Power supply configuration equalization model establishment method based on capacity and inertia market mechanism

Abstract

The invention discloses a power supply configuration equilibrium model establishment method based on a capacity and inertia market mechanism, and the method comprises the steps: S1, designing an inertia market mechanism, and enabling an inertia market to be a medium-and-long-term inertia market based on auction; s2, constructing a power supply configuration equilibrium model based on the Stackelberg game, including S2.1, constructing an upper layer model to solve the problem of profit maximization of a power producer; s2.2, a lower-layer model is constructed to solve the problem of clearing of multiple markets, and the multiple markets comprise an energy reserve joint market, a capacity market and an inertia market; and S3, solving the power supply configuration equalization model. According to the invention, by designing the inertia market and researching an inertia adequacy mechanism from the medium and long term time scale, a power generator can be effectively stimulated to invest inertia resources.

Description

Technical Field

[0001] This invention relates to the field of power system power supply optimization and allocation technology, and in particular to a method for establishing and solving a power supply allocation equilibrium model based on capacity and inertia market mechanisms. Background Technology

[0002] Given the urgent need for ample inertia in new power systems, a crucial issue in optimizing power supply configuration through decentralized decision-making is how to provide long-term incentive signals to guide power supply structures with sufficient inertia. Existing research rarely focuses on the design of inertia adequacy mechanisms, failing to discover the value of inertia or incentivize its provision. Furthermore, current research has not considered inertia adequacy guidance mechanisms, resulting in power supply structures that cannot guarantee the system's inertia adequacy.

[0003] Existing research on inertia incentive mechanisms is generally based on an operational timescale, incorporating inertia into ancillary services and calculating its marginal price. While this method is theoretically feasible, inertia is currently difficult to measure in real time, making it impossible to compensate based on the unit's real-time inertia contribution, thus limiting its applicability. Furthermore, the uncertainty of revenue in actual operation and generators' risk aversion can easily lead to underinvestment, and this problem is difficult to correct in a timely manner at the operational level, making it difficult to guarantee the system's inertia sufficiency. Therefore, it is necessary to study inertia sufficiency mechanisms on a medium- to long-term timescale, locking in generators' inertia-related revenue in advance from the spot market.

[0004] The statements herein provide only background information in relation to this invention and do not necessarily constitute prior art. Summary of the Invention

[0005] The purpose of this invention is to provide a method for establishing and solving a power configuration balancing model based on capacity and inertia market mechanisms, so as to study the power structure under the energy, reserve, capacity and inertia market mechanisms.

[0006] To achieve the above objectives, this invention provides a method for establishing a power allocation balancing model based on a capacity and inertia market mechanism, comprising: S1. Design an inertia market mechanism, wherein the inertia market is a medium- to long-term inertia market based on auctions; S2. Construct a power configuration balancing model based on Stackelberg game theory, including: S2.1 Construct an upper-level model to solve the problem of maximizing the profits of power generators; S2.2 Construct a lower-level model to solve the multi-market clearing problem, wherein the multi-market includes the energy reserve joint market, the capacity market, and the inertia market; S3. Solve the power supply configuration equalization model.

[0007] Optionally, step S1 includes: S1.1. Set the trading product, and use inertia as the trading product to be auctioned in the inertia market, and quantify it with the inertia constant H; S1.2. Define the trading participants, including setting different types of generator sets as sellers, system operators or load agents as buyers, and power system operators or regulators as market organizers. S1.3, Set up the transaction process.

[0008] Optionally, step S2.1 includes: S2.1.1 To minimize the investment costs of power generators and maximize their profits from the energy, reserve, capacity, and inertia markets, the objective function of the upper-level model is determined as follows: ; In the formula, the parameter Represents the probability of scenario s; variables include: , , , and These represent the power generation operator y's power investment cost, energy-related profit, standby-related profit, capacity market profit, and inertia market profit, respectively; unit: $; S2.1.2 Determine the constraints of the upper-level model, including power investment constraints, unit pricing constraints, and inertia constraints.

[0009] Optionally, the power investment cost The calculation formula is: ; In the formula, the set includes: This represents the set of all types of generator sets for generator y. This represents a collection of thermal power units to be built. This indicates a collection of wind power plants to be built. This represents the collection of energy storage systems to be built; parameters include: , and These represent the annualized investment costs of thermal power unit g, wind power w, and energy storage b, respectively, in $ / MW-year. This represents the annualized investment cost per unit capacity of energy storage b, expressed in $ / MWh-year; variables include: , and These represent the newly installed capacity of thermal power unit g, wind power w, and energy storage b, respectively, in MW. This indicates the newly built capacity of energy storage b, in MWh; Energy-related profits The calculation formula is: ; In the formula, the set includes: This indicates that a thermal power unit has been assembled. This indicates that there is already a wind power cluster. This indicates an existing energy storage system; parameters include: This indicates that time period t represents the number of days in a year. and These represent the operating costs of the planned thermal power unit g and wind power unit w, respectively, in $ / MWh. and Represent the operating costs of existing thermal power unit g and wind power unit w, respectively, in $ / MWh; variables include: , , and These represent the dispatch power of the planned thermal power unit g, wind power w, and energy storage b, respectively, in MW. , , and These represent the dispatchable power of existing thermal power unit g, wind power w, and energy storage b, respectively, in MW. , and The values ​​represent the energy prices at node n in scenario s during time period t, which includes thermal power unit g, wind power w, and energy storage b, respectively, in units of $ / MWh. The backup related profits The calculation formula is: ; In the formula, the variables include: and These represent the dispatch reserve of the thermal power unit g and energy storage b to be built during time period t in scenario s, respectively, in MW. and These represent the standby power generation units g and energy storage b in scenario s during time period t, respectively, in MW. Represents the reserve price for time period t in scenario s, in units of $ / MWh; The market profit of the capacity The calculation formula is: ; In the formula, the variables include: , and These represent the dispatch capacities of the planned thermal power unit g, wind power w, and energy storage b, respectively, in MW. , and These represent the dispatch capacity of existing thermal power unit g, wind power w, and energy storage b, respectively, in MW. This indicates the price per MW, in units of $ / MW-year. The inertia market profit The calculation formula is: ; In the formula, the variables include: , and Let g represent the dispatch inertia of the thermal power unit to be built, w represent the wind power unit, and b represent the energy storage unit, respectively, in seconds. , and These represent the dispatch inertia of existing thermal power unit g, wind power unit w, and energy storage unit b, respectively, in seconds. Price of inertia, in units of $ / s-year.

[0010] Optionally, the power investment constraint is: ; ; In the formula, the parameters include: The power-to-capacity conversion factor for energy storage, in hours (h). The pricing constraints for the generator set are as follows: ; ; In the formula, the set includes: Represents a set of time periods. Represents a set of random scenarios; variables include: and These represent the energy market prices for the planned and existing thermal power units (g) during time period t in scenario s, respectively, in $ / MWh. , and These represent the market prices for the planned thermal power unit g, wind power w, and energy storage b, respectively, in $ / MW-year. , and These represent the market prices for the planned thermal power unit g, wind power w, and energy storage b, respectively, in the inertia market, in units of $ / s-year. , and These represent the market prices for existing thermal power units (g), wind power (w), and energy storage (b), respectively, in $ / MW-year. , and The prices quoted in the inertia market for existing thermal power units (g), wind power (w), and energy storage (b) are respectively expressed in $ / s-year. The inertia constraint is: ; ; ; ; ; ; In the formula, the parameters include: , and Let g represent the inertia constants of the thermal power unit to be built, w represent the inertia constants of the wind power unit, and b represent the inertia constants of the energy storage unit, respectively, in seconds. , and Let g represent the inertia constants of the existing thermal power unit (g), wind power unit (w), and energy storage unit (b), respectively, in seconds. , and These represent the existing installed capacity of thermal power unit g, wind power w, and energy storage b, respectively, in MW; variables include: , and These represent the inertia levels provided to the system by the planned thermal power unit g, wind power w, and energy storage b, respectively, in seconds. , and These represent the inertia levels provided to the system by the existing thermal power unit g, wind power w, and energy storage b, respectively, in seconds.

[0011] Optionally, step S2.2 includes: To maximize the social welfare of the joint energy and reserve market, the objective function of the joint energy and reserve market is determined as follows: ; In the formula, the parameter The cost of load shedding (unit: $ / MWh), variable This represents the load shedding size of node n in time period t within scenario s (unit: MW). The constraints for determining the energy reserve joint market include power balance constraints, unit output constraints, spinning reserve constraints, coupling constraints between unit output and spinning reserve, ramping constraints, load shedding constraints, energy storage state of charge constraints, and line power flow constraints.

[0012] Optionally, step S2.2 includes: To maximize the social welfare of the capacity market, the objective function of the capacity market is determined as follows: ; In the formula, the set Represents a set of segmented capacity demand curves; parameters This represents the capacity quote for the i-th segment of the capacity demand curve, in units of $ / MW-year; variable This represents the actual capacity demand of the i-th segment of the capacity demand curve, in MW. Determine the constraints of the capacity market, including capacity demand balance constraints, unit capacity constraints, and capacity demand range constraints.

[0013] Optionally, step S2.2 includes: To maximize the social welfare of the inertia market, the objective function of the inertia market is determined as follows: ; Determine the constraints of the inertia market, including inertia demand constraints and unit inertia constraints.

[0014] Optionally, step S3 includes: S3.1 Based on the primal-dual optimality condition, the lower-level problem is replaced with its primal problem constraint, dual problem constraint and strong dual equality constraint, thereby transforming each bi-level problem into a single-level problem. The resulting single-level problem is an MPEC (Mathematical Programs with Equilibrium Constraints) problem. S3.2. Use the diagonalization method to find the Nash equilibrium among multiple generators. Different generators take turns making decisions after seeing the decisions of other generators in previous iterations. This process is repeated to solve the MPEC model of each generator. When all generators do not change their decisions, it is considered that the equilibrium point has been converged and the iteration can be terminated.

[0015] Optionally, step S3.2 includes: By setting initial values ​​and starting from the perspective of centralized optimization, the power structure with the minimum investment and total operating cost is found, and this is used as the initial value. The equilibrium solution of the model is obtained by using the diagonalization method. In different equilibrium solutions, an equilibrium solution is determined by setting different objective functions.

[0016] Compared with the prior art, the present invention has at least the following beneficial effects: 1. Ensure sufficient inertia and system security: By designing an inertia market, clearly pricing inertia, and studying the inertia sufficiency mechanism on a medium- to long-term time scale, the inertia-related income of power generators can be locked in advance in the spot market, which can effectively incentivize power generators to invest in inertia resources and fundamentally ensure the frequency stability of a high proportion of new energy power grids.

[0017] 2. Significant cost savings: Studies show that relying on thermal power units to provide inertia requires replacing 10%-33% of wind power, which is costly. This invention, however, incentivizes wind power to configure virtual inertia, requiring thermal power units to replace only 0%-2%, significantly reducing the system cost of the clean energy transition.

[0018] 3. Promoting Technological Application: This invention clarifies the economic value of virtual inertia. Under carbon tax policies, investing in virtual inertia is more cost-effective than building new thermal power plants, providing market impetus for the promotion of emerging technologies and accelerating the green transformation of the power system. Attached Figure Description

[0019] Figure 1 This is a flowchart of the power configuration equalization model establishment and solution method of the present invention; Figure 2 This is a schematic diagram of the inertia market clearing method of the present invention; Figure 3 The power supply structures corresponding to different scenarios are: (a) a balance model with an inertia market but no virtual inertia; (b) a balance model with both an inertia market and virtual inertia; (c) a balance model without an inertia market; (d) a centralized optimization model with inertia constraints but no virtual inertia; (e) a centralized optimization model with both inertia constraints and virtual inertia; and (f) a centralized optimization model without inertia constraints. Figure 4 A schematic diagram of the total system inertia for different scenarios; Figure 5 A schematic diagram of energy prices (i), (ii) and reserve prices (iii) for scenarios (a), (b) and (c); Figure 6 The following are the power supply structures for scalability testing systems under different scenarios: (a) a balanced model with an inertia market but no virtual inertia; (b) a balanced model with both an inertia market and virtual inertia; (c) a balanced model without an inertia market; (d) a centralized optimization model with inertia constraints but no virtual inertia; (e) a centralized optimization model with both inertia constraints and virtual inertia; and (f) a centralized optimization model without inertia constraints. Detailed Implementation

[0020] The following detailed description, in conjunction with the accompanying drawings and specific embodiments, further illustrates the power configuration balancing model establishment and solution method based on the capacity and inertia market mechanism proposed in this invention. The advantages and features of this invention will become clearer from the following description. It should be noted that the accompanying drawings are in a very simplified form and use non-precise scales, used only to facilitate and clearly illustrate the embodiments of this invention. Please refer to the accompanying drawings to make the objectives, features, and advantages of this invention more apparent and understandable. It should be understood that the structures, scales, sizes, etc., depicted in the accompanying drawings are only for illustrative purposes to aid those skilled in the art and are not intended to limit the implementation conditions of this invention. Therefore, they have no substantial technical significance. Any modifications to the structure, changes in the proportional relationships, or adjustments to the size, without affecting the effects and objectives achieved by this invention, should still fall within the scope of the technical content disclosed in this invention.

[0021] This invention provides a method for establishing and solving a power allocation balancing model based on capacity and inertia market mechanisms, such as... Figure 1 As shown, the method includes the following steps: S1. Design of the inertia market mechanism.

[0022] This step proposes an auction-based medium- to long-term inertia market designed to incentivize generators to invest in generators with large inertia constants or the ability to provide virtual inertia. Unlike compensating for inertia by incorporating it into frequency regulation ancillary services, this inertia market allows generators to earn additional revenue for inertia they haven't actually provided. This enables generators to receive inertia fees before the spot market, helping to stabilize revenue fluctuations and ensuring system inertia sufficiency. This inertia market mechanism is applicable to all types of generators.

[0023] Step S1 specifically includes the following steps: S1.1, Set up the trading products.

[0024] Inertia is used as a traded commodity in the inertia market and quantified by the inertia constant H to reflect the unit's ability to support system inertia. This product has the following characteristics: (1) The inertia level of a thermal power unit depends on its technical parameter: inertia constant H. Once a thermal power unit is built, its inertia constant is fixed and is unrelated to its actual dispatch output. Furthermore, once the generator is connected to the power grid, its inertia will be absorbed by the power system. Meanwhile, wind power with improved inverter control and energy storage can provide virtual inertia similar to traditional inertia. That is, once wind power with virtual inertia is built, its inertia constant is determined and is unrelated to actual dispatch output. It should be noted that the inertia contribution of different units to the system (analogous to the dispatch output of units in the energy market) is difficult to measure in real time, while the maximum inertia that a unit can provide (analogous to the installed capacity of the unit) is related to the power technology type and can be determined once the unit is built.

[0025] (2) The total inertia of a power system is the weighted sum of the inertia of all generator units, with the weight being the ratio of the rated power of each unit to the total rated power of the system. The revenue of each generator unit in the inertia market depends on its contribution to the total inertia of the system.

[0026] (3) The system’s requirement for inertia is only reflected in the size of the inertia, not in the speed provided. This is because both traditional and virtual inertia can achieve fast response and meet the system’s requirements for inertia response, so there is no need to differentiate between providing speed.

[0027] S1.2, Set up transaction participants.

[0028] As sellers, different types of generator sets participate equally in the inertia market, such as thermal power units, new energy generator sets (such as wind power), and energy storage systems. Among them, thermal power units can provide traditional rotational inertia for the power system; new energy generator sets and energy storage systems can provide virtual inertia.

[0029] As the buyer, the system operator or load agent pays for the inertia supply on behalf of the electricity consumers. This payment is used to compensate for the installed capacity costs of thermal power units and the costs of virtual inertia technology upgrades for new energy power units.

[0030] As market organizers, power system operators or regulators determine the required total system inertia based on the desired rate of frequency change. The required rate of frequency change depends on the power system's frequency stability standards and the adequacy of flexible resources, and its value varies from power system to power system.

[0031] S1.3, Set up the transaction process.

[0032] In the proposed auction-based inertia market mechanism, the inertia market determines the clearing price of inertia and the winning bids for different power generators. The execution process of this mechanism is as follows: (1) Initially, market organizers confirm some basic information: the inertia constant and installed capacity of each generator set, the frequency change rate requirement of the power system and the corresponding inertia requirement, and the trading frequency (usually an annual market).

[0033] (2) The power generator quotes a price and quantity to the market organizer. The quoted quantity is the maximum inertia that the power generator can provide to the power system. The quoted price is the minimum fee that the power generator demands for providing the inertia.

[0034] (3) The final cleared bid determines the clearing price of the momentum market (e.g., Figure 2 The clearing price is in dollars per second and is paid as a unit price to all generators whose power generation is being cleared.

[0035] (4) The inertia (unit: s) provided by the generators that have successfully cleared out will receive corresponding payment (unit: $).

[0036] The above transaction process is carried out once per auction, with delivery taking place in the following year of the auction.

[0037] S2. Construct a power configuration equilibrium model based on Stackelberg game theory.

[0038] This step establishes a two-level optimization model for each generator. The upper-level problem aims to maximize a generator's profit and obtain the corresponding optimal investment decision, predicting revenue from multiple markets. The lower-level problem represents the market clearing process, using the investment decision obtained from the upper-level problem as given parameters. Each generator has its own two-level model to maximize its profit, while their lower-level models are identical.

[0039] Step S2 specifically includes the following steps: S2.1 Construct an upper-level model to solve the problem of maximizing the profits of power generators.

[0040] Step S2.1 specifically includes the following steps: S2.1.1 Determine the objective function.

[0041] The objective function aims to minimize the investment costs of power generators and maximize their profits from the energy, reserve, capacity, and inertia markets. Energy and reserve markets employ a joint clearing mechanism, with the energy market clearing hourly to generate hourly energy and reserve prices. The capacity and inertia markets clear annually to generate annual capacity and inertia prices. Furthermore, this invention uses a scenario-based stochastic optimization method to model the uncertainties of renewable energy generation and load. The objective function is expressed as follows: (2-1) In the formula, the parameter This represents the probability of scenario s. The variables include: , , , and These represent the power generation operator y's power investment cost, energy-related profit, standby-related profit, capacity market profit, and inertia market profit (unit: $).

[0042] Among them, power investment cost The calculation formula is shown in equation (2-2). The power investment cost consists of two parts: the power cost related to the rated power and the capacity cost related to the rated capacity.

[0043] (2-2) In the formula, the set includes: This represents the set of all types of generator sets for generator y. This represents a collection of thermal power units to be built. This indicates a collection of wind power plants to be built. This represents the energy storage system to be built. Parameters include: , and These represent the annualized investment costs of thermal power unit g, wind power w, and energy storage b (unit: $ / MW-year). This represents the annualized investment cost per MWh of energy storage unit b (unit: $ / MWh-year). Variables include: , and These represent the newly installed capacity (unit: MW) of thermal power unit g, wind power w, and energy storage b, respectively. This indicates the newly built capacity of energy storage b (unit: MWh).

[0044] Among them, energy-related profits The calculation formula is shown in equation (2-3), which represents the energy-related profit that power generators obtain from the combined energy and reserve markets.

[0045] (2-3) In the formula, the set includes: This indicates that a thermal power unit has been assembled. This indicates that there is already a wind power cluster. This indicates an existing energy storage system. Parameters include: This indicates that time period t represents the number of days in a year. and These represent the operating costs of the planned thermal power unit g and wind power unit w (unit: $ / MWh). and These represent the operating costs of existing thermal power unit g and wind power unit w (unit: $ / MWh). Variables include: , , and These represent the dispatch power (unit: MW) of the thermal power unit g, wind power w, and energy storage b (discharge and charge) to be built. , , and These represent the dispatch power (unit: MW) of existing thermal power units g, wind power w, and energy storage b (discharging and charging). , and These represent the energy prices at node n in scenario s during time period t, where thermal power unit g, wind power w, and energy storage b are located (unit: $ / MWh).

[0046] Among them, the profit related to reserves The calculation formula is shown in equation (2-4), which represents the reserve-related profit obtained by power generators from the energy and reserve joint market.

[0047] (2-4) In the formula, the variables include: and These represent the scheduling reserves (unit: MW) of the thermal power unit g and energy storage b to be built during time period t in scenario s. and These represent the standby power generation units g and energy storage units b in scenario s during time period t (unit: MW). This represents the reserve price for time period t in scenario s (unit: $ / MWh).

[0048] Among them, capacity market profits The calculation formula is shown in equation (2-5), which represents the profit of the generator from the capacity market.

[0049] (2-5) In the formula, the variables include: , and These represent the dispatch capacity (unit: MW) of the thermal power unit g, wind power w, and energy storage b to be built, respectively. , and These represent the dispatch capacity (unit: MW) of existing thermal power unit g, wind power w, and energy storage b, respectively. This indicates the price per MW (unit: $ / MW-year).

[0050] Among them, the inertia market profit The calculation formula is shown in equation (2-6), which represents the profit of the generator from the inertia market.

[0051] (2-6) In the formula, the variables include: , and Let g represent the dispatch inertia (in seconds) of the thermal power unit g, wind power w, and energy storage b to be built. , and These represent the dispatch inertia (in seconds) of existing thermal power unit g, wind power w, and energy storage b, respectively. Indicates the price of inertia (unit: $ / s-year).

[0052] S2.1.2 Determine the constraints of the upper-level model.

[0053] The constraints of the upper-level model include power investment constraints, unit pricing constraints, and inertia constraints.

[0054] The power investment constraints are shown in Equations (2-7) and (2-8). Equation (2-7) indicates that the investment in thermal power units, wind power and energy storage is non-negative, and Equation (2-8) indicates the new capacity constraint for energy storage.

[0055] (2-7) (2-8) In the formula, the parameters include: The power-to-capacity conversion factor for energy storage (unit: h).

[0056] The unit pricing constraints are shown in equations (2-9) and (2-10), where equations (2-9) and (2-10) indicate that the prices of the units to be built and the existing units in all markets are non-negative.

[0057] (2-9) (2-10) In the formula, the set includes: Represents a set of time periods. This represents a set of random scenarios. Variables include: and The figures represent the energy market prices (unit: $ / MWh) for the thermal power units to be built and the existing thermal power units g in time period t of scenario s. , and These represent the market prices for the planned thermal power unit g, wind power w, and energy storage b (unit: $ / MW-year). , and These represent the prices quoted in the inertia market for the thermal power unit g, wind power w, and energy storage b to be built (unit: $ / s-year). , and These represent the market prices for existing thermal power units (g), wind power (w), and energy storage (b) (unit: $ / MW-year). , and These represent the existing prices of thermal power units g, wind power w, and energy storage b in the inertia market (unit: $ / s-year).

[0058] The inertia constraint is shown in equations (2-11)-(2-16), where equations (2-11)-(2-16) represent the magnitude of the inertia support of all units to be built and existing units to the system.

[0059] (2-11) (2-12) (2-13) (2-14) (2-15) (2-16) In the formula, the parameters include: , and Let g represent the inertia constants (in seconds) of the thermal power unit g, wind power w, and energy storage b to be built. , and Let g represent the inertia constants (in seconds) of the existing thermal power unit g, wind power w, and energy storage b, respectively. , and These represent the installed capacity (unit: MW) of existing thermal power units (g), wind power units (w), and energy storage units (b). Variables include: , and These represent the inertia levels (in seconds) provided to the system by the thermal power unit g, wind power w, and energy storage b, respectively. , and These represent the inertia levels (in seconds) provided by the existing thermal power unit g, wind power w, and energy storage b to the system.

[0060] When different power generators offer the same price, it is also necessary to consider the allocation of their winning bids in the energy, reserve, capacity, and inertia markets according to their respective installed capacity proportions. This constraint should theoretically be placed in the lower-level market clearing model, but in order to simplify the dualized mathematical model and ensure the linearity of the lower-level problem, this problem is considered in the upper-level problem. The specific processing method belongs to the prior art and is not the focus of this invention.

[0061] The variable set of the power configuration equalization model includes the upper-level variable set. and lower-level variable set , and The upper-level variable set is ={ , , , , , , , , , , , , , , , , , , , , , , , The set of lower-level variables for the energy reserve joint market is as follows: ={ , , , , , , , , , , , , , , , , , The set of lower-level variables concerning the capacity market is as follows: ={ , , , , , , , The set of lower-level variables for the inertia market is as follows: ={ , , , , , , }

[0062] S2.2 Construct a lower-level model to address the multi-market clearing problem. The multi-markets include the energy reserve joint market, the capacity market, and the inertia market.

[0063] (1) The expression for the optimal solution set when the energy reserve joint market reaches equilibrium is: .

[0064] To solve for the values ​​of each variable in the optimal solution set, the objective function of the energy reserve joint market is first determined, as shown in Equation (2-17), which aims to maximize the social welfare of the energy and reserve joint market.

[0065] (2-17) In the formula, the parameter This represents the cost of load shedding (unit: $ / MWh). Variable This represents the load shedding size of node n in time period t within scenario s (unit: MW).

[0066] Then, the constraints of the energy reserve joint market are determined, including power balance constraints, unit output constraints, spinning reserve constraints, coupling constraints of unit output and spinning reserve, ramping constraints, load shedding constraints, energy storage state of charge constraints, and line power flow constraints.

[0067] The power balance constraint is shown in equation (2-18), representing the nodal power balance. The corresponding dual variables are given in parentheses after the constraint.

[0068] (2-18) In the formula, the set includes: Represents a set of nodes. and Let n represent the sets of thermal power units to be built and the sets of existing thermal power units at node n, respectively. and Let n represent the sets of wind farms to be built and the sets of existing wind farms, respectively. and Let n represent the sets of energy storage to be built and the sets of existing energy storage at node n, respectively. This represents the nodes connected to node n. Parameters include: This represents the susceptance (unit: pu) of a transmission line (n, m). This represents the electrical load (unit: MW) of node n in time period t within scenario s.

[0069] The unit output constraints are shown in equations (2-19) to (2-26). Equations (2-19) and (2-20) represent the output constraints of the thermal power units to be built and the existing units, respectively. Equations (2-21) and (2-22) represent the output constraints of the wind power units to be built and the existing units, respectively. Equations (2-23) to (2-26) represent the charging and discharging constraints of the energy storage units to be built and the existing units.

[0070] (2-19) (2-20) (2-21) (2-22) (2-23) (2-24) (2-25) (2-26) In the formula, the parameters include: and represents the typical output coefficients of the wind power w to be built and the existing wind power w in time period t in scenario s, respectively, which is the ratio of typical dispatch output to rated power.

[0071] Among them, the spinning reserve constraints are shown in equations (2-27) to (2-31). Equations (2-27) and (2-28) represent the spinning reserve constraints provided by the thermal power plants to be built and the existing thermal power plants, respectively. Equations (2-29) and (2-30) represent the spinning reserve constraints of the energy storage plants to be built and the existing energy storage plants, respectively. Equation (2-31) gives the reserve requirements.

[0072] (2-27) (2-28) (2-29) (2-30) (2-31) In the formula, the parameters include: and Let g represent the 10-minute ramp rate coefficients of the thermal power units under construction and the existing thermal power units, respectively. and These represent the 10-minute ramp rate coefficients for the energy storage system to be built and the existing energy storage system b, respectively. This represents the reserve requirement during time period t (unit: MW).

[0073] The coupling constraints of unit output and spinning reserve are shown in equations (2-32) to (2-35). Equations (2-32) and (2-33) represent the coupling constraints of dispatch output and spinning reserve of thermal power plants to be built and existing thermal power plants, respectively, and equations (2-34) and (2-35) represent the coupling constraints of dispatch output and spinning reserve of energy storage plants to be built and existing energy storage plants, respectively.

[0074] (2-32) (2-33) (2-34) (2-35) Among them, the ramping constraints are shown in equations (2-36) and (2-37), which represent the ramping constraints of the thermal power plants to be built and the existing thermal power plants, respectively.

[0075] (2-36) (2-37) In the formula, the parameters include: and Let g represent the downward and upward gradient coefficients of the thermal power unit to be built, respectively. and These represent the downward and upward ramp coefficients of the existing thermal power unit g, respectively.

[0076] The load shearing constraint is shown in equation (2-38), which represents the range of the load shearing.

[0077] (2-38) Among them, the state of charge constraints of energy storage are shown in (2-39) to (2-44). Equations (2-39) and (2-41) represent the state of charge constraints of the energy storage to be built and the existing energy storage, respectively. Since there are losses in the charging and discharging process of energy storage, it is implicitly guaranteed that the energy storage will not be charged and discharged at the same time. Equations (2-40) and (2-42) represent the initial and final state of charge of the energy storage to be built and the existing energy storage, respectively, which are half of its rated capacity. Equations (2-43) and (2-44) represent the upper and lower limits of the state of charge constraints of the energy storage to be built and the existing energy storage, respectively.

[0078] (2-39) (2-40) (2-41) (2-42) (2-43) (2-44) In the formula, the parameters include: and These represent the charging and discharging efficiencies of the energy storage system to be built (b), respectively. and These represent the charging and discharging efficiencies of the existing energy storage b, respectively. Indicates the scheduling interval (unit: h). This represents the rated capacity (in MWh) of existing energy storage b. Variables include: and The states of charge (in MWh) represent the state of charge of the energy storage b to be built and the existing energy storage b during time period t in scenario s, respectively.

[0079] The power flow constraints of the line are shown in equations (2-45)-(2-47).

[0080] (2-45) (2-46) (2-47) In the formula, the parameter This represents the transmission capacity (in MW) of the transmission line (n, m). Variable This represents the voltage phase angle of node n in time period t within scenario s (unit: rad).

[0081] The expression for the optimal solution set when the capacity market reaches equilibrium is: ; To solve for the values ​​of each variable in the optimal solution set, the objective function of the capacity market is first determined, as shown in equation (2-48), which aims to maximize the social welfare of the capacity market.

[0082] (2-48) In the formula, the set This represents the set of segments of the capacity demand curve. Parameters This represents the capacity quote (unit: $ / MW-year) for the i-th segment of the capacity demand curve. Variable This represents the actual capacity demand (in MW) of the i-th segment of the capacity demand curve.

[0083] Then, the constraints of the capacity market are determined, including capacity demand balance constraints, unit capacity constraints, and capacity demand range constraints.

[0084] The capacity demand balance constraint is shown in equation (2-49), indicating that thermal power units, wind power, and energy storage jointly provide capacity to meet the system capacity demand. The corresponding dual variables are given in parentheses after the constraint.

[0085] (2-49) The unit capacity constraints are shown in equations (2-50) to (2-55). Equations (2-50) and (2-51) represent the range of reliable capacity for thermal power units, equations (2-52) and (2-53) give the range of reliable capacity for wind power, and equations (2-54) and (2-55) give the range of reliable capacity for energy storage. The maximum reliable capacity that wind power and energy storage can provide is the rated power after being converted according to their reliable capacity coefficients. The reliable capacity coefficients are empirical values, which are the ratio of the average output of wind power and energy storage to the rated power during historical periods of power shortage.

[0086] (2-50) (2-51) (2-52) (2-53) (2-54) (2-55) In the formula, the parameters include: and Let w represent the reliable capacity coefficients of wind power projects to be built and existing wind power projects in the capacity market, respectively. and represents the reliable capacity coefficients of energy storage b to be built and existing energy storage in the capacity market, respectively.

[0087] The capacity demand range constraint is shown in Equation (2-56), which represents the upper and lower limits of the capacity demand in the i-th segment of the capacity demand curve.

[0088] (2-56) In the formula, the parameter This represents the maximum capacity demand (in MW) of the i-th segment of the capacity demand curve.

[0089] The expression for the optimal solution set when the inertia market reaches equilibrium is: ; To solve for the values ​​of each variable in the optimal solution set, the objective function of the inertia market is first determined, as shown in equation (2-57), which aims to maximize the social welfare of the inertia market.

[0090] (2-57) Then, the constraints of the inertia market are determined, including inertia demand constraints and unit inertia constraints.

[0091] The inertia requirement constraint is shown in equation (2-58), indicating that the total inertia provided by thermal power units, wind power, and energy storage must meet the system's inertia requirements. The corresponding dual variables are given in parentheses after the constraint.

[0092] (2-58) The inertia constraints of the generating units are shown in equations (2-59) to (2-64). Equations (2-59) and (2-60) represent the upper and lower limits of the inertia provided by the thermal power units to be built and the existing thermal power units, respectively; equations (2-61) and (2-62) represent the upper and lower limits of the inertia provided by the wind power units to be built and the existing wind power units, respectively; and equations (2-63) and (2-64) represent the upper and lower limits of the inertia provided by the energy storage units to be built and the existing energy storage units, respectively. If the new energy generating units are not equipped with virtual inertia control facilities, then their inertia is zero.

[0093] (2-59) (2-60) (2-61) (2-62) (2-63) (2-64) In the formula, the parameter This represents the system's inertia requirement (unit: seconds).

[0094] S3, the solution algorithm for the power configuration balancing model.

[0095] This step presents the solution method for the proposed power allocation balancing model. Each power generator acts based on the investment decisions of other power generators; equilibrium is achieved if no power generator changes its decision.

[0096] Step S3 includes the following steps: S3.1. Based on the primal-dual optimality condition, the lower-level problem is replaced with its primal problem constraints, dual problem constraints, and strong duality equality constraints, thereby transforming each bi-level problem into a single-level problem. The resulting single-level problem is an MPEC problem.

[0097] S3.2. Use the diagonalization method to find the Nash equilibrium among multiple generators. In this diagonalization method, different generators take turns making decisions after seeing the decisions of other generators in previous iterations, and so on, solving the MPEC model for each generator iteratively. When all generators no longer change their decisions, it is considered that they have converged to the equilibrium point, and the iteration can be terminated.

[0098] Given that different initial values ​​in the diagonalization method will lead to different solutions, this invention first seeks the power supply structure that minimizes investment and total operating costs from a lumped optimization perspective in order to obtain a reasonable solution. Then, using this as the initial value, the equilibrium solution of the model is obtained through the diagonalization method.

[0099] The model may have multiple equilibrium solutions. Different objective functions can be set for different equilibrium solutions to select a desired one, such as maximizing social welfare or maximizing the profits of all generators. In this embodiment, the solution obtained by the ensemble optimization with the minimum total cost is selected as the initial value, and the final equilibrium solution is most likely the one with the minimum cost.

[0100] S4. Simulation verification of the power configuration equalization model.

[0101] This step introduces a specific calculation case based on the power configuration balancing model.

[0102] Six scenarios were set up for numerical simulations: (a) an equilibrium model with an inertia market but no virtual inertia, (b) an equilibrium model with both an inertia market and virtual inertia, (c) an equilibrium model without an inertia market, (d) a lumped optimization model with inertia constraints but no virtual inertia, (e) a lumped optimization model with both inertia constraints and virtual inertia, and (f) a lumped optimization model without inertia constraints. All numerical simulations were implemented and solved on the GAMS platform with default parameters. The NLPEC solver embedded in GAMS was used, which can provide local optima for the MPEC problem. All numerical simulations were performed on a personal laptop with an Intel Core i5 CPU with 3.20 GHz and 8GB of RAM.

[0103] The numerical simulation studies a one-year timeframe; therefore, the annualized investment cost is matched to the annual operating cost over the given time period. Eight typical days (π) were selected. s =1 / 8, σ t The model uses a 365-day period (=365) to model the uncertainties in renewable energy generation and load, representing weekdays and weekends in the four seasons, with each typical day containing 24 hours. To highlight the impact of the inertia market on the power structure, network constraints and demand-side responses are ignored in the numerical simulation. Furthermore, only spinning reserve is considered, while other types of reserve are neglected.

[0104] The technical parameters of the generators to be built and those already in use are shown in Table 4-1. Baseload thermal power is characterized by high investment costs and low operating costs (generally large coal-fired power units), while peak load thermal power is characterized by low investment costs and high operating costs (generally gas turbine units). The system's generating capacity needs to maintain a redundancy of 13.75% of the maximum load. The system's inertia level is required to be no less than 3.125 s. The price cap in the energy market is $400 / MWh, and the bid price for capacity demand is $8600 / MWh. The sum of these two prices is $9000 / MWh, representing VOLL. In the energy market, it is assumed that all units bid at their operating costs. Due to the joint clearing of energy and reserves, the reserve bid price for all units is their opportunity cost in the energy market. The capacity bid price for the peak load thermal power units to be built is their investment cost, while the bid price for the base load thermal power units to be built is 20% of their investment cost. The capacity bid price for existing thermal power units is $0 / MW-year, meaning it is assumed that the profits obtained by these generating units have fully covered their investment costs. The capacity pricing for wind power and energy storage is $0 / MW-year. In scenarios with virtual inertia, the inertia pricing for thermal power units is $0 / s-year. The inertia pricing for wind turbines and energy storage represents the investment cost of the devices enabling them to possess virtual inertia. In scenarios without virtual inertia, the inertia pricing for thermal power units under construction represents the investment cost of the virtual inertia device, reflecting the value of inertia.

[0105] Table 4-1 Power Supply Parameters

[0106] *CT represents carbon tax, which is part of the operating cost of thermal power units. In this embodiment, the carbon tax is set at $10 / MWh.

[0107] *In this embodiment, the investment cost for virtual inertia is set at $10,000 / MW-year. This is after the installation of virtual inertia-related... After installation, the inertia constant of wind power and energy storage is 4 s.

[0108] The assumptions regarding capacity market pricing are explained as follows: 1) Peak-load thermal power units under construction are generally marginal units. Their operating costs determine the price in the energy market during non-scarce periods, thus resulting in no profit during these periods. During scarcity periods, the electricity price in the energy market will reach its upper limit, $400 / MWh, exceeding the operating costs of peak-load thermal power units, thereby enabling them to profit. However, due to the reliability requirements of the power system, the total number of scarcity hours in a year is very small, usually not exceeding 20 hours. Therefore, it is difficult for peak-load thermal power units under construction to profit in the energy market, and they need to rely on the capacity market to recover almost all of their investment costs. Thus, this embodiment assumes that their pricing in the capacity market is their investment cost. 2) Base-load thermal power units under construction can profit from the energy market, thereby recovering part of their investment costs. This embodiment assumes that they recover 80% of their investment costs from the energy market. Therefore, they only need to recover 20% of their investment costs in the capacity market. 3) Existing thermal power units have been operating for many years, and it is assumed that they have already recovered all their investment costs. Therefore, their bids in the capacity market are zero. 4) Due to the near-zero operating costs of wind turbines, wind turbines can recover almost all of their investment costs in the energy market. Furthermore, due to the uncertainty and intermittency of wind power generation, power system operators typically do not consider wind turbines as capacity providers or determine reliable capacity based on their historical performance. Therefore, this embodiment assumes that wind turbines have a bid of zero in the capacity market. 5) The power generation capacity of energy storage depends on the stored energy, i.e., the state of charge. Similar to wind turbines, power system operators typically do not consider energy storage as a capacity provider or determine reliable capacity based on historical output. Therefore, this embodiment considers energy storage to have a bid of zero in the capacity market.

[0109] (1) Comparison of power supply structures in different scenarios contrast Figure 3 (a) and Figure 3 (c), or Figure 3 (d) and Figure 3 (f) shows that after considering inertia constraints, the proportion of wind turbines in the total installed capacity will decrease, while the proportion of thermal power units will increase. Because wind power has the characteristics of low operating cost and small inertia, it is the preferred choice if inertia constraints are not considered. However, when inertia constraints are considered, thermal power units with high inertia constants will replace a portion of wind power to meet the inertia requirements of the entire system.

[0110] contrast Figure 3 (b) and Figure 3 (c), or Figure 3 (e) and Figure 3(f) shows that if wind turbines are equipped with virtual inertia devices, the introduction of inertia constraints will not significantly reduce the share of wind power, but will increase the penetration rate of virtual inertia devices.

[0111] The total costs of the six scenarios, including investment and operating costs, are compared. The scenario without inertia constraints is selected as the baseline. When inertia constraints are considered and virtual inertia is included, the total cost increases. This is because inertia constraints, similar to reserve constraints, place higher demands on power systems with a high proportion of renewable energy, requiring additional costs to maintain sufficient system inertia. When inertia constraints are considered but virtual inertia is not, the total cost increases further. This is because this scenario necessitates the construction of thermal power units to replace a portion of wind power, and considering carbon taxes, investing in wind power with virtual inertia is more cost-effective than replacing wind power with thermal power units.

[0112] Compared to the results obtained from the centralized optimization model, the market-based model yielded a higher share of thermal power units. This is because thermal power units possess flexible ramp-up capabilities, reliable capacity, and high inertia constants, leading to a preference for them in the reserve, capacity, and inertia markets. Some researchers have criticized this, arguing that these markets may discriminate against renewable energy generation, thus hindering the decarbonization of the power system. However, this paper argues that reserve capacity, reliable capacity, and sufficient inertia are crucial for the long-term reliability of power supply. To achieve low-carbon goals, renewable energy generation should be encouraged to actively participate in these markets through technological upgrades, such as equipping virtual inertia devices.

[0113] In addition, energy storage is only Figure 3 (e) and Figure 3 Both appear in (f) and are results of the centralized optimization model. This is because energy storage is difficult to profit from in the proposed model. First, their output depends on the current state of charge (SOC). When energy storage sees scarce prices, the current SOC may be low, making it unable to discharge. Second, it is difficult for energy storage to predict the highest and lowest prices in the spot market to determine when to discharge and when to charge. Therefore, in the market-based model, due to the low profit margins of energy storage, power generators tend not to build energy storage. Furthermore, as a result of centralized optimization... Figure 3 Storage is also absent in (d). This is because in this scenario, inertia constraints are considered but virtual inertia is not taken into account. Since storage cannot provide inertia, system operators tend to build thermal power plants to meet the system inertia requirements.

[0114] (2) Comparison of system inertia levels in different scenarios Total system inertia in six scenarios as follows Figure 4As shown, it is necessary to consider inertia requirements in both the equilibrium model and the lumped optimization model. When inertia requirements are ignored, the system inertia will not meet the minimum inertia requirement of the power system (3.125 s). Furthermore, it can be seen that in the scenario with virtual inertia, the total system inertia is higher than that in the scenario without virtual inertia, indicating a higher inertia adequacy.

[0115] (3) Prices of different products Energy and backup costs for scenarios (a), (b), and (c) are as follows: Figure 5 As shown in (i) to (iii). The capacity price for scenarios (a), (b), and (c) is 6.853 k$ / MW-year. The inertia price for scenarios (a) and (b) is 10 k$ / s-year.

[0116] according to Figure 5 In (i) and (ii), the energy price in scenario (b) is lower than in scenario (a). This is because wind power in scenario (b) is increased by 15% compared to scenario (a). More wind power, due to its low operating costs, leads to a lower energy price. Furthermore, scenario (c) has the highest energy price. This is because more peak-load thermal power units are dispatched in scenario (c), which have the highest operating costs. It is noteworthy that although scenario (c) has the highest proportion of wind power, its installed wind power capacity is only 0.8% higher than in scenario (b). Moreover, due to the lack of inertia constraints, scenario (c) has the lowest total installed capacity, which also results in the highest utilization rate of peak-load thermal power units.

[0117] according to Figure 5 (iii) Scenario (a) has the most peak-load thermal power units installed and the lowest standby price, while scenario (c) has the fewest peak-load thermal power units installed and the highest standby price. This is because peak-load thermal power units have the highest operating costs, resulting in the lowest opportunity cost in the energy market. In a market where energy and standby are jointly cleared, the lowest opportunity cost in the energy market leads to the lowest standby price. The more peak-load thermal power units installed, the lower the standby price.

[0118] (4) Consumer spending The user's total annual expenditure and unit electricity expenditure are listed in Table 4-2. Consistent with the price trends of different products, users in scenario (c) have the highest energy expenditure, while users in scenario (b) have the lowest. Regarding reserve expenditure, users in scenario (c) have the highest reserve expenditure, while users in scenario (a) have the lowest. In the composition of unit electricity expenditure, energy fees constitute the majority, accounting for approximately 96% of the total unit electricity payment. Capacity fees account for approximately 3.4% of the total unit electricity payment. The combined reserve costs and inertia costs account for a very small proportion, approximately 0.6%.

[0119] Table 4-2 User Expenditure

[0120] (5) Extensibility test The number of existing thermal power units was increased to 54 to verify the scalability of the proposed model. The existing unit parameters are derived from the IEEE 118-bus system parameters, see Matpower 7.1. Other parameter settings are the same as in the small system test.

[0121] Power supply structure in scalability testing, such as Figure 6 As shown in (a) to (f), the numerical simulation results of the scalability test and the small system test have similar conclusions. The percentage of each type of generator set is the same as the percentage of units in the small system test. This is because the main difference in parameters between the scalability test and the small system test is the different load levels and the different existing units, which are not marginal units and do not affect the clearing price in the market. In terms of computational performance, the computation time for scenarios (a), (b), and (c) is 3.01 × 10⁻⁶. 3 s, 1.55×10 3 s and 790.71 s.

[0122] In summary, this invention proposes an auction-based inertia market mechanism and a Stackelberg game-based power allocation equilibrium model to study the power structure under the energy, reserve, capacity, and inertia market mechanism. The research results of this invention show that: First, it is necessary to consider inertia constraints in power allocation problems and to introduce an inertia incentive mechanism to ensure the sufficiency of inertia in new power systems. Second, compared to the power structure without inertia constraints, if there are inertia constraints but no virtual inertia, 10%-33% of wind turbines need to be replaced by thermal power units to ensure sufficient system inertia. If there are inertia constraints and virtual inertia, thermal power units will only replace 0%-2% of wind turbines. Third, considering carbon taxes, investing in wind turbines with virtual inertia facilities is more cost-effective than replacing zero-inertia wind turbines with thermal power units. Therefore, discovering the value of inertia, incentivizing inertia provision, and increasing the penetration rate of virtual inertia facilities to ensure sufficient inertia in new power systems is feasible and economical.

[0123] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0124] In the description of this invention, it should be understood that the terms "center," "height," "thickness," "upper," "lower," "vertical," "horizontal," "top," "bottom," "inner," "outer," "axial," "radial," and "circumferential," etc., indicating orientation or positional relationships, are based on the orientation or positional relationships shown in the accompanying drawings and are only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the invention. In the description of this invention, unless otherwise stated, "a plurality of" means two or more.

[0125] In the description of this invention, unless otherwise explicitly specified and limited, the terms "installation," "connection," "linking," and "fixing" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0126] In this invention, unless otherwise explicitly specified and limited, "above" or "below" the second feature can include direct contact between the first and second features, or contact between the first and second features through another feature between them. Furthermore, "above," "over," and "on top" of the second feature includes the first feature directly above or diagonally above the second feature, or simply indicates that the first feature is at a higher horizontal level than the second feature. "Below," "below," and "under" the second feature includes the first feature directly below or diagonally below the second feature, or simply indicates that the first feature is at a lower horizontal level than the second feature.

[0127] Although the present invention has been described in detail through the preferred embodiments above, it should be understood that the above description should not be considered as a limitation of the present invention. Various modifications and substitutions to the present invention will be apparent to those skilled in the art after reading the above description. Therefore, the scope of protection of the present invention should be defined by the appended claims.

Claims

1. A method for establishing a power allocation balancing model based on capacity and inertia market mechanisms, characterized in that, include: S1. Design an inertia market mechanism, wherein the inertia market is a medium- to long-term inertia market based on auctions; S2. Construct a power configuration balancing model based on Stackelberg game theory, including: S2.1 Construct an upper-level model to solve the problem of maximizing the profits of power generators; S2.2 Construct a lower-level model to solve the multi-market clearing problem, wherein the multi-market includes the energy reserve joint market, the capacity market, and the inertia market; S3. Solve the power supply configuration equalization model.

2. The method for establishing a power allocation balancing model based on capacity and inertia market mechanism as described in claim 1, characterized in that, Step S1 includes: S1.

1. Set the trading product, and use inertia as the trading product to be auctioned in the inertia market, and quantify it with the inertia constant H; S1.

2. Define the trading participants, including setting different types of generator sets as sellers, system operators or load agents as buyers, and power system operators or regulators as market organizers. S1.3, Set up the transaction process.

3. The method for establishing a power allocation balancing model based on capacity and inertia market mechanism as described in claim 1, characterized in that, Step S2.1 includes: S2.1.1 To minimize the investment costs of power generators and maximize their profits from the energy, reserve, capacity, and inertia markets, the objective function of the upper-level model is determined as follows: ； In the formula, the parameter Represents the probability of scenario s; variables include: , , , and These represent the power generation operator y's power investment cost, energy-related profit, standby-related profit, capacity market profit, and inertia market profit, respectively; unit: $; S2.1.2 Determine the constraints of the upper-level model, including power investment constraints, unit pricing constraints, and inertia constraints.

4. The method for establishing a power allocation balancing model based on capacity and inertia market mechanism as described in claim 3, characterized in that, The power investment cost The calculation formula is: ； In the formula, the set includes: This represents the set of all types of generator sets for generator y. This represents a collection of thermal power units to be built. This indicates a collection of wind power plants to be built. This represents the collection of energy storage systems to be built; parameters include: , and These represent the annualized investment costs of thermal power unit g, wind power w, and energy storage b, respectively, in $ / MW-year. This represents the annualized investment cost per unit capacity of energy storage b, expressed in $ / MWh-year; variables include: , and These represent the newly installed capacity of thermal power unit g, wind power w, and energy storage b, respectively, in MW. This indicates the newly built capacity of energy storage b, in MWh. Energy-related profits The calculation formula is: ； In the formula, the set includes: This indicates that a thermal power unit has been assembled. This indicates that there is already a wind power cluster. This indicates an existing energy storage system; parameters include: This indicates that time period t represents the number of days in a year. and These represent the operating costs of the planned thermal power unit g and wind power unit w, respectively, in $ / MWh. and Represent the operating costs of existing thermal power unit g and wind power unit w, respectively, in $ / MWh; variables include: , , and These represent the dispatch power of the planned thermal power unit g, wind power w, and energy storage b, respectively, in MW. , , and These represent the dispatchable power of existing thermal power unit g, wind power w, and energy storage b, respectively, in MW. , and The values ​​represent the energy prices at node n in scenario s during time period t, which includes thermal power unit g, wind power w, and energy storage b, respectively, in units of $ / MWh. The backup related profits The calculation formula is: ； In the formula, the variables include: and These represent the dispatch reserve of the thermal power unit g and energy storage b to be built during time period t in scenario s, respectively, in MW. and These represent the standby power generation units g and energy storage b in scenario s during time period t, respectively, in MW. This represents the reserve price for time period t in scenario s, in units of $ / MWh; The market profit of the capacity The calculation formula is: ； In the formula, the variables include: , and These represent the dispatch capacities of the planned thermal power unit g, wind power w, and energy storage b, respectively, in MW. , and These represent the dispatch capacity of existing thermal power unit g, wind power w, and energy storage b, respectively, in MW. This indicates the price per MW, in units of $ / MW-year. The inertia market profit The calculation formula is: ； In the formula, the variables include: , and Let g represent the dispatch inertia of the thermal power unit to be built, w represent the wind power unit to be built, and b represent the energy storage unit to be built, in seconds. , and These represent the dispatch inertia of existing thermal power unit g, wind power unit w, and energy storage unit b, respectively, in seconds. Price of inertia, in units of $ / s-year.

5. The method for establishing a power allocation balancing model based on capacity and inertia market mechanism as described in claim 4, characterized in that, The power investment constraint is: ； ； In the formula, the parameters include: The power-to-capacity conversion factor for energy storage, in hours (h). The pricing constraints for the generator set are as follows: ； ； In the formula, the set includes: Represents a set of time periods. Represents a set of random scenarios; variables include: and These represent the energy market prices for the planned and existing thermal power units (g) during time period t in scenario s, respectively, in $ / MWh. , and These represent the market prices for the planned thermal power unit g, wind power w, and energy storage b, respectively, in $ / MW-year. , and These represent the market prices for the planned thermal power unit g, wind power w, and energy storage b, respectively, in the inertia market, in units of $ / s-year. , and These represent the market prices for existing thermal power units (g), wind power (w), and energy storage (b), respectively, in $ / MW-year. , and The prices quoted in the inertia market for existing thermal power units (g), wind power (w), and energy storage (b) are respectively expressed in $ / s-year. The inertia constraint is: ； ； ； ； ； ； In the formula, the parameters include: , and Let g represent the inertia constants of the thermal power unit to be built, w represent the inertia constants of the wind power unit, and b represent the inertia constants of the energy storage unit, respectively, in seconds. , and Let g represent the inertia constants of the existing thermal power unit (g), wind power unit (w), and energy storage unit (b), respectively, in seconds. , and These represent the existing installed capacity of thermal power unit g, wind power w, and energy storage b, respectively, in MW; variables include: , and These represent the inertia levels provided to the system by the planned thermal power unit g, wind power w, and energy storage b, respectively, in seconds. , and These represent the inertia levels provided to the system by the existing thermal power unit g, wind power w, and energy storage b, respectively, in seconds.

6. The method for establishing a power allocation balancing model based on capacity and inertia market mechanism as described in claim 5, characterized in that, Step S2.2 includes: To maximize the social welfare of the joint energy and reserve market, the objective function of the joint energy and reserve market is determined as follows: ； In the formula, the parameter This represents the cost of load shedding, in units of $ / MWh, and is a variable. This represents the load shedding magnitude of node n in time period t within scenario s, in MW. The constraints for determining the energy reserve joint market include power balance constraints, unit output constraints, spinning reserve constraints, coupling constraints between unit output and spinning reserve, ramping constraints, load shedding constraints, energy storage state of charge constraints, and line power flow constraints.

7. The method for establishing a power allocation balancing model based on capacity and inertia market mechanism as described in claim 5, characterized in that, Step S2.2 includes: To maximize the social welfare of the capacity market, the objective function of the capacity market is determined as follows: ； In the formula, the set Represents a set of segmented capacity demand curves; parameters This represents the capacity quote for the i-th segment of the capacity demand curve (unit: $ / MW-year); variable This represents the actual capacity demand (in MW) of the i-th segment of the capacity demand curve. Determine the constraints of the capacity market, including capacity demand balance constraints, unit capacity constraints, and capacity demand range constraints.

8. The method for establishing a power allocation balancing model based on capacity and inertia market mechanism as described in claim 5, characterized in that, Step S2.2 includes: To maximize the social welfare of the inertia market, the objective function of the inertia market is determined as follows: ； Determine the constraints of the inertia market, including inertia demand constraints and unit inertia constraints.

9. The method for establishing a power allocation balancing model based on capacity and inertia market mechanism as described in claim 1, characterized in that, Step S3 includes: S3.1 Based on the primal-dual optimality condition, the lower-level problem is replaced with its primal problem constraint, dual problem constraint and strong duality equality constraint, thereby transforming each bi-level problem into a single-level problem. The resulting single-level problem is an MPEC problem. S3.

2. Use the diagonalization method to find the Nash equilibrium among multiple generators. Different generators take turns making decisions after seeing the decisions of other generators in previous iterations. This process is repeated to solve the MPEC model of each generator. When all generators do not change their decisions, it is considered that the equilibrium point has been converged and the iteration can be terminated.

10. The method for establishing a power allocation balancing model based on capacity and inertia market mechanism as described in claim 8, characterized in that, Step S3.2 includes: By setting initial values ​​and starting from the perspective of centralized optimization, the power structure with the minimum investment and total operating cost is found, and this is used as the initial value. The equilibrium solution of the model is obtained by using the diagonalization method. In different equilibrium solutions, an equilibrium solution is determined by setting different objective functions.

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