The Line P-Q Curve for Steady-State Voltage Stability Analysis

Generally, resistances and susceptance of transmission lines are neglected in determining voltage stability limit. Differently, this paper includes such parameters to form the P-Q curve analyzed as a rotated parabola. In the region inside the line P-Q curve, a power system can operate normally, but in the outside the system operation is impossible. The line voltage collapse coefficient is determined by using the concept of the line P-Q curve. This coefficient can be used to find weak lines in the power system. It relates to the minimal distance of the P-Q boundary curve, the probability of safe load transmission and the probability of positive bus influence on load transmission. The minimal distance and the probability of safe load transmission can be determined by equations in this paper. While the probability of positive bus influence on load transmission is given from the exact post-contingency analysis with a P-V curve. The lower the values of line voltage collapse coefficient, the weaker the transmission line. The threshold of line voltage collapse is shown in this paper. The proposed method is tested on the modified IEEE 14-bus test system. The result shows that some transmission lines would be monitored carefully to prevent voltage collapse. In practice, this method can detect the weak lines. We can solve the voltage collapse problem before it occurs.