s
PTD M SP/5510.80/Mü Erlangen, 20.01.2005
Damping resistor against relaxion oscillations ( ferro-resonance) ferro-resonance) 1
In three-phase systems, the residual voltage windings (da-dn winding) of inductive voltage transformers (VT) are connected in broken delta for the purpose of attaching a resistor for damping relaxation oscillations.
L1 L2 L3 a
a
a
n
n
n
da
da
da
dn
dn
dn
max. 110 V
I∆
RD
typical values I∆: 4 / 6 / 8 A
1.
Default values of resistors
The table lists customary values of damping resistors. The selection is the result which follows the thermal limiting output (or rated long-duration current) of the da-dn winding of the voltage transformer. da-dn winding of the voltage transformer
Damping resistor 2
Thermal limiting output
Rated long duration current
75 W
4A
25 Ohm / 500 W
100 W
6A
25 Ohm / 500 W
150 W
8A
12,5 Ohm / 1 kW
3
If these default values do not match the requirements, other values can be calculated.
2.
Calculation of the damping resistance
The damping resistance can be calculated with the data given by the nameplate of the voltage transformer. Data:
Rated thermal limiting out put Ssr for 8 h Rated voltage Usr of the da-dn winding (formerly „e-n winding “)
Demanded:
smallest value of the damping resistance RD Heat dissipation (thermal rating) of the damping resistor
1 2 3
Formerly also the term „e-n winding“ was used. The term „rated long duration current“ still is commonly used, but replaced by „rated thermal limiting output “in the current edition of the VT VT standard. Both terms describe the same issue. Two resis resis tors à 25 Ohm in parallel connection.
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The damping resistance has to match the requirement that neither the resistor nor the voltage transformer is overloaded, also under earth fault conditions.
3.
Symbols and indices
U S P R
Voltage Apparent power Active power Resistance
4. •
D r s V
Damping Rated value secondary Power dissipation
Normal, undisturbed service Voltage at the terminals of a single da-dn winding: U2 = Usr (rated voltage) Example: Rated secondary voltage
•
U 2r
=
100
V
3
Voltage at the broken delta: U∆ = 0 V, symmetrical, undisturbed service
System voltage L2
Voltage at the da-dn winding L3
3 U ‘ L 3 V / 1 0 0
Undisturbed service
U ‘L 1
U ‘ L 2
L1
Uda-dn = 0 V
L2
Service with earth fault in L1
L3
U e
L 2
3 L
e U
•
U ‘ e
L 3
110 V da
L1
5.
3 / ) V 0 0 1 3 ⋅ ( e L 2 √ ⋅ 1 U ‘ 1,
dn
Service under earth fault condition Values at the terminals of a single da-dn winding:
[F1] [F2] [F3]
Voltage Current Apparent power
U se
= 1,1 ⋅ 3 ⋅ U sr = 1,9 ⋅ U sr
Factors: 1,1
Voltage factor at fault location
√3
Earth-fault factor
1,9
Rated voltage factor 1,9 = 1,1 x √3
S sr
I se
= 1,9 ⋅ I sr = 1,9 ⋅
S se
= U se ⋅ I se = 1,9 ⋅ S sr
U sr 2
4
4
Rated voltage factor: multiple of the rated primary voltage at which the VT must comply with the relevant thermal requirements for a specified time and with the relevant accuracy requirements.
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F2: with constant load resistance the 1,9-times voltage during earth fault causes a 1,9-times current through the winding. The rated thermal limiting output S2r relates to undisturbed, normal service. S 2r is a rated value, however, does not represent the actual load carrying capacity of the winding! In fact, the residual voltage winding (da-dn winding) can be loaded with 3,6-times the rated thermal limiting output over 8 hours. •
Values at the terminals of the broken delta:
[F4]
[F5] [F6]
6.
Voltage Apparent power Current
U ∆
= 3 ⋅ (1,1 ⋅ 3 )⋅ U sr = 3,3 ⋅U sr
S ∆
= 3,3 ⋅ U sr ⋅1,9 ⋅
I ∆
= I se
S sr U sr
Typical value for Usr :
100
V
3
= 6,3 ⋅ S sr Maximum permissible value
Damping resistor
The value of the resistance is calculated by [F4] and [F5]: 2
[F7]
[F8]
7.
Resistance
Power dissipation
R D
P V
≥
U ∆ S ∆
≥
2
= 3⋅
U sr S sr
(3,3 ⋅U )2 sr
RD and PV are the minimum permissible values
R D
Worked sample
Data give on the nameplate of the voltage transformer: -
rated secondary voltage of the residual voltage winding Usr
100 V / 3
-
rated thermal limiting output Ssr ( corresponds to the former rated long duration current
100 VA 6A)
=> Damping resistance RD (according to F7) Power dissipation PV (according to F8)
≥ 19,2 Ω ≥ 630 W |19,2 Ω
Usually, for example a 25-Ohm-resistor is used, load carrying capacity 500 W (or higher).
8. Sources - Documents by Peter Dorsch and Dr. Kerstin Kunde - IEC 60044-2
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Edition: 20.01.2005
