Penetration of renewable power generation is increasing significantly in modern power systems. Wind power generation is highly intermittent and uncertain. The effect of uncertainty in wind power generation on available transfer capability was discussed, in seminar-I, using relative distance measure arithmetic.
In seminar-II, the effect of uncertainty in active and reactive power injections on the solution bounds of power flow analysis will be addressed. Power flow studies are useful in the analysis and design of power systems. Conventional power flow analysis is for a set of deterministic active and reactive power generations and demands. However, in a practical scenario, the active and reactive power demands are variable due to the significant integration of renewable energy sources, like wind and solar, into the power system. To study the effect of uncertainty in active and reactive power injections, on power flow analysis, Monte Carlo simulations are widely utilized in literature. Monte Carlo simulations are very expensive in terms of computational time and to address this issue range arithmetic methods were proposed in the literature. Affine arithmetic is a range arithmetic method used in literature. However, multiplication and division of two affine variables lead to non-affine terms that are approximated to affine terms with certain assumptions. This assumptions lead to a reduction in accuracy. In the present work, a method is proposed to carry out the power flow analysis, in the presence of uncertainty, using relative distance measure arithmetic. The uncertainty in active and reactive power is represented with intervals. Further, power injections are converted to relative distance measure variables which are continuous. The proposed relative distance measure arithmetic based power flow analysis is implemented on IEEE 30-Bus and IEEE 118-Bus systems. The detailed simulation results are discussed and compared with affine-arithmetic and Monte Carlo simulations based power flow analysis. The results clearly demonstrate that the proposed relative distance measure arithmetic based power flow analysis gives solution bounds closer to that obtained with Monte Carlo for the voltage magnitudes, bus angles, real and reactive power flows as compared to affine arithmetic-based power flow analysis