Topic 2 Reference Frame Theory
ELE847 Advanced Electromechanical Systems
2011
Edition
Bin Wu
Professor
Dept of Electrical & Computer Engineering
Office:
ENG328
Tel:
(416) 979
‐
5000 ext: 6484
Email:
[email protected]
Advanced Electromechanical Systems
ELE847 2011
‐
2
‐
Main Topics
1. Introduction
2. Transformation in the stationary reference frame
3. Transformation between different reference frames
4. Transformation of 3
‐
phase resistive circuits
5. Transformation of 3
‐
phase inductive circuits
6. Transformation of other 3
‐
phase circuits

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Advanced Electromechanical Systems
ELE847 2011
‐
3
‐
What is a reference frame?
Reference frame is a mathematical convention for the representation of
physical variables (voltage, current, flux linkage, etc.)
Purpose of developing reference frame
The system variables can be transformed from one reference frame to another
to
simplify motor dynamic models
simplify analysis, simulation and design of dynamic systems
facilitate real
‐
time digital implementation of control schemes
Most commonly
‐
used reference frames
Stationary reference frame
‐
abc
stationary reference frame
‐
dq
stationary frame (it is known as
αβ
reference frame in literature)
Rotating or arbitrary reference frames
‐
dq
rotating reference frames
Introduction
Advanced Electromechanical Systems
ELE847 2011
‐
4
‐
Three
‐
phase variable representation
Consider the three
‐
phase currents
i
a
,
i
b
and
i
c
, given by
0
5
10
15
20
25
30
-1
-0.5
0
0.5
1
Time [ms]
Amplitude [Pu]
i
a
i
b
i
c
)
sin(
ˆ
)
(
)
sin(
ˆ
)
(
)
sin(
ˆ
)
(
3
4
3
2
π
π
ω
ω
ω
−
=
−
=
=
t
i
t
i
t
i
t
i
t
i
t
i
c
b
a
Transformation in the Stationary Frame
Note:
The analysis is performed for current variables, but is applicable to
any other types of variables (voltage, flux linkage, etc.)