Sensor-less Field Oriented Control of Wind Turbine Driven Permanent Magnet Synchronous Generator Using Flux Linkage and Back EMF Estimation Methods

The study aims at the speed control of the wind turbine driven Permanent Magnet Synchronous Generator (PMSG) by sensor-less Field Oriented Control (FOC) method. Two methods of sensor-less FOC are proposed to control the speed and torque of the PMSG. The PMSG and the full-scale converter have an increasing market share in variable speed Wind Energy Conversion System (WECS). When compared to the Induction Generators (IGs), the PMSGs are smaller, easier to control and more efficient. In addition, the PMSG can operate at variable speeds, so that the maximum power can be extracted even at low or medium wind speeds. Wind turbines generally employ speed sensors or shaft position encoders to determine the speed and the position of the rotor. In order to reduce the cost, maintenance and complexity concerned with the sensor, the sensor-less approach has been developed. This study presents the sensor-less control techniques using the flux-linkage and the back EMF estimation methods. Simulations for both the methods are carried out in MATLAB/SIMULINK. The simulated waveforms of the reference speed, the measured speed, the reference torque, the measured torque and rotor position are shown for both the methods.


INTRODUCTION
Variable-speed wind generation with the PMSG and a full-scale power electronic converter is a promising but not yet a very popular wind turbine concept.A PMSG connected to a power electronic converter can operate at low speeds, so a gearbox is not required.Since the gearbox increases the weight, the losses, the costs and demands more maintenance, a gearless construction represents an efficient and a robust solution, especially for offshore applications.Also, due to the presence of the permanent magnet in the PMSG, the DC excitation system can be eliminated, further reducing the weight, the losses, the costs and the maintenance requirements (Hsieh and Hsu, 2012;Qiao et al., 2012).Thus, the efficiency of a PMSG based wind energy system is higher than other variable-speed WECS.In addition, a full-scale Insulated-Gate Bipolar Transistor (IGBT) converter allows full controllability of the system (Li et al., 2009(Li et al., , 2010)).The generator-side converter controls the generator speed to enhance the wind power extraction.The control techniques for the generator-side converter decouple the torque and flux controls.Vector control or direct control technique is used for this purpose.A rotor field oriented control is applied to the generator-side converter to control the generator speed and to obtain the maximum electromagnetic torque with the minimum current.To achieve this, the d-component of the stator currents is forced to zero and the electromagnetic torque is controlled only with the q-component of the current.When compared to the direct control, vector control achieves higher overall system efficiency, which is mainly due to the lower current distortion and the consequent lower joule losses (Freire et al., 2012).
Several techniques are available for the sensor-less position and speed estimations.In Fan et al. (2010), a digital phase-locked loop is used for the sensor-less vector control of speed and position.This controls the frequency of the output signal by a control signal that is proportional to the difference between the output phase of the system and the phase of the given signal.With this obtained frequency characteristic, the motor speed and the rotor position angle are measured.However, this frequency control technique does not work well when the motor runs at low speed.In Zhonggang et al. (2012), a Robust Extended Kalman Filter (REKF) algorithm is used for the sensor-less vector control.Although this method provides less effect of gross error on the estimation accuracy, the intensive calculations involved are difficult to compute and time consuming.
High frequency signals injection method (Consoli et al., 2001) is proven effective at low-speeds and even at standstill for both the salient and non-salient pole machines.However, the method requires additional carrier signals, resulting in unnecessary losses, current and torque distortions and acoustic noise.
A speed controller observer based on the model reference adaptive control was proposed for the Permanent Magnet Synchronous Motor (PMSM) in Saikumar and Sivakumar (2011), Maiti et al. (2008) and Kim et al. (1995).This controller requires two models, which increase the complexity in the control and the costs.In Yongchang et al. (2009), a comparison between a Luenberger observer, a sliding mode observer and an extended Kalman filter was made for the sensorless control of the induction machine.It was shown that the first two methods are more suitable when compared to the third method.
This study describes the sensor-less vector control method of the PMSG.There are several methods of sensor-less control of PMSG available.Two methods are considered namely the flux linkage estimation method and the back EMF estimation method.Simulation is carried out in MATLAB/SIMULINK for both the methods.A comparison based on the settling time of speed and torque for the two methods is shown.The simulated waveforms of the stator voltage, the stator current, the reference speed, the measured speed, the reference torque, the measured torque and the rotor position are shown for both the methods for varying reference speed and reference torque.

MATERIALS AND METHODS
Modeling of the PMSG: Equation (1) gives the mathematical model of the PMSG derived from the stator voltage equation: (1) where, v s , i s and Ψ ୱ are the space vectors of the stator voltages, the stator currents and the flux linkages, respectively.Equation ( 2) and (3) give the voltage equations in the d-q reference frame with the d-axis coinciding with the permanent magnet pole axis: where, ω e is the electrical speed in rad/s.Equation ( 4) and ( 5) give the flux linkages in the dq reference frame: where, ψ d and ψ q are the d-axis and q-axis flux linkages, respectively, L d and L q are the d-axis and the q-axis inductances, respectively and ψ m is the permanent magnet flux linkage.
Equation (6) gives the electromagnetic power from which the electromagnetic torque derived: Equation ( 7) gives the relation between the electrical and the mechanical speed: where, p = The number of pole pairs ω m = The mechanical speed of the rotor Hence, Eq. ( 8) gives the expression for the electromagnetic torque: By substituting the d-axis and the q-axis flux linkages in Eq. ( 8) and by considering that the d-axis and q-axis inductances for the surface mounted PMSG are equal, the torque relation is finally derived and given by Eq. ( 9): Equation ( 10) shows the general mechanical equation of the machine: where, T L = The load torque J = The moment of inertia B = The viscous frictional coefficient Field oriented control: Field Oriented Control (FOC) is a vector control technique, which controls the torque indirectly by controlling the stator currents.The constant torque angle control is used in this study.In this method, the torque angle is kept at 90°.The d-axis current component is set to zero and therefore the stator current has only the q-axis component.Since the torque angle and the permanent magnet flux are Fig.1: Field oriented control of the PMSG with the sensor constant, the torque depends only on the q-axis stator current.
As the current control is performed on the rotor reference frame, a transformation of coordinates is required to obtain the reference stator currents.FOC eliminates current cross coupling between the d and q axes components, which requires feed-forward compensation.In the FOC, the permanent magnet flux linkage is aligned along the d-axis.
Figure 1 gives the block diagram of the FOC of the PMSG with the sensor.In this control, the speed is sensed and compared with the reference speed.The error in speed is processed in the PI controller to obtain the reference q-axis current.The reference d-axis current is set to zero.The stator currents from the PMSG are transformed to the d-q reference frame and compared with the reference d-q currents.
For decoupling purposes, a feed-forward loop is used.This includes the components I and II, which are given by: V dc and V αβ are given to space vector modulation block to produce the gate signals for the converter switches.
q-axis current controller design: Figure 2 shows the block diagram for the design of the q-axis current controller.The various blocks are the PI block, the delay introduced by the PI, the delay introduced by the inverter, the plant that is the stator block and the delay Fig. 2: Block diagram for the design of the q-axis current controller introduced due the digital to analog conversion, which is taken to be equal to half of the delay introduced by the PI.Equation ( 11) gives the transfer function of the qaxis current controller: where, K pq = The proportional gain of the q-axis current controller T iq = The integral time constant of the q-axis current controller d -axis current controller design: The d-axis current controller is implemented in the same way as the qaxis current controller except that the L q is replaced by L d .Equation ( 12) gives the transfer function of the d-axis current controller: where, K pd = The proportional gain of the d-axis current controller q-axis speed controller design: Figure 3 shows the block diagram for the design of the speed controller, where, τ iq = L q /R s , p is the number of pole pairs, T f is the filter time constant used only when an encoder measures the speed.Equation ( 13) gives the transfer function of the PI speed controller: where, K pω = The proportional gain of the speed controller T iω = The integral time constant of the speed controller Sensor-less control: Using a sensor to encode the speed has several drawbacks like, increased cost, bigger size and lower reliability of the system.This study, therefore, presents the sensor-less control methods using the flux linkage and the back-EMF estimation methods.
Figure 4 shows the block diagram of the FOC of the PMSG without the sensor.In this control, the stator currents from the PMSG are taken and transformed to the α-β reference frame.The currents in the α-β reference frame are given to the position and speed estimation blocks.

Flux linkage estimation method:
This method is used for estimating the position of the rotor.The rotor position estimation is based on the estimation of the flux linkages.The initial rotor position is found from the flux linkage using the inductances and the stator currents (Lukko, 2000).Sensor-less control method is implemented in five steps: Step 1: Estimation of the stator flux linkages: Phase currents and voltages are assumed to be measured at a fixed sample time T s .The stator flux linkages are given in Eq. ( 14) and ( 15): where, k is the present sampling interval and k-1 is the previous sampling interval.The currents i α and i β (i.e., the stator currents in the stationary reference frame) are obtained by measuring the a, the b and the c stator phase currents.
Step 2: Stator current estimation: The stator currents are estimated by the flux linkages estimated in step 1 and the predicted rotor position in step 5.The stator currents are then estimated using Eq. ( 16) and ( 17): where, 2 Figure 5 shows the various steps involved in the estimation of rotor position.
Step 3: Position correction: In this step, the rotor position predicted in step 5 is corrected with the errors of the stator currents.The errors of the current are obtained from the difference between the measured and estimated currents.Equation ( 18) and ( 19) give the errors of the current in the d and q axes reference frames, respectively: The corrected position is obtained by adding the position error to the predicted position, as given in Eq. ( 20): where, Ө r and Ө p are the corrected and the predicted rotor angles respectively.
Step 4: Flux linkage updating: In this step, the fluxes are recalculated using the corrected rotor position and the measured stator currents.Equation ( 21) and ( 22) express the fluxes in discrete time: Step 5: Position prediction: Considering position to be a second-order polynomial, the position prediction can be expressed by Eq. ( 23): where, e, f, g are constants (Chandana Perera, 2002).

Back-EMF estimation method:
The permanent magnet flux is aligned with the d-axis, while the induced voltage of the permanent magnet flux i.e., the back-EMF is along the q-axis.This back EMF can be used to calculate the rotor position.The rotor is in the same position as that of the back EMF, as shown in Fig. 6.The position of the back EMF space vector is determined using Eq. ( 24): In order to have a simpler model, the Clarke's transformation is used.Equation ( 25) gives the relation between the abc and the α-β reference frames: By knowing the voltages of the stator in the α-ß reference frame, the stator angle is calculated as by Eq. ( 26): where, v α and v β are the stator voltages in the α-ß reference frame.Now, the variables in the α-β reference frame are transformed into a new reference frame of δ-φ, which is shown in Fig. 7.
Equation ( 27) gives the transformation matrix that converts the α-β variables to the δ-φ variables: Now, the stator voltage is aligned with the δ axis with the v φ component equal to zero.The voltage equations of the PMSG in the δ-φ co-ordinate system are given by Eq. ( 28) and ( 29): where, ω i = The rotational speed of i s e δ and e φ = Back EMFS of the stator in δ-φ reference frame, respectively They can be expressed by Eq. ( 30) and ( 31 At steady state, the currents i δ and i φ are constant, resulting in the derivative term of the Eq. ( 28) and ( 29) becoming zero.Assuming ideal conditions, the rotor position in the δ-φ reference frame is determined from Eq. ( 30) and ( 31) and is expressed by Eq. ( 32): Equation ( 33) gives the estimated rotor position:

RESULTS AND DISCUSSION
The system is simulated in MATLAB/SIMULINK for the sensor-less field oriented control with the flux linkage and back-EMF estimation methods.The initial reference speed and torque are 700 rpm and -9 Nm, respectively.Then the reference speed alone is changed to 1000 rpm at 2 sec with the same torque.At 4 sec, the reference torque is changed to -12 Nm, with the speed reference at 1000 rpm. Figure 8   Figure 11 and 12, respectively show the reference and measured speeds and the reference and measured torques for the back-EMF estimation method.
From the Fig. 8 and 11, it is found that the speed follows the reference speed.Initially, when the reference speed was set at 700 rpm, the PMSG follows the reference speed of 700 rpm.When the reference speed changes to 1000 rpm at t = 2 sec, the speed of the PMSG also changes and reaches the reference speed within 0.028 sec for the flux linkage and the back-EMF methods.There is a little oscillation in speed at t = 4 sec which is due to the change in the reference torque, which also damps out within 0.01 sec for the flux linkage method.However, some oscillations exist in back-EMF estimation method, which damps out within 0.015 sec.It is found from the Fig. 11 that, there are some oscillations speed in the system with the change in the reference speed and torque for the back EMF estimation method.
Figure 13 shows the measured and estimated rotor positions for the back-EMF estimation method.
Table 1 shows the comparison of the flux linkage and the back EMF estimation methods based on the settling time of speed and torque for change in speed and torque.
It is found from the Fig. 8, 9, 11 and 12 and the Table 1, that the response for the flux linkage method is faster than the back-EMF method.In addition, it is evident from the waveforms that, the presence of oscillations is more in the back-EMF method.

CONCLUSION
The PMSG is modelled in the d-q reference frame with the d-axis aligned with the permanent magnet axis.The PMSG is controlled with a sensor-less field oriented control for varying reference speeds and torques.The sensor-less tracking of the position and the speed of the PMSG is carried out using the flux linkage estimation method and the back-EMF estimation methods.The two control methods are simulated using the MATLAB/SIMULINK.The flux linkage estimation method shows a faster response to the change in reference speed and torque.This improves the robustness and the effectiveness of the system.In spite of the many advantages, this algorithm uses sampled data from the previous time instant, which introduces certain time delay in the system and presents integration drift problems.The back-EMF method presents certain oscillations in the system with the change in the reference speed and torque and has sensitivity problems with parameter changes.The main drawback of the back-EMF estimation method is the estimation of the position of the rotor at zero speed or low speed ranges, because the back EMF becomes zero and thus the position estimation is not possible.At low speeds, the back-EMF is very small which leads to a large error in the estimation.From the simulated results, it is observed that better control is achieved with the flux linkage estimation method as compared to the back-EMF estimation method.

Fig. 3 :
Fig. 3: Design of the speed controller T id = The integral time constant of the d-axis current controller

Fig. 4 :
Fig. 4: Field oriented control of the PMSG without the sensor

Fig. 6 :
Fig. 6: Space vector representation of the back EMF The rotor electrical speed λ m = The permanent magnet flux linkage Ө n = The estimated rotor angle in δ-φ reference frame Fig. 8: The reference and measured speeds of the PMSG for the flux linkage estimation method

Fig. 9 :
Fig. 9: The reference and measured torques of the PMSG for the flux linkage estimation method

Fig. 11 :
Fig. 11: Reference and measured speeds of the PMSG for the back-EMF estimation method

Table 1 :
Comparison of the flux linkage and back EMF methods