A Method for Controlling the Abandoned Water of Cascade Hydropower Stations Based on Multi-Objective Variable Penalty Coefficients

Abstract

The present invention discloses a cascaded hydropower station group water abandonment control method based on multi-objective variable penalty coefficients, which uses a two-layer optimal scheduling model to control the cascaded water abandonment volume. The outer layer aims to maximize the cascaded power generation and minimize the cascaded water abandonment volume, and uses the multi-objective optimization algorithm NSGA-II to optimize the time series of penalty coefficients. The inner layer aims to maximize the power generation of the upstream power station, and performs single-objective reservoir optimal scheduling calculation through the DDDP algorithm, and controls the water abandonment of the downstream power station through the penalty coefficients. This method controls the pre-flood water abandonment volume of the downstream power station through the penalty coefficients, and considering the different penalty coefficients in each period, compared with the constant penalty coefficient, the variable penalty coefficient can significantly reduce the cascaded water abandonment volume.

Description

Technical Field

[0001] The present invention belongs to the technical field of reservoir operation, and particularly relates to a method for controlling the water abandonment of cascade hydropower stations based on multi-objective variable penalty coefficients. Background Art

[0002] Water abandonment is the main problem faced by reservoir operation in hydropower-rich areas. The research on water abandonment control methods is very important for reservoir operation and is directly related to the social and economic benefits of hydropower station operation. In order to fully utilize the head benefit of the reservoir, most reservoirs operate at a high water level. However, this operation method lacks consideration for water abandonment control. Therefore, in actual operation, in addition to considering the maximum power generation, it is also necessary to minimize the water abandonment as much as possible. At present, the research on water abandonment control mainly focuses on the flood season, and there is little research on the water abandonment control method before the flood season. Generally, a penalty is imposed on the output to increase the guarantee rate. Therefore, introducing a penalty coefficient to reduce the water abandonment before the flood season is also a good method. However, most of the research using penalty coefficient control tends to keep the penalty coefficient as a fixed value and does not consider the influence brought by variable penalty coefficients. The present invention proposes a method for controlling the water abandonment before the flood season by using variable penalty coefficients. The penalty coefficients for different time periods can be determined through an optimization model, and different penalty coefficients are given for each time period to better achieve the effect of controlling water abandonment. Summary of the Invention

[0003] Based on the above technical problems, the present invention uses a two-layer optimal operation model. The outer layer aims at maximizing the cascade power generation and minimizing the cascade water abandonment, and uses the multi-objective optimization algorithm NSGA-II to optimize the time series of penalty coefficients. The inner layer aims at maximizing the power generation of the upstream power station and conducts single-objective reservoir optimal operation calculation through the DDDP algorithm.

[0004] To solve the above calculation problems, the present invention adopts the following technical solutions:

[0005] A method for controlling the water abandonment of cascade hydropower stations based on multi-objective variable penalty coefficients, comprising the following steps:

[0006] Step S1. Establish a two-layer optimal operation model, where the outer layer aims at maximizing the cascade power generation and minimizing the cascade water abandonment, and the inner layer aims at maximizing the power generation of the upstream power station;

[0007] Step S2. The outer layer uses the multi-objective optimization algorithm NSGA-II to optimize the time series of penalty coefficients, and the inner layer conducts single-objective reservoir optimal operation calculation through the DDDP algorithm, and controls the water abandonment of the downstream power station through the penalty coefficient.

[0008] Furthermore, the objective functions are as follows:

[0009] (1) There are two objective functions in the outer layer:

[0010] (i) The total cascade power generation within the scheduling period T is maximized, i.e.:

[0011]

[0012] Where: E1 is the total cascade power generation within the period T of n reservoirs; i is the reservoir serial number; n is the total number of cascade reservoirs; T is the total number of periods, t ∈ [1, T]; N it is the effective actual output of the i-th reservoir at time t; is the water diversion flow rate for power generation of the i-th reservoir at time t; is the water consumption rate of the i-th reservoir at time t; Δt is the length of the time interval;

[0013] (ii) The total cascade water abandonment within the scheduling period T is minimized, i.e.:

[0014]

[0015] Where: QS is the total water abandonment within the period T; Qqs it is the water abandonment flow rate of the i-th reservoir at time t;

[0016] (2) The inner-layer objective function is to maximize the total power generation of the upstream power station, i.e.:

[0017]

[0018] Where: E2 is the total power generation within the period T; T is the total number of periods, t ∈ [1, T]; N t is the effective actual output at time t; is the water diversion flow rate for power generation at time t; is the water consumption rate at time t; Δt is the length of the time interval.

[0019] Furthermore, the step S2 specifically includes the following sub-steps:

[0020] S21. Input the water level and flow rate data of the cascade power station to generate the initial population of penalty coefficient sequences;

[0021] S22. Substitute the initial penalty coefficient sequence into the inner-layer DDDP solution algorithm to solve the optimal operation water level of the upstream power station, calculate the discharge of the upstream power station, calculate the inflow of the downstream power station through the interval flow, and then calculate the cascade power generation and cascade water abandonment;

[0022] S23. Update the penalty coefficient sequence through the NSGA-II algorithm and calculate the Pareto solution set of penalty coefficients that meet the objectives.

[0023] Furthermore, the constraint conditions are as follows:

[0024] (1) Outer layer:

[0025] 0 ≤ α t ≤ α max (4)

[0026] Where: α t is the penalty coefficient in period t, and α max is the upper limit of the penalty coefficient;

[0027] (2) Inner layer:

[0028] (i) Includes water balance constraint, reservoir water level constraint, hydropower station head constraint, total output constraint of hydropower station, and outflow discharge constraint;

[0029] (ii) Considering the constraint condition of the full-load flow of the downstream power station units, a penalty coefficient is introduced to control the water abandonment of the downstream power station. The specific expression is as follows:

[0030]

[0031] Where: q t is the upstream power station outflow discharge in period t, Qqj t is the inter-basin flow of the downstream power station in period t, which is obtained by subtracting the upstream power station outflow discharge from the downstream power station inflow discharge, a t is the penalty coefficient in period t, q′ t is the upstream power station reservoir discharge after penalty in period t, is the full-load flow of the downstream power station units in period t.

[0032] Compared with the prior art, the present application has the following beneficial effects:

[0033] The present invention only needs to perform optimal scheduling calculations on the upstream power station, control the water abandonment of the downstream power station through the penalty coefficient, introduce a variable penalty coefficient, and optimize the penalty coefficient for each period. Compared with the case where the penalty coefficient remains unchanged, it can reduce the water abandonment of the downstream power station more, thereby reducing the cascade water abandonment. Moreover, constructing a two-layer optimization model can automatically optimize the penalty coefficient without manual adjustment, which is objective. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 is the flowchart of the present invention;

[0035] Figure 2 is the variation diagram of cascade power generation and cascade water abandonment under different penalty coefficients from January to May 2022 in the embodiment of the present invention;

[0036] Figure 3 is the variation diagram of cascade power generation and cascade water abandonment under different penalty coefficients from January to May 2012 in the embodiment of the present invention;

[0037] Figure 4This is a graph showing the changes in cascade power generation and cascade water abandonment under different penalty coefficients from January to May 2010 in the embodiments of the present invention. Detailed implementation manners

[0038] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings, embodiments and comparative examples.

[0039] Embodiment

[0040] This embodiment provides a method for controlling water abandonment in cascade hydropower stations based on multi-objective variable penalty coefficients, including the following steps:

[0041] Step S1. Establish a two-layer optimal scheduling model, where the outer layer aims to maximize the cascade power generation and minimize the cascade water abandonment, and the inner layer aims to maximize the power generation of the upstream power station;

[0042] Step S2. The outer layer uses the multi-objective optimization algorithm NSGA-II to optimize the time series of penalty coefficients, and the inner layer performs single-objective reservoir optimal scheduling calculation through the DDDP algorithm, and controls the water abandonment of the downstream power station through the penalty coefficients.

[0043] The optimal scheduling model is as follows:

[0044] (1) There are two objective functions in the outer layer:

[0045] (i) Maximize the total cascade power generation within the scheduling period T, that is:

[0046]

[0047] In the formula: E1 is the total power generation of n reservoirs within the period T; i is the reservoir number; n is the total number of cascade reservoirs; T is the total number of periods, t ∈ [1, T]; N it is the effective actual output of the i-th reservoir at the t-th period; is the power generation diversion flow of the i-th reservoir at the t-th period; is the water consumption rate of the i-th reservoir at the t-th period; Δt is the period interval length.

[0048] (ii) Minimize the total cascade water abandonment within the scheduling period T, that is:

[0049]

[0050] In the formula: QS is the total water abandonment of n reservoirs within the period T; Qqs it is the water abandonment flow of the i-th reservoir at the t-th period, and the meanings of the other symbols are the same as above.

[0051] (2) The objective function of the inner layer is to maximize the total power generation of the upstream power station, that is:

[0052]

[0053] Where: E2 is the total power generation within the time period T; T is the total number of time periods, t ∈ [1, T]; N t is the effective actual output in the t-th time period; is the water diversion flow for power generation in the t-th time period; is the water consumption rate in the t-th time period; Δt is the length of the time interval.

[0054] Constraint conditions

[0055] (1) Outer layer:

[0056] 0 ≤ α t ≤ α max (4)

[0057] Where: α t is the penalty coefficient in the t-th time period, and α max is the upper limit of the penalty coefficient.

[0058] (2) Inner layer:

[0059] (i) It includes conventional constraints such as water balance constraint, reservoir water level constraint, hydropower station head constraint, total output constraint of hydropower station, and outflow discharge constraint.

[0060] (ii) Considering the constraint condition of the full-load flow of the downstream power station units, a penalty coefficient is introduced to control the water abandonment of the downstream power station. The specific expression is as follows:

[0061]

[0062] Where: q t is the upstream power station outflow discharge in the t-th time period, Qqj t is the downstream power station interval flow in the t-th time period, a t is the penalty coefficient in the t-th time period, q′ t is the upstream power station reservoir flow after penalty in the t-th time period, is the full-load flow of the downstream power station units in the t-th time period.

[0063] Taking the Xijin Power Station, Xianyitan Power Station and Guihang Power Station in the Yujiang River Basin of Guangxi as examples, the Xijin Power Station is upstream of the Xianyitan Power Station and Guihang Power Station and is a seasonal regulation power station. The Xianyitan Power Station and Guihang Power Station are both daily regulation power stations. Since the inflow discharge is large during the water level recession period from April to May at the Xijin Power Station, there is more water abandonment. There are differences in the power stations considered in this embodiment for January - March and April - May.

[0064] Considering the constraint conditions of the installed capacity flow of Xianyitan and Guihang

[0065] (1) January to March: The main consideration is to minimize the waste of water at Xianyitan and Guihang power stations, that is, the incoming water is less than the full-load flow of their respective units. Since the full-load flow of the units at Xianyitan power station is greater than that at Guihang power station, when there is waste water at Xianyitan power station, there will definitely be waste water at Guihang power station. Therefore, the main consideration is the penalty of the waste water at Guihang power station on the outflow of Xijin power station, that is:

[0066]

[0067] (2) April to May: At this time, the incoming water at Xijin power station is relatively large. The main consideration is to minimize the waste of water at Xianyitan as much as possible, and the situation where Guihang can have waste water. Therefore, during this period, the main consideration is the penalty of the waste water at Xianyitan power station on the outflow of Xijin power station, that is:

[0068]

[0069] In equations (5) - (6): q t is the outflow of Xijin at time t, and are the sectional flows of Xianyitan and Guihang at time t, respectively obtained by subtracting the outflow of the upstream power station from the incoming water flow. a t is the penalty coefficient at time t, q' t is the outflow of Xijin at time t after penalty, 525 m 3 / s and 1100 m 3 / s are the full-load flows of the units at Guihang and Xianyitan, respectively.

[0070] The specific implementation steps are as follows:

[0071] (1) Input the incoming water flow process and the initial and final reservoir water levels of Xijin power station, the initial reservoir water levels and sectional flow processes of Xianyitan and Guihang power stations, and the characteristic curve data of the three power stations;

[0072] (2) Generate an initial penalty coefficient sequence α1, α2,..., α T , all within the range of 0 to 3, and the evolutionary generation i = 1;

[0073] (3) Determine whether the first-generation sub-penalty coefficient sequence has been generated. If it has been generated, set the evolutionary generation i = 2; otherwise, perform non-dominated sorting, selection, crossover, and mutation on the initial penalty coefficient sequence to generate the first-generation sub-penalty coefficient sequence and set the evolutionary generation i = 2;

[0074] (4) Combine the parent penalty coefficient sequence and the offspring penalty coefficient sequence into a new penalty coefficient sequence;

[0075] (5) Take the actual dispatching water levels of Xijin Power Station as the initial and final water levels for calculation. According to the conventional constraint conditions of Xijin Power Station and the constraint conditions of the downstream power stations considering the new penalty coefficient sequence, generate the initial feasible dispatching water level process z0, z1,..., z T ;

[0076] (6) According to z0, z1,..., z T , calculate the total power generation E0 of Xijin Power Station, and generate a corridor within the range of 0.1 m above and below the water level line. According to the conventional constraint conditions of Xijin Power Station and the constraint conditions of the downstream power stations, use dynamic programming to calculate the optimal dispatching water level process z′0, z′1,..., z′ T ;

[0077] (7) Calculate the total power generation E1 of Xijin Power Station corresponding to z′0, z′1,..., z′ T . If E0 = E1, proceed to the next step; otherwise, use z′0, z′1,..., z′ T to replace z0, z1,..., z T , and return to step (6);

[0078] (8) Calculate the discharge flow, power generation, and water rejection flow processes of Xijin Power Station corresponding to the process of z0, z1,..., z T . According to the interval flow processes of Xianyitan and Guihang Power Stations, calculate the inflow flow processes of Xianyitan and Guihang Power Stations. For Xianyitan and Guihang Power Stations, adopt runoff regulation to calculate their respective power generations and water rejections, and calculate the total power generation and total water rejection of Xijin, Xianyitan, and Guihang Power Stations;

[0079] (9) According to the calculated total power generation and total water rejection, perform operations such as fast non - dominated sorting and crowding degree calculation to generate a new parent penalty coefficient sequence, and perform selection, crossover, and mutation operations on the generated parent penalty coefficient sequence to generate a child penalty coefficient sequence;

[0080] (10) If i < 100, the evolutionary generation i = i + 1, return to step (4); otherwise, the program ends and outputs the pareto solution set of the penalty coefficient sequence.

[0081] Take the measured initial and final water levels of Xijin, Xianyitan, and Guihang Power Stations from January to May in the wet year 2022, normal year 2012, and dry year 2010 as the initial and final water levels for calculation, and set three calculation schemes for different penalty coefficient conditions:

[0082] (1) Scheme 1: The penalty coefficient is taken as 0 (no penalty), and with the maximum total power generation of Xijin Power Station as the goal, perform optimal dispatching calculation on Xijin Power Station using DDDP;

[0083] (2) Scheme 2: The penalty coefficients for each time period are taken as the same value. With the maximum total power generation of Xijin Power Station as the objective, the DDDP is used to optimize the dispatching calculation of Xijin Power Station. By calculating the results of multiple penalty coefficients, the penalty coefficient that maximizes the power generation is selected for the optimized dispatching calculation;

[0084] (3) Scheme 3: The penalty coefficients for each time period are different. The optimized dispatching calculation is carried out through a two-layer optimized dispatching model. The outer layer takes the maximum total power generation of the cascade of Xijin, Xianyitan and Guihang power stations and the minimum cascade water abandonment as the objectives, and the inner layer takes the maximum total power generation of Xijin Power Station as the objective.

[0085] Figures 2 to 4 They are the variation diagrams of the cascade power generation and cascade water abandonment under different penalty coefficients when the penalty coefficients for each time period are taken as the same value in the wet year 2022, normal year 2012 and dry year 2010 of Scheme 2. In order to make the cascade power generation as large as possible and the cascade water abandonment as small as possible, the results with penalty coefficients of 0, 0.3 and 0.9 are respectively selected as the final results. Tables 1 - 3 show the total power generation and total water abandonment results of Xijin, Xianyitan and Guihang power stations and the cascade under different schemes. It can be seen that compared with Scheme 1, both Scheme 2 and Scheme 3 can reduce the total cascade water abandonment, but Scheme 3 has a better effect than Scheme 2, that is, considering variable penalty coefficients has a better effect on reducing water abandonment than keeping the penalty coefficient unchanged. When the penalty coefficient remains unchanged, the effect is the best without penalty in 2022, while the effect is the best when the penalty coefficients are 0.3 and 0.9 in 2012 and 2010 respectively. In the case of variable penalty coefficients, the cascade water abandonment in 2022, 2012 and 2010 is reduced by 0.07 billion m 3 ³, 1.8 billion m 3 ³ and 0.23 billion m 3 ³ respectively compared with the case where the penalty coefficient remains unchanged, indicating that when the incoming water is too large or too small, the cascade water abandonment that can be reduced by the penalty coefficient is relatively small.

[0086] Table 1 Results of power generation and water abandonment of each power station in Scheme 1

[0087]

[0088] Table 2 Results of power generation and water abandonment of each power station in Scheme 2

[0089]

[0090] Table 3 Results of power generation and water abandonment of each power station in Scheme 3

[0091]

[0092]

[0093] The specific embodiments described herein are merely illustrative of the spirit of the present invention. Those skilled in the art to which the present invention pertains may make various modifications or supplements to the described specific embodiments or use similar means for substitution, without departing from the spirit of the present invention or exceeding the scope defined by the appended claims.

Claims

1. A cascade hydropower station group water abandonment control method based on multi-objective variable penalty coefficient, characterized in that It includes the following steps: Step S1: Establish a two-layer optimal scheduling model, where the outer layer aims to maximize the cascade power generation and minimize the cascade water abandonment, and the inner layer aims to maximize the power generation of the upstream power station. The objective functions are as follows: (1) The outer layer has two objective functions: (i) Maximize the total cascade power generation within the scheduling period T, that is: In the formula: is the total power generation of cascade within a reservoir period; is the reservoir serial number; is the total number of cascade reservoirs; is the total number of periods, ; is the effective actual output of the th reservoir in the period; is the th reservoir t in the period for the water diversion flow for power generation; is the th reservoir t in the period for the water consumption rate; is the period interval length; (ii) Minimize the total cascade water abandonment within the scheduling period T, that is: In the formula: is the total water abandonment volume within the time period; is t the water abandonment flow of the th reservoir in the time period; (2) The inner layer objective function is to maximize the total power generation of the upstream power station, that is: Wherein: is the total power generation during the time period ; is the effective actual output during the th time period; is the water diversion flow rate for power generation during the t th time period; is the water consumption rate during the t th time period. Step S2: The outer layer uses the multi-objective optimization algorithm NSGA-II to optimize the penalty coefficient time series, and the inner layer conducts single-objective reservoir optimal scheduling calculation through the DDDP algorithm, and controls the water abandonment of the downstream power station through the penalty coefficient.

2. The cascade hydropower station group water abandonment control method based on multi-objective variable penalty coefficient according to claim 1, characterized in that, The specific steps of Step S2 include the following sub-steps: S21: Input the water level and flow data of the cascade power stations to generate the initial penalty coefficient sequence population; S22: Substitute the initial penalty coefficient sequence into the DDDP solution algorithm of the inner layer to solve the optimal operation water level of the upstream power station, calculate the outflow of the upstream power station, calculate the inflow of the downstream power station through the interval flow, and then calculate the cascade power generation and cascade water abandonment; S23: Update the penalty coefficient sequence through the NSGA-II algorithm and calculate the Pareto solution set of the penalty coefficients that meet the objectives.

3. A cascaded hydropower station group water abandonment control method based on multi-objective variable penalty coefficient as claimed in claim 1, characterized in that The constraint conditions are as follows: (1) The outer layer: Wherein: is t the time period penalty coefficient, is the upper limit of the penalty coefficient; (2) The inner layer: (i) It includes water balance constraints, reservoir water level constraints, hydropower station head constraints, total hydropower station output constraints, and outflow constraints; (ii) Considering the constraint condition of the full-load flow of the downstream power station units, a penalty coefficient is introduced to control the water abandonment of the downstream power station. The specific expression is as follows: Wherein: is t the upstream power station's outflow during the period is t the inter-basin flow of the downstream power station during the period, obtained by subtracting the upstream power station's outflow from the downstream power station's inflow is t the penalty coefficient during the period is the t upstream power station's reservoir flow after penalty during the period is the downstream power station's unit t unit full-load flow during the period.

Images