Waste mine pumped storage battery modeling method considering efficiency characteristics

Abstract

The invention relates to an abandoned mine pumped storage battery modeling method considering efficiency characteristics, and belongs to the technical field of power grid energy storage, and the method comprises the following steps: S1, analyzing an abandoned mine pumped storage operation mechanism and a system structure; s2, building models of an ACEPS pump turbine, a pressure water passing system and a guide vane control mechanism; s3, establishing an optimal efficiency control strategy of the pump turbine; and S4, establishing the ACEPS battery-like model considering the efficiency external characteristics. The method breaks through the defect that a traditional model considering fixed efficiency cannot reflect the variable working condition efficiency characteristic of the system. According to the method, the complexity of the model is greatly reduced, the traditional indirect estimation mode of reservoir capacity constraint is broken through, the dynamic matching of the energy storage state and the power grid operation parameters is realized, and the method is suitable for the power system optimization scheduling problem.

Description

Technical Field

[0001] This invention belongs to the field of power grid energy storage technology, and relates to a modeling method for pumped storage batteries in abandoned mines that consider efficiency characteristics. Background Technology

[0002] Pumped storage is a promising technology for the energy storage retrofitting of abandoned mines. Scientific planning for pumped storage in abandoned mines is crucial; therefore, it is necessary to construct a model for pumped storage in abandoned mines suitable for power system optimization and dispatch. However, due to the coupling of multiple physical processes, including mechanical and electromagnetic processes, pumped storage systems exhibit strong nonlinear characteristics. Using precise models based on physical mechanisms is difficult to directly apply to comparative analysis of operational characteristics under power system optimization and dispatch scenarios due to their complex structure and high computational cost. Therefore, constructing a battery-like model of pumped storage suitable for power system optimization and dispatch is a key foundation for achieving collaborative planning of pumped storage in abandoned mines.

[0003] Currently, most pumped storage models are power models considering fixed efficiency or water balance constraints considering reservoir capacity or water level. These models cannot reflect the variable efficiency characteristics of the system under varying operating conditions, resulting in inaccuracies. Furthermore, existing research often treats the reservoir operation of pumped storage power stations as conventional hydropower stations, using reservoir capacity as a constraint variable. However, the reservoir capacity of abandoned mine pumped storage power stations is much smaller than that of conventional hydropower stations, and the water level fluctuates frequently and significantly during operation. Therefore, this approach makes it difficult to directly measure the reservoir capacity, and in hydropower conversion calculations, flow rate or water volume needs to be introduced as intermediate variables, making it difficult to intuitively determine whether the capacity constraint has been violated. Abandoned mine pumped storage currently employs unique physical models in optimization scheduling research, involving numerous non-electrical variables and lacking a unified mathematical model. Therefore, it is necessary to establish a mathematical model for abandoned mine pumped storage batteries suitable for power system optimization scheduling. Summary of the Invention

[0004] In view of this, the purpose of this invention is to provide a modeling method for pumped storage batteries in abandoned mines that takes into account efficiency characteristics.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] A method for modeling pumped-storage batteries in abandoned mines, considering efficiency characteristics, includes the following steps:

[0007] S1: Analyze the operation mechanism and system structure of pumped storage in abandoned mines;

[0008] S2: Build a model of the ACEPS pump turbine, pressurized water system, and guide vane control mechanism;

[0009] S3: Establish the optimal efficiency control strategy for water pumps and turbines;

[0010] S4: Establish a battery-like model for ACEPs that considers external characteristics of efficiency.

[0011] Furthermore, step S1 specifically includes the following steps:

[0012] S11: Analysis of the operation mechanism of pumped storage in abandoned mines: The coal seams in abandoned mines exhibit multi-layered structural characteristics. After mining activities, multiple water storage areas with certain elevation differences and open spaces are formed between different coal seams. The core mechanism of pumped storage technology is to rely on two water bodies with significant elevation differences to realize the storage and release of electrical energy through a two-way conversion process of electrical energy and gravitational potential energy.

[0013] S12: Establish the system structure framework of AC excited pumped storage (ACEPS), which consists of a reversible pump turbine, an AC excited generator motor, a pressurized water system, and a speed governor. The ACEPS unit achieves power peak shaving and frequency regulation through bidirectional energy conversion. In power generation mode, the pump turbine converts the water energy of the upstream reservoir into mechanical energy, drives the AC excited generator motor to generate electricity, and transmits the electrical energy to the power grid through the converter. In pumping mode, the unit switches to motor mode, consumes grid power to drive the pump to pump the downstream water back upstream and store potential energy.

[0014] Furthermore, step S2 specifically includes the following steps:

[0015] S21: Establish a pump-turbine model: Based on the pre-defined operating area division markers, determine the operating area of ​​the pump-turbine; retrieve the three-dimensional flow-torque full characteristic curve data grid of the corresponding area, and obtain the unit flow and unit torque parameters under the current operating conditions by looking up the table;

[0016] S22: A second-order elastic water hammer model is used to model the pressurized water system;

[0017] S23: Modeling the guide vane control mechanism: The core components of the guide vane control mechanism are a PID speed controller and a hydraulic actuator. The PID speed controller is a parallel PID speed controller; the hydraulic actuator includes a relay and a follow-up device.

[0018] Furthermore, in step S21, the ACEPS unit modeling method based on the full characteristic curve of the pump-turbine is adopted. In the full characteristic curve, the per-unit values ​​and actual values ​​of the three parameters—actual speed n, pump-turbine flow rate Q, and mechanical torque M—are as follows:

[0019]

[0020] M = M 11 HD 3 (3)

[0021] In the formula, D is the diameter of the wheel, Q 11 M 11 and n 11 These represent unit flow rate, unit torque, and unit speed, respectively; the flow rate characteristic curve Q 11 -n 11 -y and torque full characteristic curve M 11 -n 11 -y constitutes a complete characteristic curve system for water pump turbines, where y represents the guide vane opening degree;

[0022] By analyzing the working regions of the full characteristic curve, the division of the pump-turbine operating condition regions is established; using the non-uniform B-spline curve fitting method, the full characteristic curves under different guide vane openings in each region are reconstructed in three dimensions to build a three-dimensional flow full characteristic grid and a three-dimensional torque full characteristic grid.

[0023] Furthermore, in step S22, the pressurized water system adopts a second-order elastic water hammer model, as detailed below:

[0024]

[0025] In the formula, T w T is the inertial time constant of the water flow. r Let f be the pipe reflection time, and f be the pipe friction coefficient.

[0026] Furthermore, in step S23, the transfer function of the parallel PID speed controller is:

[0027]

[0028] In the formula, the unit speed difference Δw is the difference between the actual speed w and the speed reference w. ref The difference, y is the actual value of the guide vane opening, K p K I K D These are the proportional gain coefficient, integral gain coefficient, and differential gain coefficient, respectively.

[0029] In the hydraulic actuator, considering the guide vane opening speed limit, dead zone, and nonlinearity of the guide vane opening limit, y ref y is the reference value for guide vane opening, and y is the actual value for guide vane opening; T y The main relay time constant is used, and the speed limiting element is used to limit the change speed of the guide vanes and reduce head fluctuations during power regulation.

[0030] Furthermore, step S3 specifically includes the following steps:

[0031] S31: Determining the stable operating boundary of the turbine: When the unit is operating at a constant speed, the total differential form of the relationship between the actual speed n of the unit, the pump-turbine flow rate Q, and the mechanical torque M per unit value and the actual value is expressed as follows:

[0032]

[0033] Simplifying equations (6) to (8), we get:

[0034]

[0035] Equations (9) and (10) must satisfy the constraint that the right-hand side of the inequality must be positive:

[0036]

[0037]

[0038] To ensure that the turbine remains within a stable operating range during dynamic regulation, the following constraints must be met:

[0039]

[0040] In the formula, H T This represents the real-time operating head of the generator unit, with head fluctuation ΔH = β*H. T β is the head fluctuation coefficient, n' 11 H1 and H1 represent the unit rotational speed and operating head at characteristic point C1 under a specific guide vane opening, respectively. A cubic polynomial fit is performed on the unit rotational speed corresponding to the guide vane opening at all characteristic points C1 in the full characteristic curve, yielding the following functional relationship between the guide vane opening at characteristic point C1 and the unit rotational speed:

[0041] n' 11 =44.5y 3 -102.9y 2 +92.6y+70.8 (14)

[0042] Substituting β into equation (13) yields:

[0043]

[0044] Taking into account the impact of head fluctuations, the turbine operating conditions include a certain range of unstable operating conditions, which are determined using the following methods:

[0045] First, based on the current guide vane opening, the unit speed corresponding to the critical operating point C1 is calculated using equation (14); second, according to the actual unit speed, the working head H1 at this critical point is determined using equation (1); finally, the working head H1 at the current actual head H1 is verified using equation (15). TUnder these conditions, can the unit complete the dynamic adjustment process to avoid entering the unstable operating region due to head fluctuations?

[0046] S32: Optimizing the optimal speed and guide vane opening: Based on the pump-turbine output formula, the mechanical power P under power generation and pumping conditions... m They are represented as follows:

[0047] P m =Mnπ / 30=9.81HQη (16)

[0048]

[0049] In the formula, η is the efficiency of the water pump turbine, and H is the head;

[0050] Under the premise of constant head and pump-turbine output power, the minimum flow rate corresponds to the optimal efficiency in power generation mode, while the maximum flow rate achieves the optimal efficiency in pumping mode.

[0051] Furthermore, in step S32, under the power generation operating conditions, the search process for the optimal speed and guide vane opening of the pump-turbine unit is as follows:

[0052] A1: Input mechanical power P m , head H, head fluctuation coefficient β;

[0053] A2: Based on the speed adjustment range n min -n max Define the search step size Δn, and divide the speed adjustment range into j values, j = (n max -n min ) / Δn;

[0054] A3: Let i = 1, calculate the rotational speed n i =n min +i*Δn and torque M i =P m / n i , where i = 1, 2, ..., j;

[0055] A4: The unit rotational speed n is obtained from equations (1) and (3) respectively. 11i and unit torque M 11i The guide vane opening y is obtained from the torque characteristic curve of region I. i ;

[0056] A5: The unit rotational speed n at characteristic point C1 is obtained from equation (13). 11i The head H1 at characteristic point C1 is obtained from equation (1);

[0057] A6: Determine if the condition is met. If the condition is not met, then exclude the rotational speed n. iIf satisfied, Q can be obtained from the flow characteristic curve of region I. 11i Therefore, from equation (2), we can obtain Q. i And determine whether 1>Q is satisfied. i If the condition is greater than 0, then let Q = 0. i =inf, indicating that the rotational speed value is not within the search range. If it is satisfied, let i+1 and repeat steps A3-A6 until i=j;

[0058] A7: Output optimal flow rate Q op =min{Q1,Q2,Q3,…,Q j}≤1;Q op The speed and opening degree corresponding to the operating point are the optimal speed n. op and optimal opening y op , which refers to the control parameters that enable the pump-turbine to achieve optimal operating efficiency under specific output and head conditions.

[0059] Furthermore, in step S32, under the pumping operation condition, the search process for the optimal speed and guide vane opening of the pump-turbine unit is as follows:

[0060] B1: Input mechanical power P m , head H, head fluctuation coefficient β;

[0061] B2: Based on the speed adjustment range n min -n max Define the search step size Δn, and divide the speed adjustment range into j values, j = (n max -n min ) / Δn;

[0062] B3: Let i = 1, calculate the rotational speed n i =n min +i*Δn and torque M i =P m / n i , where i = 1, 2, ..., j;

[0063] B4: Determine the unit rotational speed n using equations (1) and (3) respectively. 11i and unit torque M 11i The guide vane opening y is obtained by querying the three-dimensional torque and flow full characteristic mesh of the pump turbine in region I. i and unit flow Q 11i And apply equation (2) to convert it into a per-unit value Q of the flow rate. i ;

[0064] B5: Determine if -1 is satisfied. i <0, if not satisfied, then set Q. i =0, and at the same time set the corresponding rotational speed n​i Remove from the candidate set; if satisfied, retain the parameter combination, let i+1, and repeat steps B3-B5 until i=j;

[0065] B7: Output optimal flow rate Q op =max{Q1,Q2,Q3,…,Q j}>0;Q op The speed and opening degree corresponding to the operating point are the optimal speed n. op and optimal opening y op This refers to the optimal control parameters that enable the pump-turbine to achieve the highest operating efficiency under the current output and head conditions.

[0066] Furthermore, step S4 specifically includes the following steps:

[0067] The system SoC is defined using water head as a constraint variable and then normalized.

[0068]

[0069] In the formula, E t The SOC is the normalized value of the head, with a value range of [0, 1]. H and These are the lower and upper limits of the gas pressure in the gas storage facility, respectively; considering the rated flow rate Q... p0 Rated charging time for pumping water (t) p0 Or at the rated flow rate Q g0 Rated power generation duration t g0 The change in reservoir head is

[0070] The dynamic equation for head-flow rate in a pumped storage power station is:

[0071]

[0072] In the formula, Q p Q is the pumping flow rate. g Let A(H) be the power generation flow rate, and A(H) be the surface area of ​​the reservoir at a head of H. Based on the dynamic equations, a quasi-steady-state model of the reservoir head in the form of a difference equation is established:

[0073]

[0074] In the formula, the subscript t indicates time t, Δt is the unit scheduling duration, and H t Let ε be the gas pressure in the gas storage tank at time t. RE To reflect the loss coefficient due to reservoir evaporation, seepage, or external runoff, this coefficient is set to 0 when water consumption is ignored;

[0075] The dynamic equations for the pump-turbine head SoC are derived as follows:

[0076]

[0077] The analogous battery SoC model is shown in Equation (21):

[0078]

[0079] Pumping efficiency is defined as the power consumption per unit volume of water pumped, i.e. Power generation efficiency is defined as the amount of water consumed per unit of power, i.e. In the formula All values ​​are per-unit values ​​based on design parameters; η ps and η gs Relative operating efficiency refers to the ratio of operating efficiency under varying operating conditions to rated efficiency, where η is the efficiency under rated operating conditions. ps =η gs =1;

[0080] The coupling relationship of the internal interface variables of the system under the optimal control strategy is represented by the following function:

[0081]

[0082] In the formula, Γ ps and Γ gs The external characteristic function is the one used to achieve the optimal efficiency of the system.

[0083] The simplified ACEPS-type battery model is as follows:

[0084]

[0085] In the formula, E t For ACEPS system energy storage SoC measured in head, its upper and lower limits are respectively represented by... and E t Indicates; γ ac and γ ad They represent the current E t Changes in SoC and per-unit charge / discharge power of ACEP The relationship, specifically expressed by the external characteristic function Γ under the optimal efficiency of the system. ap ,Γ ag The derivation yields the results shown in equations (27) and (28):

[0086]

[0087] In the formula, k p and k g These represent the rated pumping time and the reciprocal of the rated time, respectively.

[0088] The beneficial effects of this invention are as follows:

[0089] (1) This method proposes a battery-like modeling method that considers the efficiency characteristics of pumped storage in abandoned mines. By multi-condition partitioning interpolation and optimal speed optimization, an optimal efficiency control strategy for pump turbine based on full characteristic curves is established. Based on this, a battery-like model considering head fluctuation is established, which overcomes the shortcomings of traditional fixed efficiency models that cannot reflect the variable operating condition efficiency characteristics of the system.

[0090] (2) This method simplifies the internal coupling relationship of pumped storage in abandoned mines, degrades non-electrical physical variables such as flow rate and guide vane opening in traditional models, and obtains a battery-like model of abandoned mines with water head as the state variable. This greatly reduces the complexity of the model, breaks through the indirect estimation method of traditional storage capacity constraints, realizes the dynamic matching of energy storage state and grid operation parameters, and is applicable to power system optimization scheduling problems.

[0091] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0092] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein:

[0093] Figure 1 This is a schematic diagram of a pumped storage system based on the transformation of abandoned mine shafts.

[0094] Figure 2 This is a schematic diagram of the ACEPS system structure;

[0095] Figure 3 This shows the distribution of characteristic operating points in the full characteristic curve of the pump-turbine; where (a) is the full characteristic curve of the flow rate (Q). 11 -n 11 -y), (b) is the torque characteristic curve (M 11 -n 11 -y);

[0096] Figure 4 The full characteristic grid for pump-turbine region I is given, where (a) is the flow characteristic curve and (b) is the torque characteristic curve.

[0097] Figure 5 The full characteristic grid for pump-turbine region II is shown, where (a) is the flow characteristic curve and (b) is the torque characteristic curve.

[0098] Figure 6The full characteristic grid for pump-turbine region III is shown, where (a) is the flow characteristic curve and (b) is the torque characteristic curve.

[0099] Figure 7 Topology diagram of the transfer function of a parallel PID speed controller;

[0100] Figure 8 This is a schematic diagram of the structure of each component of a hydraulic actuator;

[0101] Figure 9 A flowchart for searching the optimal speed and guide vane opening of a pump-turbine unit under power generation conditions;

[0102] Figure 10 A flowchart for searching the optimal speed and guide vane opening of a pump-turbine unit under pumping conditions;

[0103] Figure 11 These are the optimal operating parameters of the unit under varying head and output conditions during power generation, where (a) is the optimal speed of the unit and (b) is the optimal guide vane opening of the unit.

[0104] Figure 12 These are the optimal operating parameters of the unit under pumping conditions with varying head and output, where (a) is the optimal speed of the unit and (b) is the optimal guide vane opening of the unit. Detailed Implementation

[0105] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0106] It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Therefore, the drawings only show the components related to the present invention and are not drawn according to the actual number, shape and size of the components in the actual implementation. In the actual implementation, the form, quantity and proportion of each component can be arbitrarily changed, and the layout of the components may also be more complex.

[0107] In the following description, numerous details are explored to provide a more thorough explanation of embodiments of the invention. However, it will be apparent to those skilled in the art that embodiments of the invention may be practiced without these specific details. In other embodiments, well-known structures and devices are shown in block diagram form rather than in detail to avoid obscuring embodiments of the invention.

[0108] Example 1:

[0109] This invention provides a modeling method for pumped-storage batteries in abandoned mines, considering efficiency characteristics. The method includes the following steps:

[0110] S1: Analyze the operation mechanism and system structure of pumped storage in abandoned mines.

[0111] Step 1: Analyze the operation mechanism of pumped storage in abandoned mines.

[0112] The substantial underground space resources left behind by abandoned mines provide an ideal foundation for the development of pumped storage hydroelectric power. Most coal seams in mining areas exhibit a multi-layered structure, and after mining activities, multiple water-reservoir areas with significant elevation differences and open spaces have formed between different coal seams. These reservoir-like spaces, formed by a combination of natural and artificial elements, create feasible conditions for constructing pumped storage hydroelectric power systems in abandoned mines. The core mechanism of pumped storage technology relies on two water bodies with significant elevation differences to achieve efficient storage and release of electrical energy through a bidirectional conversion process of electrical energy and gravitational potential energy. For example... Figure 1 The diagram shows a pumped storage system based on the transformation of an abandoned mine.

[0113] Step 2: Establish the system structure framework of AC excited pumped storage (ACEPS).

[0114] This invention focuses on ACEP (Accelerated Pump-Turbine System), which mainly consists of a reversible pump-turbine, an AC-excited generator-motor, a pressurized water system, and a speed governor. Its system structure is as follows: Figure 2 As shown.

[0115] ACEPS units achieve power peak shaving and frequency regulation through bidirectional energy conversion. In power generation mode, the pump-turbine converts the water energy of the upstream reservoir into mechanical energy, driving the AC excitation motor to generate electricity, which is then transmitted to the grid through a converter. In pumping mode, the unit switches to motor mode, consuming grid power to drive the pump to pump water from downstream back upstream, storing potential energy.

[0116] S2: Build a model of the ACEPPS water pump turbine, pressurized water system, and guide vane control mechanism.

[0117] Step 1: Establish a water pump turbine model.

[0118] This invention employs an ACEP (Anaerobic, Anchored, Plumbing, and Power) unit modeling method based on the full characteristic curve of a pump-turbine. In the full characteristic curve, the per-unit values ​​and actual values ​​of the three parameters—actual speed n, pump-turbine flow rate Q, and mechanical torque M—are as follows:

[0119]

[0120] M = M 11 HD 3 (3)

[0121] In the formula, D is the impeller diameter. Flow rate full characteristic curve (Q) 11 -n 11 -y) and torque full characteristic curve (M 11 -n 11 -y) constitutes a complete characteristic curve system that can fully characterize a water pump turbine. Here, Q 11 M 11 and n 11 These represent unit flow rate, unit torque, and unit speed, respectively, with y representing the guide vane opening. It's worth noting that by specifying any two of these four physical quantities, the values ​​of the other two can be calculated from the full characteristic curve. The distribution of characteristic operating points in the full characteristic curve of a pump-turbine is shown below. Figure 3 As shown in (a) and (b).

[0122] As can be seen, there is a special inverted S-shaped characteristic region within the positive range of unit speed of the full characteristic curve. Within this region, multiple different unit flow rates and torque values ​​will correspond to a single unit speed. This phenomenon brings multi-value problems to the interpolation calculation of the full characteristic curve. To solve this problem, by analyzing each working region of the full characteristic curve, the division of the pump turbine operating condition region is established as shown in Table 1.

[0123] Table 1

[0124]

[0125] After dividing the full characteristic curves of the pump-turbine into regions, it was found that the characteristic curves still overlapped in the two-dimensional coordinate plane, causing traditional interpolation methods to fail. To solve this problem, this invention employs a non-uniform B-spline curve fitting method to reconstruct the full characteristic curves under different guide vane openings within each region in three dimensions. In this way, a three-dimensional flow rate full characteristic mesh and a three-dimensional torque full characteristic mesh were successfully constructed, as detailed below. Figures 4-6 As shown in (a) and (b) in the figure, the construction of the full-feature mesh not only effectively eliminates the curve overlap problem, but also realizes the parameter query function.

[0126] Based on the aforementioned theoretical analysis, this invention establishes a dynamic simulation method system for water pump turbines. The first step involves identifying the operating area of ​​the water pump turbine according to pre-defined operating condition area division markers. The second step involves retrieving the three-dimensional flow-torque full characteristic curve data grid for the corresponding area. By looking up the table, the unit flow rate and unit torque parameters under the current operating conditions can be obtained.

[0127] Step 2: Modeling the pressurized water system

[0128] The pressurized water system of this invention adopts a second-order elastic water hammer model, as detailed below:

[0129]

[0130] In the formula, T w T is the inertial time constant of the water flow. r Let f be the pipe reflection time, and f be the pipe friction coefficient.

[0131] Step 3: Modeling the guide vane control mechanism

[0132] The core components of the guide vane control mechanism are a PID speed controller and a hydraulic actuator. The PID speed controller exists in both parallel and series configurations. Parallel PID speed controllers, with their fast response characteristics, can achieve instantaneous tracking of the guide vane opening to the set reference value; while series PID speed controllers, limited by a large time constant, exhibit significant lag in response speed. To ensure both high efficiency and flexibility in the control strategy, this invention selects a parallel PID speed controller as the control scheme. The transfer function of this speed controller is as follows: Figure 7 As shown. The transfer function of the parallel PID speed controller is:

[0133]

[0134] In the formula, the unit speed difference Δw is the difference between the actual speed w and the speed reference w. ref The difference, y is the actual value of the guide vane opening, K p K I K D These are the proportional gain coefficient, integral gain coefficient, and differential gain coefficient, respectively.

[0135] Figure 7 In the diagram, n and y represent the actual values ​​of rotational speed and guide vane opening, respectively. ref y ref These are reference values ​​for rotational speed and guide vane opening, respectively; b p This is the permanent slip coefficient.

[0136] The hydraulic actuator, a key component of the guide vane control system, mainly consists of a servo motor and a follower device. It considers nonlinear factors such as guide vane opening speed limits, dead zones, and guide vane opening amplitude limits. Its structure is as follows: Figure 8 As shown, in the hydraulic actuator, considering the guide vane opening speed limit, dead zone, and nonlinearity of the guide vane opening limit, y ref y is the reference value for guide vane opening, and y is the actual value for guide vane opening; T y The main relay time constant is used, and the speed limiting element is used to limit the change speed of the guide vanes and reduce head fluctuations during power regulation.

[0137] S3: Establish the optimal efficiency control strategy for water pumps and turbines.

[0138] The output power of ACEPS units is affected by multiple variables, including unit speed, guide vane opening, and head. Under constraints of unit speed, operating conditions, and stable operation in the inverse S-characteristic region, the optimal unit speed and optimal guide vane opening under different heads and power are obtained by searching the full characteristic curve of the pump-turbine.

[0139] Step 1: Determine the stable operating boundary of the turbine.

[0140] When a pump-turbine operates in the reverse S-shaped characteristic region, it can trigger blockage effects such as static vortices in the bladeless zone, dynamic vortices in the flow channel, and rotational stall, which seriously threaten operational stability. Since some of the turbine's operating conditions fall within this region, it is necessary to determine the stability boundary before searching for the optimal speed and guide vane opening to avoid unstable operating areas.

[0141] When the unit is operating at a constant speed, the total differential form of the equations involved in equations (1)-(3) can be specifically expressed as follows:

[0142]

[0143] Simplifying equations (6) to (8), we get:

[0144]

[0145] When the ACEPS unit operates in turbine mode, when the unit reaches steady-state operation at constant speed and guide vane opening, the trends of its working head, flow rate, and torque must remain consistent. To ensure stable operation of the unit within the turbine mode, the mathematical relationships described by equations (9) and (10) must satisfy the constraint that the right-hand side of the inequality is positive. Further, we can derive:

[0146]

[0147] According to theoretical analysis, the boundary between the steady operating region and the unstable operating region (braking operating region) of the turbine corresponds to... Figure 3Characteristic point C1 is shown in the diagram. However, dynamic adjustments during unit operation can trigger water hammer, leading to fluctuations in the operating head. To quantify this fluctuation characteristic, a head fluctuation coefficient β = ΔH / H is introduced. T Studies have shown that when β < 0, the unit speed of the turbine will increase, potentially causing the operating point to exceed the characteristic point C1 and enter the braking operating zone, thereby leading to operational instability. Therefore, to ensure that the turbine remains within a stable operating range during dynamic regulation, the following constraints must be met:

[0148]

[0149] In the formula, H T This represents the real-time operating head of the generator unit, with head fluctuation ΔH = β*H. T ,n' 11 H1 and H1 represent the unit rotational speed and operating head at characteristic point C1 under a specific guide vane opening, respectively. By performing a cubic polynomial fit on the unit rotational speed corresponding to the guide vane opening at all characteristic points C1 in the full characteristic curve, the functional relationship between the guide vane opening at characteristic point C1 and the unit rotational speed can be obtained as follows:

[0150] n' 11 =44.5y 3 -102.9y 2 +92.6y+70.8 (14)

[0151] Substituting β into equation (13) yields:

[0152]

[0153] Based on the above analysis, considering the impact of head fluctuations, the turbine operating conditions will include a certain range of unstable operating areas. To ensure the stability of unit operation, the following determination method can be adopted: First, based on the current guide vane opening, calculate the unit speed corresponding to the critical operating point C1 using equation (14); second, based on the actual unit speed, determine the operating head H1 at the critical point using equation (1); finally, verify the current actual head H1 using equation (15). T Under these conditions, can the unit complete the dynamic adjustment process to avoid entering the unstable operating region due to head fluctuations?

[0154] Step 2: Optimal rotational speed and guide vane opening

[0155] According to the power output formula of a water pump turbine, its mechanical power P under power generation and pumping conditions is... m They are represented as follows:

[0156] P m =Mnπ / 30=9.81HQη (16)

[0157]

[0158] In the formula, η is the efficiency of the water pump turbine, and H is the head.

[0159] The analysis of the above formula shows that, under the premise of constant head and pump-turbine output power, the minimum flow rate corresponds to the optimal efficiency in power generation mode, while the maximum flow rate achieves the optimal efficiency in pumping mode.

[0160] like Figure 9 The diagram shows the search process for the optimal speed and guide vane opening of the pump-turbine unit under power generation operating conditions. Figure 9 All parameters are expressed in per-unit values, where Q op n op and y op These represent the optimal flow rate, optimal speed, and optimal opening degree under specific operating conditions. By constraining the guide vane opening rate, head oscillations caused by hydraulic transients can be significantly suppressed; therefore, this invention sets the fluctuation coefficient β = 0.1. For AC excitation motors, the speed adjustment range is defined as n. min =0.9pu to n max =1.1 pu. Additionally, the rotational speed search step size Δn = 0.005 pu is selected, i.e., j = 40. Q is marked in the figure. i =inf's rotational speed n i This indicates that the speed value is not within the search range. After completing the full speed range traversal, the operating point that satisfies the constraints and has the smallest per-unit flow rate is selected. The speed and guide vane opening parameters corresponding to this point are the control parameters that enable the pump turbine to achieve optimal operating efficiency under specific output and head conditions.

[0161] like Figure 10 The diagram shows the search flow for the optimal speed and guide vane opening of the pump-turbine unit under pumping operation conditions. For the AC-excited generator-motor, its speed regulation range is defined as n. min =-1.1pu to n max = -0.9pu. Additionally, the speed search step size Δn = 0.005pu is selected, i.e., j = 40. First, based on the input mechanical power P... m and the current rotational speed n i The corresponding mechanical torque M can be calculated. i Subsequently, the unit rotational speed n is determined using equations (1) and (3) respectively. 11i and unit torque M 11i The guide vane opening y can be obtained by querying the three-dimensional torque and flow rate full characteristic mesh of the pump turbine in region I. i and unit flow Q 11i And apply equation (2) to convert it into a per-unit value Q of the flow rate. i During the parameter selection phase, Q needs to be verified.i Is it within the valid range of [-1, 0]? If it is outside this range, then set Q. i =0, and at the same time set the corresponding rotational speed n i Remove from the candidate set; if the condition is met, retain the parameter combination. After traversing the entire speed range, select the operating point with the smallest per-unit actual flow rate from all candidate operating conditions. The speed and guide vane opening parameters corresponding to this operating point are the optimal control parameters that enable the pump-turbine to achieve the highest operating efficiency under the current output and head conditions.

[0162] S4: Establish a battery-like model for ACEPs that considers external characteristics of efficiency.

[0163] Existing studies often equate the operation of pumped storage power station reservoirs with conventional hydropower stations, using reservoir capacity as a constraint variable. However, this approach has the following shortcomings: reservoir capacity needs to be indirectly estimated using a water level-capacity curve; hydropower conversion requires the introduction of flow / water volume as an intermediate variable; and it is difficult to intuitively determine whether the reservoir capacity constraint has been exceeded. Abandoned mine pumped storage power stations have small reservoir capacities, and their water levels fluctuate significantly and frequently during operation. Therefore, this invention uses head as a constraint variable to define the system SoC and performs normalization processing.

[0164]

[0165] In the formula, E t The SOC is the normalized value of the head, with a value range of [0, 1]. In the formula, H and These are the lower and upper limits of the gas pressure in the gas storage facility, respectively. Considering the rated flow rate Q... p0 Rated charging time for pumping water (t) p0 Or at the rated flow rate Q g0 Rated power generation duration t g0 The change in reservoir head is

[0166] The dynamic equation for head-flow rate in a pumped storage power station is:

[0167]

[0168] In the formula, Q p Q is the pumping flow rate. g Let A(H) be the power generation flow rate, and A(H) be the surface area of ​​the reservoir at a head of H. Based on this dynamic model in the form of a differential equation, a quasi-steady-state model of the reservoir head in the form of a difference equation is established:

[0169]

[0170] In the formula, the subscript t indicates time t, Δt is the unit scheduling duration, and H t Let ε be the gas pressure in the gas storage tank at time t.RE To reflect the loss due to evaporation, seepage, or external runoff in the reservoir, this coefficient can be taken as 0 when water consumption is ignored.

[0171] Therefore, the dynamic equation of the pump-turbine head SoC can be derived as follows:

[0172]

[0173] Analogous to the battery SoC model as shown in equation (22), the pumping efficiency can be defined as the power consumption per unit pumping volume, i.e. Power generation efficiency can be defined as the amount of water consumed per unit of power, i.e. In the formula All values ​​are per-unit values ​​based on design parameters. Under this definition, η ps and η gs Relative operating efficiency refers to the ratio of operating efficiency under varying operating conditions to rated efficiency, where η is the efficiency under rated operating conditions. ps =η gs =1.

[0174] When a pump-turbine system operates at its optimal efficiency, it corresponds to the optimal rotational speed and guide vane opening. Therefore, given a fixed head and the pump-turbine's output power, by optimizing the optimal rotational speed and guide vane opening, the optimal rotational speed and guide vane opening at its optimal efficiency can be determined. Consequently, the flow rate at optimal efficiency can be determined based on the pump-turbine's full characteristic curve.

[0175] Therefore, the coupling relationship between the internal interface variables (pumping flow rate, drainage flow rate, rotational speed, guide vane opening) and the external interface variables (head, charging power, generating power) under the optimal control strategy can be represented by the following function:

[0176]

[0177] In the formula, Γ ps and Γ gs This is the external characteristic function under optimal system efficiency.

[0178] Therefore, a simpler ACEPS-type battery model is proposed:

[0179]

[0180] In the formula, E t For ACEPS system energy storage SoC measured in head, its upper and lower limits are respectively represented by... and E t Indicates; γ ac and γ ad They describe the current E respectively t Changes in SoC and per-unit charge / discharge power of ACEP The relationship reflects the efficiency characteristics of the system under different energy storage states and output levels. Its specific expression can be derived from the external characteristic function Γ under the optimal efficiency of the system. ap ,Γ ag The derivation yields the results shown in equations (27) and (28):

[0181]

[0182] In the formula, k p and k g These represent the rated pumping time and the reciprocal of the rated time, respectively.

[0183] The simplified ACEPS scheduling model (25) mentioned above does not include non-electrical physical variables such as flow rate and guide vane opening. It has a similar form to the traditional battery SoC model and can also fully reflect the efficiency characteristics of the system under different operating conditions. It is suitable for power system optimization scheduling problems.

[0184] This embodiment takes a 300MW ACEPS as the research object, and its unit parameters are shown in Table 2.

[0185] Table 2

[0186]

[0187] This invention uses five typical head conditions (0.8 pu, 0.85 pu, 0.9 pu, 0.95 pu, and 1.0 pu) as the research object, and uses a power parameter with a search step size of 0.01 pu. A systematic search is performed on the optimal speed and guide vane opening of the pump-turbine under different output states for each head condition, obtaining the global optimization solution set of the unit's optimal operating speed and guide vane opening. This is then further analyzed using... Figure 11 and Figure 12 (a) and (b) are presented intuitively.

[0188] Through the Figure 11 and Figure 12 Analysis of the research results shows that in the power generation operation mode, the fluctuation characteristics of the unit's optimal speed exhibit a significant head dependence, while its influence from changes in output power is relatively weak. The trend of the optimal guide vane opening, however, is mainly related to output power and is relatively insensitive to head fluctuations. In the pumping operation mode, the unit's operating characteristics change significantly. The optimal speed shows strong sensitivity to changes in both head and output power, while the optimal guide vane opening remains relatively stable under different operating conditions.

[0189] Under the above basic system parameter settings, through projection and linear fitting, the characteristic function of the abandoned mine pumped storage battery considering its optimal efficiency is obtained as follows:

[0190]

[0191] Example 2:

[0192] An electronic device, comprising a memory and a processor;

[0193] The memory is used to store computer programs;

[0194] The processor is configured to implement the method described in Embodiment 1 when executing the computer program.

[0195] Example 3:

[0196] A computer-readable storage medium storing a computer program that, when executed by a processor, implements the method described in Embodiment 1.

[0197] Example 4:

[0198] A computer program product includes a computer program that, when executed by a processor, implements the method described in Example 1.

[0199] In the above embodiments, the reference to "this embodiment" in the specification indicates that a specific feature, structure, or characteristic described in connection with the embodiment is included in at least some embodiments, but not necessarily all embodiments. Multiple appearances of "this embodiment" do not necessarily refer to the same embodiment.

[0200] In the above embodiments, although the invention has been described in conjunction with specific embodiments thereof, many substitutions, modifications, and variations of these embodiments will be apparent to those skilled in the art from the foregoing description. For example, other memory structures (e.g., dynamic RAM (DRAM)) may be used with the embodiments discussed. The embodiments of the invention are intended to cover all such substitutions, modifications, and variations falling within the broad scope of the appended claims.

[0201] As will be understood by those skilled in the art, the computer-readable storage medium described in this embodiment allows for the implementation of all or part of the steps in the above method embodiments by computer program-related hardware. The aforementioned computer program can be stored in a computer-readable storage medium. When executed, the program performs the steps of the above method embodiments; and the aforementioned storage medium includes various media capable of storing program code, such as ROM, RAM, magnetic disks, or optical disks.

[0202] The electronic terminal provided in this embodiment includes a processor, a memory, a transceiver, and a communication interface. The memory and the communication interface are connected to the processor and the transceiver and complete communication between them. The memory is used to store computer programs, the communication interface is used to perform communication, and the processor and the transceiver are used to run the computer programs, so that the electronic terminal performs the steps of the above method.

[0203] In this embodiment, the memory may include random access memory (RAM) and may also include non-volatile memory, such as at least one disk storage device.

[0204] The processors mentioned above can be general-purpose processors, including central processing units (CPUs), network processors (NPs), etc.; they can also be digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components.

[0205] This invention can be used in a wide range of general-purpose or special-purpose computing system environments or configurations. Examples include: personal computers, server computers, handheld or portable devices, tablet devices, multiprocessor systems, microprocessor-based systems, set-top boxes, programmable consumer electronics, network PCs, minicomputers, mainframe computers, and distributed computing environments including any of the above systems or devices, etc.

[0206] This invention can be described in the general context of computer-executable instructions, such as program modules, that are executed by a computer. Generally, program modules include routines, programs, objects, components, data structures, etc., that perform a specific task or implement a specific abstract data type. This invention can also be practiced in distributed computing environments where tasks are performed by remote processing devices connected via a communication network. In distributed computing environments, program modules can reside in local and remote computer storage media, including storage devices.

[0207] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for modeling pumped-storage batteries in abandoned mines, considering efficiency characteristics, characterized in that: Includes the following steps: S1: Analyze the operation mechanism and system structure of pumped storage in abandoned mines; S2: Build a model of the ACEPS pump turbine, pressurized water system, and guide vane control mechanism; S3: Establish the optimal efficiency control strategy for water pumps and turbines; S4: Establish a battery-like model for ACEPs that considers external characteristics of efficiency.

2. The method for modeling abandoned mine pumped storage batteries considering efficiency characteristics according to claim 1, characterized in that: Step S1 specifically includes the following steps: S11: Analysis of the operation mechanism of pumped storage in abandoned mines: The coal seams in abandoned mines exhibit multi-layered structural characteristics. After mining activities, multiple water storage areas with certain elevation differences and open spaces are formed between different coal seams. The core mechanism of pumped storage technology is to rely on two water bodies with significant elevation differences to realize the storage and release of electrical energy through a two-way conversion process of electrical energy and gravitational potential energy. S12: Construct the system structure framework of AC-excited pumped storage (ACEPS), which consists of a reversible pump-turbine, an AC-excited generator motor, a pressurized water system, and a speed governor. The ACEPS unit achieves power peak shaving and frequency regulation through bidirectional energy conversion. In power generation mode, the pump-turbine converts the water energy of the upstream reservoir into mechanical energy, drives the AC-excited generator motor to generate electricity, and transmits the electrical energy to the power grid through a converter. In pumping mode, the unit switches to motor mode, consumes grid power to drive the pump to pump downstream water back upstream, storing potential energy.

3. The method for modeling abandoned mine pumped storage batteries considering efficiency characteristics according to claim 1, characterized in that: Step S2 specifically includes the following steps: S21: Establish a pump-turbine model: Based on the pre-defined operating area division markers, determine the operating area of ​​the pump-turbine; retrieve the three-dimensional flow-torque full characteristic curve data grid of the corresponding area, and obtain the unit flow and unit torque parameters under the current operating conditions by looking up the table; S22: A second-order elastic water hammer model is used to model the pressurized water system; S23: Modeling the guide vane control mechanism: The core components of the guide vane control mechanism are a PID speed controller and a hydraulic actuator. The PID speed controller is a parallel PID speed controller; the hydraulic actuator includes a relay and a follow-up device.

4. The method for modeling abandoned mine pumped storage batteries considering efficiency characteristics according to claim 3, characterized in that: In step S21, the ACEPS unit modeling method based on the full characteristic curve of the pump-turbine is adopted. In the full characteristic curve, the per-unit values ​​and actual values ​​of the three parameters of the unit—actual speed n, pump-turbine flow rate Q, and mechanical torque M—are as follows: M=M 11 HD 3 (3) In the formula, D is the diameter of the wheel, Q 11 M 11 and n 11 These represent unit flow rate, unit torque, and unit speed, respectively; the flow rate characteristic curve Q 11 -n 11 -y and torque full characteristic curve M 11 -n 11 -y constitutes a complete characteristic curve system for water pump turbines, where y represents the guide vane opening degree; By analyzing the working regions of the full characteristic curve, the division of the pump-turbine operating condition regions is established; using the non-uniform B-spline curve fitting method, the full characteristic curves under different guide vane openings in each region are reconstructed in three dimensions to build a three-dimensional flow full characteristic grid and a three-dimensional torque full characteristic grid.

5. The method for modeling abandoned mine pumped storage batteries considering efficiency characteristics according to claim 3, characterized in that: In step S22, the pressurized water system adopts a second-order elastic water hammer model, as follows: In the formula, T w T is the inertial time constant of the water flow. r Let f be the pipe reflection time, and f be the pipe friction coefficient.

6. The method for modeling abandoned mine pumped storage batteries considering efficiency characteristics according to claim 3, characterized in that: In step S23, the transfer function of the parallel PID speed controller is: In the formula, the unit speed difference Δw is the difference between the actual speed w and the speed reference w. ref The difference, y is the actual value of the guide vane opening, K p K I K D These are the proportional gain coefficient, integral gain coefficient, and differential gain coefficient, respectively. In the hydraulic actuator, considering the guide vane opening speed limit, dead zone, and nonlinearity of the guide vane opening limit, y ref y is the reference value for guide vane opening, and y is the actual value for guide vane opening; T y The main relay time constant is used, and the speed limiting element is used to limit the change speed of the guide vanes and reduce head fluctuations during power regulation.

7. The method for modeling abandoned mine pumped storage batteries considering efficiency characteristics according to claim 1, characterized in that: Step S3 specifically includes the following steps: S31: Determining the stable operating boundary of the turbine: When the unit is operating at a constant speed, the total differential form of the relationship between the actual speed n of the unit, the pump-turbine flow rate Q, and the mechanical torque M per unit value and the actual value is expressed as follows: Simplifying equations (6) to (8), we get: Equations (9) and (10) must satisfy the constraint that the right-hand side of the inequality must be positive: To ensure that the turbine remains within a stable operating range during dynamic regulation, the following constraints must be met: In the formula, H T This represents the real-time operating head of the generator unit, with head fluctuation ΔH = β*H. T β is the head fluctuation coefficient, and n1'1 and H1 represent the unit rotational speed and working head at characteristic point C1 under a specific guide vane opening, respectively. A cubic polynomial fit is performed on the unit rotational speed corresponding to the guide vane opening at all characteristic points C1 in the full characteristic curve, yielding the following functional relationship between the guide vane opening at characteristic point C1 and the unit rotational speed: n' 11 =44.5y 3 -102.9y 2 +92.6y+70.8 (14) Substituting β into equation (13) yields: Taking into account the impact of head fluctuations, the turbine operating conditions include a certain range of unstable operating conditions, which are determined using the following methods: First, based on the current guide vane opening, the unit speed corresponding to the critical operating point C1 is calculated using equation (14); second, according to the actual unit speed, the working head H1 at this critical point is determined using equation (1); finally, the working head H1 at the current actual head H1 is verified using equation (15). T Under these conditions, can the unit complete the dynamic adjustment process to avoid entering the unstable operating region due to head fluctuations? S32: Optimizing the optimal speed and guide vane opening: Based on the pump-turbine output formula, the mechanical power P under power generation and pumping conditions... m They are represented as follows: P m =Mnπ / 30=9.81HQη (16) In the formula, η is the efficiency of the water pump turbine, and H is the head; Under the premise of constant head and pump-turbine output power, the minimum flow rate corresponds to the optimal efficiency in power generation mode, while the maximum flow rate achieves the optimal efficiency in pumping mode.

8. The method for modeling abandoned mine pumped storage batteries considering efficiency characteristics according to claim 7, characterized in that: In step S32, under the power generation operating conditions, the search process for the optimal speed and guide vane opening of the pump-turbine unit is as follows: A1: Input mechanical power P m , head H, head fluctuation coefficient β; A2: Based on the speed adjustment range n min -n max Define the search step size Δn, and divide the speed adjustment range into j values, j = (n max -n min ) / Δn; A3: Let i = 1, calculate the rotational speed n i =n min +i*Δn and torque M i =P m / n i , where i = 1, 2, ..., j; A4: The unit rotational speed n is obtained from equations (1) and (3) respectively. 11i and unit torque M 11i The guide vane opening y is obtained from the torque characteristic curve of region I. i ; A5: The unit rotational speed n at characteristic point C1 is obtained from equation (14). 11i The head H1 at characteristic point C1 is obtained from equation (1); A6: Determine if the condition is met. If the condition is not met, then exclude the rotational speed n. i If satisfied, Q can be obtained from the flow characteristic curve of region I. 11i Therefore, from equation (2), we can obtain Q. i And determine whether 1>Q is satisfied. i If the condition is greater than 0, then let Q = 0. i =inf, indicating that the rotational speed value is not within the search range. If it is satisfied, let i+1 and repeat steps A3-A6 until i=j; A7: Output optimal flow rate Q op =min{Q1,Q2,Q3,…,Q j }≤1;Q op The speed and opening degree corresponding to the operating point are the optimal speed n. op and optimal opening y op , which refers to the control parameters that enable the pump-turbine to achieve optimal operating efficiency under specific output and head conditions.

9. The method for modeling abandoned mine pumped storage batteries considering efficiency characteristics according to claim 7, characterized in that: In step S32, under the pumping operation condition, the search process for the optimal speed and guide vane opening of the pump-turbine unit is as follows: B1: Input mechanical power P m , head H, head fluctuation coefficient β; B2: Based on the speed adjustment range n min -n max Define the search step size Δn and divide the speed adjustment range into j values. j = (n max -n min ) / Δn; B3: Let i = 1, calculate the rotational speed n i =n min +i*Δn and torque M i =P m / n i , where i = 1, 2, ..., j; B4: Determine the unit rotational speed n using equations (1) and (3) respectively. 11i and unit torque M 11i The guide vane opening y is obtained by querying the three-dimensional torque and flow full characteristic mesh of the pump turbine in region I. i and unit flow Q 11i And apply equation (2) to convert it into a per-unit value Q of the flow rate. i ; B5: Determine if -1 is satisfied. i <0, if not satisfied, then set Q. i =0, and at the same time set the corresponding rotational speed n i Remove from the candidate set; if satisfied, retain the parameter combination, let i+1, and repeat steps B3-B5 until i=j;​ B7: Output optimal flow rate Q op =max{Q1,Q2,Q3,…,Q j }>0;Q op The speed and opening degree corresponding to the operating point are the optimal speed n. op and optimal opening y op This refers to the optimal control parameters that enable the pump-turbine to achieve the highest operating efficiency under the current output and head conditions.

10. The method for modeling abandoned mine pumped-storage batteries considering efficiency characteristics according to claim 1, characterized in that: Step S4 specifically includes the following steps: The system SoC is defined using water head as a constraint variable and then normalized. In the formula, E t The SOC is the normalized value of the head, with a value range of [0, 1]. H and These are the lower and upper limits of the gas pressure in the gas storage facility, respectively; considering the rated flow rate Q... p0 Rated charging time for pumping water (t) p0 Or at the rated flow rate Q g0 Rated power generation duration t g0 The change in reservoir head is The dynamic equation for head-flow rate in a pumped storage power station is: In the formula, Q p Q is the pumping flow rate. g Let A(H) be the power generation flow rate, and A(H) be the surface area of ​​the reservoir at a head of H. Based on the dynamic equations, a quasi-steady-state model of the reservoir head in the form of a difference equation is established: In the formula, the subscript t indicates time t, Δt is the unit scheduling duration, and H t Let ε be the gas pressure in the gas storage tank at time t. RE To reflect the loss coefficient due to reservoir evaporation, seepage, or external runoff, this coefficient is set to 0 when water consumption is ignored; The dynamic equations for the pump-turbine head SoC are derived as follows: The analogous battery SoC model is shown in Equation (21): Pumping efficiency is defined as the power consumption per unit volume of water pumped, i.e. Power generation efficiency is defined as the amount of water consumed per unit of power, i.e. In the formula All values ​​are per-unit values ​​based on design parameters; η ps and η gs Relative operating efficiency refers to the ratio of operating efficiency under varying operating conditions to rated efficiency, where η is the efficiency under rated operating conditions. ps =η gs =1; The coupling relationship of the internal interface variables of the system under the optimal control strategy is represented by the following function: In the formula, Γ ps and Γ gs The external characteristic function is the one used to achieve the optimal efficiency of the system. The simplified ACEPS-type battery model is as follows: In the formula, E t For ACEPS system energy storage SoC measured in head, its upper and lower limits are respectively represented by... and E t Indicates; γ ac and γ ad They represent the current E t Changes in SoC and per-unit charge / discharge power of ACEP The relationship, specifically expressed by the external characteristic function Γ under the optimal efficiency of the system. ap ,Γ ag The derivation yields the results shown in equations (27) and (28): In the formula, k p and k g These represent the rated pumping time and the reciprocal of the rated time, respectively.

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