The increased penetration of renewables is beneficial for power systems but it poses several challenges, i.e., uncertainty in power supply, power quality issues, and other technical problems. Backup generators or storage system have been proposed to solve this problem but there are limitations remaining due to high installation and maintenance cost. Furthermore, peak load is also an issue in the power distribution system. Due to the adjustable characteristics of loads, strategies on demand side such as demand response (DR) are more appropriate in order to deal with these challenges. Therefore, this paper studies how DR programs influence the operation of the multi-microgrid (MMG). The implementation is executed based on a hierarchical energy management system (HiEMS) including microgrid EMSs (MG-EMSs) responsible for local optimization in each MG and community EMS (C-EMS) responsible for community optimization in the MMG. Mixed integer linear programming (MILP)-based mathematical models are built for MMG optimal operation. Five scenarios consisting of single DR programs and DR groups are tested in an MMG test system to evaluate their impact on MMG operation. Among the five scenarios, some DR programs apply curtailing strategies, resulting in a study about the influence of base load value and curtailable load percentage on the amount of curtailed load and shifted load as well as the operation cost of the MMG. Furthermore, the impact of DR programs on the amount of external and internal trading power in the MMG is also examined. In summary, each individual DR program or group could be handy in certain situations depending on the interest of the MMG such as external trading, self-sufficiency or operation cost minimization.