Voltage Stability Preserving Invariants for Smart Grids

Voltage stability analysis is essential in any power system. This paper addresses the voltage stability in a typical smart grid type system with multiple independent entities. A typical smart grid operation involves various loading excursions (changes in power, both generated and consumed) undertaken by all these independent entities. For a smooth functioning of any generic smart grid type system, correct behavior of all these independent entities must be preserved when one or more of these entities are subjected to various loading levels. Correct behavior of all the entities (sub-systems) will ensure correct behavior of the overall system (smart grid). Invariants, if forced to be true, ensure correct behavior on a subsystem level and thus preserve the overall system correctness. An invariant is a logical predicate on a system state that should not change its truth value if satisfied by system execution [1]. This paper derives an invariant that preserves voltage stability. This invariant is based on an online indicator which is derived from fundamental Kirchhoff's laws and will predict the proximity of voltage collapse at one or more entities in a smart grid. The efficiency of the invariant in predicting voltage collapse has been verified with simulations performed on a typical seven node smart grid system. Thus an online monitoring of the system parameters gives an indication of the system voltage stability. The voltage stability invariant works for both static and dynamic states. This method is also a fast and powerful tool to predict the voltage stability margin of a generic smart grid system by a simple monitoring of the system parameters.