spice modelling of the transformer losses and the thermal
TRANSCRIPT
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Spice Modeling of Transformer Losses and Thermal-Based Verifications
Dr. Qichen Yang, Florida State University
Dr. Ray Ridley, CEO Ridley Engineering
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I. Spice model of winding proximity loss
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A Significant Factor: Eddy Currents in Windings
Skin effect Proximity effect
Relative current density
Relative current density
AC current in an isolated conductor
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Problems of Dowell’s Equation
where
[1] P. L. Dowell, "Effects of eddy currents in transformer windings," in Proc. IEE, vol. 113, no. 8, pp. 1387-1394, August 1966.
Problem1: frequency-domain function => cannot be used in the time-domain calculation directly
Problem2: complex expressionProblem3: ideal assumptions-based (square conductors, no edge effect)
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The AC winding resistance 𝑅𝑊 is given by
𝑅𝑊𝑅𝑤,dc
= Re 𝛼ℎ coth 𝛼ℎ +𝑚2 − 1
3Re 2𝛼ℎ tanh
𝛼ℎ
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𝛼 =𝑗𝜔𝜇0𝜂
𝜌(ℎ, 𝜂: parameters of the geometry sizes;𝑚: the number of layers)
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Current components in the frequency domain
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[2] Hurley, William G., and Werner H. Wölfle. Transformers and inductors for power electronics: Theory, design and applications. John Wiley & Sons, 2013.
Every Waveform Needs Equations Derived
From [2]
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Simple and Accurate Solution: Equivalent Circuit/Spice Model
Objective: Find a series 𝑅𝐿 circuit to fit 𝑅𝑎𝑐 𝑓 data (Dowell’s or Measurement)
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Some existing works
[3] F. de Leon and A. Semlyen, "Time domain modeling of eddy current effects for transformer transients," IEEE Trans. Power Del., vol. 8, no. 1, pp. 271-280, Jan. 1993.
Basic idea of [3]:
(1) Find the Taylor expression of the Dowell’s equation:
(2) Find the Taylor expression of the series 𝑅𝐿 circuit:
(3) Match the corresponding terms:
• Con 1: The process is still kind of complex.• Con 2: It depends on try-and-error to determine the number of 𝑅𝐿 stages (𝑁 in the equations).• Con 3: It requires analytical expressions of 𝑅𝑎𝑐.
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Some existing works
Basic idea of [4]: Iterative method
[4] A. Semlyen and A. Deri, “Time domain modelling of frequency dependent three-phase transmission line impedance,” IEEE Trans. Power App. Syst., vol. PAS-104, no. 6, pp. 1549–1555, Jun. 1985.
Background of [4]:
(1) Focus: transmission line(2) Tool: Parallel 𝑅𝐿 network
From [4]From [5]
[5] J. Beerten, S. D'Arco and J. A. Suul, "Frequency-dependent cable modelling for small-signal stability analysis of VSC-HVDC systems," IET Gen., Trans. & Distrib., vol. 10, no. 6, pp. 1370-1381, 21 4 2016. 8
From large 𝑅 and 𝐿; From highest-frequency branch to lowest-frequency branch
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One of our simple methods(1) Resistance of the series 𝑅𝐿 circuit ( )
( )
( )
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ac,
dc ac,221
ac, ac,
n
n
nn n
LR R R
R L
=
= ++
(2) Selecting sampling frequency, i.e., 𝜔𝑛 𝑛 = 1⋯5ac, ac,n n n
R L=
( )
( )
( )
2 5
ac,1 ac1,Dwll 1 dc
ac,2 ac1,Dwll 2 dc
2 5 2
ac,5 ac1,Dwll 5 dc
5 2 5
1 1 1
1 1 1 1
1 1 1
1 1 1 1 1
1 1 1
1 1 1 1 1
k kR r R
R r Rk k k
R r R
k k k
+ + +−
−+ + + =
−
+ + +
(3) Equating 𝑅 𝜔𝑛 = 𝑟ac1,Dwll 𝜔𝑛• Pro 1: The idea and expression are
very simple.
• Con 1: Inverting matrix is computation-consuming
• Con 2: only fit the resistance, but not inductance
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A preliminary verification
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Modified Spice model of the transformer
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II. Spice model of the core loss
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An arithmetic based method
(2) RL circuit to simulate the core loss
(3) Fitting results(1) Fitting objective: Steinmetz’s equation
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Modified Spice model of the transformer
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An example of the Spice model
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Two switch forward converter
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III. Thermal-based verifications
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Test Setup(1) Transformers
(a) Different winding configurations
(b) Litz wire and solid copper wire
(2) Testbeds
(a) Two switch forward converter
(b) Characteristics of the transformer
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Configurations of the transformers
Transformer No. 1 Transformer No. 2
Transformer No. 3 Transformer No. 4
Transformer No. 5
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Pri. Windings in series Pri. Windings in parallel
Pri. Windings in seriesSec. Windings in series
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Approximation to the measured loss
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Co
re lo
ss a
dd
ed
Proximity effect Core loss
Dowell’s (fundamental only)
Dowell’s (full harmonics)Core loss added
Impact ofhot surroundings
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Thermal-based test
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No. Pri. winding Sec. winding
No. 1 One layer One layer
No. 2 Two non-interleaved layers in series
One layer
No. 3 Two interleaved layers in series
One layer
No. 4 Two interleaved layers in parallel
One layer
No. 5 Two interleaved layers in series
Two interleaved layers in series
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Summary
• Spice model of the winding loss with proximity effect
- Developed in the existing research direction
- Verified based on thermal test
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More questions?
• Spice model of the core loss- Better data sets are needed to improve the accuracy
Talk with Dr. Ridley in the Expo Hall Monday 5-8 pm.More details in Dr. Ridley’s seminar tomorrow morning.
Ridley Engineering booth #621