Strategy generation method for combined heat and power based on generalized nash equilibrium algorithm solving

Abstract

The application provides a strategy generation method for combined heat and power based on a generalized Nash equilibrium algorithm, comprising the following steps: constructing a combined heat and power system under related constraints; wherein the upper limit of the thermal comfort of each consumer and the relationship between the consumer utility and energy consumption are considered; the problem to be solved by each company is determined by considering the decision information of all energy companies; wherein the objective function of the combined heat and power system model is determined according to the upper limit and the lower limit of the production efficiency of each company, the production plan of the company which needs to follow the power balance and the thermal balance, and the problem to be solved by each company; when the global decision information of other companies is obtained, the decision of each company is obtained by solving based on the edge-based distributed generalized Nash equilibrium algorithm under the global decision information, including the demand and the price of thermal energy and electric energy in each round of auction.

Description

Technical Field

[0001] This invention relates to the field of market regulation technology, specifically to a strategy generation method for cogeneration based on solving a generalized Nash equilibrium algorithm. Background Technology

[0002] With the increasing adoption of combined heat and power (CHP) systems in micro smart grids, the interaction between district heating systems and the power system is becoming more frequent. Furthermore, the optimized operation of integrated energy systems is becoming more complex, as these systems incorporate various types of distributed energy resources. New types of electric boilers and high-performance heat pumps are highly competitive in reducing operating costs and carbon emissions.

[0003] In recent years, due to the singular nature of heat sources, competition in the heating market has been far less intense than in the electricity market. A key characteristic of the heating market is the localization of heat sales and production, often handled by the same heating company. Because heat transportation investment is capital-intensive, heat losses within the heating network are significant. However, the widespread use of combined heat and power (CHP) systems allows power companies to participate in the heating market, increasing their competitiveness. The coupling power generation constraints of CHP units create a strong interdependence between power generation and heating. CHP systems can play a crucial role in long-term cold regions.

[0004] One of the key characteristics of the electricity and heating markets is imperfect competition. In this context, three scenarios arise: (i) competition: different energy suppliers compete for limited demand to maximize their profits; (ii) conflict of interest: energy suppliers seek to maximize sales revenue, while consumers try to reduce their energy bills; and (iii) information asymmetry: all competitors want to protect their privacy from competitors. Therefore, we can address these issues using game theory. In this patent, we propose an algorithm applied to combined heat and power (CHP) systems. We solve the price and supply-demand problems of CHP by establishing a generalized Nash equilibrium game model.

[0005] In recent years, with the emergence of new fields such as cloud computing and big data, distributed optimization, as a "decentralized" optimization algorithm, has been widely applied in various fields. In smart grids, social networks, and optical communications, the application of generalized Nash equilibrium has received widespread attention, where non-cooperative participants need to make local decisions to optimize the objective problem. In game theory, participants cooperate at the information level, but each participant only optimizes their own interests, and each participant needs to optimize their objective function based on the decisions of other participants. Furthermore, the feasible set of each participant is determined by other participants. In these games, we use generalized Nash equilibrium to solve problems where players cannot unilaterally change their decisions to alter local utilities.

[0006] When the Nash equilibrium point is calculated, all players will work based on it. In optimizing the objective function, all agents consider not only their own local feasible sets and local constraints, but also shared coupling constraints. However, due to the large computational resources consumed by large-scale networks, the centralized form of existing solution methods may not be able to complete the operation, and existing algorithms have slow convergence speed and low accuracy. Summary of the Invention

[0007] To address the aforementioned problems, this invention provides a strategy generation method for cogeneration based on solving the generalized Nash equilibrium algorithm.

[0008] The present invention provides the following technical solution.

[0009] A strategy generation method for cogeneration based on solving the generalized Nash equilibrium algorithm includes the following steps:

[0010] Construct a combined heat and power (CHP) system model; this includes determining the upper limit of thermal comfort for each consumer and the relationship between consumer utility and energy consumption, considering the relationship function between consumer expenditure and energy consumption; and determining the objective function of the CHP system model based on the upper and lower limits of each company's production efficiency, the requirement that the company's production plan should maintain power and heat balance, and the problems to be solved for each company.

[0011] Obtain global decision information from other companies. Based on the cogeneration system model, solve the decision of each company using the edge-based distributed generalized Nash equilibrium algorithm under global decision information, including the production quantity and price of each type of commodity.

[0012] In the edge-based distributed generalized Nash equilibrium algorithm under global decision information, the solution to the generalized Nash equilibrium problem is indirectly obtained by solving the variational inequality. The condition of the variational inequality is transformed into a saddle point problem of finding monotone operators and zeros, and a metric matrix design algorithm is introduced.

[0013] Preferably, the combined heat and power model specifically includes:

[0014] The combined heat and power (CHP) system is configured to consist of C users and G energy suppliers, where C = {C1, ..., C}. C Let G be the set of consumers, where G = {G1, ..., G} G} represents the set of suppliers;

[0015] Consumer thermal comfort is expressed as:

[0016]

[0017] Considering consumers' thermal comfort, the temperature needs to be controlled within the following range:

[0018]

[0019]

[0020] The relationship between consumer utility and energy consumption is defined as follows:

[0021]

[0022]

[0023]

[0024] Consumer spending is expressed as follows:

[0025]

[0026] Define ε -j =(ε1,...,ε j-1 ,ε j+1 ,...,ε G As a strategic profile other than energy supplier j; the objective function of the problem is defined as the cost function:

[0027]

[0028] Production planning must adhere to maintaining power and thermal balance, which introduces constraints:

[0029]

[0030]

[0031] Each supplier produces different equipment, and the equipment has an upper and lower limit to its production efficiency. Constraints are introduced as follows:

[0032]

[0033] Preferably, the edge-based distributed generalized Nash equilibrium algorithm based on global decision information specifically includes:

[0034] Consider a group of participants N = {1,...,N} who are engaged in a non-cooperative game and share coupling constraints; define As an edge set, if (i,j)∈ε, it indicates that participant i communicates with participant j; participant i (i∈N) has its own strategy.

[0035] Among them, Ω i As a private feasible decision set and Introducing x = col(x1,...,x) N )∈Rn As an indirect decision-making process x=(x i ,x -i );x -i =col(x1,...,x i-1 ,x i+1 ,...,x N (f) represents the lateral decision-making process excluding participant i; each participant's objective is to find the optimal solution to their objective function: f i (x i ,x- i ):Ω→R;f i (x i ,x- i ) Subject to x -i Impact, the strategies of all participants are shared with the global set. Coupled together; the feasible strategy set of participant i is X i (x -i )={x i ∈Ω i :(x i ,x -i )∈X};

[0036] The objective function for participant i is defined as:

[0037]

[0038] Where, x * Defined as the optimal set of strategies for all participants, i.e., for all participants:

[0039]

[0040] Define the coupling set as:

[0041]

[0042] in, b i ∈R m And Ω i It is the player's private information;

[0043] Define A = [A1,...,A] N ]∈R m×n , λ = col(λ1,...,λ) N )∈R mN Under assumption 1, determine x. * It is the Nash equilibrium point in game (1); for Existence Its Karush-Kuhn-Tucker condition is satisfied:

[0044]

[0045] in, if Get Ax * -b≤0; if Get Ax * -b = 0;

[0046] The centralized form of the algorithm is written as:

[0047]

[0048] Where b = col{b1,...,b N}, C (i,j) ={(w1,w2)|w1+w2=0};

[0049] The distributed form of the algorithm is as follows:

[0050] initialization as well as

[0051] Set the initial iteration value k = 0;

[0052] When i = 1 to N, receive U ji , And update the algorithm:

[0053]

[0054]

[0055]

[0056]

[0057] After the update ends, set k = k + 1 and repeat the above update until the maximum number of iterations is reached.

[0058] The beneficial effects of this invention are:

[0059] (1) The algorithm proposed in this invention uses a locally constant step size, which can improve the flexibility of each participant. The step sizes are independent of each other and can be adjusted independently. This invention can use a wider range of step size parameters.

[0060] (2) This invention proposes a novel edge-based distributed algorithm. This algorithm performs well in large-scale model networks and demonstrates accurate convergence. The edge-based algorithm does not require a balanced weight matrix, thus reducing resource usage. Numerical experiments show that this algorithm has better convergence speed and accuracy than node-based distributed algorithms.

[0061] (3) This invention discusses the problem of finding generalized Nash equilibrium points under coupling constraints and set constraints. Furthermore, this invention employs a novel operator splitting method to design a distributed algorithm that can solve the generalized Nash equilibrium problem under a wider range of conditions. Attached Figure Description

[0062] Figure 1 This is a flowchart of an embodiment of the present invention;

[0063] Figure 2 This is a diagram illustrating the convergence process of electricity and heat prices in a single auction according to an embodiment of the present invention.

[0064] Figure 3 This is a diagram illustrating the convergence process of energy production and demand in an embodiment of the present invention.

[0065] Figure 4 This is a graph showing electricity and heat prices during multiple rounds of auctions according to an embodiment of the present invention. Detailed Implementation

[0066] This invention proposes a strategy generation method for cogeneration based on solving the generalized Nash equilibrium algorithm, such as... Figure 1-4 As shown, it specifically includes:

[0067] The objective function for participant i is defined as:

[0068]

[0069] x * Defined as the optimal set of strategies for all players, i.e., for all participants:

[0070]

[0071] Define the coupling set as:

[0072]

[0073] in b i ∈R m And Ω i It is the player's private information;

[0074] Define A = [A1,...,A] N ]∈R m×n , λ = col(λ1,...,λ) N )∈R mN Under assumption 1, determine x. * It is the Nash equilibrium point in game (1); for Existence Its Karush-Kuhn-Tucker condition is satisfied:

[0075]

[0076] in if Get Ax * -b≤0; if Get Ax * -b = 0;

[0077] Therefore, x * It is the optimal solution to the variational inequality when λ * ∈R m At that time, its Karush-Kuhn-Tucker condition is satisfied as follows:

[0078]

[0079] By comparing (3) and (4), any solution to variational inequality (2) is a generalized Nash equilibrium of game problem (1);

[0080] A compact form of the algorithm:

[0081]

[0082] Where b = col{b1,...,b N}, C (i,j) ={(w1,w2)|w1+w2=0};

[0083] The distributed form of the algorithm is as follows:

[0084] initialization as well as

[0085] Set the initial iteration value k = 0

[0086] When i = 1 to N, receive U ji , And update the algorithm:

[0087]

[0088]

[0089]

[0090]

[0091] After the update ends, set k = k + 1 and repeat the above update until the maximum number of iterations is reached.

[0092] In this embodiment:

[0093] Assume that a combined heat and power (CHP) system within a fixed area consists of C users and G energy suppliers. This can be represented as C = {C1, ..., C...}. C Let G be the set of consumers, where G = {G1, ..., G} G Let} be the set of suppliers. Consumers and suppliers communicate through the Integrated Energy Trading Center (IETC). The IETC collects consumer demand, enabling energy companies to formulate production strategies and informing consumers of new electricity and heat prices, while also informing energy companies of users' total demand. In this experiment, we focus on the game theory problem among energy supply companies. To compete with each other, energy suppliers develop their own optimal strategies and engage in game theory to maximize profits.

[0094] We stipulate that consumers can only obtain heat by purchasing heat from energy companies and by purchasing electricity using "power-to-heat" (P2H) appliances. This experiment takes into account consumer thermal comfort, which can be expressed as:

[0095]

[0096] Considering consumers' thermal comfort, the temperature needs to be controlled within the following range:

[0097]

[0098]

[0099] The relationship between consumer utility and energy consumption is defined as follows:

[0100]

[0101]

[0102]

[0103] Among them, V i P and V i H V represents the utility of obtaining electricity and heat directly from energy suppliers. iPH This indicates the effectiveness of electric heating. i h i and pth i These represent the power consumption, direct heat consumption, and power consumption via electric heating of user i's electrical equipment, respectively. σ, μ, υ, α1, α2, α3, β (1,i) β (2,i) β (3,i) This is the coefficient for adjusting utility. β (1,i) β (2,i) β (3,i) It is set according to consumer preferences. This represents the maximum value of thermal comfort. We introduce price. p and price h As the price of electricity and heat, consumer expenditure can be expressed as:

[0104]

[0105] Consumers optimize their returns based on renewable energy prices. All energy companies are engaged in a game of strategy, and we stipulate that the energy consumed by users should match the total energy produced by the energy companies. The energy produced by the energy companies can be represented as:

[0106]

[0107]

[0108] PE and HE are defined as electrical energy and thermal energy, respectively. Each energy supplier will develop a production plan. In order to obtain the maximum benefit, among which Defined as the heat output of combined heat and power (CHP), Defined as the heat output of a gas-fired boiler. Define ε. -j =(ε1,...,ε j-1 ,ε j+1 ,...,ε G As a strategic profile other than energy supplier j. The objective function of the problem can be defined as a cost function, which can be written as:

[0109]

[0110] Define δ (1,j) δ (2,j) δ (3,j) δ represents the company's cost coefficient. (4,j) TR is the cost coefficient for gas-fired boilers. j Let be the heat-to-power ratio of the combined heat and power (CHP). In this model, the production schedule must adhere to maintaining power and heat balance; therefore, we introduce the following constraints:

[0111]

[0112]

[0113] Each supplier produces different equipment, and the equipment has an upper and lower limit to its production efficiency; therefore, constraints are introduced:

[0114]

[0115]

[0116] Rewrite the cost function in Lagrange form:

[0117]

[0118] To better illustrate the experimental results, we set the total number of companies to 3 and considered 20 consumers. The parameter settings are shown in Table 1. The proposed Algorithm 1 was applied to this model, with the step size set to τ. i =0.001, σ (i,j) =0.03, γ i =0.2. Plot the convergence process of electricity and heat prices in a single auction, as shown below. Figure 2 As shown. The convergence process of energy production and demand is as follows. Figure 3 As shown. Based on the multi-round auction process of this model, the electricity and heat prices in the multi-round auctions are as follows: Figure 4 As shown.

[0119] Table 1 Parameter Settings

[0120]

[0121] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A strategy generation method for cogeneration based on solving the generalized Nash equilibrium algorithm, characterized in that, Includes the following steps: Construct a combined heat and power (CHP) system model; this includes determining the upper limit of thermal comfort for each consumer and the relationship between consumer utility and energy consumption, considering the relationship function between consumer expenditure and energy consumption; and determining the objective function of the CHP system model based on the upper and lower limits of each company's production efficiency, the requirement that the company's production plan should maintain power and heat balance, and the problems to be solved for each company. Obtain global decision information from other companies. Based on the cogeneration system model, solve the decision of each company using the edge-based distributed generalized Nash equilibrium algorithm under global decision information, including the production quantity and price of each type of commodity. In the edge-based distributed generalized Nash equilibrium algorithm under global decision information, the solution to the generalized Nash equilibrium problem is indirectly obtained by solving the variational inequality. The condition of the variational inequality is transformed into a saddle point problem of finding monotonic operators and zeros, and a metric matrix design algorithm is introduced. The edge-based distributed generalized Nash equilibrium algorithm based on global decision information specifically includes: Consider a group of participants in a non-cooperative game who share coupling constraints. ;definition As an edge set, if This indicates that the participant With participants To communicate; participants He has his own strategy ; in, Ω i As a private feasible decision set and ; Introduction As an indirect decision-making process , ; In addition to the participants Other aspects of decision-making; each participant's goal is to find the optimal solution to their objective function: ; by Impact, the strategies of all participants are shared with the global set. Coupled together; participants The set of feasible strategies is ; participants The objective function is defined as: （1） in, Defined as the optimal set of strategies for all participants, i.e., for all participants: Define the coupling set as: in, , For local data and It is the player's private information; definition , , ;in As local variables; under assumption 1, formulate It is the Nash equilibrium point in game (1); for , exists Its Karush-Kuhn-Tucker condition is satisfied: （3） in, ;if , ,get ;if , ,get ; The centralized form of the algorithm is written as: （5） in, , , ; , , Introducing the identifier operator Representing the linear operator as ,in ; , , The step-size diagonal matrix is ​​specifically represented as follows: The distributed form of the algorithm is as follows: initialization , , as well as ; Set initial iteration values ; when Receive , , , , And update the algorithm: Settings after the update ends And repeat the above update until the maximum number of iterations is reached.

2. The strategy generation method for cogeneration based on solving the generalized Nash equilibrium algorithm according to claim 1, characterized in that, The cogeneration model specifically includes: The combined heat and power system is configured to consist of C users and G energy suppliers. For a collection of consumers, A collection of suppliers; Consumer thermal comfort is expressed as: in, for Indoor temperature at all times for outdoor temperature at all times; For the building's equivalent thermal resistance, , The capacitance coefficient; Considering consumers' thermal comfort, the temperature needs to be controlled within the following range: in, , These are the lowest and highest indoor temperatures; This represents the change in indoor temperature. The relationship between consumer utility and energy consumption is defined as follows: in, and This refers to the utility of obtaining electricity and heat directly from energy suppliers. It indicates the effectiveness of electric heating; , and Representing users respectively Power consumption of electrical equipment, direct heat consumption, and power consumption through electric heating; , , , , , , , , It is a coefficient for adjusting utility; , , It is set according to consumer preferences; This is expressed as the maximum value of thermal comfort. Introduction and As the price of electricity and heat, consumer spending is expressed as: The energy produced by the energy company is represented as follows: in, and Defined as electrical and thermal energy; each energy supplier will develop a production plan. In order to obtain the maximum benefit, among which, Defined as the heat output of combined heat and power (CHP), Defined as the heat output of a gas-fired boiler; definition As an energy supplier Beyond strategic contours; defining the objective function of the problem as a cost function: definition , , This is the company's cost coefficient. This represents the cost coefficient for gas-fired boilers. The heat-to-power ratio of combined heat and power (CHP); Production planning must adhere to maintaining power and thermal balance, which introduces constraints: Each supplier produces different equipment, and the equipment has an upper and lower limit to its production efficiency. Constraints are introduced as follows: Rewrite the cost function in Lagrange form: 。

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