CN112968474A - Multi-target optimization method for photovoltaic off-grid inverter system - Google Patents

Abstract

The invention provides a multi-target optimization method for a photovoltaic off-grid inverter system, and belongs to the technical field of power electronics. The method comprises the following steps: establishing a multi-objective optimization model 1 by taking efficiency, power density, special cost and switch tube predicted service life maximization as objective functions; obtaining a four-dimensional Pareto frontier by utilizing an improved NSGA-III algorithm and normalizing; establishing a multi-objective optimization model 2 by maximizing technical advantages and profits; obtaining a two-dimensional Pareto front edge after rapid non-dominant sorting; the embodiment is selected as desired. The multi-target optimization method can not only quickly obtain the complete Pareto front edge and avoid the loss of the optimal solution, but also comprehensively evaluate the performance of different targets in the system, is more practical, and can effectively solve the problem that the four-dimensional target Pareto front edge is not visible, thereby being convenient for visually comparing the performance of different targets.

Description

Multi-target optimization method for photovoltaic off-grid inverter system

Technical Field

The invention belongs to the technical field of power electronics, relates to a multi-target optimization method of a photovoltaic off-grid inverter system, and particularly relates to a multi-target optimization method of a photovoltaic off-grid inverter system based on an improved NSGA-III algorithm.

Background

Solar energy is more and more focused and valued by people due to the influence of global energy crisis and climate warming. The performance of the photovoltaic inverter, which is used as the core of energy conversion of the photovoltaic power generation system, not only affects whether the whole photovoltaic power generation system can operate efficiently, stably, safely and reliably, but also is a main factor for determining the service life of the whole system. In recent years, the conversion efficiency of photovoltaic inverter systems has increased to over 98%, and on this basis, higher power density, system life, and lower cost are strongly sought after.

However, the performance indexes of the photovoltaic inverter are often conflicting with each other and cannot satisfy all the best performance indexes at the same time, so that the performance indexes need to be well balanced, conflicts are resolved, and a set of Pareto optimal solutions are found. Various solutions have been proposed for this purpose by many experts:

an article entitled "Multi objective optical Design of Photonic synchronous synthetic synchronous-us Boost Association, Reliability, and Cost Sav-ins" (G.Adinolfi, G.Gradii, P.Sino and A.Piccolo, IEEE Transa-fractions on Industrial information, vol.11, No.5, pp.1038-1048, Oct.2015) (Multi-objective optimization Design in Photovoltaic synchronous Boost Converters on Efficiency, Reliability and Cost savings G.Adinolfi, G.Gradii, P.Sino and A.Piccolo, IEEE Industrial information report, vol.5, vol.1038, 1048) uses NSGA-II algorithm to find the Efficiency, Reliability, Cost of the system, thereby obtaining the Reliability-Efficiency optimization of the three indexes. However, this solution has the following disadvantages:

1) vital volume indicators in the system are not considered;

2) the reliability of the system is evaluated only through an MIL-HDBK-217 handbook, and the method is simple and rough;

in the 'NSGA-III-based UPFC addressing and capacity multi-target configuration method' disclosed in 2018, 10, 12 and 8, CN105243432B, the installation position and capacity of the UPFC are optimized by adopting an NSGA-III algorithm, so that a Pareto frontier corresponding to an optimization target is obtained. However, this solution has the following disadvantages:

1) randomly generating an initial population, so that the convergence speed of the front edge of the Pareto is slowed down, and the optimal solution of the Pareto can be lost;

2) the influence of different coding modes on the convergence speed of the Pareto frontier is not eliminated;

3) only the Pareto frontier is obtained, and when the optimization target is larger than 3, the problem that the Pareto frontier is not visualized at the moment cannot be solved, and the performance of different optimization targets cannot be intuitively balanced.

Disclosure of Invention

The invention provides a multi-target optimization method of a photovoltaic off-grid inverter system based on an improved NSGA-III algorithm by adopting the NSGA-III algorithm, aiming at the defects that the existing multi-target optimization method of a photovoltaic inverter is few in performance index, simple in partial performance calculation and influenced by an initial population and a coding mode in the NSGA-III algorithm convergence speed, and the problems in the prior art are solved.

The invention aims to realize the purpose, and provides a multi-target optimization method of a photovoltaic off-grid inverter system, wherein the photovoltaic off-grid inverter system comprises a direct-current voltage source, a three-phase three-level ANPC inverter circuit, a filter circuit and a load;

the three-phase three-level ANPC inverter circuit comprises two same supporting capacitors and an inverter main circuit, wherein the two supporting capacitors are respectively recorded as supporting capacitors Cap₁And a support capacitor Cap₂Supporting capacitance Cap₁And a support capacitor Cap₂After being connected in series, the capacitor is connected between a direct current positive bus P and a direct current negative bus E of a direct current voltage source₁And a support capacitor Cap₂The connecting point of the D-type bus is marked as a direct current bus midpoint O;

the main inverter circuit comprises an A-phase bridge arm, a B-phase bridge arm and a C-phase bridge arm, each phase of bridge arm comprises 6 switching tubes with anti-parallel diodes, namely the main inverter circuit comprises 18 switching tubes with anti-parallel diodes in total, and the 18 switching tubes with the anti-parallel diodes are marked as switching tubes S_ij18 anti-parallel diodes are marked as diodes D_ijWhere i denotes three phases, i ═ a, b, c, j denote serial numbers of switching tubes and diodes, and j ═ 1, 2, 3, 4, 5, 6; the A-phase bridge arm, the B-phase bridge arm and the C-phase bridge arm are mutually connected in parallel between a direct current positive bus P and a direct current negative bus E; in IIIIn each phase arm of the phase arm, a switching tube S_i1Switch tube S_i2Switch tube S_i3Switch tube S_i4Are sequentially connected in series, and switch tube S_i1The input end of the switch tube is connected with a direct current positive bus P and a switch tube S_i1The output end of the switch tube S_i2Of the input terminal, switching tube S_i2The output end of the switch tube S_i3Of the input terminal, switching tube S_i3The output end of the switch tube S_i4Of the input terminal, switching tube S_i4The output end of the switch tube is connected with a direct current negative bus E and a switch tube S_i5Is connected with the switch tube S_i1Of the output terminal, switching tube S_i5The output end of the switch tube S is connected with a DC bus midpoint O and a switching tube S_i6The input end of the switch tube S is connected with a DC bus midpoint O and a switching tube S_i6The output end of the switch tube S_i3Of the output terminal, switching tube S_i2And a switching tube S_i3Is recorded as the inverter output point phi_i(ii) a Switch tube S_i1Switch tube S_i4Switch tube S_i5And a switching tube S_i6A power frequency switch tube with the same switching frequency, a switch tube S_i2And a switching tube S_i3The switching tubes are high-frequency switching tubes and have the same switching frequency;

the filter circuit comprises a three-phase filter inductor L and a three-phase filter capacitor C₀One end of the three-phase inductance filter L is connected with an output point phi of the inverter_iThe other end is connected with a load and a three-phase filter capacitor C₀The three-phase filter inductor L is connected between the three-phase filter inductor L and a load in parallel;

the multi-target optimization method is based on an improved NSGA-III algorithm to carry out multi-target optimization on the photovoltaic off-grid inverter system, and comprises the following specific steps:

step 1, establishing a multi-objective optimization model of the first step

Recording a photovoltaic off-grid inverter system as a system, and setting the loss, volume and purchase cost of five capacitors in the system to be ignored;

the setting system meets the following constraint conditions:

wherein, T_j，T2Is a switch tube S_a2Average junction temperature, T, at steady operation_j，maxIs a switch tube S_a2Sustainable maximum junction temperature, T_coreFor stabilizing the operating temperature, T, of the magnetic core of the three-phase filter inductor L_core，maxThe maximum temperature that the magnetic core of the three-phase filter inductor L can bear;

based on the above settings and constraints, with the efficiency f of the system₁Power density f of the system₂Specific cost f of the system₃Switch tube S in system_a2Predicted life of f₄Aiming at the goal, establishing a multi-objective optimization model of the first step, wherein the specific expression is as follows:

in the formula, P_TThe total loss, P, of 18 switching tubes and 18 anti-parallel diodes in the system_LIs the loss of three-phase filter inductance L in the system, P_WFor rated input power of the system, V_TThe total volume of 18 switch tubes and 18 anti-parallel diodes in the system, V_LIs the magnetic core volume of a single-phase filter inductor in a three-phase filter inductor L in a system, Cost_TCost for purchasing 18 switch tubes and 18 anti-parallel diodes in the system, Cost_LFor the purchase cost of the three-phase filter inductor L in the system, f_swIs the switching frequency, Nc, of the high-frequency switching tube_gFor switching tube S in the g-th switching period_a2Number of cycles of (Nf)_gFor switching tube S in the g-th switching period_a2G 1, 2, g_maxAnd g is_maxIs the maximum cycle number of the switching cycle;

will f is₁、f₂、f₃、f₄Is recorded as a first step optimization goal f_ψ，ψ＝1，2，3，4；

Step 2, solving the multi-objective optimization model of the first step by using the improved NSGA-III algorithm

In the step 2.1, the method comprises the following steps of,setting parameters, including: population size Pop, evolution algebra ζ, ζ 0, 1, 2_max，ζ_maxIs the maximum evolution algebra;

initializing zeta 0;

step 2.2, generating excellent initial parent population S by adopting different coding modes_ζThe population scale is Pop;

the different coding modes comprise binary coding, real number coding, tree coding and quantum bit coding;

generating an excellent initial parent population S_ζThe specific operation is as follows:

firstly, a binary coding mode is adopted to obtain a class of initial parent population Rm¹The population size is 0.5 Pop; obtaining two kinds of initial parent population Rm by adopting a real number coding mode²The population size is 0.5 Pop; obtaining three types of initial parent population Rm by adopting a tree type coding mode³The population size is 0.5 Pop; four kinds of initial parent population Rm are obtained by adopting a quantum bit coding mode⁴The population size is 0.5 Pop;

then starting a parent population Rm from the parallel_all＝Rm¹∪Rm²∪Rm³∪Rm⁴In the selection of Pop individuals into an excellent initial parent population S_ζ(ii) a The selecting operation specifically comprises the following steps:

(a) computing parallel initial parent population Rm_allMaximum value of each objective function in

(b) Computing and comparing parallel initial parent population Rm_allSpecific distance of middle body

Individuals with smaller special distance are stored preferentially;

step 2.3, obtaining the filial generation population P through genetic operation operators_ζThe population scale is Pop;

step 2.4, order the composite population Z_ζ＝S_ζ∪P_ζThe population size is 2Pop, and the involution population Z_ξPerforming fast non-dominant sorting to obtain original non-dominant solution sets Q with different sorting levels_λλ is a ranking level, λ is 1, 2,., 1d, 1d is a critical ranking level, and then a non-dominated solution set K is obtained according to a general constraint domination principle_ζ；

The specific operation of the fast non-dominated sorting is as follows: firstly, a combined population Z is found_ζOriginal non-dominated solution set Q with minimum middle ranking₁Let λ be 1; then the combined population Z_ζOriginal non-dominated solution set Q with medium rank λ of 1₁Removing and finding out the original non-dominant solution set Q with the minimum ranking grade in the rest population₂Let λ be 2; this is done sequentially until a critical sort level 1d is reached; individuals with smaller ranking are stored preferentially;

step 2.5, judge the non-dominated solution set K_ζIf the population size is larger than the population size Pop, entering a step 2.6 if the population size Pop is larger than the population size Pop; otherwise, changing ζ to ζ +1, and returning to the step 2.3;

step 2.6, for non-dominated solution set K_ζPerforming elite reservation operation to obtain new parent population S_ζ+1The population scale is Pop;

step 2.7, judging whether the evolution algebra zeta is larger than the maximum evolution algebra zeta_max：

If yes, outputting a new parent population S_ζ+1Efficiency f of a system with a medium rank λ of 1₁Power density f of the system₂Specific cost f of the system₃Switch tube S in system_a2Predicted life of f₄A four-dimensional Pareto frontier of composition;

otherwise, changing ζ to ζ +1, and returning to the step 2.3;

the four-dimensional Pareto frontier is a set Ma

Wherein the set Mb ═ f_ψ]，δ₁The number of sets Mb;

step 3, carrying out normalization operation on the four-dimensional Pareto front edge to obtain a normalized four-dimensional Pareto front edge, wherein the specific expression is as follows:

in the formula (I), the compound is shown in the specification,

Ga_ψfor corresponding f in any set Mb in the four-dimensional Pareto frontier_ψThe value of the one or more of,

is corresponding to f in any set Mb in the four-dimensional Pareto frontier_ψThe minimum value of the values is such that,

is corresponding to f in any set Mb in the four-dimensional Pareto frontier_ψThe maximum value of the value;

F_ψfor normalized data, include: efficiency of the normalized System F₁Normalized power density of the system F₂Normalized special cost of the system F₃Normalized switching tube S in the system_a2Predicted life F of₄；

Step 4, establishing the multi-objective optimization model of the second step

Let the technical advantage of the system be Y₁And the profit of the system is recorded as Y₂To maximize Y₁-Y₂Establishing a second-step multi-objective optimization model for the target, wherein the specific expression is as follows:

in the formula, w₁To normalize the efficiency F of the system₁Occupied weight coefficient, w₂For normalizing the power density F of the system₂Occupied weight coefficient, w₃For switching tubes S in the normalized system_a2Predicted life F of₄The occupied weight coefficient;

step 5, according to the fast non-dominated sorting method described in step 2.4, the result of step 4 is obtainedTechnical advantage Y of the system to₁And profit Y of the system₂Technical advantage Y of system for performing rapid non-dominated sorting on two-dimensional targets and outputting sorting level lambda of 1₁And profit Y of the system₂A two-dimensional Pareto front; the two-dimensional Pareto frontier is a set Mc, a set

Wherein the set Md ═ Y₁，Y₂]，δ₂The number of the sets Md;

and 6, selecting a set Md from the two-dimensional Pareto frontier as a final implementation scheme according to needs.

Preferably, the genetic operators in step 2 include selection, crossover and mutation operations, and the different coding modes implement the corresponding conventional genetic operators; the selection operation means that individuals more suitable for the environment have more opportunity to be inherited to the next generation; the cross operation refers to generating a new individual through the cross combination of chromosomes; the mutation operation refers to selecting one individual from the population, and making a segment of the code of the individual have mutation so as to generate more excellent individuals.

Preferably, the elite reservation operation in step 2 is: set K of non-dominant solutions_ζIndividuals with a medium ranking of 1 to (1d-1) are placed into a new parent population S_ζ+1And from the original non-dominated solution set Q based on the method of the reference point_ldContinuously selecting individuals and putting the individuals into a new parent population S_ζ+1Until the new parent population S_ζ+1The population size of (a) is Pop; the method based on the reference point specifically comprises the following steps:

(a) computing a non-dominated solution set K_ζMinimum value of each objective function in

(b) Computing a non-dominated solution set K_ζOf each target function on-axis intercept of y'_ψAnd adaptive to the objective function

(c) According to f'_ψSetting a reference point Z on a normalized hypercube^r；

(d) According to reference point Z^rDefining a reference line H_sComputing a non-dominated solution set K_ζIndividuals with a medium rank λ of 1 to (1d-1) and a reference point Z^rThe number of associations is denoted as J_s(ii) a The association means that the individual is associated with a reference point when the individual is closest to the reference line;

(e) until there is a reference point Z^rAnd original non-dominated solution set Q_ldIs associated with the middle individual, if J is present_sIf 0, then select the original non-dominated solution set Q_ldPutting the individuals closest to the reference point Zr in the new parent population S_ζ+1Performing the following steps; otherwise in the original non-dominated solution set Q_ldRandomly selecting individuals and putting the individuals into a new parent population S_ζ+1In (1).

Compared with the prior art, the invention has the beneficial effects that:

(1) the invention takes the efficiency f of the system into account₁Power density f of the system₂Specific cost f of the system₃And a switch tube S in the system_a2Predicted life of f₄The performance of the system is evaluated more comprehensively and objectively by four targets, and the system is more in line with the actual situation;

(2) the improved NSGA-III algorithm provided by the invention effectively eliminates the influence of the initial population and the coding mode on the convergence speed of the Pareto frontier, and simultaneously avoids the loss of the Pareto optimal solution;

(3) the two-step optimization model provided by the invention effectively avoids the problem that the four-dimensional Pareto front is not visible, and is convenient for intuitively balancing the conflict between the technical advantages and profits of the system in the two-dimensional Pareto front.

Drawings

Fig. 1 is a topology diagram of a photovoltaic off-grid inverter system in an embodiment of the invention;

FIG. 2 is a topology diagram of the inverter main circuit according to the embodiment of the present invention;

FIG. 3 is a schematic diagram of the multi-target optimization method of the present invention;

FIG. 4 is a flow chart of the multi-target optimization method of the present invention;

FIG. 5 is a normalized system optimization objective F according to an embodiment of the present invention₁-F₂-F₃-F₄A four-dimensional Pareto leading edge schematic diagram is formed;

FIG. 6 is a second step of optimizing the target Y in the embodiment of the present invention₁-Y₂Schematic diagram of the formed two-dimensional Pareto frontier.

Detailed Description

The present invention will be described in detail below with reference to the accompanying drawings.

The invention selects the photovoltaic off-grid inverter system circuit shown in fig. 1 and fig. 2 as a topology structure for case implementation. As can be seen from fig. 1 and 2, the photovoltaic off-grid inverter system includes a dc voltage source 10, a three-phase three-level ANPC inverter circuit 20, a filter circuit 30 and a load 40.

The three-phase three-level ANPC inverter circuit 20 comprises two same support capacitors and an inverter main circuit, wherein the two support capacitors are respectively recorded as support capacitors Cap₁And a support capacitor Cap₂Supporting capacitance Cap₁And a support capacitor Cap₂Connected in series between a positive DC bus P and a negative DC bus E of a DC voltage source 10, and supporting a capacitor Cap₁And a support capacitor Cap₂The connection point of (a) is denoted as the dc bus midpoint O.

The main inverter circuit comprises an A-phase bridge arm, a B-phase bridge arm and a C-phase bridge arm, each phase of bridge arm comprises 6 switching tubes with anti-parallel diodes, namely the main inverter circuit comprises 18 switching tubes with anti-parallel diodes in total, and the 18 switching tubes with the anti-parallel diodes are marked as switching tubes S_ij18 anti-parallel diodes are marked as diodes D_ijWhere i denotes three phases, i ═ a, b, c, j denote serial numbers of switching tubes and diodes, and j ═ 1, 2, 3, 4, 5, 6; the A-phase bridge arm, the B-phase bridge arm and the C-phase bridge arm are mutually connected in parallel between a direct current positive bus P and a direct current negative bus E; in each of the three-phase arms, a switching tube S_i1Switch tube S_i2Switch tube S_i3Switch tube S_i4Are sequentially connected in series, and switch tube S_i1The input end of the switch tube is connected with a direct current positive bus PS_i1The output end of the switch tube S_i2Of the input terminal, switching tube S_i2The output end of the switch tube S_i3Of the input terminal, switching tube S_i3The output end of the switch tube S_i4Of the input terminal, switching tube S_i4The output end of the switch tube is connected with a direct current negative bus E and a switch tube S_i5Is connected with the switch tube S_i1Of the output terminal, switching tube S_i5The output end of the switch tube S is connected with a DC bus midpoint O and a switching tube S_i6The input end of the switch tube S is connected with a DC bus midpoint O and a switching tube S_i6The output end of the switch tube S_i3Of the output terminal, switching tube S_i2And a switching tube S_i3Is recorded as the inverter output point phi_i(ii) a Switch tube S_i1Switch tube S_i4Switch tube S_i5And a switching tube S_i6A power frequency switch tube with the same switching frequency, a switch tube S_i2And a switching tube S_i3The switch tubes are high-frequency switch tubes and the switch frequency is the same.

The filter circuit 30 includes a three-phase filter inductor L and a three-phase filter capacitor C₀One end of the three-phase inductor L is connected with an output point phi of the inverter_iThe other end is connected with a load 40 and a three-phase filter capacitor C₀Connected in parallel between the three-phase filter inductor L and the load 40.

Fig. 3 is a schematic diagram of the multi-target optimization method of the present invention, fig. 4 is a flowchart of the multi-target optimization method of the present invention, as can be seen from fig. 3 and fig. 4, the multi-target optimization method of the present invention performs multi-target optimization on a photovoltaic off-grid inverter system based on an improved NSGA-III algorithm, and the specific steps are as follows:

step 1, establishing a multi-objective optimization model of the first step

Recording a photovoltaic off-grid inverter system as a system, and setting the loss, volume and purchase cost of five capacitors in the system to be ignored;

the setting system meets the following constraint conditions:

wherein, T_j，T2For switching tubesS_a2Average junction temperature, T, at steady operation_j，maxIs a switch tube S_a2Sustainable maximum junction temperature, T_coreFor stabilizing the operating temperature, T, of the magnetic core of the three-phase filter inductor L_core，maxThe maximum temperature that the magnetic core of the three-phase filter inductor L can bear.

Based on the above settings and constraints, with the efficiency f of the system₁Power density f of the system₂Specific cost f of the system₃Switch tube S in system_a2Predicted life of f₄Aiming at the goal, establishing a multi-objective optimization model of the first step, wherein the specific expression is as follows:

in the formula, P_TThe total loss, P, of 18 switching tubes and 18 anti-parallel diodes in the system_LIs the loss of three-phase filter inductance L in the system, P_wFor rated input power of the system, V_TThe total volume of 18 switch tubes and 18 anti-parallel diodes in the system, V_LIs the magnetic core volume of a single-phase filter inductor in a three-phase filter inductor L in a system, Cost_TCost for purchasing 18 switch tubes and 18 anti-parallel diodes in the system, Cost_LFor the purchase cost of the three-phase filter inductor L in the system, f_swIs the switching frequency, Nc, of the high-frequency switching tube_gFor switching tube S in the g-th switching period_a2Number of cycles of (Nf)_gFor switching tube S in the g-th switching period_a2G 1, 2, g_maxAnd g is_maxIs the maximum number of cycles of the switching cycle.

Will f is₁、f₂、f₃、f₄Is recorded as a first step optimization goal f_ψ，ψ＝1，2，3，4。

In this embodiment, take T_j，maxTaking T at 175 DEG C_core，max＝150℃。

Step 2, solving the multi-objective optimization model of the first step by using the improved NSGA-III algorithm

Step 2.1, setting parameters, including: population size Pop, evolution algebra ζ, ζ 0, 1, 2_max，ζ_maxIs the maximum evolution algebra;

initialization ζ is 0.

Step 2.2, generating excellent initial parent population S by adopting different coding modes_ζThe population size is Pop.

The different encoding modes comprise binary encoding, real number encoding, tree encoding and quantum bit encoding.

Generating an excellent initial parent population S_ζThe specific operation is as follows:

firstly, a binary coding mode is adopted to obtain a class of initial parent population Rm¹The population size is 0.5 Pop; obtaining two kinds of initial parent population Rm by adopting a real number coding mode²The population size is 0.5 Pop; obtaining three types of initial parent population Rm by adopting a tree type coding mode³The population size is 0.5 Pop; four kinds of initial parent population Rm are obtained by adopting a quantum bit coding mode⁴The population size is 0.5 Pop;

then starting a parent population Rm from the parallel_all＝Rm¹∪Rm²∪Rm³∪Rm⁴In the selection of Pop individuals into an excellent initial parent population S_ζ(ii) a The selecting operation specifically comprises the following steps:

(a) computing parallel initial parent population Rm_allMaximum value of each objective function in

(b) Computing and comparing parallel initial parent population Rm_allSpecific distance of middle body

Individuals with smaller specific distances are preferentially kept.

Step 2.3, obtaining the filial generation population P through genetic operation operators_ζThe population size is Pop.

The genetic operation operators comprise selection, crossing and mutation operations, and the conventional genetic operation operators corresponding to the genetic operation operators are implemented in different coding modes; the selection operation means that individuals more suitable for the environment have more opportunity to be inherited to the next generation; the cross operation refers to generating a new individual through the cross combination of chromosomes; the mutation operation refers to selecting one individual from the population, and making a segment of the code of the individual have mutation so as to generate more excellent individuals.

Step 2.4, order the composite population Z_ζ＝S_ζ∪P_ζThe population size is 2Pop, and the involution population Z_ζPerforming fast non-dominant sorting to obtain original non-dominant solution sets Q with different sorting levels_λλ is a ranking level, λ is 1, 2,., 1d, 1d is a critical ranking level, and then a non-dominated solution set K is obtained according to a general constraint domination principle_ζ；

The specific operation of the fast non-dominated sorting is as follows: firstly, a combined population Z is found_ζOriginal non-dominated solution set Q with minimum middle ranking₁Let λ be 1; then the combined population Z_ζOriginal non-dominated solution set Q with medium rank λ of 1₁Removing and finding out the original non-dominant solution set Q with the minimum ranking grade in the rest population₂Let λ be 2; this is done sequentially until a critical sort level 1d is reached; individuals with smaller rank are saved preferentially.

Step 2.5, judge the non-dominated solution set K_ζIf the population size is larger than the population size Pop, entering a step 2.6 if the population size Pop is larger than the population size Pop; otherwise, let ζ be ζ +1 and return to step 2.3.

Step 2.6, for non-dominated solution set K_ζPerforming elite reservation operation to obtain new parent population S_ζ+1The population size is Pop.

The elite reservation operation is as follows: set K of non-dominant solutions_ζIndividuals with a medium ranking of 1 to (1d-1) are placed into a new parent population S_ζ+1And from the original non-dominated solution set Q based on the method of the reference point_ldContinuously selecting individuals and putting the individuals into a new parent population S_ζ+1Until the new parent population S_ζ+1The population size of (a) is Pop; the method based on the reference point specifically comprises the following steps:

(a) computing a non-dominated solution set K_ζMinimum value of each objective function in

(b) Computing a non-dominated solution set K_ζOf each target function on-axis intercept of y'_ψAnd adaptive to the objective function

(c) According to f'_ψSetting a reference point Z on a normalized hypercube^r；

(d) According to reference point Z^rDefining a reference line H_sComputing a non-dominated solution set K_ζIndividuals with a medium rank λ of 1 to (1d-1) and a reference point Z^rThe number of associations is denoted as J_s(ii) a The association means that the individual is associated with a reference point when the individual is closest to the reference line;

(e) until there is a reference point Z^rAnd original non-dominated solution set Q_ldIs associated with the middle individual, if J is present_sIf 0, then select the original non-dominated solution set Q_ldMiddle distance reference point Z^rRecent individuals are placed in a new parent population S_ζ+1Performing the following steps; otherwise in the original non-dominated solution set Q_ldRandomly selecting individuals and putting the individuals into a new parent population S_ζ+1In (1).

Step 2.7, judging whether the evolution algebra zeta is larger than the maximum evolution algebra zeta_max：

If yes, outputting a new parent population S_ζ+1Efficiency f of a system with a medium rank λ of 1₁Power density f of the system₂Specific cost f of the system₃Switch tube S in system_a2Predicted life of f₄A four-dimensional Pareto frontier of composition; otherwise, let ζ be ζ +1 and return to step 2.3.

The four-dimensional Pareto frontier is a set Ma

Therein collectionTotal Mb ═ f_ψ]，δ₁The number of sets Mb.

Step 3, carrying out normalization operation on the four-dimensional Pareto front edge to obtain a normalized four-dimensional Pareto front edge, wherein the specific expression is as follows:

in the formula (I), the compound is shown in the specification,

Ga_ψfor corresponding f in any set Mb in the four-dimensional Pareto frontier_ψThe value of the one or more of,

is corresponding to f in any set Mb in the four-dimensional Pareto frontier_ψThe minimum value of the values is such that,

is corresponding to f in any set Mb in the four-dimensional Pareto frontier_ψThe maximum value of the value.

F_ψFor normalized data, include: efficiency of the normalized System F₁Normalized power density of the system F₂Normalized special cost of the system F₃Normalized switching tube S in the system_a2Predicted life F of₄。

FIG. 5 is a normalized system optimization objective F according to an embodiment of the present invention₁-F₂-F₃-F₄And (3) forming a four-dimensional Pareto leading edge schematic diagram.

Step 4, establishing the multi-objective optimization model of the second step

Let the technical advantage of the system be Y₁And the profit of the system is recorded as Y₂To maximize Y₁-Y₂Establishing a second-step multi-objective optimization model for the target, wherein the specific expression is as follows:

in the formula, w₁To normalize the efficiency F of the system₁Occupied weight coefficient, w₂For normalizing the power density F of the system₂Occupied weight coefficient, w₃For switching tubes S in the normalized system_a2Predicted life F of₄The occupied weight coefficient.

Step 5, according to the fast non-dominated sorting method described in step 2.4, the technical advantage Y of the system obtained in step 4 is₁And profit Y of the system₂Technical advantage Y of system for performing rapid non-dominated sorting on two-dimensional targets and outputting sorting level lambda of 1₁And profit Y of the system₂A two-dimensional Pareto front;

the two-dimensional Pareto frontier is a set Mc, a set

Wherein the set Md ═ Y₁，Y₂]，δ₂The number of sets Md.

FIG. 6 is a second step of the system optimization objective Y in the embodiment of the present invention₁-Y₂Schematic diagram of the formed two-dimensional Pareto frontier.

And 6, selecting a set Md from the two-dimensional Pareto frontier as a final implementation scheme according to needs.

In this embodiment, the efficiency f to the system₁Power density f of the system₂Specific cost f of the system₃Switch tube S in system_a2Predicted life of f₄Some of the parameters in (1) are selected and calculated as follows.

In the present embodiment, the magnetic core of the three-phase filter inductor L is composed of an amorphous ring, and the purchase Cost of the three-phase filter inductor L is_LIs obtained by the following formula:

Cost_L＝λa₁ρV_L+6λa₂(A_wai-B_nei+C_hou)Num

in the formula, λ a₁For the purchase cost per unit mass of the magnetic core of the single inductor in the three-phase filter inductor L, $ 28/kg is taken, and rho is the material density of the magnetic core of the single inductor in the three-phase filter inductor LTaking 7.8 g/cubic centimeter, lambda a₂The purchase cost per unit length of the windings of the single inductor in the three-phase filter inductor L is $ 6.2/meter.

In this embodiment, the temperature T of the magnetic core of the three-phase filter inductor L during stable operation_coreIs obtained by the following formula:

in the embodiment, the system adopts bipolar SPWM modulation, and the power factor is 1, the total loss P of 18 switching tubes and 18 anti-parallel diodes_TIs obtained by the following formula:

in the formula, P_IGBTFor conduction losses, P, of all single-phase mains-frequency switching tubes in the system_MOSFor conduction losses and switching losses, P, of all high-frequency switching tubes of a single phase in the system_diodeThe conduction loss of all anti-parallel diodes in a single phase in the system, alpha is an integral independent variable, I is a switch tube S_ijThe current flowing when conducting is taken

Ampere, V_ceTaking V as collector-emitter voltage of power frequency switch tube in system_ce0.00618I + 0.85V, R_dsonTaking R as the on-resistance of a high-frequency switch tube in the system_dson0.0062+0.0009logI ohm, D is duty ratio, and D is 0.9sin alpha, T_deadThe dead time of a high-frequency switch tube in the system is 4.26 multiplied by 10^-7Second, E_{on_nom}Selecting 2.02X 10 to obtain the turn-on loss of high-frequency switch tube under standard test condition^-3Joule, E_{off_nom}The turn-off loss of the high-frequency switch tube in the system under the standard test condition is 1.28 multiplied by 10^-3Joule, I_nomThe conduction current of a high-frequency switch tube in a system under a standard test condition is 100 amperes and V_dstestThe voltage born by the two ends of the drain electrode and the source electrode under the standard test condition is 600V_dsThe voltage at two ends of the DC voltage source is 1200V_diodeTaking V as the voltage at two ends of all anti-parallel diodes in a single phase in the system_diode0.0169I +0.8249 volts.

In the present embodiment, the magnetic core of the selected three-phase filter inductor L is composed of an amorphous ring, and the loss P of the three-phase filter inductor L is_LIs obtained by the following formula:

P_L＝3(P_cop+P_core)

in the formula, P_copFor the winding loss, P, of a single inductor in the three-phase filter inductor L_coreThe magnetic core loss of a single inductor in the three-phase filter inductor L is respectively obtained by the following formula:

winding loss P of single inductor in three-phase filter inductor L_copIs obtained by the following formula:

in the formula, La is the inductance value of the three-phase filter inductor L, I_maxIs a switch tube S_ijThe maximum value of the current flowing during conduction is taken

Ampere, m is modulation degree, 0.9, gamma is taken_cTaking 10% -20% as current ripple factor, step length is 1%, A_waiThe outer diameter of the magnetic core of a single inductor in the three-phase filter inductor L, B_neiInner diameter of magnetic core of single inductor in three-phase filter inductor L, C_houHeight, k, of the core of a single inductor in a three-phase filter inductor L_uTaking any one value of 0.3, 0.35, 0.4 and 0.45, B, for the window utilization rate of a single inductor in the three-phase filter inductor L_maxThe maximum magnetic flux density of a single inductor in the three-phase filter inductor L is any one value of 1.0, 1.1, 1.2 and 1.3, J_CuThe current density of the winding of a single inductor in the three-phase filter inductor L is 5 amperes/square millimeter, A_dFor selected commercial individual inductorsThe reference outer diameter of the magnetic core is 10.2 cm, B_dReference inner diameter of 5.7 cm, C for selected commercial single inductor core_dThe selected reference height of the commercial single inductance magnetic core is 3.3 cm, Num is the number of turns of a winding of a single inductance in the three-phase filter inductance L, rouw is the resistivity of the winding of the single inductance in the three-phase filter inductance L, and 2.3 multiplied by 10 is taken^-8Ohm x meter, R_LThe resistance of the winding of a single inductor in the three-phase filter inductor L.

Magnetic core loss P of single inductor in three-phase filter inductor L_coreIs obtained by the following formula:

in the formula I_cAverage magnetic path length L of magnetic core of single inductor in three-phase filter inductor L_gThe length of the air gap u of the magnetic core of a single inductor in the three-phase filter inductor L₀For the magnetic permeability in vacuum, take 4 π × 10^-7Tesla x meter/ampere, u_rFor the relative permeability of the magnetic core of a single inductor in the three-phase filter inductor L, 15600 and B are taken_mActual magnetic induction, K, of the magnetic core of a single inductor in a three-phase filter inductor L_cAnd alpha r and beta r are material constants of a magnetic core of a single inductor in the three-phase filter inductor L, and K is taken_c＝40.43，αr＝1.21，βr＝1.88。

In this embodiment, the switching tube S in the g-th switching period_a2Number of cycles Nc_gAnd switching tube S in the g-th switching period_a2Number of failure cycles Nf_gObtained by the following calculation:

(a) computing the g-th switching period of the switching tube S_a2Temperature difference T from chip to substrate_j，T2(g)：

In the formula, P_MOS(g)For switching tube S in the g-th switching period_a2Is lost, isConduction loss and switching loss P of all single-phase high-frequency switching tubes in system_MOSThe method is obtained by discretization, and the method comprises the following steps of,

is a switch tube S_a2Chip to supply switch tube S_a2Theta order thermal resistance of heat sink for heat dissipation, where theta is 1, 2, 3, 4, and R is taken_{th_jh1}0.0124 kelvin/watt, R_{th_jh2}0.0434 kelvin/watt, R_{th_jh3}0.0677 kelvin/watt, R_{th_jh4}0.107 kelvin/watt, Tsw is the switching period, τ_θIs a switch tube S_a2Chip to supply switch tube S_a2Theta-th order thermal time constant of heat sink₁4.44 seconds,. tau₂1.03 seconds,. tau₃0.199 sec,. tau₄0.0557 sec, T_jh，T2(g-1)For the switching tube S in the (g-1) th switching period_a2Chip to supply switch tube S_a2Temperature difference of heat sink, P_T(g)The total loss P of 18 switching tubes in the g switching period is the total loss P of 18 switching tubes and 18 anti-parallel diodes in the system_TDiscretizing to obtain R_{th_ha}For supplying a switching tube S_a2The heat resistance from the heat sink to the environment is 0.22 Kelvin/watt, and epsilon is given to the switch tube S_a2The thermal time constant from the heat sink to the environment is 10 seconds, T_ha(g-1)For the switching tube S in the (g-1) th switching period_a2Temperature difference from heat sink to ambient, T_aTaking the temperature at 25 ℃ for the ambient temperature;

(b) repeating the operation (a) until g ═ g_maxGet g_max300000, record all T_j，T2(g)A value;

(c) extracting temperature-saving T according to rain flow counting method_j，T2(g)Fluctuation value Δ T of_jAverage value T_mAnd number of cycles Nc_g；

(d) In the g switching period, the switching tube S is calculated_a2Number of failure cycles Nf_g：

Wherein, A 'and n' are experimental fitting data, and A 'is 97.2, n' is 3.129, E_aFor activation energy, 9.89X 10 was taken^-20Joule, k_nIs Boltzmann constant, and takes 1.38 × 10^-23。

Finally, the maximum value of the system technical advantage required, i.e. the top left-most corner points (0.4526, 0.6716) in fig. 6, is selected from the two-dimensional Pareto frontier as the final embodiment.

Claims (3)

1. A multi-target optimization method for a photovoltaic off-grid inverter system comprises a direct-current voltage source (10), a three-phase three-level ANPC inverter circuit (20), a filter circuit (30) and a load (40);

the three-phase three-level ANPC inverter circuit (20) comprises two same supporting capacitors and an inverter main circuit, wherein the two supporting capacitors are respectively recorded as supporting capacitors Cap₁And a support capacitor Cap₂Supporting capacitance Cap₁And a support capacitor Cap₂After being connected in series, the supporting capacitor Cap is connected between a direct current positive bus P and a direct current negative bus E of a direct current voltage source (10)₁And a support capacitor Cap₂The connecting point of the D-type bus is marked as a direct current bus midpoint O;

the main inverter circuit comprises an A-phase bridge arm, a B-phase bridge arm and a C-phase bridge arm, each phase of bridge arm comprises 6 switching tubes with anti-parallel diodes, namely the main inverter circuit comprises 18 switching tubes with anti-parallel diodes in total, and the 18 switching tubes with the anti-parallel diodes are marked as switching tubes S_ij18 anti-parallel diodes are marked as diodes D_ijWhere i denotes three phases, i ═ a, b, c, j denote serial numbers of switching tubes and diodes, and j ═ 1, 2, 3, 4, 5, 6; the A-phase bridge arm, the B-phase bridge arm and the C-phase bridge arm are mutually connected in parallel between a direct current positive bus P and a direct current negative bus E; in each of the three-phase arms, a switching tube S_i1Switch tube S_i2Switch tube S_i3Switch tube S_i4Are sequentially connected in series, and switch tube S_i1The input end of the switch tube is connected with a direct current positive bus P and a switch tube S_i1Is connected to the output terminalSwitch tube S_i2Of the input terminal, switching tube S_i2The output end of the switch tube S_i3Of the input terminal, switching tube S_i3The output end of the switch tube S_i4Of the input terminal, switching tube S_i4The output end of the switch tube is connected with a direct current negative bus E and a switch tube S_i5Is connected with the switch tube S_i1Of the output terminal, switching tube S_i5The output end of the switch tube S is connected with a DC bus midpoint O and a switching tube S_i6The input end of the switch tube S is connected with a DC bus midpoint O and a switching tube S_i6The output end of the switch tube S_i3Of the output terminal, switching tube S_i2And a switching tube S_i3Is recorded as the inverter output point phi_i(ii) a Switch tube S_i1Switch tube S_i4Switch tube S_i5And a switching tube S_i6A power frequency switch tube with the same switching frequency, a switch tube S_i2And a switching tube S_i3The switching tubes are high-frequency switching tubes and have the same switching frequency;

the filter circuit (30) comprises a three-phase filter inductor L and a three-phase filter capacitor C₀One end of the three-phase filter inductor L is connected with the output point phi of the inverter_iThe other end is connected with a load (40) and a three-phase filter capacitor C₀Is connected between the three-phase filter inductor L and the load (40) in parallel;

the method is characterized in that the multi-target optimization method carries out multi-target optimization on a photovoltaic off-grid inverter system based on an improved NSGA-III algorithm, and comprises the following specific steps:

step 1, establishing a multi-objective optimization model of the first step

Recording a photovoltaic off-grid inverter system as a system, and setting the loss, volume and purchase cost of five capacitors in the system to be ignored;

the setting system meets the following constraint conditions:

wherein, T_j，T2Is a switch tube S_a2Average junction temperature, T, at steady operation_j，maxIs a switch tube S_a2Sustainable maximum junction temperature, T_coreFor stabilizing the operating temperature, T, of the magnetic core of the three-phase filter inductor L_core，maxThe maximum temperature that the magnetic core of the three-phase filter inductor L can bear;

based on the above settings and constraints, with the efficiency f of the system₁Power density f of the system₂Specific cost f of the system₃Switch tube S in system_a2Predicted life of f₄Aiming at the goal, establishing a multi-objective optimization model of the first step, wherein the specific expression is as follows:

in the formula, P_TThe total loss, P, of 18 switching tubes and 18 anti-parallel diodes in the system_LIs the loss of three-phase filter inductance L in the system, P_wFor rated input power of the system, V_TThe total volume of 18 switch tubes and 18 anti-parallel diodes in the system, V_LIs the magnetic core volume of a single-phase filter inductor in a three-phase filter inductor L in a system, Cost_TCost for purchasing 18 switch tubes and 18 anti-parallel diodes in the system, Cost_LFor the purchase cost of the three-phase filter inductor L in the system, f_swIs the switching frequency, Nc, of the high-frequency switching tube_gFor switching tube S in the g-th switching period_a2Number of cycles of (Nf)_gFor switching tube S in the g-th switching period_a2G 1, 2, g_maxAnd g is_maxIs the maximum cycle number of the switching cycle;

will f is₁、f₂、f₃、f₄Is recorded as a first step optimization goal f_ψ，ψ＝1，2，3，4；

Step 2, solving the multi-objective optimization model of the first step by using the improved NSGA-III algorithm

Step 2.1, setting parameters, including: population size Pop, evolution algebra ζ, ζ 0, 1, 2_max，ζ_maxIs the maximum evolution algebra;

initializing zeta 0;

step 2.2, generating excellent initial parent population S by adopting different coding modes_ζThe population scale is Pop;

the different coding modes comprise binary coding, real number coding, tree coding and quantum bit coding;

generating an excellent initial parent population S_ζThe specific operation is as follows:

firstly, a binary coding mode is adopted to obtain a class of initial parent population Rm¹The population size is 0.5 Pop; obtaining two kinds of initial parent population Rm by adopting a real number coding mode²The population size is 0.5 Pop; obtaining three types of initial parent population Rm by adopting a tree type coding mode³The population size is 0.5 Pop; four kinds of initial parent population Rm are obtained by adopting a quantum bit coding mode⁴The population size is 0.5 Pop;

then starting a parent population Rm from the parallel_all＝Rm¹∪Rm²∪Rm³∪Rm⁴In the selection of Pop individuals into an excellent initial parent population S_r(ii) a The selecting operation specifically comprises the following steps:

(a) computing parallel initial parent population Rm_allMaximum value of each objective function in

(b) Computing and comparing parallel initial parent population Rm_allSpecific distance of middle body

Individuals with smaller special distance are stored preferentially;

step 2.3, obtaining the filial generation population P through genetic operation operators_ζThe population scale is Pop;

step 2.4, order the composite population Z_ζ＝S_ζ∪P_ζThe population size is 2Pop, and the involution population Z_ζPerforming fast non-dominant sorting to obtain original non-dominant solution sets Q with different sorting levels_λλ is the rank, λ 1, 2.1d and 1d are critical ordering levels, and then a non-dominated solution set K is obtained according to a general constraint domination principle_ζ；

The specific operation of the fast non-dominated sorting is as follows: firstly, a combined population Z is found_ζOriginal non-dominated solution set Q with minimum middle ranking₁Let λ be 1; then the combined population Z_ζOriginal non-dominated solution set Q with medium rank λ of 1₁Removing and finding out the original non-dominant solution set Q with the minimum ranking grade in the rest population₂Let λ be 2; this is done sequentially until a critical sort level 1d is reached; individuals with smaller ranking are stored preferentially;

step 2.5, judge the non-dominated solution set K_ζIf the population size is larger than the population size Pop, entering a step 2.6 if the population size Pop is larger than the population size Pop; otherwise, changing ζ to ζ +1, and returning to the step 2.3;

step 2.6, for non-dominated solution set K_ζPerforming elite reservation operation to obtain new parent population S_ζ+1The population scale is Pop;

step 2.7, judging whether the evolution algebra zeta is larger than the maximum evolution algebra zeta_max：

If yes, outputting a new parent population S_ζ+1Efficiency f of a system with a medium rank λ of 1₁Power density f of the system₂Specific cost f of the system₃Switch tube S in system_a2Predicted life of f₄A four-dimensional Pareto frontier of composition;

otherwise, changing ζ to ζ +1, and returning to the step 2.3;

the four-dimensional Pareto frontier is a set Ma

Wherein the set Mb ═ f_ψ]，δ₁The number of sets Mb;

step 3, carrying out normalization operation on the four-dimensional Pareto front edge to obtain a normalized four-dimensional Pareto front edge, wherein the specific expression is as follows:

in the formula (I), the compound is shown in the specification,

Ga_ψfor corresponding f in any set Mb in the four-dimensional Pareto frontier_ψThe value of the one or more of,

is corresponding to f in any set Mb in the four-dimensional Pareto frontier_ψThe minimum value of the values is such that,

is corresponding to f in any set Mb in the four-dimensional Pareto frontier_ψThe maximum value of the value;

F_ψfor normalized data, include: efficiency of the normalized System F₁Normalized power density of the system F₂Normalized special cost of the system F₃Normalized switching tube S in the system_a2Predicted life F of₄；

Step 4, establishing the multi-objective optimization model of the second step

Let the technical advantage of the system be Y₁And the profit of the system is recorded as Y₂To maximize Y₁-Y₂Establishing a second-step multi-objective optimization model for the target, wherein the specific expression is as follows:

in the formula, w₁To normalize the efficiency F of the system₁Occupied weight coefficient, w₂For normalizing the power density F of the system₂Occupied weight coefficient, w₃For switching tubes S in the normalized system_a2Predicted life F of₄The occupied weight coefficient;

step 5, according to the fast non-dominated sorting method described in step 2.4, the technical advantage Y of the system obtained in step 4 is₁And profit Y of the system₂System for performing rapid non-dominated sorting on two-dimensional targets and outputting sorting grade lambda of 1Technical advantage of (A) Y₁And profit Y of the system₂A two-dimensional Pareto front; the two-dimensional Pareto frontier is a set Mc, a set

Wherein the set Md ═ Y₁，Y₂]，δ₂The number of the sets Md;

and 6, selecting a set Md from the two-dimensional Pareto frontier as a final implementation scheme according to needs.

2. The multi-target optimization method for the photovoltaic off-grid inverter system according to claim 1, wherein the genetic operators in the step 2 comprise selection, crossing and mutation operations, and different coding modes implement corresponding conventional genetic operators; the selection operation means that individuals more suitable for the environment have more opportunity to be inherited to the next generation; the cross operation refers to generating a new individual through the cross combination of chromosomes; the mutation operation refers to selecting one individual from the population, and making a segment of the code of the individual have mutation so as to generate more excellent individuals.

3. The multi-target optimization method for the photovoltaic off-grid inverter system according to claim 1, wherein the elite reservation operation in the step 2 is as follows: set K of non-dominant solutions_ζIndividuals with a medium ranking of 1 to (1d-1) are placed into a new parent population S_ζ+1And from the original non-dominated solution set Q based on the method of the reference point_ldContinuously selecting individuals and putting the individuals into a new parent population S_ζ+1Until the new parent population S_ζ+1The population size of (a) is Pop; the method based on the reference point specifically comprises the following steps:

(a) computing a non-dominated solution set K_ζMinimum value of each objective function in

(b) Computing a non-dominated solution set K_ζMiddle per target function axial truncationDistance of y'_ψAnd adaptive to the objective function

(c) According to f'_ψSetting a reference point Z on a normalized hypercube^r；

(d) According to reference point Z^rDefining a reference line H_sComputing a non-dominated solution set K_ζIndividuals with a medium rank λ of 1 to (1d-1) and a reference point Z^rThe number of associations is denoted as J_s(ii) a The association means that the individual is associated with a reference point when the individual is closest to the reference line;

(e) until there is a reference point Z^rAnd original non-dominated solution set Q_ldIs associated with the middle individual, if J is present_sIf 0, then select the original non-dominated solution set Q_ldMiddle distance reference point Z^rRecent individuals are placed in a new parent population S_ζ+1Performing the following steps; otherwise in the original non-dominated solution set Q_ldRandomly selecting individuals and putting the individuals into a new parent population S_ζ+1In (1).

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