Data-Driven Successive Linearization for Optimal Voltage Control

Abstract

Power distribution systems are increasingly exposed to large voltage fluctuations driven by intermittent solar photovoltaic generation and rapidly varying loads (e.g., electric vehicles and storage). To address this challenge, a number of advanced controllers have been proposed for voltage regulation. However, these controllers typically rely on fixed linear approximations of voltage dynamics. As a result, the solutions may become infeasible when applied to the actual voltage behavior governed by nonlinear power flow equations, particularly under heavy power injection from distributed energy resources. This paper proposes a data-driven successive linearization approach for voltage control under nonlinear power flow constraints. By leveraging the fact that the deviation between the nonlinear power flow solution and its linearization is bounded by the distance from the operating point, we perform data-driven linearization around the most recent operating point. Convergence of the proposed method to a neighborhood of KKT points is established by exploiting the convexity of the objective function and the structural properties of the nonlinear constraints. Case studies show that the proposed approach achieves fast convergence and adapts quickly to changes in net load.

Figures (5)

• Figure 1: The voltage and reactive power at 9 nodes under four controllers in the time-invariant load setting. Convex relaxation obtains a solution that is feasible for the original nonconvex problem \ref{['eq:Optimization']}, indicating that it is globally optimal for the original problem. Data-driven successive linearization converges within a few iterations to a solution that is very close to this global optimum. Both feedback optimization and linear control converge more slowly, which also retains larger steady-state voltage deviation.
• Figure 2: Cost trajectories corresponding to Fig. \ref{['fig:static_traj_4methods']}. Convex relaxation provides a global benchmark. Feedback optimization and linear control retain high costs after convergence. The proposed data-driven successive linearization rapidly drives the cost to the convex relaxation level within a few iterations, indicating fast convergence.
• Figure 3: Comparison of log-normalized mean cost of the last 5 steps in the time-invariant load setting over 100 trials. Data-driven successive linearization consistently achieves the lowest cost, with values tightly concentrated near zero, indicating both superior performance and small deviation across trials.
• Figure 4: Trajectories of voltage, reactive power, and cost at 9 nodes under three controllers in the time-varying load setting. Data-driven successive linearization rapidly compensates for each load change, restoring voltages close to nominal, and yielding the lowest post-disturbance cost. Feedback optimization exhibits slower recovery and a larger cost after disturbances. Linear control produces the largest voltage deviations.
• Figure 5: Comparison of log-normalized mean costs in the time-varying load setting over 100 trials. Data-driven successive linearization attains the lowest cost, with values tightly concentrated near zero, indicating both low cost and small deviation across test cases. By contrast, feedback optimization exhibits a noticeably higher cost. Linear control performs worst with a substantially larger median and variability.

Theorems & Definitions (12)

• Definition 1: Sufficient excitation
• Definition 2: KKT conditions for \ref{['eq:Optimization']}
• Theorem 1
• Lemma 1
• Lemma 2
• proof
• Lemma 3
• proof
• Lemma 4
• proof