Consumer load modeling and fair mechanisms in the efficient transactive energy market

Abstract

Two significant and closely related issues pertaining to the grid-constrained transactive distribution system market are investigated in this research. At first, the problem of spatial fairness in the allocation of energy among energy consumers is addressed, where consumer agents that are located at large distances from the substation – in terms of grid layout, are charged at higher rates than those close to it. This phenomenon, arising from the grid’s voltage and flow limits is aggravated during demand peaks. Using the Jain’s index to quantify fairness, two auction mechanisms are proposed. Both approaches are bilevel, with aggregators acting as interface agents between the consumers and the upstream distribution system operator (DSO). Furthermore, in spite of maximizing social welfare, neither mechanism makes use of the agents’ utility functions. The first mechanism is cost-setting, with the DSO determining unit costs. It implements the Jain’s index as a second term to the social welfare. Next, a power setting auction mechanism is put forth where the DSO’s role is to allocate energy in response to market equilibrium unit costs established at each aggregator from an iterative bidding process among its consumers. The Augmented Lagrangian Multigradient Approach (ALMA), which is based on vector gradient descent, is proposed in this research for implementation at the upper level. The mechanism’s lower level comprises of multiple auctions realized by the aggregators. The quasi-concavity of the Jain’s index is theoretically established, and it has been shown that ALMA converges to the Pareto front representing tradeoffs between social welfare and fairness. The effectiveness of both mechanisms is established through simulations carried out using a modified IEEE 37-bus system platform. The issue of extracting patterns of energy usage from time series energy use profiles of individual consumers is the focus of the second phase of this research. Two novel approaches for non-intrusive load disaggregation based on non-negative matrix factorization (NMF), are proposed. Both algorithms distinguish between fixed and shiftable load classes, with the latter being characterized by binary OFF and ON cycles. Fixed loads are represented as linear combinations of a set of basis vectors that are learned by NMF. One approach imposes L0 normed constraints on each shiftable load using a new method called binary load decomposition. The other approach models shiftable loads as Gaussian mixture models (GMM), therefore using expectation-maximization for unsupervised learning. This hybrid NMF-GMM algorithm enjoys the theoretical advantage of being interpretable as a maximum-likelihood procedure within a probabilistic framework. Numerical studies with real load profiles demonstrate that both algorithms can effectively disaggregate total loads into energy used by individual appliances. Using disaggregated loads, a maximum-margin regression approach to derive more elaborate, temperature-dependent utility functions of the consumers, is proposed. The research concludes by identifying the various ways gleaning such information can lead to more effective auction mechanisms for multi-period operation.