Available online at www.sciencedirect.com
ScienceDirect Procedia Computer Science 86 (2016) 397 – 400
2016 International Electrical Engineering Congress, iEECON2016, 2-4 March 2016, Chiang Mai, Thailand
Experimental Validation of Vector Control of a Matrix Converter Fed Induction Generator for Renewable Energy Sources Prajak Bunpakdeea, Jessada Theeranana, Chuttchaval Jeraputrab * a
Dept. of Electrical Engineering, Bangkokthonburi University, Bangkok, Thailand b Dept. of Electrical Engineering, Mahidol University, Nakhonpathom, Thailand
Abstract Grid integration of induction generators driven by renewable energy sources requires power electronic converters to transform the grid voltage into an output voltage of appropriate magnitude and frequency. This paper presents an experimental validation on vector control of a matrix converter fed induction generator. Operation of a matrix converter is presented. The principle of vector control for induction generators is described. A matrix converter prototype 3 kW, 230V, 50Hz is developed. Rotor speed and flux are digitally controlled by 32-bit microcontrollers TMS320F28069. The experimental results confirm viability of the proposed control method. © 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license © 2016 The Authors. Published by Elsevier B.V. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-reviewunder under responsibility of Organizing the Organizing Committee of iEECON2016. Peer-review responsibility of the Committee of iEECON2016 Keywords: Maxtrix Converter; Vector Control; Induction Generator
1. Introduction Nowadays, power electronic converters play an important role in the integration of renewable energy sources to the grid. They are capable of converting ac voltages with variable magnitude and frequency to desirable ac voltages as recommended by grid requirements. These power converters can be categorized into two types:
*Corresponding author. Tel.: 662-889-2138 Ext.6501; Fax: 662-889-2138 Ext.6529. E-mail address:
[email protected]
1877-0509 © 2016 The Authors. Published by Elsevier B.V. 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 the Organizing Committee of iEECON2016 doi:10.1016/j.procs.2016.05.043
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Input voltage
Flux command
Speed Zm* command
PI Controller
PI Controller
ids i*
qs
vds*
Inverse Park’s Transformation
vqs*
PI Controller
Indirect SVPWM
IGBTs
Vector Control
Rotor flux angle
Te
ids iqs
Park’s Transformation
Output voltage
ScA Vb
ia
SaB
ib
SbB
ic
ScB
iabc,s
Vc
Zm
SaA
Phase A
SbA
Va
Matrix Converter
iqs Zm
Output side
Input side
vabc,s ids*
VA iA Phase B
VB
iB VC
SaC
Phase C
SbC
iC
ScC Wind Turbine
Fig. 1 Grid integration of a variable speed wind turbine using a matrix converter
Fig. 2 Matrix converter topology
an indirect ac/dc/ac converter and a direct ac/ac converter; i.e. a back to back PWM rectifier/inverter and a matrix converter respectively [1-2]. Although an indirect ac/dc/ac conversion system has several advantages such as being mature technology, robust and simple to control. The use of a bulky dc-link electrolytic capacitor which has a limited lifetime is a serious drawback. Instead, a direct ac/ac conversion system i.e. a matrix converter has a number of advantages such as sinusoidal input/output currents, bidirectional flow, controllable power factor, compactness, and high reliability due to lack of bulky electrolytic capacitors. In Fig. 1, a matrix converter is employed to control speed and rotor flux of an induction generator driven by a variable speed wind turbine. The real power converted from wind energy is directly fed into the grid. But the reactive power required by an induction generator and drawn from the grid can be controlled independently. In this paper, experimental validation of vector control of a matrix converter fed induction generator is presented. Operation of a matrix converter is detailed. Principles of vector control and gain selection of PI controllers are discussed. A matrix converter prototype with ratings of 3 kW, 230V, 50Hz is developed and controlled using 32-bit microcontrollers. Viability of the proposed conversion method is verified by experimental results. 2. Matrix Converter A matrix converter is represented by a switch matrix as shown in Fig. 2 It consists of nine bidirectional switches with three input phases that can be connected to any of three output phases without an energy storage element. The notations of bidirectional switches are given that small letters a, b, or c belong to the input phase and capital letters A, B or C belong to the input phases. For example, the switching state [SaA] refers to the state where the output phase A is connected to the input phase a. The operation of a matrix converter has two restrictions First, three input phases must never be shorted circuits. Second, three output phases must never be opened circuits. It is assumed that an element of a switching transfer matrix is one when a corresponding switch is closed and it becomes zero when a corresponding switch is opened. The switching transfer matrix and its constraint is expressed as, (1) ܵ ܵ ܵ Sij = 1; On state = ܁ܵ ܵ
ܵ ܵ
ܵ ൩ ܵ
Sij = 1; Off state i ^a, b, c`, j ^A, B, C`
Sୟ୧ + S + S = 1 (2) The input currents and output voltages of a matrix converter can be determined by the product of the switching function matrix and the input current vector and the output voltage vector expressed as. ܁ = ܗ܄ή ܑ܄ (3) ۷ܑ = ܁ ή ۷ܗ (4) where V0 is the output voltage vector, Vi is the input voltage vector, I i is the input current vector, I0 is the output current vector, S is the switching function matrix, and T denotes transposition of a matrix. Voltage and current conversion above require advanced modulation techniques. In this reseach, the indirect space vector PWM is adopted for the implementation [4]. This modulation has a significant advantage that it enables control of the input currents and the output voltages to be decoupled. Thus, the reactive power required by an induction generator and unity power factor at the utility side can be controlled independently.
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3. Vector Control The concept of vector control is to enable an induction generator/motor to be controlled as if it were a dc generator/motor. Dynamic stator and rotor voltage equations in the stationary abc frame of a three-phase induction generator can be expressed as, ݀ߣ,௦ ݀ߣ, (5) ݒ,௦ = ݎ௦ ݅,௦ + ݒ, = ݎ ݅, + ݀ݐ
݀ݐ
whereas subscripts s and r denote stator and rotor repectively. The stator and rotor voltages in the abc frame can be transformed into the dq frame and vice versa by Park’s transformation. 1 2ߨ 2ߨ (6) ۍcos(ߠ ) ې sin(ߠ ) ۍcos(ߠ ) cos(ߠ െ ) cos(ߠ + )ې ܂ௗ =
ێ 2 ێsin(ߠ ) 3ێ ێ1 ۏξ2
sin(ߠ െ 1
3 2ߨ ) 3
ξ2 ۑ ێ 2ߨ 2ߨ 1 ۑ ێ ିଵ ܂ௗ = ێcos(ߠ െ ) sin(ߠ െ ) ۑ 3 3 ξ2 ێ ۑ ێcos(ߠ + 2ߨ) sin(ߠ + 2ߨ) 1 ۑ 3 3 ۏ ξ2 ے
3 ۑ 2ߨ )ۑ 3 ۑ 1 ۑ ے ξ2
sin(ߠ +
ξ2
whereas șe is the electrical angle. The dynamic voltage equations (5) are transformed into the dq frame by Park’s transformation (6) and expressed as, ݒௗ௦ ݒௗ െ߱ ߣ௦ െ(߱ െ ߱ )ߣ ݅ௗ௦ ݀ߣௗ௦ Τ݀ݐ ݅ௗ ݀ߣௗ Τ݀ݐ (7) ൨+ ൨+ ቂ ቃ= ݎ ൨+ ൨ ቂ ቃ= ݎ ൨+ ൨ ݒ௦
௦
݅௦
݀ߣ௦ Τ݀ݐ
ݒ
߱ ߣௗ௦
݅
݀ߣ Τ݀ݐ
(߱ െ ߱ )ߣௗ
where Ze is the synchronous speed and Zr is the rotor speed. As the rotor being short-circuited, the rotor voltages in (7) are zero. The rotor flux in the dq frame and the slip speed Ȧslip can be expressed as, ߣௗ = ܮ ݅ௗ௦ (8) ݎ ݅௦ (9) ߱௦ = ܮ ݅ௗ௦
where Lm and Lr are the magnetizing inductance and the rotor inductance repectively and P is number of poles. The rotor flux angle șe aligned with the rotor d-axis can be derived from integration of the sum of the rotor speed and the slip speed given by eq (10). The developed torque on the rotor is expressed by eq (11). ܲ (10) ߠ = න൫߱௦ + ߱ ൯݀ݐ ܶ=
2 3ܲ ܮ ߣ ݅ 4 ܮ ௗ ௦
(11)
It is noticed that the rotor flux can be controlled by the stator current in d axis (8). Torque can be controlled by the stator current in q axis (11). The speed command and reference currents in dq frame are compared with their respective reference values and regulated by PI controllers. Closed loop block diagrams of speed control and current control are shown in Fig. 3. Zm* (s)
-
Kp
Ki
iq* (s)
T (s)
Keq
s
-
1 sJeq
* i dq (s)
Zm(s)
TL (s)
Zm(s)
Kp
i dq (s)
Ki
s
* (s) edq
v dq (s)
FEED FORWARD COMPENSATION
-
1 rs + s VLs
i dq (s)
e dq (s)
Fig.3 Block diagrams of closed loop speed control and current control
Gain selection of PI controllers are designed based on frequency response analysis. Proportional and integral gains for closed loop speed control are expressed as, ߱ଶ ܬ )ܯܲ(݊ܽݐ (12) ܭூ = ܭ= ܭ
ூ
߱
(ܭ ඥ1 + )ܯܲ(݊ܽݐଶ )
where PM is the phase margin and Ȧc is the cross over frequency, Jeq is the combined rotor and turbine inertia. The torque constant Keq is defined by, ܭ =
(13)
ܲ ܮ ଶ כ ݅ 2 ܮ ௗ௦
where Ls is the stator inductance, Lr is the rotor inductance, and Lm is the magnetizing inductance. Proportional and integral gains for closed loop current control are expressed as, (14) ߨ ݎ௦ଶ + (߱ ܮ௦ ߪ)ଶ ିଵ ߱ ܮ௦ ߪ ܯܲ(݊ܽݐെ
ܭ = ܭூ
2
+ ݊ܽݐ
ቀ
ݎ௦
ቁ)
ܭூ = ඩ
߱
ܯܲ(݊ܽݐെ
ߨ ߱ ߪܮ + ି݊ܽݐଵ( ௦ ))ଶ + 1 ݎ௦ 2
where Ȧci is the cross over frequency of current control loops. The linkage factor is defined as, ߪ = ܮ௦ ܮ െ ܮଶ
It is noted that the linkage factor must be greater than zero.
(15)
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4. Experimental Results A matrix converter prototype rated 3 kW, 230V, 50Hz is implementd. Figure 4 shows a matrix converter circuit that is comprised of three IGBT modules “APTGF50TDU120PG” by Microsemi forming nine bidirectional switches.The matrix converter is digitally controlled using two 32-bit microcontrollers operating in parallel. Vector control algorithm and indirect space vector modulation is implemented on the principal microcontroller. The second microcontroller generates precise switching pulses for the matrix converter. More detail on the development can be found in [4].
Nine bi-directional switches
Three-phase matrix converter
Test setup
Fig. 4 Matrix converter prototype and test setup ia (1A/div) iA (2.5A/div) vAB (500V/div)
Input current, output current, and output voltage
Real and reactive power
Total harmonic distortion
Fig. 5 Experimental results
Fig. 5 shows input current and output current waveforms of the matrix converter while it regulates speed of the induction generator at 1,100 rpm. It is observed that the frequency of input current is the same as the system frequency, while, the output current has frequency of 35.7Hz. Thus, the induction generator operates in the regenerative mode with the slip of -0.027. Real power of 120W is supplied into the grid. Reactive power of 231 Var is transfered to the grid as a result of input filter capacitors. The input power factor of 0.47 (leading) is obtained. The quality of the input current is analyzed using a power quality analyzer Fluke 43B. The total harmonic distorion %THD of 16.6% is achieved. Therefore, vector control of an induction generator using a matrix converter is viable. Advantages of direct ac/ac conversion and efficient vector control sigificantly improve the potential of a matrix converter to compete with typical ac/dc/ac conversion systems in the near future. 5. Conclusion Experimental validation of vector control of a matrix converter fed induction generator is presented. Operation of a matrix converter is described. Analysis of vector control for induction generators is discussed in detail. A matrix converter prototype rated at 3 kW, 230V, 50Hz is implemented and tested. Vector control algorithm and indirect space vector PWM for the matrix converter are implemented on two 32-bit microcontrollers. The experimental results verify that the proposed vector control of a matrix converter fed induction generator is practical and well suited for grid integration of renewable energy sources. Acknowledgements This project is supported by Mahidol University and the Energy Policy and Planning Office (EPPO), Ministry of Energy, Thailand.
References 1. Blaabjerg F. and Z. Chen, Power Electronics for Modern Wind Turbines, Morgan & Claypool Publishers, 2006. 2. Han Ju Cha, Analysis and Design of Matrix Converters for Adjustable Speed Drives and Distributed Power Sources, Ph.D. Thesis Texas A&M University 3. Ned Mohan, Advanced Electric Drivers Analysis Control and Modelling using Simulink, MNPERE 4. Jessada Theeranan, Development of a Matrix Converter based on Indirect Space Vector PWM for Renewable Energy Sources, M.Eng Thesis, 2014, Mahidol University.
