Light emitting diode (LED) lamps are now an established lighting technology, which is becoming prevalent in all load sectors. However, LED lamps are non-linear electrical loads, and their impact on distribution system voltage quality must be evaluated. This paper provides a detailed analysis of time domain and frequency domain approaches for developing and evaluating models suitable for use in large scale steady-state harmonic power flow analysis of the low frequency (LF) emission of LED lamps. The considered approaches are illustrated using four general categories of LED lamps, which have been shown to cover the vast majority of LED lamps currently available on the market. The aim is an in-depth assessment of the ability of commonly applied models to represent the specific design characteristics of different categories of LED lamps. The accuracy of the models is quantitatively evaluated by means of laboratory tests, numerical simulations, and statistical analyses. This provides an example, for each LED lamp category, of comprehensive information about the overall accuracy that can be achieved in the general framework of large scale LF harmonic penetration studies, particularly in the assessment of voltage quality in low voltage networks and their future evolution.