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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. REFERENCES [1] [2] [3] [4] [5] [6] [7] Zahirrudin Idris and Mustafar Kamal Hamzah, “Implementation of a new Single-phase Cycloconverter based on Single-phase Matrix Converter Topology using Sinusoidal Pulse Width Modulation with Passive Load Condition,” ICIEA 2006. Sedat Sunter and Omur Aydo gmu, “Implementation of a single-phase matrix converter induction motor drive,” Electr Eng (2008) 90:425–433. Zahirrudin Idris, Mustafar Kamal Hamzah and Ahmad Maliki Omar, “Implementation of Single-Phase Matrix Converter as a Direct AC-AC Converter Synthesized Using Sinusoidal Pulse Width Modulation with Passive Load Condition,” IEEE PEDS 2005. Siti Zaliha Mohammad Noor, Mustafar Kamal Hamzah and Ahmad Farid Abidin, “Modelling and Simulation of a DC Chopper Using Single Phase Matrix Converter Topology,” IEEE PEDS 2005. H. Mohd Hanafi, Z. Idris and M. K. Hamzah,, “Modelling & Simulation of Single-phase Matrix Converter as a Frequency Changer with Sinusoidal Pulse Width Modulation Using MATLAB/Simulink,” First International Power and Energy Coference PECon 2006, November 28-29, 2006, Putrajaya, Malaysia. Ebrahim Babaei, Seyed Hossein Hosseini and Gevorg B. Gharehpetian, “Reduction of THD and low order harmonics with symmetrical output current for single-phase ac/ac matrix converters,” Electrical Power and Energy Systems 32 (2010) 225–235. Taha Ahmad Hussein, “Voltage Spikes and Harmonics Reduction for Inductive Load Single-phase Matrix Converter Using MATLAB,” 2009 Second International Conference on Computer and Electrical Engineering.