Quantification of Additional Reinforcement Cost Driven by Voltage Constraint Under Three-Phase Imbalance

Three-phase imbalance causes uneven voltage drops across LV transformers and main feeders. With continuous load growth, the lowest phase voltage at the feeder end determines the voltage spare room, which is lower than if the same power were transmitted through balanced three phases. This imbalance causes additional reinforcement cost (ARC) beyond the balanced case. This paper proposes novel ARC models for a typical LV circuit based on primary-side voltage and current measurements. All models except the accurate model not only enable efficient utility-scale ARC calculations with sufficient accuracy but also remove the need for phasor measurements. The ARC models calculate voltage-driven reinforcement costs for the imbalanced case and the benchmark, i.e., the balanced case, where the ARC is the difference between the above values. The models include: an accurate ARC model considering imbalance in both magnitudes and phase angles; a semi-simplified ARC model assuming balanced phase angles; a fully simplified model assuming a purely resistive LV circuit and a unity power factor; and linearized ARC models considering the imbalance degree for two special cases. Test case proves that: the ARC is a monotonically increasing, convex (concave) but close-to-linear function of current (voltage) imbalance; voltage imbalance has a greater impact on ARCs than current imbalance; a higher degree of current imbalance and/or a deteriorating power factor reduce the accuracy of the fully simplified model; and the accuracy of the semi-simplified model is higher in the case of voltage angle imbalance than in the case of current angle imbalance.