[James_H._Harlow]_Electric_Power_Transformer_Engin(BookSee.org)
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Primary Current (Amps)<br />
60<br />
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TABLE 3.8.1 Harmonic Content of the Current Signal Shown in Figure 3.8.3<br />
Frequency Component Magnitude (primary amps) Percentage of Fundamental<br />
Fundamental 22.5 100.0<br />
Third 11.1 49.2<br />
Fifth 4.9 21.7<br />
Seventh 1.8 8.1<br />
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0.5 1 1.5 2 2.5<br />
Cycles<br />
FIGURE 3.8.3 Exciting current of an overexcited transformer; overvoltage of 150% applied to a 5-KVA, 230/115-<br />
V single-phase transformer.<br />
• Second harmonics are added at 120.<br />
• Third harmonics are added at 180 (they cancel out), etc.<br />
Sonnemann et al. initially claimed that the second-harmonic content of the inrush current was never<br />
less than 16 to 17% of the fundamental [22]. However, transformer energization with reduced voltages<br />
can generate inrush currents with second-harmonic content less than 10%, as will be discussed later in<br />
this section.<br />
3.8.3.2 <strong>Transformer</strong> Overexcitation<br />
The magnetic flux inside the transformer core is directly proportional to the applied voltage and inversely<br />
proportional to the system frequency. Overvoltage and/or underfrequency conditions can produce flux<br />
levels that saturate the transformer core. These abnormal operating conditions can exist in any part of<br />
the power system, so any transformer can be exposed to overexcitation.<br />
<strong>Transformer</strong> overexcitation causes transformer heating and increases exciting current, noise, and<br />
vibration. A severely overexcited transformer should be disconnected to avoid transformer damage.<br />
Because it is difficult, with differential protection, to control the amount of overexcitation that a transformer<br />
can tolerate, transformer differential protection tripping for an overexcitation condition is not<br />
desirable. Instead, use separate transformer overexcitation protection, and the differential element should<br />
not trip for these conditions. One alternative is a V/Hz relay that responds to the voltage/frequency ratio.<br />
Overexcitation of a power transformer is a typical case of ac saturation of the core that produces odd<br />
harmonics in the exciting current. Figure 3.8.3 shows the exciting current recorded during a real test of<br />
a 5-kVA, 230/115-V, single-phase laboratory transformer [24]. The current corresponds to an overvoltage<br />
condition of 150% at nominal frequency. For comparison purposes, the peak value of the transformer<br />
nominal current is 61.5 A, and the peak value of the exciting current is 57.3 A.<br />
Table 3.8.1 shows the most significant harmonics of the current signal depicted in Figure 3.8.3.<br />
Harmonics are expressed as a percentage of the fundamental component. The third harmonic is the most<br />
suitable for detecting overexcitation conditions, but either the delta connection of the CTs or the deltaconnection<br />
compensation of the differential relay filters out this harmonic. The fifth harmonic, however,<br />
is still a reliable quantity for detecting overexcitation conditions.<br />
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FIGURE 3.8.4 Harmonic content of transformer exciting current as a function of the applied voltage. (From Cooper<br />
<strong>Power</strong> Systems, <strong>Electric</strong> <strong>Power</strong> System Harmonics: Design Guide, Cooper <strong>Power</strong> Systems, Bulletin 87011, Franksville,<br />
WI, 1990. With permission.)<br />
Einval and Linders [13] were the first to propose using the fifth harmonic to restrain the transformer<br />
differential relay. They recommended setting this restraint function at 35% of fifth harmonic with respect<br />
to the fundamental. Figure 3.8.4 [25] shows the harmonic content of the excitation current of a power<br />
transformer as a function of the applied voltage. As the voltage increases, saturation and the exciting<br />
current increase. The odd harmonics, expressed as a percentage of the fundamental, first increase and<br />
then begin to decrease at overvoltages on the order of 115 to 120%. Setting the differential-relay fifthharmonic<br />
restraint to 35% ensures security for overvoltage conditions less than 140%. For greater<br />
overvoltages, which could quickly destroy the transformer in a few seconds, it is desirable to have the<br />
differential-relay fast tripping added to that of the transformer-overexcitation relay.<br />
© 2004 by CRC Press LLC<br />
© 2004 by CRC Press LLC