Risk of Phase Incoherence in Wide Area Control of Synchronous Power Networks With Time-Delayed and Corrupted Measurements

We develop a framework to quantify systemic risk measures in a class of wide-area-control (WAC) laws in power networks in the presence of noisy and time-delayed sensory data. A closed-form calculation of the risk of phase incoherence in interconnected power networks is presented, and the effect of network parameters, information flow in WAC architecture, statistics of noise, and time delays are characterized. We show that in the presence of time-delay and noise, a fundamental tradeoff between the best achievable performance (via tuning feedback gains) and value-at-risk emerges. The significance of our results is that they provide a guideline for developing algorithmic design tools to enhance the coherency and robustness of closed-loop power networks simultaneously. Finally, we validate our theoretical findings through extensive simulation examples.