Abstract: The output characteristics of photovoltaic cells vary with load and external environment. Maximum power point tracking (MPPT) circuits can fully utilize the efficiency of photovoltaic devices. Based on the advantages and disadvantages of commonly used photovoltaic power generation system control and the basic principle of MPPT, this paper proposes an adaptive duty cycle perturbation method with online parameter adjustment based on fuzzy control. Simulation results show that the system can effectively track changes in the external environment, ensuring that the system always operates near the maximum power point and exhibits good stability.
Keywords: photovoltaic cell; fuzzy control; maximum power point tracking; Matlab/Simulink
Maximum power point tracking by using fuzzy control for photovoltaic energy generation system
Abstract： The output power of PV module varies with module temperature, solar insolation and Loads, so it is necessary to track the MPP of the PV array all the time． time． According to the mechanism and control methods of Maximum Power Point Tracking (MPPT), a new modified adaptive MPP method based on fuzzy control which includes automatic parameter tuning and directly uses the DC/DC converter duty cycle as a control parameter is presented. When the external environment has changed, this method can track MPP changes rapidly． Experimental results show it can track MPP exactly and quickly．
Key words: photovoltaic; fuzzy control; MPPT (maximum power point tracking); Matlab/Simulink
introduction
The output characteristics of photovoltaic (PV) cells are greatly affected by the external environment. Changes in cell surface temperature and solar radiation intensity can lead to significant variations in output characteristics. While maximum power point tracking (MPPT) control significantly improves the conversion efficiency of PV cells, it is often limited by their inherent limitations. MPPT typically uses power as a variable for feedback control, matching the internal resistance of the PV cell to the impedance of the external load. Common MPPT control algorithms include the perturbation-observation method, the constant voltage method, the optimal gradient method, and the incremental conductance method. This paper proposes a fuzzy control method for achieving MPPT in PV systems, effectively addressing the problems of uncertain perturbation variables and overly complex control processes encountered with other methods. Simulation results demonstrate the superior performance of this control method.
1. Characteristics of photovoltaic cells
1.1 Mathematical Model of Photovoltaic Array
The following are the mathematical models for the output voltage and current of a typical polycrystalline silicon photovoltaic cell: (1)
Where I <sub>as </sub> is the dark saturation current of the photovoltaic cell; I<sub> LG </sub> is the photocurrent; q is the unit charge (1.6*10<sup> -23</sup> ); A and B are ideality factors; k is the Boltzmann constant (1.38*10<sup> -23</sup> ); V is the output voltage of the photovoltaic cell; R is the series equivalent resistance of the photovoltaic cell; TY is the reference temperature; T is the actual operating temperature of the photovoltaic cell; I<sub> OR </sub> is the dark saturation current under TY ; T<sub> LG </sub> is the short-circuit current of the photovoltaic cell under standard test conditions; K <sub>1</sub> is the temperature coefficient of the short-circuit current; and is the solar irradiance.
Parallel connection of photovoltaic cells increases the maximum output current of the system, while series connection increases the maximum output DC voltage of the power generation system. Analysis of formula (1) shows that ambient temperature and solar irradiance are the main factors affecting the output characteristics of solar cells. Ambient temperature primarily affects the open-circuit voltage of the solar cell, while solar irradiance primarily affects the short-circuit current.
Figure 1. Equivalent circuit diagram of photovoltaic cells connected to a load.
1.2 Typical photovoltaic cell characteristic curves
Figure 2 shows the power point (PU) characteristic curves of solar cells under different light intensities. It indicates that a solar cell is neither a constant voltage source nor a constant current source, but rather a nonlinear DC power source. Furthermore, the maximum power point of the solar panel differs under different solar irradiance and ambient temperatures. If the solar cell employs MPPT control, it can track the maximum power under different light intensities, thereby maximizing the photovoltaic cell's performance.
Figure 2 Voltage and power operating characteristics
1.3 MPPT Principle and Implementation of Fuzzy Control
Fuzzy controllers do not need precise mathematical models of the solar photovoltaic array, nor do they need to know the ambient temperature and solar radiation intensity. Instead, they continuously change the setpoints of controllable parameters during operation, gradually moving the current operating point closer to the peak power point, and finally operating near the maximum power point. Therefore, the fuzzy self-optimization method can be used to achieve maximum power point tracking.
Following the principle of the duty cycle perturbation observation method, the objective function is taken as the output power of the photovoltaic cell, and the controllable variable is the duty cycle D of the PWM signal used to control the Boost converter. The adjustment step size at this moment is determined based on the change in power value and the duty cycle adjustment step size of the previous moment. The input of the fuzzy controller at time n is the change in power of the photovoltaic system at time n and the duty cycle step size at time n-1. The output at time n is the duty cycle step size at time n. The following principles are followed:
(1) If the output power increases, continue the original step size adjustment direction; otherwise, adjust the step size in the opposite direction.
(2) When the distance to the maximum power point is far, a larger step size is used to speed up the tracking speed. When the distance to the maximum power point is close, a smaller step size is used to reduce power loss.
2. Basic Principles of Fuzzy Control
2.1 Determine the input and output fuzzy subsets and universe of discourse
The linguistic variables are defined as 8 and 6 fuzzy subsets, respectively:
E = {NB, NM, NS, NO, PO, PS, PM, PB}; A = {NB, NM, NS, PS, PM, PB}. Where NB, NM, NS, NO, PO, PS, PM, and PB represent fuzzy concepts such as negative large, negative small, negative zero, positive zero, positive small, and positive large, respectively. Their domains are defined as having 14 and 12 levels, respectively.
E={-6,-5,-4,-3,-2,-1,-0,+0,+1,+2,+3,+4,+5,+6}; A={-6,-5,-4,-3,-2,-1,-0,+0,+1,+2,+3,+4,+5,+6}. A=(-0.058,0.058), e=(-50,50), representing the range of actual values. These values are then assigned to different fuzzy domains using quantization factors.
2.2 Membership Function
Based on the characteristics of photovoltaic systems, a triangle is chosen as the shape of the membership function, and the closer the curve is to the origin, the steeper the curve; the farther away from the origin, the gentler the curve. The membership functions for duty cycle step size and power difference are shown in Figures 3 and 4.
2.3 Fuzzy Decision Table
The following principles are derived from the analysis of the characteristic curves between the duty cycle and output power of a photovoltaic system.
(1) If the output power increases, continue to adjust in the original step direction; otherwise, take the opposite direction.
(2) Use a smaller step size near the maximum power point to reduce search loss; use a larger step size at a greater distance from the maximum power point to speed up the tracking.
(3) When changes in factors such as temperature and solar radiation intensity cause significant changes in the power output of the photovoltaic system, the system can react quickly.
The basis is whether the output power of the photovoltaic cell can quickly reach the given required range. The fuzzy rule IF A AND B THEN C is applied to establish the fuzzy rule table as shown in Table 1.
Table 1 Fuzzy Control Rule Table
3. Simulation Experiment
3.1 Simulation Model
Based on the mathematical model of the photovoltaic array, an MPPT fuzzy control system was built using Matlab/Simulink. The solar cell model is shown in Figure 5. The PV module represents the photovoltaic cell model. The main MPPT functions are implemented by the fuzzy controller, and the S-function implements the function D(n) = D(n-1) + a(n).
Figure 5 Simulation of MPPT fuzzy control
3.2 Simulation Results
The simulation conditions are as follows: photovoltaic cell surface temperature T = 25℃; simulating external changes, the solar irradiance A increases sharply from 600 W/ m² to 900 W/ m² ; the quantization factor Ka is 0.01, and ke is 10; the load resistance R = 1.568 Ω; the simulation time is 6 s; the delay time is 0.05 s; the maximum simulation step size is set to 0.025 s; and the power output is shown in Figure 6.
Figure 6. Simulated tracking waveform of output power P
The fuzzy controller can adjust the duty cycle step size in real time according to the solar irradiance. The change in duty cycle directly regulates the load voltage, thereby causing the load power to change in the same direction. Applying fuzzy logic control to the tracking of the maximum power point of photovoltaic cells results in rapid tracking and virtually no fluctuations after reaching the maximum power point, exhibiting good dynamic steady-state characteristics and control performance.
4. Conclusion
This paper models and analyzes a photovoltaic power generation system, employing fuzzy control with the duty cycle step size as the control variable. The duty cycle is adaptively adjusted based on the magnitude of changes in photovoltaic power. Simulation experiments show that the proposed fuzzy logic control method exhibits good tracking performance and is easy to implement, addressing issues such as severe oscillations near the maximum power point, difficulty in determining the step size, and significant power loss. Real-time tracking is achieved by intelligently adjusting the step size using fuzzy logic control. Simulink simulation results demonstrate that this algorithm solves the problems existing in conventional algorithms and achieves excellent control performance.
References
[1] Wang Chuanhui, Luo Yaohua. Fuzzy control method [J]. Applied Science, 2008, 35(3), 42-45.
[2] Hui Jing. New Energy Conversion and Control Technology [M]. Beijing: Machinery Industry Press, 2008.
[3]FUNABASHI T, KOYANAGI K, YOKOYAMA R. A Review of Islanding Detection Methods for Distributed Resources[J]． Power Tech Conference Proceedings, IEEE. Bologna. 2003, 30(2):1-6．
[4]TAEYK, HOGA, KYUP, et a1. A Novel Maximum Power Point Tracking Control for Photovohaic Power System under Rapidly Changing Solar Radiation[J]． Proc IEEE Conf International Symposium on Industria Electronics, Pusan, 2001, 20(5): 1011-1014.
[5] Li Guoyong. Intelligent Control and Its MATLAB Implementation [M]. Beijing: Electronic Industry Press, 2005.
[6] Zhang Chao, He Xiangning. Application of asymmetric PID fuzzy control in maximum power point tracking [J]. Journal of Electrical Engineering, 2005, 20(10): 73-75.
About the author:
Li Huihui (1985-), female, from Linfen, Shanxi Province, is a postgraduate student in the class of 2007 at Taiyuan University of Science and Technology. Her research focuses on control technology of photovoltaic power generation systems.
Sun Zhiyi (1959-), male, from Changzhi, Shanxi Province, is a professor and doctoral supervisor at Taiyuan University of Science and Technology. His research interests include control theory and engineering.
Mailing Address: Room 633, Taiyuan University of Science and Technology; Mobile Phone: 13834143795; Email: li
