Evaluating shortfalls in mixed-integer programming approaches for the optimal design and dispatch of distributed generation systems

► We model the optimal design and dispatch of a distributed generation system. ► Our model includes performance characteristics often not considered in simpler models. ► A simpler model underestimates the optimal system capacity compared to our model. The distributed generation (DG) of combined heat and power (CHP) for commercial buildings is gaining increased interest, yet real-world installations remain limited. This lack of implementation is due, in part, to the challenging economics associated with volatile utility pricing and potentially high system capital costs. Energy technology application analyses are also faced with insufficient knowledge regarding how to appropriately design (i.e., configure and size) and dispatch (i.e., operate) an integrated CHP system. Existing research efforts to determine a minimum-cost-system design and dispatch do not consider many dynamic performance characteristics of generation and storage technologies. Consequently, we present a mixed-integer nonlinear programming (MINLP) model that prescribes a globally minimum cost system design and dispatch, and that includes off-design hardware performance characteristics for CHP and energy storage that are simplified or not considered in other models. Specifically, we model the maximum turn-down, start up, ramping, and part-load efficiency of power generation technologies, and the time-varying temperature of thermal storage technologies. The consideration of these characteristics can be important in applications for which system capacity, building demand, and/or utility guidelines dictate that the dispatch schedule of the devices varies over time. We demonstrate the impact of neglecting system dynamics by comparing the solution prescribed by a simpler, linear model with that of our MINLP for a case study consisting of a large hotel, located in southern Wisconsin, retrofitted with solid-oxide fuel cells (SOFCs) and a hot water storage tank. The simpler model overestimates the SOFC operational costs and, consequently, underestimates the optimal SOFC capacity by 15%.