A Linear Adaptive Robust Optimization Model for Day-Ahead Scheduling of Microgrid

Abstract

There are different uncertainties in microgrids’ (MG) operation such as output power of renewable energy sources (RESs), electricity price and load demand. Ignoring these existing uncertainties in the optimization problem imposes high cost to the system and the lack of reliability. This paper presents a general linear framework for microgrid optimization problem using robust optimization method. Adaptive robust optimization (ARO) model is a min-max-min problem in which the first level targets to determine the on/off status of dispatchable units, the second one aims find the worst case of uncertain parameters and eventually in third level the operational costs are minimized. This model is converted to a min-max one by using Karush-Kuhn-Tucker (KKT) conditions and then the ensuing model is linearized. A control parameter named budget of uncertainty is considered to determine the level of robustness and being conservative. The more budget of uncertainty we consider, the more robust model we obtain. An optimum point in which the expected cost is minimal and a compromise between the level of robustness and operational cost is reached. A modified IEEE-33 bus system is considered to evaluate the adequacy of proposed linear ARO model. Simulation results prove that the proposed ARO model is appropriately able to deal with the existing uncertainties and results in lower expected cost compared to deterministic model.