Rating of Transformers supplying Harmonic-Rich Loads David Chapman - - PowerPoint PPT Presentation

David Chapman Copper Development Association david.chapman@copperdev.co.uk

Copper Development Association

Rating of Transformers supplying Harmonic-Rich Loads

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Copper Development Association

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Losses in Transformers

No-load loss (‘iron loss’) – energy consumed in eddy current and hysteresis loss – present 100% of the time Load losses Resistive loss (‘copper loss’) – dependent on square of load current – most important during high load periods Eddy current loss

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Copper Development Association

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Distribution transformer efficiency standards

HD 428 & 538

Source: CENELEC

Load Losses for Distribution Transform ers No-Load Losses for Distribution Transform ers

RATED POW ER

OI L-FI LLED ( HD4 2 8 ) UP TO 2 4 kV2) DRY TYPE ( HD5 3 8 ) OI L-FI LLED ( HD4 2 8 ) UP TO 2 4 kV2) DRY TYPE ( HD5 3 8 ) LI ST A LI ST B LI ST C 1 2 kV PRI MARY

3)

LI ST A’ LI ST B’ LI ST C’ 1 2 kV PRI MARY 3) kVA W W W W W W W W 5 0 1 ,1 0 0 1 ,3 5 0 8 7 5 N/ A 1 9 0 1 4 5 1 2 5 N/ A 1 0 0 1 ,7 5 0 2 ,1 5 0 1 ,4 7 5 2 ,0 0 0 3 2 0 2 6 0 2 1 0 4 4 0 1 6 0 2 ,3 5 0 3 ,1 0 0 2 ,0 0 0 2 ,7 0 0 4 6 0 3 7 5 3 0 0 6 1 0 2 5 0 3 ,2 5 0 4 ,2 0 0 2 ,7 5 0 3 ,5 0 0 6 5 0 5 3 0 4 2 5 8 2 0 4 0 0 4 ,6 0 0 6 ,0 0 0 3 ,8 5 0 4 ,9 0 0 9 3 0 7 5 0 6 1 0 1 ,1 5 0 6 3 0 / 4 % 6 ,5 0 0 8 ,4 0 0 5 ,4 0 0 7 ,3 0 0 1 ,3 0 0 1 ,0 3 0 8 6 0 1 ,5 0 0 6 3 0 / 6 % 6 ,7 5 0 8 ,7 0 0 5 ,6 0 0 7 ,6 0 0 1 ,2 0 0 9 4 0 8 0 0 1 ,3 7 0 1 0 0 0 1 0 ,5 0 0 1 3 ,0 0 0 9 ,5 0 0 1 0 ,0 0 0 1 ,7 0 0 1 ,4 0 0 1 ,1 0 0 2 ,0 0 0 1 6 0 0 1 7 ,0 0 0 2 0 ,0 0 0 1 4 ,0 0 0 1 4 ,0 0 0 2 ,6 0 0 2 ,2 0 0 1 ,7 0 0 2 ,8 0 0 2 5 0 0 2 6 ,5 0 0 3 2 ,0 0 0 2 2 ,0 0 0 2 1 ,0 0 0 3 ,8 0 0 3 ,2 0 0 2 ,5 0 0 4 ,3 0 0

www.leonardo-energy.org

Copper Development Association

www.cda.org.uk

Distribution transformer efficiency standards

HD 428 & 538

Source: CENELEC

Load Losses for Distribution Transform ers No-Load Losses for Distribution Transform ers

RATED POW ER

OI L-FI LLED ( HD4 2 8 ) UP TO 2 4 kV2) DRY TYPE ( HD5 3 8 ) OI L-FI LLED ( HD4 2 8 ) UP TO 2 4 kV2) DRY TYPE ( HD5 3 8 ) LI ST A LI ST B LI ST C 1 2 kV PRI MARY

3)

LI ST A’ LI ST B’ LI ST C’ 1 2 kV PRI MARY 3) kVA W W W W W W W W 5 0 1 ,1 0 0 1 ,3 5 0 8 7 5 N/ A 1 9 0 1 4 5 1 2 5 N/ A 1 0 0 1 ,7 5 0 2 ,1 5 0 1 ,4 7 5 2 ,0 0 0 3 2 0 2 6 0 2 1 0 4 4 0 1 6 0 2 ,3 5 0 3 ,1 0 0 2 ,0 0 0 2 ,7 0 0 4 6 0 3 7 5 3 0 0 6 1 0 2 5 0 3 ,2 5 0 4 ,2 0 0 2 ,7 5 0 3 ,5 0 0 6 5 0 5 3 0 4 2 5 8 2 0 4 0 0 4 ,6 0 0 6 ,0 0 0 3 ,8 5 0 4 ,9 0 0 9 3 0 7 5 0 6 1 0 1 ,1 5 0 6 3 0 / 4 % 6 ,5 0 0 8 ,4 0 0 5 ,4 0 0 7 ,3 0 0 1 ,3 0 0 1 ,0 3 0 8 6 0 1 ,5 0 0 6 3 0 / 6 % 6 ,7 5 0 8 ,7 0 0 5 ,6 0 0 7 ,6 0 0 1 ,2 0 0 9 4 0 8 0 0 1 ,3 7 0 1 0 0 0 1 0 ,5 0 0 1 3 ,0 0 0 9 ,5 0 0 1 0 ,0 0 0 1 ,7 0 0 1 ,4 0 0 1 ,1 0 0 2 ,0 0 0 1 6 0 0 1 7 ,0 0 0 2 0 ,0 0 0 1 4 ,0 0 0 1 4 ,0 0 0 2 ,6 0 0 2 ,2 0 0 1 ,7 0 0 2 ,8 0 0 2 5 0 0 2 6 ,5 0 0 3 2 ,0 0 0 2 2 ,0 0 0 2 1 ,0 0 0 3 ,8 0 0 3 ,2 0 0 2 ,5 0 0 4 ,3 0 0

BA’

www.leonardo-energy.org

Copper Development Association

www.cda.org.uk

Distribution transformer efficiency standards

HD 428 & 538

Source: CENELEC

Load Losses for Distribution Transform ers No-Load Losses for Distribution Transform ers

RATED POW ER

OI L-FI LLED ( HD4 2 8 ) UP TO 2 4 kV2) DRY TYPE ( HD5 3 8 ) OI L-FI LLED ( HD4 2 8 ) UP TO 2 4 kV2) DRY TYPE ( HD5 3 8 ) LI ST A LI ST B LI ST C 1 2 kV PRI MARY

3)

LI ST A’ LI ST B’ LI ST C’ 1 2 kV PRI MARY 3) kVA W W W W W W W W 5 0 1 ,1 0 0 1 ,3 5 0 8 7 5 N/ A 1 9 0 1 4 5 1 2 5 N/ A 1 0 0 1 ,7 5 0 2 ,1 5 0 1 ,4 7 5 2 ,0 0 0 3 2 0 2 6 0 2 1 0 4 4 0 1 6 0 2 ,3 5 0 3 ,1 0 0 2 ,0 0 0 2 ,7 0 0 4 6 0 3 7 5 3 0 0 6 1 0 2 5 0 3 ,2 5 0 4 ,2 0 0 2 ,7 5 0 3 ,5 0 0 6 5 0 5 3 0 4 2 5 8 2 0 4 0 0 4 ,6 0 0 6 ,0 0 0 3 ,8 5 0 4 ,9 0 0 9 3 0 7 5 0 6 1 0 1 ,1 5 0 6 3 0 / 4 % 6 ,5 0 0 8 ,4 0 0 5 ,4 0 0 7 ,3 0 0 1 ,3 0 0 1 ,0 3 0 8 6 0 1 ,5 0 0 6 3 0 / 6 % 6 ,7 5 0 8 ,7 0 0 5 ,6 0 0 7 ,6 0 0 1 ,2 0 0 9 4 0 8 0 0 1 ,3 7 0 1 0 0 0 1 0 ,5 0 0 1 3 ,0 0 0 9 ,5 0 0 1 0 ,0 0 0 1 ,7 0 0 1 ,4 0 0 1 ,1 0 0 2 ,0 0 0 1 6 0 0 1 7 ,0 0 0 2 0 ,0 0 0 1 4 ,0 0 0 1 4 ,0 0 0 2 ,6 0 0 2 ,2 0 0 1 ,7 0 0 2 ,8 0 0 2 5 0 0 2 6 ,5 0 0 3 2 ,0 0 0 2 2 ,0 0 0 2 1 ,0 0 0 3 ,8 0 0 3 ,2 0 0 2 ,5 0 0 4 ,3 0 0

C-C’

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Full load losses in a 100kVA C-C’ transformer

12% 88% Winding Magnetic

Total loss = 1685 W

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Full load losses in a 100kVA C-C’ transformer

79% 9% 12%

Resistance Magnetic Eddy current (10% )

Total loss = 1685 W

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Copper Development Association

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Full load losses in a 100kVA C-C’ transformer

84% 4% 12% Resistance Magnetic Eddy Current (5% )

Total loss = 1685 W

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Copper Development Association

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Current waveform for a typical PC

• 2.0000
• 1.5000
• 1.0000
• 0.5000

0.0000 0.5000 1.0000 1.5000 2.0000 90 180 270 360 Degrees Current (A)

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0.0000 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Harmonic Current (A)

Harmonic profile of a typical PC

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Typical harmonic profile - 6 pulse converter

5 10 15 20 25 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Harmonic number %

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There are two issues that affect Transformers supplying harmonic-rich loads:

• Triple-n harmonic currents circulate in delta windings,

increasing resistive losses, operating temperature and reducing effective load capacity

• Harmonic currents, being of higher frequency, cause

increased magnetic losses in the core and increased eddy current and skin effect losses in the windings

Effect of harmonics on transformers

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Effect of triple-n harmonics in transformers

Triple-n harmonic currents circulate in delta windings - they do not propagate back onto the supply network

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Harmonic mitigation by transformer

Delta-star transformers

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Copper Development Association

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There are two issues that affect Transformers supplying harmonic-rich loads:

• Triple-n harmonic currents circulate in delta windings,

increasing resistive losses, operating temperature and reducing effective load capacity

• Harmonic currents, being of higher frequency, cause

increased magnetic losses in the core and increased eddy current and skin effect losses in the windings

Effect of harmonics on transformers

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Copper Development Association

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Increased Eddy current losses in transformers

2 1 2

max

h I P P

h h h h ef eh

∑ =

= = where: Peh is the total eddy current loss Pef is the eddy current loss at fundamental frequency h is the harmonic order I h is the per unit RMS current at harmonic h

Increased eddy current loss can be calculated by:

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K-Rating of Transformers

There are two approaches to rating transformers supplying harmonic rich load: -

• Designing for the anticipated duty - e.g.the

American system, established by UL and manufacturers, which specifies harmonic capability

• f the transformer - known as K-factor.
• De-rating to survive the anticipated duty - e.g.

the European system, developed by IEC, which defines de-rating factor for standard transformers

• known as factor K.

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K-Rating of Transformers - US System

2 1 2

max

h I K

h h h h

∑ =

= =

where:

h is the harmonic order I h is the RMS current at h in per unit of total current

First, calculate the K factor of the load according to:

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Copper Development Association

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For this typical PC load, the K factor is 11.6 (For worked examples see LPQI AN 3.5.2 or IEE 1100 1992)

p y 0.0000 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Harmonic Current (A )

K-Rating of Transformers - US System

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Copper Development Association

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K-Rating of Transformers - US System

Next, a transformer with a higher K rating is selected from the standard range: 4, 9, 13, 20, 30, 40, 50

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Copper Development Association

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K-Rating of Transformers - European System

In Europe, the transformer de-rating factor is calculated according to the formulae in BS 7821 Part 4. The factor K is given by:

5 . 2 2 1 2 1

1 1 ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + + =

∑

= + N n n n q

I I n I I e e K

e is ratio of eddy current loss (50 Hz) to resistive loss n is the harmonic order q is dependent on winding type & frequency, typically 1.5 to 1.7

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Copper Development Association

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K-Rating of Transformers - European System

For the same PC load, the de-rating factor is 78%

p y 0.0000 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Harmonic Current (A )

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2 4 6 8 10 12 14 16 1 2 5 10 20 41 No of Units (pairs) K Factor

Harmonic Diversity - K Factor

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K-Rating - Calculation software

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K-Rating - Calculation software

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Copper Development Association

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K-Rating - Calculation software

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Copper Development Association

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K-Rating - Calculation software

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Copper Development Association

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Full load losses in a 100kVA C-C’ transformer

41% 53% 6%

Resistance Magnetic Eddy Current

Total loss = 3245 W

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Copper Development Association

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80% load losses in a 100kVA C-C’ transformer

39% 51% 10%

Resistance Magnetic Eddy Current

Total loss = 2156 W

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Copper Development Association

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C 115 28 . 1 90 P P t temp Working

f k

° = × = × =

⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ∂ −

× = −

10 t

2 T time Life

( )

years 7 2 40 2 T time Life

5 . 2 10 P P P t

f f k

= × = × = −

− ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ − × −

Effect of additional losses on life-time

80 % load

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70% load losses in a 100kVA C-C’ transformer

38% 50% 12%

Resistance Magnetic Eddy Current

Total loss = 1699 W

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Copper Development Association

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C 75 . 90 0083 . 1 90 P P t temp Working

f k

° = × = × =

⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ∂ −

× = −

10 t

2 T time Life

( )

years 38 2 40 2 T time Life

075 . 10 P P P t

f f k

= × = × = −

− ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ − × −

Effect of additional losses on life-time

70 % load

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The real world

Selection and management small change in loading - large effect on lifetime. derate then add the ‘headroom’ management practices must maintain derating for the life of the transformer when

– adding new loads – making changes to any harmonic filters within the installation

David Chapman Copper Development Association david.chapman@copperdev.co.uk

Copper Development Association

www.cda.org.uk