CN101521438B - A design method of motor optimization based on Game Theory - Google Patents

Abstract

The invention relates to a design method of motor optimization based on Game Theory, which comprises the following steps: (1) determining variables to be optimized in motor design and establishing a partial objective functional equation and a constraint equation; (2) determining a noninferior solution set which is then taken as a strategy set in Game Theory; (3) taking an optimization objective asa player and taking a partial objective function and taking definite purpose as utilities of each player, disintegrating design variables into strategies for each player according to the correlation between the utilities and each partial objective function, and changing the solving problem of the optimal motor design scheme into a Game problem according to the above steps, wherein each player cancooperate with each other so as to maximize the utility of each player; and (4) adopting a method of cooperative Game for integratedly optimizing each optimization objective from Nash equilibrium sol ution, thus obtaining the global optimum solution. The design method of motor optimization fully takes the relation among different optimization objectives into account so as to search the integrated optimum solution, thus shortening the motor design cycle, lowering development difficulty and laying foundation for the intelligentization of motor optimization design.

Description

Based on game theoretic motor optimized design method

Technical field

The present invention relates to motor optimal design and manufacturing technology field.

Background technology

Along with the continuous development of optimized Algorithm, be optimized simultaneously at the target of a plurality of mutual conflicts, the motor optimized design method that obtains design Pareto disaggregation becomes the focus of research in recent years.This multi-objective optimization design of power method can solve the non-bad design collection that satisfies constraints, and the designer can therefrom select suitable design according to actual needs neatly.The dispersiveness in order to guarantee to separate but, the noninferior solution quantity that this multi-objective optimization algorithm obtains is more, therefrom selects optimal solution to need very strong professional knowledge and long time.

Optimal solution is searched in research from noninferior solution algorithm can reduce labour intensity, shorten the construction cycle.Japan scholar Tomoyuki Miyamoto has proposed a kind of method based on game theory search motor optimization design scheme in Selection of an Optimal Solution for Multiobjective ElectromagneticApparatus Design Based on Game Theory one literary composition, adopt the thought of non-cooperative game, separate optimization design scheme with Nash Equilibrium, certain novelty is arranged and obtained effect preferably as motor.Often have competition and conflict in the motor optimal design between the Different Optimization target, if regard optimization aim as game side, separate from Nash Equilibrium, each side all makes suitable concession, all can be beneficial to for each side.

Summary of the invention

At the deficiency of traditional design method, the present invention proposes a kind of new for game theoretic motor optimized design method, and this kind motor optimized design method has given improvement to existing based on game theoretic motor optimized design method.

The present invention adopts following technical scheme:

The game theoretic motor manufacturing method of a kind of employing comprises the following steps:

The first step: determine the variable to be optimized in the design of electrical motor, set up partial objectives for functional equation and constraint equation, design of electrical motor is converted into multi-objective optimization question.

Second the step: determine the noninferior solution collection, and with it as the set of strategies in the game theory.

The 3rd the step: with optimization aim as game side, partial objectives for function and prestige order feature are as the effectiveness of each game side, according to design variable being decomposed into the strategy of each game side with the correlation of each partial objectives for function, according to above-mentioned steps the motor best design is found the solution problem and change into a problem of game, wherein each game can be to work in coordination, and purpose is exactly to increase the effectiveness of each side as far as possible.

The 4th step: the method for employing cooperative game draws global optimum from each optimization aim of Nash Equilibrium separate complex optimum and separates.

The 5th step: draw motor each several part drawing according to optimization design scheme, linear cutting die, punch die, laminate, coiling, rule, dipping lacquer, assembling, check motor actual motion index and the index comparison that provides with design, adjust the performance accounting equation as its difference greater than set point, be optimized design again; Less than set point, the scheme typing is also produced in batches as its difference.

Above-mentioned motor optimized design method in the first step, can be optimized at the cost and the efficiency index of motor, sets up following partial objectives for functional equation, and design of electrical motor is converted into multi-objective optimization question min F (x)=min[f ₁(x), f ₂(x)]:

f ₁＝K _CuG _Cu+K _FeG _Fe+K _AlG _Al

$f_2=\mathrm{\η}=\frac{1}{1+P_{\mathrm{Cu}}^{*}+P_{\mathrm{Al}}^{*}+P_{\mathrm{Fe}}^{*}+P_{\mathrm{fw}}^{*}+P_s^{*}}$

K in the formula _Cu, K _Fe, K _Al---be respectively the unit price of copper, iron, aluminium; G _Cu, G _Fe, G _Al---be respectively the weight of every motor copper, iron, aluminium; η---electric efficiency;

---be respectively every motor stator copper loss, the loss of rotor aluminium, iron loss, wind moussing loss and stray loss;

In second step, can adopt niche genetic algorithm or particle group optimizing method to determine the noninferior solution collection;

Can be in the 3rd step based on the prestige order feature of each design of robustness theory analysis, and with it as scheme robustness index, calculate the robustness that noninferior solution is concentrated each design, with its with the partial objectives for function as game side;

In the 4th step, preferably adopt the method for tactic concession game to find the solution the Synthetical Optimization scheme in the cooperative game.

Motor optimized design method of the present invention manufactures and designs dual-feed asynchronous wind power generator, and the key dimension of this motor satisfies following formula:

$D^2{l}_{\mathrm{ef}}=C_A\frac{P\′}{n},$ $C_A=\frac{6.1}{{\mathrm{\α}}_p^{\′}{K}_{\mathrm{Nm}}{K}_{\mathrm{dp}}(1.3\·A)B_{\mathrm{\δ}}}.$

The present invention has following outstanding beneficial effect:

1. can to make all benefit allocative decisions of reaching the contract defined all be self-actualization in each stage that contract is reached or link in tactic concession game, thereby make the effect that realizes being similar to binding contract under the situation that does not have binding contract with the threat that can put letter.Be applied to the motor optimal design can optimization aim exist mutually the competition and the conflict situation under ask for comprehensive optimal solution.

2. adopt tactic concession game from numerous noninferior solutions, to search for comprehensive optimal solution, improved optimal speed, reduced technical threshold, accelerated the construction cycle.

Embodiment

Important indicator in the design of electrical motor---cost and efficient exist conflict to a certain extent, and the efficient that cost is low in the noninferior solution that multi-objective optimization algorithm obtains is also low, and the cost that efficient is high is also high.The present invention adopts tactic concession game search complex optimum scheme at this problem.

The present invention is expressed as a problem of game G with the motor multi-objective optimization question, and optimization aim is as game side, and m partial objectives for function used u as the effectiveness of each game side _iExpression, according to design variable being decomposed into the strategy of each game side with the correlation of each target function, the design Pareto disaggregation that multi-objective optimization algorithm obtains constitutes game set of strategies (policy space) S, strategy among the S satisfies all equatioies and the inequality constraints in the former problem, thereby does not need to consider restricted problem.Former like this multi-objective optimization question is equivalent to problem of game G={S; u ₁, u ₂..., u _m, wherein each game can be to work in coordination, and purpose is exactly to increase the effectiveness u of each side as far as possible _iFor above-mentioned many people, fully information, static state, limited, nonzero sum, have the cooperative game problem of the complete rational faculty and collective's rational faculty, adopt the thought of tactic concession game to find the solution its comprehensive optimal solution.

Cost and efficiency index at threephase asynchronous machine commonly used is optimized target function in the present embodiment

f ₁＝K _CuG _Cu+K _FeG _Fe+K _AlG _Al

$f_2=\mathrm{\η}=\frac{1}{1+P_{\mathrm{Cu}}^{*}+P_{\mathrm{Al}}^{*}+P_{\mathrm{Fe}}^{*}+P_{\mathrm{fw}}^{*}+P_s^{*}}---\left(1\right)$

K in the formula _Cu, K _Fe, K _Al---be respectively the unit price of copper, iron, aluminium;

G _Cu, G _Fe, G _Al---be respectively the weight of every motor copper, iron, aluminium;

η---electric efficiency;

---be respectively every motor stator copper loss, the loss of rotor aluminium, iron loss, wind moussing loss and stray loss.

The present invention at first is converted into multi-objective optimization question with design of electrical motor

min?F(x)＝min[f ₁(x)，f ₂(x)]

Adopt multi-objective optimization algorithm that above-mentioned optimization problem is optimized, for example adopt methods such as niche genetic algorithm, particle group optimizing method to draw the optimal solution set of motor optimal design.

Inevitably have error in the processing of motor, assembling process, environmental factor such as temperature, Harmonic Interference is uncertain again in the practical application, and these all can have influence on the performance of product, the serious qualification rate that also can influence motor.In order to reduce of the influence of these uncertain factors to product, the present invention is in the optimization and decision-making of design of electrical motor, introduce the notion of robustness, the optimal solution set that the utilization signal to noise ratio solves said method in design of electrical motor is estimated and is sorted, searching realizes the based Robust Design scheme that anti-various error components disturb with least cost, has bigger engineering using value.

For this class of design of electrical motor the occasion of definite target and bound thereof is arranged, can select to hope the order feature as the index of estimating robustness.The purpose of hoping the order feature is the fluctuation that reduces around mean value, and mean value is adjusted on the desired value.For hoping that the order characteristic value is y ₀, mass property y Normal Distribution N (μ _y, σ _y ²) product, hope that the purpose of order feature is to make μ _y=y ₀, and σ _y ²The smaller the better.For the single performance index, hope the signal to noise ratio of order feature be

$\mathrm{SN}=10\lg \left(\frac{{\mathrm{\μ}}_y^2}{{\mathrm{\σ}}_y^2}\right)---\left(2\right)$

μ in Practical Calculation _y ²And σ _y ²Maximal possibility estimation with them replaces

${\widetilde{\mathrm{\μ}}}_y=\stackrel{\‾}{y}---\left(3\right)$

${\widetilde{\mathrm{\σ}}}_y^2=\frac{\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{(y_i-\stackrel{\‾}{y})}^2}{N}---\left(4\right)$

Hope order feature signal to noise ratio be

$\mathrm{SN}=10\lg \left(\frac{{\stackrel{\‾}{y}}^2}{{\widetilde{\mathrm{\σ}}}_y^2}\right)---\left(5\right)$

Signal to noise ratio is big more, and the properties of product deviation is more little, and the quality of product is stable more, and qualification rate is high more.The performance index that need consider more for a long time, choose for some more important performance index of quality testing, calculate the signal to noise ratio that it hopes the order feature respectively, choose a wherein minimum signal to noise ratio, just with the signal to noise ratio of sensitive target signal to noise ratio as whole proposal as design.Can find to adapt to design production in enormous quantities, sane at an easy rate by the signal to noise ratio that compares each design.

The motor multi-objective optimization question is expressed as a problem of game G, and optimization aim and robustness index be as game side, and m partial objectives for function used u as the effectiveness of each game side ₁Expression, according to design variable being decomposed into the strategy of each game side with the correlation of each target function, the design Pareto disaggregation that multi-objective optimization algorithm obtains constitutes game set of strategies (policy space) S, strategy among the S satisfies all equatioies and the inequality constraints in the former problem, thereby does not need to consider restricted problem.Former like this multi-objective optimization question is equivalent to problem of game G={S; u ₁, u ₂..., u _m, wherein each game can be to work in coordination, and purpose is exactly to increase the effectiveness u of each side as far as possible ₁

For above-mentioned problem of game, game side i, j ∈ 1,2}, i ≠ j.The target of game side i is the effectiveness u of maximization oneself ₁(s ₁, s ₂), s wherein ₁∈ S _iIt is the policy selection of game side.Policy space S is a compact convex set, and utility function satisfies the uniqueness theorem of Rosen.Suppose that each participant is ready to make a concession, $Q_i\∈[0,S_i^N]$ Game side i is from its Nash Equilibrium in expression

The concession of making.The rule of giving way is that game side i makes a concession is the α of game side j concession _iDoubly, promptly

$Q_i=\left\{\begin{array}{cc}{\mathrm{\α}}_i{Q}_j,& {\mathrm{\α}}_i{Q}_j\≤s_i^N\\ s_i^N,& {\mathrm{\α}}_i{Q}_j>s_i^N\end{array}\right.---\left(6\right)$

The picked at random noninferior solution is separated as Nash Equilibrium, and making a concession from this scheme reaches other noninferior solutions, can be obtained the optimal solution of motor optimization problem by tactic concession theory of games:

1. work as ${{\mathrm{\α}}_i}^0={{\mathrm{\α}}_i}^m,$ ${{\mathrm{\α}}_j}^0={{\mathrm{\α}}_j}^m$ The time, if ${\mathrm{\α}}_i^0\≥\frac{{\left(s_i^N\right)}^2}{{\left(s_j^N\right)}^2}{\mathrm{\α}}_j^0,$ Tactic concession game equilibrium is separated

${\mathrm{\α}}_j^{*}={\mathrm{\α}}_j^0,$ ${\mathrm{\α}}_i^{*}={\mathrm{\α}}_i^s=\arg \underset{{\mathrm{\α}}_i\∈[\frac{{\left(s_i^N\right)}^2}{{\left(s_j^N\right)}^2}{\mathrm{\α}}_j^0,{\mathrm{\α}}_i^0]}{\max }\left\{U_i^W\left({\mathrm{\α}}_i\right)\right\}---\left(7\right)$

2. work as ${{\mathrm{\&alpha;}}_i}^0={{\mathrm{\&alpha;}}_i}^m,$ ${{\mathrm{\&alpha;}}_j}^0{<{\mathrm{\&alpha;}}_j}^m$ The time, if ${\mathrm{\&alpha;}}_i^0\&GreaterEqual;\frac{{\left(s_i^N\right)}^2}{{\left(s_j^N\right)}^2}{\mathrm{\&alpha;}}_j^m,$ Tactic concession game equilibrium is separated

${\mathrm{\&alpha;}}_j^{*}={\mathrm{\&alpha;}}_j^0,$ ${\mathrm{\&alpha;}}_i^{*}={\mathrm{\&alpha;}}_i^s=\arg \underset{{\mathrm{\&alpha;}}_i\&Element;[\frac{{\left(s_i^N\right)}^2}{{\left(s_j^N\right)}^2}{\mathrm{\&alpha;}}_j^m,{\mathrm{\&alpha;}}_i^0]}{\max }\left\{U_i^W\left({\mathrm{\&alpha;}}_i\right)\right\}---\left(8\right)$

3. work as ${{\mathrm{\&alpha;}}_i}^0={{\mathrm{\&alpha;}}_i}^m,$ ${{\mathrm{\&alpha;}}_j}^0{<{\mathrm{\&alpha;}}_j}^m$ The time, if ${\mathrm{\&alpha;}}_i^0\&le;\frac{{\left(s_i^N\right)}^2}{{\left(s_j^N\right)}^2}{\mathrm{\&alpha;}}_j^0,$ Tactic concession game equilibrium is separated

${\mathrm{\&alpha;}}_i^{*}={\mathrm{\&alpha;}}_i^0,$ ${\mathrm{\&alpha;}}_j^{*}={\mathrm{\&alpha;}}_j^s=\arg \underset{{\mathrm{\&alpha;}}_j\&Element;[\frac{{\left(s_j^N\right)}^2}{{\left(s_i^N\right)}^2}{\mathrm{\&alpha;}}_i^0,{\mathrm{\&alpha;}}_j^m]}{\max }\left\{U_j^W\left({\mathrm{\&alpha;}}_j\right)\right\}---\left(9\right)$

4. work as ${{\mathrm{\&alpha;}}_i}^0={{\mathrm{\&alpha;}}_i}^m,$ ${{\mathrm{\&alpha;}}_j}^0{<{\mathrm{\&alpha;}}_j}^m$ The time, if ${\mathrm{\&alpha;}}_j^m\&GreaterEqual;\frac{{\left(s_j^N\right)}^2}{{\left(s_i^N\right)}^2}{\mathrm{\&alpha;}}_i^0>{\mathrm{\&alpha;}}_j^0,$ Tactic concession game equilibrium is separated

${\mathrm{\&alpha;}}_j^{*}={\mathrm{\&alpha;}}_j^m,$ ${\mathrm{\&alpha;}}_i^{*}={\mathrm{\&alpha;}}_j^0---\left(10\right)$

5. work as ${{\mathrm{\&alpha;}}_i}^0<{{\mathrm{\&alpha;}}_i}^m,$ ${{\mathrm{\&alpha;}}_j}^0{<{\mathrm{\&alpha;}}_j}^m$ The time, if ${\mathrm{\&alpha;}}_i^0\&GreaterEqual;\frac{{\left(s_i^N\right)}^2}{{\left(s_j^N\right)}^2}{\mathrm{\&alpha;}}_j^m,$ Tactic concession game equilibrium is separated

${\mathrm{\&alpha;}}_j^{*}={\mathrm{\&alpha;}}_j^m,$ ${\mathrm{\&alpha;}}_i^{*}={\mathrm{\&alpha;}}_i^s=\arg \underset{{\mathrm{\&alpha;}}_i\&Element;[\frac{{\left(s_i^N\right)}^2}{{\left(s_j^N\right)}^2}{\mathrm{\&alpha;}}_j^m,{\mathrm{\&alpha;}}_i^m]}{\max }\left\{U_i^W\left({\mathrm{\&alpha;}}_i\right)\right\}---\left(11\right)$

6. work as ${{\mathrm{\&alpha;}}_i}^0<{{\mathrm{\&alpha;}}_i}^m,$ ${{\mathrm{\&alpha;}}_j}^0{<{\mathrm{\&alpha;}}_j}^m$ The time, if ${\mathrm{\&alpha;}}_i^m\&GreaterEqual;\frac{{\left(s_i^N\right)}^2}{{\left(s_j^N\right)}^2}{\mathrm{\&alpha;}}_j^m>{\mathrm{\&alpha;}}_i^0,$ Tactic concession game equilibrium is separated

${\mathrm{\&alpha;}}_j^{*}={\mathrm{\&alpha;}}_j^m,$ ${\mathrm{\&alpha;}}_i^{*}={\mathrm{\&alpha;}}_i^m---\left(12\right)$

Draw motor each several part drawing according to optimization design scheme, linear cutting die, punch die, laminate, coiling, rule, dipping lacquer, assembling, check motor actual motion index and the index comparison that provides with design, adjust the performance accounting equation as its difference greater than set point, be optimized design again; Less than set point, the scheme typing is also produced in batches as its difference.

Make dual-feed asynchronous wind power generator according to above-mentioned flow scheme design, wherein the key dimension of motor satisfies following formula:

$D^2{l}_{\mathrm{ef}}=C_A\frac{P\&prime;}{n}---\left(13\right)$

$C_A=\frac{6.1}{{\mathrm{\&alpha;}}_p^{\&prime;}{K}_{\mathrm{Nm}}{K}_{\mathrm{dp}}(1.3\&CenterDot;A)B_{\mathrm{\&delta;}}}---\left(14\right)$

D in the formula---armature internal diameter (m);

l _Ef---armature computational length (m);

P '---rated output (VA);

N---rotating speed (r/min);

α _p'---calculate pole embrace;

K _Nm---the air-gap field form factor;

K _Dp---the armature winding coefficient;

A---specific electric load (A/m);

B _δ---air gap flux density maximum (T).

1.3A represents to convert when rotor-side flows through 1/3 energy the specific electric load of stator side in the formula (14).Should determine the key dimension of motor in the design of electrical motor according to 1.3A as the motor lines load.Rated output

Here the detailed explanation that has been center deployment with embodiments of the invention, the imbody of described optimal way or some characteristic, should be understood to this specification only is to describe the present invention by the mode that provides embodiment, in fact on some details of forming, construct and using, can change to some extent, comprise the combination and the assembly of parts, these distortion and application all should belong in the scope of the present invention.

Claims (2)

1. one kind based on game theoretic motor optimized design method, is applicable to the design of threephase asynchronous machine, comprises the following steps:

The first step: cost and efficiency index at motor are optimized, and partial objectives for functional equation and constraint equation below setting up are converted into multi-objective optimization question with the threephase asynchronous machine design:

minF(x)＝min[f ₁(x)，f ₂(x)].

f ₁＝K _CuG _Cu+K _Fe+G _Fe+K _AlG _Al

$f_2=\mathrm{\&eta;}=\frac{1}{1+P_{\mathrm{Cu}}^{*}+P_{\mathrm{Al}}^{*}+P_{\mathrm{Fe}}^{*}+P_{\mathrm{fw}}^{*}+P_s^{*}}$

In the formula, K _Cu, K _Fe, K _Al---be respectively the unit price of copper, iron, aluminium; G _Cu, G _Fe, G _Al---be respectively the weight of every threephase asynchronous machine copper, iron, aluminium; η---electric efficiency;

---be respectively every threephase asynchronous machine stator copper loss, the loss of rotor aluminium, iron loss, wind moussing loss and stray loss;

Second the step: determine the noninferior solution collection, and with it as the set of strategies in the game theory;

The 3rd step: with optimization aim and robustness index as game side, the partial objectives for function is as the effectiveness of each game side, according to design variable being decomposed into the strategy of each game side with the correlation of each partial objectives for function, according to above-mentioned steps the motor best design is found the solution problem and change into a problem of game, wherein each game can be to work in coordination, and purpose is the effectiveness that increases each side as far as possible;

The 4th step: the method for employing tactic concession game draws global optimum from each optimization aim of Nash Equilibrium separate complex optimum and separates;

The 5th step: draw motor each several part drawing according to optimization design scheme, linear cutting die, punch die, laminate, coiling, rule, dipping lacquer, assembling, check motor actual motion index and the index comparison that provides with design, as its difference greater than set point, adjust the performance accounting equation, be optimized design again; Less than set point, the scheme typing is also produced in batches as its difference.

2. according to claim 1ly it is characterized in that, in second step, adopt niche genetic algorithm or particle group optimizing method to determine the noninferior solution collection based on game theoretic motor optimized design method.