Mathematical Model And Mechanism Of Total Supply Capability Curve For Distribution Networks

Total Supply Capability(TSC)is an important indicator to measure the planning and construction of the distribution network.TSC simply describes the limit load capacity under a few specific load conditions,while the total supply capacity curve(TSC curve)can completely describe the load capacity under the safety limitation of the distribution network.In consideration that the existing research has not yet established a mathematical model of the TSC curve,this thesis establishes the mathematical model of the TSC curve for the first time,and reveals the formation mechanism of the TSC curve mathematically.First,the mathematical model of the TSC curve is proposed.The model of TSC curve model is composed of multiple sub-models,and each sub-model is mathematically a set of multiple linear equations with several equations and inequalities.The strict boundary points of the distribution network and the total load value of each point are obtained by solving the model.Based on the TSC curve model,a sampling algorithm for drawing TSC curve is proposed.Second,based on the mathematical model,the intersection mechanism that can explain the shape of the TSC curve is found: the intersection variables between the equality constraints causes the redundancy of the equation-constraint summation,and the increase of the redundancy leads to the decrease of the total load of boundary points,that is,most of the curve points will drop relative to TSC.The intersection mechanism formula is derived to calculate the capability decline of the total load relative to the TSC.And the physical meaning of the intersection mechanism is that the minimum redundancy corresponds to TSC,which is the optimal backup plan,meanwhile the difference between the redundancy and the minimum redundancy is the capacity waste of the backup plan relative to the optimal backup plan.In this thesis,the intersection mechanism is compared with the backup/distribution mechanism,and the relationship between them is analyzed.The backup/distribution mechanism is explained from the perspective of network structure and the transfer process after N-1,but the intersection mechanism is explained from the perspective of mathematical model.Third,the existing TSC curve research mostly ignores the the influence of substation main transformers.This thesis reveals the law and mechanism of the influence of main transformers on the TSC curve.The laws found are: when the capacity is less than the action capacity of the main transformers,the capacity constraints of the main transformers begin to take effect.At this time,as the main transformer capacity decreases,the TSC curve moves downward as a whole,or becomes steeper,or moves downward and becomes steeper at the same time.To discover the mechanism,the security boundaries are divided into main transformer boundaries,feeder boundaries and mixed boundaries according to the functioning constraints.The feeder boundary is not affected by the main transformer.Reducing the capacity of the main transformer will cause the boundary points of the main transformer boundaries and the mixed boundaries to decrease,which will cause the TSC curve to decrease in varying degrees.Finally,the correctness of the above-mentioned theoretical work is verified by a variety of cases of typical connection modes and also a comprehensive case of the distribution network.The work in this thesis lays a mathematical foundation for the study of TSC curves and helps people to better understand the shape characteristics and formation mechanism of TSC curves.