Electrical Machine Design (equations)

Factors	DC Machine	Transformers	Induction Machines	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
Choice of Magnetic Loading	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
Choice of Electric Loading	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	Stator tooth 1.3 to 1.7 Wb/m2 Rotor tooth 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 Dovetail & T Head 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
Slot Loading	DNA	DNA	Slot Loading = Zss Is 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