Cascade hydroelectric medium-term random water level control method considering wind power random deviation

Abstract

The invention provides a cascade hydroelectric medium-term random water level control method considering wind power random deviation, and belongs to the field of novel power system dispatching. The method comprises the following steps: collecting water power and wind power actual operation and boundary condition data; clustering historical output data of the wind power plant to form a typical output scene; constructing a joint probability of each regional wind power plant group, and generating a group of time sequence output scenes of all wind power plants in the region; based on the wind power output scene, solving the cascade hydropower maximum generating capacity considering the wind power output uncertainty; respectively solving a planned water level process and a water level process under wind power in each scene to obtain a cascade hydropower water level control interval for coping with wind power uncertainty, and analyzing interval change characteristics under different water incoming conditions and different scene numbers. According to the method, the water level control interval of each cascade hydropower station can be obtained under many restrictions and wind power output uncertainty, and the method can be applied to actual dispatching work.

Description

Technical Field

[0001] This invention belongs to the field of novel power system dispatching and relates to a method for medium-term stochastic water level control of cascade hydropower considering the random deviation of wind power. Background Technology

[0002] In recent years, the installed capacity of new energy sources such as wind power and photovoltaics has continuously broken new records, and their share in the total installed capacity of the power grid has rapidly increased, gradually forming a new type of power system dominated by clean energy. Against this backdrop, understanding the operating characteristics of various power sources, improving the flexibility of regulating power sources, and promoting energy consumption to ensure the balance of power grid supply and demand have become the main research directions in the field of energy and power system dispatching. High-proportion renewable energy systems exhibit the characteristics of "stochastic superposition and counter-regulation," making it difficult for traditional deterministic dispatching methods to simultaneously achieve real-time balance and economic operation. It is urgent to address the inherent uncertainty to improve the power grid's supply guarantee and new energy consumption capabilities. In the existing power dispatching system, cascade hydropower, with its flexible start-stop and excellent regulation performance, has become an important regulating energy source for the power system. Therefore, fully exploring the regulation potential of cascade hydropower is of great significance for improving the stability and security of the power system. Hydropower has multiple guarantee and control requirements during critical dispatching periods such as the flood season and water supply season. Rationally determining the water level control range of hydropower stations is crucial for ensuring the safe operation of hydropower. From the perspective of hydropower supply and renewable energy consumption, excessively low water levels at hydropower stations lead to insufficient regulation capacity and reduced power supply support; conversely, excessively high water levels result in insufficient reservoir storage space, failing to provide adequate space for renewable energy consumption. From the perspective of scheduling cycles, long-term scheduling focuses on hydropower operation trends and power supply capacity, while short-term scheduling focuses on real-time operation and feasibility. Long-term and short-term scheduling need to be linked through medium-term scheduling to achieve dual guarantees of long-term supply and short-term safety. Due to the uncertainty of real-time operation, long-term scheduling is difficult to execute as planned, and hydropower operation has strong spatiotemporal correlation; the current operating status is affected by previous periods and continues to influence subsequent periods. Therefore, medium-term coordinated scheduling is needed to mitigate short-term operational deviations. The challenge lies in the nonlinearity of hydropower operation, the uncertainty of renewable energy output, and the spatiotemporal coupling. Therefore, characterizing the uncertainty of renewable energy directly affects the hydropower station's water level control range and operational safety. Summary of the Invention

[0003] To address the aforementioned issues, the present invention aims to provide a mid-term stochastic water level control method for cascade hydropower that considers the random bias of wind power. This method constructs a joint probability distribution model of the wind farm cluster using a multidimensional joint Copula distribution function, generates the cascade hydropower water level operation process based on wind power scenarios, and obtains the cascade hydropower water level control interval to address the uncertainty of wind power output. Specifically, the present invention constructs a joint probability distribution model of the wind farm cluster under different typical processes using a multidimensional joint Copula distribution function to characterize the uncertainty of new energy sources; with the objective of maximizing the power generation of cascade hydropower, a mid-term stochastic water level control optimization model considering the bias of multiple wind power scenarios is established; and the impact of different number of scenarios and different inflow conditions on the stochastic water level control of hydropower stations is investigated.

[0004] The technical solution adopted in this invention is as follows:

[0005] A method for mid-term stochastic water level control of cascade hydropower considering wind power stochastic bias mainly includes: constructing the joint probability of wind farm clusters in various regions, generating a set of time-series output scenarios for all wind farms in the region; solving for the maximum power generation of cascade hydropower considering the uncertainty of wind power output based on the wind power output scenarios; solving for the planned water level process and the water level process under each wind power scenario, respectively, to obtain the water level control interval for cascade hydropower to cope with wind power uncertainty, and analyzing the interval variation characteristics under different inflow conditions and different number of scenarios; the specific steps are as follows:

[0006] Step 1: Collect initial calculation conditions, including the total planned output of cascade hydropower on a daily basis for the next month, the daily wind power output for the next month, the actual wind power operation data for the past year, the operating conditions and constraints of the power station, and the power and water dispatch demand conditions.

[0007] Step 2: Based on principal component analysis dimensionality reduction and K-means clustering, typical meteorological classifications for the region are obtained. First, the historical monthly daily wind speed forecast sequences of the regional wind farm clusters are analyzed to extract representative wind speed evolution patterns. Then, historical wind power output data are classified and organized according to the identified typical wind speed processes. Finally, the monthly historical power output data of the wind farm clusters are classified according to the cluster centers of various wind speed processes to form typical power output scenarios under corresponding wind speed conditions.

[0008] Based on the C-vine Copula theory, a statistical scenario set of wind farm clusters is generated by decomposing the joint distribution of multivariate Copula functions. A C-vine structure is constructed to fit the sequential correlation between wind farms, decomposing the high-dimensional mixed Copula distribution into a series of equivalent binary conditional Copula combinations, thereby obtaining the joint probability distribution of power output of the regional wind farm cluster at different time periods. Specifically:

[0009] Determine the C-vine structure of the wind farm cluster:

[0010] By sequentially assuming each random variable as a root node, the Kendall correlation coefficient between it and other variables is calculated. A strong correlation is considered to exist between the power outputs of two wind farms when the absolute value of the correlation coefficient exceeds a certain threshold, allowing them to be included in the Copula model. The random variable corresponding to the largest sum of cumulative correlation coefficients is then selected as the root node, and the order of nodes and conditions is determined sequentially. Finally, a Copula conditional structure for the region is established based on wind farm power output data for each time period, and the wind farm selected as the root node most frequently in each time period is identified as the dominant power station in the region.

[0011] C-curve Copula Function Form Selection and Parameter Estimation:

[0012] Choose the bivariate conditional Copula function forms that constitute the Copula. Determine the parameters of the Copula function using the maximum likelihood estimation method. Construct the maximum likelihood function of the Copula. Equation (1) is given.

[0013] (1)

[0014] In the formula: This is the parameter vector of the Copula function. For the number of power stations, For sample size; This is a tree index for a C-Vine structure, specifically a power station index. The edge index in the current tree; For power station exist Output value at any given moment; For paired Copula density functions, that is, given the variables from 1 to... Establish in the case and Dependencies; In the known Power station Under the condition of exerting effort at all times, the first Power station The conditional cumulative distribution function of output at any given time.

[0015] Before performing maximum likelihood estimation, the initial parameter values ​​of each binary conditional Copula need to be obtained. The specific process is as follows: First, based on the power output samples of each power station per unit time period, the marginal distribution sequence is obtained through kernel density estimation, and the binary conditional Copula parameters corresponding to root node 1 are estimated. Then, simulated observations are generated using the obtained Copulas, and the binary conditional Copula parameters of root node 2 and subsequent nodes are estimated sequentially. Finally, the obtained parameters are used as initial values, and the BFGS algorithm in the quasi-Newton method is employed, according to equation... The maximum likelihood function is used for optimization.

[0016] Generation of output scenario sets for wind farm clusters:

[0017] Based on the distribution, R random number samples are generated, and the generated random number samples are converted into output scenario sets of each wind farm in the region during the same period through a multi-dimensional Copula joint distribution function using the inverse transformation sampling method.

[0018] Step 3: Extract the cluster fluctuation characteristics based on the EMD fluctuation decomposition algorithm and reconstruct them into the output scenario set of the wind farm cluster: First, calculate the difference between adjacent periods of the average output curve of the leading power station for 30 periods per day within a month to obtain the volatility process; then use the EMD algorithm to reduce noise to obtain the reference fluctuation sequence; finally, based on the characteristic power station, match and recombine different scenario sets according to the temporal coherence between their samples to form a complete temporal output scenario set.

[0019] Step 4: Establish a mid-term stochastic water level control optimization model with the maximum hydropower generation as the objective function, considering the conventional operation constraints of cascade hydropower stations and the stochastic wind power output deviation constraints.

[0020] (2)

[0021] In the formula: and are the power station number and the total number of power stations respectively, and it is stipulated that the one with a smaller number is located upstream; and are the dispatching period number and the total number of periods, Taking 0 and respectively represent the beginning and the end of the dispatching period; is the step size of the dispatching calculation period . is the total hydropower generation during the dispatching period, MW·h; is the hydropower station at the time period planned output, MW.

[0022] Step 5: Cascade hydropower stations need to ensure that both the planned process and the response to each scenario process meet the operation constraints to ensure operation safety.

[0023] Relationship constraints between wind power output in each scenario and planned output:

[0024] Due to the uncertainty of wind power output, the wind power output in each scenario at each time period often deviates from the planned output, as shown in Equation (3).

[0025] (3)

[0026] In the formula: is the serial number of the generated wind power scenario set; express Planned wind power output for the specified period, in MW; express Time-of-use wind power scenarios Output, MW. express Time-of-use wind power scenarios The difference between the output and the planned output, i.e. the deviation output that the cascade hydropower needs to bear, is expressed in MW.

[0027] Cascade hydropower requires adjustments to address wind power output deviations in various scenarios. To ensure the clarity of the adjustment process for cascade hydropower stations, the deviation output must be... Distribute the data to each power station and introduce the deviation output. Distribution coefficient After adjustment, the output of each power station at each time period is the sum of the planned output and the output with deviation issued, which can be expressed as equation (4). After adjustment, the total output of the cascade hydropower is the sum of the planned output and the output with deviation, which can be expressed as equation (5).

[0028] (4)

[0029] (5)

[0030] In the formula: For power station exist Time period adjustment scenario Random power output during wind power deviation output process, MW; For power station exist Time period adjustment scenario The output coefficient of wind power deviation process.

[0031] Water balance constraints:

[0032] When wind power generates electricity as planned, and the output process is a deterministic process, the hydropower station operates according to the power generation plan, and the water balance equation is shown in equation (6). (Adjustment scenario) During the wind power deviation output process, the hydropower station's power generation flow, inflow, and reservoir capacity will all change with the change in power output. The water balance equation for this stage is shown in equation (7).

[0033] (6)

[0034] (7)

[0035] In the formula: For power station During the period The final storage capacity, in m³; To adjust the scene Hydropower station with wind power deviation output process During the period The final storage capacity, in m³; , and Hydropower stations During the period Power generation flow, inter-regional flow, and wastewater discharge, m³ / s; and Adjusting the scene respectively Hydropower station with wind power deviation output process During the period The power generation flow and wastewater discharge flow, m³ / s.

[0036] Hydropower station operation boundary constraints:

[0037] Hydropower station operation must meet the constraints of power generation flow, water discharge flow, and power output boundary. During the planning stage, the constraints of power generation flow, water discharge flow, and power output boundary of hydropower station are shown in equations (8)-(10).

[0038] (8)

[0039] (9)

[0040] (10)

[0041] In the formula: , Hydropower stations During the period The upper and lower limits of power generation flow rate, in m³; For hydroelectric power station During the period The upper limit of the wastewater discharge rate, m³ / s; , Hydropower stations During the period Average output upper and lower limits, MW; , Hydropower stations During the period The upper and lower limits of the storage capacity, in m³.

[0042] Adjust scene The wind power deviation output process, the power generation flow, the water discharge flow and the output boundary constraints are shown in equations (11)-(13).

[0043] (11)

[0044] (12)

[0045] (13)

[0046] Initial and final water level constraints:

[0047] During the planning phase, the initial and final water level constraints and reservoir water level constraints are shown in equations (14)-(16).

[0048] (14)

[0049] (15)

[0050] (16)

[0051] In the formula: and Hydropower stations during the dispatching cycle The initial and final water levels, in meters; and These are the given initial water level and final water level, respectively. and Hydropower stations During the period The minimum and maximum water levels, in meters.

[0052] The initial and final water level constraints and reservoir water level constraints considering the wind power output deviation are shown in equations (17)-(19).

[0053] (17)

[0054] (18)

[0055] (19)

[0056] In the formula: and Adjusting the scene respectively Hydropower station with wind power deviation output process The initial and final water levels, in meters (m).

[0057] Hydropower output stability constraints:

[0058] A smooth power generation process at hydropower stations is beneficial for protecting downstream ecosystems and the station's generating units; therefore, fluctuations in hydropower output are limited. (Planning Phase and Adjustment Scenarios) The stability constraints of the wind power deviation output process are shown in equations (20) and (21).

[0059] (20)

[0060] (twenty one)

[0061] In the formula: For the power system to provide power to cascade power stations during time periods With time period Output variation constraint, MW;

[0062] Hydropower station head constraints:

[0063] The formulas for water level and reservoir capacity, tailwater level and discharge, head loss and net head calculation methods during the planning stage are shown in equations (22)-(25).

[0064] (twenty two)

[0065] (twenty three)

[0066] (twenty four)

[0067] (25)

[0068] In the formula: , They represent hydroelectric power stations. During the period The final water level above and below the dam, in meters; , They represent hydroelectric power stations. During the period Head loss, net head, m; , and They represent hydroelectric power stations The functions relating upstream water level to reservoir capacity, downstream water level to outflow, and head loss to power generation flow.

[0069] Adjust scene The formulas for water level and reservoir capacity, tailwater level and discharge, head loss and net head calculation methods for the wind power deviation output process are shown in equations (26)-(29).

[0070] (26)

[0071] (27)

[0072] (28)

[0073] (29)

[0074] In the formula: , These represent wind power generation scenarios. Downstream power station During the period The final water level above and below the dam, in meters; , These represent wind power generation scenarios. Downstream power station During the period Head loss, net head, m.

[0075] Hydropower station power generation function:

[0076] Planning Phase and Adjustment Scenarios The calculation methods for the output of hydropower stations during the wind power deviation output process are shown in equations (30) and (31).

[0077] (30)

[0078] (31)

[0079] In the formula: Indicates power station The dynamic characteristic function relating power output, power generation flow rate, and water head.

[0080] Step 6: After solving the optimization model based on scenario-driven construction, output the planned water level process and the water level process under wind power in each scenario. The planned water level process is the optimal water level process after comprehensively considering the wind power deviations of all scenarios, and the water level process under wind power in each scenario is the optimal water level process under each scenario. Together, they depict the water level operating space considering the uncertainty of wind power. The highest and lowest water levels at each time are statistically analyzed, and upper and lower envelope lines are drawn. Based on the envelope line interval, the optimal water level control interval is established for each power station.

[0081] Step 7: Linearize the nonlinear constraints involved in Step 5 using SOS2 constraints, and then use the method provided in Step 6 to call the solver to solve the model, thereby obtaining the optimal water level control range for each power station.

[0082] This invention offers the following advantages: It enables the determination of water level control ranges for each cascade hydropower station under various constraints and uncertainties in wind power output. Reasonably determining the water level control range of a hydropower station is crucial for ensuring the safe operation of hydropower. Too low a water level leads to insufficient regulation capacity and reduced power supply support; too high a water level results in insufficient reservoir storage space, failing to provide sufficient space for renewable energy absorption. Wind power output deviation is correlated with the water level control range of cascade hydropower stations. In the early stages, cascade hydropower stations are limited by initial water levels and operational constraints, resulting in fewer scheduling decisions and narrow water level ranges. However, as wind power deviations gradually affect the water level process, and different wind deviations may lead to completely opposite scheduling strategies, the water level operating range of cascade hydropower stations expands in the later stages. This invention demonstrates the changes in water level control ranges under different inflow rates and different scenarios, indicating that wind power has a significant impact on the hydropower water level control range. In summary, this invention can accurately determine the water level control ranges of each cascade hydropower station under uncertain wind power output, guiding actual operation and scheduling. Attached Figure Description

[0083] Figure 1 This is a map showing the coverage of historical data in the wind power scene generation area according to the present invention. The areas between dark lines represent the wind power output range of the scene, the areas between light lines represent the historical wind power output range, and the shaded areas represent the areas not covered by the generated scene.

[0084] Figure 2 This is a comparison diagram of the water level control intervals of each hydropower station during the dry season and normal water season, obtained by the present invention. In the diagram, (A) is the dry season and (B) is the normal water season; (a) is the GGQ power station, (b) is the XW power station, (c) is the MW power station, (d) is the DCS power station, (e) is the NZD power station, and (f) is the JH power station. The thin black dashed line represents the scene water level process, the thin black solid line represents the planned water level process, and the area between the thick black solid lines is the water level envelope, i.e., the water level control interval.

[0085] Figure 3 This is a comparison chart of the power output ranges of each hydropower cascade during the dry season and normal water season, where (a) is the dry season and (b) is the normal water season.

[0086] Figure 4 This diagram illustrates the changes in water level control intervals for various hydropower stations under different wind power scenarios. (a) represents the NZD power station, (b) the XW power station, (c) the GGQ power station, (d) the MW power station, (e) the DCS power station, and (f) the JH power station. The light-colored areas represent the water level control intervals for hydropower stations under 6 wind power scenarios, the dark-colored areas represent 7 scenarios, and the gray-colored areas represent 8 scenarios. Detailed Implementation

[0087] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0088] Taking a cascade hydropower group consisting of six hydropower stations in the lower reaches of a river basin and surrounding wind farms as a case study, this cascade hydropower resource utilization is full, with a total installed capacity accounting for approximately 19% of the province's total hydropower installed capacity. The uncertainty of wind power output, leading to deviations between planned and actual output, and the complex water-wind coupling relationship, pose significant challenges to the complementary and unified scheduling of the cascade hydropower group on a monthly scale. Using this region as the research object effectively verifies the rationality and effectiveness of the model proposed in this invention. Table 1 lists the required basic data for the power stations. This embodiment analyzes the 30-day simulation calculation based on the operating data of a typical dry month in 2024.

[0089] Table 1 Basic Parameters of Cascade Hydropower Stations

[0090]

[0091] The analysis using the aforementioned method for mid-term stochastic water level control in cascade hydropower considering wind power stochastic bias includes the following steps:

[0092] Step 1: Collect initial calculation conditions, including the total planned output of cascade hydropower on a daily basis for the next month, the daily wind power output for the next month, the actual wind power operation data for the past year, the operating conditions and constraints of the power station, and the power and water dispatch demand conditions.

[0093] Step 2: Based on principal component analysis dimensionality reduction and K-means clustering, typical meteorological classifications for the region are obtained. First, the historical monthly daily wind speed forecast sequences of the regional wind farm clusters are analyzed to extract representative wind speed evolution patterns. Then, historical wind power output data are classified and organized according to the identified typical wind speed processes. Finally, the monthly historical power output data of the wind farm clusters are classified according to the cluster centers of various wind speed processes to form typical power output scenarios under corresponding wind speed conditions.

[0094] Based on the C-vine Copula theory, a statistical scenario set of wind farm clusters is generated by decomposing the joint distribution of multivariate Copula functions. A C-vine structure is constructed to fit the sequential correlation between wind farms, decomposing the high-dimensional mixed Copula distribution into a series of equivalent binary conditional Copula combinations, thereby obtaining the joint probability distribution of power output of the regional wind farm cluster at different time periods. Specifically:

[0095] Determine the C-vine structure of the wind farm cluster:

[0096] By sequentially assuming each random variable as a root node, the Kendall correlation coefficient between it and other variables is calculated. A strong correlation is considered to exist between the power outputs of two wind farms when the absolute value of the correlation coefficient exceeds a certain threshold, allowing them to be included in the Copula model. The random variable corresponding to the largest sum of cumulative correlation coefficients is then selected as the root node, and the order of nodes and conditions is determined sequentially. Finally, a Copula conditional structure for the region is established based on wind farm power output data for each time period, and the wind farm selected as the root node most frequently in each time period is identified as the dominant power station in the region.

[0097] C-curve Copula Function Form Selection and Parameter Estimation:

[0098] Choose the form of each binary conditional Copula function that constitutes the Copula. Determine the parameters of the Copula function using the maximum likelihood estimation method. Construct the maximum likelihood function of the Copula as Equation (1).

[0099] (32)

[0100] In the formula: This is the parameter vector of the Copula function. For the number of power stations, For sample size; This is a tree index for a C-Vine structure, specifically a power station index. The edge index in the current tree; For power station exist Output value at any given moment; For paired Copula density functions, that is, given the variables from 1 to... Establish in the case and Dependencies; In the known Power station Under the condition of exerting effort at all times, the first Power station The conditional cumulative distribution function of output at any given time.

[0101] Before performing maximum likelihood estimation, the initial parameter values ​​of each binary conditional Copula need to be obtained. The specific process is as follows: First, based on the power output samples of each power station per unit time period, the marginal distribution sequence is obtained through kernel density estimation, and the binary conditional Copula parameters corresponding to root node 1 are estimated. Then, simulated observations are generated using the obtained Copulas, and the binary conditional Copula parameters of root node 2 and subsequent nodes are estimated sequentially. Finally, the obtained parameters are used as initial values, and the BFGS algorithm in the quasi-Newton method is employed, according to equation... The maximum likelihood function is used for optimization.

[0102] Generation of output scenario sets for wind farm clusters:

[0103] Based on the distribution, R random number samples are generated, and the generated random number samples are converted into output scenario sets of each wind farm in the region during the same period through a multi-dimensional Copula joint distribution function using the inverse transform sampling method.

[0104] Step 3: Extract the cluster fluctuation characteristics based on the EMD fluctuation decomposition algorithm and reconstruct them into the output scenario set of the wind farm cluster. First, calculate the difference between adjacent periods of the average output curve of the leading power station for 30 periods per day within a month to obtain the volatility process; then use the EMD algorithm to denoise and obtain the benchmark fluctuation sequence; finally, conditional on the characteristic power station, match and reorganize different scenario sets according to the temporal coherence between their samples to form a complete temporal output scenario set.

[0105] Step 4: Taking the maximum hydropower generation as the objective function, considering the conventional operation constraints of cascade hydropower stations and the random wind power output deviation constraints, establish a mid-term stochastic water level control optimization model.

[0106] (33)

[0107] In the formula: and are the power station numbers and the total number of power stations, and it is stipulated that the one with a smaller number is located upstream; and are the scheduling period numbers and the total number of periods, Taking 0 and when, they represent the beginning and the end of the scheduling period respectively; is the step size of the scheduling calculation period, and in this embodiment, it is taken as 1 . is the total hydropower generation during the scheduling period, MW·h; is the hydropower station at the time period planned output, MW.

[0108] Step 5: Cascade hydropower stations need to ensure that both the planned process and the response to each scenario process meet the operation constraints to ensure operation safety.

[0109] Constraint on the relationship between the output of each wind power scenario and the planned output:

[0110] Due to the uncertainty of wind power output, the output of each wind power scenario in each period often deviates from the planned output, as shown in Equation (34).

[0111] (34)

[0112] In the formula: is the serial number of the generated wind power scenario set; express The planned wind power output for the specified period is to be coordinated with hydropower output. Distinguish by using superscript. Logo, MW; express Time-of-use wind power scenarios Output, MW. express Time-of-use wind power scenarios The difference between the output and the planned output, i.e. the deviation output that the cascade hydropower needs to bear, is expressed in MW.

[0113] Cascade hydropower requires adjustments to address wind power output deviations in various scenarios. To ensure the clarity of the adjustment process for cascade hydropower stations, the deviation output must be... Distribute the data to each power station and introduce the deviation output. Distribution coefficient After adjustment, the output of each power station at each time period is the sum of the planned output and the output with deviation issued, which can be expressed as equation (35). After adjustment, the total output of the cascade hydropower is the sum of the planned output and the output with deviation, which can be expressed as equation (36).

[0114] (35)

[0115] (36)

[0116] In the formula: For power station exist Time period adjustment scenario Random power output during wind power deviation output process, MW; For power station exist Time period adjustment scenario The output coefficient of wind power deviation process.

[0117] Water balance constraints:

[0118] When wind power generates electricity as planned, and the output process is a deterministic process, the hydropower station operates according to the power generation plan, and the water balance equation is shown in equation (37). (Adjustment scenario) During the wind power deviation output process, the hydropower station's power generation flow, inflow, and reservoir capacity will all change with the change in power output. The water balance equation for this stage is shown in equation (38).

[0119] (37)

[0120] (38)

[0121] In the formula: For power station During the period The final storage capacity, in m³; To adjust the scene Hydropower station with wind power deviation output process During the period The final storage capacity, in m³; , and Hydropower stations During the period Power generation flow, inter-regional flow, and wastewater discharge, m³ / s; and Adjusting the scene respectively Hydropower station with wind power deviation output process During the period The power generation flow and wastewater discharge flow, m³ / s.

[0122] Hydropower station operation boundary constraints:

[0123] Hydropower station operation must meet the constraints of power generation flow, water discharge flow, and power output boundary. During the planning stage, the constraints of power generation flow, water discharge flow, and power output boundary of hydropower station are shown in equations (39)-(41).

[0124] (39)

[0125] (40)

[0126] (41)

[0127] In the formula: , Hydropower stations During the period The upper and lower limits of power generation flow rate, in m³; For hydroelectric power station During the period The upper limit of the wastewater discharge rate, m³ / s; , Hydropower stations During the period Average output upper and lower limits, MW; , Hydropower stations During the period The upper and lower limits of the storage capacity, in m³.

[0128] Adjust scene The wind power deviation output process, the power generation flow, the water discharge flow and the output boundary constraints are shown in equations (42)-(44).

[0129] (42)

[0130] (43)

[0131] (44)

[0132] Initial and final water level constraints:

[0133] During the planning phase, the initial and final water level constraints and reservoir water level constraints are shown in equations (45)-(47).

[0134] (45)

[0135] (46)

[0136] (47)

[0137] In the formula: and Hydropower stations during the dispatching cycle The initial and final water levels, in meters (m); and These are the given initial water level and final water level, respectively. and Hydropower stations During the period The minimum and maximum water levels, in meters.

[0138] The initial and final water level constraints and reservoir water level constraints considering the wind power output deviation are shown in equations (48)-(50).

[0139] (48)

[0140] (49)

[0141] (50)

[0142] In the formula: and Adjusting the scene respectively Hydropower station with wind power deviation output process The initial and final water levels, in meters (m).

[0143] Hydropower output stability constraints:

[0144] A smooth power generation process at hydropower stations is beneficial for protecting downstream ecosystems and the station's generating units; therefore, fluctuations in hydropower output are limited. (Planning Phase and Adjustment Scenarios) The stability constraints of the wind power deviation output process are shown in equations (51) and (52).

[0145] (51)

[0146] (52)

[0147] In the formula: For the power system to provide power to cascade power stations during time periods With time period Output variation constraint, MW;

[0148] Hydropower station head constraints:

[0149] The formulas for water level and reservoir capacity, tailwater level and discharge, head loss and net head calculation methods during the planning stage are shown in equations (53)-(56).

[0150] (53)

[0151] (54)

[0152] (55)

[0153] (56)

[0154] In the formula: , They represent hydroelectric power stations During the period The final water level above and below the dam, in meters; , They represent hydroelectric power stations During the period Head loss, net head, m; , and They represent hydroelectric power stations The functions relating upstream water level to reservoir capacity, downstream water level to outflow, and head loss to power generation flow.

[0155] Adjust scene The formulas for water level and reservoir capacity, tailwater level and discharge, head loss and net head calculation methods for the wind power deviation output process are shown in equations (57)-(60).

[0156] (57)

[0157] (58)

[0158] (59)

[0159] (60)

[0160] In the formula: , These represent wind power generation scenarios. Downstream power station During the period The final water level above and below the dam, in meters; , These represent wind power generation scenarios. Downstream power station During the period Head loss, net head, m.

[0161] Hydropower station power generation function:

[0162] Planning Phase and Adjustment Scenarios The calculation methods for the output of hydropower stations during the wind power deviation process are shown in equations (61) and (62).

[0163] (61)

[0164] (62)

[0165] In the formula: Indicates power station The dynamic characteristic function relating power output, power generation flow rate, and water head.

[0166] Step 6: After solving the optimization model based on scenario-driven construction, the planned water level process and the water level process under wind power in each scenario are output respectively. The former is the optimal water level process after comprehensively considering the wind power deviation of all scenarios, and the latter is the optimal water level process under each scenario. The two together depict the water level operation space considering the uncertainty of wind power. The highest and lowest water levels at each time are counted respectively, and the upper and lower envelopes are drawn. Based on this envelope interval, the optimal water level control interval is established for each power station.

[0167] Step 7: Linearize the nonlinear constraints involved in Step 5 using SOS2 constraints, and then use the method provided in Step 6 to call the solver to solve the model, thereby obtaining the optimal water level control range for each power station.

[0168] The simulation analysis results are as follows:

[0169] (1) Statistically calculate the maximum and minimum wind power output at each moment in the wind power generation scenario set and the historical operation dataset to obtain the corresponding upper and lower envelopes. The envelope interval represents the fluctuation range. Plot the upper and lower envelopes of the generation scenario set and the historical operation dataset. The fluctuation range of the two sets is shown in [reference needed]. Figure 1 The calculated coverage rate is 92.2%, indicating that the scenario set generated by this invention basically covers the fluctuation range of historical operating data and can effectively characterize the uncertainty of wind power output.

[0170] (2) Different inflow conditions have a direct impact on the water level control range decision of each cascade hydropower station. Considering the water level process with different wind power deviations, the upper and lower water level envelopes are plotted for each power station. The envelope interval represents the water level operating range of each power station. See Figure 2 The water level operating range basically exhibits a structural characteristic of "convergence in the early stage and divergence in the later stage." This is because, under the goal of maximizing cascade power generation, the initial water level and strict operational constraints result in very few feasible solutions for the model, leading to highly consistent scheduling decisions across all scenarios in the initial stage. The expansion of the water level operating range in the later stage is due to the different operating strategies implemented by each power station in the cascade under different scenarios. In addition, the different wind power deviations brought about by each scenario enter the water balance equation in the form of cumulative disturbances, causing the water levels at the same time period to become increasingly different over time, ultimately resulting in a larger water level operating range for each power station in the later stage.

[0171] Due to the different time periods selected, the water levels of the two hydropower stations with good regulation performance, XW and NZD, differ significantly between the dry and normal water periods, with the water level being higher during the dry season, indicating a wider adjustable range for both stations. Furthermore, water level fluctuations are more pronounced during the dry season, especially towards the end of the scheduling period. This is because the reduced adjustable water volume during the dry season makes them less capable of handling wind power fluctuations. In the dry season, with lower water inflows, there is usually a need for greater wind power output and more power balancing. Initially, NZD, located downstream, lowers its water level while XW, located upstream, maintains a high water level. Later, XW lowers its water level while NDZ stores water to raise its level, ensuring that the entire cascade hydropower system has sufficient capacity to meet grid supply and wind power consumption needs. Conversely, during the normal water period, while meeting power demand, except for NZD which experiences a significant drop in water level in the early stages, the other hydropower stations maintain water levels to ensure stable output and improve economic efficiency.

[0172] Figure 3The diagram shows the power output distribution of the cascade hydropower project calculated by the model of this invention. The calculated power generation during the dry season and normal water season are 355,826 kWh and 321,254 kWh, respectively. It can be seen that, regardless of whether it is the dry season or the normal water season, and especially in the early stages of the scheduling period, the downstream NZD and JH hydropower stations are the first to generate power. This is determined by the scheduling strategy of the cascade hydropower project, which prioritizes the output of downstream hydropower stations to lower their water levels, thereby storing subsequent incoming water and improving the overall water utilization of the cascade hydropower project. Due to the differences in the selected time periods, during the dry season when water inflow is reduced, wind power generation is high and fluctuates significantly. Therefore, more hydropower needs to be mobilized to balance the load. In the later part of the dispatch period, the output of the upstream XW and MW hydropower stations is used to balance the load, resulting in a relatively smooth output throughout the dispatch period. During the normal water season, water inflow is moderate, and the power demand for balancing wind power fluctuations is relatively low. The entire cascade hydropower station increases its output in the early stage and decreases significantly in the later stage, raising the water level to increase energy storage. Moreover, the output of upstream power stations is relatively low throughout the dispatch period, corresponding to the water level results. This indicates that both water inflow and wind power output during the selected time period have a significant impact on the power generation level of the cascade hydropower stations.

[0173] (3) By Figure 4 It can be seen that as the number of scenarios increases, the water level control interval not only changes in range but also in location. This is mainly because the wind power scenarios generated by different numbers of scenarios are different, and are not simply expansions of the original scenarios. Specifically, the NZD and XW hydropower stations, with better regulation performance, show smaller changes in their water level intervals, while other hydropower stations with relatively poorer regulation performance exhibit more significant changes in their water level intervals. It is worth noting that at the end of the scheduling period, the planned water levels of all power stations are quite close, indicating that the water level control interval proposed in this invention has good accuracy.

[0174] The quality of the generated scenarios directly impacts the water level control range obtained by the model: higher scenario quality provides more comprehensive coverage of wind power uncertainties, resulting in a more accurate water level control range. Although increasing the number of scenarios helps enhance the description of uncertainties, the wind power scenarios generated by the C-vine Copula method used in this invention are of high quality, thus increasing the number of scenarios has a limited impact on the model results. In practical applications, the number of scenarios can be appropriately controlled to improve solution efficiency.

[0175] The embodiments described above are merely illustrative of the implementation methods of the present invention, but should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the protection scope of the present invention.

Claims

1. A method for mid-term stochastic water level control in cascade hydropower projects considering wind power stochastic bias, characterized in that, include: Construct the joint probability of wind farm clusters in various regions to generate a set of time-series power output scenarios for all wind farms in the region; The maximum power generation of cascade hydropower is calculated based on the wind power output scenario, taking into account the uncertainty of wind power output. The planned water level process and the water level process under wind power in each scenario are solved separately to obtain the water level control range of cascade hydropower to cope with the uncertainty of wind power. The range change characteristics under different water inflow conditions and different number of scenarios are analyzed.

2. The method for mid-term stochastic water level control of cascade hydropower considering wind power stochastic deviations according to claim 1, characterized in that, The specific steps are as follows: Step 1: Collect initial calculation conditions, including the total planned output of cascade hydropower on a daily basis for the next month, the daily wind power output for the next month, the actual wind power operation data for the past year, the operating conditions and constraints of the power station, and the power and water dispatch demand conditions; Step 2: Obtain typical meteorological classifications for the region based on principal component analysis dimensionality reduction and K-means clustering. First, analyze the historical monthly daily wind speed forecast sequences of the regional wind farm cluster to extract representative wind speed evolution patterns. Then, classify and organize the historical wind power output data according to the identified typical wind speed processes. Finally, classify the monthly historical power output data of the wind farm cluster according to the cluster centers of various wind speed processes to form typical power output scenarios under corresponding wind speed conditions. Based on the C-vine Copula theory, the joint distribution of multivariate Copula functions is decomposed to generate a set of statistical scenarios for wind farm clusters. By constructing a C-vine structure, the sequential correlation between wind farms is fitted, and the high-dimensional mixed Copula distribution is decomposed into a series of equivalent binary conditional Copula combinations, thereby obtaining the joint probability distribution of power output of regional wind farm clusters at different times. Generation of wind farm cluster output scenarios: Based on the distribution, R random number samples are generated. The inverse transformation sampling method is used to convert the generated random number samples into a set of wind farm output scenarios in the same period within the region through the multidimensional Copula joint distribution function. Step 3: Extract cluster fluctuation features and reconstruct a wind farm cluster power output scenario set based on the EMD fluctuation decomposition algorithm: First, calculate the difference between adjacent time periods of the average power output curve of the dominant power station for 30 time periods per day within the month to obtain the fluctuation process; then, use the EMD algorithm to reduce noise and obtain the benchmark fluctuation sequence; finally, based on the characteristic power station, match and reorganize different scenario sets according to the temporal continuity between its samples to form a complete time-series power output scenario set. Step 4: Taking the maximum hydropower generation as the objective function, and considering the conventional operation constraints of the cascade hydropower stations and the random wind power output deviation constraints, establish a medium-term stochastic water level control optimization model. (2) In the formula: and are the power station number and the total number of power stations respectively, and it is stipulated that the one with a smaller number is located upstream; and are the dispatching period number and the total number of periods, taking 0 and respectively represent the beginning and the end of the dispatching period; is the step length of the dispatching calculation period ; is the total hydropower generation during the dispatching period, MW·h; is the hydropower station during the period planned output, MW; Step 5: Cascade hydropower stations must simultaneously ensure that the planned process and the response processes for each scenario meet operational constraints to guarantee operational safety. Step 6: After solving the optimization model based on scenario-driven construction, output the planned water level process and the water level process under wind power in each scenario. The planned water level process is the optimal water level process after comprehensively considering the wind power deviation of all scenarios. The water level process under wind power in each scenario is the optimal water level process under each scenario. Statistically calculate the highest and lowest water levels at each time, draw the upper and lower envelope lines, and establish the optimal water level control range for each power station based on the envelope line interval. Step 7: Linearize the nonlinear constraints involved in Step 5 using SOS2 constraints, and then use the method provided in Step 6 to call the solver to solve the model, thereby obtaining the optimal water level control range for each power station.

3. The method for mid-term stochastic water level control of cascade hydropower considering wind power stochastic deviations according to claim 1, characterized in that, The specific steps for obtaining the joint probability distribution of power output of the regional wind farm cluster in each time period in step 2 are as follows: Determine the C-vine structure of the wind farm cluster: Each random variable is assumed to be a root node, and its Kendall correlation coefficient with other variables is calculated. When the absolute value of the correlation coefficient is greater than a certain threshold, the power output of the two electric fields is considered to be strongly correlated and included in the Copula model. Then, the random variable corresponding to the largest sum of cumulative correlation coefficients is selected as the root node, and the nodes and conditions at each level are determined in turn. Finally, the Copula condition structure in the region is established based on the power output data of wind farms in each time period, and the wind farm that is selected as the root node most times in each time period is determined as the dominant power station in the region. C-curve Copula Function Form Selection and Parameter Estimation: Select the bivariate conditional Copula function forms that constitute the Copula; determine the Copula function parameters using the maximum likelihood estimation method; construct the maximum likelihood function of the Copula. For example, Equation (1); (1) In the formula: Let be the parameter vector of the C-curve Copula function; For the number of power stations, For sample size; This is a tree index for a C-Vine structure, specifically a power station index. The edge index in the current tree; For power station exist Output value at any given moment; For paired Copula density functions, that is, given the variables from 1 to... Establish in the case and Dependencies; In the known Power station Under the condition of exerting effort at all times, the first Power station The conditional cumulative distribution function of output at any given moment; Before performing maximum likelihood estimation, the initial parameter values ​​of each binary condition Copula need to be obtained. The specific process is as follows: First, based on the power output samples of each power station per unit time period, the marginal distribution sequence is obtained by kernel density estimation, and the binary condition Copula parameters corresponding to the root node 1 are estimated. Then, the obtained Copula is used to generate simulated observation values, and the binary condition Copula parameters of the root node 2 and subsequent nodes are estimated in turn. Finally, the obtained parameters are used as initial values, and the BFGS algorithm in the quasi-Newton method is used to optimize the solution with the maximum likelihood function of equation (1).

4. The method for mid-term stochastic water level control of cascade hydropower considering wind power stochastic deviations according to claim 1, characterized in that, The constraints in step 5 are as follows: Constraints on the relationship between wind power output and planned output in various scenarios: Due to the uncertainty of wind power output, the wind power output in each scenario at each time period deviates from the planned output, as shown in equation (3). (3) In the formula: The sequence number of the generated wind power scene set; express Planned wind power output for the specified period, in MW; express Time-of-use wind power scenarios Output, MW; express Time-of-use wind power scenarios The difference between the output and the planned output, i.e. the deviation output that the cascade hydropower needs to bear, in MW; Cascade hydropower requires adjustments to address wind power output deviations in various scenarios. To ensure the clarity of the adjustment process for cascade hydropower stations, the deviation output must be... Distribute the data to each power station and introduce the deviation output. Distribution coefficient The output of each power station at each time period after adjustment is the sum of the planned output and the output of the deviation issued, expressed as formula (4); the total output of the cascade hydropower after adjustment is the sum of the planned output and the output of the deviation, expressed as formula (5). (4) (5) In the formula: For power station exist Time period adjustment scenario Random power output during wind power deviation output process, MW; For power station exist Time period adjustment scenario The distribution coefficient of the wind power deviation output process; Water balance constraints: When wind power generates electricity as planned, and the output process is a deterministic process, the hydropower station operates according to the power generation plan, and the water balance equation is shown in equation (6); Adjustment scenario During the wind power deviation output process, the hydropower station's power generation flow, inflow and reservoir capacity will all change with the change in output. The water balance equation for this stage is shown in equation (7). (6) (7) In the formula: For power station During the period The final storage capacity, in m³; To adjust the scene Hydropower station with wind power deviation output process During the period The final storage capacity, in m³; , and Hydropower stations During the period Power generation flow, inter-regional flow, and wastewater discharge, m³ / s; and Adjusting the scene respectively Hydropower station with wind power deviation output process During the period The power generation flow and wastewater discharge, m³ / s; Hydropower station operation boundary constraints: The operation of a hydropower station must meet the constraints of power generation flow, water discharge flow and power output boundary; during the planning stage, the constraints of power generation flow, water discharge flow and power output boundary of the hydropower station are shown in equations (8)-(10); (8) (9) (10) In the formula: , Hydropower stations During the period The upper and lower limits of power generation flow rate, in m³; For hydroelectric power station During the period The upper limit of the wastewater discharge rate, m³ / s; , Hydropower stations During the period Average output upper and lower limits, MW; , Hydropower stations During the period The upper and lower limits of the storage capacity, in m³; Adjust scene The wind power deviation output process, the power generation flow, the water discharge flow and the output boundary constraints are shown in equations (11)-(13); (11) (12) (13) Initial and final water level constraints: During the planning phase, the initial and final water level constraints and the reservoir water level constraints are shown in equations (14)-(16); (14) (15) (16) In the formula: and Hydropower stations during the dispatching cycle The initial and final water levels, in meters; and These are the given initial water level and final water level, respectively. and Hydropower stations During the period Minimum and maximum water levels, in meters; The initial and final water level constraints and reservoir water level constraints considering the wind power output deviation are shown in equations (17)-(19); (17) (18) (19) In the formula: and Adjusting the scene respectively Hydropower station with wind power deviation output process The initial and final water levels, in meters; Hydropower output stability constraints: Planning Phase and Adjustment Scenarios The stability constraints of the wind power deviation output process are shown in equations (20) and (21), respectively; (20) (21) In the formula: For the power system to provide power to cascade power stations during time periods With time period Output variation constraint, MW; Hydropower station head constraints: The formulas for water level and reservoir capacity, tailwater level and discharge, head loss and net head calculation methods during the planning stage are shown in equations (22)-(25); (22) (23) (24) (25) In the formula: , They represent hydroelectric power stations. During the period The final water level above and below the dam, in meters; , They represent hydroelectric power stations. During the period Head loss, net head, m; , and They represent hydroelectric power stations. Functions relating upstream water level to reservoir capacity, downstream water level to outflow, and head loss to power generation flow; Adjust scene The formulas for water level and reservoir capacity, tailwater level and discharge, head loss and net head calculation methods for the wind power deviation output process are shown in equations (26)-(29); (26) (27) (28) (29) In the formula: , These represent wind power generation scenarios. Downstream power station During the period The final water level above and below the dam, in meters; , These represent wind power generation scenarios. Downstream power station During the period Head loss, net head, m; Hydropower station power generation function: Planning Phase and Adjustment Scenarios The calculation methods for the output of hydropower stations during the wind power deviation output process are shown in equations (30) and (31), respectively. (30) (31) In the formula: Indicates power station The dynamic characteristic function relating power output, power generation flow rate, and head.

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