Deriving power uncertainty intervals for low voltage grid state estimation using affine arithmetic

Pseudo-measurements are usually applied as substitutes for measurement data to obtain observability even in case of sparse measurement configurations. The quality of pseudo-measurements strongly affects the accuracy of state estimation results. Generating pseudo-measurements is not a straightforward task in particular for customers with highly stochastic behavior. This paper proposes a novel approach to obtain verified boundaries of pseudo-measurements, which are consistent to currently available measurement information. These boundaries allow to verify generated pseudo-measurements, whether they are compliant to current system conditions. Additionally, tight boundaries are suitable to generate pseudo-measurements on-line regardless of the customer's structure. The proposed algorithm applies Affine Arithmetic a self-validated numerical model to the state estimation problem and treats pseudo-measurements as main source of uncertainty. The key properties of the algorithm are rigorous, iterative, linearizing and large-scale. These properties are demonstrated by numerical simulation of two benchmark grid models of different complexity. Computational and implementation issues are addressed in detail.