A Novel Meter Placement Algorithm Based on Monte Carlo Coupled State Estimation and Iterative Nonlinear Mesh Adaptive Direct Search

Distribution system state estimation (DSSE) is widely used for real-time monitoring of power grids, where different types of metering devices such as phasor measurement units, smart meters, power quality meters, and etc. are installed. The accuracy of estimated states and the system observability level depends on the type, number and location of meters and since there are many nodes and branches in such large networks, a highly redundant measurement infrastructure is practically unattainable due to the limited investment budget. Hence, this paper proposes a novel meter placement algorithm aiming to minimize the distribution system state estimation error and enhance the system observability level considering the limited number of available meters or investment cost. To this end, on one hand, Monte Carlo simulation (MCS) is applied to a weighted least squares (WLS) based DSSE to find the nodal voltage magnitude and angle as the state variables under the uncertainty of measurements. A MCS and WLS-DSSE hybrid iterative nonlinear optimization mesh adaptive direct search (NOMADS) algorithm is proposed to obtain the best locations of the voltage measuring units considering a trade-off between the DSSE performance and the investment cost. The uncertainties associated with the voltage measurements are modeled using random errors with normal probability distribution function. The efficiency and applicability of the proposed method are analyzed by its implementation on a 25-node unbalanced radial distribution system and numerical results demonstrate that this method technically outperforms other heuristic algorithms in the literature which are usually computationally intractable or more demanding in finding the optimal meter places under uncertainties. Compared to other recently developed algorithms, the accuracy of the estimated states as well as the runtime of the proposed algorithm are improved significantly especially under severe measuring errors. Moreover, it is capable to find the minimum number of voltage meters ensuring that the system observability criterion and the expected DSSE accuracy are fulfilled under the uncertain operating conditions.