Electrical parking lots (EPLs) play a vital role in the current energy system to achieve the decarbonization goal. This paper proposes a novel structure for integrating EPLs into a multi-carrier energy system (MCES) using a Stackelberg game theory approach. The bi-level optimization is used to model the Stackelberg game. Within this bi-level optimization model

the MCES operator minimizes the MCES cost by participating in the upstream energy market at the upper level

and the EPL operators maximize their profits by participating in the local energy market between the MCES operator and themselves at the lower level. At the upper level

the MCES operator faces uncertainties in the wind and PV systems. The bi-level multi-objective information gap decision theory (MO-IGDT) is employed to address uncertainties at the upper level of the Stack-elberg game problem

resulting in a nested bi-level optimization model. The nested bi-level optimization problem is converted into a mixed-integer linear programming (MILP) optimization problem using Karush-Kuhn-Tucker (KKT) conditions. The main research assumptions pertain to EPLs' privacy and the KKT-based approach. The results demonstrate that increasing the incentive/penalty price for self-sufficiency programs from 0.0 $/% to 0.2 $/%

with a 50% self-sufficiency target

can reduce MCES operation costs by 10.19%.