An electric energy-frequency modulation market joint scheduling optimization system and method considering energy storage electrochemical-aging coupling characteristics

Abstract

The application discloses an electric energy-frequency modulation market joint scheduling optimization system and method considering energy storage electrochemical-aging coupling characteristics, and relates to the field of energy storage.The application method simplifies the calculation formula of the terminal voltage by ignoring the role of the capacitor in the equivalent circuit, and linearizes the relationship between the open-circuit voltage and the state of charge of the energy storage system and the internal resistance characteristics, thereby effectively reducing the model complexity.Meanwhile, the sequence convex programming technology is used for successive approximation of the non-convex optimization problem, and the solving efficiency and the calculation accuracy are significantly improved.This method can not only accurately depict the dynamic behavior of the energy storage system under different scenarios, but also provide a more operational optimization scheme for actual engineering application.In addition, by linearizing and approximating the power constraint, the scalability and adaptability of the model are further enhanced, so that the model is more suitable for the actual demand of multi-scenario joint scheduling.

Description

Technical Field

[0001] This invention relates to the field of energy storage, specifically to a joint scheduling optimization system and method for energy and frequency regulation markets that considers the electrochemical-aging coupling characteristics of energy storage. Background Technology

[0002] With the construction of new power systems and the increasing proportion of renewable energy, the demand for flexible adjustment resources in power systems is growing. Energy storage systems, with their precise power control capabilities and rapid response characteristics, have become a core flexible resource for building new power systems and supporting the safe operation of the power grid.

[0003] In existing energy storage dispatch optimization models, energy storage systems are generally abstracted as linear energy tank models, characterizing their physical properties by setting fixed energy conversion efficiencies and rated power. However, in reality, power limitations, capacity and conversion efficiency, as well as aging costs, are crucial issues that need to be comprehensively considered in the optimized operation of energy storage systems. These characteristics are inherently affected by operating conditions, including physical quantities such as temperature, state of charge, and current, and exhibit significant nonlinear mapping relationships. Therefore, deeply coupling complex electrochemical nonlinear characteristics in joint dispatch optimization remains a key problem that urgently needs to be addressed. Summary of the Invention

[0004] The purpose of this invention is to provide a joint scheduling optimization system and method for the energy-frequency regulation market that considers the coupling characteristics of energy storage electrochemistry-aging, so as to solve the problems mentioned in the background art.

[0005] To achieve the above objectives, the present invention provides the following technical solution: A joint dispatch optimization system for the energy-frequency regulation market that considers the electrochemical-aging coupling characteristics of energy storage includes: Energy storage modeling module: used to simulate the internal polarization, ohmic voltage drop and open-circuit voltage characteristics of energy storage based on the equivalent circuit model ECM, capture the nonlinear losses related to terminal voltage changes and current, define the state of charge (SoC) using the ampere-hour integration method, and construct a cycle life aging model that reflects electrochemical stress by combining the rainflow counting method. The day-ahead collaborative bidding decision model construction module is used to obtain electricity market price, frequency regulation market price parameters and typical frequency regulation scenario information. Using energy bidding amount and frequency regulation bidding capacity as decision variables, it constructs a day-ahead collaborative bidding decision model that includes electricity-frequency regulation collaborative market constraints and energy storage model constraints. The goal is to maximize the expected revenue of energy storage operators. The convexity processing module is used to convexize the non-convex and nonlinear power constraints in the current collaborative bidding decision model. By ignoring the effect of capacitance in the equivalent circuit, assuming a linear relationship between the open-circuit voltage and the SoC, and reasonably simplifying the internal resistance model as a linear function of the SoC, a cubic polynomial expression for power is obtained. Then, the sequential convex programming (SCP) method is used to linearize the non-convex terms using Taylor expansion, transforming them into a mixed integer convex programming subproblem. The solution module is used to initialize the parameters of the energy storage power station, market conditions, and iteration parameters, iteratively solve the subproblems after convexification, until the convergence condition is met, and output the joint scheduling optimization results.

[0006] As a further aspect of the present invention, the present invention also provides a method for joint scheduling optimization of the energy-frequency regulation market considering the coupling characteristics of energy storage electrochemistry-aging, comprising the following steps: Energy storage modeling: Based on the equivalent circuit model, the internal electrical characteristics of energy storage are simulated by circuit components such as resistors, capacitors and voltage sources. Formulas are used to calculate the terminal voltage, current and state of charge of the energy storage system at each time period. Combined with the rainflow counting method, the battery cycle life and aging cost are quantified. The day-ahead collaborative bidding decision model is constructed with the goal of maximizing expected returns. It incorporates the arbitrage returns from spot electricity, frequency regulation compensation, and aging costs. The model includes constraints on the electricity-frequency regulation collaborative market and energy storage operation. These constraints include charging and discharging power limits, response accuracy thresholds, and limits on terminal voltage and state of charge range. Model convexity processing: The nonlinear power constraints in the current collaborative bidding decision model are simplified. The non-convex terms are linearized one by one using the sequential convex programming method, and a convex approximation subproblem is constructed. The linearized working point is updated iteratively. Model Solving: Initialize the parameters of the energy storage power station, market price parameters, typical frequency regulation scenario signals and their occurrence probabilities, call the solver to iteratively solve the convex approximation subproblem until the difference between the objective functions of two consecutive iterations meets the preset convergence tolerance, and output the optimal joint bidding strategy.

[0007] As a further aspect of the present invention, the physical meaning of each parameter in the equivalent circuit model and the dynamic electrical behavior it describes are shown in the following equations: (1) (2) (3) (4) (5) In the formula: Let be the terminal voltage of the energy storage system during time period t; Let be the open-circuit voltage (OCV) of the energy storage system during time period t, representing the state of charge. function ; Let be the voltage of the first RC branch of the energy storage system during time period t; Let be the voltage of the second RC branch of the energy storage system during time period t; The total actual current of the energy storage system during time period t; and , These are the ohmic resistance and polarization resistance of the energy storage system during time period t, respectively. , Let be the polarization capacitance of the energy storage system during time period t.

[0008] As a further aspect of this invention, in the equivalent circuit model of the energy storage system, a power-type SoC definition based on ampere-hour integration is adopted. The power-type SoC is calculated by the ratio of real-time charging and discharging current to rated capacity, and its expression is as follows: (6) (7) In the formula: This refers to the rated charge capacity of the energy storage system. This represents the change in SoC of the energy storage system during time period t.

[0009] As a further aspect of the present invention, the expression for quantifying battery cycle life and aging cost using the rainflow counting method is as follows: (8) (9) In the formula: This refers to the cycle life at the corresponding depth of discharge; Depth of discharge; , , These are the fitting parameters for the battery material, and their meanings represent the baseline cycle number, the deep decay index, and the nonlinearity correction coefficient, respectively. The aging cost induced by a single cycle; This represents the total investment and construction cost of the energy storage system. This refers to cycle life.

[0010] As a further aspect of the present invention, the pre-contract collaborative bidding decision-making model is as follows: Objective function: (10) In the formula: Let be the probability of scenario s occurring; , , Let 's' represent the aging cost, energy spot arbitrage profit, and frequency regulation compensation for time period 't' in scenario 's', respectively. The specific calculation formulas are as follows: (11) In the formula: The state of charge in scene s during time period t; This represents the aging cost for a single cycle under this charged state. (12) In the formula: Let t be the electricity price for the period t. The actual net output power of the energy storage system during time period t in scenario s; For time intervals; (13) (14) (15) (16) In the formula, , , These are frequency modulation capacity gains, frequency modulation mileage gains, and deviation penalties, respectively. , , These are the prices for frequency modulation capacity, frequency modulation mileage, and deviation penalty; The frequency modulation capacity won in time period t; , These represent the average up-modulation and down-modulation frequency modulation power during time period t in scenario s; , , These represent the mileage value, average upward signal, and average downward signal of the AGC signal during time period t in scenario s, respectively. Constraints: Electricity-Frequency Regulation Coordinated Market Constraints: Charging power is defined as positive and discharging power as negative. Baseline power is defined as the amount of electricity won in the day-ahead energy market, while total power is the actual output after frequency regulation. The operational constraints are as follows: In the formula: The baseline power during time period t; The frequency modulation power during time period t in scenario s; This refers to the upper limit of the charging and discharging power of the energy storage system. , These are the state variables for charging and discharging of the energy storage system during time period t in scenario s; The frequency regulation response accuracy parameter is incorporated into the model, and a lower limit threshold is set to ensure that energy storage meets market access requirements. In the formula: The response accuracy parameters of the energy storage system to the frequency modulation signal during time period t in scenario s; This represents the minimum acceptable response accuracy for the FM market. Energy storage model constraints: The energy storage model constraints are based on the equivalent circuit model described by equations (1)-(7), and are embedded in the multi-scenario optimization framework. All physical quantities in the model are simultaneously associated with the scheduling period t and the typical frequency regulation scenario s, so as to accurately characterize the dynamic behavior and state evolution of energy storage under different scenarios. The following operational constraints are applied to some of the decision variables: In the formula, , , These represent the charging current, discharging current, and actual total current of the energy storage system during time period t in scenario s. This refers to the upper limit of the charging and discharging current of the energy storage system. , These are the upper and lower limits of the terminal voltage of the energy storage system, respectively. , These are the upper and lower limits of the state of charge of the energy storage system, respectively.

[0011] As a further aspect of the present invention, the model convexity processing method is as follows: First, construct an equivalent circuit model that combines accuracy and computational feasibility: 1) Ignore the effect of capacitance in the equivalent circuit The formula for calculating terminal voltage is simplified to: 2) The open-circuit voltage (OCV) and the system SoC (System-on-Chips) exhibit an approximately linear relationship within the main operating range. (32) In the formula: and These are the parameters for the linear fit between the open-circuit voltage and the SoC; 3) The internal resistance of the energy storage system is modeled as a linear function of the SoC. (33) In the formula: and These are the parameters for the linear fit between the battery's internal resistance and the SoC; The power constraints in the equivalent circuit model are summarized as follows: (34) The actual total current Changes in SoC This is expressed as follows: The terminal voltage within time period t is averaged and approximated, and the equation is rearranged into the following form: (35) In the formula: , , , , ; The sequential convex programming (SCP) method is used for processing, specifically for cubic terms, quadratic terms, and terms at points. Taylor expansion is performed at the point, and the obtained linear expression is used to approximate the original non-convex terms, transforming the original problem into a mixed integer convex programming (MICP) subproblem. The convex approximation subproblem is solved iteratively and the expansion point is updated until the objective function of the two iterations satisfies the preset convergence tolerance, and finally a feasible approximate solution to the original non-convex optimization problem is obtained. First, let's derive the formula for successive linearization. Let the operating point at the k-th iteration be... For each non-convex term, perform a Taylor expansion and approximate the terms by taking the first few terms: (36) (37) (38) (39) In the formula: , These are the cubic terms and the cross-difference cubic terms after successive linearization, respectively; , These are the linearized quadratic term and the cross-difference quadratic term, respectively. , These represent the SoC change in the k-th iteration of the energy storage system in scenario s during time period t and the SoC in the k-th iteration of the system in scenario s during time period t-1, respectively. The specific iterative process of the linearization approximation of power constraints using the SCP method is as follows: 1) Initialization: Set the initial iteration point ,Pick The initial point is the change in zero; 2) Construct the convex approximation subproblem for the k-th iteration: Replace the non-convex terms in the power constraint with their corresponding linearized forms: (40) 3) Solve the convex subproblem and update the iteration point: Solve the mixed integer convex optimization problem that includes the linearization constraints mentioned above to obtain the current iterative solution. The current solution is used as the linearization working point for the next iteration; 4) Convergence check: Repeat the iteration process until the difference between the objective functions of two iterations satisfies the convergence condition. (41) In the formula: To predetermine the tolerance, the solution results that satisfy the convergence condition are finally output based on the iteration records.

[0012] Compared with existing technologies, the beneficial effects of this invention are as follows: By ignoring the effect of capacitance in the equivalent circuit, the method simplifies the calculation formula for terminal voltage and linearizes the relationship between open-circuit voltage and state of charge, as well as the internal resistance characteristics of the energy storage system, thereby effectively reducing model complexity. Simultaneously, by utilizing sequential convex programming techniques to successively approximate the non-convex optimization problem, the solution efficiency and computational accuracy are significantly improved. This method not only accurately characterizes the dynamic behavior of the energy storage system under different scenarios but also provides a more operational optimization scheme for practical engineering applications. Furthermore, by linearizing the power constraints, the scalability and adaptability of the model are further enhanced, making it more suitable for the practical needs of multi-scenario joint scheduling. Attached Figure Description

[0013] Figure 1 This is a schematic diagram of the equivalent circuit model of the present invention. Detailed Implementation

[0014] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0015] Please see Figure 1 In this embodiment of the invention, a joint scheduling optimization system for the energy-frequency regulation market considering the electrochemical-aging coupling characteristics of energy storage includes: Energy storage modeling module: used to simulate the internal polarization, ohmic voltage drop and open-circuit voltage characteristics of energy storage based on the equivalent circuit model ECM, capture the nonlinear losses related to terminal voltage changes and current, define the state of charge (SoC) using the ampere-hour integration method, and construct a cycle life aging model that reflects electrochemical stress by combining the rainflow counting method. The day-ahead collaborative bidding decision model construction module is used to obtain electricity market price, frequency regulation market price parameters and typical frequency regulation scenario information. Using energy bidding amount and frequency regulation bidding capacity as decision variables, it constructs a day-ahead collaborative bidding decision model that includes electricity-frequency regulation collaborative market constraints and energy storage model constraints. The goal is to maximize the expected revenue of energy storage operators. The convexity processing module is used to convexize the non-convex and nonlinear power constraints in the current collaborative bidding decision model. By ignoring the effect of capacitance in the equivalent circuit, assuming a linear relationship between the open-circuit voltage and the SoC, and reasonably simplifying the internal resistance model as a linear function of the SoC, a cubic polynomial expression for power is obtained. Then, the sequential convex programming (SCP) method is used to linearize the non-convex terms using Taylor expansion, transforming them into a mixed integer convex programming subproblem. The solution module is used to initialize the parameters of the energy storage power station, market conditions, and iteration parameters, iteratively solve the subproblems after convexification, until the convergence condition is met, and output the joint scheduling optimization results.

[0016] As a further aspect of the present invention, the present invention also provides a method for joint scheduling optimization of the energy-frequency regulation market considering the coupling characteristics of energy storage electrochemistry-aging, comprising the following steps: Energy storage modeling: Based on the equivalent circuit model, the internal electrical characteristics of energy storage are simulated by circuit components such as resistors, capacitors and voltage sources. Formulas are used to calculate the terminal voltage, current and state of charge of the energy storage system at each time period. Combined with the rainflow counting method, the battery cycle life and aging cost are quantified. The day-ahead collaborative bidding decision model is constructed with the goal of maximizing expected returns. It incorporates the arbitrage returns from spot electricity, frequency regulation compensation, and aging costs. The model includes constraints on the electricity-frequency regulation collaborative market and energy storage operation. These constraints include charging and discharging power limits, response accuracy thresholds, and limits on terminal voltage and state of charge range. Model convexity processing: The nonlinear power constraints in the current collaborative bidding decision model are simplified. The non-convex terms are linearized one by one using the sequential convex programming method, and a convex approximation subproblem is constructed. The linearized working point is updated iteratively. Model Solving: Initialize the parameters of the energy storage power station, market price parameters, typical frequency regulation scenario signals and their occurrence probabilities, call the solver to iteratively solve the convex approximation subproblem until the difference between the objective functions of two consecutive iterations meets the preset convergence tolerance, and output the optimal joint bidding strategy.

[0017] As a further aspect of the present invention, the physical meaning of each parameter in the equivalent circuit model and the dynamic electrical behavior it describes are shown in the following equations: (1) (2) (3) (4) (5) In the formula: Let be the terminal voltage of the energy storage system during time period t; Let be the open-circuit voltage (OCV) of the energy storage system during time period t, representing the state of charge. function ; Let be the voltage of the first RC branch of the energy storage system during time period t; Let be the voltage of the second RC branch of the energy storage system during time period t; The total actual current of the energy storage system during time period t; and , These are the ohmic resistance and polarization resistance of the energy storage system during time period t, respectively. , Let be the polarization capacitance of the energy storage system during time period t.

[0018] As a further aspect of this invention, in the equivalent circuit model of the energy storage system, a power-type SoC definition based on ampere-hour integration is adopted. The power-type SoC is calculated by the ratio of real-time charging and discharging current to rated capacity, and its expression is as follows: (6) (7) In the formula: This refers to the rated charge capacity of the energy storage system. This represents the change in SoC of the energy storage system during time period t.

[0019] As a further aspect of the present invention, the expression for quantifying battery cycle life and aging cost using the rainflow counting method is as follows: (8) (9) In the formula: This refers to the cycle life at the corresponding depth of discharge; Depth of discharge; , , These are the fitting parameters for the battery material, and their meanings represent the baseline cycle number, the deep decay index, and the nonlinearity correction coefficient, respectively. The aging cost induced by a single cycle; This represents the total investment and construction cost of the energy storage system. This refers to cycle life.

[0020] As a further aspect of the present invention, the pre-contract collaborative bidding decision-making model is as follows: Objective function: (10) In the formula: Let be the probability of scenario s occurring; , , Let 's' represent the aging cost, energy spot arbitrage profit, and frequency regulation compensation for time period 't' in scenario 's', respectively. The specific calculation formulas are as follows: (11) In the formula: The state of charge in scene s during time period t; This represents the aging cost for a single cycle under this charged state. (12) In the formula: Let t be the electricity price for the period t. The actual net output power of the energy storage system during time period t in scenario s; For time intervals; (13) (14) (15) (16) In the formula, , , These are frequency modulation capacity gains, frequency modulation mileage gains, and deviation penalties, respectively. , , These are the prices for frequency modulation capacity, frequency modulation mileage, and deviation penalty; The frequency modulation capacity won in time period t; , These represent the average up-modulation and down-modulation frequency modulation power during time period t in scenario s; , , These represent the mileage value, average upward signal, and average downward signal of the AGC signal during time period t in scenario s, respectively. Constraints: Electricity-Frequency Regulation Coordinated Market Constraints: Charging power is defined as positive and discharging power as negative. Baseline power is defined as the amount of electricity won in the day-ahead energy market, while total power is the actual output after frequency regulation. The operational constraints are as follows: (17) (18) (19) (20) (twenty one) In the formula: The baseline power during time period t; The frequency modulation power during time period t in scenario s; This refers to the upper limit of the charging and discharging power of the energy storage system. , These are the state variables for charging and discharging of the energy storage system during time period t in scenario s; The frequency regulation response accuracy parameter is incorporated into the model, and a lower limit threshold is set to ensure that energy storage meets market access requirements. (twenty two) (twenty three) (twenty four) In the formula: The response accuracy parameters of the energy storage system to the frequency modulation signal during time period t in scenario s; This represents the minimum acceptable response accuracy for the FM market. Energy storage model constraints: The energy storage model constraints are based on the equivalent circuit model described by equations (1)-(7), and are embedded in the multi-scenario optimization framework. All physical quantities in the model are simultaneously associated with the scheduling period t and the typical frequency regulation scenario s, so as to accurately characterize the dynamic behavior and state evolution of energy storage under different scenarios. The following operational constraints are applied to some of the decision variables: (25) (26) (27) (28) (29) In the formula, , , These represent the charging current, discharging current, and actual total current of the energy storage system during time period t in scenario s. This refers to the upper limit of the charging and discharging current of the energy storage system. , These are the upper and lower limits of the terminal voltage of the energy storage system, respectively. , These are the upper and lower limits of the state of charge of the energy storage system, respectively.

[0021] As a further aspect of the present invention, the model convexity processing method is as follows: First, construct an equivalent circuit model that combines accuracy and computational feasibility: 1) Ignore the effect of capacitance in the equivalent circuit The formula for calculating terminal voltage is simplified to: (30) (31) 2) The open-circuit voltage (OCV) and the system SoC (System-on-Chips) exhibit an approximately linear relationship within the main operating range. (32) In the formula: and These are the parameters for the linear fit between the open-circuit voltage and the SoC; 3) The internal resistance of the energy storage system is modeled as a linear function of the SoC. (33) In the formula: and These are the parameters for the linear fit between the battery's internal resistance and the SoC; The power constraints in the equivalent circuit model are summarized as follows: (34) The actual total current Changes in SoC This is expressed as follows: The terminal voltage within time period t is averaged and approximated, and the equation is rearranged into the following form: (35) In the formula: , , , , ; The sequential convex programming (SCP) method is used for processing, specifically for cubic terms, quadratic terms, and terms at points. Taylor expansion is performed at the point, and the obtained linear expression is used to approximate the original non-convex terms, transforming the original problem into a mixed integer convex programming (MICP) subproblem. The convex approximation subproblem is solved iteratively and the expansion point is updated until the objective function of the two iterations satisfies the preset convergence tolerance, and finally a feasible approximate solution to the original non-convex optimization problem is obtained. First, let's derive the formula for successive linearization. Let the operating point at the k-th iteration be... For each non-convex term, perform a Taylor expansion and approximate the terms by taking the first few terms: (36) (37) (38) (39) In the formula: , These are the cubic terms and the cross-difference cubic terms after successive linearization, respectively; , These are the linearized quadratic term and the cross-difference quadratic term, respectively. , These represent the SoC change in the k-th iteration of the energy storage system in scenario s during time period t and the SoC in the k-th iteration of the system in scenario s during time period t-1, respectively. The specific iterative process of the linearization approximation of power constraints using the SCP method is as follows: 1) Initialization: Set the initial iteration point ,Pick The initial point is the change in zero; 2) Construct the convex approximation subproblem for the k-th iteration: Replace the non-convex terms in the power constraint with their corresponding linearized forms: (40) 3) Solve the convex subproblem and update the iteration point: Solve the mixed integer convex optimization problem that includes the linearization constraints mentioned above to obtain the current iterative solution. The current solution is used as the linearization working point for the next iteration; 4) Convergence check: Repeat the iteration process until the difference between the objective functions of two iterations satisfies the convergence condition. (41) In the formula: To predetermine the tolerance, the solution results that satisfy the convergence condition are finally output based on the iteration records.

[0022] Model solution: Initialize the parameters of each device in the system, input the capacity price and mileage price of the electric energy market and frequency regulation market, typical frequency regulation scenario signals and their occurrence probabilities, call the solver to solve the model, and obtain the joint scheduling optimization results of energy storage.

[0023] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered in all respects as exemplary and non-limiting, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

[0024] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A joint dispatch optimization system for the energy-frequency regulation market considering the electrochemical-aging coupling characteristics of energy storage, characterized in that, include: Energy storage modeling module: used to simulate the internal polarization, ohmic voltage drop and open-circuit voltage characteristics of energy storage based on the equivalent circuit model ECM, capture the nonlinear losses related to terminal voltage changes and current, define the state of charge (SoC) using the ampere-hour integration method, and construct a cycle life aging model that reflects electrochemical stress by combining the rainflow counting method. The day-ahead collaborative bidding decision model construction module is used to obtain electricity market price, frequency regulation market price parameters and typical frequency regulation scenario information. Using energy bidding amount and frequency regulation bidding capacity as decision variables, it constructs a day-ahead collaborative bidding decision model that includes electricity-frequency regulation collaborative market constraints and energy storage model constraints. The goal is to maximize the expected revenue of energy storage operators. The convexity processing module is used to convexize the non-convex and nonlinear power constraints in the current collaborative bidding decision model. By ignoring the effect of capacitance in the equivalent circuit, assuming a linear relationship between the open-circuit voltage and the SoC, and reasonably simplifying the internal resistance model as a linear function of the SoC, a cubic polynomial expression for power is obtained. Then, the sequential convex programming (SCP) method is used to linearize the non-convex terms using Taylor expansion, transforming them into a mixed integer convex programming subproblem. The solution module is used to initialize the parameters of the energy storage power station, market conditions and iteration parameters, iteratively solve the subproblems after convexification until the convergence condition is met, and output the joint scheduling optimization results. The specific iterative process of the linearization approximation of power constraints using the SCP method is as follows: 1) Initialization: Set the initial iteration point ,Pick The initial point is the change in zero; 2) Construct the convex approximation subproblem for the k-th iteration: Replace the non-convex terms in the power constraint with their corresponding linearized forms: （40） In the formula: , , , , ; , These are the cubic terms and the cross-difference cubic terms after successive linearization, respectively; , These are the linearized quadratic term and the cross-difference quadratic term, respectively. , These represent the SoC change in the k-th iteration of the energy storage system in scenario s during time period t and the SoC in the k-th iteration of the system in scenario s during time period t-1, respectively. and These are the parameters for the linear fit between the battery's internal resistance and the SoC; and These are the parameters for the linear fit between the open-circuit voltage and the SoC; This refers to the rated charge capacity of the energy storage system. 3) Solve the convex subproblem and update the iteration point: Solve the mixed integer convex optimization problem that includes the linearization constraints mentioned above to obtain the current iterative solution. The current solution is used as the linearization working point for the next iteration; 4) Convergence check: Repeat the iteration process until the difference between the objective functions of two iterations satisfies the convergence condition. （41） In the formula: To predetermine the tolerance, the solution results that satisfy the convergence condition are finally output based on the iteration records.

2. A joint scheduling optimization method for the energy-frequency regulation market considering the electrochemical-aging coupling characteristics of energy storage, characterized in that, Includes the following steps: Energy storage modeling: Based on the equivalent circuit model, the internal electrical characteristics of energy storage are simulated by circuit components such as resistors, capacitors and voltage sources. Formulas are used to calculate the terminal voltage, current and state of charge of the energy storage system at each time period. Combined with the rainflow counting method, the battery cycle life and aging cost are quantified. The day-ahead collaborative bidding decision model is constructed with the goal of maximizing expected returns. It incorporates the arbitrage returns from spot electricity, frequency regulation compensation, and aging costs. The model includes constraints on the electricity-frequency regulation collaborative market and energy storage operation. These constraints include charging and discharging power limits, response accuracy thresholds, and limits on terminal voltage and state of charge range. Model convexification: The non-convex and nonlinear power constraints in the current collaborative bidding decision model are convexified. By ignoring the effect of capacitance in the equivalent circuit, assuming a linear relationship between open-circuit voltage and SoC, and reasonably simplifying the internal resistance into a linear function of SoC, a cubic polynomial expression for power is obtained. Then, the sequential convex programming (SCP) method is used to linearize the non-convex terms using Taylor expansion, transforming it into a mixed integer convex programming subproblem. The specific iterative process of the linearization approximation of power constraints using the SCP method is as follows: 1) Initialization: Set the initial iteration point ,Pick The initial point is the change in zero; 2) Construct the convex approximation subproblem for the k-th iteration: Replace the non-convex terms in the power constraint with their corresponding linearized forms: （40） In the formula: , , , , ; , These are the cubic terms and the cross-difference cubic terms after successive linearization, respectively; , These are the linearized quadratic term and the cross-difference quadratic term, respectively. , These represent the SoC change in the k-th iteration of the energy storage system in scenario s during time period t and the SoC in the k-th iteration of the system in scenario s during time period t-1, respectively. and These are the parameters for the linear fit between the battery's internal resistance and the SoC; and These are the parameters for the linear fit between the open-circuit voltage and the SoC; This refers to the rated charge capacity of the energy storage system. 3) Solve the convex subproblem and update the iteration point: Solve the mixed integer convex optimization problem that includes the linearization constraints mentioned above to obtain the current iterative solution. The current solution is used as the linearization working point for the next iteration; 4) Convergence check: Repeat the iteration process until the difference between the objective functions of two iterations satisfies the convergence condition. （41） In the formula: To predetermine the tolerance, the solution results that satisfy the convergence condition are finally output based on the iteration records. Model Solving: Initialize the parameters of the energy storage power station, market price parameters, typical frequency regulation scenario signals and their occurrence probabilities, call the solver to iteratively solve the convex approximation subproblem until the difference between the objective functions of two consecutive iterations meets the preset convergence tolerance, and output the optimal joint bidding strategy.

3. The method for joint scheduling optimization of the energy-frequency regulation market considering the electrochemical-aging coupling characteristics of energy storage, as described in claim 2, is characterized in that... The physical meaning of each parameter in the equivalent circuit model and the dynamic electrical behavior it describes are shown in the following equations: In the formula: Let be the terminal voltage of the energy storage system during time period t; Let t be the open-circuit voltage (OCV) of the energy storage system during time period t, representing the state of charge. function ; Let be the voltage of the first RC branch of the energy storage system during time period t; Let be the voltage of the second RC branch of the energy storage system during time period t; The total actual current of the energy storage system during time period t; and , These are the internal resistance of the energy storage system during time period t, the resistance of the first RC branch, and the resistance of the second RC branch, respectively. , Let be the capacitance of the first RC branch and the capacitance of the second RC branch in the energy storage system during time period t.

4. The method for joint scheduling optimization of the energy-frequency regulation market considering the electrochemical-aging coupling characteristics of energy storage, as described in claim 3, is characterized in that... In the equivalent circuit model of the energy storage system, a power-type SoC definition based on ampere-hour integration is adopted. The power-type SoC is calculated by the ratio of real-time charging and discharging current to rated capacity, and its expression is as follows: In the formula: This refers to the rated charge capacity of the energy storage system. This represents the change in SoC of the energy storage system during time period t.

5. The method for joint scheduling optimization of the energy-frequency regulation market considering the electrochemical-aging coupling characteristics of energy storage, as described in claim 3, is characterized in that... The expression for quantifying battery cycle life and aging cost using the rainflow counting method is as follows: In the formula: This refers to the cycle life at the corresponding depth of discharge; Depth of discharge; , , These are the fitting parameters for the battery material, and their meanings represent the baseline cycle number, the deep decay index, and the nonlinearity correction coefficient, respectively. The aging cost induced by a single cycle; This represents the total investment and construction cost of the energy storage system. This refers to cycle life.

6. The method for joint scheduling optimization of the energy-frequency regulation market considering the electrochemical-aging coupling characteristics of energy storage, as described in claim 5, is characterized in that... The current collaborative bidding decision-making model is as follows: Objective function: In the formula: Let be the probability of scenario s occurring; , , Let 's' represent the aging cost, energy spot arbitrage profit, and frequency regulation compensation for time period 't' in scenario 's', respectively. The specific calculation formulas are as follows: In the formula: The state of charge in scene s during time period t; This represents the aging cost for a single cycle under this charged state. In the formula: Let t be the electricity price for the period t. The actual net output power of the energy storage system during time period t in scenario s; For time intervals; In the formula, , , These are frequency modulation capacity gains, frequency modulation mileage gains, and deviation penalties, respectively. , , These are the prices for frequency modulation capacity, frequency modulation mileage, and deviation penalty; The frequency modulation capacity won in time period t; , These represent the average up-modulation and down-modulation frequency modulation power during time period t in scenario s; , , These represent the mileage value, average upward signal, and average downward signal of the AGC signal during time period t in scenario s, respectively. Constraints: Electricity-Frequency Regulation Coordinated Market Constraints: Charging power is defined as positive and discharging power as negative. Baseline power is defined as the amount of electricity won in the day-ahead energy market, while total power is the actual output after frequency regulation. The operational constraints are as follows: In the formula: The baseline power during time period t; The frequency modulation power during time period t in scenario s; This refers to the upper limit of the charging and discharging power of the energy storage system. , These are the state variables for charging and discharging of the energy storage system during time period t in scenario s; The frequency regulation response accuracy parameter is incorporated into the model, and a lower limit threshold is set to ensure that energy storage meets market access requirements. In the formula: The response accuracy parameters of the energy storage system to the frequency modulation signal during time period t in scenario s; This represents the minimum acceptable response accuracy for the FM market. Energy storage model constraints: The energy storage model constraints are based on the equivalent circuit model described by equations (1)-(7), and are embedded in the multi-scenario optimization framework. All physical quantities in the model are simultaneously associated with the scheduling period t and the typical frequency regulation scenario s, so as to accurately characterize the dynamic behavior and state evolution of energy storage under different scenarios. The following operational constraints are applied to some of the decision variables: In the formula, , , These represent the charging current, discharging current, and actual total current of the energy storage system during time period t in scenario s. This refers to the upper limit of the charging and discharging current of the energy storage system. , These are the upper and lower limits of the terminal voltage of the energy storage system, respectively. , These are the upper and lower limits of the state of charge of the energy storage system, respectively.

7. The method for joint scheduling optimization of the energy-frequency regulation market considering the electrochemical-aging coupling characteristics of energy storage, as described in claim 6, is characterized in that... The model convexity processing method is as follows: First, construct an equivalent circuit model that combines accuracy and computational feasibility: 1) Ignore the effect of capacitance in the equivalent circuit The formula for calculating terminal voltage is simplified to: 2) The open-circuit voltage (OCV) and the system SoC (System-on-Chips) exhibit an approximately linear relationship within the main operating range. In the formula: and These are the parameters for the linear fit between the open-circuit voltage and the SoC; 3) The internal resistance of the energy storage system is modeled as a linear function of the SoC. In the formula: and These are the parameters for the linear fit between the battery's internal resistance and the SoC; The power constraints in the equivalent circuit model are summarized as follows: The actual total current Changes in SoC This is expressed as follows: The terminal voltage within time period t is averaged and approximated, and the equation is rearranged into the following form: （35） The sequential convex programming (SCP) method is used for processing, specifically for cubic terms, quadratic terms, and terms at points. Taylor expansion is performed at the point, and the obtained linear expression is used to approximate the original non-convex terms, transforming the original problem into a mixed integer convex programming (MICP) subproblem. The convex approximation subproblem is solved iteratively and the expansion point is updated until the objective function of the two iterations satisfies the preset convergence tolerance, and finally a feasible approximate solution to the original non-convex optimization problem is obtained. First, let's derive the formula for successive linearization. Let the operating point at the k-th iteration be... For each non-convex term, perform a Taylor expansion and approximate the terms by taking the first few terms: （36） （37） （38） （39） In the formula: , These are the cubic terms and the cross-difference cubic terms after successive linearization, respectively; , These are the linearized quadratic term and the cross-difference quadratic term, respectively. , These represent the SoC change during the k-th iteration of scenario s in time period t and the SoC during the k-th iteration of scenario t-1 in scenario s, respectively.

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