Matrix modelling of small-scale trigeneration systems and application to operational optimization

Combined production of electricity, heat and cooling power in trigeneration represents a key option for the development of high-efficiency and cost-effective integrated energy systems. The complexity of the possible plant schemes calls for the adoption of general models handling multiple interconnected components and energy flows of various typologies. This paper presents a comprehensive input–output matrix approach aimed at modelling small-scale trigeneration equipment taking into account the interactions among plant components and external energy networks. Starting from the definitions of specific efficiency matrices for each plant component and from a matrix representation of the relevant interconnections, an overall efficiency matrix representing the whole plant is constructed. This construction is carried out by means of an original procedure, suitable for automatic and symbolic implementation, which, exploiting graph theory concepts, explores the tree formed by the backward paths from outputs to inputs. The proposed formulation maintains the separation among the individual energy vectors, each of which can be associated to its time-dependent price, providing the basic framework for formulating optimization problems concerning management of trigeneration systems within an energy market context. A numerical example referred to the optimal operation of a composite scheme with absorption and electric chillers is illustrated and discussed. The results obtained show the modelling effectiveness of the proposed matrix formulation.