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
[email protected]
Overload Capacity of Power Transformers
t
r o t c a f d a o L
K2
K1 0
Time of day
24 h
P o w e r Q u a l i t y
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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 S p,
•
equivalent final load S k,
•
duration of the final load t k.
The above equivalent load values should be computed as a root mean square average according to the relation:
∑ S i Δt i ∑ Δt i 2
S =
(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:
K p
=
S p S n
K k
=
S k S n
(2)
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where: Snt – transformer nominal power. The permissible equivalent final load K k = 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 K p = 0.25÷1.0
•
duration of the final load t k = 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-of-
life, 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 t
r o t c a f d a o L
K2
K1 0
Time of day
24 h
Fig. 1. Equivalent two-step load cycle The load steps in figure 1 shall be K 1 and K 2, where K 2 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 K 1 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 K 1 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 K 1 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 = K 24 for continuous duty and different ambient temperatures.
Overload Capacity of Power Transformers www.leonardo-energy.org Table 2 Acceptable
load factor K 24 for continuous duty at different ambient temperatures (ON, OF and OD cooling) -25
-20
-10
0
10
20
30
40
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
AMBIENT TEMPERATURE ,
C
Hot-spot t emperature r ise, C
K 24
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 K 2 for a given duration t and a given initial load K 1. 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 K 2 = f(K 1, 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 K 2 = f(K 1, 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 K 2 /K 1. For this purpose it is necessary is to find the intersection of the curve corresponding to the duration of the load K 2 with the line of constant slope K 2 /K 1, which can be found by marking corresponding points on ordinate K 2 = 1 and abscissa K 1 = 1. Figure 1 shows the line for K 2 /K 1 = 1.75, which allows determining the factors K 2 = 1.15 and K 1 = 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 K 1 and K 2 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 k p
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 +
(3)
Θa
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 . k p
(4)
where: k p – 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.
K 2 0.7
K 1 V Δθh
0.8
V Δθh
0.9
V Δθh
1.0
V Δθh
1.1
V Δθh
1.2
V Δθh
1.3
V Δθh
1.4
V Δθh
1.5
V Δθh
1.6
V Δθh
1.7
V Δθh
1.8
V Δθh
1.9
V Δθh
2.0
V Δθh
0.25
0.50
0.70
0.80
0.90
1.00
1.10
1.20
1.30
1.40
1.50
0.003 43
0.080 46
0.032 48
0.005 51
0.012 53
0.040 56
0.093 57
0.010 59
0.020 61
0.056 64
0.117 66
0.292 67
0.023 68
0.039 70
0.091 73
0.170 74
0.377 76
1.00 78
0.056 77
0.091 73
0.178 83
0.294 84
0.566 86
1.32 87
3.72 89
0.154 87
0.236 89
0.417 92
0.621 94
1.04 95
2.06 97
5.00 99
14.9 101
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
1.45 109
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
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
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
69.0 144
97.3 147
146 149
187 151
246 153
334 155
470 157
694 159
110 161
1950 163
4190 166
282 157
394 160
587 162
745 164
971 166
1300 167
1790 169
1560 172
3830 174
6110 176
+ 179
1220 171
1690 173
2500 176
3150 177
4080 179
5410 180
7370 183
+ +
+ +
+ +
+ +
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.
