Formula Sheets: Basics of Electrical Machines | Electrical Machines - Electrical Engineering (EE) PDF Download

 Page 1


Electrical Mac hines: Basics F orm ula Sheet for
Electrical GA TE
Magnetic Circuits
• 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)
wherel is length of magnetic path (m ), µ is p ermeabilit y (Hm
-1
), A is cross-sectional
area (m
2
).
• Magnetic Field In tensit y :
H =
NI
l
(A-turns/m)
• Flux Densit y :
B =
?
A
=µH (T)
T r ansformers
• EMF Equation :
E =4.44fN?
m
(V)
where f is frequency (Hz ), N is n um b er of turns, ?
m
is m axim um flux ( Wb ).
• V oltage Ratio :
V
1
V
2
=
N
1
N
2
,
I
1
I
2
=
N
2
N
1
whereV
1
,V
2
are primary and secondary v oltages,I
1
,I
2
are curren ts,N
1
,N
2
are turns.
• Equiv alen t Resistance and Reactance (Referred to Primary) :
R
eq1
=R
1
+R
2
(
N
1
N
2
)
2
, X
eq1
=X
1
+X
2
(
N
1
N
2
)
2
where R
1
, R
2
are resistances, X
1
, X
2
are reactances.
• E?iciency :
? =
P
out
P
out
+P
core
+P
copp er
×100 (%)
where P
core
is core loss, P
copp er
=I
2
R .
1
Page 2


Electrical Mac hines: Basics F orm ula Sheet for
Electrical GA TE
Magnetic Circuits
• 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)
wherel is length of magnetic path (m ), µ is p ermeabilit y (Hm
-1
), A is cross-sectional
area (m
2
).
• Magnetic Field In tensit y :
H =
NI
l
(A-turns/m)
• Flux Densit y :
B =
?
A
=µH (T)
T r ansformers
• EMF Equation :
E =4.44fN?
m
(V)
where f is frequency (Hz ), N is n um b er of turns, ?
m
is m axim um flux ( Wb ).
• V oltage Ratio :
V
1
V
2
=
N
1
N
2
,
I
1
I
2
=
N
2
N
1
whereV
1
,V
2
are primary and secondary v oltages,I
1
,I
2
are curren ts,N
1
,N
2
are turns.
• Equiv alen t Resistance and Reactance (Referred to Primary) :
R
eq1
=R
1
+R
2
(
N
1
N
2
)
2
, X
eq1
=X
1
+X
2
(
N
1
N
2
)
2
where R
1
, R
2
are resistances, X
1
, X
2
are reactances.
• E?iciency :
? =
P
out
P
out
+P
core
+P
copp er
×100 (%)
where P
core
is core loss, P
copp er
=I
2
R .
1
Rotating Mac hines Basics
• Rotational Sp eed :
n
s
=
120f
P
()
where f is frequency (Hz ), P is n um b er of p oles.
• T orque :
T =
P
mec h
?
(Nm)
where P
mec h
is mec hanical p o w er (W ), ? =
2pn
60
is angular sp eed (rads
-1
).
• Slip (A C Mac hines) :
s=
n
s
-n
n
s
where n
s
is sync hronous sp eed, n is rotor sp eed ().
• P o w er Con v ersion :
P
mec h
=P
elec
-P
losses
where P
losses
includes copp er, core, and mec hanical losses.
DC Mac hines
• EMF Equation :
E =
P?Zn
60A
(V)
where ? is flux p er p ole ( Wb ), Z is total conductors, A is n um b er of parallel paths.
• T orque :
T =
P?ZI
a
2pA
(Nm)
where I
a
is armature curren t (A ).
• V oltage Equation (Motor) :
V =E+I
a
R
a
where R
a
is armature resistance (? ).
Key Notes
• Use SI units: V oltage (V ), Curren t (A ), Resistance (? ), P o w er (W ), T orque (Nm ),
Sp eed ( or rads
-1
).
• F or transformers, assume ideal conditions unless losses are sp ecified.
• In rotating mac hines, p ole pairs (P/2 ) affect sp eed and torque calculations.
• F or GA TE, fo cus on EMF and torque equations for DC mac hines and transformers.
• Chec k for balanced conditions in three-phase mac hines.
2