A Power Flow Method Using a New Bus Type for Computing Steady-State Voltage Stability Margins

In steady-state voltage stability analysis, it is well-known that as the load is increased toward the maximum loading condition, the conventional Newton-Raphson power flow Jacobian matrix becomes increasingly ill-conditioned. As a result, the power flow fails to converge before reaching the maximum loading condition. To circumvent this singularity problem, continuation power flow methods have been developed. In these methods, the size of the Jacobian matrix is increased by one, and the Jacobian matrix becomes non-singular with a suitable choice of the continuation parameter. In this paper, we propose a new method to directly eliminate the singularity by reformulating the power flow problem. The central idea is to introduce an AQ bus in which the bus angle and the reactive power consumption of a load bus are specified. For steady-state voltage stability analysis, the voltage angle at the load bus can be varied to control power transfer to the load, rather than specifying the load power itself. For an AQ bus, the power flow formulation consists of only the reactive power equation, thus reducing the size of the Jacobian matrix by one. This reduced Jacobian matrix is nonsingular at the critical voltage point. We illustrate the method and its application to steady-state voltage stability using two example systems.