Incremental Volt/Var Control for Distribution Networks via Chance-Constrained Optimization

TL;DR

The paper tackles voltage regulation in distribution networks with high inverter based DER penetration by introducing an incremental Volt/Var controller whose gains are designed via a chance-constrained optimization to bound voltage violations within a prescribed probability. A two level architecture computes a single set of gains at a central地点 and broadcasts them to all DERs, enabling fully decentralized real time operation with only occasional coordination and forecast dependent planning. The core methodology combines a linearized power flow model with a successive convex approximation to solve the chance constrained problem, and proves stability and equilibrium existence under reasonable assumptions. Numerical experiments on a 42-node low voltage network and the unbalanced IEEE 123-node system demonstrate improved voltage regulation and reduced reactive power usage, while tolerating forecast uncertainties; results highlight the practical benefits of forecasting informed gains over static Volt/Var rules or no control. The approach offers a scalable, communication-light solution for real world distribution networks facing increasing DER variability, with potential integration with traditional slow regulators and topology adaptations in future work.

Abstract

This paper considers an incremental Volt/Var control scheme for distribution systems with high integration of inverter-interfaced distributed generation (such as photovoltaic systems). The incremental Volt/Var controller is implemented with the objective of minimizing reactive power usage while maintaining voltages within safe limits sufficiently often. To this end, the parameters of the incremental Volt/Var controller are obtained by solving a chance-constrained optimization problem, where constraints are designed to ensure that voltage violations do not occur more often than a pre-specified probability. This approach leads to cost savings in a controlled, predictable way, while still avoiding significant over- or under-voltage issues. The proposed chance-constrained problem is solved using a successive convex approximation method. Once the gains are broadcast to the inverters, no additional communication is required since the controller is implemented locally at the inverters. The proposed method is successfully tested on a low-voltage single-phase 42-nodes network and on the three-phase unbalanced IEEE 123-node test system.

Figures (13)

• Figure 1: (a) Proposed voltage regulation strategy. Based on the forecast ${\hbox{\boldmath $\rho$}}$ and the probability $\epsilon$ to violate voltage limits, the controller gains ${\bf x}$ are computed centrally and then broadcasted to the controllable DERs. (b) Illustrative explanation of the impact of the parameter $\epsilon$ on the total amount of voltage violations. A smaller $\epsilon$ results in a more constrained optimization problem and therefore in fewer voltage violations.
• Figure 2: Comparison between different time scales of the problem, assuming $\tau = 1s$.
• Figure 3: Block diagram of the proposed framework.
• Figure 4: (a) Low-voltage 42-nodes network, (b) aggregated non-controllable active power injections, and active/reactive power consumption, (c) reactive power setpoint update for controller at node 20 around hour 20:00.
• Figure 5: Controller dynamics and voltage magnitudes for two given nodes: node 34 and node 20.

Theorems & Definitions (3)

• Remark 1
• Remark 2
• Proposition 1