A power spot market equilibrium analysis method based on a conjecture variation model

Abstract

The application discloses a power spot market equilibrium analysis method based on a conjecture variation model and belongs to the electrical engineering field.The method is based on the conjecture variation theory, an optimization problem of a generalized market operation subject is constructed, and optimal KKT conditions thereof are simultaneously established, so that the simulation operation of the power spot market game equilibrium clearing under the participation of multiple market operation subjects with multiple power generation technologies is realized.Firstly, market clearing conditions including energy supply and demand balance and a price formation mechanism are established.Secondly, a generalized optimization model of a single market operation subject is constructed with the maximum market income as the target.Thirdly, the optimal KKT conditions of all market operation subject optimization models and the market clearing conditions are simultaneously established, so that a nonlinear market equilibrium clearing model with partial differential terms is formed.Finally, a generalized conjecture variation parameter is defined and is used to replace the partial differential terms in the above model, so that the market game clearing under the participation of multiple market subjects and multiple power generation technologies can be quickly solved.

Description

Technical Field

[0001] This invention belongs to the field of electrical engineering, and more specifically, relates to a method for equilibrium analysis of the electricity spot market based on a conjecturative variational model. Technical Background

[0002] Since 2015, my country's electricity spot market construction has achieved phased results, with trial operation periods continuously extended and market participants becoming increasingly diversified. The guiding role of electricity resource optimization in allocation, through the transmission of time-series and location-based price changes, has become increasingly significant. Currently, 29 regions nationwide have launched trial operations of electricity spot markets, an unprecedented scope of construction. The overall framework of a unified electricity market has been basically established, and a market architecture of "unified market, two-tier operation" has been largely formed. In the complex spot market environment, the trading revenue / cost of each market participant is directly related to their bidding strategy. Therefore, simulating the bidding behavior of market participants and analyzing the market clearing equilibrium state is crucial for electricity market trading centers to predict electricity price trends, supervise market participant behavior, and maintain normal trading order. However, existing market clearing methods mainly follow the competitive market assumption, using the marginal cost of generating units instead of their bidding curves, failing to fully consider the trading strategies and game behavior of each market participant, and making it difficult to truly reflect the market supply and demand structure. Therefore, to better grasp the market state and verify the effective operation of the market, there is an urgent need for an easy-to-understand and conveniently calculated method for analyzing the equilibrium of the electricity spot market. Summary of the Invention

[0003] To address the shortcomings of existing technologies, the present invention aims to provide a method for equilibrium analysis of the electricity spot market based on a conjecturative variational model. This method establishes a mathematical model to determine the equilibrium clearing of the electricity spot market involving multiple market operators possessing various power generation technologies (including traditional thermal power units, new energy units, and energy storage power stations). By adjusting the conjecturative variational parameters to simulate different levels of market competition, the method calculates the market operation status and operational efficiency under different market monopoly scenarios. This method provides market operators with quantitative analysis and scientific basis for predicting clearing prices, regulating market power, and evaluating market efficiency.

[0004] To achieve the above objectives, this invention provides a method for analyzing the equilibrium of the electricity spot market based on a conjecturative variational model, comprising the following steps:

[0005] S1. Establish market clearing conditions that include energy supply and demand balance and price formation mechanisms;

[0006] S2. With the objective function of maximizing spot market profits and the constraints of spot market operation, construct a generalized optimization problem for a single market operator.

[0007] S3. Combine the optimal KKT conditions of the generalized optimization problem of all market operators with the market clearing conditions of S1 to form a nonlinear market equilibrium clearing model with partial differential terms.

[0008] S4. Define the generalized conjectured variational parameters and replace the partial differential terms in the S3 model to transform the nonlinear market equilibrium clearing model into a single-layer linear optimization model. It can be solved quickly through a business solver to simulate the market clearing operation results under the game equilibrium of market participants.

[0009] Further, step S1 includes:

[0010] S11. Establish the energy supply and demand balance equation.

[0011] S12. Introduce a linear price-demand function, construct an inverse demand function, and form a price formation mechanism.

[0012] S13. Introduce slack variables and their corresponding binary variables to construct complementary slack conditions, and then establish upper and lower limits constraints on electricity demand.

[0013] Further, step S2 includes:

[0014] S21. Optimization problem of constructing a generalized market operator: The objective function is to maximize the spot market profit (= power generation and consumption revenue- power generation and consumption cost), and the constraints are as follows: ① power generation and consumption constraints of the unit; ② power generation and consumption ramp-up constraints of the unit; ③ upper and lower limits constraints and continuity constraints of the unit's electrical energy.

[0015] S22. Based on the optimization problem formed by S21, derive its Lagrange dual function based on the theory of optimization.

[0016] Further, step S3 includes:

[0017] Based on S21 and S22, the optimal KKT conditions for the optimization problem of a single generalized market operator are constructed, specifically including: ① the equality constraints of the original problem; ② the first-order conditions of the Lagrange function; ③ the complementary relaxation conditions corresponding to the original inequality constraints. The KKT system obtained in this step contains partial differential terms.

[0018] Further, step S4 includes:

[0019] S41. Define the generalized conjecture variational parameter and the generalized conjecture price response parameter, and the conversion relationship between the two.

[0020] S42. Replace the partial differential terms in the KKT conditions obtained in S3 with linear expressions containing conjectured variational parameters, and solve them by simultaneously solving the linear KKT conditions of all market operators and the market clearing conditions (S14).

[0021] In summary, the above-described technical solutions conceived in this invention can achieve the following beneficial effects:

[0022] This invention simulates the game-theoretic behavior and pricing strategies of market participants by introducing conjectured variational parameters. Based on KKT conditional optimization theory, it transforms the complex market equilibrium problem into a single-layer optimization model, enabling market clearing simulation and equilibrium analysis under conditions of multiple market participants and varying levels of market competition. This provides a scientific basis for market operators to predict clearing prices, regulate market power, and assess market benefits. Therefore, this invention has significant practical value and can better serve participants and operators in the electricity spot market. Attached Figure Description

[0023] Figure 1 This is a flowchart illustrating a method for analyzing the equilibrium of the electricity spot market based on a conjecturative variational model, provided by the present invention.

[0024] Figure 2 Supply and demand curves for the testing system provided in this embodiment of the invention.

[0025] Figure 3 This invention provides a comparison of clearing electricity prices under three different market competition scenarios.

[0026] Figures 4(a) to 4(c) The unit output is shown in three market competition scenarios provided in the embodiments of the present invention. Detailed Implementation

[0027] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0028] like Figure 1 As shown, the electricity spot market equilibrium analysis method based on a conjecturative variational model of the present invention includes the following steps:

[0029] S1. Establish market clearing conditions that include energy supply and demand balance and price formation mechanisms. Specifically, this can be divided into the following three steps.

[0030] S11. Establish the energy supply and demand balance equation.

[0031]

[0032] Where i is the serial number of the market operator, g is the serial number of the power generation technology, and t is the time serial number; d t Let p be the system power load demand at time t. i，g，t s i，g，t These represent the power generation / consumption of the g-type power generation technology owned by the i-th market operator at time t.

[0033] S12. Introducing a linear price-demand function:

[0034] λ t (d t )=(D t -d t ) / α

[0035] Where λ t The market-clearing electricity price at time t is the system load d. t Affine function; D t Let α be the vertical intercept of the system load (i.e., the theoretical maximum value), and α be the price elasticity of the system load, which is the decrease (increase) in electricity demand caused by a one-unit increase (decrease) in market price.

[0036]

[0037] Based on this, an inverse demand function can be constructed:

[0038] d t (λ t ) = D t -α×λ t

[0039] Thus, the market price formation mechanism was established through the price-demand function and load elasticity.

[0040] S13. Introduce slack variables And construct complementary relaxation conditions:

[0041]

[0042] in These represent the upper and lower limits of the system load at time t, respectively.

[0043] Introduce the corresponding binary variables Applying linear integer relaxation to the complementarity condition, we obtain:

[0044]

[0045] This allows for the establishment of upper and lower limits for electricity demand.

[0046]

[0047] The final market clearing conditions are:

[0048]

[0049] S2. Construct a generalized optimization problem for a single market operator and derive the Lagrangian function for the generalized optimization problem. Specifically, this can be divided into the following two steps.

[0050] S21. Construct an optimization problem for a generalized market operator, with the objective function being to maximize spot market profit (= Electricity generation and consumption revenue - Electricity generation and consumption cost):

[0051]

[0052] In the objective function, λ t The clearing price at time t, determined by market clearing conditions, is p. i，g，t s i，g，t Let be the power generation / consumption of the g-type power generation technology owned by the i-th market operator at time t. These represent the marginal costs of power generation and consumption for the g-type power generation technology.

[0053] The constraints are as follows:

[0054] ① Power generation and consumption constraints of the generating unit:

[0055]

[0056] in These represent the upper and lower limits of power generation / consumption for the g-type power generation technology of the i-th market operator at time t. These are the dual variables of each constraint.

[0057] ② Power generation and consumption ramp-up constraints of the unit:

[0058]

[0059] in These are the power generation and consumption ramp-up limits for Class g power generation technologies. The initial output of the g-type power generation technology for the i-th market operator (usually assumed to be 50% of the power capacity), These are the dual variables of each constraint.

[0060] ③ Upper and lower limits of unit electrical energy and continuity constraints:

[0061]

[0062] in These represent the upper limit, lower limit, and initial value of the electrical energy state for the g-th type of power generation technology, respectively, for the i-th market operator. g The conversion efficiency (η) between electrical energy and power for the g-th type of power generation technology g <1), ε i，g，tThese are the dual variables of each constraint.

[0063] S22. Based on the optimization problem formed in S21, derive its Lagrangian function:

[0064]

[0065] S3. Establish the optimal KKT conditions for the generalized optimization problem of all market operators to form a nonlinear market equilibrium clearing model with partial differential terms: Based on S21 and S22, construct the optimal KKT conditions for the optimization problem of a single generalized market operator, specifically including:

[0066] ① Equality constraints of the original problem:

[0067]

[0068] ② First-order condition for the Lagrange function:

[0069]

[0070] It is easy to notice that the above equation constraints contain partial differential terms. This results in nonlinear constraints that are difficult to solve directly.

[0071] ③ Complementary relaxation conditions corresponding to the original inequality constraints:

[0072]

[0073] ④ Market clearing conditions:

[0074]

[0075] S4. Define the generalized conjectured variational parameters and replace the partial differential terms in the S3 model, thereby transforming the original complex problem into a single-layer optimization model that can be solved quickly using a commercial solver. Specifically, this can be divided into the following two steps.

[0076] S41. Define the generalized conjectured variational parameter. The traditional concept of conjectured variation refers to the response of all competitors of market participant i to the output (generally referring to power generation in the power industry) of participant i, that is, the sum p of the power generation of all competitors of participant i. -i Power generation p of subject i i Sensitivity (partial derivative):

[0077]

[0078] According to the economic definition, when ρ i = -1, 0, I-1 respectively represent the degree of market competition from the perspective of market subject i as a perfectly competitive market / Cournot oligopoly market / implicit collusion market.

[0079] Furthermore, we define the conjectured price response parameter for market participant i, namely, the sensitivity (partial derivative) of the market clearing price to the power generation of participant i:

[0080]

[0081] Based on market supply and demand equilibrium conditions and price elasticity of demand:

[0082]

[0083] A conversion formula between the conjectured price response parameters and the conjectured variational parameters can be further established:

[0084]

[0085] Therefore, by adjusting different conjectured variational parameter values ​​and converting them into conjectured price response parameters, different levels of market competition can be simulated.

[0086] The innovation of this invention lies in extending the traditional conjecturative variational model from power generation to power generation and consumption, to complement the model proposed in this invention. Specifically, the conjectured price response parameters and conjectured variational parameters for power generation, and the conjectured price response parameters and conjectured variational parameters for power consumption are defined respectively:

[0087]

[0088] It's easy to understand that, from the perspective of the power system, the unit electricity consumption of any market participant is the opposite of the unit electricity consumption, that is:

[0089]

[0090] Therefore, a generalized conjectured price response parameter can be defined:

[0091]

[0092] Based on the transformation relationship between the conjectured price response parameters and the conjectured variational parameters, a generalized conjectured variational parameter can be defined:

[0093]

[0094] S42. Replacing the partial differential terms in the KKT conditions obtained in S3 with a linear expression containing the conjectured variational parameters, the Lagrange first-order conditions in S3-② can be transformed into:

[0095]

[0096] in:

[0097]

[0098] Therefore, the solution can be found by simultaneously applying the linear KKT conditions and the market clearing condition (S14) to all market operators. The final market equilibrium model is as follows:

[0099]

[0100] All nonlinear complementary relaxation conditions in the above equation can be relaxed by introducing binary variables through mixed integer linear relaxation, as follows:

[0101] For complementary relaxation conditions of the following general form:

[0102] 0 ≤ μ ⊥ p(x) ≥ 0, that is, μ × p(x) = 0, μ ≥ 0, p(x) ≥ 0

[0103] Here, μ is the dual variable of the constraint p(x). Introducing a binary variable ζ∈{0,1} transforms the above nonlinear constraint into a mixed-integer linear constraint:

[0104] 0≤μ≤ζ×M,0≤p(x)≤(1-ζ)×M

[0105] Where M is a sufficiently large constant.

[0106] The specific implementation steps of this invention will be further explained below with reference to a specific testing system.

[0107] The calculation example tested in this invention has the following system supply and demand structure: 2400MW of thermal power units (including one 1000MW unit, one 600MW unit, two 300MW units, and two 100MW units), 4000MW of renewable energy power plants (including 2000MW of wind turbines and 2000MW of photovoltaic power plants), 2500MW of electrochemical energy storage power plants, and a maximum power load of 2500MW. The specific allocation of power generation capacity ownership is shown in Table 1 below:

[0108] Table 1

[0109]

[0110] The marginal costs of power generation and consumption for various power generation technologies are shown in Table 2 below:

[0111] Table 2

[0112]

[0113] The wind and solar capacity factors in this example adopt the annual wind and solar capacity factor curves of a certain province and are averaged on a daily scale; the system supply and demand curves in this example are as follows: Figure 2 As shown.

[0114] This example sets up three market competition scenarios: perfect competition (ρ = -1), mild oligopoly (ρ = -0.5), and Cournot oligopoly (ρ = 0). It then compares and analyzes electricity prices under these three scenarios. Figure 3 As shown.

[0115] Unit output in three scenarios Figures 4(a) to 4(c) As shown.

[0116] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is 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 scope of protection of the present invention.

Claims

1. A method for analyzing the equilibrium of the electricity spot market based on a conjecturative variational model, characterized in that, Includes the following steps: S1. Establish market clearing conditions that include energy supply and demand balance and price formation mechanisms; S2. With the objective function of maximizing spot market profits and the constraints of spot market operation, construct a generalized optimization problem for a single market operator. S3. Combine the optimal KKT conditions of the generalized optimization problem of all market operators with the market clearing conditions of S1 to form a nonlinear market equilibrium clearing model with partial differential terms. S4. Define the generalized conjectured variational parameters and replace the partial differential terms in the S3 model to transform the nonlinear market equilibrium clearing model into a single-layer linear optimization model and solve it to obtain the market clearing operation results under the game equilibrium of market participants. Define the generalized conjecture variational parameter With generalized conjecture price response parameters And the conversion relationship between the two: in, for Price elasticity, Let be the system power load demand at time t; Replace the partial differential terms in the KKT conditions obtained in S3 with a linear expression containing the conjectured variational parameters: in, For the serial number of the market operator, For the serial number of power generation technology, For time sequence number, These represent the marginal costs of power generation / consumption for the g-type power generation technology. It is the market-clearing electricity price at time t. Let be the power generation / consumption of the g-type power generation technology owned by the i-th market operator at time t. These are the dual variables of the four constraints: lower limit of unit power generation, upper limit of unit power generation, lower limit of unit power consumption, and upper limit of unit power consumption. These are the dual variables of the four constraints: lower limit of power generation ramp-up limit, upper limit of power generation ramp-up limit, lower limit of power consumption ramp-up limit, and upper limit of power consumption ramp-up limit. The conversion efficiency between electrical energy and power for the g-th type of power generation technology. , It is the dual variable of the unit's electrical energy continuity constraint.

2. The method for analyzing the equilibrium of the electricity spot market based on a conjecturative variational model according to claim 1, characterized in that, The market clearing conditions include: in, for The y-intercept, They are respectively The upper and lower limits.

3. The method for analyzing the equilibrium of the electricity spot market based on a conjecturative variational model according to claim 2, characterized in that, The objective function of the generalized optimization problem for a single market operator is: The constraints include: ①Power generation and consumption constraints of the generating unit: in These represent the lower limit of power generation, the upper limit of power generation, the lower limit of power consumption, and the upper limit of power consumption for the g-type power generation technology of the i-th market operator at time t. ② Power generation and consumption ramp-up constraints of the unit: in These are the power generation and consumption ramp-up limits for Class g power generation technologies. The initial output of the g-type power generation technology for the i-th market operator; ③ Upper and lower limits of unit electrical energy and continuity constraints: in Let be the upper limit, lower limit, and initial value of the electrical energy state of the g-th type of power generation technology for the i-th market operator. These are the dual variables of the two constraints: the lower limit of the unit's electrical energy and the upper limit of the unit's electrical energy.

4. The method for analyzing the equilibrium of the electricity spot market based on a conjecturative variational model according to claim 3, characterized in that, Establish the Lagrangian function for the generalized optimization problem of a single market operator. L : in, This refers to the serial number of the market operator.

5. The method for analyzing the equilibrium of the electricity spot market based on a conjecturative variational model according to claim 4, characterized in that, The nonlinear market equilibrium clearing model with partial differential terms includes: ① Equality constraints of the original problem: ② First-order condition for the Lagrange function: in It is a partial differential term; ③ Complementary relaxation conditions corresponding to the original inequality constraints: ④ Market clearing conditions: 。 6. The method for analyzing the equilibrium of the electricity spot market based on a conjecturative variational model according to claim 5, characterized in that, The constructed complementary relaxation conditions have the following general form: in Constraints The dual variable; Introduce a binary variable This transforms the nonlinear constraints into mixed-integer linear constraints: 。 7. A power spot market equilibrium analysis system based on a conjecturative variational model, characterized in that, include: Computer-readable storage media and processors; The computer-readable storage medium is used to store executable instructions; The processor is used to read executable instructions stored in the computer-readable storage medium and execute the electricity spot market equilibrium analysis method based on the conjecturative variational model as described in any one of claims 1 to 6.

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