Calculating participation factors in the maximum loadability

This work presents a methodology to analyze the participation of the load buses in the maximum loadability. Firstly, the determination of the maximum loadability for which an operational solution exists is formulated as an optimisation problem. The solution of this problem provides the largest value of a load parameter related to the demand increase and is obtained through a nonlinear version of the Interior Point Method. Then, the maximum demand is divided into a number of intervals and the Continuation method is applied to yield a sequence of optimal power flow (OFF) solutions to minimize the active power generation. Simultaneously, the sensitivities of the load parameter with respect to the load bus power injections are evaluated for each OFF solution. The integration of Lagrange multipliers and sensitivities obtained in the OFF solutions provides nodal factors, which represent the participation of the load bus in both active power generation and critical loadability.