Control method for water level drawdown of cascade reservoirs before flood season under uncertain electricity price condition

Abstract

The present application belongs to the technical field of power market and reservoir dispatching, and discloses a control method for pre-flood water level drawdown of cascade reservoirs under uncertain electricity price conditions. The present application can fully consider the influence of electricity price uncertainty on the operation of hydropower stations, and reduce the randomness of electricity price on the power generation benefit of reservoirs through scene generation clustering. The improved k-means algorithm is used to cluster the electricity price factors to determine the electricity price situation under different scenes, the electricity price scene and runoff scene are combined by using the Cartesian product idea, the cascade reservoir power generation, water abandonment, drawdown energy storage objective function is constructed, and the NSGA-II is used as the solving algorithm to deduce the optimal pre-flood drawdown water level interval under different drawdown water level combinations. Through the analysis of the engineering example of the trunk cascade hydropower station in a certain basin in southwest China, the results show that the present application can effectively improve the benefit of hydropower stations, meet the smooth operation of cascade reservoirs during the drawdown period, and improve the practicality of the drawdown scheme.

Description

Technical Field

[0001] This invention belongs to the field of electricity market and reservoir scheduling technology, and specifically relates to a method for controlling the pre-flood water level drawdown of cascade reservoirs under uncertain electricity price conditions. Background Technology

[0002] The cascade hydropower stations along the main stream of the Yangtze River play a dominant role in the power grid of Southwest my country. Reasonable water level control directly affects the effective absorption of hydropower and the safe and stable operation of the power grid. Reservoir (group) scheduling rules are an important basis and means to guide the safe, economical, and reliable operation of reservoirs (groups), and have always been a classic research topic both domestically and internationally. However, traditional research on reservoir scheduling rules mainly focuses on deriving rules based on control objectives such as guaranteed output, power generation, and cascade storage. This is then achieved through heuristic methods, optimization methods, or a combination of both to form single-reservoir or cascade scheduling curves or functions to guide reservoir scheduling operations. These methods have played an important role in actual production scheduling. However, in the past decade or so, the scheduling of the cascade hydropower stations along the main stream of the Yangtze River in Southwest my country has differed significantly from the traditional scheduling and operation mode dominated by small-scale hydropower stations. Current cascade reservoir scheduling rules no longer only focus on power generation and traditional guaranteed output, but also consider further improving the utilization of hydropower resources from the perspective of the power grid. Key water level control, including control of water levels at the beginning, end, and end of the flood season, is an important indicator for measuring the utilization rate of hydropower resources and can effectively reflect the comprehensive utilization requirements of power generation, water supply, and flood control. Therefore, in the actual scheduling of power grids and cascade hydropower station groups, key water level control at each stage has become the most commonly used and easy-to-operate scheduling control method. The pre-flood drawdown level, as the key water level connecting the dry season and the main flood season of cascade reservoirs, mainly plays a role in reducing the risk of water abandonment during the flood season. At the beginning of the flood season, it is necessary to control the drawdown to be sufficient while avoiding excessive drawdown that could affect power grid safety and subsequent power generation efficiency. How to rationally formulate pre-flood drawdown water level control rules for cascade reservoirs is one of the core issues in hydropower system scheduling and has significant practical implications for the efficient operation of the entire power grid.

[0003] Current research on the scheduling and control of cascade reservoirs during the drawdown period, such as Cao Rui et al.'s paper on multi-objective optimization methods for pre-flood drawdown control of cascade reservoir groups, introduces the concept of the Gini coefficient, analyzes the drawdown situation and power generation benefits of cascade energy storage from the perspective of the power grid, and makes optimal decisions on different drawdown modes; Zheng Yalian et al.'s paper on the pre-flood drawdown water level of reservoir groups coordinating power generation and water abandonment considers complex constraints such as unit maintenance and ecological flow, constructs a two-level optimal scheduling model, and explores the optimal pre-flood drawdown water level range of the Qingjiang cascade reservoirs. Most studies start from the reservoirs themselves, aiming at the comprehensive utilization of cascade reservoirs and the supplementary benefits of joint scheduling, and obtain reasonable drawdown control schemes through model analysis and calculation. However, few studies consider the impact of electricity price factors on water level drawdown in the context of the electricity market, which will inevitably affect the practicality of the scheduling scheme. Therefore, it is necessary to consider conducting research on the optimal pre-flood drawdown water level of cascade reservoirs under the influence of uncertain electricity prices.

[0004] To address the aforementioned problems, this invention proposes a pre-flood water level drawdown control method for cascade reservoirs that considers electricity price uncertainties, and applies it to a cascade reservoir system on the main stream of the Southwest River Basin as an engineering example. The results show that the invention can effectively improve the efficiency of hydropower stations, ensure stable operation of cascade reservoirs during the drawdown period, and enhance the practicality of the drawdown scheme. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a method for controlling the pre-flood water level drawdown of cascade reservoirs that takes into account the uncertainty of electricity prices, so as to improve the overall power generation efficiency of the reservoirs and improve the practicality of the drawdown scheme.

[0006] The technical solution of this invention:

[0007] A method for controlling pre-flood water level drawdown in cascade reservoirs under uncertain electricity prices, the key steps of which are as follows:

[0008] (1) Constructing an uncertain electricity price sample set. Based on years of market transaction electricity price data, the Latin hypercube sampling method is used to sample the electricity price data, and the t-SNE method is used to reduce the sampling results.

[0009] (2) Generating typical electricity price scenarios. The elbow method is used to select the number of clusters. Using the sum of squared errors within each cluster as the criterion, the electricity price sequence of the trading commodity is decomposed into multiple commodity electricity price sequences and converted into actual electricity price data. A typical scenario is then generated using the k-means clustering algorithm based on Grey Wolf optimization. The specific steps are as follows:

[0010] Step 1. Based on the electricity price sample, the elbow method is used to select the number of clusters K;

[0011] Step 2. Calculate the Euclidean distance and average distance between any two data points in the electricity price sample set, where a≠b; for each data point in the sample set, determine the density value centered at each point with a distance of D, using the following formula:

[0012]

[0013]

[0014]

[0015] In the formula: x a x b Two random data points are given in the low-dimensional scene set; a, b, and k are the data point numbers; d(x a ,x b ) is x a ,x b The Euclidean distance between them; D is the distance between x and x. a ,x b The average distance between them; Let f(x) be the number of pairwise combinations of n data points; f(x) is a 0-1 function; desnity(x) a ) is x a Density value at point;

[0016] Step 3. Using density as the fitness function, the Gray Wolf Optimization Algorithm is used to continuously update the positions of elite wolves and find the optimal initial cluster centers.

[0017] Step 4. Calculate the Euclidean distance from the electricity price sample data of non-cluster centers to the K cluster centers, and divide each sample data into the cluster with the closest distance;

[0018] Step 5. Calculate the centroids of the K clusters respectively, and update the K centroids as the new cluster centers.

[0019] Step 6. Repeat Steps 2 to 5 until the cluster centers no longer change. The final cluster centers are the K typical scenarios {ζ1,ζ2,...,ζ}. k}

[0020] (3) Generate electricity price-runoff combination scenarios. The generated typical electricity price scenario is combined with three runoff scenarios: abundant, normal, and dry, using the concept of Cartesian product.

[0021] (4) Construct an optimization model for pre-flood water level drawdown control of cascade hydropower stations. With the optimization objectives of maximizing power generation efficiency, minimizing water wastage, and maximizing drawdown energy storage, a multi-objective scheduling model is established, as follows:

[0022]

[0023]

[0024]

[0025] in:

[0026]

[0027]

[0028]

[0029] In the formula: E represents the maximum power generation benefit of the cascade reservoir group during the scheduling period; n and N are the trading variety number and total number, respectively; T is the scheduling period; i and M are the reservoir number and total number, respectively; Δt is the number of seconds in the t-th time period, in seconds; A i Let q be the output coefficient of the i-th reservoir; i,t Let m be the power generation flow rate of the i-th reservoir during time period t. 3 / s;H i,t Let e ​​be the water head height of the i-th reservoir during time period t, in meters. i,n,t The electricity price for the nth trading type during the t-th time period of the i-th reservoir is expressed in yuan / kWh; V q The amount of water discharged from the cascade reservoirs, in m 3 ;Qd i.t Let m be the discharge flow rate of the i-th reservoir during time period t. 3 / s;r i,n,t Ed represents the weight of the nth trading variety for the i-th reservoir during time period t in electricity trading; Ed represents the drawdown storage capacity of the cascade reservoirs, in kWh; ES i,t Calculate the energy storage (kWh) for the i-th reservoir during time period t; η i Let UV be the water consumption rate of the i-th reservoir; i,t Let m be the available water volume of the upstream reservoir during time period t for the i-th reservoir. 3 V i,t Let HS be the reservoir capacity above the dead water level of reservoir i at the end of time period t, in meters. i,t The average head (m) used to calculate the energy storage capacity of reservoir i at the end of time period t; Z i,t Let be the water level of reservoir i at the end of time period t, in meters. Let be the dead water level of reservoir i, in meters. The downstream tailwater level used to calculate the energy storage of reservoir i is selected by choosing the downstream tailwater level corresponding to 1 / 3 of the maximum power generation flow of reservoir i, in meters.

[0030] (5) Select the optimal drawdown control scheme. Use the NSGA-II algorithm to solve the benefit values ​​under different schemes, simulate and schedule different drawdown control schemes, use the congestion ranking method to select the benefit values ​​under different schemes, and select the optimal drawdown control scheme based on the maximum benefit value.

[0031] The beneficial effects of this invention are as follows: Compared with hydropower dispatching methods that consider fixed electricity prices, the improved k-means algorithm can effectively avoid getting trapped in local optima, accurately describe the uncertain electricity prices of different trading varieties, and exhibit better reliability, concentration, and practicality. The constructed cascade pre-flood drawdown control optimization model can intuitively reflect the benefit values ​​of different drawdown schemes, avoiding the randomness and irrationality of relying on subjective determination of drawdown schemes. Attached Figure Description

[0032] Figure 1 This is a diagram illustrating the overall solution framework of the method of this invention;

[0033] Figure 2 This is a flowchart of the k-means algorithm based on GWO;

[0034] Figure 3 These are electricity price charts for different scenarios; where (a) is scenario one (power station A), (b) is scenario one (power station D), (c) is scenario two (power station A), (d) is scenario two (power station D), (e) is scenario three (power station A), and (f) is scenario three (power station D).

[0035] Figure 4 It is a flowchart of the scene generation process;

[0036] Figure 5 It is the dispatch result under deterministic electricity price conditions; where (a) is the benefit of cascade power generation and (b) is the drawdown energy storage.

[0037] Figure 6 The results are the dispatch results under uncertain electricity prices; where (a) is the power generation benefit in a year with favorable wind and water conditions, (b) is the change in power generation in a year with favorable wind and water conditions, (c) is the power generation benefit in a year with normal water conditions, (d) is the change in power generation in a year with normal water conditions, (e) is the power generation benefit in a year with low water conditions, and (f) is the change in power generation in a year with low water conditions.

[0038] Figure 7 This is a comparison chart of power generation benefits and energy storage during drawdown; where (a) is the power generation benefit in a year with favorable water conditions, (b) is the energy storage during drawdown in a year with favorable water conditions, (c) is the power generation benefit in a year with normal water conditions, (d) is the energy storage during drawdown in a year with normal water conditions, (e) is the power generation benefit in a year with low water conditions, and (f) is the energy storage during drawdown in a year with low water conditions. Detailed Implementation

[0039] The specific implementation of the present invention will be further described below with reference to the accompanying drawings and technical solutions. It mainly includes three parts: typical scenario generation, modeling of the cascade pre-flood water level drawdown control optimization model, and example application.

[0040] 1. Typical Scene Generation

[0041] Because the initial cluster centers in the traditional k-means algorithm are randomly selected, they may get stuck in local optima. However, the Grey Wolf optimization algorithm based on Lévy flight has better global search capabilities, avoiding getting stuck in local optima and finding the optimal initial cluster centers more effectively. In finding the optimal initial cluster centers, the fitness function is based on maximizing density.

[0042]

[0043]

[0044]

[0045] By using an improved gray wolf optimization algorithm, the positions of elite wolves are continuously updated and iterated to find the optimal initial cluster centers. Based on the calculated Euclidean distance from each remaining low-dimensional original scene to the K cluster centers, each original scene is assigned to the nearest cluster. The center points of each of the K clusters are calculated, and these K center points are updated as new cluster centers. Through repeated calculations, the final typical scene {ζ1,ζ2,...,ζ} is determined. k The update iteration formula is as follows:

[0046]

[0047]

[0048]

[0049] In the formula: Let be the positions of the elite wolf in the (t+1)th iteration, and the positions of the α wolf and β wolf in the tth iteration, respectively. This is point-to-point multiplication; This represents the Lévy random search path. β is a random number in (0,2), typically taken as 1.5; u and v are random numbers following a normal distribution.

[0050] 2. Modeling of Optimization Model for Pre-Flood Water Level Reduction Control in Cascade Flood Zones

[0051] (2.1) Objective function: The optimization objective is to maximize the power generation benefits of the cascade hydropower stations, minimize the amount of water wasted, and maximize the drawdown storage value. The expression is as follows:

[0052]

[0053]

[0054]

[0055] in:

[0056]

[0057]

[0058]

[0059] In the formula: E represents the maximum power generation benefit of the cascade reservoir group during the scheduling period; T represents the scheduling cycle; i and M represent the reservoir number and total number, respectively; Δt represents the number of seconds in time period t; A i e is the power output coefficient of the power plant. i,t Let be the electricity price for the nth trading type at time t for the i-th reservoir, expressed in yuan / kWh. q Qd represents the amount of water discarded. i.t r is the discharge flow rate of the power station during time period t. i,n,t Let ES be the weight of the nth trading variety in electricity trading for the i-th reservoir at time t. i,t Calculate the energy storage (kWh) for the i-th reservoir during time period t. η i Let be the water consumption rate of the i-th reservoir; Let be the dead water level of reservoir i, in meters. For calculating the downstream tailwater level used in reservoir i for energy storage, this invention selects the downstream tailwater level corresponding to 1 / 3 of the maximum power generation flow of reservoir i, in meters (UV). i,t Let m be the available water volume of the upstream reservoir during time period t for the i-th reservoir. 3 Ed represents the drawdown energy storage capacity of the cascade reservoirs, in kWh.

[0060] (2.2) Constraints

[0061] 1) Water balance equation

[0062] V i,t+1 =V i,t +(Q i,t -q i,t -Qd i,t )Δt

[0063] In the formula: V i,t and V i,t+1 Q represents the reservoir capacity corresponding to the initial and final water levels in time period t. i Qd i.t This represents the inflow and outflow of water at time t in reservoir i, in meters per second (m³). 3 / s.

[0064] 2) Reservoir water level constraints

[0065]

[0066] In the formula: Z i,t , Z i,t Let t represent the water level of reservoir i at time t and its upper and lower limits, in meters.

[0067] 3) Power generation flow constraints

[0068]

[0069] In the formula: q i,t , q i,t The power generation flow rate of reservoir i in time period t and its upper and lower limits, in m³. 3 / s.

[0070] 4) Outbound flow constraints

[0071]

[0072] And there are

[0073] Q i ' ,t =q i,t +Qd i,t

[0074] In the formula: Q i ' ,t , Q i ' ,t The discharge flow rate of reservoir i at time t and its upper and lower limits, in m³. 3 / s.

[0075] 5) Output constraints

[0076]

[0077] In the formula: p i,t , p i,t Let represent the power output of reservoir i at time t and its upper and lower limits, in MW.

[0078] (2.3) Model Solution

[0079] This invention employs the NSGA-II algorithm for solution. By inputting different scenarios and corresponding solutions as boundary conditions, the NSGA-II algorithm iteratively calculates and obtains non-dominated solution sets under different solutions. Finally, a crowding algorithm is used to select the optimal solution set.

[0080] 3. Practical Application

[0081] (1) Project Background

[0082] This invention selects five cascade hydropower stations on the main stream of a river basin in southwestern my country as the research object. This cascade of hydropower stations is one of the thirteen major hydropower bases planned in my country and plays an important role in my country's energy development. Among them, stations A and D are multi-year regulating stations, while the remaining three are seasonal regulating stations with relatively poor regulation performance. Currently, stations A, D, and E are directly dispatched by the Southern Power Grid dispatch center to participate in electricity market transactions, while the hydropower stations under the control of the central control center are centrally dispatched by the Yunnan Power Grid dispatch center. Therefore, this invention simplifies the cascade system to a model of station A-station D, using the actual inflow data of the two stations from 1954 to 2022 and the actual electricity price transaction data from 2017 to 2022 as historical data for the solution. Basic data for the reservoirs of stations A and D are shown in the table.

[0083] Table 1

[0084]

[0085] (2) Model Solving

[0086] (a) Generation of typical scenarios

[0087] For power plants A and D participating in various trading varieties in the provincial electricity market, Latin hypercube sampling, t-SNE dimensionality reduction, and a k-means algorithm based on GWO were used to cluster the electricity price data. The trading variety price sequences were decomposed into four types of trading variety price sequences and transformed into actual electricity price data to generate typical scenarios. Specific electricity price scenarios are as follows: Figure 3 As shown. The obtained electricity price scenario and runoff scenario are combined using a Cartesian product, that is, let the generated electricity price scenario set be... Typical scenarios for incoming water are If the corresponding number of scenes are k and n respectively, then the number of scenes after combination is k×n. The combination flowchart is as follows: Figure 4 As shown.

[0088] (b) Model Results Analysis

[0089] The flood season in this basin is from June to October, therefore the scheduling period is chosen to be one calendar year. The water level at the beginning of June is selected as the control node; the upper limit for the remaining periods is the normal high water level, and the lower limit is the dead water level. Using a 5m scale for the pre-flood drawdown water level interval, 11 schemes are generated by adjusting the depth of the pre-flood drawdown water level at each station in the cascade, as shown in Table 2. The above basic conditions, combined with the generated scenarios and schemes, are used to simulate scheduling using the NSGA-II algorithm. The results are as follows: Figure 5-6 As shown.

[0090] Table 2

[0091]

[0092] Figure 5 The calculation results for different water inflow years under a deterministic electricity price are presented. Based on the average transaction price of cascade hydropower stations on the main stream of a river basin in Southwest China participating in the electricity market over many years, the average electricity price during the flood season is set at 0.14 yuan / kWh, and the average electricity price during the dry season is set at 0.25 yuan / kWh. These values ​​are then used in the model for simulation calculations. It can be seen that under both wet and dry years, the power generation efficiency and drawdown energy storage value of power stations A and D are maximized when the drawdown reaches the ranges of 1170–1175m and 765–770m, respectively. During dry years, to prevent excessively low water levels from affecting power generation efficiency, the power generation efficiency and drawdown energy storage value of power stations A and D are maximized when the drawdown reaches the ranges of 1170–1175m and 790–795m, respectively.

[0093] Figure 6 The calculation results for different inflow year groups under uncertain electricity prices are presented. Considering the uncertainty of electricity prices, the optimal drawdown water level ranges for the three inflow years (high, average, and low) are consistent with those under deterministic electricity prices.

[0094] Figure 7 The paper presents a comparison of two scenarios: deterministic and uncertain electricity prices. It shows that considering the impact of electricity price uncertainty on reservoir drawdown improves the overall power generation efficiency and drawdown energy storage of cascade reservoirs. Specifically, in high-water years, scenarios 1 and 4 significantly improve the overall power generation efficiency of the cascade. In normal-water years, the power generation efficiency and drawdown energy storage effectively improve in all three scenarios, averaging 14.6%, 12.74%, and 11.89% respectively, with relatively low changes in drawdown energy storage. In low-water years, the overall trends of power generation efficiency and drawdown energy storage are generally consistent, with a slight deviation of approximately 0.59% between the drawdown energy storage under uncertain electricity prices and deterministic conditions. In scenario 9, the average power generation efficiency is 1.59% lower than under deterministic electricity prices, but the error is small and the overall trend is consistent, proving that the pre-flood drawdown rules obtained by the model established in this invention are reasonable and reliable, and can provide a reference for scheduling decisions.

[0095] Through comparative analysis of different methods and schemes, it was verified that the pre-flood drawdown water level control model proposed in this invention can effectively meet the stable operation of cascade reservoirs during the drawdown period, improve the practicality of the drawdown scheme, and the results are highly reliable. While ensuring accuracy, it can effectively improve the benefits of hydropower stations and the efficiency of water energy utilization.

Claims

1. A method for controlling the pre-flood water level drawdown of cascade reservoirs under uncertain electricity price conditions, characterized by including: The following steps are required: (1) Constructing a sample set of uncertain electricity prices Based on years of market transaction electricity price data, the Latin hypercube sampling method was used to sample the electricity price data, and the t-SNE method was used to reduce the sampling results to obtain an electricity price sample set. (2) Generate typical electricity price scenarios The elbow method is used to select the number of clusters, and the sum of squared errors within each cluster is used as the criterion to decompose the electricity price series of the trading commodity into multiple commodity electricity price series, which are then converted into actual electricity price data. Typical scenarios are generated by clustering using the gray wolf-optimized k-means algorithm. The specific steps are as follows: Step 1. Based on the electricity price sample, the elbow method is used to select the number of clusters K; Step 2. Calculate the Euclidean distance and average distance between any two data points in the electricity price sample set, where a≠b; for each data point in the electricity price sample set, determine the density value centered at each data point at a distance D, using the following formula: In the formula: x a x b Two random data points are given in the low-dimensional scene set; a, b, and k are the data point numbers; d(x a ,x b ) is x a ,x b The Euclidean distance between them; D is the distance between x and x. a ,x b The average distance between them; C n 2 Let f(x) be the number of pairwise combinations of n data points; f(x) is a 0-1 function; desnity(x) a ) is x a Density value at point; Step 3. Using density as the fitness function, the Gray Wolf Optimization Algorithm is used to continuously update the positions of elite wolves and find the optimal initial cluster centers. Step 4. Calculate the Euclidean distance from the electricity price sample data of non-cluster centers to the K cluster centers, and divide each sample data into the cluster with the closest distance; Step 5. Calculate the centroids of the K clusters respectively, and update the centroids of the K clusters as the new cluster centers. Step 6. Repeat Steps 2 to 5 until the cluster centers no longer change. The final cluster centers are the K typical electricity price scenarios {ζ1,ζ2,...,ζ}. k }; (3) Generating electricity price-runoff combination scenarios The typical electricity price scenario generated is combined with three runoff scenarios—abundant, average, and dry—using the concept of the Cartesian product. (4) Construct an optimization model for the pre-flood water level drawdown control of cascade hydropower stations A multi-objective scheduling model is established with the optimization objectives of maximizing power generation efficiency, minimizing water wastage, and maximizing drawdown energy storage value, as detailed below: in: In the formula: E represents the maximum power generation benefit of the cascade reservoir group during the scheduling period; n and N are the trading variety number and total number, respectively; T is the scheduling period; i and M are the reservoir number and total number, respectively; Δt is the number of seconds in the t-th time period, in seconds; A i Let q be the output coefficient of the i-th reservoir; i,t Let m be the power generation flow rate of the i-th reservoir during time period t. 3 / s;H i,t Let e ​​be the water head height of the i-th reservoir during time period t, in meters. i,n,t The electricity price for the nth trading type during the t-th time period of the i-th reservoir is expressed in yuan / kWh; V q The amount of water discharged from the cascade reservoirs, in m 3 ;Qd i.t Let m be the discharge flow rate of the i-th reservoir during time period t. 3 / s;r i,n,t Ed represents the weight of the nth trading variety for the i-th reservoir during time period t in electricity trading; Ed represents the drawdown storage capacity of the cascade reservoirs, in kWh; ES i,t Calculate the energy storage (kWh) for the i-th reservoir during time period t; η i Let UV be the water consumption rate of the i-th reservoir; i,t Let m be the available water volume of the upstream reservoir during time period t for the i-th reservoir. 3 V i,t Let HS be the reservoir capacity above the dead water level of reservoir i at the end of time period t, in meters. i,t The average head (m) used to calculate the energy storage capacity of reservoir i at the end of time period t; Z i,t Let be the water level of reservoir i at the end of time period t, in meters. Let be the dead water level of reservoir i, in meters. The downstream tailwater level used to calculate the energy storage of reservoir i is selected from the downstream tailwater level corresponding to 1 / 3 of the maximum power generation flow of reservoir i, in meters. (5) Select the optimal dropout control scheme The NSGA-II algorithm is used to solve for the benefit values ​​under different schemes. The different drawdown control schemes are simulated and scheduled. The congestion ranking method is used to select the benefit values ​​under different schemes. The optimal drawdown control scheme is selected based on the criterion of maximizing the benefit value.

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