WO2019119413A1 - 一种耦合相对目标接近度和边际分析原理的梯级水电站多目标优化调度方法 - Google Patents

一种耦合相对目标接近度和边际分析原理的梯级水电站多目标优化调度方法 Download PDF

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WO2019119413A1
WO2019119413A1 PCT/CN2017/117988 CN2017117988W WO2019119413A1 WO 2019119413 A1 WO2019119413 A1 WO 2019119413A1 CN 2017117988 W CN2017117988 W CN 2017117988W WO 2019119413 A1 WO2019119413 A1 WO 2019119413A1
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objective
marginal
target
benefit
interval
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French (fr)
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申建建
张俊涛
程春田
牛文静
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大连理工大学
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Priority to US16/606,571 priority patent/US11009001B2/en
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B17/00—Systems involving the use of models or simulators of said systems
    • G05B17/02—Systems involving the use of models or simulators of said systems electric
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F03—MACHINES OR ENGINES FOR LIQUIDS; WIND, SPRING, OR WEIGHT MOTORS; PRODUCING MECHANICAL POWER OR A REACTIVE PROPULSIVE THRUST, NOT OTHERWISE PROVIDED FOR
    • F03B—MACHINES OR ENGINES FOR LIQUIDS
    • F03B13/00—Adaptations of machines or engines for special use; Combinations of machines or engines with driving or driven apparatus; Power stations or aggregates
    • F03B13/06—Stations or aggregates of water-storage type, e.g. comprising a turbine and a pump
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F03—MACHINES OR ENGINES FOR LIQUIDS; WIND, SPRING, OR WEIGHT MOTORS; PRODUCING MECHANICAL POWER OR A REACTIVE PROPULSIVE THRUST, NOT OTHERWISE PROVIDED FOR
    • F03B—MACHINES OR ENGINES FOR LIQUIDS
    • F03B15/00—Controlling
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/041—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a variable is automatically adjusted to optimise the performance
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q10/00—Administration; Management
    • G06Q10/04—Forecasting or optimisation specially adapted for administrative or management purposes, e.g. linear programming or "cutting stock problem"
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F05—INDEXING SCHEMES RELATING TO ENGINES OR PUMPS IN VARIOUS SUBCLASSES OF CLASSES F01-F04
    • F05B—INDEXING SCHEME RELATING TO WIND, SPRING, WEIGHT, INERTIA OR LIKE MOTORS, TO MACHINES OR ENGINES FOR LIQUIDS COVERED BY SUBCLASSES F03B, F03D AND F03G
    • F05B2260/00—Function
    • F05B2260/42—Storage of energy
    • F05B2260/422—Storage of energy in the form of potential energy, e.g. pressurized or pumped fluid
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F05—INDEXING SCHEMES RELATING TO ENGINES OR PUMPS IN VARIOUS SUBCLASSES OF CLASSES F01-F04
    • F05B—INDEXING SCHEME RELATING TO WIND, SPRING, WEIGHT, INERTIA OR LIKE MOTORS, TO MACHINES OR ENGINES FOR LIQUIDS COVERED BY SUBCLASSES F03B, F03D AND F03G
    • F05B2270/00—Control
    • F05B2270/30—Control parameters, e.g. input parameters
    • F05B2270/335—Output power or torque
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E10/00—Energy generation through renewable energy sources
    • Y02E10/20—Hydro energy
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E60/00—Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation
    • Y02E60/16—Mechanical energy storage, e.g. flywheels or pressurised fluids
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
    • Y02P70/00—Climate change mitigation technologies in the production process for final industrial or consumer products
    • Y02P70/50—Manufacturing or production processes characterised by the final manufactured product

Definitions

  • the invention relates to the field of hydropower dispatching operation, in particular to a multi-objective optimal scheduling method for cascade hydropower stations coupled with relative target proximity and marginal analysis principles.
  • This method does not destroy the physical meaning of the multi-objective problem itself, and can obtain the non-inferior solution set of the real Pareto frontier of the approximation problem.
  • Hydropower dispatching schemes but the final decision still depends on the subjective tendency of the dispatcher or the degree of target preference. Without objective decision-making metrics, it is difficult to fully reflect the decision-making benefits under the combined effects of multiple objectives.
  • the present invention relies on the National Natural Science Foundation Major Program Key Support Project (91547201) and the National Natural Science Foundation of China (51579029), and proposes a multi-objective optimal scheduling of cascade hydropower stations coupled with relative target proximity and marginal analysis principles.
  • the method is applied to test the multi-objective optimal scheduling problem of cascade hydropower stations in the middle and lower reaches of Minjiang River as the engineering background.
  • the results show that the results of the present invention can effectively meet the multi-target control requirements of peak shaving and downstream river navigation, and reduce the traditional The subjective assumption of the target decision method.
  • the technical problem to be solved by the present invention is to provide a multi-objective optimal scheduling method for cascade hydropower stations with coupling relative target proximity and marginal analysis principles, which can realize efficient processing of multi-objective optimal scheduling optimization models for cascade hydropower stations, and utilize the principle of economic marginal analysis. Analyze the change law of hydropower dispatching benefit under multi-objective action, and provide the basis for multi-objective scientific decision-making.
  • a multi-objective optimal scheduling method for cascade hydropower stations with coupling relative target proximity and marginal analysis principles including multi-objective optimization model processing, model solving and multi-objective decision making.
  • the specific steps are as follows:
  • Step1 Get positive and negative ideal points: positive ideal point Negative ideal point
  • Step2 Target vector normalization: the objective function values corresponding to any feasible solution are F 1 and F 2 ; the target vector corresponding to the feasible solution is (F 1 , F 2 ), and the normalized target vector is (g 1 , g 2 ), Therefore, the positive and negative ideal points are normalized to (0,0) and (1,1), respectively;
  • Step5 So multi-target problem Converted to a single target problem min(F);
  • the multi-objective coordination solution is selected from the optimal solution set.
  • the detailed steps are as follows:
  • Step2 the marginal benefit is greater than the marginal cost, the decision maker should increase the output; the marginal benefit is less than the marginal cost, the decision maker should reduce the output; the marginal benefit is equal to the marginal cost, then the equilibrium state is reached, and the output makes the profit the largest Search for ⁇ ' from ⁇ min to the direction of "yield" increase, so that within the interval [ ⁇ min , ⁇ ′) And This section is called the benefit-driven zone.
  • the increase of “yield” in this interval can improve the comprehensive benefit; search for ⁇ ′′ from ⁇ max to “yield” reduction, so that it is within the interval ( ⁇ ′′, ⁇ max ] And The interval is called the cost-dominated area.
  • the reduction of “yield” in this interval can improve the comprehensive benefit; the interval [ ⁇ ′, ⁇ ′′] is the equilibrium area, and the “yield” can obtain a relatively high comprehensive benefit in the interval;
  • Step3 Select the optimal solution corresponding to the target weight coefficient in the equilibrium interval as the multi-objective coordination solution.
  • the invention has the following beneficial effects: the invention constructs a relative target proximity optimization model by introducing a target positive and negative ideal point to efficiently process multi-objective optimization; proposes a complex scheduling constraint processing strategy, and couples a genetic algorithm to solve the model to determine different targets; Based on the optimal solution set of weight coefficient, a multi-objective decision-making method based on the principle of economic marginal analysis is proposed.
  • the marginal benefit and marginal cost are introduced to represent the relationship between the objective function value and the target weight coefficient.
  • the law of profit maximization, the marginal analysis of the target weight coefficient finally determines the benefit dominant zone, the cost dominant zone, and the equilibrium zone, and gives the basis of multi-objective decision-making.
  • the invention can effectively reduce the subjective cut-off in multi-objective decision-making, and is beneficial to the dispatcher to make more objective decisions according to the actual needs of the project.
  • the invention also provides a new technical approach for the scheduling decision of the large hydropower station group with comprehensive utilization requirements.
  • Figure 1 is a schematic diagram of a relative target approach
  • Figure 2 is a margin analysis process diagram
  • Figure 3 is a schematic diagram of the overall solution of the method of the present invention.
  • Figure 4 is a process diagram of marginal analysis of the weighting factor of the peak shaving target
  • Figure 5 is an optimal solution profile.
  • the counter-regulation power station operates in conjunction with the upstream cascade hydropower stations, taking into account the hydropower peak shaving and river navigation requirements, has become a theoretical and practical issue to be solved in the dispatching of power grids and cascade hydropower stations in China, and it is necessary to construct practical methods. Therefore, the peaking power station and its downstream counter-regulating power station are selected as the scheduling objects. At the same time, the combined peaking and downstream river navigation requirements of the cascade power stations are considered, and a multi-objective optimization model is established to verify the invention results.
  • the minimum residual power of the grid is used as the objective function to ensure the residual load is stable, reduce the residual load peak-to-valley difference, and avoid frequent power-on and shutdown of power plants such as thermal power plants with poor regulation performance, thus achieving grid safety and energy saving. Economic Operation.
  • this paper adopts the minimum water level deviation of the downstream river channel of the hydropower station as the objective function.
  • the water flow conditions of the channel are improved to meet the navigation requirements.
  • the multi-objective optimization model for both peak shaving and navigation requirements can be described as: under the same control conditions, determine the daily water level change process of the cascade hydropower stations, so that the system residual load variance is minimized during the dispatch period and the river channel water level variance of the reverse regulation hydropower station is minimized. In order to ensure that the scheduling scheme can balance peaking and navigation requirements.
  • V m,t+1 V m,t +3600(Q m,t -S m,t ) ⁇ t
  • V m,t is the capacity of the m power station at time t, m 3 ;Q m,t is the inflow flow of the m power station t period, m 3 /s; S m,t is the outflow of the m power station t period The flow rate, m 3 /s; q m,t is the power generation flow rate of the m power station t period, m 3 /s; d m,t is the abandoned water flow rate of the m power station t period, m 3 /s.
  • Z m,t is the upper and lower limits of the water level of the m reservoir in the t period, m.
  • Z m,0 , Z m,T are the initial reservoir water level of m hydropower station and the reservoir water level at the end of the scheduling period, m.
  • N m,t are the upper and lower limits of the average output of the m power station in the t period, MW;
  • q m,t are the upper and lower limits of the power generation flow rate of the m power station t period, m 3 /s;
  • S m,t are the upper and lower limits of the outflow of the m power station t period, m 3 /s;
  • Shipping constraints mainly include the water depth limit of the channel, the maximum variation of the daily water level of the channel, the maximum amplitude limit of the hour water level, and the water flow speed limit of the channel.
  • h t is the water depth of the channel in t period, m; h is the lower limit of the depth of the air, m; Z t is the water level of the channel in time t, m; The upper limit of the water level of the channel is m, m; For the upper limit of the hourly water level of the channel, m; v t is the water flow velocity of the channel during t, m/s; The upper limit of the water flow speed of the channel, m/s.
  • Z is the lower limit of the tail water level of the anti-regulation power station
  • H is the bottom elevation of the river section near the dam section, m
  • h is the minimum depth of the downstream channel, m
  • y ( ⁇ ) is the tail water level-discharge relationship curve of the power station.
  • Step1 Get positive and negative ideal points: positive ideal point Negative ideal point
  • Step2 Target vector normalization: The objective function values corresponding to any feasible solution are F 1 , F 2 .
  • the target vector corresponding to the feasible solution is (F 1 , F 2 ), and the normalized target vector is (g 1 , g 2 ). Therefore, the positive and negative ideal points are normalized to (0, 0) and (1, 1), respectively.
  • Step5 So multi-target problem Converted to a single target problem min(F).
  • the multi-objective coordination solution is selected from the optimal solution set.
  • the detailed steps are as follows:
  • Step2 the marginal benefit is greater than the marginal cost, the decision maker should increase the output; the marginal benefit is less than the marginal cost, the decision maker should reduce the output; the marginal benefit is equal to the marginal cost, then the equilibrium state is reached, and the output makes the profit the largest Chemical.
  • the increase of “yield” in this interval can improve the comprehensive benefit; search for ⁇ ′′ from ⁇ max to “yield” reduction, so that it is within the interval ( ⁇ ′′, ⁇ max ] And This interval is called the cost-dominated area.
  • the reduction of “yield” in this interval can improve the comprehensive benefit; the interval [ ⁇ ′, ⁇ ′′] is the equilibrium area, and the “yield” in this interval can obtain a relatively high comprehensive benefit.
  • Step3 Select the optimal solution corresponding to the target weight coefficient in the equilibrium interval as the multi-objective coordination solution.
  • the model and method of this paper are tested with the Jinghong-Olive Dam cascade hydropower station on the lower reaches of the Minjiang River as the actual engineering background.
  • the Minjiang River is developed in the middle and lower reaches of the main stream in Yunnan province according to the two reservoirs and eight levels.
  • the Jinghong-Olive Dam cascade hydropower stations are the sixth and seventh hydropower stations in the middle and lower reaches of the Minjiang River in Yunnan.
  • As the main power station in Yunnan Power Grid, Jingshui Power Station plays an important role in peak shaving in the power system. At present, with the gradual increase of peaking pressure, the contradiction between the power generation peaking of Jinghong Power Station and its downstream river navigation becomes more and more prominent.
  • the Olive Dam Power Station Located 20 kilometers downstream of Jinghong City, the Olive Dam Power Station is a counter-regulation power station of Jinghong Power Station. It mainly reverses the peak discharge and discharge of Jinghong Power Station and improves the navigation flow conditions of the Jinghong River downstream to alleviate the Jinghong Power Station. The contradiction between the peak and the downstream navigation.
  • the basic data of the power station is shown in Table 1.
  • the shipping mileage of the Jinghong Power Station-Olive Dam Power Station is 30km, and the shipping mileage of the Olive Dam Power Station-Nanlahekou section is 80km.
  • the channel grade is V
  • the depth of field is 2.5m
  • the maximum variation of the daily water level is 3.0m
  • the maximum variation of the hour water level is 1.0m
  • the maximum flow rate is 3.0m.
  • the 19 sets of target weight coefficients are selected for calculation.
  • Table 2 shows the optimal solutions for each group of target weight coefficients.
  • the marginal analysis of the peaking target weight coefficient is obtained.
  • the target weighting coefficient equalization area is shown in Table 3.
  • the marginal analysis process is shown in Figure 4.
  • Figure 5 is the optimal solution distribution of the 19 sets of target weight coefficients. It can be seen that the optimal solution corresponding to the target weight coefficient in the equilibrium region is closer to the positive ideal point.
  • Two typical target weight coefficients ⁇ 0.45-0.55, 0.70-0.30 ⁇ are selected from the equilibrium area for further analysis and calculation. The results are shown in Table 4.
  • Peak shaving The optimal demodulation peaks under the two sets of target weight coefficients are ideal.
  • the residual variance is reduced by 31.1% and 29.7%, respectively, compared with the original system load variance.
  • the peak shaving amplitude is 715MW and 680MW, respectively.
  • the peak effect is significant.
  • Navigation The optimal water level change corresponding to the optimal solution of the three sets of target weight coefficients is very stable.
  • the daily water level variation D ⁇ Z and the hourly water level maximum amplitude H ⁇ Z are far in line with the V channel requirements, and the river water level is also strictly met.
  • F 1 is the residual variance
  • F 2 is the tail water level variance
  • ⁇ N is the residual peak-to-valley difference

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Abstract

一种耦合相对目标接近度和边际分析原理的梯级水电站多目标优化调度方法，其通过引入目标正负理想点构造相对目标接近度优化模型，以高效处理多目标优化；提出复杂调度约束处理策略，并耦合遗传算法进行模型求解，确定不同目标权重系数的最优解集；以此为基础，引入边际效益和边际成本表征多目标函数值随权重系数的变化关系；依据经济学利润最大化规律，对目标权重系数进行边际分析最终确定了效益主导区、成本主导区、以及均衡区，给出多目标决策依据；所述方法有效兼顾梯级水电站多目标优化调度需求，有利于调度人员减少决策中的主观臆断性，为具有综合利用要求的特大流域水电站群调度决策提供新的技术途径。

Description

一种耦合相对目标接近度和边际分析原理的梯级水电站多目标优化调度方法 技术领域
本发明涉及水电调度运行领域，特别涉及一种耦合相对目标接近度和边际分析原理的梯级水电站多目标优化调度方法。
技术背景
特大流域梯级水电站群通常肩负发电、防洪、供水、航运、生态等综合利用任务，其调度运行是典型的多目标优化问题，其求解非常复杂，主要体现在以下两个方面：一是从数学角度来看，水电站群多目标优化调度是典型的高维、强耦合、非线性优化问题，特别是在短期，如何求解时空高度耦合约束集下的多目标优化问题，需要高超的求解技术，以兼顾计算效率和结果精度要求；二是多目标问题通常面临庞大的非劣解集，如何避免人为主观因素影响，做出科学客观的决策是面临的又一难点问题。目前多目标优化问题的求解思路主要有两类：一是将多目标转化为单目标求解包括目标权重法、约束法、序列优化法、模糊最大满意度法等，这类方法原理简单且易于实现，实质是简化了原问题、降低了优化难度，但求解过程严重依赖于目标权重系数的确定、转化为约束条件的目标函数选择、目标重要性排序、隶属度函数中目标值的伸缩范围等众多人为主观因素，极有可能对计算结果和调度决策产生重大影响。另一类是直接采用多目标优化算法获得问题的Pareto解集，这类方法不会破坏多目标问题本身的物理意义，能够获得逼近问题真实Pareto前沿的非劣解集，给出了可选的水电调度方案集，但最终决策仍依赖于调度者的主观倾向性或目标偏好程度，缺少客观的决策度量方法，难以充分体现出多个目标综合作用下的决策效益。
针对以上问题，本发明依托国家自然科学基金重大计划重点支持项目(91547201)和国家自然科学基金面上项目(51579029)，提出一种耦合相对目标接近度和边际分析原理的梯级水电站多目标优化调度方法，并以澜沧江中下游梯级水电站群多目标优化调度问题为工程背景对其进行应用测试，结果显示本发明成果可有效兼顾电站调峰和下游河道通航的多目标控制需求，同时减少了传统多目标决策方法的主观臆断性。
发明内容
本发明要解决的技术问题是提供一种耦合相对目标接近度和边际分析原理的梯级水电站多目标优化调度方法，可实现梯级水电站多目标优化调度优化模型高效处理，并利用经济学边际分析原理深入分析多目标作用下的水电调度效益变化规律，为多目标科学决策提供依据。
本发明技术方案：
一种耦合相对目标接近度和边际分析原理的梯级水电站多目标优化调度方法，主要包括多目标优化模型处理、模型求解和多目标决策三部分，具体步骤如下：
(1)初始计算条件，包括水电站运行条件和约束条件，以及电力和水力调度需求条件；
(2)求出电力调度目标函数min(F 1)、水力调度目标函数min(F 2)的上下限分别为[F 1 min,F 1 max]、
Figure PCTCN2017117988-appb-000001
构建相对目标接近度模型优化模型，将多目标优化问题转化为单目标优化问题；详细转化步骤介绍如下：
Step1.获得正负理想点：正理想点
Figure PCTCN2017117988-appb-000002
负理想点
Figure PCTCN2017117988-appb-000003
Step2.目标向量标准化：任意可行解对应的目标函数值为F 1、F 2；该可行解对应的目标向量为(F 1,F 2)，标准化目标向量为(g 1,g 2)，
Figure PCTCN2017117988-appb-000004
Figure PCTCN2017117988-appb-000005
因此正负理想点分别标准化为(0,0)和(1,1)；
Step3.设置目标权重系数、计算标准化目标向量到正负理想点的加权距离：
Figure PCTCN2017117988-appb-000006
其中λ i是目标权重系数，i＝1,2；
Step4.计算相对目标接近度：F＝S 1/(S 1+S 2)；
Step5.因此多目标问题
Figure PCTCN2017117988-appb-000007
转化为单目标问题min(F)；
(3)运用耦合复杂约束处理策略的遗传算法求解相对目标接近度单目标优化模型，获得不同目标权重系数下的最优解集为
Figure PCTCN2017117988-appb-000008
其中
Figure PCTCN2017117988-appb-000009
其中
Figure PCTCN2017117988-appb-000010
Δλ＝(λ max-λ min)/(n-1)；n是目标权重系数的个数；
(4)运用基于经济学边际分析原理的多目标决策方法，从最优解集中筛选出多目标协调解，详细步骤如下：
Step1.对“边际效益”、“边际成本”、“产量”进行对应定义；“产量”：目标权重系数
Figure PCTCN2017117988-appb-000011
其中i＝1,…,n；k∈{1,2}，取k＝1；“边际效益”：目标权重系数
Figure PCTCN2017117988-appb-000012
增加到
Figure PCTCN2017117988-appb-000013
时，目标函数min(F1)的减小幅度百分比
Figure PCTCN2017117988-appb-000014
“边际成本”：目标权重系数
Figure PCTCN2017117988-appb-000015
增加到
Figure PCTCN2017117988-appb-000016
时，目标函数min(F2)的增加幅度百分比
Figure PCTCN2017117988-appb-000017
Step2.根据经济学利润最大化规律：边际效益大于边际成本，决策者应增加产量；边际效益小于边际成本，决策者应减少产量；边际效益等于边际成本，此时达到均衡状态，产量使利润最大化；从λ min向“产量”增加方向搜索λ′，使得在区间[λ min,λ′)内
Figure PCTCN2017117988-appb-000018
且
Figure PCTCN2017117988-appb-000019
称该区间为效益主导区，该区间内增加“产量”能提高综合效益；从λ max向“产量”减少方向搜索λ″，使得在区间(λ″,λ max]内
Figure PCTCN2017117988-appb-000020
且
Figure PCTCN2017117988-appb-000021
称该区间为成本主导区，该区间内减少“产 量”能提高综合效益；区间[λ′,λ″]为均衡区，“产量”在该区间取值能获得相对高的综合效益；
Step3.选出均衡区间内目标权重系数所对应的最优解即为多目标协调解。
本发明成果有如下有益效果：本发明通过引入目标正负理想点构造相对目标接近度优化模型，以高效处理多目标优化；提出复杂调度约束处理策略，并耦合遗传算法进行模型求解，确定不同目标权重系数的最优解集；以此为基础，提出一种基于经济学边际分析原理的多目标决策方法，引入边际效益和边际成本来表征目标函数值随目标权重系数的变化关系，依据经济学利润最大化规律，对目标权重系数进行边际分析最终确定了效益主导区、成本主导区、以及均衡区，给出了多目标决策依据。相比传统多目标决策方法，本发明可有效减少多目标决策中的主观臆断性，有利于调度人员根据工程实际需求做出更加客观的决策。本发明也为具有综合利用要求的特大流域水电站群调度决策提供新的技术途径。
附图说明
图1是相对目标接近度法示意图；
图2是边际分析过程图；
图3是本发明方法总体求解框架图；
图4是对调峰目标权重系数边际分析过程图；
图5是最优解分布图。
具体实施方式
下面结合附图和技术方案，进一步说明本发明的具体实施方式。
特大流域梯级水电站普遍面临发电、防洪、通航、生态等综合利用要求。伴随水电建设事业的高速发展，干流梯级水电站群联和调度运行逐步形成，这些综合利用需求之间的矛盾日益突出，特别是对于有通航和发电调峰要求的梯级水电站群，两者矛盾更为尖锐。当水电参与系统调峰时，若无有效的调控措施，必然会造成下游河道水位频繁起伏，严重破坏航运条件，直接威胁航运安全，修建反调节电站就是必然的选择。但反调节电站如何与上游梯级水电站群联合运行，兼顾水电调峰和河道通航需求，已成为我国电网和梯级水电站群调度中亟待解决的理论和实践课题，需要构建切实可行的方法。因此选择以调峰电站及其下游反调节电站为调度对象，同时考虑梯级电站联合调峰和下游河道通航需求，建立多目标优化模型，对发明成果进行验证。
对于调峰优化目标，采用电网剩余负荷方差最小作为目标函数，以保证剩余负荷平稳，减少剩余负荷峰谷差，进而避免调节性能较差的火电站等电源频繁开机停机，实现电网安全、节能、经济运行。
Figure PCTCN2017117988-appb-000022
对于通航优化目标，本文采用反调节水电站下游河道水位方差最小作为目标函数。以减小河道水位变幅改善航道水流条件，使其满足通航要求。
Figure PCTCN2017117988-appb-000023
对于兼顾调峰和通航需求的多目标优化模型可描述为：在相同控制条件下，确定梯级水电站群的日水位变化过程，使调度期内系统剩余负荷方差最小和反调节水电站下游河道水位方差最小，以保证调度方案能兼顾调峰和通航需求。
Figure PCTCN2017117988-appb-000024
式中：T为调度时段数目；t为时段序号，t＝1,2,…,T；N t为t时段系统负荷，MW；M为水电站数目；m为电站编号，m＝1,2,…,M；N m,t为m水电站t时段的平均出力，MW；Z t为t时段反调节水电站下游水位，m；
上述目标函数需要满足以下约束条件：
水量平衡方程：
V m,t+1＝V m,t+3600(Q m,t-S m,t)Δt
其中：S m,t＝q m,t+d m,t
式中：V m,t为m电站在t时刻的库容，m 3；Q m,t为m电站t时段的入库流量，m 3/s；S m,t为m电站t时段的出库流量，m 3/s；q m,t为m电站t时段的发电流量，m 3/s；d m,t为m电站t时段的弃水流量，m 3/s。
库水位约束：
Figure PCTCN2017117988-appb-000025
式中：
Figure PCTCN2017117988-appb-000026
Z m,t分别为m水库在t时段的水位上下限，m。
始末水位控制：
Z m,0＝Z m,T
式中：Z m,0、Z m,T分别为m水电站初始库水位和调度期末库水位，m。
电站出力上下限约束：
Figure PCTCN2017117988-appb-000027
式中：
Figure PCTCN2017117988-appb-000028
N m,t分别为m电站在t时段的平均出力上下限，MW；
出力爬坡约束；
Figure PCTCN2017117988-appb-000029
式中：
Figure PCTCN2017117988-appb-000030
为m水电站相邻时段出力变幅上限，MW；
发电流量约束：
Figure PCTCN2017117988-appb-000031
式中：
Figure PCTCN2017117988-appb-000032
q m,t分别为m电站t时段的发电流量上下限，m 3/s；
出库流量约束：
Figure PCTCN2017117988-appb-000033
式中：
Figure PCTCN2017117988-appb-000034
S m,t分别为m电站t时段的出库流量上下限，m 3/s；
航运约束，主要包括航道水深限制，航道日水位最大变幅限制，小时水位最大变幅限制，航道水流速度限制。
min{h t,t＝1～T}≥ h
Figure PCTCN2017117988-appb-000035
Figure PCTCN2017117988-appb-000036
Figure PCTCN2017117988-appb-000037
式中：h t为t时段航道水深，m； h为航深下限，m；Z t为t时段航道水位，m；
Figure PCTCN2017117988-appb-000038
为航道日水位变幅上限，m；
Figure PCTCN2017117988-appb-000039
为航道小时水位变幅上限，m；v t为t时段航道水流速度，m/s；
Figure PCTCN2017117988-appb-000040
航道水流速度上限，m/s。
航运约束条件处理：
(1)航深约束处理。通过下式将航深下限约束转化为最小出库流量约束。
S m,t＝y( Z) Z＝H+ h
式中 Z为反调节电站尾水位下限；H为近坝段河道断面底标高，m； h为下游河道最小航深，m；y(·)为电站尾水位-泄流关系曲线。
(2)水位变幅约束。本文通过目标函数控制水位变幅，并将日水位最大变幅、小时水位最大变幅作为结果是否满足通航要求的评价指标。
(3)对于航道水流速度限制，根据历史经验统计，最大流速一般都能满足要求，因此本文不考虑航道流速限制。
以上述多目标优化模型为问题背景，对本发明成果进行一次的完整应用，按照下述步骤(1)-(4)予以实现：
(1)初始计算条件，包括水电站运行条件和约束条件，以及电力和水力调度需求条件；
(2)求出电力调度目标函数min(F 1)、水力调度目标函数min(F 2)的上下限分别为[F 1 min,F 1 max]、
Figure PCTCN2017117988-appb-000041
构建相对目标接近度模型优化模型将多目标优化问题转化为单目标优化问题。详细转化步骤介绍如下：
Step1.获得正负理想点：正理想点
Figure PCTCN2017117988-appb-000042
负理想点
Figure PCTCN2017117988-appb-000043
Step2.目标向量标准化：任意可行解对应的目标函数值为F 1，F 2。该可行解对应的目标向量为(F 1,F 2)，标准化目标向量为(g 1,g 2)，
Figure PCTCN2017117988-appb-000044
Figure PCTCN2017117988-appb-000045
因此正负理想点分别标准化为(0,0)和(1,1)。
Step3.设置目标权重系数、计算标准化目标向量到正负理想点的加权距离：
Figure PCTCN2017117988-appb-000046
其中λ i是目标权重系数，i＝1,2。
Step4.计算相对目标接近度：F＝S 1/(S 1+S 2)。
Step5.因此多目标问题
Figure PCTCN2017117988-appb-000047
转化为单目标问题min(F)。
(3)运用耦合复杂约束处理策略的遗传算法求解相对目标接近度单目标优化模型，获得不同目标权重系数下的最优解集为
Figure PCTCN2017117988-appb-000048
其中
Figure PCTCN2017117988-appb-000049
一般地
Figure PCTCN2017117988-appb-000050
其中k＝1,2；Δλ＝(λ max-λ min)/(n-1)；n是目标权重系数的个数；
(4)运用基于经济学边际分析原理的多目标决策方法，从最优解集中筛选出多目标协调解。详细步骤如下：
Step1.对“边际效益”、“边际成本”、“产量”进行对应定义。“产量”：目标权重系数
Figure PCTCN2017117988-appb-000051
其中i＝1,…,n；k∈{1,2}，取k＝1。“边际效益”：目标权重系数
Figure PCTCN2017117988-appb-000052
增加到
Figure PCTCN2017117988-appb-000053
时，目标函数min(F 1)的减小幅度百分比
Figure PCTCN2017117988-appb-000054
“边际成本”：目标权重系数
Figure PCTCN2017117988-appb-000055
增加到
Figure PCTCN2017117988-appb-000056
时，目标函数min(F 2)的增加幅度百分比
Figure PCTCN2017117988-appb-000057
Step2.根据经济学利润最大化规律：边际效益大于边际成本，决策者应增加产量；边际效益小于边际成本，决策者应减少产量；边际效益等于边际成本，此时达到均衡状态，产量使利润最大化。从λ min向“产量”增加方向搜索λ′，使得在区间[λ min,λ′)内
Figure PCTCN2017117988-appb-000058
且
Figure PCTCN2017117988-appb-000059
称该区间为效益主导区，该区间内增加“产量”能提高综合效益；从λ max向“产量”减少方向搜索λ″，使得在区间(λ″,λ max]内
Figure PCTCN2017117988-appb-000060
且
Figure PCTCN2017117988-appb-000061
称该区间为成本主导区，该区间内减少“产量”能提高综合效益；区间[λ′,λ″]为均衡区，“产量”在该区间取值能获得相对高的综合效益。
Step3.选出均衡区间内目标权重系数所对应的最优解即为多目标协调解。
现以澜沧江下游景洪-橄榄坝梯级水电站群为实际工程背景，对本文模型和方法进行检验。澜沧江在云南境内干流中下游河段按两库八级开发。景洪-橄榄坝梯级水电站分别是云南澜沧江中下游河段第六、第七级水电站。景洪水电站作为云南电网中的主力电站，在电力系统中担负着重要的调峰任务。目前随着调峰压力的逐渐增加，景洪电站发电调峰与其下游河道通航的矛盾愈发突出。橄榄坝电站位于景洪市下游20公里处，是景洪电站的反调节电站，主要对景洪电站的调峰泄流进行反调节，改善景洪下游河道通航水流条件，以缓解景洪电站调峰和下游通航之间的矛盾。电站基础资料如表1所示。景洪电站-橄榄坝电站区段航运里程为30km，橄榄坝电站-南腊河口区段航运里程为80km。航道等级为Ⅴ级，航深为2.5m，日水位最大变幅为3.0m，小时水位最大变幅为1.0m，最大流速为3.0m。选取19组目标权重系数进行计算。表2为各组目标权重系数下的最优解。对调峰目标权重系数进行边际分析获得目标权重系数均衡区见表3，边际分析过程详见图4。图5为19组目标权重系数下的最优解分布图，可以看出均衡区中目标权重系数对应的最优解更加接近正理想点。从均衡区选取两种典型目标权重系数{0.45-0.55,0.70-0.30}，作进一步分析计算，结果见表4。调峰方面：两组目标权重系数下的最优解调峰效果都较为理想，余荷方差相对于原系统负荷方差分别减小31.1％、29.7％，调峰幅度分别为715MW、680MW，可见调峰效果显著。通航方面：三组目标权重系数组合下的最优解对应的航道水位变化非常平稳，日水位变幅D ΔZ和小时水位最大变幅H ΔZ均远远符合Ⅴ航道要求，此外河道水位也严格满足下游河道通航最低运行水位(522.5m)要求。因此，经过目标权重系数边际分析筛选出的最优解能够有效兼顾电站调峰和下游河道通航需求，实现景洪—橄榄坝梯级水电站的联合优化调度。
表1电站基础资料
Figure PCTCN2017117988-appb-000062
表2各组目标权重系数下的最优解统计表
Figure PCTCN2017117988-appb-000063
Figure PCTCN2017117988-appb-000064
表3均衡区目标权重系数组合
Figure PCTCN2017117988-appb-000065
表4典型目标权重系数最下最优解结果统计表
Figure PCTCN2017117988-appb-000066
注：F 1为余荷方差，F 2为尾水位方差，ΔN为余荷峰谷差。

Claims (1)

  1. 一种耦合相对目标接近度和边际分析原理的梯级水电站多目标优化调度方法，其特征包括如下步骤：
    (1)初始计算条件，包括水电站运行条件和约束条件，以及电力和水力调度需求条件；
    (2)求出电力调度目标函数min(F 1)、水力调度目标函数min(F 2)的上下限分别为[F 1 min,F 1 max]、
    Figure PCTCN2017117988-appb-100001
    构建相对目标接近度模型优化模型，将多目标优化问题转化为单目标优化问题，详细转化步骤介绍如下：
    Step1.获得正负理想点：正理想点
    Figure PCTCN2017117988-appb-100002
    负理想点
    Figure PCTCN2017117988-appb-100003
    Step2.目标向量标准化：任意可行解对应的目标函数值为F 1、F 2；该可行解对应的目标向量为(F 1,F 2)，标准化目标向量为(g 1,g 2)，
    Figure PCTCN2017117988-appb-100004
    Figure PCTCN2017117988-appb-100005
    因此正负理想点分别标准化为(0,0)和(1,1)；
    Step3.设置目标权重系数、计算标准化目标向量到正负理想点的加权距离：
    Figure PCTCN2017117988-appb-100006
    其中λ i是目标权重系数，i＝1,2；
    Step4.计算相对目标接近度：F＝S 1/(S 1+S 2)；
    Step5.因此多目标问题
    Figure PCTCN2017117988-appb-100007
    转化为单目标问题min(F)；
    (3)运用耦合复杂约束处理策略的遗传算法求解相对目标接近度单目标优化模型，获得不同权重系数下的最优解集为
    Figure PCTCN2017117988-appb-100008
    其中
    Figure PCTCN2017117988-appb-100009
    一般地
    Figure PCTCN2017117988-appb-100010
    其中k＝1,2；Δλ＝(λ max-λ min)/(n-1)；n是目标权重系数的个数；
    (4)运用基于经济学边际分析原理的多目标决策方法，从最优解集中筛选出多目标协调解，详细步骤如下：
    Step1.对“边际效益”、“边际成本”、“产量”进行定义；“产量”：目标权重系数
    Figure PCTCN2017117988-appb-100011
    其中i＝1,…,n；k∈{1,2}，取k＝1；“边际效益”：目标权重系数
    Figure PCTCN2017117988-appb-100012
    增加到
    Figure PCTCN2017117988-appb-100013
    时，目标函数min(F 1)的减小幅度百分比
    Figure PCTCN2017117988-appb-100014
    “边际成本”：目标权重系数
    Figure PCTCN2017117988-appb-100015
    增加到
    Figure PCTCN2017117988-appb-100016
    时，目标函数min(F 2)的增加幅度百分比
    Figure PCTCN2017117988-appb-100017
    Step2.根据经济学利润最大化规律：边际效益大于边际成本，决策者应增加产量；边际效益小于边际成本，决策者应减少产量；边际效益等于边际成本，此时达到均衡状态，产量使利润最大化；从λ min向“产量”增加方向搜索λ′，使得在区间[λ min,λ′)内
    Figure PCTCN2017117988-appb-100018
    且
    Figure PCTCN2017117988-appb-100019
    称该区间为效益主导区，该区间内增加“产量”能提高综合效益；从λ max向“产量”减少方向搜索λ″，使得在区间(λ″,λ max]内
    Figure PCTCN2017117988-appb-100020
    且
    Figure PCTCN2017117988-appb-100021
    称该区间为成本主导区，该区间内减少“产量”能提高综合效益；区间[λ′,λ″]为均衡区，“产量”在该区间取值能获得相对高的综合效益；
    Step3.选出均衡区间内目标权重系数所对应的最优解即为多目标协调解。
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