CN108347062B

CN108347062B - micro-grid energy management distributed multi-target collaborative optimization algorithm based on potential game

Info

Publication number: CN108347062B
Application number: CN201810028818.2A
Authority: CN
Inventors: 曾君; 王侨侨; 刘俊峰
Original assignee: South China University of Technology SCUT
Current assignee: South China University of Technology SCUT
Priority date: 2018-01-12
Filing date: 2018-01-12
Publication date: 2019-12-10
Anticipated expiration: 2038-01-12
Also published as: CN108347062A

Abstract

the invention discloses a potential game-based micro-grid energy management distributed multi-target collaborative optimization algorithm, which comprises the following steps: 1) modeling a microgrid element unit, including determining a decision subject, decision variables, element constraints and multi-objective modeling; 2) potential game modeling is carried out, and both the income function and the potential function are vector functions; 3) distributed game solving based on a multi-objective optimization algorithm mainly adopts a multi-objective evolutionary algorithm to solve a pareto optimal solution set of a gain function, and solves Nash equilibrium through distributed iteration. The distributed multi-subject decision optimization method is adopted, and a potential game theory with distributed characteristics is combined, so that the expansion of the microgrid is easy to realize, local management and local decision are realized, the reliability and flexibility of the system are increased, the distributed multi-target optimization is realized in a game mode, the competition and cooperation relationship of microgrid individuals is realized, the individual benefit is ensured, and the maximization of the overall benefit of the microgrid is realized.

Description

Micro-grid energy management distributed multi-target collaborative optimization algorithm based on potential game

Technical Field

The invention relates to the technical field of operation, simulation, analysis and scheduling of a microgrid, in particular to a microgrid energy management distributed multi-target collaborative optimization algorithm based on potential game.

Background

The smart power grid has the performances of flexibility, cleanness, safety, economy, friendliness and the like, and is a development direction of a future power grid. The massive access and exploitation of distributed power sources (including stored energy) and the implementation of demand-side management are the prime movers in the development of smart grids. The microgrid is the best bridge connecting a distributed power supply with a large power grid, and is generally defined as a low-voltage distribution network or system comprising the distributed power supply, energy storage equipment and controllable loads, and can be operated off-grid (island) or be regarded as the controllable power supply or load of the large power grid. Therefore, the microgrid is also considered to be a building block of the smart grid.

With the development of information technology and physical information fusion systems (CPS), distributed power supplies and loads of more different benefit agents can access the micro-grid, and the intelligence and the self-benefit of the micro-grid are further enhanced. Distributed and plug and play are inevitable trends in the development of micro-grids, and the micro-grids are required to have flexible grid structures and good expansion performance. The following three aspects can be considered: 1. the distributed power supply, the energy storage equipment and the load are used as controllable modular element units to be connected into the microgrid; 2. the physical information deep fusion connects loose modular element units into an organic whole; 3. distributed energy management and optimization.

At present, a great deal of research focuses on centralized optimization of a microgrid, such as an evolutionary algorithm, a random planning method, a model prediction control method and a multi-objective optimization algorithm. Obviously, the centralized optimization method needs to process a large amount of data, has poor expandability and is not easy to realize plug and play. Most of the current research on distributed optimization is multi-agent systems (MAS). Fundamentally, MAS based on distributed information and computational algorithms is an excellent technical solution and does not fully express the self-benefit of distributed power sources or loads. Meanwhile, the operation optimization of the microgrid is a multi-objective optimization problem, so that a distributed multi-objective optimization algorithm considering individual self-interest is needed to be designed. The potential game theory with distributed nature is the basis of the present invention and is briefly introduced below.

The strategy game comprises three elements of people in the game, strategy and a revenue function (utility function). For policy Game Γ ═<N,{Yⁱ}_i∈N,{U_i}_i∈N>N is {1,2, …, N } is a collection of people in a office, YⁱA set of policies representing the ith office, the revenue function for office i being U_i:Y→R(Y＝Y¹×Y²×……×Yⁿis the office-man policy combination, R is the set of real numbers). Let S be a subset of N, -S be the complement of S, Y^Srepresentation of Cartesian product (Cartesian product) in book_i∈SYⁱ. For a single set of elements i, Y^-{i}Abbreviated as Y^-i. Policy combination y ═ y¹,y²,…,yⁿ) Abbreviated as y ═ yⁱ,y^-i)，yⁱ∈Yⁱ，y^-i∈Y^-i，y∈Y。

Potential game (Monderer D., Shapley L.S., positional Games [ J.)].Games&Economatic Behavior,1996,14(1): 124-: for game Γ ═<N,{Yⁱ}_i∈N,{U_i}_i∈N>y → R for the function G if presentSatisfies the following conditions:

U_i(x,y^-i)-U_i(z,y^-i)＝G(x,y^-i)-G(z,y^-i)，

Game Γ is referred to as a full potential game. Potential games have limited improvement attributes that ensure that the potential game necessarily has nash equilibrium points.

Disclosure of Invention

The invention aims to overcome the defects and shortcomings of an operation optimization algorithm of an existing microgrid energy management system, and particularly provides a microgrid energy management distributed multi-target collaborative optimization algorithm based on potential game.

In order to achieve the purpose, the technical scheme provided by the invention is as follows: a potential game-based micro-grid energy management distributed multi-objective collaborative optimization algorithm comprises the following steps:

1) Microgrid element unit modeling

Considering a typical micro-grid, which is composed of photovoltaic array (PV/PV), wind power generator (WT/WT), diesel generator (DE/DE), storage battery (BA/BA), load (LD/LD), and electric vehicle (EV/EV), etc., each component combines with corresponding power variator, sensor, controller and intelligent switch to form a controllable component unit; each element unit is provided with a Local Manager (LM) for local decision and local management, and all the LMs are interconnected through a network and can communicate with each other to realize distributed coordination control;

1.1) decision principal and decision variables

a decision main body set N composed of all element units is represented as formula (1);

Where n1 corresponds to the number of photovoltaic array assemblies PV, PV_nIs the nth group photovoltaic array, n is 1,2, …, n 1; n2 corresponds to the number of wind turbine assemblies WT, WT_nIs the nth wind power generator, n is 1,2, …, n 2; n3 corresponds to the number of diesel generator sets DE, DE_nIs the nth diesel generator, n is 1,2, …, n 3; n4 corresponds to the number of battery aggregates BA, BA_nIs the nth group of storage batteries, n is 1,2, …, n 4; n5 corresponds to the number of load sets LD, LD_nIs the nth load, n ═ 1,2, …, n 5; n6 corresponds to the number of sets EV of electric vehicles, EV_nIs the nth electric automobile, n is 1,2, …, n 6;

Assuming that the time window to be optimized contains TN optimization periods, the output power or the consumed power (decision variable) of the element unit i in the period t is P_i ^tI ∈ N, t ═ 1,2, …, TN, and positive values denote output power and negative values denote consumed power; decision vector P for element unit i_iRepresented by formula (2);

1.2) component constraint

decision variablesConstrained by upper and lower limits, as shown in formula (3);

power of element unit i in t periodlower limits of P^t _i·maxAnd P^t _i·min(ii) a At the same time, other constraints g on the element unit_i(P_i) As shown in formula (4);

g_i(P_i)≤0,i∈N (4)

All element units must satisfy the power balance constraint, as shown in equation (5);

1.3) Multi-object modeling

The multi-objective function considers two categories: a free interest goal and a collaborative goal;

The interest target refers to a target which is only related to the decision vector of the element unit and is not related to the decision vectors of other element units, and the target indicates that the interest of the element unit pursues the maximization of the interest of the element unit; the number of such targets is at least one, and the targets are two, i.e., the yield of the element unit i and the emission of pollutants, i.e., waste, and the maximum yield target is F_i ¹(P_i,ρ,γ_i)，ρ^tthe unit electricity price of the t period is t, and t is 1,2, …, TN and rho are electricity price vectors;is the unit cost coefficient of the t period, t is 1,2, …, TN, gamma_iA cost coefficient vector, as shown in equation (6);

The aim of minimizing pollutant (waste) discharge is Is the waste discharge coefficient of the period t, t is 1,2, …, TN, mu_iIs an emission coefficient vector, as shown in formula (7);

factor rho, gamma_iAnd mu_iis a non-decision vector, F without misinterpretation_i ¹(P_i,ρ,γ_i) And F_i ²(P_i,μ_i) Each of which is abbreviated as F_i ¹(P_i) Is a sum of F_i ²(P_i)；

The cooperative target refers to a target shared by decision-making main bodies, and is realized by mutual information sharing to represent interaction and influence among the decision-making main bodies; the number of the cooperative targets can be one or more, and each cooperative target at least comprises two decision-making subjects; aiming at the coordination of m decision-making main bodies of photovoltaic-fan-load, aiming at enabling the load to be consistent with the output of renewable energy sources so as to reduce the influence of the volatility on a microgrid, and aiming at the coordination of an element unit iThe cooperative targeting of element unit j is The cooperative target of the element unit k isi, j and k respectively represent a photovoltaic element, a fan element and a load, and are shown as a formula (8);

The m decision-making subjects have the same cooperative target form F^(i,j,k)(P_i,P_j,P_k) As shown in formula (9);

In the formula, avg^τ(P_i,P_j,P_k) Is N from the time period tau_wAverage value of decision variables of i, j and k within a time window, N_wIs the length of the sliding time window;

2) Potential game modeling

all decision-making main bodies are used as game players, and the game players are shown in a formula (1); decision vector P in element unit i_iThe strategy of the person in the bureau is shown as a formula (2); all decision vectors P satisfying equations (3) and (4)_iis a strategy space Y which is a strategy set of people i in the officeⁱAs shown in formula (10);

utility function U of person i in office_i(P_s)_s∈Ni.e. the payment function is a vector function, P_sthe decision vector which influences the utility function of the person i in the office is shown as a formula (11);

The utility functions for all people in a office must have the same dimensions, but the number of optimization objectives for people in each office may be different, by: classifying all optimization targets, including an economic target (income), an environmental target (pollutant emission), a photovoltaic-fan-load cooperative target and the like, in sequence in a utility function vector, placing targets of the same type, namely targets with the same dimension, at the same position, and supplementing with 0 if no targets of the same type exist; unifying the forms of all the targets, processing all the minimized targets according to the inverse number of the maximized targets, and converting all the targets into minimized treatment by the same method;

existence potential function G (P)_s)_s∈NSatisfying the potential game definition as shown in formula (12);

Establishing a distributed multi-target cooperative optimization potential game model;

3) distributed game solving based on multi-objective optimization algorithm

The game solving is realized by the following steps:

3.1) policy evaluation

directly evaluating the strategy by using a utility function, wherein the utility function is a vector function, each component is an optimization target, and a pareto optimal solution set is solved by adopting a multi-objective optimization algorithm to serve as a candidate strategy set; the multi-objective optimization algorithm comprises but is not limited to multi-objective particle swarm optimization (MOPSO) and multi-objective genetic algorithms (NSGA, NSGA-II and NSGA-III), and multi-objective evolutionary algorithms and modified forms thereof;

3.2) decision rules

The local center needs to select one strategy from the candidate strategy set as the next strategy, and the following principle is established by considering the global power balance constraint, namely equation (5): firstly, a feasible solution is prior to an infeasible solution; second, the non-dominant solution in the feasible solution is prior; solution priority with small constraint violation amount in infeasible solution;

the constraint violation quantity refers to the power balance constraint violation quantity delta P in the period t^tAs shown in formula (13);

wherein ε is the error limit, a positive number close to 0; the feasible solution satisfies the formula (13), otherwise, the feasible solution is not feasible;

According to the principle, two strategies are selected; the first method is as follows: randomly selecting, namely randomly selecting one strategy from the candidate strategy set as a next strategy; the second method comprises the following steps: the components (normalization) of the utility function are combined in a linear weighting way to obtain a decision function F_i(P_i) Strategy P for maximizing the decision function_i ^*As a next strategy, α is shown in the formula (14)_i ¹，α_i ²AndAre respectively corresponding objective functionsAndThe weighting coefficient of (2);

3.3) adjustment mechanism (policy update)

The adjusting mechanism is divided into static adjustment and dynamic adjustment;

The static adjustment means that after all the persons in the bureau select the next strategy, the strategy is not updated immediately, and the strategy is updated after all the persons in the bureau finish the current game; the strategies of other people in the bureau, which are obtained by the people in the bureau through communication, are all the strategies determined by the previous round of game;

the dynamic adjustment means that the strategy of the person in the office is updated immediately after the person in the office determines the next strategy, and the strategies of other persons in the office, which are obtained by the person in the office through communication, are all the latest strategies.

Compared with the prior art, the invention has the following advantages and beneficial effects:

1. the potential game has good convergence property, and the convergence of the model and the algorithm provided by the invention is ensured.

2. Compared with a centralized single-subject decision optimization algorithm, the distributed multi-subject decision optimization method is adopted, and a potential game theory with distributed characteristics is combined, so that the expansion of the micro-grid is easy to realize, the local management and the local decision are realized, and the reliability and the flexibility of the system are improved.

3. The method considers the self-profit (profit-by-profit) and intelligence of the microgrid and simultaneously considers the multi-objective of a decision main body, and realizes the distributed multi-objective optimization in a game mode.

4. and a collaborative optimization target among a plurality of decision-making main bodies is set, so that a competitive and cooperative relationship of individual micro-grids is realized, the individual benefit is ensured, and the maximization of the overall benefit of the micro-grid is realized.

Drawings

Fig. 1 is a diagram of a microgrid architecture.

FIG. 2 is a flow chart of a potential game-based micro-grid energy management distributed multi-objective collaborative optimization algorithm.

Detailed Description

The present invention will be further described with reference to the following specific examples.

Referring to fig. 1 and fig. 2, the distributed multi-objective collaborative optimization algorithm for energy management of a micro grid based on potential gaming provided in this embodiment specifically includes the following:

The first step is as follows: microgrid and element unit modeling thereof

A typical microgrid comprising a photovoltaic array (PV/PV), a wind generator (WT/WT), a diesel generator (DE/DE), energy storage (batteries, BA/BA), loads (LD/LD) and electric vehicles (EV/EV) is shown in FIG. 1. And the micro grid Manager (MG Manager) receives the scheduling of a distribution network management system (DMS) and realizes the conversion between grid connection and grid disconnection through a Point of Common Coupling (PCC). Photovoltaic, fan, diesel engine, battery, load and electric automobile combine corresponding sensor, controller, intelligence switch and power converter (AC/DC or AC/AC) respectively, form controllable component unit, and Local Manager (LM) is the core of this unit. And the local managers and the micro-grid managers of all the element units are interconnected through an information network, so that local decision management and collaborative optimization are realized. Furthermore, the modular component units are distributed in different regions and belong to different owners.

A photovoltaic array, a wind driven generator, a diesel generator, energy storage equipment (storage battery) and loads are selected as decision main bodies, and a decision main body set N is expressed as a formula (15). Taking day-ahead planning of the microgrid as an example, the operation of the microgrid 24 hours in the future is optimized, wherein TN is 24, and the decision vector is shown as a formula (2).

N＝{pv,wt,de,ba,ld}(15)

The decision vector of the photovoltaic array, the wind driven generator, the diesel generator, the storage battery and the load is P in sequence_pv、P_wt、P_de、P_ba、P_ldThe output power or the consumed power (i.e. the decision variable) in the t period is used respectively AndWhere t is 1,2, …, and TN, and the corresponding constraint sets are Y^pv、Y^wt、Y^de、Y^baAnd Y^ld. The element units are modeled in turn by decision bodies.

1) Photovoltaic array

The optimization target is shown as a formula (16); yield target of photovoltaic array is F_pv ¹(P_pv) (ii) a Without second target F_pv ²(P_pv) And a third target F_pv ³(P_pv) Therefore, it is set to 0; photovoltaic co-targeting is F_pv ^(wt,ld)(P_pv,P_wt,P_ld) The cooperative target of the fan is F_wt ^(pv,ld)(P_wt,P_pv,P_ld) The cooperative target of the load is F_ld ^(pv,wt)(P_ld,P_pv,P_wt) Photovoltaic-wind turbine-load cooperative target embodiment F^(pv,wt,ld)(P_pv,P_wt,P_ld) As shown in formula (17); avg^τ(P_pv,P_wt,P_ld) Is N from the time period tau_wThe average value of decision variables of photovoltaic, fan and load in a time window; rho is the electricity price vector, gamma_pvLength N of sliding time window for unit maintenance cost coefficient vector_wSet to 4.

the constraint set is as shown in formula (18), wherein P is^t _pv·maxThe maximum output power in the t (t ═ 1,2, …, TN) period is calculated by a photovoltaic maximum power prediction model.

2) wind power generator

the optimization target is shown as the formula (19), and the income target of the fan is F_wt ¹(P_wt)，γ_wta cost coefficient vector for unit maintenance of the fan element; the fan has no second target F_wt ²(P_wt) And a third target F_wt ³(P_wt) Therefore, it is set to 0; the specific form of the photovoltaic-fan-load cooperative target is as shown in formula (17).

The constraint set is as shown in formula (20), wherein P is^t _wt·maxthe maximum output power of the period t (t is 1,2, …, TN) calculated by the maximum power prediction model of the fan.

3) diesel generator

The optimization target is shown as a formula (21); the yield target of the diesel generator is F_de ¹(P_de)，γ_deIs a unit fuel cost coefficient vector, and the pollutant emission target is F_de ²(P_de)，μ_deThe waste emission coefficient vector of the diesel generator is defined as shown in a formula (7); without third target F_de ³(P_de) And a cooperative target F_de ⁽⁾(P_de)，Therefore, it is set to 0.

the constraint set is as shown in formula (22), P^t _de·maxand P^t _de·minThe time periods t are the upper and lower mechanical output limits respectively; g¹ _de(P_de) And g² _de(P_de) Is a unit ramp constraint function, R_upAnd R_downrespectively representing the ascending rate limit and the descending rate limit of the unit slope climbing in unit time.

4) Storage battery

The optimization target is shown as the formula (23), and the benefit target of the storage battery is F_ba ¹(P_ba)，γ^t _baa unit maintenance cost coefficient for the t time period of the storage battery; f_ba ³(P_ba) The method is a target for minimizing the charging and discharging switching times; without second target F_ba ²(P_ba) With co-target F_ba ⁽⁾(P_ba) Therefore, it is set to 0.

The storage battery charge-discharge model is shown as a formula (24), wherein SOC (t) is the state of charge of the storage battery at the end of the tth time period; eta_c、η_drespectively the charging efficiency and the discharging efficiency of the storage battery; e_rThe rated capacity of the storage battery; sigma is the self-discharge rate of the storage battery; and delta t is a charge-discharge time interval.

the charge of the battery is constrained as shown in formula (25), SOC_maxAnd SOC_minRespectively an upper limit and a lower limit of the charged quantity; the constraint set is as shown in formula (26), P^t _ba·maxAnd P^t _ba·minThe maximum allowable discharge power and the maximum allowable charge power of the storage battery in the t period are respectively.

5) Load(s)

The optimization objective is shown as equation (27), and the profit objective of the load is F_ld ¹(P_ld) (ii) a The revenue target without the second target is F_ld ²(P_ld) Therefore, it is set to 0; load satisfaction function of F³ _ld(P_ld) Wherein L is^t _ldpredicting load demand in a time period t, wherein lambda and mu are parameters of a load satisfaction function and are determined by a user; p^t _ld＝L^t _ld,F³ _ld(P_ld) 0, satisfaction reference point; i P^t _ld|>|L^t _ld|,F³ _ld(P_ld)>0, the relative satisfaction reference point is more satisfactory; i P^t _ld|<|L^t _ld|,F³ _ld(P_ld)<0, relative satisfaction reference point is less than satisfactory. P^t _ldand L^t _ldAre all negative numbers.

The constraint set is as shown in formula (28), P^t _ld·maxAnd P^t _ld·minRespectively, the upper and lower limits of the load demand during the t period.

The second step is that: potential game modeling

The person in the office is shown as the formula (15)The utility functions are shown as formula (29), and the utility functions corresponding to the photovoltaic array, the wind driven generator, the diesel generator, the storage battery and the load are respectively U_pv(P_s)_s∈N、U_wt(P_s)_s∈N、U_de(P_s)_s∈N、U_ba(P_s)_s∈NAnd U_ld(P_s)_s∈NThe corresponding strategy sets are respectively equations (18), (20), (22), (26) and (28).

potential function G (P)_s)_s∈NAs shown in equation (30), both the utility function and the potential function are vector functions including 4 components.

the third step: distributed game solving based on multi-objective optimization algorithm

the gain function shown in the formula (29) is used as an evaluation function of the strategy of the person in the bureau, a pareto optimal solution set of the person in the bureau is solved by using a multi-objective particle swarm optimization (MOPSO) algorithm, a random selection mode is adopted by a decision rule, and a dynamic adjustment mechanism is used for accelerating convergence.

MOPSO was proposed in 2004 by Carlos A. Coello Coello et al (Coello C. A. C., Pulido G.T., Lechuga M.S., Handling multiple objects with particle swarming [ J ]. IEEE Transactions on evolution calculation, 2004,8(3):256-279), which introduces a "elite strategy" to preserve non-inferior solutions in "on the basis of a single-target Particle Swarm Optimization (PSO) algorithm, and applies an adaptive archiving mesh method to select globally optimal particles, introduces a variation mechanism, and increases the local search capability of the algorithm. MOPSO is a very mature multi-objective optimization algorithm, and details about MOPSO are not repeated here.

the specific description of the distributed game solving based on the multi-objective optimization algorithm comprises the following steps:

step1. Algorithm initialization

Inputting data (micro-source, energy storage equipment and load operating characteristics, environmental data, electricity prices and load prediction data);

Processing data to obtain the maximum output power of the photovoltaic and the fan;

Initialization parameters (number of optimization time segments TN, maximum iteration number MaxItr, policy precision epsilon₁)；

Establishing a potential game model according to the method;

Searching and updating a person priority queue in the bureau, wherein the priority is as shown in a formula (15) from top to bottom, and the number (| N |) of persons in the bureau is set;

initializing an iteration counter k to be 1;

step2. initialize queue counter i 1

step3.i^thGambling behavior of people in a game

Request policies of other parties;

Waiting for the other persons in the bureau to reply;

Receiving a reply;

Evaluating a strategy by using a revenue function and finding out a pareto optimal solution set by using MOPSO;

Deciding and updating policy P according to decision rule^k _i(P^k _i＝[P^k _i·1,P^k _i·2,…,P^k _i·t,…,P^k _i·TN]，P^k _i·tPower corresponding to t period of kth iteration of person i in office);

Calculating the rate of change of the strategy Δ P^k _i·t(ΔP^k _i·t＝|(P^k _i·t-P^k-1 _i·t)/P^k-1 _i·t|,k≥2,ΔP¹ _i·t＝0，t＝1,2,…,TN)；

Setting the convergence status S_i(S_i＝1,||ΔP^k _i||≤ε₁；S_i＝0,||ΔP^k _i||>ε₁，ΔP^k _i＝[ΔP^k _i·1,…,ΔP^k _i·t,…,ΔP^k _i·TN])；

step4. judging i < | N non-woven phosphor

If yes, return to step 3; if not, step5 is entered;

step5. the person in the game determines the convergence state of the game through communication, if S_iif 1 holds for each player i (i e N), the game converges (nash equilibrium)

step6. judge whether reach nash equilibrium (game convergence)

If yes, step7 is entered;

If not, judging that k is less than or equal to MaxItr, namely whether the maximum iteration number is reached

if the maximum iteration number is not reached, executing k to k +1, and returning to step 2;

If the maximum iteration number is reached, step7 is entered;

step7. all persons in the bureau save game strategy result P_i(P_i,i∈N)

step8. output optimization results { P_i}_i∈N。

The above-mentioned embodiments are merely preferred embodiments of the present invention, and the scope of the present invention is not limited thereto, so that the changes in the shape and principle of the present invention should be covered within the protection scope of the present invention.

Claims

1. A potential game-based micro-grid energy management distributed multi-objective collaborative optimization algorithm is characterized by comprising the following steps:

1) Microgrid element unit modeling

Considering a typical micro-grid comprising a photovoltaic array PV/PV, a wind power generator WT/WT, a diesel generator DE/DE, a storage battery BA/BA, a load LD/LD and an electric vehicle EV/EV, each element in combination with a corresponding power variator, sensor, controller and intelligent switch constitutes a controllable element unit; each element unit is provided with a local manager LM for local decision and local management, and all the LMs are interconnected through a network and can communicate with each other to realize distributed coordination control;

1.1) decision principal and decision variables

Assuming that the time window to be optimized contains TN optimization periods, the output power or the consumption power of the element unit i in the t period, i.e. the decision variable, is P_i ^ti ∈ N, t ═ 1,2, …, TN, and positive values denote output power and negative values denote consumed power; decision vector P for element unit i_iRepresented by formula (2);

P_i＝[P_i ¹,P_i ²,…,P_i ^t,…,P_i ^TN]^T,i∈N (2)

1.2) component constraint

decision variable P_i ^tConstrained by upper and lower limits, as shown in formula (3);

The upper and lower limits of the power of the element unit i in the t period are respectively P^t _i·maxAnd P^t _i·min(ii) a At the same time, other constraints g on the element unit_i(P_i) As shown in formula (4);

g_i(P_i)≤0,i∈N (4)

1.3) Multi-object modeling

The interest target refers to a target which is only related to the decision vector of the element unit and is not related to the decision vectors of other element units, and the target indicates that the interest of the element unit pursues the maximization of the interest of the element unit; the number of such targets is at least one, and the targets are two, i.e., the yield of the element unit i and the emission of pollutants, i.e., waste, and the maximum yield target is F_i ¹(P_i,ρ,γ_i)，ρ^tThe unit electricity price of the t period is t, and t is 1,2, …, TN and rho are electricity price vectors; gamma ray_i ^tIs the unit cost coefficient of the t period, t is 1,2, …, TN, gamma_ia cost coefficient vector, as shown in equation (6);

Minimum pollutant emission target is F_i ²(P_i,μ_i)，μ_i ^tIs the waste discharge coefficient of the period t, t is 1,2, …, TN, mu_iis an emission coefficient vector, as shown in formula (7);

Factor rho, gamma_iAnd mu_iis a non-decision vector, F without misinterpretation_i ¹(P_i,ρ,γ_i) And F_i ²(P_i,μ_i) Are each abbreviated as F_i ¹(P_i) And F_i ²(P_i)；

The cooperative target refers to a target shared by decision-making main bodies, and is realized by mutual information sharing to represent interaction and influence among the decision-making main bodies; the number of the cooperative targets is at least one, and each cooperative target at least comprises two decision-making main bodies; aiming at the coordination of m decision-making main bodies of photovoltaic-fan-load, aiming at enabling the load to be consistent with the output of renewable energy sources so as to reduce the influence of the fluctuation on a micro-grid, wherein the coordination target of an element unit i is F_i ^(j,k)(P_i,P_j,P_k) The cooperative target of the element unit j is F_j ^(i,k)(P_j,P_i,P_k) The cooperative target of the element unit k is F_k ^(i,j)(P_k,P_i,P_j) I, j and k respectively represent a photovoltaic element, a fan element and a load, and are shown as a formula (8);

2) potential game modeling

max U_i(P_s)_s∈N＝[F_i ¹(P_i),-F_i ²(P_i),-F_i ^(j,k)(P_i,P_j,P_k)] (11)

the utility functions for all people in a office must have the same dimensions, but the number of optimization objectives for people in each office may be different, by: classifying all optimization targets, including an economic target, namely income, an environmental target, namely pollutant emission and a photovoltaic-fan-load cooperative target, in sequence in a utility function vector, placing the targets of the same type, namely targets with the same dimension at the same position, and supplementing with 0 if no targets of the same type exist; unifying the forms of all the targets, processing all the minimized targets according to the inverse number of the maximized targets, and converting all the targets into minimized treatment by the same method;

3) Distributed game solving based on multi-objective optimization algorithm

The game solving is realized by the following steps:

3.1) policy evaluation

directly evaluating the strategy by using a utility function, wherein the utility function is a vector function, each component is an optimization target, and a pareto optimal solution set is solved by adopting a multi-objective optimization algorithm to serve as a candidate strategy set; the multi-target optimization algorithm comprises a multi-target particle swarm algorithm, namely an MOPSO algorithm, and a multi-target genetic algorithm, namely multi-target evolutionary algorithms NSGA, NSGA-II and NSGA-III, and an improved form thereof;

3.2) decision rules

According to the principle, two strategies are selected; the first method is as follows: randomly selecting, namely randomly selecting one strategy from the candidate strategy set as a next strategy; the second method comprises the following steps: each component of the utility function, namely normalized linear weighted combination is combined to obtain a decision function F_i(P_i) Strategy P for maximizing the decision function_i ^*As a next strategy, α is shown in the formula (14)_i ¹，α_i ²And beta_i ^(j,k)Respectively corresponding objective function F_i ¹(P_i)，F_i ²(P_i) And F_i ^(j,k)(P_i,P_j,P_k) The weighting coefficient of (2);

3.3) adjustment mechanisms, i.e. policy updates