Design of MPPT for Photovoltaic Cells Based on Fuzzy Control

0 Introduction
As the global energy shortage becomes increasingly serious, renewable energy is being used more and more widely. In recent years, photovoltaic energy has been greatly developed due to its advantages such as no pollution and long-term use. Generally, photovoltaic systems hope that the photovoltaic cell array can output as much electric energy as possible under the same sunshine and temperature conditions, that is, the maximum power point tracking (MPPT) problem of photovoltaic cell arrays is proposed in theory and practice. In photovoltaic grid-connected power generation systems, since the power level of the array is generally large, the MPPT problem is particularly important. Therefore, it is undoubtedly a good choice to use the intelligence and adaptability of intelligent control methods to control nonlinear solar photovoltaic power generation systems.

1 Maximum power point of photovoltaic cells
As can be seen from Figure 1, under certain light intensity and temperature, a maximum power output point Pm can be found on the photovoltaic cell output curve. If the photovoltaic cell can be made to work at the maximum power point, the efficiency of the photovoltaic cell can be greatly improved. Therefore, its maximum power point should be found, that is, optimization should be sought.

2 Principle and design of MPPT control
The principle of MPPT control is essentially a dynamic self-optimization process. By detecting the current output voltage and current of the photovoltaic cell, the current battery output power is obtained, which is compared with the power at the previous moment. Then, according to the relationship between power and duty cycle, the duty cycle is changed to make it approach the maximum power point continuously, and this is repeated until it reaches a very small area near the maximum point. When the external light intensity and temperature change significantly, the system will search for the best again.
As shown in Figure 2, changing the duty cycle D of the pulse width modulation signal (PWM) actually changes the load of the photovoltaic cell. That is, the output power point of the photovoltaic cell is changed, thereby achieving the purpose of finding the maximum power point.

The relationship between the load RL of the photovoltaic cell and the load R and the duty cycle D is:
RL=R/D
The MPPT controller changes the load of the photovoltaic cell by adjusting the duty cycle D of the PWwM signal, thereby achieving the impedance matching function. Therefore, the size of the duty cycle D determines the size of the photovoltaic cell output power P. The PD relationship of a general photovoltaic inverter is shown in Figure 3.

Some photovoltaic power generation systems at home and abroad have generally proposed a variety of methods for the maximum power tracking control of photovoltaic cells, such as constant voltage tracking method, perturbation observation method, power feedback method and incremental conductance method. The shortcomings of these algorithms are: they do not explain how to track from one maximum power point to the next maximum power point; the amount of calculation is large and difficult to implement; the control accuracy is poor and is greatly affected by external factors. The design scheme proposed in this paper can make up for the above shortcomings by tracking the maximum power point.

3 Fuzzy controller design
In the photovoltaic grid-connected power generation system, the input and output of the system are designed using fuzzy logic, which can derive a series of control rules that can be implemented very simply by a microcomputer.
3.1 Determine the structure of the fuzzy controller
The key to MPPT control design is the design of the fuzzy controller. A dual-input single-output fuzzy controller is selected, as shown in Figure 4.

The input quantity of the fuzzy controller at the nth moment is the power change △P(n) and the power change rate at the nth moment; the output quantity at the nth moment is the duty cycle change △D(n+1) at the n+1th moment, which varies between [0, 1]. The power change △P(n)=P(n)-P(n-1), and the power change rate is calculated by △P(n)/△D(n).
3.2 Determine the fuzzy subsets of input and output quantities and the fuzzy set of the domain
△P(n) is E, the fuzzy set of △P(n)/△D(n) is EC, and the fuzzy set of △D(n) is U.
Define the linguistic variables E and U as 7 fuzzy subsets, and EC as 6 fuzzy subsets, namely:

Among them: NB, NM, NS, NO, ZO, PO, PS, PM, PB represent fuzzy concepts such as negative large, negative medium, negative small, negative zero, zero, positive zero positive small, positive medium, positive large, etc. The domain of E and U is defined as 15 levels, and the domain of EC is defined as 12 levels, namely:

3.3 Determine the membership function
The membership function of the fuzzy subset is sharp, reflecting the high sensitivity of the fuzzy set with high resolution characteristics.
Therefore, this paper chooses a triangle as the shape of the membership function. The membership functions of E and EC are shown in Figures 5 and 6, and the membership function of U is shown in Figure 7.

3.4 Determine the fuzzy control rules
According to the change in power value, the change in duty cycle at this moment is determined. By analyzing the characteristic curve between the output power P of the photovoltaic cell and the duty cycle D, and considering the influence of external environmental factors (temperature, sunshine intensity) on the output power of the photovoltaic cell, the following principles are obtained:
(1) If the output power increases, continue to adjust the original change direction, otherwise take the opposite direction;
(2) Far away from the maximum power point, use a larger change to speed up the tracking speed; near the maximum power point, use a smaller change to search to reduce the search loss;
(3) When reaching the extremely small ZO area centered on the maximum power point, the system stabilizes until the external environment changes significantly again.
(4) When the temperature, sunshine intensity and other factors change and cause the output power of the photovoltaic cell to change significantly, the system can respond quickly and search for the best again.
Following the above principles and adjusting the actual simulation results, the final control rule table is obtained, as shown in Table 1.

3.5 Defuzzification method and simulation
The fuzzy logic controller simulation selects the Mamdani type controller, and the defuzzification method is the center of gravity method, and its calculation formula is:

Where: u(Ai) is the membership degree of the i-th fuzzy output; A is the i-th fuzzy output.
After experimental simulation, the results are shown in Figure 8. When the duty cycle is controlled by MPPT fuzzy control, it can quickly track the maximum power point. It can be seen that fuzzy control can effectively overcome the nonlinearity and time lag of photovoltaic cells, and can quickly track the maximum power point and maintain this state.

4 Conclusion
The simulation found that the application of fuzzy logic control to the tracking of the maximum power point of photovoltaic cells is not only fast but also responsive. In addition, the fuzzy control table can be used to realize offline design, saving the internal storage space of the microcomputer and improving the working speed.