• Harmonic distortion can be forecasted with no specialized metering device. • Demand response meters can be used for power quality monitoring. • Artificial intelligence helps monitoring power quality at low voltage networks. • Utilities will increasingly have to cope with harmonic distortion in a near future. This paper introduces a methodology to forecast voltage total harmonic distortion (THD) at low voltage busbars of residential distribution feeders based on the data provided by a limited number of smart meters. The methodology provides relevant power quality indices to system operators using only the existing monitoring infrastructure required for demand response operation. Different algorithms for voltage THD forecasting are implemented, including artificial neural networks, and their performance is tested and compared. The necessary coverage of smart meters for the acceptable accuracy of the estimated THD is also established. The estimation algorithms are validated considering probabilistic demand load model developed based on typical harmonic injections of household devices obtained from measurements and using a typical European low voltage test-feeder with 471 residential consumers.