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This manuscript introduces a mathematically tractable and accurate model of narrowband power line noise based on experimental measurements. In this paper, the noise is expressed as a Gaussian process whose instantaneous variance is a periodic time function. With this assumption and representation, the cyclostationary features of power line noise can be described in close form. The periodic function that represents the variance is then approximated with a small number of parameters. The noise waveform generated with this model shows good agreement with that of actually measured noise. Noise waveforms generated by different models are also compared with that of the proposed model.