# Energy Loss of an Inductor

```ENERGY LOSS OF AN INDUCTOR
Stefano Medved
Enerdoor Products Manager
JACKSONVILLE, FL January 22, 2016
1
OVERVIEW
• VFD’s and Motors - The Challenge
• Inductance - Theory
• Inductance - Real
• Laboratory Testing
• Market Applications
2
VFD’S &amp; MOTORS
• VFD Output = PWM
• Similar dv/dt regardless of
output frequency
• Motor Potential
• Break down of winding
insulation.
• Arc to motor bearing
• Decreased life
3
VFD’S &amp; MOTORS
Solution – Reduce the dv/dt, and prolong the life of the motor.
This is old news:
4
INDUCTANCE - THEORY
E: Magnetic Field
An inductor, also called a coil or reactor, is an electrical component that creates a
magnetic field when current flows through it. An ‘ideal inductor’ has inductance,
but no resistance or capacitance, and does not dissipate or radiate energy. The
energy loaded from an inductor is:
E = &frac12; L I2
E = Energy
L = Inductance
I = Current
5
INDUCTANCE - THEORY
Q: Quality Factor
The quality factor, or Q is the ratio of its inductive reactance to its resistance at a
given frequency while measuring the efficiency. The higher Q factor of the inductor,
the closer it is to being considered an ideal or low loss inductor:
Q=
ωπΏ
ππ
Q = Quality Factor
ω = Resonance
L = Inductance
ππ = ππππππππππ
P: Power Loss
The Q factor increases linearly at low frequencies if L and R are constant, however,
the parameters vary with frequency. The energy loss on the wire is mostly due to
electrical resistance. The power loss would be:
P=R&middot;I2
P = Power Loss
π = ππππππππππ
πΌ = πΆπΆπΆπΆπΆπΆπΆ
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INDUCTANCE – THEORY
B: Magnetic Flux
A measure of the strength of a magnetic field over given area perpendicular to it,
equal to the product of the area and magnetic flux density
ππ
B=&micro;
π
B =magnetic flux
&micro; =magnetic permeability
N= number of turns of the inductor
l = length of the magnetic ride
7
INDUCTANCE - REAL
However, a real inductor has energy losses
Considerations:
•
Resistance of the wire
•
Inductor core material
•
Parasitic capacitance
Theory
Theory in Practice
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INDUCTANCE - REAL
Resistance of wire
•
Material &amp; cable length
P = Resistivity
L= πΏπΏπΏπΏπΏπΏ
A = Cross Sectional Area
• Considered negligible if cross
sectional area is sized correctly
•
Source: http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html
Resistance v. Frequency
Copper
Aluminum
Silver
Relative resistance versus
temperature
• At 20&ordm;C resistance is 1
• At 150&ordm;C resistance is 1.5
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INDUCTANCE - REAL
Resistance of wire
•
Change in Cross Sectional Area v. Frequency
Frequency - Skin effect
Impedance on the cross sectional area of a
power cable increases linearly with the
increase of frequency
Note: Skin effect occurs regardless of material
Example:
At 60Hz the copper skin depth is 10mm
At 1Khz the copper skin depth is 2mm
Impedance Level
Low
Medium
High
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INDUCTANCE - REAL
Resistance of wire
Example:
Power loss of AWG2/0 cable @ 240A
Conclusion
• Number of conductors is important
• Frequency level is important
11
LABORATORY TEST
Setup – Equipment For Analysis
2ft
20ft
Reactor
Transformer
480Vac 3-phase
High Frequency VFD
480Vac – 150A
Frequency output 0-3500Hz
PRODUCT A
V = 480Vac
L = 2.4mH
I = 25 A
Core Material:
Iron laminate
High Frequency Rated Motor
15HP
PRODUCT B
3-phase high frequency
V = 480Vac
L = 2.4mH
I = 25 A
Core Material:
high frequency material
LABORATORY TEST
Setup – Measurements
Determined two most important factors:
• Power Loss
•
Quality Analyzer
- Input Power
• Inductor Temperature
•
Temperature Sensors
- Inductor Core
- Copper Winding
LABORATORY TEST
Core Material product A
Power loss of Iron Core Inductor @ 480Vac v. Frequency
At 50Hz: Power loss is 1.01W/Kg
At 500Hz: Power loss is 24.66W/Kg
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LABORATORY TEST
Core Material product B
Power loss of HF Core Inductor @ 480Vac v. Frequency
At 50Hz: Power loss is
At 500Hz: Power loss is 3.5W/Kg
High performance material reduces power loss by 84% at 500Hz
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LABORATORY TEST
Energy Loss Summary
Laminated Inductor &amp; High Frequency Inductor
Energy Loss v. Frequency
16
LABORATORY TEST
Temperature Testing
•
•
Wire Temperature
Laminate Temperature
Laminated Inductor &amp; High Frequency Inductor at 300Hz
Note: Ambient Temperature = 73&ordm;F
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LABORATORY TEST
Energy Loss Calculations
• If the inductor temperature is greater than ambient, energy losses are present.
• Heat Measurement = BTU (British Thermal Unit)
• Energy required to raise the temperature of a given mass of material:
E = Energy
ΔT = Temperature Change
m = mass of copper
Cp = Material Specific Gravity
• 1 Joule = 0.00095 BTU
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LABORATORY TEST
Energy Loss Calculations
Power Dissipated as Heat - BTU Calculation Results
Frequency
Product A - Standard Reactor
Product B – HF Reactor
120Hz
1630 BTU
1050 BTU
300Hz
3067 BTU
1108 BTU
550Hz
5163 BTU
1170 BTU
Additional heat within a cabinet requires power for temperature
conditioning within an enclosure 14x14x12:
• 1000 BTU/Hr is 300W
• 3400 BTU/Hr is 1000W
• 5000 BTU/Hr is 1500W
Source: Hoffmann – Pentair – series S06
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LABORATORY TEST
Energy Loss Summary
Test at 60Hz
Temperature
Power loss
Heat
dissipation
Total power
consumption
140&deg;F
360W
300W
660W
High Frequency Reactor
80&deg;F
308W
300W
608W
Δ difference
-60&deg;F
-52W (17%)
0W
-52W ( 17%)
Test at 300Hz
Temperature
Power loss
Heat
dissipation
Total power
consumption
230&deg;F
900W
1000W
1900W
High Frequency Reactor
80&deg;F
330W
300W
630W
Δ difference
-150&deg;F
-570W (63%)
-700W ( 70%)
-1270W ( 67%)
Test at 550Hz
Temperature
Power loss
Heat
dissipation
Total power
consumption
&gt;250&deg;F
1515W
1500W
3015W
High Frequency Reactor
80&deg;F
343W
300W
643W
Δ difference
NA&deg;F
-1172W (78%)
-1200W (80%)
-2372W ( 79%)
MARKET APPLICATIONS
50/60Hz
Greater than 60Hz
Conveyer controlled by VFD
High speed spindle motor
Low speed motor
CNC machine
Automatic machine with VFD
High speed pump
Motor pump low speed
Machine Tools – Wood Machinery
Centrifuge
Medical
MARKET APPLICATIONS
•
dV/dt and overvoltage spikes damage
bearing and winding insulation reducing
motor life
•
Typical load reactor that reduce the dV/dt
and overvoltage spikes increasing the
motor life.
Measurement between VFD and motor
Measurement between VFD and motor with load reactor
MARKET APPLICATIONS
•
Sine wave filter installed. dV/dt and
overvoltage spikes completed eliminate.
•
Enerdoor snubber:
A new technology way to protect dV/dt and
overvoltage phase- phase and phase-ground.
Compact parallel device with low power loss
Measurement between VFD and motor with
sine-wave filter
*Measurement taken between VFD and
motor with Enerdoor snubber.
Questions?
(P) 207-210-6511 (F) 207-210-6512
04103 Portland, ME - USA
www.enerdoor.com [email protected]
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