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Symmetrical Components with Neg. Seq.
s 2 =1.
System Parameters: (^) ωe 377.
rad sec
:= ⋅ Vll := 480 V⋅ Vs1 := V 1 p := 4 Prot :=2950 W⋅
Machine Parameters:^ Vs2^ :=V^2
rs := 0.1 ohm⋅ xls := 0.205 ohm⋅ xlr :=0.186 ohm⋅
Vs1 = 277.1295 V xm := 7.15 ohm⋅ rr :=0.079 ohm⋅ Vs2 =13.8456 V
Calculations: (^) ωsyn
ωe
p 2
:= ωsyn 188.5 rad sec
− 1 = ⋅
ωrm := (^) ( 1 −s 1 ) ⋅ωsyn ωrm 182.
rad sec
Performance of an Induction Machine given a Slip with Negative Sequence Excitation Present
Unbalanced Phase Voltages:
j := − 1
Va 290.98 e
j 0⋅ := ⋅ ⋅V Vb 270.47 e
− j⋅ 122.54⋅deg := ⋅ ⋅V Vc 270.47 e
j 122.54⋅ ⋅deg := ⋅ ⋅V
a e
j
2 ⋅π 3
⋅ := A
a
2
a
a
a
2
V 0
V 1
V 2
A
− 1
Va
Vb
Vc
V 0 = 0.0049 V arg V( 0 ) =0 deg
V 1 = 277.1295 V arg V( 1 ) =0 deg
V 2 = 13.8456 V arg V( 2 ) =0 deg
3 V⋅ 1 = 480.00 V
V 2
V 1
V 0
V 1
− 5 = ×
Slip: (^) s 1 := 0.0333 s 2 := 2 −s 1
Symmetrical Components with Neg. Seq.
Z (^) in2 =0.4104 ohm arg Z( (^) in2) =70.33 deg
Z (^) in2 :=Z (^) f2 + rs+j x⋅ ls Z (^) in2 =0.1382 + 0.3865iohm
Z (^) in1 =2.3822 ohm arg Z( (^) in1) =26.0478 deg
Z (^) in1 :=Z (^) f1 + rs+j x⋅ ls Z (^) in1 =2.1402 + 1.0461iohm
R (^) f2 :=Re Z( (^) f2) R (^) f2 =0.0382 ohm
Z (^) f2 =0.1855 ohm arg Z( (^) f2) =78.1272 deg
Z (^) f2 Z (^) f2 =0.0382 + 0.1815iohm
j x⋅ (^) m
rr
s 2
+j x⋅lr
rr
s (^2)
+j ⋅(x (^) lr +xm)
R (^) f1 :=Re Z( (^) f1) R (^) f1 =2.0402 ohm
Z (^) f1 =2.2068 ohm arg Z( (^) f1) =22.4035 deg
Z (^) f1 Z (^) f1 =2.0402 + 0.8411iohm
j x⋅ (^) m
rr
s 1
+j x⋅lr
rr
s (^1)
+j ⋅(x (^) lr +xm)
z (^) r
z (^) r
z (^) r2 =0.1903 ohm arg z( (^) r2) =77.8135 deg
z (^) r2 z (^) r2 =0.0402 + 0.186iohm
rr
2 − s 1
:= +j x⋅lr
z (^) r1 =2.3797 ohm arg z( (^) r1) =4.483 deg
z (^) r1 z (^) r1 =2.3724 + 0.186iohm
rr
s (^1)
:= +j x⋅ lr
Symmetrical Components with Neg. Seq.
η η =0.
Pout
Pin
τ (^) out τ (^) out =422.5609 N m⋅
Pout
ωrm
Pout :=Pem −Prot Pout =77.0003 kW
τ (^) em =438.7498 N m⋅
τ (^) em :=τ (^) em1 +τ (^) em
τem
τem
τ (^) em2 τ (^) em2 =−0.691 N m⋅
( 1 −s 2 ) ⋅Pgap
( 1 −s 1 ) ⋅ωsyn
τ (^) em1 τ (^) em1 =439.4408 N m⋅
Pgap
ωsyn
Pem :=Pem1 +Pem
Pem2 :=( 1 −s 2 ) ⋅Pgap2 Pem2 =−0.1259 kW
Plossr2 :=s 2 ⋅Pgap2 Plossr2 =0.2562 kW
Pgap2 3 ( Is2) Pgap2 =0.1303 kW
2 := ⋅ ⋅R (^) f
Pem1 :=( 1 −s 1 ) ⋅Pgap1 Pem1 =80.0762 kW
Plossr1 :=s 1 ⋅Pgap1 Plossr1 =2.7584 kW
Pgap1 3 ( Is1) Pgap1 =82.8346 kW
2 := ⋅ ⋅R (^) f
Pin :=Pin1 +Pin2 Pin =87.3663 kW
Plosss :=Plosss1 +Plosss2 Plosss =4.4014 kW
Plosss
Plosss
