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.