Modeling and circuit-based simulation of photovoltaic arrays,” Proceedings of Power Electronics Conference, Bonito, Brazil, pp. 1244-1254, 2009.

[5] Y.H. Ji, D.Y. Jung, J.G. Kim, J.H. Kim, T.W. Lee and C.Y. Won, “A real maximum power point tracking method for mismatching compensation in PV array under partially shaded conditions,” IEEE Transaction on Power Electronics, vol. 26, issue 4, pp. 1001-1009, 2011.

[6] H. Patel, and V. Agarwal, “Maximum power point tracking scheme for PV systems operating under partially shaded conditions,” IEEE Transaction on Industrial Electronics, vol. 55, no. 4, pp. 1689-1698, 2008.

[7] M.G. Villalva, J.R. Gazoli, and E.R. Filho, “Comprehensive approach to modeling and simulation of photovoltaic arrays,” IEEE Transactions on Power Electronics, vol. 24, no. 5, pp. 1198-1208, 2009.

[8] Y.J. Wang, and P.C. Hsu, “Analytical modelling of partial shading and different orientation of photovoltaic modules,” IET Renewable Power Generation, vol. 4, issue 3, pp. 272-282, 2010.

[9] S. Silvestre, A. Boronat, and A. Chouder, “Study of bypass diodes configuration on PV modules,” Applied Energy, vol. 86, issue 9, pp. 1632-1640, 2009.

[10] C.S. Chin, P. Neelakantan, H.P. Yoong, S.S. Yang and K.T.K. Teo, “Maximum power point tracking for PV array under partially shaded conditions,” Proceedings of 3rd International Conference on Computational Intelligence, Communication Systems and Networks, Bali, Indonesia, pp. 72-77, 2011.


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