Improved Voltage Regulation with Optimal Design of Decentralized Volt-VAr Control

TL;DR

This work addresses voltage regulation in DER-rich distribution networks by designing decentralized Volt-VAr Control (VVC) slopes through a data-driven linearized power flow (LPF) model. It introduces a non-convex spectral-radius stability constraint, $\rho(\mathbf{J_qK}) < 1$, to guarantee asymptotic stability while minimizing steady-state voltage deviation via a regularized objective. The approach is validated on a realistic Vermont feeder, showing that LPF-based design is more accurate than LinDistFlow and that spectral-radius constraints yield superior voltage regulation compared to convex relaxations. The findings support deploying non-incremental VVC with optimal slopes and invite further work on incremental schemes, deadbands, and 3-phase extensions for robust grid operation.

Abstract

Integration of distributed energy resources has created a need for autonomous, dynamic voltage regulation. Decentralized Volt-VAr Control (VVC) of grid-connected inverters presents a unique opportunity for voltage management but, if designed poorly, can lead to unstable behavior when in feedback with the grid. We model the grid-VVC closed-loop dynamics with a linearized power flow approach, leveraging historical data, which shows improvement over the commonly used LinDistFlow model. This model is used to design VVC slopes by minimizing steady-state voltage deviation from the nominal value, subject to a non-convex spectral radius stability constraint, which has not been previously implemented within this context. We compare this constraint to existing convex restrictions and demonstrate, through simulations on a realistic feeder, that using the spectral radius results in more effective voltage regulation.

Figures (11)

• Figure 1: As proliferation of DERs increase, voltage profiles on distribution networks change faster and by larger amounts. Note that this is a cartoon for illustrative purposes only, not real data.
• Figure 2: A block diagram showing the interaction between Volt-VAr Control and the grid physics (plant model). Bold lines indicate a vector of measurements at all nodes.
• Figure 3: The IEEE prescribed standard curve with saturation limits and a deadband is shown. We choose parameters such that the curve is a straight line through the reference voltage ($V_\text{2}=V_\text{3}=V_\text{r}$ and $V_\text{L}=V_\text{1},\, V_\text{H}=V_\text{4}$). Note this is a slightly modified version of Figure H.4 from IEEE1547.
• Figure 4: Comparison of stable regions of VVC slope values ($k$) in a 2-node section of a real network using an LPF model where $\mathbf{J_q}$ = [1.5504, 1.5504; 1.5505, 1.6144];. Note that the spectral radius set is convex here, although this is not guaranteed depending on the structure of $\mathbf{J_q}$.
• Figure 5: Illustration of the single-phase section of a real feeder in Vermont on which the VVC design framework is applied and evaluated.