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In this paper, a comprehensive dedicated framework is set up to analyze distributed multi-generation (DMG) systems for the purpose of identifying and quantifying their potential to participate in real-time demand response (DR) programmes. At first, flexibility of DMG systems with multiple interconnected plant components is exploited to identify the optimal operational strategy in the presence of half-hourly pricing. Then, the costs and benefits of providing further real-time DR are assessed by taking into account different energy shifting strategies. The novel concept of electricity shifting potential is introduced to establish the upper limit to the possible reduction of the electricity flowing from the electrical grid to the DMG system. The maximum profitable energy shifting that can be activated in the presence of given DR incentives is established on the basis of a DR profitability map. The key point is that energy shifting can be deployed inside the local DMG system to respond to given DR signals without reducing the users' energy demand and thus without affecting their comfort level. Examples of real-time DR for a trigeneration system referring to half-hourly periods during selected Summer and Winter days are illustrated and discussed.