Basic Electrical and Electronics Engineering: Unit II: Electrical Machines
Torque Equation of the Synchronous Motor
I lags/leads V by an angle ϕ and lags behind Er, by an angle Ɵ. Ɵ = tan-1 (Xs /Ra)
TORQUE
EQUATION OF THE SYNCHRONOUS MOTOR
OL
= Supply voltage/phase
I
= Armature current
LM
= Back emf at a load angle of δ
OM
= Resultant voltage, ER
Er
= IZs(or I Xs if Ra is negligible)
I
lags/leads V by an angle ϕ and lags behind Er, by an angle Ɵ.
Ꮎ = tan-1
(Xs /Ra)
✓ Line NS is drawn at angle ϕ to LM
✓ LN and QS are perpendicular to NS
✓ Mechanical power developed per phase in
the rotor,
Pmech
=EbI cos Ψ
Δ
OMS, MS = I Zs cos Ψ
MS
= NS - NM = LQ - NM
I
Zs cos Ψ = Vcos (Ɵ - δ) - Eb cos Ɵ
(or) I cos Ψ = V/Zs cos (Ɵ - δ) - Eb/Zs
cos Ɵ
Pmech/phase
= Eb [V/Zs cos (Ɵ - δ) - Eb/Zs cos
Ɵ]
Pmech/phase
= EbV/Zs cos (Ɵ - δ) - Eb2/Zs
cos Ɵ]
✓ This is the expression for the mechanical power developed
in terms of load angle (α) and the internal angle of the motor for a constant
voltage V & Eb.
Maximum power developed:
✓ Condition for maximum power developed can be found
by differentiating the above expression with respect to load angle and then
equating it is zero.
sin
(Ɵ - δ) = 0 (or) Ɵ = δ
Value
of maximum power,
This shows that the maximum power and hence torque depends on V and Eb that is excitation.
Maximum
value of Ꮎ
and hence α is 90° for all values of V and Eb, this limiting value of
α is the same but maximum torque will be proportional to the maximum power
developed.
If
Ra is neglected, then Zs = Xs and Ɵ = 90°.
COS
Ɵ = 0
This
gives the value of mechanical power developed in terms of δ - the basic
variable of a synchronous machine.
Pmech(max)
= EbV/Xs when (δ = 90°)
This
corresponds to the 'pull out' torque.
To
determine the value of exitation or induced emf Eb to give maximum
power developed possible, differentiate with respect to Eb and equal
to zero.
Where
Ra
→ eflective resistance of the motor
Hence
(P mech)max = V2/4Ra
Basic Electrical and Electronics Engineering: Unit II: Electrical Machines : Tag: : - Torque Equation of the Synchronous Motor
Basic Electrical and Electronics Engineering: Unit II: Electrical Machines
Under Subject
Basic Electrical and Electronics Engineering
BE3251 2nd semester Mechanical Dept | 2021 Regulation | 2nd Semester Mechanical Dept 2021 Regulation
Basic Electrical and Electronics Engineering
BE3251 2nd Semester CSE Dept 2021 | Regulation | 2nd Semester CSE Dept 2021 Regulation
Related Subjects
Professional English II
HS3251 2nd Semester 2021 Regulation | 2nd Semester Common to all Dept 2021 Regulation
Statistics and Numerical Methods
MA3251 2nd Semester 2021 Regulation M2 Engineering Mathematics 2 | 2nd Semester Common to all Dept 2021 Regulation
Engineering Graphics
GE3251 eg 2nd semester | 2021 Regulation | 2nd Semester Common to all Dept 2021 Regulation
Physics for Electrical Engineering
PH3202 2nd Semester 2021 Regulation | 2nd Semester EEE Dept 2021 Regulation
Basic Civil and Mechanical Engineering
BE3255 2nd Semester 2021 Regulation | 2nd Semester EEE Dept 2021 Regulation
Electric Circuit Analysis
EE3251 2nd Semester 2021 Regulation | 2nd Semester EEE Dept 2021 Regulation
Physics for Electronics Engineering
PH3254 - Physics II - 2nd Semester - ECE Department - 2021 Regulation | 2nd Semester ECE Dept 2021 Regulation
Electrical and Instrumentation Engineering
BE3254 - 2nd Semester - ECE Dept - 2021 Regulation | 2nd Semester ECE Dept 2021 Regulation
Circuit Analysis
EC3251 - 2nd Semester - ECE Dept - 2021 Regulation | 2nd Semester ECE Dept 2021 Regulation
Materials Science
PH3251 2nd semester Mechanical Dept | 2021 Regulation | 2nd Semester Mechanical Dept 2021 Regulation
Basic Electrical and Electronics Engineering
BE3251 2nd semester Mechanical Dept | 2021 Regulation | 2nd Semester Mechanical Dept 2021 Regulation
Physics for Civil Engineering
PH3201 2021 Regulation | 2nd Semester Civil Dept 2021 Regulation
Basic Electrical, Electronics and Instrumentation Engineering
BE3252 2021 Regulation | 2nd Semester Civil Dept 2021 Regulation
Physics for Information Science
PH3256 2nd Semester CSE Dept | 2021 Regulation | 2nd Semester CSE Dept 2021 Regulation
Basic Electrical and Electronics Engineering
BE3251 2nd Semester CSE Dept 2021 | Regulation | 2nd Semester CSE Dept 2021 Regulation
Programming in C
CS3251 2nd Semester CSE Dept 2021 | Regulation | 2nd Semester CSE Dept 2021 Regulation