ISSN: 1693-6930
TELKOMNIKA Vol. 13, No. 3, September 2015 : 783 – 793
786 As can be seen from Equation 7-9, the structure of the single-phase IM under open-
phase fault is similar to the structure of the single-phase IM with two main and auxiliary windings. The only difference between these two types of motors is the motor parameters. In
the single-phase IM under open-phase fault it is obtained: L
ds
=M
ds
=R
ds
=0 but in the healthy single-phase IM: L
ds
≠L
qs
, M
ds
≠M
qs
and R
ds
≠R
qs
. In the next section, a vector control system based on Rotor FOC RFOC for healthy
single-phase IM is presented. It is obvious by substituting L
ds
=M
ds
=R
ds
=0, this control system can be used for faulty single-phase IM.
4. Proposed Method for Vector Control of Single-Phase IM Based on RFOC
In this section, using transformation matrix, a method for vector control of single-phase IM is presented. The reason of using this transformation matrix is changing the unbalanced
equations of the single-phase IM due to the L
ds
≠L
qs
, M
ds
≠M
qs
and R
ds
≠R
qs
to the balanced equations.
4.1. Transformation Matrix for Stator Current Variables
The idea of using this transformation matrix is obtained from equivalent circuit of the single-phase IM. Figure 2 shows the equivalent circuit of single-phase IM.
Figure 2. Equivalent circuit of single-phase IM All the parameters in Figure 2, have been defined in Appendix. It can be shown that
using following definitions,
a m
m a
V jZ
V Z
V I
I j
I
4 3
1 1
10 Figure 2 can be simplified as Figure 3 see Appendix.
Figure 3. Simplified equivalent circuit of single-phase IM
TELKOMNIKA ISSN: 1693-6930
A Novel Technique for Fault-Tolerant Control of Single-Phase IM M. Jannati 787
In Figure 3,
1 2
2 2
1 2
2 2
4 3
4 3
j Z
jZ Z
Z Z
j Z
jZ Z
Z Z
Z Z
Z Z
Z
b la
lm b
lm f
la lm
f lm
11 In 11, Z
3
and Z
4
are the parameters in terms of inductances L
ds
andor L
qs
andor M
ds
andor M
qs
. As can be seen using 10, the equivalent circuit of single-phase IM Figure 2 changed into a balanced circuit Figure 3. Equation 10 can be re-written as follows:
m a
m a
m a
m a
I I
N N
j I
jI I
N N
jI
1 1
12 And,
m a
m a
V Z
V jZ
V V
jZ V
Z jV
3 4
1 3
4 1
13 Equation 12 and 13 are transformation matrices for transformation of variables from
unbalanced set eg., Figure 2 to the balanced set eg., Figure 3. Based on 12 and 13, following transformation matrices for stator voltage and current variables can be derived:
Transformation matrix for stator voltage variables:
s qs
s ds
e e
e e
s qs
s ds
e vs
e qs
e ds
Z Z
Z Z
T
cos
sin sin
cos
3 4
3 4
14 Transformation matrix for stator current variables:
s qs
s ds
e e
qs ds
e e
qs ds
s qs
s ds
e is
e qs
e ds
i i
M M
M M
i i
T i
i
cos sin
sin cos
15 To obtain 14 and 15, following substituting have been considered in 14 and 15
superscript “e’’ indicates that the variables are in the rotating reference frame. Moreover, “ θ
e
’’ is the angle between the stationary reference frame and the rotor flux oriented reference frame.
s qs
m s
ds a
e qs
e ds
s qs
m s
ds a
e qs
e ds
ds qs
a m
e e
i I
i I
i I
i jI
v V
v V
v V
v jV
M M
N N
j
, ,
, ,
, ,
, ,
cos 1
, sin
1 1
1 1
16 It is expected by using 14 and 15 the unbalanced equations of single-phase IM
become similar to the balanced equations.
4.2. Equations of RFOC for Single-Phase IM Based on Proposed Method
