CN110633494B - A Multi-objective Optimization Design Method of Swiss Rectifier Based on NSGA-Ⅱ Algorithm - Google Patents

Abstract

The invention provides a Swiss rectifier multi-objective optimization design method based on NSGA-II algorithm, belonging to the technical field of rectifier parameter optimization design. Step 1, determining optimized components and modeling power and volume; step 2, defining a target function; step 3, initializing a population; step 4, selecting; step 5, selecting a binary tournament; step 6, crossing; step 7, mutation; step 8, merging the parent population and the child population to obtain a first generation population; step 9, forming a population by utilizing the parent population and the child population; step 10, reaching a maximum evolution algebra gen; and 11, outputting the Pareto optimal solution front edge and the parameter matrix, obtaining corresponding decision variable values, namely solutions of optimization problems, according to the selected target performance indexes, and selecting and designing components according to the parameters.

Description

A Multi-objective Optimization Design Method of Swiss Rectifier Based on NSGA-Ⅱ Algorithm

technical field

The invention relates to a Swiss rectifier multi-objective optimization design method based on NSGA-II algorithm, and belongs to the technical field of rectifier parameter optimization design.

Background technique

In recent years, with the wide application of power electronic devices, more and more research and optimization techniques on converters have been paid great attention by researchers at home and abroad, and various high-efficiency and novel rectifier topologies and digital control have emerged as the times require. , which has made the rapid development of electric vehicles and new energy technologies; the remarkable performance characteristics of the rectifier system are high frequency, high efficiency, high power density, high power factor, high reliability, etc., along with various new electromagnetic materials, electronic components The advent and application of devices and conversion technologies have made the rectifier system develop in the direction of small size, high efficiency and low cost.

However, because the Swiss rectifier has nonlinear components such as inductance, the rectifier system is a strong nonlinear system, and there are many component parameters and performances that need to be optimized, and the performances conflict and restrict each other. Another cost of performance reduction; this makes the Swiss rectifier, a complex optimization problem with multi-objective, uncertainty, nonlinearity and multi-parameters, difficult to achieve in traditional optimization methods. Judging each parameter by experience, it is impossible to guarantee its performance. Accuracy; how to use rigorous mathematical methods to select suitable devices to deal with multi-objective optimization problems with discrete variables such as rectifiers, so as to optimize the overall performance of the system, which is of great significance to the reliable operation of the system and the sustainable development of energy. ; Therefore, a multi-objective optimization method for Swiss rectifiers is imperative.

SUMMARY OF THE INVENTION

Aiming at the problems existing in the prior art, the present invention proposes a multi-objective optimal design method for Swiss rectifiers based on NSGA-II algorithm, which is beneficial to the optimal design of Swiss rectifier parameters, thereby improving the efficiency and power density of the rectifier. The technical solutions adopted are as follows:

A multi-objective optimization design method of Swiss rectifier based on NSGA-II algorithm, the optimization design method includes:

Step 1. Take the DC inductance L, the output capacitor C, the switch IGBT and the diode Diode in the basic topology circuit of the Swiss rectifier as the optimization variables that affect the performance index of the rectifier, and compare the DC inductance L, the output capacitor C, the switch IGBT and the diode Diode. Diode Diode for power and volume modeling;

Step 2. Define the objective function: take the efficiency and power density of the Swiss rectifier as the objective function to measure the performance index of the Swiss rectifier;

Step 3. Initialize the population: set the population size to N, the maximum evolutionary algebra to gen, and the number of decision variables to V; then, encode the decision variables with real numbers, and input the parameters with the established component database as the constraint The upper and lower limits of the variable; randomly generate an N-dimensional decision matrix, take the V+1 and V+2 columns of the decision matrix as the objective function values, the last two columns are the number of non-dominated layers and the crowding degree distance, a parameter vector corresponds to an individual or called a chromosome;

Step 4. Selection: Set two parameters n _i and S _i , where n _i is the number of individuals dominated by all individuals in the population, and Si is the set of individuals dominated by individual _i , using the fast non-dominated sorting to judge the solution of the matrix. Good and bad and sorting operations;

Step 5, binary tournament selection: set the tournament size to 2 and the matching pool size to N/2; in the initial population, randomly select two individuals, compare the non-dominated ranks of the two individuals, and put the lower ranking into the matching pool ; If the level is the same, compare the crowding degree distance, and the one with the larger distance is reserved; if the non-dominant level and the crowding degree distance are both the same, then randomly select an individual to retain, and repeat this step until the number of individuals in the matching pool is N/2;

Step 6, Crossover: First, randomly select two individuals in the contemporary population as the parent individuals of the crossover operation, perform crossover operation on the genes on the matching chromosomes, generate a pair of new chromosomes, repeat the crossover operation, and form a new generation of populations; Among them, the contemporary population is the parent population; the specific operation process is as follows: set the gene length of the chromosome as L, in the range of [0, L], randomly select an integer value K as the crossover position, and the matching chromosome is at the crossover position Exchange [K, L] genes at each other to form a new pair of chromosomes, that is, individuals;

Step 7: Mutation: Define a mutation operator to replace individual genes with a small probability, and apply the mutation operator to the population to change the genes of some individuals in the population and generate new alleles. The population is recorded as the offspring population;

Step 8, merge the parent population in step 6 with the child population obtained in step 7, the merged population is recorded as the first generation population (gen=1), and the population size is N;

In step 9, the first generation population obtained in step 8 is used as the parent population, and then the parent population is crossed and mutated to obtain the child population, and then the parent population and the child population in this step are merged to form a population. When the population size is 2N;

Step 10, utilize the operation process of step 4 to process the population formed in step 9, select N individuals as the new parent population, and then go through steps 6 and 7 to generate a new child population P _t+1 ; repeat steps 9, to reach the maximum evolutionary algebra gen;

Step 11: Output the Pareto optimal solution front and parameter matrix, obtain the corresponding decision variable values according to the selected target performance index, that is, the solution of the optimization problem, and select and design components according to each parameter.

Further, the process of power and volume modeling described in step 1 includes:

Calculate the power of the inductor, the power _PL of the inductor is:

Among them, u _L is the input voltage of the inductor, I _rms is the effective value of the current flowing through the inductor, f _sw is the switching frequency, and _VL is the inductor volume;

Calculate the coil volume of the inductance; the coil volume V _cl is:

Among them, ω _w is the winding width, and d _w is the winding depth;

N为线圈匝数，

为导体截面积，Calculate the conductor volume V _cd as: V _cd =k _pf V _cl , where k _pf is the filling factor of the coil,

N is the number of turns of the coil,

is the conductor cross-sectional area,

为：

则电感体积V_L为:

其中，l表示磁芯长度；Calculate core volume

for:

Then the inductor volume _VL is:

Among them, l represents the length of the magnetic core;

Calculate the on-state loss of the switch IGBT as:

表示为电压电流相位角；Among them, V _GE is the threshold voltage of the IGBT, I _IGBT is the amplitude of the current flowing through the IGBT, r _CE is the on-state equivalent resistance, M is the modulation ratio,

Expressed as the voltage and current phase angle;

The switching losses of the IGBT are:

Among them, E _sw(on) and E _sw(off) are the energy lost by the turn-on and turn-off of the IGBT respectively, I _N is the rated working current of the rectifier, u _CEN is the rated working voltage, and u _pn is the output voltage of the rectifier;

Calculate the total loss of IGBT as: P _IGBT =P _{cond, IGBT} +P _{sw, IGBT} ;

The conduction loss of the diode is:

P _{on, Diode} = V _F I _F D

Among them, V _F is the forward conduction voltage drop of the diode, _IF is the forward conduction current, D is the duty cycle, and the duty cycle of different diodes is calculated according to the four conduction circuit states;

The off-state loss of the diode is:

P _{off, Diode} = V _R I _R (1-D)

Among them, _VR is the reverse voltage drop, _IR is the diode reverse leakage current;

The switching losses of the diode are:

where V _fp and V _rp are the forward and reverse peak voltages of the diode, respectively, I _fp and I _rp are the forward and reverse peak currents flowing through the diode, respectively, t _fp is the forward recovery time, and t _b is Its reverse current fall time;

Then the total loss of the diode is: P _Diode =P _{on, Diode} +P _{off, Diode} +P _{sw, Diode} .

Further, the specific process of defining the objective function described in step 2 includes:

Define the objective function, taking the efficiency and power density of the Swiss rectifier as the objective function, and the efficiency η is:

Among them, P ₀ is the output power, and the power density ρ is:

Among them, P ₀ is the output power, P _loss is the total loss, P _l is the total loss of the inductor, P _IGBT is the total loss of the IGBT, P _Diode is the total loss of the Diode; V _total is the total volume of components, _VL is the inductor volume, V _IGBT is the IGBT volume, V _Diode is the diode volume, V _C is the output capacitor volume, C is the inductance; the power density ρ is the objective function

Further, the specific process of judging the quality of the solution and sorting described in step 4 includes:

Step 1: Select the individual whose n _i is 0 in the population, that is, the non-dominated optimal individual, and put it into the set F ₁ ;

Step ₂ : For each individual i in the set F1, find out the dominant individual set S _i corresponding to _i respectively, and for the individual j in Si, reduce the number n _j of all individuals dominating individual j in the population. One operation, namely n _j =n _j -1, excludes the influence of individual i dominating j, if n _j is 0, put individual j into the set F ₂ ;

Then the set F ₁ is the first-level non-dominated set, and the number of non-dominated layers of all individuals in F ₁ is recorded as Rank1, and the individuals in F ₂ are recorded as Rank2;

Step 3: Repeat the operations of Step 1 and Step 2 to sort all individuals in the population non-dominated. The number of non-dominated layers is from low to high. The smaller the Rank value, the better.

In the iterative process of the NSGA-II algorithm, the population size is always N, so in the selection operation, the individuals in the same Rank layer need to be selected, and the crowding degree distance C is defined, that is, the adjacent two individuals are on each sub-objective function. and have, C _k =(f _k+1,1 -f _k-1,1 )+(f _k-1,2 -f _k+1,2 ), where f _{k+1 ,1} , f _k-1,1 , f _k-1,2 and f _k+1,2 are represented as (k+1,1), (k-1,1), (k-1,2) and The objective function corresponding to (k+1,2);

Individuals with a large crowding degree distance are better than individuals with a small crowding degree distance. The number of non-dominated layers and the distance of crowding degree are used as the last two elements of the decision vector, and the quality of the solution and the sorting operation are judged by the number of non-dominated layers and the distance of crowding degree. .

Beneficial effects of the present invention:

The multi-objective optimization design method of the Swiss rectifier based on the NSGA-II algorithm proposed by the present invention performs multi-objective optimization on the Swiss rectifier, a complex problem with multi-objective, uncertainty, nonlinearity and multi-parameter properties, and solves the problem of selecting by experience. For the device selection of each component, the Pareto frontier selection performance index can be obtained through the optimization algorithm. The efficiency is increased to 95.28-96.86%, and the power density is 4.48-6.05KW/dm ³ , which makes the overall performance of the rectifier optimal.

Description of drawings

Figure 1 is the circuit topology diagram of the Swiss rectifier;

Figure 2 is a diagram of four conduction circuits of the Swiss rectifier;

Figure 3 is the flow chart of the NSGA-II algorithm;

Figure 4 is a schematic diagram of elite selection strategy;

Figure 5 is a structural diagram of a DC inductor UI core;

Figure 6 is a structural diagram of an output capacitor;

Figure 7 shows the Pareto optimal solution front.

Detailed ways

The present invention will be further described below in conjunction with specific embodiments, but the present invention is not limited by the embodiments.

Example 1:

Step 1, model the power and volume of the optimized components; Figure 5 is the UI core structure diagram of the DC inductor L, and the power _PL of the inductor is:

Where u _L is the input voltage of the inductor, I _rms is the rms value of the current flowing through the inductor, f _sw is the switching frequency, and _VL is the inductor volume.

The coil volume V _cl of the inductor is:

The conductor volume V _cd is: V _cd =k _pf V _cl , where k _pf is the filling factor of the coil,

为导体截面积，磁芯体积

为：N is the number of turns of the coil,

is the cross-sectional area of the conductor and the volume of the magnetic core

for:

Then _VL is:

The on-state loss of the switch IGBT is:

Among them, V _GE is the threshold voltage of the IGBT, I _IGBT is the current amplitude flowing through the IGBT, r _CE is the on-state equivalent resistance, and M is the modulation ratio. The switching losses of the IGBT are:

E _sw(on) and E _sw(off) are the energy lost for one turn on and one turn off of the IGBT, respectively.

Then the total loss of IGBT is: P _IGBT =P _{cond, IGBT} +P _{sw, IGBT} .

The conduction loss of the diode is:

P _{on, Diode} = V _F I _F D

V _F is the forward conduction voltage drop of the diode, _IF is the forward conduction current, and D is the duty cycle. The duty cycle of different diodes can be obtained from the four conduction circuit states shown in Figure 2.

The off-state loss of the diode is:

P _{off, Diode} = V _R I _R (1-D)

Among them, _VR is its reverse voltage drop, and _IR is diode reverse leakage current.

The switching losses of the diode are:

V _fp and V _rp are the forward and reverse peak voltages of the diode, respectively, I _fp and I _rp are the forward and reverse peak currents flowing through the diode, respectively, t _fp is the forward recovery time, and t _b is the reverse current fall time.

Then the total loss of the diode is: P _Diode =P _{on, Diode} +P _{off, Diode} +P _{sw, Diode} .

Step 2, define the objective function, take the efficiency and power density of the Swiss rectifier as the objective function, and the efficiency η is:

Among them, P ₀ is the output power, which is set to 5KW, and the power density ρ is:

Step 3: Initialize the population, set the population size to 200, the maximum evolutionary algebra to 200, and the number of decision variables to 39, encode the decision variables with real numbers, and use the established component database as constraints, input the upper and lower limits of each parameter variable, A 200×43 decision matrix is randomly generated, the 40th and 41st columns of the matrix are the objective function values, the last two columns are the number of non-dominated layers and the crowding degree distance, and a parameter vector corresponds to an individual or called a chromosome.

Step 4, select, adopt fast non-dominated sorting, need to set two parameters n _i and S _i , n _i is the number of all individuals in the population dominated by individual i, and Si is the set of individuals dominated by individual _i ;

First select the individual whose n _i is 0 in the population, that is, the non-dominated optimal individual, and put it into the set F ₁ ;

For each individual i in F ₁ , find out the dominant individual set Si corresponding to _i respectively, and subtract one operation for the individual _j in Si and n _j , that is, n _j =n _j -1, and exclude the individual i dominates the influence of j, if n _j is 0, put individual j into the set F ₂ ;

Then the set F ₁ is the first-level non-dominated set, and the number of non-dominated layers of all individuals in F ₁ is recorded as Rank1, and the individuals in F ₂ are recorded as Rank2;

Repeat the above operations to sort all individuals in the population non-dominated, the number of non-dominated layers is from low to high, the smaller the Rank value, the better the individual;

In the iterative process of the NSGA-II algorithm, the population size is always N, so in the selection operation, the individuals in the same Rank layer need to be selected, and the crowding degree distance C is defined, that is, the adjacent two individuals are on each sub-objective function. The sum of the distance differences, namely: C _k =(f _k+1,1 -f _k-1,1 )+(f _k-1,2 -f _k+1,2 );

Individuals with a large crowding degree distance are better than individuals with a small crowding degree distance. The number of non-dominated layers and the crowding degree distance are used as the last two elements of the decision vector for judging the quality of the solution and sorting operations.

Step 5, binary tournament selection, set the tournament size to 2 and the matching pool size to 100; in the initial population, randomly select two individuals, compare their non-dominant levels, and put the lower level into the matching pool; if the levels are the same, The crowding degree distance is compared, and the one with the larger distance is reserved; if the non-dominant level and the crowding degree distance are the same, an individual is randomly selected to be retained, and the above operations are repeated until there are 100 individuals in the matching pool.

Step 6, crossover, first randomly select two individuals in the contemporary population as the parent individuals of the crossover operation, and perform crossover operation on the genes on the matching chromosomes to generate a pair of new chromosomes; the specific operation process is as follows: set the genes of the chromosomes The length is L, in the range of [0, L], an integer value K is randomly selected as the crossover position, and the matched chromosomes exchange the genes of the [K,L] part of each other at the crossover position, thereby forming a new pair of chromosomes, the individual.

Step 7, mutation, define a mutation operator to replace individual genes with a small probability, and apply the mutation operator to the population to change the genes of some individuals in the population and generate new alleles.

Step 8: Merge the parent-child populations after the operations from Steps 5 to 7, and record them as the first-generation population (gen=1).

Step 9, Figure 4 is a schematic diagram of the elite selection strategy. After steps 6 and 7, the child and parent populations are merged. At this time, the population size is 400. After step 4, 200 individuals are selected as the new parent population, and then After steps 6 and 7, a new descendant population P _t+1 is generated; step 9 is repeated until the maximum evolutionary generation 200 is reached.

Step 10, Fig. 7 shows the Pareto optimal solution frontier. After 200 generations, the frontier and parameter matrix are output. The efficiency η is 95.28-96.86%, and the power density ρ is 4.48-6.05KW/dm ³ , which can be selected within this range. The performance index is obtained, and the corresponding value of each decision variable is obtained, that is, the solution of the optimization problem, and the selection and design of components are carried out according to each parameter.

Although the present invention has been disclosed above with preferred embodiments, it is not intended to limit the present invention. Anyone who is familiar with this technology can make various changes and modifications without departing from the spirit and scope of the present invention. Therefore, The protection scope of the present invention should be defined by the claims.

Claims (2)

1. a Swiss rectifier multi-objective optimization design method based on NSGA-II algorithm, is characterized in that, described optimization design method comprises: Step 1. Take the DC inductance L, the output capacitor C, the switch IGBT and the diode Diode in the basic topology circuit of the Swiss rectifier as the optimization variables that affect the performance index of the rectifier, and compare the DC inductance L, the output capacitor C, the switch IGBT and the diode Diode. Diode Diode for power and volume modeling; Step 2. Define the objective function: take the efficiency and power density of the Swiss rectifier as the objective function to measure the performance index of the Swiss rectifier; Step 3. Initialize the population: set the population size to N, the maximum evolutionary algebra to gen, and the number of decision variables to V; then, encode the decision variables with real numbers, and input the parameters with the established component database as a constraint The upper and lower limits of the variable; randomly generate an N-dimensional decision matrix, take the V+1 and V+2 columns of the decision matrix as the objective function values, the last two columns are the number of non-dominated layers and the crowding degree distance, a parameter vector corresponds to an individual or called a chromosome; Step 4. Selection: set two parameters n _i and S _i , where n _i is the number of individuals dominated by all individuals in the population, and Si is the set of individuals dominated by individual _i , using fast non-dominant sorting to judge the matrix. The quality of the solution and the sorting operation; Step 5, binary tournament selection: set the tournament size to 2 and the matching pool size to N/2; in the initial population, randomly select two individuals, compare the non-dominated ranks of the two individuals, and put the lower ranking into the matching pool ; If the level is the same, compare the crowding degree distance, and the one with the larger distance is reserved; if the non-dominant level and the crowding degree distance are both the same, then randomly select an individual to retain, and repeat this step until the number of individuals in the matching pool is N/2; Step 6, Crossover: First, randomly select two individuals in the contemporary population as the parent individuals of the crossover operation, perform crossover operation on the genes on the matching chromosomes, generate a pair of new chromosomes, repeat the crossover operation, and form a new generation of populations; Wherein, the contemporary population is the parent population; Step 7: Mutation: Define a mutation operator to replace individual genes with a small probability, and apply the mutation operator to the population to change the genes of some individuals in the population and generate new alleles. The population is recorded as the offspring population; Step 8, merge the parent population in step 6 with the child population obtained in step 7, and the merged population is recorded as the first generation population gen=1, and the population size is N; In step 9, the first generation population obtained in step 8 is used as the parent population, and then the parent population is crossed and mutated to obtain the child population, and then the parent population and the child population in this step are merged to form a population. When the population size is 2N; Step 10, utilize the operation process of step 4 to process the population formed in step 9, select N individuals as the new parent population, and then go through steps 6 and 7 to generate a new child population P _t+1 ; repeat steps 9, to reach the maximum evolutionary algebra gen; Step 11, output the Pareto optimal solution front and parameter matrix, obtain the corresponding decision variable values according to the selected target performance index, that is, the solution of the optimization problem, and select and set components according to each parameter; The power and volume modeling process described in step 1 includes: Calculate the power of the inductor, the power _PL of the inductor is:

Wherein, u _L is the input voltage of the inductor, I _rms is the rms value of the current flowing through the inductor, f _sw is the switching frequency, and _VL is the inductor volume; calculate the coil volume of the inductor; the coil volume V _cl is:

Among them, ω _w is the winding width, and d _w is the winding depth; Calculate the conductor volume V _cd as: V _cd =k _pf V _cl , where k _pf is the filling factor of the coil,

N is the number of turns of the coil,

is the conductor cross-sectional area, Calculate core volume

for:

Then the inductor volume _VL is:

Among them, l represents the length of the magnetic core; Calculate the on-state loss of the switch IGBT as:

Among them, V _GE is the threshold voltage of the IGBT, I _IGBT is the amplitude of the current flowing through the IGBT, r _CE is the on-state equivalent resistance, M is the modulation ratio,

Expressed as the voltage and current phase angle; The switching losses of the IGBT are:

Among them, E _sw(on) and E _sw(off) are the energy lost by the turn-on and turn-off of the IGBT respectively, I _N is the rated working current of the rectifier, u _CEN is the rated working voltage, and u _pn is the output voltage of the rectifier; Calculate the total loss of IGBT as: P _IGBT =P _{cond, IGBT} +P _{sw, IGBT} ; The conduction loss of the diode is: P _{on, Diode} = V _F I _F D Among them, V _F is the forward conduction voltage drop of the diode, _IF is the forward conduction current, D is the duty cycle, and the duty cycle of different diodes is calculated according to the four conduction circuit states; The off-state loss of the diode is: P _{off, Diode} = V _R I _R (1-D) Among them, _VR is the reverse voltage drop, _IR is the diode reverse leakage current; The switching losses of the diode are:

where V _fp and V _rp are the forward and reverse peak voltages of the diode, respectively, I _fp and I _rp are the forward and reverse peak currents flowing through the diode, respectively, t _fp is the forward recovery time, and t _b is Its reverse current fall time; Then the total loss of the diode is: P _Diode =P _on,Diode +P _off,Diode +P _sw,Diode ; The specific process of defining the objective function described in step 2 includes: Define the objective function, taking the efficiency and power density of the Swiss rectifier as the objective function, and the efficiency η is:

Among them, P ₀ is the output power, P _L is the inductance loss, and the power density ρ is:

Among them, P ₀ is the output power, P _loss is the total loss, P _IGBT is the IGBT total loss, P _Diode is the Diode total loss; V _total is the total volume of components, _VL is the inductor volume, V _IGBT is the IGBT volume, and V _Diode is the diode volume, V _C is the output capacitor volume, and the power density ρ is the objective function. 2. according to the described optimization design method of claim 1, it is characterized in that, the concrete process of judging the quality of solution and sorting described in step 4 comprises: Step 1: Select the individual whose n _i is 0 in the population, that is, the non-dominated optimal individual, and put it into the set F ₁ ; Step ₂ : For each individual i in the set F1, find out the dominant individual set S _i corresponding to _i respectively, and for the individual j in Si, reduce the number n _j of all individuals dominating individual j in the population. One operation, namely n _j =n _j -1, excludes the influence of individual i dominating j, if n _j is 0, put individual j into the set F ₂ ; Then the set F ₁ is the first-level non-dominated set, and the number of non-dominated layers of all individuals in F ₁ is recorded as Rank1, and the individuals in F ₂ are recorded as Rank2; Step 3: Repeat the operations of Step 1 and Step 2 to sort all individuals in the population non-dominated. The number of non-dominated layers is from low to high. The smaller the Rank value, the better. In the iterative process of the NSGA-II algorithm, the population size is always N, so in the selection operation, the individuals in the same Rank layer need to be selected, and the crowding degree distance C is defined, that is, the adjacent two individuals are on each sub-objective function. and have, C _k =(f _k+1,1 -f _k-1,1 )+(f _k-1,2 -f _k+1,2 ), where k is the solution set Any point in the frontier, f _k+1,1 , f _k-1,1 , f _k-1,2 and f _k+1,2 are represented as (k+1,1), (k-1,1 respectively ), (k-1,2) and (k+1,2) corresponding objective functions; Individuals with a large crowding degree distance are better than individuals with a small crowding degree distance. The number of non-dominated layers and the distance of crowding degree are used as the last two elements of the decision vector, and the quality of the solution and the sorting operation are judged by the number of non-dominated layers and the distance of crowding degree. .

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