A method for integrating long-, medium- and short-term scheduling of cascade hydropower considering multi-period fluctuations of renewable energy

Abstract

The present invention belongs to the technical field of modeling and solving of water, wind and solar multi-energy complementary scheduling, and particularly relates to a method for integrating long-, medium- and short-term cascade hydropower scheduling that takes into account multi-cycle fluctuations of new energy. First, based on the actual output samples of the power grid over many years of history, a method for characterizing the key fluctuation characteristics of new energy multi-cycles is proposed; then, an adjustable robust optimization and opportunity constraint modeling method is adopted to uniformly incorporate the multi-cycle volatility of new energy into the cascade hydropower scheduling modeling, and a long-, medium- and short-term nested fusion optimization scheduling model for cascade hydropower is constructed; finally, with the help of Lagrangian duality, quantile regression and MILP linearization modeling technology, the model is efficiently solved. And through cascade hydropower application examples, it is shown that compared with the traditional long-, medium- and short-term decoupled cascade hydropower optimization scheduling framework, the method proposed in the present invention more effectively takes into account the current and long-term requirements of the power grid for the regulation capacity of cascade hydropower, and significantly reduces the risk of power shortage and power abandonment in the power grid.

Description

Technical Field

[0001] The present invention belongs to the technical field of modeling and solving multi-energy complementary scheduling of water, wind and solar power, and in particular relates to a long-, medium- and short-term integrated scheduling method for cascade hydropower taking into account multi-cycle fluctuations of new energy. Background Art

[0002] The major challenges that the power grid is currently facing and will soon face are the seasonal fluctuations, extreme fluctuations, random fluctuations of new energy sources, the low proportion of flexible regulation power sources, the lack of long-term and seasonal energy storage technology, the difficulty in seasonal balance of the system, the difficulty in responding to extreme weather, and the difficulty in daily peak regulation and supply guarantee.

[0003] The regulation capacity of cascade hydropower is closely related to the energy storage of reservoirs, and the operating characteristic of water balance makes the regulation capacity of hydropower unsustainable. That is, excessive use of power generation capacity in the current period will consume too much energy storage, affecting the power support capacity in subsequent periods. Excessive water storage in the current period will affect the ability to reduce power generation and avoid it in subsequent periods. Coupled with the random fluctuations of new energy in the short term and the extreme and seasonal fluctuations in the medium and long term, how to optimize the scheduling and operation mode of cascade hydropower stations, take into account the regulation needs of new energy in the current and future periods of the power grid, and improve the regulation efficiency of the entire hydropower scheduling period has become a new scheduling problem that needs to be solved urgently in the transformation of the flexible role of hydropower.

[0004] Currently, power grids mostly use a decoupled long-, medium-, and short-term hydropower scheduling framework. This framework uses the monthly average as the basic decision-making unit at the end of the year to formulate a year-end water level scheduling plan and calculate monthly hydropower generation capacity. In the medium term, the daily average is used as the basic decision-making unit to formulate a daily water level scheduling plan for the next month or week, using the long-term scheduled end-of-month water level as the scheduling boundary. In the short term (day ahead), a 96-point output plan (in 15-minute increments) is formulated within the medium-term defined daily water and power generation boundaries. This decoupled scheduling framework is suitable for cascade hydropower scheduling that maximizes power generation, but it is difficult to meet the requirements of new power systems that require the multi-scale regulation capabilities of hydropower.

[0005] To address these issues, some researchers have begun researching scheduling methods that incorporate short-term renewable energy regulation demand into long-term models. These methods fall into two main categories: the first focuses on establishing a coupled relationship between long-term decision variables and the adequacy of short-term regulation capacity. These methods include analytical derivation and operational simulation. The former mathematically establishes analytical relationships between short-term indicators such as renewable energy curtailment risk, hydropower station curtailment risk, and residual load fluctuations, and long-term decision variables. The latter uses short-term operational simulation results to fit functional relationships between these indicators and long-term decision variables. The second category focuses on modeling methods that embed short-term regulation demand into long-term scheduling models. One approach incorporates analytically derived short-term risk quantification into the long-term scheduling model as a model constraint or objective function, while the other establishes a two-layer nested model. The outer layer allocates the monthly electricity consumption of the long-term scheduling model to daily levels, while the inner layer further considers hydropower's regulation capacity for renewable energy output fluctuations and counter-peak fluctuations within the daily electricity consumption boundary, thereby incorporating the impact of short-term regulation demand into long-term scheduling decisions. However, the essence of these studies remains the development of long-term scheduling plans, and the challenge is to more accurately quantify the daily renewable energy regulation demand for the next year.

[0006] It can be seen that scheduling modeling that achieves hourly resolution throughout the year (8760 hours) can fully take into account the long-, medium- and short-term multi-time scale regulation needs of new energy. However, this method will greatly increase the scale of problem solving, and from a practical engineering perspective, there is a lack of hourly resolution water, wind and solar resource forecast information for the next year, which makes it not very practical. Summary of the Invention

[0007] This paper develops a method for integrating the long-, medium-, and short-term scheduling of cascade hydropower plants that considers the multi-period fluctuations of renewable energy sources (in this paper, renewable energy output refers to the output of wind and photovoltaic power plants). First, a method for characterizing the key multi-period fluctuation characteristics of renewable energy sources is proposed by collecting historical data from the power grid. Subsequently, an adjustable robust optimization and opportunity-constrained modeling approach are employed to integrate the multi-period volatility of renewable energy sources into the optimization of cascade hydropower operations, constructing a cascade hydropower scheduling model that integrates long-, medium-, and short-term optimization with variable time scales. Finally, a MILP equivalent optimization solution is implemented using Lagrangian duality, quantile regression, and two-dimensional linear interpolation methods. By integrating and optimizing the multi-period scheduling plan for cascade hydropower, this paper more effectively balances the grid's current and long-term requirements for cascade hydropower regulation capacity, significantly reducing the risk of power shortages and curtailment. Simulation analysis is also conducted using cascade hydropower stations in the Lancang River basin as the research object.

[0008] Technical solution of the present invention:

[0009] A method for integrating long-, medium-, and short-term cascade hydropower scheduling considering multi-period fluctuations of renewable energy is proposed. The steps are as follows:

[0010] Step (1): Initial calculation conditions.

[0011] Historical observation data: Collect hourly wind power and photovoltaic power output data for the entire province over many years, as well as hourly runoff data for cascade hydropower stations, provincial power grid load data, and other power output data for typical years;

[0012] Basic data of hydropower stations: including installed capacity data, upper and lower limits of reservoir capacity, upper and lower limits of power generation flow, initial and final reservoir capacity, etc.

[0013] Step (2): Construct a long-, medium- and short-term integrated scheduling model for cascade hydropower.

[0014] (2.1) Objective function:

[0015] Objective function 1: Minimize the long-term power shortage and power abandonment.

[0016]

[0017] Objective function 2: Minimize medium-term power shortages and power curtailment.

[0018]

[0019] Objective function three: Minimize short-term power shortage and power abandonment.

[0020]

[0021] Where: is the long-term period (month) in the scheduling model, and its value is the number of remaining months in the year; is the medium-term scale period (days) in the scheduling model, and its value is the number of days remaining in the month; is the short-term period in the scheduling model (h); 、 are the number of hours (h) of long-, medium-, and short-scale scheduling steps in the scheduling model, respectively; 、 、 are long-term, medium-term and short-term loads (MW); For hydropower stations exist Output during the period (MW); They are the long-term actual output, medium-term forecast output, and short-term forecast output of renewable energy (MW); are the long, medium and short term outputs of other power sources (MW) respectively; from the perspective of energy conversion, the abandoned water of the hydropower station can be equivalently converted into abandoned electricity. For hydropower stations exist The abandoned water flow in the period is converted into power output (MW); is the number of hydropower stations.

[0022] (2.2) Cascade hydropower operation constraints:

[0023] (2.2.1) Reservoir water balance constraints:

[0024]

[0025]

[0026]

[0027] Where: For reservoirs exist Storage capacity at the end of the period (10 4 m 3 ); Reservoirs exist Inflow, power generation, and abandoned water flow during the period (m 3 / s); The day of the corresponding month.

[0028] (2.2.2) Cascade hydraulic connection constraints:

[0029]

[0030] Where: For reservoirs exist Natural inflow runoff during the period (m 3 / s); For the upstream cascade hydropower station To the hydropower station The water flow is stagnant.

[0031] (2.2.3) Hydropower station operation boundary constraints:

[0032] The reservoir capacity constraint, power generation flow constraint, outflow flow constraint, output constraint, and ramp constraint of a hydropower station are shown in the following formula.

[0033]

[0034]

[0035]

[0036]

[0037]

[0038] Where: and Hydropower Station exist The upper and lower limits of storage capacity in the time period (m 3 ); and Hydropower Station exist Period Upper and lower limits of power generation flow (m 3 / s); and Hydropower Station exist The upper and lower limits of outbound flow in the time period (m 3 / s); and Hydropower Station exist The upper and lower limits of output for the time period (MW); and They are the upward and downward climbing capabilities of the hydropower station.

[0039] (2.2.4) Adjustment of storage capacity constraints:

[0040]

[0041] Where: For hydropower stations Starting storage capacity (m 3 ), take the reservoir capacity at the end of 24 hours of the previous day's scheduling model.

[0042] (2.2.5) Final storage capacity constraint:

[0043]

[0044] Where: For a given hydropower station Storage capacity at the end of the year (m 3 ).

[0045] (2.2.6) Water level-reservoir capacity relationship constraints:

[0046]

[0047] Where: It is a nonlinear function of the hydropower station with respect to the reservoir capacity.

[0048] (2.2.7) Hydropower station power generation function:

[0049] According to the historical actual operation data of the hydropower station, the nonlinear hydropower station output function is fitted into the form of a two-variable quadratic polynomial.

[0050]

[0051] Where: yes and The average value of is a nonlinear hydropower station output function Parameters.

[0052] (2.2.8) Constraints on conversion from hydropower to electricity:

[0053]

[0054] Where: is the conversion function from abandoned water to abandoned power in a hydropower station.

[0055] (2.3) Uncertainty constraints of new energy:

[0056] (2.3.1) Constraints on long-term seasonal fluctuations in new energy:

[0057] We use robust optimization with adjustable uncertainty intervals to characterize the long-term output uncertainty of renewable energy. By introducing an adjustable parameter to describe the decision maker's conservative judgment regarding robust optimization, we achieve scaling of the uncertainty interval. The actual output of renewable energy is described as the sum of the output forecast and the forecast error, as shown in the following equation.

[0058]

[0059]

[0060] Where: and Respectively, new energy in the long term Actual output and forecast output for the time period (MW); For new energy in the long term Output forecast error for the time period (MW); and New energy in the long term The maximum downward output deviation and the maximum upward output deviation during the time period (MW).

[0061] Introducing new energy uncertainty budget coefficient To define the uncertainty set U of renewable energy output, we can coordinate the robustness and optimality of the optimized scheduling, as shown in the following formula.

[0062]

[0063] Where: Auxiliary variables for adjustable robust optimization with uncertainty intervals.

[0064] (2.3.2) New energy medium-term extreme volatility scenario:

[0065] Based on the historical probability of occurrence, a scenario of extreme fluctuations of new energy for several days is introduced to enhance the ability of hydropower to regulate extreme fluctuations of new energy.

[0066] The definition method for new energy extreme fluctuation events is as follows:

[0067] The average daily output of new energy Compared with the average monthly output The decline in Above and continuing The "more than 10 days" fluctuation scenario is defined as an extreme low output fluctuation event that lasts for several days. ; The average daily output of new energy Compared with the average monthly output The increase in Above and continuing The "more than 24-day" fluctuation scenario is defined as an extreme high output fluctuation event lasting for several days. , see the following formula.

[0068]

[0069]

[0070] Where: is the day index, and are the start and end times of extreme fluctuations respectively; It is the key characteristic parameter of sustained extreme volatility events.

[0071] (2.3.3) Constraints on short-term reserve regulation demand for new energy:

[0072] The reserve supply and demand relationship between hydropower and renewable energy is characterized as an opportunity constraint to quantify the demand for flexible regulation capacity of hydropower due to the short-term uncertainty of renewable energy, as shown in the following formula.

[0073]

[0074]

[0075] Where: Indicates the probability that the inequality in the brackets is true; and Respectively represent hydropower stations exist Time period up reserve and down reserve (MW); and Indicates that new energy in the short term The predicted output and actual output (MW) at time , where the actual output is a random variable; and It is the confidence level that cascade hydropower can provide sufficient backup to meet the uncertainty of new energy. .

[0076] The up and down regulation of reserve capacity of a hydropower station is mainly limited by the installed capacity and ramping capability of the hydropower station, as shown in the following formula.

[0077]

[0078]

[0079] Step (3): Model solution.

[0080] (3.1) Multi-objective optimization solution method:

[0081] The hierarchical sequence method with relative tolerance is used to solve the multi-objective optimization model. Denoted as the first-level, second-level, and third-level objectives respectively, first solve the optimal solution set of the first-level objective function; then solve the second-level objective function under the premise of ensuring that the optimal value of the first-level objective function meets the given tolerance; finally, solve the third-level objective function under the premise of ensuring that the optimal value of the second-level objective function meets the given tolerance.

[0082]

[0083]

[0084]

[0085] Where: represents the state variable of the model, i.e., storage capacity; represents the decision variables of the model, i.e., generation flow and outbound flow; represent and The feasible set of and Represent the optimal solutions of the first, second, and third level objectives of the model respectively; and Represent the optimal values ​​of the first, second, and third level objectives respectively; and Represent the tolerance of the first and second level targets respectively.

[0086] After the above process, the optimal solution of the multi-objective optimization problem is , the values ​​of the three-layer objective functions are and .

[0087] (3.2) Linearization of nonlinear functions:

[0088] (3.2.1) The absolute value function linearization process is as follows:

[0089]

[0090] Where: is a linear auxiliary variable.

[0091] (3.2.2) Constrained linearization of one-dimensional non-convex nonlinear curves: A special ordered set type II constraint (SOS2) is introduced to linearize the water level and storage capacity curve. The specific formula is:

[0092]

[0093] Where: For power stations The water level and storage capacity segmented discrete points of the water level and storage capacity curve are The weights are restricted to be non-negative and sum to 1. Constrained for SOS2; The power station is represented by the sum of the discrete points multiplied by the weights exist Water level and reservoir capacity at a given moment.

[0094] (3.2.3) Two-dimensional non-convex nonlinear surface constrained linearization: The parallelogram two-dimensional interpolation method is used to linearly approximate the nonlinear output function of hydropower without introducing 0-1 integer variables.

[0095]

[0096]

[0097]

[0098]

[0099]

[0100]

[0101]

[0102]

[0103]

[0104]

[0105]

[0106] in, and are the upper and lower limits of the hydropower station’s storage capacity respectively; and They are the upper and lower limits of the power generation flow of the hydropower station;

[0107] Firstly, the hydropower output function is discretized into a non-orthogonal grid defined by parallelograms; represents the discrete gradient of power generation flow, represents the vertices of the parallelogram, and The power generation flow is Liedi The sampling value and storage capacity of the row The sample value of the row, and . and represents the vertex index, , and denote the number of columns and rows of the parallelogram network, and represents the linear auxiliary variable.

[0108] (3.3) Robust stochastic constraint transformation based on Lagrangian duality theory: Lagrangian duality theory is used to equivalently transform the uncertainty set U into an adjustable robust dual model.

[0109]

[0110] Where: Lagrangian dual variables introduced for the transformation process.

[0111] (3.4) Opportunity constraint transformation based on quantile regression: Using the random correlation between the actual output and the predicted output of new energy, the model is transformed into a linear programming model. Separate them separately and convert them into the following expression:

[0112]

[0113]

[0114] Where: is a random variable The inverse function of the cumulative distribution function; and represent random variables Probability distribution Quantile and Quantile.

[0115] Forecasting power output with new energy As the input variable, the actual output of new energy is established based on the quantile regression method. The non-parametric probability prediction model is used to obtain The analytical expression of .

[0116] The expression of quantile regression theory is as follows:

[0117]

[0118] Where: represents the infimum; is the nominal quantile level of the quantile, .

[0119] random variable Quantile It can be expressed as:

[0120]

[0121] Where: The nominal quantile level The corresponding quantile regression model is are model parameters.

[0122] Model parameters The value of is determined by minimizing the quantile loss To estimate:

[0123]

[0124] Where: Data samples of predicted and actual output of new energy sources; is the data sample index, is the index collection; is the pinball loss function, which is expressed as follows:

[0125]

[0126] Where: Represents the independent variable of the pinball loss function.

[0127] Choose a cubic polynomial to express the nominal quantile levels The corresponding quantile regression model is used to establish the mapping relationship between the predicted output and actual output of new energy. The specific expression is:

[0128]

[0129] Where: The nominal quantile level The corresponding quantile prediction model parameters.

[0130] After the above steps, the long-, medium- and short-term integrated scheduling model of cascade hydropower considering the multi-period fluctuations of new energy has been transformed into a mixed integer linear programming problem (MILP), which can be solved directly by calling the solver.

[0131] The beneficial effects of the present invention are as follows: the present invention integrates the multi-period volatility of new energy into the optimization of cascade hydropower operation, constructs a cascade hydropower long-, medium- and short-term variable time scale fusion optimization scheduling model, and solves the key problem that traditional hydropower scheduling methods are difficult to comprehensively meet the current and long-term random call requirements of the power grid for cascade hydropower regulation capacity under the background of large-scale new energy grid connection. BRIEF DESCRIPTION OF THE DRAWINGS

[0132] Figure 1 It is the schematic diagram of the scheduling model;

[0133] Figure 2 It is a method framework diagram;

[0134] Figure 3 This is a traditional scheduling model diagram. DETAILED DESCRIPTION

[0135] The specific implementation of the present invention is further described below in conjunction with the accompanying drawings and technical solutions.

[0136] The overall process of the present invention is as follows Figure 2 shown.

[0137] This case study examines the dispatching of the five hydropower stations in the Lancang River basin of Yunnan Province: Xiaowan, Manwan, Dachaoshan, Nuozadu, and Jinghong. Xiaowan and Nuozadu, with installed capacities of 4,200 MW and 5,850 MW, respectively, have long-standing regulation capabilities and are the cornerstones of Yunnan's power grid. Load data and other power output data for Yunnan Province were referenced to actual data to establish the boundaries of hydropower regulation capacity.

[0138] Step (1): Initial calculation conditions.

[0139] Historical observation data: Hourly wind and photovoltaic power output data for Yunnan Province from January 1, 2016, to December 31, 2023, as well as hourly runoff data from the Lancang River cascade hydropower stations for three typical years, Yunnan power grid load data, and other power output data were collected from the Yunnan Power Grid Dispatching Center.

[0140] Extension Data: By integrating GIS, AI, and meteorological big data into the renewable energy output sample extension method, we constructed hourly wind power and photovoltaic power output data for Yunnan Province from 1990 to 2015.

[0141] Basic data of hydropower stations: including installed capacity data, upper and lower limits of reservoir capacity, upper and lower limits of power generation flow, initial and final reservoir capacity, etc. for the five-level hydropower stations of Xiaowan, Manwan, Dachaoshan, Nuozhadu, and Jinghong;

[0142] Step (2): Construct a long-, medium- and short-term integrated scheduling model for cascade hydropower.

[0143] (2.1) Objective function:

[0144] Objective function 1: Minimize the long-term power shortage and power abandonment.

[0145]

[0146] Objective function 2: Minimize medium-term power shortages and power curtailment.

[0147]

[0148] Objective function three: Minimize short-term power shortage and power abandonment.

[0149]

[0150] Where: is the long-term period (month) in the scheduling model, and its value is the number of remaining months in the year; is the medium-term scale period (days) in the scheduling model, and its value is the number of days remaining in the month; is the short-term period in the scheduling model (h); 、 are the number of hours (h) of long-, medium-, and short-scale scheduling steps in the scheduling model, respectively; are long-term, medium-term and short-term loads (MW); For hydropower stations exist Output during the period (MW); They are the long-term actual output, medium-term forecast output, and short-term forecast output of renewable energy (MW); are the long, medium and short term outputs of other power sources (MW) respectively; from the perspective of energy conversion, the abandoned water of the hydropower station can be equivalently converted into abandoned electricity. For hydropower stations exist The abandoned water flow in the period is converted into power output (MW); is the number of hydropower stations.

[0151] (2.2) Cascade hydropower operation constraints:

[0152] (2.2.1) Reservoir water balance constraints:

[0153]

[0154]

[0155]

[0156] Where: For reservoirs exist Storage capacity at the end of the period (10 4 m 3 ); Reservoirs exist Inflow, power generation, and abandoned water flow during the period (m 3 / s); The day of the corresponding month.

[0157] (2.2.2) Cascade hydraulic connection constraints:

[0158]

[0159] Where: For reservoirs exist Natural inflow runoff during the period (m 3 / s); For the upstream cascade hydropower station To the hydropower station The water flow is stagnant.

[0160] (2.2.3) Hydropower station operation boundary constraints:

[0161] The reservoir capacity constraint, power generation flow constraint, outflow flow constraint, output constraint, and ramp constraint of a hydropower station are shown in the following formula.

[0162]

[0163]

[0164]

[0165]

[0166]

[0167] Where: and Hydropower Station exist The upper and lower limits of storage capacity in the time period (m 3 ); and Hydropower Station exist Period Upper and lower limits of power generation flow (m 3 / s); and Hydropower Station exist The upper and lower limits of outbound flow in the time period (m 3 / s); and Hydropower Station exist The upper and lower limits of output for the time period (MW); and They are the upward and downward climbing capabilities of the hydropower station.

[0168] (2.2.4) Adjustment of storage capacity constraints:

[0169]

[0170] Where: For hydropower stations Starting storage capacity (m 3 ), take the reservoir capacity at the end of 24 hours of the previous day's scheduling model.

[0171] (2.2.5) Final storage capacity constraint:

[0172]

[0173] Where: For a given hydropower station Storage capacity at the end of the year (m 3 ).

[0174] (2.2.6) Water level-reservoir capacity relationship constraints:

[0175]

[0176] Where: It is a nonlinear function of the hydropower station with respect to the reservoir capacity.

[0177] (2.2.7) Hydropower station power generation function:

[0178] According to the historical actual operation data of the hydropower station, the nonlinear hydropower station output function is fitted into the form of a two-variable quadratic polynomial.

[0179]

[0180] Where: yes and The average value of is a nonlinear hydropower station output function Parameters.

[0181] (2.2.8) Constraints on conversion from hydropower to electricity:

[0182]

[0183] Where: is the conversion function from abandoned water to abandoned power in a hydropower station.

[0184] (2.3) Uncertainty constraints of new energy:

[0185] (2.3.1) Constraints on long-term seasonal fluctuations in new energy:

[0186] We use robust optimization with adjustable uncertainty intervals to characterize the long-term output uncertainty of renewable energy. By introducing an adjustable parameter to describe the decision maker's conservative judgment regarding robust optimization, we achieve scaling of the uncertainty interval. The actual output of renewable energy is described as the sum of the output forecast and the forecast error, as shown in the following equation.

[0187]

[0188]

[0189] Where: and New energy in the long term Actual output and forecast output for the time period (MW); For new energy in the long term Output forecast error for the time period (MW); and New energy in the long term The maximum downward output deviation and the maximum upward output deviation during the time period (MW).

[0190] Introducing new energy uncertainty budget coefficient To define the uncertainty set U of renewable energy output, we can coordinate the robustness and optimality of the optimized scheduling, as shown in the following formula.

[0191]

[0192] Where: Auxiliary variables for adjustable robust optimization with uncertainty intervals.

[0193] (2.3.2) New energy medium-term extreme volatility scenario:

[0194] Based on the historical probability of occurrence, a scenario of extreme fluctuations of new energy for several days is introduced to enhance the ability of hydropower to regulate extreme fluctuations of new energy.

[0195] The definition method for new energy extreme fluctuation events is as follows:

[0196] The average daily output of new energy Compared with the average monthly output The decline in Above and continuing The "more than 10 days" fluctuation scenario is defined as an extreme low output fluctuation event that lasts for several days. ; The average daily output of new energy Compared with the average monthly output The increase in Above and continuing The "more than 24-day" fluctuation scenario is defined as an extreme high output fluctuation event lasting for several days. , see the following formula.

[0197]

[0198]

[0199] Where: is the day index, and are the start and end times of extreme fluctuations respectively; It is the key characteristic parameter of sustained extreme volatility events.

[0200] (2.3.3) Constraints on short-term reserve regulation demand for new energy:

[0201] The reserve supply and demand relationship between hydropower and renewable energy is characterized as an opportunity constraint to quantify the demand for flexible regulation capacity of hydropower due to the short-term uncertainty of renewable energy, as shown in the following formula.

[0202]

[0203]

[0204] Where: Indicates the probability that the inequality in the brackets is true; and Respectively represent hydropower stations exist Time period up reserve and down reserve (MW); and Indicates that new energy in the short term The predicted output and actual output (MW) at time , where the actual output is a random variable; and It is the confidence level that cascade hydropower can provide sufficient backup to meet the uncertainty of new energy. .

[0205] The up and down regulation of reserve capacity of a hydropower station is mainly limited by the installed capacity and ramping capability of the hydropower station, as shown in the following formula.

[0206]

[0207]

[0208] Step (3): Model solution.

[0209] (3.1) Multi-objective optimization solution method:

[0210] The hierarchical sequence method with relative tolerance is used to solve the multi-objective optimization model. Denoted as the first-level, second-level, and third-level objectives respectively, first solve the optimal solution set of the first-level objective function; then solve the second-level objective function under the premise of ensuring that the optimal value of the first-level objective function meets the given tolerance; finally, solve the third-level objective function under the premise of ensuring that the optimal value of the second-level objective function meets the given tolerance.

[0211]

[0212]

[0213]

[0214] Where: represents the state variable of the model, i.e., storage capacity; represents the decision variables of the model, i.e., generation flow and outbound flow; represent and The feasible set of and Represent the optimal solutions of the first, second, and third level objectives of the model respectively; and Represent the optimal values ​​of the first, second, and third level objectives respectively; and Represent the tolerance of the first and second level targets respectively.

[0215] After the above process, the optimal solution of the multi-objective optimization problem is , the values ​​of the three-layer objective functions are and .

[0216] (3.2) Linearization of nonlinear functions:

[0217] (3.2.1) The absolute value function linearization process is as follows (applicable to objective functions 1, 2, and 3):

[0218]

[0219] Where: is a linear auxiliary variable.

[0220] (3.2.2) Constrained linearization of one-dimensional non-convex nonlinear curves: A special ordered set type II constraint (SOS2) is introduced to linearize the water level and storage capacity curve. The specific formula is:

[0221]

[0222] Where: For power stations The water level and storage capacity segmented discrete points of the water level and storage capacity curve are The weights are restricted to be non-negative and sum to 1. Constrained for SOS2; and The power station is represented by the sum of the discrete points multiplied by the weights exist Water level and reservoir capacity at a given moment.

[0223] (3.2.3) Two-dimensional non-convex nonlinear surface constrained linearization: The parallelogram two-dimensional interpolation method is used to linearly approximate the nonlinear output function of hydropower without introducing 0-1 integer variables.

[0224]

[0225]

[0226]

[0227]

[0228]

[0229]

[0230]

[0231]

[0232]

[0233]

[0234]

[0235] Firstly, the hydropower output function is discretized into a non-orthogonal grid defined by parallelograms; represents the discrete gradient of power generation flow, represents the vertices of the parallelogram, The power generation flow is Liedi The sampling value and storage capacity of the row The sample value of the row, and . and represents the vertex index, , and denote the number of columns and rows of the parallelogram network, and represents the linear auxiliary variable.

[0236] (3.3) Robust stochastic constraint transformation based on Lagrangian duality theory: Lagrangian duality theory is used to equivalently transform the uncertainty set U into an adjustable robust dual model.

[0237]

[0238] Where: Lagrangian dual variables introduced for the transformation process.

[0239] (3.4) Opportunity constraint transformation based on quantile regression: Using the random correlation between the actual output and the predicted output of new energy, the model is transformed into a linear programming model. Separate them separately and convert them into the following expression:

[0240]

[0241]

[0242] Where: is a random variable The inverse function of the cumulative distribution function; and represent random variables Probability distribution Quantile and Quantile.

[0243] Forecasting power output with new energy As the input variable, the actual output of new energy is established based on the quantile regression method. The non-parametric probability prediction model is used to obtain The analytical expression of .

[0244] The expression of quantile regression theory is as follows:

[0245]

[0246] Where: represents the infimum; is the nominal quantile level of the quantile, .

[0247] random variable Quantile It can be expressed as:

[0248]

[0249] Where: The nominal quantile level The corresponding quantile regression model is are model parameters.

[0250] Model parameters The value of is determined by minimizing the quantile loss To estimate:

[0251]

[0252] Where: Data samples of predicted and actual output of new energy sources; is the data sample index, is the index collection; is the pinball loss function, which is expressed as follows:

[0253]

[0254] Where: Represents the independent variable of the pinball loss function.

[0255] Choose a cubic polynomial to express the nominal quantile levels The corresponding quantile regression model is used to establish the mapping relationship between the predicted output and actual output of new energy. The specific expression is:

[0256]

[0257] Where: The nominal quantile level The corresponding quantile prediction model parameters.

[0258] After the above steps, the long-, medium- and short-term integrated scheduling model of cascade hydropower considering the multi-period fluctuations of new energy has been transformed into a mixed integer linear programming problem (MILP), which can be solved directly by calling the solver.

[0259] Step (4): Comparison of results of different methods.

[0260] In order to illustrate the advantages of the scheduling method of the present invention, two hydropower scheduling methods were set up for comparative verification.

[0261] Method 1: Call the short-term scheduling mode to perform daily rolling scheduling. The objective function and constraints are the same as the short-term scheduling part in step (2). The inclusion of short-term new energy uncertainty is shown in step (2).

[0262] Method 2: Traditional long-, medium- and short-term decoupling scheduling mode (see the traditional scheduling mode Figure 3 The objective functions and constraints of the long-term, medium-term and short-term scheduling models are the same as those in the long-term, medium-term and short-term scheduling parts in step (2). The inclusion of long-term, medium-term and short-term new energy uncertainties is shown in step (2).

[0263] Method 3: The long-, medium- and short-term integrated scheduling method proposed in the present invention (hereinafter collectively referred to as the "method of the present invention").

[0264] Based on the hydrological frequency calculation method, three typical historical years were selected: normal water year, dry year, and high water year. In each typical year, daily rolling scheduling was performed using Method 1, Method 2, and the method of the present invention for 365 days. The differences in grid-wide power balance performance achieved using the different scheduling methods are compared, as shown in Table 1.

[0265] Table 1 Operation results of different typical years under three scheduling methods

[0266]

[0267] In normal water years, Method 1 showed the highest system power shortage and curtailment, followed by Method 2. The proposed method performed best, reducing the combined power shortage and curtailment by 96.84% and 44.53% compared to Methods 1 and 2, respectively. Similarly, in both wet and dry years, the proposed method's combined power shortage and curtailment were lower than those of Methods 1 and 2, decreasing by 97.11% and 69.81% (wet years), and 91.37% and 3.58% (dry years), respectively. Except for wet years, where the power shortage indicator was slightly lower than that of Method 2, the proposed method achieved lower system curtailment and power shortages across all typical years. This demonstrates that the proposed method fully exploits the multi-cycle power regulation capabilities of hydropower and reduces the risk of system power shortages and curtailment. This is primarily because the proposed method, through the integrated optimization of the multi-cycle scheduling plan for cascade hydropower, more effectively addresses both the current and future grid requirements for the regulation capabilities of cascade hydropower.

[0268] Step (5): Method reliability analysis.

[0269] To further highlight the advantages of the method of the present invention in supporting the system power and electricity balance, typical daily high-intensity fluctuation output scenarios for each month were clustered from the historical renewable energy output data and their occurrence probabilities in each month were calculated. During the daily rolling scheduling process, 30 new energy daily high-intensity fluctuation events were randomly introduced according to probability (the high-intensity fluctuation output scenarios of the corresponding months were introduced as the new energy short-term output prediction sequence). The scheduling results of different methods in each typical year were compared, as shown in Table 2.

[0270] Table 2 Operation results of different typical years under three scheduling methods

[0271]

[0272] It can be seen that the introduction of the high-intensity intraday fluctuation scenario of renewable energy exacerbates the risk of imbalance between supply and demand in the power grid, resulting in varying degrees of increases in system power shortages and curtailment compared to before the scenario was introduced. Method 1 yielded the highest total system power shortages and curtailment in all typical years, followed by Method 2. The method of the present invention yielded the lowest total, with average decreases of 91.75% and 49.69% compared to Methods 1 and 2, respectively. After the introduction of the high-intensity intraday fluctuation scenario of renewable energy, the method of the present invention yielded the lowest increase in total system power shortages and curtailment in normal water years, with decreases of 4.56% and 79.82% compared to Methods 1 and 2, respectively. Method 1 yielded the lowest increase in total system power shortages and curtailment in both wet and dry years, with decreases of 83.71% and 22.07% (wet years), and 22.78% and 9.54% (dry years) compared to Method 2 and the method of the present invention, respectively. The total system power shortages and curtailment obtained by Method 1 are too high and are therefore not discussed in this step.

[0273] In order to further compare the reliability of different scheduling methods, scenarios of high-intensity daily fluctuations in renewable energy output were randomly introduced into a typical normal water year with different frequencies, and full-year rolling scheduling was performed under Method 2 and the method of the present invention. The results show that for every 15 days of increase in the frequency of high-intensity daily fluctuations in renewable energy output, the system power shortage and power curtailment obtained by Method 2 increased by an average of 10.48GWh and 4.28GWh, respectively; the system power shortage and power curtailment obtained by the method of the present invention increased by an average of 2.09GWh and 0.46GWh, respectively, which are only 19.94% and 10.74% of those in Method 2. Therefore, as the frequency of high-intensity daily fluctuations in renewable energy output increases, the advantages of the method of the present invention in supporting the system power and electricity balance performance will become more and more significant.

[0274] In summary, under the condition of frequent high-intensity fluctuations in new energy during the day, the method of the present invention can still enable the system to achieve less power shortages and power abandonment, showing stronger reliability.

[0275] Step (6): Sensitivity analysis under the growth prospects of new energy installed capacity.

[0276] To explore the sensitivity of the performance of different scheduling methods to the growth rate of renewable energy installed capacity, taking a typical year with normal water conditions as an example, the installed capacities of wind power and photovoltaic power were increased by 5% in steps, assuming that the load and output of other power sources remained unchanged (considering that the scheduling results of method 1 were too poor, only the method of the present invention and method 2 were compared).

[0277] As the installed capacity growth rate of wind power and photovoltaic power increases from 0% to 30%, the following conclusions are drawn: 1) The system power shortage and curtailment under the scheduling method of the present invention are always lower, and the difference between the sum of the system power shortage and curtailment under the scheduling method of the present invention and method 2 increases from 148GW to 170.7GW; 2) The system power shortage is generally on a downward trend, and the reduction is lower and more stable under the scheduling method of the present invention; 3) The system curtailment is generally on an upward trend, and the increase is smaller under the scheduling method of the present invention. Therefore, with the increase in the installed capacity of new energy, the advantages of the method of the present invention are more significant. It can not only effectively alleviate the risk of curtailment caused by the increase in the penetration rate of new energy, but also fully release the positive gain of the newly installed capacity on the system power supply reliability, thereby improving the level of new energy consumption while ensuring system safety.

Claims

1. A method for integrating long-, medium- and short-term cascade hydropower scheduling considering multi-period fluctuations of renewable energy, characterized by: Here are the steps: Step (1): initial calculation conditions; Historical observation data: Collect hourly wind power and photovoltaic power output data for the entire province over many years, as well as hourly runoff data for cascade hydropower stations, provincial power grid load data, and other power output data for typical years; Basic data of hydropower stations: including installed capacity data, upper and lower limits of reservoir capacity, upper and lower limits of power generation flow, initial and final reservoir capacity, etc. Step (2): Construct a long-, medium- and short-term integrated dispatching model for cascade hydropower; (2.1) Objective function: Objective function 1: Minimize the long-term power shortage and power abandonment; Objective function 2: Minimize medium-term power shortages and curtailment; Objective function three: Minimize short-term power shortage and power abandonment; Where: is the long-term period in the scheduling model, and its value is the number of months remaining in the year; The medium-term period in the scheduling model is the number of days remaining in the month. is the short-term period in the scheduling model; 、 、 are the number of hours of long-, medium-, and short-scale scheduling steps in the scheduling model, respectively; 、 、 They are long, medium and short term loads respectively; For hydropower stations exist Output during the time period; They are the long-term actual output of new energy, the medium-term predicted output, and the short-term predicted output; They are respectively the long, medium and short term output of other power sources; from the perspective of energy conversion, the abandoned water of the hydropower station can be equivalently converted into abandoned electricity. For hydropower stations exist The abandoned water flow in the time period is converted into power output; is the number of hydropower stations; (2.2) Cascade hydropower operation constraints: (2.2.1) Reservoir water balance constraints: Where: For reservoirs exist Storage capacity at the end of the period; Reservoirs exist Inflow, power generation, and abandoned water flow during the time period; The day of the corresponding month; (2.2.2) Cascade hydraulic connection constraints: Where: For reservoirs exist Natural inflow runoff during the period; For the upstream cascade hydropower station To the hydropower station When the water flow is stagnant; (2.2.3) Hydropower station operation boundary constraints: The reservoir capacity constraint, power generation flow constraint, outflow flow constraint, output constraint, and ramp constraint of a hydropower station are shown in the following formulas: Where: and Hydropower Station exist The upper and lower limits of storage capacity for a time period; and Hydropower Station exist Period Upper and lower limits of power generation flow; and Hydropower Station exist The upper and lower limits of outbound traffic during the time period; and Hydropower Station exist The upper and lower limits of output during the time period; and They are the up- and down-gradability of the hydropower station; (2.2.4) Adjustment of storage capacity constraints: Where: For hydropower stations The starting storage capacity is the reservoir capacity at the end of 24 hours of the previous day's scheduling model; (2.2.5) Final storage capacity constraint: Where: For a given hydropower station Year-end storage capacity; (2.2.6) Water level-reservoir capacity relationship constraints: Where: It is a nonlinear function of the hydropower station with respect to the reservoir capacity; (2.2.7) Hydropower station power generation function: According to the historical actual operation data of the hydropower station, the nonlinear hydropower station output function is fitted into the form of a two-variable quadratic polynomial: Where: yes and The average value of is a nonlinear hydropower station output function Parameters; (2.2.8) Constraints on conversion from hydropower to electricity: Where: is the conversion function from abandoned water to abandoned electricity of the hydropower station; (2.3) Uncertainty constraints of new energy: (2.3.1) Constraints on long-term seasonal fluctuations in new energy: Uncertainty interval adjustable robust optimization is used to characterize the uncertainty of long-term renewable energy output. An adjustable parameter is introduced to describe the decision maker's conservative judgment on robust optimization to achieve scaling of the uncertainty interval. The actual renewable energy output is described as the sum of the output forecast value and the forecast error, as shown in the following formula: Where: and Respectively, new energy in the long term Actual output and predicted output during the time period; For new energy in the long term Output forecast error for each time period; and Respectively, new energy in the long term The maximum downward output deviation and the maximum upward output deviation during the time period; Introducing new energy uncertainty budget coefficient , , to define the uncertainty set of new energy output , in order to coordinate the robustness and optimality of the optimized scheduling, as shown in the following formula; Where: Auxiliary variables for adjustable robust optimization of uncertainty intervals; (2.3.2) New energy medium-term extreme volatility scenario: Based on historical probability, a scenario of extreme fluctuations in renewable energy for multiple days is introduced to enhance hydropower's ability to regulate extreme fluctuations in renewable energy. The definition method for new energy extreme fluctuation events is as follows: The average daily output of new energy Compared with the average monthly output The decline in Above and continuing The "more than 10 days" fluctuation scenario is defined as an extreme low output fluctuation event that lasts for several days. ; The average daily output of new energy Compared with the average monthly output The increase in Above and continuing The "more than 24-day" fluctuation scenario is defined as an extreme high output fluctuation event lasting for several days. , see the following formula; Where: is the day index, and are the start and end times of extreme fluctuations respectively; It is the key characteristic parameter of sustained extreme volatility events; (2.3.3) Constraints on short-term reserve regulation demand for new energy: The reserve supply and demand relationship between hydropower and renewable energy is represented as an opportunity constraint to quantify the demand for flexible regulation capacity of hydropower due to the short-term uncertainty of renewable energy, as shown in the following formula; Where: represents the probability that the inequality in the brackets is true; and Represents hydropower station exist Time period upward and downward reserve; and Indicates that new energy in the short term The predicted output and actual output at time , where the actual output is a random variable; and It is the confidence level that cascade hydropower can provide sufficient backup to meet the uncertainty of new energy. ; The up and down regulation of hydropower stations is mainly limited by the installed capacity and ramping capability of the hydropower station, as shown in the following formula; Step (3): Model solution; (3.1) Multi-objective optimization solution method: The hierarchical sequence method with relative tolerance is used to solve the multi-objective optimization model. Denoted as the first-level, second-level, and third-level objectives respectively, first solve the optimal solution set of the first-level objective function; then solve the second-level objective function under the premise of ensuring that the optimal value of the first-level objective function meets the given tolerance; finally, solve the third-level objective function under the premise of ensuring that the optimal value of the second-level objective function meets the given tolerance; Where: represents the state variable of the model, i.e., storage capacity; represents the decision variables of the model, i.e., generation flow and outbound flow; represent and The feasible set of 、 and Represent the optimal solutions of the first, second, and third level objectives of the model respectively; 、 and Represent the optimal values ​​of the first, second, and third level objectives respectively; and Represent the tolerance of the first and second level targets respectively; After the above process, the optimal solution of the multi-objective optimization problem is , the values ​​of the three-layer objective functions are 、 and ; (3.2) Linearization of nonlinear functions: (3.2.1) The absolute value function linearization process is as follows: Where: is a linear auxiliary variable; (3.2.2) Constrained linearization of one-dimensional nonconvex nonlinear curves: Introducing special ordered set type II constraints The water level storage capacity curve is linearized, and the specific formula is: Where: For power stations The water level and storage capacity segmented discrete points of the water level and storage capacity curve are The weights are restricted to be non-negative and sum to 1. for constraint; and The power station is represented by the sum of the discrete points multiplied by the weights exist Water level and reservoir capacity at the moment; (3.2.3) 2D Nonconvex Nonlinear Surface Constrained Linearization: Using the 2D parallelogram interpolation method, a linear approximation model is constructed for the nonlinear hydropower output function without introducing 0-1 integer variables. in, and are the upper and lower limits of the hydropower station’s storage capacity respectively; and They are the upper and lower limits of the power generation flow of the hydropower station; Firstly, the hydropower output function is discretized into a non-orthogonal grid defined by parallelograms; represents the discrete gradient of power generation flow, represents the vertices of the parallelogram, and The power generation flow is Liedi The sampling value and storage capacity of the row The sample value of the row, and ; and represents the vertex index, , and denote the number of columns and rows of the parallelogram network, and represents linear auxiliary variables; (3.3) Robust stochastic constraint transformation based on Lagrangian duality theory: Using Lagrangian duality theory, the uncertainty set Equivalently transformed into an adjustable robust dual model; Where: Lagrangian dual variables introduced for the transformation process; (3.4) Opportunity constraint transformation based on quantile regression: Using the random correlation between the actual output and the predicted output of renewable energy, the model is transformed into a linear programming model; the random variables in the opportunity constraint are transformed into Separate them separately and convert them into the following expression: Where: is a random variable The inverse function of the cumulative distribution function; and represent random variables Probability distribution Quantile and Quantile; Forecasting power output with new energy As the input variable, the actual output of new energy is established based on the quantile regression method. The non-parametric probability prediction model is used to obtain The analytical expression of ; The expression of quantile regression theory is as follows: Where: represents the infimum; is the nominal quantile level of the quantile, ; random variable Quantile It can be expressed as: Where: The nominal quantile level The corresponding quantile regression model is are model parameters; Model parameters The value of is determined by minimizing the quantile loss To estimate: Where: Data samples of predicted and actual output of new energy sources; is the data sample index, is the index collection; is the pinball loss function, which is expressed as follows: Where: Represents the independent variable of the pinball loss function; Choose a cubic polynomial to express the nominal quantile levels The corresponding quantile regression model is used to establish the mapping relationship between the predicted output and actual output of new energy. The specific expression is: Where: The nominal quantile level The corresponding quantile prediction model parameters; After the above steps, the long-, medium- and short-term integrated scheduling model of cascade hydropower considering the multi-period fluctuations of renewable energy has been transformed into a mixed integer linear programming problem MILP, which is directly solved by calling the solver.

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