On the impact of voltage unbalance on distribution locational marginal prices

Voltage unbalance (VU) is becoming a critical operational challenge in modern distribution networks due to the increasing penetration of single-phase loads and distributed energy resources. VU affects power quality, accelerates asset degradation, and increases system losses, making its efficient management essential. 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 introduces a ‘soft limit’ framework that embeds VU penalties into a three-phase optimal power flow formulation to reflect the economic impact of asset lifetime reduction under unbalanced voltages. The approach yields unbalance-aware Distribution Locational Marginal Prices (DLMPs), providing dynamic price signals tied directly to power quality. A new analytical decomposition of DLMPs is developed to isolate energy, loss, congestion, and unbalance components, enabling transparent interpretation of their drivers. 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. • A three-phase welfare model using cost-based voltage unbalance penalties is proposed. • DLMP expressions derived with separate energy, loss, and unbalance terms. • Voltage unbalance penalties embedded in DLMPs to yield clear economic signals.