Incompletely rational power generator behavior modeling method under capacity-energy market collaborative operation

Abstract

The invention discloses an incomplete rational power generator behavior modeling method under capacity-energy market collaborative operation, and the method comprises the steps: 1), building a unit irrational quotation behavior model based on a foreground theory in behavioral economics; 2) constructing a capacity market and energy market simulation clearing model; and 3) embedding the unit irrational quotation behavior model into the capacity market and energy market simulation clearing model, and establishing a unit energy market quotation decision model considering the capacity market income influence. According to the method, a foreground theory in behavioral economics is introduced, unit irrational decision perception is embedded into a quotation decision model, a unit energy market quotation decision model considering the capacity market income influence is established, unit quotation behavior modeling considering the capacity-energy coupling influence is realized, and the unit quotation behavior modeling efficiency is improved. And the earnings of power generators in the capacity market and the energy market can be effectively improved.

Description

Technical Field

[0001] This invention relates to the field of power system and automation technology, specifically to a method for modeling the behavior of incompletely rational power generators under the coordinated operation of capacity-energy markets. Background Technology

[0002] Currently, the electricity market system is gradually extending from medium- and long-term transactions to the spot market, gradually forming a multi-tiered, multi-time-scale market structure. Due to the unique characteristics of electricity as a commodity, such as immediate balance, inability to be stored on a large scale, and security constraints, multi-market coupling and coordinated operation have become an inevitable requirement for market-oriented development. This also poses new challenges to the operation mechanism of the electricity market and its theoretical research.

[0003] The capacity market and energy market are the main sources of revenue for generating units in the electricity market. Existing research generally assumes that the bidding decisions of generating units in the capacity and energy markets are independent, and that the total market revenue of a unit is simply the sum of the revenues obtained by the unit under its independent bidding decisions in the two markets. In other words, existing research does not consider the coupling relationship between the capacity and energy markets in terms of unit bidding behavior and market revenue. However, in reality, due to the significant time scale difference between the capacity and energy markets, and the irrational behavior of market participants in actual decision-making, generating units have the motivation and sufficient time to dynamically adjust their bidding decisions in the subsequent energy market based on the capacity compensation already obtained in the preceding capacity market, thereby changing energy market revenue and total market revenue. Ignoring this coupling effect will affect the effectiveness of electricity market modeling and the revenue of power generators in the electricity market. Summary of the Invention

[0004] The purpose of this invention is to provide a method for modeling the behavior of incompletely rational power generators under the coordinated operation of capacity-energy markets, comprising the following steps:

[0005] 1) Based on prospect theory in behavioral economics, a model of irrational bidding behavior of generator units is established.

[0006] 2) Construct simulation clearing models for the capacity market and energy market.

[0007] 3) Embed the model of irrational bidding behavior of generating units into the capacity market and energy market simulation clearing model to establish a unit energy market bidding decision model that takes into account the impact of capacity market revenue.

[0008] Furthermore, the prospect theory in behavioral economics uses value functions and probability functions to model the objective benefits and objective probabilities of decision outcomes.

[0009] Furthermore, the value function is as follows:

[0010]

[0011] In the formula, v represents the decision-maker's perceived subjective benefit. R represents the objective benefit. V(·) represents the mapping from objective benefit to subjective benefit. ref This serves as a reference point for returns. α and β are both risk attitude coefficients of the value function. μ is the loss aversion coefficient.

[0012] Furthermore, the probability function is as follows:

[0013]

[0014] In the formula, w represents the subjective probability perceived by the decision-maker. p represents the objective probability. W(·) denotes the mapping from objective probability to subjective probability. R represents the objective benefit. ref This serves as a reference point for returns. θ and δ are both risk attitude coefficients of the probability function.

[0015] Furthermore, the model for the irrational bidding behavior of the generating units is as follows:

[0016]

[0017] In the formula, i is the number of the bidding unit. t is the time. s is the index of the uncertainty scenario. Let be the net energy market revenue obtained by the i-th generating unit at time t under the s-th uncertainty scenario. Let V(·) be the subjective assessment of the net income from the energy market by the i-th generating unit at time t under the s-th uncertainty scenario. V(·) represents the mapping from objective income to subjective income. Let W(·) represent the probability of occurrence of the i-th unit under the s-th uncertainty scenario at time t. W(·) represents the mapping from objective probability to subjective probability. For the i-th unit, this represents its subjective assessment of the probability of occurrence under the s-th uncertainty scenario at time t.

[0018] Furthermore, the capacity market and energy market simulation clearing model includes a two-layer optimization model.

[0019] When the capacity market and energy market simulation clearing model is a two-layer optimization model, the upper optimization model is the unit bidding decision layer. The unit aims to maximize its own interests and transmits the bidding decision to the lower optimization model.

[0020] The lower-level optimization model is the energy market clearing layer, which feeds back the market clearing results to the upper-level optimization model.

[0021] Furthermore, when the capacity market and energy market simulation clearing model is a two-level optimization model, the steps in step 3) to establish a unit energy market bidding decision model that considers the impact of capacity market revenue are as follows:

[0022] 3.1) Embed the irrational bidding behavior model of the generating units into the upper-level optimization model to establish a unit bidding decision model.

[0023] 3.2) Based on the unit pricing decision model, and considering the impact of capacity market revenue, a unit energy market pricing decision model is established.

[0024] Furthermore, the upper-level optimization model of the unit bidding decision model is shown below:

[0025]

[0026] In the formula, i is the number of the bidding unit. t is the time. s is the index of the uncertainty scenario. NS is the total number of uncertainty scenarios. Let be the expected subjective benefit of the i-th unit at time t. This refers to the bidding decision of the i-th generating unit at time t in the energy market. Let represent the allowed range for the bidding decision of the i-th unit. Let be the subjective assessment of the net revenue of the energy market by the i-th unit at time t under the s-th uncertainty scenario. For the i-th unit, this represents its subjective assessment of the probability of occurrence under the s-th uncertainty scenario at time t.

[0027] The objective function of the lower-level optimization model of the unit bidding decision model is shown below:

[0028]

[0029] In the formula, Let be the output of the i-th unit at time t corresponding to the s-th uncertainty scenario.

[0030] The constraints of the lower-level optimization model of the unit bidding decision model include power balance constraints, line power flow constraints, unit output upper and lower limit constraints, and unit ramping upper and lower limit constraints.

[0031] The power balance constraints are as follows:

[0032]

[0033] In the formula, n is the user index. D n,t,s Let t represent the load demand of the nth user in the s-th uncertain scenario at time t. This is the dual multiplier corresponding to the power balance constraint.

[0034] The power flow constraints of the line are as follows:

[0035]

[0036] In the formula, l represents the line number. Fl max F l min These represent the upper and lower limits of the transmission capacity for the l-th line, respectively. M li M is the power transfer distribution factor corresponding to the i-th unit on the l-th line. ln This is the power transfer distribution factor for the l-th line corresponding to the n-th user. This is the dual multiplier corresponding to the line power flow constraint.

[0037] The upper and lower limits of the unit's output are constrained as follows:

[0038]

[0039] In the formula, P i max P i min These are the upper and lower limits of the output of the i-th unit, respectively.

[0040] The upper and lower limits of the unit's ramp rate constraints are as follows:

[0041]

[0042] In the formula, These represent the uphill and downhill climbing capabilities of the i-th unit, respectively. Let be the output of the i-th unit under the s-th uncertainty scenario at time t-1.

[0043] Furthermore, the market clearing results output by the lower-level optimization model include net energy market revenue. probability of occurrence

[0044] The net income of the energy market probability of occurrence As shown below:

[0045]

[0046] In the formula, i is the number of the bidding unit. t is the time. s is the index of the uncertainty scenario. l is the line number. Let c be the output of the i-th unit at time t corresponding to the s-th uncertainty scenario. i Let p be the power generation cost of the i-th generating unit. s Let be the probability of the s-th uncertain scenario occurring. Let be the energy market clearing price for the i-th generating unit at time t, corresponding to the s-th uncertainty scenario. M is the dual multiplier corresponding to the power balance constraint. liLet be the power transfer distribution factor of the i-th unit corresponding to the l-th line. This is the dual multiplier corresponding to the line power flow constraint.

[0047] After the energy market clearing process, the unit's total revenue in the energy market is as follows:

[0048]

[0049] In the formula, Let be the total revenue of the i-th unit under the s-th uncertainty scenario.

[0050] Furthermore, the capacity market revenue affects the revenue reference point, which in turn affects the unit pricing decision model, thus establishing a unit energy market pricing decision model.

[0051] The relationship between the capacity market revenue and the revenue reference point is shown below:

[0052]

[0053] In the formula, i is the bidding unit number. t1 is the bidding period. tp represents the current bidding period. ρ is the reference point for the revenue of the i-th unit in the t1 bidding cycle. i,tp σ represents the percentage of total annual revenue predicted for the tp-th bidding cycle based on historical data. i To allow for flexible adjustment of coefficients. This indicates market revenue from capacity. E represents the percentage of total annual revenue earned during the t1st bidding period. i Require This indicates the expected annual revenue from electricity. This indicates the energy market revenue prior to the bidding process. (CI) i Indicates annual investment cost. (CO) i This represents the annual operating and maintenance costs. λ represents the target annual net profit margin.

[0054] The technical effects of this invention are undeniable. This invention introduces prospect theory from behavioral economics, embeds the perception of irrational decision-making by generating units into the bidding decision model, and establishes a bidding decision model for generating units in the energy market that considers the impact of capacity market revenue. This realizes the modeling of generating unit bidding behavior that considers the coupling effect of capacity and energy, which can effectively improve the revenue of power generators in the capacity market and energy market. Attached Figure Description

[0055] Figure 1 This is a flowchart of the present invention;

[0056] Figure 2 This is a schematic diagram of the value function in prospect theory.

[0057] Figure 3 This is a schematic diagram of the probability function in prospect theory;

[0058] Figure 4 This diagram illustrates the unit pricing decision-making process under different market revenue conditions. Detailed Implementation

[0059] The present invention will be further described below with reference to embodiments, but it should not be construed that the scope of the present invention is limited to the following embodiments. Various substitutions and modifications made based on ordinary technical knowledge and common practices in the art without departing from the above-described technical concept of the present invention should be included within the scope of protection of the present invention.

[0060] Example 1:

[0061] See Figures 1 to 4 A method for modeling the behavior of imperfectly rational power producers under the coordinated operation of capacity-energy markets includes the following steps:

[0062] 1) Based on prospect theory in behavioral economics, a model of irrational bidding behavior of generator units is established.

[0063] 2) Construct simulation clearing models for the capacity market and energy market.

[0064] 3) Embed the model of irrational bidding behavior of generating units into the capacity market and energy market simulation clearing model to establish a unit energy market bidding decision model that takes into account the impact of capacity market revenue.

[0065] Example 2:

[0066] The method for modeling the behavior of imperfectly rational power generators under the coordinated operation of capacity-energy markets, the main technical contents of which are described in Example 1, further utilizes the prospect theory in behavioral economics to model the objective benefits and objective probabilities of decision outcomes using value functions and probability functions.

[0067] Example 3:

[0068] A method for modeling the behavior of incompletely rational power producers under the coordinated operation of capacity-energy markets, the main technical contents of which are described in any one of Examples 1 and 2, and further, the value function is as follows:

[0069]

[0070] In the formula, v represents the decision-maker's perceived subjective benefit. R represents the objective benefit. V(·) represents the mapping from objective benefit to subjective benefit. ref This serves as a reference point for returns. α and β are both risk attitude coefficients of the value function. μ is the loss aversion coefficient.

[0071] Example 4:

[0072] A method for modeling the behavior of incompletely rational power producers under the coordinated operation of capacity-energy markets, the main technical contents of which are described in any one of Examples 1 to 3, and further, the probability function is as follows:

[0073]

[0074] In the formula, w represents the subjective probability perceived by the decision-maker. p represents the objective probability. W(·) denotes the mapping from objective probability to subjective probability. R represents the objective benefit. ref This serves as a reference point for returns. θ and δ are both risk attitude coefficients of the probability function.

[0075] Example 5:

[0076] A method for modeling the behavior of incompletely irrational power generators under the coordinated operation of the capacity-energy market, the main technical contents of which are described in any one of Examples 1 to 4, and further, the model of the irrational bidding behavior of the generating units is as follows:

[0077]

[0078] In the formula, i is the number of the bidding unit. t is the time. s is the index of the uncertainty scenario. Let be the net energy market revenue obtained by the i-th generating unit at time t under the s-th uncertainty scenario. Let V(·) be the subjective assessment of the net income from the energy market by the i-th generating unit at time t under the s-th uncertainty scenario. V(·) represents the mapping from objective income to subjective income. Let W(·) represent the probability of occurrence of the i-th unit under the s-th uncertainty scenario at time t. W(·) represents the mapping from objective probability to subjective probability. For the i-th unit, this represents its subjective assessment of the probability of occurrence under the s-th uncertainty scenario at time t.

[0079] Example 6:

[0080] A method for modeling the behavior of incompletely rational power generators under the coordinated operation of capacity and energy markets, the main technical contents of which are described in any one of Examples 1 to 5. Furthermore, the capacity market and energy market simulation clearing model includes a two-layer optimization model.

[0081] When the capacity market and energy market simulation clearing model is a two-layer optimization model, the upper optimization model is the unit bidding decision layer. The unit aims to maximize its own interests and transmits the bidding decision to the lower optimization model.

[0082] The lower-level optimization model is the energy market clearing layer, which feeds back the market clearing results to the upper-level optimization model.

[0083] The energy market is a spot market measured in hourly units. To simplify computational complexity, several typical days within the year can be selected for energy market operation simulation.

[0084] The objective function of the energy market clearing model is to minimize the total power generation cost of the system, as shown below.

[0085]

[0086] In the formula: i, y, j, t are the unit, year, operating day, and time period within a certain operating day, respectively; I E_market,y J represents the set of generating units participating in the energy market transaction in year y; J represents the set of operating days within a year; and T represents the set of clearing periods within the operating days. and These represent the bid and clearing volume of unit i in the energy market on the j-th operating day and during the t-th period of year y;

[0087] The constraints of the energy market clearing model are as follows:

[0088] a) Power balance constraints

[0089] The power balance constraints are shown below.

[0090]

[0091] In the formula: D i,y,j,t The system load for the j-th operating day of year y, during the t-th time period; This is the dual multiplier corresponding to the power balance constraint.

[0092] b) Line power flow constraints

[0093] The power flow constraints for the line are shown below.

[0094]

[0095] In the formula: l is the line number; F l max and F l min These are the upper and lower limits of transmission capacity, respectively; M li is the power transfer distribution factor of the node where unit i is located; and This is the dual multiplier corresponding to the line power flow constraint.

[0096] c) Unit output upper and lower limit constraints

[0097] The upper and lower limits of the unit's output are shown below.

[0098]

[0099] In the formula: Pi max and P i min These are the upper and lower limits of the output of unit i, respectively.

[0100] d) Unit ramping limits and upper and lower limits constraints

[0101] The unit's output is limited by its climbing ability, as shown below.

[0102]

[0103] In the formula: and These refer to the uphill and downhill climbing capabilities of unit i, respectively.

[0104] After the energy market clearing, the unit receives energy revenue based on the energy market clearing price. The total annual revenue of unit i in the energy market is calculated as follows:

[0105]

[0106] In the formula: Let i be the total revenue of unit i in the energy market in year y; Let be the energy market clearing price for unit i in the energy market during the time period t on the j-th operating day in year y.

[0107] Example 7:

[0108] A method for modeling the behavior of incompletely rational power generators under the coordinated operation of capacity and energy markets, the main technical contents of which are described in any one of Examples 1 to 6. Furthermore, when the capacity market and energy market simulation clearing model is a two-level optimization model, the steps in step 3) for establishing a unit energy market bidding decision model that considers the impact of capacity market revenue are as follows:

[0109] 3.1) Embed the irrational bidding behavior model of the generating units into the upper-level optimization model to establish a unit bidding decision model.

[0110] 3.2) Based on the unit pricing decision model, and considering the impact of capacity market revenue, a unit energy market pricing decision model is established.

[0111] Example 8:

[0112] A method for modeling the behavior of incompletely rational power generators under the coordinated operation of capacity-energy market, the main technical contents of which are described in any one of Examples 1 to 7. Furthermore, the upper-level optimization model of the unit bidding decision model is shown below:

[0113]

[0114] In the formula, i is the number of the bidding unit. t is the time. s is the index of the uncertainty scenario. NS is the total number of uncertainty scenarios. Let be the expected subjective benefit of the i-th unit at time t. This refers to the bidding decision of the i-th generating unit at time t in the energy market. Let represent the allowed range for the bidding decision of the i-th unit. Let be the subjective assessment of the net revenue of the energy market by the i-th unit at time t under the s-th uncertainty scenario. For the i-th unit, this represents its subjective assessment of the probability of occurrence under the s-th uncertainty scenario at time t.

[0115] The objective function of the lower-level optimization model of the unit bidding decision model is shown below:

[0116]

[0117] In the formula, Let be the output of the i-th unit at time t corresponding to the s-th uncertainty scenario.

[0118] The constraints of the lower-level optimization model of the unit bidding decision model include power balance constraints, line power flow constraints, unit output upper and lower limit constraints, and unit ramping upper and lower limit constraints.

[0119] The power balance constraints are as follows:

[0120]

[0121] In the formula, n is the user index. D n,t,s Let t represent the load demand of the nth user in the s-th uncertain scenario at time t. This is the dual multiplier corresponding to the power balance constraint.

[0122] The power flow constraints of the line are as follows:

[0123]

[0124] In the formula, l represents the line number. F l max F l min These represent the upper and lower limits of the transmission capacity for the l-th line, respectively. M li M is the power transfer distribution factor corresponding to the i-th unit on the l-th line. ln This is the power transfer distribution factor for the l-th line corresponding to the n-th user. This is the dual multiplier corresponding to the line power flow constraint.

[0125] The upper and lower limits of the unit's output are constrained as follows:

[0126]

[0127] In the formula, P i max P i min These are the upper and lower limits of the output of the i-th unit, respectively.

[0128] The upper and lower limits of the unit's ramp rate constraints are as follows:

[0129]

[0130] In the formula, These represent the uphill and downhill climbing capabilities of the i-th unit, respectively. Let be the output of the i-th unit under the s-th uncertainty scenario at time t-1.

[0131] Example 9:

[0132] A method for modeling the behavior of incompletely rational power generators under the coordinated operation of capacity and energy markets, the main technical contents of which are described in any one of Examples 1 to 8. Furthermore, the market clearing result output by the lower-level optimization model includes net energy market revenue. probability of occurrence

[0133] The net income of the energy market probability of occurrence As shown below:

[0134]

[0135] In the formula, i is the number of the bidding unit. t is the time. s is the index of the uncertainty scenario. l is the line number. Let c be the output of the i-th unit at time t corresponding to the s-th uncertainty scenario. i Let p be the power generation cost of the i-th generating unit. s Let be the probability of the s-th uncertain scenario occurring. Let be the energy market clearing price for the i-th generating unit at time t, corresponding to the s-th uncertainty scenario. M is the dual multiplier corresponding to the power balance constraint. li Let be the power transfer distribution factor of the i-th unit corresponding to the l-th line. This is the dual multiplier corresponding to the line power flow constraint.

[0136] After the energy market clearing process, the unit's total revenue in the energy market is as follows:

[0137]

[0138] In the formula, Let be the total revenue of the i-th unit under the s-th uncertainty scenario.

[0139] Example 10:

[0140] A method for modeling the behavior of imperfectly rational power generators under the coordinated operation of capacity and energy markets, the main technical contents of which are described in any one of Examples 1 to 9. Furthermore, the capacity market revenue affects the revenue reference point, thereby affecting the unit pricing decision model, and a unit energy market pricing decision model is established.

[0141] The relationship between the capacity market revenue and the revenue reference point is shown below:

[0142]

[0143] In the formula, i is the bidding unit number. t1 is the bidding period. tp represents the current bidding period. ρ is the reference point for the revenue of the i-th unit in the t1 bidding cycle. i,tp σ represents the percentage of total annual revenue predicted for the tp-th bidding cycle based on historical data. i To allow for flexible adjustment of coefficients. This indicates market revenue from capacity. E represents the percentage of total annual revenue earned during the t1st bidding period. i Require This indicates the expected annual revenue from electricity. This indicates the energy market revenue prior to the bidding process. (CI) i Indicates annual investment cost. (CO) i This represents the annual operating and maintenance costs. λ represents the target annual net profit margin.

[0144] Example 11:

[0145] See Figures 1 to 4 A modeling method for the behavior of incompletely rational power producers under the coordinated operation of capacity-energy markets, the main technical contents of which include:

[0146] First, a model of irrational bidding behavior by generating units is established based on prospect theory in behavioral economics. Then, this model is embedded into a capacity market and energy market simulation clearing model. Further, a unit energy market bidding decision model considering the impact of capacity market returns is established. Finally, simulations verify the rationality of considering irrational bidding behavior by generating units and the effectiveness of improving market returns. The specific steps are as follows:

[0147] (1) Modeling of Irrational Bidding Behavior of Units Based on Prospect Theory

[0148] Prospect theory explains the imperfectly rational behavior of decision-makers in reality. Experimental observations have revealed that decision-makers' actual decisions are influenced by their subjective perception of the outcomes. Decision-makers have a subjective expectation of the benefits of their decision's outcome, defined as a reference point in prospect theory. Decision-makers compare the decision outcome with this pre-set reference point; if the outcome is greater than the reference point, they experience a subjective feeling of "gain," and vice versa. During the decision-making process, decision-makers develop subjective perceptions in two aspects: the benefits of the decision and the probability of that benefit occurring. To address this, prospect theory proposes value functions and probability functions to model the subjective perception of the objective benefits and probabilities of a decision.

[0149] 1) Value Function

[0150] The value function V(·) characterizes the mapping relationship from objective gains to subjective gains, such as... Figure 2 As shown, the corresponding function form is shown in equation (1).

[0151]

[0152] In the formula: v represents the subjective benefit perceived by the decision-maker; R represents the objective benefit; R ref α is the reference point; α and β correspond to the risk attitude coefficients of the value function under the conditions of "profit" and "loss", respectively; μ is the loss aversion coefficient.

[0153] The value function has the following three characteristics:

[0154] 1. Reference point dependence

[0155] Decision-makers' subjective assessment of benefits depends on the outcome (i.e., R) and a pre-set reference point (i.e., R0). ref The reference point is the distance to the outcome, not the result itself. The reference point refers to the decision-maker's expected return based on current financial conditions and other factors. The selection of the reference point influences the decision-maker's subjective perception.

[0156] 2. Loss aversion

[0157] Decision-makers have different sensitivities to gains and losses. Decision-makers feel "losses" more strongly than "gains". Therefore, μ in equation (1) is taken as a constant greater than 1.

[0158] 3. Decreased sensitivity

[0159] Decision-makers' sensitivity to changes in returns decreases as the distance between the objective return and the reference point increases, corresponding to the range of α and β in equation (1) being (0,1). Conversely, sensitivity increases as the distance between the objective return and the reference point decreases. This reflects decision-makers' different risk attitudes towards gains and losses. In the case of "gains," decision-makers exhibit risk aversion, corresponding to a concave value function, while in the case of "losses," they exhibit risk preference, corresponding to a convex value function.

[0160] 2) Probability function

[0161] The probability function W(·) represents the mapping relationship from objective probability to subjective probability, and its functional form is shown in equation (2).

[0162]

[0163] In the formula: w is the subjective probability perceived by the decision-maker; p is the objective probability; θ and δ correspond to the risk attitude coefficients of the probability function under the conditions of "profit" and "loss", respectively.

[0164] probability functions such as Figure 3 As shown, the probability function reflects the decision-maker's biased subjective judgment of probability. Decision-makers tend to overestimate low-probability events and underestimate high-probability events. Furthermore, the choice of reference point can influence the decision-maker's subjective perception of "gain" or "loss," thus affecting their subjective judgment of probability.

[0165] When prospect theory is applied to study the bidding behavior of generator units in the energy market, the subjective assessment of the unit's profit and probability under a certain bidding decision is shown in Equations (3) and (4), respectively.

[0166]

[0167] In the formula: i is the bidding unit number; t is the bidding decision time; s is the s-th uncertainty scenario considered; The net energy market revenue obtained by unit i at time t under the uncertainty scenario s is defined as the objective revenue. For the unit The subjective assessment is defined as subjective benefit; Let the probability of occurrence of unit i under the uncertainty scenario s at time t be defined as the objective probability. For the unit The subjective assessment is defined as subjective probability.

[0168] (2) Unit Energy Market Bidding Decision Model Considering the Impact of Capacity Market Revenue

[0169] 1) A unit bidding decision model based on prospect theory

[0170] A two-layer optimization model is employed to determine the optimal bidding decision for generating units in the energy market. The upper layer is the unit bidding decision layer, and the lower layer is the energy market clearing layer. In the unit bidding decision layer, generating units aim to maximize their own interests and transmit their bidding strategies to the lower-level energy market. After the lower-level energy market clears, the market clearing results are fed back to the upper-level unit bidding decision layer. Through multiple iterations and optimization, the final bidding decision for the generating units in the energy market is determined.

[0171] The model for the upper-level unit bidding decision layer is shown in equations (5)-(6). In traditional bidding decision models, considering the uncertainties in the power system due to load, intermittent new energy sources, etc., the objective function is usually to maximize the expected value of the unit's revenue. Since the unit actually has a subjective perception of the decision-making revenue and will make decisions based on this subjective perception, the objective function in the bidding decision model proposed in this patent is to maximize the expected value of the unit's subjective revenue, corresponding to equation (5). Equation (6) is the constraint on the unit's bidding range. Assuming that the unit's power generation cost is a linear function, the corresponding bid is a constant value.

[0172]

[0173] In the formula: NS represents the total number of uncertain scenarios; The expected subjective benefit of unit i at time t is obtained by calculating the sum of the products of all possible subjective benefit outcomes and their corresponding subjective probabilities. For unit i's bidding decision in the energy market at time t; This represents the allowable range for the bidding decision of unit i.

[0174] The energy market is a day-ahead spot market, and the model of the lower-level energy market clearing layer adopts the economic dispatch model of the day-ahead spot market, as shown in equations (7)-(11).

[0175]

[0176] In the formula: D represents the output of unit i at time t under the uncertainty scenario s; n,t,s Let M be the load demand of user n at time t under the uncertain scenario s; li and M ln These are the power transfer distribution factors for the nodes corresponding to unit i and user n, and line l, respectively; F l max and F l min These represent the upper and lower limits of the transmission capacity of line l, respectively; P i max and P i minThese are the upper and lower limits of the output of unit i, respectively; and These represent the ramp-up and ramp-down limits for unit i, respectively; Equation (7) is the objective function, representing minimizing the total power generation cost of the system; Equation (8) is the system power balance constraint. Equation (9) represents the dual multiplier corresponding to the system power balance constraint; Equation (9) represents the line power flow constraint. and Equation (10) represents the dual multiplier corresponding to the power flow constraint of the line; Equation (11) represents the upper and lower limits of the unit output constraint; Equation (12) represents the upper and lower limits of the unit ramp constraint.

[0177] The corresponding energy market clearing price can be obtained. As shown in equation (12).

[0178]

[0179] Corresponding objective benefits The net income from the energy market is shown in equation (13).

[0180]

[0181] In the formula: c i,t Let be the power generation cost of unit i.

[0182] Objective probability That is, the probability p of the occurrence of the corresponding uncertain scenario s. s :

[0183]

[0184] 2) Capacity Market Revenue

[0185] Suppose that unit i makes a bidding decision at a certain bidding time t in the energy market, and has already earned revenue in the capacity market before that. Then capacity market revenue and reference points The relationship is as follows:

[0186]

[0187] In the formula: tp represents the time index; ρ i,tp ρ represents the percentage of revenue for each bidding period relative to the total annual revenue, predicted based on historical data. For example, assuming that the revenue for each bidding period (e.g., hour) is equal, then ρ i,tp =1 / 8760; the first term ρ in equation (15) i,t E i Require This represents the expected return for the current bidding period at the beginning of the year in the energy market; the second term in equation (15) This represents the expected additional revenue for the current bidding period based on actual revenue prior to the current bidding decision period; σ i The coefficients are designed for flexibility and reflect the unit's willingness to adjust its pricing decisions based on prior market revenue.

[0188] Example 12:

[0189] A modeling method for the behavior of incompletely rational power generators under the coordinated operation of capacity-energy markets, the main technical content of which is described in Example 11. Furthermore, the modeling method for the coordinated operation of capacity-energy markets based on prospect theory mainly consists of the following two steps:

[0190] (1) A model of irrational bidding behavior of generator units was established based on prospect theory in behavioral economics;

[0191] (2) Embed the unit bidding behavior model into the capacity market and energy market simulation clearing model to establish a unit energy market bidding decision model that takes into account the impact of capacity market revenue.

[0192] I. Example Explanation

[0193] Table 1 Parameters of various generator sets

[0194]

[0195] Table 2 Uncertainty Scenarios for New Energy Output

[0196]

[0197] The simulation example is based on actual power grid data from a certain region. The system includes three types of generating units: coal-fired (COAL), open-cycle gas turbine (OCGT), and combined-cycle gas turbine (CCGT). Parameters for each type of unit are shown in Table 1. The example considers six typical days, each containing hourly load and renewable energy output data. Renewable energy output includes seven uncertain scenarios, represented as discrete sequences with corresponding probabilities of occurrence, as shown in Table 2. It is assumed that a certain generating unit (coal-fired unit #18) makes a strategic bid at a certain bidding time. The unit's bid in the energy market ranges from [$35, $150] with a step size of $0.05. Its revenue in the capacity market varies from 0% to 120% of the unit's annual fixed cost, with a step size of 5%, reflecting different capacity compensation ratios for generating units in the capacity market.

[0198] II. Determining Unit Energy Market Bidding Behavior

[0199] To verify that the unit bidding behavior modeling method proposed in this embodiment can take into account the capacity-energy coupling effect, the bidding decision model based on Prospect Theory (PT) proposed in this embodiment is compared with the current traditional bidding decision model. Figure 4 This demonstrates the energy market bid situation of coal-fired unit #18 in the system at a certain bidding moment, influenced by capacity market revenue. Figure 4 As can be seen, when using the PT-based pricing decision model proposed in this embodiment, as capacity market revenue increases, the unit price begins to decline when the capacity market revenue reaches 80% of the annual fixed cost, and then remains unchanged after the capacity market revenue reaches 95% of the annual fixed cost. Throughout the entire range of capacity market revenue changes, the unit price decreased from $57.65 / MWh to $44.5 / MWh, a total decrease of 22.8%.

[0200] III. Determining the Energy Market Revenue of the Unit

[0201] As the unit's bid changes, the energy market revenue obtained by coal-fired unit #18 also changes accordingly. The results show that as it obtains more capacity revenue in the capacity market, the unit's aggressive bidding behavior weakens, and it tends to adopt a lowering bid strategy. When using the traditional bidding decision model, the unit's bidding decision remains unchanged, failing to reflect the unit's behavior of adjusting its energy market bidding decision in response to capacity market revenue. This is because the traditional bidding decision model does not model the impact of capacity market revenue.

[0202] In summary, this embodiment introduces prospect theory from behavioral economics, embedding the perception of irrational decision-making by generating units into the bidding decision model. It establishes a unit energy market bidding decision model that considers the impact of capacity market revenue, thus achieving modeling of unit bidding behavior that takes into account the coupling effect of capacity and energy. Simulation analysis verifies that this method can effectively improve the revenue of power generators in both the capacity and energy markets, providing technical support for electricity market simulation modeling.

Claims

1. A method for modeling the behavior of incompletely rational power generators under the coordinated operation of capacity-energy markets, characterized by: Includes the following steps: 1) Based on prospect theory in behavioral economics, establish a model of irrational bidding behavior of generating units; 2) Construct simulation clearing models for the capacity market and energy market; 3) Embed the model of irrational bidding behavior of generating units into the capacity market and energy market simulation clearing model to establish a unit energy market bidding decision model that takes into account the impact of capacity market revenue.

2. The method for modeling the behavior of incompletely rational power generators under the capacity-energy market collaborative operation as described in claim 1, characterized in that, The prospect theory in behavioral economics uses value functions and probability functions to model the objective benefits and objective probabilities of decision outcomes.

3. The method for modeling the behavior of incompletely rational power generators under the capacity-energy market collaborative operation as described in claim 2, characterized in that, The value function is as follows: In the formula, v represents the subjective benefit perceived by the decision-maker; R represents the objective benefit; V(·) represents the mapping from objective benefit to subjective benefit; R ref α is the reference point for returns; α and β are both risk attitude coefficients of the value function; μ is the loss aversion coefficient.

4. The method for modeling the behavior of incompletely rational power generators under the capacity-energy market collaborative operation as described in claim 2, characterized in that, The probability function is as follows: In the formula, w is the subjective probability perceived by the decision-maker; p is the objective probability; W(·) represents the mapping from objective probability to subjective probability; R is the objective benefit; R ref θ and δ are risk attitude coefficients for probability functions, serving as a reference point for returns.

5. The method for modeling the behavior of incompletely rational power generators under the capacity-energy market collaborative operation as described in claim 1, characterized in that, The model of the unit's irrational bidding behavior is shown below: In the formula, i is the number of the bidding unit; t is the time; and s is the index of the uncertainty scenario. Let be the net energy market revenue obtained by the i-th generating unit at time t under the s-th uncertainty scenario; Let V(·) be the subjective assessment of the net income of the energy market by the i-th unit at time t under the s-th uncertainty scenario; V(·) represents the mapping from objective income to subjective income. Let W(·) represent the probability of occurrence of the i-th unit under the s-th uncertainty scenario at time t; W(·) represents the mapping from objective probability to subjective probability. For the i-th unit, this represents its subjective assessment of the probability of occurrence under the s-th uncertainty scenario at time t.

6. The method for modeling the behavior of incompletely rational power generators under the capacity-energy market collaborative operation as described in claim 1, characterized in that, The capacity market and energy market simulation clearing model includes a two-level optimization model; When the capacity market and energy market simulation clearing model is a two-layer optimization model, the upper optimization model is the unit bidding decision layer. The unit aims to maximize its own interests and transmits the bidding decision to the lower optimization model. The lower-level optimization model is the energy market clearing layer, which feeds back the market clearing results to the upper-level optimization model.

7. The method for modeling the behavior of incompletely rational power generators under the capacity-energy market collaborative operation as described in claim 6, characterized in that, When the capacity market and energy market simulation clearing model is a two-level optimization model, the steps in step 3) to establish a unit energy market bidding decision model that considers the impact of capacity market revenue are as follows: 3.1) Embed the irrational bidding behavior model of the generating units into the upper-level optimization model to establish a unit bidding decision model; 3.2) Based on the unit pricing decision model, and considering the impact of capacity market revenue, a unit energy market pricing decision model is established.

8. The method for modeling the behavior of incompletely rational power generators under the capacity-energy market collaborative operation as described in claim 7, characterized in that, The upper-level optimization model of the unit bidding decision model is shown below: In the formula, i is the number of the bidding unit; t is the time; s is the index of the uncertainty scenario; NS is the total number of uncertainty scenarios; Let be the expected subjective benefit of the i-th unit at time t; For the i-th generating unit's bidding decision in the energy market at time t; This represents the allowable range for the bidding decision of the i-th generating unit. For the i-th generating unit, at time t, it is the subjective assessment of the net revenue of the energy market under the s-th uncertainty scenario; For the i-th unit, at time t, it is the subjective assessment of the probability of occurrence of the s-th uncertainty scenario; The objective function of the lower-level optimization model of the unit bidding decision model is shown below: In the formula, Let i be the output of the i-th unit at time t corresponding to the s-th uncertainty scenario; The constraints of the lower-level optimization model of the unit bidding decision model include power balance constraints, line power flow constraints, unit output upper and lower limit constraints, and unit ramping upper and lower limit constraints. The power balance constraints are as follows: In the formula, n is the user index; D n,t,s Let the load demand of the nth user at time t correspond to the sth uncertain scenario; The dual multiplier corresponding to the power balance constraint; The power flow constraints of the line are as follows: In the formula, l is the line number; These are the upper and lower limits of the transmission capacity for the l-th line, respectively; M li M is the power transfer distribution factor corresponding to the i-th unit on the l-th line; ln The power transfer distribution factor for the l-th line corresponding to the n-th user; This is the dual multiplier corresponding to the line power flow constraint; The upper and lower limits of the unit's output are constrained as follows: In the formula, These are the upper and lower limits of the output of the i-th unit, respectively; The upper and lower limits of the unit's ramp rate constraints are as follows: In the formula, These represent the uphill and downhill climbing capabilities of the i-th unit, respectively. Let be the output of the i-th unit under the s-th uncertainty scenario at time t-1.

9. The method for modeling the behavior of incompletely rational power generators under the capacity-energy market collaborative operation as described in claim 8, characterized in that, The market clearing results output by the lower-level optimization model include net energy market revenue. probability of occurrence The net income of the energy market probability of occurrence As shown below: In the formula, i is the number of the bidding unit; t is the time; s is the index of the uncertainty scenario; l is the line number. Let c be the output of the i-th unit at time t corresponding to the s-th uncertainty scenario; i p represents the power generation cost of the i-th generating unit; s Let be the probability of the s-th uncertain scenario occurring; Let be the energy market clearing price for the i-th generating unit at time t, corresponding to the s-th uncertainty scenario; M is the dual multiplier corresponding to the power balance constraint; li Let be the power transfer distribution factor corresponding to the ith line for the ith unit; This is the dual multiplier corresponding to the line power flow constraint; After the energy market clearing process, the unit's total revenue in the energy market is as follows: In the formula, Let be the total revenue of the i-th unit under the s-th uncertainty scenario.

10. The method for modeling the behavior of incompletely rational power generators under the capacity-energy market collaborative operation according to claim 7, characterized in that, The capacity market revenue affects the revenue reference point, which in turn affects the unit pricing decision model, thus establishing the unit energy market pricing decision model; The relationship between the capacity market revenue and the revenue reference point is shown below: In the formula, i is the number of the bidding unit; t1 is the bidding period; tp represents the current bidding period; ρ is the reference point for the revenue of the i-th unit in the t1 bidding cycle; i,tp σ represents the percentage of total annual revenue predicted for the tp-th bidding cycle based on historical data; i To allow for flexible adjustment of coefficients; Indicates market revenue from capacity; This represents the percentage of total annual revenue earned during the t1st bidding period. This indicates the expected annual revenue from electricity. Indicates the energy market revenue before the auction; CI i Indicates annual investment cost; CO i λ represents the annual operating and maintenance costs; λ represents the target annual net profit margin.

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