**9. Thd theory and verification calaculations**

The percentage of Total Harmonic Distortion (%THD) can be defined in two different ways, as a percentage of the fundamental component (the IEEE definition of THD) or as a percentage of the RMS (used by the Canadian Standards Association and the IEC).

$$\text{THD} = \frac{\sqrt{\sum\_{n=2}^{n} Irms} n}{I\_1} \tag{9.1}$$

Where, Irms, n is the amplitude of the harmonic component of order n (i.e., the nth harmonic). The numerator gives the RMS current due to all harmonics and I1 is the RMS value of fundamental component of current only. Given above is the mathematical form of the IEEE. According to IEC standards, the mathematical form of THD is given below:

$$\text{THID} = \frac{\sqrt{\sum\_{n=2}^{2} Irms\_n n}}{I\_1} \tag{9.2}$$

Where

226 Power Quality Harmonics Analysis and Real Measurements Data

Point 1 10.6% 10.7% 10.8% 1.5-1.6 Third Point 2 29% 28.4% 28.9% 1.5 Fifth Point 3 19.6% 19.9% 20.6% 1.5 Fifth

263 28.3A 14.8A 5.2A 0.4A 0.7A 0.1A 0.4A 0.1A 10.4 204 27.1A 13.1A 4.6A 1.4A 0.7A 0.4A 0.7A 0.1A 9.9 170 25.6A 12.5A 4.2A 1.8A 0.8A 0.4A 0.5A 0.1A 9.6

International Standards have set some limits to the most equipment on the permissible harmonic content in the electrical system during operation. The following are general limits

d. Electronic equipment: 5% voltage distortion with a maximum individual percentage of

Most utilities have adopted standards to limit the harmonic content at the point of common

The percentage of Total Harmonic Distortion (%THD) can be defined in two different ways, as a percentage of the fundamental component (the IEEE definition of THD) or as a

> 2 1

*I*

*n*

  2

*Irms n*

,

(9.1)

percentage of the RMS (used by the Canadian Standards Association and the IEC).

**Max THD in the third period** 

%age Mag. of 11th Harmonic

%age Mag. of 13th Harmonic

**Crest Factor** 

> %age Mag. of 15th Harmonic

%age Mag. of 17th Harmonic

THD %

**Highest Harmonic Order** 

**Max THD in the second period** 

Table 6. Summary of the obtained results for the three points of Bldg. 14

%age Mag. of 9th Harmonic

%age Mag. of 7th Harmonic

Table 7. Harmonic magnitudes for different No. of PC's at point 1

a. Synchronous machine: permissible stator current distortion < 1.4%

c. Cable: permissible core-shielding voltage distortion < 10%

b. Asynchronous machines: permissible stator current distortion; 1.5% to 3.5%

e. Transformer: permissible current distortion <5% at full load [ IEEE-519 ]

coupling (PCC). Some of the Standards adapted around the world include:

**Location** 

No. of PC's %age Mag. of 3rd Harmonic

**8.5 Standards and limits** 

 US/Canada IEEE 519 Europe IEC61000 3-2, 3-4 United Kingdom G5/4 -1 China GB/T 14549

for various electrical equipments:

3% depending on the equipment

**9. Thd theory and verification calaculations** 

THD =

**Max THD in the first period** 

%age Mag. of 5th Harmonic

$$\mathbf{I}\_{\text{rms}} = \sqrt{\sum\_{n=1}^{m} I\_{Imn}^{2}} \tag{9.3}$$

Where Irms, n is the amplitude of the harmonic component of order n (i.e., the nth harmonic) and Irms is the rms value of all the harmonics plus the fundamental component of the current. The later standard is referred in this study, because the apparatus used for analysis was based on IEC Standards.

The 3rd, 5th, 7th and 9th harmonics being the most significant, the definition of THD may be modified and written as in 9.4

THD = <sup>2222</sup> *Irms Irms Irms Irms* ,3 ,5 ,7 ,9 *Irms* (9.4)

The value of THD may be calculated for any number of computers using formula (9.3). Irms = 308.4 A

RMS magnitude of 3rd Harmonic= 25.6 A

RMS magnitude of 5th Harmonic= 12.5 A

RMS magnitude of 7th Harmonic= 4.2 A

RMS magnitude of 9th Harmonic= 1.8 A

$$\text{THD} = \frac{\sqrt{25, 6^2 + 12, 5^2 + 4, 2^2 + 1, 8^2}}{308, 4} = 9.36\% \tag{9.5}$$

Figure 9 is showing the magnitude of individual harmonics, when 263 PCs in building 14 were connected to the supply mains.

Fig. 7. Harmonic spectrums at point one when 263 PC's operating

Harmonics Effect in Industrial and University Environments 229

2 2 22 3 600 112 1 2271

The online value of THD was 26.8%. The percentage difference (Error) of the calculated and

According to the previous measurements it has been observed that the total harmonic distortion at point two (29 %) is much greater than that at point one (10.8%). Since there is no load connected between these two points except the Uninterruptible power supply (UPS), it is considered that UPS is the main reason for this difference. The UPS can be considered to fit 'in-line' between the loads and the mains power supply. In addition to providing power protection to the loads, it should also protect the main power supply itself from getting any harmonics generated by the loads themselves. However, it is again not commonly known that UPS and their design being power electronics oriented, also generate harmonic pollution. For any UPS this is typically stated as Total Harmonic Distortion (THD). Care has to be taken when comparing different THD values as these can differ when contrasting the two different types of on-line UPS (transformer-based and transformer less)

> %age Mag. of 9th Harmonic

263 1.6 33.7 6.4 0.1 7.6 4.4 0.1 19.7 204 1.6 33.6 4.7 0.1 7.9 3.5 0.1 20.6 170 1.4 33.5 4.3 0.1 7.8 3.5 0.1 20.6

Table 8 indicates the online value of THD is 19.7%. The difference of the calculated and experimental value of 0.37% as shown in table 9. This difference caused again by other odd harmonics being neglected, however, such low error proves the validity of measurement and it consequently plays a pivotal role for the accurate analysis of the odd harmonics.

**Location Calculated values Experimental values %age Error Point 1** 9.36 9.60 0.24 **Point 2** 26.7 26.8 0.10 **Point 3** 19.3 19.7 0.37 Table 9. Comparison of calculated and experimental values when 263 PC'S were connected

%age Mag. of 11th Harmonic

%age Mag. of 13th Harmonic

%age Mag. of 15th Harmonic THD r%

and also with regard to the percentage of load applied for each measurement.

%age Mag. of 7th Harmonic

Table 8. Magnitudes of harmonics for different numbers of PC's at point 3

= 26.7% (9.7)

RMS magnitude of 5th Harmonic= 600 A RMS magnitude of 7th Harmonic= 112 A RMS magnitude of 9th Harmonic= 1A

**10. Thd measurements discussion** 

experimental value is 0.1%.

No. of PC's (N)

%age Mag. of 3th Harmonic

%age Mag. of 5th Harmonic

THD =

The online value of THD was 9.6%. The percentage difference (Error) of the calculated and experimental value is 0.24%.

This difference caused by neglecting other odd harmonics such small error proves the validity of measurement using this PQA and it consequently plays a pivotal role for the accurate analysis of the odd harmonics.

Figure 8 explains the overall impact of individual harmonics cumulatively. Total Harmonic Distortion (THD) in line current is increasing when the electronic loads are increasing. Among odd harmonics only third harmonic plays active role whereas the other odd harmonics impact with increase in electronic loads is negligible.

By using linear interpolation, the relation between THD in current and the number of PC's (N) is given by the following equation:

 **It** = 8.143 + 0.008 x *N* (9.6)

Fig. 8. THD curve vs. No. of PC's at point 1.

Fig. 9. Harmonic spectrums at point 2 when 263 PC's operating

The value of THD may be calculated for any number of computers with formula (9.4). Figure 9 is showing the magnitude of individual harmonics, when 263 PCs were connected to the supply mains.

```
Irms = 2271 A
```
RMS magnitude of 3rd Harmonic= 3 A

RMS magnitude of 5th Harmonic= 600 A RMS magnitude of 7th Harmonic= 112 A RMS magnitude of 9th Harmonic= 1A

228 Power Quality Harmonics Analysis and Real Measurements Data

The online value of THD was 9.6%. The percentage difference (Error) of the calculated and

This difference caused by neglecting other odd harmonics such small error proves the validity of measurement using this PQA and it consequently plays a pivotal role for the

Figure 8 explains the overall impact of individual harmonics cumulatively. Total Harmonic Distortion (THD) in line current is increasing when the electronic loads are increasing. Among odd harmonics only third harmonic plays active role whereas the other odd

By using linear interpolation, the relation between THD in current and the number of PC's

 **It** = 8.143 + 0.008 x *N* (9.6)

experimental value is 0.24%.

accurate analysis of the odd harmonics.

(N) is given by the following equation:

Fig. 8. THD curve vs. No. of PC's at point 1.

to the supply mains.

RMS magnitude of 3rd Harmonic= 3 A

Irms = 2271 A

Fig. 9. Harmonic spectrums at point 2 when 263 PC's operating

The value of THD may be calculated for any number of computers with formula (9.4). Figure 9 is showing the magnitude of individual harmonics, when 263 PCs were connected

harmonics impact with increase in electronic loads is negligible.

$$\text{THD} = \frac{\sqrt{3^2} + 600^2 + 112^2 + 1^2}{2271} = 26.7\% \tag{9.7}$$

The online value of THD was 26.8%. The percentage difference (Error) of the calculated and experimental value is 0.1%.
