Voltage control in power distribution networks has been greatly challenged bythe increasing penetration of volatile and intermittent devices. These devicescan also provide limited reactive power resources that can be used to regulatethe network-wide voltage. A decentralized voltage control strategy can bedesigned by minimizing a quadratic voltage mismatch error objective usinggradient-projection (GP) updates. Coupled with the power network flow, thelocal voltage can provide the instantaneous gradient information. This paperaims to analyze the performance of this decentralized GP-based voltage controldesign under two dynamic scenarios: i) the nodes perform the decentralizedupdate in an asynchronous fashion, and ii) the network operating condition istime-varying. For the asynchronous voltage control, we improve the existingconvergence condition by recognizing that the voltage based gradient is alwaysup-to-date. By modeling the network dynamics using an autoregressive processand considering time-varying resource constraints, we provide an error bound intracking the instantaneous optimal solution to the quadratic error objective.This result can be extended to more general \textit{constrained dynamicoptimization} problems with smooth strongly convex objective functions understochastic processes that have bounded iterative changes. Extensive numericaltests have been performed to demonstrate and validate our analytical resultsfor realistic power networks.
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