Methods for determining the optimal expansion location of pumped-storage units in cascade hydropower stations
By establishing a mixed-integer linear programming model in cascade power stations and optimizing the location of pumped-storage unit expansion, the problems of long construction cycle and high cost in the integrated transformation of cascade power stations were solved, and a more accurate expansion plan and a more efficient peak-shaving effect were achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- SICHUAN ENERGY INTERNET RES INST TSINGHUA UNIV
- Filing Date
- 2023-07-12
- Publication Date
- 2026-06-30
AI Technical Summary
In existing technologies, the lack of research on the expansion location of pumped storage units during the integration and transformation of cascade power stations has led to problems such as long construction cycles, high costs, and difficulty in site selection for pumped storage. Furthermore, traditional models have not been accurate enough to pinpoint the units, resulting in operational deviations.
By simulating the expansion of pumped storage units based on existing cascade hydropower stations, a mixed integer linear programming model is established to optimize short-term peak shaving and obtain the optimal expansion location. The model includes an objective function and various constraints, and the optimal expansion scheme is obtained by linearization and CPLEX solver.
It effectively shortens the construction cycle of pumped storage, reduces costs, provides more precise selection of expansion locations, meets actual engineering needs, and improves peak-shaving efficiency.
Smart Images
Figure CN117236580B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of power plant dispatching technology, and more specifically, to a method for selecting the optimal expansion location of pumped-storage units in a cascade power plant. Background Technology
[0002] With the development of the national economy and the continuous adjustment of electricity consumption structure, power grids are facing problems such as widening peak-valley differences and severe peak-shaving challenges to varying degrees. Pumped storage power stations, as large-scale energy storage power sources that simultaneously possess the functions of "peak shaving and valley filling," can effectively solve these problems. However, pumped storage power stations require high upfront investment and have long construction periods, and relocating pumped storage power stations will also have a significant impact on the ecological environment. Integrating and upgrading existing hydropower stations can compensate for the shortcomings of pumped storage, such as long construction periods, high costs, and difficult site selection. Therefore, further exploring integrated upgrading schemes for cascade power stations is of great significance for effectively accelerating the construction of pumped storage power stations.
[0003] However, while domestic research on the optimized operation of conventional cascade hydropower stations and traditional pumped storage power stations is relatively abundant, there are few reports on the establishment of models for cascade hybrid pumped storage power stations and the introduction of peak-shaving modes. Furthermore, research on the expansion locations of pumped storage units during the integration and transformation of conventional cascade hydropower stations into cascade hybrid pumped storage systems is also lacking. In addition, for the modeling of hydropower dispatching, to facilitate research, the field often uses the power station as the smallest dispatching unit. This method improves the model's solution efficiency to some extent, but actual operation often results in some deviation due to the lack of precision down to the unit level. Summary of the Invention
[0004] The purpose of this invention is to provide a method for selecting the optimal expansion location of pumped storage units in a cascade hydropower station. This method can integrate and transform existing cascade hydropower stations to expand pumped storage units and form a cascade hybrid pumped storage power station. This can make up for the shortcomings of pumped storage, such as long construction cycle, high cost, and difficult site selection, and effectively accelerate the construction of pumped storage.
[0005] The embodiments of the present invention can be implemented as follows:
[0006] This invention provides a method for selecting the optimal expansion location of pumped-storage units in a cascade hydropower station, the method comprising:
[0007] S1: Based on existing cascade hydropower stations, simulate the expansion of pumped storage units to form a cascade hybrid pumped storage power station, and set up various operating conditions for expanding pumped storage units; among them, the operating conditions represent the expansion location of the pumped storage units.
[0008] S2: Short-term peak shaving optimization is performed on the above various operating conditions using an appropriate mixed-integer linear programming model to obtain the peak shaving optimization results for each operating condition;
[0009] S3: Compare the peak-shaving optimization results under various operating conditions to obtain the optimal expansion site selection scheme.
[0010] In an optional implementation, S2 includes:
[0011] S21: Establish the objective function for short-term peak-shaving optimization scheduling of cascade hybrid pumped storage power stations; and establish the constraints for cascade hybrid pumped storage power stations considering the combination of conventional generator units and pumped storage units.
[0012] S22: Linearize the nonlinear factors in the model to form a mixed integer linear programming model for short-term peak-shaving optimization scheduling of cascade hybrid pumped storage power stations.
[0013] S23: Solve the mixed-integer linear programming model to obtain peak-shaving optimization results for various operating conditions.
[0014] In an optional implementation, S21 includes:
[0015] The objective function is to minimize the maximum peak-to-valley difference of the remaining load of the power grid within the scheduling cycle.
[0016] In an optional implementation, the objective function is as follows:
[0017]
[0018] In the formula, F is the peak-to-valley difference of the remaining load, and C t D represents the remaining load during time period t. t The original load of the power grid in time period t. Let N be the generating capacity of unit n of power plant i during time period t, M be the total number of power plants, and N be the total generating capacity of unit n of power plant i during time period t. i The total number of units. Let M be the pumping power of pumped storage unit k in a hybrid pumped storage power station j during time period t, where t is the scheduling cycle, t∈{1,2,3…,T}, T is the total number of cycles, and M is the total number of cycles. p This represents the total number of power station serial numbers with pumped storage units. This represents the total number of pumped storage units in the hybrid pumped storage power station j.
[0019] In an optional implementation, in S21, the constraints include: hydraulic connection constraints between cascade power stations and operational constraints of individual units and power stations.
[0020] In an optional implementation, in S21, the constraints include hydraulic connection constraints between cascade power stations, power station water level constraints, water level-reservoir capacity constraints, tailrace water level-discharge constraints, unit output limit constraints, unit power generation flow limit constraints, unit vibration zone limit constraints, unit ramping limit constraints, unit output fluctuation limit constraints, unit operating status constraints, unit power generation head constraints, unit dynamic characteristic constraints, unit pumping power limit constraints, unit pumping flow limit constraints, unit power generation and pumping status constraints, unit pumping power constraints, and pumped storage unit regulation frequency constraints.
[0021] In an optional implementation, S21 includes:
[0022] When building a mixed-integer linear programming model, the following coding techniques can be used:
[0023] All units are assumed to be equipped with pumping capabilities;
[0024] For conventional generator sets, the upper and lower limits of their power generation are the actual values, while the upper and lower limits of their pumping power are 0.
[0025] For the expanded pumped storage units, the upper and lower limits of their power generation and pumping power are actual values.
[0026] In an optional implementation, in S21, the method for distinguishing between pumped-storage units and conventional generator units is as follows:
[0027] like Then, unit n in power station i is a pumped-storage unit;
[0028] like Then, unit n in power station i is a conventional generator unit;
[0029] In the formula, This is the maximum pumping power limit for unit n in power plant i.
[0030] In an optional implementation, S22 includes:
[0031] A linear transformation is performed on the objective function of the model by adding 0-1 auxiliary variables.
[0032] For the water level-reservoir capacity constraint and the tailwater level-discharge constraint in the model, a piecewise linear approximation method is used for linear transformation.
[0033] To address the unit output fluctuation constraint in the model, an auxiliary variable with the number of adjustment records is used for linear transformation.
[0034] The discrete head linear method is used to address the unit dynamic characteristic constraints and the unit pumping power limit constraints in the model. By using the unit power generation and pumping power curves to partition the model according to the head sensitivity, a linear constraint is formed with the power generation flow and pumping flow as linear functions. Finally, the law of large numbers is used to relax the constraints.
[0035] In an optional implementation, S3 includes:
[0036] The mixed-integer linear programming model established above was solved using the CPLEX solver in the JAVA environment, and the generating power, generating flow, pumping power, pumping flow, and power station water level of the unit at 96 time points under various optimal operating conditions were obtained.
[0037] The beneficial effects of the method for selecting the optimal expansion location of pumped-storage units in a cascade hydropower station, as provided in this embodiment, include:
[0038] 1. The established model takes the power station's generating units as the smallest scheduling unit, making the scheduling objects more detailed and closer to the actual engineering situation. It can also meet the normal operation requirements of hydropower stations, even for cascade hybrid pumped storage power stations with more complex operating modes.
[0039] 2. Expanding pumped storage units based on existing cascade hydropower stations to form cascade hybrid pumped storage power stations can make up for the shortcomings of pumped storage units, such as long construction period, high cost and difficult site selection, and effectively accelerate the construction of pumped storage units;
[0040] 3. By obtaining peak-shaving optimization results under different operating conditions through this model and conducting comparative analysis, it can provide a useful reference for subsequent site selection and expansion of pumped storage units to form a cascade hybrid pumped storage power station. Attached Figure Description
[0041] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.
[0042] Figure 1 A flowchart illustrating the method for selecting the optimal expansion location of pumped-storage units in a distinguishable cascade power station according to an embodiment of the present invention;
[0043] Figure 2 This is a diagram showing the reservoir water level and outflow of power station 1 in operating condition 1 during the implementation of this invention;
[0044] Figure 3 This is a diagram illustrating the operation of pumped-storage unit 4 in power plant 1 under operating condition 1 during the implementation of this invention.
[0045] Figure 4 This is a diagram illustrating the operation of Unit 1 of Power Plant 1 in Operating Condition 1 during the implementation of this invention.
[0046] Figure 5 This is a diagram illustrating the operation of Unit 1 of Power Plant 2 in Operating Condition 1 during the implementation of this invention.
[0047] Figure 6 This is a diagram illustrating the operation of Unit 3 of the power plant in Working Condition 1 during the implementation of this invention.
[0048] Figure 7 This is a diagram illustrating the operation of Unit 2 of Power Plant 4 in Working Condition 1 during the implementation of this invention. Detailed Implementation
[0049] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.
[0050] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.
[0051] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.
[0052] It should be noted that, where there is no conflict, the features in the embodiments of the present invention can be combined with each other.
[0053] Please refer to Figure 1 This embodiment provides a method for selecting the optimal expansion location of pumped-storage units in a cascade power station (hereinafter referred to as the "method"), which can provide the optimal site selection scheme for the integrated transformation of cascade power stations.
[0054] The method includes the following steps:
[0055] S1: Based on existing cascade hydropower stations, simulate the expansion of pumped storage units to form a cascade hybrid pumped storage power station, and set up various operating conditions for expanding pumped storage units.
[0056] The operating condition represents the location of the pumped-storage unit expansion, for example, the operating condition is to build pumped-storage unit b at power station a.
[0057] S2: Short-term peak shaving optimization is performed on the above various operating conditions using an adaptive mixed integer linear programming (MILP) model to obtain peak shaving optimization results for various operating conditions.
[0058] The steps involved in establishing a mixed-integer linear programming model are as follows:
[0059] S21: Establish the objective function for short-term peak-shaving optimization scheduling of cascade hybrid pumped storage power stations; and establish the constraints for cascade hybrid pumped storage power stations considering the combination of conventional generator units and pumped storage units.
[0060] Specifically, taking the minimum maximum peak-to-valley difference of the remaining load of the receiving-end power grid within the scheduling cycle as the objective function, the objective function is as follows:
[0061]
[0062] In the formula, F is the peak-to-valley difference of the remaining load, and C t D represents the remaining load during time period t. t The original load of the power grid in time period t. Let N be the generating capacity of unit n of power plant i during time period t, M be the total number of power plants, and N be the total generating capacity of unit n of power plant i during time period t. i Let be the total number of generating units in power station i. Let M be the pumping power of pumped storage unit k in a hybrid pumped storage power station j during time period t, where t is the scheduling cycle, t∈{1,2,3…,T}, T is the total number of cycles, and M is the total number of cycles. p This represents the total number of power stations equipped with pumped storage units. This represents the total number of pumped storage units in hybrid pumped storage power station j.
[0063] The constraints mainly include hydraulic connection constraints between cascade power stations and operational constraints of individual units and power stations. Specifically, the constraints include hydraulic connection constraints between cascade power stations, power station water level constraints, water level-reservoir capacity constraints, tailrace water level-discharge constraints, unit output limit constraints, unit power generation flow limit constraints, unit vibration zone limit constraints, unit ramping limit constraints, unit output fluctuation limit constraints, unit operating status constraints, unit power generation head constraints, unit dynamic characteristic constraints, unit pumping power limit constraints, unit pumping flow limit constraints, unit power generation and pumping status constraints, unit pumping power constraints, and pumped storage unit regulation frequency constraints.
[0064] S22: Linearize the nonlinear factors in the model to form a mixed integer linear programming (MILP) model for short-term peak-shaving optimization scheduling of cascade hybrid pumped storage power stations.
[0065] S23: Solve the mixed-integer linear programming model to obtain peak-shaving optimization results for various operating conditions.
[0066] S3: Compare the peak-shaving optimization results under various operating conditions to obtain the optimal expansion site selection scheme.
[0067] Example
[0068] Taking a four-stage cascade hydropower station in Southwest China as an example, the detailed information of the cascade hydropower station is shown in Table 1 below:
[0069] Table 1: Detailed Information on Cascade Hydropower Stations
[0070]
[0071] For the aforementioned cascade power stations, a method for selecting the optimal expansion location of pumped-storage units in the cascade power stations is adopted, including the following steps:
[0072] Step 1: Establish four operating conditions for expanding pumped storage units.
[0073] Specifically, one pumped-storage unit was added to each of the four cascade hydropower stations. In this embodiment, all added pumped-storage units have variable-speed operation capabilities, with a maximum generating capacity of 100MW, a maximum pumping capacity of 133.4MW, a vibration range of [30, 70], and a ramp rate of 40MW / 15min. For ease of study, it is assumed that the pumped water comes entirely from the upstream reservoir of the next cascade hydropower station, thus preventing situations where there is insufficient downstream water or pumping failure. The operating conditions of the four types of added pumped-storage units are shown in Table 2 below.
[0074] Table 2: Operating Conditions of Four Types of Expanded Pumped Storage Units
[0075] Operating condition classification Detailed operating conditions Operating Condition 1 Add one pumped-storage unit to Power Station No. 1. Operating Condition 2 Add one pumped-storage unit to Power Station No. 2. Operating Condition 3 Add one pumped-storage unit to Power Station No. 3. Operating Condition 4 Add one pumped-storage unit to Power Station No. 4.
[0076] Step 2: Short-term peak shaving optimization is performed on the above four operating conditions using an appropriate mixed-integer linear programming model to obtain the peak shaving optimization results for each operating condition.
[0077] The steps involved in establishing a mixed-integer linear programming model are as follows:
[0078] Step 21: Establish the objective function for short-term peak-shaving optimization scheduling of cascade hybrid pumped storage power stations; and establish the constraints for cascade hybrid pumped storage power stations considering the combination of conventional generator units and pumped storage units.
[0079] Specifically, taking the minimum maximum peak-to-valley difference of the remaining load of the receiving-end power grid within the scheduling cycle as the objective function, the objective function is as follows:
[0080]
[0081] In the formula, F is the peak-to-valley difference of the remaining load, and C t D represents the remaining load during time period t. t The original load of the power grid in time period t. Let N be the generating capacity of unit n of power plant i during time period t, M be the total number of power plants, and N be the total generating capacity of unit n of power plant i during time period t. i Let be the total number of generating units in power station i. Let M be the pumping power of pumped storage unit k in a hybrid pumped storage power station j during time period t, where t is the scheduling cycle, t∈{1,2,3…,T}, T is the total number of cycles, and M is the total number of cycles. p This represents the total number of power stations equipped with pumped storage units. This represents the total number of pumped storage units in hybrid pumped storage power station j.
[0082] Among them, the original load of the power grid D t The values are shown in Table 3 below:
[0083] Table 3: Original load of the power grid D t Value
[0084]
[0085] The constraints are established as follows:
[0086] 1) Establish hydraulic connection constraints between cascade power stations, as shown in the following formula:
[0087]
[0088] Among them, V i,t R represents the reservoir capacity of power station i at the end of time period t. i,t Let be the flow rate between power station i and power station i-1. Let i-1 be the power generation flow rate of power plant i-1 during time period t. Let Δt be the total amount of water pumped by power station i-1 during time period t, and Δt be the time step.
[0089] R i,t Taking March 14, 2016 as a typical scenario, the interval traffic flow is set according to the actual situation on that day.
[0090] 2) Establish the power station water level constraint, the formula is as follows:
[0091]
[0092]
[0093] in, ΔZ represents the initial and final water levels at the upstream dam of reservoir i, as well as the allowable water level range for scheduling. In order to regulate the water level in front of the i reservoir dam during the first period, To regulate the water level in front of the dam of reservoir i during time period T. Among them, Given the conditions; the allowable fluctuation range of the water level ΔZ is set to 0.5m.
[0094] 3) Establish water level-reservoir capacity constraints, using the following formula:
[0095] V i,t =f i,zv (Z i,t )
[0096] Among them, f i,zv (·) represents the water level-capacity relationship function of reservoir i, Z i,t Let V be the water level of reservoir i in time period t. i,t Let be the reservoir capacity of reservoir i during time period t.
[0097] 4) Establish tailwater level-discharge constraint, the formula is as follows:
[0098]
[0099] Among them, f i,zu (·) represents the tailwater level-discharge relationship function of reservoir i, Q i,t Let i be the discharge volume of reservoir i in time period t. Let be the tailwater level of reservoir i during time period t.
[0100] 5) Establish unit output limit constraints, as shown in the following formula:
[0101]
[0102] in, Let n be the power generation capacity of unit n of power plant i during time period t. These are the upper and lower limits of the generating power of unit n in power plant i, respectively. Let n be the operating status of unit n of power plant i during time period t. If the unit is in power generation mode, then on the contrary
[0103] 6) Unit power generation flow limit constraints, the formula is as follows:
[0104]
[0105] in, Let n be the power generation flow of unit n of power plant i during time period t. The ratio represents the upper and lower limits of the generating power of unit n in power plant i.
[0106] 7) Establish the vibration zone constraint for the unit, using the following formula:
[0107]
[0108] in, These are the upper and lower limits of the output of the m-th vibration zone of unit n in power plant i, respectively.
[0109] 8) Establish unit ramp-up constraints, using the following formula:
[0110]
[0111] Wherein, ΔP i,n Let α be the ramp-up limit for unit n of power plant i, and α be the allowable fluctuation range of this unit within a unit time period. i,n,t ∈{0,1}、β i,n,t ∈{0,1} represents the power generation regulation index parameter of n generating units of power plant i during time period t, α i,n,t =1 indicates that the power is adjusted upward in time period t+1, β i,n,t =1 indicates that the power is adjusted downward in time period t+1; conversely, when it is equal to 0, the power does not change during that time period.
[0112] 9) Establish constraints to limit unit output fluctuations, using the following formula:
[0113]
[0114] ξ = 1, 2, ..., t a -1
[0115] Where ξ is the independent variable representing the number of time periods, and t a t represents the minimum number of time periods that a conventional generator set needs to maintain during the processing. a >1. This constraint reduces losses caused by frequent fluctuations in the unit's power generation.
[0116] 10) Establish unit operating state constraints, using the following formula:
[0117]
[0118] in, Let n be the unit n of power plant i during time period t. If it is equal to 1, the unit is started; if it is equal to 0, the unit is not started. Similarly, but it describes operation when the computer is off; 1 means the computer is off and 0 means the computer is on. Let be the minimum continuous start-up and shutdown times of unit n in power plant i, respectively. Let n be the maximum start-up time of unit n in power plant i.
[0119] 11) Establish the generator head constraint, the formula is as follows:
[0120]
[0121] Among them, H i,n,t , These represent the net head and head loss of unit n of power station i during time period t.
[0122] 12) Establish the unit's dynamic characteristic constraints, as shown in the following formula:
[0123]
[0124] in, Let be the function relating the output of unit n of power plant i to the power generation flow rate and the power generation head.
[0125] 13) Establish the unit's pumping power limit constraint, as shown in the following formula:
[0126]
[0127] in, Let k be the operating state of unit k in hybrid pumped storage power station j during time period t. If k is equal to 1, the unit is in pumping state; if k is equal to 0, the unit is in non-pumping state. These represent the maximum and minimum pumping power limits of unit k in power plant j, respectively, M p Let j be the total number of power stations. Let k be the total number of units. Let K be the pumping power of unit k in power plant j.
[0128] 14) Establish the unit's pumping flow rate limit constraint, as shown in the following formula:
[0129]
[0130] in, These are the maximum and minimum pumping flow limits for unit k of power plant j, respectively. Let be the pumping flow rate of unit k of power plant j during time period t.
[0131] 15) Establish the unit's power generation pumping state constraints, as shown in the following formula:
[0132]
[0133]
[0134] The above formula describes the mutual exclusion relationship between the power generation and pumping states of the unit. Unit n of power plant i cannot simultaneously be in the two states of pumping and power generation during time period t; and there will be no rapid transition between the power generation and pumping states.
[0135] 16) Establish the unit's pumping power constraint, as shown in the following formula:
[0136]
[0137] Among them, f j,k (·) is the function relating the pumping power of unit n in power plant i to the pumping flow rate and pumping head.
[0138] 17) Establish constraints on the number of regulation cycles for pumped-storage units, using the following formula:
[0139]
[0140] in, Let be the power generation regulation parameters for n generating units of power plant i during time period t. This indicates that the power will be adjusted upwards during time period t+1. This indicates that the power is adjusted downwards during time period t+1; conversely, when it equals 0, the power does not change during that time period, and υ is the limit of the optimal number of adjustments during the output of the pumped storage unit.
[0141] When establishing a mixed-integer linear programming model, the following coding techniques can be used: assume all units have pumping capacity. For conventional units, the upper and lower limits of their pumping power are 0; for expanded pumped-storage units, the upper and lower limits of their pumping power are the actual values.
[0142] When differentiating between pumped-storage units and conventional generator units, judgment statements are used for identification. The specific identification method for pumped-storage units and conventional generator units is shown in Table 4 below:
[0143] Table 4: Methods for distinguishing between pumped-storage units and conventional generator units
[0144]
[0145] In Table 4, This is the maximum pumping power limit for unit n in power plant i.
[0146] Step 22: Linearize the nonlinear factors in the model to form a mixed integer linear programming model for short-term peak-shaving optimization scheduling of cascade hybrid pumped storage power stations.
[0147] Specifically, a linear transformation is performed on the objective function of the model by adding 0-1 auxiliary variables. The specific method is as follows:
[0148]
[0149] In the formula: R max R min These are auxiliary variables for the linearization objective function.
[0150] For the water level-reservoir capacity constraint and tailwater level-discharge constraint in the model, a piecewise linear approximation method can be used for linear transformation. In particular, for power stations with seasonal regulation or above, the daily water level change is relatively small, and linear fitting can be performed at the initial water level.
[0151] To address the unit output fluctuation constraints in the model, a linear transformation is performed using an auxiliary variable that sets the number of adjustment records. The specific method is as follows:
[0152]
[0153] In the formula: α i,n,t ∈{0,1}、β i,n,t ∈{0,1} represents the power generation regulation index parameter of n generating units of power plant i during time period t, α i,n,t =1 indicates that the power is adjusted upward in time period t+1, β i,n,t A value of 1 indicates that the power is adjusted downwards during time period t+1; conversely, a value of 0 indicates that the power remains unchanged during that time period. α This refers to the period of minimum continuous output of the generator unit.
[0154] To address the unit dynamic characteristic constraints and pumping power limit constraints in the model, a linear method based on discrete head is employed. This involves partitioning the model based on the unit's power generation and pumping power curves, taking into account head sensitivity, to form linear constraints where power generation flow and pumping flow are linear functions. Finally, the law of large numbers is used to relax these constraints, as follows:
[0155] The relaxation constraints for power generation are as follows:
[0156]
[0157]
[0158] In the formula, Let be the relationship function between the power generation flow and power generation of unit n in power plant i during time period t.
[0159] The relaxation constraints on pumping power are as follows:
[0160]
[0161]
[0162] In the formula, Let be the function relating the pumping flow rate and pumping power of unit k in power plant j during time period t.
[0163] Step 23: Solve the mixed-integer linear programming model to obtain peak-shaving optimization results for various operating conditions.
[0164] Specifically, the CPLEX solver is used in the JAVA environment to solve the mixed integer linear programming model established above. Finally, the optimization results of the unit's power generation, power generation flow, pumping power, pumping flow, and power station water level at 96 time points under the optimal conditions of the four operating conditions can be obtained.
[0165] Step 3: Compare the peak-shaving optimization results under various operating conditions to obtain the optimal expansion site selection scheme.
[0166] Specifically, the peak-shaving optimization results obtained under the four operating conditions were compared and analyzed, as shown in Table 5 below, to obtain the optimal expansion site selection scheme.
[0167] Table 5: Peak-to-valley difference of residual load under various operating conditions
[0168]
[0169] As can be seen from Table 5, compared with the other three operating conditions, the maximum value of the peak-valley difference of the remaining load is the smallest under operating condition 1, and the reduction is the largest compared with the original load, which is 36.4%. Therefore, the optimal expansion site selection scheme is the scheme corresponding to operating condition 1 in Table 2: add one pumped storage unit to the No. 1 power station.
[0170] To demonstrate the effectiveness of the model solution method of this invention, the actual scheduling optimization process of working condition 1 is used as an example. Figure 2 The diagram shows the reservoir water level changes and outflow during the operation of Power Plant 1 under Working Condition 1, where the reservoir water level meets the allowable fluctuation range of 0.5m. Figure 3 , Figure 4 , Figure 5 , Figure 6 and Figure 7 The power output process of some units during the scheduling process is shown separately. Figure 4-7 It can be seen that the output of the conventional units all operates within the safe zone and meets the minimum continuous output time constraint, and the minimum start-up and shutdown of the units also meet the actual situation; from Figure 3-4 It can be seen that the output of the pumped-storage units meets the regulation frequency requirements, and while the pumped-storage units are operating, the other conventional units of the power station are shut down, indicating that the power station's operating state constraints are met. The peak-shaving optimization results all satisfy the model parameter settings and constraint requirements, further verifying the effectiveness of the model and solution method of this invention.
[0171] The beneficial effects of the method for selecting the optimal expansion location of pumped-storage units in a cascade hydropower station, as provided in this embodiment, include:
[0172] 1. Expanding pumped storage units based on existing cascade hydropower stations to form cascade hybrid pumped storage power stations can make up for the shortcomings of pumped storage, such as long construction period and high cost, and effectively accelerate the construction of pumped storage.
[0173] 2. The model established in this invention takes the generating unit as the smallest scheduling unit, and the scheduling objects are more detailed and closer to the actual engineering situation. It can also meet the short-term peak-shaving needs for cascade hybrid pumped storage power stations with more complex operation modes.
[0174] 3. By obtaining peak-shaving optimization results under different operating conditions through this model and conducting comparative analysis, it can provide a useful reference for subsequent site selection and expansion of pumped storage units to form a cascade hybrid pumped storage power station.
[0175] The above are merely specific embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.
Claims
1. A method for selecting the optimal expansion position of pumped storage units in a distinguishable cascade power station, characterized in that, The method includes: S1: Based on existing cascade hydropower stations, simulate the expansion of pumped storage units to form a cascade hybrid pumped storage power station, and establish various operating conditions for expanding pumped storage units; wherein, the operating conditions represent the expansion location of the pumped storage units. S2: Short-term peak shaving optimization is performed on the above various operating conditions using an appropriate mixed-integer linear programming model to obtain the peak shaving optimization results for each operating condition; S3: Compare the peak-shaving optimization results under various operating conditions to obtain the optimal expansion site selection scheme; S2 also includes: S21: Establish the objective function for short-term peak-shaving optimization scheduling of cascade hybrid pumped storage power stations; and establish the constraints for cascade hybrid pumped storage power stations considering the combination of conventional generator units and pumped storage units. S22: Linearize the nonlinear factors in the model to form a mixed integer linear programming model for short-term peak-shaving optimization scheduling of cascade hybrid pumped storage power stations. S23: Solve the mixed-integer linear programming model to obtain peak-shaving optimization results for various operating conditions; The objective function in S21 is as follows: In the formula, The difference between peak and valley loads is the remaining load. for Remaining load for the period For the power grid The original load of the power grid during the period, For power station unit exist The generating capacity of the unit during the time period The total number of power stations. The total number of units. Hybrid pumped storage power station Pumped storage units exist Pumping power of the unit during the time period For the scheduling period, T is the total number of periods. This represents the total number of power station serial numbers with pumped storage units. Hybrid pumped storage power station The total number of pumped storage unit serial numbers; The constraints in S21 include hydraulic connection constraints between cascade power stations, power station water level constraints, water level-reservoir capacity constraints, tailrace water level-discharge constraints, unit output limit constraints, unit power generation flow limit constraints, unit vibration zone limit constraints, unit ramping limit constraints, unit output fluctuation limit constraints, unit operating status constraints, unit power generation head constraints, unit dynamic characteristic constraints, unit pumping power limit constraints, unit pumping flow limit constraints, unit power generation and pumping status constraints, unit pumping power constraints, and pumped storage unit regulation frequency constraints. S22 includes: When establishing the mixed-integer linear programming model, the following coding techniques are used: All units are assumed to be equipped with pumping capabilities; For conventional generator sets, the upper and lower limits of their power generation are the actual values, while the upper and lower limits of their pumping power are 0. For the expanded pumped storage units, the upper and lower limits of their power generation and pumping power are actual values.
2. The method for selecting the optimal expansion location of pumped-storage units in a distinguishable cascade power station according to claim 1, characterized in that, S21 includes: The objective function is to minimize the maximum peak-to-valley difference of the remaining load of the power grid within the scheduling cycle.
3. The method for selecting the optimal expansion location of pumped-storage units in a distinguishable cascade power station according to claim 1, characterized in that, In S21, the method for distinguishing between pumped-storage units and conventional generator units is as follows: like Then the power station medium-sized units For pumped storage units; like Then the power station medium-sized units It is a conventional generator set; In the formula, For power station medium-sized units Maximum pumping power limit.
4. The method for selecting the optimal expansion location of pumped-storage units in a distinguishable cascade power station according to claim 1, characterized in that, S22 includes: A linear transformation is performed on the objective function of the model by adding 0-1 auxiliary variables. For the water level-reservoir capacity constraint and the tailwater level-discharge constraint in the model, a piecewise linear approximation method is used for linear transformation. To address the unit output fluctuation constraint in the model, an auxiliary variable with the number of adjustment records is used for linear transformation. The discrete head linear method is used to address the unit dynamic characteristic constraints and the unit pumping power limit constraints in the model. By using the unit power generation and pumping power curves to partition the model according to the head sensitivity, a linear constraint is formed with the power generation flow and pumping flow as linear functions. Finally, the law of large numbers is used to relax the constraints.
5. The method for selecting the optimal expansion location of pumped-storage units in a distinguishable cascade power station according to claim 1, characterized in that, S3 include: The mixed-integer linear programming model was solved using the CPLEX solver in the JAVA environment to obtain the unit's power generation, power generation flow, pumping power, pumping flow, and power station water level at 96 time points under various optimal operating conditions.