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The paper deals with the problem of comprehensive analysis of heat supply reliability for consumers. It implies a quantitative assessment of the impact of all stages of heat energy production and distribution on heat supply reliability for each consumer of the heat supply system. A short review of existing methods for the analysis of fuel and heat supply reliability is presented that substantiates the key approaches to solving the problem of comprehensive analysis of heat supply reliability. A methodological approach is suggested, in which mathematical models and methods for nodal evaluation of heat supply reliability for consumers are developed and the studies on the impact of different elements of fuel and heat supply systems on its level are described. Mathematical modeling is based on the Markov random processes, models of flow distribution in a heat network, deterministic dependences of thermal processes of heat energy consumption and some other models.

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The problem of determining the effective (optimal) heat supply radius is considered. Heat supply radius is transportation distance of heat energy in the district heating systems (DHS), under which the highest indices of economic efficiency of district heating to consumers are respected. To solve this difficult and multifactorial problem, a bi-level approach has been proposed. This approach allows finding the optimal frameworks of territorial areas of district heating while fulfilling the necessary requirements for thermal-hydraulic modes in heat networks and for reliability of heating to consumers. Methodology for solving the formulated problem is based on bi-level programming methods, models of Theory of hydraulic circuits, nonlinear optimization methods, nodal reliability indices (availability factor, failure-free operation probability), Markov random processes models and other methods and models. A case study has been conducted using the developed methodological apparatus for the actual DHS scheme of the Irkutsk city (Russia, Siberia).