Flexible Continuous-Time Modeling for Multi-Objective Day-Ahead Scheduling of CHP Units

Increasing applications of CHP units have turned the problem of finding the best optimization model into a significant subject for scholars. In this respect, this paper is aimed at driving a novel formulation to the multi-objective day-ahead scheduling of CHP units using Bernstein polynomials, which more optimally schedules power and heat generations as well as ramping trajectories. This procedure includes yielding an affine function that closely approximates real-time net-load and generation trajectories, which is demonstrated to have a superior performance to the conventional hourly day-ahead scheduling of CHP units based on discrete-time approximation. The problem of how to handle various objective functions by function space method is also addressed. The simulations conducted on the sample test systems, which consist of CHP systems, thermal and heat-only units, as well as thermal and electrical loads, show that the suggested multi-objective model can perfectly cover the total heat and electrical loads in terms of economic and environmental criteria. More importantly, the results indicate that the accuracy of the proposed approach renders cost saving of 1.67% and emission saving of 1.46% in comparison with the conventional hourly-based model, apart from leading to fewer ramping scarcities in real-time operations.