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Transcript
A Simple Control Scheme for Single-Phase Matrix
Converter Operating as Frequency Changer
V.Sravan Kumar,
S.Senthil Kumar,
N. NagaSekhara Reddy,
(LM-ISTE, AM-IETE)
(M-IEEE)
(Ph.D Scholar)
M.B.Chakkravaarthy,
(LM-ISTE, AM-IETE, M-IEEE)
EEE, Lakireddy Bali Reddy
College of Engineering,
Mylavaram, A.P., India.
[email protected]
EEE, National Institute of
Technology, Tiruchirappalli,
Tamilnadu, India.
[email protected]
IIT Hyderabad,
Telangana, India.
[email protected]
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 converter 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 dc-link 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 four-quadrant
power supply without any additional power hardware [7]; power is converted from ac unregulated frequency and 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.
II.
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 are shown in Fig.1. SPMC operates in two modes for converting given frequency into required frequency which are
stated below the figure.
S1A
S2B
S1B
S2A
Vo, fo
Vin, fin
LOAD
S3B
S3A
S4A
S4B
Fig.1 SPMC for A.C. to A.C. Power Conversion.
A. Modes of Operation:
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. 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 so that the fundamental of the
output voltage will be as in eqn. 2. The Matrix Converter operates in different modes by which the required output voltage
is obtained [2]. The different modes are shown by eqn. 3, among which mode - 3 in not useful.
 Vin (t )

Vo (t )   Vin (t )
 0

Mode-1 S1 & S4 are on
…... (3)
Mode-2 S2 & S3 are on
Mode-3 S1 & S2 or S3 & S4 are on
Mode-1: It is for obtaining the positive half cycle of output by appropriate switching. In this mode switches S1A and S4A
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), and it can be considered as state-1.
S1A
S2B
S1B
I
N
P
U
T
S1A
S2A
I
N
P
U
T
LOAD
S3A
S3B
S4A
S2A
LOAD
S3A
S3B
S4B
Fig.2 (a) For +ve half cycle of input
S2B
S1B
S4A
S4B
Fig.2 (b) For -ve half cycle of input
By Fig2 (b) it is clear that for obtaining positive half cycle of output in the negative half of the input switches S2 A and
S3A are in on state either by a pulse or PWM by which the input voltage can be applied across the load, and it is considered
as state-3. Now in positive and negative half cycles of input we are able to obtain positive half cycle of the output.
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 B and S3B on and the negative half of the
input is fed directly across load as S1B and S4B 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
S1A
S2A
I
N
P
U
T
LOAD
S3A
S3B
S2B
S1B
S4A
S2A
LOAD
S3A
S3B
S4B
Fig.3 (a) For +ve half cycle of input
S4A
S4B
Fig.3 (b) For -ve half cycle of input
In each state of operation in addition to the two switches to be operated, one more switch is made on by direct pulse
for commutation. The information regarding the switch that is to be made on in each state is given by the following table
(Table I). The commutation switch that is to be made on in states one and two is S2A and in states three and four is S1B.
(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.
A generalized switching logic is developed for different frequency conversions for SPMC operating as A.C. to A.C.
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
State
Regular switch
ON
Commutation
switch ON
50
50
100
150
25
12.5
1
2
1
3
4
2
1
3
1
2
4
2
1
4
3
2
1
4
1
4
3
2
3
2
1
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
S1a,
S4a
S2a
S2b
S2a
S1b
S1a
S2b
S2a
S1b
S2a
S2b
S1a
S2b
S2a
S1a
S1b
S2b
S2a
S1a
S2a
S1a
S1b
S2b
S1b
S2b
S2a
The generalized logic developed is presented in table II. It automatically selects the switching states based up on the
sample signals of input and required output signals.
Table II. Generalized logic for different frequency conversions
Input wave
Positive
Positive
Negative
Negative
Output wave
Positive
Negative
Positive
Negative
Switching state
State-1
State-3
State-4
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..
Modulating
Signal Vo, fo
S4a for sine
PWM
S4b for sine
PWM
S1a, S2a
S1b, S2b
Mode-1
Mode-2
Mode-1
Mode-2
Fig.4 Switching Pulses
Fig.5 Block diagram of Proposed control scheme for SPMC
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. 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.
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.
PIcontroller
q*
Modulation
technique
fo
q =V0/Vin
Fig.6 Closed loop structure
Control
logic
fin
Driver
Circuit
Control pulses
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.
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. 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
v in
>=
0
4a
S4a
input
3a
S3a
3b
S3b
>=
0
4b
1
q
v out
S4b
>=
q
Modulating Signal
-1
>=
Out1
Carrier Signal
S2a
S1a
S1b
S2b
Fig.9 Proposed control logic for SPMC
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.
Voltage
Current
Voltage
Fig.10 Closed Loop Results for fin=50Hz, fo=50Hz, fs=2000Hz
Current
FFT analysis
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.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%.
Voltage
Fig.12 Closed Loop Results for fin=50Hz, fo=25Hz, fs=2000Hz
Current
FFT analysis
Current
Voltage
FFT analysis
Fig.13 Closed Loop Results for fin=50Hz, fo=12.5Hz, 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%.
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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[2]
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[6]
[7]
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