A microgrid energy-reserve joint market bidding method based on cost mapping

Abstract

The application discloses a kind of based on cost mapping's microgrid energy-reserve joint market bidding method, steps include: obtaining the operating parameter of distributed power supply, energy storage, flexible load and establishing microgrid operation model, with the active power of microgrid, upper reserve power and lower reserve power as planning parameter, the cost of microgrid is to be optimized solution, establish unified offer model and carry out microgrid energy-reserve-cost mapping analytical expression, obtain linear cost domain under different planning parameters;Establish microgrid bidding model based on linear cost domain and distribution network energy-reserve market lower layer joint clearing model, as Stackelberg double game model upper and lower layer respectively and be converted into single-layer mixed integer linear programming model and be solved, obtain the optimal bidding strategy of the active power of microgrid, upper reserve power and lower reserve power.The application can accurately characterize the real operation cost of microgrid under zero bias, with good calculation efficiency.

Description

Technical Field

[0001] This invention relates to the field of power market and microgrid optimal dispatch technology, specifically to a microgrid energy-reserve joint market bidding method based on cost mapping. Background Technology

[0002] The coordinated interaction between distribution networks and microgrids is a crucial foundation for building new power systems. With the continuous increase in renewable energy penetration and the deepening of power market reforms, microgrids, as effective carriers for aggregating distributed resources, are gradually transforming from passive consumption units into active participants in market transactions. Exploring their potential for participation in various trading markets, including the electricity market and ancillary services market, is of key significance for improving the overall operational flexibility of the power system, promoting renewable energy consumption, and optimizing resource allocation efficiency.

[0003] Currently, scholars both domestically and internationally have conducted extensive research on microgrid participation in market bidding and optimal scheduling, primarily focusing on two aspects: market mechanism modeling and bidding strategy optimization. Regarding market mechanism design, existing research has proposed collaborative power trading models between distribution networks and microgrids, aiming to achieve a win-win situation for both. Other studies have addressed the collaborative clearing problem of microgrid participation in the power and reserve service markets, establishing a two-layer optimal scheduling model and verifying the positive impact of participating in diversified markets on improving microgrid profitability and system flexibility. However, most of these studies assume complete transparency of internal microgrid information to the market or employ simplified linear cost models for bidding, failing to fully consider the non-convexity and coupling of equipment constraints and the nonlinear characteristics of cost functions in actual operation. This leads to a significant discrepancy between bidding strategies and actual operating costs, known as the "model mismatch" problem.

[0004] In terms of bidding strategy optimization, to adapt to market rules and reduce information leakage, existing research mainly focuses on the following directions: First, designing new market mechanisms to simplify interactions, such as proposing a two-stage day-ahead / intraday trading mechanism of "reporting quantity but not price," or a P2P trading mechanism based on iterative unified price auctions. These methods attempt to circumvent the disclosure of detailed cost information through mechanism design, but they typically rely heavily on specific, non-standardized market rule designs, making them difficult to apply directly to the existing standardized electricity market centered on clear price signals. Second, employing distributed optimization algorithms to achieve privacy protection, such as using the enhanced Benders decomposition method to achieve joint bidding among multiple microgrids, or designing distributed algorithms based on alternating direction multiplier methods for coordinated scheduling. These methods seek the optimal solution through multiple rounds of boundary information iteration among participants. While this protects privacy to some extent, the iterative process usually requires frequent communication and long convergence times, making it difficult to meet the stringent computational timeliness requirements of current market clearing. Third, privacy abstraction can be achieved using cryptographic techniques or by constructing aggregation models, such as privacy-preserving transaction protocols based on homomorphic encryption or blockchain, or by constructing aggregation models such as "virtual energy storage" to hide internal operational details. However, cryptographic methods typically introduce huge computational and communication overhead, while aggregation models are often too macroscopic and difficult to output accurate marginal cost information that can be directly used to guide bidding decisions. Summary of the Invention

[0005] The technical problem this invention aims to solve is to provide a cost-mapping-based microgrid energy-reserve joint market bidding method that can accurately characterize the real operating cost of microgrids with zero bias and has good computational efficiency, addressing the aforementioned problems in existing technologies. To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows: A cost-mapping-based microgrid energy-reserve joint market bidding method includes the following steps: The operating parameters of distributed power sources, energy storage, and flexible loads within the microgrid are obtained. Based on these operating parameters, a microgrid operation model including distributed power sources, energy storage, and flexible loads is established. The active power, upper reserve power, and lower reserve power of the microgrid are used as planning parameters, and the cost of the microgrid is the solution to be optimized. A unified bidding model with market bidding volume as the objective is established. An analytical expression of the microgrid energy-reserve-cost mapping is performed on the unified pricing model to obtain the linear cost domain of the microgrid under different planning parameters; A microgrid bidding model based on the linear cost domain is established as the upper-level model, and a lower-level joint clearing model of the distribution network energy-reserve market is established as the lower-level model, thus obtaining the Stackelberg two-level game model of energy-reserve. By utilizing the KKT optimality condition and strong duality principle of the lower-level model, the Stackelberg two-level game model is transformed into a single-level mixed-integer linear programming model. The solver is used to solve the single-layer mixed integer linear programming model to obtain the optimal bidding strategy for the active power, upper reserve power and lower reserve power of the microgrid, and generate the corresponding dispatch instructions to control the microgrid to operate according to the optimal bidding strategy.

[0006] Furthermore, the mathematical expression of the unified pricing model is as follows:

[0007]

[0008]

[0009] in, For the cost of microgrids, x The vector of variables to be optimized. y To plan the variable vector, , The vector of variables to be optimized The cost function coefficient matrix, , , The vector of variables to be optimized and planning variable vector y The constraint variable coefficient matrix, The microgrid can provide active power at time t. and The upper and lower backup power that the microgrid can provide at time t are respectively: for t The renewable energy output of distributed power sources at all times, for t The backup power provided by renewable energy at all times for t The output of the micro gas turbine of the distributed power source at all times. and They are respectively t The upper and lower backup power provided by the micro gas turbine at all times. and They represent t Energy storage charging and discharging power at all times, and They represent t The backup power provided by energy storage at all times. for t Real-time flexible load demand and for tFlexible loads can provide backup power at all times.

[0010] Furthermore, when performing an analytical expression of the microgrid energy-reserve-cost mapping for the unified pricing model, the specific steps include: Construct the Lagrangian function and first-order KKT conditions for the unified pricing model; Based on the optimal variable vector of the Lagrange function and the first-order KKT condition setting parameters when they change within the feasible region, the original constraints of the unified pricing model are divided into active constraints and inactive constraints using the optimal variable vector. For the effective constraints, the explicit mapping linear analytical relationship between different variables is obtained by Gaussian elimination; Based on the explicit mapping linear analytical relationship, a unique linear mapping expression between the optimal cost and the planning parameters is obtained, and the space for variation of the planning parameters is divided into critical regions based on the inactive constraints and the explicit mapping linear analytical relationship. When planning variables y When the critical region changes, a piecewise linear analytical function and critical region partitioning are obtained on a bounded closed domain, thereby obtaining a piecewise analytical mapping relationship of microgrid cost-energy-reserve and using it as the linear cost domain of microgrid under different planning parameters.

[0011] Furthermore, the mathematical expression for the piecewise analytical mapping relationship of microgrid cost-energy-reserve is as follows:

[0012] in, for t The cost of microgrids at any time This is the parameter coefficient vector within the Nth critical region. The constant coefficients within the Nth critical region. This is the Nth critical region.

[0013] Furthermore, when the space of variation of planning parameters is divided into critical regions based on the ineffective constraints and the explicit mapping linear analytical relationship, the mathematical expression is as follows:

[0014]

[0015]

[0016] in, This is the critical region. and For the sorted-out first n The parameter coefficient vector and constant coefficients within each critical region, with subscripts... a ,b These represent active and inactive constraints, respectively. and This is the rearranged parameter coefficient vector. This is the optimal variable vector.

[0017] Furthermore, the upper-level model aims to maximize the total revenue minus operating costs in the energy and reserve markets, and its mathematical expression is as follows:

[0018] In the formula: Total profit of the microgrid; for t Time Node i Marginal electricity price of microgrids and They are respectively t Time Node i The clearing price for reserve capacity in microgrids is adjusted upwards and downwards; for t Time Node i Microgrid active power bidding and They are respectively t Time Node i Microgrids adjust the reserve market bidding capacity by both upward and downward. for t Time Node i Microgrid costs; The mathematical expressions for the constraints of the upper-level model are as follows:

[0019]

[0020]

[0021] in, For auxiliary binary variables, for t Time Node i The microgrid bidding variable vector, where M is the maximum value. and They are nodes i The parameter coefficient vector and constant coefficients within the nth critical region. and They are nodes i The parameter coefficient vector and constant coefficients within the nth critical region.

[0022] Furthermore, the lower-level model aims to minimize the overall social welfare of distribution network energy and reserves, and its mathematical expression is as follows:

[0023] In the formula: , , These are the cost coefficients for active power, upper reserve, and lower reserve of the gas turbine unit, respectively. , , These are the active power output, upper reserve power, and lower reserve power of the gas turbine unit, respectively. The constraints of the lower-level model include node power balance constraints, system reserve demand constraints, line transmission capacity constraints, gas turbine unit operation and reserve constraints, and their mathematical expressions are as follows:

[0024]

[0025]

[0026]

[0027]

[0028]

[0029]

[0030]

[0031]

[0032] In the formula: For nodes i exist t The load demand at any time, For the route ij exist t Transmission power at any given moment; and Representing nodes respectively i exist t The need for up-and-down backup at all times. and They represent the lines respectively. ij exist t Always-on backup and backup support; The line indicates the maximum transmission power; and Representing nodes respectively i Minimum and maximum output of the gas turbine unit; and Representing nodes respectively iDownhill and uphill speed limits; Representing nodes respectively i Maximum upper and lower reserve capacities; , , , express t Timetable ij The cost of transmission power and line congestion caused by redundancy; and express t Time Node i Price constraints based on the lower and upper limits of gas turbine unit output. and express t Time Node i Gas turbine unit ramp rate constraint price, and express t Time Node i Price constraints on standby and reserve capacity of gas turbine units.

[0033] Furthermore, the mathematical expression of the Stackelberg two-layer game model is as follows:

[0034] In the formula: This represents the decision vector of the upper-level model; This represents the decision vector for the lower-level model. and These are the sets of equality and inequality constraints for the upper-level model, respectively. and These are the sets of equality and inequality constraints for the lower-level model, respectively. and These are the dual variable vectors of equal and inequality constraints in the lower-level model, respectively.

[0035] Furthermore, when transforming the Stackelberg two-level game model into a single-level mixed-integer linear programming model by utilizing the KKT optimality condition and strong duality principle of the lower-level model, the specific steps include: Calculate the Lagrangian function of the lower-level problem in the Stackelberg two-level game model; The initial single-level mixed-integer linear programming model is obtained by replacing the lower-level model of the Stackelberg two-level game model with the KKT conditions of the Lagrange function of the lower-level problem. The bilinear terms of the objective function in the single-layer mixed-integer linear programming model are linearized using the strong duality principle, and the complementary relaxation condition nonlinear coupling terms in the single-layer mixed-integer linear programming model are linearized using the Big M method, resulting in the final single-layer mixed-integer linear programming model.

[0036] Furthermore, the KKT conditional mathematical expression for the Lagrangian function of the lower-level problem is as follows:

[0037] in, This represents the decision vector of the upper-level model in the Stackelberg two-level game model. This represents the decision vector of the lower-level model in the Stackelberg two-level game model. For gradient operators; The objective function for the lower-level model; and These are the sets of equality and inequality constraints for the lower-level model, respectively. and These are the dual variable vectors of equal and inequality constraints in the lower-level model, respectively. This indicates their complementary relaxation constraints, i.e. .

[0038] Compared with the prior art, the advantages of the present invention are as follows: 1) The cost mapping-based bidding strategy proposed in this invention generates an explicit piecewise linear mapping between microgrid bidding volume and operating cost through multi-parameter programming analysis. It can accurately characterize the real operating cost of microgrid with a deviation of less than 0.01%, thus solving the model mismatch problem.

[0039] 2) By submitting the aggregated cost domain instead of the detailed internal data, this invention effectively protects sensitive information such as the internal equipment parameters, cost coefficients, and real-time operating status of the microgrid, thus achieving a balance between privacy protection and bidding effectiveness.

[0040] 3) This invention efficiently transforms the complex Stackelberg game two-level model into a single-level mixed-integer linear programming model, significantly improving computational efficiency and making it suitable for the current market's tight timeframes. The computation time is significantly reduced compared to centralized optimization methods. 4) Based on the proposed strategy, microgrids can flexibly optimize their regulation capabilities between the energy and reserve markets according to real-time market price signals, verifying the effectiveness of the multi-market collaborative participation strategy in improving microgrid profits. Attached Figure Description

[0041] Figure 1 This is a flowchart of a method according to an embodiment of the present invention.

[0042] Figure 2 This is a schematic diagram of the Stackelberg two-layer game model framework according to an embodiment of the present invention.

[0043] Figure 3 Diagram of a micro-distribution network simulation system. Figure 4 This is a schematic diagram of the renewable energy output, flexible load adjustable capacity, load demand, and system reserve demand curves of a typical daily microgrid.

[0044] Figure 5 This is a schematic diagram of the three-dimensional mapping surface of active power, reserve, and cost in a microgrid.

[0045] Figure 6 This is a schematic diagram of the active power market clearing results and microgrid node electricity prices on a typical day.

[0046] Figure 7 This is a schematic diagram illustrating the typical clearing results of the Sunrise standby market.

[0047] Figure 8 This is a schematic diagram illustrating the typical clearing results of the Nisshoku standby market. Detailed Implementation

[0048] The present invention will be further described below with reference to the accompanying drawings and specific preferred embodiments, but this does not limit the scope of protection of the present invention.

[0049] This embodiment proposes a cost-mapping-based microgrid energy-reserve joint market bidding method, achieving accurate, efficient, and privacy-preserving characterization of microgrid operating costs, and formulating optimal market bidding strategies accordingly. Figure 1 As shown, the method includes the following steps: Step S1: Establish a refined operation model of the microgrid, including distributed power sources, energy storage, and flexible loads, and determine a unified bidding model with market bidding volume as the target. Specifically, obtain the operation parameters of distributed power sources, energy storage, and flexible loads within the microgrid; establish a microgrid operation model including distributed power sources, energy storage, and flexible loads based on the operation parameters; and establish a unified bidding model with market bidding volume as the target, using the microgrid's bidding volume as the planning parameter and the microgrid's cost as the optimization solution. The microgrid's bidding volume includes active power, upper reserve power, and lower reserve power. Step S2: Based on the unified pricing model obtained in Step S1, an analytical expression of the microgrid energy-reserve-cost mapping is performed using multi-parameter programming theory. Specifically, multi-parameter programming theory is used to perform an analytical expression of the microgrid energy-reserve-cost mapping of the unified pricing model, obtaining the linear cost domain of the microgrid under different planning parameters; Step S3: Based on the linear cost domain expressed in Step S2, construct a Stackelberg game bidding-clearing two-layer model for the distribution network and microgrids. Specifically, establish a microgrid bidding model based on the linear cost domain as the upper-layer model, and a lower-layer joint clearing model for the distribution network energy-reserve market as the lower-layer model, to obtain the Stackelberg two-layer game model for energy-reserve. Step S4: Using the KKT optimality condition and strong duality principle of the lower-level model, the Stackelberg two-level game model constructed in step S3 is transformed into a single-level mixed integer linear programming model. Step S5: Based on the MATLAB platform and YALMIP toolbox, build the single-layer mixed integer linear programming model of step S4. Use the GUROBI solver to solve the single-layer mixed integer linear programming model to obtain the optimal bidding strategy for the active power, upper reserve power and lower reserve power of the microgrid. Then generate the corresponding scheduling instructions to control the microgrid to operate according to the optimal bidding strategy.

[0050] The following provides a detailed explanation of each step.

[0051] In step S1 of this embodiment, when obtaining the operating parameters of distributed power sources, energy storage, and flexible loads within the microgrid, specifically, the predicted output data of renewable energy sources, the output limit and ramp rate of micro gas turbines, the state of charge and maximum charging / discharging power of energy storage, and the adjustable capacity range of flexible loads are obtained. The specific process for establishing a microgrid operation model including distributed power sources, energy storage, and flexible loads based on these operating parameters is as follows: Distributed power sources include renewable energy and micro gas turbines. Micro gas turbines not only provide active power during operation but also provide a certain amount of backup power, as shown in the following expression: (1) (2) (3) (4) In the formula: for t Real-time renewable energy output forecast for t Real-time renewable energy output forecast for t The micro gas turbine output is always available. and They are respectively t The upper and lower limits of the gas turbine's ramp rate at all times. and They are respectivelyt The upper and lower backup power provided by the micro gas turbine at all times.

[0052] Electric energy storage requires binary variable constraints to ensure mutual exclusion during charging and discharging. The resulting non-convexity leads to the curse of dimensionality in optimization solutions, making it difficult to quickly obtain efficient solutions. Therefore, a convex model is constructed based on the vertex information of the feasible operating region of energy storage. Furthermore, in addition to participating in energy regulation, energy storage can also provide some backup support for the system. The final model is expressed in the following form: (5) (6) (7) (8) (9) (10) (11) (12) (13) In the formula: express t Constant energy storage state of charge, Indicates the energy storage charging and discharging efficiency. and They represent t Energy storage charging and discharging power at all times; and They represent t Maximum charge and discharge power of energy storage at all times; and These represent the upper and lower limits of energy storage capacity, respectively. and They represent t The backup power provided by the energy storage at all times.

[0053] Flexible loads can be adjusted while ensuring user comfort, and this paper assumes that all flexible loads regulated by the microgrid have signed agreements and are willing to accept dispatch arrangements. These loads can not only participate in energy regulation but also provide some backup support for the microgrid, as shown below.

[0054] (14) (15) (16) In the formula: for t Real-time flexible load demand; and They are respectively t The upper and lower limits of the flexible load can be adjusted at any time. and for t Flexible loads can provide backup power at all times.

[0055] The overall power balance constraints of the microgrid mentioned above include power balance constraints and upper and lower reserve balance constraints, as shown below: (17) (18) (19) In the formula: for t Microgrid load demand at all times; and For respectively t The uplink and downlink backup requirements of microgrids at all times; for t Microgrids can provide active power at any time. and They are respectively t Microgrids can provide both upstream and downstream backup power. for t The backup power provided by renewable energy sources at all times.

[0056] In step S1 of this embodiment, before establishing the unified pricing model, a cost function for the microgrid is also constructed. Operating costs of micro gas turbine units Energy storage operating costs Flexible load cost Composition, represented in the following form: (20) (twenty one) (twenty two) (twenty three) In the formula: Let t be the expected value of the flexible load. This represents the cost coefficient for micro gas turbines. and These are the power cost coefficients for upper and lower reserves of micro gas turbines, respectively. and This refers to the charging and discharging cost coefficient for energy storage. and These are the cost coefficients for upper and lower standby power of energy storage, respectively; The flexible load penalty cost coefficient, and The cost coefficient for standby power above and below flexible loads.

[0057] In step S1 of this embodiment, when establishing a unified pricing model targeting market bidding volume, specifically... , and For planning parameters, the cost of microgrids To find the optimal solution, the energy-reserve-cost expression for the microgrid is analyzed, and the established unified pricing model can be expressed in the following compact form: (twenty four) (25) (26) (27) (28) (29) (30) (31) (32) (33) (34) (35) (36) (37) (38) (39) (40) (41) (42) (43) In the formula, x The vector of variables to be optimized. y For planning variable vectors; , The vector of variables to be optimized in equation (26) obtained by rearranging equations (20)-(23) The cost function coefficient matrix is ​​shown in equations (27) and (28); , , The vector of variables to be optimized in equation (26) obtained by rearranging equations (1)-(19) and planning variable vector y The constraint variable coefficient matrix. Specifically, Depend on , , and composition, The vector of variables to be optimized obtained by rearranging equations (1)-(4) The coefficient matrix is ​​shown in equation (30); The vector of variables to be optimized obtained by rearranging equations (5) to (13) The coefficient matrix is ​​shown in equation (31); The vector of variables to be optimized obtained by rearranging equations (14)-(16) The coefficient matrix is ​​shown in equation (32); The vector of variables to be optimized obtained by rearranging equations (17)-(19) The coefficient matrix is ​​shown in equation (33). Depend on , , and composition, The result of rearranging equations (1) to (4) regarding the vector of variables y The coefficient matrix is ​​shown in equation (35), where It is a 3x8 matrix of zeros; The result of rearranging equations (5) to (13) regarding the vector of variables y The coefficient matrix is ​​shown in equation (36), where It is a 3x13 matrix of zeros; The result of rearranging equations (14) to (16) regarding the variable vectors y The coefficient matrix is ​​shown in equation (37), where It is a 3x6 matrix of zeros; The result of rearranging equations (17) to (19) regarding the vector of variables y The coefficient matrix is ​​shown in equation (38). Depend on , , and composition, The constant vector obtained by rearranging equations (1) to (4) is shown in equation (40); The constant vector obtained by rearranging equations (5) to (13) is shown in equation (41); The constant vector obtained by rearranging equations (14)-(16) is shown in equation (42); The constant vector obtained by rearranging equations (17) to (19) is shown in equation (43).

[0058] In step S2 of this embodiment, when using multi-parameter programming theory to perform an analytical expression of the microgrid energy-reserve-cost mapping for the unified pricing model, the specific process is as follows: S21: Construct the Lagrangian function and first-order KKT conditions of the unified pricing model. To solve for the optimal solution of equations (24)-(26) in the unified pricing model, the Lagrangian function and its first-order KKT conditions of equations (24)-(26) are constructed as follows: (44) (45) In the formula: is a Lagrange multiplier vector.

[0059] S22: When the parameters vary within the feasible region, the optimal variable vector for the parameters varying within the feasible region can be set according to the Lagrangian function and the first-order KKT conditions. Thus, the optimal variable vector is used. The original constraints of the unified pricing model are further divided into active constraints. and ineffective constraints It is represented as follows: (46) (47) In the formula: subscript a , b These represent active and inactive constraints, respectively.

[0060] S23: For the constraints in equation (46), the explicit linear analytical relationships between different variables can be obtained by Gaussian elimination, as shown below: (48) In the formula: and This is the rearranged parameter coefficient vector.

[0061] S24: Based on the explicit mapping linear analytical relationship, the unique linear mapping expression between the optimal cost and the planning parameters is obtained, as shown in equation (49). Based on the inactive constraint shown in equation (47) and the explicit mapping linear analytical relationship shown in equation (48), a planning parameter variation space can be divided into a critical region, that is, the critical region is defined. As shown in equation (50): (49) (50) In the formula: , , and For the sorted-out first n The parameter coefficient vector and constant coefficients within each critical region.

[0062] S25: When planning variables y In the critical region During internal changes, there is always a unique optimal mapping relationship. Based on multi-parameter programming theory, by enumerating all combinations of active and inactive constraints, a piecewise linear analytic function and critical domain partitioning on a bounded closed domain can be obtained. This yields the piecewise analytic mapping relationship of microgrid cost-energy-reserve, which serves as the linear cost domain of the microgrid under different planning parameters. The final mathematical expression for the piecewise analytic mapping relationship of microgrid cost-energy-reserve is as follows: (51) in, for t The cost of microgrids at any time This is the parameter coefficient vector within the Nth critical region. The constant coefficients within the Nth critical region. This is the Nth critical region.

[0063] In step S3 of this embodiment, the specific process of constructing the Stackelberg game two-layer model of the distribution network and microgrid is as follows: S31: Constructing the upper-level model. In this embodiment, the upper-level model adopts a microgrid upper-level bidding model based on the cost domain, which aims to maximize the total revenue minus the operating cost in the energy and reserve markets. The mathematical expression is as follows: (52) In the formula: Total profit of microgrids; for t Time Node i The marginal electricity price of microgrids and They are respectively t Time Node i The clearing price for reserve capacity on microgrids was increased or decreased; for t Time Node i Microgrid active power volume won in the bidding and They are respectively t Time Node i The micro-network adjusted and lowered the reserve market bidding adjustment capacity; for t Time Node i Microgrid cost.

[0064] In this embodiment, the constraint of the upper-level model is that the bidding combination must be located within the piecewise linear critical region characterized by equation (50), and each critical region This can be described by a set of linear inequalities. To handle the piecewise structure shown in the optimization, auxiliary binary variables can be introduced. Linearization with the Big M method. It can be expressed in the following form: (53) (54) In the formula: Let M be the vector of bidding variables for node i in the microgrid at time t, and M be the maximum value. and Let be the parameter coefficient vector and constant coefficients, respectively, within the nth critical region of node i. and These are the parameter coefficient vector and constant coefficients within the nth critical region of node i, respectively.

[0065] Under this constraint, the microgrid can only select one critical region in each time period, and if a critical region is selected... k ,Right now Microgrid bidding variable vector All linear inequality constraints in this region must be satisfied; otherwise, these constraints should be relaxed, and the total cost of the microgrid will be reduced. It must match the selected area, as shown below: (55) Since the objective function is to maximize profit, the inequality in constraint (55) will cause [the following] during the optimization process: Get the selected area k The corresponding actual linear cost value. If... Then the constraint changes Greater than And it will make Equal to that value cost; if If the constraint is relaxed, it will have no effect.

[0066] S32: Constructing the lower-level model. In this embodiment, the lower-level model adopts a joint clearing model for the distribution network energy-reserve market. Market operators aggregate bids from energy and reserve entities. The clearing objective of the lower-level model is to maximize the overall social welfare of energy and reserves, as expressed mathematically below: (56) In the formula: , , These are the cost coefficients for active power, upper reserve, and lower reserve of the gas turbine unit, respectively. , , These are the active power output, upper reserve power, and lower reserve power of the gas turbine unit, respectively.

[0067] In this embodiment, the constraints of the lower-level model include node power balance constraints, system reserve demand constraints, line transmission capacity constraints, gas turbine unit operation, and reserve constraints, and their mathematical expressions are as follows: (57) (58) (59) (60) (61) (62) (63) (64) (65) In the formula: For nodes i exist t The load demand at any time, For the route ij exist t Transmission power at any given moment; and Representing nodes respectively i exist t The need for up-and-down backup at all times. and They represent the lines respectively. ij exist t Always-on backup and backup support; The line indicates the maximum transmission power; and Representing nodes respectively i Minimum and maximum output of the gas turbine unit; and Representing nodes respectively i Downhill and uphill speed limits; Representing nodes respectively i Maximum upper and lower reserve capacities; , , , express t Timetable ij The cost of transmission power and line congestion caused by redundancy; and express t Time Node i Price constraints based on the lower and upper limits of gas turbine unit output. and express t Time Node i Gas turbine unit ramp rate constraint price, and express t Time Node i Price constraints on standby and reserve capacity of gas turbine units.

[0068] The upper-level model established by equations (52)-(55) and the lower-level model established by equations (56)-(65) constitute an energy-reserve Stackelberg two-level game as shown in equation (66).

[0069] (66) In the formula: This represents the decision vector of the upper-level model; This represents the decision vector for the lower-level model. and These are the sets of equality and inequality constraints for the upper-level model, respectively. and These are the sets of equality and inequality constraints for the lower-level model, respectively. and These are the dual variable vectors of equal and inequality constraints in the lower-level model, respectively.

[0070] like Figure 2As shown, in the upper-level model, the microgrid aggregates distributed resources such as internal wind and solar turbines, gas turbines, energy storage devices, and flexible loads. Based on the physical operating parameters and cost characteristics of each device, multi-parameter programming theory is used to analytically express the energy-reserve-cost relationship of the microgrid, generating a piecewise linear cost domain with bidding quantities (active power, upper reserve, lower reserve) as planning parameters. This cost domain accurately represents the actual operating cost of the microgrid under different bidding combinations, serving as the endogenous cost basis for the microgrid to participate in market bidding, while effectively protecting sensitive information such as internal device parameters and operating status.

[0071] The lower-level model is operated by the distribution network market operator. The market operator aggregates the mapping cost information (i.e., piecewise linear cost domain) submitted by the microgrids with the power generation resources, network topology and load demand information on the distribution network side, and performs unified clearing with the goal of maximizing social welfare, determining the node marginal electricity price and reserve clearing price.

[0072] The upper and lower layers achieve collaboration through information exchange: the upper-layer microgrid generates a cost domain based on its internal operating status and submits it to the lower layer; after the lower-layer market operator completes the clearing process, it feeds back the clearing results (marginal electricity price, winning bid volume, and reserve capacity) to the upper layer, guiding the microgrid to formulate the optimal bidding strategy. This framework accurately represents the true operating cost of the microgrid with zero deviation while realizing the coordinated and optimized operation of the microgrid and the distribution network.

[0073] In this embodiment, to improve computational efficiency, the Stackelberg two-layer game model is transformed into a single-layer mixed-integer linear programming model in step S4 by utilizing the KKT optimality condition and strong duality principle of the lower-level model. The specific process is as follows: S41: Calculate the Lagrangian function of the lower-level problem in the Stackelberg two-level game model. Since the physical constraints of the power system ensure the existence of strictly internal points in the feasible solution set, the Slater conditions are satisfied. Therefore, strong duality holds, and the KKT conditions can be used to replace the lower-level optimization problem, transforming the two-level model into a single-level mixed-integer linear programming problem for solution. The Lagrangian function of the lower-level problem is expressed as: (67) Its KKT conditions are expressed as: (68) In the formula: This represents the decision vector of the upper-level model in the Stackelberg two-level game model. This represents the decision vector of the lower-level model in the Stackelberg two-level game model. For gradient operators; The objective function for the lower-level model; This indicates their complementary relaxation constraints, i.e. .

[0074] S42: Replace the lower-level model of the Stackelberg two-level game model with the KKT conditions of the Lagrangian function of the lower-level problem to obtain the initial single-level mixed-integer linear programming model. By replacing the original model with the KKT conditions of the lower-level problem, the two-level game between the microgrid and the market operator is transformed into a single-level mixed-integer linear programming problem that can be solved efficiently, as shown in Equation (69). (69) S43: The bilinear terms of the objective function in the single-layer mixed integer linear programming model are linearized using the strong duality principle. For the bilinear terms of the objective function (52) in the original problem, a linearization transformation is performed using the strong duality principle, as shown in equation (70): (70) S44: The complementary relaxation condition nonlinear coupling terms in the single-layer mixed integer linear programming model are linearized using the Big M method. For the complementary relaxation condition nonlinear coupling terms that are widely present in model (69), the Big M method is used for linearization. The linearized form is shown below: (71) In the formula: For the first k A complementary relaxation constraint For the first k The complementary relaxation constraints correspond to the binary variables.

[0075] Through the processing of steps S41 to S44 above, the final single-layer mixed integer linear programming model is obtained.

[0076] The specific process of step S5 in this embodiment is as follows: The corresponding model in step S4 is built based on the MATLAB platform and the YALMIMP toolbox. The day-ahead scheduling data and system equipment parameters are substituted into it. After determining the maximum profit obtained by the microgrid as the objective function, the model is solved using the GUROBIO solver.

[0077] For the optimal bidding strategy of active power, upper reserve power, and lower reserve power of the microgrid obtained by solving, scheduling instructions are generated for the internal equipment of the microgrid, and each equipment is controlled to operate according to the scheduling instructions so that the power exchange between the microgrid and the upper-level distribution network meets the optimal bidding strategy. The specific logic is as follows: 1. The optimal bidding strategy obtained from the solution (active power bidding amount, upper and lower reserve bidding amount, etc.) is first used as the power exchange intention submitted by the microgrid to the upper distribution network or the power market.

[0078] 2. Based on market clearing or optimized scheduling, the distribution network dispatch center formulates a formal power exchange plan (or dispatch instruction) and issues it to the microgrid.

[0079] 3. The microgrid energy management system (EMS) adjusts its internal controllable devices (distributed power sources, energy storage, flexible loads, etc.) in real time according to the power exchange plan, so that the actual power exchanged between the microgrid and the upper-level grid tracks the bid value.

[0080] The effectiveness of the method in this embodiment will be further verified through experiments below.

[0081] An improved IEEE 13-bus distribution network was used as the test system. Figure 3 The topology is shown. Distribution system node 4 is connected to a microgrid. Within the microgrid, a micro gas turbine unit has a rated power of 2000 kW, an energy storage capacity of 800 kWh, a maximum charge / discharge power of 150 kW, micro renewable energy output, adjustable capacity for flexible loads, and load and reserve requirements as shown. Figure 4 As shown in Table 1, the cost coefficients of each device in the microgrid are as follows.

[0082] Table 1. Cost coefficients of microgrid equipment

[0083] Based on microgrid market bidding volume Using the planning parameters, its energy-reserve-cost domain is obtained. This cost domain is a piecewise linear function, reflecting the minimum operating cost of the microgrid under different bidding combinations. Figure 4 Showing t =12 Microgrid cost is related to active power and reserve adjustment in a three-dimensional slice surface. The surface in the figure is composed of multiple planar curves.

[0084] Figure 5 The mid-cost domain is a piecewise linear surface, with each plane corresponding to a critical region. This represents a specific combination of operating states of the microgrid's internal equipment within the region. The slope of the surface reflects the change in marginal cost of the microgrid under different combinations of output and reserve. The transitions between segments correspond to the switching of the internal equipment's operating state between providing active power or reserve.

[0085] By comparing the regional characteristics in different directions, it can be seen that when a microgrid, such as in Region 3, mainly provides up-load backup, its marginal cost is relatively low; while in Region 5, the marginal cost increases significantly with the increase in active power output demand. In the same direction, the cost in Region 1 is low and changes gradually, corresponding to an operating state with sufficient renewable energy output; in Region 2, energy storage is in a charging or idle state, and the marginal cost is mainly determined by the energy storage operating cost; in Regions 4 and 6, which are dominated by micro gas turbines and flexible loads, the cost exhibits a quadratic function, leading to a rise in marginal cost.

[0086] Figure 6 The results of the active power market clearing and its marginal nodal price are presented. The active power clearing price fluctuated between 400 and 600 yuan / MW, with an average price of 533.1 yuan / MW. The price trend showed a pattern of low prices in the morning and evening, and high prices during the midday and evening peak periods. The load peaked between the 12th and 13th hour, coinciding with the peak clearing price, reflecting the tight supply situation during peak load periods. Traditional gas turbine units bore the brunt of the system's power supply, while the microgrid provided its maximum active power output for most of the time, offering additional power support to the system and alleviating system pressure.

[0087] Figure 7 and Figure 8 The clearing results and marginal node prices of the upper and lower reserve markets are presented separately. The microgrid's reserve provision decisions reflect its economic optimization as a flexibility resource and its responsiveness to system demand. In the first 18 hours, the microgrid provided 0.32 MW of active power and 3.3 MW of upper reserve, allocating operational space to the higher-priced upper reserve service to maximize revenue. In the 23rd hour, the microgrid provided 4.7 MW of lower reserve, utilizing its rapid adjustment capabilities to address system balancing needs during load decline phases. Based on market price signals and system demand, it can dynamically optimize its operating mode under operational space constraints, improving its own revenue and providing crucial ancillary service support to the system.

[0088] To verify the practicality of the method in this embodiment and the impact of different microgrid participation strategies on the distribution network market clearing results, the following four schemes were set up for comparative analysis: Option 1: Microgrids do not participate in the energy market and the backup market, but sell energy and backup at the average market price.

[0089] Option 2: The microgrid participates only in the energy market, and the standby power is sold at a fixed market price.

[0090] Option 3: The microgrid participates only in the backup market, and sells its active power at a fixed market price.

[0091] Option 4: Microgrids can participate in both the energy market and the backup market, and can flexibly provide active power and backup services.

[0092] Table 2 shows the market clearing results, total system cost, and microgrid revenue of the four schemes. The economics and impact on system operation of different participation strategies of microgrids are evaluated by comparison.

[0093] Table 2. Economic indicators of microgrids in different scenarios

[0094] Table 2's economic indicator analysis reveals the economic differences of different market participation strategies for microgrids. Scheme 2, which only participates in the energy market, achieves the highest electricity sales revenue, but its operating costs are high. This is mainly due to the quadratic nature of the generation cost function, leading to a sharp increase in marginal costs. Comparing Schemes 1, 2, and 3 shows that participating in both the active power market and the reserve market can bring incremental revenue. A comprehensive comparison of Schemes 2, 3, and 4 reveals that Scheme 4's simultaneous participation strategy achieves the best balance, avoiding the problem of rapidly rising marginal costs caused by over-focusing on a single market. Simultaneously, it generates additional revenue by providing reserve services. Although the total revenue is slightly lower than Scheme 2, the more effective control of operating costs ultimately achieves the optimal profit. By flexibly participating in multiple markets, microgrids can optimize the allocation of their limited capacity resources, maximizing economic benefits and verifying the effectiveness of the method in this embodiment.

[0095] In summary, this invention proposes a cost-mapping-based bidding method for the microgrid energy-reserve joint market. First, the refined operation model within the microgrid is reconstructed into a multi-parameter programming problem with market bid volume as the planning parameter. An explicit piecewise linear mapping relationship between bid volume and operating cost is generated analytically. Second, a Stackelberg game-based bidding-clearing two-layer model is constructed based on this endogenous cost domain. Finally, utilizing the KKT conditions and strong duality principle of the lower-level clearing model, the original problem is efficiently transformed into a solvable single-layer mixed-integer linear programming model. Experiments demonstrate that the proposed method can accurately characterize the true operating cost of the microgrid with zero bias, with a deviation of less than 0.01% between the reported cost and the internal true minimum cost. It also effectively protects sensitive information such as internal equipment parameters and operating status, and possesses good computational efficiency, making it suitable for microgrids to quickly and securely formulate bidding strategies in the standardization-day market.

[0096] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-readable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create a machine for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to operate in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The functions specified in one or more boxes. These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable apparatus for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0097] The above description is merely a preferred embodiment of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principles of the present invention should also be considered within the scope of protection of the present invention.

Claims

1. A microgrid energy-reserve joint market bidding method based on cost mapping, characterized in that, Includes the following steps: The operating parameters of distributed power sources, energy storage, and flexible loads within the microgrid are obtained. Based on these operating parameters, a microgrid operation model including distributed power sources, energy storage, and flexible loads is established. The active power, upper reserve power, and lower reserve power of the microgrid are used as planning parameters, and the cost of the microgrid is the solution to be optimized. A unified bidding model with market bidding volume as the objective is established. An analytical expression of the microgrid energy-reserve-cost mapping is performed on the unified pricing model to obtain the linear cost domain of the microgrid under different planning parameters; A microgrid bidding model based on the linear cost domain is established as the upper-level model, and a lower-level joint clearing model of the distribution network energy-reserve market is established as the lower-level model, thus obtaining the Stackelberg two-level game model of energy-reserve. By utilizing the KKT optimality condition and strong duality principle of the lower-level model, the Stackelberg two-level game model is transformed into a single-level mixed-integer linear programming model. The solver is used to solve the single-layer mixed integer linear programming model to obtain the optimal bidding strategy for the active power, upper reserve power and lower reserve power of the microgrid, and generate the corresponding dispatch instructions to control the microgrid to operate according to the optimal bidding strategy.

2. The microgrid energy-reserve joint market bidding method based on cost mapping according to claim 1, characterized in that, The mathematical expression for the unified pricing model is as follows: in, For the cost of microgrids, x The vector of variables to be optimized. y To plan the variable vector, , The vector of variables to be optimized The cost function coefficient matrix, , , The vector of variables to be optimized and planning variable vector y The constraint variable coefficient matrix, The microgrid can provide active power at time t. and The upper and lower backup power that the microgrid can provide at time t are respectively: for t The renewable energy output of distributed power sources at all times, for t The backup power provided by renewable energy at all times for t The output of the micro gas turbine of the distributed power source at all times. and They are respectively t The upper and lower backup power provided by the micro gas turbine at all times. and They represent t Energy storage charging and discharging power at all times, and They represent t The backup power provided by energy storage at all times. for t Real-time flexible load demand and for t Flexible loads can provide backup power at all times.

3. The microgrid energy-reserve joint market bidding method based on cost mapping according to claim 2, characterized in that, When performing an analytical expression of the microgrid energy-reserve-cost mapping for the unified pricing model, the specific steps include: Construct the Lagrangian function and first-order KKT conditions for the unified pricing model; Based on the optimal variable vector of the Lagrange function and the first-order KKT condition setting parameters when they change within the feasible region, the original constraints of the unified pricing model are divided into active constraints and inactive constraints using the optimal variable vector. For the effective constraints, the explicit mapping linear analytical relationship between different variables is obtained by Gaussian elimination; Based on the explicit mapping linear analytical relationship, a unique linear mapping expression between the optimal cost and the planning parameters is obtained, and the space for variation of the planning parameters is divided into critical regions based on the inactive constraints and the explicit mapping linear analytical relationship. When planning variables y When the critical region changes, a piecewise linear analytical function and critical region partitioning are obtained on a bounded closed domain, thereby obtaining a piecewise analytical mapping relationship of microgrid cost-energy-reserve and using it as the linear cost domain of microgrid under different planning parameters.

4. The microgrid energy-reserve joint market bidding method based on cost mapping according to claim 3, characterized in that, The mathematical expression for the segmented analytical mapping relationship of microgrid cost-energy-reserve is as follows: in, for t The cost of microgrids at any time This is the parameter coefficient vector within the Nth critical region. The constant coefficients within the Nth critical region. This is the Nth critical region.

5. The microgrid energy-reserve joint market bidding method based on cost mapping according to claim 3, characterized in that, When the space of variation of planning parameters is divided into critical regions based on the ineffective constraints and the explicit mapping linear analytical relationship, the mathematical expression is as follows: in, This is the critical region. and For the sorted-out first n The parameter coefficient vector and constant coefficients within each critical region, with subscripts... a , b These represent active and inactive constraints, respectively. and This is the rearranged parameter coefficient vector. This is the optimal variable vector.

6. The microgrid energy-reserve joint market bidding method based on cost mapping according to claim 1, characterized in that, The upper-level model aims to maximize the total revenue from the energy and reserve markets minus operating costs, and its mathematical expression is as follows: In the formula: Total profit of the microgrid; for t Time Node i Marginal electricity price of microgrids and They are respectively t Time Node i The clearing price for reserve capacity in microgrids is adjusted upwards and downwards; for t Time Node i Microgrid active power bidding and They are respectively t Time Node i Microgrids adjust the reserve market bidding capacity by both upward and downward. for t Time Node i Microgrid costs; The mathematical expressions for the constraints of the upper-level model are as follows: in, For auxiliary binary variables, for t Time Node i The microgrid bidding variable vector, where M is the maximum value. and They are nodes i The parameter coefficient vector and constant coefficients within the nth critical region. and They are nodes i The parameter coefficient vector and constant coefficients within the nth critical region.

7. The microgrid energy-reserve joint market bidding method based on cost mapping according to claim 6, characterized in that, The lower-level model aims to minimize the overall social welfare of distribution network energy and reserves, and its mathematical expression is as follows: In the formula: , , These are the cost coefficients for active power, upper reserve, and lower reserve of the gas turbine unit, respectively. , , These are the active power output, upper reserve power, and lower reserve power of the gas turbine unit, respectively. The constraints of the lower-level model include node power balance constraints, system reserve demand constraints, line transmission capacity constraints, gas turbine unit operation and reserve constraints, and their mathematical expressions are as follows: In the formula: For nodes i exist t The load demand at any time, For the route ij exist t Transmission power at any given moment; and Representing nodes respectively i exist t The need for up-and-down backup at all times. and They represent the lines respectively. ij exist t Always-on backup and backup support; The line indicates the maximum transmission power; and Representing nodes respectively i Minimum and maximum output of the gas turbine unit; and Representing nodes respectively i Downhill and uphill speed limits; Representing nodes respectively i Maximum upper and lower reserve capacities; , , , express t Timetable ij The cost of transmission power and line congestion caused by redundancy; and express t Time Node i Price constraints based on the lower and upper limits of gas turbine unit output. and express t Time Node i Gas turbine unit ramp rate constraint price, and express t Time Node i Price constraints on standby and reserve capacity of gas turbine units.

8. The microgrid energy-reserve joint market bidding method based on cost mapping according to claim 7, characterized in that, The mathematical expression of the Stackelberg two-level game model is as follows: In the formula: This represents the decision vector of the upper-level model; This represents the decision vector for the lower-level model. and These are the sets of equality and inequality constraints for the upper-level model, respectively. and These are the sets of equality and inequality constraints for the lower-level model, respectively. and These are the dual variable vectors of equal and inequality constraints in the lower-level model, respectively.

9. The microgrid energy-reserve joint market bidding method based on cost mapping according to claim 1, characterized in that, When transforming the Stackelberg two-level game model into a single-level mixed-integer linear programming model using the KKT optimality condition and strong duality principle of the lower-level model, the specific steps include: Calculate the Lagrangian function of the lower-level problem in the Stackelberg two-level game model; The initial single-level mixed-integer linear programming model is obtained by replacing the lower-level model of the Stackelberg two-level game model with the KKT conditions of the Lagrange function of the lower-level problem. The bilinear terms of the objective function in the single-layer mixed-integer linear programming model are linearized using the strong duality principle, and the complementary relaxation condition nonlinear coupling terms in the single-layer mixed-integer linear programming model are linearized using the Big M method, resulting in the final single-layer mixed-integer linear programming model.

10. The microgrid energy-reserve joint market bidding method based on cost mapping according to claim 9, characterized in that, The mathematical expression for the KKT condition of the Lagrangian function of the lower-level problem is as follows: in, This represents the decision vector of the upper-level model in the Stackelberg two-level game model. This represents the decision vector of the lower-level model in the Stackelberg two-level game model. For gradient operators; The objective function for the lower-level model; and These are the sets of equality and inequality constraints for the lower-level model, respectively. and These are the dual variable vectors of equal and inequality constraints in the lower-level model, respectively. This indicates their complementary relaxation constraints, i.e. .

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