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Probabilistic Assessment of Available Transfer Capacity via Market Linearization

Uncertainties associated with bus loading and components' availability lead to uncertainties in different system variables based on the system physical and economical relationships. Line flows, bus voltages, different prices, and other variables and indices, such as available transfer capacity (ATC), are stochastic and cannot be expressed as a determined quantity. Traditionally, in order to model the stochastic nature of power systems, a stochastic power flow algorithm is used. In this paper, stochastic-algebraic method is applied to find the probability density function (pdf) of ATC. The algorithm linearizes the optimal power flow formulation and uses Gram-Charlier expansion to find the pdf of the ATC, based on the statistical moments. The main contribution of this paper is that the market clearing equations are linearized instead of the power flow equations. In addition, in most of previous studies, the effects of system uncertainties have been neglected in ATC calculations. The other advantage of the proposed method is that the program execution time is very short. The proposed method is tested on the IEEE Reliability Test System, and the results are compared with those drawn using Monte Carlo simulation to show the effectiveness of the proposed method.