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A novel measurement approach for power-flow analysis in medium-voltage (MV) networks, based on load power measurements at low-voltage level in each secondary substation (SS) and only one voltage measurement at the MV level at primary substation busbars, was proposed by the authors in previous works. In this paper, the method is improved to cover the case of temporary unavailability of load power measurements in some SSs. In particular, a new load power estimation method based on artificial neural networks (ANNs) is proposed. The method uses historical data to train the ANNs and the real-time available measurements to obtain the load estimations. The load-flow algorithm is applied with the estimated load powers, and the MV network state variables are obtained. The proposed method is validated for the real MV distribution network of the island of Ustica. The loads of selected SSs are estimated for two full days of different seasons. In comparison with previous works, satisfactory results are obtained in terms of uncertainty in the calculated power flows, thus suggesting the applicability of the proposed method for real-time monitoring of MV distribution networks. [ABSTRACT FROM AUTHOR]

In this paper, we discuss how the extreme learning machine (ELM) framework can be effectively employed in the unsupervised context of multivariate density estimation. In particular, two algorithms are introduced, one for the estimation of the cumulative distribution function underlying the observed data, and one for the estimation of the probability density function. The algorithms rely on the concept of F -discrepancy, which is closely related to the Kolmogorov–Smirnov criterion for goodness of fit. Both methods retain the key feature of the ELM of providing the solution through random assignment of the hidden feature map and a very light computational burden. A theoretical analysis is provided, discussing convergence under proper hypotheses on the chosen activation functions. Simulation tests show how ELMs can be successfully employed in the density estimation framework, as a possible alternative to other standard methods. [ABSTRACT FROM PUBLISHER]