Methods, systems, equipment, and media for clearing and dispatching pumped storage units participating in the spot market, taking into account the impact of head.

By constructing a head relationship model and formulating head constraint conditions to optimize the clearing plan of pumped storage units, the problem of the head effect not being considered in the existing technology was solved, and the accuracy of output calculation and the stability of the power system were improved.

CN121906561BActive Publication Date: 2026-06-30BEIJING QU CREATIVE TECH CO LTD

Patent Information

Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
BEIJING QU CREATIVE TECH CO LTD
Filing Date
2026-03-23
Publication Date
2026-06-30

AI Technical Summary

Technical Problem

In existing technologies, the clearing model for pumped storage units participating in the spot market does not consider the impact of the power station head on the maximum pumping power and maximum generating power, resulting in a mismatch between the clearing results and the actual operating conditions, which affects the safe operation of the power grid.

Method used

Construct a model relating the maximum pumping output of the pumped storage unit to the power station head, and the maximum power generation output to the power station head. Formulate head-based constraints and optimize the clearing plan through a clearing model to ensure that the output results match the actual operating conditions of the unit.

Benefits of technology

To improve the accuracy of power output calculations and the feasibility of optimization results, ensure the safe and stable operation of the power system, give full play to the flexible adjustment characteristics of pumped storage units, and promote the safety and flexibility of the power system.

✦ Generated by Eureka AI based on patent content.

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Abstract

This application proposes a method, system, equipment, and medium for clearing and scheduling pumped-storage units participating in the spot market, considering the impact of head. The method includes: analyzing actual operating data of the pumped-storage power station and constructing relationship models between the unit's maximum pumping and generating output and the head; determining the head value of the unit at time period t, and calculating the unit's maximum pumping and generating output at time period t using the relationship models; obtaining the unit's application information for participating in the spot electricity market, and using the calculated maximum output to formulate multiple constraints; based on these constraints and the application information, performing spot electricity market clearing calculations to obtain the output plan for time period t+1; and performing iterative calculations to obtain the unit's output plan curve for each operating day. This method ensures that the output results conform to the actual operating conditions of the pumped-storage unit, improves the accuracy of the unit's output calculation results and clearing optimization results, and guarantees the reliability of the pumped-storage output plan execution.
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Description

Technical Field

[0001] This application relates to the field of pumped storage unit control technology, and in particular to a method, system, equipment and medium for clearing and scheduling pumped storage units participating in the spot market that takes into account the influence of head. Background Technology

[0002] Pumped storage units possess advantages such as fast response speed and high regulation precision. In addition to their core peak shaving and valley filling functions, they can also provide various regulation services such as frequency regulation, reserve capacity, and ramp-up, making them an ideal regulation means to ensure the safe and stable operation of the power system and enhance system flexibility. With the deepening development of the electricity market, pumped storage units are gradually participating in the spot market's declaration and clearing process. Their dispatch and operation plans are determined through market mechanisms, allowing them to fully leverage their flexible regulation role and contribute to the construction of a new type of power system.

[0003] In related technologies, during the process of pumped storage units participating in the spot market declaration and clearing, the clearing model usually sets the maximum pumping power and maximum power generation of the pumped storage unit as fixed constants, and optimizes the clearing by setting boundary constraints based on these constants, thereby obtaining the pumping operation curve and power generation operation curve of the pumped storage unit.

[0004] However, in actual operation of pumped storage units, the maximum pumping power and maximum generating power are not fixed, but are directly related to the water levels of the upper and lower reservoirs of the pumped storage power station. Because the clearing models in related technologies do not consider the impact of the power station head on the maximum pumping power and maximum generating power of the pumped storage units, there are problems such as a mismatch between the clearing results and the actual operation of the pumped storage, the units being unable to execute the clearing plan, and affecting the safe operation of the power grid. Summary of the Invention

[0005] This application aims to at least partially address one of the technical problems in the related art.

[0006] Therefore, the first objective of this application is to propose a clearing and scheduling method for pumped storage units participating in the spot market that takes into account the influence of head. This method considers the maximum pumping output constraint and maximum power generation constraint of the pumped storage unit based on the head relationship in the clearing model, ensuring that the output results are consistent with the actual operating conditions of the pumped storage unit and improving the accuracy of the output calculation results and the clearing optimization results.

[0007] The second objective of this application is to propose a clearing and dispatching system for pumped storage units participating in the spot market that takes into account the impact of head.

[0008] The third objective of this application is to propose an electronic device.

[0009] The fourth objective of this application is to provide a computer-readable storage medium.

[0010] To achieve the above objectives, the first aspect of this application is to propose a method for clearing and dispatching pumped-storage units participating in the spot market, taking into account the impact of head, comprising the following steps:

[0011] By analyzing the actual operating data of pumped storage power stations, we constructed relationship models between the maximum pumping output of pumped storage units and the power station head, as well as relationship models between the maximum power generation output and the power station head.

[0012] Determine the head value of the pumped storage unit in time period t, and based on the head value, calculate the maximum pumping output and maximum power generation output of the pumped storage unit in time period t through the constructed relational model, where t is any positive integer;

[0013] Obtain the application information of pumped storage units participating in the spot electricity market, and formulate multiple constraints on pumped storage units using the water head status and the maximum pumping output and maximum power generation output of the pumped storage units in the time period t. Based on the multiple constraints and the application information, perform spot electricity market clearing calculation through a clearing model to obtain the output plan of the pumped storage units in the time period t+1.

[0014] Based on the power output plan for the t+1 time period, the head value, maximum power output, and spot electricity market clearing calculations are performed cyclically to obtain the power output plan curve of the pumped storage unit on the operating day.

[0015] Optionally, the step of constructing the relationship models between the maximum pumping output of the pumped storage unit and the power station head, and the relationship models between the maximum power generation output and the power station head, respectively, includes: performing statistical analysis and fitting calculations on the relationship data between the head value of the pumped storage power station and the pumping power and power generation of the pumped storage unit, respectively, to obtain the linear relationship between the maximum pumping power and the head, and the linear relationship between the maximum power generation output and the head; constructing the relationship model between the maximum pumping output and the power station head based on the linear relationship between the maximum pumping power and the head, and constructing the relationship model between the maximum power generation output and the power station head based on the linear relationship between the maximum power generation output and the head.

[0016] Optionally, obtaining the application information for pumped storage units to participate in the spot electricity market includes: obtaining the expected head value at the end of the operating day.

[0017] Optionally, the multiple constraints of the pumped storage unit include: a maximum pumping power constraint for the pumped storage power station, used to constrain the range of the maximum pumping power of the pumped storage power station based on the linear relationship between the maximum pumping power and the water head; and a maximum power generation constraint for the pumped storage power station, used to constrain the range of the maximum power generation of the pumped storage power station based on the linear relationship between the maximum power generation and the water head, using the interval where the water head is located in the current time period.

[0018] Optionally, the multiple constraints of the pumped storage unit also include: head state constraints of the pumped storage power station, used to constrain the range of head during the operation of the pumped storage power station; head constraints of the pumped storage power station at the beginning and end of the operating day, used to constrain the head value of the pumped storage power station at the beginning of the current operating day to be equal to the head clearing value at the end of the adjacent previous operating day, and to constrain the head value at the end of the current operating day to be equal to the declared expected head value; and state constraints of the pumped storage power station at different times within one hour, used to constrain the pumped storage power station to have a unique candidate state at different times within one hour, the candidate state including pumping state and power generation state.

[0019] Optionally, the cycle performs head calculation, maximum output calculation, and spot market clearing operation to obtain the pumped storage unit's output plan curve for the operating day. This includes: calculating the head value for time period t+1 based on the output plan for time period t+1; calculating the maximum pumping output and maximum power generation output of the pumped storage unit for time period t+1 based on the head value for time period t+1; performing spot market clearing operation based on the maximum pumping output and maximum power generation output of the pumped storage unit for time period t+1 to obtain the pumped storage unit's output plan for time period t+2, and switching to the next time period for calculation, until the output plans for each time period of the operating day are obtained.

[0020] To achieve the above objectives, a second aspect of this application also proposes a clearing and dispatching system for pumped storage units participating in the spot market, taking into account the impact of head, comprising the following modules:

[0021] The module is used to analyze the actual operating data of pumped storage power stations and build models showing the relationship between the maximum pumping output of the pumped storage unit and the power station head, as well as the relationship between the maximum power generation output and the power station head.

[0022] The calculation module is used to determine the head value of the pumped storage unit in time period t, and based on the head value, calculate the maximum pumping output and maximum power generation output of the pumped storage unit in time period t through the constructed relational model, where t is any positive integer;

[0023] The clearing module is used to obtain the application information of pumped storage units participating in the spot electricity market, and to formulate multiple constraints on the pumped storage units by using the water head status and the maximum pumping output and maximum power generation output of the pumped storage units in the time period t. Based on the multiple constraints and the application information, the clearing module performs spot electricity market clearing calculation through the clearing model to obtain the output plan of the pumped storage units in the time period t+1.

[0024] The cyclic module is used to perform cyclic calculations of head value, maximum output, and spot electricity market clearing based on the output plan for the t+1 time period, so as to obtain the output plan curve of the pumped storage unit on the operating day.

[0025] To achieve the above objectives, a third aspect of this application also provides an electronic device, comprising: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to execute a clearing and scheduling method for pumped storage units participating in the spot market, taking into account the head effect, as described in any one of the first aspects above.

[0026] To achieve the above objectives, the fourth aspect of this application also proposes a computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, it implements the clearing and scheduling method for pumped storage units participating in the spot market, taking into account the head effect, as described in any one of the first aspects above.

[0027] The technical solutions provided by the embodiments of this application bring at least the following beneficial effects: This application establishes a model relating the maximum pumping power and maximum generating power of a pumped storage power station to the head size of the power station, and quantitatively models and manages the maximum pumping and generating power of the pumped storage power station, improving the scientificity and rationality of the determined maximum pumping and generating power of the pumped storage power station. Furthermore, this application proposes a spot electricity market clearing and scheduling model based on the maximum pumping output constraint and maximum generating output constraint of the pumped storage power station's head relationship. The model establishes relevant constraints such as the maximum pumping power constraint, maximum generating power constraint, head state constraint, and head constraints at the start and end of the operating day, ensuring that the planned clearing results of the pumped storage power station conform to the actual situation of the unit, and ensuring the feasibility and effectiveness of the plan, thus guaranteeing the safe and stable operation of the power system. Therefore, this application can effectively promote the participation of pumped storage power stations in the spot market electricity market, fully consider the output and operation characteristics of pumped storage power stations, and optimize the dispatch clearing curve to maximize the regulatory value of pumped storage power stations on the power system, effectively promote the safety and flexibility of the power system, and meet the needs of the construction and safe and stable operation of new power systems.

[0028] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0029] The above and / or additional aspects and advantages of this application will become apparent and readily understood from the following description of the embodiments taken in conjunction with the accompanying drawings, wherein:

[0030] Figure 1 A flowchart illustrating a method for clearing and scheduling pumped storage units participating in the spot market, taking into account the impact of head, as proposed in an embodiment of this application.

[0031] Figure 2 This is a schematic diagram illustrating a specific pumped-storage unit participating in the spot market clearing process according to an embodiment of this application;

[0032] Figure 3 This is a schematic diagram illustrating the relationship between the maximum power output of a pumped storage power station and the water head, as proposed in an embodiment of this application.

[0033] Figure 4 This is a schematic diagram of a clearing and dispatching system for pumped storage units participating in the spot market, taking into account the influence of water head, as proposed in an embodiment of this application. Detailed Implementation

[0034] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0035] It should be noted that in the relevant embodiments, pumped storage units (hereinafter referred to as pumped storage units) participate in the spot market to determine the actual scheduling operation curve of the unit on the operating day. They generally participate in the spot market declaration and clearing by means of "reporting quantity and price". That is, the pumped storage unit's power generation, pumping corresponding quantity and price curves, and reservoir capacity and other parameters are determined after the scheduling model in the spot market is optimized and cleared, thus determining the pumping price, power generation price, pumping output curve and power generation output curve of the pumped storage unit.

[0036] In the optimization and clearing scheduling of the spot market, the maximum pumping power and maximum power generation of pumped storage units are mainly considered as fixed constants, which are used as important boundary constraints. Multiple constraints such as the reservoir capacity status of pumped storage units are also set. Based on these constraints, optimization and clearing are carried out according to the declared data.

[0037] For example, in terms of constraints, additional constraints related to pumped storage power stations are added to the existing constraints, including reservoir capacity constraints and reservoir capacity constraints at the start and end of the operating day of the pumped storage power station.

[0038] Among them, the reservoir capacity state constraint of the pumped storage power station is used to ensure that the reservoir capacity of the pumped storage power station is within the upper and lower limits during operation, and can be expressed by the following formula:

[0039]

[0040] in, Indicates pumped storage power station ps During the period t Storage capacity; and These represent pumped storage power stations. ps During the period t The upper and lower limits of the storage capacity; and These represent pumped storage power stations. ps The pumping power-storage capacity conversion factor and the power generation-storage capacity conversion factor; Indicates the length of the time period.

[0041] The reservoir capacity constraints at the start and end of the operating day of a pumped storage power station are used to ensure that the reservoir capacity at the start of the operating day is equal to the cleared capacity at the end of the previous operating day, and that the reservoir capacity at the end of the operating day is equal to the declared expected capacity. This constraint can be expressed by the following formula:

[0042]

[0043] in, and These represent pumped storage power stations. ps Storage capacity at the beginning and end of the operating day; Indicates pumped storage power station ps Storage capacity at the end of the previous operating day; Indicates pumped storage power station ps The expected storage capacity at the end of the declared operating day.

[0044] The spot market clearing model in the relevant embodiments defaults to the maximum pumping power of the pumped storage unit. and maximum discharge power It is a constant (fixed value) and is not affected by other parameters. Therefore, the pumping / power generation operation curve and corresponding price of the unit are obtained through clearing optimization.

[0045] However, in actual operation, the maximum pumping power and maximum generating power of pumped-storage units are not fixed, but rather linearly related to the head of the pumped-storage power station. When the head is low, the maximum pumping power and maximum generating power are generally lower than their rated pumping power and generating power.

[0046] In this context, the head of a pumped storage power station refers to the water level difference between the upper and lower reservoirs of the pumped storage unit, which can be understood as the gravitational potential energy of water flowing from a high place to a low place.

[0047] As mentioned above, the spot market clearing model for electricity in the relevant embodiments does not consider the influence of the maximum pumping power and maximum generating power of pumped storage units on the power station head. This will lead to a mismatch between the spot clearing results and the actual operating conditions of the pumped storage units. In particular, during the period when the clearing results show the maximum pumping power or maximum generating power, due to the decline in reservoir water level and changes in head, the actual maximum pumping / generating output that the unit can achieve is lower than the maximum pumping / generating output (fixed value), making it impossible to execute the clearing plan curve. The deviation of the unit output from the plan may disrupt the power balance of the power grid, causing voltage and frequency fluctuations, affecting the stability of the power grid, and in severe cases, may cause system oscillations, power outages, and other accidents, endangering the safe and stable operation of the power grid.

[0048] To address this, this application proposes a clearing and dispatching method, system, equipment, and medium for pumped-storage units participating in the spot market, considering the impact of head. The clearing model further considers the maximum pumping output and maximum generating output constraints of the pumped-storage units based on head relationships, ensuring that the output results conform to the actual operating conditions of the pumped-storage units. Furthermore, by replacing reservoir capacity constraints with state constraints based on the head of the pumped-storage power station, the application fully considers the changes in head with the output of the pumped-storage units, further improving the accuracy of the calculation of maximum pumping output and maximum generating output. Therefore, this application can improve the feasibility and effectiveness of the pumped-storage unit clearing plan, fully leverage the flexible adjustment characteristics of pumped storage, ensure the safe and stable operation of the power system, and better promote the participation of pumped storage in the electricity market.

[0049] The following description, with reference to the accompanying drawings, describes a method, system, equipment, and medium for clearing and scheduling pumped storage units participating in the spot market, taking into account the influence of head.

[0050] Figure 1 This is a flowchart illustrating a method for clearing and scheduling pumped storage units participating in the spot market, taking into account the impact of head, as proposed in an embodiment of this application. Figure 2 This is a schematic diagram illustrating a specific pumped-storage unit participating in the spot market clearing process as proposed in an embodiment of this application. Figure 1 As shown, the method includes the following steps:

[0051] Step S101: By analyzing the actual operating data of the pumped storage power station, a relationship model between the maximum pumping output of the pumped storage unit and the power station head, and a relationship model between the maximum power generation output and the power station head are constructed respectively.

[0052] Specifically, this step utilizes measured operational data from pumped-storage power stations to analyze the head characteristics of these stations, thereby constructing a relationship model between the maximum pumping output and maximum power generation output of the pumped-storage units and the power station head. It should be noted that output in this application refers to power; for example, the maximum power generation output of the unit is the same as its maximum power output. The relationship model constructed in this step can be expressed through relevant functional relationships.

[0053] In pumped storage power stations, head refers to the water level difference between the upper and lower reservoirs, which can be understood as the gravitational potential energy of water flowing from a higher to a lower elevation. That is, the greater the elevation difference between the upper and lower reservoirs, the higher the head, and for pumped storage power stations of the same scale, the higher the maximum pumping power and maximum generating power. Therefore, head management is of great significance for determining the maximum pumping power and maximum generating power of pumped storage units, ensuring the scientific clearing and stable operation of pumped storage unit output plans.

[0054] In one embodiment of this application, a relationship model between the maximum pumping power output of the pumped storage unit and the power station head, and a relationship model between the maximum power generation output and the power station head are constructed respectively. This includes: performing statistical analysis and fitting calculations on the relationship data between the head value of the pumped storage power station and the pumping power and power generation of the pumped storage unit, respectively, to obtain the linear relationship between the maximum pumping power and the head of the pumped storage unit and the linear relationship between the maximum power generation output and the head of the pumped storage unit; constructing a relationship model between the maximum pumping power output and the power station head based on the linear relationship between the maximum pumping power and the head of the pumped storage unit, and constructing a relationship model between the maximum power generation output and the power station head based on the linear relationship between the maximum power generation output and the head of the pumped storage unit.

[0055] Specifically, this application analyzes the historical operating data of the measured pumped storage power station, performs statistical analysis and fitting calculation on the corresponding data of pumping power and power generation of the pumped storage unit under different water head sizes, and determines that the maximum pumping power and maximum power generation of the pumped storage unit are approximately linearly related to the water head.

[0056] Among them, such as Figure 3 As shown, the maximum power output of a pumped-storage unit generally exhibits a multi-segment linear relationship with the water head, while the maximum pumping output can be approximated as a single-segment linear relationship with the water head. Therefore, the maximum pumping power and maximum power output of a pumped-storage unit should be functions of the water head relationship, which can be expressed by the following formula:

[0057]

[0058]

[0059] in, and These represent the power generation and pumping output of the pumped-storage unit during time period t, respectively. and The pumped storage units are respectively located at the water head. Maximum power generation and maximum pumping capacity at that time The head of the pumped storage unit during time period t is the water head.

[0060] Based on the above analysis, a model can be established to represent the relationship between the maximum pumping power and maximum generating power of pumped-storage units and the water head. The specific relationship between the maximum generating output and the power station head can be expressed by the following formula:

[0061]

[0062] The relationship between maximum pumping capacity and power station head can be specifically expressed by the following formula:

[0063]

[0064] in, , … , , … , , For different fitting coefficients, all are fixed values; The pumped storage unit's head during time period t; This is the maximum head of the pumped storage unit.

[0065] Therefore, the relational model constructed in this application takes into account the changes in the maximum pumping power and maximum generating power of the energy storage power station with the water head, ensuring the accuracy of the set unit parameters.

[0066] Step S102: Determine the head value of the pumped storage unit in time period t, and calculate the maximum pumping output and maximum power generation output of the pumped storage unit in time period t based on the head value and the constructed relational model, where t is any positive integer.

[0067] Specifically, this step first determines the head of the pumped-storage unit at any given time period t. For example, each time period can be set to 15 minutes, where t is any positive integer from 0 to 96. Then, the head of time period t is substituted into the relationship models between maximum pumping capacity and power station head, and between maximum power generation capacity and power station head, constructed in the previous step, to calculate the maximum pumping capacity and maximum power generation capacity of the pumped-storage unit at time period t. Step S103 involves obtaining the application information for the pumped-storage unit to participate in the spot electricity market. Using the head status and the maximum pumping capacity and maximum power generation capacity of the pumped-storage unit at time period t, multiple constraints are established for the pumped-storage unit. Based on these constraints and the application information, a clearing model is used to perform a clearing operation in the spot electricity market to obtain the planned output of the pumped-storage unit at time period t+1.

[0068] Specifically, this step first obtains various information submitted by pumped-storage units when participating in the spot electricity market. This information includes, but is not limited to, pumping volume and price curves, power generation and price curves, and the expected head at the end of the operating day. Then, using parameters such as the maximum pumping capacity and maximum power generation capacity of the pumped-storage units calculated in the previous step for time period t, multiple constraints are established. Based on the submitted information from market participants such as pumped-storage units and the established constraints, a spot market clearing process is conducted using a relevant clearing model to obtain the pumped-storage units' planned output for time period t+1.

[0069] In one embodiment of this application, obtaining the declaration information of pumped storage units participating in the spot electricity market includes: obtaining the pumping output price curve and the discharge output price curve of the pumped storage unit, wherein each output price curve includes multiple output segments, and each output segment includes the start point of the output range, the end point of the output range, and the output price; and obtaining the expected head value at the end of the operating day.

[0070] Specifically, in this embodiment, the pumped-storage unit participates in the spot electricity market declaration as usual, obtaining output price curves for both pumping and discharging. Multiple output segments can be declared for both pumping and discharging, with each segment requiring the declaration of the starting point (MW), the ending point (MW), and the output price (RMB / MWh) for that segment. The declaration information and related parameters for this part are consistent with the electricity market declaration model in related embodiments.

[0071] Furthermore, this embodiment considers that the pumped storage unit can further submit the expected head value at the end of the operating day. If the unit submits the submission, the obtained expected value (i.e., the expected head value) will be used as the boundary condition for spot market clearing; if it does not submit the submission, the expected head value will be determined by spot market clearing.

[0072] Furthermore, several constraints were established for pumped storage units to participate in spot market clearing, and clearing calculations were performed using a spot electricity market clearing model.

[0073] As one possible implementation, the clearing model, based on conditions such as power balance and grid security constraints, aims to minimize the total operating cost of generator units. It determines the unit combination, start-up and shutdown status, and real-time output for the following day by summing the results for each time period and unit separately. The appropriate clearing model can be selected for calculation according to actual needs.

[0074] The objective function of the Security-Constrained Unit Commitment (SCUC) model selected for use in this example, which can be applied to the day-ahead energy market clearing of pumped storage units, is shown in the following formula:

[0075]

[0076] Where N represents the total number of generator sets; T represents the total number of time periods considered, where D days consist of 15-minute time periods, for a total of 96 time periods considered; This represents the output of generator unit i during time period t; and Let represent the operating cost and startup cost of generator unit i in time period t, respectively. The operating cost of the unit is a multi-segment linear function related to the output range declared by the unit and the corresponding electricity price. MS and ML These represent the network flow constraint relaxation penalty factor and the load balancing constraint relaxation penalty factor used for market clearing optimization, respectively. and They represent the lines respectively. l The forward and reverse power flow relaxation variables, where NL is the total number of lines; and Representing cross-sections s The forward and reverse power flow relaxation variables, where NS is the total number of cross sections; PS This indicates the total number of pumped storage power stations; and These represent pumped storage power stations. ps Pumping power and discharge power during time period t; and These represent pumped storage power stations. ps Pumping and power generation costs during time period t.

[0077] In one embodiment of this application, the established constraints for pumped storage units include: system load balance constraints, system positive reserve capacity constraints, system negative reserve capacity constraints, system spinning reserve constraints, unit output upper and lower limit constraints, unit ramp-up constraints, unit minimum continuous start-up and shutdown time constraints, unit maximum start-up and shutdown frequency constraints, renewable energy power station output constraints, and multiple pumped storage constraints. The various constraints established in this embodiment are described in detail below.

[0078] For each time period, the load balance constraint can be expressed by the following formula:

[0079]

[0080] in, Indicates the contact line j In time period t, the planned power (input is positive, output is negative), NT represents the total number of tie lines. This represents the system load during time period t.

[0081] The system's positive and negative standby capacity constraints are used to ensure that the total daily uptime capacity meets the system's minimum standby capacity. This constraint can be described as follows:

[0082]

[0083] in, To demonstrate the unit i During the start / stop state of time period t For the unit i Maximum electrical energy output during time period t The system's positive standby capacity requirement for time period t.

[0084] The system negative reserve capacity constraint can be described as:

[0085]

[0086] in, For the unit i The minimum electrical energy output in time period t; The system's negative backup capacity requirement for time period t.

[0087] The system spinning reserve constraint, used to ensure that the sum of the upward and downward adjustment capabilities of the unit output in each time period meets the actual operating requirements for upward and downward spinning reserve adjustments, can be expressed by the following formula:

[0088]

[0089]

[0090] in, For the unit i Maximum uphill speed, This represents the maximum downhill / climb rate of unit i. and These represent the upward and downward adjustment of the rotational reserve requirements for time period t, respectively.

[0091] The upper and lower limits of generator output are used to ensure that the generator output is within the range formed by its maximum and minimum output. This constraint can be described as follows:

[0092]

[0093] in, and They represent the generating units. i The maximum and minimum technical output during time period t.

[0094] The unit ramp-up constraint is used to ensure that the ramp-up rate requirement is met when the unit is ramping uphill or downhill. This constraint can be described as follows:

[0095]

[0096]

[0097] in, For the unit i Maximum uphill speed, For the unit i Maximum downhill / climbing speed.

[0098] Due to the physical properties and actual operational requirements of pumped-storage units, a minimum continuous start / stop time constraint is imposed, requiring pumped-storage units to meet a minimum continuous start / stop time. This constraint can be described as follows:

[0099]

[0100]

[0101] in, and These are the minimum continuous operating time and minimum continuous downtime of the unit. and For the unit i The continuous power-on time and continuous power-off time at time t can be represented by state variables. This can be expressed using the following formula:

[0102] ,

[0103] When setting the maximum number of start-stop cycles for the unit, first define the switching variables for start-up and shutdown, and define... Indicates the unit i Whether the system switches to shutdown mode during time period t can be expressed by the following formula:

[0104]

[0105] The output constraint of new energy power plants is expressed by the following formula:

[0106]

[0107] in, E For the collection of new energy power stations, For new energy power stations i The predicted power output for time period t. That is, the day-ahead market power output of new energy power plants should be less than the predicted power output of new energy power plants.

[0108] In this embodiment, multiple pumped storage constraints include: pumping power and power generation constraints of the pumped storage power station, used to constrain the range of pumping power and power generation of the pumped storage power station, and restricting pumping and power generation states from being mutually exclusive within the same time period; maximum pumping power constraint of the pumped storage power station, used to constrain the range of maximum pumping power of the pumped storage power station based on the linear relationship between maximum pumping power and water head; and maximum power generation constraint of the pumped storage power station, used to constrain the maximum power generation of the pumped storage power station based on the linear relationship between maximum power generation and water head, utilizing the interval of water head in the current time period. The scope includes: head state constraints for pumped storage power stations, used to constrain the range of head during the operation of the pumped storage power station; head constraints at the start and end of the operating day, used to constrain the head value at the start of the current operating day to be equal to the head clearing value at the end of the adjacent previous operating day, and to constrain the head value at the end of the current operating day to be equal to the declared expected head value; and state constraints for pumped storage power stations at different times within one hour, used to constrain the pumped storage power station to have a unique candidate state at different times within one hour, the candidate state including pumping state and power generation state.

[0109] The various pumped storage constraints established in the embodiments of this application will be described in detail below.

[0110] In this embodiment, the pumping power and power generation constraints of the pumped storage power station indicate that for a pumped storage power station whose pumping and power generation can be continuously adjusted, its pumping and power generation must be within upper and lower limits, and it cannot pump and generate power simultaneously. This constraint can be expressed by the following formula:

[0111]

[0112]

[0113]

[0114]

[0115] in, and These represent pumped storage power stations. ps The upper and lower limits of pumping power during time period t; and These represent pumped storage power stations. ps The upper and lower limits of power generation during time period t; and These represent pumped storage power stations. ps The 0-1 variables representing the pumping and power generation states during time period t, =1 indicates a pumped storage power station ps During time period t, the pumping operation is in progress. =1 indicates pumping. ps It is in a power generation state during time period t.

[0116] The maximum pumping power constraint of a pumped storage power station represents the relationship between the maximum pumping power and the water head. As shown in the above examples, the maximum pumping power of a pumped storage power station has a single-segment linear relationship with the water head. Therefore, this constraint can be expressed by the following formula:

[0117]

[0118] in, It is a maximum constant.

[0119] When setting the maximum power generation constraint for pumped storage power stations, as shown in the above examples, the maximum power generation of a pumped storage power station has a multi-segment linear relationship with the water head. Therefore, it is necessary to first determine whether the water head in time period t is within the specified range. The specific formula used for the interval is as follows:

[0120]

[0121]

[0122] in, Indicates whether the head of the pumped storage power station is at 0-1 variables in the interval Indicates the water head at time t. interval, This indicates that it is not within that range; It is a maximum constant; This represents the total number of head intervals.

[0123] Then, the relationship between the maximum power generation of the pumped storage power station and the water head is clarified, and the specific expression is as follows:

[0124]

[0125] in, and They are respectively Fitting coefficients between power generation output and water head of pumped storage power stations in different intervals; It is a maximum constant.

[0126] The head constraint for pumped storage power stations is used to limit the head of the pumped storage power station to within upper and lower limits during operation. This can be expressed by the following formula:

[0127]

[0128]

[0129]

[0130] in, Indicates pumped storage power station ps The water head at time t; and These represent pumped storage power stations. ps The upper and lower limits of the head in time period t; and These represent pumped storage power stations. ps The conversion coefficient between pumping power and head and the conversion coefficient between power generation and head; Indicates the length of the time period.

[0131] The head constraints at the start and end of the operating day of a pumped storage power station are used to ensure that the head at the start of the operating day is equal to the head clearing value at the end of the previous operating day, and that the head at the end of the operating day is equal to the declared expected value. This can be expressed by the following formula:

[0132]

[0133] in, and These represent the head of the pumped storage power station at the beginning and end of its operating day, respectively. This indicates the head of the pumped storage power station at the end of the previous operating day. This represents the expected head value at the end of the declared operation date for a pumped storage power station.

[0134] The state constraints of a pumped-storage power station at different times within an hour are used to restrict the power station from being in a pumping state during a certain time period within a single hour, and vice versa. Specifically, if the power station is in a pumping state during a certain time period within a single hour, it is not allowed to be in a pumping state during other times. This can be expressed by the following formula:

[0135]

[0136] in, and These represent pumped storage power stations. ps The 0-1 variables for pumping and power generation states at hour t; =1 indicates a pumped storage power station ps Pumping occurred within hour t. =1 indicates a pumped storage power station ps A power generation state occurred within hour t; and These represent pumped storage power stations. ps The 0-1 variables for pumping and power generation states at hour h; =1 indicates a pumped storage power station ps Pumping occurred within hour h. =1 indicates a pumped storage power station ps The generator was generated within the time frame h.

[0137] Therefore, this embodiment, based on the spot price model, adjusts the expected reservoir capacity value at the end of the submitted operating day to the expected head value at the end of the submitted operating day, thereby better matching the maximum pumping / generating power constraints of the pumped storage power station. Furthermore, the clearing model in related embodiments only considers the reservoir capacity-related constraints of pumped storage, failing to measure the maximum pumping / generating power, leading to a risk that the clearing results may deviate from the actual operating conditions of the unit. This embodiment introduces a head variable to improve constraints such as maximum pumping power and maximum generating power, ensuring the feasibility of the clearing results.

[0138] Furthermore, under the constraints of the aforementioned multiple conditions, the obtained declaration information can be used to perform spot electricity market clearing calculations through the clearing model to obtain the power output plan of pumped storage units in the t+1 period.

[0139] For example, the spot electricity market clearing model, as a mixed integer programming problem, is generally solved using commercial solvers such as GUROBI or CPLEX. Based on the aforementioned constraints related to pumped storage units, and according to the declaration information and boundary conditions from both the power generation and consumption sides, the spot electricity market is cleared, yielding the planned output curves for 96 points (15-minute intervals, totaling 96 intervals) of the generator unit's daily operating days, including the pumped storage units.

[0140] Therefore, based on the head of the pumped storage unit in time period t determined in step S102, the clearing and output plan of the pumped storage unit in time period t+1 can be calculated in the manner shown in the above embodiment, including the power output value of the unit.

[0141] Step S104: Based on the power output plan for time period t+1, the head value, maximum power output, and spot electricity market clearing calculation are performed cyclically to obtain the power output plan curve of the pumped storage unit on the operating day.

[0142] Specifically, based on the clearing and output plan of the pumped storage unit in time period t+1, this step can also calculate the head of the pumped storage unit in time period t+1, and repeat the above steps S102 to S104 in a loop to form a coupled loop, and finally obtain the head of the unit and the final output plan for each time period of the operating day.

[0143] In one embodiment of this application, the calculation of head value, maximum output, and spot electricity market clearing are performed cyclically to obtain the output plan curve of the pumped storage unit on the operating day. This includes: calculating the head value of time period t+1 based on the output plan of time period t+1; calculating the maximum pumping output and maximum power generation output of the pumped storage unit in time period t+1 based on the head value of time period t+1; performing spot electricity market clearing based on the maximum pumping output and maximum power generation output of the pumped storage unit in time period t+1 to obtain the output plan of the pumped storage unit in time period t+2, and switching to the next time period for calculation, until the output plan for each time period of the operating day is obtained.

[0144] Specifically, this embodiment calculates the head of the pumped-storage unit in time period t+1 based on the clearing and output plan for time period t+1. As one possible implementation, the operating condition is first determined based on the clearing and output plan for time period t+1. Then, for the determined pure power generation, pure pumping, or shutdown operating conditions, the head for time period t+1 is initially calculated using conversion coefficients and parameters such as the calculated total power generation or total pumping volume. Finally, the boundary verification of the initially calculated head for time period t+1 is performed.

[0145] Furthermore, based on the head of the pumped-storage unit in time period t+1, and following the method described in the above embodiment, the maximum pumping power and maximum generating power of the pumped-storage unit in time period t+1 can be iteratively calculated, and the clearing operation is repeated to obtain the clearing output plan of the pumped-storage unit in time period t+2. The above steps are then repeated for the next time period, forming a coupled loop, until the last time period of the current operating day is reached. Finally, the output plans for each time period are spliced ​​together to obtain the output plan curve for the operating day.

[0146] Therefore, the pumped storage unit head and final output plan for each time period of the operating day are finally obtained, which serve as the final clearing result and operating plan of the pumped storage unit.

[0147] In summary, the clearing and scheduling method for pumped storage units participating in the spot market, considering the impact of head, as described in this application, establishes a model relating the maximum pumping power and maximum generating power of a pumped storage power station to the head size of the station. This model quantitatively models and manages the maximum pumping and generating power of the pumped storage power station, improving the scientific validity and rationality of the determined maximum pumping and generating power. Furthermore, this method proposes a spot market clearing and scheduling model based on the maximum pumping output constraint and maximum generating output constraint of the pumped storage power station's head relationship. The model establishes relevant constraints such as the maximum pumping power constraint, maximum generating power constraint, head state constraint, and head constraints at the start and end of the operating day. This ensures that the planned clearing results of the pumped storage power station conform to the actual situation of the unit, guarantees the feasibility and effectiveness of the plan, and ensures the safe and stable operation of the power system. Therefore, this method can effectively promote the participation of pumped storage power stations in the spot market for electricity, fully consider the output and operation characteristics of pumped storage power stations, and optimize the dispatch clearing curve to maximize the regulatory value of pumped storage power stations for the power system, effectively promote the safety and flexibility of the power system, and meet the needs of the construction and safe and stable operation of new power systems.

[0148] To achieve the above embodiments, this application also proposes a clearing and dispatching system for pumped storage units participating in the spot market, taking into account the impact of water head. Figure 4 This is a schematic diagram of a clearing and dispatching system for pumped storage units participating in the spot market, taking into account the impact of water head, as proposed in an embodiment of this application. Figure 4 As shown, the system includes:

[0149] Module 100 is used to analyze the actual operating data of pumped storage power stations to construct models showing the relationship between the maximum pumping output of the pumped storage unit and the power station head, as well as the relationship between the maximum power generation output and the power station head.

[0150] The calculation module 200 is used to determine the head value of the pumped storage unit in time period t, and based on the head value, calculate the maximum pumping output and maximum power generation output of the pumped storage unit in time period t through the constructed relational model, where t is any positive integer.

[0151] The clearing module 300 is used to obtain the application information of pumped storage units participating in the spot electricity market, and to formulate multiple constraints on the pumped storage units by using the water head status and the maximum pumping output and maximum power generation output of the pumped storage units in time period t. Based on the multiple constraints and application information, the clearing module performs spot electricity market clearing calculations through the clearing model to obtain the output plan of the pumped storage units in time period t+1.

[0152] The cyclic module 400 is used for the output plan based on the t+1 time period. It cyclically calculates the head value, the maximum output, and the spot electricity market clearing operation to obtain the output plan curve of the pumped storage unit on the operating day.

[0153] It should be noted that the explanation of the aforementioned embodiment of the method for clearing and dispatching pumped storage units that take into account the impact of water head in the spot market also applies to the system of this embodiment, and will not be repeated here.

[0154] In summary, the clearing and dispatching system for pumped storage units participating in the spot market, which considers the impact of head in this application embodiment, takes into account the maximum pumping output constraint and maximum power generation constraint of the pumped storage unit based on the head relationship in the clearing model, ensuring that the output results are consistent with the actual operating conditions of the pumped storage unit and improving the accuracy of the output calculation results and clearing optimization results.

[0155] To implement the above embodiments, this application also proposes an electronic device, including: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to execute the clearing and scheduling method for pumped storage units participating in the spot market, taking into account the head effect, as described in any one of the first aspect embodiments above.

[0156] To implement the above embodiments, this application also proposes a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements a clearing and scheduling method for pumped storage units participating in the spot market, taking into account the head effect, as described in any one of the first aspect embodiments above.

[0157] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this application. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0158] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this application, "multiple" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0159] Any process or method described in the flowchart or otherwise herein can be understood as representing a module, segment, or portion of code comprising one or more executable instructions for implementing custom logic functions or processes, and the scope of the preferred embodiments of this application includes additional implementations in which functions may be performed not in the order shown or discussed, including substantially simultaneously or in reverse order depending on the functions involved, as should be understood by those skilled in the art to which embodiments of this application pertain.

[0160] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-included system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device. More specific examples (a non-exhaustive list) of computer-readable media include: an electrical connection having one or more wires (electronic device), a portable computer disk drive (magnetic device), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Alternatively, the computer-readable medium may be paper or other suitable media on which the program can be printed, since the program can be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in a computer memory.

[0161] It should be understood that various parts of this application can be implemented using hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented using software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0162] Those skilled in the art will understand that all or part of the steps of the methods in the above embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, the program includes one or a combination of the steps of the method embodiments.

[0163] Furthermore, the functional units in the various embodiments of this application can be integrated into a processing module, or each unit can exist physically separately, or two or more units can be integrated into a module. The integrated module can be implemented in hardware or as a software functional module. If the integrated module is implemented as a software functional module and sold or used as an independent product, it can also be stored in a computer-readable storage medium.

[0164] The storage medium mentioned above can be a read-only memory, a disk, or an optical disk, etc. Although embodiments of this application have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting this application. Those skilled in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of this application.

Claims

1. A method for clearing and dispatching pumped-storage units participating in the spot market, considering the impact of head, characterized in that, Includes the following steps: By analyzing the actual operating data of pumped storage power stations, we constructed relationship models between the maximum pumping output of pumped storage units and the power station head, as well as relationship models between the maximum power generation output and the power station head. Determine the head value of the pumped storage unit in time period t, and based on the head value, calculate the maximum pumping output and maximum power generation output of the pumped storage unit in time period t through the constructed relational model, where t is any positive integer; Obtain the application information of pumped storage units participating in the spot electricity market, and formulate multiple constraints on pumped storage units using the water head status and the maximum pumping output and maximum power generation output of the pumped storage units in the time period t. Based on the multiple constraints and the application information, perform spot electricity market clearing calculation through a clearing model to obtain the output plan of the pumped storage units in the time period t+1. Based on the power output plan for the t+1 time period, the head value, maximum power output, and spot electricity market clearing calculation are performed cyclically to obtain the power output plan curve of the pumped storage unit on the operating day. The pumped storage unit has several constraints, including: The maximum pumping power constraint of a pumped storage power station is used to constrain the range of the maximum pumping power of the pumped storage power station based on the linear relationship between the maximum pumping power and the water head. The maximum power generation constraint of a pumped storage power station is used to constrain the range of the maximum power generation of the pumped storage power station based on the linear relationship between the maximum power generation and the water head, using the interval where the water head is located in the current time period. Head state constraints for pumped storage power stations are used to constrain the range of head during the operation of pumped storage power stations. The head constraints at the start and end of the operating day of a pumped storage power station are used to constrain the head value at the start of the current operating day to be equal to the head clearing value at the end of the adjacent previous operating day, and to constrain the head value at the end of the current operating day to be equal to the declared expected head value. The state constraints of a pumped storage power station at different times within one hour are used to ensure that the pumped storage power station has a unique candidate state at different times within one hour. The candidate state includes pumping state and power generation state.

2. The method according to claim 1, characterized in that, The construction of models relating the maximum pumping capacity of pumped storage units to the hydroelectric head and the maximum power generation capacity to the hydroelectric head includes: Statistical analysis and fitting calculations were performed on the relationship data between the head value of the pumped storage power station and the pumping power and power generation of the pumped storage unit, respectively, to obtain the linear relationship between the maximum pumping power and the head of the pumped storage unit and the linear relationship between the maximum power generation and the head of the pumped storage unit. Based on the linear relationship between the maximum pumping power and the water head, a relationship model between the maximum pumping output and the power station water head is constructed. Similarly, based on the linear relationship between the maximum power generation and the water head, a relationship model between the maximum power generation and the power station water head is constructed.

3. The method according to claim 1, characterized in that, The acquisition of application information for pumped storage units to participate in the spot electricity market includes: Obtain the expected head value at the end of the operating day.

4. The method according to claim 1, characterized in that, The cycle calculates the head value, maximum output, and clears the spot electricity market to obtain the planned output curve of the pumped storage unit on the operating day, including: Calculate the head value for time period t+1 based on the power output plan for time period t+1. Based on the head value during time period t+1, calculate the maximum pumping output and maximum power generation output of the pumped storage unit during time period t+1. Based on the maximum pumping capacity and maximum power generation capacity of the pumped storage unit in the t+1 time period, a spot electricity market clearing calculation is performed to obtain the power output plan of the pumped storage unit in the t+2 time period, and then the calculation is switched to the next time period until the power output plan for each time period of the operating day is obtained.

5. A clearing and dispatching system for pumped-storage units participating in the spot market, considering the impact of head, characterized in that... Includes the following modules: The module is used to analyze the actual operating data of pumped storage power stations and build models showing the relationship between the maximum pumping output of the pumped storage unit and the power station head, as well as the relationship between the maximum power generation output and the power station head. The calculation module is used to determine the head value of the pumped storage unit in time period t, and based on the head value, calculate the maximum pumping output and maximum power generation output of the pumped storage unit in time period t through the constructed relational model, where t is any positive integer; The clearing module is used to obtain the application information of pumped-storage units participating in the spot electricity market, and to formulate multiple constraints on the pumped-storage units using the water head status and the maximum pumping and generating output of the pumped-storage units in time period t. Based on the multiple constraints and the application information, the clearing module performs spot electricity market clearing calculations through a clearing model to obtain the output plan of the pumped-storage units in time period t+1. The multiple constraints on the pumped-storage units include: The maximum pumping power constraint of a pumped storage power station is used to constrain the range of the maximum pumping power of the pumped storage power station based on the linear relationship between the maximum pumping power and the water head. The maximum power generation constraint of a pumped storage power station is used to constrain the range of the maximum power generation of the pumped storage power station based on the linear relationship between the maximum power generation and the water head, using the interval where the water head is located in the current time period. Head state constraints for pumped storage power stations are used to constrain the range of head during the operation of pumped storage power stations. The head constraints at the start and end of the operating day of a pumped storage power station are used to constrain the head value at the start of the current operating day to be equal to the head clearing value at the end of the adjacent previous operating day, and to constrain the head value at the end of the current operating day to be equal to the declared expected head value. State constraints for pumped storage power stations at different times within one hour are used to ensure that the pumped storage power station has a unique candidate state at different times within one hour. The candidate state includes pumping state and power generation state. The cyclic module is used to perform cyclic calculations of head value, maximum output, and spot electricity market clearing based on the output plan for the t+1 time period, so as to obtain the output plan curve of the pumped storage unit on the operating day.

6. The system according to claim 5, characterized in that, The building module is specifically used for: Statistical analysis and fitting calculations were performed on the relationship data between the head value of the pumped storage power station and the pumping power and power generation of the pumped storage unit, respectively, to obtain the linear relationship between the maximum pumping power and the head of the pumped storage unit and the linear relationship between the maximum power generation and the head of the pumped storage unit. Based on the linear relationship between the maximum pumping power and the water head, a relationship model between the maximum pumping output and the power station water head is constructed. Similarly, based on the linear relationship between the maximum power generation and the water head, a relationship model between the maximum power generation and the power station water head is constructed.

7. An electronic device, comprising: At least one processor; as well as A memory communicatively connected to the at least one processor; wherein, The memory stores instructions that can be executed by the at least one processor, which, when executed by the at least one processor, enables the at least one processor to perform a clearing and scheduling method for pumped storage units participating in the spot market, taking into account the head effect, as described in any one of claims 1-4.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the clearing and scheduling method for pumped storage units participating in the spot market, taking into account the head effect, as described in any one of claims 1-4.