CN102096728A - Power electronic circuit optimizing method based on estimation of distribution algorithms - Google Patents

Abstract

The invention relates to a power electronic circuit optimizing method based on estimation of distribution algorithms. The automatic optimal design of the power electronic circuit is an important technology of enhancing the design quality and the design efficiency of the power electronic circuit. In the invention, the estimation of the distribution algorithms is applied to the automatic optimal design of the power electronic circuit and two fields of the power electronic circuit and the intelligent computation are related. In the method provided by the invention, a histogram probability model is applied to estimate the optimal value distribution of each electronic component in the power electronic circuit; and in the meantime, the self-adaptive local optimum operation is introduced into the estimation of the distribution algorithms to enhance the efficiency of the algorithm optimization. Through a test on the optimal design of a buck converter, the method provided by the invention is proved to be very effective.

Description

Power electronic circuit optimization method based on distribution estimation algorithm

The technical field is as follows:

the invention relates to two fields of power electronic circuits and intelligent calculation, in particular to a power electronic circuit optimization method based on a distribution estimation algorithm.

Background art:

power electronic circuit technology is widely used in various everyday electronic devices. It uses power electronic components to regulate and control the supply current or voltage to suit the requirements of the user's load. With the rapid development of semiconductor technology and related fields such as computer science technology, automatic optimization design of power electronic circuits becomes possible, and has become an important technology for improving the design quality and efficiency of power electronic circuits.

The traditional power electronic circuit optimization method is mainly a deterministic optimization method, such as a Newton method, a steepest descent method and the like. The disadvantage of these algorithms is that they tend to fall into local optima. For a more complex circuit, it is difficult to obtain a high-quality design effect by using a traditional optimization method. In recent years, successive learners have succeeded in optimizing the design of power electronic circuits by using intelligent algorithms such as genetic algorithm and particle swarm algorithm. These intelligent algorithms do not require strict mathematical derivations and specialized power circuit domain knowledge in optimizing circuit designs, but rather only require an objective function. Moreover, the objective function need not satisfy constraints that can be micro, derivative, domain-continuous, etc. The algorithm can optimize the problem even in the case of an objective function without an explicit mathematical expression (e.g., the objective function value is obtained by analog simulation). Therefore, the intelligent algorithm has very strong universality and is particularly suitable for optimizing the power circuit.

Distribution estimation algorithms are an emerging class of intelligent algorithms. The probability model is adopted to estimate the distribution of the optimal solution, and the iterative evolution form guiding algorithm of the probability model is improved to find the approximate optimal solution or even the optimal solution of the problem through sampling and sample evaluation. Compared with other intelligent algorithms, the distribution estimation algorithm has the greatest characteristic that the optimal value distribution of the variables is estimated by adopting a probability model. The search form based on probability statistics is very suitable for solving the problem that problem variables have noises (such as a power electronic circuit optimization problem), and at present, a distribution estimation algorithm is successfully used for solving complex optimization problems, such as a protein optimization problem, a work scheduling problem, a network control problem, a material management problem and the like.

The invention content is as follows:

a distribution estimation algorithm is used herein in power circuit optimization. The probability model adopted by the distribution estimation algorithm is a histogram model with a fixed width.

The algorithm comprises the following steps:

(1) the probabilistic model and associated parameters are initialized.

(2) And generating N initial samples according to the value range of each electronic element, and calculating the objective function values of all the initial samples.

(3) And sequencing the current sample set according to the objective function values, and selecting S samples with larger objective function values.

(4) And counting the selected S sample information, and updating the current histogram probability model.

(5) N new samples are sampled from the updated probability model, and the objective function values of all the new samples are evaluated.

(6) And comparing the N new samples with the original N samples pairwise in sequence, reserving the better individuals, and finally obtaining the updated N samples to participate in the subsequent operation.

(7) A local optimization operation is performed on the optimal sample found so far.

(8) And adaptively adjusting the step length of the next local optimization according to the feedback condition of the local optimization.

(9) And (4) terminating if the algorithm reaches the end condition, otherwise, executing the step (3).

The distribution estimation algorithm is a population-based intelligent algorithm. In the optimization process, the algorithm can optimize N potential solutions at the same time, so that the method has strong global search capability. In order to further accelerate the convergence rate of the algorithm, the invention introduces a self-adaptive local optimization operator in the distribution estimation algorithm, thereby effectively improving the solving speed and precision of the algorithm.

Description of the drawings:

FIG. 1 basic block diagram of a power electronic circuit

FIG. 2 is a flow chart of a distributed estimation algorithm for optimizing power electronic circuits

Fig. 3 schematic diagram of a buck converter

The specific implementation mode is as follows:

the method of the present invention is further described below with reference to the accompanying drawings.

The basic block diagram of the power electronic circuit is shown in fig. 1, which includes two parts, a power delivery and a feedback network. It is assumed here that the circuitry of the power transfer part is fixed and that only the circuitry of the more complex feedback network part is optimized. The feedback network part comprises I_FA resistance J_FAn inductance and K_FA capacitor. The passive elements are represented by a vector:

<math><mrow><msub><mi>&Theta;</mi><mi>F</mi></msub><mo>=</mo><mfenced open='[' close=']'><mtable><mtr><mtd><msub><mover><mi>R</mi><mo>&OverBar;</mo></mover><mi>F</mi></msub></mtd><mtd><msub><mover><mi>L</mi><mo>&OverBar;</mo></mover><mi>F</mi></msub></mtd><mtd><msub><mover><mi>C</mi><mo>&OverBar;</mo></mover><mi>F</mi></msub></mtd></mtr></mtable></mfenced></mrow></math>

wherein, <math><mrow><msub><mover><mi>R</mi><mo>&OverBar;</mo></mover><mi>F</mi></msub><mo>=</mo><mfenced open='[' close=']'><mtable><mtr><mtd><msub><mi>R</mi><mn>1</mn></msub></mtd><mtd><msub><mi>R</mi><mn>2</mn></msub><mo>&CenterDot;</mo><mo>&CenterDot;</mo><mo>&CenterDot;</mo><msub><mi>R</mi><msub><mi>I</mi><mi>F</mi></msub></msub></mtd></mtr></mtable></mfenced><mo>,</mo></mrow></math> <math><mrow><msub><mover><mi>L</mi><mo>&OverBar;</mo></mover><mi>F</mi></msub><mo>=</mo><mfenced open='[' close=']'><mtable><mtr><mtd><msub><mi>L</mi><mn>1</mn></msub></mtd><mtd><msub><mi>L</mi><mn>2</mn></msub><mo>&CenterDot;</mo><mo>&CenterDot;</mo><mo>&CenterDot;</mo><msub><mi>L</mi><msub><mi>J</mi><mi>F</mi></msub></msub></mtd></mtr></mtable></mfenced><mo>,</mo></mrow></math> <math><mrow><msub><mover><mi>C</mi><mo>&OverBar;</mo></mover><mi>F</mi></msub><mo>=</mo><mfenced open='[' close=']'><mtable><mtr><mtd><msub><mi>C</mi><mn>1</mn></msub></mtd><mtd><msub><mi>C</mi><mn>2</mn></msub><mo>&CenterDot;</mo><mo>&CenterDot;</mo><mo>&CenterDot;</mo><msub><mi>C</mi><msub><mi>K</mi><mi>F</mi></msub></msub></mtd></mtr></mtable></mfenced><mo>.</mo></mrow></math>

the objective function is defined as follows:

<math><mrow><msub><mi>&Phi;</mi><mi>F</mi></msub><mrow><mo>(</mo><mi>X</mi><mo>)</mo></mrow><mo>=</mo><munderover><mi>&Sigma;</mi><mrow><msub><mi>R</mi><mi>L</mi></msub><mo>=</mo><msub><mi>R</mi><mrow><mi>L</mi><mo>,</mo><mi>min</mi></mrow></msub><mo>,</mo><msub><mi>&delta;R</mi><mi>L</mi></msub></mrow><msub><mi>R</mi><mrow><mi>L</mi><mo>,</mo><mi>max</mi></mrow></msub></munderover><munderover><mi>&Sigma;</mi><mrow><msub><mi>V</mi><mi>in</mi></msub><mo>=</mo><msub><mi>V</mi><mrow><mi>in</mi><mo>,</mo><mi>min</mi></mrow></msub><mo>,</mo><msub><mi>&delta;v</mi><mi>in</mi></msub></mrow><msub><mi>V</mi><mrow><mi>in</mi><mo>,</mo><mi>max</mi></mrow></msub></munderover></mrow></math> [F₁(R_L，v_in，X)+F₂(R_L，v_in，X)+F₃(R_L，v_in X)+F₄(R_L，v_in，X)]

wherein X is a set of input variables, R_L，min，R_L，max，v_in，minAnd v_in，maxThe minimum and maximum values of the load and input voltage, respectively. Delta R_LAnd δ v_inThen the step sizes of the changes of the load and the input voltage, respectively. F₁，F₂，F₃，F₄Four evaluation indices considered for circuit optimization. The four evaluation indexes are defined and calculated as follows:

1.F₁: this target is used to estimate the steady state error of the output voltage. Is defined as

${\mathrm{<figure-callout\; id="1"\; label="F"\; filenames="HSA00000367182900021.png"\; state="\{\{state\}\}">F</figure-callout>}}_1=K_1{e}^{-E_2/K_2}$

2.F₂: this target is used to evaluate the maximum overshoot, the maximum undershoot during start-up and the settling time of the output voltage. Is defined as:

F₂＝OV(R_L，v_in，X)+UV(R_L，v_in，X)+ST(R_L，v_in，X)

where OV is the maximum overshoot, UV is the maximum undershoot, and ST is the settling time of the output voltage. They are defined as follows:

$\mathrm{OV}=\frac{K_{10}}{1+e^{\frac{M_p-M_{p0}}{K_{11}}}}$

wherein K₁₀Is the maximum value of the objective function, M_p0Is the maximum overshoot, M_pIs practicalOvershoot, K₁₁Is the pass band constant.

$\mathrm{UV}=\frac{K_{12}}{1+e^{\frac{M_v-M_{v0}}{K_{13}}}}$

Wherein K₁₂Is the maximum value of the objective function, M_v0Is the maximum undershoot, M_vIs a real undershoot, K₁₃Is the pass band constant.

$\mathrm{ST}=\frac{K_{14}}{1+e^{\frac{T_s-T_{s0}}{K_{15}}}}$

Wherein K₁₄Is the maximum value of the objective function, T_s0Is a constant, T_sIs the actual setup time, K₁₅For adjusting the sensitivity. T is_sIs defined as v_dThe settling time falling within the a ± σ% passband. That is to say, the position of the nozzle is,

|v_d(t)|≤0.01σ，t≥T_s

3.F₃: this target is used to calculate the steady state ripple voltage on the output voltage. The definition is as follows:

$F_3=K_5{e}^{-{\mathrm{<figure-callout\; id="1"\; label="A"\; filenames="HSA00000367182900021.png"\; state="\{\{state\}\}">A</figure-callout>}}_1/K_6}$

4.F₄: this target is used to evaluate the dynamic performance of the circuit in case of input voltage and output resistance disturbances. The definition is as follows:

<math><mrow><msub><mi>F</mi><mn>4</mn></msub><mo>=</mo><munderover><mi>&Sigma;</mi><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><msub><mi>N</mi><mi>T</mi></msub></munderover><mi>OV</mi><mrow><mo>(</mo><msub><mi>R</mi><mrow><mi>L</mi><mo>,</mo><mi>i</mi></mrow></msub><mo>,</mo><msub><mi>v</mi><mrow><mi>in</mi><mo>,</mo><mi>i</mi></mrow></msub><mo>,</mo><mi>X</mi><mo>)</mo></mrow><mo>+</mo><mi>UV</mi><mrow><mo>(</mo><msub><mi>R</mi><mrow><mi>L</mi><mo>,</mo><mi>i</mi></mrow></msub><mo>,</mo><msub><mi>v</mi><mrow><mi>in</mi><mo>,</mo><mi>i</mi></mrow></msub><mo>,</mo><mi>X</mi><mo>)</mo></mrow><mo>+</mo><mi>ST</mi><mrow><mo>(</mo><msub><mi>R</mi><mrow><mi>L</mi><mo>,</mo><mi>i</mi></mrow></msub><mo>,</mo><msub><mi>v</mi><mrow><mi>in</mi><mo>,</mo><mi>i</mi></mrow></msub><mi>X</mi><mo>)</mo></mrow></mrow></math>

wherein N is_TIs the number of inputs and load disturbances in the performance test.

Fig. 2 shows an overall flow chart of the algorithm optimized power circuit design of the present invention. The following describes the specific implementation of the whole algorithm in steps with respect to the contents of the flow chart:

1. and (5) initializing.

The invention adopts a histogram probability model with fixed width to estimate the optimal value distribution of each electronic element in the power electronic circuit; assume an electronic component with a value range of [ a, b ]]The number of the square columns is n, and the heights are h respectively₁，h₂，...h_nThen, the intervals represented by the square bars are as follows:

[a，a+Δ]，[a+Δ，a+2Δ]，...，[b-Δ，b]，

where Δ ═ b-a)/n is the width of the interval, and the probability of the electronic component taking a value in the interval i is:

h₁/N，h₂/N，...，h_n/N

wherein N is h₁+h₂+...+h_n. . In the initialization stage of the algorithm, the initial histogram probability model is:

$H=\left[\begin{array}{c}{h}_{11},h_{12},...,h_{1n}\\ h_{21,}{h}_{22},...,h_{2n}\\ ...\\ {\mathrm{<figure-callout\; id="1"\; label="h\; D"\; filenames="HSA00000367182900021.png"\; state="\{\{state\}\}">h</figure-callout>}}_D,h_{D2},...,h_{\mathrm{Dn}}\end{array}\right]=\left[\begin{array}{c}\mathrm{0,0},...,0\\ \mathrm{0,0},...,0\\ ...\\ \mathrm{0,0},...,0\end{array}\right]$

wherein D is the number of the electronic elements, and n is the number of the square columns corresponding to each electronic element. And then generating N initial samples according to the value range of each electronic element, and calculating the objective function values of all the initial samples. Assume that the N initial samples generated are:

$\mathrm{POP}=\left[\begin{array}{c}{I}_1\\ I_2\\ ...\\ I_N\end{array}\right]=\left[\begin{array}{c}{x}_{11},x_{12},...,x_{1D}\\ x_{21},x_{22},...,x_{2D}\\ ...\\ x_{\mathrm{<figure-callout\; id="1"\; label="N"\; filenames="HSA00000367182900021.png"\; state="\{\{state\}\}">N</figure-callout>}1},z_{N2},...,x_{\mathrm{ND}}\end{array}\right]$

2. and updating the probability model.

This step selects S samples with a larger objective function value from the current sample set, and updates the histogram probability model according to the S samples. The histogram probability model is updated in the following manner:

h_ij＝β·h_ij+(1-β)·h′_ij

wherein, beta is ∈ [0, 1]]Is the learning rate, h'_ijIs the number of the ith variable of the selected S samples in the jth square column.

3. A new sample is generated.

This operation generates N new samples from the updated histogram probability model and evaluates the objective function values of all the new samples. The values of the variables of the new sample are generated as follows:

<math><mrow><msub><mi>x</mi><mi>i</mi></msub><mo>=</mo><mfenced open='{' close=''><mtable><mtr><mtd><mi>rand</mi><mrow><mo>(</mo><msub><mi>l</mi><mi>i</mi></msub><mo>,</mo><msub><mi>u</mi><mi>i</mi></msub><mo>)</mo></mrow><mo>,</mo><mi>ifq</mi><mo>&le;</mo><mi>&alpha;</mi></mtd></mtr><mtr><mtd><mi>R</mi><mrow><mo>(</mo><mi>i</mi><mo>)</mo></mrow><mo>,</mo><mi>otherwise</mi></mtd></mtr></mtable></mfenced></mrow></math>

where a ∈ [0, 1] is the rate of variation, q is a random value over the [0, 1] interval, and R (i) is a value generated according to a histogram probability model. The generation process of r (i) comprises two substeps: (1) selecting one of the higher squares by roulette selection based on the height of each square for the ith variable; (2) and generating a random value in the area corresponding to the square column according to uniform distribution.

4. And (5) replacing operation.

And comparing the N new samples with the original N samples pairwise in sequence, and reserving the better individuals. The N samples that are finally left are subjected to the subsequent operations.

5. And (4) performing self-adaptive local optimization operation.

Suppose X_b＝(x_b1，x_b2，...，x_bD) Is the best sample found by the algorithm so far. The adaptive local optimization operation comprises two sub-steps:

(1) m temporary samples are generated in the neighborhood of the sample and their objective function values are evaluated. The values of the variables of the temporary sample are generated as follows:

wherein v is a random value between 0 and 1, r_iIs the radius of the neighborhood.

(2) If the optimal temporary individuals are better than X_bThen replace X with the temporary entity_bAnd the neighborhood radius is enlarged, thereby improving the efficiency of subsequent local search. Otherwise, the neighborhood radius is reduced, thereby improving the precision of the next local optimization. The updating mode of the neighborhood radius is as follows:

where ρ ∈ [0, 1] is the neighborhood radius reduction rate.

To test and evaluate the performance of the algorithm of the present invention, a test was conducted using an optimized design of a buck converter as an example. The schematic diagram of the buck converter is shown in fig. 3, where the electronic component of the feedback network to be optimized is R₁，R₂，R_C3，R₄，C₂，C₃And C and₄。

the parameter settings of the algorithm of the present invention are shown in the following table:

parameter(s)	Value taking	Description of the invention
			N	200	Total sample size
S	100	Selecting a sample size for updating a probabilistic model
			M	20	Temporary sample size
α	0.1	Rate of variation
			β	0.7	Learning rate
ρ	0.9	Neighborhood radius shrinkage
			n	20	Number of columns contained in each variable

Genetic algorithms and particle swarm algorithms which have been successfully used for optimizing power electronic circuits at present also optimize the design of the same circuits. The final result shows that the algorithm of the invention does not fall into local optimization in multiple simulation tests, and the average optimization effect is superior to that of a genetic algorithm and a particle swarm algorithm. This demonstrates that the invention is very effective in optimizing the design of power electronic circuits.

Claims (3)

1. A power electronic circuit optimization method based on a distribution estimation algorithm is characterized by comprising the following steps:

(1) initializing a probability model and related parameters;

(2) generating N initial samples according to the value range of each electronic element, and calculating the objective function values of all the initial samples;

(3) sequencing the current sample set according to the objective function values, and selecting S samples with larger objective function values;

(4) counting the selected S sample information, and updating the current histogram probability model;

(5) sampling N new samples from the updated probability model, and evaluating objective function values of all the new samples;

(6) comparing the N new samples with the original N samples pairwise in sequence, reserving better individuals in the samples, and finally obtaining updated N samples to participate in subsequent operations;

(7) performing local optimization operation on the optimal sample found so far;

(8) according to the feedback condition of the local optimization, adaptively adjusting the step length of the next local optimization;

(9) and (4) terminating if the algorithm reaches the end condition, otherwise, executing the step (3).

2. The power electronic circuit optimization method based on the distribution estimation algorithm of claim 1, wherein: estimating the optimal value distribution of each electronic element in the power electronic circuit by adopting a histogram probability model with fixed width; assume an electronic component with a value range of [ a, b ]]The number of the square columns is n, and the heights are h respectively₁，h₂，...h_nThen, the intervals represented by the square bars are as follows:

[a，a+Δ]，[a+Δ，a+2Δ]，...，[b-Δ，b]，

where Δ ═ b-a)/n is the width of the interval, and the probability of the electronic component taking a value in the interval i is:

h₁/N，h₂/N，...，h_n/N

wherein N is h₁+h₂+...+h_n。

3. The power electronic circuit optimization method based on the distribution estimation algorithm of claim 1, wherein: introducing a self-adaptive local optimization operator for further accelerating the convergence speed of the algorithm and improving the solving precision of the algorithm; suppose X_b＝(x_b1，x_b2，...，x_bD) Is the optimal sample found by the algorithm so farThen, the specific method of the adaptive local optimization operation includes the following two sub-steps:

(1) at X_bThe neighborhood of (2) generates M temporary samples, wherein the values of the variables of the temporary samples are generated as follows:

wherein v is a random value between 0 and 1, r_iIs the radius of the neighborhood;

(2) if the optimal temporary individuals are better than X_bThen replace X with the temporary entity_bAnd expanding the neighborhood radius, otherwise, reducing the neighborhood radius, wherein the updating mode of the neighborhood radius is as follows:

where ρ ∈ [0, 1] is the neighborhood radius reduction rate.

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