A linear programming energy and environment model for space heating

The linear programming (LP) model of space heating covers the whole building stock and the main heat production methods that can be used in meeting its heating energy demand. The model documented in this report is a mathematical representation of resource allocation alternatives in this sector of the national energy economy. It is developed for the investigation of feasible and optimal resource allocation structures under varying assumptions. These assumptions define availabilities of primary resources, process alternatives, technological development trends, production capacities, environmental factors, construction norms, consumption patterns and objectives applied in optimisation. Fuels, electricity and solar insulation are the most important energy resources in space heating. For all building types several heat production alternatives are available. These alternatives differ from each other with respect to raw energy or heat production technology. The flows of resources, heat, emissions etc. form a network in which an optimal flow structure is to be determined according to the objectives defined. The model documented here is a static one period model. It can be extended to a dynamic LP model or to a model which is regionally divided. The model is developed as a part of a national energy model research project. The objective of the project is to develop independent models of the most important sectors of Finnish energy economy. These models can be integrated to form a national energy model. The approach for LP model construction applied here can be summarised as follows: Linear programming is a mathematical theory of resource allocation. To construct an LP model of space heating amounts to a though study of the real resource allocation alternatives in the heat production-consumption system. The results are documented in the form of the constraint matrix of the mathematical problem. Standard forms are developed for the definition of constraints, variables and parameters.