State estimation (SE) is based on an iterative process for solving weighted least squares (WLS) via the so‐called normal equations (NE). This process is prone to numerical instability and may lead to an ill‐conditioned state estimator in many cases. Although several methods have been proposed in the past to deal with the ill‐conditioning problem in high‐voltage transmission systems, the SE stability of low‐voltage distribution systems remains a challenge due to fewer measurements and high R/X ratios. This paper highlights the main reasons for the ill‐conditioning problem and focuses on the impact of the R/X ratio of the distribution systems. NE‐based SE uses a comparatively simple algorithm with much lower storage size. Hence, this paper proposes a regularized version of the WLS state estimator to solve the problem of ill‐conditioning using an adjustable regularization parameter. Simulation results on U.K. 18‐bus and radial 33‐bus distribution systems show improved performance in terms of reducing the computational complexity, measurements redundancy, the impact of high R/X ratios and improving the accuracy and numerical stability of the SE solution. © 2018 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.