inrush current

1. Inrush Current
Tutorial Session
Ramsis Girgis
IEEE Standards
Transformers Committee
Oct 15, 2001
Orlando, Florida

2. Inrush Current in Power Transformers
n Calculation & typical values of inrush current
parameters requested by customers
n Peak value
n Wave-shape
n integral of i2dt (Energy parameter)
n Maximum di/dt
n Minimum % ratio of 2nd harmonic / peak
n Effect of transformer design parameters
n Number of phases and Winding connection
n Size of transformer
n Core material, geometry, design induction, and type of joint

3. General Inrush Current Equation
n U = applied voltage
n zt = total impedance under inrush, including system
n ϕ = energization angle
n t0 = point at which core saturates (function of BR, BS, BN, ϕ )
n BR = remenant flux density
n BS = saturation flux density
n BN = normal rated flux density
n t = time constant of transformer winding under inrush conditions
n α = function of t0
n KW = accounts for 3 phase winding connection
n KS = accounts for short-circuit power of network
Sw
tt
t
KKet
z
U o
⋅⋅








⋅−−
−−
αϕω τ sin)sin(
2
)(

4. Calculated Inrush Current Waveshape
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0 5 10 15 20
Time [ms]
Amps

5. Calculated Peak inrush current
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0 20 40 60 80 100
Cycle
Current[A]

6. Inrush Current Energy Parameter
n General Equation
( ) ( )
( )∫
∫
∝
⋅=
dtti
dttitv
2
Users ask for this value
over the first cycle

7. Calculated for RGO Grade∫ dti2
0
5000
10000
15000
20000
25000
30000
0 45 90 135 180 225 270 315 360
Degrees
integralofi2
dt
1.80 T
1.75 T
1.50 T
1.20 T
Flux Density

8. Minimum % Ratio of 2nd Harmonic / Peak
n Customers use this value to distinguish
between Inrush current and short circuit
current
n This minimum % ratio occurs when the
transformer is energized at voltage-angle = 0º ;
which is also the condition that results in the
maximum peak inrush current value

9. Inrush current
0
500
1000
1500
2000
2500
3000
3500
4000
4500
0 10 20 30 40 50 60 70 80 90
Voltage angle °
Peakcurrentamps
Peak of Inrush
Peak of second harmonic

10. Inrush Current for First Cycle
-2000
-1500
-1000
-500
0
500
1000
1500
2000
0 5 10 15 20
Time [ms]
Current[A]
-400
-300
-200
-100
0
100
200
300
400
di/dt[A/ms]
Inrush Current 1st Peak
di/dt of 1st Cycle
n Value used in setting size of vacuum switch

11. Effect of Design Parameters
n Number of Phases and Winding connection
n Inrush current in 3 phase transformers is equal to, or less (by
30-40%), than 1 phase, depending on winding connection
n delta, wye, grounded wye, auto, etc
n winding connection combination of energized and secondary
windings
n Transformer Size (MVA)
n Generally inrush/rated current ratio is lower for larger MVA
n Time constant for inrush current is larger for larger MVA
n Core Steel Material
n HiB materials have lower remenance, but slightly higher
saturation level compared to RGO materials
n Thus, HiB materials are associated with lower peak inrush
currents & higher min % 2nd harmonic / peak ratio

12. Effect of Design Parameters
n Core Geometry
n affects core remenance
n affects the magnetic field distribution in the core (which
hence affects core air inductance)
n Design induction
n peak inrush increases with induction
n min % 2nd harmonic / peak decreases with induction
n Joint type
n transformer core has lower remenance than material of the
core because of the high reluctance of the joints
n non step lap core has slightly lower peak inrush current
than the step lap core
n lower core remenance