A Day-ahead Spot Market Electricity Price Forecasting Method Based on Multi-Agent Game Equilibrium

Abstract

This invention discloses a day-ahead spot market electricity price forecasting method based on multi-agent game equilibrium. The method comprises the following steps: S1, obtaining the technical parameters of thermal power units; S2, defining decision variables; S3, establishing a clearing model for the day-ahead electricity market; S4, calculating the daily revenue of thermal power units; S5, calculating the probability coefficients of each bidding strategy and reselecting a bidding strategy; S6, determining whether the thermal power unit power system is in game equilibrium. If so, the system marginal electricity price at which the thermal power unit power system reaches game equilibrium is used as the predicted market price; otherwise, S3 is repeated. This invention simulates the market behavior of thermal power units through multi-agent simulation. Based on learning from historical bidding results, the agents continuously optimize their bidding strategies until market equilibrium is reached, with the system marginal electricity price at equilibrium serving as the predicted market price. This provides a method for predicting day-ahead spot market prices.

Description

Technical Field

[0001] This invention relates to the field of power market planning and design technology, and in particular to a day-ahead spot market electricity price forecasting method based on multi-agent game equilibrium. Background Technology

[0002] Currently, my country is actively promoting the reform of the electricity spot market. The transaction settlement under the "dual-track" system of planned and market transactions has generated a large amount of imbalance costs, and the calculation of various imbalance costs is based on the prediction of market prices. To analyze the magnitude of the imbalance costs corresponding to the marginal electricity price of the system when the spot market matures and reaches game equilibrium, it is urgent to use the equilibrium market price for calculation.

[0003] In the early stages of the electricity spot market, given the lack of historical market price data, intelligent agents can simulate the market behavior of thermal power units bidding in the day-ahead spot market. How to utilize the historical bidding results simulated by intelligent agents to continuously optimize its own bidding strategy until market equilibrium is a problem that the electricity spot market needs to solve. Summary of the Invention

[0004] This invention provides a day-ahead spot market electricity price forecasting method based on multi-agent game equilibrium to overcome the above-mentioned technical problems.

[0005] To achieve the above objectives, the technical solution of the present invention is as follows:

[0006] A day-ahead spot market electricity price forecasting method based on multi-agent game equilibrium includes the following steps:

[0007] S1. Obtain the next day's load information of the power system of thermal power units, the technical parameters of transmission lines, and determine the technical parameters of each thermal power unit.

[0008] S2. Assuming that thermal power units bid in segments between rated active power and minimum stable technical output, define the size of the next day's bid range and the bid value of the last segment of thermal power units as decision variables, in order to establish a set of bidding strategies for thermal power units and generate the initial bid curve of thermal power units.

[0009] S3. Establish a clearing model for the day-ahead electricity market to obtain the operating costs of thermal power units, the winning bid volume, and the nodal electricity price;

[0010] S4. Based on the operating cost of the thermal power unit, the winning bid volume and the node price, calculate the daily revenue of the thermal power unit and obtain the tendency coefficient of each bidding strategy in the set of bidding strategies for the thermal power unit.

[0011] S5: Based on the propensity coefficient, calculate the probability coefficient of each bidding strategy and reselect the bidding strategy to generate a new bidding curve;

[0012] S6. Determine whether the thermal power unit power system is in a game equilibrium state based on the probability coefficient. If the system is in a game equilibrium state, use the marginal electricity price of the system when the thermal power unit power system reaches game equilibrium as the predicted market price; otherwise, repeat S3.

[0013] Furthermore, the set of pricing strategies for thermal power units in S2 is established as follows:

[0014]

[0015] In the formula, Let J be the m-th bidding strategy for thermal power unit j; J be the number of thermal power units; M be the number of bidding strategies in the set of bidding strategies for thermal power units; and N be the number of segmented combinations of bidding strategies for thermal power units.

[0016] Furthermore, the clearing model of the day-ahead electricity market in S3 includes a security-constrained unit combination model and a security-constrained economic dispatch model for the day-ahead electricity market.

[0017] Furthermore, the calculation formula for the safety-constrained unit combination model of the day-ahead electricity market is as follows:

[0018]

[0019] In the formula, The operating cost of unit j in the thermal power unit during time period t; Let be the startup cost of unit j in time period t; NT is the set of time periods; J is the set of thermal power units.

[0020] The operating cost of the thermal power unit is calculated as follows:

[0021]

[0022] In the formula, A j The operating cost of thermal power unit j under minimum technical output; v j,t It is a Boolean variable representing the on / off status of unit j during time period t, where 0 indicates shutdown and 1 indicates on / off; λ l,j The electricity price quote for thermal power unit j in section l; δ l,j,t p represents the actual power generation of thermal power unit j during time period t in segment l of the segmented pricing function; j,t The winning bid amount for thermal power unit j during time period t; P j These represent the maximum and minimum technical outputs of thermal power unit j, respectively; E l,j NL represents the upper limit of the power generation capacity of segment l in the piecewise linear pricing function. j The number of segments in the piecewise linear electricity price function;

[0023] in,

[0024] In the formula: a j b is the coefficient of the quadratic term of the operating cost of unit j; j c is the coefficient for the first-order term of the operating cost of unit j; j For the constant term coefficient of unit j's operating cost;

[0025] The startup cost of the thermal power unit is calculated as follows:

[0026]

[0027] In the formula, This is the startup quote for thermal power unit j.

[0028] Furthermore, the security-constrained economic dispatch model for the day-ahead electricity market includes power system balance constraints for thermal power units, load reserve constraints, operating boundary constraints for thermal power units, and power flow constraints.

[0029] S31: The power balance constraints of the thermal power unit's power system are calculated as follows:

[0030] ∑ j∈J p j,t =D t (5)

[0031] In the formula: D t The system load demand for time period t;

[0032] S32: The load reserve constraint is calculated as follows:

[0033]

[0034] In the formula, ε d The power system load reserve rate for thermal power units; Let J be the maximum possible power generation of thermal power unit j during time period t;

[0035] S33: The power flow constraints are calculated as follows:

[0036]

[0037] In the formula, L h,t Let represent the line power flow of branch h during time period t; LM is the system sensitivity matrix; ΔP is the net power injected into the node; L maxh The transmission capacity limit for branch h;

[0038] S34: The operating boundary constraints of the thermal power unit include the output range constraint, the ramp rate constraint, the minimum start-up time constraint, and the minimum downtime constraint.

[0039] Furthermore, in S34, the constraints on the output range of the thermal power unit, the ramp rate constraint, the minimum start-up time constraint, and the minimum downtime constraint are calculated as follows:

[0040] S331: The output range constraint of the thermal power unit is calculated as follows:

[0041]

[0042] S332: The calculation of the gradeability constraint for the thermal power unit is as follows:

[0043]

[0044] In the formula, RU j Ramp-up rate for thermal power unit j; RD j SU represents the ramp rate under operating conditions for thermal power unit j; j SD represents the starting ramp rate of thermal power unit j; j Let be the shutdown ramp rate of thermal power unit j;

[0045] S333: The minimum start-up time constraint for the thermal power unit is calculated as follows:

[0046]

[0047] In the formula, NT represents the minimum start-up time of thermal power unit j; G represents the number of cycle periods; j This represents the number of time periods during which the thermal power unit must be started at the beginning of cycle j; Ins j It is the continuous operating time at the end of the previous cycle of thermal power unit j;

[0048] S334: The minimum downtime constraint for the thermal power unit is calculated as follows:

[0049]

[0050] In the formula, L represents the minimum downtime of thermal power unit j; j This represents the number of time periods during which the thermal power unit must be shut down at the beginning of cycle j.

[0051] S335: The formula for calculating the nodal electricity price is as follows:

[0052]

[0053] In the formula, LMP j,t Let ρ be the nodal price of thermal power unit j at time t; t The marginal electricity price at time t is the shadow value of the load balance constraint; These are the shadow values ​​of trend constraints; G l,j This is the sensitivity matrix of the power system for thermal power units.

[0054] Furthermore, the daily revenue of the thermal power unit in S4 is calculated as follows:

[0055]

[0056] In the formula, R j For the daily revenue of thermal power unit J; LMP j,t Let be the nodal electricity price of thermal power unit j at time t;

[0057] The propensity coefficients for each bidding strategy within the set of bidding strategies for thermal power units are calculated as follows;

[0058]

[0059] In the formula, Update the propensity coefficient for the bidding strategy selected by agent j in the nth round; q jm (n) represents the updated propensity coefficients for strategies not selected; m c m represents the selected bidding strategy; r represents the unselected bidding strategy; e represents the forgetting factor; and q represents the empirical parameter. jm (0) represents the initial tendency coefficient of each bidding strategy in the m-th bidding strategy set of thermal power unit j.

[0060] Furthermore, the probability coefficients of each bidding strategy in S5 are calculated as follows:

[0061]

[0062] In the formula, p j,m (n) represents the probability coefficient of the m-th bidding strategy of thermal power unit j in the nth round; c is the cooling coefficient;

[0063] Furthermore, the proportional selection method is used to reselect the pricing strategy in S5.

[0064]

[0065] In the formula, Let be the cumulative probability of thermal power unit j in the nth round and the mth time.

[0066] Furthermore, the method for determining whether the power system of thermal power units is in a game equilibrium state is as follows:

[0067] If the probability coefficient of a certain bidding strategy for all thermal power units in the thermal power unit power system is greater than the convergence coefficient, then the thermal power unit power system is determined to be in a game equilibrium state.

[0068] Right now

[0069] In the formula, δ is the convergence coefficient;

[0070] Otherwise, it is determined that the power system of the thermal power unit is not in a game equilibrium state.

[0071] Beneficial effects: The present invention provides a day-ahead spot market electricity price forecasting method based on multi-agent game equilibrium. The agents simulate the market behavior of thermal power units in strategic bidding in the day-ahead spot market. Based on learning from the bidding results of historical bidding strategies, the agents continuously optimize their bidding strategies until market equilibrium is reached, with the principle of maximizing their own interests. The system marginal electricity price at equilibrium is used as the predicted market price, thus providing a method for forecasting day-ahead spot market prices. Attached Figure Description

[0072] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0073] Figure 1 This is a technical flowchart of the day-ahead spot market electricity price forecasting method of the present invention;

[0074] Figure 2 This is a schematic diagram of the price curve for the day-ahead spot market electricity price forecasting method of the present invention;

[0075] Figure 3 This is a system structure diagram of the day-ahead spot market electricity price forecasting method of the present invention;

[0076] Figure 4 The load curve for the next day of the day-ahead spot market electricity price forecasting method of the present invention;

[0077] Figure 5a This is the initial price curve for thermal power unit G1 in the day-ahead spot market electricity price forecasting method of the present invention;

[0078] Figure 5b This is the initial price curve for thermal power unit G2 in the day-ahead spot market electricity price forecasting method of the present invention;

[0079] Figure 5c The initial price curve for thermal power unit G3 in the day-ahead spot market electricity price forecasting method of the present invention;

[0080] Figure 6a The present invention provides a system equilibrium price curve for the thermal power unit G1 quotation in the day-ahead spot market electricity price forecasting method of the present invention.

[0081] Figure 6b The present invention provides the G2 price curve for thermal power units during system equilibrium in the day-ahead spot market electricity price forecasting method.

[0082] Figure 6c The figure shows the G3 price curve of thermal power units at the system equilibrium time of the day-ahead spot market electricity price forecasting method of the present invention. Detailed Implementation

[0083] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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, 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.

[0084] This embodiment provides a day-ahead spot market electricity price forecasting method based on multi-agent game equilibrium. It acquires the next day's system load data, maximum transmission power of power lines, and technical parameters of thermal power units. Using the size of the last bidding range and the bid value of each thermal power unit as decision variables, it generates a set of bidding strategies for thermal power units and provides an initial bidding curve. A clearing model for the day-ahead electricity market is established, and the winning bid volume and nodal price for thermal power units are calculated from the clearing model. The revenue of each thermal power unit is calculated based on the clearing results. The propensity coefficient and selection probability coefficient of each strategy within the bidding strategy set are adjusted based on the revenue of the thermal power units. A new bidding strategy is then reselected using a proportional selection method based on the selection probability, generating a new bidding curve. The system is judged to have reached game equilibrium based on the selection probability coefficient of each strategy. If equilibrium has not been reached, the new bidding curve is sent back to the day-ahead spot market clearing model for re-execution. If game equilibrium has been reached, the marginal electricity price at the point of equilibrium is used as the predicted day-ahead market electricity price. Specifically, in this embodiment, the agent refers to a thermal power unit; one thermal power unit constitutes one agent, and multiple thermal power units constitute multiple agents.

[0085] Specifically, it includes the following steps:

[0086] S1. Obtain the next day's load information of the thermal power unit power system, transmission line technical parameters, and determine the technical parameters of each thermal power unit; the thermal power unit power system load information includes system load demand; the transmission line technical parameters include transmission capacity limits; the thermal power unit technical parameters include: maximum technical output of the thermal power unit, minimum technical output of the thermal power unit, continuous operating time of the thermal power unit at the end of the previous cycle, minimum downtime of the thermal power unit, minimum start-up time of the thermal power unit, uphill ramp rate, downhill ramp rate, and start-up cost;

[0087] S2. Assuming that thermal power units bid in segments between rated active power and minimum stable technical output, define the size of the next day's bid range and the bid value of the last segment of thermal power units as decision variables, in order to establish a set of bidding strategies for thermal power units and generate the initial bid curve of thermal power units.

[0088] Specifically, the set of pricing strategies for thermal power units is established as follows:

[0089] The construction of the pricing strategy set should follow these principles: For thermal power units with a minimum stable technical output that is not zero, the starting point of the first output interval is the unit's minimum stable technical output, and the ending point of the last output interval is the unit's rated active power. The starting point of each pricing segment is the ending point of the previous pricing segment. The length of each pricing segment cannot be less than 10% of the difference between the thermal power unit's rated active power and its minimum stable technical output. The pricing curve increases monotonically with output, as shown in the attached figure. Figure 2 As shown.

[0090] Specifically, thermal power units are bid in N segments between their rated active power and minimum stable technical output. The first to N-1 segments are bid on at marginal cost. The Nth segment's bid is a combination of the unit's marginal cost (MP) and the bid ceiling (Ccap). The length of the Nth segment's bid interval is the decision variable x, where x represents the percentage of the Nth segment's bid interval length relative to the difference between the unit's rated active power and minimum stable technical output. Following this combination, there are a total of 2N bidding strategies.

[0091]

[0092] In the formula, Let J be the m-th bidding strategy for thermal power unit j; J be the number of thermal power units; M be the number of bidding strategies in the set of bidding strategies for thermal power units; and N be the number of segmented combinations of bidding strategies for thermal power units.

[0093] The initial pricing curve for each pricing range is based on the marginal cost of the generator unit. A schematic diagram of the initial pricing curve is attached. Figure 1 As shown.

[0094] S3. Establish a clearing model for the day-ahead electricity market, which includes a safety-constrained unit combination model and a safety-constrained economic dispatch model for the day-ahead electricity market. The clearing model clears the day-ahead spot market based on the bid curves submitted by thermal power units to obtain the operating costs of thermal power units, the winning bid volume, and the nodal price. Specifically...

[0095] The safety-constrained unit combination model for the day-ahead electricity market includes the operating cost and start-up cost of thermal power units, and its calculation formula is as follows:

[0096]

[0097] In the formula, The operating cost of unit j in the thermal power unit during time period t; Let be the startup cost of unit j in time period t; NT is the set of time periods; J is the set of thermal power units.

[0098] The operating cost of the thermal power unit is calculated as follows:

[0099]

[0100] In the formula, A j The operating cost of thermal power unit j under minimum technical output; v j,t λ is a Boolean variable representing the start-up and shutdown status of a thermal power unit, indicating the start-up and shutdown status of unit j during time period t, where 0 represents shutdown and 1 represents start-up; l,j The electricity price quote for thermal power unit j in section l; δ l,j,t p represents the actual power generation of thermal power unit j during time period t in segment l of the segmented pricing function; j,t The winning bid amount for thermal power unit j during time period t; P j These represent the maximum and minimum technical outputs of thermal power unit j, respectively; E l,j NL represents the upper limit of the power generation capacity of segment l in the piecewise linear pricing function. j The number of segments in the piecewise linear electricity price function;

[0101] in,

[0102] In the formula: a j b is the coefficient of the quadratic term of the operating cost of unit j; j c is the coefficient for the first-order term of the operating cost of unit j; j For the constant term coefficient of unit j's operating cost.

[0103] The startup cost of the thermal power unit is calculated as follows:

[0104]

[0105] In the formula, This is the startup quote for thermal power unit j.

[0106] The security-constrained economic dispatch model for the day-ahead electricity market includes power system balance constraints for thermal power units, load reserve constraints, thermal power unit operating boundary constraints, and power flow constraints.

[0107] S31: The power balance constraint calculation of the thermal power unit power system is as follows:

[0108] ∑j∈J p j,t =D t (5)

[0109] In the formula: D t The system load demand for time period t;

[0110] S32: The load reserve constraint is calculated as follows:

[0111]

[0112] In the formula, ε d The power system load reserve rate for thermal power units; Let J be the maximum possible power generation of thermal power unit j during time period t;

[0113] S33: The power flow constraints are calculated as follows:

[0114]

[0115] In the formula, L h,t Let represent the line power flow of branch h during time period t; LM is the system sensitivity matrix; ΔP is the net power injected into the node; L maxh This is the transmission capacity limit for branch h.

[0116] S34: The operating boundary constraints of the thermal power unit include the output range constraint of the thermal power unit, the ramp rate constraint, the minimum start-up time constraint, and the minimum downtime constraint.

[0117] S331: The output range constraint of the thermal power unit is calculated as follows:

[0118]

[0119] S332: The calculation of the gradeability constraint for the thermal power unit is as follows:

[0120]

[0121] In the formula, RU j Ramp-up rate for thermal power unit j; RD j SU represents the ramp rate under operating conditions for thermal power unit j; j SD represents the starting ramp rate of thermal power unit j; j Let be the shutdown ramp rate of thermal power unit j;

[0122] S333: The minimum start-up time constraint for the thermal power unit is calculated as follows:

[0123]

[0124] In the formula, NT represents the minimum start-up time of thermal power unit j; G represents the number of cycle periods; j This represents the number of time periods during which the thermal power unit must be started at the beginning of cycle j; Ins j It is the continuous operating time of unit j at the end of the previous cycle. Continuous operation is represented by a positive value, and continuous shutdown is represented by a negative value. It is a known quantity.

[0125] S334: The minimum downtime constraint for the thermal power unit is calculated as follows:

[0126]

[0127] In the formula, L represents the minimum downtime of thermal power unit j; j This represents the number of time periods during which the thermal power unit must be shut down at the beginning of cycle j. It is a known quantity, obtained from the results of the previous cycle.

[0128] The calculated unit start-up and shutdown status v j,t As a known quantity, due to the start-up and shutdown state v of the thermal power unit j,t Since these constraints are already fixed, the day-ahead electricity market's safety-constrained economic dispatch model does not include minimum start-up time constraints and minimum downtime constraints for thermal power units. The winning bid amount and nodal price for the units are obtained from the safety-constrained economic dispatch model.

[0129] S335: The formula for calculating the nodal electricity price is as follows:

[0130]

[0131] In the formula, LMP j,t Let ρ be the nodal price of thermal power unit j at time t; t The marginal electricity price at time t is the shadow value of the load balance constraint; These are the shadow values ​​of trend constraints; G l,j This is the sensitivity matrix of the power system for thermal power units.

[0132] S4. Calculate the daily revenue of the thermal power unit based on the operating cost, the winning bid volume, and the node price, and obtain the tendency coefficient of each bidding strategy in the bidding strategy set of the thermal power unit based on the daily revenue of the thermal power unit.

[0133] The daily revenue of the thermal power unit is calculated as follows:

[0134]

[0135] In the formula, R j For the daily revenue of thermal power unit J; LMP j,t Let be the nodal electricity price of thermal power unit j at time t;

[0136] The propensity coefficients for each bidding strategy within the set of bidding strategies for thermal power units are calculated as follows;

[0137]

[0138] In the formula, Update the propensity coefficient for the bidding strategy selected by agent j in the nth round; q jm (n) represents the updated propensity coefficients for strategies not selected; m c q represents the selected bidding strategy; m represents the unselected bidding strategy; r is the forgetting factor, which inhibits the increase of the tendency coefficient of each behavior over time. The purpose of introducing the forgetting factor is to reduce the influence of past experience and enhance the influence of present experience; e is the experience parameter, which encourages the agent's past successful experience; jm (0) represents the initial tendency coefficient of each bidding strategy in the m-th bidding strategy set of thermal power unit j.

[0139] S5: Calculate the probability coefficient of each bidding strategy based on the propensity coefficient, and reselect the bidding strategy using the proportional selection method based on the probability coefficient to generate a new bidding curve;

[0140] The probability coefficients for each pricing strategy are calculated as follows:

[0141]

[0142] In the formula, p j,m (n) is the probability coefficient of the m-th bidding strategy of thermal power unit j in the nth round; c is the cooling coefficient, which determines the degree of influence of the propensity coefficient on the selection probability;

[0143] The ratio selection method is as follows:

[0144]

[0145] In the formula, Let be the cumulative probability of thermal power unit j in the nth round and the mth time.

[0146] The basic idea behind the proportional selection method is that the probability of each bidding strategy being selected is directly proportional to the proportion of that bidding strategy among all available bidding strategies. The larger the proportion of a bidding strategy, the greater the probability of selecting that strategy in the next round.

[0147] The cumulative probability is obtained by accumulating the probability coefficients calculated by formula (13). The probability coefficient accumulated to the last pricing strategy will definitely be 1. A random number generator generates J random numbers Rand(j) at a time, with values ​​ranging from (0,1); starting from the first accumulated probability, these are compared with the random number Rand(j), up to the m-th accumulated probability. If the Rand(j) is greater than that of the j-th unit, then the m-th bidding strategy is selected, and the bidding curve corresponding to this strategy is used for the next round of market clearing.

[0148] The pricing strategy corresponds to the probability level of selecting each pricing curve from the pricing strategy set. In each iteration, the generator agent of the intelligent agent reselects a certain pricing curve from the pricing strategy set according to the selection probability using a proportional selection method.

[0149] Therefore, the generation of a new price curve is as follows: the probability level of each price curve is selected from the set of price strategies corresponding to the strategy. In each iteration, the generator agent of the intelligent agent reselects a certain price curve from the set of price strategies according to the selection probability using a proportional selection method.

[0150] S6. Determine whether the thermal power unit power system is in a game equilibrium state based on the probability coefficient. If the system is in a game equilibrium state, use the marginal electricity price of the system when the thermal power unit power system reaches game equilibrium as the predicted market price; otherwise, repeat S3.

[0151] Specifically, the method for determining whether a thermal power unit's power system is in a game equilibrium state is as follows:

[0152] If the probability coefficient of a certain bidding strategy for all thermal power units in the thermal power unit power system is greater than the convergence coefficient, then the thermal power unit power system is determined to be in a game equilibrium state.

[0153] Right now

[0154] In the formula, δ is the convergence coefficient;

[0155] At this point, the marginal electricity price of the system at which the game equilibrium is reached is used as the predicted market price.

[0156] Otherwise, it is determined that the power system of the thermal power unit is not in a game equilibrium state, and the process returns to step S3.

[0157] Specifically, one embodiment of the present invention is as follows:

[0158] S1. Obtain the next day's load information of the power system of thermal power units, the technical parameters of transmission lines, and determine the technical parameters of each thermal power unit.

[0159] (1) Load data

[0160] The electrical load of the system is shown in Table 1, and the daily load curve is attached. Figure 4 As shown. (Attached) Figure 3 In this example, nodes 1-6 represent node changes; G1-G3 represent thermal power unit numbers; and L1-L3 represent the load demand of the corresponding nodes. In this example, L1 represents 20% of the power system load demand of the thermal power units, while L2 and L4 both represent 40% of the power system load demand of the thermal power units.

[0161] Table 1. Load power at different times of the day (unit: MW)

[0162]

[0163]

[0164] (2) Technical parameters of transmission lines

[0165] Table 2 Technical parameters of transmission lines

[0166]

[0167] (3) Unit technical parameters

[0168] The test system has 3 units, and the technical parameters of the units are shown in Table 3.

[0169] Table 3 Technical parameters of the generating unit

[0170]

[0171] S2. Assuming that thermal power units bid in segments between rated active power and minimum stable technical output, define the size of the next day's bid range and the bid value of the last segment of thermal power units as decision variables, in order to establish a set of bidding strategies for thermal power units and generate the initial bid curve of thermal power units.

[0172] S21. Establish a set of pricing strategies for thermal power units:

[0173] The construction of the pricing strategy set should follow the following principles: For generator sets whose minimum stable technical output is not zero, the starting point of the first output range is the minimum stable technical output of the unit, and the ending point of the last output range is the rated active power of the unit. The starting point of each pricing range is the output ending point of the previous pricing range. The length of each pricing range should not be less than 10% of the difference between the rated active power and the minimum stable technical output of the unit. The pricing curve increases monotonically with the output.

[0174] The unit pricing strategy is as follows: Assume the unit is priced in three segments. The first segment's pricing interval is selected based on 30% of the difference between the unit's rated active power and its minimum stable technical output. The second and third segments are discretized with increments of 10%. The first and second segments are based on the unit's marginal cost. The third segment is based on both the unit's marginal cost (MP) and the price cap (Ccap), with Ccap set at $50 / MW. The pricing action set is denoted as...

[0175]

[0176] There are a total of 6 possible price combinations for thermal power units, namely (0.3, 0.1, 0.6), (0.3, 0.2, 0.5), (0.3, 0.3, 0.4), (0.3, 0.4, 0.3), (0.3, 0.5, 0.2), and (0.3, 0.6, 0.1). Therefore, N is 6; M = 2 * 6 = 12, meaning there are a total of 12 pricing strategies, as shown in Table 4.

[0177] Table 4 Unit Electricity Pricing Strategy

[0178]

[0179] S22. Select the initial price curve for the generator set:

[0180] The initial bid curves for the generating units are segmented according to a ratio of 0.3:04:0.3. All three bid ranges are based on the marginal cost of the generating units, meaning the initial bid curves for the generating units are based on the bid curve corresponding to Strategy 3 in Table 4. The initial bid curves for each generating unit are shown in the attached table. Figure 5a , Figure 5b and Figure 5c As shown.

[0181] S3. Establish a clearing model for the day-ahead electricity market, which includes a safety-constrained unit combination model and a safety-constrained economic dispatch model. The day-ahead electricity market clearing model performs day-ahead spot market clearing based on the bid curves submitted by thermal power units to obtain the operating costs of thermal power units, the winning bid volume, and the nodal price. The safety-constrained unit combination model for the day-ahead electricity market includes the operating costs and start-up costs of thermal power units.

[0182]

[0183] The operating cost of a thermal power unit can be calculated using the following formula:

[0184]

[0185] The start-up cost of a thermal power unit can be calculated using the following formula:

[0186]

[0187] The security-constrained economic dispatch model for the day-ahead electricity market includes power system balance constraints for thermal power units, load reserve constraints, thermal power unit operating boundary constraints, and power flow constraints.

[0188] S31: The power balance constraint calculation of the thermal power unit power system is as follows:

[0189] ∑ j∈J p j,t =D t (5)

[0190] S32: The load reserve constraint is calculated as follows:

[0191]

[0192] Where, ε d The value is 5%.

[0193] S33: The power flow constraints are calculated as follows:

[0194]

[0195] S34: The operating boundary constraints of the thermal power unit include the output range constraint of the thermal power unit, the ramp rate constraint, the minimum start-up time constraint, and the minimum downtime constraint.

[0196] S331: The output range constraint of the thermal power unit is calculated as follows:

[0197]

[0198] S332: The calculation of the gradeability constraint for the thermal power unit is as follows:

[0199]

[0200] S333: The minimum start-up time constraint for the thermal power unit is calculated as follows:

[0201]

[0202] S334: The minimum downtime constraint for the thermal power unit is calculated as follows:

[0203]

[0204] The calculated start-up and shutdown status v of the thermal power unit j,tAs known quantities, since the start-up and shutdown states (vj,t) of thermal power units are fixed, the day-ahead electricity market's safety-constrained economic dispatch model does not include minimum start-up time constraints and minimum shutdown time constraints for thermal power units. The winning bid amount and nodal price for the units are obtained from the safety-constrained economic dispatch model.

[0205] S335: The formula for calculating the nodal electricity price:

[0206]

[0207] Based on the results of the spot market clearing model, the daily revenue of thermal power units is calculated, and the tendency coefficients of each bidding strategy in the bidding strategy set of thermal power units are adjusted according to the daily revenue of the units. Then, the selection probability of the bidding strategy is adjusted according to the tendency coefficients, and the bidding strategy is reselected by the proportional selection method according to the selection probability to generate a new bidding curve.

[0208] S4: The daily revenue of the thermal power unit is calculated as follows:

[0209]

[0210] In the formula, R j For the daily revenue of thermal power unit J; LMP j,t Let J be the nodal electricity price of thermal power unit j at time t;

[0211] The propensity coefficients for each bidding strategy within the set of bidding strategies for thermal power units are calculated as follows;

[0212]

[0213] In the formula, q represents the initial propensity coefficient for the concentrated bidding behavior of each unit. j,m (0) takes the value 0, r takes the value 0.03, and e takes the value 0.97.

[0214] S5: Update the probability coefficients of each bidding action in the bidding action set of each unit:

[0215]

[0216] In the formula, p represents the initial probability coefficient of the bidding behavior of each unit. j,m (0) takes the value 1 / 12.

[0217] Select a new pricing curve:

[0218] The strategy corresponds to the probability level of selecting each price curve from the set of price bidding behaviors. In each iteration, the generator agent of the intelligent agent reselects a certain price curve from the set of price bidding strategies according to the selection probability in a proportional manner.

[0219] S6. Determine whether the system has reached game equilibrium based on the probability coefficients. If all thermal power units in the system have a probability value greater than the convergence coefficient for a certain strategy, then the system is considered to be in game equilibrium. In this case, the marginal electricity price of the system at the time of game equilibrium is used as the predicted market price. The game equilibrium condition can be further explained as follows:

[0220]

[0221] If the system does not reach game equilibrium, the selected new price curve is sent back to step S3 to re-execute the day-ahead spot market clearing calculation.

[0222] Multiple equilibrium results show that the equilibrium state of unit G1 is between the 7th and 12th pricing strategies. At this time, regardless of the proportion of the last pricing segment, unit G1 chooses to bid according to the upper limit of the market price. This is because, under this market condition, among the three units, unit G1 has the lowest marginal cost and the largest market share, giving it a monopoly position. It tends to raise the market price to increase additional revenue.

[0223] Unit G2 is in a balanced state between the first and sixth bidding strategies. At this time, regardless of the proportion of the last bidding segment, Unit G2 chooses to bid according to the marginal cost. This is because, under this market condition, Unit G2 has the highest marginal cost and the middle market share among the three units. In order to increase the winning bid volume, it tends to bid conservatively.

[0224] Unit G3 is in equilibrium between the 7th and 12th bidding strategies. At this point, regardless of the proportion of the last bidding segment, Unit G3 chooses to bid at the upper limit of the market price. This is because, under market conditions, Unit G3's marginal cost is in the middle among the three units and its market share is the lowest. Changes in the proportion of the third bidding segment have little impact on the unit's revenue. Moreover, as a price taker, G3 may obtain additional revenue by bidding higher prices.

[0225] Table 5 shows the percentage of each bidding range for each unit, the bid price for each range, and the probability of selection at equilibrium in a certain game. The bidding curves for each unit at system equilibrium are attached. Figure 6a , Figure 6b and Figure 6c As shown.

[0226] Table 5. Equilibrium Results (Unit: $ / MW)

[0227]

[0228] The market prices at system equilibrium are shown in Table 6.

[0229] Table 6. Market Prices at System Equilibrium (Unit: $ / MW)

[0230]

[0231] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A day-ahead spot market electricity price forecasting method based on multi-agent game equilibrium, characterized in that, It comprises the following steps: S1, obtaining next-day load information of a thermal power unit power system, transmission line technical parameters, and determining technical parameters of each thermal power unit; S2, assuming that the thermal power unit is segmented between the rated active power and the minimum stable technical output to make a bid, defining the size of the last segment of the next-day bid interval and the bid value of the thermal power unit as decision variables, to establish a thermal power unit bidding strategy set, and generate an initial bidding curve of the thermal power unit; The thermal power unit bidding strategy set in S2 is established as follows: (1) In the formula, thermal power generating units thermal power generating units the first thermal power generating units thermal power generating units thermal power generating units S3, establishing a day-ahead electricity market clearing model to obtain the operation cost of the thermal power unit, the winning electricity quantity, and the node electricity price; The day-ahead electricity market clearing model in S3 comprises a security constrained unit commitment model of the day-ahead electricity market and a security constrained economic dispatch model of the day-ahead electricity market; The security constrained unit commitment model of the day-ahead electricity market has the following calculation formula: (2) wherein is a unit j At t the operating cost of a thermal power unit for a time period; is a unit j At t the start-up cost of a thermal power unit for a time period; NT is a set of time periods; J is a set of thermal power units; The operation cost of the thermal power unit is calculated as follows: (3) In the formula, is a thermal power unit j The operation cost under the minimum technical output; is a Boolean variable, indicating whether the unit j is in operation or not; t is the on-off state of the time period, 0 for shutdown and 1 for startup; is a thermal power unit j The electricity quantity bid in the l segment; is j a thermal power unit t The actual power generation of the l segment in the piecewise pricing function; is a thermal power unit j The winning electricity quantity in the t segment; , are the maximum technical output and the minimum technical output of the thermal power unit j respectively; is the upper limit of the power generation of the l segment in the piecewise linear pricing function; is the number of segments in the piecewise linear pricing function; wherein, wherein: is the set of units j the quadratic coefficient of the operating cost; is the set of units j the linear coefficient of the operating cost; is the set of units j the constant coefficient of the operating cost; The start-up cost of the thermal power unit is calculated as follows: (4) In the formula, The starting offer of the thermal power generating unit j ; The security constrained economic dispatch model of the day-ahead electricity market comprises a thermal power unit power system power balance constraint, a load reserve constraint, a thermal power unit operation boundary constraint, and a power flow constraint; The thermal power unit power system power balance constraint is calculated as follows: (5) In the formula: is t system load demand for the period; The load reserve constraint is calculated as follows: (6) In the formula, is the load reserve rate of the thermal power unit power system; is the thermal power unit j In t the maximum possible power generation power of the period; The power flow constraint is calculated as follows: (7) wherein is a branch h In t line flow at a time period; LM is a sensitivity matrix of the system; is a net injection power at a node; is h a transmission capacity limit of a branch; The thermal power unit operation boundary constraint comprises a thermal power unit output range constraint, a ramp rate constraint, a minimum start-up time constraint, and a minimum shutdown time constraint; In S34, the thermal power unit output range constraint, the ramp rate constraint, the minimum start-up time constraint, and the minimum shutdown time constraint are calculated as follows, respectively: The thermal power unit output range constraint is calculated as follows: (8) The thermal power unit ramp rate constraint is calculated as follows: (9) In the formula, the operating up-ramp rate of the thermal power unit j ; the operating down-ramp rate of the thermal power unit j ; the start-up ramp rate of the thermal power unit j ; the shut-down ramp rate of the thermal power unit j ; The thermal power unit minimum start-up time constraint is calculated as follows: (10) In the formula, is the minimum start-up time of the thermal power unit; j is the minimum start-up time of the thermal power unit; NT is the number of periodic time periods; is the minimum start-up time of the thermal power unit; j is the minimum start-up time of the thermal power unit; ; is the minimum start-up time of the thermal power unit; j is the continuous running time at the end of the previous cycle; The thermal power unit minimum shutdown time constraint is calculated as follows: (11) In the formula, the minimum downtime of the thermal power unit; j the minimum downtime of the thermal power unit; the number of periods in which the thermal power unit j must be shut down at the beginning of the period, ; The node electricity price calculation formula is as follows: In the formula, is thermal power unit the nodal price at the moment; is the system marginal price at the moment, which is the shadow value of the load balance constraint; , respectively, the shadow value of the power flow constraint; is the sensitivity matrix of the thermal power system. S4, calculating the daily income of the thermal power unit according to the operation cost of the thermal power unit, the winning electricity quantity, and the node electricity price, and obtaining the tendency coefficient of each bidding strategy in the thermal power unit bidding strategy set; S5, calculating the probability coefficient of each bidding strategy according to the tendency coefficient, and reselecting the bidding strategy to generate a new bidding curve; S6, judging whether the thermal power unit power system is in a game equilibrium state according to the probability coefficient, if the system is in the game equilibrium state, taking the system marginal electricity price when the thermal power unit power system reaches the game equilibrium as the predicted market price; otherwise, repeating S3. 2.The day-ahead spot market electricity price forecasting method based on multi-agent game equilibrium according to claim 1, characterized in that, The daily income of the thermal power unit in S4 is calculated as follows: (12) In the formula, is the daily income of the thermal power unit; is the thermal power unit the node electricity price at the moment The tendency coefficient of each bidding strategy in the thermal power unit bidding strategy set is calculated as follows: (13) In the formula, is the first wheel agent the updated result of the propensity coefficient of the selected bid strategy; is the updated result of the propensity coefficient of the unselected strategy; is the selected bid strategy; m is a selected bid strategy; r is a forgetting factor; e is an experience parameter; is a thermal power unit j The initial inclination coefficient of each bid strategy in the first m bid strategy set.

3. The method of claim 2, wherein, The probability coefficient of each bidding strategy in S5 is calculated as follows: (14) In the formula, for thermal power generating units j The first m The first bidding strategy in the first The probability coefficient of the first round; The cooling coefficient; 4. The method of claim 3, wherein, The reselected bidding strategy in S5 adopts a proportional selection method as follows: (15) In the formula, for thermal power generating units j the first wheel the m cumulative probability.

5. The method of claim 4, wherein, The method for judging whether the thermal power unit power system is in a game equilibrium state is as follows: If the probability coefficient of all thermal power units in the thermal power unit power system existing a certain bidding strategy is greater than the convergence coefficient, it is determined that the thermal power unit power system is in a game equilibrium state. That is (16) In the formula, is the convergence coefficient; Otherwise, it is determined that the thermal power unit power system is not in a game equilibrium state.

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