Open AccessThis article succeeds the former A. P. K nko’ and A. I. Kuzmina’ ubl t on titled "A mathematical model of urban distribution electro-network considering its future development" (electronic scientific and technical magazine "Science and education" No. 5, 2014).
The article offers a model of urban power distribution network as a set of transformer and distribution substations and cable lines. All elements of the network and new consumers are determined owing to vectors of parameters consistent with them.
A problem of the urban power distribution network design, taking into account a prospective development of the city, is presented as a problem of discrete programming. It is in deciding on the optimal option to connect new consumers to the power supply network, on the number and sites to build new substations, and on the option to include them in the power supply network.
Two methods, namely a reduction method for a set the nested tasks of global minimization and a decomposition method are offered to solve the problem.
In reduction method the problem of prospective development of power supply network breaks into three subtasks of smaller dimension: a subtask to define the number and sites of new transformer and distribution substations, a subtask to define the option to connect new consumers to the power supply network, and a subtask to include new substations in the power supply network. The vector of the varied parameters is broken into three subvectors consistent with the subtasks. Each subtask is solved using an area of admissible vector values of the varied parameters at the fixed components of the subvectors obtained when solving the higher subtasks.
In decomposition method the task is presented as a set of three, similar to reduction method, reductions of subtasks and a problem of coordination. The problem of coordination specifies a sequence of the subtasks solution, defines the moment of calculation termination. Coordination is realized by introducing the vectors of parameters of limiting and stimulating coordination into the problem. Vector components of limiting coordination mean the minimum numbers of substations to be built. Vector components of stimulating coordination define "usefulness" of new substations to be built on possible sites. There are two offered options to determine parameters of stimulating coordination.
The offered methods of reduction and decomposition generally generate a large number of the optimization algorithms. Subsequent publications are expected to consider these algorithms and a software to implement them.