A method for dynamic control of lower limit of water level of cascade hydropower stations supporting power grid supply

Abstract

The application provides a cascade hydropower station water level lower limit dynamic control method for supporting power grid supply, and belongs to the field of multi-energy power system planning. The method is based on the runoff and new energy output prediction data of the dry representative year, and sets a supply period under the premise of meeting the operation parameters and constraints of hydropower. In order to guarantee the supply demand of hydropower in the period, the "water by electricity" algorithm coupling the fourth-order Runge-Kutta method and the success-failure search method is innovatively used to solve the required power generation flow. Further, combined with the water balance principle, the initial reservoir capacity is calculated through reverse iteration, and the initial water level lower limit is determined by using the piecewise linear interpolation method, and finally the operation constraints are corrected. In the simulation period, the rolling calculation strategy is used to dynamically update the water level lower limit, and a complete water level lower limit dynamic control curve is formed. The method has the advantages of simple solution, convenient parameter adjustment, high calculation efficiency, and fast response to real-time power grid supply instructions by directly reverse recursion of the physical process.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of multi-energy power system planning, in particular to a method for dynamically controlling the lower limit of the water level of a cascade hydropower station to support power grid supply. BACKGROUND

[0002] The large-scale grid connection of new energy represented by wind power and photovoltaic power brings great challenges to the safe and stable operation of the power grid due to its inherent intermittency, volatility and uncertainty. The power grid is facing increasingly severe peak regulation, frequency regulation and reserve pressure. In particular, during the peak load period, when new energy output suddenly drops or extreme weather events occur, power supply becomes a top priority for the national economy and people's livelihood. Hydropower stations, especially cascade control stations with reservoir regulation capacity, are one of the most important flexible resources and power supply foundations for the power grid due to their rapid start-up, flexible regulation, large regulation range and low operating cost. The lower limit of the water level, as the "lifeline" of the regulation capacity of the cascade hydropower station, fundamentally determines the physical boundary of the system in response to upstream water fluctuation, support for downstream cascade regulation and accommodation of wind and light fluctuations. Especially when the power grid is under continuous multi-day power supply pressure, the available storage capacity above the dead water level of the control reservoir directly restricts the limit of the cascade hydropower station's "topping" and "stability". The rigid setting of the current static lower limit of the water level makes this lifeline unable to respond dynamically to the demand for power supply: a large amount of effective storage capacity is occupied by the conservative operation above the dead water level, resulting in the idle of regulation potential during the power supply period and the decay of cross-day support capacity. How to scientifically control this key lower limit has become the primary proposition for unlocking the potential of cascade hydropower supply.

[0003] Although existing research focuses on the support of power grid flexibility by hydropower bases, such as Zhang Juntao, Cheng Chuantian, Shen Jianjian, et al. Short-term joint optimization scheduling method for high-proportion renewable energy power grid considering wind and light uncertainty [J]. Proceedings of the Chinese Society of Electrical Engineering, 2020, 40(18):5921-5932. DOI:10.13334 / j.0258-8013.pcsee.191200, it has not yet systematically responded to the systemic imbalance at the monthly to annual scale under high penetration of new energy. From the control period, most current research focuses on short-term requirements, such as Liu Xinyu, Luo Bin, Chen Yongcan, et al. Short-term scheduling model for mixing and storage-wind and light considering wind and light joint output uncertainty [J]. Journal of Hydroelectric Engineering, 2025, 44(05):44-60. In particular, seasonal power gaps and wind and light accommodation period fluctuations have significantly exceeded the regulation capacity limit of pumping and storage and electrochemical storage, and it is urgent to tap the cross-seasonal regulation potential of hydropower bases.

[0004] From the perspective of considering power grid demand, most studies focus on wind and solar power consumption and economic requirements for reservoir water level operation, such as: Ke Xianbo, Wu Chen, Liu Pan, et al. Impact of wind and solar power consumption on the operation of cascade reservoirs [J]. China Rural Water Conservancy and Hydropower, 2024, (04): 210-216. For future extreme weather or bundled new energy less frequent, there are few studies on water level operation boundary control to meet the safety demand of power grid power supply.

[0005] Secondly, from the optimization method, the current cascade hydropower station water level control research mainly focuses on the forward optimization model driven by the objective function, such as: Xie Mengfei, Xu Hang, Zhang Juntao, et al. Cascade hydropower station water level control method to support power grid power supply and consumption [J]. People's Yangtze River, 2025, 56(03): 191-199. DOI: 10.16232 / j.cnki.1001-4179.2025.03.026. This paper takes the minimum expected power shortage period and the minimum total energy storage of reservoir group as the objective function, inputs the constructed typical scenario into the simulation MILP model, sets the constraint condition, and determines the water level operation interval by forward optimization. But the traditional model depends on the prediction accuracy too much, and there are some shortcomings such as long-term prediction error accumulation leading to the deviation of the dispatching scheme from the actual power supply demand and the sharp drop in reliability under extreme scenarios, secondly, there are problems such as complex solution, difficult parameter adjustment, high time-consuming of large-scale matrix operation calculation, and inability to respond to real-time power supply instructions of power grid. Thirdly, the forward optimization model driven by the objective function is not as intuitive as the direct reflection of the physical process reverse recursion method.

[0006] The engineering pain point of the lack of quantitative basis for the reserved lack of regulation reservoir capacity of cascade hydropower in the 7-day or more medium and long-term power supply scenarios of provincial power grid, it is urgent to develop a water level lower limit fast calculation method based on boundary constraint, which can convert the power supply demand into executable dynamic water level control instructions under the premise of ensuring engineering safety (dead water level). SUMMARY

[0007] The technical problem to be solved by the present application is to provide a dynamic control method for supporting power grid supply guarantee of a cascade hydropower station, which is a boundary solution for the lower limit of the water level of a cascade control reservoir suitable for medium and long-term supply guarantee requirements. The result can be used as a water level control point in the integrated scheduling of water, wind and light in the cascade, that is, the water level of the cascade control reservoir should not be lower than the water level boundary during operation and scheduling, so as to ensure the support capacity of the cascade hydropower in the future supply guarantee period, and further improve the continuous power supply capacity of the integrated cluster of water, wind and light in the basin. Taking the Jinguan cascade project group as an application example, the lower limit of the water level of the leading reservoir Jinyi hydropower station is calculated, and the results show that the application can effectively determine the cascade supply guarantee warning and provide guidance for water level control. Compared with the traditional model based on the optimization of the objective function, the present application has the advantages of simple solution, convenient parameter adjustment, high calculation efficiency and quick response to real-time power grid supply instructions. The output result is intuitive and has strong interpretability, which can provide effective guidance for the supply guarantee warning and fine water level control of the cascade hydropower station.

[0008] The technical scheme of the present application is as follows:

[0009] A dynamic control method for supporting power grid supply guarantee of a cascade hydropower station, comprising the following steps:

[0010] Step (1): initial calculation condition collection.

[0011] Runoff data: collect long series of historical runoff data. Through the conversion of flow and runoff, and the accumulation of monthly runoff, the annual runoff is obtained. The mean, deviation coefficient and variation coefficient are obtained by using the Pearson III distribution curve to estimate the moment method, hydrological frequency calculation and line adjustment of the annual runoff. Finally, the design annual runoff under the hydrological guarantee rate of 10%, 50% and 90% is calculated. The daily runoff process corresponding to the hydrological guarantee rate close to 90% (i.e. the dry water representative year) is selected as the model input.

[0012] New energy data: download wind speed data, solar radiation intensity data and air temperature data from the European Meteorological Center open source dataset ERA5 (https: / / cds.climate.copernicus.eu / cdsapp#! / dataset / reanalysis-era5-single-levels?tab=app) to calculate the daily average output coefficient (output divided by installed capacity) of the wind power cluster and the daily average output coefficient of the photovoltaic cluster and use them as the model input.

[0013] Power station characteristic parameters: according to the water level, output, flow boundary specified in the scheduling regulations. Including normal high water level, flood control water level, dead water level, upper and lower limits of discharge flow and power generation flow, upper and lower limits of reservoir capacity, adjustable reservoir capacity value, etc.

[0014] Power station basic curve: water level-storage capacity relationship curve, tail water level-discharge relationship curve for interpolation.

[0015] According to the power supply requirements of the power grid, determine the power supply reference load rate of hydropower, wind power and photovoltaic, set the power supply period T cycle length (7 days and above), and determine the simulation period N time span.

[0016] Model data step: To reflect the extreme volatility of new energy for several consecutive days and the uncertainty of runoff, the step is set to one day.

[0017] Step (2): Solve the minimum discharge boundary of the upstream control hydropower station.

[0018] Assume that all bundled new energy planning capacities and hydropower stations in the cascade water, wind and light cluster have been put into production. Due to the small reservoir of the downstream daily regulation hydropower station of the cascade control hydropower station, the medium and long-term regulation effect of the power supply period T can be ignored, and the fixed water level operation mode is adopted.

[0019] Step (2.1) Calculate the power supply demand output of hydropower. According to the output basis of water, wind and light cluster (power supply reference load rate and new energy output credible capacity), calculate the total power supply reference load, and then deduct the actual output of bundled new energy to obtain the actual output demand list of downstream hydropower station per day in simulation period N. The calculation formula is as follows:

[0020]

[0021] In the formula: is the constrained target output of hydropower, is the installed capacity of hydropower, is the total power supply reference load, is the actual output of bundled new energy; wherein The calculation formula of is as follows:

[0022]

[0023] In the formula: represents the type of new energy, respectively representing hydropower, wind power and photovoltaic; is the installed capacity corresponding to the type of new energy, is the power supply reference load rate corresponding to the type of new energy.

[0024] Step (2.2) Solve the power generation flow corresponding to the power supply demand output by trial method. Since it is operated at a fixed water level, the initial and final water levels remain unchanged, and the minimum power generation flow per day is determined according to the actual power supply output. To solve the power generation flow of hydropower station, the algorithm adopts the method of "determining water by electricity". The algorithm flow of "determining water by electricity" is as follows:

[0025] The water head is solved by success-failure search algorithm in this step, which involves methods including dichotomy, optimization algorithm, and curve interpolation. The specific process is as follows. First, estimate the initial flow according to the water head experience value: the output calculation uses KQH to calculate the theoretical power generation flow required by dividing the target output by the comprehensive output coefficient and the water head experience value. If the estimated value is within the power generation flow boundary, the flow is taken as the initial flow of the algorithm, which is brought into the output formula calculation to obtain the corresponding actual output. The output calculation formula is as follows:

[0026]

[0027]

[0028] In the formula: is the output, is the comprehensive output coefficient, is the power generation flow, is the power generation water head, are the initial and final water levels, respectively, is the tail water level, which is obtained by curve interpolation according to the tail water level-discharge relationship.

[0029] Calculate the error and the target output minus the actual output. According to whether the error converges, determine the search direction. If the actual output is less than the target output, the power generation flow needs to be increased, otherwise it needs to be decreased. Adjust according to the step size a. The initial step size a is set according to the following formula:

[0030]

[0031] In the formula: is the given output, is the calculated output, is the maximum output, is the maximum power generation flow.

[0032] If the flow needs to be increased, the updated power generation flow is equal to the previous generation flow plus the step size, otherwise, the step size is reversed and halved. According to the success-failure search method, iterative search is performed. Set the maximum number of iterations and the minimum allowable error. If the conditions are met, exit the loop, stop searching and record the best power generation flow.

[0033] Step (2.3) solves the corresponding upstream discharge under the final power generation flow. Under the condition of known inflow in the downstream reservoir area, the power supply output demand of the downstream daily regulation hydropower station can be converted into the minimum outflow boundary of the upstream control hydropower station step by step by using water balance and hydraulic connection between upstream and downstream of the cascade.

[0034] The mathematical model of water balance is as follows:

[0035]

[0036] wherein: is the reservoir In the reservoir capacity at the end of the period (m 3 ), is the reservoir In the period, the inflow, power generation flow, and abandoned water flow of the reservoir (m 3 / s), is the length of the period (in seconds).

[0037] The cascade hydraulic connection model is as follows:

[0038]

[0039] wherein: is the reservoir In the period, the natural inflow of the reservoir (m 3 / s); is the water flow lag time from the upstream hydropower station to the hydropower station .

[0040] Step (2.4) obtains the daily minimum discharge boundary of the upstream control reservoir in the simulation period N, which is taken as a new constraint condition and brought into the calculation of the next step. This step can reflect the influence of the downstream power station's demand for power supply on the upstream cascade control reservoir.

[0041] Step (3): Obtain the lower limit of the power supply water level of the upstream control power station.

[0042] Step (3.1): Calculate the power supply demand of the cascade control power station, which is calculated in the same way as the downstream power station. According to the water, wind, and light cluster output benchmark (power supply benchmark load rate and new energy output credible capacity), the power supply benchmark total load is calculated, and then the actual output of the bundled new energy is deducted to obtain the actual output demand list of the upstream control power station in the simulation period N. The calculation formula is as follows:

[0043]

[0044] wherein: is the water power target output after constraint, is the water power installed capacity, is the power supply benchmark total load, is the actual output of the bundled new energy; wherein The calculation formula of

[0045]

[0046] wherein: New energy type, respectively, hydropower, wind power, photovoltaic, For the installed capacity corresponding to the new energy type, For the installed capacity corresponding to the new energy type,

[0047] Step (3.2) compares the minimum outflow calculated in step (2) with the minimum outflow in the dispatching rules to obtain a new outflow boundary.

[0048] Step (3.3) assumes that one day in simulation period N is , and considers the supply period T as the calculation window, and the last day of the supply support period is the dead water level, and the daily forward recursion optimization is used to solve the daily initial water level limit of the cascade control hydropower station with the daily power generation capacity greater than or equal to the actual power demand, until , the final daily water level boundary result is obtained.

[0049] Step (3.4) summarizes the optimization solution process as solving the power generation flow under the corresponding supply demand power using the trial method, and determining the minimum daily power generation flow according to the actual supply power, and the algorithm uses the "electricity determines water" algorithm. The process is as follows:

[0050] The electricity determines water in this step is different from step 2, and is solved by combining the Runge-Kutta numerical algorithm and the success-failure search algorithm, which involves methods such as bisection method, optimization algorithm, and curve interpolation. The specific process is as follows. First, estimate the initial flow according to the head experience value: the outflow calculation uses KQH calculation, and the target outflow divided by the comprehensive outflow coefficient and the head experience value can obtain the theoretical required power generation flow. If the estimated value is within the power generation flow boundary, then this flow is taken as the initial flow of the algorithm, which is brought into the outflow calculation formula to obtain the corresponding actual outflow. The outflow calculation formula is as follows:

[0051]

[0052]

[0053] In the formula: is the outflow, represents the comprehensive outflow coefficient, represents the power generation flow, represents the power generation head, are the initial and final water levels of the period, is the tail water level, which is obtained by curve interpolation according to the tail water level-outflow relationship.

[0054] And the calculation of the period end water level uses the fourth-order Runge-Kutta method, and the reservoir capacity change is described by the continuity equation as follows:

[0055]

[0056] In the formula: For storage capacity, The incoming water flow rate This refers to the outflow from the reservoir (including power generation flow and wastewater discharge flow).

[0057] at discrete time step Within 24 hours, the fourth-order Runge-Kutta method (RK4) is used to solve for the change in reservoir capacity in reverse. The differential equation for the change in reservoir capacity over time is defined as a function (note: the time step is negative during reverse calculation):

[0058]

[0059] The steps and formulas for RK4 are as follows:

[0060]

[0061]

[0062] In the formula: Indicates the initial storage capacity for the period. This represents the reservoir capacity at the end of the time period. In this way, the reservoir capacity at the beginning of the time period (24 hours ago) can be deduced from the known end reservoir capacity (obtained by interpolation of dead water level), and this deduction can be continued until the beginning of the supply guarantee period.

[0063] in The outflow rate is a function related to reservoir capacity, including power generation flow and water release. The calculation formula is as follows:

[0064]

[0065] In the formula: Let represent power generation flow and water discharge, respectively. Both are related to reservoir capacity and are obtained through trial calculations using a success-failure search method. Each iteration calculates the power generation flow, and then updates the reservoir capacity using a fourth-order Runge-Kutta method. Derivative to flow rate Storage capacity Storage capacity calculation also depends on This forms a nested iteration.

[0066] The success-failure search method involves the following steps: Calculate the error and the target output minus the actual output, using this as the optimization function value. Determine the search direction based on whether the error converges. If the actual output is less than the target output, increase the power generation flow rate; otherwise, decrease it. Adjustments are made according to the step size 'a'. The initial step size 'a' is set using the following formula:

[0067]

[0068] In the formula: For a given output, To calculate the output force, To maximize output, This represents the maximum power generation flow rate.

[0069] If a larger flow rate is needed, the updated power generation flow rate equals the sum of the previous generation's power generation flow rate and the step size; conversely, the step size is reversed and halved. An iterative search is performed using a success-failure search method, setting a maximum number of iterations and a minimum allowable error. The loop exits when the condition is met, the search stops, and the optimal power generation flow rate is recorded. Nested iteration consists of an outer iteration (success-failure search method) and an inner iteration (RK4 method).

[0070] Step (3.5) The condition for water discharge is whether the initial reservoir capacity of the calculated period is higher than the reservoir capacity under normal water storage level. If it is higher, water discharge is required. The total discharge flow is equal to the sum of the power generation flow and the water discharge flow, which is used to calculate the initial reservoir capacity of the period for water balance.

[0071] The mathematical model for water balance is as follows:

[0072]

[0073] In the formula: For reservoir exist Storage capacity at the end of the period (m) 3 ); Reservoirs exist Inflow, power generation, and wastewater discharge (m³) during the specified time period 3 / s); The number of seconds for each time period.

[0074] Step (3.6) uses interpolation to obtain the initial water level for each time period and then corrects it. The obtained initial water level result must meet the water level constraint. If the initial water level is higher than the normal high water level, it is corrected to the normal high water level. This indicates that even if the head reservoir operates at the normal high water level during the supply guarantee period, the cascade will not meet the supply guarantee period requirements due to insufficient water inflow or excessive hydropower generation caused by insufficient renewable energy generation. If the initial water level is lower than the dead water level, it is corrected to the dead water level. This indicates that even if the head reservoir maintains the dead water level without leaving excess storage capacity during the supply guarantee period, the cascade will still meet the supply guarantee requirements due to sufficient water inflow or low hydropower generation demand. The mathematical expression is as follows:

[0075]

[0076] In the formula, For hydroelectric power station No. Water level over a period of time, in meters. For hydroelectric power station No. Normal high water level for a given period, in meters (m). For hydroelectric power station No. Dead water level for a given period, in meters (m).

[0077] Step (3.7) Dynamic result output: The simulation period N is the total time range for constructing a complete forward-looking dynamic lower limit water level control curve, covering multiple supply guarantee periods T, reflecting the continuous dynamic control process under long-term scheduling background. A rolling calculation control strategy is adopted during the simulation period: each day forward (time step is one day), the supply guarantee period T window is moved forward by one day, and the reverse iterative calculation is re-executed. That is, each time, starting from a new initial date, a control interval of length T is extended forward to construct a new supply guarantee period T water level lower limit calculation window. The water level lower limit control results obtained from each rolling calculation are summarized and connected in chronological order to form a dynamic control curve for the lower limit water level of the cascade hydropower stations covering the entire simulation period N. Different lengths of supply guarantee periods T (such as 7 days, 10 days, 15 days, 30 days) can be set according to actual scheduling needs, and the optimization results under different supply guarantee periods can be compared and analyzed to evaluate the model's adaptability and regulation effect.

[0078] The beneficial effects of this invention are as follows: This invention first constructs a water level determination algorithm based on electricity demand, combining a fourth-order Runge-Kutta method and a success-failure search method, and uses a rolling window period reverse recursion method to solve for the lower limit of the operating water level for power supply guarantee. This method considers the nonlinearity of the hydropower generation function and the hydraulic connection between upstream and downstream cascades, and provides a dynamic control scheme for the lower limit of the water level to support the power grid's power supply needs in the event of extreme weather or reduced power generation due to bundled renewable energy sources. Based on this, it provides a medium- to long-term control cycle of 7 days or more, which can tap the cross-seasonal regulation potential of hydropower bases. This method proposes a water level determination algorithm based on electricity demand, coupled with a fourth-order Runge-Kutta method and a success-failure search method, combined with a reverse recursion method that directly reflects the physical process to solve for the lower limit of operation. This algorithm does not use the traditional objective function-driven optimization model, and has the advantages of simple solution, easy parameter adjustment, low computation time without large-scale matrix operations, and the ability to respond to real-time power grid power supply guarantee commands. Furthermore, the output results of the reverse recursion method are more intuitive and have better interpretability. This invention proposes for the first time a rapid calculation method for the lower limit boundary of water level in cascade control reservoirs that meets the needs of medium- and long-term water supply, effectively providing guidance for cascade water supply early warning and water level control. Attached Figure Description

[0079] Figure 1 This is a roadmap of the overall solution technology of the present invention;

[0080] Figure 2 and Figure 3 These are runoff input data diagrams for the Jin Yi and Guan Di hydropower stations, respectively.

[0081] Figure 4 and Figure 5 These are the daily power output coefficients of wind power and photovoltaic clusters, respectively.

[0082] Figure 6 This is a comparison chart of the calculation results of the lower limit of water level for multiple supply guarantee periods. Detailed Implementation

[0083] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0084] This embodiment uses the Jinguan hydro-wind-solar integrated project cluster located in the Yalong River Basin of Sichuan Province as an implementation case to verify the present invention. The Yalong River Basin has abundant hydro-wind-solar clean energy resources. Faced with the problem of high-level consumption and supply security of such a large-scale hydro-wind-solar renewable energy source, there is an urgent need to answer how to avoid the problem of supply support caused by the excessively low operating position of the leading hydropower station, and to provide a technology for solving the lower limit boundary of the supply water level of cascade control reservoirs that can be used for a supply guarantee period of more than 7 days.

[0085] Step (1): Collection of initial calculation conditions.

[0086] Runoff Data: Monthly flow and inter-regional inflow data for the Jinping I and Guandi hydropower stations from 1993 to 2023 were collected for a total of 31 years. By converting flow to runoff and summing the monthly runoff, the annual runoff for the 31 years was obtained. Using the Pearson Type III distribution curve, the annual runoff was estimated using the method of moments, hydrological frequency calculation, and alignment adjustment to obtain the mean, coefficient of deviation, and coefficient of variation. Finally, the design annual runoff under three hydrological guarantee rates of 10%, 50%, and 90% was statistically calculated. The daily runoff process in 2023, corresponding to a hydrological guarantee rate close to 90% (i.e., a dry year), was selected as the model input. (See...) Figure 2 and Figure 3 .

[0087] New energy data: Hourly wind speed data, solar radiation intensity data, and air temperature data for the Yalong River basin in 2023 were downloaded from the European Centre for Meteorological Research (ECMR) open-source dataset ERA5 (https: / / cds.climate.copernicus.eu / cdsapp#! / dataset / reanalysis-era5-single-levels?tab=app). The daily average power output coefficient (output divided by installed capacity) of the wind power cluster and the daily average power output coefficient of the photovoltaic cluster in the Jinguan project group were calculated using power output data from surrounding operational new energy power plants and historical meteorological data from 2023, and used as model inputs. Due to data availability limitations, it is temporarily assumed that the power output coefficients of the new energy clusters connected to Jinyi and Guandi are the same. See [link to new energy power output coefficients]. Figure 4 andFigure 5 The overall data collection process is as follows: Figure 1 Module 1.

[0088] Power plant characteristic parameters: water level, output, and flow boundaries as specified in the dispatching regulations. These include normal high water level, flood control limit water level, dead water level, upper and lower limits of outflow and power generation, upper and lower limits of reservoir capacity, and adjustable reservoir capacity, etc.

[0089] Basic curves of the power station: water level-reservoir capacity relationship curve and tailwater level-discharge flow relationship curve are used for interpolation.

[0090] Supply guarantee load rate and period: The supply guarantee load rate for hydropower stations is set at 70% of installed capacity, for wind power clusters at 30% of installed capacity, and for photovoltaic clusters at 20% of installed capacity. The supply guarantee period is set at 7 days, 10 days, 15 days, and 30 days. The simulation period N spans the entire year of 2023.

[0091] Model data step size: To reflect the extreme volatility of new energy sources over multiple days and the uncertainty of runoff, the step size is set to daily.

[0092] Step (2): Solve for the minimum outflow boundary of the upstream controlling hydropower station.

[0093] Assuming that all bundled new energy planned capacity and hydropower stations within the Jinguan cascade hydro-wind-solar cluster have been put into operation, and since the Guandi Reservoir, the daily regulating hydropower station downstream of Jinping I, the first-level cascade control hydropower station, is relatively small, its medium- and long-term regulating effect during the supply guarantee period T can be ignored, and a constant water level operation mode is adopted.

[0094] Step (2.1) calculates the power output required for supply guarantee by the hydropower station. Based on the power output benchmarks of the hydropower-wind-solar cluster (power supply benchmark load rate and reliable capacity of new energy output), the total power supply benchmark load is calculated. Then, the actual output of bundled new energy is deducted to obtain the daily actual power output demand list for the downstream hydropower station during the simulation period N. The calculation formula is as follows:

[0095]

[0096] In the formula: To generate power for the constrained hydropower target, For hydropower installed capacity, To ensure the supply of the baseline total load, To make actual contributions to the bundling of new energy, among which The calculation formula is as follows:

[0097]

[0098] In the formula: These indicate the types of new energy sources, specifically hydropower, wind power, and photovoltaic power. To correspond to the installed capacity of new energy types, This is the benchmark load rate for ensuring the supply of the corresponding new energy type.

[0099] Step (2.2) uses a trial-and-error algorithm to determine the power generation flow rate under the corresponding power supply demand. Since the initial and final water levels remain constant during constant water level operation, the minimum daily power generation flow rate is determined based on the actual power supply output. The algorithm for determining the hydropower station's power generation flow rate adopts a "power-determined water" approach, see [link to relevant documentation]. Figure 1 Module 2. The algorithm flow for determining water usage by electricity is as follows:

[0100] In this step, the power-to-water ratio is determined using a success-failure search algorithm, which involves methods such as bisection, optimization algorithms, and curve interpolation. The specific process is as follows: First, the initial flow rate is estimated based on the empirical head value. The power output is calculated using KQH. Dividing the target power output by the comprehensive power output coefficient and the empirical head value yields the theoretically required power generation flow rate. If the estimated value is within the power generation flow rate boundary, this flow rate is used as the initial flow rate for the algorithm. It is then substituted into the power output formula to obtain the corresponding actual power output. The power output calculation formula is as follows:

[0101]

[0102]

[0103] In the formula: To contribute, Indicates the overall output coefficient. Indicates power generation flow rate. Indicates the head of the generator. These represent the water levels at the beginning and end of the time period, respectively. The tailwater level is obtained by interpolation based on the tailwater level-discharge flow rate relationship curve.

[0104] The calculation involves subtracting the actual output from the target output. The search direction is determined based on whether the error converges. If the actual output is less than the target output, the power generation flow rate needs to be increased; conversely, if it is greater, the flow rate should be decreased. Adjustments are made according to a step size 'a'. The initial step size 'a' is set using the following formula:

[0105]

[0106] In the formula: For a given output, To calculate the output force, To maximize output, This represents the maximum power generation flow rate.

[0107] If a larger flow rate is needed, the updated power generation flow rate equals the sum of the previous generation's power generation flow rate and the step size; otherwise, the step size is reversed and halved. An iterative search is performed using a success-failure search method, setting a maximum number of iterations and a minimum allowable error. The loop exits when the conditions are met, the search stops, and the optimal power generation flow rate is recorded.

[0108] Step (2.3) solves for the upstream discharge flow corresponding to the final power generation flow. Using water balance and the hydraulic connection between upstream and downstream of the cascade, under the condition that the inflow of water in the downstream reservoir section is known, the daily power supply demand of the downstream regulating hydropower station can be converted into the minimum outflow boundary of the upstream controlling hydropower station step by step.

[0109] The mathematical model for water balance is as follows:

[0110]

[0111] In the formula: For reservoir exist Storage capacity at the end of the period (m) 3 ); Reservoirs exist Inflow, power generation, and wastewater discharge (m³) during the specified time period 3 / s); The number of seconds for each time period.

[0112] The cascade hydraulic connection model is as follows:

[0113]

[0114] In the formula: For reservoir Natural inflow runoff during the time period (m3 / s); For upstream hydropower stations in the cascade To the hydroelectric power station The water flow stagnates.

[0115] Step (2.4) yields the daily minimum discharge boundary of the upstream controlling reservoir during the simulation period N, which is then used as a new constraint in the calculation of the next step. This step reflects the impact of the downstream power station's supply demand on the upstream cascade controlling reservoirs.

[0116] Step (3): Determine the lower limit of the water level for the upstream control power station to ensure water supply.

[0117] Step (3.1) Calculate the power output required to meet the supply needs of the cascade control hydropower stations, using the same method as the downstream power stations. Calculate the total supply benchmark load based on the power output benchmark of the hydro-wind-solar cluster (supply benchmark load rate and reliable capacity of new energy output), then subtract the actual output of bundled new energy sources to obtain the daily actual power output demand list for the upstream control power stations during the simulation period N. The calculation formula is as follows:

[0118]

[0119] In the formula: To generate power for the constrained hydropower target, For hydropower installed capacity, To ensure the supply of the baseline total load, To make actual contributions to the bundling of new energy, among which The calculation formula is as follows:

[0120]

[0121] In the formula: These indicate the types of new energy sources, specifically hydropower, wind power, and photovoltaic power. To correspond to the installed capacity of new energy types, This is the benchmark load rate for ensuring the supply of the corresponding new energy type.

[0122] Step (3.2) compares the minimum outflow from step (2) with the minimum discharge flow in the scheduling procedure to obtain a new discharge flow boundary.

[0123] Step (3.3) assumes that one day in the simulation period N is The day is considered as the calculation window, with the supply guarantee period T being the last day of the supply guarantee support cycle. The day-end water level is set at the dead water level of 1800m. The optimization solution is then used to iteratively calculate the lower limit of the initial water level for each day's control hydropower station, ensuring that the daily power generation capacity is greater than or equal to the actual output demand, until... Finally, the daily water level boundary results were obtained. See the diagram for the supply guarantee and downstream production line optimization method. Figure 1 Module 3.

[0124] Step (3.4) optimization process can be summarized as follows: using a trial-and-error algorithm to solve for the power generation flow rate under the corresponding supply demand, determining the minimum daily power generation flow rate according to the actual supply demand, and the algorithm adopts the "electricity-determined water" approach. Figure 1 Module 2. The algorithm flow for determining water usage by electricity is as follows:

[0125] The method of determining water flow based on electricity differs from step 2. It combines the Runge-Kutta numerical algorithm with a success-failure search algorithm for solution. Methods involved include bisection, optimization algorithms, and curve interpolation. The specific process is as follows: First, the initial flow rate is estimated based on empirical head values. Power output is calculated using the KQH algorithm. Dividing the target output by the comprehensive output coefficient and the empirical head value yields the theoretically required power generation flow rate. If the estimated value is within the power generation flow rate boundary, this flow rate is used as the initial flow rate for the algorithm. This flow rate is then substituted into the output formula to obtain the corresponding actual output. The output calculation formula is as follows:

[0126]

[0127]

[0128] In the formula: To contribute, Indicates the overall output coefficient. Indicates power generation flow rate. Indicates the head of the generator. These represent the water levels at the beginning and end of the time period, respectively. The tailwater level is obtained by interpolation based on the tailwater level-discharge flow rate relationship curve.

[0129] The calculation of the water level at the end of the period is performed using the fourth-order Runge-Kutta method. The change in reservoir capacity is described by the continuity equation as follows:

[0130]

[0131] In the formula: For storage capacity, The incoming water flow rate This refers to the outflow from the reservoir (including power generation flow and wastewater discharge flow).

[0132] at discrete time step Within 24 hours, the fourth-order Runge-Kutta method (RK4) is used to solve for the change in reservoir capacity in reverse. The differential equation for the change in reservoir capacity over time is defined as a function (note: the time step is negative during reverse calculation):

[0133]

[0134] The steps and formulas for RK4 are as follows:

[0135]

[0136]

[0137] In the formula: Indicates the initial storage capacity for the period. This represents the reservoir capacity at the end of the time period. In this way, the reservoir capacity at the beginning of the time period (24 hours ago) can be deduced from the known end reservoir capacity (obtained by interpolation of dead water level), and this deduction can be continued until the beginning of the supply guarantee period.

[0138] in The outflow rate is a function related to reservoir capacity, including power generation flow and water release. The calculation formula is as follows:

[0139]

[0140] In the formula: Let represent power generation flow and water discharge, respectively. Both are related to reservoir capacity and are obtained through trial calculations using the success-failure search method, which will be introduced later. In this way, the power generation flow is iterated once each time, and the reservoir capacity is updated using a fourth-order Runge-Kutta method. Derivative to flow rate Storage capacity Storage capacity calculation also depends on This forms a nested iteration.

[0141] The success-failure search method involves the following steps: Calculate the error and the target output minus the actual output, using this as the optimization function value. Determine the search direction based on whether the error converges. If the actual output is less than the target output, increase the power generation flow rate; otherwise, decrease it. Adjustments are made according to the step size 'a'. The initial step size 'a' is set using the following formula:

[0142]

[0143] In the formula: For a given output, To calculate the output force, To maximize output, This represents the maximum power generation flow rate.

[0144] If a larger flow rate is needed, the updated power generation flow rate equals the sum of the previous generation's power generation flow rate and the step size; conversely, the step size is reversed and halved. An iterative search is performed using a success-failure search method, setting a maximum number of iterations and a minimum allowable error. The loop exits when the condition is met, the search stops, and the optimal power generation flow rate is recorded. Nested iteration consists of an outer iteration (success-failure search method) and an inner iteration (RK4 method).

[0145] Step (3.5) The condition for water discharge is whether the initial reservoir capacity of the calculated period is higher than the reservoir capacity under normal water storage level. If it is higher, water discharge is required. The total discharge flow is equal to the sum of the power generation flow and the water discharge flow, which is used to calculate the initial reservoir capacity of the period for water balance.

[0146] The mathematical model for water balance is as follows:

[0147]

[0148] In the formula: For reservoir exist Storage capacity at the end of the period (m) 3 ); Reservoirs exist Inflow, power generation, and wastewater discharge (m³) during the specified time period 3 / s); The number of seconds for each time period.

[0149] Step (3.6) uses interpolation to obtain the initial water level for each time period and then corrects it. The obtained initial water level result must meet the water level constraint. If the initial water level is higher than the normal high water level by 1880m, it is corrected to the normal high water level. This indicates that even if the head reservoir operates at the normal high water level during the supply guarantee period, the cascade will not meet the supply guarantee period requirements due to insufficient water inflow or excessive hydropower generation caused by insufficient renewable energy generation. If the initial water level is lower than the dead water level, it is corrected to the dead water level. This indicates that even if the head reservoir maintains the dead water level without leaving excess storage capacity during the supply guarantee period, the cascade will still meet the supply guarantee requirements due to sufficient water inflow or low hydropower generation demand. The mathematical expression is as follows:

[0150]

[0151] In the formula, For hydroelectric power station No. Water level over a period of time, in meters. For hydroelectric power station No. Normal high water level for a given period, in meters (m). For hydroelectric power station No. Dead water level for a given period, in meters (m).

[0152] Step (3.7) Dynamic result output: The simulation period N is the total time range for constructing a complete forward-looking dynamic lower limit water level control curve, covering multiple supply guarantee periods T, reflecting the continuous dynamic control process under long-term scheduling background. A rolling calculation control strategy is adopted during the simulation period: each day forward (time step is one day), the supply guarantee period T window is moved forward by one day, and the reverse iterative calculation is re-executed. That is, each time, starting from a new initial date, a control interval of length T is extended forward to construct a new supply guarantee period T water level lower limit calculation window. The water level lower limit control results obtained from each rolling calculation are summarized and connected in chronological order to form a dynamic control curve for the lower limit water level of the cascade hydropower stations covering the entire simulation period N. Different lengths of the supply guarantee period T can be set according to actual scheduling needs (in this case, they are set to 7 days, 10 days, 15 days, and 30 days respectively), and the optimization results under different supply guarantee periods are compared and analyzed to evaluate the model's adaptability and regulation effect.

[0153] Analyze the calculation results, see Figure 6 It can be seen that the longer the supply guarantee period, the higher the lower limit of the water level. The diagram shows the cascade supply guarantee coordinated control method:

[0154] From January to early June, the lower limit of the water level for ensuring water supply needs to be stabilized at a certain level according to the water supply cycle in order to cope with extreme water inflows and insufficient power generation of new energy sources. Specifically, the lower limit of the water level for the 7-day water supply period needs to be maintained at around 1816 meters, the lower limit of the water level for the 10-day water supply period needs to be maintained at around 1822 meters, the lower limit of the water level for the 15-day water supply period needs to be maintained at around 1831 meters, and the lower limit of the water level for the 30-day water supply period needs to be maintained at around 1854 meters.

[0155] Before mid-June: The lower limit of the water supply level for the 7-30 day cycle needs to be kept above the dead water level to cope with the low runoff.

[0156] From mid-June to mid-July, the lower limit of the water level needs to be raised by about 10 meters above the dead water level to retain some energy storage in order to cope with extreme situations.

[0157] In late July, the water inflow is abundant and concentrated, and the lower limit of the water level may briefly drop to the dead water level of 1800 meters.

[0158] From mid-September to the end of the year, the overall runoff will decrease, and the lower limit of the water level needs to be gradually raised according to the length of the supply guarantee period, and it needs to rise back to the level at the beginning of the year by the end of the year.

Claims

1. A cascade hydropower station water level lower limit dynamic control method for supporting power grid supply, characterized in that, The steps are as follows: Step (1): initial calculation of conditions collection; The calculation conditions include runoff data, power station characteristic parameters, and power station basic curve; The supply guarantee period T cycle length is set, and the N time span of the simulation period is determined; The model data step is set to day; Step (2): solving the minimum outflow boundary of the upstream control hydropower station; Step (2.1): calculating the supply guarantee demand output of the hydropower station, calculating the supply guarantee total load according to the water, wind and light cluster output benchmark, i.e. the supply guarantee load rate and the new energy output credible capacity, and then deducting the bundled new energy actual output to obtain the actual output demand list of the downstream hydropower station in the simulation period N; The calculation formula is as follows: In the formula: is the water and electricity target output after constraint, is the water and electricity installed capacity, is the total load of the supply guarantee reference, is the actual output of the bundled new energy; wherein The calculation formula is as follows: In the formula: represents a new energy type, and respectively represents water power, wind power, and photovoltaic power; is the installed capacity corresponding to the new energy type, is the load rate corresponding to the new energy type. Step (2.2): solving the power generation flow under the corresponding supply guarantee demand output by using the trial method, so the initial and final water levels remain unchanged, and the minimum power generation flow of each day is determined according to the actual supply guarantee output; the power generation flow of the hydropower station is solved, and the "electricity determines water" algorithm is used; the process of the "electricity determines water" algorithm is as follows: The successful and failed search algorithm is used for solving, and the specific process is as follows: first, estimate the initial flow according to the water head empirical value: the output calculation uses KQH to calculate, the target output is divided by the comprehensive output coefficient and the water head empirical value to obtain the theoretical power generation flow required, if the estimated value is within the power generation flow boundary, then the flow is taken as the initial flow of the algorithm, which is brought into the output formula calculation to obtain the corresponding actual output, the output calculation formula is as follows: In the formula: is the output, represents the comprehensive output coefficient, represents the power generation flow, represents the power generation water head, , are the initial and final water levels of the period, respectively, is the tail water level, which is obtained by interpolation according to the tail water level-discharge relationship curve; Calculate the error and the target output minus the actual output, and determine the search direction according to whether the error converges, if the actual output is less than the target output, then the power generation flow needs to be increased, otherwise it needs to be reduced, and the step a is adjusted; If the flow needs to be increased, then the updated power generation flow is equal to the sum of the last generation flow and the step, otherwise, the step is reversed and halved; Iterative search is performed according to the successful and failed search method, the maximum number of iterations and the minimum allowable error are set, the condition is met to jump out of the loop, the search is stopped and the best power generation flow is recorded; Step (2.3): solving the corresponding upstream discharge flow under the final power generation flow, using water balance and the hydraulic connection between the upstream and downstream of the cascade, under the condition that the inflow of the downstream reservoir area is known, the supply guarantee output demand of the downstream daily regulation hydropower station can be converted into the minimum outflow boundary of the upstream control hydropower station step by step; Step (2.4): obtaining the minimum discharge flow boundary of the upstream control reservoir in the simulation period N, which is taken as a new constraint condition and brought into the calculation of the next step; Step (3): obtaining the lower limit of the supply guarantee water level of the upstream control power station; Step (3.1): calculating the supply guarantee demand output of the cascade control hydropower station, the calculation method is the same as that of the downstream power station; calculating the supply guarantee total load according to the water, wind and light cluster output benchmark, i.e. the supply guarantee load rate and the new energy output credible capacity, and then deducting the bundled new energy actual output to obtain the actual output demand list of the upstream control power station in the simulation period N; Step (3.2): comparing the minimum outflow calculated in step (2) with the minimum discharge in the dispatching rules to obtain a new discharge boundary; Step (3.3) assumes a day in simulation period N as the calculation window, and the last day of the support period as the end water level, and recursively solves the lower limit of the initial water level of each day for the power generation capacity of the cascade control hydropower station to be greater than or equal to the actual power output demand, until the final day, and finally obtains the water level boundary results of each day ; The process of step (3.4) optimization solution is summarized as follows: the power generation flow under the corresponding supply-demand output is solved by trial method, the minimum power generation flow per day is determined according to the actual supply-demand output, and the "water by electricity" algorithm is used; the process of water by electricity algorithm is as follows: The Runge-Kutta method and the success-failure search algorithm are combined to solve the problem, and the specific process is as follows: firstly, the initial flow is estimated according to the water head experience value: the output calculation uses KQH calculation, the target output is divided by the comprehensive output coefficient and the water head experience value to obtain the theoretical required power generation flow, if the estimated value is within the boundary of power generation flow, the flow is taken as the initial flow of the algorithm, which is brought into the output formula calculation to obtain the corresponding actual output, the output calculation formula is as follows: In the formula: is the output, represents the comprehensive output coefficient, represents the power generation flow, represents the power generation water head, are the initial and final water levels of the period, respectively, is the tail water level, which is obtained by interpolation according to the tail water level-discharge relationship curve; And the calculation of the water level at the end of the period uses the fourth-order Runge-Kutta method, and the reservoir capacity change is described by the continuity equation as follows: In the formula: is the storage capacity, is the inflow; is the outflow, including the power generation flow and the abandoned water flow; At discrete time steps Within each time step, the change in storage volume is solved backwards using the fourth-order Runge-Kutta method, RK4; the differential equation for the change in storage volume over time is defined as a function: The step formula of RK4 is as follows: In the formulae: denotes the initial reservoir volume at the beginning of the period, denotes the final reservoir volume at the end of the period; Thus, the initial reservoir capacity at the beginning of the period is obtained from the known final reservoir capacity, and the initial reservoir capacity at the beginning of the period is continuously obtained until the beginning of the supply period; wherein Qout represents the outflow, is a function of the reservoir capacity, and includes the power generation flow and the abandoned water amount, and the calculation formula is as follows: wherein: respectively represent the power generation flow and the abandoned water, both of which are related to the reservoir capacity, and are obtained by trial and error; the power generation flow is updated once per trial iteration, and the reservoir capacity is updated by the fourth-order Runge-Kutta, the outflow depends on the reservoir capacity, the reservoir capacity calculation depends on , forming a nested iteration; The success-failure search method steps are as follows: calculate the error and the target output minus the actual output as the function value of optimization, determine the search direction according to whether the error converges, if the actual output is less than the target output, the power generation flow needs to be increased, otherwise the power generation flow needs to be decreased, and the step size a is adjusted; If the flow needs to be increased, the updated power generation flow is equal to the sum of the last generation flow and the step size, otherwise, the step size is reversed and halved; According to the success-failure search method, the maximum iteration number and the minimum allowable error are set, the conditions are met to jump out of the loop, the search is stopped and the best power generation flow is recorded; The nested iteration is composed of the success-failure search method of the outer iteration and the RK4 method of the inner iteration; The judgment condition of step (3.5) is whether the calculated initial reservoir capacity at the beginning of the period is higher than the reservoir capacity under the normal water level, if it is higher, water needs to be abandoned, and the total discharge flow is equal to the sum of the power generation flow and the abandoned water flow, which is used for water balance to obtain the initial reservoir capacity at the beginning of the period; Step (3.6) uses interpolation to obtain the initial water level of each period, and corrects it; the obtained initial water level result needs to meet the water level limit constraint, if the initial water level is higher than the normal high water level, it is corrected to the normal high water level; if the initial water level is lower than the dead water level, it is corrected to the dead water level; the mathematical expression is as follows: wherein is the water power station the water level of the time period, in m, is the water power station the normal high water level of the time period, in m, is the water power station the dead water level of the time period, in m; Step (3.7) outputs the dynamic results, the rolling calculation control strategy is used in the simulation period: every day, the supply period T window is moved one day forward, and the reverse iteration calculation is performed again; that is, every time a new initial date is taken as the starting point, a control interval with a length of T is extended forward, a new supply period T water level lower limit calculation window is constructed; the water level lower limit control results obtained by each rolling calculation are summarized and connected in time sequence, which can form the cascade headwater water level lower limit dynamic control curve covering the entire simulation period N.

2. The method according to claim 1, characterized in that, The data in step (1) includes: Runoff data: Collect long series of historical runoff data; through the conversion of flow and runoff, and the accumulation of monthly runoff, the annual runoff is obtained; the mean, coefficient of deviation and coefficient of variation are obtained by using Pearson III distribution curve to estimate the annual runoff by moment method, hydrological frequency calculation and curve fitting adjustment; finally, the design annual runoff under the hydrological guarantee rate of 10%, 50% and 90% is calculated; the daily runoff process corresponding to the hydrological guarantee rate close to 90% is selected as the model input; New energy data: download wind speed data, solar radiation intensity data and air temperature data from the open source dataset ERA5 of the European Meteorological Center; calculate the daily average output coefficient of wind power cluster and the daily average output coefficient of photovoltaic cluster and use them as model inputs; Power station characteristic parameters: according to the water level, output and flow boundaries specified in the dispatching regulations; including normal high water level, flood control water level, dead water level, upper and lower limits of discharge flow and power generation flow, upper and lower limits of reservoir capacity, adjustable reservoir capacity value; Power station basic curve: water level-storage capacity curve, tail water level-discharge flow curve for interpolation.

3. The method according to claim 1, characterized in that, In steps (2.3) and (3.5), the mathematical model of water balance is as follows: In the formula: V is the reservoir At the end of the period; V is the reservoir At the inflow, power generation flow, and abandoned water flow of the period; is the number of seconds for each period; In step (2.3), the cascade hydraulic connection model is as follows: wherein: is the reservoir natural inflow to the reservoir during the time period; is the upstream hydropower plant to the hydropower plant water flow lag time.

4. The method according to claim 1, characterized in that, In steps (2.2) and (3.4), the initial step a is set according to the following formula: wherein: Pmax is the maximum output, Pcalc is the calculated output, Pmax is the maximum output, Pmax is the maximum output.

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