This paper proposes a restricted earth fault protection based on the wavelet transform (REFW) for detecting ground faults close to the transformer neutral point (turn-to-ground faults) and supporting the conventional phase differential protection, which presents limitations in this kind of faults. The proposed REFW protection uses only high-frequency components instead of phasor estimation, speeding up the detection of turn-to-ground faults. A performance comparison between the proposed wavelet-based restricted earth-fault differential protection and the respective conventional restricted earth-fault (REF) unit was accomplished considering simulated turn-to-ground faults, involving a few winding turns. The proposed method is more efficient and faster than the conventional one, reaching a success rate of 100%.

This paper proposes a two-stage stochastic market clearing (SMC) model based on a semidefinite programming (SDP) relaxation. The SMC model aims at determining the day-ahead schedule (DA) and the real-time (RT) balance settlement that minimize the total expected production cost. The network capacity constraints are considered in the proposed model through an AC power flow formulation, while the uncertainty in the renewable-based generation is taking into account using a set of stochastic scenarios. In order to solve the proposed non-linear programming model, a SDP relaxation is used. An illustrative example (3-bus test system) and the IEEE Reliability 24-bus test system are used to show the effectiveness and accuracy of the proposed model. Results shown that the proposed SDP relaxation introduce a negligible error, when compared with the solution after solving the original non-linear model.