Section A: Balanced systems
EDEE2063 Modern Power Systems/
Practice
Title
Total Marks
Class
Due Date
:4
: Symmetrical Components
: 5%
: 1 April 2022
: 5 April 2022
Date submitted :
Final Awarded Marks
25 / 04 / 22
NAME
Student ID
Lim
Li
Sheng
Submission Checklist (To be filled-up by marker)
Report
Turn-it-in Report
Extension Granted (YES/NO)
Overall Comments:
Signature
: …………………………
Marker : Lau Kim Boon
Date
:
0130208
Fig.1: Balanced systems
The subscripts in all three systems of symmetrical components denote the components in various stages.
The sum of the appropriate components of the distinct sequences in a phase equals the total voltage of
that phase. Our symmetrical components, notably those referring to the a phase, can now be written in
terms of three ways.
Symmetrical voltage
1.0a
�� = ��0 + ��1 + ��2
1.0b
�� = ��0 + ��1 + ��2
1.0c
�� = ��0 + ��1 + ��2
After simplification the notation is as follows; define
1.1a
�0 = ��0
1.1b
�1 = ��1
�2 = ��2
1.1c
After substituting their equivalent values
1.2a
�� = � 0 + �1 + �2
�� = �0 + �2 �1 + ��2
�� = �0 + ��1 + �2 �2
1.2b
1.2c
These equations may be manipulated to solve for V0, Vl, and V2 in terms of
Va,Vb
�0 =
1
( � + � �� + � 2 �� )
3 �
1
�2 = ( �� + � �� + � 2 �� )
3
�1 =
1.3a
1
( � + �� + �� )
3 �
1.3b
1.3c
These equations may be manipulated to solve for V0, Vl, and V2 in terms of Va,Vb
Phase Current
�� = �0 + � + �2
1.4a
�� = �0 + �2 �1 + ��2
1.4b
�� = �0 + ��1 + �2 �2
1.4c
Sequence Current
1.5a
�0 =
�1 =
1.5b
�2 =
1.5c
1
( � + �� + �� )
3
1
( � + � �� + �2 �� )
3 �
1
( � + � �� + �2 �� )
3
The unbalanced system is therefore defined in
terms of three balanced systems. Eq 1.2 may
be used to convert phase voltages (or currents)
to symmetrical component voltages (or
currents) and vice versa [Eq 1.3]
Section B: Symmetrical components
Fig.2
Power Quality Teaching Toy
Fig.3 symmetrical components
In conclusion the subsequent lines for ��0 , ��0 ��� ��0 are zero sequence. ��1 , ��1 and . Values are
positive sequence. ��2 , ��2 and ��2 values indicate negative sequence. The dotted line diagram indicates
the line remains flat. In a balanced power system in Fig 1, the phasors have equal amplitudes and are
displaced 120° relative to each other. By the definition of symmetrical components, ��1 always lags
��1 by a fixed angle of 120° and always has the same magnitude as ��1 . Similarly ��1 leads ��1 by
120°.