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We investigate the sensitivity of the transient performance of power systemscontrolled by Distributed Power-Imbalance Allocation Control (DPIAC) on theparameters of the control law. We model the disturbances at power loads asGaussian white noises and measure the transient performance of the frequencydeviation and control cost by the H_2 norm. For a power system with acommunication network of the same topology as the power network, analysis showsthat the transient performance of the frequency can be greatly improved byaccelerating the convergence of the frequencies to the nominal value through asinge control gain coefficient. However, the control cost increases linearly asthis control gain coefficient increases. Hence, in the feedback control law,DPIAC, there is a trade-off between the frequency deviation and control costwhich is determined by this control gain coefficient. By increasing anothercontrol gain coefficient, the control cost can be decreased with an acceleratedconsensus of the marginal costs during the transient phase. Furthermore, thebehavior of the state approaches that of a centralized control law when theconsensus of the marginal costs is accelerated.

Transient Performance of Power Systems with Distributed Power-Imbalance Allocation Control