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Power flow (PF) is a fundamental tool for operation, automation and optimization of the power systems. Due to the nonlinearity of the PF system equations, the classical PF solutions are computationally very demanding. As a common approach in solving the nonlinear equations, linearization is a potential technique which can simplify and accelerate the PF calculations. In this context, this paper proposes a linear fast iterative method based on the fixed-point iteration technique in which a linearized model of generator along with a ZI load model are integrated in a simplified system of linear equations (SLE) of Yv = i. The relaxation method is used during the deriving process of generator equivalent current in this approach. However, the already developed ZI load model based on the curve-fitting technique has been exploited in this work. The accuracy of the proposed PF method has been compared with calculated results from DIgSILENT PowerFactory on the benchmark IEEE 33-bus test system and on a large medium voltage network in Germany.INDEX TERMS Linearization, fixed-point iteration technique, current injection model, relaxation method. NOMENCLATUREThe main notation used in this paper is provided below; other symbols are defined as required.

Data-driven approaches based on Distributed Artificial Intelligence (DAI) such as Artificial Neural Networks (ANN) could be used to perform estimation of voltage magnitude in distribution systems for monitoring purposes. These methods may offer high accuracy and yet require relatively few measurement inputs and low computational power compared to conventional state estimation techniques. However, the number of required measurements may vary from system to system depending on several factors. Furthermore, it is important to ensure that these estimators are robust to input noise. Moreover, a factor to be considered in presence of sparse electrical measurements is that other additional inputs may be used to improve the accuracy of estimation. This paper investigates the decisive factors that affect the minimum number of input measurements for an ANN-based estimator. Furthermore, it discusses how the ANN should be designed to handle measurement noise properly in practice. Simulations are performed on benchmark networks to support the discussion.

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