Equilibrium Analysis of Power Systems

Abstract
The flow function of a power system is the vector of node powers expressed in terms of the node angles. The Jacobian is the matrix of partial derivatives of the flow vector with respect to the angle vector. The ratio of the determinant of the Jacobian to the value which it has when the node angles are set to zero is a dimensionless stability margin which lies between one and zero (steady-state in- stability) and is easily computed from a load flow. The margin of torque is the least change in power flows that will cause instability. Maximizing the torque margin or maximizing the stability margin with a load constraint yields the optimum dispatching change to maximize security.