Mathematical Mechanism of Total Supply Capability Curve for Distribution Networks

Abstract

The complete supply capacity of the distribution network shows a curve called the TSC curve. The mathematical model of TSC curve is established and the formation mechanism of TSC curve is revealed in this article. Firstly, the concept of TSC and the TSC curve is briefly introduced. In general, a TSC curve is a declining curve; the peak point of the curve is TSC point; other non-TSC curve points are lower than TSC p-oint. Secondly, a mathematical model of TSC curve is established. Thirdly, the intersection mechanism is discovered: it is the common variable constrained by different equations that causes TSC curve to decline, which is called the intersection variable. The intersection variables cause redundancy in the equation-constraint summation, and the value of redundancy determines whether TSC curve declines and the degree of decline. Furthermore, the intersection mechanism formula is derived to calculate the value of the decline, and its physical meaning is analyzed: for a TSC point, the redundancy value reaches the minimum, which means the distribution network is in the optimal backup state with no capacity waste; while for a non- TSC point, the capacity waste appears, with the redundancy value increasing, and the value increased is the capacity waste, which is also equal to the decline of the point compared with TSC point. Finally, the wiring mode and IEEE_RBTS examples are used to demonstrate and verify the intersection mechanism.