New Value Set Approach for Robust Stability of Power Systems with Wind Power Penetration

A new value set approach is developed to examine the robust stability analysis of power systems, such as power systems with wind power penetration. The new approach has several advantages compared with our previous work. It also applies to the D-stability problem considering the damping ratio constraint for power system analysis. The well-known mapping theorem is applied to compute the value sets of ${{\det(}}\bf{I}- \bf{M}(s)\Delta $ ), which gives a sufficient condition for stability evaluation. To reduce the conservativeness of the mapping theorem, the multivariable stability margin $K_{m}$ , a necessary and sufficient condition, is calculated to evaluate the robust stability. It is shown that by inspection of the value sets of ${{\det(}}\bf{I}- \bf{M}(s)\Delta $ ), the impact of the uncertainties becomes transparent. The introduced results are tested on a classical 4-generator 11-bus test power system and a 547-machine 8647-bus model of the actual North China system.