Guide for electrical design engineers
Power Quality
Katarzyna Strzalka-Goluszka
Doctoral Student of Faculty of Electrical Engineering,
Automatics, IT & Electronics
AGH University of Science & Technology
kstrzalka@op.pl
Overload Capacity of Power
Transformers
Load factor
t
K2
0
Time of day
24 h
Power Quality
K1
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1. Introduction
For over three decades, since the early seventies, the principles of sizing oilimmersed 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:
S=
∑ S Δt
∑ Δt
2
i
i
(1)
i
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:
Kp =
Sp
S nt
Kk =
2
Sk
S nt
(2)
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where: Snt – transformer nominal power.
The permissible equivalent final load Kk = f(Kp, tk) is given in standard PN-71/E81000 [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.
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Table 1 : Currents and temperature limits applicable to loading beyond
nameplate rating
TYPE OF LOADING
Normal cyclic load:
Current
Hot-spot temperature
[p.u.]
[°C]
Top-oil temperature
[°C]
Long-time emergency cyclic loading:
Current
Hot-spot temperature
Top-oil temperature
Short-time emergency loading:
Current
Hot-spot temperature
Top-oil temperature
DISTRIBUTION
TRANSFORMERS
MEDIUM POWER
TRANSFORMERS
LARGE POWER
TRANSFORMERS
1.5
140
105
1.5
140
105
1.3
120
105
1.8
150
115
1.5
140
115
1.3
130
115
2.0
-
1.8
160
115
1.5
160
115
[p.u.]
[°C]
[°C]
[p.u.]
[°C]
[°C]
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-oflife, expressed in terms of "normal" days, i.e. equivalent days of operation with
rated power at the ambient temperature 20ºC.
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3. Method of representing an actual load by an equivalent
two-step load cycle
Load factor
t
K2
K1
0
Time of day
24 h
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.
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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.
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Table 2 Acceptable load factor K24 for continuous duty at different ambient
temperatures (ON, OF and OD cooling)
AM BIENT TEM PER ATU RE , °C
-25
-20
-10
0
10
20
30
40
Hot-spot temperature rise, °C
123
118
108
98
88
78
68
58
ONAN
1.37
1.33
1.25
1.17
1.09
1.00
0.91
0.81
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
K24
Distribution
transformers
Medium and large
power
transformers
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
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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 hotspot temperature rise ΔΘh for distribution transformers with ONAN cooling and
duration t = 4 h.
Table 3 Conversion factor related to the ambient temperature
40°C
30°C
20°C
10°C
0°C
-10°C
-20°C
-25°C
10
3.2
1
0.32
0.1
0.032
0.01
0.0055
AMBIENT
TEMPERATURE°C
Conversion factor kp
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.
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- 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.
K2
K1
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
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
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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.
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