2014 6th International Conference on Information Technology and Electrical Engineering (ICITEE), Yogyakarta, Indonesia
Maximum Power Point Tracking Algorithm for Photovoltaic System Under Partial Shaded Condition by Means Updating β Firefly Technique Yanuar Mahfudz Safarudin, Ardyono Priyadi
Mauridhi Hery Purnomo, Margo Pujiantara
Instrumentation, Measurement, and Power Systems Identification Laboratory Department of Electrical Engineering
[email protected],
[email protected]
Institut Teknologi Sepuluh Nopember, Surabaya, Indonesia 60111
[email protected],
[email protected]
Abstract—This paper proposes new Simplified Firefly Algorithm (SFA) with an updated β coefficient to maximum power point tracking (MPPT) of photovoltaic system under partial shading condition. The different from standard firefly algorithm is neglected α and γ coefficients to simplify an algorithm. The other new feature is updated β coefficient for each iteration step in order to achieve faster convergence. This proposed algorithm is to obtain the optimal solution for MPPT of PV system under three shaded conditions. The simulation results are compared with traditional Perturbation and Observation (P&O) and standard Firefly Algorithm (FA) to verify the proposed method performance. Highest maximum powers and efficiencies are produced by the proposed algorithm. The ripple in steady state condition is also better than P&O and standard FA. The main advantage of proposed algorithm is simpler and faster convergence yet still accurate compared to standard firefly. Keywords—Firefly Algorithm (FA); Simplified Firefly Algorithm (SFA); Maximum Power-Point Tracking (MPPT); Partial shaded condition (PSC); Photovoltaik (PV) systems.
I.
INTRODUCTION
Nowadays, solar energy plays an important role for renewable energy resource since it offers clean energy with free abundant source of power. Photovoltaic (PV) is a tool used to convert solar energy into electric energy. PV generators have advantage such as low maintenance cost, no emission, and free source of abundant solar energy. However it requires high initial cost.
Some researchers have published the MPPT methods such as modified P&O [3], PSO [4], firefly algorithm [5], and its combinations [6] for solving partial shading problems. In the newest reference, FA is currently best method for optimizing MPPT of PV system under partial shaded condition. The advantages of this method are simple computation, fast convergence, may implemented in low cost microprocessor, and the most important is may track multiple peaks optimization problem in case of partial shading [5]. This paper proposes new Simplified Firefly Algorithm (SFA) with an updated β coefficient to maximum power point tracking (MPPT) of photovoltaic system under partial shading condition. The different from standard firefly algorithm is neglected α and γ coefficients to simplify an algorithm. The other new feature is updated β coefficient for each iteration step in order to achieve faster convergence. This proposed algorithm is to obtain the optimal solution for MPPT of PV system under three shaded conditions. The simulation results are compared with traditional Perturbation and Observation (P&O) and standard Firefly Algorithm (FA) to verify the proposed method performance. II.
PHOTOVOLTAIC UNDER PARTIAL SHADED CONDITION MODELLING
This section explains the PV model and partial shaded condition used in this paper. A. PV Model
PV system currently must be optimized to convert the electricity at maximum rate. The MPPT is a method to track maximum power of PV system may convert in any temperature and solar insolation condition. The MPPT requires DC-DC converter and/or inverter to control the PV output power. The problem occurred when an obstacle object block up solar insolation to some part of PV surfaces. This condition is named partial shading condition (PSC). The effect of PSC on PV system has been investigated by researchers in several publications. However it varies depend on configuration of PCS and bypass diode [1]-[2]. PV system under partial shading condition becomes more complex since it is presence of multiple peaks.
Figure 1. PV Modeling From photovoltaic model in figure 1, output current (I0) can be written as [4]:
978-1-4799-5303-5/14/$31.00 ©2014 IEEE
(1)
2014 6th International Conference on Information Technology and Electrical Engineering (ICITEE), Yogyakarta, Indonesia
Where Ipv represent short circuit current affected by solar insolation and surface temperature. Ipv can be calculated by following equation: (2) 2
S is solar insolation in W/m , and Sref is reference of solar insolation. T is PV survace temperature in Kelvin, and Tref is reference of PV surface temperature. Isco is PV module short circuit current in standart insolation and temperature written in PV specification. Id is diode current can be expressed by follows: Figure 3. P-V curve of partial shading condition scheme
(3) Where Isat is diode saturation current, and Vt is thermal voltage that can be calculated using following equation: (4) Ș is PV ideality factor, k is Boltzmann’s constant in joule per kelvin, Ns is number of series cells, and q is electronic charge in coulombs. The power generated by photovoltaic (Ppv) can be expressed by following equation: (5) B. PV System and Partial Shading Condition In this paper, four PVs connected in series are used for simulation model. Every single PV has parameter is stated in Table I, and every single PV connected into bypass diode. TABLE I PARAMETER OF SINGLE PHOTOVOLTAIC MODULE Parameter Value Maximum power (Pmax) 60.46 W Open Circuit Voltage (VOC) 21.98 V Maximum Power Voltage (VMP) 21.12 V Short Circuit Current (ISCO) 2.95 A Maximum Power Current (IMP) 2.863 A Three schemes of partial shading conditions are used for simulation model to test the performance of proposed algorithm. The differences of each scheme are the number of multiple peaks that represent level of complicate optimization. Optimization problem become more complicate if there are more peaks occurred. There is only one string of series photovoltaic used in this paper since multiple peaks problem depends on configuration of bypass diodes connected in series [1]. Partial shading condition and its P-V curve are described in figure 2-3.
Figure 2. Three scheme of partial shading condition
Figure 3 shows P-V curve of partial shading condition scheme used in the simulation model. The shading scheme can be explained as follows: Shading scheme 1 has two peaks, and the global maximum power is 218.4 W. And then shading scheme 2 has three peaks, and the global maximum power is 143.4 W. Finally shading scheme 3 has four power peaks, and the global maximum power is 68.83 W. The proposed algorithm should detect global maximum power, and not be trapped into local maximum power. The DCDC converter used in this paper is buck type converter with resistive load. Buck converter parameters are given in Table II. TABLE II PARAMETER OF BUCK CONVERTER Parameter Value Capacitor, C 470 μF Inductor, L 2.7 mH Internal resistance of Inductor, RL 0.2 ȍ Switching frequency, f 20 kHz The objective function is to maximize power generated by photovoltaic and represented in equation (5). Then duty cycle of DC-DC converter become control variable of optimization problem. The duty cycle may change voltage and current generated by photovoltaic. It means that the power generated by photovoltaic will change. III.
PROPOSED ALGORITHM
This paper proposes a modified firefly algorithm in order to simplify algorithm and faster computation. Basic firefly algorithm is based on firefly phenomena. The less bright firefly will move to brighter firefly. Basic of firefly movement can be calculated using following equation [7]: (6) Xi and Xj represent less bright firefly i and brighter firefly j position. ȕ is firefly attractiveness factor, and Ȗ is light absorption coefficient. And then Į represent random coefficient, and represent random vector. In MPPT application, the objective function is photovoltaic output power and firefly position represent duty cycle. There are two kind of modification is proposed in this paper. First, it neglects an unnecessary parameter to simplify algorithm. Second, it updates ȕ coefficient for each iteration
2014 6th International Conference on Information Technology and Electrical Engineering (ICITEE), Yogyakarta, Indonesia
step in order to achieve faster convergence and increase tracking speed.
The number of firefly is chosen as 5, and its initial position is manually chosen as 0.05, 0.25, 0.5, 0.75, and 0.95.
A. Simplify Algorithm Firefly algorithm is widely used to solve many optimization problems. It is necessary to use standard firefly as equation (6) if control variable presented as firefly position is more than one, and ranged widely.
B. Updated ȕ Coefficient In basic firefly algorithm, ȕ coefficient represent firefly attractiveness factor that ranging from 0 to 1. Higher ȕ coefficient will guarantee faster computation, but less accurate. And then, low ȕ coefficient will make the computation slow, but more accurate.
In MPPT application, there is only one control variable which is duty cycle. Then duty cycle applied in DC-DC buck converter is ranged from 0 to 1. It means that the range of firefly position as control variable is very narrow. Therefore, the Ȗ and Į factor are not required. Besides, the first position of firefly can be selected manually ranging from 0 to 1. It depends on the number of firefly. So, it is also unnecessary to randomize first position of firefly. The simple firefly equation can be written as:
In this paper, the ȕ coefficient will be updated each iteration in order to make it faster for convergence, but still accurate. At first we set ȕ coefficient as 0.3. It means that firefly will move slowly into the brightest one. Each iteration, ȕ coefficient will be added by 0.25. It means that each next iteration firefly will move faster than the last iteration. This modification will make the proposed algorithm faster than standard firefly, but still accurate.
(7)
Figure 4. Simulation result of shading scheme 1
Figure 5. Simulation result of shading scheme 2
2014 6th International Conference on Information Technology and Electrical Engineering (ICITEE), Yogyakarta, Indonesia
IV.
SIMULATION RESULTS AND DISCUSSION
Figures 4-6 show solving shading scheme 1-3 respectively to verify the performance of proposed method. The simulation has done using MATLAB Simulink software. The P&O and standard FA are also described for comparison. The power in W, voltage in V, current in A, and duty cycle are used for performance measurement. The constant parameter of traditional P&O is chosen as 0.01. And then the standard firefly parameter of ȕ, Ȗ, and Į is chosen as 0.5, 0.98, and 0.0012. It is observed that P&O algorithm trapped into local maximum power at shading scheme 2 and 3. P&O tracking speed very much based on constant parameter. Higher constant parameter means faster but less accurate of searching. And then
there is much ripple when output power reaches steady state level. It is also observed that the standard firefly may track global maximum power in shading scheme 1 and 2, but still less accurate in shading scheme 3. It may say that shading scheme 3 is the most complicated optimization problem, because the presence of four peaks. The proposed method has worked properly, and may track global maximum power at all shading scheme. Beta update has also worked properly so that the tracking speed of proposed method has been a bit faster than standard firefly. The accuracy is also better than standard FA. There are no ripples when it reaches steady state since duty cycle has been convergent. It means that no duty cycle ripple exists.
Figure 6. Simulation result of shading scheme 3 TABLE III RESULT OF THREE SHADING SCHEMES Shading Scheme
1
2
3
Tracking Method
Power Tracked (Watt)
Voltage (Volts)
Current (Amperes)
PnO Standard FA Proposed FA PnO Standard FA Proposed FA PnO Standard FA Proposed FA
207.8764 217.1206 217.1533 124.5787 143.019 143.1954 37.9081 57.4265 68.6766
84.22527 87.3549 87.37157 87.22166 65.3025 65.38603 90.36496 19.67807 42.92288
2.4681 2.4855 2.4854 1.4283 2.1901 2.19 0.4195 2.9183 1.6
Table III shows the comparison of the three shading schemes are calculated by PnO, standard FA and proposed FA. The shading scheme, power tracked, voltage, current, tracking speed, maximum power, steady state ripple and tracking efficiency are also shown. It is observed that proposed FA is faster, more accurate, and simpler computation than P&O and
Tracking Speed Maximum (s) Power (Watts) 2.404 2.611 2.18 1.805 2.565 1.801 0.924 2.302 1.901
218.4
143.4
68.83
Steady State Ripple
Tracking Efficiency (%)
poor minimum minimum poor minimum minimum average minimum minimum
95.18150183 99.41419414 99.42916667 86.87496513 99.73430962 99.85732218 55.07496731 83.43236961 99.77713206
standard FA algorithm to track maximum power. The proposed method is also never trapped into local optimum and produce efficiency always above 95%. Table IV shows the comparison between proposed method and FA algorithm with various ȕ factors. The power tracked,
2014 6th International Conference on Information Technology and Electrical Engineering (ICITEE), Yogyakarta, Indonesia
voltage, current, tracking speed, maximum power, steady state ripple and tracking efficiency are also shown in three shading schemes. It is observed that tracking speed and accuracy in
case of value of ȕ factors are compromised in the proposed algorithm.
TABLE IV VARIOUS BETA VALUES Shading Scheme
1
2
3
Tracking Method Standard FA (ɴ=0.3) Standard FA (ɴ=0.5) Standard FA (ɴ=0.75) Proposed FA Standard FA (ɴ=0.3) Standard FA (ɴ=0.5) Standard FA (ɴ=0.75) Proposed FA Standard FA (ɴ=0.3) Standard FA (ɴ=0.5) Standard FA (ɴ=0.75) Proposed FA
V.
Power Tracked (Watt) 216.86 217.1206 216.8464 217.1533 143.1153 143.019 143.1012 143.1954 68.7187 57.4265 57.2215 68.6766
Voltage (Volts) 87.25005 87.3549 87.24107 87.37157 65.34945 65.3025 65.34301 65.38603 42.95187 19.67807 29.28729 42.92288
CONCLUSSIONS
Simplified firefly algorithm with beta update has been proposed. There are two new features proposed in this paper. First, it neglects an unnecessary parameter to simplify algorithm. Second, it updates ȕ coefficient for each iteration step in order to achieve faster convergence and increase tracking speed. The main advantage of proposed algorithm is simpler algorithm, faster convergence and tracking speed, high accuracy, and never been trapped into local optimum. It means that Simplified Firefly Algorithm (SFA) may also solve the MPPT optimization problems. This paper only deals with software simulation to test the performance of proposed algorithm. Hardware implementation and comparison with other algorithm will be investigated in the next paper. ACKNOWLEDGMENT First author would to thanks to Indonesian Directorate General of Higher Education for giving the full financial support to study in Master program at ITS, Surabaya. And also thank you for my parents and my teacher.
REFERENCES [1]
[2]
[3]
[4]
Current Tracking Speed Maximum (Amperes) (s) Power (Watts) 2.4855 5.6458 2.4855 2.611 218.4 2.4856 1.6647 2.4854 2.18 2.19 5.556 2.1901 2.565 143.4 2.19 1.614 2.19 1.801 1.5999 4.606 2.9183 2.302 68.83 1.9538 1.409 1.6 1.901
A. Dolara, G.C Lazaroiu, S. Leva, “Experimental Investigation of Partial Shading Scenarios on PV (Photovoltaic) Modules”, ScienceDirect, Energy 55 (2013), p466-475. Y. J. Wang and P. C. Hsu, “Analytical modelling of partial shading and different orientation of photovoltaic modules”, IET Renew. Power Gener., vol. 4, no. 3, pp. 272-282, May 2010. H.Renaudineau, A. Houari, J.-P. Martin, S. Pierfederici, F. M. Tabar, “A New Approach in Tracking Maximum Power Under partially Shaded Condition with Consideration of Converter Losses”, ScienceDirect, Solar Energy 85 (2011), p2580-2588. K. Ishaque, Z. Salam, “A Deterministic Particle Swarm Optimization Maximum Power Point Tracker for Photovoltaic System Under Partial
[5]
[6]
[7]
Steady State Tracking Ripple Efficiency (%) minimum 99.29487179 minimum 99.41419414 minimum 99.28864469 minimum 99.42916667 minimum 99.80146444 minimum 99.73430962 minimum 99.7916318 minimum 99.85732218 minimum 99.83829725 minimum 83.43236961 minimum 83.13453436 minimum 99.77713206
Shading Condition”, IEEE Trans. Industrial Electronics, vol. 60, no. 8, pp. 3195-3206, August. 2013. K. Sundareswaran, S. Peddapati, S. Palani, “MPPT of PV Systems Under Partial Shaded Conditions Through a Colony of Flashing Fireflies”, IEEE Trans. Energy Conversion (2014), early acces K.L. Lian, J.H. Jhang, I.S. Tian,“ A Maximum Power Point tracking Method Based on Perturb-and-Observe Combined with Particle Swarm Optimization”, IEEE Journal of Photovoltaics, vol. 4, no. 2, pp. 626-633, March. 2014. X.-S. Yang, Nature-Inspired Metaheuristic Algorithm, Beckington, U.K.: Luniver Press, 2008.
