CN103839177A - Improved Shapley value method distribution method of micro-grid load gaming - Google Patents

Abstract

The invention discloses an improved Shapley value method distribution method of micro-grid load gaming. The improved Shapley value method distribution method includes the following steps: (1) building a micro-grid load gaming model, (2) achieving the improved Shapley value method, and (3) solving a fine adjustment coefficient with the particle swarm optimization. According to the improved Shapley value method distribution method, the improved Shapley value method for carrying out searching through the earning fine adjustment coefficient and stabilization indexes is provided, earnings after cooperation can be redistributed, it can be guaranteed that the earnings obtained by a gamer in a full cooperation union are higher than the earnings obtained by the gamer after the gamer quits the full cooperation union, and therefore the stability of the full cooperation union is guaranteed.

Description

The improvement Shapley value method distribution method of microgrid load game

Technical field

Project of the present invention relates to a kind of microgrid load game distribution of income method research, particularly a kind of distribution of income method based on improving Shapley value method.

Background technology

Along with fossil energy gradually shortage and environmental pollution day by day serious, utilize distributed power source (the Distributed Generation of clean energy resource, DG) put on schedule, and microgrid (Microgrid) can be integrated various DG, energy-storage units and load effectively, it is the important component part of following intelligent grid.But the large-scale development of microgrid is still subject to the impact of the many factors such as micro-source cost of investment, regional characteristics, output energy, reliability, the quality of power supply, variable load.

Game theory, as a kind of advanced person's mathematical method, day by day receives publicity in recent years.It,, for studying interbehavior complicated between independent player, is applicable to solve the mutual relationship between multiagent, multiple goal.The present invention takes into full account the interests of load, follow and how to realize that interests between microgrid load maximize and the thinking of micro-source capacity configuration economical and efficient, taking load income and microgrid capacity as strategy, set up the betting model of non-cooperation and cooperation, utilized Linear Iterative Method to solve game equilibrium strategy.Appropriate allocation scheme is most important for cooperative game, therefore how the income after cooperation is redistributed, and becomes the study hotspot of cooperative game.Shapley value method (Shapley) be Shapley L S in nineteen fifty-three provide for solving a kind of method of n people's cooperative game problem, can be directly used in distribution of interests problem.Shapley value method carries out distribution of interests according to game person to the size of alliance's contributrion margin, makes each game person can obtain incomes more when not coalizing.But traditional Shapley value method is a kind of allocative decision of equalization, and in cooperation, the risks and assumptions that different interests individuality is born may be different, if carry out distribution of income according to all taking risks, obviously unreasonable for the large game person of the factor of accepting the risk, alliance's potentially unstable after distribution, game person has the possibility that exits alliance.Given this, the improvement Shapley value method that the present invention proposes to utilize income fine setting coefficient and stability index to search for is redistributed cooperative game income, makes to cooperate full alliance and keeps stable.

Summary of the invention

The present invention will overcome traditional Shapley value method and distribute and have the shortcoming unstable, cooperative alliances is failed at cooperation benefit, improvement Shapley value method distribution method based on the game of microgrid load is proposed, improved Shapley value method the redistributing of game income of cooperating, distribution of income after improvement has the allocation rule of Pareto improvement character, can strengthen intrinsic alliance, the integral benefit that maintains alliance is greater than income sum when wherein each member manages separately.

The present invention is taking into full account on the basis of mutual relationship between micro-source cost, micro-source capacity, load cost, load power consumption, has set up micro-source and the load betting model with Game Relationship, and objective function under non-cooperation and cooperative game.Utilize Linear Iterative Method to carry out game and solve, realized the optimum of objective function.The improvement Shapley value method that utilizes income fine setting coefficient and stability index to search for is finally proposed, in income fine setting coefficient solution procedure, the present invention utilizes particle cluster algorithm to carry out optimizing and solves, pass through carry improvement Shapley value method the income after cooperating is redistributed, ensured to cooperate the stability of full alliance.

Based on the improvement Shapley value method distribution method of microgrid load game, comprise the following steps:

Step 1, set up microgrid load betting model;

Step 2, improvement Shapley value method are realized;

Step 3, PSO Algorithm fine setting coefficient;

Further, in step 1, set up the concrete steps of microgrid load betting model as follows:

1-1), set up payoff function model;

Consider a microgrid containing m node, getting M is node set, and game person's set, for Γ, comprises a n game person, Γ=i|i=1,2 ..., n}, obviously,

n≤m.Load game side set L and micro-source game side S set all use game person i (i ∈ Γ) to represent, S ∪ L=Γ.I load game person's pure control strategy is x _i=p _i, p _irepresent the load power of this load bus; I micro-source game person's pure control strategy is x _i=s _i, s _irepresent micro-source capacity of this micro-source node.A n game person's pure strategy is combined as x={x ₁, x ₂..., x _i..., x _n, x _-i={ x ₁..., x _i-1, x _i+1..., x _nrepresent except tactful x _iother outer strategy combination.

Further, step (1-1) can be made up of following steps:

111), determine electricity charge function;

The electricity charge function of constructing has following features: 1) electricity price is along with the increase that micro-source game person invests capacity increases gradually, and rate of growth reduces gradually.When the investment capacity in micro-source hour, may not reach the single-machine capacity in micro-source, therefore unit cost is higher; And along with the investment capacity in micro-source increases gradually, its unit cost increases gradually, but tend towards stability.2) electricity price is along with the increase of load game person demand increases gradually, and rate of growth strengthens gradually.According to the feature of market economy, when supply exceed demand, electricity price is lower, along with the reverse of supplydemand relationship, certainly will occur competing the situation of electricity consumption, causes electricity price to rise violently.Therefore, constructed electricity price cost function is as described below:

$C_{\mathrm{CHR}}=k\sqrt{\underset{i=1}{\overset{n_s}{\mathrm{\Σ}}}{s}_i}{\left(\underset{i=1}{\overset{n_l}{\mathrm{\Σ}}}{p}_i\right)}^2---\left(1\right)$

Wherein, C _cHRfor total income of electricity charge of a year of all micro-source game persons, unit is unit/year; K is the unit cost coefficient in micro-source; p _ibe i load game person's planned supply and use of electric power amount, s _iit is i micro-source game person's tactful capacity; n _sfor the nodes in micro-source, n _lfor the nodes of load.

112), determine the payoff function in micro-source:

Micro-source game person's payoff function has comprised the electricity charge of collecting to load and the cost of investment in micro-source, is expressed as:

$H_{\mathrm{DGi}}={\mathrm{ks}}_i{\left(\underset{i=1}{\overset{n_l}{\mathrm{\Σ}}}{p}_i\right)}^2/\sqrt{\underset{i=1}{\overset{n_s}{\mathrm{\Σ}}}{s}_i}-\frac{R{(1+R)}^T}{{(1+R)}^T-1}{s}_i{c}_{\mathrm{DGi}}---\left(2\right)$

Wherein, H _dGiit is i micro-source game person's payoff function; R is annual rate, the pay back period of investment that T is micro-source, c _dGiit is the unit capacity cost in i micro-source.

113), determine the payoff function of load:

Load game person's payoff function be the income that participates in main business with the difference of payment electricity price expense, be defined as:

H _Li=u _i,SEL-C _i,CHR (3)

Wherein, H _liit is i load game person's payoff function; u _{i, SEL}for load participates in main business, the income that production marketing brings; C _{i, CHR}for load needs the electricity charge that pay.

The output value of load is:

$u_{i,\mathrm{SEL}}={8760c}_{i,\mathrm{SEL}}=8760(a_i{p}_i^2+b_i{p}_i)---\left(4\right)$

Wherein, c _{i, SEL}for the output value per hour of different load, become secondary relevant with the electric weight of load, unit be first/hour; a _iand b _ifor the related coefficient of load output value quadratic function, it is the coefficient of colligation obtaining on the basis of the expenses such as raw material, artificial, maintenance considering.

The electricity charge that load game person pays are:

$C_{i,\mathrm{CHR}}=C_{\mathrm{CHR}}\×\frac{p_i}{\underset{i=1}{\overset{n_l}{\mathrm{\Σ}}}{p}_i}---\left(5\right)$

114), determine each game person's payoff function

To every kind of pure strategy combination x, construct each game person's payoff function u _i(x _i, x _-i) be:

$u_i(x_i,x_{-i})=\left\{\begin{array}{cc}{\mathrm{ks}}_i{\left(\underset{i=1}{\overset{n_s}{\mathrm{\Σ}}}{p}_i\right)}^2/\sqrt{\underset{i=1}{\overset{n_s}{\mathrm{\Σ}}}{s}_i}-\underset{i=1}{\overset{n_s}{\mathrm{\Σ}}}\frac{R{(1+R)}^T}{{(1+R)}^T-1}{s}_i{c}_{{\mathrm{DG}}_i}& i\∈S\\ 8760(a_i{p}_i^2+b_i{p}_i)-k\sqrt{\underset{i=1}{\overset{n_l}{\mathrm{\Σ}}}{s}_i}\left(\underset{i=1}{\overset{n_l}{\mathrm{\Σ}}}{p}_i\right)p_i& i\∈L\end{array}\right.---\left(6\right)$

In formula (1), R is annual rate, the pay back period of investment that T is micro-source, c _dGfor the unit capacity cost in micro-source, n _sfor the nodes in micro-source, n _lfor the nodes of load, k is micro-source unit cost coefficient, a _i, b _ifor the coefficient entry of load revenue function.

Strategy meets constraint:

$\left\{\begin{array}{cc}\underset{i=1}{\overset{n_s}{\mathrm{\Σ}}}{s}_i\≥\underset{i=1}{\overset{n_l}{\mathrm{\Σ}}}{p}_i& i\∈\mathrm{\Γ}\\ s_i\≥0& i\∈S\\ p_i\≥0& i\∈L\\ & \end{array}\right.---\left(7\right)$

In the time that game person is micro-source node, this game person's payoff function is made up of sale of electricity electricity price income and the difference of micro-source cost of investment.In the time that game person is load bus, this game person's payoff function is made up of the income of load point main business and the difference of the electricity price expense that pays.

1-2), determine game person's objective function model:

In non-cooperative game, between each game person, there is no binding agreement, independently seek separately number one and maximize.Corresponding objective function is:

${x_i}^{*}=\arg \underset{x_i}{\max }{u}_i(x_i,x_{-i})---\left(8\right)$

In cooperative game, between each game person, taking collective rationality as basis, first realize the maximization of alliance's income, then by the suitable distribution of income being maximized to each game person's income.When n game person's cooperative game of note, will produce X kind game play mode, every kind of cooperation is all with the interests u under this pattern _xbe objective function to the maximum, be expressed as:

${x_i}^{*}=\arg \underset{x_i}{\max }{u}_X(x_i,x_{-i})---\left(9\right)$

Further, the concrete steps that step (2) improvement Shapley value method is realized are as follows:

2-1), Shapley value method is realized:

The concrete steps of step (2-1) are as follows:

211) determine alliance:

In n-person game, game person gathers with N={1, and 2 ..., n} represents, the random subset S of N is called an alliance;

212) determine fundamental function:

A given n-person game, S is an alliance, v (S) refer to S and

two-person game in the maximum utility of S, v (S) is called the fundamental function of the S of alliance;

213) determine allocative decision:

For cooperative game (N, v), N={1,2 ..., n}, to each game person i ∈ N, gives a real-valued parameters u _i, form n-dimensional vector u={u ₁, u ₂..., u _i..., u _n, and it meets: u _i>=v (i}),

claim u={u ₁, u ₂..., u _i..., u _nit is an allocative decision of the S of alliance;

214) determine distribution of income value:

To each game (N, v), there is unique u (v)=(u ₁(v), u ₂(v) ..., u _i(v) ..., u _n(v)) value, is defined as Sharp's profit value, is now assigned to the income u of game person i _i(v) be

$u_i\left(v\right)=\underset{S\⋐N/\left\{i\right\}}{\mathrm{\Σ}}\frac{\left|S\right|!(n-|S|-1)!}{n!}[v(S\∪\{i\left\}\right)-v\left(S\right)]---\left(10\right)$

Wherein, | S| represents the number of all game persons in the S of alliance;

2-2) improve Shapley value method:

Implementation method main thought is: first carry out distribution of interests according to Shapley value method, afterwards, from the large game person's hand of income, regain a part of interests, and all re-starting fine setting in member, make each member's income all meet rationality constraint.

Further, for step (2-2), determining step is as follows:

221), determine income fine setting coefficient;

Making the income fine setting coefficient of game person i is Δ λ _i, meet:

$\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\Δ\λ}}_i=0---\left(11\right)$

Use Δ λ _irevise Shapley value u _i(v), the Shapley value u that is improved _i(v) *:

$u_i\left(v\right)*=u_i\left(v\right)+{\mathrm{\Δ\λ}}_i\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{u}_i\left(v\right)---\left(12\right)$

Obviously, $v\left(N\right)=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{u}_i\left(v\right)=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{u}_i\left(v\right)*;$

222), determine stability index:

In order to try to achieve the income fine setting coefficient delta λ meeting the demands _i, the income growth pattern of game person i after improving the distribution of Shapley value is carried out to quantification treatment, definition stability index δ _ι:

${\mathrm{\δ}}_i=\frac{u_i{\left(v\right)}^{*}}{v\left(\right\{i\left\}\right)}---\left(13\right)$

Obviously, only has the δ of working as _i>=1 o'clock, game person i was just ready to participate in cooperation.Stability index value is larger, and alliance's result is more stable.

Therefore, improve Sharpley Value Method and can be described as finding optimum income fine setting coefficient delta λ _i, make following objective function maximum:

$\mathrm{\δ}=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\δ}}_i---\left(14\right)$

Constraint condition is:

$\left\{\begin{array}{c}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\Δ\λ}}_i=0\\ {\mathrm{\δ}}_i\≥1\end{array}\right.---\left(15\right)$

Further, the concrete steps of step (3) PSO Algorithm fine setting coefficient are as follows:

3-1), initiation parameter:

Be provided for solving the parameter of the particle cluster algorithm of fine setting coefficient, comprise the particle number, inertia weight value, the study factor of iterations, the population of population etc.And input the distribution of income value of each game side that traditional Sharp profit value distribution method obtains;

3-2), initialization population position, speed and target function value:

The initialized location of random definition population particle, remember that this position vector is X:

X=(x ₁,x ₂,…,x _m) （16）

Wherein, x _irefer to fine setting coefficient delta λ _i; M value is the number of fine setting coefficient, the number that needs to distribute income side.It should be noted that fine setting restricted coefficients of equation condition (15), summation is 0.If the position of random initializtion does not meet this constraint condition, need its making zero, make it meet constraint condition;

The initialization speed of random definition particle cluster algorithm, remember that this velocity vector is V:

V=(v ₁,v ₂,…,v _m) （17）

According to the initialized position of particle, by formula (12) and formula (14), calculate the stability index of each particle, i.e. the initial target functional value of each particle;

3-3), initialization pbest and gbest variable:

Positional value initial each particle and target function value are made as to the initial value of population pbest variable (the historical optimal value of each particle), and select a wherein particle of target function value maximum, be made as the initial value of gbest variable (whole population is when the optimal value of time iteration);

3-4), the renewal of population position and speed:

According to the more new formula of the speed of particle cluster algorithm and position, position and speed to each particle are upgraded.The more new formula adopting is as follows:

v _i,t+1=wv _i,t+c ₁×R×(pbest _t-x _i,t)+c ₂×R×(gbest _t-x _i,t) （18）

x _i,t+1=x _i,t+v _t （19）

Wherein, w refers to inertia weight value, generally gets 1.5; x _i,tposition while being the t time iteration of particle i; v _i,tthe speed of the t time iteration of particle i.C ₁, c ₂the representative study factor, generally gets 2.0; The random random function that produces numeral between 0～1 of R representative.Here also it is noted that if the new positional value of the particle obtaining does not meet constraint condition (15), need new making zero of positional value to process;

3-5), the renewal of particle target function value:

According to the positional value after each particle renewal, recalculate the target function value of each particle by formula (12) and formula (14);

3-6), upgrade pbest, gbest variable:

According to the more new formula of particle cluster algorithm pbest, upgrade the pbest variable of each particle, formula is as described below:

${\mathrm{pbest}}_{i,I_{\mathrm{ter}}+1}=\left\{\begin{array}{ccc}{X}_{i,I_{\mathrm{ter}}+1}& \mathrm{if}& H\left(X_{i,I_{\mathrm{ter}}+1}\right)>H\left({\mathrm{pbest}}_{i,I_{\mathrm{ter}}}\right)\\ {\mathrm{pbest}}_{i,I_{\mathrm{ter}}}& \mathrm{if}& H\left(X_{i,I_{\mathrm{ter}}+1}\right)<H\left({\mathrm{pbest}}_{i,I_{\mathrm{ter}}}\right)\end{array}\right.---\left(20\right)$

Wherein, H () represents the computing formula of objective function.Then the individuality of choosing target function value maximum in pbest is made as gbest variable;

3-7), judge whether convergence:

Whether evaluation algorithm restrains, if no convergence re-starts step 3-4, if algorithm convergence is carried out next step;

3-8), Output rusults:

According to the final result of particle cluster algorithm, export the fine setting coefficient of each point of formula, and the distribution income being improved after Sharp's profit method.

Technical conceive of the present invention is: taking realize between microgrid load that interests maximize and micro-source capacity configuration economical and efficient as tactful, taking into full account on the basis of mutual relationship between micro-source cost, micro-source capacity, load cost, load power consumption, set up micro-source and the load betting model with Game Relationship, and objective function under non-cooperation and cooperative game.Then utilize linear iteration to carry out game and solve, the optimum of function to achieve the objective.The improvement Shapley value method that utilizes income fine setting coefficient and stability index to search for is finally proposed, in income fine setting coefficient solution procedure, the present invention utilizes particle cluster algorithm to carry out optimizing and solves, pass through carry improvement Shapley value method the income after cooperating is redistributed, ensured to cooperate the stability of full alliance.

Advantage of the present invention is: considered that between microgrid load, interests maximize and the capacity high-efficient disposition of micro-source simultaneously, set up micro-source and the microgrid load betting model with Game Relationship.Shortcoming for traditional Sharp profit value in cooperation distributes, the present invention proposes the improvement Shapley value method that utilizes income fine setting coefficient and stability index to search for, this is improved one's methods and can redistribute the income after cooperation, can ensure that game person is greater than it in the income of cooperating to obtain under full alliance and exits the financial value obtaining under cooperative alliances, thereby ensure to cooperate the stability of full alliance.

Brief description of the drawings

Fig. 1 PSO Algorithm process flow diagram of the present invention

The relation of the income in micro-source and micro-source capacity, total load under Fig. 2 non-cooperative game of the present invention

1 the income of loading under Fig. 3 non-cooperative game of the present invention and the relation of total load

Income under Fig. 4 cooperative game of the present invention

Capacity and power consumption under Fig. 5 cooperative game of the present invention

embodiment

With reference to accompanying drawing:

Based on the microgrid load game distribution of income method of improving Shapley value method, comprise the following steps:

1), set up microgrid load betting model:

1-1), set up payoff function model;

Consider a microgrid containing m node, getting M is node set, and game person's set, for Γ, comprises a n game person, Γ=i|i=1,2 ..., n}, obviously,

n≤m.Load game side set L and micro-source game side S set all use game person i (i ∈ Γ) to represent, S ∪ L=Γ.I load game person's pure control strategy is x _i=p _i, p _irepresent the load power of this load bus; I micro-source game person's pure control strategy is x _i=s _i, s _irepresent micro-source capacity of this micro-source node.A n game person's pure strategy is combined as x={x ₁, x ₂..., x _i..., x _n, x _-i={ x ₁..., x _i-1, x _i+1..., x _nrepresent except tactful x _iother outer strategy combination.

Step (1-1) is specifically made up of following steps:

111), determine electricity charge function;

The electricity charge function of constructing has following features: 1) electricity price is along with the increase that micro-source game person invests capacity increases gradually, and rate of growth reduces gradually.When the investment capacity in micro-source hour, may not reach the single-machine capacity in micro-source, therefore unit cost is higher; And along with the investment capacity in micro-source increases gradually, its unit cost increases gradually, but tend towards stability.2) electricity price is along with the increase of load game person demand increases gradually, and rate of growth strengthens gradually.According to the feature of market economy, when supply exceed demand, electricity price is lower, along with the reverse of supplydemand relationship, certainly will occur competing the situation of electricity consumption, causes electricity price to rise violently.Therefore, constructed electricity price cost function is as described below:

$C_{\mathrm{CHR}}=k\sqrt{\underset{i=1}{\overset{n_s}{\mathrm{\&Sigma;}}}{s}_i}{\left(\underset{i=1}{\overset{n_l}{\mathrm{\&Sigma;}}}{p}_i\right)}^2---\left(1\right)$

Wherein, C _cHRfor total income of electricity charge of a year of all micro-source game persons, unit is unit/year; K is the unit cost coefficient in micro-source; p _ibe i load game person's planned supply and use of electric power amount, s _iit is i micro-source game person's tactful capacity; n _sfor the nodes in micro-source, n _lfor the nodes of load;

112), determine the payoff function in micro-source:

Micro-source game person's payoff function has comprised the electricity charge of collecting to load and the cost of investment in micro-source, is expressed as:

$H_{\mathrm{DGi}}={\mathrm{ks}}_i{\left(\underset{i=1}{\overset{n_l}{\mathrm{\&Sigma;}}}{p}_i\right)}^2/\sqrt{\underset{i=1}{\overset{n_s}{\mathrm{\&Sigma;}}}{s}_i}-\frac{R{(1+R)}^T}{{(1+R)}^T-1}{s}_i{c}_{\mathrm{DGi}}---\left(2\right)$

Wherein, H _dGiit is i micro-source game person's payoff function; R is annual rate, the pay back period of investment that T is micro-source, c _dGiit is the unit capacity cost in i micro-source;

113), determine the payoff function of load:

Load game person's payoff function be the income that participates in main business with the difference of payment electricity price expense, be defined as:

H _Li=u _i,SEL-C _i,CHR (3)

Wherein, H _liit is i load game person's payoff function; u _{i, SEL}for load participates in main business, the income that production marketing brings; C _{i, CHR}for load needs the electricity charge that pay;

The output value of load is:

$u_{i,\mathrm{SEL}}={8760c}_{i,\mathrm{SEL}}=8760(a_{\mathrm{<figure-callout\; id="2"\; label="i\; p\; i"\; filenames="DEST\_PATH\_HDA0000487851730000022.png,DEST\_PATH\_HDA0000487851730000023.png"\; state="\{\{state\}\}">i</figure-callout>}}{p}_i^{}{}_2^{}+b_i{p}_i)---\left(4\right)$

Wherein, c _{i, SEL}for the output value per hour of different load, become secondary relevant with the electric weight of load, unit be first/hour; a _iand b _ifor the related coefficient of load output value quadratic function, it is the coefficient of colligation obtaining on the basis of the expenses such as raw material, artificial, maintenance considering.

The electricity charge that load game person pays are:

$C_{i,\mathrm{CHR}}=C_{\mathrm{CHR}}\&times;\frac{p_i}{\underset{i=1}{\overset{n_l}{\mathrm{\&Sigma;}}}{p}_i}---\left(5\right)$

114), determine each game person's payoff function

To every kind of pure strategy combination x, construct each game person's payoff function u _i(x _i, x _-i) be:

$u_i(x_i,x_{-i})=\left\{\begin{array}{cc}{\mathrm{ks}}_i{\left(\underset{i=1}{\overset{n_s}{\mathrm{\&Sigma;}}}{p}_i\right)}^2/\sqrt{\underset{i=1}{\overset{n_s}{\mathrm{\&Sigma;}}}{s}_i}-\underset{i=1}{\overset{n_s}{\mathrm{\&Sigma;}}}\frac{R{(1+R)}^T}{{(1+R)}^T-1}{s}_i{c}_{{\mathrm{DG}}_i}& i\&Element;S\\ 8760(a_{\mathrm{<figure-callout\; id="2"\; label="i\; p\; i"\; filenames="DEST\_PATH\_HDA0000487851730000022.png,DEST\_PATH\_HDA0000487851730000023.png"\; state="\{\{state\}\}">i</figure-callout>}}{p}_i^{}{}_2^{}+b_i{p}_i)-k\sqrt{\underset{i=1}{\overset{n_l}{\mathrm{\&Sigma;}}}{s}_i}\left(\underset{i=1}{\overset{n_l}{\mathrm{\&Sigma;}}}{p}_i\right)p_i& i\&Element;L\end{array}\right.---\left(6\right)$

In formula (1), R is annual rate, the pay back period of investment that T is micro-source, c _dGfor the unit capacity cost in micro-source, n _sfor the nodes in micro-source, n _lfor the nodes of load, k is micro-source unit cost coefficient, a _i, b _ifor the coefficient entry of load revenue function.

Strategy meets constraint:

$\left\{\begin{array}{cc}\underset{i=1}{\overset{n_s}{\mathrm{\&Sigma;}}}{s}_i\&GreaterEqual;\underset{i=1}{\overset{n_l}{\mathrm{\&Sigma;}}}{p}_i& i\&Element;\mathrm{\&Gamma;}\\ s_i\&GreaterEqual;0& i\&Element;S\\ p_i\&GreaterEqual;0& i\&Element;L\\ & \end{array}\right.---\left(7\right)$

In the time that game person is micro-source node, this game person's payoff function is made up of sale of electricity electricity price income and the difference of micro-source cost of investment.In the time that game person is load bus, this game person's payoff function is made up of the income of load point main business and the difference of the electricity price expense that pays;

1-2), determine game person's objective function model:

In non-cooperative game, between each game person, there is no binding agreement, independently seek separately number one and maximize.Corresponding objective function is:

${x_i}^{*}=\arg \underset{x_i}{\max }{u}_i(x_i,x_{-i})---\left(8\right)$

In cooperative game, between each game person, taking collective rationality as basis, first realize the maximization of alliance's income, then by the suitable distribution of income being maximized to each game person's income.When n game person's cooperative game of note, will produce X kind game play mode, every kind of cooperation is all with the interests u under this pattern _xbe objective function to the maximum, be expressed as:

${x_i}^{*}=\arg \underset{x_i}{\max }{u}_X(x_i,x_{-i})---\left(9\right)$

2), improving Sharp's profit value realizes;

2-1), Shapley value method is realized;

Further, for step (3-1), determining step is as follows:

211) determine alliance:

In n-person game, game person gathers with N={1, and 2 ..., n} represents, the random subset S of N is called an alliance.

212) determine fundamental function:

A given n-person game, S is an alliance, v (S) refer to S and

two-person game in the maximum utility of S, v (S) is called the fundamental function of the S of alliance;

213) determine allocative decision:

For cooperative game (N, v), N={1,2 ..., n}, to each game person i ∈ N, gives a real-valued parameters u _i, form n-dimensional vector u={u ₁, u ₂..., u _i..., u _n, and it meets: u _i>=v (i}),

claim u={u1, u2 ..., ui ..., un} is an allocative decision of the S of alliance;

214) determine distribution of income value:

To each game (N, v), there is unique u (v)=(u ₁(v), u ₂(v) ..., u _i(v) ..., u _n(v)) value, is defined as Sharp's profit value, is now assigned to the income u of game person i _i(v) be

$u_i\left(v\right)=\underset{S\&Subset;N/\left\{i\right\}}{\mathrm{\&Sigma;}}\frac{\left|S\right|!(n-|S|-1)!}{n!}[v(S\&cup;\{i\left\}\right)-v\left(S\right)]---\left(10\right)$

Wherein, | S| represents the number of all game persons in the S of alliance;

2-2) improve Shapley value method:

Implementation method main thought is: first carry out distribution of interests according to Shapley value method, afterwards, from the large game person's hand of income, regain a part of interests, and all re-starting fine setting in member, make each member's income all meet rationality constraint.

Further, for step (2-2), determining step is as follows:

221), determine income fine setting coefficient;

Making the income fine setting coefficient of game person i is Δ λ _i, meet:

$\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&Delta;\&lambda;}}_i=0---\left(11\right)$

Use Δ λ _irevise Shapley value u _i(v), the Shapley value u that is improved _i(v) *:

$u_i\left(v\right)*=u_i\left(v\right)+{\mathrm{\&Delta;\&lambda;}}_i\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{u}_i\left(v\right)---\left(12\right)$

Obviously, $v\left(N\right)=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{u}_i\left(v\right)=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{u}_i\left(v\right)*;$

222), determine stability index:

In order to try to achieve the income fine setting coefficient delta λ meeting the demands _i, the income growth pattern of game person i after improving the distribution of Shapley value is carried out to quantification treatment, definition stability index δ _ι:

${\mathrm{\&delta;}}_i=\frac{u_i{\left(v\right)}^{*}}{v\left(\right\{i\left\}\right)}---\left(13\right)$

Obviously, only has the δ of working as _i>=1 o'clock, game person i was just ready to participate in cooperation.Stability index value is larger, and alliance's result is more stable.

Therefore, improve Sharpley Value Method and can be described as finding optimum income fine setting coefficient delta λ _i, make following objective function maximum:

$\mathrm{\&delta;}=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&delta;}}_i---\left(14\right)$

Constraint condition is:

$\left\{\begin{array}{c}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&Delta;\&lambda;}}_i=0\\ {\mathrm{\&delta;}}_i\&GreaterEqual;1\end{array}\right.---\left(15\right)$

3) PSO Algorithm fine setting coefficient, solves process flow diagram as shown in Figure 1:

3-1), initiation parameter:

Be provided for solving the parameter of the particle cluster algorithm of fine setting coefficient, comprise the particle number, inertia weight value, the study factor of iterations, the population of population etc.And input the distribution of income value of each game side that traditional Sharp profit value distribution method obtains;

3-2), initialization population position, speed and target function value:

The initialized location of random definition population particle, remember that this position vector is X:

X=(x ₁,x ₂,…,x _m) （16）

Wherein, x _irefer to fine setting coefficient delta λ _i; M value is the number of fine setting coefficient, the number that needs to distribute income side.It should be noted that fine setting restricted coefficients of equation condition (15), summation is 0.If the position of random initializtion does not meet this constraint condition, need its making zero, make it meet constraint condition;

The initialization speed of random definition particle cluster algorithm, remember that this velocity vector is V:

V=(v ₁,v ₂,…,v _m) （17）

According to the initialized position of particle, by formula (12) and formula (14), calculate the stability index of each particle, i.e. the initial target functional value of each particle;

3-3), initialization pbest and gbest variable:

Positional value initial each particle and target function value are made as to the initial value of population pbest variable (the historical optimal value of each particle), and select a wherein particle of target function value maximum, be made as the initial value of gbest variable (whole population is when the optimal value of time iteration);

3-4), the renewal of population position and speed:

According to the more new formula of the speed of particle cluster algorithm and position, position and speed to each particle are upgraded.The more new formula adopting is as follows:

v _i,t+1=wv _i,t+c ₁×R×(pbest _t-x _i,t)+c ₂×R×(gbest _t-x _i,t)c （18）

x _i,t+1=x _i,t+v _t （19）

Wherein, w refers to inertia weight value, generally gets 1.5; x _i,tposition while being the t time iteration of particle i; v _i,tthe speed of the t time iteration of particle i.C ₁, c ₂the representative study factor, generally gets 2.0; The random random function that produces numeral between 0～1 of R representative.Here also it is noted that if the new positional value of the particle obtaining does not meet constraint condition (15), need new making zero of positional value to process;

3-5), the renewal of particle target function value:

According to the positional value after each particle renewal, recalculate the target function value of each particle by formula (12) and formula (14);

3-6), upgrade pbest, gbest variable:

According to the more new formula of particle cluster algorithm pbest, upgrade the pbest variable of each particle, formula is as described below:

${\mathrm{pbest}}_{i,I_{\mathrm{ter}}+1}=\left\{\begin{array}{ccc}{X}_{i,I_{\mathrm{ter}}+1}& \mathrm{if}& H\left(X_{i,I_{\mathrm{ter}}+1}\right)>H\left({\mathrm{pbest}}_{i,I_{\mathrm{ter}}}\right)\\ {\mathrm{pbest}}_{i,I_{\mathrm{ter}}}& \mathrm{if}& H\left(X_{i,I_{\mathrm{ter}}+1}\right)<H\left({\mathrm{pbest}}_{i,I_{\mathrm{ter}}}\right)\end{array}\right.---\left(20\right)$

Wherein, H () represents the computing formula of objective function.Then the individuality of choosing target function value maximum in pbest is made as gbest variable;

3-7), judge whether convergence:

Whether evaluation algorithm restrains, if no convergence re-starts step 3-4, if algorithm convergence is carried out next step;

3-8), Output rusults:

According to the final result of particle cluster algorithm, export the fine setting coefficient of each point of formula, and the distribution income being improved after Sharp's profit method;

Case analysis

Yi Mou industrial park is example, in order to avoid too much permutation and combination, the present invention to choose 4 game persons in game process, is respectively micro-source investor G ₁and the load game person G being formed by different factories ₂, G ₃, G ₄.

In particle cluster algorithm, choose 200 particles, iterations is 500 times, inertia weight w=1.5, study factor c1=c2=2.0.Systematic parameter is as shown in table 1.

Table 1 systematic parameter

A), non-cooperative game

Choose formula (8) as non-cooperative game target, draw micro-source and each load power consumption change curve and income result under non-cooperative game, as shown in Figure 2.

The income variation tendency in micro-source when the representation of a surface micro-source capacity in Fig. 2 and total load change.In figure, red area represents that income is high, and blue region represents that income is low.Obviously, ideally, larger, micro-source capacity of loading is more, and the income in micro-source is also higher.But in this paper non-cooperative game, the actual change situation of micro-source yield curve is as shown in red curve in figure.In the incipient stage of game, along with the increase of load and micro-source capacity, micro-source income progressively raises by red curve in figure.When load increases to A point in figure, after 952kW, load is considering, under the prerequisite of number one, will can not increase electricity consumption again, therefore, continues to increase micro-source capacity and will cause micro-source utilization factor to reduce, and causes micro-source income to reduce gradually along red curve in figure.

Fixing micro-source capacity, 1 income variation tendency can obtain loading when the total load shown in Fig. 3 changes.As seen from Figure 3, if when load general power consumes completely on load 1, load 1 Income Maximum, as B point (400 in figure, 400,5.34E6), otherwise, along with the increase of other load power consumption, the income of load 1 reduces linearity, as the blue straight line in figure.This straight line has formed the curved surface of Fig. 3 in the movement in space.If total load remains unchanged, along with the increase of load 1 power consumption, will there is obvious convex function characteristic in load 1 income, first increase gradually, after reduce gradually.

Non-cooperative game result is as shown in table 2, and Nash break-even point is (952kW, 236kW, 326kW, 390kW), and all game persons all reach interests separately and maximize, and now the corresponding electricity charge are 1.67 yuan/kWh.From table 2, the load G that the output value is less ₂corresponding power consumption and income are relatively little, the load G that the output value is larger ₄the power consumption needing is relative with income higher.Micro-source G ₁capacity be subject to the total quantitative limitation of workload demand, continue dilatation only can cause microgrid operator income reduce.3 loads are 25:35:40 to the electricity charge ratio of micro-source payment.Micro-source and load game person's total revenue is 28,053,585 yuan/year.

Table 2 non-cooperative game result

There are 4 game persons herein, the raw 14 kinds of cooperative game patterns of common property, as shown in table 3.Choose interests under every kind of pattern and maximize as game target, can draw unit electricity price under various cooperative games, micro-source and respectively load power consumption and income result as shown in table 3, Fig. 4 and Fig. 5, payoff detailed data is as shown in table 4.

Table 3 cooperative game pattern

Table 4 cooperative game result

From table 3, Fig. 4 and Fig. 5:

1) full alliance state, i.e. the total revenue maximum of pattern 14.Under this pattern, load side and micro-source side are in cooperation state, and they are considering on the basis of inner link between load side income, micro-source cost and the electricity charge, make final micro-source configuration capacity and load power consumption all larger.But it is noted that under full alliance state, unit electricity price is very high, reach 4.26 yuan/hour.If game person's income separately is still calculated according to payoff function separately, may cause the income of load is negative value (as shown in pattern in Fig. 44,5,7,8,10,11,14).Therefore need to adopt rational distribution mechanism to reallocate to total revenue.

2), for micro-source game person, preferred manner is and load cooperation.In addition, the load composition alliance less with income can be considered in micro-source, and for example, the capacity in 4,10 and 11 times micro-sources of pattern is all larger.This is because the load under cooperation state is no longer considered the impact (internal-neutralized) of electricity price on its income, only determines production scale by the percent saturation of market of product.This cooperation, is expanded the capacity in micro-source.But this alliance also causes raising of unit electricity price, corresponding electricity price is all greater than 3 yuan/hour substantially.So high electricity price needs all to be born by the load of not participating in alliance, and therefore can final total revenue higher than the income under non-cooperation, depends on the game person's who does not participate in alliance income and electricity consumption situation completely, needs concrete condition concrete analysis.

3) for load game person, preferred manner is cooperate with micro-source, if selection does not participate in alliance, can expect that other load also do not cooperate with micro-source.For example, for the G of simply connected alliance ₂, Income Maximum under mode 3; For the G of simply connected alliance ₃, 2 times Income Maximums of pattern.In pattern 1,2,3, basic charge as per installed capacity all only has about 1.5 yuan/hour.When either party in micro-source and other load forms alliance, all can cause the rising of non-partner unit electricity price.

4) between load alliance and with micro-source in race condition, or sub-load and Wei Yuan alliance carry out game with other load again, these two kinds of modes have all been subdued both sides' interests, the final total revenue making is less than the income under non-cooperation.For example, in pattern 13, load and micro-source opposite in game completely, limit mutually, do not give in mutually.Therefore micro-source capacity does not increase, and electricity price is minimum, is 1.31 yuan/hour; Meanwhile, load power consumption does not increase yet, and benefit cannot embody.

C), improving Sharp's profit value distributes

Utilize particle cluster algorithm to formula (13) optimizing, obtain income fine setting coefficient and stability index as shown in table 5.

From table 5, under the prerequisite that is zero in income fine setting coefficient summation, find and made each game person's stability index all be greater than 1 solution.Bring the data of table 3 into formula (12) income under full alliance is improved to Sharp's profit value distribution, and compare with the allocation result of traditional Shapley value method.As shown in table 6.Visible, when full alliance, system benefit is higher than non-cooperation state, also higher than each fundamental function value under cooperation state.But Shapley value method allocation result shows, G ₄the income (9,537,443) obtaining is less than its fundamental function (10,931,208), is also less than the income (10,180,562) under non-cooperation state, therefore, and G ₄can trend towards exiting alliance, cause full alliance state labile.But after utilizing improvement Shapley value method in this paper to distribute, each game person's financial value is not only greater than under non-cooperation state income separately, and is all greater than fundamental function value separately, now, all game persons all obtain optimum interests under full alliance state, have kept the stability of alliance.

Table 5 income fine setting coefficient delta λ _iand stability index δ _ι

The comparison of table 6 income

Illustrate by above case, under non-cooperative game, the total revenue in microgrid load and micro-source is lower, and inappropriate alliance even can further reduce system-wide income, and the total revenue under the cooperative game of full alliance is the highest; Improvement Shapley value method based on income fine setting coefficient and stability index can be realized the stable allocation in alliance, makes full alliance become stable game core; By calculating power consumption and the financial value of microgrid load, can instruct microgrid to plan that micro-source exerts oneself, be conducive to reasonable disposition resource, reach the object of energy-saving and emission-reduction.

Content described in this instructions case study on implementation is only enumerating of way of realization to inventive concept; protection scope of the present invention should not be regarded as only limiting to the concrete form that case study on implementation is stated, protection scope of the present invention also and conceive the equivalent technologies means that can expect according to the present invention in those skilled in the art.

Claims (4)

1. the improvement Shapley value method distribution method based on the game of microgrid load, comprises the following steps:

Step 1, set up microgrid load betting model;

Step 2, improvement Shapley value method are realized;

Step 3, PSO Algorithm fine setting coefficient.

2. the method for claim 1, is characterized in that: the concrete steps of setting up microgrid load betting model in step 1 are as follows:

1-1), set up payoff function model;

Consider a microgrid containing m node, getting M is node set, and game person's set, for Γ, comprises a n game person, Γ=i|i=1,2 ..., n}, obviously,

n≤m; Load game side set L and micro-source game side S set all use game person i (i ∈ Γ) to represent, S ∪ L=Γ.I load game person's pure control strategy is x _i=p _i, p _irepresent the load power of this load bus; I micro-source game person's pure control strategy is x _i=s _i, s _irepresent micro-source capacity of this micro-source node; A n game person's pure strategy is combined as x={x ₁, x ₂..., x _i..., x _n, x _-i={ x ₁..., x _i-1, x _i+1..., x _nrepresent except tactful x _iother outer strategy combination;

Specifically comprise:

111), determine electricity charge function;

The electricity charge function of constructing is as described below:

Wherein, C _cHRfor total income of electricity charge of a year of all micro-source game persons, unit is unit/year; K is the unit cost coefficient in micro-source; p _ibe i load game person's planned supply and use of electric power amount, s _iit is i micro-source game person's tactful capacity; n _sfor the nodes in micro-source, n _lfor the nodes of load;

112), determine the payoff function in micro-source:

Micro-source game person's payoff function has comprised the electricity charge of collecting to load and the cost of investment in micro-source, is expressed as:

Wherein, H _dGiit is i micro-source game person's payoff function; R is annual rate, the pay back period of investment that T is micro-source, c _dGiit is the unit capacity cost in i micro-source;

113), determine the payoff function of load:

Load game person's payoff function be the income that participates in main business with the difference of payment electricity price expense, be defined as:

H _Li=u _i,SEL-C _i,CHR (3)

Wherein, H _liit is i load game person's payoff function; u _{i, SEL}for load participates in main business, the income that production marketing brings; C _{i, CHR}for load needs the electricity charge that pay;

The output value of load is:

Wherein, c _{i, SEL}for the output value per hour of different load, become secondary relevant with the electric weight of load, unit be first/hour; a _iand b _ifor the related coefficient of load output value quadratic function, it is the coefficient of colligation obtaining on the basis of the expenses such as raw material, artificial, maintenance considering;

The electricity charge that load game person pays are:

114), determine each game person's payoff function

To every kind of pure strategy combination x, construct each game person's payoff function u _i(x _i, x _-i) be:

In formula (1), R is annual rate, the pay back period of investment that T is micro-source, c _dGfor the unit capacity cost in micro-source, n _sfor the nodes in micro-source, n _lfor the nodes of load, k is micro-source unit cost coefficient, a _i, b _ifor the coefficient entry of load revenue function;

Strategy meets constraint:

In the time that game person is micro-source node, this game person's payoff function is made up of sale of electricity electricity price income and the difference of micro-source cost of investment.In the time that game person is load bus, this game person's payoff function is made up of the income of load point main business and the difference of the electricity price expense that pays;

1-2), determine game person's objective function model:

In non-cooperative game, between each game person, there is no binding agreement, independently seek separately number one and maximize.Corresponding objective function is:

In cooperative game, between each game person, taking collective rationality as basis, first realize the maximization of alliance's income, then by the suitable distribution of income being maximized to each game person's income; When n game person's cooperative game of note, will produce X kind game play mode, every kind of cooperation is all with the interests u under this pattern _xbe objective function to the maximum, be expressed as:

。

3. method as claimed in claim 2, is characterized in that: the concrete steps that step (2) is improved Shapley value method realization are as follows:

2-1), Shapley value method realize, concrete steps are as follows:

211) determine alliance:

In n-person game, game person gathers with N={1, and 2 ..., n} represents, the random subset S of N is called an alliance;

212) determine fundamental function:

A given n-person game, S is an alliance, v (S) refer to S and

two-person game in the maximum utility of S, v (S) is called the fundamental function of the S of alliance;

213) determine allocative decision:

For cooperative game (N, v), N={1,2 ..., n}, to each game person i ∈ N, gives a real-valued parameters u _i, form n-dimensional vector u={u ₁, u ₂..., u _i..., u _n, and it meets: u _i>=v (i}),

claim u={u ₁, u ₂..., u _i..., u _nit is an allocative decision of the S of alliance;

214) determine distribution of income value:

To each game (N, v), there is unique u (v)=(u ₁(v), u ₂(v) ..., u _i(v) ..., u _n(v)) value, is defined as Sharp's profit value, is now assigned to the income u of game person i _i(v) be

Wherein, | S| represents the number of all game persons in the S of alliance;

2-2) improve Shapley value method:

First carry out distribution of interests according to Shapley value method, afterwards, from the large game person's hand of income, regain a part of interests, and all re-starting fine setting in member, make each member's income all meet rationality constraint;

Concrete steps are as follows:

221), determine income fine setting coefficient;

Making the income fine setting coefficient of game person i is Δ λ _i, meet:

Use Δ λ _irevise Shapley value u _i(v), the Shapley value u that is improved _i(v) *:

Obviously,

222), determine stability index:

In order to try to achieve the income fine setting coefficient delta λ meeting the demands _i, the income growth pattern of game person i after improving the distribution of Shapley value is carried out to quantification treatment, definition stability index δ _ι:

Obviously, only has the δ of working as _i>=1 o'clock, game person i was just ready to participate in cooperation.Stability index value is larger, and alliance's result is more stable;

Therefore, improve Sharpley Value Method and can be described as finding optimum income fine setting coefficient delta λ _i, make following objective function maximum:

Constraint condition is:

。

4. method as claimed in claim 3, is characterized in that: the concrete steps of step (3) PSO Algorithm fine setting coefficient are as follows:

3-1), initiation parameter:

Be provided for solving the parameter of the particle cluster algorithm of fine setting coefficient, comprise iterations, the particle number of population, inertia weight value, the study factor of population, and input the distribution of income value of each game side that traditional Sharp profit value distribution method obtains;

3-2), initialization population position, speed and target function value:

The initialized location of random definition population particle, remember that this position vector is X:

X=(x ₁,x ₂,…,x _m) （16）

Wherein, x _irefer to fine setting coefficient delta λ _i; M value is the number of fine setting coefficient, the number that needs to distribute income side; It should be noted that fine setting restricted coefficients of equation condition (15), summation is 0.If the position of random initializtion does not meet this constraint condition, need its making zero, make it meet constraint condition;

The initialization speed of random definition particle cluster algorithm, remember that this velocity vector is V:

V=(v ₁,v ₂,…,v _m) （17）

According to the initialized position of particle, by formula (12) and formula (14), calculate the stability index of each particle, i.e. the initial target functional value of each particle;

3-3), initialization pbest and gbest variable:

Positional value initial each particle and target function value are made as to the initial value of population pbest variable (the historical optimal value of each particle), and select a wherein particle of target function value maximum, be made as the initial value of gbest variable (whole population is when the optimal value of time iteration);

3-4), the renewal of population position and speed:

According to the more new formula of the speed of particle cluster algorithm and position, position and speed to each particle are upgraded; The more new formula adopting is as follows:

v _i,t+1=wv _i,t+c ₁×R×(pbest _t-x _i,t)+c ₂×R×(gbest _t-x _i,t) （18）

x _i,t+1=x _i,t+v _t （19）

Wherein, w refers to inertia weight value, generally gets 1.5; x _i,tposition while being the t time iteration of particle i; v _i,tthe speed of the t time iteration of particle i.C ₁, c ₂the representative study factor, generally gets 2.0; The random random function that produces numeral between 0～1 of R representative.Here also it is noted that if the new positional value of the particle obtaining does not meet constraint condition (15), need new making zero of positional value to process;

3-5), the renewal of particle target function value:

According to the positional value after each particle renewal, recalculate the target function value of each particle by formula (12) and formula (14);

3-6), upgrade pbest, gbest variable:

According to the more new formula of particle cluster algorithm pbest, upgrade the pbest variable of each particle, formula is as described below:

Wherein, H () represents the computing formula of objective function.Then the individuality of choosing target function value maximum in pbest is made as gbest variable;

3-7), judge whether convergence:

Whether evaluation algorithm restrains, if no convergence re-starts step 3-4, if algorithm convergence is carried out next step;

3-8), Output rusults:

According to the final result of particle cluster algorithm, export the fine setting coefficient of each point of formula, and the distribution income being improved after Sharp's profit method.

Images