Electric power spot market equilibrium analysis method based on conjecture variation model

Abstract

The invention discloses an electric power spot market equilibrium analysis method based on a conjecture variation model, and belongs to the field of electrical engineering. According to the method, on the basis of the conjecture variation theory, by constructing an optimization problem of a generalized market operation subject and establishing an optimal KKT condition of the generalized market operation subject in parallel, simulation operation of balanced clearing of the electric power spot market game under participation of a plurality of market operation subjects with multiple types of power generation technologies is achieved. The method comprises the following steps: firstly, establishing market clearing conditions including energy supply and demand balance and a price formation mechanism; secondly, constructing a generalized optimization model of a single market operation main body by taking the maximum market income as a target; thirdly, a nonlinear market equilibrium clearing model with partial differential items is formed by simultaneously establishing the optimal KKT conditions and the market clearing conditions of all the market operation main body optimization models; finally, generalized conjecture variation parameters are defined and replace partial differential items in the model, and therefore rapid solving of market game clearing under the participation of multiple market subjects and multiple power generation technologies can be achieved.

Description

Technical Field

[0001] The present invention belongs to the field of electrical engineering, and more specifically, relates to an equilibrium analysis method for a power spot market based on a conjecture variational model. Technical Background

[0002] Since 2015, my country's electricity spot market construction has achieved phased results, the trial operation cycle has been continuously extended, and market players have become increasingly diversified. Through the changes in electricity prices that transmit timing and location signals, the guiding role of optimizing the allocation of power resources has become increasingly significant. At present, 29 regions across the country have carried out trial operations of electricity spot markets, with an unprecedented coverage of construction. The overall framework of the unified electricity market has also been basically established, and the market structure of "unified market, two-level operation" has basically taken shape. In the complex spot market environment, the transaction benefits / costs of various market players are directly related to their bidding strategies. Therefore, simulating the bidding behavior of market players and analyzing the market clearing equilibrium state are crucial for the power market trading center to predict electricity price trends, regulate the behavior of market players, and maintain normal trading order. However, the existing market clearing methods mainly follow the competitive market hypothesis, replace the unit's marginal cost with its bidding curve, fail to fully consider the trading strategies and game behaviors of various market players, and are difficult to truly reflect the market supply and demand structure. Therefore, in order to better grasp the market status and verify the effective operation of the market, there is an urgent need for an easy-to-understand and easy-to-calculate electricity spot market equilibrium analysis method. Summary of the invention

[0003] In view of the defects of the prior art, the purpose of the present invention is to provide a method for analyzing the equilibrium of the electricity spot market based on a conjectural variational model, which aims to establish a mathematical model to balance the clearing of the electricity spot market with the participation of multiple market operators with various types of power generation technologies (including traditional thermal power units, new energy units, energy storage power stations, etc.), and adjust the conjectural variational parameters to simulate different degrees of market competition, so as to calculate the market operation status and operating benefits under different market monopoly situations. This method can provide quantitative analysis and scientific basis for market operators to predict clearing prices, regulate market power, and evaluate market benefits.

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

[0005] S1. Establish market clearing conditions including energy supply and demand balance and price formation mechanism;

[0006] S2. Taking the maximum profit of the spot market as the objective function and the spot market operation constraints as the constraints, a generalized optimization problem of a single market operator is constructed;

[0007] S3, combine the optimal KKT conditions of the generalized optimization problem of all market operators, and combine them with the market clearing conditions of S1 to form a nonlinear market equilibrium clearing model with partial differential terms;

[0008] S4. Define the generalized conjecture variational parameters and replace the partial differential terms in the S3 model, transforming the nonlinear market equilibrium clearing model into a single-layer linear optimization model, which can be quickly solved by a commercial solver to simulate the market clearing operation results under the game equilibrium of market players.

[0009] Furthermore, the step S1 comprises:

[0010] S11. Establish an 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, construct complementary slack conditions, and then establish upper and lower limit constraints on electricity demand.

[0013] Furthermore, the step S2 comprises:

[0014] S21. Constructing the optimization problem of the generalized market operating entity: the objective function is to maximize the spot market profit (= power generation and consumption income - power generation and consumption cost), and the constraints are: ① unit power generation and consumption power constraints; ② unit power generation and consumption power ramping constraints; ③ unit power energy upper and lower limit constraints and continuity constraints.

[0015] S22. Based on the optimization problem formed in S21 and optimization theory, derive its Lagrangian dual function.

[0016] Furthermore, the step S3 comprises:

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

[0018] Furthermore, the step S4 comprises:

[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 the conjectured variational parameters, and solve them by combining the linear KKT conditions of all market operators with the market clearing conditions (S14).

[0021] In general, the above technical solutions conceived by the present invention can achieve the following beneficial effects:

[0022] The present invention simulates the game behavior and bidding strategy between market operators by introducing conjectured variational parameters. At the same time, based on the KKT conditional optimization theory, the complex market equilibrium problem is transformed into a single-layer optimization model, realizing the market clearing simulation and equilibrium analysis under the participation of multiple market operators and different market competition levels, thereby providing a scientific basis for market operators to predict clearing prices, regulate market power, and evaluate market benefits. Therefore, the present invention has significant practical value and can better serve the participants and operators of the electricity spot market. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 A schematic flow chart of a method for analyzing equilibrium in a power spot market based on a conjectural variational model provided by the present invention.

[0024] Figure 2 A supply and demand curve of a test system provided in an embodiment of the present invention.

[0025] Figure 3 A comparison of clearing electricity prices for three market competition scenarios provided in an embodiment of the present invention.

[0026] Figure 4(a) to Figure 4(c) The unit output conditions of three market competition scenarios provided in the embodiments of the present invention. DETAILED DESCRIPTION

[0027] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments.

[0028] like Figure 1 As shown, the electric power spot market equilibrium analysis method based on the conjecture variational model of the present invention comprises the following steps:

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

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

[0031]

[0032] Among them, 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 is the system power load demand at time t, p i，g，t ,s i，g，t They are respectively the power generation / power consumption of the g-th type of power generation technology owned by the ith market operator at time t.

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

[0034] λ t (d t )=(D t -d t ) / α

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

[0036]

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

[0038] d t (λ t )=D t -α×λ t

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

[0040] S13. Introducing slack variables And construct the complementary slack condition:

[0041]

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

[0043] Introduce the corresponding binary variable Linear integer relaxation of the complementarity condition yields:

[0044]

[0045] This can establish upper and lower constraints on electricity demand.

[0046]

[0047] The final market clearing condition is:

[0048]

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

[0050] S21. Construct the optimization problem of the generalized market operator, and the objective function is to maximize the spot market profit (= power generation and consumption income - power generation and consumption cost):

[0051]

[0052] In the objective function, λ t is the clearing electricity price at time t determined by the market clearing condition, p i，g，t ,s i，g，t are the power generation / power consumption of the g-th type of power generation technology owned by the i-th market operator at time t, are the marginal costs of power generation and consumption of the g-th type of power generation technology respectively.

[0053] The constraints are:

[0054] ① Constraints on power generation and consumption of units:

[0055]

[0056] in are the upper and lower limits of power generation and consumption of the g-th type of power generation technology of the i-th market operator at time t, is the dual variable of each constraint.

[0057] ② Constraints on power generation and consumption ramping of the unit:

[0058]

[0059] in are the power ramp limits of the g-type power generation technology, is the initial output of the g-th type of power generation technology of the i-th market operator (usually assumed to be 50% of the power capacity), is the dual variable of each constraint.

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

[0061]

[0062] in are the upper limit, lower limit and initial value of the electric energy state of the g-th type of power generation technology of the i-th market operator, respectively, g is the conversion efficiency between electric energy and power of the g-type power generation technology (η g <1), ε i，g，tis the dual variable of each constraint.

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

[0064]

[0065] S3. Combine the optimal KKT conditions for the generalized optimization problems 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, including:

[0066] ①Original problem equality constraint:

[0067]

[0068] ②The first-order condition of Lagrangian function:

[0069]

[0070] It is easy to notice that the above equality constraints contain partial differential terms. This causes the constraints to be nonlinear and difficult to solve directly.

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

[0072]

[0073] ④ Market clearing conditions:

[0074]

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

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

[0077]

[0078] According to the economic definition, when ρ i When =-1, 0, I-1, it means that from the perspective of market entity i, the degree of market competition is perfectly competitive market / Cournot oligopoly market / implicit collusion market respectively.

[0079] Furthermore, the conjectured price response parameter of market subject i is defined, that is, the sensitivity (partial derivative) of the market clearing price to the power generation of subject i:

[0080]

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

[0082]

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

[0084]

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

[0086] The innovation of the present invention is to expand the above-mentioned traditional conjecture variational model from power generation to power generation and consumption to match the model proposed by the present invention. Specifically, firstly, the conjecture price response parameters and conjecture variational parameters of power generation, as well as the conjecture price response parameters and conjecture variational parameters of power consumption are defined respectively:

[0087]

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

[0089]

[0090] Therefore, the generalized conjecture price response parameters can be defined as:

[0091]

[0092] According to the conversion relationship between the conjectured price response parameters and the conjectured variational parameters, the generalized conjectured variational parameters can be defined:

[0093]

[0094] S42. Replace the partial differential terms in the KKT conditions obtained in S3 with linear expressions containing the conjectured variational parameters, then the Lagrangian first-order conditions of S3-② can be changed to:

[0095]

[0096] in:

[0097]

[0098] At this point, the solution can be obtained by combining the linear KKT conditions of all market operators and the market clearing conditions (S14). The final market equilibrium model is as follows:

[0099]

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

[0101] For complementary slack conditions have the following general form:

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

[0103] where μ is the dual variable of the constraint p(x). A binary variable ζ∈{0,1} is introduced to transform the above nonlinear constraints into mixed integer linear constraints:

[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 the present invention are further described below in conjunction with a specific test system.

[0107] The example tested in this invention has the following system supply and demand structure: 2400MW thermal power units (including 1 1000MW unit, 1 600MW unit, 2 300MW units, 2 100MW units), 4000MW renewable energy power station (including 2000MW wind turbines and 2000MW photovoltaic power stations), 2500MW electrochemical energy storage power station, and a maximum power load of 2500MW. The specific power generation technology capacity ownership distribution is shown in Table 1 below:

[0108] Table 1

[0109]

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

[0111] Table 2

[0112]

[0113] The wind power and photovoltaic capacity factors in this example adopt the annual wind and solar capacity factor curve of a certain province and average it on a daily scale; the system supply and demand curve of this example is as follows: Figure 2 shown.

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

[0115] The unit output under three scenarios is as follows Figure 4(a) to Figure 4(c) shown.

[0116] It will be easily understood by those skilled in the art that the above description is only 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 in the protection scope of the present invention.

Claims

1. A method for analyzing equilibrium of the electricity spot market based on a conjectural variational model, characterized in that: The following steps are involved: S1. Establish market clearing conditions including energy supply and demand balance and price formation mechanism; S2. Taking the maximum profit of the spot market as the objective function and the spot market operation constraints as the constraints, a generalized optimization problem of a single market operator is constructed; S3, combine the optimal KKT conditions of the generalized optimization problem of all market operators, and combine them with the market clearing conditions of S1 to form a nonlinear market equilibrium clearing model with partial differential terms; S4. Define the generalized conjecture variational parameters and replace the partial differential terms in the S3 model, 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 players.

2. The method for analyzing the equilibrium of the electricity spot market based on the conjecture variational model according to claim 1 is characterized in that: The market clearing conditions include: Among them, 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 is the system power load demand at time t, p i，g，t ,s i，g，t are the power generation / power consumption of the g-th power generation technology owned by the i-th market operator at time t, λ t is the market clearing price at time t, and is the system load d t Function of D t is the vertical intercept of system load, α is the price elasticity of system load, are the upper and lower limits of the system load at time t respectively.

3. The method for analyzing the equilibrium of the electricity spot market based on the conjecture variational model according to claim 1 is characterized in that: The objective function of the generalized optimization problem of a single market operator is: Among them, λ t is the clearing electricity price at time t determined by the market clearing condition, p i，g，t ,s i，g，t are the power generation / power consumption of the g-th type of power generation technology owned by the i-th market operator at time t, are the marginal costs of electricity generation / consumption of the g-th type of power generation technology; The constraints include: ① Constraints on power generation and consumption of units: in are the upper and lower limits of power generation and consumption of the g-th type of power generation technology of the i-th market operator at time t, is the dual variable of each constraint condition; ② Constraints on power generation and consumption ramping of the unit: in are the power ramp limits of the g-type power generation technology, is the initial output of the g-th type of power generation technology of the i-th market operator, is the dual variable of each constraint condition; ③ Upper and lower limits and continuity constraints of unit electric energy: in are the upper limit, lower limit and initial value of the electric energy state of the g-th type of power generation technology of the i-th market operator, respectively, g is the conversion efficiency between electric energy and power of the g-type power generation technology (η g <1), ε i，g，t is the dual variable of each constraint.

4. The method for analyzing the equilibrium of the electricity spot market based on the conjecture variational model according to claim 1 is characterized in that: Establish the Lagrangian function L of the generalized optimization problem of a single market operator: Among them, i is the serial number of the market operator.

5. The method for analyzing equilibrium of the electricity spot market based on the conjecture variational model according to claim 1 is characterized in that: The nonlinear market equilibrium clearing model with partial differential terms includes: ①Original problem equality constraint: ②The first-order condition of Lagrangian function: in is the partial differential term; ③ The complementary relaxation conditions corresponding to the original inequality constraints: ④ Market clearing conditions:

6. The method for analyzing equilibrium of the electricity spot market based on the conjecture variational model according to claim 1, characterized in that: The step S4 comprises: S41. Define the generalized conjecture variational parameter and the generalized conjecture price response parameter, and the conversion relationship between the two: S42. Replace the partial differential term in the KKT condition obtained in S3 with a linear expression containing the conjectured variational parameters, and the resulting market equilibrium model is as follows:

7. The method for analyzing equilibrium of the electricity spot market based on the conjecture variational model according to claim 6 is characterized in that: The complementary slack conditions constructed have the following general form: 0≤μ⊥p(x)≥0, that is, μ×p(x)=0, μ≥0, p(x)≥0 where μ is the dual variable of the constraint p(x); Introduce a binary variable θ∈{0,1} to transform the above nonlinear constraints into mixed integer linear constraints:

8. A power spot market equilibrium analysis system based on a conjectural variational model, characterized in that: include: A computer readable storage medium and a processor; The computer-readable storage medium is used to store executable instructions; The processor is used to read the executable instructions stored in the computer-readable storage medium to execute the electricity spot market equilibrium analysis method based on the hypothetical variational model as described in any one of claims 1 to 7.

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