A method for quantifying flexibility of cascade hydropower in a power market environment

Abstract

The present application belongs to the technical field of dispatching operation of power system and market operation of hydropower, and discloses a method for quantifying flexibility of cascade hydropower under the environment of electricity market. Data is collected and preprocessed; dynamic climbing constraints driven by electricity price quantile are constructed from the two dimensions of technical availability and economic rationality, five flexible characteristic regions of electricity price sensitivity are divided; a double-objective dispatching model of optimal peak shaving effect and maximum economic benefit is established, a constraint condition system is established, and the optimal output and flexibility configuration scheme of cascade hydropower are obtained by using mixed integer linear programming. The present application deeply integrates the quantification of hydropower flexibility technology and the spot electricity price signal, solves the problems of spatial and temporal mismatch of supply and demand of flexibility, separation of technology and market, and single dispatching target, etc., and can significantly improve the matching degree of supply and demand of flexibility, the level of new energy consumption and the economic benefit of hydropower, and is suitable for the market dispatching of cascade hydropower and efficient use of flexible resources under the scenario of high proportion of new energy grid connection.

Description

Technical Field

[0001] This invention relates to the technical field of power system dispatching and operation and hydropower market operation, specifically to a method for quantifying the flexibility of cascade hydropower in a power market environment. Background Technology

[0002] The highly random, intermittent, and volatile nature of renewable energy output places extremely high demands on the flexibility and regulation capabilities of the power system. Cascade hydropower, with its advantages of fast response, low operating costs, and wide regulation range, has become the most important flexibility and regulation resource in scenarios with a high proportion of renewable energy connected to the grid.

[0003] However, the current flexible utilization of cascade hydropower still faces three core problems: First, there is a mismatch between the supply and demand of flexibility in time and space, with both excess and shortage of regulation capacity, making it difficult to adapt to the real-time fluctuations of new energy sources; second, there is a disconnect between the quantification of flexibility and market mechanisms, with regulation potential being assessed only from a technical perspective without considering the impact of spot price fluctuations on the economic value of flexibility, resulting in the inability to effectively reflect the value of flexibility through the market; and third, there is insufficient coordination between dispatching decisions and the electricity market, with traditional dispatching models struggling to simultaneously ensure the safe operation of the power grid and the economic benefits of hydropower companies, thus restricting the efficient allocation of flexibility resources and the improvement of new energy consumption levels.

[0004] Existing research has made some progress in defining hydropower flexibility and multi-energy complementary dispatch, but there are still obvious shortcomings: most studies focus on analyzing the technical characteristics of hydropower such as its ramp-up capability and output range, without incorporating electricity market price signals into the flexibility quantification system, resulting in a disconnect between the supply capacity for regulation and market demand; there is a lack of dynamic matching mechanisms, and the correlation between flexibility supply and demand and electricity price signals has not been established, making it impossible to achieve accurate matching of flexibility on a spatiotemporal scale; dispatch models mostly aim at optimizing the single peak-shaving effect, without fully considering the market-oriented profit demands of hydropower companies, making it difficult to promote and apply them in the electricity market environment.

[0005] Therefore, there is an urgent need to propose a method for quantifying and optimizing the flexible allocation of cascade hydropower that simultaneously considers technological availability and economic rationality, in order to solve the problems of the disconnect between technology and the market and the structural mismatch between supply and demand, and to achieve synergistic optimization of power grid security and hydropower economic benefits. Summary of the Invention

[0006] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method for quantifying the flexibility of cascade hydropower in the context of the power market. This method serves as a supply and demand coordination quantification method for cascade hydropower flexibility in the context of high-proportion renewable energy grid connection, as well as a technical-economic dual-objective optimization method driven by electricity price signals. This method addresses the problems of flexibility quantification being fragmented with the market, supply and demand mismatch, and single scheduling objective.

[0007] The technical solution of this invention is as follows: A method for quantifying the flexibility of cascade hydropower in an electricity market environment, comprising the following steps:

[0008] Step 1: Basic data collection and preprocessing;

[0009] Step 2: Construct a quantitative method for the flexible supply capacity of hydropower;

[0010] Step 2.1: Determine the basic climbing constraints based on historical climbing data from a technical perspective, define the climbing range, and perform upward and downward cumulative frequency fitting on the historical climbing data. Select the values ​​corresponding to the 95th percentile of the cumulative frequency curve as the basic constraints for upward and downward climbing, respectively.

[0011] Step 2.2: Introduce the electricity price percentile level parameter from the economic dimension to construct a dynamic ramp constraint driven by the electricity price percentile. Through the linear regression formula, the value of the dynamic ramp constraint is continuously and dynamically adjusted between the 90th percentile and the 98th percentile of the cumulative frequency of upward adjustment and the cumulative frequency of downward adjustment, so that the flexible supply capacity of hydropower changes with the electricity price signal.

[0012] Step 2.3: Based on dynamic ramping constraints and the upper limit of hydropower station output, quantify the flexible supply capacity of hydropower supply during different time periods for upward and downward adjustments.

[0013] Step 2.4: Divide the hydropower flexibility characteristic zones, including the single-transformer zone for increasing flexibility, the single-transformer zone for decreasing flexibility, the economic operation gain zone, the economic operation stability zone, and the multi-objective coordinated control zone, and limit the power output of the hydropower station to the non-single-transformer zone;

[0014] Step 3: Construct a dual-objective scheduling model for the flexibility of cascade hydropower;

[0015] Step 3.1: With the goal of achieving the best peak-shaving effect, establish an objective function that minimizes the peak-to-valley difference of the system's remaining load;

[0016] Step 3.2: With the goal of maximizing economic benefits, establish an objective function that maximizes the net revenue from the sale of hydropower electricity in the market;

[0017] Step 3.3: The two objectives of optimal peak-shaving effect and maximum economic benefit are integrated into an overall objective function using the linear weighting method. A normalized benchmark value is introduced to eliminate the difference in dimensions, and an adjustable weight coefficient is set to adapt to different operating requirements.

[0018] Step 3.4: Establish a constraint system, including technical safety constraints, market rule constraints, hydropower flexibility supply capacity, and hydropower flexibility characteristic area non-single transformer area constraints. Among them, technical safety constraints include at least water balance constraints, reservoir capacity constraints, hydropower station output constraints, dynamic ramping constraints, water flow lag constraints, and ecological flow constraints. Market rule constraints include at least cascade total transaction volume constraints and single power station transaction volume allocation constraints. Hydropower flexibility supply capacity and hydropower flexibility characteristic area non-single transformer area constraints are respectively the hydropower upward and downward flexibility supply capacity in Step 2.3 and the hydropower flexibility characteristic area in Step 2.4.

[0019] Step 4: Solving and optimizing the dual-objective scheduling model for the flexibility of cascade hydropower.

[0020] In step 2, the specific method for quantifying the technical dimensions is as follows:

[0021] The gradient of time period t is defined as:

[0022]

[0023] In the formula, Let be the slope gradient during time period t. This represents the actual output of the hydropower station during time period t. This represents the actual output of the hydropower station during time period t-1. >0 indicates upregulation. <0 indicates downward adjustment, and the absolute value of the downward adjustment gradient is taken;

[0024] Cumulative frequency fitting was performed on the preprocessed historical climbing data to obtain cumulative frequency curves for both upward and downward climbing magnitudes. The values ​​corresponding to the 95th percentile of the upward and downward cumulative frequency curves were selected as the technical constraints for upward basic climbing. With lowering the basic ramp constraint .

[0025] In step 2, the specific method for constructing the dynamic ramp-up constraint driven by electricity price quantiles is as follows:

[0026] Introducing electricity price percentile level parameters The calculation formula is:

[0027]

[0028] In the formula, k is a number that satisfies λ(k)≤λ t Integers less than λ(k+1); λ t This indicates the electricity price t days prior. The value range is [0,1]. The smaller the value, the lower the electricity price during that period; The larger the value, the higher the electricity price during that period;

[0029] The linear regression formula with adjusted ramp constraint is:

[0030]

[0031] The linear regression formula for reducing the climbing constraint is:

[0032]

[0033] In the formula, , These are the upward ramping constraint values ​​corresponding to the 90th percentile of the cumulative frequency and the downward ramping constraint values ​​corresponding to the 90th percentile of the cumulative frequency, respectively. , These are the upward ramping constraint values ​​corresponding to the 98th percentile of the cumulative frequency, and the downward ramping constraint values ​​corresponding to the 98th percentile of the cumulative frequency, respectively. , These are the upward ramping constraint value corresponding to the 95th percentile of the cumulative frequency and the downward ramping constraint value corresponding to the 95th percentile of the cumulative frequency, respectively, which are the basic ramping constraints.

[0034] In step 2, the hydropower flexibility characteristic zone is divided into 5 areas, including:

[0035] Increase flexibility in single-variable zones: Hydropower stations only have the capacity to increase flexible supply, among which This is the upper limit of the hydropower station's output.

[0036] Reduce flexibility in single-variable zones: Hydropower stations only have the capacity to reduce flexible supply.

[0037] Economic operating gain zone: And the corresponding electricity price percentile level During periods of high electricity prices (>0.5), hydropower station output is in a high-yield range.

[0038] Stable economic operation zone: And the corresponding electricity price percentile level During periods of low electricity prices (≤0.5), the output of hydropower stations remains within a stable range.

[0039] Multi-objective coordinated control zone: Hydropower station output spans multiple zones;

[0040] The output of hydropower stations will be limited to non-single-transformer zones, namely the economic operation gain zone or the economic operation stability zone, in order to maintain both upward and downward flexibility in supply capacity.

[0041] In step 3, the objective function of the dual-objective scheduling model for the flexibility of cascade hydropower is:

[0042] The optimal goal for peak shaving effect is to minimize the difference between peak and valley loads of the system's remaining load.

[0043]

[0044] In the formula, ΔP is the peak-to-valley difference of the remaining load, in MW; The remaining load for time period t is expressed in MW, and the formula is:

[0045]

[0046] in, The total system load for time period t is expressed in MW. , The figures represent the predicted wind power and solar power output for time period t, in MW.

[0047] The objective of maximizing economic benefits is to maximize the net revenue from the sale of hydropower electricity in the market.

[0048]

[0049] In the formula, R represents the daily net revenue from hydropower, in ten thousand yuan; N represents the total number of cascade hydropower stations. d represents the output of the i-th hydropower station in time period t, in MW; d represents the unit price of water wastage, in yuan / m³, which is determined based on a combination of water resource fees and power generation revenue. Δt represents the discharge flow of the i-th hydropower station during time period t, in m³ / s; Δt represents the duration of the time period, in hours.

[0050] The overall objective function adopts a linear weighted method:

[0051]

[0052] In the formula, , The target weight coefficient satisfies + =1, reflecting the importance of economic targets and peak-shaving targets respectively; The maximum net profit obtained when optimizing economic objectives individually, expressed in ten thousand yuan; The maximum remaining load peak-to-valley difference, expressed in MW, is obtained when optimizing the peak-shaving target independently; a normalized baseline value is introduced. and This eliminates the dimensional differences between the two objectives, making the weighted results comparable.

[0053] Step 1 specifically involves:

[0054] Step 1.1: Collect historical ramp-up data of hydropower stations, electricity market transaction data, and predicted output data of new energy sources;

[0055] Step 1.2: Perform outlier removal, missing value imputation, and normalization on the collected raw data.

[0056] Step 4 specifically involves:

[0057] Step 4.1: Input basic data, including hydropower station parameters, electricity price data, predicted output data of new energy sources, and historical ramp-up data of hydropower stations;

[0058] Step 4.2: Following Step 2, calculate the flexible supply capacity of cascade hydropower in each time period to obtain the hydropower flexibility characteristic zone;

[0059] Step 4.3: Construct a dual-objective scheduling model for cascade hydropower flexibility, whose objective function is the overall objective function in Step 3.3:

[0060]

[0061] The constraints are the same as the constraint system in step 3.4;

[0062] Step 4.4: Set the solver parameters, call the mixed integer linear programming solver to solve the dual-objective scheduling model of cascade hydropower flexibility, and obtain the optimal power output plan, reservoir water level plan and water abandonment plan for each time period of cascade hydropower.

[0063] Step 4.5: Output the optimization results and perform flexibility supply and demand matching analysis, peak shaving effect analysis, and economic analysis.

[0064] The beneficial effects of this invention are:

[0065] (1) This invention constructs a method for quantifying hydropower flexibility from the dual dimensions of technological availability and economic rationality, and accurately delineates five major characteristic zones of hydropower flexibility based on the dynamic response relationship between electricity price percentiles and ramp constraints. These characteristic zones clearly define the operational boundaries and optimization directions under different scenarios, guide the power output of regulating power stations to focus on the core high-efficiency range, avoid the risk of regulation imbalance, and efficiently release the regulation potential of cascade hydropower stations.

[0066] (2) The dynamic ramp constraint driven by the price quantification proposed in this invention enables the deep integration of hydropower flexibility technology quantification and market mechanism, and binds flexibility quantification with electricity market signals, thus solving the problem of the separation of technology quantification and market mechanism in traditional methods and the difficulty in reflecting the value of flexibility.

[0067] (3) The cascade hydropower flexibility dual-objective scheduling model constructed in this invention realizes the coordinated optimization of power grid security (peak shaving) and hydropower economic benefits, solves the problem of insufficient coordination between traditional scheduling and the power market, and significantly improves the comprehensive benefits of hydropower while ensuring power grid security. Attached Figure Description

[0068] Figure 1 This is a general technical roadmap of the method of the present invention;

[0069] Figure 2 These are the cumulative frequency curves and frequency histograms of the gradient of the hydropower station, where (a) is the cumulative frequency curve of upward adjustment, (b) is the cumulative frequency curve of downward adjustment, (c) is the frequency histogram of upward adjustment, and (d) is the frequency histogram of downward adjustment.

[0070] Figure 3 It includes a curve showing the relationship between the flexible supply capacity and output of hydropower, and a distribution map of five major characteristic areas;

[0071] Figure 4 This is a typical graph showing the relationship between daily electricity prices and dynamic ramp-up constraints for hydropower.

[0072] Figure 5 This is a supply and demand comparison chart of the flexibility adjustment method of the present invention;

[0073] Figure 6 This is a supply and demand comparison chart of the flexibility of the method of the present invention.

[0074] Figure 7 This is a diagram illustrating the hydropower output and peak-shaving process of the method of this invention. Detailed Implementation

[0075] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0076] A method for quantifying the flexibility of cascade hydropower in an electricity market environment includes the following steps:

[0077] Step 1: Basic data collection and preprocessing;

[0078] This step aims to provide high-quality foundational data for subsequent flexibility quantification and optimized scheduling. The accuracy and completeness of the data directly affect the reliability of the final results.

[0079] Step 1.1: Data Acquisition;

[0080] Collect the following four types of basic data:

[0081] Historical ramp-up data for hydropower stations: High-resolution historical operating data of 15 minutes for 5 years were collected from all hydropower stations in the cascade, including unit output, reservoir water level, inflow, outflow, power generation, and water discharge for each time period. The data sampling frequency was 15 minutes / time.

[0082] Electricity market transaction data: Collects day-ahead spot electricity price data from the electricity market, including nodal prices and system average prices for each time period.

[0083] New energy power output forecast data: Collect historical operating data of wind power and photovoltaic power, including 15-minute forecast and actual power output data of each wind farm and photovoltaic power station.

[0084] System operation data: Collect the total load data of the target power grid for 15 minutes.

[0085] Step 1.2: Data preprocessing;

[0086] Preprocess the collected raw data to eliminate noise and outliers and improve data quality;

[0087] Outlier removal: The 3σ criterion is used to remove outlier data. For a time series of a variable, its mean μ and standard deviation σ are calculated. Data that exceeds the range [μ-3σ, μ+3σ] are considered outliers and replaced with the average of adjacent time periods.

[0088] Missing value imputation: For a small number of missing data, linear interpolation is used for imputation; for data that is missing for more than 3 consecutive time periods, the average value of historical data in the same period is used for imputation.

[0089] Data normalization: To eliminate the influence of different units of measurement on subsequent calculations, all data are normalized, mapping the data to the interval [0,1]. The normalization formula is as follows:

[0090]

[0091] In the formula, x′ represents the normalized data; x represents the original data; x min and x max These are the minimum and maximum values ​​of the variable, respectively.

[0092] Step 2: Construct a quantitative method for the flexible supply capacity of hydropower;

[0093] From the dual dimensions of technological availability and economic rationality, a quantitative method for cascade hydropower flexibility under the power market environment is established, and five major response characteristic zones of hydropower flexibility are accurately delineated.

[0094] 2.1 Quantification of technical dimensions: Determination of basic ramp-up constraints based on historical data;

[0095] The gradient of time period t is defined as:

[0096]

[0097] In the formula, ΔP ramp,t The gradient (MW) is the gradient during time period t. This represents the actual power output (MW) of the hydropower station during time period t. This represents the actual power output (MW) of the hydropower station during time period t-1. Wherein, ΔP ramp,t >0 indicates upward adjustment, meaning the hydropower station increases its output during time period t; ΔP ramp,t <0 indicates a downward adjustment, meaning the hydropower station reduces its output during time period t. To eliminate the influence of positive and negative values ​​on the statistics, the absolute value of the downward adjustment gradient is taken.

[0098] Cumulative frequency fitting was performed on the preprocessed 5-year historical climbing data, and the results are as follows: Figure 2 The cumulative frequency curves for adjusting the ramp rate upwards and downwards are shown. The value corresponding to the 95th percentile of the cumulative frequency curves is selected as the upper limit of the technical ramp rate adjustment constraints, i.e., the basic constraint for adjusting the ramp rate upwards. With lowering the basic constraints of the ramp .

[0099] Taking the Lancangjiang DCS hydropower station as an example, the station has a total installed capacity of 1350MW. Based on historical operating data from 2020 to 2024, the upward slope basic constraint is calculated to be 239.04MW / 15min, and the downward slope basic constraint is calculated to be 245.47MW / 15min.

[0100] 2.2 Quantification from an economic perspective: Construction of dynamic ramp-up constraints driven by electricity price quantiles;

[0101] This invention introduces the electricity price percentile level parameter. This represents the relative position of the electricity price during a given time period within the daily distribution. First, a distribution sequence of the daily electricity price is constructed: {λ1, λ2, ..., λ...} 24 Then, the distribution sequence of the daily electricity price is sorted from smallest to largest to obtain the sorted electricity price sequence {λ}. (1) ,λ (2) ,...,λ (24) For any time period t, the electricity price λ t Its electricity price percentile level The calculation formula is:

[0102]

[0103] In the formula, k is a number that satisfies λ(k)≤λ t Integers less than λ(k+1). The value range is [0,1]. The smaller the value, the lower the electricity price during that period; The larger the value, the higher the electricity price during that period.

[0104] Based on the electricity price percentile level parameter, a linear dynamic adjustment mechanism for hydropower ramping constraints is constructed to achieve continuous dynamic adjustment between the 90th percentile and the 98th percentile.

[0105] Adjusting the climbing constraint linear regression formula:

[0106]

[0107] Lowering the climbing constraint linear regression formula:

[0108]

[0109] In the formula, , These are the upward ramping constraint values ​​corresponding to the 90th percentile of the cumulative frequency and the downward ramping constraint values ​​corresponding to the 90th percentile of the cumulative frequency, respectively. , These are the upward ramping constraint values ​​corresponding to the 98th percentile of the cumulative frequency, and the downward ramping constraint values ​​corresponding to the 98th percentile of the cumulative frequency, respectively. , These are the upward ramp constraint value corresponding to the 95th percentile of the cumulative frequency and the downward ramp constraint value corresponding to the 95th percentile of the cumulative frequency, respectively, which are the basic ramp constraints.

[0110] From the above formula, it can be seen that when When the slope constraint decreases from 0.5 to 0, it smoothly increases from the basic constraint to the 98th percentile, gradually improving the flexible supply capacity of hydropower and adapting to scenarios with large-scale renewable energy generation and strong demand for flexibility; when When the slope constraint is increased from 0.5 to 1, the ramp constraint decreases smoothly from the basic constraint to the 90th percentile, and the flexible supply capacity of hydropower gradually shrinks, prioritizing high-output operation to capture peak electricity price benefits.

[0111] By coupling the aforementioned technical constraints of differentiated power adjustment with electricity price signals, a precise quantitative model of the flexible supply capacity of hydropower during different time periods (upward and downward adjustments) can be constructed:

[0112] Flexible supply capacity of hydropower during peak hours:

[0113]

[0114] In the formula, F up,t For time period t, the flexible supply capacity of hydropower (MW); P h,max,tThe maximum output (MW) of the hydropower station during time period t is determined by factors such as reservoir water level and unit capacity. The actual power output (MW) of the hydropower station during time period t; The ramp-up constraint (MW / 15min) is obtained by linear regression of electricity price quantiles for time period t.

[0115] Flexible supply capacity of hydropower during peak hours:

[0116]

[0117] In the formula, The flexible supply capacity of hydropower during the time period t (MW); The lower limit of hydropower station output (MW) for time period t is determined by factors such as ecological flow and minimum technical output of the unit; The downward ramp-up constraint (MW / 15min) is obtained by linear regression of electricity price quantiles for time period t.

[0118] 2.3 Division of Hydropower Flexibility Characteristic Zones and Operation Strategies;

[0119] Based on the flexibility of hydropower supply and the price percentile, hydropower output is divided into five price-sensitive hydropower flexibility characteristic zones, clarifying the operational boundaries and optimization directions under different scenarios. The output range, price characteristics, and operational strategies for each characteristic zone are as follows:

[0120] Table 1. Hydropower Flexibility Characteristics Zone

[0121]

[0122] Limiting the output of hydropower stations to non-single-transformer zones (i.e., economically profitable zones or economically stable zones) can simultaneously maintain a high level of flexibility in both upward and downward adjustments of hydropower supply, which is the optimal operating range for hydropower.

[0123] Step 3: Construct a dual-objective scheduling model for the flexibility of cascade hydropower;

[0124] Using the quantitative results of the flexibility of electricity price-sensitive hydropower as the core input, a dual-objective scheduling model for the flexibility of cascade hydropower is constructed, which achieves the best peak-shaving effect and the greatest economic benefits, realizing the synergistic optimization of power grid security and hydropower economic benefits.

[0125] 3.1 Construction of the objective function;

[0126] 3.1.1 Optimal peak-shaving effect;

[0127] The peak-to-valley difference in residual load directly reflects the system's demand for flexible adjustment resources. The smaller the peak-to-valley difference, the lower the system's peak-shaving pressure and the more stable the operation. The objective function for achieving optimal peak-shaving effect is to minimize the peak-to-valley difference in the system's residual load.

[0128]

[0129] In the formula, ΔP is the peak-to-valley difference of the remaining load (MW); The remaining load (MW) for time period t is calculated using the following formula:

[0130]

[0131] in, The total system load (MW) is given by time period t. , The forecasted output (MW) of wind power and photovoltaic power are respectively for time period t.

[0132] 3.1.2 Maximizing economic benefits;

[0133] The objective function that maximizes the net revenue from selling electricity in the hydropower market is the one that optimizes economic returns.

[0134]

[0135] In the formula, R represents the daily net revenue from hydropower (in ten thousand yuan); λ t The price of electricity t days in advance (yuan / MWh); N is the total number of cascade hydropower stations; d represents the power output (MW) of the i-th hydropower station in time period t; d represents the unit price of water wastage (yuan / m³), which is determined based on a combination of water resource fees and power generation revenue. Let t be the discharge flow of the i-th hydropower station during time period t (m³ / s); Δt is the duration of the time period (h), where Δt = 0.25h.

[0136] 3.1.3 Overall objective function;

[0137] Optimizing peak shaving efficiency and maximizing economic benefits are two conflicting objectives. To transform the dual-objective optimization problem into a single-objective optimization problem for easier solution, a linear weighted method is used to integrate the two objective functions into a single overall objective function:

[0138]

[0139] In the formula, ω1 and ω2 are target weight coefficients, satisfying ω1+ω2=1, which respectively reflect the importance of economic targets and peak-shaving targets; The maximum net profit (in ten thousand yuan) obtained when optimizing the economic objective alone; This is the maximum remaining load peak-to-valley difference (MW) obtained when optimizing the peak-shaving target independently. A normalized baseline value is introduced. and This eliminates the dimensional differences between the two objectives, making the weighted results comparable.

[0140] The target weighting coefficient can be adjusted according to the actual operating needs of the power system. When the system faces high peak-shaving pressure and new energy consumption is difficult, the value of ω2 should be increased to prioritize peak-shaving performance; when power supply is tight and electricity prices are high, the value of ω1 should be increased to prioritize the economic benefits of hydropower.

[0141] 3.2 Constraint System;

[0142] The constraint system covers two categories: technical security constraints and market rule constraints, ensuring the feasibility and compliance of the scheduling plan.

[0143] 3.2.1 Technical security constraints;

[0144] Water balance constraint: describes the relationship between reservoir capacity and time, and is the most basic constraint condition for hydropower dispatch.

[0145]

[0146] In the formula, Let be the reservoir capacity (m³) of the i-th hydropower station during time period t; Let be the inflow rate (m³ / s) of the i-th hydropower station during time period t; Let be the power generation flow rate (m³ / s) of the i-th hydropower station during time period t; Let be the discharge flow rate (m³ / s) of the i-th hydropower station during time period t.

[0147] Reservoir capacity constraints: The reservoir capacity cannot be lower than the dead storage capacity, nor higher than the capacity corresponding to the normal storage level, in order to ensure the safe operation and comprehensive utilization benefits of the reservoir.

[0148]

[0149] In the formula, , These represent the dead storage capacity and the storage capacity corresponding to the normal water level of the i-th hydropower station, respectively (m³).

[0150] Hydropower station output constraints: The output of a hydropower station cannot be lower than the minimum technical output of the generating unit, nor can it be higher than the installed capacity.

[0151]

[0152] In the formula, , These represent the lower and upper limits (MW) of the output of the i-th hydropower station.

[0153] Dynamic ramp constraint: The core constraint of this invention enables the dynamic adjustment of hydropower flexibility supply capacity in response to electricity price signals.

[0154]

[0155] In the formula, , These represent the upward and downward dynamic ramping constraints (MW / 15min) for the i-th hydropower station during time period t.

[0156] Water flow delay constraint: describes the water flow transmission relationship between the upstream and downstream of a cascade hydropower station, that is, the outflow from the upstream hydropower station becomes the inflow from the downstream hydropower station after a certain time delay.

[0157]

[0158] In the formula, For the upstream (i-1)th hydropower station, the time period t−τ i−1 Outflow rate (m³ / s); τ i−1 The flow delay (h) from the (i-1)th upstream hydropower station to the ith hydropower station.

[0159] Ecological flow constraint: In order to protect the river's ecological environment, the discharge flow of hydropower stations must meet the minimum ecological flow requirements.

[0160]

[0161] In the formula, Let be the outflow (m³ / s) of the i-th hydropower station during time period t; Let be the minimum ecological flow (m³ / s) of the i-th hydropower station.

[0162] 3.2.2 Market rule constraints;

[0163] Total transaction volume constraint at different levels: The total transaction volume declared by hydropower companies in the day-ahead market must be consistent with the actual power generation, otherwise they will face deviation assessment.

[0164]

[0165] In the formula, This represents the total daily electricity traded by the cascade hydropower stations (MWh).

[0166] Constraints on the allocation of electricity traded by a single power station: The total electricity traded by a cascade hydropower station group needs to be reasonably allocated among the power stations in order to give full play to the regulation performance of each power station.

[0167]

[0168] In the formula, , These represent the lower and upper limits (MWh) of the daily trading volume of the i-th hydropower station.

[0169] Step 4: Solve the model;

[0170] The bi-objective scheduling model constructed in this invention is a mixed-integer linear programming (MILP) model. It employs Python programming to quantify supply and demand flexibility and calls the Gurobi commercial mathematical programming solver to solve the model. The Gurobi solver boasts advantages such as fast solution speed, high accuracy, and good stability, making it a mainstream tool for solving large-scale linear programming and mixed-integer linear programming problems.

[0171] The specific solution steps are as follows:

[0172] Input basic data, including hydropower station parameters, electricity price data, predicted output data of new energy sources, and system load data.

[0173] Following step 2, calculate the flexible supply capacity of cascade hydropower in each time period to obtain the hydropower flexibility characteristic zone;

[0174] Construct the objective function and constraints of a dual-objective scheduling model for cascade hydropower flexibility, and generate an LP file that can be recognized by the Gurobi solver.

[0175] The Gurobi solver parameters are set, including the solution time limit, MIP gap, and optimization objective. In this invention, the solution time limit is set to 300s, and the MIP gap is set to 0.1%.

[0176] The model is solved using the Gurobi solver to obtain the optimal power output plan, reservoir water level plan, and water discharge plan for each time period of the cascade hydropower project.

[0177] Output optimization results and perform flexibility supply and demand matching analysis, peak shaving effect analysis, and economic analysis.

[0178] The overall technical route of the present invention is as follows: Figure 1 As shown.

[0179] This invention is tested using a real-world scenario involving the Lancang River cascade hydropower stations and a high proportion of wind and solar power grid integration in the Yunnan power grid. By the end of 2025, Yunnan's total installed hydropower capacity exceeded 80 million kW, and the total installed capacity of wind and solar power surpassed 70 million kW. This high proportion of new energy grid integration poses a significant challenge to the safe operation of the power grid. Six cascade hydropower stations in the Lancang River basin—GGQ, XW, MW, DCS, NZD, and JH—were selected as the research subjects, with a total installed capacity of 15,670 MW, covering various regulation capabilities including daily, weekly, and multi-year regulation. Calculations were performed using typical daily data from the pre-flood dry season.

[0180] Step 1: Initial data collection;

[0181] Historical output data for six hydropower stations from 2020 to 2024 were collected in 15-minute increments. The ramp rate for each station was statistically analyzed, yielding the 95th percentile basic ramp constraint and the 90th and 98th percentile ramp constraints. For example, the basic ramp constraint for the DCS hydropower station (1350MW installed capacity) with an upward ramp rate is 239.04MW / 15min, with a 90th percentile of 173.25MW / 15min and a 98th percentile of 323.66MW / 15min; the basic ramp constraint with a downward ramp rate is 245.47MW / 15min, with a 90th percentile of 181.35MW / 15min and a 98th percentile of 330.54MW / 15min.

[0182] Collect day-ahead spot electricity price data for typical 24-hour periods. Collect historical forecast and actual output data of wind and solar power in Yunnan power grid in 2024 for quantile regression modeling. Collect system load data for typical days.

[0183] 1.2 Basic Data Preparation;

[0184] Collect and preprocess the following basic data:

[0185] Parameters of cascade hydropower stations: regulation cycle, installed capacity, normal water level, dead water level, reservoir capacity curve, tailrace level-outflow curve, unit characteristic curve, core technical parameters, etc. for each hydropower station.

[0186] Historical operating data: 15-minute output data, reservoir water level data, and inflow data of the three flexible regulating power stations (GGQ, MW, and DCS) for five consecutive years.

[0187] Electricity market data: Day-ahead spot electricity price data for a typical day.

[0188] New energy data: Historical forecast and actual output data of wind and solar power for the target power grid for one consecutive year, as well as forecast output data of wind and solar power for typical days.

[0189] System data: Total load data of the target power grid system on a typical day.

[0190] Key parameters of the model are set as follows: unit cost of water disposal d = 0.0011 yuan / m³; dual objective weighting coefficients ω1 = 0.9, ω2 = 0.1; quantile regression confidence level 90%; ramp constraint adjustment quantiles are 90% and 98%.

[0191] Step 2: Quantify the flexible supply capacity of hydropower;

[0192] 2.1 Quantification of technical dimensions: Calculation of basic ramp constraints;

[0193] We statistically analyzed the 15-minute output ramp-up data of three flexible regulating power stations (GGQ, MW, and DCS) from 2020 to 2024, and calculated the cumulative frequency curves of the upward and downward ramp-up amplitudes for each power station. The values ​​corresponding to the 90%, 95%, and 98% quantiles were selected as the ramp-up constraint parameters for each power station.

[0194] The DCS hydropower station has the strongest climbing ability, with its 95th percentile climbing constraint being 239.04MW / 15min, which is about 17.7% of its installed capacity and close to the standard regulation rate of hydropower units (20% / min).

[0195] 2.2 Quantification of Economic Dimensions: Calculation of Dynamic Climbing Constraints;

[0196] Based on day-ahead spot electricity price data for typical days in 2025, the electricity price percentile level for each time period is calculated. The dynamic ramping constraints for each power station at each time period are obtained. Taking a DCS hydropower station as an example, its typical daily dynamic ramping constraints and electricity price changes are as follows: Figure 4 As shown.

[0197] Depend on Figure 4 It can be seen that the dynamic ramping constraint of the DCS hydropower station has a clear negative correlation with the electricity price. During daytime hours when the electricity price is low (10:00~16:00), the ramping constraint is larger, and the flexibility of hydropower supply is stronger. During peak hours when the electricity price is higher (08:00~10:00 and 18:00~22:00), the ramping constraint is smaller, the flexibility of hydropower supply is weaker, and priority is given to ensuring the output of electrical energy. This pattern of change is highly consistent with the pattern of change in the system's flexibility demand, achieving a temporal match between flexibility supply and demand.

[0198] 2.3 Calculation of flexible supply capacity and division of characteristic areas;

[0199] By combining the real-time upper limit and actual output of each power station, the upward and downward flexibility supply capacity of a single power station in each time period is calculated. The flexibility supply capacity of the three flexible regulation power stations is then superimposed to obtain the total flexibility supply capacity of the cascade hydropower stations.

[0200] The output of cascade hydropower stations is divided into five major flexibility characteristic zones, and the results are as follows: Figure 3 As shown. By Figure 3 It can be seen that on a typical day, the output of the cascade hydropower stations is mainly distributed in the stable economic operation zone and the economic operation gain zone, avoiding entering the single variable zone of upward and downward adjustment of flexibility, thus maintaining a high supply capacity for both upward and downward adjustment of flexibility.

[0201] Step 3: Solving the dual-objective scheduling model and analyzing the results;

[0202] Call the Gurobi solver to solve the model.

[0203] 4.1 Analysis of the effectiveness of flexible supply and demand matching;

[0204] Calculate the supply and demand deviation parameter This parameter reflects the overall degree of matching between flexible supply and demand; the closer the R value is to 1, the better the matching effect.

[0205] Increase flexibility in supply and demand: such as Figure 5 As shown, the increased flexible supply capacity can meet the increased flexibility demand of new energy sources, with no supply gap. The increased flexible supply capacity ranges from 597.49 to 802.17 MW during peak daytime photovoltaic (PV) output, indicating a higher model supply capacity and stronger adaptability. During nighttime periods of low PV output, the model's increased flexible supply capacity shrinks to 452.6 to 523.8 MW. The average increased R-value is 4.14, demonstrating excellent supply-demand matching performance of the model.

[0206] Reduce flexibility in supply and demand: such as Figure 6 As shown, the model optimizes the flexible supply capacity of cascade hydropower through price-sensitive dynamic ramping constraints. The flexible supply capacity remains between 436.42 and 810.64 MW throughout the day, exceeding the flexible demand from renewable energy sources, with no supply gap, thus ensuring grid stability. The model's average downward adjustment R is 1.10, indicating that supply dynamically contracts with demand, with no surplus at night.

[0207] 4.2 Peak shaving effect analysis;

[0208] Calculate the peak-to-valley difference of the remaining load, such as Figure 7 As shown, the residual load peak-to-valley difference of the model is 0MW, indicating that the model proposed in this invention can maintain excellent peak-shaving effect while meeting the flexibility requirements of wind and solar power.

[0209] 4.3 Economic Analysis;

[0210] The daily net revenue from hydropower was calculated, and the results show that, without any water wastage, the model's total daily electricity sales revenue exceeds 19.8 million yuan. The model, through dynamic ramp constraints, guides hydropower to increase output during periods of high electricity prices, fully capturing the revenue potential of these periods.

[0211] Step 4: Analysis of the mechanism for improving the flexibility and comprehensive benefits of hydropower;

[0212] The core mechanism by which this invention achieves a dual improvement in the flexibility of hydropower supply and overall economic benefits can be summarized in the following three aspects:

[0213] The economic guiding role of electricity price signals: As a core lever for resource allocation, electricity price signals guide hydropower output towards high-yield periods. During periods of high electricity prices, ramp-up constraints contract, and hydropower reduces its flexible supply to prioritize the output of high-value electricity; during periods of low electricity prices, ramp-up constraints expand, and hydropower increases its flexible supply to support the system's absorption of new energy sources. This dynamic adjustment mechanism maximizes the economic benefits of hydropower while ensuring system security.

[0214] The operational constraints of the flexibility characteristic zone: By limiting the output of hydropower stations to non-single-transformer zones, hydropower is prevented from entering operating ranges with only single-regulation capabilities, thus maintaining a high level of flexibility in both upward and downward regulation. This enables hydropower to quickly respond to various regulation demands of the system, effectively improving the system's flexibility availability.

[0215] The synergistic regulation effect of cascade hydropower stations: By fully leveraging the advantages of hydropower stations with varying regulation capabilities, multi-year regulating stations undertake seasonal water volume regulation tasks, while daily and weekly regulating stations handle intraday flexibility regulation tasks. Through the coordinated efforts of cascade hydropower stations, optimal utilization of water resources and optimized allocation of flexible resources in the basin are achieved.

Claims

1. A method for quantifying the flexibility of cascade hydropower in an electricity market environment, characterized in that, The steps are as follows: Step 1: Basic data collection and preprocessing; Step 2: Construct a quantitative method for the flexible supply capacity of hydropower; Step 2.1: Determine the basic climbing constraints based on historical climbing data from a technical perspective, define the climbing range, and perform upward and downward cumulative frequency fitting on the historical climbing data. Select the values ​​corresponding to the 95th percentile of the cumulative frequency curve as the basic constraints for upward and downward climbing, respectively. Step 2.2: Introduce the electricity price percentile level parameter from the economic dimension to construct a dynamic ramp constraint driven by the electricity price percentile. Through the linear regression formula, the value of the dynamic ramp constraint is continuously and dynamically adjusted between the 90th percentile and the 98th percentile of the cumulative frequency of upward adjustment and the cumulative frequency of downward adjustment, so that the flexible supply capacity of hydropower changes with the electricity price signal. Step 2.3: Based on dynamic ramping constraints and the upper limit of hydropower station output, quantify the flexible supply capacity of hydropower supply during different time periods for upward and downward adjustments. Step 2.4: Divide the hydropower flexibility characteristic zones, including the single-transformer zone for increasing flexibility, the single-transformer zone for decreasing flexibility, the economic operation gain zone, the economic operation stability zone, and the multi-objective coordinated control zone, and limit the power output of the hydropower station to the non-single-transformer zone; Step 3: Construct a dual-objective scheduling model for the flexibility of cascade hydropower; Step 3.1: With the goal of achieving the best peak-shaving effect, establish an objective function that minimizes the peak-to-valley difference of the system's remaining load; Step 3.2: With the goal of maximizing economic benefits, establish an objective function that maximizes the net revenue from the sale of hydropower electricity in the market; Step 3.3: The two objectives of optimal peak-shaving effect and maximum economic benefit are integrated into an overall objective function using the linear weighting method. A normalized benchmark value is introduced to eliminate the difference in dimensions, and an adjustable weight coefficient is set to adapt to different operating requirements. Step 3.4: Establish a system of constraints, including technical security constraints, market rule constraints, hydropower flexibility supply capacity, and constraints on non-single-transformer areas within the hydropower flexibility characteristic zone. The technical safety constraints include at least water balance constraints, reservoir capacity constraints, hydropower station output constraints, dynamic ramping constraints, water flow lag constraints, and ecological flow constraints; the market rule constraints include at least total cascade trading volume constraints and single power station trading volume allocation constraints; the constraints on hydropower flexibility supply capacity and hydropower flexibility characteristic area non-single transformer area are respectively the hydropower upward and downward flexibility supply capacity in step 2.3 and the hydropower flexibility characteristic area in step 2.

4. Step 4: Solving and optimizing the dual-objective scheduling model for the flexibility of cascade hydropower.

2. The method for quantifying the flexibility of cascade hydropower in a power market environment according to claim 1, characterized in that, In step 2, the specific method for quantifying the technical dimensions is as follows: The gradient of time period t is defined as: In the formula, Let be the slope gradient during time period t. This represents the actual output of the hydropower station during time period t. This represents the actual output of the hydropower station during time period t-1. >0 indicates upregulation. <0 indicates downward adjustment, and the absolute value of the downward adjustment gradient is taken; Cumulative frequency fitting was performed on the preprocessed historical climbing data to obtain cumulative frequency curves for both upward and downward climbing magnitudes. The values ​​corresponding to the 95th percentile of the upward and downward cumulative frequency curves were selected as the technical constraints for upward climbing magnitude adjustments. With lowering the basic constraints of the climbing slope .

3. The method for quantifying the flexibility of cascade hydropower in a power market environment according to claim 1, characterized in that, In step 2, the specific method for constructing the dynamic ramping constraint driven by electricity price quantiles is as follows: Introducing electricity price percentile level parameters The calculation formula is: In the formula, k is a number that satisfies λ(k)≤λ t Integers less than λ(k+1); λ t This indicates the electricity price t days prior. The value range of is [0,1]. The smaller the value, the lower the electricity price during that period; The larger the value, the higher the electricity price during that period; The linear regression formula with adjusted ramp constraint is: The linear regression formula for reducing the climbing constraint is: In the formula, , These are the upward ramping constraint values ​​corresponding to the 90th percentile of the cumulative frequency and the downward ramping constraint values ​​corresponding to the 90th percentile of the cumulative frequency, respectively. , These are the upward ramping constraint values ​​corresponding to the 98th percentile of the cumulative frequency, and the downward ramping constraint values ​​corresponding to the 98th percentile of the cumulative frequency, respectively. , These are the upward ramping constraint value corresponding to the 95th percentile of the cumulative frequency and the downward ramping constraint value corresponding to the 95th percentile of the cumulative frequency, respectively, which are the basic ramping constraints.

4. The method for quantifying and optimizing the flexibility of cascade hydropower in a power market environment according to claim 1, characterized in that, In step 2, the hydropower flexibility characteristic zone is divided into 5 areas, including: Increase flexibility in single-variable zones: Hydropower stations only have the capacity to increase flexible supply, among which This is the upper limit of the hydropower station's output. Reduce flexibility in single-variable zones: Hydropower stations only have the capacity to reduce flexible supply. Economic operating gain zone: And the corresponding electricity price percentile level During periods of high electricity prices (>0.5), hydropower station output is in a high-yield range. Stable economic operation zone: And the corresponding electricity price percentile level During periods of low electricity prices (≤0.5), the output of hydropower stations remains within a stable range. Multi-objective coordinated control zone: Hydropower station output spans multiple zones; The output of hydropower stations will be limited to non-single-transformer zones, namely the economic operation gain zone or the economic operation stability zone, in order to maintain both upward and downward flexibility in supply capacity.

5. The method for quantifying the flexibility of cascade hydropower in a power market environment according to claim 1, characterized in that, In step 3, the objective function of the dual-objective scheduling model for the flexibility of cascade hydropower is: The optimal goal for peak shaving effect is to minimize the difference between peak and valley loads of the system's remaining load. In the formula, ΔP is the peak-to-valley difference of the remaining load, in MW; The remaining load for time period t is expressed in MW, and the formula is: in, The total system load for time period t is expressed in MW. , The figures represent the predicted wind power and solar power output for time period t, in MW. The objective of maximizing economic benefits is to maximize the net revenue from the sale of hydropower electricity in the market. In the formula, R represents the daily net revenue from hydropower, in ten thousand yuan; N represents the total number of cascade hydropower stations. d represents the output of the i-th hydropower station in time period t, in MW; d represents the unit price of water wastage, in yuan / m³, which is determined based on a combination of water resource fees and power generation revenue. Δt represents the discharge flow of the i-th hydropower station during time period t, in m³ / s; Δt represents the duration of the time period, in hours. The overall objective function adopts a linear weighted method: In the formula, , Let the target weight coefficient satisfy... + =1, reflecting the importance of economic targets and peak-shaving targets respectively; The maximum net profit obtained when optimizing economic objectives individually, expressed in ten thousand yuan; The maximum remaining load peak-to-valley difference, expressed in MW, is obtained when optimizing the peak-shaving target independently; a normalized baseline value is introduced. and This eliminates the dimensional differences between the two objectives, making the weighted results comparable.

6. The method for quantifying the flexibility of cascade hydropower in a power market environment according to claim 1, characterized in that, Step 1 specifically involves: Step 1.1: Collect historical ramp-up data of hydropower stations, electricity market transaction data, and predicted output data of new energy sources; Step 1.2: Perform outlier removal, missing value imputation, and normalization on the collected raw data.

7. The method for quantifying the flexibility of cascade hydropower in a power market environment according to claim 1, characterized in that, Step 4 specifically involves: Step 4.1: Input basic data, including hydropower station parameters, electricity price data, predicted output data of new energy sources, and historical ramp-up data of hydropower stations; Step 4.2: Following Step 2, calculate the flexible supply capacity of cascade hydropower in each time period to obtain the hydropower flexibility characteristic zone; Step 4.3: Construct a dual-objective scheduling model for cascade hydropower flexibility, whose objective function is the overall objective function in Step 3.3: The constraints are the same as the constraint system in step 3.4; Step 4.4: Set the solver parameters, call the mixed integer linear programming solver to solve the dual-objective scheduling model of cascade hydropower flexibility, and obtain the optimal power output plan, reservoir water level plan and water abandonment plan for each time period of cascade hydropower. Step 4.5: Output the optimization results and perform flexibility supply and demand matching analysis, peak shaving effect analysis, and economic analysis.

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