mains harmonics(zm mhlongo)
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University of KwaZulu±Natal
School of Electrical, Electronic and Computer Engineering
Mains Harmonics
ZM Mhlongo
208528095
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Abstract
This report investigates the mains distortion caused by non linear loads. A rectifier connected to a
resistive load is used as the non linear load. After observations are made with regards to performance
various harmonic curbing techniques are investigated. Inductive coupling and 5th
harmonic filter are
employed and the results are discussed in terms of the effect each has on the system. Simulink
SimPowerSystems library is used to simulate those circuits. The Analysis is done using the PowerGui FFT
analysis tool. A comparison is made with the schemes given in five circuits and simulations divided,
correspondingly to five parts.
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Introduction
Electric utilities supply power at sinusoidally varying voltages, the frequency of these sinusoids is
ussually 50 or 60Hz. In South Africa the standard is 50Hz. There are basically two types of loads, linear
and non linear. The linear loads do not present a problem since the current drawn by them is sinusoidal
as well. The problem comes when the loads connected to the power supply are non linear, these devices
draw a non linear current and thus cause a distortion in the input current.
The resulting waveform can be approximated using sinusoids via the Fourier analysis. The resulting
sinusoids start at the power system frequency and appear as interger multiples of the fundamental
frequency. The effect of these devices is not very desirable and can cause a decay in porformance of thepower grid.
Theory
Definition
Harmonics are a mathematical way of describing distortion to a voltage or current waveform. Fourier
analysis allows for the use of sinusoids to represent any waveform by a sum of sinusoids. The term
harmonic refers to a component of a waveform that occurs at an integer multiple of the fundamental
frequency. Figure 1 illustrates how harmonics affect the fundamental current.
Figure 1: Effects of harmonics on the fundamental frequency sinusoid.
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After a process of observing the load current and adjusting the resistive load, the current was set to 1A
with some ripple. This was achieved when the resistor was set at 300 ohms. The waveform of the
current through the load is shown in figure 3.
Figure 3 : Load Current Waveform
The supply voltage waveform is shown in figure 4. Some harmonic distortion is present, although not
alarmingly large. The rectifier shows minimal disturbance in the supply voltage.
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Figure 4 : Supply Voltage Waveform
The supply current waveform differs much from a sinusoid, indicating large harmonic distortion present
in the current due to current blocking in the diodes in the rectifier. This is shown in figure 5.
Figure 5 : Supply Current Waveform
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The load voltage is displayed in figure 6, with a ripple but centered to approximately 300V.
Figure 6 : Load Voltage Waveform
The ripple in the voltage is calculated in this way
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Figure 7 : FFt Analysis Tool for Part 1
Using the Power GUI analysis tool the results obtained were analyzed to give the following
Fundamental value of input current(rms)
Total harmonic distortion
Total input current(rms) =
3. Harmonic Numbers Present
Current : 5, 7, 11, 13, 17, 19
Voltage : 2, 4
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4. & 5.
Figure 8 : Diode Voltage and Current Waveform
For the diode current
Fundamental value of input current(rms)
Total harmonic distortion
Total input current(rms) =
6. Diode rating
A safety factor of 1.5 was used and the values obtained from the graph of the diodes current and
voltage waveforms, together with the FFT tool for the current.
The PIV was found to be approximately 325V
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Figure 11 : Current Waveforms for circuit two.
The inrush of current during starting causes the capacitor to add a proportinal voltage this causes a
transient a during the circuits startup. The voltage observed during startup peaks at an excess of 600V.
After the current reaches a stedy varying waveform, the voltage stabilizes with some ripple.
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Figure 12 : Voltage Waveform Across the Load
This ripple is larger by 22.2% when compared to that of part one.
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Figure 13: FFT Analysis Results.
Fundamental value of input current(rms)
Total harmonic distortion
Total input current(rms) =
3. Harmonic Numbers Present
Current : From 2 to 19 are present
Voltage : None
Virtually no harmonics can be are present in the voltage waveform, the current shows more harmonics
and the effect of 2 to 19, as shown by the FFT tool, is evident.
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Figure 14 : Diode Voltage & Current plot
For the diode current
Fundamental value of input current(rms)
Total harmonic distortion
Total input current(rms) =
6. Diode rating
PIV rating = 1.5(PIV )= 1.5*(346) = 519V
Irms rating = 1.5*I = 1.5*1.036 = 1.554A
Conclusion.
The addition of the capacitor reduces the harmonics in the supply voltage. This can be seen as a goodresult. However, the total harmonic distortion in the current waveform increased from 66.72% to
216.74%. This coupled with the fact that the current waveforms appear different from each other leads
to the conclusion that the capacitor is detrimental to the system.
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Part 3
Inductors were added in the circuit of part two to form the third circuit. The effect of linking the rectifier
and supply with inductors is investigated next. The model used is shown in figure
Figure 15 : Model for Part 3
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The voltage outpu from the supply is smoother, with less harmonics affecting it. As evident in figure 16.
Figure 16 : Supply Voltage Against time
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The addition of the inductors positively influenced the durrent waveform, less harmonic distortion is
observed. Although the harmonics were reduced, the problem of different pahse current magnitudes is
not solved by this addition.
Figure 17 : Supply Current After the Addition of Inductors
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Figure 18 : Load Voltage waveform
Besides the increase in the magnitude of the transient, a lower ripple is observed as compared to parts 1
and 2. The ripple voltage is 41% lower than that of part one.
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Figure 19: FFT Results
Fundamental value of input current(rms)
Total harmonic distortion
Total input current(rms) =
3. Harmonic Numbers Present
Current : 5, 7, 11, 13
Voltage : None
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Figure 20 : Diode Voltage and Current waveforms
For the diode current
Fundamental value of input current(rms)
Total harmonic distortion
Total input current(rms) =
6. Diode rating
PIV rating = 1.5(PIV )= 1.5*(329) = 493.5V
Irms rating = 1.5*I = 1.5*1.036 = 0.924A
Conclusion
The total harmonic distortion has decreased to 66.72%, from the 216.74% when there was no inductivelink. The diodes use will require a lower rating since the PIV is lower and the rms Input current as well.
The inductive link can be regarded as a good addition since it improved all aspects of the circuits.
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Part 4
Part four investigates the effect of inductively linking the parallel RC load with the rectifier. The effects if
this is shown on the supply voltage and current as well as the load.
Figure 21 : Model Used to simulate Circuit Four
Figure 22 : Supply Voltage Plot Against Time
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The supply voltage deteriorated with this new configuration. There is more distortion, although close
resemblance to a sinusoid is evident. The method used earlier, in circuit three is better.
Figure 23 : Supply Current Plot
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Figure 24 : DC Output Voltage
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Fundamental value of input current(rms)
Total harmonic distortion
Total input current(rms) =
3. Harmonic Numbers Present
Current : 3, 5, 7
Voltage : None
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For the diode current
Fundamental value of input current(rms)
Total harmonic distortion
Total input current(rms) =
6. Diode rating
PIV rating = 1.5(PIV )= 1.5*(325) = 487.5V
Irms rating = 1.5*I = 1.5*0.578 = 0.867A
Conclusion
Although this scheme causes some distortion in the supply voltage waveform, the distortion is quite
small. The main benefit that differs from the previous scheme is that the current waveforms are the
same and the distortion is less (56.52% compared to 68.2%). The ripple voltage is the same
Part 5
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The DC ripple voltage is varies and its maximum is :
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While its minimum is
Fundamental value of input current(rms)
Total harmonic distortion
Total input current(rms) =
3. Harmonic Numbers Present
Current : 5
Voltage : 5
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For the diode current
Fundamental value of input current(rms)
Total harmonic distortion
Total input current(rms) =
6. Diode rating
PIV rating = 1.5(PIV)= 1.5*(355) = 532.5V
Irms rating = 1.5*I = 1.5*1.206 = 1.8087A
Conclusion
The filter increases the distortion of the voltage and current. From the FFT analysis it can be seen that
the 5th
order harmonic which is supposed to be filtered, is the more prominent one compared to the
other harmonics. This might be a result of the limited elements available for its design. The input current
shows an increase also. The ratings of the diode have to be increased as well if the filter is in use
campared to the other schemes
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Overall Conclusion
Harmonics are detrimental to the power system and the equipment adjacent to the device causing
them. Various schemes to minimize this were investigated, inductive coupling of the load, inductive
coupling of the source with the rectifier and the fifth order filter were simulated and analyzed in this
practical. Some results were rather difficult to explain. The differences between these schemes were
observed in the simulations. From the simulation, linking the rectifier and the supply with inductors
proved most effective albeit the different current waveforms for the different phases.
In an application where the current waveform similarity is crucial, the method of inductively linking the
load is prudent. The filter, although thought to be the best manner to handle harmonics, proved
ineffective and actually detrimental.
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References
1.Ellis, R., 2001. Power System Harmonics. [Online].
http://samplecode.rockwellautomation.com/idc/groups/literature/documents/wp/mvb-wp011_-en-p.pdf [01 June
2011]
2. http://www.joliettech.com/abb_guide-to-harmonics-with-ac-drives.htm [01 June 2011]
3. Kreide, P., Power Quality [Online] http://www.docstoc.com/docs/21314824/REDUCTION-OF-LINE-
LOSSES-VOLTAGE-STABILIZATION-POWER-FACTOR [01 June 2011]
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