The document discusses transformer metering, heating, and harmonics. It covers harmonic conditions and their effects on three-phase transformers and current transformers. It presents standards for harmonic distortion limits. Finite element analysis was used to model and analyze a three-phase isolation transformer under harmonic conditions. Experimental results validated the finite element model. Temperature rise calculations were also presented for a 2.5MVA three-phase isolation transformer.

1. Transformers: Metering, Heating and
Harmonics
Michael Robert Larkin
Managing Director at Tortech Pty Ltd
ENGINEERS
AUSTRALIA
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OUTLINE
 Harmonics and three phase
transformers
 Three-phase metering units for solar
installation
 CT design under power grid harmonic
conditions
 Temperature rise calculation of three-
phase isolation transformers
Design of suitable enclosure for three-
phase transformers under harmonic
conditions2

4. Harmonics and three phase transformers
What Are Harmonics?
4
+
+
+
+
50 Hz
(Fundamental
Frequency)
150 Hz
(h=3)
250 Hz
(h=5)
350 Hz
(h=7)
450 Hz
(h=9)
Non-Sinusoidal Signal
 Defined by ANSI/IEEE Std. 519-1981
 Distorting the waveform and changing its magnitude.
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5. Three-phase metering units for solar installation
33KV Metering Unit
22 KV Metering Unit with 3 phase Current Transformers
22 KV Metering Unit 12 Core CT's
J.S Hansom Pty. Ltd.5
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CT design under power grid harmonic conditions
 The phase angle error affects the accuracy of the measurement when
harmonic powers are measured.
 The magnetizing current is the cause of angle error.
 The lower the ferromagnetic core permeability the larger becomes the
magnetizing current and the phase angle error.
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CT design under power grid harmonic conditions
Power frequencies Magnetic error
Higher frequencies Capacitive error
Increase the apparent permeability of the magnetic core
Decrease the number of turns in the ratio windings
To be Minimized
To be Minimized
7

8. CT design under power grid harmonic conditions
550kv Current Transformer for ECNSW
Cascade HV Magnetic Voltage Transformer
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9. Effect Of Harmonics On Transformers:
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Harmonics and three phase transformers
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Harmonics and three phase transformers
Fluke 435 series II power quality and energy analyser
EEP Electrical Engineering Portal10

11. ANSI/IEEE standard 519-2014: Voltage harmonic distortion limits
Harmonics and three phase transformers
Bus voltage V at PCC Individual harmonic (%) Total Harmonic Distortion (%)
V ≤ 1kV 5 8
1 kV < V ≤ 69 kV 3 5
69 kV < V ≤ 161 kV 1.5 2.5
161 kV < V 1 1.5
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12. Odd harmonics non-
multiple of 3
Odd harmonics
multiple of 3
Even harmonics
Order h Harmonic
voltage %
Order h Harmonic
voltage %
Order h Harmonic
voltage %
5 6 3 5 2 2
7 5 9 1.5 4 1
11 3.5 15 0.3 6 0.5
13 3 21 0.2 8 0.5
17 2 >21 0.2 10 0.5
19 1.5 12 0.2
23 1.5 >12 0.2
25 1.5
>25 0.2+1.3×(25/h)
NOTE: Total Harmonic Distortion (THD)=8%
Australia/New Zealand standard AS/NZS 61000-3-6 limits- Assessment of emission limits for distorting load in
MV and HV power systems
Harmonics and three phase transformers
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13. IEC Standard 61000-3-6: Compatibility levels for individual harmonics voltages in low and medium voltage
networks in percent of fundamental voltage
Harmonics and three phase transformers
Odd harmonics non-multiple
of 3
Odd harmonics multiple
of 3
Even harmonics
Order h Harmonic
%
Order h Harmonic
voltage %
Order h Harmonic voltage
%
5 6 3 5 2 2
7 5 9 1.5 4 1
11 3.5 15 0.3 6 0.5
13 3 21 0.2 8 0.5
17≤h≤49 2.27×(17/h)-0.27 21<h≤45 0.2 10≤h≤50 0.25× (10/h)+0.25
NOTE: NOTE: Total Harmonic Distortion (THD)=8%
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14. EN 50160:2010 Voltage characteristics of electricity supplied by public electricity networks
Harmonics and three phase transformers
Odd harmonics non-
multiple of 3
Odd harmonics multiple
of 3
Even harmonics
Order h Harmonic
voltage %
Order h Harmonic
voltage %
Order h Harmonic
voltage %
5 6 3 5 2 2
7 5 9 1.5 4 1
11 3.5 15 0.5 6…24 0.5
13 3 21 0.5
17 2
19 1.5
23 1.5
25 1.5
NOTE: No values are given for harmonics of order higher than 25, as they
usually small, but largely unpredictable due to resonance effects.
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15. IEEE C57.110-2008
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𝑃𝑡𝑜𝑡 = 𝑃𝐿 + 𝑃𝐶
𝑃𝐿 = 𝑃 𝐷𝐶 + 𝑃𝐸𝐶 + 𝑃𝑂𝑆𝐿
𝑃 𝐷𝐶−ℎ = 𝑅 𝐷𝐶 ×
ℎ=1
ℎ 𝑚𝑎𝑥
𝐼ℎ 𝑟𝑚𝑠
2
𝑃𝐸𝐶−ℎ = 𝑃𝐸𝐶−𝑅 ×
ℎ=1
ℎ 𝑚𝑎𝑥
𝐼ℎ 𝑟𝑚𝑠
𝐼1
2
× ℎ2
𝑃𝐶 = 𝑃 𝐻 + 𝑃𝐸 = 𝑘 𝐻 × 𝑓 × 𝐵 𝑚
𝑛
+ 𝑘 𝐸 × 𝑓2
× 𝑡2
× 𝐵 𝑚
2
𝑃𝐶−ℎ = 𝑃𝐶−𝑟 ×
1
ℎ
𝑉𝑝−ℎ
𝑉𝑝−𝑟
𝑚
×
1
ℎ2.6
𝑃𝑂𝑆𝐿−ℎ = 𝑃OSL−𝑅 ×
ℎ=1
ℎ 𝑚𝑎𝑥
𝐼ℎ 𝑟𝑚𝑠
𝐼1
2
× ℎ0.8
15

16. Finite Element Analysis of Three-phase Transformers under
Harmonics
 FEM has proven itself as an effective numerical method that
takes into account the geometry complexity, material
properties, saturation effects and non-linearities
 A real three-phase isolation transformer is analyzed and
modelled in Ansys Electronic Desktop (AED)
 Different tests were performed to obtain the initial results
and check the transformer characteristics.
Three-phase isolation transformer employed
for FEM simulations
Majid Malekpour, Michael Larkin, Ganesh Surendran, and Toan Phung, “Core Loss Studies using FEM of a Three Phase Isolation Transformer
under Harmonic Conditions”, the 2nd IEEE International Conference on Electrical Materials and Power Equipment (ICEMPE 2019), April 7th-
10th, 2019, Guangzhou, China.
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17. Finite Element Analysis of Three-phase Transformers under Harmonics
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Detailed flowchart of the proposed model in FEM
(2.5MVA, 80kVA, and 300VA three-phase isolation
transformers
17

18. Finite Element Analysis of Three-phase Transformers under Harmonics
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Magnetizing curve of the core material Core loss curves of the core material
3D modelling of the isolation transformer under mesh operation
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19. Finite Element Analysis of Three-phase Transformers under Harmonics
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EXPERIMENTAL AND SIMULATION RESULTS
Core loss curves at different frequencies
20

21. Finite Element Analysis of Three-phase Transformers under Harmonics
Primary voltages obtained for an 80kVA three-phase isolation transformer
Secondary voltages obtained for an 80kVA three-phase isolation transformer21

22. Finite Element Analysis of Three-phase Transformers under Harmonics
Primary currents obtained for an 80kVA three-phase isolation transformer
Core loss obtained for an 80kVA three-phase isolation transformer22

23. Finite Element Analysis of Three-phase Transformers under Harmonics
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Eddy current and hysteresis losses obtained in FEM
23
Eddy current loss
Hysteresis loss
Eddy current loss
Hysteresis loss

24. Finite Element Analysis of Three-phase Transformers under Harmonics
 The model in FEM requires validation
 Experiments are carried out to evaluate the proposed
modelling approach.
 A 3-phase, 300 VA, YD, 415/415 V, 50 Hz, isolation
transformer is fed through the AMETEK CSW55
programmable power supply
 Current is measured through a current probe and sent to
computer via a National Instruments PCI 6024E data
acquisition board.
UNSW High Voltage Laboratory
24
AMETEK
CSW55
Transformer
Set up Inside
the Cage
Personal
Computer
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25. Finite Element Analysis of Three-phase Transformers under Harmonics
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The measured core loss under pure sinusoidal input voltage is 8.381 W and 7.2194 W for experiment and FEM, respectively.
The results show 13.86% difference between FEM and experiment which demonstrates the accuracy of the FEM model
Primary Current
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EXPERIMENTAL AND SIMULATION RESULTS
Case I:
Fundamental Frequency
100%
2nd Harmonic Component 8th Harmonic Component
0%0%
Core Loss (Experiment) = 8.381 W
Core Loss (FEM) = 7.2194 W
Primary Voltage Primary Current
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EXPERIMENTAL AND SIMULATION RESULTS
Case II:
Fundamental Frequency
100%
2nd Harmonic Component 8th Harmonic Component
2.5%10%
Core Loss (Experiment) = 8.405 W
Core Loss (FEM) = 7.2298 W
Primary Voltage Primary Current
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EXPERIMENTAL AND SIMULATION RESULTS
Case III:
Fundamental Frequency
100%
2nd Harmonic Component 8th Harmonic Component
10%10%
Core Loss (Experiment) = 9.28571 W
Core Loss (FEM) = 7.8962 W
Primary Voltage Primary Current
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EXPERIMENTAL AND SIMULATION RESULTS
Case IV: Highest percentage of each harmonic order defined by IEC 61000-3-6 Standard
Core Loss (Experiment) = 16.19 W
Core Loss (FEM) = … W
Primary Voltage Primary Current
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EXPERIMENTAL AND SIMULATION RESULTS
INCREASED LOSS PERCENTAGE BETWEEN CASE I AND OTHER CASES (%)
Experiment FEM
Case I - -
Case II 0.28 % 0.15 %
Case III 10.8 % 9.37 %
Case IV 94.78 % -
30
Case I:
Fundamental Frequency
100%
2nd Harmonic Component 8th Harmonic Component
0%0%
Case II: 100% 2.5%10%
Case III: 100% 10%10%
Case IV: Highest percentage of each harmonic order defined by IEC 61000-3-6 Standard

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K-Factor Transformers
 As derived from ANSI/IEEE C57.110, a K-factor of 1.0 indicates a linear load (no harmonics). The higher the
K-factor, the greater the harmonic heating effects.
 Transformers come in basic K-factors such as 4, 9,13, 20, 30, 40, and 50.
K-Factor = 1
34 𝑖ℎ×ℎ 2
1
34 𝑖ℎ
2
h is the harmonic number
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K-Factor Transformers
 shield between the two windings
 smaller conductor section size
 larger overall conductors
 larger neutral conductors
 high quality magnetic steel core
 thinner laminations
 larger overall core size
 enhanced cooling system
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33. Tortech Pty Ltd
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Temperature rise calculation
2.5 MVA three-phase isolation transformer
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34. Temperature rise calculation
Temperature Rise Test Without Enclosure
Cold
Circumstances
test data
Cold resistance 𝐑 𝟏(Ω) Temperature 𝛉 𝟎𝟏
HV 0.2343 LV 0.0002766 8.9 ℃
No-load test Heat resistance 𝐑 𝟐(Ω) Temperature 𝛉 𝟎𝟐 Core temperature 𝛉 𝟏
HV 0.2363 LV 0.0002916 9.2 ℃ 89.1 ℃
Coil temperature rise
∆𝑄 𝑒=
𝑅2
𝑅1
× (235 + 𝜃01)-(235+𝜃02)
HV 1.7 K LV 12.38 K
Load test data Heat resistance 𝐑 𝟐𝐥(Ω) Temperature 𝛉 𝟎𝟐𝐥 Core temperature 𝛉 𝟏𝐥
HV 0.31548 LV 0.000372 8.9 ℃ 74 ℃
Coil temperature rise
∆𝑄𝑐=
𝑅2𝑙
𝑅1
× (235 + 𝜃01)-(235+𝜃02𝑙)
HV 81.04 K LV 80.67 K
Results Coil temperature rise
∆𝐐 𝐜𝐭= ∆𝐐 𝐜 × 𝟏 +
∆𝐐 𝐞
∆𝐐 𝐜
𝟏.𝟐𝟓 𝟎.𝟖
Core temperature
𝐓 = 𝛉 𝟏 − 𝛉 𝟎𝟐
HV 81.56 K LV 86.82 K 79.90 K
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35. Tortech Pty Ltd
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Temperature rise calculation
Temperature rise analysis for the 2.5MVA three-phase isolation transformer
based on the results obtained by FEM and open-air test set up
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36. Tortech Pty Ltd
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Temperature rise calculation
Number of Doors:
Section Row Column
Total Amount
of Louvres
A0
Row (L)
(m)
A0
Column (H)
(m)
A0
Total
(m^2)
A1 Total
(m^2)
φ
= A1/A0
A0
Total
(m^2)
A1 Total
(m^2)
φ
= A1/A0
A0
Total
(m^2)
A1 Total
(m^2)
φ
= A1/A0
4
Per Door:
Bottom Section (Inlet) 9 6 54 0.88 0.22 0.1936 0.00702 0.036260331 0.1936 0.00702 0.036260331
Top Section (Outlet) 9 6 54 0.88 0.22 0.1936 0.00702 0.036260331 0.1936 0.00702 0.036260331
Total for All Four Doors 432 1.5488 0.05616 0.036260331 0.7744 0.02808 0.036260331 0.7744 0.02808 0.036260331
HV Side:
Bottom Left (Inlet) 12 4 48 1.18 0.136 0.16048 0.00624 0.03888335 0.16048 0.00624 0.03888335
Bottom Centre (Inlet) 12 8 96 1.18 0.304 0.35872 0.01248 0.034790366 0.35872 0.01248 0.034790366
Bottom Right (Inlet) 12 4 48 1.18 0.136 0.16048 0.00624 0.03888335 0.16048 0.00624 0.03888335
Top Left (Outlet) 20 4 80 1.98 0.136 0.26928 0.0104 0.038621509 0.26928 0.0104 0.038621509
Top Centre (Outlet) 6 8 48 0.58 0.304 0.17632 0.00624 0.0353902 0.17632 0.00624 0.0353902 Length
Top Right (Outlet) 20 4 80 1.98 0.136 0.26928 0.0104 0.038621509 0.26928 0.0104 0.038621509 Width
Middle Left (Outlet) 18 4 72 1.78 0.136 0.24208 0.00936 0.038664904 0.26928 0.0104 0.038621509 Height
Middle Centre (Outlet) 18 8 144 1.78 0.304 0.54112 0.01872 0.034594914 0.26928 0.0104 0.038621509 Thickness
Middle Right (Outlet) 18 4 72 1.78 0.136 0.24208 0.00936 0.038664904 0.26928 0.0104 0.038621509
Total for HV 400 1.39456 0.052 0.037287747 0.71488 0.02704 0.03782453 0.67968 0.02496 0.036723164
LV Side:
Bottom Left (Inlet) 12 4 48 1.18 0.136 0.16048 0.00624 0.03888335 0.16048 0.00624 0.03888335
Bottom Centre (Inlet) 12 8 96 1.18 0.304 0.35872 0.01248 0.034790366 0.35872 0.01248 0.034790366
Bottom Right (Inlet) 12 4 48 1.18 0.136 0.16048 0.00624 0.03888335 0.16048 0.00624 0.03888335
Top Left (Outlet) 19 4 76 1.88 0.136 0.25568 0.00988 0.038642053 0.25568 0.00988 0.038642053
Top Right (Outlet) 18 4 72 1.78 0.136 0.24208 0.00936 0.038664904 0.24208 0.00936 0.038664904
Middle Left (Outlet) 21 4 84 2.08 0.136 0.28288 0.01092 0.038602941 0.24208 0.00936 0.038664904
Middle Centre (Outlet) 26 8 208 2.58 0.304 0.78432 0.02704 0.034475724 0.24208 0.00936 0.038664904
Middle Right (Outlet) 16 4 64 1.58 0.136 0.21488 0.00832 0.038719285 0.24208 0.00936 0.038664904
Total for LV 340 1.17744 0.0442 0.037539068 0.49776 0.01924 0.038653166 0.67968 0.02496 0.036723164
Total for Enclosure 1172 4.1208 0.15236 0.036973403 1.98704 0.07436 0.037422498 2.13376 0.078 0.036555189
86.82
19
40
145.82
Outlet
21875
A0 = Total Ventilation Area
2500kVA Unit
Losses: (W)
1.6
2.55
0.003
Centre line from Inlet to Outlet: (m)
Surface Cooling Area:
Dimensions of Enclosure: (m)
A2
Louvre Size (m^2):
0.00013
Key:
Total Inlet
2.3
1.3
Signature:
A1 = Total Ventilation Open (Slot) Area
A2 = Area of Single Opening (Slot)
Transformer Temperature Rise Class F (155°C)
Enclosure Temperature Comment:
Ambient Temperature The total temperature rise is less than the
insulation material class.Total Temperature Rise
Temperature Rise Test
Temperature Rise Measured Results (°C) Insulation Class
Inlet and outlet louvre geometry consideration for the 2.5MVA three-
phase isolation transformer
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37. Tortech Pty Ltd
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Temperature rise calculation
The designed Louvre size and geometry for
the 2.5MVA three-phase isolation
transformer
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38. Tortech Pty Ltd
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Temperature rise calculation
The designed enclosure for the 2.5MVA three-phase isolation
transformer
38

39. Magnetically Controlled Reactor (MCR)
Oil-immersed and Dry type Magnetically Controlled
Reactors (MCRs)
 Suppressing overvoltage
 Mitigating secondary ARC current
 Compensating the reactive power
 Voltage stabilization
 Mitigating voltage/current harmonics
It is a multifunctional device to increase the power quality by:
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40. Magnetically Controlled Reactor (MCR)
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Schematic diagram of primary part of MSVC complete unitMagnetic structure of the MCR
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41. Magnetically Controlled Reactor (MCR)
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Magnetic Core
Thyristors
Enclosure
MCR
Control Panel
Epoxy cast
winding

42. Magnetically Controlled Reactor (MCR)
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Angle View
Side View
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Magnetically Controlled Reactor (MCR)

44. Thank You
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Questions?