The stochastic-algebraic evaluation of available transfer capability for transmission expansion

In power transmission systems, due to uncertainty in bus loading and transmission asset status, the evaluation of the available transfer capability (ATC) also becomes uncertain. The ATC is a measure of 'available room' in a power system to transmit power between two given points beyond already committed uses.; Using a linearized model, the stochastic ATC can be calculated from the probabilistic models. A linear transformation transforms bus load statistics to statistics of the ATC. A new method, termed the stochastic-algebraic method is developed and illustrated for the calculation of ATC statistics. The limitations considered in the stochastic-algebraic ATC calculation algorithm are: transmission line thermal rating limits, bus voltage magnitude limits, and the phase angle difference across transmission lines (i.e. security limits).; The linear transformation matrix used to obtain the ATC is the system power flow study Jacobian matrix at the ATC solution point. Once uncertainties of each of the several ATC limitations are found, the probability density function of the ATC is calculated using a statistical property of the minimum of several given random variables. The calculation of stochastic ATC with transmission asset status is performed using a modified transmission outage table. Statistical moments are used, therefore a Gram-Charlier type A series can be used to approximate the probability density of the ATC.; The stochastic-algebraic calculation of ATC is tested using the WECC 179 bus system. The stochastic-algebraic calculation of the ATC is compared to a computationally intensive Monte Carlo calculation of the ATC. Results show that the stochastic-algebraic calculation has a computation time much shorter than the Monte Carlo solution. Calculations including and not including transmission element uncertainty are also compared. Results show that various statistical measures of the ATC between two points drastically change when including the transmission element uncertainty.; The stochastic ATC calculation is considered in possible transmission expansion scenarios of the system. A cost to benefit analysis example of transmission expansion is preformed using the WECC 179 bus system. Results show that transmission expansion can possibly be justified by considering the sale of ATC as the sole contributor to the payback of the transmission expansion.