CN103839109A - Microgrid power source planning method based on game and Nash equilibrium - Google Patents

Abstract

The invention discloses a microgrid power source planning method based on game and Nash equilibrium. Cooperative game optimal configuration models are established with identities of different participants respectively, generated output characteristics of micro sources of different kinds in a microgrid and various constraint conditions are taken into full consideration, a game is carried out between revenue functions formed by microgrid electricity sell revenue, investment cost of the microgrid, system losses cost, environment cost and interactive power cost and revenue functions formed by loss reduction revenue of large power grid loss, electricity sell revenue to the microgrid, discharged exhaust gas cost due to electricity sell to the microgrid and hot standby cost saved by a large power grid, solving is carried out by adopting a game iterative algorithm, and the power source planning problem of the game models is solved. Simulated analytical investigation is carried out by adopting a typical microgrid structure, simulation results show that cooperative the game between the microgrid and the large power grid can achieve better revenue, and therefore sound development of the microgrid can be promoted by combining power of all interested parties.

Description

A kind of microgrid power source planning method based on game Nash Equilibrium

Technical field

The present invention relates to a kind of microgrid power source planning method based on game Nash Equilibrium, belong to microgrid field.

Background technology

Along with being on the rise of environmental problem and energy crisis; the mode that conventional electric power system produces electric energy and long Distance Transmission by consumption of fossil fuels is difficult to meet energy-saving and emission-reduction, alleviates environmental pollution, reduces network loss, improves the quality of power supply and improves the requirements such as power supply reliability; the proportion of renewable energy power generation, all in Devoting Major Efforts To Developing new forms of energy and regenerative resource, is improved in countries in the world.Meanwhile, user requires constantly to promote to the quality of power supply and power supply reliability, requires electrical network that electric power supply safer, reliable, clean, high-quality can be provided, and can adapt to the needs of various energy resources type generation mode, and therefore, the concept of microgrid is arisen at the historic moment.

Relatively large electrical network, microgrid (Microgrid) is a kind of organic system being jointly made up of micro-power supplys (distributed power source, DG) such as wind-power electricity generation, photovoltaic generation, miniature gas turbine and energy storage device, load.Microgrid can effectively be integrated the advantage of various distributed power sources, give full play to economic benefit and environmental benefit that distributed power source brings, can better meet user to the quality of power supply and the higher requirement of power supply reliability, can realize the peak load shifting of electrical network, improve the cascade utilization of the energy.

In micro-grid system, the power source planning of micro-power supply is the Focal point and difficult point problem of microgrid research, has caused people's extensive concern.Present Domestic outward existing a large amount of scholar conducts a research to distributing rationally of DG, mainly sets about from aspects such as technical factor, economic benefit, Environmental costs considering, and has obtained certain achievement in research.But above method has certain limitation, be all to carry out the planning of micro-power supply based on microgrid or the large different investor of electrical network.Microgrid and large electrical network may belong to different investors, while distributing rationally for micro-power supply, the investor of each side wishes can be to configure optimum capacity under the prerequisite of self maximum benefit, so also needs the optimization allocation of micro-power supply in micro-grid system further to launch in breadth and depth further investigation.

Summary of the invention

The present invention sets up game theory Nash Equilibrium model and analyzes the optimization allocation of micro-power supply capacity in microgrid, taking microgrid and the participant of large electrical network as game, adopt game theory iterative algorithm to solve and analyze the Nash Equilibrium result having compared under each pattern, iterative computation result proves to adopt modality for co-operation can better realize distributing rationally of micro-power supply in microgrid, ensure the efficient utilization of the energy, the complex art economic benefit of General Promotion microgrid and large electrical network.

1 model construction

The microgrid that the present invention considers comprises photovoltaic generation (Photovoltaic, PV), wind-power electricity generation (Wind Turbine, WT), miniature gas turbine (Micro Gas Turbine, MT), and energy storage device (Energy Storage Systems, ESS), thereby set up based on game theoretic microgrid and large network optimization allocation models.In game theory, a game comprises the key element of multiple indispensabilities, is indispensable comprising participant, strategy, revenue function, equilibrium.

Game theory factor analysis

1) participant

Taking microgrid and the participant of large electrical network as game, thereby form two-person game, use respectively Mic, Mac represents two participants.

2) participant's strategy

Participant Mic, Mac is in the time carrying out game, and its strategy is mainly the capacity that determines micro-power supply by cooperation and noncooperation game play mode, is expressed as P _pV, P _wT, P _mT, P _eSS, due to decision variable continuous value within the scope of certain, each participant has continuous policy space S _pV, S _wT, S _mT, S _eSS, be specially:

$\left\{\begin{array}{c}{P}_{\mathrm{PV}}=\∈\{S_{\mathrm{PV}}=[P_{\mathrm{PV}}^{\min },P_{\mathrm{PV}}^{\max }\left]\right\}\\ P_{\mathrm{WT}}\∈\{S_{\mathrm{WT}}=[P_{\mathrm{WT}}^{\min },\left]P_{\mathrm{WT}}^{\max }\right]\}\\ P_{\mathrm{MT}}\∈\{S_{\mathrm{MT}}=[P_{\mathrm{MT}}^{\min },P_{\mathrm{MT}}^{\max }\left]\right\}\\ P_{\mathrm{ESS}}\∈\{S_{\mathrm{ESS}}=[P_{\mathrm{ESS}}^{\min },P_{\mathrm{ESS}}^{\max }\left]\right\}\end{array}\right.---\left(1\right)$

Wherein,

for the bound of photovoltaic generation capacity;

for the bound of wind-power electricity generation capacity; for the bound of miniature gas turbine capacity; for the bound of capacity of energy storing device.

3) participant's income

Participant Mic, the revenue function of Mac is respectively:

1. the revenue function of microgrid:

$C_B^{\mathrm{Mic}}=C_{\mathrm{Benefit}}-C_C---\left(2\right)$

In formula:

for the targeted yield of microgrid; C _benefitfor microgrid is the power selling income in 1 year period; C _cfor microgrid is for the financial cost of micro-power supply, comprise cost of investment, installation cost, operation and maintenance cost, Environmental costs and to large electrical network power purchase cost.Concrete objective function is:

In formula, the kind that Nb is micro-power supply, wherein 1 is PV, and 2 is WT, and 3 is MT, and 4 is ESS, Nb is 4; N _dlfor scheduling slot, τ _dlit is the time of dl scheduling slot; λ _dlelectricity price while being dl scheduling slot; r _dlit is the electricity price subsidy of dl scheduling slot;

it is the electricity sales amount of dl scheduling slot of the micro-power supply of i kind; C _i, C _{o & M}, C _f, C _e, C _gRIDbe respectively the cost of investment present value of annuity, operation and maintenance cost, fuel cost, Environmental costs of micro-power supply and to large electrical network power purchase cost; I _i,e, I _i,facquisition cost and the installation cost of the micro-power supply of i kind respectively; P _iit is the specified installed capacity of the micro-power supply of i kind;

be respectively the operation and maintenance cost of i Zhong Wei power supply unit generated energy; C _gasfor the price of unit cubic meter rock gas, be generally 2.5 yuan/m ³; C (d, n) is that discount rate is the PVIFAi, n that is n in d serviceable life; E _i,k, E ' _{i, k}be respectively environmental value cost and the pollution punishment cost of the k kind dusty gas of i Zhong Wei power supply unit generated energy discharge; M is the kind of micro-power supply exhaust emission gas;

for microgrid is dl scheduling slot load short of electricity rate; C is the purchase electricity price of microgrid to large electrical network;

for microgrid is at the workload demand of dl scheduling slot; for active power loss; B is the network loss electricity price of microgrid.

2. the revenue function of large electrical network

With respect to microgrid, the income of large electrical network is mainly the grid integration due to microgrid, and in electric system, falling of network loss damaged income C _loss, to the sale of electricity income C of microgrid _mG, due to the waste gas cost C of the fossil fuel discharge consuming to microgrid sale of electricity _emission, the stand-by heat expense C that saves of large electrical network _reserve.

$\left\{\begin{array}{c}{C}_B^{\mathrm{Mac}}=C_{\mathrm{loss}}+C_{\mathrm{MG}}-C_{\mathrm{emission}}-C_{\mathrm{reserve}}\\ C_{\mathrm{loss}}=\underset{\mathrm{dl}=1}{\overset{N_{\mathrm{dl}}}{\mathrm{\&Sigma;}}}(a\&times;\mathrm{\&Delta;}{\stackrel{\&OverBar;}{P}}_{\mathrm{dl}}^{\mathrm{loss}})\&times;{\mathrm{\&tau;}}_{\mathrm{dl}}\\ C_{\mathrm{MG}}=\underset{\mathrm{dl}=1}{\overset{N_{\mathrm{dl}}}{\mathrm{\&Sigma;}}}{\mathrm{\&tau;}}_{\mathrm{dl}}\&CenterDot;c\&CenterDot;{\mathrm{\&delta;}}_{\mathrm{dl}}^{\mathrm{LPSP}}\&CenterDot;P_{\mathrm{dl}}^L\\ C_{\mathrm{emission}}=\underset{\mathrm{dl}=1}{\overset{N_{\mathrm{dl}}}{\mathrm{\&Sigma;}}}\underset{k=1}{\overset{M}{\mathrm{\&Sigma;}}}{\mathrm{\&tau;}}_{\mathrm{dl}}(E_k+E_k^{\&prime;})\&CenterDot;{\mathrm{\&delta;}}_{\mathrm{dl}}^{\mathrm{LPSP}}\&CenterDot;P_{\mathrm{dl}}^L\\ C_{\mathrm{reserve}}=\underset{\mathrm{dl}=1}{\overset{N_{\mathrm{dl}}}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{\mathrm{Nb}}{\mathrm{\&Sigma;}}}{\mathrm{\&tau;}}_{\mathrm{dl}}\&CenterDot;{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA0000398471720000011.png,HDA0000398471720000021.png"\; state="\{\{state\}\}">c</figure-callout>}}_1\&CenterDot;\mathrm{\&alpha;}\&CenterDot;P_i\end{array}\right.---\left(4\right)$

In formula:

be dl the network loss variable quantity that the large electrical network of scheduling slot reduces due to the access of microgrid; A is network loss electricity price; E _k, E ' _kbe respectively environmental value cost and the pollution punishment cost of the k kind dusty gas of fired power generating unit unit's generated energy discharge; Due to the grid integration of microgrid, both met the demand of local power supply reliability, simultaneously large electrical network has also reduced the demand of stand-by heat, therefore C _reservefor the stand-by heat expense that large electrical network is saved, c ₁for the stand-by heat expense of unit quantity of electricity, α is the proportion of the shared total installation of generating capacity of stand-by heat.

4) information set

For the microgrid of cooperative game and large electrical network, information set be guarantee system can be safely, reliably and the constraint condition of stable operation.

1. equality constraint, i.e. node power flow equation.

$\left\{\begin{array}{c}{P}_{j,\mathrm{dl}}^{\mathrm{net}}=-P_{j,\mathrm{dl}}^D+P_{j,\mathrm{dl}}^{\mathrm{DG}}\\ Q_{j,\mathrm{dl}}^{\mathrm{net}}=-Q_{j,\mathrm{dl}}^D+Q_{j,\mathrm{dl}}^{\mathrm{DG}}\end{array}\right.---\left(5\right)$

$\left\{\begin{array}{c}{P}_{j,\mathrm{dl}}^{\mathrm{net}}=U_{j,\mathrm{dl}}\underset{r=1}{\overset{N}{\mathrm{\&Sigma;}}}{U}_r(G_{\mathrm{jr}}\cos {\mathrm{\&theta;}}_{\mathrm{jr}}+B_{\mathrm{jr}}\sin {\mathrm{\&theta;}}_{\mathrm{jr}})\\ Q_{j,\mathrm{dl}}^{\mathrm{net}}=U_{j,\mathrm{dl}}\underset{r=1}{\overset{N}{\mathrm{\&Sigma;}}}{U}_r(G_{\mathrm{jr}}\sin {\mathrm{\&theta;}}_{\mathrm{ijr}}-B_{\mathrm{jr}}\cos {\mathrm{\&theta;}}_{\mathrm{jr}})\\ \mathrm{\&Delta;}{P}_{\mathrm{dl}}^{\mathrm{loss}}=\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}{P}_{j,\mathrm{dl}}^{\mathrm{net}}\end{array}\right.---\left(6\right)$

In formula: be respectively the meritorious and reactive power network loss of node j at dl scheduling slot electrical network;

be respectively the meritorious and reactive power of node j dl scheduling slot electrical network demand;

be respectively the meritorious and reactive power that node j sends at dl scheduling slot DG; U _{j, dl}for node j is at the voltage magnitude of dl scheduling slot; G _jr, B _jrbe respectively real part and the imaginary part of the admittance matrix of system; θ _jrfor the phase difference of voltage of node j and node r; N is the nodes of microgrid.

2. inequality constrain

A. access capacity-constrained

$P_{i,\min }\&le;P_i^{\mathrm{DG}}\&le;P_{i,\max }---\left(7\right)$

In formula, P _{i, min}, P _{i, max}be respectively the bound of the access capacity of the micro-power supply of i kind.

B. voltage constraint

U _min≤U _j,dl≤U _max （8）

In formula, U _{j, dl}for node j is at the magnitude of voltage of dl scheduling slot; U _min, U _maxfor the bound of quality of voltage.

C. miniature gas turbine climbing constraint

$|P_{t,\mathrm{dl}}^{\mathrm{MT}}-P_{t-1,\mathrm{dl}}^{\mathrm{MT}}|\&le;P_{\max }^{\mathrm{MT}}---\left(9\right)$

In formula,

power upper limit during for consideration gas turbine climbing constraint.

D. energy storage device operation constraint

$S_{\mathrm{OC}}^{\min }\&le;S_{\mathrm{OC}}\&le;S_{\mathrm{OC}}^{\max }---\left(10\right)$

In formula, for lower limit and the upper limit of the constraint of energy storage device dump energy;

5) balance policy

Suppose for the Nash Equilibrium strategy of betting model, due to both can the forming cooperative alliances game and also can realize non-cooperative game of microgrid and large electrical network, represent that this strategy can realize the maximization of each alliance income.

Brief description of the drawings

Fig. 1 is microgrid structure principle chart

Fig. 2 is local solar irradiation radiant quantity

Fig. 3 is local wind speed situation of change

Fig. 4 is load condition

Fig. 5 is Spot Price curve

Fig. 6 is network loss comparison diagram under cooperative game pattern

Fig. 7 is the generated output of each micro-power supply

Embodiment

Below in conjunction with accompanying drawing, embodiment is elaborated.Should be emphasized that, following explanation is only exemplary, instead of in order to limit the scope of the invention and to apply.

(1) Optimal Allocation Model of game Nash Equilibrium

The microgrid of setting up is herein that the integral benefit that will ensure all participants maximizes with large electrical network cooperative game Optimal Allocation Model, form cooperative alliances by participant and realize maximize revenue, and then carry out the reasonable distribution of income, finally ensure that participant's individual interest maximizes.Therefore, suppose

for the Nash Equilibrium strategy of betting model, cooperative game model is:

(2) model solution

For the Optimized model of cooperative game, be the optimization problem of non-linear a, multiple constraint, therefore introduce tactful probability matrix, with solving model.Game Optimal Allocation Model becomes:

Participant: the participant of game is targeted yield separately, i.e. ξ=1,2 ..., n}, however for microgrid with the game of large electrical network all for the interests that realize self maximize, therefore n=2, wherein 1 targeted yield that is microgrid, 2 targeted yields that are large electrical network.

Game strategies: suppose in game process, all participants are " rationality people ", and share game play space, i.e. a S={S ₁, S ₂, wherein S ₁represent cooperation policy, S ₂represent non-cooperation policy.

Gain matrix: cause income different according to the different policy selection of each participant, therefore, in game bout, participant can obtain a new gain matrix, each time

wherein u _ijrepresent the income of when participant i takes strategy, participant j being brought.

Revenue function: for each participant, its ultimate yield is realized maximum and turned to

represent each game participant all pursue realize interests maximize.

Strategy probability matrix: the action that participant i takes in game process can have influence on the financial value of participant j.Participant j is the tactful probability to participant i according to the situation of Profit adjustment after each game.Strategy probability matrix is wherein p _ijfor participant j chooses the probability of cooperation policy, initial value is 0.5, and later each game finishes, and adjusts this value according to gain matrix U.If

increase Probability p _ji; If

reduce Probability p _ji.

Food concentration adaptive value matrix; Owing to adopting self-adaptation artificial fish-swarm algorithm to carry out iterative herein, therefore must carry out the calculating of food concentration adaptive value to it, suppose

be the individual i of the t time iteration,

food concentration adaptive value be

like this participant to each target have a preference degree (0 to 100),, pass through taked strategy and upgrade each target preference (cooperation+10, non-cooperation-10) each target preference identical (being 50) in original state.Participant can be converted to weight vector w to the preference of each target _i=(w _i1, w _i2..., w _in) ^t, in conjunction with the food concentration adaptive value in artificial fish-swarm k generation be

participant i just can seek optimum solution according to strategy thus.

Step1: the input of raw data.Comprise device parameter, climatic environment correlation parameter (as wind speed, intensity of illumination etc.), system loading situation of the network parameter of micro-grid system, micro-power supply etc.

Step2: set up cooperative game and non-cooperative game model.Correlation parameter in Step1 is brought in model, and sets up the microgrid and large electrical network cooperative game Optimal Allocation Model based on game Nash Equilibrium according to formula (11), (12);

Step3: balance policy initialization.Owing to adopting game theoretic iterative algorithm to solve balance policy, therefore, first set the initial value of balance policy, suppose (P _pV, P _wT, P _mT, P _eSS) be the Nash Equilibrium strategy initial value of betting model.

Step4: game solves.According to cooperative game model, each participant will, according to betting model optimization strategy separately, ensure the income of self.Calculate food concentration adaptive value matrix simultaneously, constantly update tactful probability matrix and revenue function.

Step5: Output rusults.Judge whether to have reached Nash Equilibrium, be also

if reached game Nash Equilibrium, Output rusults.

(3) sample calculation analysis

1) real data

The real data of choosing certain load center in Shanxi Province, China area is herein carried out the research of distributing rationally of micro-power supply capacity, wherein microgrid structure principle chart as shown in Figure 1, wherein in Fig. 1, load 1 for resident load, maximum active power is 15kW, and load 2 is Commercial Load, maximum active power is 30kW, load 3 is industrial load, and maximum active power is 30kW, belongs to interruptible load, load 4 is industrial load, and maximum active power is 40kW.Consider the feature of the radial network structure of distribution and low-voltage circuit parameter, line taking road resistance R=0.64 Ω/km, X=0.1 Ω/km.The correlation parameter of micro-power supply is as shown in table 1.Solar radiation amount and wind speed situation of change are as shown in Figure 2,3.Fig. 4 is the dynamic changing curve of load in certain 24 hours day of typical case.By this area's load data of a year is added up, its load condition is as shown in table 2.Fig. 5 is Spot Price curve, suppose that industrial load, Commercial Load and resident load all adopt same Spot Price curve, but owing to adopting distributed new to generate electricity by way of merging two or more grid systems, photovoltaic rate for incorporation into the power network scheme and wind-powered electricity generation mark post rate for incorporation into the power network that National Development and Reform Committee announced July 31, be respectively 1.15 yuan/kWh, 0.58 yuan/kWh.The initial dump energy S of energy storage device _oC(0)=0.5, dump energy variation range is 0.1～0.9.In artificial fish-swarm algorithm, the state of Artificial Fish is 2 dimension space vectors, and Artificial Fish adds up to 100, and iterations was 40 generations, and number of attempt is 200 times, and crowding is 0.618.

The systematic parameter of the micro-power supply of table 1

Table 2 scheduling slot

Table 3 environment conversion cost and emission factor (unit/MWh)

2) optimum results and analysis

The cooperative game model of setting up according to the present invention, in conjunction with the condition such as weather conditions and micro-power parameter in given somewhere, Shanxi, adopts the artificial fish-swarm iterative algorithm of game Nash Equilibrium to solve, and optimum results is:

Under table 4 cooperation and non-cooperative game pattern, distribute result rationally

Table 5 microgrid gain on investments and correlative charges

The large electrical network income of table 6 and correlative charges

Find out that by the analysis of his-and-hers watches 4 installed capacity of the miniature gas turbine under cooperative game pattern is 108.34kW, the installed capacity of aerogenerator is 26.86kW, the installed capacity of photovoltaic cell is 10.54, the installed capacity of energy storage device is 40kW/320kW.h, the installed capacity of finding out cooperative game pattern apparatus for lower wind genset by the analysis of his-and-hers watches 4 is significantly large than the installed capacity of photovoltaic cell, can find out in conjunction with Fig. 2 and Fig. 3, the wind resource of this area is relatively abundant, mean wind speed is in 6m/s left and right, and whole day can be continuous generating, good with the matching of load, and photovoltaic cell only have illumination by day time just can generated output, can not whole day mutually mate with load, and for the weather conditions of this area, as can be drawn from Figure 2, the average radiation amount of this area is 5000MJ/m ³, be the comparatively poor place of solar energy resources, these all will certainly increase the configuration capacity of miniature gas turbine and energy storage device, and therefore, the photovoltaic cell capacity relative of configuration is little.

And compare distributed power generation, miniature gas turbine has very large advantage, because it is controlled micro-power supply, has good matching with load, so configure larger capacity, but because the harmful gas discharging in its power generation process and higher cost of electricity-generating have also limited its capacity.

As can be seen from Table 5, for microgrid, the gas fuel cost C of miniature gas turbine _fbe 215130 yuan, accounted for 50% of whole cost of electricity-generating, have the greatest impact for the cost of electricity-generating of whole system, therefore, under the prerequisite of the installed capacity of reasonable disposition miniature gas turbine, reasonable start and stop.For the operation and maintenance cost C of the micro-power supply of variety classes in microgrid _{o & M}being 23258 yuan, is ingredient important in cost of electricity-generating, by with the contrast of conventional fired power generating unit, can find out that microgrid has significant environmental benefit, can greatly promote social low carbon development.As can be seen from Table 6, for large electrical network, the stand-by heat expense C that large electrical network is saved _reservebe 92158 yuan, also proved the access of microgrid, improved greatly the stability of system, reduced stand-by heat expense, and under cooperative game, large electrical network can obtain to microgrid sale of electricity electricity income C _mGbe 5173.9 yuan, this is by the support that further promotes large electrical network to microgrid development.And from the mutual power of large electrical network and microgrid and the waste gas of consumption of fossil fuels discharge can be found out the feature of environmental protection of microgrid.In microgrid access power distribution network, the network loss of system has reduced a lot, just can find out from Fig. 6, has important effect for the voltage, the stability that improve system.Fig. 7 has provided the generated output situation of the micro-power supply of variety classes in workload demand situation, as seen from Figure 7,1 o'clock-4 o'clock this stage, due to the undulatory property of blower fan and solar energy power generating power, and they are non-scheduling power supplys, Spot Price is now all lower, at this moment mating between the main balance that discharges and recharges holding power by accumulator system and load; Along with the growth of Spot Price, the generated output of miniature gas turbine increases, and particularly, in 5 o'clock-19 o'clock, when generated output is greater than load power, electric power surplus relies on accumulator to absorb completely.And in the time there is electric power vacancy at 20 o'clock-24 o'clock, Spot Price is lower, the main energy storage system discharges that relies on makes up, because the restriction of energy or power can not be discharged while reaching burden requirement, miniature gas turbine can be used as standby power supply afterpower is provided, and this can improve system reliability to a certain extent.

In a word; although the Installed capital cost of microgrid is higher; if but from microgrid the overall interests with large electrical network; consider microgrid in the benefit that improves the aspects such as reliability, energy-saving and cost-reducing, protection of the environment; the investment of microgrid is economical; by associating Stake Holders' strength, could promote the sound development of microgrid.

Claims (1)

1. the present invention sets up the microgrid and large network optimization allocation models based on game Nash Equilibrium, the microgrid taking into full account comprises photovoltaic generation (Photovoltaic, PV), wind-power electricity generation (Wind Turbine, WT), miniature gas turbine (Micro Gas Turbine, MT), and energy storage device (Energy Storage Systems, ESS), and in game theory, a game comprises the key element of multiple indispensabilities, is indispensable comprising participant, strategy, revenue function, equilibrium.

Game theory factor analysis

1) participant

Taking microgrid and the participant of large electrical network as game, thereby form two-person game, use respectively Mic, Mac represents two participants.

2) participant's strategy

Participant Mic, Mac is in the time carrying out game, and its strategy is mainly the capacity that determines micro-power supply by cooperation and noncooperation game play mode, is expressed as P _pV, P _wT, P _mT, P _eSS, due to decision variable continuous value within the scope of certain, each participant has continuous policy space S _pV, S _wT, S _mT, S _eSS, be specially:

$\left\{\begin{array}{c}{P}_{\mathrm{PV}}=\&Element;\{S_{\mathrm{PV}}=[P_{\mathrm{PV}}^{\min },P_{\mathrm{PV}}^{\max }\left]\right\}\\ P_{\mathrm{WT}}\&Element;\{S_{\mathrm{WT}}=[P_{\mathrm{WT}}^{\min },\left]P_{\mathrm{WT}}^{\max }\right]\}\\ P_{\mathrm{MT}}\&Element;\{S_{\mathrm{MT}}=[P_{\mathrm{MT}}^{\min },P_{\mathrm{MT}}^{\max }\left]\right\}\\ P_{\mathrm{ESS}}\&Element;\{S_{\mathrm{ESS}}=[P_{\mathrm{ESS}}^{\min },P_{\mathrm{ESS}}^{\max }\left]\right\}\end{array}\right.$

Wherein,

for the bound of photovoltaic generation capacity; for the bound of wind-power electricity generation capacity;

for the bound of miniature gas turbine capacity;

for the bound of capacity of energy storing device.

3) participant's income

Participant Mic, the revenue function of Mac is respectively:

1. the revenue function of microgrid:

$C_B^{\mathrm{Mic}}=C_{\mathrm{Benefit}}-C_C$

In formula: for the targeted yield of microgrid; C _benefitfor microgrid is the power selling income in 1 year period; C _cfor microgrid is for the financial cost of micro-power supply, comprise cost of investment, installation cost, operation and maintenance cost, Environmental costs and to large electrical network power purchase cost.Concrete objective function is:

In formula, the kind that Nb is micro-power supply, wherein 1 is PV, and 2 is WT, and 3 is MT, and 4 is ESS, Nb is 4; N _dlfor scheduling slot, τ _dlit is the time of dl scheduling slot; λ _dlelectricity price while being dl scheduling slot; r _dlit is the electricity price subsidy of dl scheduling slot;

it is the electricity sales amount of dl scheduling slot of the micro-power supply of i kind; C _i, C _{o & M}, C _f, C _e, C _gRIDbe respectively the cost of investment present value of annuity, operation and maintenance cost, fuel cost, Environmental costs of micro-power supply and to large electrical network power purchase cost; I _i,e, I _i,facquisition cost and the installation cost of the micro-power supply of i kind respectively; P _iit is the specified installed capacity of the micro-power supply of i kind;

be respectively the operation and maintenance cost of i Zhong Wei power supply unit generated energy; C _gasfor the price of unit cubic meter rock gas, be generally 2.5 yuan/m ³; C (d, n) is that discount rate is the PVIFAi, n that is n in d serviceable life; E _i,k, E ' _{i, k}be respectively environmental value cost and the pollution punishment cost of the k kind dusty gas of i Zhong Wei power supply unit generated energy discharge; M is the kind of micro-power supply exhaust emission gas;

for microgrid is dl scheduling slot load short of electricity rate; C is the purchase electricity price of microgrid to large electrical network;

for microgrid is at the workload demand of dl scheduling slot; for active power loss; B is the network loss electricity price of microgrid.

2. the revenue function of large electrical network

With respect to microgrid, the income of large electrical network is mainly the grid integration due to microgrid, and in electric system, falling of network loss damaged income C _loss, to the sale of electricity income C of microgrid _mG, due to the waste gas cost C of the fossil fuel discharge consuming to microgrid sale of electricity _emission, the stand-by heat expense C that saves of large electrical network _reserve.

$\left\{\begin{array}{c}{C}_B^{\mathrm{Mac}}=C_{\mathrm{loss}}+C_{\mathrm{MG}}-C_{\mathrm{emission}}-C_{\mathrm{reserve}}\\ C_{\mathrm{loss}}=\underset{\mathrm{dl}=1}{\overset{N_{\mathrm{dl}}}{\mathrm{\&Sigma;}}}(a\&times;\mathrm{\&Delta;}{\stackrel{\&OverBar;}{P}}_{\mathrm{dl}}^{\mathrm{loss}})\&times;{\mathrm{\&tau;}}_{\mathrm{dl}}\\ C_{\mathrm{MG}}=\underset{\mathrm{dl}=1}{\overset{N_{\mathrm{dl}}}{\mathrm{\&Sigma;}}}{\mathrm{\&tau;}}_{\mathrm{dl}}\&CenterDot;c\&CenterDot;{\mathrm{\&delta;}}_{\mathrm{dl}}^{\mathrm{LPSP}}\&CenterDot;P_{\mathrm{dl}}^L\\ C_{\mathrm{emission}}=\underset{\mathrm{dl}=1}{\overset{N_{\mathrm{dl}}}{\mathrm{\&Sigma;}}}\underset{k=1}{\overset{M}{\mathrm{\&Sigma;}}}{\mathrm{\&tau;}}_{\mathrm{dl}}(E_k+E_k^{\&prime;})\&CenterDot;{\mathrm{\&delta;}}_{\mathrm{dl}}^{\mathrm{LPSP}}\&CenterDot;P_{\mathrm{dl}}^L\\ C_{\mathrm{reserve}}=\underset{\mathrm{dl}=1}{\overset{N_{\mathrm{dl}}}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{\mathrm{Nb}}{\mathrm{\&Sigma;}}}{\mathrm{\&tau;}}_{\mathrm{dl}}\&CenterDot;c_1\&CenterDot;\mathrm{\&alpha;}\&CenterDot;P_i\end{array}\right.$

In formula:

be dl the network loss variable quantity that the large electrical network of scheduling slot reduces due to the access of microgrid; A is network loss electricity price; E _k, E ' _kbe respectively environmental value cost and the pollution punishment cost of the k kind dusty gas of fired power generating unit unit's generated energy discharge; Due to the grid integration of microgrid, both met the demand of local power supply reliability, simultaneously large electrical network has also reduced the demand of stand-by heat, therefore C _reservefor the stand-by heat expense that large electrical network is saved, c ₁for the stand-by heat expense of unit quantity of electricity, α is the proportion of the shared total installation of generating capacity of stand-by heat.

4) information set

For the microgrid of cooperative game and large electrical network, information set be guarantee system can be safely, reliably and the constraint condition of stable operation.

1. equality constraint, i.e. node power flow equation.

$\left\{\begin{array}{c}{P}_{j,\mathrm{dl}}^{\mathrm{net}}=-P_{j,\mathrm{dl}}^D+P_{j,\mathrm{dl}}^{\mathrm{DG}}\\ Q_{j,\mathrm{dl}}^{\mathrm{net}}=-Q_{j,\mathrm{dl}}^D+Q_{j,\mathrm{dl}}^{\mathrm{DG}}\end{array}\right.$

$\left\{\begin{array}{c}{P}_{j,\mathrm{dl}}^{\mathrm{net}}=U_{j,\mathrm{dl}}\underset{r=1}{\overset{N}{\mathrm{\&Sigma;}}}{U}_r(G_{\mathrm{jr}}\cos {\mathrm{\&theta;}}_{\mathrm{jr}}+B_{\mathrm{jr}}\sin {\mathrm{\&theta;}}_{\mathrm{jr}})\\ Q_{j,\mathrm{dl}}^{\mathrm{net}}=U_{j,\mathrm{dl}}\underset{r=1}{\overset{N}{\mathrm{\&Sigma;}}}{U}_r(G_{\mathrm{jr}}\sin {\mathrm{\&theta;}}_{\mathrm{ijr}}-B_{\mathrm{jr}}\cos {\mathrm{\&theta;}}_{\mathrm{jr}})\\ \mathrm{\&Delta;}{P}_{\mathrm{dl}}^{\mathrm{loss}}=\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}{P}_{j,\mathrm{dl}}^{\mathrm{net}}\end{array}\right.$

In formula:

be respectively the meritorious and reactive power network loss of node j at dl scheduling slot electrical network;

be respectively the meritorious and reactive power of node j dl scheduling slot electrical network demand;

be respectively the meritorious and reactive power that node j sends at dl scheduling slot DG; U _{j, dl}for node j is at the voltage magnitude of dl scheduling slot; G _jr, B _jrbe respectively real part and the imaginary part of the admittance matrix of system; θ _jrfor the phase difference of voltage of node j and node r; N is the nodes of microgrid.

2. inequality constrain

A. access capacity-constrained

$P_{i,\min }\&le;P_i^{\mathrm{DG}}\&le;P_{i,\max }$

In formula, P _{i, min}, P _{i, max}be respectively the bound of the access capacity of the micro-power supply of i kind.

B. voltage constraint

U _min≤U _j,dl≤U _max

In formula, U _{j, dl}for node j is at the magnitude of voltage of dl scheduling slot; U _min, U _maxfor the bound of quality of voltage.

C. miniature gas turbine climbing constraint

$|P_{t,\mathrm{dl}}^{\mathrm{MT}}-P_{t-1,\mathrm{dl}}^{\mathrm{MT}}|\&le;P_{\max }^{\mathrm{MT}}$

In formula, power upper limit during for consideration gas turbine climbing constraint.

D. energy storage device operation constraint

$S_{\mathrm{OC}}^{\min }\&le;S_{\mathrm{OC}}\&le;S_{\mathrm{OC}}^{\max }$

In formula,

for lower limit and the upper limit of the constraint of energy storage device dump energy;

5) balance policy

Suppose

for the Nash Equilibrium strategy of betting model, due to both can the forming cooperative alliances game and also can realize non-cooperative game of microgrid and large electrical network, represent that this strategy can realize the maximization of each alliance income.

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