An asymptotically stable attraction domain calculation method applied to thermal power combined market

Abstract

The application discloses a kind of asymptotic stability attraction domain calculation method applied to thermal power combined market, the calculation method includes the following steps: based on game theory, establish energy supplier production strategy model, terminal user optimal energy purchase model and transaction center market clearing model;According to the optimal strategy model constructed above, design dynamic market transaction mechanism and based on KKT condition and gradient method depict the optimal economic behavior model of each market subject;Based on the optimal economic behavior model established above, the state space equation of thermal power combined market is constructed;According to Lyapunov stability theorem, derive the attraction domain calculation formula.The calculation method of the application describes economic behavior based on game theory, converts economic behavior into state space equation describing market operation, and then derives the explicit expression of the attraction domain, which shows the influence of system parameters on the size of the attraction domain, can quantify the robustness of the market to maintain stable operation, and has high academic value and engineering guiding significance.

Description

Technical Field

[0001] This invention relates to the field of joint trading in the electricity and heat markets, specifically a method for calculating the asymptotically stable attraction domain applied to the combined heat and power market. Background Technology

[0002] From a global perspective, many countries have established carbon reduction timelines to fulfill their commitments to reduce CO2 emissions. Combined heat and power (CHP) units and heat pumps have received increasing attention due to their higher energy efficiency and environmental friendliness. In recent years, with the proliferation of CHP units and heat pumps, the coupling between the power system and district heating systems has become increasingly stronger. The actual physical processes of energy production impose substantial constraints on the energy traded in the market. CHP units and heat pumps connect the electricity market and the heating market on the supply and demand sides, respectively. To further improve overall efficiency and equitable resource allocation, many countries are reforming their electricity and heat markets, introducing more competition into these markets.

[0003] Although the competitiveness of the heat market is far lower than that of the electricity market, the operational and marketization challenges of combined heat and power (CHP) systems have attracted significant attention from academia and government agencies. Due to the physical coupling between different energy systems, electricity trading cannot be fully described through single-market analysis but must be analyzed in conjunction with the heat market. A dynamic trading mechanism for the CHP market is necessary, as well as a method for calculating the attraction domain to ensure asymptotic stability. Therefore, this paper proposes a method for calculating the asymptotically stable attraction domain in the CHP market. Summary of the Invention

[0004] The purpose of this invention is to provide a method for calculating the asymptotically stable attraction domain in the combined heat and power market. By simulating the multi-round bidding mechanism of the combined heat and power market, the range of the stability domain is quantified, ensuring that the market is asymptotically stable as long as the initial point is within the attraction domain. This guarantees that transactions can proceed smoothly and are physically executable. The invention provides a rigorous mathematical proof and conditions for the asymptotic stability of the market, and provides an effective reference for the design of the architecture and trading mechanism of the combined heat and power market.

[0005] The objective of this invention can be achieved through the following technical solutions:

[0006] A method for calculating the asymptotically stable attraction domain applied to the combined heat and power market, the method comprising the following steps:

[0007] Step 1: Based on game theory, establish an energy supplier production strategy model, an end-user optimal energy purchase model, and a trading center market clearing model.

[0008] Step 2: Based on the optimal strategy model constructed above, design a dynamic market trading mechanism and characterize the optimal economic behavior model of each market participant based on KKT conditions and gradient method.

[0009] Step 3: Based on the optimal economic behavior model established above, construct the state-space equations for the combined heat and power market.

[0010] Step 4: Derive the formula for calculating the attraction field based on Lyapunov's stability theorem.

[0011] Furthermore, the specific operation of step one is as follows:

[0012] S1: Establish a production strategy model for energy suppliers based on game theory.

[0013] S2: Establish an energy purchase strategy model for end users based on game theory.

[0014] S3: Establish a clearing model for the trading center based on market clearing requirements.

[0015] Furthermore, step two specifically includes the following operations:

[0016] S1: Energy supplier action sequence based on game theory and gradient method

[0017] Based on the gradient method, find information about , and The gradient is obtained as follows:

[0018]

[0019]

[0020]

[0021] in , and Indicates the first k Energy suppliers in rounds of iteration i Electricity output, heat output, and wind power output. h Indicates time interval, Indicates energy supplier i The ability to regulate It is a projection operation, representing a projection onto a set. The projection on is specifically defined as follows:

[0022]

[0023] In the formula, This represents the 2-norm.

[0024] S2: End-user action sequence based on game theory and gradient method

[0025] Based on the gradient method, find information about , and The gradient is obtained as follows:

[0026]

[0027]

[0028]

[0029] In the formula, Indicates end user j The ability to regulate , and Indicates the first k End users in round iteration j The pure electric load, the heat load, and the electric load generated by the use of electric heating equipment.

[0030] S3: Trading center action sequence based on game theory and gradient method:

[0031]

[0032]

[0033]

[0034]

[0035]

[0036]

[0037]

[0038] In the formula, , , , and This represents the trading center's electricity price regulation capability, voltage phase angle regulation capability, multiplier regulation capability corresponding to the temperature loss equation, node temperature regulation capability, and multiplier regulation capability corresponding to power flow security constraints. Indicates busbar n In the k The nodal electricity price in the next iteration. Represents a node m In the k Node heat price in the next iteration Indicates pipeline l The Lagrange multiplier corresponding to the temperature loss constraint is in the first... k The value in the next iteration Indicates pipeline l In the k The final temperature in the next iteration. Indicates the first k In the next iteration, from the heating network nodes m The temperature of the flowing water The Lagrange multiplier corresponding to the power flow constraint is in the first position. k Values ​​in the next iteration, symbols in the formula Represents the projection operation, when hour, ;when hour, .

[0039] Furthermore, step three involves constructing the state-space equations for the combined heat and power market, specifically including:

[0040] S1, the state-space equation of the energy supplier:

[0041]

[0042]

[0043] In the formula , , , NG This indicates the total number of energy suppliers. When When, it indicates the unit i It belongs to Category A energy suppliers. and These are vectors composed of nodal electricity prices and nodal heat prices, respectively. and Represents the correlation matrix of the generator units. Indicates the unit i Connected to the power grid bus j superior, Indicates the unit i Connected to the heating network node j Above; if not connected, then , , , and yes NG × NG A diagonal matrix consisting of cost coefficients. , and yes NG A vector of cost coefficients, which is 1 ×1.

[0044] S2, the state-space equation of the end user:

[0045]

[0046]

[0047]

[0048] In the formula , , , ND Indicates the number of end users. and Represents the user association matrix. Indicates user i Connected to the power grid bus j superior, Indicates user i Connected to the heating network node j Above; if not connected, then , . , , yes ND × ND The diagonal matrix consisting of utility coefficients. , and yes ND A 1-dimensional vector consisting of utility coefficients.

[0049] S3, the state-space equation of the trading center:

[0050] In addition to nodal price vectors and node heat price vector The state vector of the trading center also includes the voltage phase angle vector. dual vector and Node temperature vector and the temperature vector at the end of the pipe Indicates the number of heating network pipes. Indicates the number of power grid lines. M Indicates the number of nodes in the heating network. N This indicates the number of power grid buses.

[0051]

[0052]

[0053]

[0054]

[0055]

[0056]

[0057]

[0058] In the formula, the matrix A yes Bus-line correlation matrix, matrix The correlation matrix after removing the column of the balancing node. It is the bus voltage phase angle vector after eliminating the slack node. yes The diagonal matrix, where the elements on the diagonal are the susceptance of the line. These are the upward correlation matrix and downward correlation matrix of the heating network, respectively. It is a matrix A and The extended matrix, , The elements on the right side of the formula are as follows:

[0059]

[0060] In the formula, , R It is a rotation matrix. yes The vector is composed of the maximum capacity of the line.

[0061] To simplify the expression, the state-space equations can be written in the following compact form:

[0062]

[0063]

[0064]

[0065]

[0066]

[0067]

[0068] in , All the uncertainties All and This is reflected in the Chinese context.

[0069] Furthermore, step four specifically includes:

[0070] Assumption It is the equilibrium point of the state equation, therefore:

[0071]

[0072] definition , And Lyapunov equations:

[0073]

[0074] in and It is a real symmetric positive definite matrix, and and Substitution and ,have to:

[0075]

[0076] Substituting into the equation, we get...

[0077]

[0078] beg The derivative with respect to time:

[0079]

[0080] Will and Substituting into the formula, simplifying, and combining like terms, we get:

[0081]

[0082] Using the non-extensibility of projection, we obtain Therefore, the formula satisfies the following equation:

[0083]

[0084] because Therefore, according to Cauchy's inequality, we get Assuming It is a positive definite diagonal matrix, composed of orthogonal nonzero real eigenvectors Composition, therefore ,in yes The eigenvalues, considering the equilibrium point ,satisfy ,get:

[0085]

[0086] in Representation matrix The largest eigenvalue, due to It is a positive vector, which can be represented by a set of orthogonal vectors. express ,in ,make We can obtain:

[0087]

[0088] in Representation matrix The smallest eigenvalue, if It is a Hurwitz matrix, for any There exists a positive definite matrix. The following Lyapunov equations must be satisfied:

[0089]

[0090] Therefore:

[0091]

[0092] in, It is a matrix The smallest eigenvalue. Definition for If the 2-norm is 0, then:

[0093]

[0094] definition In summary:

[0095]

[0096] The above formula is equivalent to:

[0097]

[0098] in To ensure The following two equations must be true:

[0099]

[0100]

[0101] Will Substituting into the formula, we get:

[0102]

[0103]

[0104]

[0105] In conclusion, when For a set to be valid, it must simultaneously satisfy the following conditions: a compact set is defined here. E

[0106]

[0107] Assuming compact set E Contains a strict subset:

[0108]

[0109] Among them when hour, It's about the attraction field of the equilibrium point.

[0110] Furthermore, the equilibrium solution satisfies There are two possibilities, the first is... The second type is ,when The equilibrium solution is in the set E On the boundary, not in the set In, that is, set There is only one equilibrium point in it.

[0111] The beneficial effects of this invention are:

[0112] 1. The calculation method of this invention describes the internal operating mechanism of the joint-venture cogeneration market based on its characteristics. Then, based on game theory, it characterizes the economic behavior of energy suppliers, end users and trading centers, and transforms the economic behavior into state-space equations describing the market operation. Thus, based on the study of its stability, it derives the sufficient conditions for asymptotic stability.

[0113] 2. The calculation method of this invention further derives the explicit expression of the asymptotically stable attraction domain of the entire economic system based on the sufficient condition of asymptotic stability. In order to ensure the stability of market transactions, the explicit expression of the attraction domain can intuitively show the influence of system parameters on the size of the attraction domain.

[0114] The calculation method of this invention quantifies the range of the stability region, ensuring that the market is asymptotically stable as long as the initial point is within the attraction region. This guarantees that transactions can be carried out smoothly and are physically executable, providing a valid reference for the design of the architecture and transaction mechanism of the combined heat and power market. Attached Figure Description

[0115] The invention will now be further described with reference to the accompanying drawings.

[0116] Figure 1 This is the IEEE-30 network topology of the present invention;

[0117] Figure 2 This is the 51-node heat network topology of the present invention;

[0118] Figure 3 This invention relates to the influence of wind farm location and uncertainty on the size of the attraction domain. Detailed Implementation

[0119] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0120] A method for calculating the asymptotically stable attraction domain applied to the combined heat and power market, combined with Figures 1 - 3 As shown, the power grid in the calculation method adopts the basic parameters in the IEEE-30 standard example, and the heating network adopts a 51-node heating network. The calculation method selects 2 conventional units and 3 cogeneration units. The initial operating conditions of the units and the network are shown in Table 1:

[0121]

[0122] Table 1

[0123] The calculation method includes the following steps:

[0124] Step 1: Based on game theory, establish an energy supplier production strategy model, an optimal energy purchase model for end users, and a market clearing model for the trading center.

[0125] Energy suppliers are divided into two categories: Category A consists of traditional energy suppliers that only own conventional combined heat and power (CHP) units, which are adjustable and often used to balance changes in system load. Category B consists of power generators that only own wind turbine units.

[0126] Class A energy suppliers formulate their optimal energy production strategies based on local nodal electricity prices and nodal heat prices, i.e., solve the following optimization problem:

[0127] Max (1)

[0128] s.t. (2)

[0129] In the formula Indicates energy supplier i Connected to the power grid n The node electricity price received on the No. 1 bus, Indicates supplier i Connected to the heating network m The node heat price received on node number 1 They represent energy suppliers. i Electricity and heat production plans, Indicates energy supplier i The cost function is typically expressed in the form of a quadratic equation:

[0130] (3)

[0131] in These are all cost coefficients, which are given as known conditions. The feasible operating region of the unit is represented by the following formula:

[0132] (4)

[0133] (5)

[0134] in Indicates the unit's minimum / maximum thermal output. and To characterize the parameters of the feasible region, all combined heat and power (CHP) units operate on a "heat-driven power generation" basis, therefore the feasible region of electrical output is... The size is determined by the feasible thermal output domain Decide.

[0135] Category B energy suppliers only own wind farms because they face the following optimization challenges:

[0136] Max (6)

[0137] s.t. , (7)

[0138] In the formula Indicates Category B energy suppliers i The actual electrical output, This refers to the cost of electricity generation; for wind turbines, this cost is close to zero. This refers to the costs incurred when other turbines are used as backups due to the uncertainty of wind power. Indicates the power output range of the fan. These represent the minimum and maximum output of the fan, respectively. Used to represent the uncertainty of wind power, when When the wind power output is underestimated, it indicates that the wind power output may be underestimated, and at this time, there may be a phenomenon of "wind curtailment"; when This indicates that wind power output is overestimated, resulting in insufficient supply and necessitating the use of backup units to compensate for the power shortage. In this invention, only the following is considered: Given this situation, the following cost formula is given:

[0139] (8)

[0140] (9)

[0141] In the formula This represents the cost coefficient.

[0142] Secondly, an energy purchase strategy model for end users is established based on game theory.

[0143] Assume the set of users is Users have only two ways to obtain heat energy. The first is to obtain heat energy directly from the heating network through a heat exchanger, i.e., to purchase heat energy directly from the energy supplier; the second is through household electric-to-heat equipment, which first purchases electricity and then converts it into heat energy. End users Total utility obtained through the consumption of electricity and heat It can be calculated using the following formula:

[0144] (10)

[0145] (11)

[0146] (12)

[0147] (13)

[0148] In the formula , and These represent the utility gained through the direct consumption of electrical energy, the use of electric heating equipment, and the direct consumption of thermal energy, respectively. , and These represent the electrical energy directly consumed by the user, the electrical energy consumed by the electro-thermal conversion equipment, and the heat energy consumed by the user, respectively. , , , , , These are all utility coefficients, and each user's goal is to maximize utility. Therefore, the following optimization problem arises:

[0149] Max (14)

[0150] s.t. (15)

[0151] (16)

[0152] (17)

[0153] (18)

[0154] In the formula Indicates user j With the power grid bus n Connected and busbar n The node electricity price is Similarly, Indicates user j With heating network nodes m Connected, the node heat price on this node is . , and These represent the feasible regions of user energy consumption. Indicates minimum / maximum power consumption. This indicates the minimum / maximum power consumption of the electric heating equipment. This indicates the minimum / maximum heat consumption.

[0155] Establish a trading center clearing model based on market clearing requirements:

[0156] The trading center has overall social benefits SW To maximize energy production and consumption using nodal electricity and nodal heat pricing, the following optimization problem needs to be solved:

[0157] Max (19)

[0158] s.t. (20)

[0159] (twenty one)

[0160] , , , (twenty two)

[0161] (twenty three)

[0162] (twenty four)

[0163] (25)

[0164] in Represents the cost of the unit, set G Represents the set of all generators. and Representing the connection with the power grid bus n A connected set of energy suppliers and end-users. Represents the set of power grid buses. Indicates connection with the power grid bus n A set of connected busbars Indicates power lines Line susceptance between Indicates the phase angle of the node voltage. Indicates the line Maximum power transmission capacity, Indicates from heating network node m The temperature of the flowing water Indicates pipeline l The product of the specific heat capacity and mass flow rate of water. Indicates pipeline l Terminal water temperature, and These represent the nodes of the heating network. m A connected set of energy suppliers and end-users. Represents the set of nodes in the heating network. Indicates pipeline l Length, This represents the temperature drop per unit length. Represented by node m The initial collection of pipes, Represents a node m Feasible temperature range Indicates heating network nodes m Minimum / maximum temperature, , These are the dual multipliers of constraints (21) and (24), respectively.

[0165] Constraint (20) indicates that the active power of each bus in the power grid is balanced, condition (21) ensures that the power flow does not exceed the limit, condition (23) indicates that the heat power of each node in the heating network is balanced, (24) is used to describe the temperature loss during transmission, and (25) indicates that the temperature of each node in the heating network is within a reasonable range.

[0166] Step 2: Based on the optimal strategy model constructed above, design a dynamic market trading mechanism and characterize the optimal economic behavior of each market participant based on KKT conditions and the gradient method.

[0167] The negotiation process of the entire dynamic market is described using iterative action sequences and state variables. We note that the optimization problem for energy suppliers, end users, and trading centers is a convex problem satisfying strong duality. Therefore, the KKT optimality condition can determine a unique market equilibrium point, as follows:

[0168] S1. Energy supplier action sequence based on game theory and gradient method

[0169] Based on the gradient method, find the relationship between (1) and (6) with respect to... , and The gradient is obtained as follows:

[0170] (26)

[0171] (27)

[0172] (28)

[0173] in , and Indicates the first k Energy suppliers in rounds of iteration i Electricity output, heat output, and wind power output. h Indicates time interval, Indicates energy supplier i The ability to regulate It is a projection operation, representing a projection onto a set. The projection onto the surface is specifically defined as follows:

[0174] (29)

[0175] In the formula, This represents the 2-norm.

[0176] S2. End-user action sequences based on game theory and gradient method

[0177] Based on the gradient method, find (10) about , and The gradient is obtained.

[0178] (30)

[0179] (31)

[0180] (32)

[0181] In the formula, Indicates end user j The ability to regulate , and Indicates the first k End users in round iteration j The pure electric load, the heat load, and the electric load generated by the use of electric heating equipment.

[0182] S3. Trading Center Action Sequence Based on Game Theory and Gradient Method

[0183] (33)

[0184] (34)

[0185] (35)

[0186] (36)

[0187] (37)

[0188] (38)

[0189] (39)

[0190] In the formula, , , , and This represents the trading center's electricity price regulation capability, voltage phase angle regulation capability, multiplier regulation capability corresponding to the temperature loss equation, node temperature regulation capability, and multiplier regulation capability corresponding to power flow security constraints. Indicates busbar n In the k The nodal electricity price in the next iteration. Represents a node m In the k Node heat price in the next iteration Indicates pipeline l The Lagrange multiplier corresponding to the temperature loss constraint is in the first... k The value in the next iteration Indicates pipeline l In the k The final temperature in the next iteration. Indicates the first kIn the next iteration, from the heating network nodes m The temperature of the flowing water The Lagrange multiplier corresponding to the power flow constraint is in the first position. k The value in the next iteration, the symbol in formula (39) Represents the projection operation, when hour, ;when hour, .

[0191] Step 3: Based on the optimal economic behavior model established above, the economic behavior of all market participants is treated as a generalized controlled object, and the state-space equations of the combined heat and power market are constructed. The construction process includes:

[0192] (1) The following two assumptions are given:

[0193] Assumption 1: All market participants are aware of their equipment parameters, and their economic activities are all within the feasible domain of the equipment.

[0194] Assumption 2: Sampling time interval h Very short, for any variable x and adjust speed s The following formula is true

[0195] (40)

[0196] (2) Write the state-space equations of the energy supplier:

[0197] (41)

[0198] (42)

[0199] In the formula , , , NG Indicates the total number of energy suppliers; when When, it indicates the unit i It belongs to Category A energy suppliers. and These are vectors composed of nodal electricity prices and nodal heat prices, respectively. and Represents the correlation matrix of the generator units. Indicates the unit i Connected to the power grid bus j superior, Indicates the unit i Connected to the heating network node j Above; if not connected, then , , , and yes NG × NG A diagonal matrix consisting of cost coefficients. , and yes NG A vector of cost coefficients, which is 1 ×1.

[0200] (3) Write the state-space equations for the end user:

[0201] (43)

[0202] (44)

[0203] (45)

[0204] In the formula , , , ND Indicates the number of end users. and Represents the user association matrix. Indicates user i Connected to the power grid bus j superior, Indicates user i Connected to the heating network node j Above; if not connected, then , , , yes ND × ND The diagonal matrix consisting of utility coefficients. , and yes ND A 1-dimensional vector consisting of utility coefficients.

[0205] (4) Write the state-space equations of the trading center:

[0206] In addition to nodal price vectors and node heat price vector The state vector of the trading center also includes the voltage phase angle vector. dual vector and Node temperature vector and the temperature vector at the end of the pipe Indicates the number of heating network pipes. Indicates the number of power grid lines. MIndicates the number of nodes in the heating network. N This indicates the number of power grid buses.

[0207] (46)

[0208] (47)

[0209] (48)

[0210] (49)

[0211] (50)

[0212] (51)

[0213] (52)

[0214] In the formula, the matrix A yes Bus-line correlation matrix, matrix The correlation matrix after removing the column of the balancing node. It is the bus voltage phase angle vector after eliminating the slack node. yes The diagonal matrix, where the elements on the diagonal are the susceptance of the line. These are the upward correlation matrix and downward correlation matrix of the heating network, respectively. It is a matrix A and The extended matrix, , The elements on the right side of formula (52) are as follows:

[0215] (53)

[0216] In the formula, , R It is a rotation matrix. yes The vector is composed of the maximum capacity of the line.

[0217] To simplify the expression, the state equations (41)-(52) can be written in the following compact form.

[0218] (54)

[0219]

[0220] (55)

[0221] (56)

[0222] (57)

[0223] (58)

[0224] in , All the uncertainties All and This is reflected in the text.

[0225] Step 4: Based on Lyapunov's stability theorem, derive the formula for calculating the attraction field. The derivation process is as follows:

[0226] Assumption It is the equilibrium point of the state equation (54), so we have:

[0227] (59)

[0228] definition , And Lyapunov equations:

[0229] (60)

[0230] in and It is a real symmetric positive definite matrix, and and Substitute (54) and ,have to:

[0231] (61)

[0232] Substituting (59) into (61), we get:

[0233] (62)

[0234] beg The derivative with respect to time:

[0235] (63)

[0236] Will and Substituting into formula (63), and after rearranging and combining like terms, we get:

[0237] (64)

[0238] Using the non-extensibility of projection, we obtain Therefore, formula (64) satisfies the following equation:

[0239] (65)

[0240] because Therefore, according to Cauchy's inequality, we get Assuming It is a positive definite diagonal matrix, composed of orthogonal nonzero real eigenvectors Composition, therefore ,in yes The eigenvalues, considering the equilibrium point ,satisfy ,get:

[0241] (66)

[0242] in Representation matrix The largest eigenvalue, due to It is a positive vector, which can be represented by a set of orthogonal vectors. express ,in ,make We can obtain:

[0243] (67)

[0244] in Representation matrix The smallest eigenvalue. If It is a Hurwitz matrix, for any There exists a positive definite matrix. The following Lyapunov equations must be satisfied:

[0245] (68)

[0246] Therefore:

[0247] (69)

[0248] in, It is a matrix The smallest eigenvalue. Definition for If the 2-norm is , then we have:

[0249] (70)

[0250] definition Combining (70), we can obtain

[0251] (71)

[0252] The above expression is equivalent to:

[0253] (72)

[0254] in To ensure The following two equations must be true:

[0255] (73)

[0256] (74)

[0257] Will Substituting into formula (74), we get:

[0258] (75)

[0259] (76)

[0260] (77)

[0261] In conclusion, when For a condition to hold, (73) and (75) must be satisfied simultaneously. Here, a compact set is defined. E:

[0262] (78)

[0263] Assuming compact set E Contains a strict subset:

[0264] (79)

[0265] Among them when hour, Regarding the region of attraction at the equilibrium point, note that there are two equilibrium solutions that can satisfy... The first one is:

[0266] (80)

[0267] The second type is:

[0268] (81)

[0269] The second case was obtained. At this point, the equilibrium solution is in the setE On the boundary, not in the set In, that is, set There is only one equilibrium point (80).

[0270] In the description of this specification, references to terms such as "an embodiment," "example," "specific example," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0271] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the claimed invention.

Claims

1. A method for calculating the asymptotically stable attraction domain applied to combined heat and power markets, characterized in that, The calculation method includes the following steps: Step 1: Establish an energy supplier production strategy model, an optimal energy purchase model for end users, and a market clearing model for the trading center based on game theory; the specific operations are as follows: S1: Establish an energy supplier production strategy model based on game theory. Energy suppliers are divided into two categories: Category A consists of traditional energy suppliers that only own traditional combined heat and power units, and Category B consists of power generators that only own wind turbine units. Class A energy suppliers formulate optimal energy production strategies based on local nodal electricity prices and nodal heat prices, i.e., solve the following optimization problem: Max （1） st （2） In the formula, Indicates energy supplier i Connected to the power grid n The node electricity price received on the No. 1 bus. Indicates supplier i Connected to the heating network m The node heat price received on node number 1 They represent energy suppliers. i Electrical and thermal output, Indicates energy supplier i The cost function is typically expressed in the form of a quadratic equation: （3） in All are cost coefficients. The feasible operating region of the unit is represented by the following formula: （4） （5） in, Indicates the unit's minimum / maximum thermal output. and The parameters used to characterize the feasible region are the electric output feasible region. The size is determined by the feasible thermal output domain Decide; Type B energy suppliers only own wind farms, so the following optimization problem needs to be solved: Max （6） st ， （7） In the formula, Indicates Category B energy suppliers i The actual electrical output, Refers to the cost of electricity generation. This refers to the costs incurred when other turbines are used as backups due to the uncertainty of wind power. This indicates the power output range of the fan. These represent the minimum and maximum output of the fan, respectively. Used to represent the uncertainty of wind power, when When the wind power output is underestimated, wind curtailment may occur; when When the wind power output is overestimated, the supply is insufficient and it is necessary to call in backup units to compensate for the power shortage. S2: Establish an optimal energy purchase model for end users based on game theory. End users Total utility is obtained through the consumption of electricity and heat. The calculation method is as follows: （10） （11） （12） （13） In the formula, , and These represent the utility obtained through directly consuming electrical energy, using electric heating equipment, and directly consuming thermal energy, respectively. , and These represent the electrical energy directly consumed by the user, the electrical energy consumed by the electro-thermal conversion equipment, and the heat energy consumed by the user, respectively. , , , , , The utility coefficient Represents a set of users; End users With the goal of maximizing utility, we solve the following optimization problem: Max （14） st （15） （16） （17） （18） In the formula, Indicates user j With the power grid bus n Connected and busbar n The node electricity price is , Indicates user j With heating network nodes m Connected, the node heat price on this node is ; , and These represent the feasible regions of user energy consumption. Indicates minimum / maximum power consumption. This indicates the minimum / maximum power consumption of the electric heating equipment. Indicates the minimum / maximum heat consumption; S3: Establish a market clearing model for the trading center based on market clearing requirements. The trading center has overall social benefits SW With the objective of maximizing energy production and consumption, and using nodal electricity and nodal heat prices to settle energy production and consumption, the following optimization problem needs to be solved: Max （19） st （20） （21） ， ， ， （22） （23） （24） （25） In the formula, Represents the cost of the unit, set G Represents the set of all generators. and Representing the connection with the power grid bus n A connected set of energy suppliers and end-users. Represents the set of power grid buses. Indicates connection with the power grid bus n A set of connected busbars Indicates power lines Line susceptance between Indicates the phase angle of the node voltage. Indicates the line Maximum power transmission capacity, Indicates from heating network node m The temperature of the flowing water Indicates pipeline l The product of the specific heat capacity and mass flow rate of water. Indicates pipeline l Terminal water temperature, and These represent the nodes of the heating network. m A connected set of energy suppliers and end-users. Represents the set of nodes in the heating network. Indicates pipeline l Length, This represents the temperature drop per unit length. Represented by node m The initial collection of pipes, Represents a node m Feasible temperature range Indicates heating network nodes m Minimum / maximum temperature, , These are the dual multipliers of constraints (21) and (24), respectively; Constraint (20) indicates that the active power of each bus in the power grid is balanced, constraint (21) ensures that the power flow does not exceed the limit, constraint (23) indicates that the heat power of each node in the heating network is balanced, constraint (24) is used to describe the temperature loss during transmission, and constraint (25) indicates that the temperature of each node in the heating network is within a reasonable range. Step Two: Based on the optimal strategy model constructed above, design a dynamic market trading mechanism and characterize the optimal economic behavior model of each market participant based on KKT conditions and the gradient method; specific operations include: S1: Energy supplier action sequence based on game theory and gradient method Based on the gradient method, find the relationship between (1) and (6) with respect to... , and The gradient is obtained as follows: （26） （27） （28） in, , and Indicates the first k Energy suppliers in rounds of iteration i Electricity output, heat output, and wind power output. h Indicates time interval, Indicates energy supplier i The ability to regulate It is a projection operation, representing a projection onto a set. The projection onto the surface is specifically defined as follows: （29） In the formula, Represents the 2-norm; S2: End-user action sequence based on game theory and gradient method Based on the gradient method, find (10) about , and The gradient is obtained. （30） （31） （32） In the formula, Indicates end user j The ability to regulate , and Indicates the first k End users in round iteration j Pure electric load, heat load, and electric load generated by the use of electric heating equipment; S3: Trading center action sequence based on game theory and gradient method: （33） （34） （35） （36） （37） （38） （39） In the formula, , , , and This represents the trading center's electricity price regulation capability, voltage phase angle regulation capability, multiplier regulation capability corresponding to the temperature loss equation, node temperature regulation capability, and multiplier regulation capability corresponding to power flow security constraints. Indicates busbar n In the k The nodal electricity price in the next iteration. Represents a node m In the k The node heat price in the next iteration. Indicates pipeline l The Lagrange multiplier corresponding to the temperature loss constraint is in the first... k The value in the next iteration Indicates pipeline l In the k The final temperature in the next iteration. Indicates the first k In the next iteration, from the heating network nodes m The temperature of the flowing water The Lagrange multiplier corresponding to the power flow constraint is in the first position. k The values ​​in the next iteration, the symbols in formula (39) Represents the projection operation, when hour, ;when hour, ; Step 3: Based on the optimal economic behavior model established above, construct the state-space equations for the combined heat and power market; specific operations include: S1, the state-space equation of the energy supplier: （41） （42） In the formula, , , , NG Indicates the total number of energy suppliers; when When, it indicates the unit i It belongs to Category A energy suppliers. and These are vectors composed of nodal electricity prices and nodal heat prices, respectively. and Represents the correlation matrix of the generator units. Indicates the unit i Connected to the power grid bus j superior, Indicates the unit i Connected to the heating network node j Above; if not connected, then , , , and yes NG × NG A diagonal matrix consisting of cost coefficients. , and yes NG A vector consisting of cost coefficients of size ×1; S2, the state-space equation of the end user: （43） （44） （45） In the formula, , , , ND Indicates the number of end users. and Representing the user association matrix, Indicates user i Connected to the power grid bus j superior, Indicates user i Connected to the heating network node j Above; if not connected, then , , yes ND × ND The diagonal matrix consisting of utility coefficients. , and yes ND A 1-dimensional vector consisting of utility coefficients; S3, the state-space equation of the trading center: In addition to nodal price vectors and node heat price vector The state vector of the trading center also includes the voltage phase angle vector. dual vector and Node temperature vector and the temperature vector at the end of the pipe Indicates the number of heating network pipes. Indicates the number of power grid lines. M Indicates the number of nodes in the heating network. N Indicates the number of power grid buses; （46） （47） （48） （49） （50） （51） （52） In the formula, the matrix A yes Bus-line correlation matrix, matrix The incidence matrix after removing the column of balancing nodes; It is the bus voltage phase angle vector after eliminating the slack node. yes The diagonal matrix, where the elements on the diagonal are the susceptance of the line. These are the upward correlation matrix and downward correlation matrix of the heating network, respectively. It is a matrix A and The extended matrix, , The elements on the right side of formula (52) are as follows: （53） In the formula, , R It is a rotation matrix. yes The vector is composed of the maximum capacity of the line; To simplify the expression, the state equations (41)-(52) are written in the following compact form: （54） （55） （56） （57） （58） in , All uncertainties All and This is reflected in the middle; Step 4: Based on Lyapunov's stability theorem, derive the formula for calculating the attraction field. The derivation process is as follows: Assumption It is the equilibrium point of the state equation (54), so we have: （59） definition , And Lyapunov equations: （60） in and It is a real symmetric positive definite matrix, and and Substitute (54) and ,have to: （61） Substituting (59) into (61), we get; （62） beg The derivative with respect to time: （63） Will and Substituting into formula (63), and after rearranging and combining like terms, we get: （64） Using the non-extensibility of projection, we obtain Therefore, formula (64) satisfies the following equation: （65） because Therefore, according to Cauchy's inequality, we get , assuming It is a positive definite diagonal matrix, composed of orthogonal nonzero real eigenvectors Composition, therefore ,in yes The eigenvalues, considering the equilibrium point ,satisfy ,get: （66） in Representation matrix The largest eigenvalue, due to It is a positive vector, which consists of a set of orthogonal vectors. express ,in ,make We can obtain: （67） in Representation matrix The smallest eigenvalue; if It is a Hurwitz matrix, for any There exists a positive definite matrix. The following Lyapunov equations must be satisfied: （68） Therefore: （69） in, It is a matrix The smallest eigenvalue; definition for If the 2-norm is , then we have: （70） definition Combining (70) we get （71） The above expression is equivalent to: （72） in In order to ensure The following two equations must be true: （73） （74） Will Substituting into formula (74), we get: （75） （76） （77） In conclusion, when For a condition to hold, (73) and (75) must be satisfied simultaneously; here we define a compact set. E: （78） Assuming compact set E Contains a strict subset: （79） Among them when hour, It concerns the region of attraction of the equilibrium point, where the equilibrium solution satisfies... There are two possibilities. The first is: （80） The second type is: （81） The second case was obtained. At this point, the equilibrium solution is in the set E On the boundary, not in the set In, that is, set There is only one equilibrium point in it. .

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