Electrical Power Systems Quality, Second Edition phần 5 pps

range of power system equipment, most notably capacitors, transform￾ers, and motors, causing additional losses, overheating, and overload￾ing. These harmonic currents can also cause interference with

telecommunication lines and errors in power metering. Sections 5.10.1

through 5.10.5 discuss impacts of harmonic distortion on various power

system components.

5.10.1 Impact on capacitors

Problems involving harmonics often show up at capacitor banks first.

As discussed in Secs. 5.9.3 and 5.9.4, a capacitor bank experiences high

voltage distortion during resonance. The current flowing in the capac￾itor bank is also significantly large and rich in a monotonic harmonic.

Figure 5.32 shows a current waveform of a capacitor bank in resonance

with the system at the 11th harmonic. The harmonic current shows up

distinctly, resulting in a waveform that is essentially the 11th har￾monic riding on top of the fundamental frequency. This current wave￾form typically indicates that the system is in resonance and a capacitor

bank is involved. In such a resonance condition, the rms current is typ￾ically higher than the capacitor rms current rating.

IEEE Standard for Shunt Power Capacitors (IEEE Standard 18-

1992) specifies the following continuous capacitor ratings:

■ 135 percent of nameplate kvar

■ 110 percent of rated rms voltage (including harmonics but excluding

transients)

■ 180 percent of rated rms current (including fundamental and har￾monic current)

■ 120 percent of peak voltage (including harmonics)

Table 5.1 summarizes an example capacitor evaluation using a com￾puter spreadsheet that is designed to help evaluate the various capac￾itor duties against the standards.

The fundamental full-load current for the 1200-kvar capacitor bank

is determined from

IC


50.2 A

The capacitor is subjected principally to two harmonics: the fifth and

the seventh. The voltage distortion consists of 4 percent fifth and 3 per￾cent seventh. This results in 20 percent fifth harmonic current and 21

percent seventh harmonic current. The resultant values all come out

1200

3 13.8

kvar3

3 kVLL

210 Chapter Five

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well below standard limits in this case, as shown in the box at the bot￾tom of Table 5.1.

5.10.2 Impact on transformers

Transformers are designed to deliver the required power to the con￾nected loads with minimum losses at fundamental frequency.

Harmonic distortion of the current, in particular, as well as of the volt￾age will contribute significantly to additional heating. To design a

transformer to accommodate higher frequencies, designers make dif￾ferent design choices such as using continuously transposed cable

instead of solid conductor and putting in more cooling ducts. As a gen￾eral rule, a transformer in which the current distortion exceeds 5 per￾cent is a candidate for derating for harmonics.

There are three effects that result in increased transformer heating

when the load current includes harmonic components:

1. RMS current. If the transformer is sized only for the kVA require￾ments of the load, harmonic currents may result in the transformer

rms current being higher than its capacity. The increased total rms

current results in increased conductor losses.

2. Eddy current losses. These are induced currents in a transformer

caused by the magnetic fluxes. These induced currents flow in the

windings, in the core, and in other conducting bodies subjected to

the magnetic field of the transformer and cause additional heating.

This component of the transformer losses increases with the square

of the frequency of the current causing the eddy currents. Therefore,

Fundamentals of Harmonics 211

0 10 20 30

–200

–150

–100

–50

0

50

100

150

200

Time (ms)

Current (A)

Figure 5.32 Typical capacitor current from a system in 11th-harmonic resonance.

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this becomes a very important component of transformer losses for

harmonic heating.

3. Core losses. The increase in core losses in the presence of harmon￾ics will be dependent on the effect of the harmonics on the applied

voltage and the design of the transformer core. Increasing the volt￾age distortion may increase the eddy currents in the core lamina￾tions. The net impact that this will have depends on the thickness of

212 Chapter Five

Recommended Practice for Establishing Capacitor Capabilities

When Supplied by Nonsinusoidal Voltages IEEE Std 18-1980

Capacitor Bank Data:

Bank Rating: 1200 kVAr

Voltage Rating: 13800 V (L-L)

Operating Voltage: 13800 V (L-L)

Supplied Compensation: 1200 kVAr

Fundamental Current Rating: 50.2 Amps

Fundamental Frequency: 60 Hz

Capacitive Reactance: 158.700 Ω

Harmonic Distribution of Bus Voltage:

Harmonic

Number

Frequency

(Hertz)

Volt Mag Vh (% of Fund.)

Volt Mag Vh (Volts)

Line Current Ih (% of Fund.)

1 60 100.00 7967.4 100.00

3 180 0.00 0.0 0.00

5 300 4.00 318.7 20.00

7 420 3.00 239.0 21.00

11 660 0.00 0.0 0.00

13 780 0.00 0.0 0.00

17 1020 0.00 0.0 0.00

19 1140 0.00 0.0 0.00

21 1260 0.00 0.0 0.00

23 1380 0.00 0.0 0.00

25 1500 0.00 0.0 0.00

Voltage Distortion (THD): 5.00 %

RMS Capacitor Voltage: 7977.39 Volts

Capacitor Current Distortion: 29.00 %

RMS Capacitor Current: 52.27 Amps

Capacitor Bank Limits:

Calculated Limit Exceeds Limit

Peak Voltage: 107.0% 120% No

RMS Voltage: 100.1% 110% No

RMS Current: 104.1% 180% No

kVAr: 104.3% 135% No

TABLE 5.1 Example Capacitor Evaluation

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the core laminations and the quality of the core steel. The increase

in these losses due to harmonics is generally not as critical as the

previous two.

Guidelines for transformer derating are detailed in ANSI/IEEE

Standard C57.110-1998, Recommended Practice for Establishing

Transformer Capability When Supplying Nonsinusoidal Load

Currents. The common K factor used in the power quality field for

transformer derating is also included in Table 5.2.2

The analysis represented in Table 5.2 can be summarized as follows.

The load loss PLL can be considered to have two components: I2R loss

and eddy current loss PEC:

PLL
I2

R  PECW (5.27)

The I2R loss is directly proportional to the rms value of the current.

However, the eddy current is proportional to the square of the current

and frequency, which is defined by

PEC
KEC I2 h2 (5.28)

where KEC is the proportionality constant.

The per-unit full-load loss under harmonic current conditions is

given by

PLL
∑ Ih

2  (∑ Ih

2 h2 ) PEC  R (5.29)

where PEC  R is the eddy current loss factor under rated conditions.

The K factor3 commonly found in power quality literature concerning

transformer derating can be defined solely in terms of the harmonic

currents as follows:

Fundamentals of Harmonics 213

TABLE 5.2 Typical Values of PEC  R

Type MVA Voltage PEC  R, %

Dry 1 — 3–8

1.5 5 kV HV 12–20

1.5 15 kV HV 9–15

Oil-filled 2.5 480 V LV 1

2.5–5 480 V LV 1–5

5 480 V LV 9–15

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K
(5.30)

Then, in terms of the K factor, the rms of the distorted current is

derived to be

∑ Ih 2
 (pu) (5.31)

where PEC  R
eddy current loss factor

h
harmonic number

Ih
harmonic current

Thus, the transformer derating can be estimated by knowing the per￾unit eddy current loss factor. This factor can be determined by

1. Obtaining the factor from the transformer designer

2. Using transformer test data and the procedure in ANSI/IEEE

Standard C57.110

3. Typical values based on transformer type and size (see Table 5.2)

Exceptions. There are often cases with transformers that do not appear

to have a harmonics problem from the criteria given in Table 5.2, yet are

running hot or failing due to what appears to be overload. One common

case found with grounded-wye transformers is that the line currents

contain about 8 percent third harmonic, which is relatively low, and the

transformer is overheating at less than rated load. Why would this

transformer pass the heat run test in the factory, and, perhaps, an over￾load test also, and fail to perform as expected in practice? Discounting

mechanical cooling problems, chances are good that there is some con￾ducting element in the magnetic field that is being affected by the har￾monic fluxes. Three of several possibilities are as follows:

■ Zero-sequence fluxes will “escape” the core on three-legged core

designs (the most popular design for utility distribution substation

transformers). This is illustrated in Fig. 5.33. The 3d, 9th, 15th, etc.,

harmonics are predominantly zero-sequence. Therefore, if the winding

connections are proper to allow zero-sequence current flow, these har￾monic fluxes can cause additional heating in the tanks, core clamps,

etc., that would not necessarily be found under balanced three-phase

or single-phase tests. The 8 percent line current previously mentioned

1  PEC  R

1  K PEC  R

∑ (Ih

2 h2

)

∑ Ih

2

214 Chapter Five

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