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This paper derives a set of sufficient conditions guaranteeing that the load-flow problem in unbalanced three-phase distribution networks with wye and delta constant-power, constant-current, and constant-impedance loads (ZIP loads) has a unique solution over a region that can be explicitly calculated from the network parameters. It is also proved that the well-known Z-Bus iterative method is a contraction...
For a single-phase distribution network with constant-power, constant-current, and constant-impedance loads (ZIP loads), sufficient conditions are presented that explicitly define a region where a unique load-flow solution exists. The Z-Bus method is shown to be a contraction mapping iteration, which upon initialization within this region, is guaranteed to converge to the unique load-flow solution...
This paper is concerned with the Z-Bus method to solve the load-flow problem in three-phase distribution networks with wye and delta constant-power, constant-current, and constant-impedance loads (ZIP loads). The Z-Bus method is viewed as a fixed-point iteration. By leveraging the contraction mapping theorem, a set of sufficient conditions is then presented that guarantees a) the existence of a unique...
Voltage regulation in distribution networks featuring high penetration of distributed photovoltaic (PV) generation is particularly challenging due to the stochastic nature of solar energy. To ensure that voltage levels remain within safety margins, this paper introduces a real and reactive power optimization model that penalizes the conditional value-at-risk of the voltage deviation from its nominal...
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