This document discusses inrush current in power transformers. It provides calculations and typical values for inrush current parameters such as peak value, wave shape, energy parameter, and maximum di/dt. It also examines the effect of transformer design parameters like the number of phases, winding connection, size, core material, geometry, design induction, and joint type on inrush current values. General equations are presented for calculating inrush current waveform based on factors like applied voltage, impedance, energization angle, and core material properties.

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