  Heating, ventilation, and air-conditioning (HVAC) systems are ideal
demand-side flexible resources to provide regulation services. However, finding
the best hourly regulation capacity offers for HVAC systems in a power market
ahead of time is challenging because they are affected by non-Gaussian
uncertainties from regulation signals. Moreover, since HVAC systems need to
frequently regulate their power according to regulation signals, numerous
thermodynamic constraints are introduced, leading to a huge computational
burden. This paper proposes a tractable chance-constrained model to address
these challenges. It first develops a temporal compression approach, in which
the extreme indoor temperatures in the operating hour are estimated and
restricted in the comfortable range so that the numerous thermodynamic
constraints can be compressed into only a few ones. Then, a novel
convexification method is proposed to handle the non-Gaussian uncertainties.
This method leverages the Gaussian mixture model to reformulate the chance
constraints with non-Gaussian uncertainties on the left-hand side into
deterministic non-convex forms. We further prove that these non-convex forms
can be approximately convexified by second-order cone constraints with marginal
optimality loss. Therefore, the proposed model can be efficiently solved with
guaranteed optimality. Numerical experiments are conducted to validate the
superiority of the proposed method.
