Formula Sheets: DC Machines | Basic Electrical Technology - Electrical Engineering (EE) PDF Download

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Electrical Mac hines: DC Mac hines F orm ula Sheet for
Electrical GA TE
DC Mac hine Basics
• EMF Equation :
E =
P?Zn
60A
(V)
where P is n um b er of p oles, ? is flux p er p ole ( Wb ), Z is total armature conductors,
n is sp eed (), A is n um b er of parallel paths.
• T orque Equation :
T =
P?ZI
a
2pA
(Nm)
where I
a
is armature curren t (A ).
• P o w er Con v ersion :
P
elec
=EI
a
(W), P
mec h
=T? (W)
where ? =
2pn
60
is angular sp eed (rads
-1
).
DC G enerator
• V oltage Equation :
V =E-I
a
R
a
(V)
where V is terminal v oltage, R
a
is armature resistance (? ).
• T yp es of Generators :
– Separately Excited: I
f
(field curren t) indep enden t.
– Sh un t: I
f
=
V
R
f
, I
L
=I
a
-I
f
.
– Series: I
a
=I
f
=I
L
.
– Comp ound: Com bination of sh un t and series.
• P o w er Output :
P
out
=VI
L
(W)
where I
L
is load curren t.
DC Motor
• V oltage Equation :
V =E+I
a
R
a
(V)
• Bac k EMF :
E??n
1
Page 2


Electrical Mac hines: DC Mac hines F orm ula Sheet for
Electrical GA TE
DC Mac hine Basics
• EMF Equation :
E =
P?Zn
60A
(V)
where P is n um b er of p oles, ? is flux p er p ole ( Wb ), Z is total armature conductors,
n is sp eed (), A is n um b er of parallel paths.
• T orque Equation :
T =
P?ZI
a
2pA
(Nm)
where I
a
is armature curren t (A ).
• P o w er Con v ersion :
P
elec
=EI
a
(W), P
mec h
=T? (W)
where ? =
2pn
60
is angular sp eed (rads
-1
).
DC G enerator
• V oltage Equation :
V =E-I
a
R
a
(V)
where V is terminal v oltage, R
a
is armature resistance (? ).
• T yp es of Generators :
– Separately Excited: I
f
(field curren t) indep enden t.
– Sh un t: I
f
=
V
R
f
, I
L
=I
a
-I
f
.
– Series: I
a
=I
f
=I
L
.
– Comp ound: Com bination of sh un t and series.
• P o w er Output :
P
out
=VI
L
(W)
where I
L
is load curren t.
DC Motor
• V oltage Equation :
V =E+I
a
R
a
(V)
• Bac k EMF :
E??n
1
• Sp eed Regulation :
SR=
n
no-load
-n
full-load
n
full-load
×100 (%)
• Sp eed-T orque Relation :
n=
V -I
a
R
a
k?
, T ??I
a
where k is a constan t.
• T yp es of Motors :
– Sh un t: Constan t sp eed, T ?I
a
.
– Series: T ?I
2
a
, high starting torque.
– Comp ound: Com bined c haracteristics.
Losses and E?iciency
• Losses :
– Copp er Loss: P
cu
=I
2
a
R
a
+I
2
f
R
f
(W ).
– Core Loss: Hysteresis and eddy curren t losses (constan t for fixed sp eed/flux).
– Mec hanical Loss: F riction and windage.
• E?iciency :
? =
P
out
P
in
×100=
P
out
P
out
+P
cu
+P
core
+P
mec h
×100 (%)
where P
out
=VI
L
(generator) or T? (motor).
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 GA TE, fo cus on EMF, torque, and e?iciency calculations.
– Chec k motor/generator t yp e ( sh un t, series, comp ound) for sp ecific equations.
– Armature reaction and comm utation ma y affect p erformance but are t ypically sim-
plified.
– Use consisten t units for sp ee d (n in , ? in rads
-1
).
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