Compensation of negative sequence stator flux of doubly-fed induction generator using polar voltage control-based direct torque control under unbalanced grid voltage condition Badrinarayan Bansilal Pimple, Vishal Yashwant Vekhande, Baylon G. Fernandes Department of Electrical Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India E-mail:
[email protected] Published in The Journal of Engineering; Received on 11th August 2014; Accepted on 2nd December 2014
Abstract: This study proposes a polar voltage control-based direct torque control method to reduce the effects of unbalanced grid voltage on doubly-fed induction generator (DFIG)-based wind turbine system. Under unbalanced grid voltage, the stator flux has a negative sequence component which leads to second harmonic pulsation in torque, stator active power, stator reactive power, stator current and rotor current. In the control scheme, the negative sequence rotor voltage vector is controlled to compensate the negative sequence stator flux by negative sequence rotor flux. Simulation study is carried out on a 2 MW DFIG system using MATLAB/SIMULINK. Feasibility of the proposed control strategy is experimentally verified on a 1.5 kW DFIG system.
1
Introduction
Doubly-fed induction generators (DFIGs) are widely equipped for multi-megawatt wind turbines because of its capability to provide variable speed operation, independent torque and reactive power control from rotor side converter. As the stator side of DFIG is directly connected to the grid, it is very sensitive to the unbalance in grid voltage. DFIG-based wind turbines are often installed in offshore and remote rural areas. Owing to the increase and gradual use of single phase and non-linear loads, and unsymmetrical grid faults, unbalance and harmonic distortion (typically the fifth and seventh orders) are commonly occurring in the rural grid and distribution network [1]. The remote wind farms connected to weak networks periodically experience voltage unbalance level beyond 2% [2]. Unbalanced grid voltage establishes negative sequence stator flux, which is responsible for the second harmonic pulsations in electromagnetic torque. Torque pulsation results in acoustic noise at low levels of unbalance, and at high levels can even damage the rotor shaft, gearbox or blade assembly. Negative sequence stator flux induces negative sequence voltage in the rotor. This results in large negative sequence current in the rotor. The unbalanced currents cause unequal heating in the stator and rotor windings. As a result, DFIGs without unbalanced voltage control may have to be disconnected from the grid when network voltage unbalance is more than 6% [3]. Control schemes to reduce the effects of unbalanced grid voltage on DFIG are well reported in the literature. The control is normally achieved using field oriented control technique based on rotating synchronous reference frame (SRF). In [4], the stator unbalanced currents and voltages of DFIG are compensated by injecting negative sequence currents into the grid using grid side converter (GSC) for stand-alone load. In [5, 6], the rotor side converter (RSC) is used to provide precise control of the positive and negative sequence rotor currents to reduce pulsations in any one of the following; torque, active power, stator current or rotor current. Field oriented control technique is used to control the RSC and simulation results are presented. To compensate for unbalanced stator voltages in the case of stand-alone DFIG, predictive current control for RSC is presented in [7]. Control schemes based on coordinated control between RSC and GSC are presented in [1, 2, 8], in which the control is achieved using sequential decomposition of stator and rotor currents. To compensate the effects of unbalanced grid voltage, RSC control is used in [9, 10], in which the positive sequence rotor currents are regulated by proportional J Eng 2015 doi: 10.1049/joe.2014.0213
and integral (PI) regulator while the harmonic components of rotor current are regulated individually by resonant regulator tuned at individual harmonic frequency. In [11], the control is achieved using RSC, in which the reference rotor voltages are generated based on the pulsation in the stator active power. In [12], the RSC is controlled in stationary reference frame to reduce the torque pulsation. The error in torque is processed by a resonant regulator along with a PI regulator. The PI regulator regulates the steady component of torque while fluctuating component of torque is processed by a resonant regulator. In [13], the RSC and GSC are controlled independently under unbalanced grid voltage condition. The effects of compensation using RSC and GSC control are compared. The behaviour of DFIG under asymmetric grid faults and voltage dip condition is analysed and compensation using RSC is presented in [14–16]. In [17–19], the direct power control (DPC) method is used to compensate for the effects of unbalanced grid. In [17], the stator active power oscillations are eliminated without the rotor current regulators and the decomposition process of positive and negative sequence rotor currents. The experimental verification of DPC scheme using RSC is carried out in [18] and it is demonstrated that only one control objective is fully achieved at a time such as balanced sinusoidal stator currents or a constant active or reactive power. In [19], the DPC scheme based on the sliding mode control is presented, where the instantaneous active and reactive powers are directly regulated in the stationary reference frame. An overview of most recent research in the field of control systems for the operation of DFIGs under balanced and unbalanced grid voltage conditions is summarised in [20]. The key contribution of this paper is to present a direct torque control (DTC)-based control approach which reduces all the major effects of unbalanced grid voltage, rather than choosing the individual target such as torque pulsation, active power pulsation, stator current or rotor current pulsation. This is achieved by compensating the negative sequence stator flux by negative sequence rotor flux. This paper is organised as follows. Section 2 gives DFIG system description. Section 3 deals with a new polar voltage control (PVC)-based DTC method of DFIG. Section 4 explores the operation and implementation of new PVC-based DTC of DFIG under unbalanced grid voltage condition. The effects of negative sequence stator flux compensation are justified in Section 5. The simulation results and experimental results are discussed in Section 6. Finally, Section 7 concludes this paper.
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2
DFIG system description
The stator of DFIG is directly connected to the grid, while controlled voltage in terms of frequency, magnitude and angle is fed to the rotor terminals via voltage source inverter. The frequency of rotor voltage vector is controlled so that speed of rotor flux vector is same as the speed of stator flux vector. The magnitude of rotor voltage vector decides the reactive power exchange between stator and grid, and by controlling the angle of rotor voltage vector, the torque of DFIG is controlled. The equivalent circuit of DFIG in SRF is given in Fig. 1. The circuit equations are d c+ dqs + jvs c+ qds dt
(1)
dc+ dqr + jvslip c+ qdr dt
(2)
+ V+ dqs = Rs Idqs +
+ V+ dqr = Rr Idqr +
where
vslip = vs − vr
(3)
Fig. 2 Phasor diagram of DFIG for sub-synchronous generation mode in stator flux oriented reference frame
reference frame. The angle (δ + α) gives the position of rotor voltage vector with respect to the stator flux vector ψs. The angle of stator flux vector, θs is estimated from stationary frame stator flux components as follows
The stator and rotor flux linkage equations are
csds =
+ + c+ dqs = Lm Idqr + Ldqs Idqs
(4)
+ + c+ dqr = Lm Idqs + Ldqr Idqr
(5)
This dynamic model of DFIG, normally used for balanced grid voltage, is also valid for unbalanced grid voltage condition. Under unbalanced grid voltage condition, the stator and rotor currents, voltage and flux vectors can be represented in terms of their respective positive and negative sequence components in the positive and negative SRFs [9] + + + − −j2vs t F+ dqs = F dqs+ + F dqs− = F dqs+ + F dqs− e
csqs =
3 Description of PVC-based DTC of DFIG under balanced grid voltage condition In doubly-fed induction machines, the stator flux vector ψs and rotor flux vector ψr are separated by an angle δ, called torque angle. For generator operation, the rotor flux vector leads the stator flux vector. The rotor voltage vector Vr leads (sub-synchronous speed) or lags (super-synchronous speed) the rotor flux vector by an angle α, (rotor impedance angle). Fig. 2 shows the phasor diagram of DFIG for sub-synchronous operation in stator flux oriented
s V sqs − Rs Iqs dt
(7)
(8)
The angle of stator flux vector is
us = tan−1
csqs csds
(9)
In stator flux oriented reference frame
(6)
where F represents the voltage, current and flux. The superscripts + , − represent the positive and negative synchronously rotating reference frames, whereas subscripts + , − represent positive and negative sequence components.
s s V ds − Rs Ids dt
cqs = 0 and cds = cs = constant
(10)
V ds = 0 and
(11)
V qs = V s = constant
The block diagram representation for the implementation of the proposed PVC-based DTC scheme is shown in Fig. 3. In control scheme, two independent regulating loops are used for rotor flux and torque regulation. The rotor flux regulating loop gives the magnitude of rotor voltage vector Vr, whereas the torque regulating loop gives the angle (δ + α) [21]. From Fig. 3, the control equations can be written as |V r | = Kp1 (cr, ref − cr, act ) + Ki1 (cr, ref − cr, act ) dt d + a = Kp2 (Tref − Tact ) + Ki2 (Tref − Tact ) dt
(12) (13)
where Kp′ s and Ki′ s are the PI gain constants, respectively. The magnitude, Vr and angle, (δ + α + θs) completely describes the rotor voltage vector. The components of rotor voltage vector in SRF aligned with stator flux vector are obtained using the angle, (δ + α). The SRF components of rotor voltage are transformed into rotor reference frame (RRF) components using the angle information (θs − θr). The rotor flux components are estimated in stationary reference frame as follows
Fig. 1 Equivalent circuit of DFIG in positive synchronously rotating reference frame This is an open access article published by the IET under the Creative Commons Attribution-NonCommercial License (http://creativecommons.org/licenses/by-nc/ 3.0/) 2
s s csdr = Lm Ids + Ldr Idr
(14)
s csqr = Lm Iqs + Lqr Iqrr
(15)
J Eng 2015 doi: 10.1049/joe.2014.0213
Fig. 3 Block diagram of PVC-based DTC of DFIG under balanced grid voltage condition
The magnitude of net rotor flux is given by
cr =
cdrs 2 + cqrs 2
(16)
The magnitude of reference rotor flux depends on the operating condition of DFIG, such as torque developed by DFIG and its reactive power interaction with grid. During high wind condition, DFIG should generate maximum active power and during light wind condition, the DFIG should support reactive power to grid. However, the maximum value of rotor flux is restricted by the magnetising current of the rotor [22]. The electromagnetic torque developed by the DFIG is estimated as Te =
Pe vr
oscillations appear in torque, active and reactive powers. Such oscillations have a pulsation of 2ωs [23]. By neglecting the stator resistance drop, the instantaneous active and reactive powers output of stator [6] are written as Ps, unb−g = Ps, av + Ps, sin2 sin (2vs t) + Ps, cos 2 cos (2vs t)
(18)
Qs, unb−g = Qs, av + Qs, sin 2 sin (2vs t) + Qs, cos 2 cos (2vs t)
(19)
The electromagnetic power imported from the rotor shaft given in (29) (in Appendix) can be summarised as Pe, unb−g = Pe0 + Pe, sin 2 sin (2vs t) + Pe, cos 2 cos (2vs t)
(20)
(17) The electromagnetic torque under unbalanced grid is given by
In the control scheme, the rotor voltages are generated without the inner current control loops and the associated coordinate transformation. Hence the scheme has simple control structure. 4 PVC-based DTC of DFIG under unbalanced grid voltage condition 4.1 Description of unbalanced grid voltage condition Unsymmetrical grid voltage establishes negative sequence components in all the relevant quantities. Therefore the harmonic
Te, unb−g =
Pe, unb−g vr
(21)
To tackle the second harmonic oscillations, the control approach based on the compensation of negative sequence stator flux is discussed. For the implementation of the scheme, the negative sequence quantities are required. The estimation of positive and negative sequence quantities are discussed in the next section.
Fig. 4 Block diagram of PVC-based DTC scheme under unbalanced grid voltage condition J Eng 2015 doi: 10.1049/joe.2014.0213
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4.2 Calculation of positive and negative sequence quantities Phase locked loop is implemented to calculate the stator flux angle θs, under unbalanced grid voltage condition. The three-phase quantities, that is, voltage, current and flux are decomposed into positive and negative sequence components using stator flux vector angle, θs. The rotation of SRF in positive direction (eθs) gives the positive sequence quantity as dc and appears the negative sequence quantity at twice the supply frequency. The notch filter is used to eliminate double frequency components. Similarly, the rotation of SRF in negative direction (e−θs) gives the negative sequence quantity as dc and the positive sequence quantity appearing at twice the supply frequency is eliminated using the notch filter. The magnitude of net negative sequence stator flux is given by
cs− =
c2ds− + c2qs−
(22)
The magnitude of negative sequence rotor flux, required for the replacement of the negative sequence stator flux is calculated as
cr− =
c2dr− + c2qr−
(23)
The magnitude of actual rotor flux is calculated as
cr+ =
c2dr+ + c2qr+
is no change in the procedure for calculation of positive sequence rotor voltages. The net voltage applied to rotor is given by V rabcr = V (dqr+) ej(us −ur ) + V (dqr−) ej(−us −ur )
(25)
The positive and negative sequence rotor voltages are generated without the inner current control and the associated coordinate transformation. Hence, the scheme has simple control structure loop under unbalanced grid voltage condition. 5
Justification of the compensation
1. As the controlled negative sequence rotor voltage vector produces the negative sequence rotor flux vector, ψr−, which occupies the position of negative sequence stator flux ψs−. Thus, stator currents are relieved from producing the negative sequence stator flux and improve the stator current waveform. The magnitude and position of negative sequence rotor voltage vector Vr− to produce the required ψr− is shown in Fig. 5. 2. Under unbalanced grid voltage condition, negative sequence voltage is induced in the rotor, this voltage causes large negative sequence rotor current. Negative sequence rotor current can be eliminated by injecting a negative sequence voltage of suitable magnitude and angle at rotor terminals. This can be explained from Figs. 6a and b. In the absence of negative sequence injected voltage, the negative sequence current drawn by rotor is given by
(24) ′
Irn = 4.3 Control scheme under unbalanced grid voltage condition In this paper, the rotor side converter is controlled to reduce the effects of the unbalanced grid voltages on DFIG. The PVC-based DTC method is explored to control the RSC in stator flux oriented reference frame. In this scheme, the magnitude and angle of negative sequence rotor voltage vector are controlled to produce the negative sequence rotor flux, ψr− which has same magnitude and direction of ψs−. The complete block diagram for the implementation of the proposed scheme under unbalanced grid voltage condition is shown in Fig. 4. During implementation, the d-axis component of negative sequence stator flux, ψds− is taken as reference and compared with the d-axis component of negative sequence rotor flux, ψdr−. The error between them is processed by the PI regulator to obtain the magnitude of Vdr−. Similarly, the negative sequence stator flux, ψqs− is taken as reference and compared with the negative sequence rotor flux, ψqr−. The error between them is processed by PI regulator to obtain the magnitude of Vqr−. The controlled negative sequence rotor voltages in synchronously rotating reference frame are then transformed to the RRF using angle, (−θs −θr). Under unbalanced grid voltage condition, there
Fig. 5 Position of negative sequence rotor flux and negative sequence rotor voltage vector
0 − Esn / b (R′r /(2 − s)) + jXr′
(26)
From Fig. 6b, in the presence of negative sequence injected voltage, the reduced negative sequence rotor current is given by ′
Irn =
′
(V r /(2 − s)) / fr − Esn / b (R′r /(2 − s)) + jXr′
(27)
In the proposed scheme, the controlled injection of negative sequence rotor voltage nullifies the effects of negative sequence stator flux. This reduces the negative sequence rotor induced voltage, and hence the negative sequence rotor current. 3. For a multi-megawatt DFIG system, the stator to rotor turns ratio is
