The proliferation of distributed energy assets necessitates the provision of flexibility to efficiently operate modern distribution systems. In this paper, we propose a flexibility market through which the DSO may acquire flexibility services from asset aggregators in order to maintain network voltages and currents within safe limits. A max-min fair formulation is proposed for the allocation of flexibility. Since the DSO is not aware of each aggregator's local flexibility costs, we show that strategic misreporting can lead to severe loss of efficiency. Using mechanism design theory, we provide a mechanism that makes it a payoff-maximizing strategy for each aggregator to make truthful bids to the flexibility market. While typical truthful mechanisms only work when the objective is the maximization of Social Welfare, the proposed mechanism lets the DSO achieve incentive compatibility and optimality for the the max-min fairness objective.

This paper presents a new linear optimal power flow model for three-phase unbalanced electrical distribution systems considering binary variables. The proposed formulation is a mixed-integer linear programming problem, aiming at minimizing the operational costs of the network while guaranteeing operational constraints. Two new linearizations for branch current and nodal voltage magnitudes are introduced. The proposed branch current magnitude linearization provides a discretization of the Euclidean norm through a set of intersecting planes; while the bus voltage magnitude approximation uses a linear combination of the L1 and the L norm. Results were obtained for an unbalanced distribution system, in order to assess the accuracy of the linear formulation when compared to a nonlinear power flow with fixed power injections, showing errors of less than 4% for currents and 0.005% for voltages.

This paper presents a new linear optimal power flow model for three-phase unbalanced electrical distribution systems considering binary variables. The proposed formulation is a mixed-integer linear programming problem, aiming at minimizing the operational costs of the network while guaranteeing operational constraints. Two new linearizations for branch current and nodal voltage magnitudes are introduced. The proposed branch current magnitude linearization provides a discretization of the Euclidean norm through a set of intersecting planes; while the bus voltage magnitude approximation uses a linear combination of the L1 and the L∞ norm. Results were obtained for an unbalanced distribution system, in order to assess the accuracy of the linear formulation when compared to a nonlinear power flow with fixed power injections, showing errors of less than 4\% for currents and 0.005\% for voltages.

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This paper proposes an algorithm for the optimal operation of community energy storage systems (ESSs) using a machine learning (ML) model, by solving a nonlinear programming (NLP) problem iteratively to obtain synthetic data. The NLP model minimizes the network's total energy losses by setting the operation points of a community ESS. The optimization model is solved recursively by Monte Carlo simulations in a distribution system with high PV penetration, considering uncertainty in exogenous parameters. Obtained optimal solutions provide the training dataset for a stochastic gradient boosting trees (SGBT) ML algorithm. The predictions obtained from the ML model have been compared to the optimal ESS operation to assess the model's accuracy. Furthermore, the sensitivity of the ML model has been tested considering the sampling size and the number of predictors. Results showed an accuracy of 98% for the SGBT model compared to optimal solutions, even after a reduction of 83% in the number of predictors.