CN109919658A - A kind of duty control method and system based on game theory - Google Patents
A kind of duty control method and system based on game theory Download PDFInfo
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Abstract
The present invention relates to a kind of duty control method and system based on game theory obtains historical data and real time meteorological data as forecast sample data;The electricity price of more power generation main bodies is formulated according to forecast sample data;The workload demand of the electricity price of more power generation main bodies and load side is input in the betting model constructed in advance as dynamic game particle, the Nash Equilibrium point of more power generation main body maximum revenue targets is met using particle swarm optimization algorithm;The historical data includes workload demand historical data, photovoltaic power generation historical data and history meteorological data.The present invention establishes the economical optimum model of more Interest Main Body transaction, is based on dynamic game theory, the Nash Equilibrium problem about electricity pricing and workload demand is solved using dynamic particles colony optimization algorithm, to realize the benefit of more power generation main bodies.
Description
Technical field
The present invention relates to the technical fields of Automation of Electric Systems, and in particular to a kind of load control system side based on game theory
Method and system.
Background technique
As electricity market is further reformed, each self-forming independence interests master of the renewable energy operator greatly developed
Body, and tradition will no longer be suitable for the electric energy scheduling method that power distribution network Income Maximum turns to target containing the new of more power generation main bodies
Type operation of power networks environment.Therefore under the premise of meeting user demand, using more power generation main body Income Maximums as target, formulate renewable
Force information, the fluctuation of intermittent photovoltaic power output to only rely on history power generation data and workload demand information hardly possible the energy a few days ago
Economy, energy loss are caused to meet perfect precision requirement;Because electricity pricing and load need between more power generation main bodies and user
It asks there are the conflict of interest, traditional multiple target solves the real time reaction for being unfavorable for Electricity Price Strategy, and obtained noninferior solution cannot accurate visitor
The representative common interest of sight.
Summary of the invention
To solve the real time reaction that above-mentioned multiple target solution traditional in the prior art is unfavorable for Electricity Price Strategy, what is obtained is non-bad
Solution accurately cannot objectively represent the problem of common interest, and the object of the present invention is to provide a kind of load control systems based on game theory
Method and system, the present invention establish the economical optimum model of more Interest Main Body transaction, are based on dynamic game theory, utilize dynamic grain
Subgroup optimization algorithm solves the Nash Equilibrium problem about electricity pricing and workload demand, to realize the interests of more power generation main bodies
It maximizes.
The purpose of the present invention is adopt the following technical solutions realization:
The present invention provides a kind of duty control method based on game theory, thes improvement is that:
Historical data and real time meteorological data are obtained as forecast sample data;
The electricity price of more power generation main bodies is formulated according to forecast sample data;
The workload demand of the electricity price of more power generation main bodies and load side is input to preparatory structure as dynamic game particle
In the betting model built, the Nash Equilibrium of more power generation main body maximum revenue targets is met using particle swarm optimization algorithm
Point;
The historical data includes workload demand historical data, photovoltaic power generation historical data and history meteorological data;
Real time meteorological data includes at least temperature and season data.
Further: the electricity price that more power generation main bodies are formulated according to forecast sample data, comprising:
Forecast sample data are input in preset RBF neural network model and predict photovoltaic power output a few days ago, are obtained
Photovoltaic power generation output forecasting value a few days ago;
The electricity consumption data of load side, the electricity consumption data system based on load side are determined according to the value of photovoltaic power generation output forecasting a few days ago
The electricity price of fixed more power generation main bodies.
Further: described forecast sample data are input in preset RBF neural network model is predicted a few days ago
Photovoltaic power output, obtains photovoltaic power generation output forecasting value a few days ago, comprising:
The forecast sample data are normalized;
RBF neural network model is trained based on the forecast sample data after normalized, obtains photovoltaic a few days ago
Power output predicted value.
Further: the expression formula that the forecast sample data are normalized is as follows:
Wherein, x ' (t) is the forecast sample data after normalized, and x (t) is the forecast sample data of input, min (x
It (t)) is the minimum data in x (t), max (x (t)) is the maximum data in x (t);
The forecast sample data based on after normalized are trained RBF neural network model, obtain a few days ago
The expression formula of photovoltaic power generation output forecasting value is as follows:
ym(t)=w1h1+w2h2+...+wjhj+...+wmhm
hj=G | | x ' (t)-hj||2
In formula: hjFor the output of j-th of neuron of hidden layer, network inputs be forecast sample data x (t)=
[x1x2...xm]T, w1w2...wmFor the weight of network.
Further: described using the workload demand of the electricity price of more power generation main bodies and load side as dynamic game particle
It is input in the betting model constructed in advance, meets more power generation main body maximum revenue targets using particle swarm optimization algorithm
Nash Equilibrium point, comprising:
Game optimizing is carried out using the workload demand of the electricity price of more power generation main bodies and load side as dynamic game particle,
Obtain the game strategies set of more power generation main bodies and load side;
Meet in conjunction with the game strategies set, in the betting model constructed in advance using particle swarm optimization algorithm more
Power generation main body maximum revenue and the optimal Nash Equilibrium point of load side benefit;
The betting model includes the revenue function of more power generation main bodies, the revenue function of load side and constraint condition.
Further: the revenue function expression formula of more power generation main bodies is as follows:
Wherein: EmulFor the revenue function of more power generation main bodies,The power generation electricity price formulated for t period more power generation main bodies;For t period more power generation main bodies to load side generate electricity electricity;UtIt indicates to buy or go out to power distribution network in t period more power generation main bodies
Electricity sales amount;It is power generation main bodies more within the t period to distribution online shopping, the electricity price of electricity sales amount;It is more power generation main bodies to distribution
The electricity that online shopping is bought or sold;Co,iFor i-th of photovoltaic unit cost of electricity-generating;For the actual power generation electricity of i-th of photovoltaic of t period
Amount;ηzIndicate energy storage depreciable cost coefficient;Indicate i-th of energy storage device in the cycle-index of t period;CinsFor energy storage installation
Cost;For energy storage device maintenance cost;For charge volume or discharge capacity;T indicates the preassigned period;
The revenue function expression formula of the load side is as follows:
Wherein: EloadFor the revenue function of load side,For load side be adjusted load participate in scheduling electric energy electricity price,Indicate load side deferrable load electricity consumption.
Further: the constraint condition includes:
Power-balance constraint:
Wherein,To be lost in the power transmission of t moment;
Workload demand responds electricity tariff constraint:
Wherein, Cload,minFor sale of electricity floor price, that is, the marginal cost to generate electricity;Cload,maxFor sale of electricity ceiling price;
Photovoltaic units limits:
Wherein, Pi,min、Pi,maxRespectively indicate the generated output upper and lower limit of photovoltaic i;
Stored energy capacitance constraint:
Wherein, Pwi,minAnd Pwi,maxThe upper and lower limit of respectively the wi energy storage output power;
Charge and discharge constraint:
Wherein,For the charge volume of t period energy storage i,The discharge capacity of period energy storage i;For t period energy storage i
Charge volume maximum value,The maximum value of the discharge capacity of period energy storage i.
Further: in conjunction with the game strategies set, the game mould constructed in advance using particle swarm optimization algorithm
The expression formula for meeting more power generation main body maximum revenues and the optimal Nash Equilibrium point of load side benefit in type is as follows:
G={ N;{Si}i∈N;{Ui}i∈N}
In formula: G is betting model, and N is participant, including more power generation main bodies and load;SiFor game strategies set, including
The workload demand that the power generation electricity price and load side that more power generation main bodies are formulated in game use;UiFor the income or branch of workload demand
It pays.
Further: described using particle swarm optimization algorithm to meet receiving for more power generation main body maximum revenue targets assorted
After equilibrium point, further includes:
The workload demand of load side is controlled according to the Nash Equilibrium point;
It is described that the workload demand of load side is controlled according to the Nash Equilibrium point, comprising:
Based on Nash Equilibrium point, load electricity consumption is adjusted according to load side demand, and carry out electricity price view with more power generation main bodies
Valence makes the strategy set in game consistently achieve Nash Equilibrium;
The electricity price is negotiated a price
More power generation main bodies update electricity price, load side updates workload demand, and both sides propose respective operation reserve in turn.
The present invention also provides a kind of load control systems based on game theory, the improvement is that:
Module is obtained, for obtaining forecast sample data;
Module is formulated, for formulating the electricity price of more power generation main bodies according to forecast sample data;
Module is solved, for using the workload demand of the electricity price of more power generation main bodies and load side as dynamic game particle
It is input in the betting model constructed in advance, meets more power generation main body maximum revenue targets using particle swarm optimization algorithm
Nash Equilibrium point;
The forecast sample data include at least photovoltaic history power generation data, workload demand information, temperature, season and in real time
Meteorological data.
Further: the formulation module, comprising:
Input submodule predicts light a few days ago for forecast sample data to be input in preset RBF prediction model
Volt power output;
It determines submodule, following electricity consumption data is determined for contributing according to the photovoltaic a few days ago of prediction, based on following use
Relationship between electric data and electricity pricing and workload demand formulates the electricity price of more power generation main bodies.
Further: the input submodule, comprising:
Normalization unit, for the forecast sample data to be normalized;
Training unit is predicted for being trained based on the forecast sample data after normalized to RBF neural
Obtain photovoltaic power output a few days ago.
Further: the expression formula that the forecast sample data are normalized is as follows:
Wherein, x ' (t) is the forecast sample data after normalized, and x (t) is the forecast sample data of input, min (x
It (t)) is the minimum data in forecast sample data x (t) after normalized, max (x (t)) is pre- test sample after normalized
Maximum data in notebook data;
The forecast sample data based on after normalized are trained RBF neural, and prediction obtains a few days ago
The expression formula of photovoltaic power output is as follows:
ym(t)=w1h1+w2h2+...+wjhj+...+wmhm
hj=G | | xj-hj||2
In formula: hjFor the output of j-th of neuron of hidden layer, network inputs are forecast sample data x=[x1x2...xm]T,
w1w2...wmFor the weight of network.
Further: the solution module, comprising:
Optimizing submodule, for using the workload demand of the electricity price of more power generation main bodies and load side as dynamic game grain
Son carries out game optimizing, obtains the game strategies set of more power generation main bodies and load side;
Submodule is solved, for being constructed in advance using particle swarm optimization algorithm in conjunction with the game strategies set
Meet more power generation main body maximum revenues and the optimal Nash Equilibrium point of load side benefit in betting model;
The betting model includes the revenue function of more power generation main bodies, the revenue function of load side and constraint condition.
Further: the revenue function expression formula of more power generation main bodies is as follows:
Wherein: EmulFor the revenue function of more power generation main bodies,The power generation electricity price formulated for t period more power generation main bodies;For t period more power generation main bodies to load side generate electricity electricity;UtIt indicates to buy or go out to power distribution network in t period more power generation main bodies
Electricity sales amount;It is power generation main bodies more within the t period to distribution online shopping, the electricity price of electricity sales amount;It is more power generation main bodies to power distribution network
Purchase or the electricity sold;Co,iFor i-th of photovoltaic unit cost of electricity-generating;For the actual power generation electricity of i-th of photovoltaic of t period
Amount;ηzIndicate energy storage depreciable cost coefficient;Indicate i-th of energy storage device in the cycle-index of t period;CinsFor energy storage installation
Cost;For energy storage device maintenance cost;For charge volume or discharge capacity;T indicates the preassigned period;
The revenue function expression formula of the load side is as follows:
Wherein: EloadFor the revenue function of load side,For load side be adjusted load participate in scheduling electric energy electricity price,Indicate load side deferrable load electricity consumption.
Further: the constraint condition includes:
Power-balance constraint:
Wherein,To be lost in the power transmission of t moment;
Workload demand responds electricity tariff constraint:
Wherein, Cload,minFor sale of electricity floor price, that is, the marginal cost to generate electricity;Cload,maxFor sale of electricity ceiling price;
Photovoltaic units limits:
Wherein, Pi,min、Pi,maxRespectively indicate the generated output upper and lower limit of photovoltaic i;
Stored energy capacitance constraint:
Wherein, Pwi,minAnd Pwi,maxThe upper and lower limit of respectively the wi energy storage output power;
Charge and discharge constraint:
Wherein,For the charge volume of t period energy storage i,The discharge capacity of period energy storage i;For t period energy storage i
Charge volume maximum value,The maximum value of the discharge capacity of period energy storage i.
Further: in conjunction with the game strategies set, the game mould constructed in advance using particle swarm optimization algorithm
The expression formula for meeting more power generation main body maximum revenues and the optimal Nash Equilibrium point of load side benefit in type is as follows:
G={ N;{Si}i∈N;{Ui}i∈N}
In formula: G is betting model, and N is participant, including more power generation main bodies and load;SiFor strategy set, in game
In, the workload demand for power generation electricity price and the load side use formulated including more power generation main bodies;UiFor workload demand income or
Payment.
Further: further include:
Control module, for being controlled according to the Nash Equilibrium point the workload demand of load side, comprising:
Agreed-upon price module adjusts itself workload demand according to load side demand response, passes through tune for being based on Nash Equilibrium point
It saves load electricity consumption and more power generation main bodies carries out electricity price agreed-upon price, the strategy set in game is made to consistently achieve Nash Equilibrium.
Compared with the immediate prior art, technical solution provided by the invention is had the beneficial effect that
The present invention provides a kind of duty control method based on game theory, obtains historical data and real time meteorological data conduct
Forecast sample data;The electricity price of more power generation main bodies is formulated according to forecast sample data;By the electricity price of more power generation main bodies and bear
The workload demand of lotus side is input in the betting model constructed in advance as dynamic game particle, is asked using particle swarm optimization algorithm
Solution meets the Nash Equilibrium point of more power generation main body maximum revenue targets;The historical data include workload demand historical data,
Photovoltaic power generation historical data and history meteorological data;Real time meteorological data includes at least temperature and season data.By to photovoltaic
The influence factors associated prediction such as power output, the historical data of workload demand, temperature, season, weather information, further increases load control
The accuracy of system and electric energy scheduling.
The present invention also carries out electric energy consumption using energy storage and adjustable load, realizes under the premise of meeting user demand
The commercialized running of more power generation main bodies, to pursue the maximization of more power generation main body benefits;Simultaneously in view of more power generation main bodies with
Dynamic competition problem between user demand optimizes it based on dynamic game theory, solves traditional optimization because adjusting
Degree personnel's subjectivity bring one-sidedness problem.
Detailed description of the invention
Fig. 1 is a kind of flow chart of duty control method based on game theory provided by the invention;
Fig. 2 is the structural schematic diagram of the duty control method based on game theory.
Specific embodiment
Specific embodiments of the present invention will be described in further detail with reference to the accompanying drawing.
The following description and drawings fully show specific embodiments of the present invention, to enable those skilled in the art to
Practice them.Other embodiments may include structure, logic, it is electrical, process and other change.Embodiment
Only represent possible variation.Unless explicitly requested, otherwise individual component and function are optional, and the sequence operated can be with
Variation.The part of some embodiments and feature can be included in or replace part and the feature of other embodiments.This hair
The range of bright embodiment includes equivalent obtained by the entire scope of claims and all of claims
Object.Herein, these embodiments of the invention can individually or generally be indicated that this is only with term " invention "
For convenience, and if in fact disclosing the invention more than one, the range for being not meant to automatically limit the application is to appoint
What single invention or inventive concept.
Embodiment one,
The present invention provides a kind of duty control method based on game theory, comprising:
Historical data and real time meteorological data are obtained as forecast sample data;
The electricity price of more power generation main bodies is formulated according to forecast sample data;
The workload demand of the electricity price of more power generation main bodies and load side is input to preparatory structure as dynamic game particle
In the betting model built, the Nash Equilibrium of more power generation main body maximum revenue targets is met using particle swarm optimization algorithm
Point;
The historical data includes workload demand historical data, photovoltaic power generation historical data and history meteorological data;
Real time meteorological data includes at least temperature and season data.
Further: the electricity price that more power generation main bodies are formulated according to forecast sample data, comprising:
Forecast sample data are input in preset RBF neural network model and predict photovoltaic power output a few days ago, are obtained
Photovoltaic power generation output forecasting value a few days ago;
The electricity consumption data of load side, the electricity consumption data system based on load side are determined according to the value of photovoltaic power generation output forecasting a few days ago
The electricity price of fixed more power generation main bodies.
Further: described forecast sample data are input in preset RBF neural network model is predicted a few days ago
Photovoltaic power output, obtains photovoltaic power generation output forecasting value a few days ago, comprising:
The forecast sample data are normalized;
RBF neural network model is trained based on the forecast sample data after normalized, obtains photovoltaic a few days ago
Power output predicted value.
Further: the expression formula that the forecast sample data are normalized is as follows:
Wherein, x ' (t) is the forecast sample data after normalized, and x (t) is the forecast sample data of input, min (x
It (t)) is the minimum data in x (t), max (x (t)) is the maximum data in x (t);
The forecast sample data based on after normalized are trained RBF neural network model, obtain a few days ago
The expression formula of photovoltaic power generation output forecasting value is as follows:
ym(t)=w1h1+w2h2+...+wjhj+...+wmhm
hj=G | | x ' (t)-hj||2
In formula: hjFor the output of j-th of neuron of hidden layer, network inputs be forecast sample data x (t)=
[x1x2...xm]T, w1w2...wmFor the weight of network.
Further: described using the workload demand of the electricity price of more power generation main bodies and load side as dynamic game particle
It is input in the betting model constructed in advance, meets more power generation main body maximum revenue targets using particle swarm optimization algorithm
Nash Equilibrium point, comprising:
Game optimizing is carried out using the workload demand of the electricity price of more power generation main bodies and load side as dynamic game particle,
Obtain the game strategies set of more power generation main bodies and load side;
Meet in conjunction with the game strategies set, in the betting model constructed in advance using particle swarm optimization algorithm more
Power generation main body maximum revenue and the optimal Nash Equilibrium point of load side benefit;
The betting model includes the revenue function of more power generation main bodies, the revenue function of load side and constraint condition.
Further: the revenue function expression formula of more power generation main bodies is as follows:
Wherein: EmulFor the revenue function of more power generation main bodies,The power generation electricity price formulated for t period more power generation main bodies;For t period more power generation main bodies to load side generate electricity electricity;UtIt indicates to buy or go out to power distribution network in t period more power generation main bodies
Electricity sales amount;It is power generation main bodies more within the t period to distribution online shopping, the electricity price of electricity sales amount;It is more power generation main bodies to power distribution network
Purchase or the electricity sold;Co,iFor i-th of photovoltaic unit cost of electricity-generating;For the actual power generation electricity of i-th of photovoltaic of t period
Amount;ηzIndicate energy storage depreciable cost coefficient;Indicate i-th of energy storage device in the cycle-index of t period;CinsFor energy storage installation
Cost;For energy storage device maintenance cost;For charge volume or discharge capacity;T indicates the preassigned period;
The revenue function expression formula of the load side is as follows:
Wherein: EloadFor the revenue function of load side,For load side be adjusted load participate in scheduling electric energy electricity price,Indicate load side deferrable load electricity consumption.
Further: the constraint condition includes:
Power-balance constraint:
Wherein,To be lost in the power transmission of t moment;
Workload demand responds electricity tariff constraint:
Wherein, Cload,minFor sale of electricity floor price, that is, the marginal cost to generate electricity;Cload,maxFor sale of electricity ceiling price;
Photovoltaic units limits:
Wherein, Pi,min、Pi,maxRespectively indicate the generated output upper and lower limit of photovoltaic i;
Stored energy capacitance constraint:
Wherein, Pwi,minAnd Pwi,maxThe upper and lower limit of respectively the wi energy storage output power;
Charge and discharge constraint:
Wherein,For the charge volume of t period energy storage i,The discharge capacity of period energy storage i;For t period energy storage i
Charge volume maximum value,The maximum value of the discharge capacity of period energy storage i.
Further: in conjunction with the game strategies set, the game mould constructed in advance using particle swarm optimization algorithm
The expression formula for meeting more power generation main body maximum revenues and the optimal Nash Equilibrium point of load side benefit in type is as follows:
G={ N;{Si}i∈N;{Ui}i∈N}
In formula: G is betting model, and N is participant, including more power generation main bodies and load;SiFor game strategies set, including
The workload demand that the power generation electricity price and load side that more power generation main bodies are formulated in game use;UiFor the income or branch of workload demand
It pays.
Further: described using particle swarm optimization algorithm to meet receiving for more power generation main body maximum revenue targets assorted
After equilibrium point, further includes:
The workload demand of load side is controlled according to the Nash Equilibrium point;
It is described that the workload demand of load side is controlled according to the Nash Equilibrium point, comprising:
Based on Nash Equilibrium point, load electricity consumption is adjusted according to load side demand, and carry out electricity price view with more power generation main bodies
Valence makes the strategy set in game consistently achieve Nash Equilibrium;
The electricity price is negotiated a price
More power generation main bodies update electricity price, load side updates workload demand, and both sides propose respective operation reserve in turn.
The present invention is described as follows according to flow chart 1 and structure chart 2:
(1) the economic optimization scheduling model of more power generation main body photovoltaic power generations is established:
(1) optimization aim:
Wherein, T indicates the when number of segment in a dispatching cycle;N indicates the number of more power generation main body distributed photovoltaics;
The power generation electricity price formulated for t period more power generation main bodies;For t period more power generation main bodies to load side generate electricity electricity;Ut=1 table
Show and buys electricity to power distribution network in t period more power generation main bodies;Ut=-1 indicates to go out sale of electricity to power distribution network in t period more power generation main bodies
Amount;It is power generation main bodies more within the t period to distribution online shopping, the electricity price of electricity sales amount;It is bought for more power generation main bodies to power distribution network
Or the electricity sold;Co,iFor i-th of photovoltaic unit cost of electricity-generating;For i-th of photovoltaic power generation electricity of t period;ηzIndicate storage
It can depreciable cost coefficient;Indicate i-th of energy storage device in the cycle-index of t period;CinsFor energy storage installation cost;For storage
It can cost of equipment maintenance;For charge volume or discharge capacity.
(2) power-balance constraint:
Wherein,To be lost in the power transmission of t moment.
(4) workload demand responds electricity tariff constraint:
Wherein, Cload,minFor sale of electricity floor price, that is, the marginal cost to generate electricity;Cload,maxFor sale of electricity ceiling price.
(3) photovoltaic units limits:
Wherein, Pi,min、Pi,maxRespectively indicate the generated output bound of photovoltaic i.
(4) stored energy capacitance constrains:
Wherein, Pwi,minAnd Pwi,maxThe bound of respectively the wi energy storage output power.
(5) charge and discharge constrain:
Wherein,The respectively charge and discharge amount of t period energy storage i;Respectively t period energy storage i
Charge and discharge amount maximum value.
(1) each Interest Main Body generates electricity information, workload demand, temperature, season and real time meteorological data according to history to predict
Photovoltaic force information establishes neural network prediction model, and (there are the peak valley phases for load electricity consumption here for photovoltaic power output situation a few days ago for prediction
Refer to that the fluctuation of T period internal loading has differences, predicts that this electricity consumption peak valley phase is to make system power more to reduce peak valley difference value
Add stabilization.Electricity hereafter is according to the actual power generation electricity of scheduling strategy photovoltaic):
Since the behind of photovoltaic power output fluctuation must have certain inherent laws, to realize photovoltaic power generation output forecasting, need pair
Its inherent laws is sought.RBF neural can realize fitting to the non-linear relation between inputoutput data easily, and
There are cracking learning ability and convergence rate, has a clear superiority in terms of prediction processing.Photovoltaic power generation output forecasting model foundation mistake
Journey is as follows:
(1) in order to reduce influence of the data to precision of prediction itself, pretreatment is normalized to data first:
Wherein, x ' (t) is the data after normalization, and x (t) is forecast sample input data, min (x (t)), max (x (t))
For minimum, the maximum value in sample data x (t);It is apparent from: 0≤x ' (t)≤1.
(2) RBF neural is trained using forecast sample data:
RBF neural is made of three-layer network, and the input layer including input signal carries out the hidden layer of NONLINEAR CALCULATION
With the output layer for linear transformation.The selection of RBF neural input layer quantity has much relations to precision of prediction, defeated
Ingress is very few, and matched curve is not accurate enough;Input node is excessive, and model is complicated and is easily trapped into local optimum.In this regard, comprehensive
Temperature, weather information, season equal samples parameter are intended choosing input node with heuristic on the basis of previous experiences.It is implicit
The activation primitive of layer selects Gaussian function, is determining input, output data sample and error range, is constantly adjusting hidden layer
Number makes to predict that error drops to setting value hereinafter, obtaining the number of nodes of final hidden layer at this time.Output layer number can basis
The prediction step number of model built is chosen.It finally selects algorithm appropriate to carry out learning training to hidden layer and output layer, obtains
The weight of corresponding network is obtained, can be obtained required prediction data after substituting into known load data.
(3) RBF neural prediction model is evaluated:
Wherein, RMSE is root-mean-square error, and n is training data sum,For predicted value, x (t) is sample value, and t is sample
Notebook data serial number.Error assessment is carried out to model, it can be seen that the superiority and inferiority of prediction model.When being predicted using trained network
It carries out anti-normalization processing and obtains the actual prediction value of photovoltaic power output a few days ago.Described be input to forecast sample data presets
RBF prediction model in predict a few days ago photovoltaic power output, comprising:
The forecast sample data are normalized;
RBF neural is trained based on the forecast sample data after normalized, prediction obtains photovoltaic a few days ago
Power output;
More power generation main bodies are contributed according to photovoltaic a few days ago, and (there are peaks for load electricity consumption here for determining demand history electricity consumption data
The paddy phase refers to that the fluctuation of T period internal loading has differences, and predicts that this electricity consumption peak valley phase is to match system to reduce peak valley difference value
Electricity is more stable.Electricity hereafter is according to the actual power generation electricity of scheduling strategy photovoltaic), according to electricity pricing and workload demand
Between relationship formulate the electricity prices of more power generation main bodies.
(3) it is discussed based on dynamic game thought to above-mentioned model, and utilizes PSO Algorithm Nash Equilibrium
Point:
For more power generation main bodies, predicts to obtain photovoltaic force information a few days ago using RBF neural, gone through by load
History power generation data, can substantially estimate the load peak valley phase.Electricity pricing has certain understanding to the reaction of workload demand;Secondly,
For load, more power generation main body photovoltaic power generation information can substantially understand electricity price a few days ago by weather information rule, and right
This makes positive counter-measure.Since every terms of information variation is dynamic in gambling process, therefore the present invention is based on Complete Informations
Dynamic game theory studies it, carries out game in the case where both sides' rationality, tries hard to maximize number one.Specifically
Mode is as follows:
The expression formula of the game strategies set of more power generation main bodies and load side is as follows:
G={ N;{Si}i∈N;{Ui}i∈N}
To the game function optimizing, game strategies set is obtained, comprising:
If the plan being made of each strategy of the workload demand strategy of the Electricity Price Strategy and load side of more power generation main bodies
Analects (S1 *,...,Sn *) in, the strategy of the Electricity Price Strategy of more power generation main body iIt is the workload demand strategy set to load side
Best strategy, then game strategies collection is combined intoWherein i is more power generation main bodies: n is more power generation main bodies
Number;Or
The strategy of the workload demand i' of load sideSet is then won to the Best strategy of the Electricity Price Strategy of more power generation main bodies
Playing chess strategy set isWherein i' is more power generation main bodies: n ' is the number of workload demand.
(1) revenue function of game participant:
Power generation main body revenue function more than 1.:
Its strategy combination includes the cost and demand response of cost of electricity-generating, operation, amortization charge and power distribution network pricing
The income of electricity price.Revenue function is the net profit of more power generation main bodies, as shown in formula (9):
2. load revenue function:
Load side is negotiated a price using between the deferrable load electricity consumption and more power generation main bodies of demand response, revenue function
For income and disbursement difference, as shown in formula (10):
(2) existence proof of Nash Equilibrium point:
The present invention uses Complete Information Dynamic Game, and strategy is Pure strategy nash equilibria, according to Pure strategy nash equilibria
Known to existence result: in multilateral Game, if the pure strategy set of each participant be a non-empty on Euclidean space,
Closing, bounded convex set, revenue function it is continuous about strategy combination and intend it is recessed, then there are Pure strategy nash equilibrias for the game.
By the revenue function of more power generation main bodies and load it is found that their revenue function can be divided into linear segment (line
Property function be clearly a kind of concave function) and non-linear partial, but non-linear partial does not change with strategy change, therefore can be seen
Work is a kind of constant, in conclusion it is quasiconcave function.Therefore there are Nash Equilibrium Solutions.
(3) existed according to above-mentioned Nash Equilibrium, solved using dynamic particles group's algorithm:
Particle swarm optimization algorithm is a kind of evolutionary computing based on swarm intelligence method, is by doctor earliest
Eberhart and Kennedy is derived from the research to flock of birds predation.It is random in solution space by the cooperation between group
Search, the process of approximate optimal solution is eventually found by iteration.
When external environment changes, in ordinary particle group's algorithm particle due to can not sensing external environment variation,
Therefore real-time response can not be carried out, lack dynamic optimization ability.Increase sensitive particles in the ordinary particle of population and obtains one kind
The particle swarm algorithm of dynamic environment, the algorithm incude external environment by the size of the difference of the adjacent function of fitness value twice
Variation, when the difference of fitness value be more than certain threshold value when triggering response, at this time algorithm according to a certain percentage renewal speed and
Particle, thus the ability with dynamic environment optimizing.
Detailed process is as follows:
1) feas ible space is divided into n1A uniform subspace, and in every sub-spaces random initializtion n2A sensitive particles,
Calculate sensitive particles fitness value.
2) parameter value of particle swarm algorithm is inputted, inertia weight, Studying factors, Dynamic trigger response lag give photovoltaic
Power output predicted value, initializes particle position, particle rapidity.
3) according to the revenue function of more power generation main bodies and load side, feasible solution is determined with particle position.According to fitness letter
Number calculates each particle fitness value, finds the individual extreme value p of particlebestWith all extreme value gbest, individual extreme value fitness value is
fpbest, group's extreme value fitness value is fgbest。
4) speed and the position that more new particle is distinguished in new group, handle constraint condition, are calculated according to fitness function
The fitness value of each particle, updates part, globally optimal solution in new group.
5) sensitive particles fitness value is calculated, and calculates the difference of adjacent fitness value twice and sums, if required
Greater than given threshold, then 3) initialization population and particle rapidity in proportion, go to step.
6) judged whether to terminate iteration according to required precision or maximum number of iterations, if meeting, output is qualified most
Excellent particle (i.e. approximate solution);Otherwise, return step 3)
Embodiment two,
Based on same inventive concept, the present invention also provides a kind of load control systems based on game theory, comprising:
Module is obtained, for obtaining historical data and real time meteorological data as forecast sample data;
Module is formulated, for formulating the electricity price of more power generation main bodies according to forecast sample data;
Module is solved, for using the workload demand of the electricity price of more power generation main bodies and load side as dynamic game particle
It is input in the betting model constructed in advance, meets more power generation main body maximum revenue targets using particle swarm optimization algorithm
Nash Equilibrium point;
The historical data includes workload demand historical data, photovoltaic power generation historical data and history meteorological data.
The formulation module, comprising:
Input submodule predicts light a few days ago for forecast sample data to be input in preset RBF prediction model
Volt power output;
It determines submodule, following electricity consumption data is determined for contributing according to the photovoltaic a few days ago of prediction, based on following use
Relationship between electric data and electricity pricing and workload demand formulates the electricity price of more power generation main bodies.
The input submodule, comprising:
Normalization unit, for the forecast sample data to be normalized;
Training unit is predicted for being trained based on the forecast sample data after normalized to RBF neural
Obtain photovoltaic power output a few days ago.
The expression formula that the forecast sample data are normalized is as follows:
Wherein, x ' (t) is the forecast sample data after normalized, and x (t) is the forecast sample data of input, min (x
It (t)) is the minimum data in forecast sample data x (t) after normalized, max (x (t)) is pre- test sample after normalized
Maximum data in notebook data;
The forecast sample data based on after normalized are trained RBF neural, and prediction obtains a few days ago
The expression formula of photovoltaic power output is as follows:
ym(t)=w1h1+w2h2+...+wjhj+...+wmhm
hj=G | | xj-hj||2
In formula: hjFor the output of j-th of neuron of hidden layer, network inputs are forecast sample data x=[x1x2...xm]T,
w1w2...wmFor the weight of network.
The solution module, comprising:
Optimizing submodule, for using the workload demand of the electricity price of more power generation main bodies and load side as dynamic game grain
Son carries out game optimizing, obtains the game strategies set of more power generation main bodies and load side;
Submodule is solved, for being constructed in advance using particle swarm optimization algorithm in conjunction with the game strategies set
Meet more power generation main body maximum revenues and the optimal Nash Equilibrium point of load side benefit in betting model;
The betting model includes the revenue function of more power generation main bodies, the revenue function of load side and constraint condition.
The revenue function expression formula of more power generation main bodies is as follows:
Wherein: EmulFor the revenue function of more power generation main bodies,The power generation electricity price formulated for t period more power generation main bodies;For t period more power generation main bodies to load side generate electricity electricity;UtIt indicates to buy or go out to power distribution network in t period more power generation main bodies
Electricity sales amount;It is power generation main bodies more within the t period to distribution online shopping, the electricity price of electricity sales amount;It is more power generation main bodies to power distribution network
Purchase or the electricity sold;Co,iFor i-th of photovoltaic unit cost of electricity-generating;For the actual power generation electricity of i-th of photovoltaic of t period
Amount;ηzIndicate energy storage depreciable cost coefficient;Indicate i-th of energy storage device in the cycle-index of t period;CinsFor energy storage installation
Cost;For energy storage device maintenance cost;For charge volume or discharge capacity;T indicates the preassigned period;
The revenue function expression formula of the load side is as follows:
Wherein: EloadFor the revenue function of load side,For load side be adjusted load participate in scheduling electric energy electricity price,Indicate load side deferrable load electricity consumption.
The constraint condition includes:
Power-balance constraint:
Wherein,To be lost in the power transmission of t moment;
Workload demand responds electricity tariff constraint:
Wherein, Cload,minFor sale of electricity floor price, that is, the marginal cost to generate electricity;Cload,maxFor sale of electricity ceiling price;
Photovoltaic units limits:
Wherein, Pi,min、Pi,maxRespectively indicate the generated output upper and lower limit of photovoltaic i;
Stored energy capacitance constraint:
Wherein, Pwi,minAnd Pwi,maxThe upper and lower limit of respectively the wi energy storage output power;
Charge and discharge constraint:
Wherein,For the charge volume of t period energy storage i,The discharge capacity of period energy storage i;For t period energy storage i
Charge volume maximum value,The maximum value of the discharge capacity of period energy storage i.
Meet in conjunction with the game strategies set, in the betting model constructed in advance using particle swarm optimization algorithm more
Power generation main body maximum revenue and the expression formula of the optimal Nash Equilibrium point of load side benefit are as follows:
G={ N;{Si}i∈N;{Ui}i∈N}
In formula: G is betting model, and N is participant, including more power generation main bodies and load;SiFor strategy set, in game
In, the workload demand for power generation electricity price and the load side use formulated including more power generation main bodies;UiFor workload demand income or
Payment.
Further include:
Control module, for being controlled according to the Nash Equilibrium point the workload demand of load side, comprising:
Agreed-upon price module adjusts itself workload demand according to load side demand response, passes through tune for being based on Nash Equilibrium point
It saves load electricity consumption and more power generation main bodies carries out electricity price agreed-upon price, the strategy set in game is made to consistently achieve Nash Equilibrium.
The present invention provides a kind of duty control method based on game theory, by contributing to photovoltaic, the history of workload demand
The influence factors associated prediction such as data, temperature, season, weather information further increases the essence of load control system and electric energy scheduling
Exactness.
The present invention also carries out electric energy consumption using energy storage and adjustable load, realizes under the premise of meeting user demand
The commercialized running of more power generation main bodies, to pursue the maximization of more power generation main body benefits;Simultaneously in view of more power generation main bodies with
Dynamic competition problem between user demand optimizes it based on dynamic game theory, solves traditional optimization because adjusting
Degree personnel's subjectivity bring one-sidedness problem.
It should be understood by those skilled in the art that, embodiments herein can provide as method, system or computer program
Product.Therefore, complete hardware embodiment, complete software embodiment or reality combining software and hardware aspects can be used in the application
Apply the form of example.Moreover, it wherein includes the computer of computer usable program code that the application, which can be used in one or more,
The computer program implemented in usable storage medium (including but not limited to magnetic disk storage, CD-ROM, optical memory etc.) produces
The form of product.
The application is referring to method, the process of equipment (system) and computer program product according to the embodiment of the present application
Figure and/or block diagram describe.It should be understood that every one stream in flowchart and/or the block diagram can be realized by computer program instructions
The combination of process and/or box in journey and/or box and flowchart and/or the block diagram.It can provide these computer programs
Instruct the processor of general purpose computer, special purpose computer, Embedded Processor or other programmable data processing devices to produce
A raw machine, so that being generated by the instruction that computer or the processor of other programmable data processing devices execute for real
The device for the function of being specified in present one or more flows of the flowchart and/or one or more blocks of the block diagram.
These computer program instructions, which may also be stored in, is able to guide computer or other programmable data processing devices with spy
Determine in the computer-readable memory that mode works, so that it includes referring to that instruction stored in the computer readable memory, which generates,
Enable the manufacture of device, the command device realize in one box of one or more flows of the flowchart and/or block diagram or
The function of being specified in multiple boxes.
These computer program instructions also can be loaded onto a computer or other programmable data processing device, so that counting
Series of operation steps are executed on calculation machine or other programmable devices to generate computer implemented processing, thus in computer or
The instruction executed on other programmable devices is provided for realizing in one or more flows of the flowchart and/or block diagram one
The step of function of being specified in a box or multiple boxes.
The above embodiments are merely illustrative of the technical scheme of the present invention and are not intended to be limiting thereof, although referring to above-described embodiment pair
The present invention is described in detail, those of ordinary skill in the art still can to a specific embodiment of the invention into
Row modification perhaps equivalent replacement these without departing from any modification of spirit and scope of the invention or equivalent replacement, applying
Within pending claims of the invention.
Claims (18)
1. a kind of duty control method based on game theory, it is characterised in that:
Historical data and real time meteorological data are obtained as forecast sample data;
The electricity price of more power generation main bodies is formulated according to forecast sample data;
The workload demand of the electricity price of more power generation main bodies and load side is input to as dynamic game particle and is constructed in advance
In betting model, the Nash Equilibrium point of more power generation main body maximum revenue targets is met using particle swarm optimization algorithm;
The historical data includes workload demand historical data, photovoltaic power generation historical data and history meteorological data.
2. duty control method as described in claim 1, it is characterised in that: described to formulate multiple electricity according to forecast sample data
The electricity price of main body, comprising:
Forecast sample data are input in preset RBF neural network model and predict photovoltaic power output a few days ago, are obtained a few days ago
Photovoltaic power generation output forecasting value;
The electricity consumption data that load side is determined according to the value of photovoltaic power generation output forecasting a few days ago, the electricity consumption data based on load side are formulated more
The electricity price of power generation main body.
3. duty control method as claimed in claim 2, it is characterised in that: described be input to forecast sample data sets in advance
Photovoltaic power output a few days ago is predicted in fixed RBF neural network model, obtains photovoltaic power generation output forecasting value a few days ago, comprising:
The forecast sample data are normalized;
RBF neural network model is trained based on the forecast sample data after normalized, obtains photovoltaic power output a few days ago
Predicted value.
4. duty control method as claimed in claim 3, it is characterised in that: place is normalized to the forecast sample data
The expression formula of reason is as follows:
Wherein, x ' (t) is the forecast sample data after normalized, and x (t) is the forecast sample data of input, min (x (t))
For the minimum data in x (t), max (x (t)) is the maximum data in x (t);
The forecast sample data based on after normalized are trained RBF neural network model, obtain photovoltaic a few days ago
The expression formula for predicted value of contributing is as follows:
ym(t)=w1h1+w2h2+...+wjhj+...+wmhm
hj=G | | x ' (t)-hj||2
In formula: hjFor the output of j-th of neuron of hidden layer, network inputs are forecast sample data x (t)=[x1x2...xm]T,
w1w2...wmFor the weight of network.
5. duty control method as described in claim 1, it is characterised in that: the electricity price by more power generation main bodies and negative
The workload demand of lotus side is input in the betting model constructed in advance as dynamic game particle, is asked using particle swarm optimization algorithm
Solution meets the Nash Equilibrium point of more power generation main body maximum revenue targets, comprising:
Game optimizing is carried out using the workload demand of the electricity price of more power generation main bodies and load side as dynamic game particle, is obtained
The game strategies set of more power generation main bodies and load side;
In conjunction with the game strategies set, meet multiple electricity in the betting model constructed in advance using particle swarm optimization algorithm
Main body maximum revenue and the optimal Nash Equilibrium point of load side benefit;
The betting model includes the revenue function of more power generation main bodies, the revenue function of load side and constraint condition.
6. duty control method as described in claim 1, it is characterised in that: the revenue function expression formula of more power generation main bodies
It is as follows:
Wherein: EmulFor the revenue function of more power generation main bodies,The power generation electricity price formulated for t period more power generation main bodies;For t
Period more power generation main bodies to load side generate electricity electricity;UtIt indicates to buy in t period more power generation main bodies to power distribution network or electricity sales amount out;It is power generation main bodies more within the t period to distribution online shopping, the electricity price of electricity sales amount;For more power generation main bodies to power distribution network buy or
The electricity of sale;Co,iFor i-th of photovoltaic unit cost of electricity-generating;For the actual power generation electricity of i-th of photovoltaic of t period;ηzTable
Show energy storage depreciable cost coefficient;Indicate i-th of energy storage device in the cycle-index of t period;CinsFor energy storage installation cost;
For energy storage device maintenance cost;For charge volume or discharge capacity;T indicates the preassigned period;
The revenue function expression formula of the load side is as follows:
Wherein: EloadFor the revenue function of load side,For load side be adjusted load participate in scheduling electric energy electricity price,Table
Show load side deferrable load electricity consumption.
7. such as duty control method described in claim 5 or 6, it is characterised in that: the constraint condition includes:
Power-balance constraint:
Wherein,To be lost in the power transmission of t moment;
Workload demand responds electricity tariff constraint:
Wherein, Cload,minFor sale of electricity floor price, that is, the marginal cost to generate electricity;Cload,maxFor sale of electricity ceiling price;
Photovoltaic units limits:
Wherein, Pi,min、Pi,maxRespectively indicate the generated output upper and lower limit of photovoltaic i;
Stored energy capacitance constraint:
Wherein, Pwi,minAnd Pwi,maxThe upper and lower limit of respectively the wi energy storage output power;
Charge and discharge constraint:
Wherein,For the charge volume of t period energy storage i,The discharge capacity of period energy storage i;For the charging of t period energy storage i
Maximum value is measured,The maximum value of the discharge capacity of period energy storage i.
8. duty control method as claimed in claim 5, it is characterised in that: in conjunction with the game strategies set, using particle
Meet more power generation main body maximum revenues in the betting model that colony optimization algorithm solution constructs in advance and load side benefit is optimal
The expression formula of Nash Equilibrium point is as follows:
G={ N;{Si}i∈N;{Ui}i∈N}
In formula: G is betting model, and N is participant, including more power generation main bodies and load;SiFor game strategies set, including game
In the workload demand of power generation electricity price and load side use formulated of more power generation main bodies;UiFor the income or payment of workload demand.
9. duty control method as described in claim 1, it is characterised in that: described to be met using particle swarm optimization algorithm
After the Nash Equilibrium point of more power generation main body maximum revenue targets, further includes:
The workload demand of load side is controlled according to the Nash Equilibrium point;
It is described that the workload demand of load side is controlled according to the Nash Equilibrium point, comprising:
Based on Nash Equilibrium point, load electricity consumption is adjusted according to load side demand, and carry out electricity price agreed-upon price with more power generation main bodies, made
Strategy set in game consistently achieves Nash Equilibrium;
The electricity price is negotiated a price
More power generation main bodies update electricity price, load side updates workload demand, and both sides propose respective operation reserve in turn.
10. a kind of load control system based on game theory, it is characterised in that:
Module is obtained, for obtaining historical data and real time meteorological data as forecast sample data;
Module is formulated, for formulating the electricity price of more power generation main bodies according to forecast sample data;
Module is solved, for inputting the workload demand of the electricity price of more power generation main bodies and load side as dynamic game particle
Into the betting model constructed in advance, meet receiving for more power generation main body maximum revenue targets using particle swarm optimization algorithm
Assorted equilibrium point;
The historical data includes workload demand historical data, photovoltaic power generation historical data and history meteorological data.
11. load control system as claimed in claim 10, it is characterised in that: the formulation module, comprising:
Input submodule predicts that photovoltaic goes out a few days ago for forecast sample data to be input in preset RBF prediction model
Power;
It determines submodule, following electricity consumption data is determined for contributing according to the photovoltaic a few days ago of prediction, based on following electricity consumption number
Relationship accordingly and between electricity pricing and workload demand formulates the electricity price of more power generation main bodies.
12. load control system as claimed in claim 11, it is characterised in that: the input submodule, comprising:
Normalization unit, for the forecast sample data to be normalized;
Training unit, for being trained based on the forecast sample data after normalized to RBF neural, prediction is obtained
Photovoltaic is contributed a few days ago.
13. load control system as claimed in claim 12, it is characterised in that: carry out normalizing to the forecast sample data
The expression formula for changing processing is as follows:
Wherein, x ' (t) is the forecast sample data after normalized, and x (t) is the forecast sample data of input, min (x (t))
For the minimum data in forecast sample data x (t) after normalized, max (x (t)) is forecast sample number after normalized
Maximum data in;
The forecast sample data based on after normalized are trained RBF neural, and prediction obtains photovoltaic a few days ago
The expression formula of power output is as follows:
ym(t)=w1h1+w2h2+...+wjhj+...+wmhm
hj=G | | xj-hj||2
In formula: hjFor the output of j-th of neuron of hidden layer, network inputs are forecast sample data x=[x1x2...xm]T,
w1w2...wmFor the weight of network.
14. load control system as claimed in claim 12, it is characterised in that: the solution module, comprising:
Optimizing submodule, for using the workload demand of the electricity price of more power generation main bodies and load side as dynamic game particle into
Row game optimizing obtains the game strategies set of more power generation main bodies and load side;
Submodule is solved, the game constructed in advance using particle swarm optimization algorithm in conjunction with the game strategies set is used for
Meet more power generation main body maximum revenues and the optimal Nash Equilibrium point of load side benefit in model;
The betting model includes the revenue function of more power generation main bodies, the revenue function of load side and constraint condition.
15. load control system as claimed in claim 14, it is characterised in that: the revenue function of more power generation main bodies is expressed
Formula is as follows:
Wherein: EmulFor the revenue function of more power generation main bodies,The power generation electricity price formulated for t period more power generation main bodies;For
T period more power generation main bodies to load side generate electricity electricity;UtIndicate t period more power generation main bodies to power distribution network buy or sale of electricity out
Amount;It is power generation main bodies more within the t period to distribution online shopping, the electricity price of electricity sales amount;It is bought for more power generation main bodies to power distribution network
Or the electricity sold;Co,iFor i-th of photovoltaic unit cost of electricity-generating;For the actual power generation electricity of i-th of photovoltaic of t period;ηz
Indicate energy storage depreciable cost coefficient;Indicate i-th of energy storage device in the cycle-index of t period;CinsFor energy storage installation cost;For energy storage device maintenance cost;For charge volume or discharge capacity;T indicates the preassigned period;
The revenue function expression formula of the load side is as follows:
Wherein: EloadFor the revenue function of load side,For load side be adjusted load participate in scheduling electric energy electricity price,Table
Show load side deferrable load electricity consumption.
16. load control system as claimed in claim 14, it is characterised in that: the constraint condition includes:
Power-balance constraint:
Wherein,To be lost in the power transmission of t moment;
Workload demand responds electricity tariff constraint:
Wherein, Cload,minFor sale of electricity floor price, that is, the marginal cost to generate electricity;Cload,maxFor sale of electricity ceiling price;
Photovoltaic units limits:
Wherein, Pi,min、Pi,maxRespectively indicate the generated output upper and lower limit of photovoltaic i;
Stored energy capacitance constraint:
Wherein, Pwi,minAnd Pwi,maxThe upper and lower limit of respectively the wi energy storage output power;
Charge and discharge constraint:
Wherein,For the charge volume of t period energy storage i,The discharge capacity of period energy storage i;For filling for t period energy storage i
Electricity maximum value,The maximum value of the discharge capacity of period energy storage i.
17. load control system as claimed in claim 10, it is characterised in that: in conjunction with the game strategies set, using grain
Meet more power generation main body maximum revenues in the betting model that optimization algorithm solution in subgroup constructs in advance and load side benefit is optimal
Nash Equilibrium point expression formula it is as follows:
G={ N;{Si}i∈N;{Ui}i∈N}
In formula: G is betting model, and N is participant, including more power generation main bodies and load;SiFor strategy set, in game, including
The workload demand that the power generation electricity price and load side that more power generation main bodies are formulated use;UiFor the income or payment of workload demand.
18. load control system as claimed in claim 10, it is characterised in that: further include:
Control module, for being controlled according to the Nash Equilibrium point the workload demand of load side, comprising:
Agreed-upon price module adjusts itself workload demand according to load side demand response, is born by adjusting for being based on Nash Equilibrium point
Lotus electricity consumption and more power generation main bodies carry out electricity price agreed-upon price, and the strategy set in game is made to consistently achieve Nash Equilibrium.
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