Formula Sheets: Electromechanical Energy Conversion Principles | Electrical Machines - Electrical Engineering (EE) PDF Download

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Electrical Mac hines: Electromec hanical Energy
Con v ersion Principles F orm ula Sheet for Electrical
GA TE
Magnetic Field Basics
• Magnetomotiv e F orce (MMF) :
F =NI (A-turns)
where N is n um b er of turns, I is curre n t (A ).
• Magnetic Flux :
?=
F
R
(Wb)
whereR is reluctance (A-turns/Wb ).
• Reluctance :
R=
l
µA
(A-turns/Wb)
where l is magnetic path length (m ), µ is p ermeabilit y (Hm
-1
), A is cross-sectional
area (m
2
).
• Magnetic Field In tensit y :
H =
F
l
=
NI
l
(A-turns/m)
• Flux Densit y :
B =
?
A
=µH (T)
Energy in Magnetic Systems
• Magnetic Field Energy :
W
m
=
1
2
LI
2
(J)
where L is inductance (H ), I is curren t (A ).
• Energy Densit y :
w
m
=
1
2
BH =
B
2
2µ
(Jm
-3
)
• Co-energy :
W
'
m
=
1
2
?I (J)
where ? is flux linkage ( Wb-turns ), ?=LI .
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Electrical Mac hines: Electromec hanical Energy
Con v ersion Principles F orm ula Sheet for Electrical
GA TE
Magnetic Field Basics
• Magnetomotiv e F orce (MMF) :
F =NI (A-turns)
where N is n um b er of turns, I is curre n t (A ).
• Magnetic Flux :
?=
F
R
(Wb)
whereR is reluctance (A-turns/Wb ).
• Reluctance :
R=
l
µA
(A-turns/Wb)
where l is magnetic path length (m ), µ is p ermeabilit y (Hm
-1
), A is cross-sectional
area (m
2
).
• Magnetic Field In tensit y :
H =
F
l
=
NI
l
(A-turns/m)
• Flux Densit y :
B =
?
A
=µH (T)
Energy in Magnetic Systems
• Magnetic Field Energy :
W
m
=
1
2
LI
2
(J)
where L is inductance (H ), I is curren t (A ).
• Energy Densit y :
w
m
=
1
2
BH =
B
2
2µ
(Jm
-3
)
• Co-energy :
W
'
m
=
1
2
?I (J)
where ? is flux linkage ( Wb-turns ), ?=LI .
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Electromec hanical Energy Con v ersion
• Energy Balance :
W
elec
=W
m
+W
mec h
+W
loss
where W
elec
is electrical input energy , W
m
is stored magnetic energy , W
mec h
is me-
c hanical output energy , W
loss
is losses.
• F orce in Magnetic Field :
F =
dW
m
dx




constan t I
(N)
or
F =-
dW
'
m
dx




constan t ?
(N)
where x is displacemen t (m ).
• T orque in Rotating Systems :
T =
dW
m
d?




constan t I
(Nm)
or
T =-
dW
'
m
d?




constan t ?
(Nm)
where ? is angular displacemen t (rad ).
Rotating Mac hines
• EMF Induced :
e=
d?
dt
=N
d?
dt
(V)
where ? is flux p er p ole ( Wb ).
• T orque in Rotating Mac hines :
T =k?I
a
(Nm)
where k is mac hine constan t, I
a
is armature curren t (A ).
• P o w er Con v ersion :
P
mec h
=T? (W)
P
elec
=eI
a
(W)
where ? is angular sp eed (rads
-1
).
• Sp eed Relation :
? =
2pn
60
, n=
120f
P
()
where f is frequency (Hz ), P is n um b er of p oles.
2
Page 3


Electrical Mac hines: Electromec hanical Energy
Con v ersion Principles F orm ula Sheet for Electrical
GA TE
Magnetic Field Basics
• Magnetomotiv e F orce (MMF) :
F =NI (A-turns)
where N is n um b er of turns, I is curre n t (A ).
• Magnetic Flux :
?=
F
R
(Wb)
whereR is reluctance (A-turns/Wb ).
• Reluctance :
R=
l
µA
(A-turns/Wb)
where l is magnetic path length (m ), µ is p ermeabilit y (Hm
-1
), A is cross-sectional
area (m
2
).
• Magnetic Field In tensit y :
H =
F
l
=
NI
l
(A-turns/m)
• Flux Densit y :
B =
?
A
=µH (T)
Energy in Magnetic Systems
• Magnetic Field Energy :
W
m
=
1
2
LI
2
(J)
where L is inductance (H ), I is curren t (A ).
• Energy Densit y :
w
m
=
1
2
BH =
B
2
2µ
(Jm
-3
)
• Co-energy :
W
'
m
=
1
2
?I (J)
where ? is flux linkage ( Wb-turns ), ?=LI .
1
Electromec hanical Energy Con v ersion
• Energy Balance :
W
elec
=W
m
+W
mec h
+W
loss
where W
elec
is electrical input energy , W
m
is stored magnetic energy , W
mec h
is me-
c hanical output energy , W
loss
is losses.
• F orce in Magnetic Field :
F =
dW
m
dx




constan t I
(N)
or
F =-
dW
'
m
dx




constan t ?
(N)
where x is displacemen t (m ).
• T orque in Rotating Systems :
T =
dW
m
d?




constan t I
(Nm)
or
T =-
dW
'
m
d?




constan t ?
(Nm)
where ? is angular displacemen t (rad ).
Rotating Mac hines
• EMF Induced :
e=
d?
dt
=N
d?
dt
(V)
where ? is flux p er p ole ( Wb ).
• T orque in Rotating Mac hines :
T =k?I
a
(Nm)
where k is mac hine constan t, I
a
is armature curren t (A ).
• P o w er Con v ersion :
P
mec h
=T? (W)
P
elec
=eI
a
(W)
where ? is angular sp eed (rads
-1
).
• Sp eed Relation :
? =
2pn
60
, n=
120f
P
()
where f is frequency (Hz ), P is n um b er of p oles.
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Key Notes
• Use SI units: V oltage (V ), Curren t (A ), P o w er (W ), T orque (Nm ), Flux (Wb ), Sp eed
( or rads
-1
).
• F or GA TE, fo cus on torque, EMF, and energy con v ersion equations.
• Assume linear magnetic systems unless sp ecified (no saturation).
• Use co-energy for systems with constan t flux linkage.
• Reluctance and flux linkage are k ey for analyzing energy storage.
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