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Topological Task of Distributed Generation Placement Using a Pareto optimization

It is suggested to use the topological task (TT) for select the placement of distributed generation (DG). A TT can’t be solved by methods of functional analysis, because it is a problem with variable parameters. The solution of the TT is suggested to represent in the form of the Pareto-optimal area. Nonlinearity of target functions of the TT of DG placement leads to the expansion of the Pareto-optimal solutions in the direction of the global extremums according to certain criteria. It is shown that TT can be described analytically, provided that the conduction cross sections are unchanged in the domain of admissible solutions. In this case, the polygon of the objective functions extremums sufficiently clearly describes the Pareto set. This situation will be observed with considerable resistance of the power electrical system source both at autonomous feeding of consumers from DG, and at work of DG in parallel with the power system. Changing the cross sections of conductors due to the implementation of technical limitations on emergency modes causes the first-order gap in the target functions. This leads to a significant expansion of the Pareto set. At the same time, the growth of the numerical values of individual criteria on the boundary of the Pareto set can be doubled in comparison with the minimum values. This should be taken into account when making a final decision on the placement of the DG.