UNIFICATION AND CLASSIFICATION OF ALGEBRAIC TESTS FOR LOSS OF VOLTAGE STABILITY

ABSTRACT

Three distinct types of algebraic bifurcations are shown to occur in both a load flow model and in a transient midterm stability model. Angle bifurcation results in significant angle change and no voltage change at the point of bifurcation. Voltage bifurcation results in significant voltage change and no angle change at the bifurcation point. Voltage and angle bifurcation result in both voltage and angle change at the bifurcation point. Angle bifurcation occurs due to reaching the real power transfer capability across some interface or boundary of the network. Voltage bifurcation is due to inability to transfer needed reactive power to a bus or area across a boundary due to insufficient voltage control and thus reactive supply capability in the region. Voltage and angle bifurcation results when reactive power can' be transferred to a bus or area across a boundary due to insufficient reactive supply and excessive reactive losses (I²X and shunt capacitive reactive withdrawal due to voltage drop) caused by real power transfer. Unique tests for the three types of load flow bifurcation are given. All the load flow voltage instability proximity measures are then classified in terms of which of these three types of load flow bifurcations they test for at the points of collapse. PQ controllability tests are shown to test for voltage, bifurcation and voltage and angle bifurcation. Any proximity test of reactive power versus voltage relationships also tests for voltage bifurcation and voltage and angle bifurcation. Proximity to all three types of load flow bifurcation are measured by either (a) tests of the singularity of the load flow jacobian or (b) proximity measures that test real power transfer or loading effects on voltage. Since equivalent voltage, angle, and voltage and angle bifurcations occur in a transient stability model, the load flow proximity measure tests can be applied on a transient stability model. This paper, thus, classifies and unifies the various proximity measure tests and point of collapse tests for voltage instability on both a load flow and transient stability model.