A Study On The Modeling And Solving Methods Of Complex Constraints For The Operation Of Hydropower Stations In Southwest China

Southwest China spans three gradient terrains of China,and has large terrain differences and dense rivers.Southwest China has richest water resources in China.Over the past 20 years,many large-scale hydropower systems,such as the Jinsha River,Lancang River,Yalong River,Wujiang River,Dadu River and Hongshui River,have been built in the Southwest China.These hydropower stations present complex features such as large-scale,high-head,large-capacity,gaint units,complex operation requirements,and sensitive hydraulic coupling.These characteristics exacerbate the difficulty of modeling and solving the optimal scheduling problem of hydropower in the Southwest China.This paper focuses on the four major and difficult problems in the optimal operation of hydropwer reservoirs in the Southwest China,that is,the large-scale hydropwer scheduling problem under high-dimensional coupling constraints,the large-scale hydropwer scheduling problem under highly nonconvex nonlinear characteristic curves,and the scheduling problem with sensitive hydraulic connection and the hydro unit commitment problem in the complex irregular vibration zone,are taken as the main research content and solved from the perspective of processing complex constraint and solution.The main results are as follows:1.Spatiotemporal coupling constraints connect the state variables of each reservoir at each time period as a whole,making large-scale hydropower scheduling problems a serious" curse of dimensionality" phenomenon.To solve this problem,the penalty function method is first used to transform the original constrained optimization problem into an unconstrained optimization problem that uses the water level of each hydropower station at each time period as the variables.A progressive optimal algorithm is then used to decouple the original high-dimensional multistage problem into several low-dimensional two-stage sub-problems in the time direction.The two-stage sub-problem is an unconstrained optimization problem with the water level as the optimization variable.An improved discrete gradient descent method is then introduced to solve this sub-problem.Finally,the results for application in the Lancang River Basin in Southwest China show the efficiency of the method.2.The nonconvex nonlinear characteristic curve of the giant hydropower station in Southwest China is prominent,which increases the difficulty of solving large-scale problems.First,constraint aggregation technology is used to aggregate the reservoir characteristic curve into a single three-dimensional surface constraint of the power generation function.Afterward,the surface is meshed using the rectangular meshing technology,and the approximate surface is modeled by the SOS2 constraint modeling method.Finally,the binary branch scheme is used to reconstruct the SOS2 constraints.The application of the deterministic optimization model and the two-stage stochastic optimization model in the Lancang River Basin in Southwest China demonstrates the efficiency of the method.3.Backwater is a sensitive hydraulic connection widely existing in the hydropower systems in Southwest China.To model the backwater,the nonlinear constraints of the hydropower station are aggregated into the four-dimensional hypersurface constraint(FDHC)of the equivalent hydro production function under backwater.A FDHC modeling method based on the SOS2 constraint is proposed.The algorithm was verified in a cascade hydropower system affected by backwater in Southwest China.The results proved the effectiveness and efficiency of the algorithm.Comparing the results of the model without and with backwater shows the necessity of considering the effect of backwater.4.Irregular vibration zone(VZ)widely exists in giant hydro units in the Southwest China,which seriously affects the safe and economic operation of hydropower stations and power grids,and becomes a technical bottleneck restricting the safe and economic operation of hydropower in Southwest China,The general mathematical expressions of VZ constraints,VZ error constraints,and VZ crossing constraints are first proposed.Based on the general mathematical expression,an automatic modeling method of irregular VZ constraint based on optimal convex partition and convex analysis theory,an automatic correction method of vibration area based on Minkowski sum method,and a graph theory-based automatic modeling method of VZ crossing constraints,are successively proposed.The models are verified in the peak shaving model of giant reservoirs with irregular VZs in Southwest China.The results show the constraints related to the VZs are adequately considered,and the peak shaving capacity of hydropower is fully utilized.The above modeling methods are all realized automatically,without manual processing,and are suitable for general problems such as peak shaving,frequency modulation,and power market transactions,and have wide adaptability and versatility.