This paper presents a bi-directional AC-DC matrix converter for the power supply systems of hybrid electric vehicles. Compared to conventional PWM rectifier and associated DC-DC converter, large DC bus capacitor banks are eliminated. The converter converts three-phase AC power into the desired DC output with higher energy density via a single power stage. A closed-loop control strategy based on indirect space vector modulation is proposed and the validity has been verified. The strategy ensures that the output voltage can be regulated tightly against different loads and wide input variation and high-quality input current can be achieved

CSNamuduri

Donald

Ejea

H.A.N.

Holmes

Keping

Lequesne

Vlatkovic

Wang

Zhuang Xu

Xu, Zhuang

Name not available

An indirect space-vector modulated three-phase AC-DC matrix converter for hybrid electric vehicles

Crossref

Energy Procedia

An Indirect Space-vector Modulated Three-phase AC-DC Matrix Converter for Hybrid Electric Vehicles

Nottingham ePrints

1876-6102 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).Peer-review under responsibility of Applied Energy Innovation Institutedoi: 10.1016/j.egypro.2015.07.242  Energy Procedia  75 ( 2015 )  1968 – 1974 ScienceDirectThe 7th International Conference on Applied Energy – ICAE2015 An Indirect Space-Vector Modulated Three-Phase AC-DC Matrix Converter for Hybrid Electric Vehicles Zhuang Xu*The University of Nottingham, China campus, 199 Taikang East Road, Ningbo, 315100, China Abstract This paper presents a bi-directional AC-DC matrix converter for the power supply systems of hybrid electric vehicles. Compared to conventional PWM rectifier and associated DC-DC converter, large DC bus capacitor banks are eliminated. The converter converts three-phase AC power into the desired DC output with higher energy density via a single power stage. A closed-loop control strategy based on indirect space vector modulation is proposed and the validity has been verified. The strategy ensures that the output voltage can be regulated tightly against different loads and wide input variation and high-quality input current can be achieved. Keywords: AC-DC; matrix converter; closed-loop control; indirect space vector modulation  1. Introduction The average electrical power absorbed by the loads of automobiles reaches above 10 kW. In order to pursue constantly high performance, high reliability and intelligence, more electronic equipment is installed in automotive, etc. [1]. Researchers, automobile manufacturers, and parts manufacturers set up the standards of the power nets for automobiles. If the total power remains unchanged, the current can be reduced by 2/3. Considering 10kW for example, 14V power supply system needs wires that can withstand current up to 714A, while the 42V voltage needs wires carrying 238A current [2]. Therefore, it is necessary to implement 42V power supply for automobiles with the developments of technologies. TheHEV power train is of the series-parallel type, such as the one found in the Toyota Prius car [1]. This HEV has two kinds of motive power sources: an electric motor and an internal combustion engine (ICE), in order to increase the drive train efficiency and reduce air pollution. The electrical subsystem as shown in Fig.1 is composed of four parts: The electrical motor, the generator, the battery, and the DC/DC converter. However, the three-phase rectifier bridge produces fifth and seventh high order harmonics. The traditional rectifier circuit requires large DC bus capacitors which increase the overall system size and maintenance costs. The alternating current produced first goes through the rectifier and then the chopper Buck circuit and undergoes two-stage power conversion. This reduces the energy transfer density [3]. * Corresponding author. Tel.: +86-0574-88189135; fax: +86-0574-88180175. E-mail address: zhuang.xu@nottingham.edu.cn. Available online at www.sciencedirect.com Zhuang Xu /  Energy Procedia  75 ( 2015 )  1968 – 1974 1969Considering the above drawbacks of conventional power converters, a novel AC-DC matrix converter is proposed. It has many inherent advantages which power converter cannot compare with. These advantages include [3-5]: x No large capacity storage devices, fast dynamic response and longer life span x Wide input voltage range x Low input current harmonic content and only high-order harmonics x High power density conversion x Compact, reduced number of devices in series, highly efficient and easy to be implemented modularly The new topological structure of the proposed AC-DC matrix converter is derived from three-phase to three-phase matrix converter. The paper [5] records the theoretical study of the AC-DC new topologies, derived AC-DC rectifier control algorithm based on AC-AC modulation, and carried out simulation investigation. The authors in [6] implemented a low power AC-DC matrix converter in the laboratory and obtained sinusoidal input current which is in the same phase with the input voltage. However, input current waveform is not sinusoidal as expected and the switching sequence pattern in the modulation strategy should be further improved. In order to solve electrical isolation problems for the AC-DC matrix converter, the paper [7] introduced high-frequency isolation transformer to the AC-DC matrix converter design and added a rectification transformation. This would reduce the efficiency and lose the benefits of matrix converter. When the load change is in wide range for the open-loop matrix converter, the output may become unregulated or even unstable. This paper adopts a closed-loop control strategy based on indirect space vector modulation to overcome the downsides of the open-loop control. This paper describes in details the operating principle and closed-loop modulation strategy for the proposed AC-DC matrix converter, verifies its effectiveness, and presents the proven results. 2. Operation Principles       Since the maximum voltage modulation ratio of a 3 phase-3 phase matrix converter is 0.866, the matrix converter is generally used as a buck converter. For rectification purpose, the three-phase output in the original three-phase to three-phase conversion can be reduced by one phase and changed into AC-DC matrix converter [5]. The topological structure of the three-phase to three phase matrix converter is shown in Fig. 2 [4].                               Fig.1. The electrical subsystem of power train systems.                       Fig.2. The circuit of 3 phase-3 phase matrix converter On the basis of the topological structure of matrix converter, its mathematical model as well as its limitations, an AC-DC converter is derived from three-phase to three-phase matrix converter. Its modulation strategy must meet the following requirements: (1) To comply with the matrix converter principle. (2) The output frequency is zero. (3) DC output voltage is equal to the maximum phase voltage.The AC-DC matrix converter topology, as shown in Fig 3, consists of six bi-directional switches which directly realize the conversion from the input of three-phase AC into the output of DC. The closed-loop 1970   Zhuang Xu /  Energy Procedia  75 ( 2015 )  1968 – 1974 control of the matrix converter ensures that the output voltage is tight against different loads and a wide range of input changes. Fig.3. The topology of the AC-DC matrix converter      The bi-directional switch-off states are defined by the function below:  ^ `1,S0,S, ; ( , , )jkjkjkSj p n k a b c­° ®°¯ RQRII                                     (1) It is known from the structure of the matrix converter that the inputs cannot be short circuited and the outputs cannot be disconnected. The constraints are:1{ , }ja jb jcS S Sj p n                                                                     (2) The AC-DC matrix converter facilitates a direct AC to DC power conversion without any DC capacitors. This gives more advantages, such as controllable input power factor, highly reliable and compact structure. A space vector modulation method for AC-DC matrix converter is adopted to control the six bi-directional switches. 3. Modulation algorithms for the AC-DC matrix converter Indirect space vector modulation algorithm is based on "virtual DC-link" concept. It regards the matrix converter equivalent in theory to a virtual connection of a rectifier and an inverter. The concept of space vector PWM can be applied to matrix converter and used to modulate the pulse width of "virtual rectifier" and "virtual inverter" respectively. Finally, the two processes were synthesized in order to achieve sinusoidal input and output waveforms and controllable input power factor [6]. The proposed AC-DC matrix converter is deduced with reference to the indirect space vector modulation algorithm. Indirect space vector modulation is divided into two processes. The first stage is the rectification and the other is the inversion process [7]. Fig 4 shows the decomposition diagram illustrating the AC-DC modulation process, which is quite similar to the traditional AC-DC-AC conversion system except that there's no DC bus capacitor. Thus, a DC bus capacitor placed across p and n gives a more virtual illustration of indirect space vector modulation principle. Fig.4. Illustration of the “virtual DC-link" concept.  Zhuang Xu /  Energy Procedia  75 ( 2015 )  1968 – 1974 1971The process of AC-DC matrix converter can be expressed in the form of mathematical matrix expressions, the virtual DC bus voltage is obtained during the rectification process.pn r iV F V                                                 (3) Where Fr is the transfer function of the rectification pro-cess, while Vi is the three-phase input voltage vector. Output voltage is supposed to be Vo, and the expression of output voltage in the inversion stage is shown in (4).o i pnV F V                                           (4)  Fi is the transfer function of the inversion process. Similarly, input line current II can be expressed together by the rectification process and the inversion process, as shown in (5) where Io is the output current vector. T Ti r i oI F F I                                         (5) 3.1. Rectifying StageThe purpose of rectification is to obtain a virtual DC bus voltage Vpn and maintain the input power factor unity. The DC voltage is modulated by six switches s1 ~ s6 from three-phase input phase voltages. It is known from the principle that the inputs of matrix converters must not be short-circuited. There are six active switching states and three inactive switching states for s1 ~ s6. The space vector hexagon according to the space vector modulation method is drawn as shown in Fig. 5. Six active switching states correspond respectively to the six switching space vectors in the space vector hexagon. The remaining three inactive switching states correspond to the three zero space vectors. A randomly placed space vector can be synthesized by its two adjacent switching vectors. For example, Viin Fig.5 is a synthesis of VD and VE, and și is the angle between Vi and VD. At this moment, switching vector duty cycle can be expressed respectively as follows: Fig.5 Rectifier space vector hexagon sin(60 )c iT mD T $                                       (6) sin( )c iT mE T                                            (7) 0 1T T TD E                                             (8) where mc is the modulation ratio, 0İmcİ1. Transfer function Fr in the rectification process can be established by means of space vectors through six switching functions s1 ~ s6. The element number of Fr is determined by the numbers of input phases. since it is a three-phase input,  Fr has three elements and can be expressed as: > @1 2 3r r r rF F F F       where 1 1 4rF s s  ; 2 3 6rF s s   ; 3 5 2rF s s                     (9) 1972   Zhuang Xu /  Energy Procedia  75 ( 2015 )  1968 – 1974 the displacements between Fr2, Fr3 and Fr1 are 120 degrees and +120 degrees respectively. Below is the expression of Vpn1.5pn c mV m V                                        (10) 3.2. Synthesis ProcessFor the six bi-directional switches shown in Fig 3, the logical expression of the six switches can be expressed as 1 3 1 3 54 2 4 6 2pa pb pcna nb ncS S S sw sw s s ssw sw s s sS S Sª º ª º ª º « » « » « »¬ ¼ ¬ ¼¬ ¼              (11) The AC-DC matrix converter modulation strategy can be implemented by using a DC output voltage outer loop and a current inner loop. The control block diagram is shown in Figure 6.       Fig.6 Block diagram of closed-loop control strategy based on indirect                         Fig.7. The converter test bench.                                    space vector modulation The indirect space vector modulation method eases the requirements for the control circuits. This modulation doesn’t require the imposition of low-frequency harmonics onto output phase voltage in order to reach the maximum voltage utilization ratio of the matrix transformation device. The arbitrary control of the input current phase differences can be realized. 4. Experimental Results The experimental test rig (Fig.7) has been set up for the three-phase AC-DC matrix converter consisting of bidirectional IGBTs from Eupec. The configuration of the main circuit is illustrated as shown in Fig.3. The controller board deploys TMS320F2812 DSP and Altera MAX II CPLD. Experiments have been carried out to test the closed-loop control strategy that is based on indirect space vector modulation.  Fig. 8 (a) plots the waveforms of the input phase voltage Ua and current Ia when the 3-phase AC programmable power supply was set to line frequency of 50Hz and line voltage of 80V. It is seen that Ua and Ia are in phase and the power factor is unity. The DC output Upn and filtered Udc are illustrated in Fig. 8 (b). The smooth Udc has been regulated tightly against the load change. Fig. 8 (c) shows the plots of Upn and Uab where Upn closely follows the top envelope of Uab indicating that due to the switching action, Upn connects and disconnects to the line to line voltage of the supply. When the bidirectional switches were conducting, Upn is generated by Uab. To appreciate the advantages of the circuit, more tests have been done to verify the effectiveness. Fig.9 (a) shows that when the frequency and amplitude of the supply were reconfigured to 150Hz and 110V, Udc is still able to be maintained against the load change. Even the frequency and amplitude of the supply decrease further to 25Hz and 50V, the system is still capable of producing satisfactory results as shown in Fig.9 (c).     Zhuang Xu /  Energy Procedia  75 ( 2015 )  1968 – 1974 1973   Fig. 8.  Input line voltage 80V,50Hzˈ(a) Phase Ua and Ia  (b) Upn and Udc  (c) Upn and Uab Fig. 9.  Input line voltage 110V, 150Hzˈ(a) Phase Ua and Ia (b) Upn and Udc (c) Upn and Udc @25Hz and line voltage of 50V 5. Conclusions (1). According to the topology and mathematical models of the traditional three-phase to three-phase matrix converters, an AC-DC matrix conversion has been derived. (2). For the proposed AC-DC converter, a new type of closed-loop control strategy is proposed based on the indirect space vector modulation algorithm. (3). According to the closed-loop control strategy, experiments have been carried out to verify the feasibility of closed-loop control of the proposed AC-DC matrix converter, which has proved the effectiveness of the proposed system. Acknowledgements The project is supported by Ningbo Science and Technology Bureau (2014A610146), China.  References        [1] Lequesne, B. EV/HEV Technology: Are We There Yet? Viewpoint: Electrification Magazine, IEEE, Volume: 2 , Issue: 2 2014. [2] CSNamuduri, BVMurty, MG Reynolds, Load dump transient control of a 42v automotive generator[C] In Proc.35th Annu. IEEE Power Electronics Specialists Conf., 2004: 389–394. [3] V. Vlatkovic, D. Borojevic, and F. C. Lee, “A Zero-Voltage Switched,Three-Phase Isolated PWM Buck Rectifier”. IEEE Transaction on Power Electronics, 1995, 10(2): 148 - 157. [4] Y.Wang. Matrix Converter's Space Vector Modulation, System Integration and Applied Research [D]. Hang Zhou: Zhe Jiang University, 2005. [5] DG Holmes, TA Lipo. Implementation of a controlled Rectifier Using ac-ac Matrix Converter theory[C] In Conf. Rec. 1989 IEEE Power Elec.Spec. Conf., 1989: 353-359.Ua:50V/DivI a:5A/DivTime: 5ms/Div              (a)Ua Ia Udc:20V/DivUpnUdcUpn:50V/DivUab:50V/DivTime: 1ms/Div          (b)Time: 1ms/Div           (c)Upn Uab Ua:50V/Div Ua Ia I a:5A/DivTime: 2.5ms/Div              (a) Upn:50V/DivUpn:50V/DivUdc:20V/DivTime: 1ms/Div           (b) UpnUdcUpn:50V/DivUdc:20V/DivTime 5ms/Div          (c)Upn Udc 1974   Zhuang Xu /  Energy Procedia  75 ( 2015 )  1968 – 1974 [6] K.Sun, D.N.Zhou, Y.Mei. Matrix converter technology and its applications. Bei Jing: China Machine Press, 2007. [7] J B Ejea, E Sanchis-Kilders, J A Carrasco, et al. Espí. High-Frequency Bi-directional Three-Phase Rectifier with Power Factor Correction[C], IEEE 32nd Annual Power Electronics Specialists Conference, 2001, 3: 1303-1308.  [8] HAN JU CHA. Analysis and Design of Matrix Converters for Adjustable Speed Drives and Distributed Power Sources[D]. Texas A&M University, 2004. [9] Donald G Holmes, Thomas A Lipo. Implementation of a Controlled Rectifier Using AC-AC Matrix Converter Theory[J]. IEEE Transaction on Power Eletronics, 1992: 240-250 [10] Keping You. A New Bidirectional AC-DC Converter Using Matrix Converter and Z-source Converter Topologies[D]. The University of New South Wales, 2007 Biography  Dr Zhuang Xu works with the University of Nottingham Ningbo China. Zhuang Xu received his Ph.D. degree in electrical engineering from the University of New South Wales, Sydney, Australia. His research has been focused on power electronics and high-performance electrical drives. 

AbstractThis paper presents a bi-directional AC-DC matrix converter for the power supply systems of hybrid electric vehicles. Compared to conventional PWM rectifier and associated DC-DC converter, large DC bus capacitor banks are eliminated. The converter converts three-phase AC power into the desired DC output with higher energy density via a single power stage. A closed-loop control strategy based on indirect space vector modulation is proposed and the validity has been verified. The strategy ensures that the output voltage can be regulated tightly against different loads and wide input variation and high-quality input current can be achieved

Elsevier - Publisher Connector 

An Indirect Space-vector Modulated Three-phase AC-DC Matrix Converter for Hybrid Electric Vehicles 

1876-6102 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license 
(http://creativecommons.org/licenses/by-nc-nd/4.0/).
Peer-review under responsibility of Applied Energy Innovation Institute
doi: 10.1016/j.egypro.2015.07.242 
 Energy Procedia  75 ( 2015 )  1968 – 1974 
ScienceDirect
The 7th International Conference on Applied Energy – ICAE2015 
An Indirect Space-Vector Modulated Three-Phase AC-DC 
Matrix Converter for Hybrid Electric Vehicles 
Zhuang Xu*
The University of Nottingham, China campus, 199 Taikang East Road, Ningbo, 315100, China 
Abstract 
This paper presents a bi-directional AC-DC matrix converter for the power supply systems of hybrid electric vehicles. 
Compared to conventional PWM rectifier and associated DC-DC converter, large DC bus capacitor banks are 
eliminated. The converter converts three-phase AC power into the desired DC output with higher energy density via a 
single power stage. A closed-loop control strategy based on indirect space vector modulation is proposed and the 
validity has been verified. The strategy ensures that the output voltage can be regulated tightly against different loads 
and wide input variation and high-quality input current can be achieved. 
Keywords: AC-DC; matrix converter; closed-loop control; indirect space vector modulation  
1. Introduction 
The average electrical power absorbed by the loads of automobiles reaches above 10 kW. In order to 
pursue constantly high performance, high reliability and intelligence, more electronic equipment is 
installed in automotive, etc. [1]. Researchers, automobile manufacturers, and parts manufacturers set up 
the standards of the power nets for automobiles. If the total power remains unchanged, the current can be 
reduced by 2/3. Considering 10kW for example, 14V power supply system needs wires that can withstand 
current up to 714A, while the 42V voltage needs wires carrying 238A current [2]. Therefore, it is 
necessary to implement 42V power supply for automobiles with the developments of technologies. The
HEV power train is of the series-parallel type, such as the one found in the Toyota Prius car [1]. This 
HEV has two kinds of motive power sources: an electric motor and an internal combustion engine (ICE), 
in order to increase the drive train efficiency and reduce air pollution. The electrical subsystem as shown 
in Fig.1 is composed of four parts: The electrical motor, the generator, the battery, and the DC/DC 
converter. However, the three-phase rectifier bridge produces fifth and seventh high order harmonics. The 
traditional rectifier circuit requires large DC bus capacitors which increase the overall system size and 
maintenance costs. The alternating current produced first goes through the rectifier and then the chopper 
Buck circuit and undergoes two-stage power conversion. This reduces the energy transfer density [3]. 
* Corresponding author. Tel.: +86-0574-88189135; fax: +86-0574-88180175. 
E-mail address: zhuang.xu@nottingham.edu.cn. 
Available online at www.sciencedirect.com
 Zhuang Xu /  Energy Procedia  75 ( 2015 )  1968 – 1974 1969
Considering the above drawbacks of conventional power converters, a novel AC-DC matrix converter 
is proposed. It has many inherent advantages which power converter cannot compare with. These 
advantages include [3-5]: 
x No large capacity storage devices, fast dynamic response and longer life span 
x Wide input voltage range 
x Low input current harmonic content and only high-order harmonics 
x High power density conversion 
x Compact, reduced number of devices in series, highly efficient and easy to be implemented modularly 
The new topological structure of the proposed AC-DC matrix converter is derived from three-phase to 
three-phase matrix converter. The paper [5] records the theoretical study of the AC-DC new topologies, 
derived AC-DC rectifier control algorithm based on AC-AC modulation, and carried out simulation 
investigation. The authors in [6] implemented a low power AC-DC matrix converter in the laboratory and 
obtained sinusoidal input current which is in the same phase with the input voltage. However, input 
current waveform is not sinusoidal as expected and the switching sequence pattern in the modulation 
strategy should be further improved. In order to solve electrical isolation problems for the AC-DC matrix 
converter, the paper [7] introduced high-frequency isolation transformer to the AC-DC matrix converter 
design and added a rectification transformation. This would reduce the efficiency and lose the benefits of 
matrix converter. 
When the load change is in wide range for the open-loop matrix converter, the output may become 
unregulated or even unstable. This paper adopts a closed-loop control strategy based on indirect space 
vector modulation to overcome the downsides of the open-loop control. This paper describes in details the 
operating principle and closed-loop modulation strategy for the proposed AC-DC matrix converter, 
verifies its effectiveness, and presents the proven results. 
2. Operation Principles  
     Since the maximum voltage modulation ratio of a 3 phase-3 phase matrix converter is 0.866, the 
matrix converter is generally used as a buck converter. For rectification purpose, the three-phase output in 
the original three-phase to three-phase conversion can be reduced by one phase and changed into AC-DC 
matrix converter [5]. The topological structure of the three-phase to three phase matrix converter is shown 
in Fig. 2 [4]. 
                              
Fig.1. The electrical subsystem of power train systems.                       Fig.2. The circuit of 3 phase-3 phase matrix converter 
On the basis of the topological structure of matrix converter, its mathematical model as well as its 
limitations, an AC-DC converter is derived from three-phase to three-phase matrix converter. Its 
modulation strategy must meet the following requirements: (1) To comply with the matrix converter 
principle. (2) The output frequency is zero. (3) DC output voltage is equal to the maximum phase voltage.
The AC-DC matrix converter topology, as shown in Fig 3, consists of six bi-directional switches which 
directly realize the conversion from the input of three-phase AC into the output of DC. The closed-loop 
1970   Zhuang Xu /  Energy Procedia  75 ( 2015 )  1968 – 1974 
control of the matrix converter ensures that the output voltage is tight against different loads and a wide 
range of input changes. 
Fig.3. The topology of the AC-DC matrix converter 
     The bi-directional switch-off states are defined by the function below: 
 ^ `
1,S
0,S
, ; ( , , )
jk
jk
jk
S
j p n k a b c
­° ®
°¯
 
RQ
RII                                     (1) 
It is known from the structure of the matrix converter that the inputs cannot be short circuited and the 
outputs cannot be disconnected. The constraints are:
1
{ , }
ja jb jcS S S
j p n
   

                                                                  (2) 
The AC-DC matrix converter facilitates a direct AC to DC power conversion without any DC 
capacitors. This gives more advantages, such as controllable input power factor, highly reliable and 
compact structure. A space vector modulation method for AC-DC matrix converter is adopted to control 
the six bi-directional switches. 
3. Modulation algorithms for the AC-DC matrix converter 
Indirect space vector modulation algorithm is based on "virtual DC-link" concept. It regards the matrix 
converter equivalent in theory to a virtual connection of a rectifier and an inverter. The concept of space 
vector PWM can be applied to matrix converter and used to modulate the pulse width of "virtual rectifier" 
and "virtual inverter" respectively. Finally, the two processes were synthesized in order to achieve 
sinusoidal input and output waveforms and controllable input power factor [6]. The proposed AC-DC 
matrix converter is deduced with reference to the indirect space vector modulation algorithm. Indirect 
space vector modulation is divided into two processes. The first stage is the rectification and the other is 
the inversion process [7]. Fig 4 shows the decomposition diagram illustrating the AC-DC modulation 
process, which is quite similar to the traditional AC-DC-AC conversion system except that there's no DC 
bus capacitor. Thus, a DC bus capacitor placed across p and n gives a more virtual illustration of indirect 
space vector modulation principle. 
Fig.4. Illustration of the “virtual DC-link" concept. 
 Zhuang Xu /  Energy Procedia  75 ( 2015 )  1968 – 1974 1971
The process of AC-DC matrix converter can be expressed in the form of mathematical matrix 
expressions, the virtual DC bus voltage is obtained during the rectification process.
pn r iV F V                                                 (3) 
Where Fr is the transfer function of the rectification pro-cess, while Vi is the three-phase input 
voltage vector. Output voltage is supposed to be Vo, and the expression of output voltage in the inversion 
stage is shown in (4).
o i pnV F V                                           (4) 
 Fi is the transfer function of the inversion process. Similarly, input line current II can be expressed 
together by the rectification process and the inversion process, as shown in (5) where Io is the output 
current vector. 
T T
i r i oI F F I                                         (5) 
3.1. Rectifying Stage
The purpose of rectification is to obtain a virtual DC bus voltage Vpn and maintain the input power 
factor unity. The DC voltage is modulated by six switches s1 ~ s6 from three-phase input phase voltages. 
It is known from the principle that the inputs of matrix converters must not be short-circuited. There are 
six active switching states and three inactive switching states for s1 ~ s6. The space vector hexagon 
according to the space vector modulation method is drawn as shown in Fig. 5. 
Six active switching states correspond respectively to the six switching space vectors in the space 
vector hexagon. The remaining three inactive switching states correspond to the three zero space vectors. 
A randomly placed space vector can be synthesized by its two adjacent switching vectors. For example, Vi
in Fig.5 is a synthesis of VD and VE, and și is the angle between Vi and VD. At this moment, switching 
vector duty cycle can be expressed respectively as follows: 
Fig.5 Rectifier space vector hexagon 
sin(60 )c iT mD T 
$                                       (6) 
sin( )c iT mE T                                            (7) 
0 1T T TD E                                             (8) 
where mc is the modulation ratio, 0İmcİ1. 
Transfer function Fr in the rectification process can be established by means of space vectors through 
six switching functions s1 ~ s6. The element number of Fr is determined by the numbers of input phases. 
since it is a three-phase input,  Fr has three elements and can be expressed as: 
> @1 2 3r r r rF F F F       where 1 1 4rF s s  ; 2 3 6rF s s   ; 3 5 2rF s s                     (9) 
1972   Zhuang Xu /  Energy Procedia  75 ( 2015 )  1968 – 1974 
the displacements between Fr2, Fr3 and Fr1 are 120 degrees and +120 degrees respectively. Below is 
the expression of Vpn
1.5pn c mV m V                                        (10) 
3.2. Synthesis Process
For the six bi-directional switches shown in Fig 3, the logical expression of the six switches can be 
expressed as 
1 3 1 3 5
4 2 4 6 2
pa pb pc
na nb nc
S S S sw sw s s s
sw sw s s sS S S
ª º ª º ª º
 « » « » « »
¬ ¼ ¬ ¼¬ ¼
              (11) 
The AC-DC matrix converter modulation strategy can be implemented by using a DC output voltage 
outer loop and a current inner loop. The control block diagram is shown in Figure 6. 
      
Fig.6 Block diagram of closed-loop control strategy based on indirect                         Fig.7. The converter test bench. 
                                   space vector modulation 
The indirect space vector modulation method eases the requirements for the control circuits. This 
modulation doesn’t require the imposition of low-frequency harmonics onto output phase voltage in order 
to reach the maximum voltage utilization ratio of the matrix transformation device. The arbitrary control 
of the input current phase differences can be realized. 
4. Experimental Results 
The experimental test rig (Fig.7) has been set up for the three-phase AC-DC matrix converter 
consisting of bidirectional IGBTs from Eupec. The configuration of the main circuit is illustrated as 
shown in Fig.3. The controller board deploys TMS320F2812 DSP and Altera MAX II CPLD. 
Experiments have been carried out to test the closed-loop control strategy that is based on indirect space 
vector modulation.  Fig. 8 (a) plots the waveforms of the input phase voltage Ua and current Ia when the 
3-phase AC programmable power supply was set to line frequency of 50Hz and line voltage of 80V. It is 
seen that Ua and Ia are in phase and the power factor is unity. The DC output Upn and filtered Udc are 
illustrated in Fig. 8 (b). The smooth Udc has been regulated tightly against the load change. Fig. 8 (c) 
shows the plots of Upn and Uab where Upn closely follows the top envelope of Uab indicating that due to 
the switching action, Upn connects and disconnects to the line to line voltage of the supply. When the 
bidirectional switches were conducting, Upn is generated by Uab. To appreciate the advantages of the 
circuit, more tests have been done to verify the effectiveness. Fig.9 (a) shows that when the frequency and 
amplitude of the supply were reconfigured to 150Hz and 110V, Udc is still able to be maintained against 
the load change. Even the frequency and amplitude of the supply decrease further to 25Hz and 50V, the 
system is still capable of producing satisfactory results as shown in Fig.9 (c).    
 Zhuang Xu /  Energy Procedia  75 ( 2015 )  1968 – 1974 1973
   
Fig. 8.  Input line voltage 80V,50Hzˈ(a) Phase Ua and Ia  (b) Upn and Udc  (c) Upn and Uab 
Fig. 9.  Input line voltage 110V, 150Hzˈ(a) Phase Ua and Ia (b) Upn and Udc (c) Upn and Udc @25Hz and line voltage of 50V 
5. Conclusions 
(1). According to the topology and mathematical models of the traditional three-phase to three-phase 
matrix converters, an AC-DC matrix conversion has been derived. 
(2). For the proposed AC-DC converter, a new type of closed-loop control strategy is proposed based 
on the indirect space vector modulation algorithm. 
(3). According to the closed-loop control strategy, experiments have been carried out to verify the 
feasibility of closed-loop control of the proposed AC-DC matrix converter, which has proved the 
effectiveness of the proposed system. 
Acknowledgements 
The project is supported by Ningbo Science and Technology Bureau (2014A610146), China.  
References  
      [1] Lequesne, B. EV/HEV Technology: Are We There Yet? Viewpoint: Electrification Magazine, IEEE, Volume: 2 , Issue: 2 
2014. 
[2] CSNamuduri, BVMurty, MG Reynolds, Load dump transient control of a 42v automotive generator[C] In Proc.35th Annu. 
IEEE Power Electronics Specialists Conf., 2004: 389–394. 
[3] V. Vlatkovic, D. Borojevic, and F. C. Lee, “A Zero-Voltage Switched,Three-Phase Isolated PWM Buck Rectifier”. IEEE 
Transaction on Power Electronics, 1995, 10(2): 148 - 157. 
[4] Y.Wang. Matrix Converter's Space Vector Modulation, System Integration and Applied Research [D]. Hang Zhou: Zhe Jiang 
University, 2005. 
[5] DG Holmes, TA Lipo. Implementation of a controlled Rectifier Using ac-ac Matrix Converter theory[C] In Conf. Rec. 1989 
IEEE Power Elec.Spec. Conf., 1989: 353-359.
U
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0V
/D
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5A
/D
iv
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             (a)
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Ia 
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5A
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             (a) 
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1974   Zhuang Xu /  Energy Procedia  75 ( 2015 )  1968 – 1974 
[6] K.Sun, D.N.Zhou, Y.Mei. Matrix converter technology and its applications. Bei Jing: China Machine Press, 2007. 
[7] J B Ejea, E Sanchis-Kilders, J A Carrasco, et al. Espí. High-Frequency Bi-directional Three-Phase Rectifier with Power 
Factor Correction[C], IEEE 32nd Annual Power Electronics Specialists Conference, 2001, 3: 1303-1308.  
[8] HAN JU CHA. Analysis and Design of Matrix Converters for Adjustable Speed Drives and Distributed Power Sources[D]. 
Texas A&M University, 2004. 
[9] Donald G Holmes, Thomas A Lipo. Implementation of a Controlled Rectifier Using AC-AC Matrix Converter Theory[J]. 
IEEE Transaction on Power Eletronics, 1992: 240-250 
[10] Keping You. A New Bidirectional AC-DC Converter Using Matrix Converter and Z-source Converter Topologies[D]. The 
University of New South Wales, 2007 
Biography  
Dr Zhuang Xu works with the University of Nottingham Ningbo China. Zhuang Xu 
received his Ph.D. degree in electrical engineering from the University of New South 
Wales, Sydney, Australia. His research has been focused on power electronics and high-
performance electrical drives. 


Nottingham eTheses

1876-6102 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).Peer-review under responsibility of Applied Energy Innovation Institutedoi: 10.1016/j.egypro.2015.07.242  Energy Procedia  75 ( 2015 )  1968 – 1974 ScienceDirectThe 7th International Conference on Applied Energy – ICAE2015 An Indirect Space-Vector Modulated Three-Phase AC-DC Matrix Converter for Hybrid Electric Vehicles Zhuang Xu*The University of Nottingham, China campus, 199 Taikang East Road, Ningbo, 315100, China Abstract This paper presents a bi-directional AC-DC matrix converter for the power supply systems of hybrid electric vehicles. Compared to conventional PWM rectifier and associated DC-DC converter, large DC bus capacitor banks are eliminated. The converter converts three-phase AC power into the desired DC output with higher energy density via a single power stage. A closed-loop control strategy based on indirect space vector modulation is proposed and the validity has been verified. The strategy ensures that the output voltage can be regulated tightly against different loads and wide input variation and high-quality input current can be achieved. Keywords: AC-DC; matrix converter; closed-loop control; indirect space vector modulation  1. Introduction The average electrical power absorbed by the loads of automobiles reaches above 10 kW. In order to pursue constantly high performance, high reliability and intelligence, more electronic equipment is installed in automotive, etc. [1]. Researchers, automobile manufacturers, and parts manufacturers set up the standards of the power nets for automobiles. If the total power remains unchanged, the current can be reduced by 2/3. Considering 10kW for example, 14V power supply system needs wires that can withstand current up to 714A, while the 42V voltage needs wires carrying 238A current [2]. Therefore, it is necessary to implement 42V power supply for automobiles with the developments of technologies. TheHEV power train is of the series-parallel type, such as the one found in the Toyota Prius car [1]. This HEV has two kinds of motive power sources: an electric motor and an internal combustion engine (ICE), in order to increase the drive train efficiency and reduce air pollution. The electrical subsystem as shown in Fig.1 is composed of four parts: The electrical motor, the generator, the battery, and the DC/DC converter. However, the three-phase rectifier bridge produces fifth and seventh high order harmonics. The traditional rectifier circuit requires large DC bus capacitors which increase the overall system size and maintenance costs. The alternating current produced first goes through the rectifier and then the chopper Buck circuit and undergoes two-stage power conversion. This reduces the energy transfer density [3]. * Corresponding author. Tel.: +86-0574-88189135; fax: +86-0574-88180175. E-mail address: zhuang.xu@nottingham.edu.cn. Available online at www.sciencedirect.com Zhuang Xu /  Energy Procedia  75 ( 2015 )  1968 – 1974 1969Considering the above drawbacks of conventional power converters, a novel AC-DC matrix converter is proposed. It has many inherent advantages which power converter cannot compare with. These advantages include [3-5]: No large capacity storage devices, fast dynamic response and longer life span Wide input voltage range Low input current harmonic content and only high-order harmonics High power density conversion Compact, reduced number of devices in series, highly efficient and easy to be implemented modularly The new topological structure of the proposed AC-DC matrix converter is derived from three-phase to three-phase matrix converter. The paper [5] records the theoretical study of the AC-DC new topologies, derived AC-DC rectifier control algorithm based on AC-AC modulation, and carried out simulation investigation. The authors in [6] implemented a low power AC-DC matrix converter in the laboratory and obtained sinusoidal input current which is in the same phase with the input voltage. However, input current waveform is not sinusoidal as expected and the switching sequence pattern in the modulation strategy should be further improved. In order to solve electrical isolation problems for the AC-DC matrix converter, the paper [7] introduced high-frequency isolation transformer to the AC-DC matrix converter design and added a rectification transformation. This would reduce the efficiency and lose the benefits of matrix converter. When the load change is in wide range for the open-loop matrix converter, the output may become unregulated or even unstable. This paper adopts a closed-loop control strategy based on indirect space vector modulation to overcome the downsides of the open-loop control. This paper describes in details the operating principle and closed-loop modulation strategy for the proposed AC-DC matrix converter, verifies its effectiveness, and presents the proven results. 2. Operation Principles       Since the maximum voltage modulation ratio of a 3 phase-3 phase matrix converter is 0.866, the matrix converter is generally used as a buck converter. For rectification purpose, the three-phase output in the original three-phase to three-phase conversion can be reduced by one phase and changed into AC-DC matrix converter [5]. The topological structure of the three-phase to three phase matrix converter is shown in Fig. 2 [4].                               Fig.1. The electrical subsystem of power train systems.                       Fig.2. The circuit of 3 phase-3 phase matrix converter On the basis of the topological structure of matrix converter, its mathematical model as well as its limitations, an AC-DC converter is derived from three-phase to three-phase matrix converter. Its modulation strategy must meet the following requirements: (1) To comply with the matrix converter principle. (2) The output frequency is zero. (3) DC output voltage is equal to the maximum phase voltage.The AC-DC matrix converter topology, as shown in Fig 3, consists of six bi-directional switches which directly realize the conversion from the input of three-phase AC into the output of DC. The closed-loop 1970   Zhuang Xu /  Energy Procedia  75 ( 2015 )  1968 – 1974 control of the matrix converter ensures that the output voltage is tight against different loads and a wide range of input changes. Fig.3. The topology of the AC-DC matrix converter      The bi-directional switch-off states are defined by the function below: 1,S0,S, ; ( , , )jkjkjkSj p n k a b c                                    (1) It is known from the structure of the matrix converter that the inputs cannot be short circuited and the outputs cannot be disconnected. The constraints are:1{ , }ja jb jcS S Sj p n                                                                  (2) The AC-DC matrix converter facilitates a direct AC to DC power conversion without any DC capacitors. This gives more advantages, such as controllable input power factor, highly reliable and compact structure. A space vector modulation method for AC-DC matrix converter is adopted to control the six bi-directional switches. 3. Modulation algorithms for the AC-DC matrix converter Indirect space vector modulation algorithm is based on "virtual DC-link" concept. It regards the matrix converter equivalent in theory to a virtual connection of a rectifier and an inverter. The concept of space vector PWM can be applied to matrix converter and used to modulate the pulse width of "virtual rectifier" and "virtual inverter" respectively. Finally, the two processes were synthesized in order to achieve sinusoidal input and output waveforms and controllable input power factor [6]. The proposed AC-DC matrix converter is deduced with reference to the indirect space vector modulation algorithm. Indirect space vector modulation is divided into two processes. The first stage is the rectification and the other is the inversion process [7]. Fig 4 shows the decomposition diagram illustrating the AC-DC modulation process, which is quite similar to the traditional AC-DC-AC conversion system except that there's no DC bus capacitor. Thus, a DC bus capacitor placed across p and n gives a more virtual illustration of indirect space vector modulation principle. Fig.4. Illustration of the “virtual DC-link" concept.  Zhuang Xu /  Energy Procedia  75 ( 2015 )  1968 – 1974 1971The process of AC-DC matrix converter can be expressed in the form of mathematical matrix expressions, the virtual DC bus voltage is obtained during the rectification process.pn r iV F V                                                (3) Where Fr is the transfer function of the rectification pro-cess, while Vi is the three-phase input voltage vector. Output voltage is supposed to be Vo, and the expression of output voltage in the inversion stage is shown in (4).o i pnV F V                                          (4)  Fi is the transfer function of the inversion process. Similarly, input line current II can be expressed together by the rectification process and the inversion process, as shown in (5) where Io is the output current vector. T Ti r i oI F F I                                       (5) 3.1. Rectifying StageThe purpose of rectification is to obtain a virtual DC bus voltage Vpn and maintain the input power factor unity. The DC voltage is modulated by six switches s1 ~ s6 from three-phase input phase voltages. It is known from the principle that the inputs of matrix converters must not be short-circuited. There are six active switching states and three inactive switching states for s1 ~ s6. The space vector hexagon according to the space vector modulation method is drawn as shown in Fig. 5. Six active switching states correspond respectively to the six switching space vectors in the space vector hexagon. The remaining three inactive switching states correspond to the three zero space vectors. A randomly placed space vector can be synthesized by its two adjacent switching vectors. For example, Viin Fig.5 is a synthesis of V  and V , and i is the angle between Vi and V . At this moment, switching vector duty cycle can be expressed respectively as follows: Fig.5 Rectifier space vector hexagon sin(60 )c iT m                                       (6) sin( )c iT m                                            (7) 0 1T T T                                           (8) where mc is the modulation ratio, 0 mc 1. Transfer function Fr in the rectification process can be established by means of space vectors through six switching functions s1 ~ s6. The element number of Fr is determined by the numbers of input phases. since it is a three-phase input,  Fr has three elements and can be expressed as: 1 2 3r r r rF F F F       where 1 1 4rF s s ; 2 3 6rF s s  ; 3 5 2rF s s                    (9) 1972   Zhuang Xu /  Energy Procedia  75 ( 2015 )  1968 – 1974 the displacements between Fr2, Fr3 and Fr1 are 120 degrees and +120 degrees respectively. Below is the expression of Vpn1.5pn c mV m V                                      (10) 3.2. Synthesis ProcessFor the six bi-directional switches shown in Fig 3, the logical expression of the six switches can be expressed as 1 3 1 3 54 2 4 6 2pa pb pcna nb ncS S S sw sw s s ssw sw s s sS S S              (11) The AC-DC matrix converter modulation strategy can be implemented by using a DC output voltage outer loop and a current inner loop. The control block diagram is shown in Figure 6.       Fig.6 Block diagram of closed-loop control strategy based on indirect                         Fig.7. The converter test bench.                                    space vector modulation The indirect space vector modulation method eases the requirements for the control circuits. This modulation doesn’t require the imposition of low-frequency harmonics onto output phase voltage in order to reach the maximum voltage utilization ratio of the matrix transformation device. The arbitrary control of the input current phase differences can be realized. 4. Experimental Results The experimental test rig (Fig.7) has been set up for the three-phase AC-DC matrix converter consisting of bidirectional IGBTs from Eupec. The configuration of the main circuit is illustrated as shown in Fig.3. The controller board deploys TMS320F2812 DSP and Altera MAX II CPLD. Experiments have been carried out to test the closed-loop control strategy that is based on indirect space vector modulation.  Fig. 8 (a) plots the waveforms of the input phase voltage Ua and current Ia when the 3-phase AC programmable power supply was set to line frequency of 50Hz and line voltage of 80V. It is seen that Ua and Ia are in phase and the power factor is unity. The DC output Upn and filtered Udc are illustrated in Fig. 8 (b). The smooth Udc has been regulated tightly against the load change. Fig. 8 (c) shows the plots of Upn and Uab where Upn closely follows the top envelope of Uab indicating that due to the switching action, Upn connects and disconnects to the line to line voltage of the supply. When the bidirectional switches were conducting, Upn is generated by Uab. To appreciate the advantages of the circuit, more tests have been done to verify the effectiveness. Fig.9 (a) shows that when the frequency and amplitude of the supply were reconfigured to 150Hz and 110V, Udc is still able to be maintained against the load change. Even the frequency and amplitude of the supply decrease further to 25Hz and 50V, the system is still capable of producing satisfactory results as shown in Fig.9 (c).     Zhuang Xu /  Energy Procedia  75 ( 2015 )  1968 – 1974 1973   Fig. 8.  Input line voltage 80V,50Hz (a) Phase Ua and Ia  (b) Upn and Udc  (c) Upn and Uab Fig. 9.  Input line voltage 110V, 150Hz (a) Phase Ua and Ia (b) Upn and Udc (c) Upn and Udc @25Hz and line voltage of 50V 5. Conclusions (1). According to the topology and mathematical models of the traditional three-phase to three-phase matrix converters, an AC-DC matrix conversion has been derived. (2). For the proposed AC-DC converter, a new type of closed-loop control strategy is proposed based on the indirect space vector modulation algorithm. (3). According to the closed-loop control strategy, experiments have been carried out to verify the feasibility of closed-loop control of the proposed AC-DC matrix converter, which has proved the effectiveness of the proposed system. Acknowledgements The project is supported by Ningbo Science and Technology Bureau (2014A610146), China.  References        [1] Lequesne, B. EV/HEV Technology: Are We There Yet? Viewpoint: Electrification Magazine, IEEE, Volume: 2 , Issue: 2 2014. [2] CSNamuduri, BVMurty, MG Reynolds, Load dump transient control of a 42v automotive generator[C] In Proc.35th Annu. IEEE Power Electronics Specialists Conf., 2004: 389–394. [3] V. Vlatkovic, D. Borojevic, and F. C. Lee, “A Zero-Voltage Switched,Three-Phase Isolated PWM Buck Rectifier”. IEEE Transaction on Power Electronics, 1995, 10(2): 148 - 157. [4] Y.Wang. Matrix Converter's Space Vector Modulation, System Integration and Applied Research [D]. Hang Zhou: Zhe Jiang University, 2005. [5] DG Holmes, TA Lipo. Implementation of a controlled Rectifier Using ac-ac Matrix Converter theory[C] In Conf. Rec. 1989 IEEE Power Elec.Spec. Conf., 1989: 353-359.Ua:50V/DivI a:5A/DivTime: 5ms/Div              (a)Ua Ia Udc:20V/DivUpnUdcUpn:50V/DivUab:50V/DivTime: 1ms/Div          (b)Time: 1ms/Div           (c)Upn Uab Ua:50V/Div Ua Ia I a:5A/DivTime: 2.5ms/Div              (a) Upn:50V/DivUpn:50V/DivUdc:20V/DivTime: 1ms/Div           (b) UpnUdcUpn:50V/DivUdc:20V/DivTime 5ms/Div          (c)Upn Udc 1974   Zhuang Xu /  Energy Procedia  75 ( 2015 )  1968 – 1974 [6] K.Sun, D.N.Zhou, Y.Mei. Matrix converter technology and its applications. Bei Jing: China Machine Press, 2007. [7] J B Ejea, E Sanchis-Kilders, J A Carrasco, et al. Espí. High-Frequency Bi-directional Three-Phase Rectifier with Power Factor Correction[C], IEEE 32nd Annual Power Electronics Specialists Conference, 2001, 3: 1303-1308.  [8] HAN JU CHA. Analysis and Design of Matrix Converters for Adjustable Speed Drives and Distributed Power Sources[D]. Texas A&M University, 2004. [9] Donald G Holmes, Thomas A Lipo. Implementation of a Controlled Rectifier Using AC-AC Matrix Converter Theory[J]. IEEE Transaction on Power Eletronics, 1992: 240-250 [10] Keping You. A New Bidirectional AC-DC Converter Using Matrix Converter and Z-source Converter Topologies[D]. The University of New South Wales, 2007 Biography  Dr Zhuang Xu works with the University of Nottingham Ningbo China. Zhuang Xu received his Ph.D. degree in electrical engineering from the University of New South Wales, Sydney, Australia. His research has been focused on power electronics and high-performance electrical drives. 

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An indirect space-vector modulated three-phase AC-DC matrix converter for hybrid electric vehicles

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