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This study presents a new method for tracing voltage power curves in unbalanced radial distribution power systems. The proposed method starts with the base case loading conditions and leading to the maximum loading point (MLP) whereas no ill-conditioning problems were detected. The calculation is performed by first-order polynomial secant predictor and the solution is corrected using the backward/forward radial power-flow method. Adaptive stepwise control is implemented to improve the overall solution process and reduce the number of the calculated points along the traced curve. The results calculated using the developed method are for both a 33-bus radial feeder and the unbalanced IEEE 13-node and IEEE123-node feeders. The results show that the developed method accurately traces the voltage power curves up to MLP. Comprehensive analysis on unbalanced scenarios shows that load unbalance greatly affects the stability limit of the study system.