Space Vector Modulation Techniques for Common mode Voltage Elimination in the Threelevel Voltage Source Inverter

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1 Space Vector Modulation Techniques for Common mode Voltage Elimination in the Threelevel Voltage Source Inverter Piotr Lezynski University of Zielona Gora Abstract- The low common mode voltage vector modulation technique for the three-level cascaded voltage source inverter is presented in the paper. The large number of available states for multilevel inverters can make implementation vector control strategies complicated. The main characteristic of the proposed modulation technique is its simplicity of implementation due to the fact that any available vector modulators can be used. implementation and characterizes by decreased the common mode voltage. VDC SA+ SB+ SC+ A B VDC C D VDC E F SD+ SE+ SF+ I. INTRODUCTION The negative effect of converting electrical energy by means of power converters is the emission of significant level of conducted electromagnetic disturbances [5]. The impulse output voltage of the inverter forms high frequency disturbance currents, which are created as a result of the impulse output voltage and parasite coupling in the system (mainly capacitive) [5]. Electromagnetic disturbances generated by the converter can cause several problems related to the immunity of electronic systems operating in its vicinity [] [5]. The application of multilevel topology inverter allows increased range of inverter output voltage and power. Additionally, in systems with multilevel inverters, lower level of electromagnetic disturbances occurs and there is a higher energy conversion efficiency compared with two-level inverters. [] [8] [5]. The cascade inverter (IHBI) (Fig. ) belongs to one of the modern multi-level inverter family. The three-level cascade inverter transforms electrical energy from three sources of DC energy to AC voltage energy []. This property predisposes cascaded inverters to couple energy from renewable energy sources []. Cascaded inverters are not widely used for drive systems because of the need to use isolation transformers. However, they can be successfully used in electric vehicles, where batteries can be easily divided into three separate groups. In order to obtain high dynamic in electric drive systems space vector control strategies are preferred [9] []. Scalar modulation strategies are easiest to implement in multilevel inverters [] [4] Vector strategy for multilevel inverters can be complicated due to the large number of available output voltage vectors. The classical decomposition method, commonly used for multilevel inverters is complicated when applied for cascade inverter topology [] [4]. In the paper new vector modulation technique for threelevel cascaded inverter is presented, which is very simple in 86 LfDM LfCM * Fig.. Three-level inverter with EMI filter. II. CfDM * * RfDM CCM VP VP VP COMMON MODE VOLTAGE Particularly important for electromagnetic compatibility of electronic systems are emitted conducted common mode disturbances (CM) which spread in the ground circuit. The danger of common node disturbances is related to disturbance currents propagated in large circuits. CM currents circuits are difficult to identify and they can cover other devices [5]. The source of common mode currents in the inverter system is the common mode voltage (V CM ). The common mode voltage is the potential of the star point of the load with respect to the ground, which is equal to the sum of all instantaneous values of phase voltages divided by their number. The common mode voltage in inverter systems most often is reduced through passive or active EMI filters at the output of the inverter [][5] (Fig..). Decreasing the level of the common mode voltage in inverters is also possible by using appropriate modulation techniques. The common mode voltage receives a specific value for a certain state of inverter s connectors. The base vectors of the inverter output voltages derived from the transformation () is shown in Figure.. = β V CM SA- SB- SC- SD- SE- SF- RCM V p V p V p LOAD ()

2 The common mode voltage in three-level inverter may take seven levels (Table I). To reduce maximal level of common mode voltage in the modulation process, vectors with low levels of V CM should be used only. Seven of base space vectors generate zero level of V CM. Modulation using only these vectors has been proposed and described in [4]. The disadvantage of this solution was a significant reduction in quality parameters of the inverter output voltages. Compromise can be reached by eliminating from the process the modulation of 8 vectors with the highest levels of disturbance. The common mode voltage is then limited to ±/V DC. Vector modulation technique for reducing high level of common mode voltage in multilevel inverters is relatively difficult to implement because of the need to choose an appropriate sequence of vectors. Despite the work carried out in recent years no vector modulation technique that allows reduction of V CM for multilevel inverters has received overwhelming advantage over the others. III. SPACE VECTOR MODULATION FOR MULTILEVEL INVERTERS In the three-level inverter there are 7 different combinations of the phase output voltage. The reference voltage vector is mostly formed of the next three base vectors. For multilevel inverters, due to the redundancy of the vectors, there might be a problem with determining which base vectors should be chosen. The figure shows a fragment of the base vector grid for three-level inverter. Depending on where the reference vector is located inside the triangle (a...d) different sequences of base vectors may be chosen. In Table II, selected switching sequences are written for the reference vector placed in the triangle (Fig.). Every sequence in table two have only one switching at the transition between selected vectors. It means that selected vectors in the sequence are located at the corners of the smallest corresponding triangle. To select switching sequences (appropriate vectors) decomposition method is commonly used. - V CM (c) β Fig.. Available space vectors for the three-level inverter. TABLE I - - COMMON MODE VOLTAGE LEVELS Level of V CM Number of vectors +V DC +/V DC +/V DC 6 7 -/V DC 6 -/V DC -V DC (d) - - Fig.. A piece of the base grid of space vectors for the three-level inverter. TABLE II SEQUENCES OF VECTORS CHOSEN FOR THE SELECTED PART OF THE VECTOR Triangle GRID Switching sequences (V) (V) (V) (V) () > () > () > () () > (-) > (--) > (---) () > () > () > (-) () > () > (-)> (--) () > (-)> (-)>(-) (c) () >( -) > (-)>(--) () > ()> ( -) > (-) (d) () > (-)>( --)>(--) IV. DECOMPOSITION METHOD Decomposition method is based on split multi-level inverter space vectors hexagon into smaller two-level inverter hexagons, as shown in Figure 4. Determining switching sequences for the three-level inverter starts by a selection of

3 one out six small hexagons, based on the phase angle of reference voltage vector. In the next step, the reference vector is decomposed into two vectors - the displacement vector V p and vector. Then the vector ' is formed the same way as the reference vector in a two-level inverter []. The sequence of base vectors is obtained from the submission of the displacement vector V p and the sequence of vectors corresponding to the vector ' V p S A+ S B+ S A S B State Tag V DC A V AN V N -V DC - SA- S B- V DC V Fig. 6. H-bridge module and its output states. V. PROPOSED SOLUTION WITH TWO SEPARATE MODULATORS Redundancy vectors in multilevel inverters allow the implementation of additional purposes, such as reducing common mode voltage at the output of the inverter. This additional functionality requires a special control method witch determine the sequence of states restricting high levels of V CM. The classical decomposition in such situation cannot be used. We have proposed a method of modulation with two vectors, in which the two modulators are controlled by vectors of length equal to a half length of the reference vector (Figure 7b, where V R = / V R =- /). This solution contributes to a balanced transistor switching during PWM period and to reduce the level of common mode. Additionally significant improved conditions for filtration of CM disorders are achieved [6]. V r Fig. 4. Space vector hexagon of three-level inverter. Decomposition method allows standardization of procedure for determining required sequences of the space vector for the three-level inverter. For example, for vector ' of Figure 4 sequence ()>()>()>() is obtained. Displacement vector V p which is marked () after the submission with ' gives the sequence ()>(-)>(-)>(--). The obtaining sequence corresponds to the sequence number 6 from Table II. After determining the sequence of vectors and calculation of switching times of individual vectors, it is necessary to determine the states of switches corresponding to the selected vectors. For the cascade inverter topology there is redundancy of switches states. For instance in the three-level inverter are 6 different combinations of switches states for 7 available space vectors. In the single H-bridge module (Fig. 6) V output state is obtained for two switching states combinations. This means that one must specify which combination of switches will represent a zero in the particular period. For cascade inverter It is possible to control switches of the inverter using two separate vector modulators. This solution is easy in implementation and greatly simplifies the modulation process. In Figure 7a we illustrate the modulation process with two separate modulators, giving for the cascade inverters identical results as the decomposition method. V r V r V r Fig. 7. Reference vectors for modulation with two separate modulators. a) equivalent of decomposition method b) proposed modulation technique. 88

4 Figure 8a shows how the reference vectors of VR and VR are created from basis vectors in hexagon, and Figure 8b shows control signals waveforms in the selected sector. V V r T V V 4 T 4 V 4 T V T 5 V 5 V r V V7 V The above correlations illustrate that the modulation process eliminate states with high level of common mode voltage. Sample switching sequence and the resulting levels of V CM is shown in Table III. The common mode voltage in the concerned sector does not exceed the range from -V DC / to V DC /. The same conclusion is drawn from the analysis of the other sectors. Executed sequences and the resulting common mode voltage levels are shown in Table III. The CM voltage in the considered sector does not exceed the range from -V DC / V DC / The same conclusion is drawn from analysis of other sectors. TABLE III SEQUENCES OF VECTORS AND THE RESULTING VOLTAGE LEVELS Sequence V r () () () () Sequence V r () () () () Sequence for () V CM level [V] (-) () +V DC/ (--) (-) -V DC/ V () S A S C S E S B S D V 5 T/ T T T T 7 T4 T5 T T 7 V r V r VI. SIMULATION RESULTS A simulation tests for two described modulation techniques, was performed in Matlab. The pulsation of reference vector was 4 rad/s and assumed frequency PWM waveform equal to 6kHz. Voltage values, obtained at a modulation depth M =.8 were related to the voltage level of the V DC In Figure 9 waveforms of phase voltages for both modulation techniques and the resulting common mode voltage waveform is presented. Common mode voltage in the proposed modulation technique is two times lower than in the decomposition method, and in most of the PWM period the common mode voltage is equal zero. Such conditions make common mode disorders much easier for passive or active filtration, and prevent the possibility of magnetic core saturation [] [] [6] [7]. S F Fig. 8. The reference vectors shaping, using the base vectors a) vector plot b) control signal waveforms. In the proposed modulation technique, switching times of individual switches are defined as follows: T 4 = T T 5 = T T 7 = T U π T T = sin U DC T U T = sin( ) U DC VP/VDC VP/VDC VP/VDC VCM/VDC

5 VP/VDC VP/VDC VP/VDC VCM/VDC Fig. 9. Phase voltage and CM voltage waveforms for modulation techniques: a) Decomposition method b) proposed modulation technique. In the Figure the line to line voltage of the inverter for two simulated modulation techniques is presented. Line to line voltage.5 The voltage waveform is significantly different in the shape and envelope for two presented modulation technique. In the proposed modulation technique voltage fluctuation occur V DC, which results from having more than one transistor switches at the same time. Filtration conditions for differential mode disorders worsen, which should be taken into consideration when designing differential filters. VII. EXPERIMENTAL RESULTS In order to verify the results obtained in the simulation a laboratory three-level inverter were built. A control system of the inverter consists of a control module with a digital signal processor TMSF8. DC voltage was 6V. The system was tested without a load (does not affect the CM voltage waveforms). Results obtained in the experimental arrangement correspond to results of the simulation V P V P V AC /V DC V P V CM -.5 VAC/VDC Line to line voltage V P V P V P V CM Fig.. Phase voltage and CM voltage waveforms for modulation techniques: a) Decomposition method b) proposed modulation technique Fig.. Line to line voltage waveforms for modulation: Decomposition method proposed modulation technique. 9

6 Additionally, better conditions for filtration of common mode disorders are obtained. In comparison with the decomposition method, the proposed modulation technique produces more distorted waveforms of output voltages, thus increased differential mode disorders. Therefore, the proposed modulation technique can be used in systems where occur problems from common mode disorders (interfering with other devices, bearing currents, faulty operation of RCDs). ACKNOWLEDGMENT This research work has been supported by Estonian Archimedes Foundation (project Doctoral School of Energy and Geotechnology II ). Fig.. Line to line voltage waveforms for modulation: Decomposition method proposed modulation technique. VIII. SUMMARY In the paper the vector modulation technique with two separate modulators was presented. This method can be used only for cascaded inverters and cannot be extend for other multilevel inverter topologies. Advantages of the proposed modulation technique, compared with the classical decomposition method are very easy implementation and a significant reduction of common mode voltage maximum level. We can restrict in this way, the main source of EMC problems of systems with power electronic inverters. REFERENCES [] H. Akagi, S. Tamura, A passive EMI filter for eliminating both bearing current and ground leakage current from an inverter-driven motor power electronics, IEEE Trans. on Power Electronics, vol., 6. [] D.G. Holmes, T.A. Lipo, Pulse Width Modulation for Power Converters, Principles and Practice, IEEE Press Series on Power Engineering, Wiley-IEEE Press,. [] P. Lezynski, (in polish) Warunki kompensacji napięcia zaburzeń wspólnych w falownikach napięcia przy modulacji sinusoidalnej PWM z dodatkiem przebiegów o częstotliwości trzeciej harmonicznej, Przegląd Elektrotechniczny, vol. 6,. [4] P.C. Loh, D.G. Holmes, Y. Fukuta, T. A. Lipo, Reduced common mode carrier-based modulation strategies for cascaded multilevel inverters, Industry Applications Conference, 7th IAS Annual Meeting,. [5] A. Kempski, (in polish) Elektromagnetyczne zaburzenia przewodzone w układach napędów przekształtnikowych, Oficyna Wydawnicza Uniwersytetu Zielonogórskiego, 5. [6] A. Kempski, R. Smolezski, P. Lezynski, Conditions of CM voltage cancellation in multilevel voltage inverters with conventional and improved carrier-based SVPWM, Przegląd Elektrotechniczny vol., 8. [7] R. Smolenski, A. Kempski, J. Bojarski, P. Lezyzski, Determination of flux density produced by multilevel inverters in CM voltage filter. COMPEL : The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, vol., no,. [8] N. Pluschke, T. Grasshoff, More Efficiency for -Level Inverters, Power Electronics Europe, Issue March. [9] K. Zhou and D. Wang, Relationship Between Space-Vector Modulation and Three-Phase Carrier-Based PWM: A Comprehensive Analysis, IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, vol. 49,. 9