On the Impact of Voltage Unbalance on Distribution Locational Marginal Prices

TL;DR

Voltage unbalance from widespread single‑phase devices degrades power quality and inflates costs in distribution networks. The paper embeds voltage unbalance as penalties within a three‑phase OPF to produce DLMPs and decomposes them into energy, losses, congestion, and unbalance components. It introduces both hard‑limit and soft‑limit formulations and analyzes two benchmark networks to reveal how unbalance signals influence dispatch and prices, including nuanced effects like middle phases incurring higher penalties and proximity to the feeder mitigating unbalance. The framework provides practitioners with asset‑aware signals for planning, DER siting, and market design, and demonstrates that soft limits offer scalable, informative economic incentives for managing power quality.

Abstract

Finding clear economic signals for distribution-network operation and expansion is increasingly important as single-phase loads and distributed energy resources escalate. These devices create phase-to-phase imbalances that manifest as voltage unbalance, a power quality issue that accelerates insulation aging in machines and increases network losses, thereby raising costs for operators and consumers. Traditional grid codes address unbalance via disparate hard limits on various indices thresholds that differ across standards, offer no dynamic economic incentive and undermine optimality. This paper proposes instead to treat voltage unbalance as a `soft limit' by adding penalty terms to grid operation costs within a three-phase optimal power flow to reflect the cost of the decrease in lifetime of assets due to being subject to voltage unbalance. This unified approach yields dynamic economic signals unbalance-aware Distribution Locational Marginal Prices (DLMP) that reflect the cost of power quality deviations. A novel mathematical decomposition of DLMP is developed, isolating the energy, loss, congestion, and unbalance components. Case studies conducted on two benchmark networks demonstrate the effectiveness and practical value of the proposed method. The results indicate that unbalance penalties reshape nodal prices, produce unexpected phase-level effects, and even allow scenarios where added load reduces unbalance and lowers costs, while providing planners and market designers with actionable insights to balance investment, operation, and power quality in modern distribution systems.

Figures (9)

• Figure 1: Single-line diagram of test case 1, 'simple network'.
• Figure 2: Active and reactive loads of 'simple network'.
• Figure 3: Shadow prices of active power of 'simple network' under four scenarios.
• Figure 4: Shadow prices of reactive power of 'simple network' under four scenarios.
• Figure 5: Schematic for the modified European LV network.