Multi-phase inverter Space Vector Modulation

Abstract—This paper presents the comparison between two

switching techniques for a multi-phase voltage source inverter (VSI) using Space Vector Modulation (SVPWM). Two different techniques which based on large vectors and the combination of large and medium vectors have been examined under a two-level five-phase inverter. The performance of these techniques are observed and evaluated in terms of harmonic contents for voltage waveform by employing MATLAB/Simulink software. It can be observed that the unwanted harmonic contents is produced in the auxiliary subspace (d3-q3) and embedded in the fundamental subspace (d1-q1). It can also be observed that the switching technique using combination of large and medium vectors has rapidly reduced the harmonic contents produced by d3-q3 subspace especially the 3rd and 7th harmonics order.

Index Terms—Multi-phase Inverter, Voltage Source Inverter, Space Vector Modulation, Five-phase Machines.

I. INTRODUCTION HE use of three-phase electrical drives especially in locomotive, naval, aerospace, renewable energy systems

and electrical vehicles industry have been replaced by multi-phase electrical drives due to various benefits inherits by multi-phase electrical drives over three-phase electrical drives as mentioned in [1-18]. This is supported by the development of efficient modulation techniques such as sinusoidal carrier-based PWM (SPWM) and space vector PWM (SVPWM).

SVPWM is preferable when designing a multi-phase VSI since this technique provide wide choice of switching combinations [4, 8]. The numbers of vectors in multi-phase VSI increase with the number of level and number of phase ( , where m is the number of VSI level and n is the number of phase). Switching vectors in a two-level VSI can be projected into , two-dimensional subspaces (d1-q1, d3-q3, … dn-qn). Unlike fundamental subspace (d1-q1), all the remaining subspaces are the source of low-order harmonics. A two-level five-phase VSI has a total of 32 vectors projected into 2 subspaces (d1-q1 and d3-q3).

This research was supported by the MARA University of Technology

(UiTM) under the Research Intensive Faculty (RIF), 600-RMI/DANA 5/3/RIF (83/2012).

The authors are with Centre for Electrical Power Engineering Studies (CEPES), Universiti Teknologi MARA, Shah Alam, MALAYSIA. (e-mail: [email protected]; [email protected]; [email protected]; [email protected]).

The harmonics in d3-q3 subspace can be eliminated using

the switching technique proposed in [3, 17]. In addition, this technique can produce phase voltage close to sinusoidal waveform.

This paper presents switching techniques using Space Vector Modulation that can be applied to a two-level five-phase VSI. The performances of these techniques are compared and verified using simulation results from MATLAB/Simulink software.

II. TWO-LEVEL FIVE-PHASE VSI A constant dc voltage can be converted to ac voltage by

using a voltage source inverter (VSI). Fig. 1 shows the circuit topology of a two-level five-phase VSI composed of 10 power switches (IGBT1~IGBT10), two power switches connected in series for each phase leg. Pole voltage (V1~V5) is equals to Vdc when the upper switch is turned on and become 0V when it is turned off. The upper switch of each phase leg works alternately with the lower switch. When upper switch is turned on, lower switch will turn off and vice versa. Phase-to-neutral voltages, (V1n~V5n) can be determined from the relationship with inverter pole voltages [8]. ∑ , , if x<5 ∑ , , if x=5

Fig. 1: Two-Level 5-Phase VSI

In general, an n-phase two-level VSI has 2n total possible combinations of switching states and can be represented in space vector subspace [19]. Thus, for a five-phase VSI, 32 combinations of switching states are available and can be presented in two space vector subspaces (d1-q1 and d3-q3) comprising of 30 active vectors and 2 zero vectors (00000 and 11111) in both subspace .

Multi-phase Inverter Space Vector Modulation Wan Noraishah Wan Abdul Munim, IEEE, Mohd Firdaus Ismail, Ahmad Farid Abidin, IEEE, and

Harizan Che Mat Haris, IEEE

T

(1)

978-1-4673-5074-7/13/$31.00 ©2013 IEEE

2013 IEEE 7th International Power Engineering and Optimization Conference (PEOCO2013), Langkawi, Malaysia. 3-4 June 2013

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From phase-to-neutral voltages calculated in (1), the 32 switching state can be represented in d-q plane using (2) and (3). Five binary numbers labeled on each space vectors represent the operation of upper switches in the inverter. Bit ‘0’ means that the upper switch is off while bit ‘1’ means the upper switch is on. Two zero vectors, (00000 and 11111) become the middle point of three concentrated decagons produced by the remaining 30 active vectors. The magnitudes of innermost, middle and outer decagons are 0.2472, 0.4, and 0.6472 respectively.

(2)

3

Where: cos sin cos sin cos sin cos sin

As shown in Fig. 2 and Fig. 3, each switching state will

produce two vectors in the d1-q1 (fundamental) and d3-q3 (auxiliary) respectively. From Fig. 2 and Fig. 3, the order of vectors map into the fundamental subspace is ABCDE while in the auxiliary subspace; vectors are map in the order of ABCDE [3, 10, 14, 17, 20]. It can be observed that the vectors in the outer decagon of d1-q1 subspace are represented in the inner decagon of d3-q3 subspace whereas the vectors in the inner decagon of d1-q1 subspace are represented in the outer decagon of d3-q3 subspace. The middle decagon in both subspaces is map in the same region [18].

The conduction time for the whole decagon is

. If the fundamental frequency is 50 Hz, the conduction time for the whole decagon is 20 ms and the conduction time for each sector is 2 .

Fig. 2: Switching State in d1-q1 Subspace (Fundamental)

Fig. 3: Switching State in d3-q3 Subspace (Auxiliary)

III. SWITCHING TECHNIQUE I: USING LARGE VECTORS ONLY For this switching technique, only the space vectors in the

outer decagon of the fundamental subspace are considered. This is the simplest space vector modulation switching technique of five-phase VSI. The switching vector moves to the neighbouring space vector in counter-clockwise direction starting from V1 until V10 as shown in Fig. 4.

Fig. 4: Switching Sequence Using Large Vectors Only

The conduction time of each switching state is calculated in

(4). The switching pattern of the upper IGBT in each phase leg is shown in Fig. 5.

(4)


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Where: = Modulation Index

= Position of reference voltage = Sector number = Switching frequency

Sector 1 Sector 2 Sector 3 Sector 4 Sector 5

T1 T1 T1 T1 T1

IGBT1

IGBT3

IGBT5

IGBT7

IGBT9

V1 V2 V3 V4 V5

Sector 6 Sector 7 Sector 8 Sector 9 Sector 10

T1 T1 T1 T1 T1

IGBT1 IGBT3 IGBT5 IGBT7 IGBT9

V6 V7 V8 V9 V10

Fig. 5: Switching Pattern Using Large Vectors Only

IV. SWITCHING TECHNIQUE II: USING COMBINATION OF LARGE AND MEDIUM VECTORS

As emphasized in [21], multi-phase inverter with an odd number should implement active space vectors with one less than the number of inverter phases. Instead of only using two active vectors as in Section III, another switching technique which uses four active vectors (2 large vectors and 2 medium vectors) is used for five-phase VSI.

As mentioned earlier, the order of vectors map into the fundamental subspace is ABCDE while in the auxiliary subspace; vectors are map in the order of ACEBD. It can be deduced that the auxiliary subspace represents a distortion voltage system producing 3rd order harmonics, embedded in the fundamental subspace [17, 22]. Hence, this switching technique is used with the purpose of eliminating the low order harmonics produced by the auxiliary subspace (d3-q3) components by producing output phase voltage closest to sinusoidal voltage waveform.

From fundamental subspace in Fig. 2, it can be observed that in a particular sector, the vector in the outer decagon aligns with the vector in the middle decagon but fall diagonally opposite each other in the auxiliary subspace (Fig. 3). Thus, in can be deduced that if the state duration ratio of the large and medium vector is the same, the resulting vector in the auxiliary subspace will be zero hence eliminate the harmonics component. As mentioned in paper [17], elimination of harmonic components in the auxiliary subspace can be done by applying large vector 1.618 times longer than medium vector. Equation (5-8) shows how this value is obtained based on vectors in Section 1 of fundamental subspace. In Sector 1 of fundamental subspace, large vectors are V1 and V2 while V11 and V12 are medium vectors. In auxiliary subspace, V1 is map into the innermost decagon with magnitude of -0.2472 and V11 is map into the outer decagon with magnitude of 0.4.

0 (5) 0.2472 0.4 0 (6) 0.40.2472 1.618 7

1.618 and 1.618 (8) Fig. 6 shows the position of four time switching applied in

each sector. These time switching can be calculated using equation (9-11) [3, 7, 10]

Fig. 6: Time Switching in Each Sector

sin 36 (9) sin 36 1 (10) | || |

| | (11)

| | | || |

Fig. 7 shows the switching sequence using combination of

large and medium vectors. The reference voltage, Vref transition from one sector to the next sector requires minimum


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number of switching [21]. This unique switching pattern requires two switching when transiting from one vector to the next switching vector.

Fig. 7: Switching Sequence Using Combination of Large and Medium

Vectors

V. SIMULATION RESULTS A simulation using MATLAB Simulink software is done to

determine the performance of the space vector simulation based on both switching technique. This simulation was performed to identify the effectiveness of switching technique using combination of medium and large vectors compared to only using large vectors. In the simulation model, the variables are fundamental frequency, switching frequency, modulation index, and DC input voltage. The values of variables used in the simulation are tabulated in III. Two separate programs are written to perform the overall switching process using both techniques based on the switching sequence in Fig. 4 and Fig. 7. The program is embedded into simulation model using S-Function block.

TABLE III

SIMULATION VARIABLES AND ITS VALUES

Variable Value Fundamental frequency, f 50 Hz Switching frequency, fC 500 Hz Modulation index, MA 1.0 DC input voltage, VDC 100 V

Fig. 9 and Fig. 10 illustrate the output waveforms using

large vectors and the combination of large and medium vectors respectively. It can be observed that by using the combination of large and medium vectors, phase voltage produced is closer to sinusoidal waveform as compared to phase voltage produced by using large vectors.

Fig. 9: Output Waveforms Using Large Vectors

Fig. 10: Output Waveforms Using Combination of Large and Medium

Vectors

As mentioned in the previous section, harmonics will be produced in the auxiliary subspace (d3-q3) and embedded into the fundamental subspace (d1-q1). Thus, to evaluate the performance of both switching techniques, the harmonic contents especially in low-order harmonics in the phase voltage and line-to-line voltage are observed and tabulated in Table IV and Table V.

In the simulation, this technique produced 33.35% of the 3rd harmonic and 14.29% of the 7th harmonic in phase voltage. By using large and medium vectors, 3rd and 7th harmonics are reduced to 0.9% and 2.39% respectively. This indicates that this technique able to balance the component in the auxiliary subspace (d3-q3) and reduced the harmonic component produced in this subspace.

TABLE IV HARMONIC CONTENT IN PHASE VOLTAGE

Switching Technique

Harmonic Content (%) 3rd 5th 7th 9th 11th 13th

I 33.35 0.01 14.29 11.13 9.09 7.07 II 0.90 0.03 2.39 11.89 10.20 6.61

TABLE V HARMONIC CONTENT IN LINE-TO-LINE VOLTAGE

Switching Technique

Harmonic Content (%) 3rd 5th 7th 9th 11th 13th

I 53.96 0.02 23.12 11.14 9.08 12.46 II 1.46 0.03 3.84 11.90 10.19 10.66


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VI. CONCLUSION Comparison between two switching techn

level five-phase inverter using SVPWM haHarmonics content and output phase volobserved and evaluated in simulationMATLAB/Simulink software and results othat switching technique based on combinatmedium vectors shows better result as comptechnique using large vectors by producing phase voltage and smaller harmonic content.

VII. ACKNOWLEDGMENT The authors would like to acknowle

Associate Professor John E. Fletcher fromsupport and contribution.

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IX. BIOGRAPH Wan Noraishah WMalaysia, on July Diploma in (TelecommunicationMalaysia (UTM), Technology in EleLumpur (UniKL), aEngineering with Strathclyde, Glascowand 2009 respectivel

She is currently a lecturer at Universiti Tek Mohd Firdaus Bin March 10, 1989. Electrical EngineerTeknologi MARA in

He is currently inElectrical EngineerMARA. Ahmad Farid AbiDecember 25, 1978Engineering in EleEngineering from U(UKM), M.Sc. in Universiti Teknologdegree from Universin 2000, 2005, and 2

He is currently a Electrical Power EnUniversiti Teknolog

d Power Electronics Conference 09. Twenty-Fourth Annual IEEE,

prehensive Relationship Between Vector PWM in a Five-Phase

ransactions on, vol. 24, pp. 2379-

voglia, and D. Casadei, "Power n Electrical Systems for Aircraft, ARS), 2010, 2010, pp. 1-6. ni, G. Serra, and D. Casadei, es in IGBT Multiphase Inverters dth Modulation," Industrial n, vol. 57, pp. 3695-3706, 2010. etcher, and B. W. Williams,

odulation strategies for five phase wer Electronics, Machines and ond International Conference on 50-655 Vol.2. F. B. Hussin, and I. Musirin,

hase voltage source inverter," in ering Research (SHUSER), 2012 9-593. rieto, and F. Barrero, "Switching Vector PWM Schemes for Five-e Inverters—Part 1: Flux

Industrial Electronics, IEEE 9-2798, 2011. r Modulation Strategies For Five ing Medium Vectors," Faculty of University of Technology, Shah

and AC Drives. New Jersey: John

Space Vector Switching Strategy Inverter Drives," Industrial

n, vol. 57, pp. 2332-2343, 2010.

HIES

Wan Abdul Munim was born in 10, 1982. She received her

Electrical Engineering n) from university Teknologi

Bachelor of Engineering ectrical from Universiti Kuala and M.Sc. in Electrical Power Business from University of

w, Scotland, UK in 2003, 2009 ly. knologi MARA (UiTM).

Ismail was born in Malaysia, on He received his Diploma of

ring (Power) from Universiti n 2010. n his final year in Bachelor of ring at Universiti Teknology

idin was born in Malaysia on 8. He received his Bachelor of ctrical, Electronic, and System

Universiti Kebangsaan Malaysia Electrical Engineering from

gi MARA (UiTM), and Ph.D siti Kebangsaan Malaysia (UKM) 011 respectively. lecturer and Head of Centre for

ngineering Studies (CEPES) at gi MARA (UiTM). His main


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https://www.researchgate.net/publication/224170516_Switching_Ripple_Characteristics_of_Space_Vector_PWM_Schemes_for_Five-Phase_Two-Level_Voltage_Source_Inverters-Part_1_Flux_Harmonic_Distortion_Factors?el=1_x_8&enrichId=rgreq-c53963d137a62da9a6501e5e5920471b-XXX&enrichSource=Y292ZXJQYWdlOzI2MTM0NjIyODtBUzoxNjE4NzI4NjcyNDE5ODdAMTQxNTYwNDkwNzk0OA==


















research interests are in power stability, power qualitprotection.

Harizan Che Mat Haris wasJanuary 29, 1964. He receiEngineering in Electrical Universiti Teknologi Malaysia

He is registered as P(P.Eng) with Board of engineand a Competent Engineer toMalaysia.

He was the Deputy DiSupply Department Malaysia of Facilities Management Depcurrently a lecturer at Universi

ty, and power system

s born in Malaysia on ived his Bachelor of

Engineering from a (UTM) in 1987. rofessional Engineer eers, Malaysia (BEM) o Suruhanjaya Tenaga

irector of Electricity and Deputy Director

partment UiTM. He is iti Teknologi MARA.


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Multi-phase inverter Space Vector Modulation

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