【文章內(nèi)容簡介】 onic Distortion in Electronic Drive Applications Larry Ray, PE。 Louis Hapeshis, PE December 2020 Abstract This paper provides an overview of harmonic considerations for designing industrial and mercial electric power distribution systems. These power systems must serve a bination of loads, many of which produce nonsinusoidal current when energized from a sinusoidal ac voltage source. While conventional power distribution systems acmodate a significant amount of nonsinusoidal current, the design engineer can utilize existing IEEE guidelines and basic software tools to avoid some special circuit and load configurations that exacerbate harmonic distortion problems. Introduction Power system harmonic distortion has existed since the early 1900’s, as long as ac power itself has been available. The earliest harmonic distortion issues were associated with third harmonic currents produced by saturated iron in machines and transformers, socalled ferromagic loads. Later, arcing loads, like lighting and electric arc furnaces, were shown to produce harmonic distortion as well. The final type, electronic loads, burst onto the power scene in the 1970’s and 80’s, and has represented the fastest growing category ever since. A better understanding of power system harmonic phenomena can be achieved with the consideration of some fundamental concepts, especially, the nature of nonlinear loads, and the interaction of harmonic currents and voltages within the power system. Harmonic Distortion Basics What’s Flowing on the Wire? By definition, harmonic (or nonlinear) loads are those devices that naturally produce a nonsinusoidal current when energized by a sinusoidal voltage source. Each “waveform” on the right, for example, represents the variation in instantaneous current over time for two different loads each energized from a sinusoidal voltage source (not shown on the graph). For each load, instantaneous current at some point in time (at the start of the graph, for example) is zero. Its magnitude quickly increases to a maximum value, then decreases until it returns to zero. At this point, the current direction appears to reverse – and the maximumtozeromagnitude trend repeats in the negative direction. This pattern is repeated continuously, as long as the device is energized, creating a set of largelyidentical waveforms that adhere to a mon time period. Both current waveforms were produced by turning on some type of load device. In the case of the current on the left, this device was probably an electric motor or resistance heater. The current on the right could have been produced by an electronic variablespeed drive, for example. The devices could be single or threephase, but only one phase current waveform is shown for illustration. The other phases would be similar. How to Describe What’s Flowing on the Wire? Fourier Series While the visual difference in the above waveforms is evident, graphical appearance alone is seldom sufficient for the power engineer required to analyze the effects of nonsinusoidal loads on the power system. The degree of nonlinearity must be objectively established, and the method of quantifying the harmonic distortion must also facilitate future analysis and mitigation. One method of describing the nonsinusoidal waveform is called its Fourier Series. Jean Fourier was a French mathematician of the early 19th century who discovered a special characteristic ofperiodic waveforms. Periodic waveforms are those waveforms prised of identical values that repeat in the same time interval, like those shown above. Fourier discovered that periodic waveforms can be represented by a series of sinusoids summed together. The frequency of these sinusoids is an integer multiple of the frequency represented by the fundamental periodic waveform. The waveform on the left above, for example, is described entirely by one sinusoid, the fundamental, since it contains no harmonic distortion. The distorted (nonlinear) waveform, however, deserves further scrutiny. This waveform meets the continuous, periodic requirement established by Fourier. It can be described, therefore, by a series of sinusoids. This example waveform is represented by only three harmonic ponents, but some realworld waveforms (square wave, for example) require hundreds of sinusoidal ponents to fully describe them. The magnitude of these sinusoids decreases with increasing frequency, often allowing the power engineer to ignore the effect of ponents above about the50th harmonic. The concept that a distorted waveform (even a square wave!) can be represented by a series of sinusoids is difficult for many engineers. But it is absolutely essential for understanding the harmonic analysis and mitigation to follow. It’s important for the power engineer to keep in mind a few facts: ? The equivalent harmonic ponents are just a representation – the instantaneous current as described by the distorted waveform is what’s actually flowing on the wire. ? This representation is necessary because it facilitates analysis of the power system. The effect of sinusoids on typical power system ponents (transformers, conductors, capacitors) is much easier to analyze than distorted signals. ? Power engineers fortable with the concept of harmonics often refer to individual harmonic ponents as if each really exists as a separate entity. For example, a load might be described as producing “30 amperes of 5th harmonic”. What’s intended is not that the load under consideration produced 30 A of current at 300 Hz, but rather that the load produced a distorted (but largely 60 Hz) current, one sinusoidal ponent of which has a frequency of 300 Hz with an rms magnitude of 30 A. ? The equivalent harmonic ponents, while imaginary, fully an