High Performance Direct Power Control of Three-Phase PWM Boost Rectifier under Different Supply Voltage Conditions Abdelouahab Bouafia (1), Jean-Paul Gaubert (2), Abdelmadjid Chaoui (1) Laboratoire d’Electronique de Puissance et Commande Industrielle (LEPCI), université de Sétif 1, Algérie. (2) Laboratoire d’Informatique et d’Automatique pour les Systèmes (LIAS), ENSIP, université de Poitiers, France. Tel.: +33 / (0) – 549.45.36.78 Fax: +33 / (0) – 549.45.40.34 E-Mail:
[email protected],
[email protected],
[email protected] URL: http://www.univ-setif.dz, http://www.lias-lab.fr (1)
Keywords «Converter control», «Direct power control», «Pulse width modulation (PWM)», «Voltage source converter», «DC power supply».
Abstract Conventional direct power control (DPC) technique is a simple and efficient control strategy for threephase PWM rectifier. However, its performance is deteriorated when the converter is supplied by unbalanced or distorted grid voltages. This paper presents the design and implementation of a new DPC scheme based on disturbance rejection principle to achieve sinusoidal input currents operation of three-phase PWM rectifier under different supply voltage conditions. In the proposed DPC, instantaneous active and reactive powers provided by harmonic component of input currents are chosen as controlled variables. Both controlled power reference are given from the outside of the controller and are set to zero to achieve full rejection of any grid disturbance. Moreover, the control strategy minimizes a cost function to select the optimum converter voltage vector allowing the best tracking of controlled powers. Finally, the effectiveness of the proposed DPC scheme is verified through several simulation and experimental tests. Results have proven an excellent performance and good robustness of the proposed DPC under different supply voltage conditions, compared to lookup table-based conventional DPC.
Introduction Over the past few years, considerable research work has been carried out on the control of three-phase PWM rectifiers. The proposed control strategies can be classified for their use of current loop controllers or active/reactive power controllers [1]. The most commonly used control technique for current control of this type of converter is called voltage-oriented control (VOC) [2-5]. It resembles the field-oriented control, used for vector-controlled ac motors. Direct power control (DPC) is a simple and efficient control strategy which has been developed analogously with the well-known direct torque control (DTC) used for adjustable speed drives [6-20]. It has become very popular and has constantly been developed and improved. In DPC, the instantaneous active and reactive powers are taken as the output signals to be regulated. Various DPC schemes have been presented in recent works for three-phase PWM rectifier. Initially, the developed DPC scheme directly controls active and reactive powers by selecting the appropriate switching states from a lookup table (LUT) based on supply voltage vector position [6-7,9-12 ] or virtual-flux (VF) vector position in the stationary reference frame [8,13,15]. The performance of this DPC scheme depends on the choice of the switching table [10-11]. Another DPC schemes with space-vector modulation (SVM) have been proposed in [13]. They join important advantages of SVM with DPC
features such as constant switching frequency. Next, several DPC schemes combined with predictive approaches have also been proposed in order to enhance control performance [21-24]. All the above mentioned DPC schemes deal with the case of balanced sinusoidal supply voltages which rarely occur in a real utility-based power distribution system. When the converter is supplied by unbalanced or distorted grid voltages the performance of the system is highly deteriorated and low order harmonic contents appear in input currents. This paper proposes a new DPC scheme which aims to achieve sinusoidal input currents operation of three-phase PWM rectifier under different supply voltage conditions. The control strategy employs the principle of disturbance rejection to compensate the effect of any grid disturbance on the quality of input currents, such as unbalanced and/or distorted voltages. Instantaneous active and reactive powers provided by harmonic component of input currents are chosen as controlled variables in the proposed DPC. Both controlled power commands are given from the outside of the controller and are set to zero. Moreover, only the optimum voltage vector minimizing a cost function is applied during one control period. Finally, the developed DPC strategy was tested both in simulation and experimentally. Results confirm the effectiveness and the high performance of the proposed DPC controller compared to lookup table-based conventional DPC (LUT-DPC).
DPC Based on Disturbance Rejection Principle System Configuration The configuration of the proposed direct power control (DPC) for three-phase PWM rectifier is shown in Fig. 1. Its concept is based on disturbance rejection principle to achieve sinusoidal input currents and constant dc-bus voltage under different supply voltage conditions. For this purpose, active and reactive powers provided by harmonic component of input currents, Ph and qh respectively, are chosen as controlled variables. As shown in Fig. 1, both power commands Ph* and qh* are given from the outside of the controller and are set to zero for full rejection of grid disturbance such as unbalanced and/or distorted supply voltages. The dc-bus voltage is regulated by adjusting the magnitude of fundamental term of input current Imax. Moreover, the proposed DPC introduces a predictive approach to select the optimum voltage vector to be applied during the next control period. The vector selection is based on minimizing a cost function for all possible voltage vectors of the converter showed in Fig.2.
Principle of optimum converter voltage vector selection As shown in Fig.2, three-phase PWM rectifier provides six non-zero voltage vectors (vi for i= 1,...,6) and two zero voltage vectors (v0 and v7). They are given by the following relation:
vα i = vαβ i .cos ( (i − 1).π 3 ) vα 0 = 0 (1) For i = 1, 2, ..., 6 and Where: vαβ i = 2 3.vdc vβ 0 = 0 vβ i = vαβ i .sin ( (i − 1).π 3 ) For a given voltage vector vαβi, and by neglecting R, the change in input current can be expressed as: ∆ iα ( k ) iα ( k + 1) − iα ( k ) Ts eα ( k ) vα i (2) ∆ i ( k ) = i ( k + 1) − i ( k ) = − v e ( k ) L β β β β β i So, the resulting change in active and reactive power can be estimated for the next control period as:
Ts Ts 2 2 ∆P (k )i = L eα (k ) + eβ (k ) − L eα ( k ).vα i + eβ ( k ).vβ i ∆q (k ) = Ts e (k ).v − e (k ).v α βi β αi i L
(3)
On the other hand, harmonic component of input currents and their associated powers are given as follows:
iah i ia1 * a * ibh = ib − ib1 , i * ich c ic1
Ph = ea .iah + eb .ibh + ec .ich 1 ( eb − ec ) .iah + ( ec − ea ) .ibh + ( ea − eb ) .ich qh = 3
(4)
Since both commands Ph* and qh* are set to zero, tracking errors of controlled powers at sampling instant k are:
ε Ph (k ) = − Ph (k ) ε qh (k ) = −qh (k )
(5)
Tracking errors at the next control period are predicted using the following equations:
ε Ph (k + 1) = ε Ph (k ) − ∆Pi (k ) ε qh (k + 1) = ε qh (k ) − ∆qi (k )
(6)
The optimum converter voltage vector, to be applied in the next control period, is the best one minimizing the cost function: 2
f i = ε Ph ( k ) − ∆ Pi ( k ) + ε q h ( k ) − ∆ q i ( k )
2
For i =1,2,...,6
(7)
Idc ea
~ e ~ ebc ~
L
R
ia
va
ib ic
vb
C
β axis
RL
θ5
vc
θ6 Sa
P L L
θ3
v2
θ7
Sc
Sb
v3
θ4
Optimum Voltage Vector Selection min(ƒi)
∆Pi(k)
vdc
Calculation of ∆Pi(k) and ∆qi(k)
ea,b,c
-
εph
εqh
∆qi(k)
vdc +
PI
ia1*
× -+ × ib1* × ic1* ia,b,c
-+ -+
Calculation of powers Ph and qh
v1
θ8 θ9
v5
θ10
θ1
α axis
v6
θ12 θ11
Fig. 2 : Rectifier voltage vectors: v1(100), v2(110), v3(010), v4(011), v5(001), v6(101), v0(000), v7(111).
-+ -+
qh*=0 Ph*=0
vdc*
θ2
θ
v4
2 3.E
Imax
Fig. 1: Block diagram of the proposed DPC.
Simulation and Experimental Results To verify the effectiveness and the performance of the proposed DPC scheme, both simulation and experimental tests are carried out for different supply voltage conditions. The test bench is developed in LIAS-laboratory, ENSIP, University of Poitiers, France. The electrical parameters of the power circuit and control data are listed in Table I. We present in this section some simulation and experimental results and measurements, which are in well accordance, for the proposed DPC and the conventional LUT-DPC under the same conditions. It can be clearly seen that the proposed DPC guarantees full rejection of grid disturbance and maintains near-sinusoidal input current waveforms (THD
