A Contribution to the Conception of Madagascar’s Interprovincial Network Topology Using Graph Theory and Power Flow

The purpose of this paper is to propose Madagascar Interprovincial Network using Graph Theory with Power Flow. This is accomplished by simulating the electrical network's topology using algorithms programmed with the Python language. The initial phase of the proposed algorithms consists in establishing connections between 17 source nodes and 94 load nodes, using the shortest path and maximizing the number of load nodes. The next phase consists in removing triangular links deemed superfluous. The third phase involves giving priority to load nodes located close to an electrical source node. The final phase involves removing any remaining superfluous links and applying the (n-k) rule. After the calculations, eight topologies of the Madagascar Interprovincial Network were established. Topology number 8 is the optimal one, comprising 126 links with optimal total distances of 7324 km. Based on this last topology, we carried out simulations of the transit and flow of energy in the static regime across the different busbars of the major mining projects and the different provinces of Madagascar by the PowerFactory software using the Newton-Raphson method. In the transmission line, we used the THTB 220 kV voltage. The simulation revealed, firstly, the location of reactive energy compensation devices, secondly, the removal and installation of new links, and thirdly, the placing on hold of 120 MW of electrical power out of the 300 MW of the slack bus Sahofika hydroelectric plant. For 2030 - 2040, with hydroelectric power plants generating a total of 1,454 MW and loads with a total capacity of 1,344.5 MW, the simulation results showed voltage drop levels with a ∆U value of ± 5% in all busbars and losses of 4.5% in relation to total production. In perspective, further studies in dynamic regime, interactions between emerging technologies and the power system across all voltage levels are to be carried out on the development of the Madagascar Interprovincial Network.