A double-layer deduction method for spot quotation strategy of thermal power generating unit group

Abstract

The present application relates to the technical field of power spot market transaction and thermal power unit operation optimization, in particular to a double-layer deduction method for thermal power unit group spot bidding strategy, which adopts a double-layer optimization model for solution, the upper layer is a similar layer of price unit value, the target is to minimize the weighted relative deviation of market simulation price and historical real price, and the upper and lower limits of segmented bidding and bidding quantity are set according to the capacity scale of the unit to set differentiated constraints; the lower layer is a market clearing layer, the target is to minimize the total system cost, and the system power balance, unit operation, new energy consumption, power transmission safety and other system operation and market clearing full-dimensional constraints are met, the optimal bidding strategy combination is obtained through the iterative interaction of bidding and price signals, the method adopts DE-PSO hybrid algorithm for solution, can accurately fit the real market price law, provides scientific bidding decision basis for power suppliers, and is suitable for different market operation scenes such as heating period and non-heating period, etc.

Description

Technical Field

[0001] This invention relates to the field of electricity spot market trading and thermal power unit operation optimization technology, specifically a two-layer deduction method for spot pricing strategies of thermal power unit groups. Background Technology

[0002] With the continuous advancement of my country's power market reform, the spot market for electricity has become the core carrier for the optimal allocation of power resources. As the main power source and core regulator of the power system, the pricing strategies of thermal power units in the spot market directly affect not only the market revenue of power generators themselves, but also are closely related to the safe and economical operation of the power system and the stable formation of market electricity prices. During the operation of the electricity spot market, the overall pricing behavior of thermal power unit groups is the core driving factor for market price formation. Thermal power units with different capacities, risk appetites, and market influence exhibit significantly differentiated pricing behaviors. At the same time, the market clearing process needs to comprehensively consider physical operational constraints such as unit generation costs, start-up and shutdown characteristics, and ramp-up capabilities, as well as multiple market and grid operation requirements such as system power balance, reserve demand, renewable energy consumption, transmission safety, and market boundary conditions. This makes the systematic deduction of the pricing strategies of thermal power unit groups a core technical challenge for market participants in market competition and for market operators in analyzing market behavior.

[0003] Current technologies for pricing strategies in the spot market for thermal power units mostly focus on maximizing the revenue of a single unit, making it difficult to systematically and holistically extrapolate the overall pricing behavior of the entire thermal power unit group. Some solutions employing multi-layer optimization models fail to fully consider the differences in market power and risk appetite characteristics of units with different capacities to set differentiated pricing and quantity constraints, thus failing to accurately reproduce the pricing behavior patterns of different types of units in the real market. Furthermore, existing market clearing simulation models do not fully cover the physical operational constraints and market rule constraints of the day-ahead spot market, resulting in a significant deviation between the simulated clearing price and the historical real price. This makes it difficult to provide power generators with pricing decision-making basis that aligns with market realities, and also hinders accurate fitting and in-depth analysis of the market price formation mechanism. Therefore, in light of the above situation, there is an urgent need to develop a two-layer extrapolation method for spot pricing strategies of thermal power unit groups to overcome the shortcomings in current practical applications. Summary of the Invention

[0004] The purpose of this invention is to provide a two-layer deduction method for spot pricing strategies of thermal power unit groups, so as to solve the problems mentioned in the background art.

[0005] To achieve the above objectives, the present invention provides the following technical solution: A two-layer derivation method for spot pricing strategies of thermal power unit groups includes the following steps: S1. Construct a two-layer optimization model for solving the spot price strategy of thermal power unit groups. The two-layer optimization model includes an upper layer of similar per-unit electricity prices and a lower layer of market clearing. S2. Through the upper-level electricity price per unit value similarity layer, with the optimization objective of minimizing the weighted relative deviation between the market simulation electricity price and the historical real electricity price, differentiated segmented pricing and upper and lower limits of the quotation are set according to the capacity scale of thermal power units, and the pricing strategy of thermal power unit group is output. S3. Through the lower market clearing layer, with the pricing strategy output by the upper layer as input and minimizing the total system cost as the optimization objective, market clearing simulation is performed under the full-dimensional constraints of power system operation and electricity spot market clearing, and the simulated market electricity price is output. S4. Feed back the market simulation electricity price output from the lower layer to the upper layer of electricity price per unit value similarity layer. Through iterative interaction of the bidding signals and electricity price signals of the two-layer model, the optimal bidding strategy combination of the thermal power unit group is obtained until convergence.

[0006] As a further aspect of the present invention: in step S2, the weighted relative deviation is a weighted relative deviation based on setting weight coefficients for peak periods, normal periods and valley periods respectively, and the weight coefficients are used to distinguish the importance of electricity price deviations in different periods.

[0007] As a further aspect of the present invention: In step S2, thermal power units are divided into three categories according to their capacity: small-capacity units, medium-capacity units, and large-capacity units. Differentiated upper and lower limits for segmented pricing and upper and lower limits for segmented quantity reporting are set for the three categories of units respectively. The upper and lower limits of segmented pricing and segmented quotation are set based on the historical pricing data characteristics, risk appetite, and market power differences of the corresponding capacity units.

[0008] As a further aspect of the present invention: in step S3, the total system cost includes the full-cycle power generation cost of the thermal power unit, which includes the operating cost, start-up cost, and no-load cost of the thermal power unit.

[0009] As a further aspect of the present invention: in step S3, the full-dimensional constraints include system load balance constraints, system reserve capacity constraints, physical constraints of thermal power unit operation, constraints of new energy consumption, power transmission security constraints, and constraints of electricity spot market boundary conditions. The power transmission safety constraints include line power flow transmission limit constraints and cross-sectional power flow transmission limit constraints. The boundary conditions constraints of the electricity spot market include the tie-line planning constraints corresponding to inter-provincial medium and long-term transactions, the mandatory start-up and shutdown constraints of generating units, and the N-1 safe and stable operation constraints of the power grid.

[0010] As a further aspect of the present invention: the system reserve capacity constraint includes the system positive reserve capacity constraint, the system negative reserve capacity constraint and the system rotating reserve constraint, wherein the system rotating reserve constraint includes system-level rotating reserve constraint and partition-level rotating reserve constraint.

[0011] As a further aspect of the present invention: the physical constraints on the operation of the thermal power unit include upper and lower limits of unit output, unit ramp rate constraints, minimum continuous start-stop time constraints, and maximum number of start-stop cycles constraints.

[0012] As a further aspect of the present invention: the constraint on the absorption of new energy sources is: The day-ahead market cleared power of new energy generating units in each time period shall not exceed the output forecast value declared by the unit for the corresponding time period.

[0013] As a further aspect of the present invention: the DE-PSO hybrid intelligent optimization algorithm is used to solve the two-layer optimization model, wherein the DE-PSO hybrid intelligent optimization algorithm integrates the global search capability of the differential evolution algorithm and the fast convergence characteristic of the particle swarm optimization algorithm; When solving the aforementioned two-layer optimization model, a solution framework consisting of an intelligent optimization outer loop and a mathematical programming inner solution is adopted. The outer layer uses the DE-PSO hybrid intelligent optimization algorithm to perform a global search on the segmented bidding and quantity decision variables of thermal power units, while the inner layer uses a mathematical programming solver to accurately solve the lower-level market clearing model.

[0014] As a further aspect of the present invention, the specific steps for solving the bi-layer optimization model include: Step 1: Input historical electricity price data, thermal power unit parameters, new energy output forecast data and market operation boundary conditions, encode the segmented bidding and quantity decision variables of thermal power units into a vector form that the algorithm can process, and initialize the value range of the decision variables based on the unit capacity type; Step 2: Randomly generate an initial population of a preset size. Each individual in the population corresponds to a complete thermal power unit group pricing strategy. Step 3: For each individual in the population, the decoded unit price parameters are used as fixed inputs and substituted into the lower-level market clearing model. The market clearing results are obtained by solving the mathematical programming solver. The market clearing results include the system marginal electricity price and unit output arrangement for each time period. Step 4: Compare the simulated electricity price obtained from the lower layer with the historical real electricity price, substitute it into the upper layer optimization objective function, and calculate the fitness value of the corresponding individual; Step 5: Based on the fitness value, iteratively update the individuals in the population using the evolutionary update rules of the DE-PSO hybrid intelligent optimization algorithm. Repeat steps 3 to 4 until the preset iteration termination condition is reached, output the optimal individual and decode to obtain the optimal bidding strategy combination of the thermal power unit group.

[0015] Compared with the prior art, the beneficial effects of the present invention are: This invention constructs a two-layer extrapolation model for spot pricing strategies of thermal power unit groups. Through iterative interaction of pricing and price signals between the upper-layer per-unit price similarity layer and the lower-layer market clearing layer, it can converge to obtain a set of optimal thermal power unit group pricing strategies under the premise of meeting the requirements of safe and economical operation of the power system. This achieves a high degree of fit between simulated market prices and historical real prices, providing a scientific and feasible decision-making basis for power generators to participate in the spot market competition. The upper-level optimization model of this invention sets differentiated segmented bidding and upper and lower limits on bidding quantity for three different types of thermal power units: small-capacity, medium-capacity, and large-capacity. The setting of the constraints combines the characteristics of historical bidding data of the units, the risk preferences of different types of units, and the differences in market power. It can accurately match the bidding behavior characteristics of different units in the real market, avoid the simulation distortion problem caused by homogeneous constraints, and greatly improve the accuracy and feasibility of bidding strategy deduction. The lower-level market clearing model of this invention takes minimizing the total system cost as its optimization objective. It fully incorporates the entire lifecycle power generation cost, including the operating cost, start-up cost, and no-load cost of thermal power units. At the same time, it sets day-ahead market clearing constraints in all dimensions, such as system load balance, positive / negative reserve capacity, spinning reserve, upper and lower limits of unit output, ramp-up, minimum continuous start-stop time, maximum number of start-stop cycles, line power flow, cross-sectional power flow, renewable energy consumption, and boundary conditions. It can accurately reproduce the day-ahead clearing process of the real electricity spot market, ensuring that the simulation clearing results are completely consistent with the actual market operation rules and grid safety operation requirements, and providing accurate and reliable electricity price feedback signals for the upper-level model. This invention employs a DE-PSO hybrid intelligent optimization algorithm to solve a two-layer optimization model. This algorithm integrates the strong global search capability of differential evolution algorithm with the fast convergence characteristic of particle swarm optimization algorithm. It achieves efficient collaboration through a two-layer nested structure of "intelligent optimization outer loop + inner DE enhanced search": the outer PSO guides particles to quickly approach the optimal region, while the inner DE performs mutation and crossover operations on the solution vector after each position update to enhance diversity. Its evolution update rules adopt the standard PSO velocity-position update formula and the DE mutation-crossover-selection mechanism, respectively. The core parameter setting rules include linearly decreasing inertia weight w (0.9→0.4), learning factor c1=c2=2.0, mutation factor F∈[0.4,0.9], crossover probability CR=0.8, population size N≥5d, and maximum number of iterations of 200 generations, ensuring that those skilled in the art can completely reproduce the solution process of this algorithm based on this specification.

[0016] By using the solution framework of "intelligent optimization outer loop + mathematical programming inner solution", the problem that the two-layer optimization model is difficult to solve directly by traditional mathematical programming methods is effectively solved. Under the premise of satisfying multiple complex constraints, it can automatically optimize and generate the typical daily segmented price curve of the unit, effectively balancing the solution efficiency and solution accuracy of large-scale market simulation problems. This invention can effectively adapt to the differences in the operating characteristics of the electricity market during the heating season and the non-heating season. It can accurately capture the market quotation patterns and electricity price formation mechanisms under different supply and demand scenarios and different seasons. According to actual data verification, the simulated electricity price obtained by simulation is basically consistent with the real market electricity price trend and has a high degree of similarity. It can effectively cover different typical scenarios such as loose market supply and demand and tight supply, and has strong engineering practicality and market scenario adaptability. Attached Figure Description

[0017] Figure 1 This is a diagram of the two-layer optimization model architecture for the spot pricing strategy of thermal power unit groups in an embodiment of the present invention.

[0018] Figure 2 This is a graph showing the overall price curve of a typical day for a thermal power unit group during the heating season in an embodiment of the present invention.

[0019] Figure 3 This is a graph showing the overall price curve of the thermal power unit group 2 on a typical day during the heating season in an embodiment of the present invention.

[0020] Figure 4 This is a graph showing the overall price curve of a typical 3-unit thermal power plant group during the heating season in an embodiment of the present invention.

[0021] Figure 5 This is a comparison chart of the actual electricity price and the simulated electricity price on a typical day during the heating season in an embodiment of the present invention.

[0022] Figure 6 This is a comparison chart of the actual electricity price and the simulated electricity price on a typical day during the heating season in this embodiment of the invention.

[0023] Figure 7 This is a comparison chart of the actual electricity price and the simulated electricity price on a typical day during the heating season in this embodiment of the invention.

[0024] Figure 8 This is a graph showing the overall price curve of a typical day's thermal power unit group during the non-heating season in an embodiment of the present invention.

[0025] Figure 9 This is a graph showing the overall price curve of a typical day for a thermal power unit group 2 during the non-heating season in an embodiment of the present invention.

[0026] Figure 10 This is a graph showing the overall price curve of a typical 3-unit thermal power plant group during the non-heating season in an embodiment of the present invention.

[0027] Figure 11 This is a comparison chart of the actual electricity price and the simulated electricity price on a typical day during the non-heating season in an embodiment of the present invention.

[0028] Figure 12 This is a comparison chart of the actual electricity price and the simulated electricity price on a typical day during the non-heating season in this embodiment of the invention.

[0029] Figure 13 This is a comparison chart of the actual electricity price and the simulated electricity price on a typical day during the non-heating season in this embodiment of the invention. Detailed Implementation

[0030] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0031] The specific implementation of the present invention will be described in detail below with reference to specific embodiments.

[0032] Please see Figures 1-13 This invention provides a two-layer derivation method for spot pricing strategies of thermal power unit groups. This method constructs a two-layer optimization model based on historical electricity price data to optimize and deduce pricing strategies for thermal power unit groups in the electricity spot market. While ensuring the safe and economical operation of the power system, it provides a scientific decision-making basis for power generators to participate in market competition. This method is applicable to the scenario of optimizing pricing strategies for thermal power unit groups in the day-ahead electricity market and conforms to the trading rules of domestic provincial electricity spot markets and the requirements of grid operation and management.

[0033] 1. Overall Framework of the Two-Layer Deduction Method for Spot Pricing Strategies of Thermal Power Unit Clusters The two-layer derivation method for spot pricing strategies of thermal power unit groups described in this embodiment uses a two-layer optimization model to solve the pricing strategies of all thermal power units in the electricity market. The two-layer optimization model includes an upper layer of similar per-unit electricity prices and a lower layer of market clearing. The two layers interact iteratively through pricing and electricity price signals, and finally converge to a set of optimal pricing strategy combinations.

[0034] The upper layer is the per-unit price similarity layer, which aims to minimize the weighted relative deviation between the predicted and actual electricity prices during typical periods. It also sets reasonable upper and lower limits for unit segmented bidding and quotation based on factors such as unit capacity, risk appetite, and market influence. The lower layer is the market clearing layer, which aims to minimize the total system cost after considering costs such as generation costs and start-up and shutdown fees. It also strictly meets physical and market constraints such as power balance, unit operation, ramp-up, reserve, renewable energy consumption, and transmission safety.

[0035] 2. Upper-level model: Optimization and adjustment of pricing strategies This layer of the model is the pricing strategy optimization and adjustment layer. Its core is to guide the optimization of the unit's pricing strategy through historical electricity price data, so that the electricity price pattern in the simulated market is highly consistent with the historical real market.

[0036] 2.1 Optimization Objectives The optimization objective of this upper-level model is to minimize the deviation between the simulated market electricity price and the historical real electricity price. The objective function is shown in equation (3-1): (3-1); In the formula, , , These are the weighting coefficients for peak, average, and trough periods (reflecting the importance of deviations in different periods); The market simulation price (or clearing price) for the i-th generating unit (or small-capacity generating unit i) during peak hours. The historical true electricity price of the i-th generating unit during peak hours (used as a benchmark for comparison); and These represent the simulated electricity price and the historical real electricity price for the i-th generating unit during normal periods, respectively. and These represent the simulated electricity price and the historical actual electricity price of the i-th generating unit during the off-peak period, respectively. This optimization objective uses a weighted relative deviation calculation method, which distinguishes the importance of deviations in different time periods by using the weight coefficients of peak, flat, and valley periods. This can accurately match the temporal distribution characteristics of historical electricity prices, avoid fitting distortion caused by single electricity price deviations, and ensure that the optimized pricing strategy can highly reproduce the real market's electricity price formation patterns.

[0037] 2.2 Constraints This layer of the model sets upper and lower limits for bids and quantities for thermal power units of different capacities, matching the market power, risk appetite, and operating characteristics of different units. The specific constraints are as follows: 2.2.1 Pricing constraints for small-capacity units (3-2); (3-3); (3-4); In the formula, and These represent the minimum / maximum allowable bids for small-capacity unit i in the b-th bidding segment (or time period / interval); This is the actual price quoted for small-capacity unit i in the b-th price segment; and These represent the minimum / maximum generating power (or capacity) of small-capacity unit i in the b-th bidding segment. This refers to the actual declared power (or capacity) of small-capacity unit i in the b-th bidding segment. This represents the maximum power capacity of the i-th unit (node / unit / load).

[0038] 2.2.2 Pricing Constraints for Medium-Capacity Units (3-5); (3-6); (3-7); In the formula, and These represent the minimum and maximum allowable bids for medium-capacity unit j in the b-th bidding segment, respectively. This is the actual price quoted for medium-capacity unit j in the b-th price segment; and These represent the minimum and maximum generating power of medium-capacity unit j in the b-th bidding segment, respectively. This represents the actual declared power of medium-capacity unit j in the b-th bidding segment. This represents the maximum power capacity of the i-th unit (node / unit / load).

[0039] 2.2.3 Pricing Constraints for Large-Capacity Units (3-8); (3-9); (3-10); In the formula, and These represent the minimum / maximum allowable bids for large-capacity unit k in the b-th bidding segment; This is the actual price quoted for large-capacity unit k in the b-th price segment; and These represent the minimum and maximum generating power of the large-capacity generator unit k in the b-th bidding segment, respectively. For the actual declared power of the large-capacity unit k in the b-th bidding segment, This represents the maximum power capacity of the i-th unit (node / unit / load).

[0040] The upper and lower limits of the unit's price will be set based on the characteristics presented in historical price data, and in combination with the differences in risk preferences and market power of different types of units.

[0041] By setting differentiated pricing and quotation constraints for units of different capacities (large, medium, and small), the model can accurately match the market power level, risk tolerance, and physical operating characteristics of different units, avoiding pricing strategies that exceed the reasonable operating range of the units. At the same time, it ensures that the constraints match the pricing behavior characteristics of units of different capacities in the real market, greatly improving the simulation accuracy and feasibility of the strategy.

[0042] 3. Lower-level model: Market simulation clearing This layer of the model is the market clearing simulation layer. Its core is based on the unit bidding strategy output by the upper-layer model, simulating the day-ahead clearing process of the real electricity spot market, and providing simulated electricity price feedback signals for the upper-layer model. Day-ahead electricity market clearing is usually solved using the Safety Constrained Unit Combination (SCUC) model, which coordinates unit start-up and shutdown and output arrangements to meet system safety and supply-demand balance requirements.

[0043] 3.1 Optimization Objectives The optimization objective of this lower-level model is to minimize the total power generation cost of the system, and the objective function is shown in equation (3-11): (3-11); In the formula, N represents the total number of units; T represents the total number of time periods considered. The rolling calculation period is the next three days. Day 1 (D) considers 96 time periods, Day 2 (D+1) considers 24 time periods, and Day 3 (D+2) considers 24 time periods, for a total of 144 time periods. Therefore, T is 144. This represents the output of unit i during time period t; and Let $i$ be the operating cost and startup cost of unit i during time period $t$, where the operating cost of unit i is $t$. It is a multi-segment linear function related to the output ranges declared by the generating unit and the corresponding energy prices; Let M be the idle cost of unit i during time period t; M is the network flow constraint relaxation penalty factor. and These are the forward and reverse power flow relaxation variables for line l, respectively; NL is the total number of lines. and , , represent the forward and reverse tidal current relaxation variables for section s, respectively; NS represents the total number of sections.

[0044] This optimization objective fully covers the power generation cost of thermal power units throughout their entire lifecycle, including operating costs, start-up costs, and no-load costs, closely aligning with the actual power generation cost structure of thermal power units. Simultaneously, it incorporates relaxation penalty factors for network power flow and cross-sectional power flow constraints, ensuring that the market clearing model conforms to real market rules while avoiding the problem of infeasible solutions due to overly tight constraints, thus balancing the model's accuracy and robustness.

[0045] 3.2 Core Parameter Expressions 3.2.1 Unit output expression (3-12); (3-13); In the formula, NM represents the total number of price segments for the generator set. The winning bid for the power of unit i in the m-th output interval of time period t. and These are the upper and lower limits of the m-th output range declared by unit i, respectively.

[0046] By dividing the output range into multiple linear segments, it is possible to accurately match the trading rules of segmented bidding for thermal power units in the spot electricity market, fully restore the correspondence between the output range declared by the unit and the winning bid electricity, and ensure that the market clearing calculation is completely consistent with the actual market trading rules.

[0047] 3.2.2 Expression for Unit Operating Costs (3-14); In the formula, the unit operating cost NM represents the total number of power unit price segments, and Ci,m represents the energy price corresponding to the m-th output segment declared by power unit i. This represents the winning bid power for unit i in the m-th output interval of time period t. This expression is directly related to the unit's segmented bidding, enabling precise calculation of the unit's operating costs under different winning bid outputs. It aligns with the core rule of "segmented bidding and segmented settlement" in the electricity spot market, ensuring the accuracy of cost calculation.

[0048] 3.2.3 Expression for Unit Start-up Costs (3-15); In the formula, The startup cost of unit i during time period t. The single start-up cost declared for unit i. This usually represents the efficiency coefficient of the i-th unit in the t-th time period.

[0049] This expression fully incorporates the cost of a single unit start-up, accurately reflects the cost of thermal power unit start-up and shutdown, and ensures that the clearing model can comprehensively consider the economics of unit start-up and shutdown, consistent with the unit operation and scheduling logic of the real power grid.

[0050] 3.3 Constraints The constraints of this layer's model are full-dimensional constraints on the day-ahead electricity market clearing SCUC, as follows: 3.3.1 System load balance constraints For each time period t, the load balancing constraint can be described as: (3-16); In the formula, This represents the output of unit i during time period t. This represents the planned power of tie line j in time period t (input is positive, output is negative), where NT is the total number of tie lines. Let t be the system load during time period t.

[0051] This constraint is the core constraint for the safe operation of the power system, ensuring that the sum of the total power generation output of the system and the power of the tie lines in each time period can fully match the system load demand, and ensuring that the market clearing result meets the basic requirements of system power balance.

[0052] 3.3.2 System Positive and Negative Reserve Capacity Constraints (3-17); In the formula, This indicates the start / stop status of unit i during time period t. This indicates that the generator unit has stopped. This indicates that the generator unit is started; This represents the maximum output of unit i during time period t. The system's positive standby capacity requirement for time period t.

[0053] This constraint ensures that the total operating capacity of the system can meet the minimum positive reserve capacity requirement, effectively cope with the system load forecast deviation and the system supply and demand imbalance fluctuations caused by various actual operating accidents, and greatly improve the safety and stability of the power system operation.

[0054] 3.3.3 System Negative Reserve Capacity Constraint (3-18); In the formula, Let be the minimum output of unit i during time period t; The system's negative backup capacity requirement for time period t.

[0055] This constraint, in conjunction with the positive and backup constraints, fully covers the two-way adjustment needs of system supply and demand fluctuations, effectively avoiding system frequency anomalies caused by sudden load drops and ensuring the stability of system operation.

[0056] 3.3.4 System Rotational Standby Constraints (3-19); (3-20); (3-21); (3-22); In the formula, This represents the maximum ramp rate of unit i. This represents the maximum downhill / climb rate of unit i. and These are the maximum and minimum output of unit i during time period t, respectively; and These represent adjustments to the rotational reserve requirements for time period t, respectively. M j Let be the number of generating units in the j-th partition's rotating standby area. and These represent the upward and downward adjustment of the rotational reserve requirement within the j-th partition's rotational reserve area for time period t, respectively.

[0057] This constraint not only considers the system-level spinning reserve requirements but also incorporates zonal spinning reserve constraints. In addition, it combines the unit ramp rate limits to ensure that the reserved spinning reserve can respond effectively within the specified time, which conforms to the reserve management rules of the real power system and avoids the problem of unavailable reserve capacity.

[0058] 3.3.5 Upper and lower limits of unit output constraints (3-23); This indicates the start / stop status of unit i during time period t. This represents the maximum output of unit i during time period t. Let i be the output of unit i during time period t. The minimum output of unit i in time period t is defined by this constraint. This constraint ensures that the actual output of the unit is within the maximum / minimum output range allowed by its physical characteristics, avoiding clearing results that exceed the unit's operating limits, and perfectly matching the actual operating characteristics of the thermal power unit.

[0059] 3.3.6 Unit ramping constraints (3-24); (3-25); In the formula, This represents the maximum ramp rate of unit i. This represents the maximum downhill / climb rate of unit i. Let i be the output of unit i during time period t. This indicates the start / stop status of unit i during time period t. This indicates the start / stop status of unit i during time period t-1. Let i be the output of unit i during time period t-1. This represents the maximum output of unit i during time period t. Let be the minimum output of unit i during time period t.

[0060] This constraint limits the range of output variation between adjacent time periods, ensuring that it meets the unit's maximum uphill and downhill ramp rate requirements, preventing equipment damage caused by sudden output changes, and guaranteeing the safety and stability of unit operation.

[0061] 3.3.7 Minimum Continuous Start-up and Shutdown Time Constraints for Units (3-26); (3-27); In the formula, This indicates the start / stop status of unit i during time period t. and The duration of continuous operation and continuous shutdown of unit i during time period t can be represented by state variables. To express.

[0062] This constraint aligns with the physical properties and actual operational needs of thermal power units, avoids frequent start-ups and shutdowns, ensures the safety and service life of unit operation, and is consistent with the dispatching and operation rules of thermal power units in the real power grid.

[0063] 3.3.8 Maximum number of start-ups and shutdowns of the unit First, define the start-up and stop switching variables, define... Whether unit i switches to startup state during time period t; Define This indicates whether unit i switches to a shutdown state during time period t. , The following conditions must be met: (3-28); The start-stop limit for unit i can be expressed as follows: (3-29); (3-30); In the formula, and These represent the maximum number of starts and stops for unit i within the scheduling cycle, respectively.

[0064] This constraint further limits the number of times a unit can be started and stopped within the scheduling cycle, avoiding equipment damage and increased costs caused by frequent unit starts and stops, while ensuring that the model's clearing results meet the actual operation and management requirements of thermal power units.

[0065] 3.3.9 Line power flow constraints (3-31); In the formula, Let i be the output of unit i during time period t. Gl−i is the power flow transmission limit of line l; Gl−i is the generator output power transfer distribution factor of the node where unit i is located to line l; Gl−j is the generator output power transfer distribution factor of the node where tie line j is located to line l. Let Gl−k represent the planned power of tie line j in time period t (positive input, negative output), K be the number of nodes in the system, Gl−k be the generator output power transfer distribution factor of node k to line l, and Dk,t be the bus load value of node k in time period t. and These are the forward and reverse power flow relaxation variables for line l, respectively.

[0066] This constraint calculates line power flow based on the generator output power transfer distribution factor, ensuring that the line transmission power does not exceed its transmission limit. At the same time, slack variables are set to avoid the model having no feasible solution, fully covering the power system's transmission security constraints, and ensuring that the clearing results meet the physical transmission limits of the power grid.

[0067] 3.3.10 Cross-sectional power flow constraints (3-32); In the formula, and Gs−i is the power flow transmission limit of section s; Gs−i is the generator output power transfer distribution factor of node i to section s; Gs−j is the generator output power transfer distribution factor of node j to section s; and Gs−k is the generator output power transfer distribution factor of node k to section s. and These are the forward and reverse kinetic flow relaxation variables for section s, respectively.

[0068] This constraint sets transmission limit constraints for key sections of the power grid, which can effectively prevent power grid safety risks caused by exceeding the limits of the sections and is in line with the safety and stability operation management requirements of the provincial power grid.

[0069] 3.3.11 Output Constraints of New Energy Units (3-33); In the formula, E represents the set of new energy generating units. The predicted output of renewable energy unit i in time period t. That is, at each time point, the day-ahead market-cleared electricity value of renewable energy units should not exceed the predicted output value declared by the renewable energy units.

[0070] This constraint ensures that the cleared power output of new energy units does not exceed their declared power output forecast, which is in line with the market rule of prioritizing the consumption of new energy. It can fully reproduce the impact of new energy output on the power market clearing results and the formation of electricity prices, and improve the simulation realism of the model.

[0071] 3.3.12 Boundary Condition Constraint Set (3-34); In the formula, This refers to the set of various boundary conditions for unit i during time period t, including the power transmission curve of the interconnection line formed by inter-provincial medium- and long-term transactions, units that must be started or stopped due to safety constraints, voltage support, heating for the people or government requirements, and N-1 safety constraints of main transformers, cross-sections, and lines at voltage levels of 220kV and above. In other words, the output of unit i during time period t satisfies the various boundary condition constraints of the day-ahead market.

[0072] This constraint set fully incorporates various boundary conditions of the current market, ensuring that the simulation boundary of the model is completely consistent with the operating boundary of the real market, further improving the accuracy and reliability of the model simulation results, and enabling the optimized pricing strategy to be directly applied to real market scenarios.

[0073] 4. Model Solution Method This implementation method uses the day-ahead electricity price and related boundary condition data of Shanxi Province for the whole year of 2024 and from January to May 2025. It employs the DE-PSO hybrid intelligent optimization algorithm (differential evolution-particle swarm optimization hybrid algorithm) to solve the two-layer model for generating the above typical daily unit price curve.

[0074] Due to its nested structure of "upper-level decision-making and lower-level feedback," the two-level optimization model is usually difficult to solve directly analytically using traditional mathematical programming methods. In this model, the upper level is a nonlinear absolute value objective function, and the lower level is a large-scale market clearing problem involving mixed integer programming (MIP). To address this characteristic, this method uses the DE-PSO hybrid intelligent optimization algorithm as the core solver. This algorithm combines the strong global search capability of differential evolution (DE) with the fast convergence characteristic of particle swarm optimization (PSO). By encoding the decision variables of the upper-level model (the segmented bid and bid quantity of the agency) as "particles" or "individuals," a parallel heuristic search is performed in the solution space, forming a framework of "intelligent optimization outer loop + mathematical programming inner solution," which effectively balances the solution efficiency and accuracy.

[0075] The specific steps of the algorithm to solve the problem are as follows: Step 1: Input historical electricity price data for Shanxi Province, unit parameters, and boundary conditions such as predicted output of new energy sources.

[0076] All decision variables of the upper-level model, namely the bids of each unit i in each bid segment b, are considered. With Reporting Volume These are encoded sequentially to form a high-dimensional real-valued vector, which serves as an "individual" or "particle". .

[0077] Based on the risk appetite and market power settings according to the unit capacity type (large, medium, small), initialize the value range of each variable. , ]and[ , ].

[0078] By encoding the decision variables, the complex unit segmented pricing strategy can be transformed into a vector form that can be processed by the intelligent algorithm. At the same time, by initializing the variable range based on the unit capacity type, the search space of the algorithm can be reduced and the solution efficiency can be improved.

[0079] Step 2: Randomly generate an initial population of size NP. , ,..., Each individual unit represents a complete unit pricing curve scheme.

[0080] By randomly generating the initial population, the algorithm's global search capability in the solution space can be guaranteed, avoiding getting trapped in local optima.

[0081] Step 3: Solving the Lower-Level Model: For each individual in the population, the decoded price parameters are used as fixed inputs and substituted into the lower-level market clearing model. This lower-level model is a mixed-integer linear programming problem with the objective of minimizing total electricity purchase and reserve costs. An efficient mathematical programming solver is used to solve it precisely, yielding the optimal clearing result, including the system marginal electricity price for each time period, actual unit output, and reserve arrangements.

[0082] By using a mathematical programming solver to accurately solve the lower-level model, it can be ensured that the market clearing results corresponding to each set of bidding strategies fully comply with market rules and system constraints, providing accurate feedback data for the fitness calculation of the upper-level model.

[0083] Step 4: Upper-level objective calculation: The clearing price obtained from the lower-level solution is categorized by peak, flat, and valley periods, compared with the corresponding historical real electricity prices, and substituted into the upper-level objective function to calculate the total weighted per-unit price deviation for that individual. This deviation is used as the fitness value for that individual. The smaller the fitness value, the closer the market electricity price pattern simulated by the pricing strategy is to the historical reality.

[0084] This step enables iterative interaction between the upper and lower level models, using the electricity price deviation as the fitness value to guide the algorithm's search direction, ensuring that the final converged pricing strategy can best reflect the electricity price formation patterns in the real market.

[0085] Step 5: Iterative optimization: Based on the fitness value, the individuals in the population are iteratively updated through the evolution and update rules of the DE-PSO hybrid algorithm. Steps 3 to 4 are repeated until the preset number of iterations or convergence accuracy is reached. Finally, the individual with the best fitness value is output, and the optimal segmented bidding strategy combination of the thermal power unit group is decoded.

[0086] The DE-PSO solution method successfully transforms the complex bi-level optimization problem into an automated iterative calculation process. It fully utilizes the global search advantage of intelligent algorithms and the accurate solution capability of mathematical programming models. Under multiple complex constraints such as unit pricing, output, system operation, and market clearing, it aims to minimize the weighted deviation between simulated and real electricity prices and automatically optimizes and generates typical daily segmented pricing curves for units, providing quantitative basis for market strategy analysis.

[0087] 5. Validation of the effectiveness of the two-layer deduction method for spot pricing strategies of thermal power unit groups. Peak, flat, and valley time weighting coefficients (k) peak , k flat , k valley The specific value of k is defined in the formula. peak =0.4, k flat =0.2, kvalley =0.4.

[0088] Practical capacity standards (MW) for classifying large, medium and small capacity units: large units ≥300MW, medium units 100-300MW, small units <100MW.

[0089] The network flow constraint relaxation penalty factor M=500.

[0090] The specific termination criteria for the DE-PSO hybrid algorithm are as follows: the convergence criteria of the algorithm need to be clearly defined, the maximum number of iterations (200 times) and the relative change of the fitness function value being less than a certain threshold (1e-4).

[0091] 5.1 Validation of Examples During the Heating Season Based on boundary information such as load, wind and solar output, and tie-line plans for three typical days of heating season cluster 1, as well as electricity prices, the method of this implementation is used to deduce the pricing strategy, obtain the overall pricing curve for the three typical days, and compare and analyze the characteristics of the pricing curve and the difference between the actual electricity price and the simulated electricity price.

[0092] The results show that the overall price curves for the three typical days within a cluster are quite similar. Each curve shows a trend of increasing bid price as bid volume increases, which is consistent with the general law of increasing marginal cost. Among them, the slope of typical day 2 changes relatively gently in the medium bid volume range, reflecting a relatively loose market supply on that day; typical day 3 shows a significant price increase in the high bid volume range, indicating tight supply or expected tightening.

[0093] The above results verify that this method can generate a consistent price curve that conforms to market rules based on the similar boundary conditions of typical days in the same cluster, and accurately capture the market price characteristics under different supply and demand scenarios.

[0094] Further comparison of the actual and simulated electricity prices on three typical days shows that, overall, the trends of simulated and actual electricity prices are basically consistent, and the similarity between simulated and actual electricity prices is high, proving the effectiveness of the two-layer model and solution method constructed in this paper.

[0095] The discrepancy between simulated and actual electricity prices during certain periods is due to the fact that the net load during those periods is higher than during other periods, but the actual electricity price is lower. This is a special fluctuation in the real market and does not affect the overall effectiveness of this method.

[0096] 5.2 Verification of Examples During Non-Heating Season In the electricity market system, the bidding behavior and electricity price formation mechanism during the non-heating season exhibit significantly different characteristics from those during the heating season due to the absence of heating load, increased volatility in renewable energy output, and changes in system regulation demand. Based on the boundary information such as load, wind and solar output, and electricity price of three typical days in cluster 1 of the non-heating season, the bidding strategy is simulated using the method of this implementation, resulting in the overall bidding curve for the three typical days. The characteristics of the bidding curve and the differences between the actual electricity price and the simulated electricity price are then compared and analyzed.

[0097] The results show that, overall, the price curve during the non-heating season still follows the law of increasing marginal cost, but compared with the heating season, the slope of the curve is generally slower, reflecting that the system adjustment pressure is relatively reduced.

[0098] Specific characteristics include: significant inter-cluster differences; on typical day 1, prices rise rapidly even in the low-demand electricity range, indicating that market participants in this cluster are highly price-sensitive or have expectations of supply shortages; on typical day 2, the curve is relatively flat, indicating high price elasticity; on typical day 3, a "step-like" jump occurs, possibly related to unit start-up and shutdown costs and pricing strategies. Meanwhile, intraday time-period characteristics are significant. Comparing the pricing curves for peak, flat, and low periods for each cluster reveals a significantly steeper slope during peak periods, especially on typical day 1, which shows a near-vertical rise near the load peak, reflecting tight peak-shaving resources.

[0099] The above results verify that this method can accurately capture the differences in market operation characteristics between the non-heating season and the heating season, and generate differentiated pricing strategies that conform to the market rules of different seasons.

[0100] Further comparison of the actual and simulated electricity prices on three typical days during the non-heating season revealed that the overall trend of the simulated and actual electricity prices closely matched, verifying that the method also possesses extremely high simulation accuracy and effectiveness in the non-heating season scenario.

[0101] It should be noted that, in this invention, although the specification describes the embodiments, not every embodiment contains only one independent technical solution. This way of describing the specification is only for clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A two-layer deduction method for spot pricing strategies of thermal power unit groups, characterized in that, Includes the following steps: S1. Construct a two-layer optimization model for solving the spot price strategy of thermal power unit groups. The two-layer optimization model includes an upper layer of similar per-unit electricity prices and a lower layer of market clearing. S2. Through the upper-level electricity price per unit value similarity layer, with the optimization objective of minimizing the weighted relative deviation between the market simulation electricity price and the historical real electricity price, differentiated segmented pricing and upper and lower limits of the quotation are set according to the capacity scale of thermal power units, and the pricing strategy of thermal power unit group is output. S3. Through the lower market clearing layer, with the pricing strategy output by the upper layer as input and minimizing the total system cost as the optimization objective, market clearing simulation is performed under the full-dimensional constraints of power system operation and electricity spot market clearing, and the simulated market electricity price is output. S4. Feed back the market simulation electricity price output from the lower layer to the upper layer of electricity price per unit value similarity layer. Through iterative interaction of the bidding signals and electricity price signals of the two-layer model, the optimal bidding strategy combination of the thermal power unit group is obtained until convergence.

2. The two-layer deduction method for spot pricing strategy of thermal power unit groups according to claim 1, characterized in that, In step S2, the weighted relative deviation is a weighted relative deviation based on weighting coefficients set for peak periods, normal periods, and valley periods. The weighting coefficients are used to distinguish the importance of electricity price deviations in different periods.

3. The two-layer deduction method for spot pricing strategy of thermal power unit groups according to claim 1, characterized in that, In step S2, thermal power units are divided into three categories according to their capacity: small-capacity units, medium-capacity units, and large-capacity units. Differentiated upper and lower limits for segmented pricing and upper and lower limits for segmented quantity are set for the three categories of units. The upper and lower limits of segmented pricing and segmented quotation are set based on the historical pricing data characteristics, risk appetite, and market power differences of the corresponding capacity units.

4. The two-layer deduction method for spot pricing strategy of thermal power unit groups according to claim 1, characterized in that, In step S3, the total system cost includes the full-cycle power generation cost of the thermal power unit, which includes the operating cost, start-up cost, and no-load cost of the thermal power unit.

5. The two-layer deduction method for spot pricing strategy of thermal power unit groups according to claim 1, characterized in that, In step S3, the full-dimensional constraints include system load balance constraints, system reserve capacity constraints, physical constraints of thermal power unit operation, constraints of new energy consumption, power transmission security constraints, and boundary condition constraints of the electricity spot market. The power transmission safety constraints include line power flow transmission limit constraints and cross-sectional power flow transmission limit constraints. The boundary conditions constraints of the electricity spot market include the tie-line planning constraints corresponding to inter-provincial medium and long-term transactions, the mandatory start-up and shutdown constraints of generating units, and the N-1 safe and stable operation constraints of the power grid.

6. The two-layer deduction method for spot pricing strategy of thermal power unit groups according to claim 5, characterized in that, The system reserve capacity constraints include system positive reserve capacity constraints, system negative reserve capacity constraints, and system spinning reserve constraints. The system spinning reserve constraints include system-level spinning reserve constraints and partition-level spinning reserve constraints.

7. The two-layer deduction method for spot pricing strategy of thermal power unit groups according to claim 5, characterized in that, The physical constraints on the operation of thermal power units include upper and lower limits of unit output, unit ramp rate constraints, minimum continuous start-stop time constraints, and maximum number of start-stop cycles constraints.

8. The two-layer deduction method for spot pricing strategy of thermal power unit groups according to claim 5, characterized in that, The constraint on the absorption of new energy sources is: The day-ahead market cleared power of new energy generating units in each time period shall not exceed the output forecast value declared by the unit for the corresponding time period.

9. The two-layer deduction method for spot pricing strategy of thermal power unit groups according to claim 1, characterized in that, The DE-PSO hybrid intelligent optimization algorithm is used to solve the two-layer optimization model. The DE-PSO hybrid intelligent optimization algorithm combines the global search capability of the differential evolution algorithm with the fast convergence characteristic of the particle swarm optimization algorithm. When solving the aforementioned two-layer optimization model, a solution framework consisting of an intelligent optimization outer loop and a mathematical programming inner solution is adopted. The outer layer uses the DE-PSO hybrid intelligent optimization algorithm to perform a global search on the segmented bidding and quantity decision variables of thermal power units, while the inner layer uses a mathematical programming solver to accurately solve the lower-level market clearing model.

10. The two-layer deduction method for spot pricing strategy of thermal power unit groups according to claim 9, characterized in that, The specific steps for solving the bi-level optimization model include: Step 1: Input historical electricity price data, thermal power unit parameters, new energy output forecast data and market operation boundary conditions, encode the segmented bidding and quantity decision variables of thermal power units into a vector form that the algorithm can process, and initialize the value range of the decision variables based on the unit capacity type; Step 2: Randomly generate an initial population of a preset size. Each individual in the population corresponds to a complete thermal power unit group pricing strategy. Step 3: For each individual in the population, the decoded unit price parameters are used as fixed inputs and substituted into the lower-level market clearing model. The market clearing results are obtained by solving the mathematical programming solver. The market clearing results include the system marginal electricity price and unit output arrangement for each time period. Step 4: Compare the simulated electricity price obtained from the lower layer with the historical real electricity price, substitute it into the upper layer optimization objective function, and calculate the fitness value of the corresponding individual; Step 5: Based on the fitness value, iteratively update the individuals in the population using the evolutionary update rules of the DE-PSO hybrid intelligent optimization algorithm. Repeat steps 3 to 4 until the preset iteration termination condition is reached, output the optimal individual and decode to obtain the optimal bidding strategy combination of the thermal power unit group.

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