Section 3 Section 3 AWS
Copyrighted material - Taylor & Francis
Formulae for electrical power technology
Three-phase systems Star IL = Ip
D.c. machines
√ VL = 3 Vp
Delta VL = Vp IL =
√ 3 Ip
√ P = 3 VL IL cos φ
or
Generated e.m.f. E =
(c = 2 for wave winding, c = 2 p for lap winding)
P = 3Ip2 Rp
Efficiency, η =
√ (P1 − P2 ) 3 (P1 + P2 )
I0 =
Efficiency, η =
2 + I 2) (IM C
Torque =
IM = I0 sin φ0 Ic = I0 cos φ0 E = 4.44 f m N Regulation =
Section 3
× 100%
VI − Ia2 Ra − If V − C VI
× 100%
pZIa EIa = ∝ Ia 2πn πc
V1 V2
Efficiency, η = 1 −
f nS = s= p
× 100%
Equivalent circuit: Re = R1 + R2
Xe = X1 + X2
Three-phase induction motors
E2 − E1 E2
VI 2 VI + Ia Ra + If V + C
E = V − I a Ra
Motor:
Transformers V1 N1 I2 = = V2 N2 I1
Generator: E = V + Ia Ra
Two-wattmeter method:
P = P1 + P2 tan φ =
2 pn Z ∝ ω c
2 Ze =
V1 V2
2
(Re2 + X e2 )
fr = sf
s
× 100
N2 N1
E1 I 2 R2 Er s= r Ir = = Zr P2 [R22 + (s X 2 )2 ]
Output power = V2 I2 cosφ2 Total loss = copper loss + iron loss
Torque, ⎛
Input power = output power + losses N1 N2
Xr = s X2
Pm η= = P1
ns − nr ns
Efficiency,
losses input power
Resistance matching: R1 =
2 RL
input − stator loss − rotor copper loss − friction & windage loss input power
⎞ N2 2
⎜m N ⎟ s E 12 R2 s E 12 R2 ⎜ ⎟ 1 ∝ T =⎜ ⎟ 2 ⎝ 2πn s ⎠ R2 + (s X 2 )2 R22 + (s X 2 )2
These formulae are available for downloading at the website: www.routledge.com/cw/bird
Formulae for electrical power technology
Three-phase systems Star IL = Ip
D.c. machines
√ VL = 3 Vp
Delta VL = Vp IL =
√ 3 Ip
√ P = 3 VL IL cos φ
or
Generated e.m.f. E =
(c = 2 for wave winding, c = 2 p for lap winding)
P = 3Ip2 Rp
Efficiency, η =
√ (P1 − P2 ) 3 (P1 + P2 )
I0 =
Efficiency, η =
2 + I 2) (IM C
Torque =
IM = I0 sin φ0 Ic = I0 cos φ0 E = 4.44 f m N Regulation =
Section 3
× 100%
VI − Ia2 Ra − If V − C VI
× 100%
pZIa EIa = ∝ Ia 2πn πc
V1 V2
Efficiency, η = 1 −
f nS = s= p
× 100%
Equivalent circuit: Re = R1 + R2
Xe = X1 + X2
Three-phase induction motors
E2 − E1 E2
VI 2 VI + Ia Ra + If V + C
E = V − I a Ra
Motor:
Transformers V1 N1 I2 = = V2 N2 I1
Generator: E = V + Ia Ra
Two-wattmeter method:
P = P1 + P2 tan φ =
2 pn Z ∝ ω c
2 Ze =
V1 V2
2
(Re2 + X e2 )
fr = sf
s
× 100
N2 N1
E1 I 2 R2 Er s= r Ir = = Zr P2 [R22 + (s X 2 )2 ]
Output power = V2 I2 cosφ2 Total loss = copper loss + iron loss
Torque, ⎛
Input power = output power + losses N1 N2
Xr = s X2
Pm η= = P1
ns − nr ns
Efficiency,
losses input power
Resistance matching: R1 =
2 RL
input − stator loss − rotor copper loss − friction & windage loss input power
⎞ N2 2
⎜m N ⎟ s E 12 R2 s E 12 R2 ⎜ ⎟ 1 ∝ T =⎜ ⎟ 2 ⎝ 2πn s ⎠ R2 + (s X 2 )2 R22 + (s X 2 )2
These formulae are available for downloading at the website: www.routledge.com/cw/bird
