Midpoint-radius interval-based method to deal with uncertainty in power flow analysis

- A novel formulation of the interval-based power flow problem is proposed.
- The proposed formulation is based on midpoint-radius interval arithmetic.
- The proposed method is compared with the Monte Carlo method and previous approaches.
- The proposed method is as accurate as Monte Carlos if uncertainty is moderate.
- The complexity of the proposed method is lower than in previous approaches.

This paper presents a novel method based on midpoint-radius interval arithmetic to deal with uncertainties in the power flow problem. The proposed technique aims at finding a balance between accuracy and computational efficiency. It relies on an original decoupling of the interval power flow equations into midpoint 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 interval solution while preserving uncertainty. The proposed technique proves to be more efficient than existing approaches based on interval and affine arithmetic and as accurate as the conventional Monte Carlo method.