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A Simple Control Scheme for Single-Phase Matrix Converter
Operating as Frequency Changer
V.Sravan Kumar,
Dr. S.Senthil
Kumar,
(LM-ISTE, AM-IETE)
Asst.Prof., EEE, Lakireddy
Bali Reddy College of
Engineering, Mylavaram,
A.P., India.
(M-IEEE)
EEE, NIT,
Tiruchirappalli,
Tamilnadu, India.
[email protected]
[email protected]
N. NagaSekhara Reddy,
M.B.Chakkravaarthy,
(Ph.D Scholar)
IIT Hyderabad, Telangana,
India.
(LM-ISTE, AM-IETE, M-IEEE)
Assoc. Prof., EEE, Lakireddy Bali
Reddy College of Engineering,
Mylavaram, A.P., India.
[email protected]
Abstract-
This paper presents the simple control scheme for
single-phase matrix converter (SPMC) for A.C. to A.C. power
conversion. A generalized switching logic for different frequency
conversions has been developed. A sinusoidal pulse width
modulation (SPWM) technique is proposed using low cost
operational amplifiers and logic gates for the operation of
SPMC. Inductive loads results spikes in the output for which safe
commutation is incorporated. And for controlling the magnitude
of output voltage a simple closed loop modulation index based
controller is developed. The proposed controller adjusts the pulse
width and switching states for obtaining required magnitude and
frequency respectively. Mat lab/Simulink simulations have also
been carried out. The simulated results show the working and
usefulness of the op-amp based controller for single-phase matrix
converter applications.
Key words: SPMC, SPWM.
I.
INTRODUCTION
The A.C. to A.C. power converters, in which ac power at
one frequency is directly converted to ac power at another
frequency, constitute converter-inverter modules for which
Matrix converter is the alternative topology as it is more reliable
and efficient for A.C. to A.C. power conversion without any
intermediate dc conversion link [1-3]. Matrix converters are
single stage, bi-directional converters giving all-silicon solution
for A.C. to A.C. power conversion with sinusoidal input and
output wave forms irrespective of load [4]. They eliminate energy
storage components, i.e., temperature sensitive electrolytic dclink capacitors. Because of which Matrix converters are used
where reduction of installation area is essential [5]. The numbers
of phases on input and output sides are independent of each other
in case of matrix converter. There is no limitation on output
frequency [6]. A matrix converter can be used as a full fourquadrant power supply without any additional power hardware
[7]; power is converted from ac unregulated frequency & voltage
to ac regulated frequency & voltage.
The main purpose of this paper is to present a generalized
logic for implementing SPMC as frequency converter and
describe successful implementation of the SPMC performing all
the basic functions of a direct AC-AC converter using proposed
generalized technique.
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given frequency into required frequency which are stated below
the figure.
S1A
Single-Phase Matrix Converter
The single-phase matrix converter (SPMC) consists of four
bidirectional switches connecting the single-phase input to the
single-phase output. Namely switches S1, S2, S3, and S4 which
are capable of conducting current in both directions are used and
are shown in Fig.1. SPMC operates in two modes for converting
S2A
Vo, fo
Vin, fin
LOAD
S3B
S4B
S4A
S3A
Fig.1 SPMC for A.C. to A.C. Power Conversion.
The topology depicted in Fig. 1 converts the input voltage,
Vin(t) with constant amplitude and frequency, through the four
bi-directional switches to the output terminals in accordance with
pre-calculated switching angles.
A. Modes of Operation.
The input voltage of the matrix converter presented in
above figure is given by
Vin (t )  Vi cos i t .
....... (1)
The matrix converter is controlled in such a manner that the
fundamental of the output voltage Vo(t) is
Vo (t )  Vo cos ot .
....... (2)
With input voltage from eqn. 1, the matrix converter switching
angles will be calculated and operates in different modes (eqn. 3)
by which the required output voltage (eqn. 2) is obtained [2].
 Vin (t )

Vo (t )   Vin (t )
 0

Mode-1 S1 & S4 are on
Mode-2 S2 & S3 are on
…... (3)
Mode-3 S1 & S2 or S3 & S4 are on
Mode-1: It is for obtaining the positive half cycle of output by
appropriate switching.
S1A
II.
S2B
S1B
S2B
S1B
I
N
P
U
T
S2A
LOAD
S3B
S3A
S4A
Fig.2 (a) For +ve half cycle of input
S4B
In this mode switches S1 and S4 are in on state either by a
pulse or PWM in positive cycle of the input by which the input
voltage can be applied directly across the load and it is shown in
Fig.2 (a), which is considered as state-1.
By Fig2 (b) it is clear that for obtaining positive half cycle
of output in the negative half of the input switches S2 and S3 are
in on state either by a pulse or PWM by which the input voltage
can be applied across the load, which can be considered as state3. Now in positive and negative half cycles of input we are able
to obtain positive half cycle of the output.
power converter. From the Table-1 it is clear that different
switching states should be implemented for different frequency
conversions [1].
Table I. Switching states for different frequency conversions
Input
frequency
Output
frequency
50
100
S1A
S2B
S1B
I
N
P
U
T
S2A
LOAD
150
S3B
S3A
S4A
S4B
50
25
Fig.2 (b) For -ve half cycle of input
Mode-2:It is for obtaining the negative half cycle of output by
appropriate switching. For obtaining negative half cycle of output
the positive half of the input is inverted and fed across load by
making S2 and S3 on and the negative half of the input is fed
directly across load as S1 and S4 are made on. This can be clearly
understood by Fig.3 (a) and (b) which can be considered as state
4 and 2 respectively
S1A
S2B
S1B
I
N
P
U
T
S3A
S4A
S2B
S1B
I
N
P
U
T
S4B
S2A
LOAD
S3B
S3A
Commutation
switch ON
1
2
1
3
4
2
1
3
1
2
4
2
1
4
3
2
1
4
1
4
3
2
3
2
S1a, S4a
S1b, S4b
S1a, S4a
S2b, S3b
S2a, S3a
S1b, S4b
S1a, S4a
S2b, S3b
S1a, S4a
S1b, S4b
S2a, S3a
S1b, S4b
S1a, S4a
S2a, S3a
S2b, S3b
S1b, S4b
S1a, S4a
S2a, S3a
S1a, S4a
S2a, S3a
S2b, S3b
S1b, S4b
S2b, S3b
S1b, S4b
S2a
S2b
S2a
S1b
S1a
S2b
S2a
S1b
S2a
S2b
S1a
S2b
S2a
S1a
S1b
S2b
S2a
S1a
S2a
S1a
S1b
S2b
S1b
S2b
The generalized logic developed is as in table II. It
automatically selects the switching states based up on the sample
signals of input and required output signals.
Fig.3 (a) For +ve half cycle of input
S1A
Regular
switch ON
S2A
LOAD
S3B
12.5
State
S4A
S4B
Table II. Generalized logic for different frequency
conversions
Input wave
Output wave
Switching state
Positive
Positive
State-1
Positive
Negative
State-3
Negative
Positive
State-4
Negative
Negative
State-2
Fig.4 gives the switching pulses for a frequency conversion of
50Hz-50Hz [5], from which it is evident that one of the two
switches is given by pwm pulse where as the other (&
commutation switch) is given by direct pulse..
Fig.3 (b) For -ve half cycle of input
In each state of operation in addition to the two switches to
be operated for commutation one more switch is made on by
direct pulse. The information regarding this given in Table - 1 by
which it is clear that in states one and two is S2 is on and in states
three and four is S1 in on. (For practical implementation there
should be a delay in between every state of operation mentioned
in order to eliminate short circuits).
B. Generalized control logic for different frequency
conversions.
Modulating
Signal Vo, fo
S4a for sine
PWM
S4b for sine
PWM
S1a, S2a
S1b, S2b
A generalized switching logic is developed for different
frequency conversions for SPMC operating as A.C. to A.C.
Mode-1
Mode-2
Mode-1
Fig.4 Switching Pulses
Mode-2
Low cost op-amp based logic circuit is developed for the
implementation of generalized logic given in Table-II for SPMC
operating as frequency changer, and it is shown in Fig.5 whose
operation is as follows.
In closed loop for changing the output magnitude q is compared
with q*, (calculated in accordance with the reference/required
voltage) and the error is fed to controller which gives modified q.
Then by using the controller output the pulses are generated using
the respective switching technique and control logic. Then the
generated control pulses are fed to SPMC.
III.
SIMULATION RESULTS
SPMC is a single stage A.C. to A.C. converter, eliminated the
bulky capacitor banks which reduces more area while
installation. It has the advantages as economic, sensitive, cost
effective and bi-directional conversion. Hence SPMC has gained
importance and number of techniques for its operation has been
proposed, likely different modulation and commutation
techniques. The SPMC is simulated in MATLAB/SIMULINK
environment for all the proposed techniques.
Fig.5 Block diagram of Proposed control scheme for SPMC
Initially two sample signals are generated with voltages
magnitudes and frequencies as Vin, fin and Vo, fo of input &
required output respectively. Then they are inverted and both
inverted and non-inverted samples zero crossings are found out
because of which we can get positive and negative halves of
input and output waves, so that the logic stated in table-II is
implemented. And the pulses are generated, (one direct pulse and
one pwm pulse) incorporated with this logic using AND gates.
This is a simple logical circuit by which SPMC can be operated
as frequency changer for any frequency conversion with variable
magnitude.
C. Closed Loop Control of SPMC
A simple closed loop structure is incorporated for SPMC in
order to achieve the output of required magnitude and frequency
exactly. Keeping the ramp signal (carrier wave) magnitude
constant and varying the modulating wave (sinusoidal)
magnitude directly varies the output magnitude. In closed loop
the magnitude of the modulating wave is varied by a controller,
so that the output magnitude reaches the required value. The
block diagram showing the above mentioned arrangement is
shown by Fig.6.
Fig.7 Simulink model of SPMC
Fig.8 Closed Loop circuit of SPMC
The SPMC is simulated in MATLAB/SIMULINK environment
for the proposed technique. The results of the proposed technique
are observed and analyzed. Fig.7 gives the Simulink model of
SPMC and Fig.8 gives the modulation index based closed loop
which is proposed above in Fig.6.
v in
>=
0
4a
S4a
input
3a
S3a
3b
0
S3b
>=
4b
As the required output frequency is directly related to
modulating wave frequency, until and unless it is changed the
output frequency cannot be changed even in closed loop.
Similarly in order to obtain the required output magnitude the
modulating signal magnitude has to be changed. As it is
mentioned that the ramp wave (carrier) is maintained constant the
ratio of modulation wave and ramp signal (q) is directly
proportional to magnitude of modulating wave. Therefore
changing q means changing the magnitude of modulating wave.
1
q
v out
S4b
>=
q
Modulating Signal
-1
>=
Out1
Carrier Signal
S2a
S1a
S1b
S2b
PIcontroller
q*
Modulation
technique
fo
q =V0/Vin
Control
logic
fin
Driver
Circuit
Control pulses
Fig.6 Closed loop structure
Fig.9 Proposed control logic for SPMC
The proposed generalized control scheme of SPMC for
different frequency conversions shown in Fig.4 is implemented in
Matlab / Simulink and the results are shown below (Fig.10 Fig.13). Fig.9 shows the Simulink model of proposed generalized
control scheme which can be easily implemented by low cost
operational amplifiers and logic gate ICs, whose results shows
the usefulness of proposed generalized controlscheme.
Simulation parameters for all the operating modes are as follows
Input voltage
: 10V
Modulation Index
: 0.5
Switching frequency
: 1000Hz
Load parameters
: R=50Ω, L=5mH
Fig.10 gives the Simulink results and harmonic analysis of output
voltage and currents with which we can say that output current is
0.994Amps with 28.74% harmonics and output voltage is 49.76V
with 28.74%. The results regarding conversion of frequency from
one frequency (50Hz) to the other (100Hz) can be observed from
Fig.11.
Fig.12 gives the Simulink results and harmonic analysis of output
voltage and currents with which we can say that fo=25Hz, output
current is 0.998Amps with 57.60% harmonics and output voltage
is 49.5V with 57.60%.
FFT analysis
FFT analysis
Current
Voltage
Fig.12 Closed Loop Results for fin=50Hz, fo=25Hz, fs=2000Hz
Fig.13 gives the Simulink results and harmonic analysis of output
voltage and currents with which we can say that fo=12.5Hz,
output current is 1Amps with 54.44% harmonics and output
voltage is 50.1V with 54.44%.
Fig.10 Closed Loop Results for fin=50Hz, fo=50Hz, fs=2000Hz
The results of all the techniques are observed and compared.
Fig.6 gives the Simulink results and harmonic analysis of output
voltage and currents with which we can say that output current is
0.994Amps with 28.74% harmonics and output voltage is 49.76V
with 28.74%. The results regarding conversion of frequency from
one frequency (50Hz) to the other (100Hz) can be observed from
Fig.7.
Voltage
Current
FFT analysis
Current
Voltage
FFT analysis
Fig.11 Closed Loop Results for fin=50Hz, fo=100Hz, fs=2000Hz
Fig.11 gives the Simulink results and harmonic analysis of output
voltage and currents with which we can say that fo=100Hz,
output current is 0.998Amps with 35.78% harmonics and output
voltage is 49.5V with 35.78%.
Fig.13 Closed Loop Results for fin=50Hz, fo=12.5Hz, fs=2000Hz
From the simulation results it is clear that the proposed
generalized logic can be used for any frequency conversion and
modulation index based closed loop is successful in obtaining the
required output voltage.
IV.
CONCLUSION
This paper briefly explains successful implementation of SPMC
as frequency changer using SPWM with a generalized switching
logic. This added feature will enable the ease of SPMC to operate
as A.C. to A.C. power converter at any frequency conversion
with low operating cost and it increases the band of SPMC
applications. Matlab/Simulink simulations are carried out. The
simulated results show the working and usefulness of the op-amp
based controller for single-phase matrix converter applications.
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