A novel approach of maximizing energy harvesting in photovoltaic systems based on bisection search theorem

Transcription

1 A novel approach of maximizing energy harvesting in photovoltaic systems based on bisection search theorem Peng Wang, Haipeng Zhu, Weixiang Shen, Fook Hoong Choo and Poh Chiang Loh and Kuan Khoon Tan School of Electrical and Electronic Engineering Nanyang Technological University, Singapore {epwang, HPZHU, wxshen, efhchoo, epcloh, Abstract This paper presents a new approach of maximizing energy harvesting in photovoltaic (PV) systems using bisection search theorem (BST). The fundamental of the BST and its application into maximum power point tracker (MPPT) in PV systems are described. A microcontroller is used to control a DC/DC boost converter to realize the MPPT function. Experimental results from solar array simulator show that the proposed technique can track maximum power point very fast within a few steps. The feasibility of the proposed MPPT is also verified in natural environment condition with two solar modules in parallel. Since the proposed technique is simple in computation, cheap in implementation and fast in tracking, it is expected to be widely used to replace conventional MPPT techniques in PV systems. I. INTRODUCTION With ever-increasing concerns on environment and energy conservation, the research and development of photovoltaic (PV) system technology has been accelerated recently due to its free of pollution, silent operation, long life time and low maintenance [1]. Although the improvement of solar cell technologies and the increasing demand for PV systems have led to a reduction of the price of PV module [2], the costs of PV systems are still too high. Therefore, it is an important to design the PV systems which can maximize energy harvesting from Sun through solar modules. The output power of solar module varies as a function of solar radiance, temperature and operating point because of its nonlinear current-voltage (I-V) relationship [3]. Therefore, the maximum power point tracker (MPPT) is widely used to maximize the power output of the solar module. As such, many MPPT techniques have been developed and implemented. The techniques vary in sensors required, tracking speed, complexity and cost of hardware implementation, such as Hill Climbing/P&O and its variants [4-7], Incremental Conductance and its variants [8-9], Factional Open-Circuit Voltage [10], [11] and Fractional Short-Circuit Current [12]. For those techniques, the qualitative comparison and the quantitative comparison in terms of simulation and experiment have been conducted [13-15], respectively. The results show that Hill Climbing/P&O and Incremental Conductance are in general the most efficient techniques. For these two techniques, the derivatives of voltage and power measured from the solar module are still required. In this paper, a novel MPPT technique based on bisection search theorem (BST) is proposed without the necessity of derivative computation. Thus, the new technique is even simpler in computation, cheaper in implementation and faster in tracking. The experimental results from solar array simulator in the laboratory show that the proposed technique can track maximum power point very fast within a few steps. The feasibility of the proposed technique is also verified under real solar modules at the presence of natural environmental conditions. Thus, it is expected to be widely used to replace conventional MPPT techniques in PV systems. II. BISECTION SEARCH THEOREM AND MPPT APPLICATION A. Prinple of bisection search theorem The bisection search theorem is one of the bracketing methods for finding roots of equations [16], [17]. Assume that function y = f (x) and an interval [ a, b] which contains a root x * of f (x) that lies somewhere in the interval as shown in Fig. 1 such that f ( c) = 0. (a) if f (c) and f (b) have opposite sign, then squeeze from left (b) if f (a) and f (c) have opposite sign, then squeeze from right Fig. 1 Decision process for bisection search This work is supported by The National Research Foundation (NRF) of Singapore through the research project NRF-G-CRP /10/$ IEEE 2143

2 The BST systematically moves the endpoints of the interval closer and closer together in the pace of halving interval for each step until an interval of arbitrarily small width that brackets the zero is obtained. The decision step for this process is first to choose the midpoint c = ( a + b) / 2 and then to analyze the three possibilities that might rise: 1). If f (a) and f (b) have opposite signs, a zero lies in [ a, c]. 2) If f (a) and f (b) have opposite signs, a zero lies in [ c, b]. 3) if f ( c) = 0, then the zero is c. If either case (1) or (2) occurs, an interval half as wide as the original interval that contains the root is found as shown in Fig.1. If the process continues, c 1, c2, c3,... c n represents the sequence of midpoints which * converges to the root x within a certain degree of accuracy (DOA), namely n * n c x ( b a) / 2 for n = 1, 2,, (1) From (1), it can be seen that increasing n can make c n more * n closer to x at the DOA in terms of the value of ( b a) / 2. B. MPPT technique based on BST In order to apply the BST into the MPPT technique in PV systems, the function of y = f (x) and the variable x should be chosen carefully. Fig. 2 shows a real current-voltage ( I V ) curve of a solar module and its corresponding power-voltage ( P V ) curve tested in a sunny day in Singapore. Current (A) Voltage (V) Power (W) Fig. 3 Typical change in power versus voltage curve power point is essential to find the root in the function Δ P by regulating the voltage of solar module or solar array. As a result, the function y = f (x) can be regarded as the change in power Δ P, where the variable x is the voltage of solar module or solar array and can be written as: y = ΔP( V m ) (2) where V m is the voltage across the solar module. To regulate the voltage V m, converters are conventionally required as interface between solar modules and loads. A DC/DC booster converter is adopted to implement the proposed MPPT technique in this paper. Fig. 4 shows the schematic diagram of the system. When the converter works at continuous mode, the relationship between the duty cycle and the voltage of solar modules at steady-state is written as: V = ( 1 D) (3) m V out where V out is the output voltage of the converter. Thus, the duty cycle D ( 0 D 1 ) can be used to regulate the voltage of solar module or solar array [18]. Fig. 2 Typical current-voltage and power-voltage curves From the P V curve, it can be observed that the change in power Δ P with respect to voltage approaches zero at the maximum power point as illustrated in Fig. 3. Obviously, the powers at short circuit voltage (0 V) and open circuit voltage ( V oc ) are zero, so maximum power should not happen in these two particular points even though the changes in power at these two points are also zero, which is caused by the small powers around these two points. Thus, tracking the maximum Fig. 4 DC-DC boost converter for MPPT 2144

3 The working principle of the system can be described as follows. The entire system is controlled by a microcontroller. The voltage and current of solar modules are continuously sampled and the duty cycle of the converter is calculated by the microcontroller based on the proposed MPPT technique using the BST. The flowchart of the program embedded in the microcontroller is shown in Fig. 5. III. EXPERIMENTAL SETUP To verify the feasibility and effectiveness of the proposed MPPT technique, the hardware of the system has been set up. Two sources were used to test the proposed MPPT. One is a real solar module working under natural environmental conditions while the other is a solar array simulator which simulates different sizes of solar modules under different conditions. A. Solar modules The solar module is a power source of PV systems. In this experimental setup, solar array consists of two solar modules connected in parallel. The specifications of the solar module are shown in Table 1. TABLE I. SPECIFICATIONS OF SOLAR MODULE Item Value Nominal Maximum Output (Pin) 45W Nominal Open Circuit Voltage (Voc) 18V Nominal Short Circuit Current (Isc) 3.45A Nominal Maximum Output Voltage (Vmpp) 14.5V Nominal Maximum Output Current (Impp) 3.11A Nominal Weight 5.3kg These two solar modules have almost the same I-V characteristics, then the output voltage of the solar array is equal to the output voltage of one solar module, and the output current is twice as much as the output current of one solar module. Thus, for this solar array at a sunny day, the voltage at the maximum power should be around 14.5 V while the current at the maximum power should be around 6.2 A, as shown in Fig. 6. Fig. 6 Two solar modules for testing MPPT Fig. 5 Flowchart of program for MPPT implementation B. Solar array simulator The solar array simulator (SAS) is the important tools to investigate the PV systems. It can create the I-V curve of different sizes of solar array under various environmental conditions. It can also test the response time of the MPPT when solar radiation changes from one into another. Fig

4 shows the Agilent SAS model of E4360. It can output power up to 1200W with maximum open circuit voltage of 130V and maximum short circuit current of 10 A. Therefore, any size of solar array within the above-mentioned ranges can be simulated by using this SAS. The first type of test is to prove its feasibility and show the steps of how the proposed MPPT tracks the maximum power point under constant solar radiation, where the SAS repeat generating one I-V curve. The results of tracking process which shows variation of voltage, current and power are illustrated in Fig. 9. It can be seen that seven steps are approximately required for the proposed MPPT to track the maximum power which is equivalent to about 1.5 seconds. Fig. 7 Solar array simulator for testing MPPT C. Hardware implementation of MPPT The proposed MPPT based on the BST is realized by a Freescale MC9S08AW60 Microcontroller. The inputs of the microcontroller are the voltage and current sensed from solar array and the output of the microcontroller is the pulse width modulation (PWM) pulse which is used to control the dutycycle of the IGBT in the DC-DC boost converter through a gate driver circuit as shown in Fig. 4, where the parameters of major components are illustrated in Table II. The C-language program is employed in this controller. The experimental setup of the proposed MPPT is shown in Fig. 8. TABLE II. PARAMETERS OF MAJOR COMPONENTS Item Value Booster inductor, L (mh) 0.2mH Smoothing capacitor, C (uf) 470uF Switching frequency, fs (khz) 40khz IGBT (type) IRG4PC50UD Fig. 9 Verification of feasibility and steps to track maximum power for the proposed MPPT The second type of test is to investigate its tracking capability under slow variation of solar radiation, where the SAS generates two I-V curves repetitively with a defined interval in between. The results of tracking process which shows the variation of voltages, currents and powers under the conditions of the changing solar radiations are illustrated in Fig. 10. It indicates that the proposed MPPT can still track the maximum power point despite the changing solar radiation. Fig. 8 Experimental setup of MPPT based on BS theorem IV. EXPERIMENTAL RESULTS AND DISCUSSIONS A. Experimental results Three types of tests have been conducted on the experimental setup of the MPPT technique based on BST. Fig. 10 Investigation of tracking capability of the proposed MPPT under variation of solar radiation 2146

5 The third type of test is to operate the proposed MPPT under natural environmental conditions, where the MPPT controller is connected to two solar modules in parallel as shown in Fig. 6. The experimental results are illustrated in Table III. Under different times (or solar radiations), the duty cycle of power converter can stabilize at 40.6% and 32.7% (see Figs. 11 and 12), respectively, which are very close to the values of duty cycles: 41% and 33%. These two values are corresponding to the maximum powers for the solar modules at the times indicated in Table III. TABLE III EXPERIMENTAL RESULTS FOR PROPOSED MPPT TO OPERATE UNDER TWO SOLAR MODULES IN PARALLEL AT DIFFERENT TIMES (DIFFERENT SOLAR RADIATIONS) 15:05, 8 May, 2009 Duty cycle 80% 70% 60% 50% 41% 40% 30% 20% Output Voltage 12.05V 13.16V 14.17V 15.29V 16.03V 15.83V 14.66V 11.43V Output Power 4.84W 5.77W 6.69W 7.79W 8.57W 8.35W 7.16W 4.35W 16:34, 8 May, 2009 Duty cycle 80% 70% 60% 50% 40% 33% 30% 20% Output Voltage 13.74V 15.31V 17.13V 19.27V 21.13V 21.56V 21.30V 16.92V Output Power 6.29W 7.81W 9.78W 12.38W 14.88W 15.49W 15.12W 9.54W Fig. 12 Power converter at duty cycle of 32.7% B. Discussions According to the description of the proposed MPPT technique and its experimental results, some observations can be made and discussed here. Firstly, there is no any requirement of derivatives of voltage and power measured from solar array, which reduces the complexity in computation and hence implementation. Therefore, the proposed MPPT technique is very suitable for the use of PV systems. Secondly, the control signal of IGBT can be easily generated due to the fact that every time the new duty cycle is simply taken by halving the sum of its previous value and current value. Thus, tracking maximum power point can be very fast within a few steps. Finally, although some ripples of voltage, current and power can be seen from the experimental data which is not evitable for the DC/DC booster converter, the proposed MPPT technique can still work well, which show a certain degree of robust and reliability of the proposed MPPT technique. V. Fig. 11 Power converter operating at duty cycle of 40.6% ONCLUSIONS AND FUTURE WORK In this paper, a novel MPPT technique based on bisection search theorem has been presented. A microcontroller together with a DC-DC boost converter is applied to implement the proposed MPPT control system. Experimental results from solar array simulator show that the proposed MPPT technique can track the maximum power very fast under slow variation of solar radiation within a few steps. The feasibility of the proposed MPPT control system has also been verified in natural environmental conditions. Further research can be conducted on how the proposed MPPT can track the maximum power at fast change of solar radiation and how it can identify the global maximum and local maxima under the partially-shaded solar modules. 2147

6 REFERENCES [1] Bialasiewicz, J.T., Renewable Energy Systems with Photovoltaic Power Generators: Operation and Modeling, IEEE Trans. on Industrial Electronics, vol. 55, no. 7, pp , July [2] D. Poponi, Analysis of diffusion paths for photovoltaic technology based on experience curves, Solar Energy, vol. 1, no. 74, pp , [3] Tomas Markvart, Solar electricity, John Wiley & Sons Inc [4] E. Koutroulis, K. Kalaitzakis, and N. C. Voulgaris, Development of a microcontroller-based, photovoltaic maximum power point tracking controlsystem, IEEE Trans. Power Electron., vol. 16, no. 21, pp , Jan [5] O. Wasynczuk, Dynamic behavior of a class of photovoltaic power systems, IEEE Trans. Power App. Syst., vol. 102, no. 9, pp , Sep [6] S. Jain andv.agarwal, A newalgorithm for rapid tracking of approximatemaximum power point in photovoltaic systems, IEEE Power Electron. Lett., vol. 2, no. 1, pp , Mar [7] N. Femia, G. Petrone, G. Spagnuolo, and M. Vitelli, Optimization of perturb and observe maximum power point trackingmethod, IEEE Trans. Power Electron., vol. 20, no. 4, pp , Jul [8] K. H. Hussein and I. Mota, Maximum photovoltaic power tracking: An algorithm for rapidly changing atmospheric conditions, in IEE Proc. Generation Transmiss. Distrib., 1995, pp [9] Y.-C. Kuo, T.-J. Liang, and J.-F. Chen, Novel maximum-power-point tracking controller for photovoltaic energy conversion system, IEEE Trans. Ind. Electron., vol. 48, no. 3, pp , Jun [10] G. W. Hart, H. M. Branz, and C. H. Cox, Experimental tests of open loop maximum-power-point tracking techniques, Solar Cells, vol. 13, pp , [11] M. A. S. Masoum, H. Dehbonei, and E. F. Fuchs, Theoretical and experimental analyses of photovoltaic systems with voltage and current-based maximum power-point tracking, IEEE Trans. Energy Convers., vol. 17, no. 4, pp , Dec [12] S. Yuvarajan and S. Xu, Photo-voltaic power converter with a simple maximum-power-point-tracker, in Proc Int. Symp. Circuits Syst., 2003, pp. III-399 III-402. R. M. Hilloowala and A. M. [13] T. Esram, P.L. Chapman, Comparison of photovoltaic array maximum power point tracking techniques, IEEE Trans. on Energy Conversion, vol. 22, pp , June [14] R. Faranda, S. Leva, Energy comparison of MPPT techniques for PV systems, WSEAS Transaction on Power systems, vol. 3, no. 6, pp , June 2008 [15] M. Berrera, A. Dolara, R. Faranda, S. Leva, Experimental test of seven widely-adopted MPPT algorithms, in Proc Int. Conf. Power Tech, 2009, June 28th - July 2nd, Bucharest, Romania. [16] Horst A. Eiselt, Carl-Louis Sandblom, Linear programming and its applications, Springer, [17] John H. Mathews and Kurtis K. Fink, Numerical method using Matlab, Prentice-Hall Inc., Upper saddle river, New Jersey, USA, [18] N. Mohan, T. M. Undeland, and W. P. Robbins, Power Electronics- Converters, Applications, and Design, John Wiley & Sons,