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This paper presents a method for monitoring multiple harmonic sources in a power system using a reduced number of harmonic monitoring stations. Artificial neural networks are used to provide initial estimates of the harmonic sources based on the measured harmonics and fundamental load flows. State estimation is then utilised to improve the estimates. This approach is tested on a simulated power system based on the IEEE 14-bus test system with several harmonic-producing loads. The outlined method can be used to reduce the number of required measurements in many real state estimation problems.