Nonlinear, robust, interval state estimation for distribution systems based on fixed-point expansion considering uncertainties

Abstract

Interval state estimation (ISE) is widely used due to its ability to handle uncertainty and the simple parameters that are required. Existing ISE methods have some problems that need improvements, such as conservatism of results, lack of completeness, and limitations in the error range. Therefore, this paper proposes a nonlinear robust ISE method for distribution systems. First, the quadratic Taylor-series expansions of measurement equations are transformed into fixed-point expansions without truncation errors, which reduces errors introduced by measurement conversion and the approximation process. Second, an exponentially weighted least-squares ISE model considering power-flow constraints is proposed based on the fixed-point expansion (FPE), which avoids calculating inverse matrices of the Jacobian matrices containing interval numbers and improves the estimation accuracy. To improve the model’s robustness, an interval weight correction strategy is proposed. Then, the interval Taylor-series method is used to calculate the range of interval functions to reduce the expansion of the interval arithmetic, thereby obtaining narrower intervals for the state variables. Finally, based on an analysis of the 34-bus and the 123-bus systems, it can be seen that the proposed method has good performance for different error ranges and poor measurement ranges.