Square Domain Forensic Analysis for Power Systems

Power systems are prone to unforeseen outages which can cause congestion, loop flows and flow-reversals, leading to cascading failures. Theses occurrences may result in blackouts. Several simulations in are required to pin down the cause of the blackout. Simulations work forward in time starting with initial conditions which is tantamount to disregarding the past history. It is necessary to trace the events back in time from given abnormal conditions to determine the cause. Square domain analysis proposed in this paper can do this. To this end, phasor-domain variables are transformed into square-domain (SD) variables which are used to derive SD-coefficients. These mathematically relate system-variables to the source-power. There are different SD-coefficients for lineflows and for the load-voltages. SD-coefficients lend to computation back in time – the process being termed as forensic analysis of power systems. A dynamic equation is derived for frequency-dependent impedances. Lineflows and load-voltages can then be calculated on the entire frequency trajectory from frequency-modified SDcoefficients. The cause of failure or abnormality is traceable with numerical certainty. Illustrative examples are given.