Stochastic optimization with value function approximation for micro-grid operation

Abstract

Operational planning of a small and isolated energy system having a large wind farm and a battery storage device is studied. Operational planning decisions are to be made in two time-scales: daily unit commitment (UC) and hourly dispatch. For this problem, Markov decision process (MDP) and stochastic programming (SP) are combined to account for both daily and hourly changes of wind uncertainty. Two stage SP is formulated for day-ahead UC decision and dispatch decisions considering a number of scenarios regarding uncertainty with respect to hourly ramping of the wind within a day. Here, the value of the end state of daily unit commitment and battery with respect to the future beyond the day (value function), which is estimated from the MDP formulation, is included in the objective function to ensure that longer term implications of the decisions are considered. In the MDP formulation, daily evolving exogenous information on wind speed is captured, and the value function is approximated with a linear model. The coefficient vector of the linear model is recursively updated with sampled observations estimated from the daily SP model. In connection with this, a general wind model for timescales from seasonal to hourly is developed to enable seamless connection of the decision making across the scales. The results of the proposed integrated method are compared to those of just the two-stage SP model through a case study and real wind data.