Electric energy inertia joint market clearing method based on level set method

Abstract

The application discloses a power energy inertia joint market clearing method based on a level set method, and comprises the following steps: establishing a power energy-inertia joint clearing model with the minimum system total cost as an objective; in view of the non-convex characteristics of the power energy-inertia joint clearing model, constructing a Lagrange dual function of the original problem, converting the dual problem into a sub-problem of unit profit maximization and a main problem based on a cutting plane linear programming; establishing a stable iteration solving framework combining a cutting plane and a level set projection; in the solving process, the profit and the sub-gradient of each unit under the current price are obtained through the sub-problem, the cutting plane is added, the upper limit and the temporary price are obtained by solving the main problem, and the new price is obtained through the level set projection; when convergence is achieved, the dual variable of the system minimum inertia constraint is extracted, and the inertia shadow price under the convex hull pricing is obtained. The method can reasonably quantify the inertia economic value under the premise of guaranteeing the system frequency safety, significantly reduces the up-regulation cost, and has obvious advantages in calculation efficiency and pricing fairness.

Description

Technical Field

[0001] This invention relates to the fields of power system optimization and electricity market, specifically to a joint market clearing method based on the level set method for electrical energy inertia. Background Technology

[0002] With the continuous increase in the installed capacity of new energy sources such as wind power and photovoltaics, the equivalent rotational inertia of the power system has decreased significantly, and transient frequency indicators (such as the rate of frequency change and the frequency minimum point) tend to deteriorate, exacerbating the risk of frequency instability. To ensure system frequency security, it is urgent to quantify the economic value of inertia through market mechanisms to incentivize synchronous units and virtual inertia resources to actively provide inertia support. Existing technologies mostly use integer relaxation methods to handle unit start-up and shutdown variables, which are difficult to accurately reflect the actual marginal value of inertia.

[0003] In the clearing of the electricity market, the day-ahead unit combination model exhibits non-convex characteristics due to the inclusion of integer variables. Traditional nodal marginal pricing methods struggle to meet incentive compatibility requirements, leading to a discrepancy between unit self-dispatch profits and market dispatch profits—i.e., upward adjustment costs—affecting market fairness. Convex hull pricing, by constructing a convex hull relaxation model of the primal problem to solve for the dual variable as the market price, theoretically minimizes upward adjustment costs and represents a cutting-edge approach to solving non-convex pricing problems.

[0004] In recent years, researchers have proposed various convex hull description methods based on the operating characteristics of generating units, such as state-space characterization based on continuous operating periods, and have attempted to solve these problems using algorithms such as Lagrange duality and Benders decomposition. However, these methods either depend on specific unit constraint forms or experience a sharp increase in model size when dealing with various ancillary services such as inertia. For example, while the convex hull pricing framework based on Dantzig-Wolfe decomposition and column generation algorithms has strong versatility, the size of the main problem continuously increases during iteration, leading to a heavier computational burden and slow convergence in large-scale systems. Summary of the Invention

[0005] To address the following issues in existing technologies: 1) the difficulty in quantifying the economic value of inertia in high-proportion renewable energy power systems and the lack of a reasonable pricing mechanism for synchronous generator inertia services; 2) the high cost and incentive incompatibility of traditional nodal pricing methods under non-convex market clearing models; and 3) the low computational efficiency of existing convex hull pricing methods, such as those based on Dantzig-Wolfe decomposition and column generation algorithms, as the main problem size increases with iteration in large-scale systems.

[0006] This invention provides a joint market clearing method for electrical energy inertia based on the level set method. This method introduces the level set method, constructs a Lagrangian dual function, and employs a stabilization iterative strategy combining cutting planes and level set projections to directly solve for the convex hull price in the price space, avoiding the dimensionality explosion problem caused by convex combinations of feasible regions. This method has a fixed dimension of the main problem variables, exhibits stable and smooth convergence, and can reasonably quantify the economic value of inertia while ensuring system frequency security, significantly reducing upward adjustment costs. Compared with existing pricing methods such as integer relaxation, it has significant advantages in computational efficiency and pricing fairness.

[0007] The technical solution adopted in this invention is as follows: The joint market clearing method for electric energy inertia based on the level set method includes the following steps: S1: Obtain basic power system data and frequency security thresholds, derive the minimum synchronous inertia requirement constraint based on the frequency dynamic response process, and establish an energy-inertia joint clearing model with the goal of minimizing the total system cost and taking into account power balance and minimum inertia constraint; S2: To address the non-convexity of the joint clearing model of electric energy and inertia, a Lagrangian dual function is constructed for the original problem, transforming the dual problem into a subproblem of maximizing unit profits and a main problem based on cutting plane linear programming. S3: Introduce the level set method to establish a stable iterative solution framework that combines the cutting plane and the projection of the level set; S4: During the iterative solution process, the profit and subgradient of each unit under the current price are obtained through subproblems, and a cutting plane is added to solve the main problem to obtain the upper bound and temporary price. Then, the new price is obtained by projection through the horizontal set. S5: Extract the dual variable of the minimum inertia constraint of the system during convergence, which is the inertia shadow price under convex hull pricing.

[0008] In step S1, the system transient frequency stability constraint is transformed into a minimum synchronization inertia requirement constraint, which is expressed as follows: (5); (8); In the formula: This represents the minimum synchronization inertia requirement for the system. The larger of the synchronization inertia requirements calculated from the frequency change rate constraint and the frequency minimum point constraint is taken as the minimum synchronization inertia requirement of the system. This represents the minimum synchronous inertia level required to satisfy the system's rate of change constraint. This represents the minimum synchronous inertia level required to satisfy the system's minimum frequency deviation constraint. This represents the actual online inertia of the system; The system's rated frequency; This refers to the system disturbance fault power. for RoCoF Protection setting value; The number of synchronous generators in the system; The primary frequency regulation response rate of the system's synchronous generator; This refers to the operating status of the synchronous generator; This refers to the allowable range of frequency extreme values. This is a primary frequency modulation dead zone; For generator The inertial time constant; For generator The upper limit of output.

[0009] An energy-inertia joint clearing model considering power balance and minimum inertia constraints is established. The objective function of the model is to minimize the total system scheduling cost, expressed as: (6); In the formula: This represents the minimum total scheduling cost of the system; The number of hours for the scheduling period; This refers to the number of synchronous generators. For generator During the period The power generation operating cost, , , , These are the coefficients of the cost function; For generator During the period The output value; For generator During the period Start-stop status; Indicates generator During the period The start / stop status; For generator During the period Startup costs; The constraints include power balance constraints, minimum inertia constraints, unit output constraints, minimum start-up and shutdown time constraints, and unit ramp / slippage rate constraints. Among these, ①: The power balance constraint is: (7); In the formula: Indicates the synchronous generator set number; The number of synchronous generators in the system; For generator During the period The output value; for The power output of the wind farm during the specified time period; For time period The total load that the system needs to meet.

[0010] ②: The minimum inertia requirement constraint is: (8); In the formula, For generator During the period The start / stop status; The number of synchronous generators in the system; For generator The inertial time constant; For generator The upper limit of output; For time period Minimum inertia requirements of the system.

[0011] ③: The unit output constraint is: (9); In the formula: , The first The upper and lower limits of the generator's output; for t Forecast wind power output for the specified time period.

[0012] ④: The minimum start-up and shutdown time constraints for the unit are: (10); In the formula: , The first One generator in front The continuous power-on and power-off times for each time period; , The first Minimum continuous start-up and shutdown time for the generator.

[0013] ⑤: The unit's ramp / slope rate constraint is: (11); In the formula: , The first The upper and lower limits of the generator's active power output climbing and landslide capabilities.

[0014] To solve the electric energy-inertia joint clearing model using the level set method, the compact form of the primal problem can be expressed as: (12); In the formula, For the unit The cost of electricity generation, Indicates generator During the period The output value; The table represents generators. During the period The start / stop status; Startup costs; Indicates the starting variable; , Indicates generator During the period The start / stop status; Indicates the total number of time periods within the scheduling period; Indicates the number of synchronous generator sets participating in the scheduling; It represents the set of output variables, which consists of the active power output variables of each unit in each time period; This represents the set of start-up and shutdown variables, which consist of the start-up and shutdown status variables of each unit in each time period. Indicates the time period of the wind farm The output value; Indicates time period The system must meet the total load requirements; , These represent the Lagrange dual multipliers corresponding to the power balance constraint and the minimum inertia requirement constraint, respectively. For the unit The feasible operating domain (including constraints such as upper and lower limits of output, ramping, and minimum start and stop time). Indicates the synchronous generator set number; The table represents the time period. The predicted wind power value; Indicates the scheduling time period number.

[0015] Lagrange multipliers are introduced for power balance constraints and inertia demand constraints, respectively. (Electricity price) and (Inertia price).

[0016] In S2, the Lagrange dual function is expressed as: (twenty three); In the formula, Represent the Lagrange dual function; Indicates the unit The active power output variables, start / stop status variables, and start variables throughout the entire scheduling cycle satisfy their operational feasible domain constraints. Indicates the unit The feasible domain; Indicates the first Start-up and shutdown status variables of the generator set during the scheduling cycle; Indicates the first The output of the generator unit during the scheduling cycle; Indicates the starting variable; Represent the Lagrange function; Represents the set of unit output variables Set of unit start-up and shutdown state variables Unit startup variable set Wind power output variable set Electricity price vector and inertia price vector The Lagrangian function of the variable; Represents the set of unit output variables; This represents the set of unit start-up and shutdown state variables; Represents the set of unit startup variables; Represents the set of wind power output variables; This indicates that at a given price of electricity and inertia price Maximize the profit of the generator unit; Represents the inertia-price vector; This represents the inertia-price vector.

[0017] Let the first After the next iteration, there are already organic groups set of cutting planes ,in: For the unit In price The sub-gradient component, , Indicates that, given a price vector Maximize the profit of the generator unit; The subgradient vector is represented by the subgradient vector. Price vector The inner product; The main problem under the multi-cut form is: (twenty two); In the formula, Represents the price vector Belongs to the preset price feasible region , This represents a set of variables composed of approximate auxiliary variables related to the profits of each generating unit; Indicates that it is composed of all The auxiliary variable vector; Indicates time period The Lagrange multipliers corresponding to the power balance constraints; Indicates the total system load; Indicates time period The Lagrange multipliers corresponding to the system's minimum synchronization inertia requirement constraint; Indicates the unit The set of synchronous generator sets that participated in the clearing process; Indicates the synchronous generator set number; This refers to the set of synchronous generator sets that participate in the joint clearing of electrical energy and inertia. Indicates the unit In the The cutting plane intercept term formed at the next iteration; Indicates the historical cutting plane number; This indicates the current iteration number.

[0018] In each iteration of the level set method, given the current price signal... , Indicates the first The energy price vector obtained from the next iteration; Indicates the first The electricity price vector obtained from the next iteration; it is necessary to calculate the profit maximization problem for each unit to obtain the dual function value. And construct the subgradient information required for the cutting plane. For each thermal power unit Its profit function : (16); In the formula, , , The coefficients of the cost function; Indicates the unit During the period The initiation variable, Indicates the unit Startup costs; In S3, the level set projection and level set method generate the cutting plane using the Kelly method: 1) Kelly method: Kelly's method considers maximizing the concave function. The problems include: For price vectors, For compact convex sets, the price range constraint is used in this section; concave functions have the following important properties: at any point At that point, the function value and one of its hypergradients , The following inequalities must be satisfied: (twenty four); In the formula, The hypergradient vector is represented by the hypergradient vector. Difference from price vector The inner product of.

[0019] In other words, a hyperplane is a global upper approximation of the original function. Based on this property, the Kelly method constructs a series of hyperplanes iteratively. upper approximation function The definition is as follows: (25); In the formula, For the first The price point of the next iteration This corresponds to the hypergradient. Due to concavity, we know that... For all It holds true, and with the number of iterations... As the number increases, the approximation becomes increasingly precise. In the... In the next iteration, the following main problem is solved to obtain new candidate points. and the Upper Realm : (26); In the formula, Indicates that it is composed of all The auxiliary variable vector; This problem is a linear programming problem, with price as the variable. and auxiliary variables represent The value of . Its optimal value It is an upper bound on the maximum value of the original dual function, while the optimal solution This is the new iteration point. At the same time, the current point is calculated... The actual function value can be used to update the lower bound: (27); In the formula, Indicates the first Lower bound of the dual function at the next iteration; Indicates the first Historical price vector The true dual function value obtained at the calculated location; The historical iteration numbers range from iteration 0 to iteration 1. The next iteration; Indicates the first The lower bound of the dual function after the next iteration update; Indicates taking the first The next iteration already has a lower bound. With new price points The true dual function value The larger value in the middle is used as the first... The lower bound of the next iteration; Indicates the new price point The true dual function value.

[0020] The difference between the upper and lower bounds provides a convergence criterion. The algorithm terminates when the convergence tolerance is satisfied. (28); In the formula, This indicates the convergence tolerance.

[0021] Kelly's method can be summarized as follows: Step 1: Initialize parameters: Select initial price Set the iteration count The lower realm Upper Realm The set of cutting planes is empty.

[0022] Step 2: Solve the subproblem: for the current price Calculate the value of the dual function. and hypergradient Update the Nether .

[0023] Step 3: Add a cutting plane: Add the new cutting plane Add to the main question.

[0024] Step 4: Solve the main problem: We obtain... and temporary prices .

[0025] Step 5: Update iteration point: Let , .

[0026] Step 6: Convergence Check: If... Stop if the maximum number of iterations is reached; otherwise, proceed to Step 2.

[0027] 2) Level set stabilization strategy: The level set method uses the current point Projected onto the level set To generate new iteration points, the projection problem can be expressed as the following quadratic programming problem: (twenty one); In the formula, It is an approximate function; Indicates the first The new price vector obtained in the next iteration; Represents the price vector to be optimized in the projection problem. It belongs to the preset price feasible region Q; Indicates the first The price vector for the next iteration; Represents the square of the Euclidean distance; The objective value for the level set; The plane constant is the cutting plane constant. It is the inner product of the gradient vector and the price vector.

[0028] The goal of this problem is to minimize the Euclidean distance to the current point while ensuring that the new point lies within the level set. Solving this quadratic programming problem yields the new price. .

[0029] Horizontal parameters The choice of has a significant impact on algorithm performance. When When the level set degenerates into the maximum point of the upper approximation function, the level set method degenerates into the Kelley method; when When the level set is the entire region above the lower bound, the iteration point will not move.

[0030] In S3, the level set method sets the level parameter. , define the first The horizontal objective value for the next iteration is By giving the current upper bound and the lower realm The level set is a set that satisfies the condition that the value of the upper approximation function is not less than 1 The set of price points and These represent the range of values ​​for the price of electrical energy and the price of inertia, respectively.

[0031] (20); In the formula, Indicates the first The level set constructed in the next iteration, i.e., within the price feasible region The set of price points that ensure the current approximate function value is not lower than the horizontal target value; This is the current approximate function; The target value for the level set.

[0032] The approximate function values ​​corresponding to all points within this price point set are no less than the target value. The level set method uses the current point... Projected onto the level set Then generate new iteration points.

[0033] In S4, the iterative solution process specifically includes: The optimal solution to the subproblem is: , , Indicates the unit At the current price vector The optimal active power output and start-stop scheme are determined.

[0034] Then the contribution component of the unit to the gradient for: (18); In the formula, Indicates the first Next iteration timing group The contribution component to the gradient of the price vector; Indicates the first Next iteration price vector Next, the unit During the period The optimal active power output; Indicates the first Next iteration price vector Next, the unit During the period The optimal start / stop state; Indicates by the unit The vector composed of the optimal active power output values ​​for each scheduling period. Since wind power has no start-stop constraints and its marginal cost is zero, the corresponding subgradient contribution is: (29); in, Indicates the first The contribution of the wind farm to the price vector gradient in the next iteration; This represents a vector consisting of the optimal power output values ​​of the wind farm during each scheduling period; Indicates the first Next iteration price vector Under these circumstances, wind farms during certain time periods The optimal output value.

[0035] The overall gradient components are: (30); in, Indicates the first The overall gradient contribution component formed by all synchronous generator units and wind farms in the next iteration.

[0036] Furthermore, in each iteration of the level set method, the main problem utilizes all current historical cutting planes to pair with the dual function. We perform an upper approximation and calculate the maximum value of the approximate function to obtain the upper bound of the maximum value of the dual function. And using the function constructed from the cutting plane: (31); in, Indicates the first The dual function constructed from the existing historical cutting plane in the next iteration The upper approximation function; Indicates the first The gradient vector of each historical cutting plane Price vector The inner product; Indicates the first The intercept term of each historical cutting plane; This indicates the current iteration number.

[0037] satisfy The main problem is equivalent to maximizing ; Solving for the upper bound yields the solution. and temporary prices .

[0038] A new price was obtained after further investigation of the projection issue; details are as follows: Projection problem will Projected to This can be expressed as a quadratic programming problem: (twenty one); in, It is an approximate function; Indicates the first k+1 The new price vector obtained in the next iteration; This represents the price vector that minimizes the objective function. π Represent the price vector to be optimized in the projection problem; Represents the price vector to be optimized π It belongs to the preset price feasible region Q; Represents the gradient vector Price vector The inner product; Indicates the unit i In the j The intercept term of the cutting plane formed at each historical price point; Indicates the first k The horizontal target value for the next iteration; Indicates the unit i It belongs to the collection of synchronous generator sets that participate in the joint clearing of electrical energy and inertia; Indicates the historical cutting plane number; k This indicates the current iteration number.

[0039] In step S5, when the iteration satisfies the convergence condition, the Lagrange multipliers corresponding to the minimum inertia requirement constraint of the system are extracted from the optimal solution of the last solved main problem. The multiplier is the inertia shadow price under convex hull pricing. Specifically: The convergence condition is that the difference between the current upper bound and the lower bound is less than or equal to the preset convergence tolerance, that is: (28); in, Indicates the convergence tolerance. .

[0040] This invention discloses a joint market clearing method for electrical energy and inertia based on the level set method, with the following technical advantages: 1) This invention transforms the transient frequency stability constraint into the minimum synchronous inertia requirement constraint of the system, and embeds an electric energy-inertia joint pricing and clearing model to ensure that transient indicators such as the rate of frequency change and the minimum frequency point do not exceed the limits after the expected disturbance, thereby ensuring frequency safety and incentivizing synchronous generators to actively provide inertia services.

[0041] 2) This invention uses the convex hull pricing mechanism combined with the level set method to directly solve the convex hull price through the stabilization iteration of the cutting plane and the level set projection in the Lagrange dual space. This can reasonably quantify the economic value of inertia, effectively reduce the upward adjustment costs in the market, provide fair and transparent price signals for market participants, and enhance incentive compatibility.

[0042] 3) The level set method of this invention has a fixed dimension of the main problem variable, which does not increase with the number of iterations, thus avoiding the problem of the main problem size expansion in traditional column generation algorithms. Compared with existing convex hull pricing methods, it significantly improves the computational efficiency in large-scale systems, and the convergence process is smooth and stable with good robustness.

[0043] 4) The model framework of this invention has no special requirements on the form of unit constraints, has strong versatility, and can be easily extended to scenarios where new energy virtual inertia and energy storage participate in inertial response, providing theoretical and algorithmic support for the construction of a high-proportion new energy power system inertial auxiliary service market. Attached Figure Description

[0044] The present invention will be further described below with reference to the accompanying drawings and examples; Figure 1 This is the improved wiring diagram of the IEEE 10 machine with 39 nodes according to the present invention.

[0045] Figure 2 The curves showing the predicted load and wind power values ​​in the 39-node example of this invention are shown.

[0046] Figure 3 The curves showing the predicted load and wind power values ​​in the 118-node example of this invention are shown.

[0047] Figure 4This is the minimum synchronization inertia requirement curve for the system in this embodiment of the invention.

[0048] Figure 5 This is the convergence curve of the level set method in this embodiment of the invention.

[0049] Figure 6 This is a clearing price curve for electrical energy and inertia in an embodiment of the present invention.

[0050] Figure 7 This is a comparison chart of inertia shadow prices under different wind power capacity ratios in embodiments of the present invention.

[0051] Figure 8 This is a bar chart comparing the computation time of the level set method and the Dantzig-Wolfe decomposition method in this embodiment of the invention.

[0052] Figure 9 The curves show the influence of different level parameters α on the convergence performance in the embodiments of the present invention. Detailed Implementation

[0053] like Figures 1-9 As shown, a joint market clearing method for electric energy inertia based on the level set method is presented, with the following specific steps and pricing clearing model: Step 1: Obtain basic power system data and frequency security thresholds, derive the minimum synchronous inertia requirement of the system based on the frequency dynamic response process, and establish an energy-inertia joint clearing model with the goal of minimizing the total system cost and taking into account power balance and minimum inertia constraints. The system transient frequency indices include the maximum and minimum frequencies of the system frequency change rate, which can be obtained from the system's dynamic frequency response process after a disturbance. The fundamental cause of frequency fluctuations is the imbalance between the mechanical and electromagnetic power of the generator. Considering only the inertial response of the synchronous generator and primary frequency regulation measures, the system's dynamic frequency response after a disturbance is expressed by the rotor motion equation of the equivalent generator: (1); In the formula: The system's rated frequency, For a moment The frequency of the system's center of inertia For a moment The frequency deviation, in Hz; This refers to the active power regulation of primary frequency modulation, with units of . ; , , They are time points The mechanical and electromagnetic power of the system's equivalent generator, in MW; The damping coefficient of the load is expressed in MW / Hz. This is a primary frequency modulation dead zone; Power imbalance under fault or disturbance, unit: .

[0054] Since the primary frequency regulation process of the synchronous generator set is jointly undertaken by all the units that are started within a unit time, assuming that the primary frequency regulation of the synchronous generator set is linear at a certain ramp rate... Increase, among which For the unit Total reserve capacity of primary frequency modulation power. For the unit The ramp-up time constant for the primary frequency modulation power to reach its maximum value is then... .

[0055] When the system has When there are 1 generator, the system's inertia is a linear combination of the inertia of all operating units, and its expression is: (2); In the formula, For generator Rated power; To characterize the generator The status variables for start and stop are 0 when the machine is stopped and 1 when the machine is started.

[0056] Considering the frequency modulation dead zone of the synchronous machine Therefore, in the initial stage of a disturbance, system frequency regulation mainly relies on the inertial capacity of the synchronous generator to release rotor kinetic energy, increase electromagnetic power, reduce unbalanced power, and suppress further deterioration of RoCoF. Thus, the occurrence of RoCoF at the moment of disturbance is only related to the system disturbance fault power and the inertia level of the synchronous machine. (3); In the formula: , These represent the maximum RoCoF value during system disturbance and the RoCoF limit threshold set by the system, respectively.

[0057] As can be seen from the frequency change curve, the frequency continues to drop, with the lowest frequency occurring when RoCoF is zero. To avoid secondary accidents caused by low-frequency load shearing due to excessively low frequency, After the generator governor actuates, the minimum frequency of the constrained system, combined with the inertial response and primary frequency regulation, is calculated through integration, and then set... The expression for frequency deviation is derived as follows: (4); In the formula: and These represent the extreme value of the frequency deviation and the limit threshold of the frequency deviation when the system is disturbed, respectively. This is the dead zone of a frequency modulation (FM) frequency, measured in units of 1. .

[0058] Based on the RoCoF constraint in equation (3) and the frequency deviation extreme value constraint in equation (4), it is found that in the transient frequency safety of the system, the inertial response plays an important supporting role in maintaining frequency safety. The magnitude of the inertial time constant directly affects the strength of the transient frequency safety constraint. Therefore, in order to avoid triggering RoCoF protection, low-frequency load shedding / high-frequency tripping, the minimum inertia level range required to maintain frequency stability by relying on inertial response and primary frequency modulation measures is derived as follows: (5); In the formula, Minimum inertia requirement for the system, in MW. s.

[0059] Based on the traditional unit combination model, a joint pricing and clearing model for electrical energy inertia that takes inertia constraints into account is constructed, and a pricing and clearing model that considers the system's minimum synchronous inertia requirement constraint is established. The objective function is to minimize the total system scheduling cost, which includes the synchronous unit generation cost and start-up and shutdown costs. The constraints include power balance constraints, minimum inertia requirement constraints, unit output, unit ramp / slippage rate constraints, and minimum start-up and shutdown time constraints.

[0060] The objective function of the established pricing clearing model is: (6); In the formula: This represents the total time period of the research cycle; This refers to the number of generators. For generator exist t Power generation operating costs during the period ,in , , The coefficients of the cost function are... For generator exist t Output value over a given period; For generator exist t Start / stop status during a given time period; For generator exist t Startup costs for a given period of time.

[0061] The constraints of the established pricing clearing model are: ①. Power balance constraint: (7); In the formula: Let t be the power output of the wind farm during time period t; Let t represent the load demand during time period t.

[0062] ②. System minimum inertia constraint: (8); In the formula: For the system in t The minimum inertia required to maintain a stable frequency over a given period of time.

[0063] ③. Unit output constraints: (9); In the formula: , The first The upper and lower limits of the generator's output; for t Forecast wind power output for the specified time period.

[0064] ④. Minimum start-up and shutdown time constraints for the generating unit (10); In the formula: , The first One generator in front The continuous power-on and power-off times for each time period; , The first Minimum continuous start-up and shutdown time for the generator.

[0065] ⑤. Unit ramp / landslide rate constraints: (11); In the formula: , The first The upper and lower limits of the generator's active power output climbing and landslide capabilities.

[0066] The simplified pricing clearing model is as follows: (12); In the formula: For the unit The cost of electricity generation, For start-up costs, Indicates the start-up variable , For the unit The feasible operating region (including output upper and lower limits, ramp rate, minimum start-stop time, etc.) is defined. Power balance constraints and inertia requirement constraints are respectively introduced using Lagrange multipliers. (Electricity price) and (Inertia price).

[0067] Step 2: Construct the Lagrange dual function of the original problem. Introduce the price multiplier of electrical energy. and inertia price multiplier By relaxing the power balance constraint and the system minimum inertia constraint into the objective function, the Lagrangian function is obtained, and then the dual function is defined. The dual problem is decomposed into subproblems of maximizing the profits of each unit: given a price signal... Each unit independently solves its profit maximization problem to obtain the optimal output plan, start-up and shutdown scheme, and corresponding subgradient. In this embodiment, the Gurobi solver is used to solve all subproblems in parallel. The construction and iterative solution of the main problem will be described in subsequent steps.

[0068] By relaxing the power balance constraint and the minimum inertia constraint of the system into the objective function, the Lagrangian function is obtained as follows: (13); Then the Lagrange dual function is: (14); The dual function can be further decomposed into the sum of the following parts: (15); Given the current price signal It is necessary to calculate the profit maximization problem for each unit in order to obtain the dual function value. And construct the subgradient information required for the cutting plane. Where: For the unit The maximum profit at a given price is obtained by solving the profit maximization subproblem: (16); Let be the maximum profit of wind power at a given electricity price. Since the marginal cost of wind power is zero and its output has an upper limit, its profit function is: (17); This subproblem is a mixed-integer linear programming problem, which can be solved using the commercial solver Gurobi. After solving, the unit's... The optimal profit. Let the optimal solution to the subproblem be denoted as . Then the contribution component of the unit to the gradient. for: (18); Since wind turbines have no start-stop constraints and their marginal cost is zero, the corresponding sub-gradient contribution is... .

[0069] Step 3: Introduce the level set method to establish a stable iterative solution framework that combines the cutting plane and the projection of the level set.

[0070] In the In this iteration, the horizontal target value is defined as follows: (19); level set To satisfy the requirement that the value of the upper approximate function is not lower than Price point set: (20); in This is the current approximate function.

[0071] Projection problem will Projected to This can be expressed as a quadratic programming problem: (twenty one); in: For the unit In price gradient components at that point, Then the first k The main problem of the next iteration is: (twenty two); in: Price range constraints, As an auxiliary variable, it represents the effect on the unit. The profit function is the lower approximation formed by the cutting plane. The optimal value of the main problem. Maximum value of dual function An upper bound is given by the function formed by the cutting plane. ,satisfy The main problem is equivalent to maximizing Solving for the upper bound yields the answer. and temporary prices .

[0072] Step 4: Based on the stable iterative framework established in Step 3, perform iterative solutions. Let the current iteration number be... The current price is Each iteration executes the following sub-steps: 1) Initialization: Select the initial price and set the iteration count. , Upper Realm Initialize the cut plane set of all units to empty; 2) Solving subproblems and updating the lower bound: for the current price The profit is obtained by solving the subproblems of each unit in parallel. and gradient components Calculate wind power profits and its subgradient contribution ; Calculate the value of the dual function Update the lower bound ; 3) Add cutting planes: for each unit Calculate the cleavage constant ; cut the plane Add to the constraint set of the main problem; 4) Solve the main problem: Solve the linear programming problem (22) to obtain the upper bound. and temporary prices .

[0073] 5) Horizontal set projection: Calculate the target value of the horizontal set. Solve the quadratic programming equation (21) to obtain the new price. .

[0074] 6) Convergence check: If Then stop and output. As the price of the convex hull; otherwise, let Proceed to step 2.

[0075] Step 5: Then, when the iteration satisfies the convergence condition... When the iteration terminates, extract the Lagrange multipliers corresponding to the minimum inertia requirement constraint of the system from the optimal solution of the last solved main problem. The multiplier is the inertia shadow price under convex hull pricing.

[0076] Example: The embodiments provided by this invention are two improved systems: one with 10 machines and 39 nodes, and the other with 54 machines and 118 nodes. For example... Figure 1 The system shown comprises 10 synchronous generator sets with a total installed capacity of 1662 MW and a total system inertia of 13795.2 MW•s. The system operates on a 24-hour scheduling timeframe, and the anticipated fault power during system disturbances is 10%. The rated frequency is 50Hz. It is assumed that all synchronous generator sets in the system can participate in primary frequency regulation, and the primary frequency regulation dead zone is 0.005Hz. System RoCoF The protection setting value is 0.5Hz / s, and the initial start frequency for low-frequency load shearing is 49Hz. The price range Q is [-50, 50], and the horizontal parameters... a The convergence tolerance is 0.2. For 1e-3 and the number of iterations k maxThe technical parameters for 500.10 synchronous generator sets are shown in Table 1, and the economic parameters are shown in Table 2. The example tests different methods on the two systems.

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[0078]

[0079] 1) Test 1: like Figure 2 The data shows 24-hour wind power and load forecasts. Based on the system's minimum synchronous inertia demand expression, the minimum synchronous inertia demand for each time period within 24 hours is calculated. Then, a synchronous pricing and clearing model is established based on the specific system parameters. The model is solved using Python and the Gurobi solver. The dual multipliers of the minimum synchronous inertia demand constraint are extracted from the optimal solution to obtain the shadow price and electricity price of synchronous inertia for each time period, as shown below. Figure 4 As shown. Figure 4 This indicates that Scheme 2 of the pricing clearing model under the inertia safety constraint of the present invention maintains a relatively sufficient and stable inertia level in all time periods. Compared with Scheme 1 of the traditional unit combination model that does not consider inertia demand constraints, the inertia value of the scheme proposed in this invention is increased by 20% to 55% in the period of weak inertia. For example, it increases from 4231MW·s to 5543MW·s in period 4 and increases significantly from 8463MW·s to 12838MW·s in period 13.

[0080] Depend on Figure 5 It can be seen that the entire convergence process of the level set method is smooth and stable, without obvious oscillations, as shown by the equation. The calculation method and iteration curve of the convergence tolerance demonstrate the effectiveness of the projection strategy in convergence using the level set method. This is achieved through solving... Figure 6 The results of the energy and inertia clearing show that the inertia price is significantly higher in the 10th-12th period than in other periods. This is because the load demand is high during this period, resulting in a large disturbance power. Due to the low marginal cost of wind power, it squeezes out the power generation share of synchronous generators under priority dispatch. In order to meet the system power balance and inertia demand, more synchronous generators are started during this period. However, the system inertia reserve decreases, and inertia resources become increasingly scarce. Therefore, the inertia price is high, which further verifies the effectiveness of the pricing method proposed in this paper.

[0081] 2) Test Two: To verify whether the model can overcome the limitations of high computational cost and its applicability to large-scale systems under the level set algorithm, Example 2 tested and analyzed the improved IEEE 118-node system. This system consists of 54 thermal power units, 91 load points, and 3 wind farms. The total installed capacity of the thermal power units is 7220MW, and the wind farms are located at nodes 14, 54, and 95. Load forecast data and wind power forecast data are as follows: Figure 3 As shown, wind farm data is collected from five system operation scenarios. By changing the installed capacity of wind farms connected to the system, the simulation results are compared and analyzed under different wind farm capacity ratios. The total installed capacity of wind farms in the system and their proportions are shown in Table 3. Meanwhile, the predicted wind speed values ​​for each time period are kept the same under different wind farm installed capacities, and the system load power values ​​remain unchanged. For detailed wind power prediction values ​​and load power data, please refer to... Figure 3 .

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[0083] The joint pricing and clearing model proposed in this invention is used to analyze the price changes of synchronous inertia under different wind farm capacity ratios. Example 2 shows the 24-hour inertia price change curves under different wind farm capacity ratios, as follows: Figure 7 As shown. By Figure 7 It is evident that the higher the proportion of wind farm capacity, the longer the period during which the inertia price is greater than zero. Further analysis reveals that, since the system inertia originates from thermal power units, when considering wind turbines without regard to operating costs and inertia, under power balance constraints, a higher proportion of wind power capacity results in less output from thermal power units under economically viable system conditions. This leads to fewer units starting up the system, making it easier for the system's online inertia to meet the minimum inertia constraint, thus increasing the inertia margin. Therefore, the larger the proportion of wind power capacity, the scarcer the system's online inertia, and the more periods there are when inertia pricing is available.

[0084] Furthermore, during most periods, the shadow price of inertia increases with the increase in the proportion of wind farm capacity. Taking the 12th period as an example, although the wind farm capacity is high and priority is given to dispatch under economic considerations, the load power is large during this period, resulting in large disturbance power, higher transient frequency constraints, and a larger minimum inertia requirement for the system. Therefore, the online inertia requirement is higher under the premise of safe operation, and inertia reserve is also required. The smaller the value, the less room there is for backup units to be scheduled, and the higher the shadow price of inertia.

[0085] Table 4 shows a further comparison of the increased costs under different wind farm capacity ratios.

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[0087] As shown in Table 4, with the increase in wind power capacity share from 10% to 40%, both the MILP function value and the LB function value show a downward trend, indicating a decrease in power generation costs, while the upward adjustment cost increases slightly. This trend reflects that under high wind power penetration, thermal power units need to adjust their operating status more frequently to balance changes in wind power output, amplifying the impact of unit start-up and shutdown in optimization. At the same time, constraints such as ramping, start-up and shutdown, and inertia constraints are more stringent in high wind power scenarios. The start-up and shutdown decisions of each thermal power unit have a significantly greater impact on system cost and reliability, while the power generation cost of wind power is negligible. Therefore, under the condition of meeting power requirements, wind power generation is prioritized, reducing the total system cost. Under low wind power penetration, the system mainly relies on thermal power units for base load, and the start-up and shutdown status of the units is relatively stable, with limited impact from integer variables.

[0088] To further compare the effectiveness of the proposed method in reducing the upward adjustment fee, two different pricing and settlement methods for the upward adjustment fee were set. Scheme 1: 0-1 integer relaxation pricing method (Q1); Scheme 2: the horizontal set inertia-based economic value pricing method proposed in this chapter (Q3).

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[0090] Table 5 compares the increased costs of the two pricing schemes under different wind power penetration rates. Among them, the convex hull pricing method of the level set method proposed in Q3 is better than the integer relaxation method in Q1 under each wind power capacity ratio, which verifies the core advantage of convex hull pricing in minimizing the increased costs. As the wind power penetration rate increases from 10% to 40%, the increased costs of both methods show an upward trend, indicating that the influence of integer variables in the system is amplified under high wind power penetration, and the constraints of unit start-up and shutdown and inertia are more intense. However, the level set method also cannot completely eliminate the non-convexity in the clearing model, so that the increased costs disappear completely.

[0091] To further verify the performance advantage of the level set method in large-scale systems, its solution efficiency was compared with that of the Dantzig-Wolfe (DW) decomposition method under four wind power capacity ratio scenarios. The number of iterations for the two methods is as follows: Figure 8 As shown: Figure 8 The data shows that at a wind power penetration rate of 10%, the two algorithms have similar iteration counts, with the level set method performing slightly better. Further comparison of the convergence performance metrics of the two methods is shown in Table 6.

[0092] Figures 4-9It can be seen that, except for the 10% wind power penetration rate, the number of iterations for the DW decomposition is less than that for the level set method. However, in terms of computation time, the solution time of the DW decomposition decreases significantly with increasing wind power penetration rate, while the computation time of the level set method only increases slightly. Although the level set method has more iterations at high wind power penetration rates, its high efficiency per iteration makes its overall computation time superior to the DW decomposition for all wind power capacity percentage scenarios. This indicates that the level set method trades slightly more iterations for higher efficiency per iteration, lower overall computational cost, and more stable convergence performance, verifying its applicability for large-scale electricity market pricing.

[0093] Horizontal parameters It is a key parameter in the level set method that balances convergence speed and stability. This section compares different... The convergence performance under various parameters was analyzed, and parameter sensitivity was examined to provide a basis for parameter selection in practical applications. Other parameters remained constant: wind power penetration rate 30%, convergence tolerance ε = 1e-4, and maximum number of iterations 500. (Horizontal parameters...) The value range is [0.1, 0.9]. The convergence performance of the algorithm under different parameter levels is compared as follows: Figure 9 As shown: Figure 9 The level set method is demonstrated with different level parameters. Convergence performance within the range of (0.1~0.9). As can be seen from the figure, The algorithm performs best in the range of 0.2 to 0.8, with relatively stable iteration count and computation time. When the level parameter is 0.1 or 0.9, the algorithm's convergence performance decreases slightly, while the number of iterations and computation time increase accordingly. This indicates that the level set method is robust to level parameters and maintains good convergence performance over a wide parameter range, achieving an optimal balance between convergence speed and stability.

[0094] This invention incorporates synchronous inertial response into the paid ancillary services market. Assuming transient frequency stability, it derives the minimum synchronous inertia requirement for the system and, based on the traditional unit combination model, establishes a joint pricing and clearing model for energy and inertia that considers the constraint of the minimum synchronous inertia requirement. To address the non-convexity of the market pricing model and effectively reduce upward adjustment costs while improving solution efficiency, this invention introduces a level set method: It constructs the Lagrangian dual function of the primal problem, transforming the dual problem into a subproblem of maximizing unit profits and a master problem based on cutting plane linear programming. Through a level set projection strategy, the current price point is stably projected onto a level set defined by the cutting plane, iteratively approximating the convex hull price. Upon convergence, the dual variable of the minimum inertia constraint is extracted to obtain the inertia shadow price under convex hull pricing, which is then used to price the system's inertial ancillary services.

[0095] The pricing model proposed in this invention can not only reasonably assess the value of synchronous inertial services and provide market participants with good economic signals, ensuring the safety and stability of system frequency, but also effectively reduce the system's upswing costs under the convex hull pricing mechanism. At the same time, compared with traditional column generation algorithms, it significantly improves the solution efficiency and convergence stability of large-scale systems, and enhances market transparency and incentive compatibility.

Claims

1. A joint market clearing method for electrical energy inertia based on the level set method, characterized in that... Includes the following steps: S1: Based on the frequency dynamic response process, derive the minimum synchronous inertia requirement constraint of the system, and establish an electric energy-inertia joint clearing model with the goal of minimizing the total system cost and taking into account power balance and minimum inertia constraint; S2: To address the non-convexity of the joint clearing model of electric energy and inertia, a Lagrangian dual function is constructed for the original problem, transforming the dual problem into a subproblem of maximizing unit profits and a main problem based on cutting plane linear programming. S3: Introduce the level set method to establish a stable iterative solution framework that combines the cutting plane and the projection of the level set; S4: During the iterative solution process, the profit and subgradient of each unit under the current price are obtained through subproblems, and a cutting plane is added to solve the main problem to obtain the upper bound and temporary price. Then, the new price is obtained by projection through the horizontal set. S5: Extract the dual variable of the minimum inertia constraint of the system during convergence, which is the inertia shadow price under convex hull pricing.

2. The electric energy inertia joint market clearing method based on the level set method according to claim 1, characterized in that: In step S1, the system transient frequency stability constraint is transformed into a minimum synchronization inertia requirement constraint, which is expressed as follows: （5）； （8）； In the formula: This represents the minimum synchronization inertia requirement for the system. The larger of the synchronization inertia requirements calculated from the frequency change rate constraint and the frequency minimum point constraint is taken as the minimum synchronization inertia requirement of the system. This represents the minimum synchronous inertia level required to satisfy the system's rate of change constraint. This represents the minimum synchronous inertia level required to satisfy the system's minimum frequency deviation constraint. This represents the actual online inertia of the system; The system's rated frequency; This refers to the system disturbance fault power. for RoCoF Protection setting value; The number of synchronous generators in the system; The primary frequency regulation response rate of the system's synchronous generator; This refers to the operating status of the synchronous generator; This refers to the allowable range of frequency extreme values. This is a primary frequency modulation dead zone; For generator The inertial time constant; For generator The upper limit of output.

3. The joint market clearing method for electrical energy inertia based on the level set method according to claim 2, characterized in that: An energy-inertia joint clearing model considering power balance and minimum inertia constraints is established. The objective function of the model is to minimize the total system scheduling cost, expressed as: （6）； In the formula: This represents the minimum total scheduling cost of the system; The number of hours for the scheduling period; This refers to the number of synchronous generators. For generator During the period The power generation operating cost, , , , These are the coefficients of the cost function; For generator During the period The output value; For generator During the period The start / stop status; Indicates generator During the period The start / stop status; For generator During the period Startup costs.

4. The joint market clearing method for electrical energy inertia based on the level set method according to claim 3, characterized in that: The constraints include power balance constraints, minimum inertia constraints, unit output constraints, minimum start-up and shutdown time constraints, and unit ramp / slippage rate constraints. in, ①: The power balance constraint is: （7）； In the formula: Indicates the synchronous generator set number; The number of synchronous generators in the system; For generator During the period The output value; for The power output of the wind farm during the specified time period; For time period The system must meet the total load requirements; ②: The minimum inertia requirement constraint is: （8）； In the formula, For generator During the period The start / stop status; The number of synchronous generators in the system; For generator The inertial time constant; For generator The upper limit of output; For time period The system's minimum inertia requirement; ③: The unit output constraint is: （9）； In the formula: , The first The upper and lower limits of the generator's output; for t Forecast wind power output for the specified time period; ④: The minimum start-up and shutdown time constraints for the unit are: （10）； In the formula: , The first One generator in front The continuous power-on and power-off times for each time period; , The first Minimum continuous start-up and shutdown time of the generator; ⑤: The unit's ramp / slope rate constraint is: （11）； In the formula: , The first The upper and lower limits of the generator's active power output climbing and landslide capabilities.

5. The joint market clearing method for electrical energy inertia based on the level set method according to claim 4, characterized in that: To solve the electric energy-inertia joint clearing model using the level set method, the primal problem is expressed in a compact form as follows: （12）； In the formula, For the unit The cost of electricity generation, Indicates generator During the period The output value; The table represents generators. During the period The start / stop status; Startup costs; Indicates the starting variable; , Indicates generator During the period The start / stop status; Indicates the total number of time periods within the scheduling period; Indicates the number of synchronous generator sets participating in the scheduling; It represents the set of output variables, which consists of the active power output variables of each unit in each time period; This represents the set of start-up and shutdown variables, which consist of the start-up and shutdown status variables of each unit in each time period. Indicates the time period of the wind farm The output value; Indicates time period The system must meet the total load requirements; , These represent the Lagrange dual multipliers corresponding to the power balance constraint and the minimum inertia requirement constraint, respectively. For the unit The feasible operating domain; Indicates the synchronous generator set number; The table represents the time period. The predicted wind power value; Indicates the scheduling period number; power balance constraints and inertia demand constraints respectively introduce Lagrange multipliers. and These correspond to the price of electrical energy and the price of inertia, respectively.

6. The joint market clearing method for electrical energy inertia based on the level set method according to claim 5, characterized in that: In S2, the Lagrange dual function is expressed as: （23）； In the formula, Represent the Lagrange dual function; Indicates the unit The active power output variables, start / stop status variables, and start variables throughout the entire scheduling cycle satisfy their operational feasible domain constraints. Indicates the unit The feasible domain; Indicates the first Start-up and shutdown status variables of the generator set during the scheduling cycle; Indicates the first The output of the generator unit during the scheduling cycle; Indicates the starting variable; Represent the Lagrange function; Represents the set of unit output variables Set of unit start-up and shutdown state variables Unit startup variable set Wind power output variable set Electricity price vector and inertia price vector The Lagrangian function of the variable; Represents the set of unit output variables; This represents the set of unit start-up and shutdown state variables; Represents the set of unit startup variables; Represents the set of wind power output variables; This indicates that at a given price of electricity and inertia price Maximize the profit of the generator unit; Represents the inertia-price vector; This represents the inertia-price vector.

7. The joint market clearing method for electric energy inertia based on the level set method according to claim 6, characterized in that: Let the first After the next iteration, there are already organic groups set of cutting planes ,in: For the unit In price The sub-gradient component, , Indicates that, given a price vector Maximize the profit of the generator unit; The subgradient vector is represented by the subgradient vector. Price vector The inner product; The main problem under the multi-cut form is: （22）； In the formula, Represents the price vector Belongs to the preset price feasible region , This represents a set of variables composed of approximate auxiliary variables related to the profits of each generating unit; Indicates that it is composed of all The auxiliary variable vector; Indicates time period The Lagrange multipliers corresponding to the power balance constraints; Indicates the total system load; Indicates time period The Lagrange multipliers corresponding to the system's minimum synchronization inertia requirement constraint; Indicates the unit The set of synchronous generator sets that participated in the clearing process; Indicates the synchronous generator set number; This refers to the set of synchronous generator sets that participate in the joint clearing of electrical energy and inertia. Indicates the unit In the The cutting plane intercept term formed at the next iteration; Indicates the historical cutting plane number; Indicates the current iteration number; In each iteration of the level set method, given the current price signal... , Indicates the first The energy price vector obtained from the next iteration; Indicates the first The electricity price vector obtained from the next iteration; it is necessary to calculate the profit maximization problem for each unit to obtain the dual function value. And construct the subgradient information required for the cutting plane; for each thermal power unit Its profit function : （16）； In the formula, , , The coefficients of the cost function; Indicates the unit During the period The initiation variable, Indicates the unit Startup costs.

8. The joint market clearing method for electric energy inertia based on the level set method according to claim 7, characterized in that: In S3, the level set projection and level set method generate the cutting plane using the Kelly method: 1) Kelly method: Kelly's method considers maximizing the concave function. The problems include: For price vectors, For compact convex sets, the price range constraint is used in this section; concave functions have the following important properties: at any point At that point, the function value and one of its hypergradients , The following inequalities must be satisfied: （24）； In the formula, The hypergradient vector is represented by the hypergradient vector. Difference from price vector The inner product; That is, a hyperplane is a global upper approximation of the original function; based on this property, the Kelly method constructs a series of hyperplanes iteratively. upper approximation function The definition is as follows: （25）； In the formula, For the first The price point of the next iteration This corresponds to the hypergradient; due to concavity, we know that... For all It holds true, and with the number of iterations... As the number of iterations increases, the approximation becomes increasingly precise; in the 1st... In the next iteration, the following main problem is solved to obtain new candidate points. and the Upper Realm : （26）； In the formula, Indicates that it is composed of all The auxiliary variable vector; This problem is a linear programming problem, with price as the variable. and auxiliary variables represent The value; its optimal value It is an upper bound on the maximum value of the original dual function, while the optimal solution This is the new iteration point; at the same time, by calculating the current point... The actual function value can be used to update the lower bound: （27）； In the formula, Indicates the first Lower bound of the dual function at the next iteration; Indicates the first Historical price vector The true dual function value obtained at the calculated location; The historical iteration numbers range from iteration 0 to iteration 1. The next iteration; Indicates the first The lower bound of the dual function after the next iteration update; Indicates taking the first The next iteration already has a lower bound. With new price points The true dual function value The larger value in the middle is used as the first... The lower bound of the next iteration; Indicates the new price point The true dual function value is found; The difference between the upper and lower bounds provides a convergence criterion; the algorithm terminates when the convergence tolerance is satisfied. （28）； In the formula, Indicates the convergence tolerance; The Kelly method follows the following steps: Step 1: Initialize parameters: Select initial price Set the iteration count The lower realm Upper Realm The set of cutting planes is empty; Step 2: Solve the subproblem: for the current price Calculate the value of the dual function. and hypergradient Update the Nether ; Step 3: Add a cutting plane: Add the new cutting plane Add to the main question; Step 4: Solve the main problem: We obtain... and temporary prices ; Step 5: Update iteration point: Let , ; Step 6: Convergence Check: If... Stop if the maximum number of iterations is reached; otherwise, proceed to Step 2. 2) Level set stabilization strategy: The level set method uses the current point Projected onto the level set To generate new iteration points, the projection problem can be expressed as the following quadratic programming problem: （21）； In the formula, It is an approximate function; Indicates the first The new price vector obtained in the next iteration; Represents the price vector to be optimized in the projection problem. It belongs to the preset price feasible region Q; Indicates the first The price vector for the next iteration; Represents the square of the Euclidean distance; The objective value for the level set; The plane constant is the cutting plane constant. It is the inner product of the gradient vector and the price vector; The goal of this problem is to minimize the Euclidean distance to the current point while ensuring that the new point lies within the level set; solving this quadratic programming problem yields the new price. ; Horizontal parameters The choice of has a significant impact on algorithm performance; when When the level set degenerates into the maximum point of the upper approximation function, the level set method degenerates into the Kelley method; when When the level set is the entire region above the lower bound, the iteration point will not move.

9. The joint market clearing method for electrical energy inertia based on the level set method according to claim 8, characterized in that: In S3, the level set method sets the level parameter. , define the first The horizontal objective value for the next iteration is By giving the current upper bound and the lower realm The level set is a set that satisfies the condition that the value of the upper approximation function is not less than 1 The set of price points and These represent the range of values ​​for the price of electrical energy and the price of inertia, respectively. （20）； In the formula, Indicates the first The level set constructed in the next iteration, i.e., within the price feasible region The set of price points that ensure the current approximate function value is not lower than the horizontal target value; This is the current approximate function; The objective value for the level set; The approximate function values ​​corresponding to all points within this price point set are no less than the target value. The level set method uses the current point Projected onto the level set Then generate new iteration points.

10. The joint market clearing method for electric energy inertia based on the level set method according to claim 9, characterized in that: In S4, the iterative solution process specifically includes: The optimal solution to the subproblem is: , , Indicates the unit At the current price vector The optimal active power output and start-stop scheme are determined; Then the contribution component of the unit to the gradient for: （18）； In the formula, Indicates the first Next iteration timing group The contribution component to the gradient of the price vector; Indicates the first Next iteration price vector Next, the unit During the period The optimal active power output; Indicates the first Next iteration price vector Next, the unit During the period The optimal start / stop state; Indicates by the unit The vector composed of the optimal active power output values ​​in each scheduling period; since wind power has no start-stop constraints and its marginal cost is zero, the corresponding subgradient contribution is: （29）； in, Indicates the first The contribution of the wind farm to the price vector gradient in the next iteration; This represents a vector consisting of the optimal power output values ​​of the wind farm during each scheduling period; Indicates the first Next iteration price vector Under these circumstances, wind farms during certain time periods The optimal output value; The overall gradient components are: （30）； in, Indicates the first The overall gradient contribution component formed by all synchronous generator units and wind farms in the next iteration; Furthermore, in each iteration of the level set method, the main problem utilizes all current historical cutting planes to pair with the dual function. We perform an upper approximation and calculate the maximum value of the approximate function to obtain the upper bound of the maximum value of the dual function. And using the function constructed from the cutting plane: （31）； in, Indicates the first The dual function constructed from the existing historical cutting plane in the next iteration The upper approximation function; Indicates the first The gradient vector of each historical cutting plane Price vector The inner product; Indicates the first The intercept term of each historical cutting plane; Indicates the current iteration number; satisfy The main problem is equivalent to maximizing ; Solving for the upper bound yields the solution. and temporary prices ; A new price was obtained after further investigation of the projection issue; details are as follows: Projection problem will Projected to This can be expressed as a quadratic programming problem: （21）； in, It is an approximate function; Indicates the first k+1 The new price vector obtained in the next iteration; This represents the price vector that minimizes the objective function. π Represent the price vector to be optimized in the projection problem; Represents the price vector to be optimized π It belongs to the preset price feasible region Q; Represents the gradient vector Price vector The inner product; Indicates the unit i In the j The intercept term of the cutting plane formed at each historical price point; Indicates the first k The horizontal target value for the next iteration; Indicates the unit i It belongs to the collection of synchronous generator sets that participate in the joint clearing of electrical energy and inertia; Indicates the historical cutting plane number; k This indicates the current iteration number.

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