ИСТИНА

An energy market typically includes its own transmission system. We consider a problem of its optimization and aim to maximize the social welfare with account of production costs, consumers’ utilities and costs of transmission capacities increments. The problem turns out to be NP-hard under positive fixed costs of transmission lines expansion. For a market with a tree-type network we propose a method of the supply-demand balances transfer to the root node. The method proceeds from the known Welfare Theorem and provides a solution of the auxiliary problem of convex optimization with zero fixed costs of the lines expansion. Complexity of the method is quadratic with respect to the number of nodes. We modify the method in order to obtain an approximate solution of the original problem. For exact solution, we propose a method based on the concept of the welfare function supermodularity with respect to the set of expanded lines. For chain-type networks we confirm efficiency of the method by results of computational experiments. The problem of transmission system optimal development till a given planning horizon is also discussed. We provide the formal setting and reduce finding of the optimal plan to the finite set of convex auxiliary problems.