Pareto-Optimal Allocation of Transactive Energy at Market Equilibrium in Distribution Systems: A Constrained Vector Optimization Approach
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In a grid constrained transactive distribution system market, distribution locational marginal pricing DLMP is influenced by the distance from the substation to an energy user, thereby causing households that are further away from the substation to be charged more. The Jain index of fairness has been recently applied to alleviate this undesirable effect in efficient energy allocations. In this research a bilevel distributed mechanism is described, where at the lower level, auction mechanisms are invoked simultaneously at each aggregator to obtain energy costs under market equilibrium conditions. A constrained multi-gradient ascent approach, ALMA, Augmented Lagrangian Multigradient Approach is proposed to for implementation at the upper level to attain Pareto optimal energy allocations that represent tradeoffs between efficiency and fairness. Theoretical issues pertaining to Pareto optimality of the solutions are addressed. The overall effectiveness of the proposed approach is confirmed through a set of MATLAB simulations implemented on a modified IEEE 37-bus system testbed.
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