Cascade hydropower short-term scheduling method and system considering interval runoff uncertainty

Abstract

The invention discloses a cascade hydropower short-term scheduling method and system considering interval runoff uncertainty, and the method comprises the steps: obtaining interval incoming water flow historical data, carrying out the fitting processing of the interval incoming water flow historical data, and obtaining the probability distribution of the interval incoming water flow and a typical interval flow scene; introducing the conditional value-at-risk into the cascade hydropower dispatching model to evaluate the risk faced by the cascade hydropower generating capacity under the intra-day interval runoff uncertainty, and obtaining a cascade hydropower short-term dispatching model based on the conditional value-at-risk; and inputting the typical interval flow scene into the cascade hydropower short-term scheduling model based on the conditional value-at-risk, performing linearization processing on nonlinear constraints in the cascade hydropower short-term scheduling model based on the conditional value-at-risk, and converting the model into a mixed integer linear programming problem for solving to obtain an optimal solution. According to the invention, effective risk assessment guidance is provided for daily production scheduling of cascade hydropower operation subjects.

Description

Technical Field

[0001] The present invention relates to the technical field of cascade hydropower optimization scheduling, and in particular to a cascade hydropower short-term scheduling method and system taking into account interval runoff uncertainty. Background Art

[0002] First, the hydropower-dominated power grid is very different from the traditional coal-fired power generation, gas-fired power generation and other dominated power grids. Coal-fired power plants and gas-fired power plants only rely on the supply of raw materials, and can arrange the supply of power generation raw materials according to market changes, while the source of hydropower generation raw materials is the interval runoff with uneven temporal and spatial distribution and strong randomness. Second, cascade hydropower is closely connected with hydraulic power and has many nonlinear constraints. The cascade development of hydropower leads to a very strong coupling effect between the inflow and outflow flow and water level between different power stations; furthermore, there are many nonlinear relationships in the power generation process of hydropower stations. The unit output, power generation flow and head of cascade hydropower are nonlinear relationships, which leads to the cascade hydropower optimization scheduling model is a decision variable with large scale, high dimension, strong constraint coupling and partial constraint nonlinearity.

[0003] Moreover, the existing cascade hydropower optimization scheduling method does not take into account the uncertainty risk of interval runoff, and cannot provide effective risk assessment guidance for the daily production scheduling of cascade hydropower operators. Summary of the invention

[0004] The technical problem to be solved by the present invention is that the existing cascade hydropower optimization scheduling method does not consider the uncertainty risk of interval runoff, and cannot provide effective risk assessment guidance for the daily production scheduling of cascade hydropower operators; in addition, the existing scheduling model has strong constraint coupling and many nonlinear constraints, which leads to problems such as long solution time. The purpose of the present invention is to provide a cascade hydropower short-term scheduling method and system that considers the uncertainty of interval runoff. The research is carried out on the cascade hydropower scheduling problem under the uncertainty of intra-day interval runoff. The scheduling of two cascade hydropower stations in a river basin in the southwest region is analyzed through examples, and the total power generation is obtained when the optimal confidence level is 0.9, which provides effective risk assessment guidance for the daily production scheduling of cascade hydropower operators.

[0005] The present invention is achieved through the following technical solutions:

[0006] In a first aspect, the present invention provides a cascade hydropower short-term scheduling method considering interval runoff uncertainty, the method comprising:

[0007] Obtain the historical data of interval water flow, perform fitting processing on the historical data of interval water flow, and obtain the probability distribution of interval water flow and typical interval flow scenarios;

[0008] The conditional risk value is introduced into the cascade hydropower dispatch model to evaluate the risk of cascade hydropower generation under the uncertainty of intra-day interval runoff, and a cascade hydropower short-term dispatch model based on conditional risk value is obtained.

[0009] The typical interval flow scenario is input into the cascade hydropower short-term scheduling model based on conditional value at risk, and the complex nonlinear constraints in the cascade hydropower short-term scheduling model based on conditional value at risk are linearized. The model is converted into a mixed integer linear programming problem for solution to obtain the optimal solution.

[0010] Furthermore, the probability distribution of interval water flow and typical interval flow scenarios are obtained, including:

[0011] Fitting the historical data of interval water flow to obtain the probability density function of interval water flow as the probability distribution of interval water flow;

[0012] The original interval traffic scene is obtained based on Latin hypercube sampling, and K-means clustering is used to reduce the original interval traffic scene to obtain the typical interval traffic scene.

[0013] Furthermore, the objective function of the cascade hydropower short-term scheduling model based on conditional risk value is:

[0014]

[0015] Where: W is the total number of scenes; ω w is the probability of scene w; δ is the confidence; P w is the total power generation under scenario w, WM·h; I is the total number of hydropower stations; T is the total number of scheduling time periods; P i,t,w represents the output of hydropower station i in scenario w during the dispatching period t, MW; Δt represents the number of hours in the dispatching period t; ζ, η w In order to calculate the auxiliary variable introduced based on the conditional risk value, the optimal value of ζ is based on the conditional risk value, that is, the VaR value; η w =[ζ-P w ] + represents the maximum value function max{ζ-P w ,0}, if the benefit of scenario w is P w is greater than the VaR value, i.e. ζ, then η w is equal to 0; otherwise η w is ζ and P w The difference.

[0016] Furthermore, the hydropower station constraints of the cascade hydropower short-term scheduling model based on conditional risk value include water balance constraints, hydraulic connection constraints, initial and final water level constraints, water level constraints, outflow flow constraints, power station output constraints, power generation flow constraints, unit output climbing constraints, unit start-up and shutdown duration constraints, net head calculation constraints, reservoir capacity-water level relationship function constraints, discharge flow tail water level relationship function constraints, head loss function constraints and unit output function constraints.

[0017] Furthermore, the complex nonlinear constraints in the conditional value-at-risk short-term dispatch model of cascade hydropower are linearized, including:

[0018] One-dimensional nonlinear function fitting and linearization processing: Based on the one-dimensional quartic polynomial fitting method, the reservoir capacity water level relationship function constraint, the discharge tail water level relationship function constraint, and the head loss function constraint are fitted respectively; and the piecewise linearization method is used to linearize the fitted function;

[0019] Binary nonlinear function line fitting and linearization processing: The binary quadratic polynomial fitting method is used to fit and linearize the unit output function constraints.

[0020] Furthermore, the model is transformed into a mixed integer linear programming problem for solution, including:

[0021] Set the initial conditions for calculation, including the number of scheduling time periods within the day, the initial and final water level control values ​​of each hydropower station, the outflow and power generation flow upper limit of each power station, and the upper limit of the unit output, etc.;

[0022] Fit and linearize the historical data of the hydropower station to obtain the linearized constraints and objective function of the hydropower station; the historical data of the hydropower station include reservoir water level, tail water level of discharge flow, head loss and unit output characteristics;

[0023] The linearized constraints and objective functions of the hydropower station are modeled through YALMIP, and the interval water inflow of typical interval flow scenarios is input. The cascade hydropower short-term scheduling model based on conditional value at risk is solved through the mature commercial solver GUROBI, and the conditional value at risk (CVaR value) at a certain confidence level, the water level changes of the hydropower station under various scenarios, the power generation flow and the unit output are output.

[0024] Furthermore, before fitting the historical data of the interval water flow, the method further includes:

[0025] The historical data of water flow in the interval is normalized, and the normalization formula is: in, is the normalized historical interval water flow of the hydropower station i at time t, m 3 / s;Qi,t is the interval water flow of the hydropower station at time t, m 3 / s; T is the number of statistical time periods for historical water flow inflow in one day.

[0026] In a second aspect, the present invention further provides a cascade hydropower short-term dispatching system considering interval runoff uncertainty, the system comprising:

[0027] A typical scenario acquisition unit is used to obtain the historical data of the interval water flow, perform fitting processing on the historical data of the interval water flow, and obtain the probability distribution of the interval water flow and the typical interval flow scenario;

[0028] The dispatch model building unit is used to introduce the conditional risk value into the cascade hydropower dispatch model to evaluate the risk faced by the cascade hydropower generation under the uncertainty of intra-day interval runoff, and obtain the cascade hydropower short-term dispatch model based on the conditional risk value;

[0029] The model solving unit is used to input typical interval flow scenarios into the cascade hydropower short-term scheduling model based on conditional risk value, and linearize the complex nonlinear constraints in the cascade hydropower short-term scheduling model based on conditional risk value, and convert the model into a mixed integer linear programming problem for solving to obtain the optimal solution.

[0030] Furthermore, the typical scene obtaining unit includes:

[0031] The fitting subunit is used to perform fitting processing on the historical data of the interval water flow, and obtain the probability density function of the interval water flow as the probability distribution of the interval water flow;

[0032] The scenario sub-unit is used to obtain the original interval traffic scenario based on Latin hypercube sampling, and use K-means clustering to reduce the original interval traffic scenario to obtain the typical interval traffic scenario.

[0033] In a third aspect, the present invention further provides a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, it implements the above-mentioned cascade hydropower short-term scheduling method considering the uncertainty of interval runoff.

[0034] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0035] The present invention provides a short-term scheduling method and system for cascade hydropower considering the uncertainty of interval runoff. The present invention conducts research on the scheduling problem of cascade hydropower under the uncertainty of intraday interval flow, obtains the probability distribution function by fitting the historical interval flow, and performs scene reduction by clustering algorithm, which effectively reduces the solution pressure; in the process of cascade hydropower modeling, the nonlinear elements in the model are linearized by polynomial fitting, piecewise linearization and plane projection method, and the MILP model is constructed to improve the solution efficiency to meet the timeliness requirements of short-term scheduling in the day ahead; finally, CVaR is introduced in the constructed cascade hydropower model to evaluate the risks faced by cascade hydropower generation under the uncertainty of intraday interval flow. The present invention analyzes the scheduling of two cascade hydropower stations in a river basin in the southwest region through examples, and obtains the total power generation when the optimal confidence level is 0.9, providing effective risk assessment guidance for the intraday production scheduling of cascade hydropower operators. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] The drawings described herein are used to provide a further understanding of the embodiments of the present invention, constitute a part of this application, and do not constitute a limitation of the embodiments of the present invention. In the drawings:

[0037] Figure 1 This is a flow chart of the cascade hydropower short-term scheduling method considering the uncertainty of interval runoff in the present invention;

[0038] Figure 2 It is a schematic diagram of the piecewise linearization of the water level-storage capacity curve of the present invention;

[0039] Figure 3 This is a schematic diagram of the output curved surface projection of the hydroelectric unit of the present invention;

[0040] Figure 4 (a) Projection of the power generation function of the hydropower station unit on the two-dimensional plane where the power generation flow and net water head are located, (b) coefficient values ​​of the vertices of the plane rectangle;

[0041] Figure 5 Solve the framework diagram for the present invention;

[0042] Figure 6 It is a schematic diagram of interval flow in different scenarios of cascade hydropower stations of the present invention;

[0043] Figure 7 is the risk value under different confidence levels of the present invention;

[0044] Figure 8 The water level changes of the hydropower station in different scenarios when the confidence level of the present invention is 0.9;

[0045] Fig. 9 The output of the hydropower station in different scenarios when the confidence level of the present invention is 0.9;

[0046] Fig.10 This is a structural block diagram of the cascade hydropower short-term scheduling system that takes into account the uncertainty of interval runoff in the present invention. DETAILED DESCRIPTION

[0047] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with embodiments and drawings. The exemplary embodiments of the present invention and their description are only used to explain the present invention and are not intended to limit the present invention.

[0048] In the current process of power market reform and construction, the production and operation of hydropower enterprises have undergone a huge transformation, from the original power generation according to dispatching arrangements to power generation through bidding. This requires hydropower enterprises to consider the uncertainty of interval runoff in the process of market competition and to be able to issue the winning bid electricity on time and in quantity. Therefore, hydropower enterprises need a set of quantitative and evaluation models that can effectively evaluate the risks of cascade hydropower generation, so as to increase the benefits of hydropower participating in the power market and reduce transaction risks. The present invention proposes a cascade hydropower short-term scheduling model based on conditional value at risk (CVaR). Firstly, the historical data of interval water flow are processed to obtain the probability distribution of interval flow, and then the interval flow under typical scenarios is obtained; secondly, in order to comprehensively evaluate the uncertainty risk of power generation under typical scenarios and control the tail risk, the conditional value at risk is introduced into the cascade hydropower scheduling model to perform model risk management; finally, in order to improve the model solving efficiency and adapt to the timeliness of short-term scheduling, the complex nonlinear constraints in the model are linearized, and the model is converted into a mixed integer linear programming (MILP) problem for solution, so as to provide effective risk assessment guidance for the daily production scheduling of cascade hydropower operators.

[0049] 1) In order to address the uncertainty problem of interval runoff in the process of cascade hydropower scheduling, the present invention proposes a cascade hydropower day-ahead short-term scheduling model based on conditional risk value. The model constructs a day-ahead uncertain interval flow scenario through historical interval flow, and embeds the conditional risk value model in the cascade hydropower scheduling model to quantitatively evaluate the impact of potential interval flow uncertainty on hydropower output results in the day-ahead short-term scheduling of cascade hydropower, in order to provide auxiliary decision-making for the scheduling of cascade hydropower under intra-day interval flow uncertainty.

[0050] 2) In the process of complex modeling of cascade hydropower, in order to be close to engineering reality and reduce deviations, the present invention uses polynomial fitting, piecewise linearization and plane projection method to linearize the nonlinear constraints in the model, and constructs a MILP model to improve the solution efficiency to meet the timeliness requirements of short-term scheduling before the day is over.

[0051] Example 1

[0052] like Figure 1 As shown, the present invention provides a short-term scheduling method for cascade hydropower considering uncertainty of interval runoff, the method comprising:

[0053] Step 1, obtaining the historical data of the interval water flow, performing fitting processing on the historical data of the interval water flow, and obtaining the probability distribution of the interval water flow and the typical interval flow scenario;

[0054] In this embodiment, the probability distribution of the interval water flow and the typical interval flow scenario are obtained, including:

[0055] Fitting the historical data of interval water flow to obtain the probability density function of interval water flow as the probability distribution of interval water flow;

[0056] The original interval traffic scene is obtained based on Latin hypercube sampling, and K-means clustering is used to reduce the original interval traffic scene to obtain the typical interval traffic scene.

[0057] Step 2, introduce conditional risk value into the cascade hydropower scheduling model to evaluate the risk faced by cascade hydropower generation under the uncertainty of intra-day interval runoff, and obtain a cascade hydropower short-term scheduling model based on conditional risk value;

[0058] In current existing research, most of the CVaR model is used to describe the loss function problem, that is, the loss of an investment portfolio over a period of time. However, the present invention adopts the CVaR model to describe the return of an investment portfolio over a period of time, such as solving the problem of power grid safety margin, the profit problem of new energy manufacturers, the calculation of wind power plant grid-connected capacity, the profit problem of wind power companies, etc.

[0059] The power generation in the cascade hydropower generation scheduling process is a revenue function of the interval flow of the uncertainty factor. In order to describe the impact of interval flow uncertainty on power generation, the revenue-based CVaR is introduced to characterize it. The constructed optimization objective function can be given by the following discrete expression:

[0060]

[0061] Where: W is the total number of scenes; ω w is the probability of scene w; δ is the confidence; P w is the total power generation under scenario w, WM·h; I is the total number of hydropower stations; T is the total number of scheduling time periods; P i,t,w represents the output of hydropower station i in scenario w during the dispatching period t, MW; Δt represents the number of hours in the dispatching period t; ζ, η w In order to calculate the auxiliary variable introduced based on the conditional risk value, the optimal value of ζ is based on the conditional risk value, that is, the VaR value; ηw =[ζ-P w ] + represents the maximum value function max{ζ-P w ,0}, if the benefit of scenario w is P w is greater than the VaR value, i.e. ζ, then η w is equal to 0; otherwise η w is ζ and P w The difference.

[0062] Hydropower station constraints include:

[0063] 1) Water balance constraints:

[0064] V i,t =V i,t-1 +3600(I i,t -Q i,t )Δt (4)

[0065] Where: V i,t represents the storage capacity of hydropower station i at the end of dispatching time period t, m 3 ; V i,t-1 represents the storage capacity of hydropower station i at the end of the previous dispatching period t-1, m 3 ;I i,t represents the average inflow value of hydropower station i in the dispatching time period t, m 3 / s;Q i,t represents the average outflow value of hydropower station i in the dispatching time period t, m 3 / s; Δt represents the number of hours in the scheduling time period t, and h; 3600 represents the number of seconds in an hour.

[0066] 2) Hydraulic connection constraints:

[0067] I i,t =Q i-1,t-τ +B i,t (5)

[0068]

[0069] Where: Q i-1,t-τ represents the average outflow value of hydropower station i-1 in the dispatching period t-τ after considering the water flow lag, m 3 / s; τ represents the water flow delay from the upstream hydropower station i-1 to the downstream hydropower station i, h; B i,t represents the average interval flow value of the upstream hydropower station i-1 and the downstream hydropower station i in the scheduling time period t, m 3 / s; represents the power generation flow value of hydropower station i in the scheduling time period t, m 3 / s; represents the abandoned water flow value of hydropower station i in the scheduling period t, m 3 / s.

[0070] 3) Initial and final water level constraints:

[0071]

[0072] Where: Z i,begin is the initial water level above the dam during the dispatching period, m; Z i,end The expected value of the water level on the dam at the end of the dispatch period is generally formulated according to the long-term or periodic operation requirements of the power station, m; ΔZ i is the allowable deviation value of the final water level of hydropower station i, which is related to the regulation performance of the hydropower station, m;

[0073] 4) Water level constraint:

[0074]

[0075] in: and are the lower and upper limits of the water level of hydropower station i in the dispatching time period t, m; Z i,t is the water level of hydropower station i in the dispatching time period t, m;

[0076] 5) Outbound flow constraints:

[0077]

[0078] in: and are the lower and upper limits of the outflow rate of hydropower station i in the dispatching time period t, respectively, 3 / s;Q i,t represents the average outflow value of hydropower station i in the dispatching time period t, m 3 / s;

[0079] 6) Power station output constraints:

[0080]

[0081] in: and are the lower and upper limits of the output of hydropower station i in the dispatching time period t, MW; P i,t represents the output of hydropower station i in the dispatching time period t, MW; u i,t ∈{0,1} is the unit operation status indicator variable of the hydropower station unit i in the dispatching time period t. When it is 1, it means the unit is turned on, and when it is 0, it means the unit is turned off;

[0082] 7) Power generation flow constraints:

[0083]

[0084] in: and are the lower and upper limits of the power generation flow of hydropower station i in the dispatching time period t, respectively, 3 / s;

[0085] 8) Unit output climbing constraints:

[0086] -ΔP i ≤P i,t+1 -P i,t ≤ΔP i (12)

[0087] Where: ΔP i is the climbing capacity of unit i of the hydropower station, MW / h;

[0088] 9) Unit start and stop duration constraints:

[0089]

[0090] in: is the startup variable of the i unit of the hydropower station in the dispatching time period t. When it is 1, it means the unit is turned on, otherwise it means the unit is turned off; is the stop variable of the i unit of the hydropower station in the dispatching time period t. When it is 1, it means the unit is shut down, otherwise it means the unit is turned on; T i on and T i off are the minimum startup and shutdown durations of unit i of the hydropower station during the entire dispatch period; It is the maximum number of startup times of unit i in the hydropower station during the entire scheduling period, avoiding frequent startup and shutdown of the unit and reducing the loss of the unit.

[0091] 10) Net head calculation constraints:

[0092]

[0093] Where: h i,t is the net head value of hydropower station i in the dispatching time period t, m; is the tailwater level of hydropower station i in the dispatching time period t, m; is the head loss value of hydropower station i in the dispatching time period t, m.

[0094] 11) Reservoir capacity and water level relationship function constraints:

[0095]

[0096] Where: f i v(·) is the storage capacity-water level function relationship of hydropower station i, which is a univariate nonlinear function.

[0097] 12) Discharge flow tail water level relationship function constraints:

[0098]

[0099] Where: f i tail (·) is the discharge flow-tailwater level function relationship of hydropower station i, which is a univariate nonlinear function.

[0100] 13) Head loss function constraints:

[0101]

[0102] Where: f i loss (·) is the head loss function relationship of hydropower station i, which is a univariate nonlinear function;

[0103] 14) Unit output function constraints:

[0104]

[0105] Where: f i p (·) is the unit output function relationship of hydropower station i, which is a binary nonlinear function.

[0106] Step 3: Input the typical interval flow scenario into the cascade hydropower short-term scheduling model based on conditional risk value, linearize the complex nonlinear constraints in the cascade hydropower short-term scheduling model based on conditional risk value, convert the model into a mixed integer linear programming problem and solve it to obtain the optimal solution.

[0107] Considering that the cascade hydropower scheduling model in step 2 contains many nonlinear constraints, including univariate nonlinear functions (15), (16), (17) and binary nonlinear function (18), the constructed model cannot be solved directly using the MILP method. Therefore, it is necessary to use linearization processing to convert the nonlinear constraints in the model into linear constraints within a certain accuracy range, and then solve the model using the MILP method.

[0108] In this embodiment, the complex nonlinear constraints in the cascade hydropower short-term scheduling model based on conditional value at risk are linearized, including:

[0109] 1) One-dimensional nonlinear function fitting and linearization processing:

[0110] It is important to consider what mathematical model is used by the above-mentioned univariate nonlinear function to accurately describe the relationship between the water level and reservoir capacity of the hydropower station, the relationship between the discharge flow and the tail water level of the hydropower station, and the relationship between the discharge flow and the head loss. The present invention adopts polynomial fitting. The higher the polynomial order, the higher the fitting accuracy is. However, the higher the polynomial order, the lower the overall calculation efficiency of the model. When the fitting order exceeds the fourth order, the trend of improving the fitting accuracy is small. Therefore, the fourth-order polynomial fitting is adopted. Formula (15) is fitted as follows:

[0111]

[0112] Among them: a1, a2, a3, a4, a5 are the coefficients of the fitted fourth-order polynomial function of the relationship between the water level and reservoir capacity of the hydropower station.

[0113] Formula (16) is fitted as follows:

[0114]

[0115] Among them: b1, b2, b3, b4, b5 are the coefficients of the fitted fourth-order polynomial function of the relationship between the discharge flow and tailwater level of the hydropower station.

[0116] Formula (17) is generally fitted as:

[0117]

[0118] Where: c1 and c2 are the fitted coefficients of the hydropower station head loss function.

[0119] The present invention adopts a piecewise linearization method for a univariate nonlinear function. Taking the relationship function between the water level and the reservoir capacity of a hydropower station as an example, C+1 points are selected within the upper and lower limits of the water level to divide it into C segments. The reservoir capacity in each water level interval c is calculated by two-point interpolation. Figure 2 As shown, Figure 2 It is a schematic diagram of piecewise linearization of water level-reservoir capacity curve;

[0120]

[0121] in: is a 0-1 indicator variable for the c-th water level interval of hydropower station i in the dispatching time period t. When the water level is in the c-th water level interval, on the contrary It is used to ensure that the water level of the hydropower station can only be within one water level range within a scheduling period; is the water level value of water level interval c; the water level Z of hydropower station i at any time t i,t and V i,tIt can be expressed by equations (25) and (26). Similarly, the same piecewise linearization method is used to deal with the relationship between the discharge flow and the tailwater level, and the relationship between the discharge flow and the head loss of the hydropower station, which will not be repeated here.

[0122] 2) Binary nonlinear function line fitting and linearization processing:

[0123] The unit output function of a hydropower station is a binary nonlinear function. How to reasonably linearize it has always been a difficult problem. This paper describes this binary nonlinear function using a binary quadratic polynomial function:

[0124]

[0125] Among them: d1, d2, d3, d4, d5, d6 are the fitted polynomial function coefficients of the hydropower station units.

[0126] A plane projection method is used to project the three-dimensional surface of the unit output, power generation flow, and net water head onto the two-dimensional plane where the power generation flow and the net water head are located, and then the plane is divided. The present invention divides the plane into rectangles, and only allows one rectangle to be selected at a time, thereby ensuring that the unit output at a time corresponds to the net water head and power generation flow. Since the error of piecewise linearization is large when processing the unit output function, the present invention adopts a plane projection method, which is described below. Figure 3 This is a schematic diagram of the curved projection of the hydropower unit output.

[0127] Figure 4 (a) is the projection diagram of the power output function of the hydropower station unit on the two-dimensional rectangular grid plane where the power generation flow and net water head are located. For the convenience of expression, the power station number i and time t are omitted here. The actual output, power generation flow and water head should correspond to the specific power station number i and time t. The horizontal axis represents the discretization of the net water head, which is discretized into J-1 intervals, and the vertical axis represents the discretization of the power generation flow, which is discretized into K-1 intervals. P j,k =f i p (p j ,h k ) is the discrete power generation flow p j With discrete net water head h k The corresponding unit output value. Figure 4 (b) is a schematic diagram of the coefficient values ​​corresponding to the vertices of each rectangle after the projection plane is divided into (J-1)×(K-1) rectangles.

[0128] The plane projection linearization method of the unit output function of the hydropower station is as follows:

[0129]

[0130] Where: k,j is the coefficient value of the corresponding vertex of the plane rectangle, which is a non-negative value; α j is the discrete net water head h j The sum of the coefficient values ​​in the column, similarly, β k is the discrete power generation flow p k The sum of the coefficient values ​​of the row; the role of equations (30) and (31) is to restrict {α1,α2,...,α k ,...,α K The sequence has at most two non-zero variables, and the positions of non-quantity variables must be adjacent. Through the action of equations (28)-(34), only one rectangle is selected at a time, and the sum of the four vertex coefficients is 1 or 0, which is 1 when the unit is turned on and 0 when the unit is turned off; at this time, the net water head, power flow, and unit output are limited to the selected rectangle when the unit is running. The net water head, power flow, and unit output when the unit is running at a certain time are given by equations (32)-(34), thereby achieving the purpose of linearization.

[0131] As a further implementation, before fitting the historical data of the interval water flow in step 1, the following steps are further included:

[0132] The historical data of water flow in the interval is normalized, and the normalization formula is:

[0133]

[0134] in, is the normalized historical interval water flow of the hydropower station i at time t, m 3 / s;Q i,t is the interval water flow of the hydropower station at time t, m 3 / s; T is the number of statistical time periods for historical water flow inflow in one day.

[0135] After normalizing the historical data, we can get a set of historical interval water flow. Due to statistical errors or the influence of extreme weather conditions, outlier data are eliminated, and then the appropriate interval step size is selected to divide the data set and perform frequency statistics. The probability density function of the interval flow is obtained by probability distribution fitting.

[0136] At present, the interval water flow is considered to be normally distributed and the description effect is good, so the present invention fits the interval water flow according to the normal distribution. After processing the historical interval flow data, the mean and standard deviation of the normal distribution probability density function are obtained by normal distribution fitting.

[0137] After the probability density function is obtained, Latin Hypercube Sampling (LHS) is used for stratified sampling to enable the samples to fully cover the entire distribution range. Due to the large number of scenes generated by sampling, if all scenes are input into the model for calculation, the model solution calculation time scale will increase sharply. In order to shorten the model solution time, the present invention uses K-means clustering to reduce the scenes, and the reduced scenes are input into the model for solution calculation.

[0138] Therefore, through the above linearization method, the original model is transformed from a complex nonlinear model to a mixed integer linear programming model, with the objective function (1) and the constraints (2)-(18), (22)-(26), (28)-(34). The model is built through the YALMIP toolbox, and the mature commercial solver GUROBI is called to solve the model. Figure 5 As shown in the figure, the model solution process is as follows:

[0139] Step A: Process the historical data of water flow in the interval and fit the probability density function. The original scene is obtained by Latin hypercube sampling, and then the scene is reduced by K-means clustering to obtain a typical interval flow scene.

[0140] Step B, setting the initial conditions for calculation, including the number of scheduling time periods within a day, the initial and final water level control values ​​of each hydropower station, the outflow and power generation flow upper limits of each power station, and the upper limit of the unit output, etc.;

[0141] Step C, fitting and linearizing the historical data of the hydropower station to obtain linearized constraints and objective functions of the hydropower station; the historical data of the hydropower station include reservoir water level, tail water level of discharge flow, head loss and unit output characteristics, etc.; specifically, the linearization process adopts the above-mentioned univariate nonlinear function line fitting and linearization process, and the bivariate nonlinear function line fitting and linearization process;

[0142] In step D, the linearized constraints and objective functions of the hydropower station are modeled through YALMIP, the interval water inflow of the typical interval flow scenario is input, and the cascade hydropower short-term scheduling model based on conditional value at risk is solved through the mature commercial solver GUROBI, and the conditional value at risk (CVaR value) at a certain confidence level is output, as well as the water level changes, power flow and unit output of the hydropower station under various scenarios.

[0143] In order to verify the effectiveness of the method and model proposed in this invention, a cascade hydropower station in a river basin in southwest my country was selected as the research object. The upstream and downstream power stations are represented by power station A and power station B respectively. The detailed characteristic parameters of the hydropower station are shown in Table 1. 1d is the scheduling cycle and 1h is the scheduling period. The water level at the beginning and end of the scheduling is set to be the same, that is, ΔZi To avoid affecting the initial dispatching water level in the next dispatching period, it also highlights the impact of water inflow uncertainty on cascade hydropower generation.

[0144] Table 1 Hydropower station operation parameters

[0145]

[0146] After normalizing the historical data, fitting was performed to obtain the distribution function. 1000 different water inflow scenarios were generated through Latin hypercube sampling. K-means clustering was used to reduce the dimension of the scenarios, and 5 interval flow scenarios were obtained as possible water inflow scenarios on the scheduling day, such as Figure 6 shown.

[0147] The simulation running environment is a laptop computer with Win11 operating system and the hardware configuration is Intel(R) Core(TM) i5-8300H CPU @ 2.30 GHz, 8.0 GB RAM. The MILP model is set with a maximum solution time of 500 s and a gap parameter of 0.001.

[0148] 1) CVaR confidence value verification and analysis

[0149] Since the selection of confidence δ has a great impact on CVaR and VaR, it also has an impact on tail risk. In order to obtain the optimal confidence δ, the CVaR, VaR and tail risk values ​​under different confidence values ​​are optimized with a step size of 0.025 in the confidence interval [0.2, 0.95].

[0150] Depend on Figure 7 It can be seen that from the trend of the change of tail loss, if the confidence is too large or too small, it will affect the optimal tail loss value, thereby affecting the risk assessment of the total power generation of cascade hydropower under the uncertainty of interval flow. If the confidence δ is too small, it means that the trust in the generated typical scenario is too low, and the reference risk for the day-ahead dispatch is too high, and there is a high probability that there will be a large deviation from the actual dispatch situation, resulting in economic losses; and if the confidence δ is too large, it means that the trust in the generated typical scenario is too high, but the potential risks that may exist are ignored, resulting in a decrease in total power generation and an increase in tail loss when the day-ahead dispatch plan is in the actual environment. It can be seen from the simulation of the example that the tail loss of the example is the smallest when the confidence δ is around 0.9, and the optimal confidence δ of the present invention is 0.9.

[0151] Table 2 Comparison of power generation between deterministic model and CVaR model

[0152]

[0153]

[0154] Table 2 compares the power generation of the deterministic model and the CVaR model. The interval flows in deterministic model 1, deterministic model 2, and deterministic model 3 are the interval flows under scenario 3, scenario 4, and scenario 5, respectively, as the determined interval flow values. There is a deviation between the optimization results of the CVaR model and the optimization results of the deterministic model. The reason is that the deterministic model believes that the interval flow under the typical scenario fully represents the entire situation of the intraday interval flow. If the intraday interval flow is lower than the interval flow under the typical scenario, the production scheduling results of the deterministic model will be difficult to adapt to the actual market situation, which will cause losses to the hydropower operator. Therefore, the advantage of quantifying the uncertainty risk of intraday interval flow highlighted by the CVaR model can provide an effective risk information reference for cascade hydropower operators.

[0155] 2) Model effectiveness analysis

[0156] Figure 8 , Fig. 9 To optimize the dispatching when the confidence level δ is 0.9, the daily water level changes and power station output under each scenario are obtained. Figure 8 It can be seen that in the five scenarios, the water level change amplitude of power station A does not exceed 0.26m, and the water level change amplitude of power station B does not exceed 0.44m, which is more consistent with the actual dispatching and operation of cascade hydropower stations; compared with the traditional method of simple linearization near the initial water level, the piecewise linearization process effectively avoids excessive deviation caused by insufficient segmentation. Fig. 9 It can be seen that the output of the two hydropower stations meets the operating constraints. Combined with the water level changes in various scenarios, the water level changes are consistent with the power station output, that is, the hydropower station stores water when the power station has low output, and the water level shows a downward trend when the hydropower station increases its output.

[0157] In optimization problems, calculation accuracy and calculation time are usually contradictory, so the dispatcher should choose the appropriate linearization processing scheme according to actual needs (Scheme 1 is the linearization segmentation scheme actually adopted in the present invention). Table 3 shows the optimization scheduling results of head, power generation flow, tail water level-outflow flow curve, and water level-storage capacity curve under different numbers of segments. The more segments there are, the closer the solution result is to the true value and the higher the calculation accuracy is. However, as the number of segments increases, the constraints and 0-1 variables in the model also increase, and the corresponding calculation time is also getting longer and longer. The CVaR values ​​of the optimization results in the three schemes are not much different. Considering the timeliness requirements of day-ahead scheduling, the solution time of Schemes 1 and 2 under the number of segments is 42s and 415s respectively, which can better meet the time requirements of short-term hydropower scheduling, fully demonstrating the efficient solution capability of the MILP model.

[0158] Table 3 Solution results under different linearization segment numbers

[0159]

[0160] Example 2

[0161] like Fig.10 As shown, the difference between this embodiment and embodiment 1 is that this embodiment provides a cascade hydropower short-term scheduling system considering the uncertainty of interval runoff, and the system has a one-to-one correspondence with the cascade hydropower short-term scheduling method considering the uncertainty of interval runoff in embodiment 1; the system includes:

[0162] A typical scenario acquisition unit is used to obtain the historical data of the interval water flow, perform fitting processing on the historical data of the interval water flow, and obtain the probability distribution of the interval water flow and the typical interval flow scenario;

[0163] The dispatch model building unit is used to introduce the conditional risk value into the cascade hydropower dispatch model to evaluate the risk faced by the cascade hydropower generation under the uncertainty of intra-day interval runoff, and obtain the cascade hydropower short-term dispatch model based on the conditional risk value;

[0164] The model solving unit is used to input typical interval flow scenarios into the cascade hydropower short-term scheduling model based on conditional risk value, and linearize the complex nonlinear constraints in the cascade hydropower short-term scheduling model based on conditional risk value, and convert the model into a mixed integer linear programming problem for solving to obtain the optimal solution.

[0165] As a further implementation, the typical scene obtaining unit includes:

[0166] The fitting subunit is used to perform fitting processing on the historical data of the interval water flow, and obtain the probability density function of the interval water flow as the probability distribution of the interval water flow;

[0167] The scenario sub-unit is used to obtain the original interval traffic scenario based on Latin hypercube sampling, and use K-means clustering to reduce the original interval traffic scenario to obtain the typical interval traffic scenario.

[0168] Among them, the execution process of each unit can be executed according to the process steps of the cascade hydropower short-term scheduling method considering interval runoff uncertainty in Example 1, and will not be repeated one by one in this embodiment.

[0169] At the same time, the present invention also provides a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, it implements the above-mentioned cascade hydropower short-term scheduling method considering the uncertainty of interval runoff.

[0170] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application may adopt the form of a computer program product implemented in one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that include computer-usable program code.

[0171] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0172] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0173] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0174] The specific implementation methods described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific implementation method of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A short-term dispatching method for cascade hydropower considering uncertainty of interval runoff, characterized in that: The method includes: Acquire historical data of water flow in the interval, perform fitting processing on the historical data of water flow in the interval, and obtain probability distribution of water flow in the interval and typical interval flow scenarios; The conditional risk value is introduced into the cascade hydropower dispatch model to evaluate the risk of cascade hydropower generation under the uncertainty of intra-day interval runoff, and a cascade hydropower short-term dispatch model based on conditional risk value is obtained. The typical interval flow scenario is input into the cascade hydropower short-term scheduling model based on conditional value at risk, and the nonlinear constraints in the cascade hydropower short-term scheduling model based on conditional value at risk are linearized, and the model is converted into a mixed integer linear programming problem for solution to obtain the optimal solution.

2. The cascade hydropower short-term scheduling method considering interval runoff uncertainty according to claim 1 is characterized in that: Obtain the probability distribution of interval water flow and typical interval flow scenarios, including: Performing fitting processing on the historical data of the interval water flow rate to obtain a probability density function of the interval water flow rate as a probability distribution of the interval water flow rate; The original interval traffic scene is obtained based on Latin hypercube sampling, and K-means clustering is used to reduce the original interval traffic scene to obtain a typical interval traffic scene.

3. The cascade hydropower short-term scheduling method considering interval runoff uncertainty according to claim 1 is characterized in that: The objective function of the cascade hydropower short-term scheduling model based on conditional risk value is: Where: W is the total number of scenes; ω w is the probability of scene w; δ is the confidence; P w is the total power generation under scenario w; I is the total number of hydropower stations; T is the total number of scheduling time periods; P i,t,w represents the output of hydropower station i under scenario w in the dispatching time period t; Δt represents the number of hours in the dispatching time period t; ζ, η w In order to calculate the auxiliary variable introduced based on the conditional risk value, the optimal value of ζ is based on the conditional risk value, that is, the VaR value; η w =[ζ-P w ] + represents the maximum value function max{ζ-P w ,0}, if the benefit of scenario w is P w is greater than the VaR value, i.e. ζ, then η w is equal to 0; otherwise η w is ζ and P w The difference.

4. The cascade hydropower short-term scheduling method considering interval runoff uncertainty according to claim 1 is characterized in that: The hydropower station constraints of the cascade hydropower short-term scheduling model based on conditional risk value include water balance constraints, hydraulic connection constraints, initial and final water level constraints, water level constraints, outflow flow constraints, power station output constraints, power generation flow constraints, unit output climbing constraints, unit start-up and shutdown duration constraints, net head calculation constraints, reservoir capacity-water level relationship function constraints, discharge flow tail water level relationship function constraints, head loss function constraints and unit output function constraints.

5. The cascade hydropower short-term scheduling method considering interval runoff uncertainty according to claim 4 is characterized in that: The nonlinear constraints in the conditional value at risk cascade hydropower short-term dispatch model are linearized, including: One-dimensional nonlinear function fitting and linearization processing: Based on the one-dimensional quartic polynomial fitting method, the reservoir capacity water level relationship function constraint, the discharge tail water level relationship function constraint, and the head loss function constraint are fitted respectively; and the piecewise linearization method is used to linearize the fitted function; Binary nonlinear function line fitting and linearization processing: The binary quadratic polynomial fitting method is used to fit and linearize the unit output function constraints.

6. The cascade hydropower short-term scheduling method considering interval runoff uncertainty according to claim 5 is characterized in that: The model is transformed into a mixed integer linear programming problem for solution, including: Setting initial calculation conditions, including the number of scheduling time periods within a day, the initial and final water level control values ​​of each hydropower station, the outflow and power generation flow upper limits of each power station, and the upper limit of the unit output; Fitting and linearizing historical data of the hydropower station to obtain linearized constraints and objective functions of the hydropower station; the historical data of the hydropower station include reservoir water level, tail water level of discharge flow, head loss and unit output characteristics; The linearized constraints and objective functions of the hydropower station are modeled through YALMIP, the interval water inflow of the typical interval flow scenario is input, and the cascade hydropower short-term scheduling model based on conditional risk value is solved through the solver to output the water level changes, power generation flow and unit output of the hydropower station under various scenarios based on conditional risk value at a certain confidence level.

7. The cascade hydropower short-term scheduling method considering interval runoff uncertainty according to claim 1 is characterized in that: Before fitting the historical data of water flow in the interval, the method further includes: The historical data of water flow in the interval is normalized, and the normalization formula is: in, is the normalized historical interval water flow of the hydropower station i at time t; Q i,t is the interval water flow at time t of the hydropower station i; T is the number of statistical time periods for the historical interval water flow in one day.

8. A cascade hydropower short-term dispatching system considering interval runoff uncertainty, characterized by: The system includes: A typical scenario acquisition unit is used to obtain the historical data of the interval water flow, perform fitting processing on the historical data of the interval water flow, and obtain the probability distribution of the interval water flow and the typical interval flow scenario; The dispatch model building unit is used to introduce the conditional risk value into the cascade hydropower dispatch model to evaluate the risk faced by the cascade hydropower generation under the uncertainty of intra-day interval runoff, and obtain the cascade hydropower short-term dispatch model based on the conditional risk value; The model solving unit is used to input the typical interval flow scenario into the cascade hydropower short-term scheduling model based on conditional risk value, linearize the nonlinear constraints in the cascade hydropower short-term scheduling model based on conditional risk value, convert the model into a mixed integer linear programming problem for solving, and obtain the optimal solution.

9. The cascade hydropower short-term dispatching system considering interval runoff uncertainty according to claim 8 is characterized in that: The typical scene obtaining unit comprises: A fitting subunit is used to perform fitting processing on the historical data of the interval water flow rate to obtain a probability density function of the interval water flow rate as a probability distribution of the interval water flow rate; The scenario sub-unit is used to obtain the original interval traffic scenario based on Latin hypercube sampling, and to reduce the original interval traffic scenario by using K-means clustering to obtain a typical interval traffic scenario.

10. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the method for short-term scheduling of cascade hydropower considering uncertainty of interval runoff as described in any one of claims 1 to 7 is implemented.

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