


ARTICLE 

Year : 2012  Volume
: 2
 Issue : 1  Page : 5262 

Fixed Pitch Wind TurbineBased Permanent Magnet Synchronous Machine Model for Wind Energy Conversion Systems
Janardan Gupta^{1}, Ashwani Kumar^{2}
^{1} M.Tech. Scholar, Department of Electrical Engineering, NIT Kurukshetra, India ^{2} Associate Professor, Department of Electrical Engineering, NIT Kurukshetra, India
Date of Web Publication  24Mar2012 
Correspondence Address: Janardan Gupta M.Tech. Scholar, Department of Electrical Engineering, NIT Kurukshetra India
Source of Support: None, Conflict of Interest: None  Check 
DOI: 10.4103/09768580.94226
Abstract   
The countries all over the world have emphasis on green energy and wind systems can play a vital role for renewable energy systems. In this work, real value model of wind turbine has been formulated. The mechanical torque and power captured by the wind turbine has also been verified for the real value WT Model. The fixed pitch winddriven wind turbine model has been utilized for generation of power with permanent magnet synchronous machine (PMSM). This paper presents a dynamic model of a microturbine generation system. The components of the system are built from the dynamics of each part with their interconnections. The model is implemented in the MATLAB/Simulink using SimPower Systems library. The performance of the implemented model is studied with an isolated load. The SIMULINK model of the entire system with wind turbine has been developed and the results are obtained for voltage and current waveforms on load end side as well as for PMSM. The current and voltage waveforms are obtained with RL and LCL filter. Keywords: Distributed generation, filter and converter controller units, microturbine, permanent magnet synchronous machine
How to cite this article: Gupta J, Kumar A. Fixed Pitch Wind TurbineBased Permanent Magnet Synchronous Machine Model for Wind Energy Conversion Systems. J Eng Technol 2012;2:5262 
How to cite this URL: Gupta J, Kumar A. Fixed Pitch Wind TurbineBased Permanent Magnet Synchronous Machine Model for Wind Energy Conversion Systems. J Eng Technol [serial online] 2012 [cited 2019 Mar 25];2:5262. Available from: http://www.onlinejet.net/text.asp?2012/2/1/52/94226 
1. Introduction   
DUE to the increasing concern about the environment and the depletion of natural resources such as fossil fuels, much research is now focused on obtaining new environmentally friendly sources of power. The wind energy conversion system is becoming popular all over the world for emissionfree power generation and green power. Electrical power generation using wind energy is possible in two ways, viz., constant speed operation and variable speed operation using power electronic converters. Variable speed power generation is attractive, because maximum electric power can be generated at all wind velocities. Wind energy has been harnessed by many generations for thousands of years to mill grain, pump water and sailing ^{[1]} . It was not until the late ninteenth century when the development of a 12 kW windmill generator was used to generate electricity ^{[1]} . Just in last decade, the wind energy industry has experienced a growth of almost 30 percent each year ^{[2]} There are two main types of wind energy conversion systems (WECS)s:
 Fixedspeed WECS and
 Variablespeed WECS
The variablespeed WECS uses power maximization techniques and algorithms to extract as much power as possible from the wind.
1.1 Fixed Speed Wind Energy Conversion Systems
Normally, induction (or asynchronous) generators are used in fixed speed WECSs because of its inherent insensitivity to changes in torque. The rotational speed of an induction machine varies with the force applied to it, but in practice, the difference between its speed at peak power and at idle mode (at synchronous speed) is very small ^{[3],[4],[5]} . The fixed speed wind systems have the generator stator directly coupled to the grid.
Due to the mechanical characteristics of the induction generator and its insensitivity to changes in torque, the rotor speed is fixed at a particular speed dictated by the grid frequency, regardless of the wind speed ^{[6]} . The construction and performance of fixedspeed wind turbines are dependent on the turbine's mechanical characteristic. Squirrelcage induction generators (SCIG) are typically used in fixed speed systems ^{[7],[8]} .
With respect to variable speed wind turbines, fixed speed turbines are wellestablished, simple, robust, reliable, cheaper, and maintenancefree ^{[8],[9]} . But because the system is fixed at a particular speed, variation in wind speed will cause the turbine to generate highly fluctuating output power to the grid ^{[9]} . These load variations require a stiff power grid to enable stable operation and the mechanical design must be robust enough to absorb high mechanical stresses ^{[9]} . Also, since the turbine rotates at a fixed speed, maximum WEC efficiency can be only achieved at one particular wind speed ^{[10]} . This is because for each wind speed, there is a particular rotor speed that will produce the TSR that gives the maximum CP value.
1.2 Variable Speed Wind Turbine Systems ^{[11]}
In variable speed wind turbine systems, the turbine is not directly connected to the utility grid. Instead, a power electronic interface is placed between the generator and the grid to provide decoupling and control of the system. Thus, the turbine is allowed to rotate at any speed over a wide range of wind speeds ^{[12]} . By using control algorithms and/or mechanical control schemes (i.e., pitch controlled, etc), the turbine can be programmed to extract maximum power from any wind speed by adjusting its operating point to achieve the TSR for maximum power capture. The mechanical stresses on the wind turbine are reduced since gusts of wind can be absorbed ^{[12],[13]} . Another advantage of this system is that the power quality can be improved by the reduction of power pulsations due to its elasticity ^{[12],[13]} . The disadvantages of the variable speed system include the additional cost of power converters and the complexity of the control algorithms ^{[14]} .
Permanent magnet synchronous generators (PMSG) are common in low power, variable speed WECSs ^{[15],[16]} . The advantages of using PMSGs are its high efficiency and small size.
In this paper, the real value system model of WT is implemented in order to make the turbine model compatible with the real value components of the WECS. This paper presents a dynamic model of a microturbine generation system. The components of the system are built from the dynamics of each part with their interconnections. The model is implemented in the MATLAB/Simulink using SimPower library. The performance of the implemented model is studied with an isolated load. The SIMULINK model of the entire system with wind turbine has been developed and the results are obtained for voltage and current waveforms on load end side as well as for PMSM. The current and voltage waveforms are obtained with RL and LCL filter.
2. Wind Turbine Characteristics and Model   
The wind turbine can operate at constant speed with variable pitch angle control that permits the machine to generate power directly at 60/50 Hz and can be tied to the grid. A variablespeed wind generation system generates variable frequency, variable voltage power that is converted to constant frequency, constant voltage before connecting to the grid. Although the latter system is expensive, the energy capture is large enough that it makes the lifecycle costs lower. Recent technological advances in wind turbine, power electronics, and AC drives make the constantspeed system practically obsolete.
The proposed model in this paper of wind turbine is based upon the real value system. Conventional wind model was not suited to a real value system. In order to make the wind turbine model compatible with the real value component, the simulink model of WT is modeled from a per unit system to a real value system. Certain assumptions have been made to the given MATLAB/Simulink wind turbine model. First, the wind turbine model was changed from a per unit system to a real value system in order to make the turbine model compatible with the real value components of the WECS. Second, the variable pitch turbine model has been changed to represent a fixed pitch turbine. Actually the fixed pitch model was used to isolate the effects of electrical control rather than mechanical control because pitch control is achieved through hydraulic manipulation. Since the power coefficient characteristic is a nonlinear curve that reflects the aerodynamic behavior a wind turbine, this curve must be defined. The characteristic forms the basis for the custom turbine model. The nonlinear, dimensionless Cp characteristic is represented as:
where C _{1} = 0.5176, C _{2} = 116, C _{3} = 0.4, C _{4} = 5, C _{5} = 21, C _{6} = 0.0068
First, the wind turbine model was changed from a per unit system to a real value system in order to make the turbine model compatible with the real value components of the WECS. Second, the original model represents a variable pitch model, while for the purpose of this thesis the model was changed to represent a fixed pitch turbine. For this purpose substitute the value of pitch angle to be zero.
The fixed pitch model was used to isolate the effects of electrical control rather than mechanical control because pitch control is achieved through hydraulic manipulation. Therefore the new power coefficient equation is derived as:
This new power coefficient curve is illustrated in [Figure 3]. The power and torque characteristics of a wind turbine are governed by equations (4) and (5). With the power coefficient function given by (3), the mechanical power of the turbine can now be represented as:
The torque is defined as
The customized turbine model's specifications are summarized by [Table 1]. With the main focus of the shaft modeling on the correctness of the torque and speed transfer to the generator, the main relationship between the turbine output torque and the generator rotor speed is given by (6).
Where T _{m} is the mechanical torque from the wind turbine, J _{s} is the total system inertia, and ω is the angular velocity of the turbine shaft. The total system inertia, J _{s} , is given by:
Where J _{T} is the inertia of the turbine, J _{G} is the inertia of the machine, and G is the gear ratio between the turbine and the generator.
The complete real system wind turbine system has been built in SIMULINK, and is as illustrated in [Figure 1]. The Cp Vs TSR graph is shown in [Figure 2] with wind speed 12 m/s and having the infinite simulation time.
By modeling the PWM MPPT controller in Matlab/Simulink Sim Power Systems library for variable speed wind turbine high efficiency drive control system for the WTG system can be implemented ^{[17]} .
The wind turbine model can be represented as [Figure 3] in MATLAB/SIMULINK corresponding to real value system. This model focuses on the energy transfer characteristics within a wind turbine and does not include the aerodynamic characteristics.
The mechanical turbine power Vs generator speed has been determined keeping the wind velocity 12 m/s, and the simulation time taken as 50 sec. The relationship of turbine mechanical power vs. generator speed is shown in [Figure 4]. Mechanical Turbine torque vs. generator speed has also been calculated for the wind turbine and is shown in [Figure 5].
As we know that the mode of operation is governed by the sign of the mechanical torque T _{m} (positive for motor mode, negative for generator mode), it is observed from the [Figure 6] and [Figure 7] that after certain interval of time the turbine torque becomes negative and used to feed the T _{m} of PMSM and works as a generator. There is a gear box (G = ω_{h} / ω_{l} ) generally installed between the turbine shaft and generator rotor shaft to increase the turbine low shaft speed to High Generator rotor speed. Here in this case this gear ratio taken is 30.  Figure 6: dqaxis equivalent circuit model of the PMSM (a) daxis (b) qaxis
Click here to view 
3. Mathematical Modeling of PMSM   
3.1 Permanent Magnet Synchronous Machine Model
The mathematical model of a PMSM is similar to that of the wound rotor synchronous machine. The permanent magnets used in the PMSM are of modern rareearth variety with high resistivity. Hence induced currents in the rotor are negligible. In addition, there is no difference between the back EMF produced by a permanent magnet that produced by an excited coil. Hence the mathematical model of a PMSM is similar to that of the wound rotor synchronous machine (SM). The PMSM block operates in either generator or motor mode. The mode of operation is dictated by the sign of the mechanical torque (positive for motor mode, negative for generator mode) ^{[15]} . The electrical and mechanical parts of the machine are each represented by a second order statespace model. The model assumes that the flux established by the permanent magnets in the stator is sinusoidal, which implies that the electromotive forces are sinusoidal.
The block implements the following equations expressed in the rotor reference frame (dq frame).
The stator dqaxis voltage equations of the PMSM in the rotor reference frame are given by"
With the flux linkage, in d direction, λ_{d} = L _{d} i _{d} + λ_{m} and in q direction, λ_{q} = L _{q} i _{q}
A rotor current term is not included because it is assumed that no rotor winding is present. Following equations are obtained from the above equations.
This is standard current dynamics model (for control purposes) of a PMSM where, the stator resistance is denoted by R _{s} , the daxis and qaxis inductances are L _{d} and L _{q} , respectively, λ_{m} is the flux linkage due to the permanent magnets, V_{d} and V_{q} are dqaxis voltages, ω_{r} is the rotor speed, i _{d} and i _{q} are dqaxis current components. The d and qaxis equivalent circuit in shown in below [Figure 6].
The d, q variables are obtained from a, b, c variables through the Park's transformation as defined in below. The θ_{r} is the rotor angular position.
The a, b, c variables are obtained from the d, q variables through the inverse of the Park's transformation as defined in below:
The expression for the electromagnetic torque developed by the machine can be obtained from the component of the input power that is transferred across the air gap. The total input power that is transferred across the air gap. The total input power into the machine is given by:
When the stator phase quantities are transformed to the rotor dq reference frame that rotates at a speed ω_{r} =dθ_{r}/dt, equation becomes:
Where, the zero sequence quantities are neglected. The mathematical output power P_{out} can be obtained by replacing V_{d} and V_{q} with the associated speed voltages as:
For a Ppole machine, with ω_{r} = (P/2) ω_{rm} , where ω_{rm} is the rotor speed in mechanical radians per second.
The equation for electromagnetic torque T_{e} is obtained by dividing output power with mechanical speed ω_{rm} , and is given as:
If P is the number of pole pairs then electromagnetic torque becomes:
It is apparent from the above equation that the produced torque is composed of two distinct mechanisms. The first term corresponds to "reluctance torque" due to the saliency (difference in the daxis and qaxis reluctance or inductance), while the second term corresponds to the "excitation torque" (occurring between i _{q} and the permanent magnet λ_{m}). For nonsalient PMSM (L _{d} = L _{q}) the electromagnetic torque becomes:
And the relationship between the electromagnetic torque and the load torque is given as
Where B is the friction coefficient, T_{l} is the load torque and J is the moment of inertia. For simulation of the dynamic characteristics of the drive, we can rewrite the equation in two first order equations as
Where T _{e} is the electromagnetic torque, B is combined viscous friction of rotor and load, ω_{r} is the rotor speed, and J is the moment of inertia, θ_{r} is the rotor angular position and T _{m} is shaft mechanical torque. The differential equations governing the system can be represented as:
Electrical system:
Where (all quantities in the rotor reference frame are referred to the stator)
Mechanical system:
Where,
3.2 Machine Side Converter Control
Machine side converter control includes two loop control structure, using inner and outer loops in dq synchronous reference frame. The inner loop controls the electrical dynamics and the outer loop controls the mechanical dynamics. For machine drive, the electrical dynamics are faster than the mechanical dynamics. The electrical state variables appear to have reached their equilibrium values when viewed by the slower mechanical state. On the other hand, the mechanical state is seen to be essentially constant at their initial values when viewed by the electrical subsystem. Usually, the mechanical constant is many times greater than the electrical time constant.
The inner loop current controller has the ability to force the motor current to follow their command values. Thus under the control action, the equilibrium currents are actually equal to the commanded values.
The outer loop regulates the speed of the machine at their maximum output by issuing current commands to inner current loop. The outer speed loop ensures that the actual speed is always equal to the commanded speed and any transient will be overcome within the system dynamics, without exceeding the motor and inverter capabilities. The inner current loop also assures fast current response within the drive system. The drive is fed in such a way that the qaxis current provides the desired torque ^{[18],[19],[20]} .
[Figure 7] shows the implemented model of the machine side converter controller in Matlab/Simulink SimPower Systems library ^{[21]} . It is the highefficiency drive control system for the WTG system. The commanded speed ω_{ref} is precalculated according to the turbine output power and set to the optimum speed ^{[21]} .
Based on the speed error the commanded qaxis reference current i_{qref} is determined through the speed controller. In this system the following PI controller is employed as the speed controller.
Where, K _{pω} and K _{Iω} are the proportional and integral gains of the speed controller, respectively. While, eω is the error between the reference speed and the measured speed.
Based on the current errors, the dq axis reference voltages are determined by the PI controllers as given below:
where, K _{pi} and K _{Ii} are the proportional and integral gains of the controller, respectively. e _{d} = i _{dref} − i _{d} is the daxis current error and e _{q} = i _{qref} ZapfEllipt BT i _{q} is the qaxis current error ^{[22]} . The commanded dq  axis voltages (V _{d} , V _{q}) are transformed into a, b, c quantities (V _{a}, V _{b}, V _{c}) and given to PWM generator to generate the gate pulse for machine side converter.
3.3 Line Side Converter Control
The objective of the Line side converter is to keep the DC link voltage constant, regardless of the magnitude and direction of the rotor power. A vector control approach is used here, with the reference frame oriented along the Line voltage vector position. This enables independent control of the voltage and frequency between the load and Line side converter. The PWM converter is current regulated, where the direct axis current component is used to regulate the DC link voltage and quadrature axis current component is used to regulate the reactive power ^{[22],[23]} .
[Figure 8] shows the implemented model of the Line side converter controller in Matlab/Simulink SimPower Systems library ^{[21]} . The Line side converter operates as a controlled power source. The standard PI  controllers are used to regulate the Line currents in the dq synchronous frame in the inner control loops and the DC voltage in the outer loop. It is seen that a PI controller regulates the DC bus voltage by imposing an i_{d} current component. i_{d} represents the active component of the injected current into the Line, and i_{q} is its reactive component. In order to obtain only a transfer of active power, the i_{q} current reference is set to zero. The decoupling terms are used to have independent control of id and iq . A PLL is used to synchronize the converter with the Line. The philosophy of the PLL is that the difference between Line phase angle and the inverter phase angle can be reduced to zero using PI controller.
3.4 Simulation Model of WTG System
[Figure 9] shows the complete model of the MTG system, which is implemented in the Matlab/Simulink SimPower Systems library. The Wind Turbine Generation (WTG) system takes wind speed and angular speed of PMSM as input. The torque output of the wind turbine is given as an input mechanical torque (T_{m} ) for the PMSM. The direction of torque T_{m} is positive during motoring mode and made negative during generating mode of PMSM ^{[15]} .
The machine side converter controller takes the rotor speed and three phase stator current signals of the PMSM as input. Both, machine side and line side converters uses the sinusoidal pulse width modulation (SPWM) with triangular carrier signal. The machine side and line side converters are IGBTbased VSC, which is available in universal bridge block in the Simulink of the Matlab. The three phaseactive LCL filter circuit is used as to reduce the highorder harmonics distortion and supplies the reactive power to the system and it will be maintains the Load endside voltage and current wave forms as sinusoidal.
Traditionally, conversion of ac generator voltages in wind systems to DC link voltages has been dominated by phase controlled or diode rectifiers. But this thesis has been changed this diode rectifier to IGBT converter gated by MPPT PWM converter which takes line current and generator speed as a input. This change has been done because the nonideal character of the input current drawn by these rectifiers approach creates a number of problems for the power distribution network and for other electrical systems in the vicinity of the rectifier including:
 Phase displacement of the current and voltage fundamentals requires that the source and distribution equipment handle reactive power increasing their voltampere ratings;
 High input current harmonics and low input power factor;
 Lower rectifier efficiency because of the large rms values of the input current;
 Input AC mains voltage distortion because of the associated higher peak currents;
 High reactive components size.
4. Results and Discussions   
The complete WECS was built in SIMULINK, and is as illustrated in [Figure 9]. The Cp Vs TSR graph is shown in [Figure 2] after the simulation of wind model with wind speed 12 m/s and having the infinite simulation time.
The PWM MPPT controller is implemented in Matlab/Simulink SimPower Systems library ^{[17],[21]} . It is the highefficiency drive control system for the WTG system. The commanded speed ω_{ref} is precalculated according to the turbine output power and set to the optimum speed ^{[23]} . It helps to draw the maximum power by the generator. This algorithm of MPPT requires the wind speed, generator speed, reference generator speed and machine current as an input.
The generator speed input allows the algorithm to determine whether the generator speed has reached the reference speed as desired.
4.1 PMSM Side Voltage and Current Waveforms
The obtained PMSM voltage and current waveforms have been shown in [Figure 10], when the WTG system model has been used with the LCL filter. It is observed that PMSM was running as a generator, when the DC source is removed at t = 0.8 sec from the system.  Figure 10: PMSM Voltage and current waveform with LCL filter (Low time frame)
Click here to view 
It is observed that, the obtained PMSM voltage and current waveforms have been shown in [Figure 11], when the WTG system model has been used with the RL filter  Figure 11: PMSM Voltage and current waveform with RL filter (Low time frame)
Click here to view 
The voltage and current wave forms were determined for 1 second. It is observed that the waveforms are very close and difficult to interpret. Therefore, the voltage and current waveforms have been determined for lower time range from 0.435 to 0.455 seconds.
4.2 Load EndSide Current and Voltage Waveform
The obtained Load end side voltage and current waveforms have been shown in [Figure 12], when the WTG system model has been used with the LCL filter.
[Figure 12] shows the load side phase voltage and current wave forms determined for 1 second. It is observed that the waveforms are very close and difficult to interpret. Therefore, the voltage and current waveforms have been determined for lower time range from 0.4 to 0.5 seconds and have been shown in [Figure 13].  Figure 12: Load endside voltage (phase to phase) and line current waveform with LCL filter
Click here to view 
 Figure 13: Load endside voltage (phase to phase) and line current waveform with LCL filter (low time frame)
Click here to view 
It is observed from figure that the WTG system will not deliver the rated active power to the load and the voltage and current waveforms are not sinusoidal when LCL filter is used.
The obtained load end side voltage and current waveforms have been shown in [Figure 14], when the WTG system model has been used with the RL filter and the reactive power is not injected into the system. The voltage and current wave forms were determined for 1 second. It is observed that the waveforms are very close and difficult to interpret. Therefore, the voltage and current waveforms have been determined for lower time range from 0.438 to 0.456 seconds and have been shown in [Figure 14].  Figure 14: Load endside voltage (phase to phase) and line current waveform with RL filter (low time frame)
Click here to view 
The obtained load end side voltage and current waveforms have been shown in [Figure 15], when the WTG system model has been used with the LCL filter and RL filter, respectively when the reactive power is not injected into the system. It is observed that the voltage and current waveforms are not sinusoidal completely.  Figure 15: Load endside voltage and current waveform with LCL filter and reactive power injection into the system (low timeframe)
Click here to view 
4.3 Load EndSide Current and Voltage Waveform with Reactive Power Injection
Now there is need to inject the reactive power to WTG system model used with the LCL filter ^{[18]} to make the sinusoidal voltage and current waveforms. The Load endside voltage (phase to phase) and line current waveform with LCL filter and with reactive power injection is given in [Figure 15]. The voltage and current waveforms have been determined for lower time range from 0.4 to 0.5 seconds and have been shown in [Figure 15]. From [Figure 15], it is observed that the WTG system delivered the rated active power to the load and the voltage and current waveforms are sinusoidal. The obtained DC link voltage waveform has been shown in [Figure 16], when the WTG system model has been used with the LCL filter and the reactive power is not injected into the system. [Figure 17] shows the DC link voltage waveform with RL filter and it can be easily concluded that for wind system, RL filter is possess less disturbances is DC link waveform as compared to the LCL filter.  Figure 16: DC Link voltage with LCL filter and reactive power is not injected into the system
Click here to view 
 Figure 17: DC Link voltage with RL filter and reactive power is not injected into the system
Click here to view 
5. Conclusions   
In this paper, the real value system model of WT is implemented in order to make the turbine model compatible with the real value components of the WECS. With the simulation of the complete WECS using MATLAB/SIMULINK model all the results have been obtained for fixed pitch wind turbinebased PMSM. With fixed pitch real system WT model the performance of Mechanical turbine Power/Torque Vs generator speed has been obtained. Using the RL and LCL filter, the load end side voltage and current and DC link voltage has been obtained. PMSM voltage and current waveforms obtained are sinusoidal. The DC link voltage has less harmonics level and gives the better results in case of RL filter rather than LCL filter. Load endside voltage and current waveforms are sinusoidal with RL filter. The performances have been taken by both injecting or without injecting the reactive power and with reactive power injection the results are sinusoidal with LCL filter also.
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Authors   
Janardhan Gupta did his masters in power systems form Dept of Electrical Engg. NIT Kurukshetra in 2010. Presently he is working with IBM, New Delhi. He has interests in the area of power systems,and wind energy conversion systems.
Ashwani Kumar is an Associate Prof. with the Dept of Electrical Engineering, NIT Kurukshetra, India. He did his B. tech. from GBPUA and Tech. Pant Nagar in 1988, masters from Punjab University Chandigarh in 1994 in nhonors and PhD from IIT Kanpur in 2003. He was post doctoral fellow at Tennessee Technological University USA in 2008. His research interests includes power system restructuring, power systems dynamics, demand side management, distributed generation, and price forecasting. He has number of publications in Int./nat. Journals and conferences and many awards to his credit. He is a life member of ISTE, IEI, India, and IEEE/IEEE PES.
[Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5], [Figure 6], [Figure 7], [Figure 8], [Figure 9], [Figure 10], [Figure 11], [Figure 12], [Figure 13], [Figure 14], [Figure 15], [Figure 16], [Figure 17]
[Table 1]
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