Electrical Machine Design (equations)

DC Machine

Synchronous Machines

Output Equation Pa=CoD2Ln, where Pa=P/h for generators, Pa=P for motors For Single Phase
Q=2.22 f Bm Ai Kw Aw d 10-3
For Three Phase
Q=3.33 f Bm Ai Kw Aw d 10-3
Q=CoD2 L ns
KVA Input Q=
HP * 0.746 / Cos f * h
Q=CoD2 L ns
KVA Input Q=
HP * 0.746 / Cos f * h
For Turbo alternators
Q=1.11Bavac KwsVa2 L 10-3/ns
Output Coefficient Co=Bav ac* 10-3 where Bav-magnetic loading and ac - electric loading DNA Co=11 Kws Bav ac 10-3 Co=11 Kws Bav ac 10-3
Flux Density in Teeth Frequency of Flux Reversals Size of machine DNA Magnetizing current, Flux Density, Iron loss Iron loss, Stability, Voltage Rating, Parallel Operation, Transient ShortCircuit current
Temperature rise,
speed of machine, Voltage, Armature reaction, Commutation
DNA Overload Capacity, Copper losses, Temperature rise, Leakage Reactance Copper loss, Synchronous reactance, Temperature rise, Stray Load losses,
Voltage rating
Flux Density
Yoke – 1.3 to 1.6 Wb/m2
Pole – 1.2 to 1.7
Air Gap – 0.4 to 0.6
Armature teeth – 1.5 – 2.2
Armature core – 1.0 to 1.5
1. 0 to 1.4 wb/m2 for Distribution Transformer
1.2 to 1.5 for power Transformers
1.3 to 1.7 Wb/m2
1.3 to 1.7 Wb/m2
Current Density
Large Machine with strap wound conds – 4.5A/mm2
Small M/c with wire wound conds – 5A/mm2
High speed - 6 to 7A/mm2
General - 4 to 7A//mm2
1.1 to 2.2 A/mm2- small Tr..
2.2 to 3.2 – large power Tr..
5.4 to 6.2 – Large power Tr with Forced circulation
In rotor bar 4 to 7A/mm2 Current density in armature conductor
d = 3 to 5A/mm2
Main Dimension D- Diameter of the armature, L- Armature Length Hw (Height of window) and Ww (width of Window) D –diameter of stator bore
L- Length of Stator core
D –diameter of stator bore
L- Length of Stator core
L/τ Ratio
0.45 to 1.1
b/τ =0.64 to 0.72
(for Square pole face and Square Pole Section)
DNA minimum cost L/t =1.5- 2
good pf L/t = 1 – 1.25
good h L/t =1.5
overall design L/t =1
best pf t =Ö0.18L
L/t = 0.6 to 0.7
L/t = 1 to 5
Choice of Number of Poles Frequency Between 25 to 50 HZ
Current per parallel path is limited to 200A.
The Armature MMF Should not be large.
DNA DNA
For Bolted pole
Va = 50 m/s
Va=80 m/s
Length of Air Gap lg=(0.5 to 0.7)* ac* τ * 1.6*106 Bg Kg DNA Lg= 0.2 + 2ÖDL
Lg=0.2 + D
Lg=0.125+0.35D+L+0.015Va
Lg=(1.6ÖD) – 0.25
M/c with open type slots
L g/t = 0.01 to 0.015
M/c with maximum o/p
L g /t = 0.02
Turbo Alternator
Lg=0.5SCR act Kf10-6/Kg Bav
Slot Information Slot Area = Conductor area/ slot space Factor DNA Stator Slot Pitch Yss=p D/Ss Values of Stator slot pitch
Yss < 25mm – Low Volt M/c
Yss < 40mm – for 6KV & less
Yss < 60mm - m/c upto 15kV
Tooth Information DNA DNA width of stator tooth
Wts min = fm / 1.7(Ss/p) Li
Width of rotor tooth
Wtr min = fm / 1.7(Sr/p) Li
DNA
Core D=Di+2dc+2ds
Di Inner Dia.of armature
dc Depth of core
ds Depth of slot
Square Core Kc = 0.45
Two stepped core Kc = 0.56
Three stepped core Kc=0.6
Kc – core area factor = Ai/d2
Depth of stator core
dcs = fm / 2 Bcs Li
Depth of rotor core
dcr = fm / 2 Bcr Li
DNA
Armature MMF/Pole Up to 100Kw- 5000 or less
100 to 200Kw- 5000 –7000
500 to1000Kw 7500-10000
over1500Kw –Upto 12,500
DNA DNA
Armature MMF/pole
ATa = 2.7 Ip Tph Kws / p
Field MMF
ATf =SCR * Ata
Dispersion Coefficient DNA DNA s = Im/Isci
Im-Magnetizing current
Isci – ideal Short ckt current
DNA
Short Circuit Ratio
DNA DNA DNA The ratio of field current required to produce rated voltage on OC to field current required to circulate rated current at SC.
SCR = 1/Xd
Conds/slot Zss=6Ts/Ss
Stator Conds = Ss Zss
DNA
Additional Information Current/Parallel path = Ia/p
For Wave Winding Ia/2
number of tubes =
[(Pi +Pc/q)-12.5 St] /8.8p dt lt
Rotor Bar current
Ib = 0.85 6Is Ts/Sr
End ring current
Ie=Sr Ib/p p
(Ss-Sr) should not be equal to
0,±p, ±2p, ±3p, ±5p, ±1, ±2, ±(p±1) ±(p±2)
Current thru the conductor
Iz = Iph/a
Peripheral Speed
Va = p D ns
DNA - Data Not Available (Data or the concept may not be there).
Reference: Electrical Machine design by A. K Sawhney

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