There are several uncertainties associated with a power system network like intermittent renewable power generation, uncertainty in network parameters, system topological changes, forecasting errors, measurement errors, etc. One simpler way of incorporating uncertainty into power system analysis is using Monte Carlo (MC) simulations, where a large number of samples are extracted within the uncertainty range, and a repeated analysis is carried out with each of the extracted samples. However, it requires a very large computational time due to the repeated number of simulations.

In the present work, modified affine arithmetic (AA) based power flow and static voltage stability analysis of a transmission network, with uncertainty in power injections, are proposed. Existing AA operations generate additional noise terms as a result of nonaffine operations like multiplication, division, and sinusoidal operations. The proposed modified AA based method do not generate any extra noise terms, as in the case of existing AA method, thereby improving accuracy in solution bounds. As static voltage stability analysis used for a transmission network is not suitable for a distribution network, backward/forward sweep (BFS) algorithm based static voltage stability analysis of a radial distribution network is also proposed. The proposed modified AA based methods are implemented on 5 bus, IEEE 57, European 1354, Polish 2383 bus transmission systems and 33, 874 bus radial distribution systems. The detailed simulation results will be presented.