Albeit numerous studies discussing manifold issues of combined cooling, heating and power (CCHP) systems, there is still lack of theoretical studies indicating to what extent the energy mismatch and the deviating working conditions affect the CCHP performance, absence of reports systematically summarizing the multiple effects of energy saving units (ESUs), and deficiency of research quantifying the benefits from ESUs to energy savings. The shortage of such studies will confuse some CCHP designers when a CCHP system is designed. Therefore, in this research, theoretical discussions have been undertaken about the energy mismatch issue between CCHP systems and their users as well as the multiple effects of ESUs on CCHP systems. An improved calculational method of energy storage rate (ESR) has been adopted to evaluate the energy savings performance of CCHP systems. Two general heat-to-electricity ratios (R-user for CCHP users and R-CCHP for CCHP systems) have been used to quantify the energy mismatch between CCHP systems and their users. In the regime of priority of providing cooling', the ESR reaches its maximum when R-user is equal to R-CCHP. Otherwise, the ESR tends to decrease rapidly, especially when the electrical demand must be supplemented from the grid. Furthermore, when the CCHP system produces more electricity than required, the payment mode of extra electricity from the CCHP system will significantly affect the ESR. Therefore, it is imperative to reach an international consensus regarding the dispose of extra CCHP products. The theoretical analyses also corroborate the advantages of incorporating an ESU into a CCHP system. The ESU enables the CCHP system components to operate at their optimal working conditions. Meanwhile, the power generation unit and the absorption refrigerator capacities can then be reduced. Moreover, the ESU also promotes the productivity of electricity and ensures an undiminished ESR regardless of what extra electricity payment mode is adopted. Copyright (c) 2016 John Wiley & Sons, Ltd.