psma...pi select a pi +1 calculate turns calculate j o select wires calculate copper loss calculate...
TRANSCRIPT
![Page 1: PSMA...pi Select A pi +1 Calculate Turns Calculate J o Select Wires Calculate Copper Loss Calculate Core Loss A c W a MLT m Select A p Calculate High Frequency Losses B max ≤ B sat](https://reader030.vdocuments.net/reader030/viewer/2022013002/5e7658f63f038068f1703923/html5/thumbnails/1.jpg)
PSMA
1Power Electronics Research Centre, NUI Galway
High Frequency Effects in the Core
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Losses in Magnetic Components
2Power Electronics Research Centre, NUI Galway
Copper losses
Core losses
Hysteresis loss
Eddy current loss
Skin effect loss
Proximity effect loss
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Ferromagnetic Materials
3Power Electronics Research Centre, NUI Galway
(a) Hard magnetic materials (b) Soft magnetic materials
B
Br
HHc-Hc
-Br
(a)
B
H
(b)
Br
Hc-Hc
-Br
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Core Loss
4Power Electronics Research Centre, NUI Galway
Hysteresis loss in a ferromagnetic material Eddy current loss in a ferromagnetic material
dB
0
a
H
B
bc
die ie/n
t
ˆfe cP K f Bα β=
Hysteresis loss is the area inside the B-H loop Eddy current loss is reduced by laminations in steel Eddy current loss is reduced by higher resistivity in ferrites
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Ferromagnetic Materials
5Power Electronics Research Centre, NUI Galway
Soft magnetic materials are classified as:
Ferrites
Laminated iron alloys
Powered iron
Amorphous alloys
Nanocrystalline materials
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Core Shapes
6Power Electronics Research Centre, NUI Galway
Toroid core PQ core Pot core RS/DS core RM core
EP core
EE core EI core ER core EFD core ETD core
U coreUR core C core Planar core
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Core Loss Density vs Frequency
7Power Electronics Research Centre, NUI Galway
B=0.1 T
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Performance Factor
8Power Electronics Research Centre, NUI Galway
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Fringing (Flux)
9Power Electronics Research Centre, NUI Galway
Gap in the centre leg Gap in the outer leg
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10Power Electronics Research Centre, NUI Galway
Transformer Design
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Basic Equations
11Power Electronics Research Centre, NUI Galway
Kv =4.44 for a sinewave=4.00 for a squarewave
Voltage equation
Power equation
rmsˆ v cV K f NBA=
Vrms: the rms value of the applied voltageKv: the voltage waveform factorf: the frequency of the applied voltageJo: the current density in each winding
: the maximum flux density in the coreIi: the current in winding iNi: the number of turns in winding iAwi: the conductor area in winding iku: the window utilisation factor
ˆVA v i i c
i o wi
K fB N I AI J A
= ⋅ ⋅∑ ∑=
Window utilisation factor
ˆVA v o u a cK fBJ k W A=∑
wi1
n
ii
u
a
N Ak
W=∑
=
secp a cA W A
Windowarea cross tional area= ×
× −
B
ˆv u p oVA K fBk A J=∑
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Transformer Losses
12Power Electronics Research Centre, NUI Galway
Winding losses
Total resistive losses
is window utilization factor
is volume of the windings
Core losses
Typical layout of a transformer
22 wi
cu1
wi
( )ni o
wi
N MLT J AP RIA
ρ=
= =∑ ∑
2
cu w w u oP V k Jρ=
wi1
n
ii
u
a
N Ak
W=∑
=
w aV MLT W= ×
feˆ=Vc cP K f Bα β
Volume ofcore,VC
Cross-sectionalarea, AC
Mean Length of a Turn, MLT
Volume ofwindings,VW
Window area,Wa
2ro
Heat loss by convection
total cu fe= c tP P P h A T+ = ∆
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Dimensional Analysis
13Power Electronics Research Centre, NUI Galway
kw=10, kc =5.6 and kt=40 are typical values
Typical layout of a transformer
3/4 2
cu w w p u oP k A k Jρ=3/4
feˆ=k c p cP A K f Bα β
Volume ofcore,VC
Cross-sectionalarea, AC
Mean Length of a Turn, MLT
Volume ofwindings,VW
Window area,Wa
2ro
3/4w w pV k A=
3/4c c pV k A=
1/2t t pA k A=
(14)
(15)
1/2
total =h c t pP k A T∆ˆ
v u p oVA K fBk A J=∑
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Losses Optimization
14Power Electronics Research Centre, NUI Galway
Winding losses
Total losses
Core losses
At a given operation frequency,
The minimum losses occur when
2
cu 2 2
VAˆ ˆw w u
v f u p
aP V kK fBk k A f B
ρ ∑= =
feˆ ˆ= c cP V K f B bf Bα β α β=
2 2ˆ
ˆaP bf B
f Bα β= +
1
2 3
2 ˆ 0ˆ ˆP a bf BB f B
α β∂ β∂
−= − + =
cu fe2P Pβ
= total cu
2P Pββ+
=
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Losses Optimization
15Power Electronics Research Centre, NUI Galway
Winding, core and total losses at different frequencies
The first step in the design is to establish whether the optimum flux density given by the optimization criterion is greater or less than the saturation flux density.
A
B
C
D
Losses
Flux densityBoptD BoptBBsat
P
Pfe
Pcu
P
Pfe
Pcu
50Hz50kHz
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Losses Optimization
Power Electronics Research Centre, NUI Galway 16
( )8 27
7 2 7( )8 7 2
[ ]2( 2) [ ][ ] VA
t v uo o o
w w c c
hk T K kf B fk k K
β α β ββ ρ
− − ∆
= + ∑
8/74/7 VA2 1ˆ
w wp
t u v o
kAhk k T K fBρ β
β +
= ∆
∑
1/41
2t
ow u p
hk TJk k A
ββ ρ
∆=
+
3/4 2
cu w w p u oP k A k Jρ=3/4
feˆ=k c p cP A K f Bα β
1/2
total =h c t pP k A T∆
ˆv u p oVA K fBk A J=∑
Core size
Current density
Optimum flux density
total cu
2P Pββ+
=
total fe
22
P Pβ +=
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Core Losses Correction
17Power Electronics Research Centre, NUI Galway
ˆ( ) 1cr
V ccr
fP K fB ff
αβ α β−
= +
feˆ=Vc cP K f Bα β
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Core size v Frequency
18Power Electronics Research Centre, NUI Galway
27 127
47 2 8( )22 2 2
7 22( 2) ( 2)7
VA( ) ( 2)( )
2
c w w cp
t v u
k k KA fhk K k T
ββ
βα βββ ββ
β β β
ρ β
β+
−−+−
+ +
+ = ∆
∑
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Optimum Core Size
19Power Electronics Research Centre, NUI Galway
27 127
48
7 2 8( ) 7 222 2 27 2
2( 2) ( 2)7
VA( ) ( 2) 1( )
2
cr
c w w cp o
t crv u
k k K fA fhk fK k T
ββ
β αα β βββ ββ
β β β
ρ β
β+
−− −+−
+ +
+ = + ∆
∑
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Design Methodology
20Power Electronics Research Centre, NUI Galway
Specifications : ∑VA,K,f,ku,ΔT
Select Material : Bsat,ρc,Kc,α,β
Calculate Bo
AcWaMLTm
Bo < Bsat
Yes No
Calculate Ap
Select Ap
Calculate Api
Select Api+1
Calculate Turns
Calculate Jo
Select Wires
Calculate Copper Loss
Calculate Core Loss
AcWa
MLTm
Calculate High Frequency LossesSelect Ap
Bmax ≤ Bsat
Calculate Efficiency, η
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21Power Electronics Research Centre, NUI Galway
Push-pull Converter TransformerCircuit Waveforms
+
_
vp2
is1
+
_
vs1
Lo
Co
+
_
Vo
is2
+
_
vs2
+
_
vp1
D1
D2
Np : Ns
Vs
+
_
S2 S1
t0
Vp,Vs
t0
ΦVs
Io
ip1 ip2
t0
Io
2oI
t0
Io
2oI
is1
is2
TDT’ T’
τ
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22Power Electronics Research Centre, NUI Galway
Push-pull Converter: Specifications
Input 36 → 72 V
Output 24 V, 300 W
Frequency, f 50 kHz
Temperature Rise, ΔT 35 ºC
Ambient Temperature, Ta 45 ºC
Kc 9.12
α 1.24
β 2.0
Bsat 0.4 T
Design specifications Core data: EPCOS N67 Mn-Zn
fe c mP K f Bα β=
Core loss
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Push-pull Converter: Voltage factor
23Power Electronics Research Centre, NUI Galway
Calculations:
(1) Voltage waveform factor KvVp,Vs
t0
ΦVs
τTDT’ T’
Push-pull converter voltage and flux waveforms
4 4.88vKD
= =
24 0.6736
D = =
max maxs max'
4 4V = = = = / 2p p c p c p c p c
B Bd dBN N A N A N A fN A Bdt dt DT DT Dφ
=
rms max max4V = = K s p c v p cDV fN B A fN B AD
=
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Push-pull Converter: Power factor
24Power Electronics Research Centre, NUI Galway
Calculations:
(2) Power factor kpp, kps
( )rms rms; 12
o os s s
V IV DV I DD
= = = +
'
0
1( ) ( ) '2
DT
s s s s
Dp v t i t dt V I DT V IT
< >= = =∫
rms rms rms rms
1 ; 12pp ps
p p s s
p p Dk kV I V I D< > < >
= = = =+
rms rms
1 1 12 2
os s o o
D D PV I V ID D+ +
= =
rms rms; ( / 2) ; p s p sV DV I D I= =
t0
Vp,Vs
t0
ΦVs
Io
ip1 ip2
t0
Io
2oI
t0
Io
2oI
is1
is2
TDT’ T’
τ
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25Power Electronics Research Centre, NUI Galway
Push-pull Converter: Core sizeCalculations:
(4) Optimum Ap
The optimum flux density is less than Bsat
(3) VA ratings of the windings
1 1 122 2 2 2
1 0.672 (300) 898.6 VA0.67
o o o oo
pp ps
P P P P DVA Pk k D
+ = + + + = +∑
+= + =
[ ][ ]
18 7 2.07 2 (7 1.24 2)7 2
7 2.0 278 28
(10)(40)(35)2 2.0 4.899 (0.4)ˆ 50000(2.0 2) 898.6[(1.72 10 )(10)] (5.6)(9.12)
0.127T
oB× − − × −
× −−
× = • + × =
4/7 8/784(1.72 10 )(10) 2.0 2 1 898.6 2.54cm
(10)(40) 2.0 0.4 35 (4.899)(50000)(0.127)pA− × +
= = ×
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ETD44 Core Data
Power Electronics Research Centre, NUI Galway 26
Ac 1.73 cm2
Wa 2.10 cm2
Ap 3.63 cm4
Vc 17.70 cm3
kf 1.0
ku 0.4
MLT 7.77 cm
ρ20 1.72 µΩ-cm
α20 0.00393
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Fringing (Flux)
27Power Electronics Research Centre, NUI Galway
Gap in the centre leg Gap in the outer leg
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Fringing (Different Frequencies)
28Power Electronics Research Centre, NUI Galway
Frequency 1kHz Frequency 100kHz
Width of conductor: 0.2mm Core: Magnetics® port core
Magnetic Field Intensity
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Fringing (Different Frequencies)
29Power Electronics Research Centre, NUI Galway
Frequency 1kHz Frequency 100kHz
Magnetic Flux
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Fringing (Different Frequencies)
30Power Electronics Research Centre, NUI Galway
Frequency 1kHz Frequency 100kHz
Current Density
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31Power Electronics Research Centre, NUI Galway
High Frequency Effects in the Windings
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High Frequency Effects
32Power Electronics Research Centre, NUI Galway
High frequency
effects
Windings optimization
Skin effect
Proximity effect
Core optimization Eddy current
Windings arrangement
Thickness optimization
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Design Issues for High Frequency
33Power Electronics Research Centre, NUI Galway
High frequency winding loss
Core loss: Steinmetz equation, iGSE.
Parasitic parameters: leakage inductance, stray capacitance
Proximity effect
I I I I
H0
Primary SecondaryH1
Core Eddy currents
Skin effect
2r
Jz
Eddy current
r
Fringing effect
Gap
Core
Ohm loss
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Eddy Current in the Core
34Power Electronics Research Centre, NUI Galway
Eddy current losses in a toroidal core Equivalent core inductance versus frequency
The inductance terms of the core impendence is
coileddy
current
ac flux
magnetic material with ferrite conductivityand relativepermeability
σ
rμ- +0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0
SLL
The inductance of the toroid under the lower frequency 2
00
r c
c
N AL µ µ=
4
0 4
0 3 4
1 2.112 1.43
1 1 1 2.116 16
sL L
L
∆ = − ∆ < + ∆ = + + ∆ > ∆ ∆ ∆
core radiusskin depth
bδ
∆ = =
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Eddy Current in the Core
35Power Electronics Research Centre, NUI Galway
Fig. 7.7 Resistivity of P type ferrite Inductance and rel. permeability v frequency and
Complex permeability 4
4
3 4
' 1 2.112 1.43
1 1 1 2.116 16
rs r
r
µ µ
µ
∆= − ∆ < + ∆ = + + ∆ > ∆ ∆ ∆
core radiusskin depth
bδ
∆ = =
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Eddy Current Core Losses
36Power Electronics Research Centre, NUI Galway
The equivalent core resistance:
The core losses may be reduced by increasing the electrical resistivity or reducing the electrical conductivity of the core material.
The use of a smaller core cross-section to reduce eddy current losses suggests the use of laminations.
The average power loss in the core due to eddy currents is
22 2
2 00 4 2
r cs
c
N l bR L fl
µ µ πω π σ ∆
= =
2 2 2
max
4f B bp π σ π
=
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Eddy Current Core Losses
37Power Electronics Research Centre, NUI Galway
Performance Factor:
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Flux Distribution in the Core
38Power Electronics Research Centre, NUI Galway
Assumptions:Homogeneous coreConstant resistivityConstant permeabilityNo dielectric effects
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Axial Flux Distribution in the Core
39Power Electronics Research Centre, NUI Galway
1. Flux bunches to the surface2. Flux is higher at the surface
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Axial Flux Distribution in the Core
40Power Electronics Research Centre, NUI Galway
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Core Losses (GSE, iGSE)
41Power Electronics Research Centre, NUI Galway
Steinmetz equation:
The time-average power loss with non-sinusoidal excitation using the iGSE
fe maxcP K f Bα β=
0 0
1 ( ) 1 ( )
( )
T T
v i i
i
dB t dB tP k B dt k B dtT dt T dt
dB tk Bdt
α αβ α β α
αβ α
− −
−
= ∆ = ∆∫ ∫
= ∆
21 1
02 cosc
i
Kkdαπβ απ θ θ− −
=∫
where
A useful approximation is
1 1 6.82442 1.10441.354
ci
Kkβ απ
α− −
= + +
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Push-pull Converter Transformer
42Power Electronics Research Centre, NUI Galway
Core data: ETD44
Kc 9.12
α 1.24
β 2.0
Bsat 0.4 T
Core data: EPCOS N67 Mn-Zn
Ac 1.73 cm2
Wa 2.78 cm2
Ap 4.81 cm4
Vc 17.70 cm3
kf 1.0
ku 0.4
MLT 7.77 cm
ρ20 1.72 µΩ-cm
α20 0.00393
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Push-pull Converter Transformer
43Power Electronics Research Centre, NUI Galway
Flux waveform for the push-pull converter
Calculations:
(1) power loss per unit volume
-Bmax
t
v
Bmax
0 DT/2 T/2 (1+D)T/2 T
ΔB
p
/2 (1 ) /2 1
0 /2
1 1 2 ( )/ 2 / 2
DT D T
Tv i i
B BP k B dt dt k B B DTT DT DT T
α αβ α β α α α− −+ − ∆ ∆ = ∆ + ≈ ∆ ∆∫ ∫
1 1
2.0 1 1.24 1
6.82442 1.10441.354
9.12 0.92756.82442 1.1044
1.24 1.354
ci
Kkβ απ
α
π
− −
− −
= + +
= = + +
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Compare iGSE and GSE
44Power Electronics Research Centre, NUI Galway
Calculations:
(2) ΔB
(3) The core loss per unit volume
(5) The total core loss by GSE = 1.466 W
[ ]
1
2.0 1.24 1.24 1 1.24
5 3
1 2 ( )
(0.9275)(0.232) (50000) (2 0.232) (0.67 / (50000))0.871 10 W/m
v iP k B B DTT
β α α α− −
− −
= ∆ ∆
= × ×
= ×
(4) The total core loss
max 4
0.67(36) 0.116 T(4.88)(50000)(6)(1.73 10 )
d
p cv
cDVBK fN A −
= = =×
max2 0.232 TB B∆ = =
6 517.71 10 0.871 10 1.543 W−× × × =