Model-Free Optimal Voltage Control via Continuous-Time Zeroth-Order Methods

Abstract

In power distribution systems, the growing penetration of renewable energy resources brings new challenges to maintaining voltage safety, which is further complicated by the limited model information of distribution systems. To address these challenges, we develop a model-free optimal voltage control algorithm based on projected primal-dual gradient dynamics and continuous-time zeroth-order method (extreme seeking control). This proposed algorithm i) operates purely based on voltage measurements and does not require any other model information, ii) can drive the voltage magnitudes back to the acceptable range, iii) satisfies the power capacity constraints all the time, iv) minimizes the total operating cost, and v) is implemented in a decentralized fashion where the privacy of controllable devices is preserved and plug-and-play operation is enabled. We prove that the proposed algorithm is semi-globally practically asymptotically stable and is structurally robust to measurement noises. Lastly, the performance of the proposed algorithm is further demonstrated via numerical simulations.

Improve Single-Point Zeroth-Order Optimization Using High-Pass and Low-Pass Filters

“…Rationale of ES Control. The rationale behind (6) is that when parameter a is small and ω is large, the ES dynamics (6) using only output feedback behaves approximately like the gradient descent flow ẋ = −∇f (x), which can steer x to a (local) minimum x * ∈ arg min x f (x) under appropriate conditions. Specifically, with a large value of ω, the ES dynamics (6) exhibits a timescale separation property, where the fast time variation is caused by the high-frequency sinusoidal signal sin(ωt), while the slow variation induced by the integrator dominates the evolution of x.…”

“…With a small value of a, we consider the Taylor expansion of the output f (x + a sin(ωt)) around x: f (x + a sin(ωt)) = f (x) + a sin(ωt)∇f (x) + O(a). Then one can compute the average dynamics of (6), which is given by ẋ = − h ave (x) and…”

“…with T = 2π ω . Hence, the average dynamics of the ES system (6) with small a and large ω can be regarded as the gradient descent flow plus a small perturbation term O(a). Besides, the ES control method can be easily extended to the multivariate case [6,15] by using a probing signal vector sin(ωt) = [sin(ω 1 t), • • • , sin(ω d t)] with ω i = ω j for all i = j.…”

“…To this end, zeroth-order (or derivative-free) methods [2] are developed for black-box optimization, which essentially estimate the gradients using perturbed function evaluations. Zeroth-order optimization (ZO) has attracted a great deal of recent attention and has been used for a broad spectrum of applications, such as reinforcement learning [3,4], adversarial training [5], power system control [6,7], online sensor management [8], etc.…”