ИСТИНА

Markets of energy resources play an important role in economies of many countries. Every such market includes its own transmission network system. We consider the welfare optimization problem with account of the production costs, consumers’ utilities and the costs of transmission lines expansion. A formal model for transmission system’s optimization generalizes two well-known optimization problems. The first one is the transport problem. The second related problem is the social welfare optimization for a market with several goods under perfect competition. The optimal solution of our problem determines the maximal total welfare value that can further be reallocated in order to obtain any Pareto-optimal outcome. The difficulty of the problem is that an expansion of any line requires valuable fixed costs. If the optimal set of expanded lines was known, the problem would be convex. However, the efficient search of this set requires special methods. The problem in general is NP-hard since the transport problem with non-convex transmission costs is NP-hard. For a market with a tree-type network we propose the method of S-D balance transfer to the root of the tree. The method proceeds from the known Welfare Theorem and provides a precise solution of the problem without fixed costs. In general the method permits to obtain an approximate solution and estimate the welfare loss. We also determine sufficient conditions for the solution to be precise.