New Direct Torque Control of DFIG under Balanced and Unbalanced Grid Voltage

Transcription

1 1 New Direct Torque Control of DFIG under Balanced and Unbalanced Grid Voltage B. B. Pimple, V. Y. Vekhande and B. G. Fernandes Department of Electrical Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 476, India. Tel Fax bbpimple@ee.iitb.ac.in,vekhande@ee.iitb.ac.in,bgf@ee.iitb.ac.in Abstract This paper presents a direct torque control method for doubly-fed induction generator (DFIG) based wind power generation systems. The angle and magnitude of rotor voltage are controlled to achieve independent control of electromagnetic torque and reactive power respectively. Space vector modulation is used to address the limitations like, variable switching frequency and torque ripple, of hysteresis based schemes. Further, this paper presents a technique to reduce the torque pulsations of DFIG under unbalanced grid voltage condition. Under unbalanced grid voltage condition, the torque angle (δ) is controlled so that electromagnetic torque pulsations are reduced. To achieve this, a compensation method based on proportional-integral and resonant (PI+R) controller is explored. The proposed control method does not require rotating frame transformations and it maintains the simplicity of DTC. It has fast dynamic response, which is comparable to vector control. Simulation results for a MW DFIG system demonstrates the effectiveness of the proposed control strategy with various loading conditions under both balanced and unbalanced grid voltage. Index Terms Doubly-Fed Induction Generator, Direct Torque Control, Unbalanced Grid Voltage, Torque pulsations, Proportional-Integral and Resonant Controller. I. INTRODUCTION DOUBLY-FED Induction Generators (DFIGs) are used mainly for wind energy conversion in MW range. The stator is directly connected to grid while the rotor is fed through power electronic converter. The power electronic converter is rated at 5% to 3% of the generator rating for a variation in synchronous speed around ±5%. The major advantages of the DFIG based wind turbines are variable speed operation and stator power factor control from rotor side converter. The direct torque control (DTC) method is an alternative to vector control for DFIG based wind power generation. Variable switching frequency and high torque ripple are the main limitations of hysteresis based DTC. To address these limitations, DTC with space vector modulation based on synchronous reference frame transformation, predictive control and deadbeat control are reported in the literature [1], []. This paper proposes a new DTC method wherein rotor voltage vector is generated in polar form. Hence, the implementation of DTC using space vector modulation becomes simple compared to above mentioned methods. The method is also capable of independent control of torque and reactive power. When the stator of DFIG is connected to unbalanced grid, the torque produced by doubly-fed induction generator would pulsate. The torque has periodic pulsations at twice the grid frequency, which can result in acoustic noise at low levels and at high levels can damage the rotor shaft, gearbox or blade assembly. Also, DFIG connected to an unbalanced grid will draw unbalanced current. These unbalanced current tend to increase the grid voltage unbalance. Generally the wind power generator in the range of 1 to 5 MVA are connected to 11 to 66 kv grid. For this voltage level, the permissible unbalance is up to 3% [3]. Methods to compensate the effects of unbalanced grid voltage based on positive sequence and negative sequence rotating reference frame theory are well reported in literature. In [5], control of DFIG with grid side converter (GSC) was explored. The stator unbalanced currents and voltages were compensated by injecting currents into grid by GSC. In this paper, two synchronously rotating reference frames were used to determine positive and negative sequence stator currents. In [6], the positive and negative sequence rotor currents were controlled to reduce pulsations in any one of the following; torque, active power, stator current or rotor current. In [7], grid side converter and rotor side converter control were used to compensate the effects of unbalanced grid. In [8], rotor side control based on positive sequence rotating frame was used. The positive sequence rotor current was regulated by PI regulator while negative sequence rotor current appears at double frequency was regulated by resonant regulator. Reduction of torque pulsation under unbalanced grid voltage with direct torque control is not explored in literature. This paper proposes the reduction of torque pulsation of DFIG connected to unbalanced grid. The magnitude and angle of rotor voltage vector are controlled independently. The torque angle δ, is controlled in such a way that torque pulsations are reduced. To achieve this a proportional-integral and resonant (PI+R) controller are used. The proposed control method is a scalar control method, it does not require multiple reference frame transformation, sequential decomposition and notch filters to remove second harmonic components. The scheme of (PI+R) control in stationary frame is simple and complexity in calculations is significantly reduced /1/$6. 1 IEEE TENCON 1 154

2 II. DYNAMIC MODEL OF DOUBLY-FED INDUCTION GENERATOR The voltage equations of DFIG in stationary reference frame are as follows: V s = R s I s + dψ s (1) V r = R r I r + dψ r jω rψ r () V ds = R s I ds + dψ ds V qs = R s I qs + dψ qs V dr = R r I dr + dψ dr (3) (4) + ω r ψ qr (5) V qr = R r I qr + dψ qr ω r ψ dr (6) where ω r, is the rotor angular speed in radian per second. The stator and rotor flux linkages are ψ ds = L m I dr + L ds I ds (7) ψ qs = L m I qr + L qs I qs (8) ψ dr = L m I ds + L dr I dr (9) ψ qr = L m I qs + L qr I qr (1) III. DIRECT TORQUE CONTROL OF DFIG UNDER BALANCED GRID VOLTAGE CONDITION In DFIG, the rotor flux vector ψ r leads the stator flux vector ψ s by an angle δ. The rotor voltage vector V r leads (subsynchronous speed) or lags (super-synchronous speed) the rotor flux vector by an angle α, rotor impedance angle. The angle (δ +α) gives the position of rotor voltage vector with respect to the stator flux vector ψ s. The stator flux angle θ s is calculated as ψ ds = (V ds R s I ds ) (11) ψ qs = (V qs R s I qs ) (1) The stator flux angle is θ s =tan 1 ψ qs (13) ψ ds The total angle (δ + α + θ s ) gives the position of rotor voltage vector with respect to the stationery axis. The phasor diagram for sub-synchronous operation of DFIG is shown in Fig. 1. The block diagram for the implementation of proposed control scheme is shown in Fig.. The DFIG is modelled in stationary reference frame and space vector notation is used to represent the variables. The error between the reference torque and actual torque is processed by the PI controller. The output of the PI controller is proportional to (δ + α) [4]. Similarly, the error between reference rotor flux vector and actual rotor flux vector is processed by the PI controller. The output of the PI controller is proportional to the magnitude of rotor voltage vector V r.using this magnitude and angle (δ + α + θ s ), the d-axis and q-axis components of reference rotor voltage are determined. These stationary reference frame (SRF) components are transformed to rotor reference frame components (RRF) using the rotor position 155 Fig. 1. Phasor Diagram of DFIG for Sub-synchronous Generation angle θ r. Under balanced grid voltage condition, the function of grid side converter (GSC) is to maintain a constant dc link voltage and to draw unity power factor current from the grid. A. Rotor Flux and Torque Estimation The magnitudes of the rotor fluxes are determined in stationery reference frame as follows: ψ dr = L m I ds + L dr I dr (14) ψ qr = L m I qs + L qr I qr (15) The magnitude of net rotor flux is given by ψ r = ψdr + ψ qr (16) The reference rotor flux is calculated using the reference reactive power or power factor. Here, the magnitude of reference rotor flux is selected such that, the stator operates at nearly unity power factor for rated torque. For torque less than the rated value, stator of DFIG supplies reactive power to the grid. The maximum limit of reference rotor flux is decided by the reactive component of rotor current. In order to maintain the stability, the reactive component of current drawn by the rotor should not be greater than twice the net magnetizing current of the DFIG [1]. The electromagnetic torque developed by DFIG is estimated as T e = 3 p (ψ dri qr ψ qr I dr ) (17) The magnitude of reference torque is determined by wind speed. B. Salient Features of New Direct Torque Control Scheme 1. It is a scalar control. No synchronously rotating reference frame transformation is required.. As the controlled rotor voltage is in polar form, it is easy to apply space vector modulation. Therefore, switching frequency of inverter remains constant. 3. It reduces the torque ripple and makes the stator current almost sinusoidal. 4. As there are no cascaded regulating loops, its structure is simple and easy to implement. 5. Fast dynamic response of rotor flux and torque. 6. As the angle and magnitude of rotor voltage vector is controlled independently, decoupled control of torque and reactive power is possible. 7. By controlling δ, the direct torque control method can be

3 Fig.. Block Diagram of New Direct Torque Control of DFIG Under Balanced Grid Voltage Condition explored to reduce torque pulsations under unbalanced grid voltage condition. IV. DIRECT TORQUE CONTROL OF DFIG UNDER UNBALANCED GRID VOLTAGE CONDITION The torque developed by DFIG is also given by T e = 3 p L m L r L ψ s ψ r sinδ (18) s where L s = L s L m L r (19) and δ is the angle between stator flux vector and rotor flux vector. Under balanced condition, the reference torque and actual torque are steady (dc) quantities. Single PI regulator is required to process the error between reference torque and actual torque. The output of PI regulator generates the signal proportional to (δ+α). Under unbalanced grid voltage condition, the stator flux vector consists of double frequency component which results in the oscillation of torque at this frequency. To eliminate the torque oscillation, it is required to modulate the rotor flux vector by controlling δ. Under unbalanced grid condition, the actual torque has an average dc value along with double frequency component. To process this double frequency fluctuating component of torque, the resonant regulator tuned at same frequency is used. PI regulator offers infinite gain for steady quantity, while resonant regulator offers an infinite gain at the selected resonant frequency. In addition, there is no phase shift and gain at other frequencies [9]. The block diagram of proportional-integral and resonant (PI+R) controller is shown in Fig. 3. The output of PI regulator is a steady value of angle (δ + α) which corresponds to steady error between reference torque and average value of actual torque. The output of resonant regulator is a double frequency component of torque angle. As a result, the proposed PI+R controller forces the steadystate errors to be null for both steady and double frequency components of torque. The open loop transfer function (OLTF) Fig. 3. Block Diagram of Proportional-Integral and Resonant Regulator of PI+R regulator is as follows: OLTF = K p + K I s + sk R s + ω () where, K R is the gain of resonant regulator, ω is the tuned resonant frequency, which is selected as, double the supply frequency. It may be noted that a low value of K R gives a very narrow frequency band. The block diagram for the implementation of proposed control scheme is shown in Fig. 4. Under unbalanced grid voltage condition, the grid side converter (GSC) maintains the dc link voltage constant. V. SIMULATION RESULTS Simulation of the proposed direct torque control strategy for a DFIG based wind generation system is carried out using MATLAB/ Simulink. The parameters of DFIG are taken from [7] and given in Table 1. Fig. 5 shows the torque developed by DFIG for step change in reference torque under balanced grid voltage condition. At t=5 s, rated torque is applied and the corresponding stator current waveform is shown in Fig. 6. The stator current is almost sinusoidal. Fig. 7 shows the stator voltage and current waveforms. It can be seen that, the stator operates nearly at unity power factor for rated torque. For below rated torque condition, it supplies reactive power to the grid. Fig. 8 shows the dynamic response of rotor flux for step change in

4 Fig. 4. Block Diagram of New Direct Torque Control of DFIG Under Unbalanced Grid Voltage Condition reference flux. Similarly, dynamic response of torque can be seen in Fig. 9. For the same DFIG system, simulation study is carried out for 3% unbalance in grid voltage. Fig. 1 shows the torque developed by DFIG for step changes in reference torque, after compensation under unbalanced grid voltage condition. Fig. 11 shows the reduction in second harmonic pulsation in torque. At t=6 s, resonant regulator is enabled. For the generated torque of 4 Nm, the torque pulsation before compensation is 9 Nm and torque pulsation after compensation is 17 Nm. Fig. 1 shows output of resonant regulator which is a double frequency component of torque angle. Fig Stator voltage and current of DFIG stator voltage (V) stator current (A) flux in Wb act. rotor flux ref. rotor flux Fig. 5. Direct torque control of DFIG under balanced grid voltage condition Fig. 8. Response of rotor flux for step change in reference flux stator current in amp Fig. 6. Stator current of DFIG under balanced grid voltage condition Fig ref. torque act. torque Response of torque for step change in reference torque 157 4

5 Fig. 1. Torque of DFIG for step change in reference torque after compensation under unbalanced grid condition Fig. 1. delta in rad Output of resonant regulator Fig Reduction of second harmonic pulsation in torque after compensation VI. CONCLUSION This paper presents a new direct torque control method for DFIG based on polar control of rotor voltage. The control scheme is simple and space vector modulation is used. The stator current is nearly sinusoidal and there is a significant reduction in torque ripple. The same direct torque control method is explored to control DFIG under unbalanced grid voltage condition. A torque angle control strategy based on PI+R controller is proposed. Without using the rotating reference frame and sequential decomposition, the control scheme reduces the pulsations in the torque. Simulation results show the effectiveness of proposed control strategies. [] Y. Lai and J. Chen, A New Approach to Direct Torque Control of Induction Motor Drives for Constant Inverter Switching Frequency and Torque Ripple Reduction, IEEE Trans. Energy Conversion, vol. 16, no. 3, pp. -7, Sept. 1. [3] The Central Electricity Authority, (Technical Standards for Connectivity to the Grid) Regulations, 7, /X/STD(CONN)/GM/CEA, Feb. 7. [4] J. Rodriguez, J. Pontt, C. Silva, R. Huerta and H. Miranda, Simple direct torque control of induction machine using space vector modulation, Eectronics Letters, vol. 4, no. 7, April 4. [5] Ruben Pena, Roberto Cardenas, Enrique Escobar, Jon Clare, Pat Wheeler, Control strategy for a Doubly-Fed Induction Generator feeding an unbalanced grid or stand-alone load, Electric Power Systems Research, vol. 79, issue, pp , February 9. [6] Lie Xu and Yi Wang, Dynamic Modeling and Control of DFIG-Based Wind Turbines Under Unbalanced Network Conditions, IEEE Trans. on Power Systems, vol., no. 1, pp , February 7. [7] Lie Xu, Coordinated Control of DFIGs Rotor and Grid Side Converters During Network Unbalance, IEEE Trans. on Power Systems, vol. 3, no. 3, pp , May 8. [8] Jiabing Hu, Yikang He, Modeling and enhanced control of DFIG under unbalanced grid voltage conditions, Electric Power Systems Research, vol. 79, issue, pp , February 9. [9] R. Teodorescu, F. Blaabjerg, M. Liserre and P.C. Loh, Proportionalresonant controllers and filters for grid-connected voltage-source converters, IEE Proc.-Electr. Power Appl., vol. 153, no. 5, pp , September 6. [1] Andreas Petersson et al, Modeling and Experimental Verification of Grid Interaction of a DFIG Wind Turbine, IEEE Trans. on Energy Conversion, vol., no. 4, pp , Dec 5. TABLE I DATA OF DFIG Rated Power MW Stator Voltage 69 V Stator Frequency 5 Hz Stator to Rotor turns ratio.333 Stator Resistance, Rs.579 Ω Rotor Resistance, Rr.88 Ω Mutual Inductance.547 mh Stator Leakage Inductance.778 mh Rotor Leakage Inductance.8335 mh Number of Poles 4 REFERENCES [1] D. Zhi and L. Xu, Direct Power Control of DFIG With Constant Switching Frequency and Improved Transient Performance, IEEE Trans. Energy Conversion, vol., no. 1, pp , March