In this study, the peak shaving idea for storing energy during off-peak hours with low price and its use during peak hours with high price is investigated. The present work introduces an innovative storage-generation configuration for the distributed generation of energy through a combination of Liquefied Natural Gas regasification (LNG), Liquid Air Energy Storage (LAES), Molten Carbonate Fuel Cell (MCFC), and Organic Rankine Cycle (ORC). To compress and liquefaction of air, 108 MW electricity is required on the off-peak. The liquefied air and wasted heat from the intermediate cooling of the compressors are stored on the off-peak. The LNG stream after the regasification operation enters the MCFC cycle as fuel on the on-peak. The output heat from the fuel cell and the stored heat on the off-peak are used for preheating, the ORC, and the gas power system. At the on-peak condition, the MCFC, the gas power system and ORC generate 210.8 MW of power at a high price of electricity. The innovative system for peak shaving purposes and reduction of pollution by employing a fuel cell instead of combustion chambers is developed. The present work evaluated the thermodynamic and exergetic performances of each component and overall integrated system. The overall exergy efficiency of an integrated system, exergy efficiency in peak hours, and fuel cell efficiency decrease when methane content increases. Furthermore, with raising methane content, the irreversibility of the new structure and storage efficiency increase. Results show the highest exergy destruction is associated with the MCFC with 33.28% and heat exchangers with 25.41%. The system's round-trip efficiency is achieved to be 69.31% that improves 5.11%, whereas storage efficiency is obtained to be 86.22%, which increases 12.82% rather than the reference system. In addition, system exergy efficiency and storage exergy efficiency are obtained to 60.25% and 80.78%, respectively.