Optimal configuration of a power grid system with a dynamic performance sharing mechanism

Performance sharing is an effective policy for a power grid system to satisfy the power demand of different districts to greatest extent. Through transmission lines, the districts with sufficient power can share the redundant power with the districts with power deficit. The existing research has incorporated the performance sharing mechanism into systems with simple structures such as parallel systems and series-parallel systems. However, little concentration has been spent on more complex structures. This necessitates the need of this paper that models a power distribution with a more complex reliability structure. We assume that the system is composed of generators and nodes. Both the performance of each generator and the demand of each node in the network are assumed to be random variables. This paper first proposes a dynamic performance sharing policy to minimize the unsupplied demand for a given system with fixed capacity and demand. The optimal allocation of generators, which minimizes the expected system unsupplied demand, is then studied. Numerical examples are proposed to illustrate the applications of the proposed procedures.