  In this paper, we investigate the problem of minimizing the long-term total
cost (i.e., the sum of energy cost and thermal discomfort cost) associated with
a Heating, Ventilation, and Air Conditioning (HVAC) system of a multizone
commercial building under smart grid environment. To be specific, we first
formulate a stochastic program to minimize the time average expected total cost
with the consideration of uncertainties in electricity price, outdoor
temperature, the most comfortable temperature level, and external thermal
disturbance. Due to the existence of temporally and spatially coupled
constraints as well as unknown information about the future system parameters,
it is very challenging to solve the formulated problem. To this end, we propose
a realtime HVAC control algorithm based on the framework of Lyapunov
optimization techniques without the need to predict any system parameters and
know their stochastic information. The key idea of the proposed algorithm is to
construct and stabilize virtual queues associated with indoor temperatures of
all zones. Moreover, we provide a distributed implementation of the proposed
realtime algorithm with the aim of protecting user privacy and enhancing
algorithmic scalability. Extensive simulation results based on real-world
traces show that the proposed algorithm could reduce energy cost effectively
with small sacrifice in thermal comfort.
