Nowadays, enhanced knowledge of the nature of the electricity demand is achieved through the progressively increasing deployment of smart meters and advanced data analysis techniques. One of the major challenges is to exploit this knowledge to support the introduction of strategies to modify the demand according to relevant objectives to be achieved, like users' participation in demand response programmes. A key point for facing this challenge is to characterize the demand flexibility. In spite of many discussions about the concept of flexibility, the few mathematical definitions of flexibility available do not address the variation in time of the overall demand aggregation. This paper starts from the analysis of time-variable patterns of aggregate residential customers, ending up with suitable definitions of expected flexibility for aggregate demand. These definitions are based on assessing positive and negative pattern variations and are identified from the analysis of the collective behavior of the aggregate users. A set of results is shown for different numbers of aggregate customers, by considering different values of the averaging time step for load pattern representation.

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The transformation of a conventional power system to a smart grid has been underway over the last few decades. A smart grid provides opportunities to integrate smart homes with renewable energy resources (RERs). Moreover, it encourages the residential consumers to regulate their home energy consumption in an effective way that suits their lifestyle and it also helps to preserve the environment. Keeping in mind the techno-economic reasons for household energy management, active participation of consumers in grid operations is necessary for peak reduction, valley filling, strategic load conservation, and growth. In this context, this paper presents an efficient home energy management system (HEMS) for consumer appliance scheduling in the presence of an energy storage system and photovoltaic generation with the intention to reduce the energy consumption cost determined by the service provider. To study the benefits of a home-to-grid (H2G) energy exchange in HEMS, photovoltaic generation is stochastically modelled by considering an energy storage system. The prime consideration of this paper is to propose a hybrid optimization approach based on heuristic techniques, grey wolf optimization, and a genetic algorithm termed a hybrid grey wolf genetic algorithm to model HEMS for residential consumers with the objectives to reduce energy consumption cost and the peak-to-average ratio. The effectiveness of the proposed scheme is validated through simulations performed for a residential consumer with several domestic appliances and their scheduling preferences by considering real-time pricing and critical peak-pricing tariff signals. Results related to the reduction in the peak-to-average ratio and energy cost demonstrate that the proposed hybrid optimization technique performs well in comparison with different meta-heuristic techniques available in the literature. The findings of the proposed methodology can further be used to calculate the impact of different demand response signals on the operation and reliability of a power system.

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