Convex relaxation of two-stage network-constrained stochastic programming for CHP microgrid optimal scheduling

Different from most studies only incorporating economic aspect into operation scheduling, this paper develops a novel network-constrained framework that can address both economic and secure issues for combined heating and power (CHP) microgrids integrated with wind power considering uncertainties. According to quadratically constrained programs, a two-stage network-constrained stochastic programming (TSNCSP) model is formulated to improve economic benefits and meanwhile capture active/reactive power and off-nominal bus voltage constraints in the full decision variable domain. In the first stage, namely day-ahead, the schedule of transacted electricity with the upstream power grid and the generation cost of heat is determined according to the forecast information. In the second stage, namely real-time, a recourse function of adjustable resources is defined to reduce the expected cost incurred by the perturbation of random wind power outputs. Moreover, the original non-convex problem is innovatively transformed into a semidefinite programming through incorporation of demand response program (DRP), duality, complementary slackness, and relaxation techniques to improve the solving efficiency. Finally, a proposition is presented and proved that provides a sufficient condition for the exactness of the proposed convex relaxation. Numerical simulations on the 33-bus test system verify the effectiveness of the proposed framework in multi-period scenario-based scheduling problems.