Affine arithmetic based methods for voltage and transient stability assessment of power systems with intermittent generation sources

This paper presents novel methods based on Affine Arithmetic (AA) for voltage and transient stability assessment of power systems, considering uncertainties of power injections from intermittent generation sources such as wind and solar. These methods, which are an alternative to the well-known sampling and probabilistic based approaches, are able to improve the computational efficiency as compared to simple Monte Carlo (MC) simulations, with reasonably accuracy. The presented AA-based voltage stability method computes the hull of PV curves associated with the assumed uncertainties, and results are discussed in detail for a 5-bus test system. On the other hand, the proposed AA-based transient stability method solves the set of differential-algebraic equations in affine form, based on a trapezoidal integration approach, that yields the hull of the dynamic response of the system, for a set of assumed contingencies and uncertainties; this approach is demonstrated on a generator-infinite bus test system. In both presented stability studies, MC simulations are used for comparison and validation purposes.