Simple Model for the Shortest Medium-Voltage Cable to Supply Sustainable Loads

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Abstract
Passive loads in power systems are well-known, but sustainable loads (SL's), due to distributed renewable energy sources and possible reverse active power flow (RAPF) from a low voltage level through a medium-voltage (MV) cable towards a high voltage level, introduce new challenges. In this paper, a simple model for the shortest MV cable required to supply SL's is introduced. The concept of unconstrained and constrained domains to design the shortest cable, at which the limiting constraint for the thermal capacity and the limiting constraint for the voltage drop are equal, is proposed. In this case, the cable can be fully used, that is, using the whole feasible region at the shortest length. A sample 2-node/1-cable network shows that the power-voltage relationship can theoretically be nonlinear within the unconstrained domains, but it can be well linearized within the proposed constrained domains. Another 3-node/2-cable network is developed to show the effects when using different cables types (copper and aluminium) and power factors. It is shown that the developed model can simply be used for estimating the active power domains of new SL's while considering the shortest length of MV cables.

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