Benha University
Faculty of Engineering at Shoubra EPE312 - Electric Machines (2) “AC Rotating Machines”
Electrical Engineering Department
EPE312 - Electric Machines (2) “AC Rotating Machines”
First Part – Lecture (3)
Presented By
Dr. Eng. Mohamed Sharawy
10/17/2023 7:24 AM First Part, Lecture (3) – Dr. Eng. Mohamed Sharawy Page No. 1 of 25
Benha University
Faculty of Engineering at Shoubra EPE312 - Electric Machines (2) “AC Rotating Machines”
Electrical Engineering Department
Lecture (3) Outline
❖First Part Objectives
❖Magnetomotive Force (MMF)
➢ Ampere Turns for Single Coil
➢ Ampere Turns For Group of Coils – One layer
➢ Ampere Turns For Group of Coils – Two Layers – Single Phase
➢ Ampere Turns for 3-Phase Winding
10/17/2023 7:24 AM First Part, Lecture (3) – Dr. Eng. Mohamed Sharawy Page No. 2 of 25
Benha University
Faculty of Engineering at Shoubra EPE312 - Electric Machines (2) “AC Rotating Machines”
Electrical Engineering Department
First Part Objectives
❖Introduction to AC Rotating Machines
❖AC Winding
➢ Basics of AC Winding
➢ Single Layer AC Winding
➢ 2-Layer AC Winding
❖Electromotive Force (EMF)
➢ Fundamental Principles of AC Rotating Machines
➢ EMF Induced in Chorded and Distributed AC Winding
➢ Fundamental EMF and Its Harmonics Induced in AC Winding
10/17/2023 7:24 AM First Part, Lecture (3) – Dr. Eng. Mohamed Sharawy Page No. 3 of 25
Benha University
Faculty of Engineering at Shoubra EPE312 - Electric Machines (2) “AC Rotating Machines”
Electrical Engineering Department
First Part Objectives
❖Magnetomotive Force (MMF)
➢ Ampere Turns for Single Coil
➢ Ampere Turns For Group of Coils – One layer
➢ Ampere Turns For Group of Coils – Two Layers – Single Phase
➢ Ampere Turns for 3-Phase Winding
10/17/2023 7:24 AM First Part, Lecture (3) – Dr. Eng. Mohamed Sharawy Page No. 4 of 25
Benha University
Faculty of Engineering at Shoubra EPE312 - Electric Machines (2) “AC Rotating Machines”
Electrical Engineering Department
Magnetomotive Force (MMF)
Bar Magnet
Rotating Magnetic Field Produced By The Rotor
10/17/2023 7:24 AM First Part, Lecture (3) – Dr. Eng. Mohamed Sharawy Page No. 5 of 25
Benha University
Faculty of Engineering at Shoubra EPE312 - Electric Machines (2) “AC Rotating Machines”
Electrical Engineering Department
Magnetomotive Force (MMF)
N S
Fixed Magnetic Field Produced By Rotating Magnetic Field Produced By
Field Winding and DC Supply 3-Phase Winding and 3-Phase Supply
(DC Machines) (AC Machines)
10/17/2023 7:24 AM First Part, Lecture (3) – Dr. Eng. Mohamed Sharawy Page No. 6 of 25
Benha University
Faculty of Engineering at Shoubra EPE312 - Electric Machines (2) “AC Rotating Machines”
Electrical Engineering Department
Magnetomotive Force (MMF)
N S
Synchronous Reluctance Motors Induction Motors
Rotating Magnetic Field Produced By
Synchronous Motors Interior Permanent Magnet (IPM) 3-Phase Winding and 3-Phase Supply
Motors (AC Machines)
10/17/2023 7:24 AM First Part, Lecture (3) – Dr. Eng. Mohamed Sharawy Page No. 7 of 25
Benha University
Faculty of Engineering at Shoubra EPE312 - Electric Machines (2) “AC Rotating Machines”
Electrical Engineering Department
Magnetomotive Force (MMF)
❑ Ampere Turns for Single Coil
➢ Consider a single coil with number of turns N and carrying AC current with instantaneous value i.
➢ The coil placed in stator to produce 2-pole machine and full pitched.
➢ The purpose is to produce MMF waves and cutting the rotor with certain value of ampere turn (AT).
➢ The value of AT is designed mainly to overcome the air gap reluctance while the stator and rotor
core reluctance is neglected.
AT = Ni = mmf = ර H𝑙 Ni = 2 Hg 𝑙𝑔 + 4 Hi𝑙𝑖
Ni = 2 Hg𝑙𝑔 = 2 F𝑚 F𝑚 = Hg𝑙𝑔 = N i/2
Hg, Hi are the field strength in air gap and iron core.
lg, li are the air gap and iron core length.
Fm is mmf required by the air gap. Full Pitch Single Coil on Stator
10/17/2023 7:24 AM First Part, Lecture (3) – Dr. Eng. Mohamed Sharawy Page No. 8 of 25
Benha University
Faculty of Engineering at Shoubra EPE312 - Electric Machines (2) “AC Rotating Machines”
Electrical Engineering Department
Magnetomotive Force (MMF)
❑ Ampere Turns for Single Coil
Full Pitch Single Coil on Stator Lines of Forces For a Single Coil
10/17/2023 7:24 AM First Part, Lecture (3) – Dr. Eng. Mohamed Sharawy Page No. 9 of 25
Benha University
Faculty of Engineering at Shoubra EPE312 - Electric Machines (2) “AC Rotating Machines”
Electrical Engineering Department
Magnetomotive Force (MMF)
❑ Ampere Turns for Single Coil
Pulsating or Fluctuating Magnetic Field
Magnetic Field Produced by Single Coil fed from AC Current
10/17/2023 7:24 AM First Part, Lecture (3) – Dr. Eng. Mohamed Sharawy Page No. 10 of 25
Benha University
Faculty of Engineering at Shoubra EPE312 - Electric Machines (2) “AC Rotating Machines”
Electrical Engineering Department
Magnetomotive Force (MMF)
❑ Ampere Turns for Single Coil
➢ Lines of forces directed from stator to rotor >> mmf is positive value.
➢ Lines of forces directed from rotor to stator >> mmf is negative value.
➢ A horizontal axis divides mmf waveform into two parts of equal area.
Ni
F Fm =
2
θ
π
MMF Waveform For a Single Coil
10/17/2023 7:24 AM First Part, Lecture (3) – Dr. Eng. Mohamed Sharawy Page No. 11 of 25
Benha University
Faculty of Engineering at Shoubra EPE312 - Electric Machines (2) “AC Rotating Machines”
Electrical Engineering Department
❑ Ampere Turns for Single Coil
MMF in air gap :
Ni −
Fm = AT ( A )
2
MMF in air gap as function of position using fourier analysis :
Ft (θ) = Fm1 cos (θ) + Fm3 cos (3θ) + Fm5 cos (5θ) + ..... + Fmn cos (nθ)
4 Fm 4 1 Ni
Fn (θ) = Fmn cos (θ) , Fmn = =
n n 2
NI
If i = 2 I sin (ωt) then, Fn (θ,t) = 0.9 sin (ωt) cos (θ)
n
N → no. of coil turns, θ → space angle in elec. degree
n → harmonic order, I → rms value of coil current
10/17/2023 7:24 AM First Part, Lecture (3) – Dr. Eng. Mohamed Sharawy Page No. 12 of 25
Benha University
Faculty of Engineering at Shoubra EPE312 - Electric Machines (2) “AC Rotating Machines”
Electrical Engineering Department
Magnetomotive Force (MMF)
❑ Ampere Turns For Group of Coils – One layer
Ftn (θ) = q Fmn K dn cos (nθ)
4 Fm
=q K dn cos (nθ)
n
q N I K dn
Ftn (θ,t) = 0.9 sin (ωt) cos (nθ)
n
q → no. of coils (slots/pole/phase)
K dn → distribution factor for the n th harmonic
10/17/2023 7:24 AM First Part, Lecture (3) – Dr. Eng. Mohamed Sharawy Page No. 13 of 25
Benha University
Faculty of Engineering at Shoubra EPE312 - Electric Machines (2) “AC Rotating Machines”
Electrical Engineering Department
Magnetomotive Force (MMF)
1 2 3 1\ 2\ 3\
❑ Ampere Turns For Group of Coils – One layer X X X • • •
Coil 3-1\
θ
Coil 2-2\
θ
Coil 1-3\
θ
Resultant
10/17/2023 7:24 AM First Part, Lecture (3) – Dr. Eng. Mohamed Sharawy Page No. 14 of 25
Benha University
Faculty of Engineering at Shoubra EPE312 - Electric Machines (2) “AC Rotating Machines”
Electrical Engineering Department
Magnetomotive Force (MMF)
❑ Ampere Turns For Group of Coils – Two Layers – Single Phase
N ph
Fph,n (θ) = 2 q Fmn K dn K cn cos (nθ) , N =
2P q
2
Fph,n (θ) = N ph K wn i cos (nθ)
πnP
N ph I K wn
Fph,n (θ,t) = 0.9 sin (ωt) cos (nθ)
nP
^ ^ N ph I K wn
= Fph,n sin (ωt) cos (nθ) , Fph,n = 0.9
nP
K cn → chording factor for the n th harmonic
K wn → winding factor for the n th harmonic
N ph → no. of turns per phase, 2P → no. of poles
10/17/2023 7:24 AM First Part, Lecture (3) – Dr. Eng. Mohamed Sharawy Page No. 15 of 25
Benha University
Faculty of Engineering at Shoubra EPE312 - Electric Machines (2) “AC Rotating Machines”
Electrical Engineering Department
Magnetomotive Force (MMF)
❑ Ampere Turns Produced by Three Phase Winding
MMF Waveform Produced by Single Phase Supply (Pulsating Magnetic Field)
10/17/2023 7:24 AM First Part, Lecture (3) – Dr. Eng. Mohamed Sharawy Page No. 16 of 25
Benha University
Faculty of Engineering at Shoubra EPE312 - Electric Machines (2) “AC Rotating Machines”
Electrical Engineering Department
Magnetomotive Force (MMF)
❑ Ampere Turns Produced by Three Phase Winding
➢ 3-phase winding are displaced in the stator with 120o (elec. Degree). The currents feeding the
phases are sinusoidal and shifted in phase by 120o. For sequence ABC then the mmf
(fundamental and harmonics) produced from 3-phase winding are:
i A = 2 I sin (ωt) , i B = 2 I sin (ωt -120 ) , i C = 2 I sin (ωt-240 )
2
Fph,n (θ) = N ph K wn i cos (nθ)
πnP
N ph I K wn
FA,n (θ,t) = 0.9 sin (ωt) cos (nθ)
nP
N ph I K wn
FB,n (θ,t) = 0.9 sin (ωt -120 ) cos n(θ-120 )
nP
N ph I K wn
FC,n (θ,t) = 0.9 sin (ωt-240 ) cos n(θ-240 )
nP
10/17/2023 7:24 AM First Part, Lecture (3) – Dr. Eng. Mohamed Sharawy Page No. 17 of 25
Benha University
Faculty of Engineering at Shoubra EPE312 - Electric Machines (2) “AC Rotating Machines”
Electrical Engineering Department
Magnetomotive Force (MMF)
❑ Ampere Turns Produced by Three Phase Winding
➢ 3-phase winding are displaced in the stator with 120o (elec. Degree). The currents feeding the
phases are sinusoidal and shifted in phase by 120o. For sequence ABC then the mmf
(fundamental and harmonics) produced from 3-phase winding are:
3 ^
F3ph,n (θ,t) = FA + FB + FC = Fph,n sin (nθ ωt),
2 F19 F13 F7 F1
^ 3 ^ N ph I K wn
F3ph,n = Fph,n = 1.35
2 nP
➢ n = 3, 9, …… >> F3ph,3, F3ph,9, …. = 0
➢ n = 6m+1 >> n = 7, 13, …. >> F7, F13, … F17 F11 F5
waves rotates in the same direction of F1.
➢ n = 6m-1 >> n = 5, 11, …. >> F5, F11, … waves rotates in the opposite direction with respect to F1.
10/17/2023 7:24 AM First Part, Lecture (3) – Dr. Eng. Mohamed Sharawy Page No. 18 of 25
Benha University
Faculty of Engineering at Shoubra EPE312 - Electric Machines (2) “AC Rotating Machines”
Electrical Engineering Department
Magnetomotive Force (MMF)
❑ Ampere Turns Produced by Three Phase Winding
MMF Waveform Produced by 3-Phase Supply
10/17/2023 7:24 AM First Part, Lecture (3) – Dr. Eng. Mohamed Sharawy Page No. 19 of 25
Benha University
Faculty of Engineering at Shoubra EPE312 - Electric Machines (2) “AC Rotating Machines”
Electrical Engineering Department
Magnetomotive Force (MMF)
❑ Ampere Turns Produced by Three Phase Winding
MMF Waveform Produced by 3-Phase Supply (Rotating Equivalent Space Vectors
10/17/2023 7:24 AM First Part, Lecture (3) – Dr. Eng. Mohamed Sharawy Page No. 20 of 25
Benha University
Faculty of Engineering at Shoubra EPE312 - Electric Machines (2) “AC Rotating Machines”
Electrical Engineering Department
Magnetomotive Force (MMF)
❑ Ampere Turns Produced by Three Phase Winding
N ph I K wn
❖ For n = 1 >> Fundamental mmf for 3-phase winding: F3ph,1 (θ,t) = 1.35 sin (θ − ωt)
P
➢ The MMF Produced is called rotating magnetic field.
➢ Constant amplitude: (1.35 Nph I Kwn / P) AT.
➢ Constant rotational speed: Ns = 60 fs / P (rpm)
➢ Ns is called Synchronous speed.
➢ Speed of rotation value can be controlled by changing
no. of poles (2P) or changing the supply frequency (fs).
➢ If any two phases of 3-phase supply are interchanged
(ABC >> BAC) , the direction of rotation of MMF
only is reversed
10/17/2023 7:24 AM First Part, Lecture (3) – Dr. Eng. Mohamed Sharawy Page No. 21 of 25
Benha University
Faculty of Engineering at Shoubra EPE312 - Electric Machines (2) “AC Rotating Machines”
Electrical Engineering Department
Magnetomotive Force (MMF)
❑ Ampere Turns Produced by Three Phase Winding
N S N S
Clockwise direction (ABC) Counterclockwise direction (BAC)
10/17/2023 7:24 AM First Part, Lecture (3) – Dr. Eng. Mohamed Sharawy Page No. 22 of 25
Benha University
Faculty of Engineering at Shoubra EPE312 - Electric Machines (2) “AC Rotating Machines”
Electrical Engineering Department
Magnetomotive Force (MMF)
❑ Ampere Turns Produced by Three Phase Winding
Rotating Magnetic Field of 2-Pole Stator Rotating Magnetic Field of 4-Pole Stator
10/17/2023 7:24 AM First Part, Lecture (3) – Dr. Eng. Mohamed Sharawy Page No. 23 of 25
Benha University
Faculty of Engineering at Shoubra EPE312 - Electric Machines (2) “AC Rotating Machines”
Electrical Engineering Department
Magnetomotive Force (MMF)
❑ Ampere Turns Produced by Three Phase Winding
❖ ABC sequence: Clockwise direction
of fundamental MMF.
N ph I K wn
F3ph,1 (θ,t) = 1.35 sin (θ − ωt)
P
❖ BAC sequence: Counterclockwise
direction of fundamental MMF.
N ph I K wn
F3ph,1 (θ,t) = 1.35 sin (θ + ωt)
P
Reversing Direction of Rotation of Rotating Magnetic Field
10/17/2023 7:24 AM First Part, Lecture (3) – Dr. Eng. Mohamed Sharawy Page No. 24 of 25
Benha University
Faculty of Engineering at Shoubra EPE312 - Electric Machines (2) “AC Rotating Machines”
Electrical Engineering Department
End of Lecture (1)
10/17/2023 7:24 AM First Part, Lecture (3) – Dr. Eng. Mohamed Sharawy Page No. 25 of 25
Benha University
Faculty of Engineering at Shoubra EPE312 - Electric Machines (2) “AC Rotating Machines”
Electrical Engineering Department
End of First Part
10/17/2023 7:24 AM First Part, Lecture (3) – Dr. Eng. Mohamed Sharawy Page No. 26 of 25
