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Purpose
The purpose of this guide is to provide basic information about transformer through-fault damage curves and characteristic landmarks necessary for plotting on time-current curves, for the purpose of equipment overcurrent protection. Damage curves are defined in the IEEE standards in per unit on the nominal base rating (kVA) of the transformer, and are not adjusted with changes to the core, winding material or method of cooling.
Full Load Amps (FLA)
FLA is the rated continuous current carrying capacity of a transformer at a referenced ambient temperature and allowable temperature rise, see table 1. The FLA label is located on a time-current curve (TCC) in top decade at 1000 seconds.
The total temperature rise of an OA 65°C transformer, at an average/maximum ambient temperature of 30/40°C, is 110/120°C. These temperatures do exceed the transformer insulation rating of 105°C, and are allowed by the standards.
Table 1 Transformer temperature ratings
|
Cooling
Method
|
Ave/Max
Amb. Temp.
|
Hot Spot
Temp.
|
Temp.
Rise
|
Total Temp.
Rise
|
Insul.
Temp.
|
Max Winding
SC Temp.
|
|
AA
|
30°C/40°C
|
15°C
20°C
25°C
30°C
30°C
|
75°C
90°C
115°C
130°C
150°C
|
120°C/130°C
140°C/150°C
170°C/180°C
190°C/200°C
210°C/220°C
|
130°C
150°C
180°C
200°C
220°C
|
300°C
350°C
400°C
425°C
450°C
|
|
ONAN (OA)
|
30°C/40°C
|
10°C
15°C
|
55°C
65°C
|
95°C/105°C
110°C/120°C
|
105°C
|
200°C-Al
250°C-CU
|
SC Withstand Capability (Damage) Curves
ANSI C57.109 defines damage characteristics for oil-filled, power transformers see tables 2-5. ANSI C57.12.59 defines damage characteristics for dry-type transformers see table 6 and 7. The through-fault current damage curves are not intended for overload capability. The standards state, “if fault current penetrates the limits of the thermal damage curve insulation may be damaged, or if fault current penetrates the limits of the mechanical damage curve cumulative mechanical damage may occur. The validity of these damage limit curves can not be demonstrated by test, since the effects are progressive over the transformer lifetime. They are based principally on informed engineering judgment and favorable, historical field experience.”
The damage curves are plotted in the top 3 decades of a TCC from 2 to 1000 seconds.
|
Table 2 Category I Liquid-Immersed Transformers
|
|
5-500kVA 1-Ø
|
|
15-500kVA 3-Ø
|
|
Frequent (Mechanical Damage)
or Infrequent Faults (Thermal Damage)
|
|
x Rated Current
|
Time
|
I2t
|
1-Ø
|
3-Ø
|
|
(A p.u.)
|
(sec.)
|
(A p.u.-sec.)
|
(kVA)
|
(kVA)
|
|
2
|
1800
|
7200
|
5-500
|
15-500
|
|
3
|
300
|
2700
|
5-500
|
15-500
|
|
4.75
|
60
|
1354
|
5-500
|
15-500
|
|
6.3
|
30
|
1191
|
5-500
|
15-500
|
|
11.3
|
10
|
1277
|
5-500
|
15-500
|
|
25
|
2
|
1250
|
5-500
|
15-500
|
|
35
|
1.02
|
1250
|
5-100
|
15-300
|
|
40
|
0.78
|
1250
|
5-75
|
15-75
|
|
Table 3 Category II Liquid-Immersed Transformers
|
|
501-1667kVA 1-Ø
|
|
501-5000kVA 3-Ø
|
|
Infrequent Faults (Thermal Damage)
|
|
x Rated Current
|
Time
|
I2t
|
|
(A p.u.)
|
(sec.)
|
(A p.u.-sec.)
|
|
2
|
1800
|
7200
|
|
3
|
300
|
2700
|
|
4.75
|
60
|
1354
|
|
6.3
|
30
|
1191
|
|
11.3
|
10
|
1277
|
|
25
|
2
|
1250
|
|
Frequent Faults (Include Infrequent Points Plus)
|
|
Mechanical Damage Points
|
|
x Rated Current
|
Time
|
I2t
|
|
(A p.u.)
|
(sec.)
|
(A p.u.-sec.)
|
|
0.7 / Z
|
2551 Z2
|
1250
|
|
0.7 / Z
|
4.08
|
K
|
|
1.0 / Z
|
2
|
K
|
|
Table 4 Category III Liquid-Immersed Transformers
|
|
1668-10,000kVA 1-Ø
|
|
5001-30,000kVA 3-Ø
|
|
Infrequent Faults (Thermal Damage)
|
|
x Rated Current
|
Time
|
I2t
|
|
(A p.u.)
|
(sec.)
|
(A p.u.-sec.)
|
|
2
|
1800
|
7200
|
|
3
|
300
|
2700
|
|
4.75
|
60
|
1354
|
|
6.3
|
30
|
1191
|
|
11.3
|
10
|
1277
|
|
25
|
2
|
1250
|
|
Frequent Faults (Include Infrequent Points Plus)
|
|
Mechanical Damage Points
|
|
x Rated Current
|
Time
|
I2t
|
|
(A p.u.)
|
(sec.)
|
(A p.u.-sec.)
|
|
0.5 / Z
|
5000 Z2
|
1250
|
|
0.5 / Z
|
8
|
K
|
|
1.0 / Z
|
2
|
K
|
| Table 5 Category IV Liquid-Immersed Transformers |
|
1668-10,000kVA 1-Ø
|
|
5001-30,000kVA 3-Ø
|
|
Frequent (Mechanical Damage)
or Infrequent Faults (Thermal Damage)
|
|
x Rated Current
|
Time
|
I2t
|
|
(A p.u.)
|
(sec.)
|
(A p.u.-sec.)
|
|
2
|
1800
|
7200
|
|
3
|
300
|
2700
|
|
4.75
|
60
|
1354
|
|
6.3
|
30
|
1191
|
|
11.3
|
10
|
1277
|
|
25
|
2
|
1250
|
|
Frequent (Mechanical Damage)
or Infrequent Faults (Thermal Damage)
|
|
x Rated Current
|
Time
|
I2t
|
|
(A p.u.)
|
(sec.)
|
(A p.u.-sec.)
|
|
0.5 / Z
|
5000 Z2
|
1250
|
|
0.5 / Z
|
8
|
K
|
|
1.0 / Z
|
2
|
K
|
IEEE Std C57.12.01 defines 3 categories of dry-type transformers. However, IEEE Std C57.12.59 only defines damage curves for Category I and II transformers. Damage curves for Category III transformers, 1668-10,000kVA 1-Ø, 5001-30,000kVA 3-Ø are not defined.
Magnetizing Inrush Current Point(s)
One or more inrush current points may be plotted on a TCC. Inrush currents are expressed in peak amps. The most common point is 8-12 times rated FLA at 0.1 seconds. Another less common point is 25 times rated FLA at 0.01 seconds.
Example 1
Plot the characteristic landmarks for a 1000kVA, 65°C, 4160-480/277V, Δ-YG, oil-filled, substation transformer with an impedance of 6.0%. Consider both the frequent and infrequent fault cases for this application.
Solution
Step 1 – Calculate the FLA
FLA = 1000kVA / (1.732 x 4.16kV) = 139 amps
Step 2 – Determine the Applicable Category
This is a Category II transformer based on the nominal rating of 1000kVA
Step 3 – Calculate the infrequent fault data points from Table 3
I 1800 sec = 2 x 139 amps = 278 amps
I 300 sec = 3 x 139 amps = 417 amps
I 60 sec = 4.75 x 139 amps = 660 amps
I 30 sec = 6.3 x 139 amps = 876 amps
I 10 sec = 11.3 x 139 amps = 1571 amps
I 2 sec = 25 x 139 amps = 3475 amps
Since the transformer is connected Δ-YG a separate set of data points must be calculated for primary-side protective devices. Primary-side devices will only see 58% of a secondary-side, single-line-to-ground fault.
I 1800 sec = 0.58 x 2 x 139 amps = 161 amps
I 300 sec = 0.58 x 3 x 139 amps = 242 amps
I 60 sec = 0.58 x 4.75 x 139 amps = 383 amps
I 30 sec = 0.58 x 6.3 x 139 amps = 508 amps
I 10 sec = 0.58 x 11.3 x 139 amps = 911 amps
I 2 sec = 0.58 x 25 x 139 amps = 2016 amps
Step 4 – Calculate the frequent fault data points from Table 3
I 2 sec = 139 amps / Z = 139 amps / 0.06 = 2316 amps
I 4.08 sec = 0.7 x 139 amps / Z = 97.3 amps / 0.06 = 1622 amps
t 1622 amps = 2551 (0.06)2 = 9.2 seconds
Again, shift the data points by 0.58.
I 2 sec = 0.58 x 139 amps / 0.06 = 1344 amps
I 4.08 sec = 0.58 x 97.3 amps / 0.06 = 941 amps
Step 5 – Calculate Inrush Points
12 x Inrush = 12 x 139 amps = 1668 amps
25 x Inrush = 25 x 139 amps = 3475 amps
The results are plotted in figure 1.
Example 2
Repeat Example 1 but now assume the secondary is high-resistance grounded (HRG).
Solution
Step 1 – Same as Example 1
Step 2 – Same as Example 1
Step 3 – Same as Example 1
No shifting of the damage curve is required with a HRG secondary. In this case the primary-side protective devices will not see a ground fault on the secondary-side. Ground fault magnitudes will always be much lower than load current levels.
Step 4 – Same as Example 1
Again, no shifting of data points is required.
Step 5 – Same as Example 1
The results are plotted in figure 2.
Fig. 1 1000kVA, Δ-YG, liquid-immersed transformer damage curves
Fig. 2 1000kVA, Δ-YG (HRG), liquid-immersed transformer damage curves
Example 3
Plot the characteristic landmarks for a 1500kVA, 150°C, 13800-480/277V, Δ-Δ, dry-type, substation transformer with an impedance of 5.75%. Consider the infrequent fault case for this application.
Solution
Step 1 – Calculate the FLA
FLA = 1500kVA / (1.732 x 13.8kV) = 62.8 amps
Step 2 – Determine the Applicable Category
This is a dry-type, Category II transformer based on the nominal rating of 1500kVA
Step 3 – Calculate the infrequent fault data points from Table 7
I 100 sec = 3.5 x 62.8 amps = 220 amps
I 10 sec = 11.2 x 62.8 amps = 703 amps
I 2 sec = 25 x 62.8 amps = 1570 amps
Since the transformer is connected Δ-Δ a separate set of data points must be calculated for primary-side protective devices. Primary-side devices will only see 87% of a secondary-side, line-to-line fault.
I 100 sec = 0.87 x 3.5 x 62.8 amps = 191 amps
I 10 sec = 0.87 x 11.2 x 62.8 amps = 612 amps
I 2 sec = 0.87 x 25 x 62.8 amps = 1366 amps
Step 4 – Calculate Inrush Points
12 x Inrush = 12 x 62.8 amps = 754 amps
25 x Inrush = 25 x 62.8 amps = 1570 amps
The results are plotted in figure 3.
Fig. 3 1500kVA, Δ- Δ, dry-type transformer damage curves
References
- Other Application Guides offered by SKM Systems Analysis at www.skm.com
- ABB Protective Relaying Theory and Application, 2nd Edition, 2004
The latest revision of:
- IEEE Std 242, IEEE Recommended Practice for Protection and Coordination of Industrial and Commercial Power Systems (IEEE Buff Book)
- IEEE Std C57.12.00, IEEE Standard General Requirements for Liquid-Immersed Distribution, Power and Regulating Transformers
- IEEE Std C57.12.01, IEEE Standard General Requirements for Dry-Type Distribution and Power Transformers Including Those with Solid-Cast and/or Resin-Encapsulated Windings
- IEEE Std C57.12.59, IEEE Guide for Dry-Type Transformer Through-Fault-Current Duration
- IEEE Std C57.109, IEEE Guide for Liquid-Immersed Transformer Through-Fault-Current Duration
Insulating materials
