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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Demand response plays an important role in the development of the smart grid, which can effectively manage society's energy consumption. Cooling devices, such as refrigerators and freezers, are ideal devices for demand-response programs because their energy states can be controlled without reducing the lifestyle and comfort of the residents. Conversely, managing air conditioning and space heating would affect a resident's comfort level. Direct compressor control and thermostat control methods have been proposed in the past for controlling cooling devices but they are never studied concurrently. This paper proposes a new control mechanism and compares the effectiveness of the three control mechanisms for cooling devices in demand response. In addition, this paper illustrates the need for a damping strategy to mitigate demand oscillations that occur from synchronous fleet control.

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