Use of p-q curve with rectangular probability distribution of bus load in voltage stability study

Practically, the idea of P-V and Q-V curve is used to determine the maximal reactive margin at load buses to avoid voltage instability. Sometimes the voltage stability study may be limited to identify the violation of the bus voltage constraints. In this paper the p-q curve for the critical bus voltage magnitude is created. Using this p-q curve the probability of the critical voltage violation is estimated for uniformly distributed active and reactive power at a given load bus. The p-q curve is created on the basis of bus impedance, which can be measured or calculated. To illustrate the usefulness of p-q idea the simple numerical example is presented.