A mixed interval power flow analysis based on affine arithmetic

A rectangular interval power flow (RIPF) method is proposed to evaluate solutions' intervals of power flow including uncertain loads and output of generators. It is based on affine arithmetic which is a more accurate method to compute intervals, and it obtains intervals through optimization methods to enhance efficiency of interval calculation. Because no approximation is used, RIPF can acquire narrower intervals of voltage phase results than polar interval power flow (PIPF), which is an excellent method raised before. However, RIPF is no better than PIPF in estimating intervals of voltage amplitude, since it could not satisfy the voltage equations of interval power flow. Therefore, a mixed interval power flow (MIPF) is established to incorporate merits of RIPF in computing intervals of voltage phase and PIPF's advantages in evaluating intervals of voltage magnitude. The IEEE118 system is analyzed to conclude that MIPF can acquire more accurate power flow intervals than PIPF.