Analysis on Optimal Design of PFC Control Circuit Using Genetic Algorithm

This paper discusses the improvement of genetic algorithm operation method and its influence on the performance of genetic algorithm, and further introduces the specific implementation of the genetic operation to be adopted. On this basis, the control parameters of the feedback compensation network of PFC control circuit are optimized by using the improved genetic algorithm, and the simulation results are given.

1 PFC control circuit current loop compensation network design

PFC technology adapts to the development direction of power electronics technology. Its control principle is to complete the conversion from DC voltage to DC voltage under a certain regular conduction ratio control, 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 Bootst converter, within the range between the filter resonant frequency band (LCO) and the switch 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:

Among them, 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 cut-off 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 design 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 problem 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) Crossover operation Consider using two-point crossover to combine excellent gene patterns as much as possible.

On this basis, the algorithm is improved as follows:

① Protect outstanding 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, allowing it to enter the next generation directly. This can prevent excellent individuals from being destroyed during crossover or mutation operations and ensure global convergence.

②Adaptive mutation strategy.

Adopt an adaptive strategy based on adaptive temperature for crossover and mutation operators. This adaptive strategy is applied to both crossover and mutation operations and is defined as adaptive temperature:

Among them, 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 appropriately selected constants, and the operator and the adaptive temperature T are in a simple linear relationship.

③Comprehensive conditions terminate evolution.

The algorithm is judged to terminate the evolution by combining two conditions: first, whether the genetic generation reaches the fixed maximum genetic generation; second, whether the difference or variance of the average fitness of 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 to meet the conditions for terminating the evolution.

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 uses a single-zero double-pole network as shown in Figure 2.

Then the open-loop transfer function of the current loop is:

Among them: 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, and is the switching frequency. The design variables are selected as X=[x1, x2, x3, x4]=[RCI, *, 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, *, RCZ, CCZ], which is a multi-parameter optimization problem. Each parameter is represented by a 10-bit Gray code, and the beginning and the end are connected in series to form a 40-bit chromosome string. The initial population X=[x1, x2, x3, x4]=[RCI, *, RCZ, CCZ] The initial value is centered on the value X* of each parameter in the preliminary design in the previous section, and the values ​​are taken 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; One optimal individual is retained after each genetic operation;

The genetic operator coefficients are taken as:

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.

Using the large variation strategy PC, the PM ranges from 0.6 to 0.8 and 0.01 to 0.2.

Combine the open-loop crossover frequency WCI of the current loop transfer function TI(s) under the unit step function of the system, and take certain weights as the *cost 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 two cost factors, which are taken as 0.5 in the optimization process.

Because continuous parameter coding is used, and component parameters in actual engineering are standardized parameters, dynamic programming ideas are used for partial design during the optimization process. That is:

First, encode and optimize the four parameters, compare the optimal value 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 Table 1 and Table 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, conducts circuit analysis and preliminary design of control parameters for the average current control power factor control circuit, optimizes the control parameters using the improved genetic algorithm, and conducts simulation analysis on the optimization results.

The following issues need to be further studied in the future work: using 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 has a short enough running time to achieve digital online optimization control.