Scenario based robust control design for uninterruptible power supplies

Abstract

The paper presents the designing of a robust control scheme for uninterruptible power supplies (UPS) by implementing scenario based approach which is a probabilistic solution framework to synthesize and analyze the problems that can be expressed in the form of minimization of a linear objective subject to convex constraints parameterized by uncertainty terms. The scenario based problem being a standard convex optimization problem possesses the solution which is approximately feasible for the infinite set of constraints and is obtained by appropriate sampling of uncertain constraints. The load variation of UPS affects the output voltage and hence is considered as a linear uncertain parameter with a known range in the dynamic model of UPS. An LPV H-infinity optimization problem is formulated in the presence of load variations maintaining the output voltage to the desired value. To design the control problem guaranteeing an a-priori particular probabilistic robustness we use the scenario based approach by randomly selecting the finite number of uncertain scenarios for the load variations instead of using conventional ploytopic approach which covers and comments on the entire uncertainty set for UPS and the solution of scenario problem is computed efficiently by solving the optimization problem using linear matrix inequalities (LMIs). Numerical simulations and comparisons with LPV H-infinity and with linear PID control design shows the proposed scheme makes the system more robust towards uncertainties as well as exogenous disturbances to make it stable and improving its THD and transient performance.