【正文】 ivalent 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 and accurately represent the distorted current. As one test, try summing the instantaneous current Total Harmonic Distortion The series of harmonic ponents that represent a distorted waveform are often described by a single number, total harmonic distortion. This number is calculated in two different ways, depending somewhat on the engineer’s geographic location. In the United States, total harmonic distortion is calculated as the sum of all the harmonic ponents (except the fundamental), divided by the magnitude of the fundamental. This value is represented as THD (all upper case). Or, in equation form: Note that the ponents are summed vectorially, not algebraically, because they have different phase angles. For a waveform represented by a fundamental current of 100 A, a 5th ponent of 20 A, and a 7th ponent of 12 A, for example, Ih would equal thesquare root of (202 + 122), or 23 A, not (20 + 12) = 32 A. The THD is, therefore, 23/100 = or 23%. It is possible for the USconvention THD to exceed or 100%, since it is possible for the magnitude of harmonic current to exceed the magnitude of fundamental current. This is the primary distinction between the US and European convention. The European convention, thd (all lower case) equals the harmonic ponents divided by the total rms current (harmonics plus fundamental). This thd value can never exceed 100%. Voltage and Current Distortion Harmonic Current Flow The current drawn by nonlinear loads passes through all of the impedance between the system source and load. This current produces harmonic voltages for each harmonic as it flows through the system impedance. These harmonic voltages sum and produce a distorted voltage when bined with the fundamental. The voltage distortion magnitude is dependent on the source impedance and the harmonic voltages produced. Figure 4 illustrates how the distorted voltage is created. As illustrated, nonlinear loads are typically modeled as a source of harmonic current. With low source impedance the voltage distortion will be low for a given level of harmonic current. If harmonic current increases, however, system impedance changes due to harmonic resonance (discussed below), voltage distortion can increase significantly. Circuit Impedance – Without Power Factor Correction While the preceding discussion focused on distorted current waveforms, it is important to note that ac voltage can also show the effects of harmonic distortion. The degree of distortion is determined by applying the same techniques as described earlier for current. So, what is therelationship between voltage distortion and current distortion? Higherfrequency (harmonic) ponents of ac voltage and current follow the same power system rules as 60Hz voltages and currents – Kirchoff’s Voltage and Current Laws, Ohm’s Law, etc. One basic principle is that voltage and current are related by impedance. As with ac voltage and current, impedance is a plex term, consisting of resistance, capacitance, and inductance. While resistance is largely independent of frequency, impedance associated with capacitance and inductance changes as the frequency of the signal changes. For the typical industrial power system, the impedance as seen by the loads is dominated by inductance. Since inductive reactance is directly proportional to the frequency of the current, the system impedance approximates a straight line, as illustrated below. Frequency (Hz) Frequency (Hz) Frequency (Hz)For this typical power system, the impedance encountered by the 300 Hz (5th harmonic) ponent of current is approximately five times the impedance encountered by the 60Hz (fundamental) ponent. With this type of power system, the amount of voltage distortion can be estimated by summing the voltage drop at each harmonic ponent, as summarized in the following table. The table assumes that the circuit load is represented by the single harmonic source shown earlier, with a total Irms = A, and ITHD = 23%, with a nominal system voltage of 480 Vrms. Circuit Impedance – With Power Factor Correction Power factor correction capacitors are often utilized in industrial and mercial power systems to reduce power factor penalties, release circuit capacity, improve voltage regulation, and reduce resistive heating losses in circuit conductors. While power factor correction capacitors do not inject harmonic distortion (that is, PFC’s are linear loads – they produce a sinusoidal current waveform when energized from a sinusoidal voltage source), their presence on a power system dramatically changes the circuit impedance. These impedance changes can adversely affect power system ponents, and worsen harmonic distortion concerns. When power factor correction capacitors are installed, a frequency of high impedance known as the resonance point results from the new binati