Abstract-This paper introduces the cumulant method for the probabilistic optimal power flow (P-OPF) problem. By noting that the inverse of the Hessian used in the logarithmic barrier interior point can be used as a linear mapping, cumulants can be computed for unknown system variables.Results using the proposed cumulant method are compared against results from Monte Carlo simulations (MCSs) based on a small test system. The Numerical Results section is broken into two sections: The first uses Gaussian distributions to model system loading levels, and cumulant method results are compared against four MCSs. Three of the MCSs use 1500 samples, while the fourth uses 20 000 samples. The second section models the loads with a Gamma distribution. Results from the proposed technique are compared against a 1000-point MCS.The cumulant method agrees very closely with the MCS results when the mean value for variables is considered. In addition, the proposed method has significantly reduced computational expense while maintaining accuracy.Index Terms-Cumulants, optimal power flow (OPF), probabilistic optimization.

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The problem of optimally sizing hybrid energy storage systems (HESS) installed in electric railway systems, considering the effect of regenerative braking is studied in this paper. HESSs combine traditional batteries and newly developed ultracapacitors, taking advantage of the high energy capacity of batteries and of the flexibility and ability to capture high power density of ultracapacitors. A novel mixed integer linear programming formulation that includes the counting of battery cycles is presented. Some particularities of battery operation are included in the model, like the dependence of its performance on the number of cycles and the depth of discharge (DOD). Results are reported first for a illustrative case study, allowing us to perform sensitivity studies for several parameters; results are also reported and for a larger case, closely resembling the problem faced by railway energy systems planners and operators.Index Terms-Electric railway systems, hybrid energy storage sizing, mixed integer linear programming. NOMENCLATUREThis section describes the sets, parameters, and variables used in the paper. A. Sets Set of batteries.Time period set. AC/DC inverter set. DC/DC inverter set. B. ParametersMinimum battery unit (MBU) cost .Daily MBU cost for each battery .Minimum ultracapacitor unit (MUU) cost .

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The expansion on the use of Electric Vehicles demands new mechanisms to ease the charging process, making it autonomous and with a reduced user intervention. This paper reviews the technologies applied to the wireless charge of Electric Vehicles. In particular, it focuses on the technologies based on the induction principle, the capacitive-based techniques, those that use radiofrequency waves and the laser powering. As described, the convenience of each technique depends on the requirements imposed on the wireless power transfer. Specifically, we can state that the power level, the distance between the power source and the electric vehicle or whether the transfer is executed with the vehicle on the move or not or the cost are critical parameters that need to be taken into account to decide which technology to use. In addition, each technique requires some complementary electronics. This paper reviews the main components that are incorporated into these systems and it provides a review of their most relevant configurations.

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