Overload capacity of power transformers
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This document discusses the principles and standards, especially the PN-IEC 60354, for evaluating the overload capacity of oil-immersed transformers, detailing factors like ambient temperature and thermal ageing. It highlights the methodology for calculating permissible transformer loads based on different loading types and conditions, providing guidelines for thermal behaviour and insulation life evaluation. The paper presents tables and curves derived from thermal calculations to assist engineers in determining the allowable operational limits for transformers under various circumstances.
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1. Introduction
For over three decades, since the early seventies, the principles of sizing oil-
immersed transformers and evaluation their overload capacity have been defined
in standard PN-71/E-81000 [1]. These principles are presented in the course
book [3], and examples of practical calculations and transformers sizing are
provided in the course book [4].
The basic criterion adopted in standard [1] for determining power transformers
loading limits is the thermal life of insulation. The standard defines transformer
overload capacity assuming nominal transformer insulation life and reduced
insulation life expectancy corresponding to overloading a transformer under
disturbed conditions.
The basis for consideration in standard [1] was a representative two-step load
cycle determined from the known or expected ordered 24-hour load curve of a
transformer, described by:
• equivalent initial load Sp,
• equivalent final load Sk,
• duration of the final load tk.
The above equivalent load values should be computed as a root mean square
average according to the relation:
(1)
where:
Si – load over the time interval Δti,
Δti – the considered time interval.
The initial and final equivalent loads are determined from the representative load:
(2)
nt
p
p
S
S
K =
nt
k
k
S
S
K =
∑
∑
Δ
Δ
=
i
ii
t
tS
S
2](https://image.slidesharecdn.com/gedeoverloadcapacitypowertransformers-190729125610/85/Overload-capacity-of-power-transformers-2-320.jpg)
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where: Snt – transformer nominal power.
The permissible equivalent final load Kk = f(Kp, tk) is given in standard PN-71/E-
81000 [1] in the form of curves and tables, assuming the following parameters:
• ambient temperature ϑo = - 10, 0, 10, 20 and 30ºC
• equivalent initial load Kp = 0.25÷1.0
• duration of the final load tk = 0.5, 1, 2, 4, 8, 12 and 24h.
Standard PN-IEC 60354 [2] implemented in 1999 considerably alters the
principles of determining the overload capacity of oil-immersed transformers. The
most important changes are discussed further in this paper.
2. Main assumptions of the standard PN-IEC 60354
methodology
The normal service life of transformer is a conventional reference basis for
continuous operation in normal ambient temperature under nominal operating
conditions. Loading beyond nameplate rating and/or higher ambient temperature
involves a risk and results accelerated insulation ageing. Both the loading and
temperature rise above the rated values will result in risk of premature failure of a
transformer that may occur either immediately or after certain time, due to
deterioration of the transformer components. The standard gives guidelines on
transformer loading in relation to the operating temperature rise and thermal
ageing of insulation; the insulation relative ageing rate is assessed using the hot
spot temperature. Since the transformer sensitivity to overloading depends
evidently on its size, the standard specifies three categories of transformers:
• Distribution transformers (with maximum power of 2500 kVA), for which
only the hot-spot temperature and thermal deterioration have to be
considered;
• Medium power transformers (not exceeding 100 MVA), in which the cooling
modes shall be considered;
• Large power transformers (exceeding 100 MVA), where the effects of stray
leakage flux are significant and the consequences of failure are severe.
For each category the standard defines separate requirements.
Table 1 shows limit currents and temperatures for the above transformer
categories, applicable to loading beyond nameplate rating.](https://image.slidesharecdn.com/gedeoverloadcapacitypowertransformers-190729125610/85/Overload-capacity-of-power-transformers-3-320.jpg)
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Table 1 : Currents and temperature limits applicable to loading beyond
nameplate rating
As can be seen from table 1, the standard recommendations apply to three types
of transformer loading:
• continuous loading,
• cyclic loading,
• long-time emergency cyclic loading.
Standard [2] provides the method for determining thermal behaviour of
transformers with various cooling modes and comprises computation results in
the form of thermal characteristics for adopted assumptions, among which the
most important are:
• ambient temperature Θa = 20ºC,
• hot-spot temperature rise ΔΘhr = 78ºC.
As the basis for analysis of transformer insulation thermal ageing the rule of 6ºC
is taken, i.e. the rate of insulation ageing doubles for every increment of
approximately 6ºC.
Assuming the relative rate of ageing V at the hot-spot temperature Θh = 98ºC
equals unity V = 1, thus at the temperature Θh = 104ºC V = 2, and at
Θh = 110ºC V = 4.
Standard [2] provides the method for calculation of transformer daily loss-of-
life, expressed in terms of "normal" days, i.e. equivalent days of operation with
rated power at the ambient temperature 20ºC.
TYPE OF LOADING DISTRIBUTION
TRANSFORMERS
MEDIUM POWER
TRANSFORMERS
LARGE POWER
TRANSFORMERS
Normal cyclic load:
Current [p.u.]
Hot-spot temperature [°C]
Top-oil temperature [°C]
1.5
140
105
1.5
140
105
1.3
120
105
Long-time emergency cyclic loading:
Current [p.u.]
Hot-spot temperature [°C]
Top-oil temperature [°C]
1.8
150
115
1.5
140
115
1.3
130
115
Short-time emergency loading:
Current [p.u.]
Hot-spot temperature [°C]
Top-oil temperature [°C]
2.0
-
-
1.8
160
115
1.5
160
115](https://image.slidesharecdn.com/gedeoverloadcapacitypowertransformers-190729125610/85/Overload-capacity-of-power-transformers-4-320.jpg)
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3. Method of representing an actual load by an equivalent
two-step load cycle
Fig. 1. Equivalent two-step load cycle
The load steps in figure 1 shall be K1 and K2, where K2 is the peak load. The
duration of the peak load is t hours. Standard [2] describes the method of
determining this duration for different shapes of actual load cycles. In the case
of a load cycle with one peak the value of t should be selected on the equal
areas basis as indicated in Fig. 2. For the off-peak portion of the load cycle, the
value of K1 is selected to correspond to the average off-peak load.
Fig. 2. Load cycle with one peak
In the case where there are two peaks of nearly equal amplitude but different
duration (Fig. 3), the value of time t is determined for the peak of a longer
duration and the value of K1 is selected to correspond to the average of the
remaining daily load.
Time of day
Loadfactor
t
24 h0
K2
K1](https://image.slidesharecdn.com/gedeoverloadcapacitypowertransformers-190729125610/85/Overload-capacity-of-power-transformers-5-320.jpg)
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Fig. 3. Load cycle with two peaks of equal amplitude and different duration
For the load cycle where two peaks occur in close succession (Fig. 4), the value
of t is made long enough to enclose both peaks, and K1 is selected accordingly to
the average load during the remaining portion of the day.
Fig. 4. Load cycle with peaks in close succession
4. Determining permissible transformer load for various
types of loadings
For a normal continuous loading, which shows no pronounced variation over
a day, the standard [2] recommends the use of a constant equivalent load
current. Table 2 gives an acceptable load factor K = K24 for continuous duty
and different ambient temperatures.](https://image.slidesharecdn.com/gedeoverloadcapacitypowertransformers-190729125610/85/Overload-capacity-of-power-transformers-6-320.jpg)
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Table 2 Acceptable load factor K24 for continuous duty at different ambient
temperatures (ON, OF and OD cooling)
For normal cycling loading and various types of transformers and eight
different ambient temperatures (Θa = -25, -20, -10, 0, 10, 20, 30 and 40°C)
standard PN-IEC 60354: 1999 [2] gives curves that can be used to determine the
permissible peak load K2 for a given duration t and a given initial load K1. If the
ambient temperature value falls between two values, the standard
recommends interpolation between the two nearest curves. Figure 5 shows an
example of relations K2 = f(K1, t) for distribution transformers with ONAN cooling,
and the ambient temperature Θa = +20°C.
Fig. 5. Permissible loading of distribution transformers at the ambient
temperature 20°C
AM BIENT TEM PERATURE, °C -25 -20 -10 0 10 20 30 40
Hot-spot temperature rise, °C 123 118 108 98 88 78 68 58
K24 Distribution
transformers
ONAN 1.37 1.33 1.25 1.17 1.09 1.00 0.91 0.81
Medium and large
power
transformers
ON 1.33 1.30 1.22 1.15 1.08 1.00 0.92 0.82
OF 1.31 1.28 1.21 1.14 1.08 1.00 0.92 0.83
OD 1.24 1.22 1.17 1.11 1.06 1.00 0.94 0.87](https://image.slidesharecdn.com/gedeoverloadcapacitypowertransformers-190729125610/85/Overload-capacity-of-power-transformers-7-320.jpg)
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If the supply voltage remains constant the curves K2 = f(K1, t) can also be used
for determining the rated power of a transformer (with normal life duration) for a
given rectangular load profile defined as the ratio K2/K1.
For this purpose it is necessary is to find the intersection of the curve
corresponding to the duration of the load K2 with the line of constant slope K2/K1,
which can be found by marking corresponding points on ordinate K2 = 1 and
abscissa K1 = 1. Figure 1 shows the line for K2/K1 = 1.75, which allows
determining the factors K2 = 1.15 and K1 = 0.66 for duration t = 8h.
For emergency cyclic loading the standard PN-IEC 60354: 1999 [2] gives
tables that can be used to ascertain whether a load characterized by particular
values K1 and K2 is permissible for a given ambient temperature, and
determine a daily loss of life expressed in "normal" days. These tables
correspond to six duration values t (0.5 to 24 h) and four types of transformers.
The below example table 4 determines relative ageing rates V and winding hot-
spot temperature rise ΔΘh for distribution transformers with ONAN cooling and
duration t = 4 h.
Table 3 Conversion factor related to the ambient temperature
In order to determine whether a daily load diagram characterized by particular
values of K1 and K2 is permissible and to evaluate the daily loss of life entailed,
the following steps should be preceded:
- From table 4 find the hot-spot temperature rise ΔΘh and determine the hot-spot
temperature Θh from the formula:
Θh = ΔΘh + Θa (3)
where: Θa - ambient temperature
- If the resulting hot-spot temperature exceeds the limit stated in table 1, the
loading is not permissible.
AMBIENT
TEMPERATURE°C
40°C 30°C 20°C 10°C 0°C -10°C -20°C -25°C
Conversion factor kp 10 3.2 1 0.32 0.1 0.032 0.01 0.0055](https://image.slidesharecdn.com/gedeoverloadcapacitypowertransformers-190729125610/85/Overload-capacity-of-power-transformers-8-320.jpg)
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5. Conclusion
The standard PN-IEC 60354 implemented in 1999, introduced considerable
changes to the principles of assessing thermal effects of transformers
overloading under various types of load. An essential advantage of the
recommended methods of verification of overloading capacity of transformers is
that the size and cooling modes of transformers are considered.
The tables and curves, provided in this standard, being the result of thermal
calculations allow determining permissible loading of transformers under different
operating conditions.
References
[1] PN-71/E-81000 Transformers. Loading of oil-immersed transformers.
[2] IEC 60354: Loading guide for oil immersed transformers.
[3] Strojny J., Strzałka J.: Design of Electric Power Equipment, (in Polish),
SU1609, AGH-UST Publisher, Krakow 2001.
[4] Strzałka J.: Electric Power Equipment ― Problem Book, (in Polish), SU1674,
AGH-UST Publishers Krakow 2005.](https://image.slidesharecdn.com/gedeoverloadcapacitypowertransformers-190729125610/85/Overload-capacity-of-power-transformers-10-320.jpg)
Overload capacity of power transformers
- 1. PowerQuality Guide for electrical design engineers Katarzyna Strzalka-Goluszka Doctoral Student of Faculty of Electrical Engineering, Automatics, IT & Electronics AGH University of Science & Technology kstrzalka@op.pl Power Quality Overload Capacity of Power Transformers Time of day Loadfactor t 24 h0 K2 K1
- 2. Power Quality 2 www.leonardo-energy.org 1. Introduction For over three decades, since the early seventies, the principles of sizing oil- immersed transformers and evaluation their overload capacity have been defined in standard PN-71/E-81000 [1]. These principles are presented in the course book [3], and examples of practical calculations and transformers sizing are provided in the course book [4]. The basic criterion adopted in standard [1] for determining power transformers loading limits is the thermal life of insulation. The standard defines transformer overload capacity assuming nominal transformer insulation life and reduced insulation life expectancy corresponding to overloading a transformer under disturbed conditions. The basis for consideration in standard [1] was a representative two-step load cycle determined from the known or expected ordered 24-hour load curve of a transformer, described by: • equivalent initial load Sp, • equivalent final load Sk, • duration of the final load tk. The above equivalent load values should be computed as a root mean square average according to the relation: (1) where: Si – load over the time interval Δti, Δti – the considered time interval. The initial and final equivalent loads are determined from the representative load: (2) nt p p S S K = nt k k S S K = ∑ ∑ Δ Δ = i ii t tS S 2
- 3. Overload Capacity of PowerTransformers 3 www.leonardo-energy.org where: Snt – transformer nominal power. The permissible equivalent final load Kk = f(Kp, tk) is given in standard PN-71/E- 81000 [1] in the form of curves and tables, assuming the following parameters: • ambient temperature ϑo = - 10, 0, 10, 20 and 30ºC • equivalent initial load Kp = 0.25÷1.0 • duration of the final load tk = 0.5, 1, 2, 4, 8, 12 and 24h. Standard PN-IEC 60354 [2] implemented in 1999 considerably alters the principles of determining the overload capacity of oil-immersed transformers. The most important changes are discussed further in this paper. 2. Main assumptions of the standard PN-IEC 60354 methodology The normal service life of transformer is a conventional reference basis for continuous operation in normal ambient temperature under nominal operating conditions. Loading beyond nameplate rating and/or higher ambient temperature involves a risk and results accelerated insulation ageing. Both the loading and temperature rise above the rated values will result in risk of premature failure of a transformer that may occur either immediately or after certain time, due to deterioration of the transformer components. The standard gives guidelines on transformer loading in relation to the operating temperature rise and thermal ageing of insulation; the insulation relative ageing rate is assessed using the hot spot temperature. Since the transformer sensitivity to overloading depends evidently on its size, the standard specifies three categories of transformers: • Distribution transformers (with maximum power of 2500 kVA), for which only the hot-spot temperature and thermal deterioration have to be considered; • Medium power transformers (not exceeding 100 MVA), in which the cooling modes shall be considered; • Large power transformers (exceeding 100 MVA), where the effects of stray leakage flux are significant and the consequences of failure are severe. For each category the standard defines separate requirements. Table 1 shows limit currents and temperatures for the above transformer categories, applicable to loading beyond nameplate rating.
- 4. Power Quality 4 www.leonardo-energy.org Table 1 : Currents and temperature limits applicable to loading beyond nameplate rating As can be seen from table 1, the standard recommendations apply to three types of transformer loading: • continuous loading, • cyclic loading, • long-time emergency cyclic loading. Standard [2] provides the method for determining thermal behaviour of transformers with various cooling modes and comprises computation results in the form of thermal characteristics for adopted assumptions, among which the most important are: • ambient temperature Θa = 20ºC, • hot-spot temperature rise ΔΘhr = 78ºC. As the basis for analysis of transformer insulation thermal ageing the rule of 6ºC is taken, i.e. the rate of insulation ageing doubles for every increment of approximately 6ºC. Assuming the relative rate of ageing V at the hot-spot temperature Θh = 98ºC equals unity V = 1, thus at the temperature Θh = 104ºC V = 2, and at Θh = 110ºC V = 4. Standard [2] provides the method for calculation of transformer daily loss-of- life, expressed in terms of "normal" days, i.e. equivalent days of operation with rated power at the ambient temperature 20ºC. TYPE OF LOADING DISTRIBUTION TRANSFORMERS MEDIUM POWER TRANSFORMERS LARGE POWER TRANSFORMERS Normal cyclic load: Current [p.u.] Hot-spot temperature [°C] Top-oil temperature [°C] 1.5 140 105 1.5 140 105 1.3 120 105 Long-time emergency cyclic loading: Current [p.u.] Hot-spot temperature [°C] Top-oil temperature [°C] 1.8 150 115 1.5 140 115 1.3 130 115 Short-time emergency loading: Current [p.u.] Hot-spot temperature [°C] Top-oil temperature [°C] 2.0 - - 1.8 160 115 1.5 160 115
- 5. Overload Capacity of PowerTransformers 5 www.leonardo-energy.org 3. Method of representing an actual load by an equivalent two-step load cycle Fig. 1. Equivalent two-step load cycle The load steps in figure 1 shall be K1 and K2, where K2 is the peak load. The duration of the peak load is t hours. Standard [2] describes the method of determining this duration for different shapes of actual load cycles. In the case of a load cycle with one peak the value of t should be selected on the equal areas basis as indicated in Fig. 2. For the off-peak portion of the load cycle, the value of K1 is selected to correspond to the average off-peak load. Fig. 2. Load cycle with one peak In the case where there are two peaks of nearly equal amplitude but different duration (Fig. 3), the value of time t is determined for the peak of a longer duration and the value of K1 is selected to correspond to the average of the remaining daily load. Time of day Loadfactor t 24 h0 K2 K1
- 6. Power Quality 6 www.leonardo-energy.org Fig. 3. Load cycle with two peaks of equal amplitude and different duration For the load cycle where two peaks occur in close succession (Fig. 4), the value of t is made long enough to enclose both peaks, and K1 is selected accordingly to the average load during the remaining portion of the day. Fig. 4. Load cycle with peaks in close succession 4. Determining permissible transformer load for various types of loadings For a normal continuous loading, which shows no pronounced variation over a day, the standard [2] recommends the use of a constant equivalent load current. Table 2 gives an acceptable load factor K = K24 for continuous duty and different ambient temperatures.
- 7. Overload Capacity of PowerTransformers 7 www.leonardo-energy.org Table 2 Acceptable load factor K24 for continuous duty at different ambient temperatures (ON, OF and OD cooling) For normal cycling loading and various types of transformers and eight different ambient temperatures (Θa = -25, -20, -10, 0, 10, 20, 30 and 40°C) standard PN-IEC 60354: 1999 [2] gives curves that can be used to determine the permissible peak load K2 for a given duration t and a given initial load K1. If the ambient temperature value falls between two values, the standard recommends interpolation between the two nearest curves. Figure 5 shows an example of relations K2 = f(K1, t) for distribution transformers with ONAN cooling, and the ambient temperature Θa = +20°C. Fig. 5. Permissible loading of distribution transformers at the ambient temperature 20°C AM BIENT TEM PERATURE, °C -25 -20 -10 0 10 20 30 40 Hot-spot temperature rise, °C 123 118 108 98 88 78 68 58 K24 Distribution transformers ONAN 1.37 1.33 1.25 1.17 1.09 1.00 0.91 0.81 Medium and large power transformers ON 1.33 1.30 1.22 1.15 1.08 1.00 0.92 0.82 OF 1.31 1.28 1.21 1.14 1.08 1.00 0.92 0.83 OD 1.24 1.22 1.17 1.11 1.06 1.00 0.94 0.87
- 8. Power Quality 8 www.leonardo-energy.org If the supply voltage remains constant the curves K2 = f(K1, t) can also be used for determining the rated power of a transformer (with normal life duration) for a given rectangular load profile defined as the ratio K2/K1. For this purpose it is necessary is to find the intersection of the curve corresponding to the duration of the load K2 with the line of constant slope K2/K1, which can be found by marking corresponding points on ordinate K2 = 1 and abscissa K1 = 1. Figure 1 shows the line for K2/K1 = 1.75, which allows determining the factors K2 = 1.15 and K1 = 0.66 for duration t = 8h. For emergency cyclic loading the standard PN-IEC 60354: 1999 [2] gives tables that can be used to ascertain whether a load characterized by particular values K1 and K2 is permissible for a given ambient temperature, and determine a daily loss of life expressed in "normal" days. These tables correspond to six duration values t (0.5 to 24 h) and four types of transformers. The below example table 4 determines relative ageing rates V and winding hot- spot temperature rise ΔΘh for distribution transformers with ONAN cooling and duration t = 4 h. Table 3 Conversion factor related to the ambient temperature In order to determine whether a daily load diagram characterized by particular values of K1 and K2 is permissible and to evaluate the daily loss of life entailed, the following steps should be preceded: - From table 4 find the hot-spot temperature rise ΔΘh and determine the hot-spot temperature Θh from the formula: Θh = ΔΘh + Θa (3) where: Θa - ambient temperature - If the resulting hot-spot temperature exceeds the limit stated in table 1, the loading is not permissible. AMBIENT TEMPERATURE°C 40°C 30°C 20°C 10°C 0°C -10°C -20°C -25°C Conversion factor kp 10 3.2 1 0.32 0.1 0.032 0.01 0.0055
- 9. Overload Capacity of PowerTransformers 9 www.leonardo-energy.org - From table 4 find relative ageing rate V and determine the daily insulation loss of life L from the formula: L = V . kp (4) where: kp – the conversion factor related to the ambient temperature according to table 3. Table 4 relative ageing rate V (daily loss of life) and winding hot-spot temperature rise Dqh for distribution transformers with ONAN cooling and duration t = 4 h. 0.25 0.50 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50 0.7 V Δθh 0.003 43 0.080 46 0.032 48 0.8 V Δθh 0.005 51 0.012 53 0.040 56 0.093 57 0.9 V Δθh 0.010 59 0.020 61 0.056 64 0.117 66 0.292 67 1.0 V Δθh 0.023 68 0.039 70 0.091 73 0.170 74 0.377 76 1.00 78 1.1 V Δθh 0.056 77 0.091 73 0.178 83 0.294 84 0.566 86 1.32 87 3.72 89 1.2 V Δθh 0.154 87 0.236 89 0.417 92 0.621 94 1.04 95 2.06 97 5.00 99 14.9 101 1.3 V Δθh 0.455 98 0.677 100 1.12 103 1.56 104 2.36 106 4.02 108 8.13 110 20.5 112 64.7 114 1.4 V Δθh 1.45 109 2.11 111 3.36 114 4.50 115 6.38 117 9.76 119 16.8 121 34.7 123 90.6 125 302 127 1.5 V Δθh 4.94 120 7.09 122 11.00 125 14.4 127 19.7 128 28.2 130 43.7 132 76.1 134 160 137 431 139 1510 141 1.6 V Δθh 17.9 132 25.5 134 38.8 137 50.1 139 66.8 140 93.7 142 135 144 211 146 371 149 790 151 2200 153 1.7 V Δθh 69.0 144 97.3 147 146 149 187 151 246 153 334 155 470 157 694 159 110 161 1950 163 4190 166 1.8 V Δθh 282 157 394 160 587 162 745 164 971 166 1300 167 1790 169 1560 172 3830 174 6110 176 + 179 1.9 V Δθh 1220 171 1690 173 2500 176 3150 177 4080 179 5410 180 7370 183 + + + + + + + + 2.0 V Δθh 5540 184 + + + + + + + + + + + + + + + + + + + + K1 K2
- 10. Power Quality 10 www.leonardo-energy.org 5. Conclusion The standard PN-IEC 60354 implemented in 1999, introduced considerable changes to the principles of assessing thermal effects of transformers overloading under various types of load. An essential advantage of the recommended methods of verification of overloading capacity of transformers is that the size and cooling modes of transformers are considered. The tables and curves, provided in this standard, being the result of thermal calculations allow determining permissible loading of transformers under different operating conditions. References [1] PN-71/E-81000 Transformers. Loading of oil-immersed transformers. [2] IEC 60354: Loading guide for oil immersed transformers. [3] Strojny J., Strzałka J.: Design of Electric Power Equipment, (in Polish), SU1609, AGH-UST Publisher, Krakow 2001. [4] Strzałka J.: Electric Power Equipment ― Problem Book, (in Polish), SU1674, AGH-UST Publishers Krakow 2005.