This paper presents a novel method based on midpoint-radius interval arithmetic to deal with uncertainties in the power ow problem. The proposed technique aims at nding a balance between accuracy and computational e ciency. It relies on an original decoupling of the interval power ow equations into mid- point and radius parts. This representation allows avoiding the factorisation of an interval Jacobian matrix. Moreover, the proposed formulation is combined with an optimisation problem in order to prevent overestimation of the inter- val solution while preserving uncertainty. The proposed technique proves to be more e cient than existing approaches based on interval and a ne arithmetic and as accurate as the conventional Monte Carlo method.