This paper presents a control scheme in order to minimize energy cost with annually energy positive constraint as following daily demand fluctuations. Generally, the more energy positive by biomass fuelled combined heat and power (CHP), the more expensive in energy cost. The control scheme consists of Lagrangian relaxation based two optimization functions: (A) the annual scheduling function which does forecast correction and rescheduling monthly, and (B) the daily scheduling function which does the gap evaluation between the forecasted and the actual load every thirty minutes and does forecast correction and rescheduling if needed. By the two functions rescheduling, the control scheme create robust operation schedule. The proposed scheme is verified by numerical simulations for HIKARI building in Lyon, France. The simulation shows that the scheme can achieve cost minimization and Positive Energy Buildings (PEB) by rescheduling under conditions of demand fluctuations.