CN115906608A - Game theory-based virtual power plant model and optimized operation method - Google Patents
Game theory-based virtual power plant model and optimized operation method Download PDFInfo
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Abstract
The invention discloses a virtual power plant model based on a game theory and an optimized operation method. The invention comprises the following steps: 1) Building a virtual power plant based on 'producer and consumer' cluster aggregation and transaction driving, and building a customized building mechanism mathematical model of the transaction-driven virtual power plant; 2) Constructing a non-cooperative game architecture in a virtual power plant, and establishing a non-cooperative game competitive model among producers and consumers; 3) Constructing a virtual power plant customization method considering condition risk value; establishing a virtual power plant optimized operation model based on a game theory; 4) And constructing a distributed solving algorithm of the Stackelberg game model of the virtual power plant. The method integrates 'producer and consumer' clusters into a virtual power plant, adopts a transaction driving and non-cooperative game theory to construct an optimized operation method of the virtual power plant, and solves the problem that distributed power resources are difficult to directly participate in power transaction due to the influence of the characteristics of scattered power generation positions, power consumption requirements and uncertain power generation capacity of the distributed power resources.
Description
Technical Field
The invention relates to the field of virtual power plants, in particular to a virtual power plant model based on a game theory and an optimized operation method.
Background
With the development of new energy power generation technology, distributed power supplies such as roof photovoltaic, park wind power and energy storage equipment are remarkably increased, a large number of power consumers are converted into ' producers and consumers ' integrating power production resources and power consumption resources through equipping small distributed new energy power generation devices, under the mode of ' producers ' and consumers ', the power consumers can flexibly convert the roles of ' producers ' and ' consumers ' according to the relative sizes of self power generation capacity and power consumption requirements, and when the power consumers are converted into power resource producers, the power consumers can serve as distributed power supplies to provide power supply services for power grids. However, the ability of the "producer and consumer" to supply electric energy to the grid cannot directly participate in grid scheduling or electric power trading due to the dispersion of distributed generation locations, the uncertainty of generation capacity and power demand, and even challenges are brought to the safe and stable operation of the grid, so that the electric energy of the "producer and consumer" can only be purchased by the grid at an extremely low grid-connected electricity price, but the insufficient electric energy needs to be purchased from the electricity vendor at a retail electricity price, and the economic benefit is low for individuals.
In order to effectively solve the problems, the virtual power plant technology provides an effective way for distributed resources to participate in power transaction, the virtual power plant is used as a technology for aggregating the distributed resources to perform unified coordination optimization, and the distributed resources with smaller volume and scattered positions are coordinated and optimized through advanced information communication and control technology, so that the distributed resources can perform power transaction between users in the virtual power plant or aggregate into the virtual power plant to participate in power grid dispatching and power transaction in a unified manner. At present, the main researches on how a virtual power plant participates in power trading are as follows:
baringo A et al put forward a Day-Ahead Self-optimization Scheduling model of a Virtual Power Plant as a price receiver simultaneously participating in electric Energy and standby Markets in Day-Ahead Self-Scheduling of a Virtual Power Plant in Energy and Reserve electric Markets Under the premise, and adopt confidence intervals to represent Uncertainty of wind Power output and standby calling requirements and utilize a multi-scenario method to construct a market price model. Gazijahani F S et al propose a double-layer Decision-Making framework With a virtual power plant as a Price Maker to participate in a day-ahead and day-in balance market simultaneously in IGDT-Based compensatory Approach for evaluating With daily statistical Decision Making of Price-Maker VPP configuration evaluating Flexibility, the upper layer takes the maximum profit of the virtual power plant as a target, the lower layer takes the maximum social benefit as a target, the uncertainty of new energy output is processed by adopting an information gap Decision theory, and a reference basis is provided for Price Making decisions of the virtual power plant in market transactions. The Hu Dynasty and the like regard a plurality of virtual power plants as a cooperation union to participate in market bidding, and propose a sharing method of income and reward punishment according to the output characteristics of each virtual power plant; the Zhou Bo et al enables a plurality of virtual power plants to form a non-cooperative game relationship, and predicts the influence of other virtual power plants on the decision according to the market simulation result to form a market bidding strategy for realizing the maximum profit.
Compared with the situation that distributed resources are independently participated in power transaction, the organization difficulty of the power distributed market can be reduced by aggregating distributed resource clusters into a virtual power plant to participate in the power transaction, but because the technology and system mechanism which can support the distributed transaction at present in China are not mature, the feasibility of the power distributed transaction can be effectively improved by taking the virtual power plant as an intermediary of the distributed resources to participate in the power transaction in the current power market development stage.
In view of this, the present application is specifically made.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the existing distributed power resources are difficult to directly participate in power transactions. The virtual power plant model and the optimized operation method based on the game theory solve the problem that distributed power resources are difficult to directly participate in power transaction due to the influence of the characteristics of scattered power generation positions, power consumption requirements and uncertain power generation capacity of the distributed power resources.
The invention is realized by the following technical scheme:
the invention provides a game theory-based virtual power plant model and an optimized operation method, which comprises the following steps:
1) Building a virtual power plant based on 'producer and consumer' cluster aggregation and transaction driving, and building a customized building mechanism mathematical model of the transaction-driven virtual power plant;
2) Establishing a non-cooperative game framework in a virtual power plant, and establishing a non-cooperative game competitive model among 'producers and consumers';
3) Constructing a virtual power plant customization method considering condition risk value; establishing a virtual power plant optimized operation model based on a game theory;
4) And constructing a distributed solving algorithm of the Stackelberg game model of the virtual power plant.
Further, in the above-mentioned case,
the step 1) of constructing the virtual power plant based on the aggregation and transaction driving of the 'producer and consumer' cluster comprises the following steps: the PRS of the 'producer and the consumer' cluster, the nodes of the distribution network 2, 3, 8230, 823013 and the point of connection 1; the distribution network node 2 is connected with the distribution network nodes 3, 5 and 7, the distribution network node 3 is connected with the distribution network node 4, the distribution network node 5 is connected with the distribution network node 6, the distribution network node 7 is connected with the distribution network nodes 2, 8, 10 and 13, the distribution network node 8 is connected with the distribution network node 9, and the distribution network node 10 is connected with the distribution network nodes 11 and 12; and the grid-connected point 1 is connected with the distribution network node 2.
The "prosumer" clustered PRS includes: the system comprises a distributed power resource gas turbine, a photovoltaic system, energy storage equipment, a controllable load and an uncontrollable load;
the distribution network node comprises: each distribution network node is a "prosumer" cluster PRS.
In a further aspect of the present invention,
the transaction-driven customized construction mechanism mathematical model of the virtual power plant is as follows:
in the formula: p is t N And
respectively the power of the virtual power plant in the contract at the day before and the corresponding electricity price; g i,t Representing PRS i Generated power of d i,t Representing PRS i The power consumption of (2); superscripts min and max represent the minimum and maximum values of the respective term, respectively; />
And &>
A Virtual Power Plant Operator (VPPO) to power Distribution System Operator (DSO) quote factor.
In a further aspect of the present invention,
the establishment of the non-cooperative game competitive bidding model among the 'producers and the consumers' comprises the following steps:
calculating GDR for each PRS to determine self identity;
a quadratic utility function is adopted to measure the satisfaction degree of the power users when consuming different electric quantities;
bidding strategies when establishing PRSs as producers or consumers, respectively, include: price sensitivity coefficient, power selling limit and bidding strategy set.
In a further aspect of the present invention,
the GDR is calculated for each PRS as:
in the formula: when GDR is used t When the PRS is more than or equal to 1, the PRS is a producer, otherwise, the PRS is a consumer.
The satisfaction degree of the power consumer when consuming different electric quantities is as follows:
in the formula: mu.s t Is a user preference parameter representing the electricity utilization behavior of a user, v is a parameter which is determined by the user, P t con Is the power usage of the PRS (power usage from PRSs),
and &>
Respectively are the upper and lower limits of the PRS power demand.
When the PRS is used as a producer, i is used as a producer number, and the PRS i The bidding strategy submitted comprises a price sensitivity coefficient a i,t And selling electricity power limit
Creating a bidding strategy set +>
Ψ denotes the set of PRS producers.
Wherein the amount of electricity available for sale is sensitive to price:
in the formula:
as PRS i Selling electricity power in a local market; />
As PRS i Price elastic coefficient of electricity sold in local market; />
Representing PRS i (ii) willingness to sell electricity in a local market; />
As PRS i Is on the basis of the maximum electricity selling power->
Is the internal load minimum power requirement; g is a radical of formula i,t As PRS i And predicting the day ahead generated power. Wherein PRS i Carrying out day-ahead optimization by taking the maximized utility as a target, wherein the target function is as follows:
in the formula: lambda i,t The unit power generation cost is the distributed power supply in the text, the distributed power supply is a photovoltaic power generation system, so the power generation cost is the sum of the unit power generation cost and the equipment operation and maintenance cost, which are obtained by dividing the equipment investment cost into the daily power generation amount, and the sum is a fixed value;
and uniformly acquiring the power value for the power grid.
The objective function needs to satisfy the following constraints:
1) And (4) power balance constraint. PRS i The sum of the consumed power and the sold power should equal the total generated power.
2) And (4) flexible load restraint. PRS i The self-consumption power is equal to the power of the air conditioning system
And uncontrollable load power->
Sum, PRS considering the tunable potential of flexible load resources i The electric power for the central air conditioner is between the upper limit and the lower limit of the own power demand.
3) Price elastic constraint. PRS i The price elasticity of the system is restricted by the power utilization intention and the power selling intention of the user, and should not exceed every timeMaximum price factor of each user.
When the PRS is used as a consumer, j is used as a consumer number, and the submitted bidding strategy comprises a price sensitivity coefficient
And electricity purchasing power limit>
Creating a bidding strategy set +>
Ω denotes the PRS consumer set.
The relation between the electricity purchasing power of the PRS and the local electricity selling price is as follows:
in the formula:
as PRS j Electrical power purchased in a local market; />
As PRS j Price elastic coefficient of electricity purchased in local market; />
Representing PRS j The willingness to purchase electricity in the local market; />
As PRS j Is greater than or equal to the maximum purchasing power, i.e. its upper power demand limit->
Wherein the PRS j Carrying out day-ahead optimization by taking the maximized utility as a target, wherein the target function is as follows:
the objective function needs to satisfy the following constraints:
1) And (4) power balance constraint. PRS j The sum of the electric power purchased in the local market and the self-generated power is equal to the total electric power.
2) And (4) flexible load restraint. As a constraint when PRS is the producer.
3) Price elastic constraints. PRS j The price elasticity of the system is constrained by the own power utilization intention and the power purchase intention of the users, and is not lower than the own minimum price elasticity coefficient of each user.
Further, in the above-mentioned case,
the method for constructing the virtual power plant customization considering the condition risk value comprises the following steps: simulating uncertainty of new energy output, user load demand and transaction contract default punishment by adopting a multi-scenario technology, so as to convert a random optimization problem into a deterministic optimization problem to solve; and carrying out risk measurement on the default part of the transaction contract of the virtual power plant by adopting the conditional risk value, and reasonably balancing the operation income and the potential risk of the virtual power plant.
Further, in the above-mentioned case,
the establishment of the game theory-based virtual power plant optimization operation model comprises the following steps:
establishing an optimization model objective function for carrying out a day-ahead optimization decision by taking the minimized virtual power plant customization cost as a target;
calculating each part of the target function;
and establishing the constraint condition of the objective function.
Further, in the above-mentioned case,
the objective function of the optimization model is as follows:
in the formula: gamma-shaped VPP Customizing costs for the virtual power plant;
the power purchase cost of VPPO under the x-th PRS power sale scene;
the power selling income of VPPO under the power purchasing scene of the y-th PRS; r con Earnings obtained by signing a power contract for VPPO; omega x And omega y Scene probabilities corresponding to an X-th PRS electricity selling scene and a Y-th PRS electricity purchasing scene respectively, wherein the PRS electricity selling scene is X in total, and the electricity purchasing scene is Y in total; gamma is the risk aversion coefficient of VPPO; v risk Customizing a conditional risk value of the problem for the virtual power plant; XI is a decision variable set of the optimization model; xi is the risk value of the virtual power plant customization problem; delta xyh For linearizing V risk But an auxiliary variable introduced.
Each part in the objective function is calculated as:
in the formula:
VPPO slave PRS for x-th PRS electricity selling scene i The amount of electricity purchased; />
VPPO to PRS under the situation of electricity purchasing for the y PRS j The amount of electricity sold; />
A transaction price specified for the contract; p t N Customizing output for a virtual power plant specified by a contract; delta t is the unit transaction time interval duration; α is the confidence level; omega h And (4) sharing a contract default penalty price scene in H for the scene probability corresponding to the H type of contract default penalty price.
The objective function needs to satisfy the following constraints:
1) And (4) power balance constraint. The external net output of the virtual power plant is not lower than the customized output value specified by the contract.
2) And (5) restricting the price of electricity purchased. The electricity purchasing price of the VPPO for the production type PRS is between the unified electricity purchasing price of the power grid and the contract trading price, and the electricity selling price of the VPPO for the consumption type PRS is between the contract trading price and the retail market price.
3) And (4) risk constraint. It is considered that if the actual delivery power of VPPO is lower than the contract specified value, the contract default needs to be paid for the deviation powerAnd (6) punishing. Wherein the conditional risk value V risk Auxiliary variable delta in xyh The following constraints should be satisfied:
in the formula:
VPPO contract default punishment under an x type PRS electricity selling scene, a y type PRS electricity purchasing scene and an h type contract default punishment price scene; />
The penalty price is given to the h type contract default under the condition of insufficient delivery amount; [ v ] of] + Indicating that the greater of v and 0 is taken.
Wherein the deviation between the actual trading value and the projected value of the VPPO and PRS cluster follows a normal distribution:
in the formula: mu.s b And σ b 、μ s And σ s VPPO and PRS sets respectivelyThe group conducts the expected value and standard deviation of the actual delivery amount obtained by the electricity purchasing and selling transaction.
Further, in the above-mentioned case,
the distributed solving algorithm for constructing the Stackelberg game model of the virtual power plant comprises the following steps:
constructing a Stackelberg game model solving algorithm;
and a step length control method is adopted to improve the convergence of the distributed solving algorithm.
Further, in the above-mentioned case,
the Stackelberg game model solving algorithm is as follows;
the step length control method comprises the following steps:
1) After the local market price is updated in the r-th round of VPPO, a certain number of PRSs are randomly selected to prohibit the PRSs from changing the bidding strategy in the next round of iteration:
in the formula:
the PRS number for forbidding bidding to update the bidding strategy; n is a radical of PRS For the total number of PRSs to participate in the virtual plant customization, RMP ∈ [0,1]Is a climbing coefficient.
2) When other unselected PRSs perform bidding decision in the virtual power plant optimization model, the decision result of the bidding coefficient is further constrained by adopting the following formula:
Δ＝|RMP t (r+1)·a i,t (r)| (35)
in the formula: a is a i,t (r) is the r-th iteration processThe decision value of the bidding coefficient obtained in the step (1),
and obtaining the optimal value of the bidding coefficient in the (r + 1) th iteration process.
Compared with the prior art, the invention has the following advantages and beneficial effects: the 'producer and consumer' clusters are aggregated into a virtual power plant with unified scheduling, an optimized operation method of the virtual power plant is constructed by adopting a transaction driving and non-cooperative game theory, and the problem that distributed power resources are difficult to directly participate in power transaction due to the influence of the characteristics of scattered power generation positions, power consumption requirements and uncertain power generation capacity is solved.
Drawings
In order to more clearly illustrate the technical solutions of the exemplary embodiments of the present invention, the drawings that are required to be used in the embodiments will be briefly described below, it should be understood that the following drawings only illustrate some embodiments of the present invention and therefore should not be considered as limiting the scope, and that for those skilled in the art, other related drawings can be obtained from these drawings without inventive effort.
FIG. 1 is a schematic diagram of a virtual power plant based on "producer and consumer" cluster aggregation according to the present invention;
FIG. 2 is a schematic diagram of a non-cooperative game architecture in a virtual power plant provided by the invention;
fig. 3 is a flow chart of a distributed solving algorithm of a virtual power plant Stackelberg game model provided by the invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail below with reference to the following detailed description and the accompanying drawings, and the exemplary embodiments and descriptions thereof are only used for explaining the present invention and are not used as limitations of the present invention.
The first embodiment is as follows: aiming at the problem that the existing distributed power resources are difficult to directly participate in power transaction, the invention provides a virtual power plant model based on a game theory and an optimized operation method, which comprises the following steps:
step one, constructing a virtual power plant based on 'producer and consumer' cluster aggregation and transaction driving, and establishing a customized construction mechanism mathematical model of the transaction-driven virtual power plant;
step two, constructing a non-cooperative game architecture in the virtual power plant, and establishing a non-cooperative game competitive model among 'producers and consumers';
step three, constructing a virtual power plant customization method considering condition risk values, and establishing a virtual power plant optimized operation model based on a game theory;
and fourthly, constructing a distributed solving algorithm of the Stackelberg game model of the virtual power plant.
The second embodiment is as follows: constructing a virtual power plant based on aggregation and transaction driving of "producer and consumer" clusters as shown in fig. 1, the virtual power plant comprising: the PRS of the 'producer and the consumer' cluster, the nodes of the distribution network 2, 3, 8230, 823013 and the point of connection 1; the distribution network node 2 is connected with distribution network nodes 3, 5 and 7, the distribution network node 3 is connected with a distribution network node 4, the distribution network node 5 is connected with a distribution network node 6, the distribution network node 7 is connected with distribution network nodes 2, 8, 10 and 13, the distribution network node 8 is connected with a distribution network node 9, and the distribution network node 10 is connected with distribution network nodes 11 and 12; the grid-connected point 1 is connected with a distribution network node 2; the "prosumer" clustered PRS includes: the system comprises a distributed power resource gas turbine, a photovoltaic system, energy storage equipment, a controllable load and an uncontrollable load; the distribution network node comprises: each distribution network node is a "prosumer" cluster PRS.
The transaction-driven customized construction mechanism mathematical model of the virtual power plant is as follows:
in the formula: p t N And
respectively the power of the virtual power plant in the contract at the day and the corresponding electricity price; g i,t Representing PRS i Generated power of d i,t Representing PRS i The power consumption of (2); superscripts min and max represent the minimum and maximum values of the respective term, respectively; />
And
a power Distribution System Operator (DSO) quote factor for a Virtual Power Plant Operator (VPPO).
The third concrete implementation mode: the non-cooperative game architecture in the virtual power plant shown in fig. 2 is constructed as follows: the whole is a Stackelberg game formed by a VPPO and a PRS cluster, the VPPO serves as a leader to issue a local market price signal, the PRS serves as a follower, a self bidding strategy is optimized based on the local market price signal, bidding information is fed back to the VPPO, the VPPO adjusts the local market price signal, and the process is repeated in a circulating mode until the Stackelberg game is balanced.
Individuals in the PRS cluster at the bottom layer optimize bidding strategies with the self benefit maximization as the target, and mutually compete with each other to form a non-cooperative game.
The establishment of the non-cooperative game competitive bidding model among the 'producers and the consumers' is realized by the following steps:
step A, calculating GDR for each PRS to determine self identity:
in the formula: when GDR is used t When the PRS is more than or equal to 1, the PRS is a producer, otherwise, the PRS is a consumer. Since the power generation capacity and the power demand of the PRS in each time period are different, the identities of the PRS in different time periods may be different.
B, measuring the satisfaction degree of the power users when consuming different electric quantities by adopting a quadratic utility function:
in the formula: mu.s t Is a user preference parameter representing the electricity consumption behavior of a user, v is a parameter which is respectively determined by the user, P t con Is the power usage of the PRS,
and &>
The upper limit and the lower limit of the PRS power utilization requirement are respectively.
And step C, when the i is used as a producer number and the PRS is used as a producer, electricity can be sold to the VPPO on the basis of meeting the self electricity demand. PRS i The bidding strategy submitted comprises a price sensitivity coefficient a i,t And power selling limit
Form bidding strategy set->
Ψ denotes a PRS producer set.
Because the PRS is internally provided with flexible loads with adjustable power, such as a central air conditioner, an energy storage device and the like, the amount of electricity which can be sold is sensitive to price:
in the formula:
as PRS i Selling electricity power in a local market; />
As PRS i The acquisition price of the local market can be known according to the price elasticity coefficient of the electricity sold in the local market>
Higher, PRS i The more electricity that is willing to be sold in the local market; />
Representing PRS i Willingness to sell electricity in local market, PRS i The premise of selecting electricity sold in the local market is the acquisition price of the local market
Not less than the unified purchase price of the power grid>
Can hereby be>
As PRS i Should meet the minimum power requirement of the internal load>
The external electricity selling is considered on the basis; g i,t As PRS i And predicting the day-ahead generated power.
PRS i The benefits of (c) include the following: utility of electricity, income from selling electricity in local market, surplus of electricity, and cost of electricity generation, PRS i Day-ahead optimization is performed with the goal of maximizing utility, which is shown below.
In the formula: lambda [ alpha ] i,t The unit power generation cost is the distributed power supply in the text, the distributed power supply is a photovoltaic power generation system, so the power generation cost is the sum of the unit power generation cost and the equipment operation and maintenance cost, which are obtained by dividing the equipment investment cost into the daily power generation amount, and the sum is a fixed value;
and uniformly acquiring the power value for the power grid.
The objective function needs to satisfy the following constraints:
1) And (4) power balance constraint. PRS i The sum of the consumed power and the sold power should be equal to the total generated power.
2) Flexible load restraint. PRS i The self-consumption power is equal to the power of the air conditioning system
And uncontrollable load power->
Sum, allowing for tunable potential of flexible load resources, PRS i The electric power for the central air conditioner is between the upper limit and the lower limit of the own power demand.
3) Price elastic constraints. PRS i The price elasticity of the system is constrained by the power utilization intention and the power selling intention of the users, and the maximum price elasticity coefficient of each user is not exceeded.
Step D, when j is used as a consumer number and PRS is used as a consumer, the submitted bidding strategy comprises a price sensitivity coefficient
And the power purchasing limit->
Creating a bidding strategy set +>
Ω denotes the PRS consumer set.
The VPPO can sell electricity to the PRS at a local market electricity price between the retail market electricity price and the contract electricity price, and the electricity utilization power of the PRS is changed by adjusting the local market electricity price, so that the external output of the virtual power plant meets the customized requirement. The relationship between the power consumption of the PRS and the price of the electricity sold locally is as follows.
In the formula:
as PRS j Electrical power purchased in a local market; />
As PRS j The price elasticity coefficient of the electricity purchased in the local market can indicate the electricity selling price->
The higher, the PRS j The more electricity that is willing to be sold in the local market; />
Representing PRS j Willingness to purchase electricity in local market, PRS j The premise of selecting the local market for purchasing electricity is that the price of electricity sold in the local market
Is not higher than the selling price of electricity in the retail market>
Can be hereby taken>
As PRS j Is greater than or equal to the maximum purchasing power, i.e. its upper power demand limit->
PRS j The benefits of (a) include the following: utility of self-electricity, cost of electricity purchase in local market, cost of self-electricity generation, PRS j To maximize the efficiencyDay-ahead optimization was performed with the objective function as shown below.
1) And (4) power balance constraint. PRS j The sum of the electricity purchasing power and the self electricity generating power in the local market is equal to the total electricity using power.
2) And (4) flexible load restraint. As a constraint when PRS is the producer.
3) Price elastic constraint. PRS j The price elasticity of the system is constrained by the own electricity utilization desire and the electricity purchase desire of the users, and should not be lower than the own minimum price elasticity coefficient of each user.
The fourth concrete implementation mode: the method for constructing the virtual power plant customization considering the condition risk value comprises the following steps: simulating the uncertainty of new energy output, user load demand and transaction contract default punishment by adopting a multi-scenario technology, so as to convert the random optimization problem into a deterministic optimization problem to solve; and carrying out risk measurement on the default part of the transaction contract of the virtual power plant by adopting the conditional risk value, and reasonably balancing the operation income and the potential risk of the virtual power plant.
The establishment of the game theory-based virtual power plant optimized operation model is realized by the following steps:
step a, carrying out day-ahead optimization decision by a Virtual Power Plant Operator (VPPO) according to a bidding strategy submitted by 'producer and consumer' PRS (personal reference service), with the aim of minimizing the customization cost of the virtual power plant, wherein the objective function of an optimization model is as follows:
in the formula: gamma-shaped VPP Customizing costs for the virtual power plant;
the power purchase cost of VPPO under the x-th PRS power sale scene;
the power selling income of VPPO under the power purchasing scene of the y-th PRS; r is con Earnings obtained by signing an electric power contract for the VPPO; omega x And ω y Scene probabilities corresponding to an X-th PRS electricity selling scene and a Y-th PRS electricity purchasing scene respectively, wherein the PRS electricity selling scene is X in total, and the electricity purchasing scene is Y in total; gamma is the risk aversion coefficient of VPPO; v risk Customizing a conditional risk value of the problem for the virtual power plant; the xi is a decision variable set of the optimization model; xi is the risk value of the virtual power plant customization problem; delta xyh For linearizing V risk But an auxiliary variable introduced.
Each part in the objective function is calculated as follows:
in the formula:
VPPO slave PRS for x-th PRS electricity selling scene i The amount of electricity purchased; />
VPPO to PRS under scenario of electricity purchasing for the y-th PRS j The amount of electricity sold; />
For contract-stipulated transactionThe price is easy; p t N Customizing output for a virtual power plant specified by a contract; delta t is the unit transaction time interval duration; α is the confidence level; omega h And (4) sharing a contract default penalty price scene in H for scene probability corresponding to the H type of contract default penalty price.
The objective function needs to satisfy the following constraints:
1) And (4) power balance constraint. The external net output of the virtual power plant is not lower than the customized output value specified by the contract.
2) And (5) restricting the price of electricity purchased. The electricity purchasing price of the VPPO for the production type PRS is between the unified electricity purchasing price of the power grid and the contract trading price, and the electricity selling price of the VPPO for the consumption type PRS is between the contract trading price and the retail market price.
3) And (4) risk constraint. And if the actual VPPO delivery electric quantity is lower than the contract specified value, punishing the contract default for the deviation electric quantity payment. Wherein the conditional risk value V risk Auxiliary variable delta in xyh The following constraints should be satisfied:
in the formula:
VPPO contract default punishment under the x type PRS electricity selling scene, the y type PRS electricity purchasing scene and the h type contract default punishment price scene; />
The penalty price is default for the h type contract under the condition of insufficient delivery amount; [ v ] of] + Indicating that the greater of v and 0 is taken.
Wherein the deviation between the actual trading value and the projected value of the VPPO and PRS cluster obeys a normal distribution:
in the formula: mu.s b And σ b 、μ s And σ s The expected value and standard deviation of the actual delivery amount obtained by conducting electricity purchasing and selling transactions for the VPPO and PRS clusters, respectively.
The fifth concrete implementation mode is as follows: constructing a distributed solving algorithm of a virtual power plant Stackelberg game model shown in figure 3; the convergence of the algorithm is improved by adopting a step length control method, so that the algorithm obtains a fixed solution in a limited iteration number. The step size control method introduces a climbing coefficient RMP epsilon [0,1] to act on an updating process of a PRS bidding strategy, and comprises two parts of contents of limiting the number of PRSs subjected to bidding strategy updating and limiting the change amplitude of each PRS bidding coefficient.
The step length control method comprises the following steps:
1) After the local market price is updated in the r-th round of VPPO, a certain number of PRSs are randomly selected to prohibit the PRSs from changing the bidding strategy in the next round of iteration:
in the formula:
the PRS number for forbidding bidding to carry out bidding strategy updating; n is a radical of PRS A total number of PRSs customized for participation in the virtual power plant.
2) When the rest of the unselected PRSs perform bidding decision in the virtual power plant optimization model in the step two, the decision result of the bidding coefficient is further constrained by adopting the following formula:
Δ＝|RMP t (r+1)·a i,t (r)| (35)
in the formula: a is a i,t (r) is a bidding coefficient decision value obtained in the process of the r-th iteration,
and obtaining the optimal value of the bidding coefficient in the (r + 1) th iteration process.
The above-mentioned embodiments are intended to illustrate the objects, technical solutions and advantages of the present invention in further detail, and it should be understood that the above-mentioned embodiments are merely exemplary embodiments of the present invention, and are not intended to limit the scope of the present invention, and any modifications, equivalent substitutions, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (6)
1. A virtual power plant model and an optimized operation method based on game theory are characterized in that: the method comprises the following steps:
1) Building a virtual power plant based on 'producer and consumer' cluster aggregation and transaction driving, and building a customized building mechanism mathematical model of the transaction-driven virtual power plant;
2) Establishing a non-cooperative game framework in a virtual power plant, and establishing a non-cooperative game competitive model among 'producers and consumers';
3) Constructing a virtual power plant customization method considering condition risk value; establishing a virtual power plant optimized operation model based on a game theory;
4) And constructing a distributed solving algorithm of the Stackelberg game model of the virtual power plant.
2. The game theory-based virtual power plant model and optimization operation method according to claim 1, wherein the step 1) of constructing a virtual power plant based on 'producer and consumer' cluster aggregation and transaction driving, and the establishing of the transaction-driven virtual power plant customized construction mechanism mathematical model comprises the following steps:
the PRS of the 'producer and the consumer' cluster, the nodes of the distribution network 2, 3, 8230, 823013 and the point of connection 1; the distribution network node 2 is connected with distribution network nodes 3, 5 and 7, the distribution network node 3 is connected with a distribution network node 4, the distribution network node 5 is connected with a distribution network node 6, the distribution network node 7 is connected with distribution network nodes 2, 8, 10 and 13, the distribution network node 8 is connected with a distribution network node 9, and the distribution network node 10 is connected with distribution network nodes 11 and 12; the grid-connected point 1 is connected with a distribution network node 2;
the "prosumer" clustered PRS includes: the system comprises a distributed power resource gas turbine, a photovoltaic system, energy storage equipment, a controllable load and an uncontrollable load;
the distribution network node comprises: at each distribution network node is a "prosumer" cluster PRS,
the transaction-driven customized construction mechanism mathematical model of the virtual power plant is as follows:
in the formula: p t N And
respectively the power of the virtual power plant in the contract at the day and the corresponding electricity price; g i,t Representing PRS i Generated power of d i,t Representing PRS i The power consumption of (2); superscripts min and max represent the minimum and maximum values of the respective term, respectively; />
And &>
A Virtual Power Plant Operator (VPPO) to power Distribution System Operator (DSO) quote factor.
3. The virtual power plant model and the optimized operation method based on the game theory as claimed in claim 1, wherein the step 2) of constructing a non-cooperative game architecture in the virtual power plant and the step of establishing the non-cooperative game bidding model among the producers and the consumers comprises the following steps:
1) Calculating GDR for each PRS to determine self identity;
2) A quadratic utility function is adopted to measure the satisfaction degree of power users consuming different electric quantities;
3) Bidding strategies when setting up PRSs as producers or consumers, respectively, include: price sensitivity coefficient, power selling limit and bidding strategy set.
4. The virtual power plant model and optimal operation method based on game theory as claimed in claim 1, wherein the step 3) of constructing a virtual power plant customization method considering conditional risk values comprises the following steps:
1) Simulating uncertainty of new energy output, user load demand and transaction contract default punishment by adopting a multi-scenario technology, so as to convert a random optimization problem into a deterministic optimization problem to solve;
2) And carrying out risk measurement on the default part of the transaction contract of the virtual power plant by adopting the conditional risk value, and reasonably balancing the operation income and the potential risk of the virtual power plant.
5. The virtual power plant model and optimal operation method based on game theory as claimed in claim 1, wherein the step 3) of establishing the virtual power plant optimal operation model based on game theory comprises:
1) Establishing an optimization model objective function for carrying out day-ahead optimization decision by taking the minimized virtual power plant customization cost as a target;
2) Calculating each part of the objective function;
3) And establishing the constraint condition of the objective function.
6. The virtual power plant model and optimized operation method based on game theory as claimed in claim 1, wherein the step 4) of constructing the distributed solving algorithm of the virtual power plant Stackelberg game model comprises:
1) Constructing a Stackelberg game model solving algorithm;
2) And a step length control method is adopted to improve the convergence of the distributed solving algorithm.
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