Mathematical Model and Formation Mechanism of Total Supply Capability Curve for Distribution Networks

The complete power supply capacity of a distribution network shows a curve (TSC curve). The value of a curve point is the sum of the load at a strict security boundary point, and the values of most points decrease compared to the total supply capability (TSC). In this paper, the formation mechanism of the TSC curve was revealed based on its mathematical model. Firstly, the mathematical model of the TSC curve was established for the first time. Secondly, an intersection mechanism was discovered based on the mathematical model. The intersection variables between some equation constraints caused the redundancy of the sum of equation constraints in the formula. The decrease of total load at the boundary points, that is, the decline of TSC curve, was caused by the increase in redundancy variables. Thirdly, the intersection mechanism formula was derived to calculate the value of the decline. Then, the physical meaning of the intersection mechanism was obtained: the minimum of redundancy corresponded to TSC, which was the optimal backup solution; the difference between redundancy variables and the minimum of redundancy corresponded to the waste of the ordinary backup solution compared with the optimal backup solution. Finally, the intersection mechanism was verified by typical connection modes and a distribution network case, comparing with the backup/distribution mechanism in existing literatures. The backup/distribution mechanism is from N-1 transfer process, while the intersection mechanism is from the mathematical model, which is more concise. © 2021 Chin. Soc. for Elec. Eng.