Mathematical model and mechanism of TSC curve for distribution networks

Abstract The total supply capability (TSC) is an important index of a distribution network and the network’s complete supply capability can be represented by a curve, named TSC curve. This paper proposes the mathematical model of the TSC curve and reveals the mechanism that determines the shape of a TSC curve. Firstly, the concept and mathematical model of the TSC curve are introduced. The operation points in a TSC curve have different power supply capabilities and their power supply capabilities are usually less than TSC. Such ‘capability decline’ exists widely in the distribution network. Secondly, the mathematical mechanism that determines the shape of a curve is discovered. It is found that the ‘intersection variable’ in the model causes the capability decline, and ultimately forms the curve. The intersection variable is a shared variable in equation constraints. It induces redundancy in the summation equation which is obtained by adding all equality constraints together. The value of the redundancy will determine how much the capability declines. Furthermore, the mathematical mechanism formula is derived to calculate the capability decline, and the physical meaning of the mathematical mechanism is revealed: a TSC operation point has the minimum redundancy, which means the distribution network works in the optimal backup state with no capacity waste; while for a non-TSC operation point, the redundancy causes the capacity waste and the wasted capacity is equal to the difference between the actual redundancy and the minimum redundancy. Finally, some wiring mode cases and IEEE_RBTS case are used to verify the proposed model and the mechanism.