Research on the Application of Genetic Algorithm in Optimal Design of PFC Control Circuit

0 Introduction
Genetic algorithms mainly rely on the diversity of population genotypes to provide evolutionary opportunities and produce continuous evolutionary effects. According to pattern theory, the search of genetic algorithms is a process of sampling patterns implicit in the coding string and reconstructing patterns between coding strings, and there is implicit parallelism. This paper discusses the improvement of genetic algorithm operation methods and their impact on the performance of genetic algorithms, and further introduces the specific implementation of the genetic operations to be adopted. On this basis, the control parameters of the feedback compensation network of the PFC control circuit are optimized by using the improved genetic algorithm, and the simulation results are given.

1 Design of current loop compensation network of PFC control circuit
PFC technology adapts to the development direction of power electronics technology. Its control principle is to complete the transformation from DC voltage to DC voltage under the control of a certain regular conduction ratio, and control the input current waveform to track the input voltage waveform to achieve the purpose of power factor correction. The PFC control circuit adopts the average current control method. The average current control circuit structure is shown in Figure 1.

For the Boost converter, within the range between the resonant frequency band (LCO) of the filter and the switching frequency band, the current loop open loop is a first-order integral system, and the transfer function of the current loop control signal to the input current is:

where VRS is the voltage across the input current detection resistor RS, VCEA is the output voltage of the current error amplifier, VO is the DC output voltage, VS is the peak-to-peak value of the oscillator triangle wave, and sL is the inductor impedance of the Boost converter.

To ensure the stable operation of the system, the current loop must be compensated. The zero point of the current regulator must be at or below the maximum cutoff frequency fCI, at which point the system has a phase margin of 45°. In order to eliminate the system's sensitivity to noise at the switching frequency, a pole should be introduced into the current regulator. The pole frequency is 1/2 of the switching frequency. When the pole frequency is greater than 1/2 of the switching frequency, the pole will not affect the frequency response of the current loop.
The current loop compensation network is shown in Figure 2:

Its transfer function:

2 Improved design of genetic algorithm
When applying genetic algorithm to optimize controller parameters, this paper makes the following designs based on the standard genetic algorithm:
(1) In terms of coding scheme, Gray coding is used to overcome the "Hamming cliff" of binary coding;
(2) In the selection operation, the expected value method is used instead of the fitness value ratio method to avoid the situation that when the number of individuals is not too large, the fitness value ratio method sometimes cannot correctly reflect the fitness of individuals when selecting individuals based on random numbers;
(3) The crossover operation considers the use of two-point crossover to combine excellent gene patterns as much as possible.
On this basis, the algorithm is improved as follows:
① Protect excellent individuals.
In each generation of the population, the individual with the largest fitness value is retained and does not participate in the crossover and mutation process, so that it directly enters the next generation. This can prevent excellent individuals from being destroyed in the crossover or mutation operation and ensure global convergence.
② Adaptive mutation strategy.
An adaptive strategy based on adaptive temperature is adopted for the crossover and mutation operators. This adaptive strategy is applied to both crossover and mutation operations and is defined as the adaptive temperature:
where f and fmax are the average and optimal individual fitness values ​​of a generation, respectively. It is easy to know that as the iteration proceeds, the "temperature" gradually decreases. Then the genetic operator is designed based on T:

PC = a + bT, PM = c - dT.
a, b, c, d are properly selected constants, and the operator and the adaptive temperature T are in a simple linear relationship.

③Terminate evolution based on comprehensive conditions.
The algorithm terminates evolution based on two conditions: first, whether the genetic generation reaches the fixed maximum genetic generation; second, whether the difference or variance of the average fitness of individuals in the previous and next generations is less than the set minimum threshold. When the two conditions are met, that is, when one of the two conditions is met, it is considered that the evolution termination condition is met.

3 Genetic algorithm control parameter optimization design
In order to make the PFC circuit have better stability and dynamic performance, the current loop and voltage loop must be feedback integrated, and the zero poles must be reasonably configured through an appropriate compensation network to improve the circuit characteristics.
The current loop feedback compensation network adopts a single zero point double pole network as shown in Figure 2.
Then the open loop transfer function of the current loop is:

Where: RS is the current sampling resistor, VO is the output voltage, is the main circuit inductor, △V is the peak value of the triangular wave of the PWM controller, is the switching frequency
Select the design variables as X=[x1, x2, x3, x4]=[RCI, CCP, RCZ, CCZ], then the relationship between the open-loop transfer function of the current loop and the design variables can be obtained:

The program is written in C language and simulated with SIMULINK.
The control parameters to be optimized are X=[x1, x2, x3, x4]=[RCI, CCP, RCZ, CCZ], which is a multi-parameter optimization problem. Each parameter is represented by a 10-bit Gray code and connected end to end to form a 40-bit chromosome string. The initial population X=[x1, x2, x3, x4]=[RCI, CCP, RCZ, CCZ] takes the initial value X* of each parameter in the preliminary design in the previous section as the center, and takes values ​​on both sides within a certain range, that is, X0=X*×(1±δ), and δ=0.3.
Population size: N=31; Maximum number of iterations: Gmax=400; After each genetic operation, one optimal individual is retained;
The coefficients of the genetic operator are:
a=0.6, b=0.2, c=0.2, d=0.19, that is: PC=a+bT=0.6+0.2T, PM=c-dT=0.2-0.19T.
The large mutation strategy PC is adopted, and the variation range of PM is 0.6~0.8 and 0.01~0.2. The open-loop crossover frequency WCI of the current loop transfer function TI(s)
under the unit step function of the system is combined, and a certain weight is taken as the evaluation function. However, because the genetic algorithm only targets the maximum value and cannot be negative, the fitness function is taken as its reciprocal:
Among them, k1 and k2 are the weights of the two evaluation factors, which are taken as 0.5 in the optimization process.
Because continuous parameter encoding is used, and the component parameters in actual engineering are standardized parameters, dynamic programming ideas are used for partial design in the optimization process. That is,
first, encode and optimize the four parameters, compare the optimal value obtained with the standard parameter, select the parameter value that is closest to the standard parameter or can be obtained by connecting at most two standard components in series (or in parallel), and determine it. Then, re-encode the remaining three parameters, optimize them, and determine the second parameter. And so on, until all four parameters are determined.

4 Experimental results analysis
We applied the modified genetic algorithm (MGA) proposed in this paper to optimize the parameters. The results were compared with the preliminary design results in the frequency domain and the transient response performance indicators of the current loop under the two sets of parameters are shown in Tables 1 and 2 respectively:

Two sets of parameter step responses are used for simulation respectively, and the simulation results are compared in Figure 4:

It can be clearly seen from Figure 4 that the overshoot is reduced, the transition time is shortened, and the time domain performance indicators of the control system are greatly improved. The simulation results illustrate the effectiveness and superiority of the optimized parameters.

Combined with frequency domain analysis, the frequency characteristic indicators before and after the current loop optimization are shown in Table 3.

The frequency characteristics of the open-loop transfer function of the current loop before and after the optimization design are shown in Figure 5.

From the above optimization design results, it can be seen that compared with the preliminary design values, after optimization, the gain margin and phase margin of the current loop are increased, the stability performance of the current loop is improved, and the switching noise suppression capability is also better than before optimization.

5 Conclusion
Based on the analysis and research of the basic principles and operation methods of genetic algorithms, this paper improves the operation methods of genetic algorithms, and conducts circuit analysis and preliminary design of control parameters for the average current control power factor control circuit. The control parameters are optimized using the improved genetic algorithm. The optimization results are simulated and analyzed. The
following issues need to be further studied in future work: Applying genetic algorithms to optimize the control parameters offline, using analog devices to achieve control, and whether the algorithm can be further optimized in the future so that the algorithm occupies a small enough memory space and the running time is short enough to achieve digital online optimization control.