We consider a demand response program in which a block of apartments receive a discount from their electricity supplier if they ensure that their aggregate load from air conditioning does not exceed a predetermined threshold. The goal of the participants is to obtain the discount, while ensuring that their individual temperature preferences are also satisfied. As such, the apartments need to collectively optimise their use of air conditioning so as to satisfy these constraints and minimise their costs. Given an optimal cooling profile that secures the discount, the problem that the apartments face then is to divide the total discounted cost in a fair way. To achieve this, we take a coalitional game approach and propose the use of the Shapley value from cooperative game theory, which is the normative payoff division mechanism that offers a unique set of desirable fairness properties. However, applying the Shapley value in this setting presents a novel computational challenge. This is because its calculation requires, as input, the cost of every subset of apartments, which means solving an exponential number of collective optimisations, each of which is a computationally intensive problem. To address this, we propose solving the optimisation problem of each subset suboptimally, to allow for acceptable solutions that require less computation. We show that, due to the linearity property of the Shapley value, if suboptimal costs are used rather than optimal ones, the division of the discount will be fair in the following sense: each apartment is fairly "rewarded" for its contribution to the optimal cost and, at the same time, is fairly "penalised" for its contribution to the discrepancy between the suboptimal and the optimal costs. Importantly, this is achieved without requiring the optimal solutions.
Over the past few years, domestic heating automation systems (DHASs) that optimize the domestic space heating control process with minimum user-input, utilizing appropriate occupancy prediction technology, have emerged as commercial products (e.g, the smart thermostats from Nest and Honeywell). At the same time, many houses are being equipped with, potentially grid-connected, intermittent energy resources (IERs), such as rooftop photovoltaic systems and/or small wind turbine generators. Now, in many regions of the world, such houses can sell energy to the grid but at a lower price than the price of buying it. In this context, and given the anticipated increase in electrification of heating, the next generation DHASs need to incorporate advanced economic control (AEC). Such AEC can exploit the energy buffer that heating loads provide, in order to shift the consumption of electricity-based heating systems to follow the intermittent energy generation of the house. By so doing, the energy imported from the grid can be minimized and considerable monetary gains for the household can be achieved, without affecting the occupants' schedule. These benefits can be amplified still further in domestic coalitions, where a number of houses come together and share their IER generation to minimize their cumulative grid energy import.Given the above, in this work we extend a state-of-the-art DHAS, to propose AdaHeat+, a practical DHAS, that, for the first time, incorporates AEC. Our work is applicable to both individual houses and domestic coalitions and comes complete with an allocation mechanism to share the coalition gains. Importantly, we propose an effective heuristic heating schedule planning approach for collective AEC which: (i) has a complexity that scales in a linear and parallelizable manner with the coalition size, and (ii) enables AdaHeat+ to handle the distinct preferences, in balancing heating cost and thermal discomfort, of the households. Our approach relies on stochastic IER power output predictions. In this context, we propose a simple and effective formulation for the site-specific calibration of such predictions based on adaptive Gaussian process modeling. Finally, we demonstrate the effectiveness of AdaHeat+ through real data evaluation, to show that collective AEC can improve heating cost-efficiency by up to 60%, compared to independent AEC (and even more when compared to no-AEC).
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