This paper presents the design and optimum scheduling of a solar CCHP (combined cool, heat and power) system which is powered by a Stirling engine in the presence of an AA-CAES (advanced adiabatic compressed air energy storage) system for a residential energy sector. An absorber and a thermal energy storage tank are employed to absorb and store all collected solar radiation for continuous energy supplied when sunlight is insufficient, and nighttime. In this paper, an ASHP (air source heat pump) that is equipped with two inside and outside air fans, an expansion valve, compressor, condenser and an evaporator is installed to cool and heat a benchmark residential building under hot and cold climate conditions, respectively. The AA-CAES system is modeled with injected and produced power constraints, storage, air balance and operation limits. A comprehensive energy and exergy based optimization is developed as a mixed-integer nonlinear program to minimize total energy procurement cost in the presence of ASHP, prime mover and AA-CAES's constraints. It is found that the use of AA-CAES results in 21.79% and 22.36% lower operational costs in the cooling and the heating modes, respectively. (C) 2016 Elsevier Ltd. All rights reserved.