A Method for Analyzing Opportunity Cost Losses of Hydropower Projects Considering Nodal Marginal Electricity Pricing Mechanisms

Abstract

This invention discloses a method for analyzing the opportunity cost loss of hydropower projects considering the nodal marginal electricity price mechanism, comprising the following steps: Step 1) Constructing a general electricity market clearing model and, based on the general electricity market clearing model, constructing nodal marginal electricity price expressions for hydropower participants; Step 2) Constructing an actual autonomous dispatch model for hydropower participants under nodal marginal electricity prices; Step 3) Solving the actual autonomous dispatch model to obtain the optimal self-dispatch strategy and maximum revenue under nodal marginal electricity prices; Step 4) Constructing and solving the expected autonomous dispatch model; Step 5) Calculating the opportunity cost loss of hydropower participants based on the difference between the optimal self-dispatch revenue and the actual revenue when complying with market clearing dispatch instructions.

Description

Technical Field

[0001] This invention relates to the field of power systems and their automation, specifically a method for analyzing the opportunity cost loss of hydropower projects that considers the nodal marginal electricity price mechanism. Background Technology

[0002] As the global energy system transitions towards affordability, low-carbon, and sustainability, electricity market reform is progressing steadily worldwide and holds significant strategic importance. A well-designed market mechanism is fundamental to promoting renewable energy integration, ensuring system reliability, and providing effective long-term investment signals. The spot market is the core of the modern electricity market architecture, determining real-time scarcity signals and guiding short-term operational choices. The effectiveness of the spot market largely depends on its price mechanism, which needs to guide market participants to adopt system-optimal behavior in a way that is both scientifically sound and economically rational.

[0003] Node marginal price (LMP) has become the mainstream pricing paradigm in organized electricity spot markets. Rooted in marginal cost theory, LMP determines the price of a node by calculating the incremental system cost incurred by adding one unit of load to that node. In traditional power systems dominated by thermal power, where the main cost structure and operating characteristics are relatively homogeneous, LMP has proven effective. However, with the rapid integration of diverse low-carbon resources such as wind, solar, and hydropower driving profound power system transformation, the cost curves, flexibility attributes, and timing constraints of market participants differ significantly. This increasingly challenges the fundamental assumptions of traditional LMP, raising critical concerns about its adaptability and incentive compatibility.

[0004] Existing research on the adaptability of the LMP can be broadly divided into two categories: The first focuses on the basic applicability of the LMP in resource systems with a high proportion of near-zero marginal costs. One view argues that the uniform energy price signal of the LMP is insufficient to accurately characterize and compensate for the differentiated flexibility services required by different resources, leading to incentive problems such as "missing money." The other view argues that the LMP framework remains effective and indispensable, and that challenges should be addressed by improving market design rather than abandoning the marginal cost principle.

[0005] The second category of research starts from the evolution of technological needs in modern power systems, and extends or modifies pricing mechanisms. This mainly includes models and pricing expressions for the coordinated optimization of energy and ancillary services, stochastic clearing frameworks for uncertainty management, and LMP extensions that internalize renewable fluctuation-related costs.

[0006] Despite a relatively rich body of research, significant gaps remain: compared to the grid connection issues of wind and solar power, the incentive attributes of LMP (Lower-Level Performance Management) for hydropower entities (especially large-scale cascade hydropower systems) have not been fully and systematically explained theoretically. This issue is both crucial and urgent in practice. Taking Yunnan Province, China, as an example, hydropower accounts for nearly half of the installed capacity, requiring market design capable of effectively absorbing and utilizing this dominant low-carbon resource. Experience in the Yunnan spot market has shown that hydropower entities experience significant incentive mismatch under LMP, manifested as substantial opportunity cost losses, thereby weakening their willingness to comply with dispatch signals. However, the root causes of opportunity cost losses remain unclear at the theoretical level, affecting the formation of targeted solutions. Summary of the Invention

[0007] The purpose of this invention is to provide a method for analyzing the opportunity cost loss of hydropower projects that considers the nodal marginal electricity price mechanism, comprising the following steps:

[0008] Step 1) Construct a general electricity market clearing model, and based on the general electricity market clearing model, construct nodal marginal electricity price expressions for hydropower participants;

[0009] Step 2) Construct a real autonomous scheduling model for hydropower participants under the nodal marginal electricity price;

[0010] Step 3) Solve the actual autonomous scheduling model to obtain the optimal autonomous scheduling strategy and maximum revenue under the node marginal electricity price;

[0011] Step 4) Construct and solve the desired autonomous scheduling model;

[0012] Step 5) Calculate the opportunity cost loss of hydropower participants based on the difference between the optimal self-scheduling revenue and the actual revenue when following market-clearing scheduling instructions.

[0013] Furthermore, the objective function of the general electricity market clearing model is as follows:

[0014] (1)

[0015] Wherein, the subscript i represents the index of the hydropower station, and its order reflects the upstream and downstream relationship: the i-th hydropower station is located upstream of the (i+1)-th station and downstream of the (i-1)-th station; v is the index of other unit types; t is the index of the settlement period. This represents the bidding parameters for hydropower station i; This indicates the coefficient for penalties related to power rationing and water supply restrictions. The bidding parameters for unit v; Let i be the output of hydropower station i during time period t; The output of unit v during time period t; Let represent the power curtailment amount of hydropower station i during time period t.

[0016] Furthermore, the constraints of the general electricity market clearing model include system constraints related to grid operation, individual operation constraints of hydropower stations, cascade coupling constraints of hydropower stations, and independent operation constraints of other types of generating units besides hydropower.

[0017] The system constraints related to power grid operation are as follows:

[0018] (2)

[0019] The individual operational constraints of the hydropower station are as follows:

[0020] (3)

[0021] The cascade coupling constraints of the hydropower station are shown below:

[0022] (4)

[0023] The independent operating constraints for other types of generating units besides hydropower are as follows:

[0024] (5)

[0025] Where n is the consumer index; This represents the demand of consumer n during time period t; The variable representing the water storage capacity of hydropower station i during time period t; This represents the reservoir water level variable of hydropower station i during time period t; The net head variable represents hydropower station i during time period t; This represents the total outflow of hydropower station i during time period t; This represents the water consumption variable for power generation of hydropower station i during time period t; This represents the overflow variable of hydropower station i during time period t; , , , , For variables or parameters in each constraint , , , The coefficient vector; , , , This represents the constant vector within each constraint; , , , For each constraint, the dual multiplier is used. Let i be the output of hydropower station i during time period t; The output of unit v during time period t; Let i be the power curtailment amount of hydropower station i during time period t; , , , , , , , for , , , , , , , The coefficient vector.

[0026] Furthermore, the expression for the water and electricity price is as follows:

[0027] (6)

[0028] In the formula, For water and electricity prices; For coefficient vectors; It is a dual multiplier.

[0029] Furthermore, the actual autonomous scheduling model The objective function is shown below:

[0030] (7)

[0031] in, It is the power generation cost coefficient of hydropower plant i; This is used to quantify the power curtailment losses borne by the hydropower plant itself.

[0032] Furthermore, the actual autonomous scheduling model The constraints are as follows:

[0033] (8)

[0034] in, The real feasible domain represents hydropower plant i.

[0035] Furthermore, in step 3), after calculating the maximum actual benefit, the marginal cost (LOC) of hydropower participant i is also calculated.

[0036] If the marginal cost (LOC) of hydropower participant i is less than or equal to a preset threshold Then proceed directly to step 4).

[0037] If the marginal cost (LOC) of hydropower participant i is greater than a preset threshold If necessary, adjust the scheduling instructions until the marginal cost (LOC) of hydropower participant i is less than or equal to a preset threshold. Then proceed to step 4).

[0038] Furthermore, under the optimal marginal price, the marginal cost LOC of hydropower participant i is... As shown below:

[0039] (9)

[0040] in, and These are the actual autonomous scheduling models. The optimal solution and maximum profit; and It is a market dispatch instruction.

[0041] Furthermore, the objective function of the desired autonomous scheduling model is as follows:

[0042] (10)

[0043] In the formula, This refers to the price of water and electricity.

[0044] Furthermore, the constraints of the expected autonomous scheduling model are as follows:

[0045] (11)

[0046] (12)

[0047] in, , It is a market dispatch instruction; hydropower plant i in the model The feasible region in the middle is denoted as Within the feasible region of hydropower plant i, the decision variables of other participants are fixed to their optimal solution for market clearing.

[0048] The technical effects of this invention are undeniable. This invention quantifies the profit difference between hydropower entities following market-cleared dispatch instructions and autonomous dispatch under price signals, assesses the opportunity cost loss of hydropower, and thus achieves quantitative verification of the incentive compatibility of hydropower entities under the nodal marginal electricity price mechanism. This provides a basis for assessing the feasibility of clearing results, early warning of dispatch compliance risks, and the formulation of compensation / assessment mechanisms. Attached Figure Description

[0049] Figure 1 This is a flowchart of the method. Detailed Implementation

[0050] 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.

[0051] Example 1:

[0052] See Figure 1 A method for analyzing the opportunity cost loss of hydropower projects that considers the nodal marginal electricity price mechanism includes the following steps:

[0053] Step 1) Construct a general electricity market clearing model, and based on the general electricity market clearing model, construct nodal marginal electricity price expressions for hydropower participants;

[0054] Step 2) Construct a real autonomous scheduling model for hydropower participants under the nodal marginal electricity price;

[0055] Step 3) Solve the actual autonomous scheduling model to obtain the optimal autonomous scheduling strategy and maximum revenue under the node marginal electricity price;

[0056] Step 4) Construct and solve the desired autonomous scheduling model;

[0057] Step 5) Calculate the opportunity cost loss of hydropower participants based on the difference (absolute value of the difference) between the optimal self-scheduling revenue and the actual revenue when complying with market clearing scheduling instructions.

[0058] Example 2:

[0059] A method for analyzing the opportunity cost loss of hydropower projects considering the nodal marginal electricity price mechanism, with the same technical content as in Example 1, further wherein the objective function of the general electricity market clearing model is as follows:

[0060] (1)

[0061] Wherein, the subscript i represents the index of the hydropower station, and its order reflects the upstream and downstream relationship: the i-th hydropower station is located upstream of the (i+1)-th station and downstream of the (i-1)-th station; v is the index of other unit types; t is the index of the settlement period. This represents the bidding parameters for hydropower station i; This indicates the coefficient for penalties related to power rationing and water supply restrictions. The bidding parameters for unit v; Let i be the output of hydropower station i during time period t; The output of unit v during time period t; Let represent the power curtailment amount of hydropower station i during time period t.

[0062] Example 3:

[0063] A method for analyzing the opportunity cost loss of hydropower considering the nodal marginal electricity price mechanism, with the same technical content as any one of Examples 1-2. Furthermore, the constraints of the general electricity market clearing model include system constraints related to grid operation, individual operation constraints of hydropower stations, cascade coupling constraints of hydropower stations, and independent operation constraints of other types of generating units besides hydropower.

[0064] The system constraints related to power grid operation are as follows:

[0065] (2)

[0066] The individual operational constraints of the hydropower station are as follows:

[0067] (3)

[0068] The cascade coupling constraints of the hydropower station are shown below:

[0069] (4)

[0070] The independent operating constraints for other types of generating units besides hydropower are as follows:

[0071] (5)

[0072] Where n is the consumer index; This represents the demand of consumer n during time period t; The variable representing the water storage capacity of hydropower station i during time period t; This represents the reservoir water level variable of hydropower station i during time period t; The net head variable represents hydropower station i during time period t; This represents the total outflow of hydropower station i during time period t; This represents the water consumption variable for power generation of hydropower station i during time period t; This represents the overflow variable of hydropower station i during time period t; , , , , For variables or parameters in each constraint , , , The coefficient vector; , , , This represents the constant vector within each constraint; , , , For each constraint, the dual multiplier is used. Let i be the output of hydropower station i during time period t; The output of unit v during time period t; Let i be the power curtailment amount of hydropower station i during time period t; , , , , , , , for , , , , , , , The coefficient vector.

[0073] Example 4:

[0074] A method for analyzing the opportunity cost loss of hydropower projects considering the nodal marginal electricity price mechanism, with the same technical content as any one of Examples 1-3, further wherein the hydropower price expression is as follows:

[0075] (6)

[0076] In the formula, For water and electricity prices; For coefficient vectors; It is a dual multiplier.

[0077] Example 5:

[0078] A method for analyzing the opportunity cost loss of hydropower projects considering the nodal marginal electricity price mechanism, with technical content the same as any one of embodiments 1-4, further including an actual autonomous scheduling model. The objective function is shown below:

[0079] (7)

[0080] in, It is the power generation cost coefficient of hydropower plant i; This is used to quantify the power curtailment losses borne by the hydropower plant itself.

[0081] Example 6:

[0082] A method for analyzing the opportunity cost loss of hydropower projects considering the nodal marginal electricity price mechanism, with technical content identical to any one of embodiments 1-5, further including an actual autonomous scheduling model. The constraints are as follows:

[0083] (8)

[0084] in, The real feasible domain represents hydropower plant i.

[0085] Example 7:

[0086] A method for analyzing the opportunity cost loss of hydropower considering the nodal marginal electricity price mechanism, with the same technical content as any one of embodiments 1-6, further, in step 3), after calculating the maximum actual benefit, the marginal cost LOC of hydropower participant i is also calculated;

[0087] If the marginal cost (LOC) of hydropower participant i is less than or equal to a preset threshold Then proceed directly to step 4).

[0088] If the marginal cost (LOC) of hydropower participant i is greater than a preset threshold If necessary, adjust the scheduling instructions until the marginal cost (LOC) of hydropower participant i is less than or equal to a preset threshold. Then proceed to step 4).

[0089] Specifically, if LOC ≤ θ, it indicates that the profit motive for deviating from the scheduling instruction is weak and the clearing result is executable. In this case, you can directly proceed to step 4 and evaluate according to the subsequent process. If LOC > θ, it indicates that the subject has a significant deviation motive. You should first take corrective measures to "reduce LOC" before proceeding to step 4. For example, on the clearing / scheduling side, you can model the entire entity (cascade hydroelectric battery) or adjust the instructions to make them closer to the subject's real feasible domain, thereby reducing opportunity costs from the root. Alternatively, you can set up compensation / assessment (deviation cost) in the settlement mechanism to ensure that the net benefit of complying with the instructions is not lower than the autonomous optimal benefit. Continue only after the LOC is recalculated and meets the threshold.

[0090] Example 8:

[0091] A method for analyzing the opportunity cost loss of hydropower projects considering the nodal marginal electricity price mechanism, with technical content identical to any one of embodiments 1-7, further defining the marginal cost (LOC) of hydropower participant i under the optimal marginal price. As shown below:

[0092] (9)

[0093] in, and These are the actual autonomous scheduling models. The optimal solution and maximum profit; and It is a market dispatch instruction.

[0094] Example 9:

[0095] A method for analyzing the opportunity cost loss of hydropower projects considering the nodal marginal electricity price mechanism, with the same technical content as any one of embodiments 1-8, further wherein the objective function of the autonomous scheduling model is as follows:

[0096] (10)

[0097] In the formula, This refers to the price of water and electricity.

[0098] Example 10:

[0099] A method for analyzing the opportunity cost loss of hydropower projects considering the nodal marginal electricity price mechanism, with the same technical content as any one of embodiments 1-9, further wherein the constraints of the autonomous scheduling model are expected to be as follows:

[0100] (11)

[0101] (12)

[0102] in, , It is a market dispatch instruction; hydropower plant i in the model The feasible region in the middle is denoted as Within the feasible region of hydropower plant i, the decision variables of other participants are fixed to their optimal solution for market clearing.

[0103] Example 11:

[0104] A method for analyzing the opportunity cost loss of hydropower considering the nodal marginal electricity price mechanism, with the same technical content as any one of Examples 1-10, further wherein when solving the actual autonomous scheduling model and the expected autonomous scheduling model, hydropower is equivalent to an independent entity and solved using MATLAB tools.

[0105] Example 12:

[0106] A method for analyzing the opportunity cost loss of hydropower projects that considers the nodal marginal electricity price mechanism is as follows:

[0107] (1) Derivation of the general market clearing model and LMP

[0108] First, the general form of market clearing model that includes hydropower is defined as follows:

[0109] 1) Objective function

[0110] The goal of the multi-phase market clearing model is to minimize the total operating cost of the system, which includes the operating costs declared by each unit and the curtailment costs of clean energy.

[0111]

[0112] Wherein, the subscript i represents the index of the hydropower station, and its order reflects the upstream and downstream relationship: the i-th hydropower station is located upstream of the (i+1)-th station and downstream of the (i-1)-th station; v is the index of other unit types; t is the index of the settlement period. This represents the bidding parameters for hydropower station i; This indicates the coefficient for penalties related to power rationing and water supply restrictions. The bidding parameters for unit v; Let i be the output of hydropower station i during time period t; The output of unit v during time period t; Let represent the power curtailment amount of hydropower station i during time period t.

[0113] 2) Constraints

[0114]

[0115]

[0116]

[0117]

[0118] Where n is the consumer index; This represents the demand of consumer n during time period t; The variable representing the water storage capacity of hydropower station i during time period t; This represents the reservoir water level variable of hydropower station i during time period t; The net head variable represents hydropower station i during time period t; This represents the total outflow of hydropower station i during time period t; This represents the water consumption variable for power generation of hydropower station i during time period t; This represents the overflow variable of hydropower station i during time period t; the vector is as follows: , , , , Equal to the variables or parameters in each constraint , , , The coefficient vector; , , , Equations are constant vectors in each constraint; , , , Equal to the dual multipliers of each constraint.

[0119] Equation (1) describes the system constraints related to power grid operation, including system power balance constraints and transmission line capacity constraints. Equation (2) describes the individual operation constraints of a single hydropower station, including water level-reservoir capacity constraints, water volume-outflow balance constraints, upper and lower water level limits, upper and lower power output limits, and hydropower coupling constraints. Equation (3) describes the cascade coupling constraints of multiple hydropower stations, including spatiotemporally coupled water volume balance constraints. Equation (4) describes the independent operation constraints of other types of generating units.

[0120] Based on the original definition of the Lowest Optimal Load Price (LMP), the price expression for hydropower is derived as follows:

[0121] This expression conforms to the current LMP mechanism. As a pricing signal for electricity services.

[0122] (2) Analytical expression of hydropower opportunity cost loss

[0123] Opportunity cost (LOC) is a core indicator for measuring whether the optimal market price (LMP) can provide effective incentives for hydropower participants. It is defined as the difference between the optimal profit a hydropower station could obtain through autonomous dispatch based on price signals and the actual profit obtained by following market dispatch instructions. LOC quantifies the motivation to deviate from dispatch and reflects the degree to which dispatch compatibility (or competitive equilibrium) is compromised.

[0124] To represent the LOC analytically, we constructed the node marginal price (LMP) signal of hydropower participant i. The actual autonomous scheduling model under (denoted as) ):

[0125] 1) Objective function (profit maximization)

[0126]

[0127] in, It is the power generation cost coefficient of hydropower plant i (consistent with the bidding parameters in market clearing, excluding strategic bidding). This is used to quantify the power curtailment losses borne by the hydropower plant itself (usually lower than the system's power curtailment penalty amount during market clearing).

[0128] 2) Constraints

[0129]

[0130] in, This represents the true feasible region of hydropower plant i, which reflects the actual operational flexibility of the hydropower plant.

[0131] Therefore, under the optimal marginal price (LMP), the marginal cost (LOC) of hydropower participant i can be analytically expressed as:

[0132]

[0133] in, and These are models The optimal solution and maximum profit; and It is also the market dispatch instruction (i.e., the optimal solution of the market clearing model). Because the dispatch instruction is always... Therefore, the feasible solution is that following the scheduling instructions will not yield a benefit greater than the optimal benefit of autonomous scheduling. .

[0134] (3) Analysis of the opportunity cost loss mechanism of hydropower under LMP

[0135] Competitive equilibrium requires that market scheduling instructions be autonomous scheduling decisions that maximize the profits of participants (i.e., This section will use duality theory and KKT conditions to analyze the incentive compatibility of nodal marginal price (LMP) for hydropower.

[0136] 4.1 Expected Autonomous Scheduling Model

[0137] Since LMP is based on the market clearing model Derived from the dual multipliers, we define the expected autonomous scheduling model of hydropower participant i (denoted as ). ):

[0138] 1) Objective function

[0139]

[0140] 2) Constraints

[0141]

[0142]

[0143] Among them, hydropower plant i in the model The feasible region in the middle is denoted as Within the feasible region of hydropower plant i, the decision variables of other participants are fixed to their optimal solutions for market clearing. Equation 11 imposes the same constraints on hydropower plant i as in Equation 3; compared to Equation 4, Equation 12 fixes the decision variables of all other entities besides hydropower plant i to their optimal solutions in the market clearing model.

[0144] 4.2 Theorem 1 and its proof

[0145] Theorem 1: If the market dispatch instruction is a market clearing model The optimal solution, and the actual autonomous scheduling model With the expected autonomous scheduling model If the optimal solutions are the same, then the nodal marginal price (LMP) mechanism can guarantee... .

[0146] prove:

[0147] Market clearing model The KKT conditions are as follows:

[0148] 1) Initial feasibility

[0149] Satisfying Equation 2-5

[0150] 2) Stability

[0151]

[0152]

[0153]

[0154]

[0155]

[0156]

[0157]

[0158]

[0159]

[0160] 3) Duality feasibility

[0161]

[0162] 4) Complementary relaxation

[0163]

[0164]

[0165]

[0166]

[0167] Desired autonomous scheduling model The KKT conditions are as follows:

[0168] 1) Initial feasibility

[0169] Satisfying equations 11 and 12

[0170] 2) Stability

[0171]

[0172]

[0173]

[0174]

[0175]

[0176]

[0177]

[0178]

[0179] 3) Duality feasibility

[0180]

[0181] 4) Complementary relaxation

[0182]

[0183]

[0184] Substitute price expression 6 into equation 28 and compare it with the market clearing model. With the expected autonomous scheduling model According to the KKT conditions, for any hydropower participant i, The optimal scheduling instruction and the corresponding dual multiplier satisfy The KKT conditions. Therefore, under price signal 6, the market clearing scheduling instruction is the expected autonomous scheduling model. The optimal solution. Furthermore, combining expression 9 for opportunity loss cost, when the actual autonomous scheduling model of hydropower participants... Rather than the expected autonomous scheduling model When there is consistency, the participant will not incur opportunity cost in following the scheduling instructions, thus proving Theorem 1.

[0185] Therefore, by the proof of Theorem 1, it can be seen that under price signal 6, the market clearing scheduling instruction is the expected autonomous scheduling model. The optimal solution. But compared with the actual autonomous scheduling model of hydropower participants. Rather than the expected autonomous scheduling model It can be observed that the objective functions and feasible regions of the two models are not necessarily completely identical. For example, in the expected autonomous dispatch model, the decision variables of upstream and downstream power plants are fixed to their market clearing outcomes, which is equivalent to using these outcomes as the boundaries defining the feasible region of operation for each participant; while the actual autonomous dispatch model may not actively accept such constraints imposed by the decisions of upstream and downstream power plants. This difference means that the optimal solutions of the two models may not be the same. In other words, under price signal 6, the dispatching instructions for market clearing are not those of the actual autonomous dispatch model. The optimal solution will result in opportunity cost.

[0186] Example 13:

[0187] The verification of a hydropower opportunity cost loss analysis method considering the nodal marginal electricity price mechanism is as follows:

[0188] (1) Data collection

[0189] To conduct opportunity cost loss analysis of hydropower under the nodal marginal electricity price mechanism, we first organized the basic data of the power grid and generating units, including nodal load and time period division, line transmission capacity and network connection relationship, price / cost and output boundary of conventional generating units, as well as the reservoir capacity-water level-output coupling, water inflow process, upstream and downstream cascade relationship and upper and lower operating limits of hydropower stations, forming an input dataset that can be used for multi-time period joint optimization.

[0190] (2) Spot market clearing and acquisition of nodal tariffs

[0191] Given system data, a multi-period market clearing calculation framework is constructed. With the goal of minimizing the total system operating cost, the framework comprehensively considers power balance, line constraints, operating boundaries of various generating units, and individual constraints and cascade coupling constraints of hydropower stations. The clearing output of generating units and the operating trajectory of reservoirs in each period are obtained. At the same time, based on the marginal information in the clearing results, LMP price sequences of each node in each period are generated as price signals and scheduling instructions released to the market.

[0192] (3) Modeling of actual self-dispatch of hydropower

[0193] After obtaining the LMP price signal, an "actual self-dispatch" decision model is established for hydropower entities: with the goal of maximizing their own profits, they optimize output and water volume within their actual feasible operating range, and allow them to adopt different benefit / loss trade-offs than system clearing (e.g., different internalization methods for water / electricity waste losses); thus, the optimal self-dispatch strategy of hydropower under the price signal and the corresponding maximum obtainable benefit are obtained.

[0194] (4) Calculation of opportunity cost

[0195] Based on the difference between the "optimal self-dispatch benefit" and the "actual benefit when complying with market-clearing dispatch instructions," the opportunity cost (LOC) loss of hydropower entities is calculated, and further statistical comparisons can be made by power station, time period, or scenario. This indicator is used to quantify the strength of hydropower's motivation to deviate from dispatch instructions, thereby evaluating the effectiveness of the LMP mechanism in incentivizing hydropower entities to "obey dispatch."

[0196] (5) Incentive compatibility mechanism

[0197] The decisions of entities other than the target hydropower entity are fixed as market clearing results, and their optimal responses should be analyzed under the same price signals. Then, the expected self-scheduling and the actual self-scheduling are compared to identify the sources of inconsistency. The focus is on characterizing the boundary effects of upstream and downstream coupling constraints under different entities / different perspectives, as well as the impact of factors such as differences in objective function parameters on incentive compatibility.

[0198] (5) Analysis method for hydropower opportunity cost loss considering nodal marginal electricity price mechanism

[0199] As mentioned earlier, the opportunity cost loss of hydropower under LMP (Low-Level Multiplication) stems from the inconsistency between the actual self-scheduling model and the expected self-scheduling model. Therefore, without considering factors such as vibration zones and water abandonment penalties, the main factor leading to opportunity cost loss is the upstream and downstream cascade coupling constraint. To analyze the impact of this coupling constraint on opportunity cost loss and verify the theoretical conclusions, two market clearing scenarios are set up:

[0200] M1: The market clearing model considers upstream and downstream tiered coupling constraints.

[0201] M2: The market clearing model ignores the upstream and downstream cascade coupling constraints, that is, it assumes that each hydropower station is only subject to its own independent constraints and is not subject to cascade coupling constraints.

[0202] Under the M1 scenario, we further assume that the actual self-dispatch model of the hydropower entity has three perspectives:

[0203] P1: When a single hydropower station is self-dispatched, it voluntarily complies with the water inflow restrictions of its upstream power station.

[0204] P2: Cascade hydropower stations with upstream and downstream coupling relationships are self-dispatched as a whole "consortium / hydropower cell", and the coupling relationship is resolved internally.

[0205] P3: When a single hydropower station is self-dispatch, it is not restricted by upstream water inflow, and its discharge is not constrained by downstream power stations.

[0206] In scenario M2, only P2 and P3 are considered.

[0207] The example uses a two-node system: node 1 is connected to hydropower station H1, thermal power unit G1, and load D1; node 2 is connected to hydropower station H2, thermal power unit G2, and load D2. The boundary parameters for market clearing are shown in Table 1.

[0208] Table 1 Boundary Parameter Settings

[0209] Table 2 Market-clearing electricity prices (node ​​prices)

[0210]

[0211] Table 3 Clearing Results and Self-Scheduling Results (Including Revenue and Opportunity Cost Losses)

[0212]

[0213] The electricity prices at each time period are obtained by solving M1 and M2, as shown in Table 2; the clearing results, self-dispatch results, profits and opportunity cost losses of H1 and H2 under each scenario are shown in Table 3.

[0214] The results show that when there is no upstream and downstream cascade coupling relationship between hydropower stations (corresponding to M2), the hydropower entity will not incur opportunity cost losses. When there are cascade coupling constraints (corresponding to M1), the hydropower entity may incur opportunity cost losses, and the magnitude depends on the perspective from which the "actual self-schedule" is characterized.

[0215] From P1's perspective: For H1, its actual self-scheduling model is not constrained by the decision variables of downstream power plants, while its expected self-scheduling model is subject to the boundary constraints implicit in the decisions of downstream power plants. Since LMP can only support competitive equilibrium when H1 follows the expected self-scheduling model, the difference in feasible regions leads to opportunity cost losses for H1. In contrast, both the actual and expected self-scheduling models of H2 consider constraints from upstream power plant H1; and since H2 has no downstream power plants, it is no longer constrained by downstream factors. Therefore, the two models are consistent, and H2 does not incur opportunity cost losses. This phenomenon is consistent with the conclusion of Theorem 1.

[0216] From P2's perspective: When two hydropower stations participate as a whole and conduct joint self-dispatch, the upstream and downstream coupling constraints are internalized into the overall operational constraints. Without considering factors such as vibration zones and water discharge penalties, the actual self-dispatch of this whole is consistent with the expected self-dispatch, thus incurring no opportunity cost loss.

[0217] From P3's perspective: Both H1 and H2 incur opportunity cost losses, for reasons similar to those of H1 from P1's perspective, namely, the actual feasible region is inconsistent with the expected feasible region.

Claims

1. A method for analyzing the opportunity cost loss of hydropower projects considering the nodal marginal electricity price mechanism, characterized in that, Includes the following steps: Step 1) Construct a general electricity market clearing model, and based on the general electricity market clearing model, construct nodal marginal electricity price expressions for hydropower participants; Step 2) Construct a real autonomous scheduling model for hydropower participants under the nodal marginal electricity price; Step 3) Solve the actual autonomous dispatch model to obtain the optimal autonomous dispatch strategy under the node marginal price, and the maximum actual revenue when following the market clearing dispatch instruction; Step 4) Construct and solve the expected autonomous scheduling model to obtain the optimal self-scheduling benefit; Step 5) Calculate the opportunity cost loss of hydropower participants based on the difference between the optimal self-scheduling revenue and the maximum actual revenue when following market-clearing scheduling instructions. If the opportunity cost loss is 0, then the optimal self-scheduling strategy is executed to achieve power clearing; If the opportunity cost loss is not zero, a warning will be issued that the scheduling strategy is not executable.

2. The method for analyzing the opportunity cost loss of hydropower projects considering nodal marginal electricity pricing mechanisms according to claim 1, characterized in that, The objective function of the general electricity market clearing model is shown below: （1） Where, the subscript i represents the index of the hydropower station, and its order reflects the upstream and downstream relationship: the i-th hydropower station is located upstream of the (i+1)-th station and downstream of the (i-1)-th station; v is the index for other unit types; t is the index for the settlement period. This represents the bidding parameters for hydropower station i; This indicates the coefficient for penalties related to power rationing and water supply restrictions. The bidding parameters for unit v; Let i be the output of hydropower station i during time period t; The output of unit v during time period t; Let represent the power curtailment amount of hydropower station i during time period t.

3. The method for analyzing the opportunity cost loss of hydropower projects considering the nodal marginal electricity price mechanism according to claim 1, characterized in that, The constraints of the general electricity market clearing model include system constraints related to grid operation, individual operation constraints of hydropower stations, cascade coupling constraints of hydropower stations, and independent operation constraints of other types of generating units besides hydropower. The system constraints related to power grid operation are as follows: （2） The individual operational constraints of the hydropower station are as follows: （3） The cascade coupling constraints of the hydropower station are shown below: （4） The independent operating constraints for other types of generating units besides hydropower are as follows: （5） Where n is the consumer index; This represents the demand of consumer n during time period t; The variable representing the water storage capacity of hydropower station i during time period t; This represents the reservoir water level variable of hydropower station i during time period t; The net head variable represents hydropower station i during time period t; This represents the total outflow of hydropower station i during time period t; This represents the water consumption variable for power generation of hydropower station i during time period t; This represents the overflow variable of hydropower station i during time period t; , , , , For variables or parameters in each constraint , , , The coefficient vector; , , , These are the constant vectors in each constraint; , , , For each constraint, the dual multiplier is used. Let i be the output of hydropower station i during time period t; The output of unit v during time period t; Let i be the power curtailment amount of hydropower station i during time period t; , , , , , , , for , , , , , , , The coefficient vector.

4. The method for analyzing the opportunity cost loss of hydropower projects considering the nodal marginal electricity price mechanism according to claim 1, characterized in that, The expression for water and electricity prices is as follows: （6） In the formula, For water and electricity prices; For coefficient vectors; It is a dual multiplier.

5. The method for analyzing the opportunity cost loss of hydropower projects considering nodal marginal electricity pricing mechanisms according to claim 1, characterized in that, Actual autonomous scheduling model The objective function is shown below: （7） in, It is the power generation cost coefficient of hydropower plant i; This is used to quantify the power curtailment losses borne by the hydropower plant itself.

6. The method for analyzing the opportunity cost loss of hydropower projects considering nodal marginal electricity pricing mechanisms according to claim 1, characterized in that, Actual autonomous scheduling model The constraints are as follows: （8） in, The real feasible domain represents hydropower plant i.

7. The method for analyzing the opportunity cost loss of hydropower projects considering nodal marginal electricity pricing mechanisms according to claim 1, characterized in that, In step 3), after calculating the maximum actual benefit, the marginal cost (LOC) of hydropower participant i is also calculated. If the marginal cost (LOC) of hydropower participant i is less than or equal to a preset threshold Then proceed directly to step 4). If the marginal cost (LOC) of hydropower participant i is greater than a preset threshold If necessary, adjust the scheduling instructions until the marginal cost (LOC) of hydropower participant i is less than or equal to a preset threshold. Then proceed to step 4).

8. The method for analyzing the opportunity cost loss of hydropower projects considering the nodal marginal electricity price mechanism according to claim 7, characterized in that, Marginal cost (LOC) of hydropower participant i As shown below: （9） in, and These are the actual autonomous scheduling models. The optimal solution and maximum profit; and It is a market dispatch instruction.

9. The method for analyzing the opportunity cost loss of hydropower projects considering nodal marginal electricity pricing mechanisms according to claim 1, characterized in that, The objective function of the desired autonomous scheduling model is shown below: （10） In the formula, This refers to the price of water and electricity.

10. The method for analyzing the cost loss of hydropower opportunities considering nodal marginal electricity pricing mechanisms according to claim 1, characterized in that, The constraints for the expected autonomous scheduling model are as follows: （11） （12） in, , It is a market dispatch instruction; hydropower plant i in the model The feasible region in the middle is denoted as Within the feasible region of hydropower plant i, the decision variables of other participants are fixed to the optimal solution for market clearing.

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