Lecture 1 electric machinery fundamental

Advanced Power Systems

Dr. Kar
U of Windsor


Dr. Kar
271 Essex Hall
Email:
Office Hour: Thursday, 12:00-2:00 pm
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GA: TBA
B20 Essex Hall
Email: TBA & TBA
Office Hour: -----


Course Text Book:









Electric Machinery Fundamentals by Stephen J. Chapman, 4th Edition,
McGraw-Hill, 2005
Electric Motor Drives – Modeling, Analysis and Control by R. Krishnan
Pren. Hall Inc., NJ, 2001

Power Electronics – Converters, Applications and Design by N. Mohan, J.
Wiley & Son Inc., NJ, 2003
Power System Stability and Control by P. Kundur, McGraw Hill Inc., 1993
Research papers

Grading Policy:
Attendance
Project
Midterm Exam
Final Exam

(5%)
(20%)
(30%)
(45%)


Course Content


Working principles, construction, mathematical modeling,
operating characteristics and control techniques for
synchronous machines



Working principles, construction, mathematical modeling,
operating characteristics and control techniques for
induction motors



Introduction to power switching devices



Rectifiers and inverters



Variable frequency PWM-VSI drives for induction motors



Control of High Voltage Direct Current (HVDC) systems


Exam Dates



Midterm Exam:



Final Exam:


Term Projects
Group 1:

Student 1 ()
Student 2 ()
Student 3 ()
Project Title:
Group 2:
Student 1 ()
Student 2 ()
Student 3 ()
Project Title:
Group 3:
Student 1 ()
Student 2 ()
Student 3 ()


Synchronous Machines


Construction



Working principles



Mathematical modeling



Operating characteristics


CONSTRUCTION


Salient-Pole Synchronous Generator
1. Most hydraulic turbines have to turn at low speeds
(between 50 and 300 r/min)
2. A large number of poles are required on the rotor

d-axis

Nonuniform airgap

N

D ≈ 10 m
q-axis

Turbin
e

Hydro (water)

Hydrogenerator

S

S

N


Salient-Pole Synchronous Generator

Stator

otor
r
e
l
o
t-p
Salien


Cylindrical-Rotor Synchronous Generator

Stator

Cylindrical rotor


Damper Windings


Operation Principle
The rotor of the generator is driven by a prime-mover

A dc current is flowing in the rotor winding which
produces a rotating magnetic field within the machine

The rotating magnetic field induces a three-phase
voltage in the stator winding of the generator


Electrical Frequency
Electrical frequency produced is locked or synchronized to
the mechanical speed of rotation of a synchronous
generator:
 
 

fe =

nm P
120

where fe = electrical frequency in Hz
P = number of poles
nm= mechanical speed of the rotor, in r/min


Direct & Quadrature Axes

d-axis
Stator winding
N

Uniform air-gap
Stato
r

q-axis

Rotor winding
Rotor
S

Turbogenerator


PU System
Per unit system, a system of dimensionless parameters, is used for
computational convenience and for readily comparing the performance
of a set of transformers or a set of electrical machines.
PU Value =

Actual Quantity
Base Quantity

Where ‘actual quantity’ is a value in volts, amperes, ohms, etc.
[VA]base and [V]base are chosen first.
I base =

[VA ] base
[V ] base

Pbase = Qbase = S base = [VA ] base = [V ] base [ I ] base

Rbase = X base = Z base
Ybase =
Z

PU

[ I ] base
[V ] base

=

Z

ohm

Z base

2
2
[V ] base [V ] base
[V ] base
=
=
=
[ I ] base S base [VA ] base


Classical Model of Synchronous Generator



The leakage reactance of the armature coils, Xl



Armature reaction or synchronous reactance, Xs



The resistance of the armature coils, Ra



If saliency is neglected, Xd = Xq = Xs
jXs

jXl

Ra

+
+
E δ

Ia
Vt

0o

Equivalent circuit of a cylindrical-rotor synchronous machine

Phasor Diagram

q-axis
E
IaXs

δ
φ

IaRa
Ia

d-axis

Vt

IaXl


The following are the parameters in per unit on machine rating of a 555
MVA, 24 kV, 0.9 p.f., 60 Hz, 3600 RPM generator
Lad=1.66

Laq=1.61

Ll=0.15

Ra=0.003

(a)When the generator is delivering rated MVA at 0.9 p. f. (lag) and rated
terminal voltage, compute the following:
(i) Internal angle δi in electrical degrees
(ii) Per unit values of ed, eq, id, iq, ifd
(iii) Air-gap torque Te in per unit and in Newton-meters


(b) Compute the internal angle δi and field current ifd using the following
equivalent circuit


Direct and Quadrature Axes










The direct (d) axis is centered magnetically in the center of the north pole
The quadrature axis (q) axis is 90o ahead of the d-axis
θ: angle between the d-axis and the axis of phase a
Machine parameters in abc can then be converted into d/q frame using θ
Mathematical equations for synchronous machines can be obtained from
the d- and q-axis equivalent circuits
Advantage: machine parameters vary with rotor position w.r.t. stator, θ,

thus making analysis harder in the abc axis frame. Whereas, in the d/q
reference frame, parameters are constant with time or θ.
Disadvantage: only balanced systems can be analyzed using d/q-axis
system


d- and q-Axis Equivalent Circuits

+

Rfd

+

pψkd1

+
-

-

pψfd

vfd

ψq

Xl

Xfd

Ifd

Ikd1

Ra

Id

Imd

Rkd1

Xmd

Vtd

p ψd

Xkd1

-

d-axis
Imd=-Id+Ifd+Ikd1
− ψd

Xl

+

pψkq1

-

Ikq1
Rkq1

Ra

Imq=-Iq+Ikq1

Iq

Imq
Xmq

p ψq

Xkq1

q-axis

Vtq


Small disturbances in a power system
o
o
o

Gradual changes in loads
Manual or automatic changes of excitation
Irregularities in prime-mover input, etc.

Importance of steady-state stability
o

Knowledge of steady-state stability provides valuable information about
the dynamic characteristics of different power system components and
assists in their design
- Power system planning
- Power system operation
- Post-disturbance analysis


Related Terms
o
o
o

o

o
o

o

Generator Modeling using the d- and q-axis equivalent circuits
Transmission System Modeling with a RL circuit

A Small Disturbance is a disturbance for which the set of equations
describing the power system may be linearized for the purpose of
analysis
Steady-State Stability is the ability to maintain synchronism when the
system is subjected to small disturbances
Loss of synchronism is the usual symptom of loss of stability
Infinite Bus is a system with constant voltage and constant frequency,
which is the rest of the power system
Eigen values and eigen vectors are used to identify system steady-state
stability condition


The Flux Equations

(

)

ψ d = − X md + X l id + X md ikd1 + X md i fd

(

)

(

)

ψ kd1 = − X md id + X md + X kd1 ikd1 + X md i fd

(

)

ψ fd = − X md id + X md ikd 1 + X md + X fd i fd

(

)

ψ q = − X mq + X l iq + X mq ikq1

(

)

ψ kq1 = − X mq iq + X mq + X kq1 ikq1