Planning models for optimal routing of radial distribution systems

<span>This paper presents three planning models for optimal routing of radial distribution systems. In the first two models, the cost function includes capital cost of lines, energy loss cost, and bays cost. The constraints equations include power balance equations, voltage drop equations, radiality equations, logic equations, thermal limit equations, and bus voltage limit equations. The first model considers the energy loss equation in its quadratic form while the second model approximates the energy loss equation of each cable size by a simple linear segment considering the economic loading of each cable size. In the third model, two sub-models are used where the first one gets the optimal radial network configuration regardless of the cable sizes and voltage constraints. In the second sub-model the best cable size on each selected line of the first model is determined to minimize the system costs while considering the bus voltage limit constraint and thermal limit constraint. Verification of the proposed planning models has been made using a real 11 kV 34-bus distribution network with 68 initial lines.</span>