Direct Power Control of Three-phase Voltage Source ... - Core

Available online at www.sciencedirect.com

ScienceDirect Procedia Computer Science 86 (2016) 365 – 368

2016 International Electrical Engineering Congress, iEECON2016, 2-4 March 2016, Chiang Mai, Thailand

Direct Power Control of Three-Phase Voltage Source Converters using Feedback Linearization Technique Nirawit Muangruka,*, Suksun Nungamb Department of Electrical and Computer Engineering, Faculty of Engineering King Mongkut’s University of Technology North Bangkok, 1518 Pracharat 1 Road, Wongsawang, Bangsue, Bangkok 10800, Thailand

Abstract This paper describes the direct power control (DPC) of a three-phase voltage source converter (VSC) using feedback linearization technique. This technique transforms nonlinear model of the VSC into a linear one so that the controller design is easy and independent of the operating point. The problem is formulated in the DPC framework. The DPC with space-vector modulation (DPC-SVM) is adopted because of its constant switching frequency operation. The control scheme is implemented on a STM32F4DISCOVERY board. The validity of the scheme has been verified through experiment which shows that the proposed control strategy provides the VSC operation with wide operating range and fast transient responses. © 2016 2016The TheAuthors. Authors. Published by Elsevier © Published by Elsevier B.V.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. Peer-review under responsibility of the Organizing Committee of iEECON2016 Keywords: Direct power control, Feedback linearization, Three-phase converter ;

1. Introduction A three-phase voltage source converter (VSC) offers many advantages, namely bidirectional power flow, low harmonic distortion of line current and regulation of input power factor to unity. These advantages are made possible by means of control strategies. Direct power control (DPC) for the VSC has attracted the attention of many researchers. In the original DPC strategy [1], the conventional current control loops and PWM modulator are replaced by a lookup table control scheme to obtain fast transient responses. However, this scheme causes problem

* Corresponding author. Tel.: +66 86 234-5656. 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.2016.05.100

366

Nirawit Muangruk and Suksun Nungam / Procedia Computer Science 86 (2016) 365 – 368

of variable switching frequency. In [2], the DPC with space-vector modulation (DPC-SVM) is proposed, providing the VSC with a constant switching frequency operation without sacrificing the original DPC performance. Since the dynamic model of the VSC is nonlinear, controllers are conventionally designed using the linearized model of the VSC around an operating point. This presents the problem that the controller design is dependent on the operating point. On the other hand, the feedback linearization technique [3] transforms the nonlinear system into a linear decoupled one. This technique is applied for VSC in [4-5], resulting in fast transient responses and operation on whole operating range. However, due to the complexity of the control algorithm, it is difficult to implement in practice. Further improvement has been proposed in [6], where the energy stored in the output capacitor, instead of DC bus voltage, is chosen as a state variable. Applying feedback linearization to this state variable gives rise to a much simpler control algorithm. This paper proposes to use the power of the output capacitor as a state variable of the system, and to apply feedback linearization technique in the framework of the DPC. Problem formulation is described and the experimental results are illustrated. The proposed control strategy provides the VSC with fast transient responses and the control performances do not depend on the operating point. 2. Mathematical model of the VSC and feedback linearization technique The power circuit of the VSC under investigation is shown in Fig. 1, where RL is a resistive load. The dynamic model of the VSC in the rotating d-q frame can be expressed by Eq. 1 where R, L are resistance and inductance of the line reactor; C is the capacitance of the DC bus capacitor; Ȧ is the angular frequency of the line voltage; id, iq, ed, eq are currents and supply voltages in the d-q axis. Pconv Vsa = VmcosȦt

Pc

Vsb Vsc

Pload

Vdc R

RL

L

ªid º « » «iq » «» ¬ Pc ¼

ª R º ª 1 «  ˜ id  Z ˜ iq » « L « » « L R « » « « Z ˜ id  L ˜ iq »« 0 « » « 2 «3 § R · » « 3 ˜ Vm V i i P Z ˜ ˜  ˜  ˜  ˜ ¨ ¸ m d q c « » © L ¹ RL ˜ C ¬2 ¼ ¬« 2 ˜ L

º 0» » 1 » ªed  vd º ˜« » L » ¬ eq  vq ¼ » 0» ¼»

(1)

Fig. 1. Power circuit of the VSC

vd, vq are the control input voltages; Pc is the power in the capacitor. Note that the power in the DC bus capacitor, Pc is chosen as a state variable. By defining, Pc (3 / 2) ˜  ed ˜ id  eq ˜ iq  Vdc 2 / RL , Pconv (3 / 2) ˜  ed ˜ id  eq ˜ iq and PLoad Vdc 2 / RL , and using the power balance principle in Fig. 1, we obtain Pc Pconv  PLoad . Feedback linearization technique assumes the plant to be described in the following form; x

f ( x )  g ( x) ˜ u

y

(2)

h( x )

(3)

where x, u and y are state vectors, control inputs and outputs respectively. We propose to regulate Vdc at a reference value by directly controlling, Pc; it is named as direct power control. The power factor at the AC-side is controlled by iq. Therefore, Pc and iq are chosen as the dummy outputs in Eq. 3. Hence, from Eq. 1, Eq. 2 and Eq. 3 we have,

ª f1 (x) º « » « f 2 (x) » «¬ f 3 (x) »¼

u

Where

ª R º «  ˜ id  Z ˜ iq » « L » R « »  ˜  ˜ Z i i d q « » L « » 2 «3 § R · » « 2 ˜ Vm ˜ ¨©  L ˜ id  Z ˜ iq ¸¹  R ˜ C ˜ Pc » ¬ ¼ L ªed  vd º «e  v » ¬ q q¼

ªud º «u » ¬ q¼

> x1

x2

T

x3 @

»id

iq

Pc ¼º

T

(4)

g (x)

ª g1 0 º « 0 g 2» « » «¬ g 3 0 »¼

(6)

h(x)

ª y1 º «y » ¬ 2¼

and ed = Vm, eq = 0.

ª Pc º «i » ¬ q¼

ª 1 « L « « 0 « « « 3 ˜ Vm ¬« 2 ˜ L

º 0» » 1» L» » 0» ¼»

(5)

(7)

367

Nirawit Muangruk and Suksun Nungam / Procedia Computer Science 86 (2016) 365 – 368

Feedback linearization technique is applied by differentiating the output, Eq. 7 only once and the control inputs show up. We then define the intermediate inputs Vd, Vq whereby linear control techniques can be applied to these inputs and the outputs. We then have, ª y1 º « y » ¬ 2¼

ªu d º A(X)  E (X) ˜ « » ¬u q ¼

E (X)

ª 3 ˜ Vm « 2˜ L « « 0 ¬«

ªVd º « » ¬Vq ¼

º 0» » 1» L ¼»

(8)

A(X)

ª f3 º « » ¬ f2 ¼

(10)

ªu d º « » ¬u q ¼

ª ªVd º º E 1 (X) ˜ «  A(X)  « » » ¬Vq ¼ ¼» ¬«

Vsa,Vsb

AC/DC Converters Current/Voltage Measurement

PLL , ed , eq , id , iq Pc estimation

Pcmea Vdc* +

PI

Pc * + X

-

PI

0 +

PI - iq

Load

ed = Vm +

Vd

ud -

Vq

Feedback Linearization uq Eq. 11

-

(11)

Isa,Isb

n iq

(9)

+

Vdref

Sa S b S c SVPWM

Vqref eq = 0

Fig. 2. DPC with feedback linearization technique

The feedback linearization-based DPC diagram is shown in Fig. 2. A phase-lock-loop (PLL) algorithm estimates the phase angle of the line voltage. The line currents, Isa and Isb are measured and transformed into id and iq currents in the rotating d-q frame. The Pcmea is then estimated and used as a controlled variable. The q-axis current, iq is controlled with its reference set to zero to ensure the unity power factor at the AC-side. Since the transformed system Eq. 8 becomes a first-order linear system, PI controllers can be simply applied for both and inner loops and pole-placement is used for tuning the controllers. The outer loop control of Vdc follows the design of direct power control described in [2], where a PI controller is also utilized. 3. Implementation and Experimental results The experimental setup is shown in Fig. 3. The feedback linearization control algorithm, the space vector PWM algorithm (SVPWM) and the phase lock loop (PLL) are implemented on a STM32F4DISCOVERY board. The resistance and the inductance of the line reactor are 0.8 Ÿ and 5 mH respectively. The system operates at the input phase voltage of 80 V / 50 Hz, with 820 μF output capacitor and 300 Ÿ resistive load. The switching frequency is chosen to be 10 KHz. Fig. 4 shows the step response of the DC bus voltage when the reference changes from 300 V to 350 V and back again. It can be seen that the fast transient response can be achieved. Fig. 5 shows the DC bus voltage when load changes from 300 Ÿ to 150 Ÿ; the load current is doubled. The system reacts almost instantaneously to the load change. Phase voltage and current are illustrated in Fig 6. It can be seen that current and voltage are in phase which means that the converter operates at unity input power factor. The experiment has been carried out for several output voltages and the results are consistent with the ones presented here. Thanks to the feedback linearization technique, the performances do not depend on the operating points. Although the simulation results are not shown here, there is very good agreement between simulation and experimental results.

368

Nirawit Muangruk and Suksun Nungam / Procedia Computer Science 86 (2016) 365 – 368

Volt = 50 V/div Time = 100 ms/div

Vdc 300 V

Fig. 3. Experimental setup

Vdc 300 V

Vdc 350 V

Fig. 4. Transient response of DC bus voltage

Volt = 50 V/div Amp = 1 A/div Time = 100 ms/div

Vsa

Volt = 50 V/div Time = 100 ms/div

Isa

Load Current 1 A

Load Current 2 A

Fig. 5. DC Bus voltage when the load changes

Fig. 6. AC-side voltage and current

4. Conclusions The direct power control of VSC using feedback linearization technique has been described. The dynamic model of the VSC in the rotating d-q frame with a resistive load has been investigated. The power in the output capacitor, Pc and the q-axis current are chosen as the outputs for the feedback linearization. This choice of output gives rise to a constant decupling matrix, which reduces the complexity of the control algorithm. In this formation, the conventional control loop of d-axis current has been replaced by the direct power control loop of Pc and hence fast transient responses result. The DPC-SVM control scheme is utilized for the sake of its constant switching frequency operation. With feedback linearization, the control design becomes easy and independent of the operating point. The experimental results show fast voltage response due to step load change, suggesting the possibility of reducing the size of the output capacitor. In addition, the performances of the VSC are virtually the same regardless of operating points. References [1] Toshihiko Noguchi, Hiroaki Tomiki, Seiji Kondo and Isao Takahashi, Direct Power Control of PWM Converter Without Power-Source Voltage Sensors, IEEE Trans. Ind. Applicat., Vol. 34, No. 3, May/Jun 1998. [2] Mariusz Malinowski and Marian P. Kazmierkowski, Simple Direct Power Control of Three-Phase PWM Rectifier Using Space-Vector Modulation (DPC-SVM), IEEE Trans. Power Electron., Vol. 51, No. 2, Apr. 2004. [3] J. E. Slotine andW. Li, Applied Nonlinear Control. Englewood Cliffs, NJ: Prentice-Hall, 1991. [4] D.-C. Lee, Advanced nonlinear control of three-phase PWM rectifiers, IEE Proc.-Electr. Power Appl., Vol. 147, No. 5, Sept 2000. [5] D.-C. Lee, G.-M. Lee, and K.-D. Lee, DC-bus voltage control of three-phase ac/dc PWM converters using feedback linearization, IEEE Trans. Ind. Applicat., Vol. 36, No. 3, May 2000. [6] Phruksarangruk.T and Nungam.S, A Novel Control of Three-Phase Converters using Feedback Linearization Technique, Proceedings of the 7th Conference of Electrical Engineering Network of Rajamangala University of Technology 2015. [7] Marzouki.A, Hamouda.M, Fnaiech.F, Sensorless Nonlinear Control for a Three-Phase PWM AC-DC Converter, IEEE Conference Publications 2010. p. 1052-1057.