On the Impact of Voltage Unbalance on Distribution Locational Marginal Prices (2511.13971v1)

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.