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Sustainable Energy Technologies and Assessments 19 (2017) 114–124 Contents lists available at ScienceDirect Sustainable Energy Technologies and Assessments journal homepage: www.elsevier.com/locate/seta Original article Design, modeling and simulation of variable speed Axial Flux Permanent Magnet Wind Generator Sriram S. Laxminarayan a,⇑, Manik Singh a, Abid H. Saifee b, Arvind Mittal a a b Energy Centre, Maulana Azad National Institute of Technology, Bhopal, India Dept. of Electronics and Communication, All Saints’ College of Technology, Bhopal, India a r t i c l e i n f o Article history: Received 15 June 2016 Revised 19 October 2016 Accepted 12 January 2017 Keywords: Axial Flux Permanent Magnet Generator Single Stator Double Rotor Horizontal Axis Wind Turbine MATLAB/Simulink Modeling Simulation a b s t r a c t Variable speed wind energy systems using permanent magnet generators are increasingly becoming popular for both standalone and grid connected applications. Axial Flux Permanent Magnet Generators (AFPMG) are a relatively new class of generators which are being considered as effective alternative to conventional Radial Flux generators, especially in wind applications, owing to their special features and attractive benefits. This paper presents the design of an Axial Flux Permanent Magnet Generator well suited for variable speed wind applications. A 2000 VA, 240 V, 3 phase, 10 pole, 5 rps AFPMG with Single Stator Double Rotor configuration has been considered for the design and analysis. The behaviour of the AFPM wind generator is investigated for different wind conditions, through dynamic modeling and simulation. The comprehensive modeling of AFPMG along with the details of the models for the Horizontal Axis Wind Turbine (HAWT), drive train, speed controller and pitch controller have been presented. The complete system model is implemented on MATLAB/Simulink platform and simulations are carried out for various wind conditions. The response of the generator for both constant wind input and variable wind pattern have been presented and discussed. The functioning of pitch controller is also verified for high wind speed conditions. Ó 2017 Elsevier Ltd. All rights reserved. Introduction In the prevailing global energy deficit scenario, generating energy from renewable energy sources has emerged as the most viable and sustainable solution. Although the presence of renewable energy systems is ubiquitous in the present landscape of energy, the renewable energy sector is still beset with many technical issues. However, a strong commitment exists to address such issues and make the renewable energy option attractive and competitive compared to the conventional energy systems. In line with this, significant efforts are being made to maximise the production of energy from renewable energy sources while keeping the prime focus on improving their associated economic aspects. Among the renewables, wind energy has historically been a front runner for both large scale and small scale applications, still holding huge scope for exploitation in many parts of the world. Wind energy conversion systems have undergone vast transformations over the years, achieving remarkable technical progress and is presently considered a matured technology [1]. Traditional wind ⇑ Corresponding author at: ‘Anugraha’, SARA 59-A, Puthen Road, Vazhappally Jn., Fort P.O., Trivandrum, Kerala, 695023, India E-mail address: [email protected] (S.S. Laxminarayan). http://dx.doi.org/10.1016/j.seta.2017.01.004 2213-1388/Ó 2017 Elsevier Ltd. All rights reserved. energy systems have been constant speed systems which were designed to give their optimal performance at certain wind speeds. They use gear boxes to couple the wind turbine with the generator and hence suffer a lot of related problems such as complexity in their control, high fatigue, noise and maintenance requirements. The newer wind energy systems have therefore moved on to gearless direct drive concept in which the turbine and generator are coupled directly without a gear box. Such systems, known as variable speed systems, have superior low speed performance and improved energy capture capability [2]. However, variable speed systems require a generator with a large number of poles since the speed of operation would be lower, limited by the directly coupled wind turbine. With the advent of high strength permanent magnets and the remarkable advancements that occurred in their field lately, electrical machines using permanent magnets have been increasingly sought after owing to their relatively simple design, compact structure and robustness. Permanent magnet generators have been found most suitable for variable speed systems wind systems since their construction allows the inclusion of a large number of poles easily which would have been difficult in the case of conventional field excited generators [3,4]. S.S. Laxminarayan et al. / Sustainable Energy Technologies and Assessments 19 (2017) 114–124 Axial Flux machines with conventional field poles machines were developed almost a century ago, though their successful foray into the field of electric machines was hindered owing to certain complexities involved in their construction and difficulties encountered in providing ventilation. Hence, traditionally electric machines have been commonly of radial flux type. However, the huge popularity of permanent magnet generators has kindled an immense interest in Axial Flux Permanent Magnet Generators (AFPMG) recently, since the use of permanent magnets enables easier design and construction. These machines hold a promising future, offering many exciting features and advantages over radial flux machines. They have been brought into the limelight of active research ever since, with commendable studies already been conducted on its performance and applications, especially as generators in wind energy conversion systems [5,6]. From the comprehensive literature survey conducted on the subject it is seen that abundant work has been carried out in terms of designing and modeling of permanent magnet machines, albeit majority of them consider radial flux machines. The relatively lesser research efforts intended towards axial flux machines seem to focus on the physical design, design optimization, thermal analysis etc. using various tools and techniques. Various electromagnetic and mechanical design procedures for Axial Flux Permanent Magnet Generators of different topologies have been discussed in [6– 10]. The studies presented in [11–13] deal with the modeling analysis of permanent magnet generators of radial flux type in variable speed wind systems while those presented in [14–16] deal with analytical modeling of Axial Flux Permanent Magnet machines. It can be seen that comprehensive studies comprising design of an AFPMG for wind systems, both the mathematical and tool based dynamic modeling of the entire system and subsequent simulation studies to understand the generator characteristics, is fairly limited. In this paper, an Axial Flux Permanent Magnet Generator (AFPMG) has been designed, which is most suited to be used as a wind generator in variable speed systems. Then, the mathematical model of the system consisting of the AFPMG directly coupled to a pitch controlled Horizontal Axis Wind Turbine (HAWT) is obtained and is implemented in MATLAB/Simulink platform. Simulations have been carried out to examine the behaviour of the wind generator under different wind speed conditions and the results have been discussed. is sandwiched between two rotors carrying permanent magnet poles [22,23]. The arrangement of permanent magnets is in such a way that the North Pole of one rotor faces the South Pole of the other rotor and vice versa (NS-SN configuration). The unique feature of this particular configuration is that the magnetic flux passes from one rotor to the other crossing the stator axially completing the magnetic circuit, without passing through the stator disc itself in a radial direction, i.e., the stator disc does not necessarily serve any purpose for the path of the magnetic flux, other than supporting the three phase windings. This allows the generator to have a non-magnetic non-conducting material such as plastic or wood for the stator disc, making it lighter in weight. This also eliminates iron losses and makes the machine more efficient. Design of Axial Flux Permanent Magnet Generator The AFPMG under consideration has a SSDR structure with NSSN configuration for permanent magnets as shown in Fig. 1. This configuration of the AFPMG makes it most suitable for wind applications since the short axial length of the machine enables it to be comfortably accommodated in the nacelle of the wind turbine (which usually has space constraints). Since the machine is compact, a nacelle of smaller size could be employed. Also, lesser weight of the generator would mean that the weight of the nacelle is reduced. Moreover, it offers a higher power density and higher efficiency since iron losses are absent. The AFPMG has been designed following the fundamentals of permanent magnet machine design [24,25] and the basic design equations have been presented below. The sizing equation of the AFPMG is given by Pout ¼ p2 8 Bav ac 1 k2 ð1 þ kÞ D3so Ns ð1Þ where Pout is the output power Bav is the average air gap flux density or specific magnetic loading (chosen as 0.6 Wb/m2), ac is the specific electric loading, Dso is the outer diameter of stator, Ns is the speed of rotation and k is the diameter ratio, which is the ratio of inner diameter (Dsi Þ to outer diameter of stator ðDso Þ. Considering the disc forms of stator and rotor, the specific electric loading is worked out as, Axial Flux Permanent Magnet Generator (AFPMG) In an AFPMG, the stator and rotor are in the shape of discs stacked or mounted on a shaft and the magnetic flux traverses from one disc to the other in a direction parallel to the shaft (i.e. axial direction). When compared to their Radial Flux counterparts, Axial Flux Permanent Magnet Generators possess a multitude of attractive features such as better design flexibility, higher power to weight ratio, negligible cogging torque, lower noise, adjustable planar air gap, higher energy efficiency, possibility of modular construction etc. They can be designed in a wide variety of topologies having multiple stators and rotors in the same machine with different assemblies for stator winding and different configurations for the placement of permanent magnets [17–21]. Axial Flux Permanent Magnet Generators can also be designed with several stages of stator-rotor units mechanically coupled together on the same shaft and electrically connected together in series or parallel as required. By doing so, the electrical output that can be generated from the available wind increases as many folds as generated by a single stage, with minimal increase in overall size. Among the various configurations, Single Stator Double Rotor (SSDR) configuration is found to have better operational features and in this configuration, the stator carrying three phase winding 115 Fig. 1. AFPMG with SSDR (NS-SN) configuration. 116 S.S. Laxminarayan et al. / Sustainable Energy Technologies and Assessments 19 (2017) 114–124 3 Iph Zph p Dso 2þDsi ac ¼ ð2Þ where Iph is the stator phase current, Zph is the number of stator conductors per phase. Voltage induced by the permanent magnet poles on the stator conductors is given by, Vph ¼ Ke Ns ð3Þ where Ke is the induced emf constant in given by the following relation, p Ke ¼ 4 Zph Bav ðD2so D2si Þ ð4Þ Number of turns per phase in stator, Tph Zph ðDso þ Dsi Þ ¼ ¼ ac p 2 6 Iph 2 Iph J ð5Þ ð6Þ Length of Mean Turn in mm, Lmt ¼ ðDso Dsi Þ 103 þ Loht þ Lohb Ld ¼ l0 T2ph p D2so D2si 4 0:8 þ Lg 2 þ Lsb ð17Þ Quadrature axis inductance, Lq ¼ l0 T2ph p ðD2so D2si Þ ð18Þ 4 fðLp þ 0:8 þ Lg Þ 2 þ Lsb g Direct axis reactance, Xd ¼ 2 p f Ld ð19Þ Quadrature axis reactance, For a current density of J (chosen as 4.1 A/mm2), the area of conductor, as ¼ where Lp is the thickness of pole (taken as 12.5 mm), Lg is the air gap length (taken as 1 mm) and Lsb is the bottom thickness of the stator.Direct axis inductance, Xq ¼ 2 p f Lq ð20Þ For this particular design of AFPMG, the iron losses are absent, copper losses are present in stator winding only and neglecting the mechanical losses, the efficiency equation can be written as g¼ Pout cos £ 100 ðPout cos £Þ þ pscu ð21Þ where cos £ is the power factor. ð7Þ where Loht and Lohb are top and bottom overhangs of the stator winding. The other coil dimensions are worked out as per standard designing procedure. The stator resistance per phase at 20 °C and 75 °C is given by, Rph20 ¼ 1:732 108 Lmt Tph 1:08 as ð8Þ Rph75 ¼ 1:3 Rph20 1:08 ð9Þ Design output The SSDR AFPMG is rated at 2000 VA, 240 V(phase), 10 pole, 3 phase, 25 Hz, 5 rps and its design output has been listed in Table 1. Higher specific magnetic and electric loadings are chosen so that the machine has reduced volume and size. The diameter ratio, k, is an influencing parameter in the design of AFPMG as the copper losses depends on this factor [25]. Hence an optimized value has been chosen for k as 0.23 for this design to maximise the efficiency of AFPMG. Stator copper loss, pscu ¼ 3 I2ph Rph75 ð10Þ For P number of Poles on each rotor disc, Pole Pitch Top and Pole Pitch Bottom is given by, p p st ¼ Dso and sb ¼ Dsi respectively: P P ð11Þ Flux per Pole in the rotor, p £p ¼ 4P ðD2so D2si Þ Bav ð12Þ Thickness of rotor end plate, Lrep ¼ £p 103 Bmax ðDso Dsi Þ ð13Þ where Bmax is the maximum flux density in the rotor end plate which is assumed as 1.55 Wb/m2.Electromagnetic torque, C¼ Pout 103 2 p Ns ð14Þ Shaft Diameter, Dshaft sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 4C 3 ¼ p rmax ð15Þ where rmax is the maximum permissible shear stress Length of machine, L ¼ ½ðLp þ 0:8 þ Lg Þ 2 þ Lsb þ 2 Lrep ð16Þ Table 1 Design Output for 2000 VA, 240 V, 3 phase, 10 pole, 25 Hz AFPMG. Parameter Symbol Value Unit Generator output Frequency Rated phase voltage No. of phases Rated Speed No. of poles Average flux density in air gap Specific Electric Loading Diameter ratio Outer diameter of stator Inner diameter of stator Induced emf constant Number of conductors per phase Area of Conductor Length of mean turn Stator Resistance per phase at 75 °C Thickness of pole Height of pole Pole Pitch Top Pole Pitch Bottom Pole Arc to Pole Pitch Ratio Pole Arc Top Pole Arc Bottom Electromagnetic torque Shaft diameter Length of machine Direct Axis Inductance Quadrature Axis Inductance Stator Copper Loss Efficiency Pout f Vph Phase Ns P Bav Ac k Dso Dsi Ke Zph as Lmt Rph75 Lp Hp 2000 25 240 3 5 10 0.6 17666 0.23 0.301 0.069 50.16 1240 0.811 0.43 7.39 12.5 116 94.56 21.67 0.7 66.2 15.18 63.661 21.11 0.696 0.247 0.066 170.6 92.14 VA Hz V – rps – Wb/m2 A-cond/m – m m V/rps – mm2 m O mm mm mm mm – mm mm Nm mm m H H W % st sb – – – C Dshaft L Ld Lq pscu g S.S. Laxminarayan et al. / Sustainable Energy Technologies and Assessments 19 (2017) 114–124 117 Modeling of Axial Flux Permanent Magnet Wind Generator The direct drive variable speed system under consideration consists of SSDR AFPMG directly coupled to a Horizontal Axis Wind Turbine (HAWT) without any gear box using a simple shaft. The auxiliary components of this system include speed controller and pitch controller. The focus of this study is on the dynamic modeling and simulation of the AFPMG operated as a wind generator to understand its response under different wind conditions using MATLAB/Simulink platform. The development of the model for each component has been presented below. Model of HAWT A conventional three bladed HAWT is considered for the analysis and its mathematical modeling equations have been given below [11–13]. Mechanical Power generated by turbine, Pm ¼ 1 Cp q A U3w 2 Fig. 2. Power Coefficient (Cp ) vs. Tip Speed Ratio (k) for different values of Pitch angle (b). ð22Þ where q is the air density (taken as 1.225 kg/m3 at normal temperature), A is the area swept by the turbine blades (in m2), Uw is the upstream wind speed (in m/s) and Cp is the power coefficient. Power coefficient ðCp ) is the ratio of mechanical power generated by the turbine to the power available in the wind. It is a non-linear function of tip speed ratio (k) and pitch angle of the blades (b). The theoretical maximum value of Cp is 0.59 (limited by Betz criterion) while practical values lie between 0.4 and 0.45. Although many variations of the equation for power coefficient exists, a standard equation has been used here as follows. Cp ¼ C1 C C2 5 C3 b C4 e ki þ C6 k ki ð23Þ The coefficients are taken as: C1 = 0.5176, C2 = 116, C3 = 0.4, C4 = 5, C5 = 21 and C6 = 0.0068 Tip Speed Ratio, k¼ xm R Uw ð24Þ Model of AFPMG where xm is the blade tip speed, which is equal to the rotor angular speed (in rad/s) and R is the radius of the turbine rotor. ki ¼ 1 0:035 k þ 0:08b b3 þ 1 ð25Þ Mechanical torque developed by turbine, Tm ¼ Pm xm Fig. 3. Mechanical Power ðPm Þ vs. Angular Speed ðxm Þ for different Wind speeds ðUw Þ. ð26Þ The variation of power coefficient Cp with respect to tip speed ratio k for different values of pitch angle b is shown in Fig. 2. As seen from the figure, the power coefficient decreases as pitch angle is increased for the same tip speed ratio. From the equation for tip speed ratio, it is clear that there exists an optimal value for k for every wind speed Uw . The value of xm corresponding to this k is considered to be optimum for extracting the maximum power from the particular wind speed. The variation of power developed by the turbine with respect to the variation in angular rotational speed for different wind speeds has been shown in Fig. 3. A MATLAB/Simulink model for the wind turbine has been developed using the above modeling equations as shown in Fig. 4. The dynamic model of AFPMG is developed using synchronous d-q rotating reference frame on the lines of Permanent Magnet Synchronous Generator [7,13,26,27]. In this frame it is considered that the q-axis is 90° ahead of d-axis. The transformation of the three phase system to d-q frame is maintained by Park’s transformation and the reverse transformation by Inverse Park’s Transformation as given below. 2 3 2 32 3 cos xt cosðxt 120Þ cosðxt þ 120Þ ua ud 6 7 2 6 sin xt sinðxt 120Þ sinðxt þ 120Þ 76 7 4 uq 5 ¼ 4 5 4 ub 5 3 1 1 1 u0 uc 2 2 2 2 3 2 32 3 ud ua cos xt sin xt 1 6 7 6 76 7 4 ub 5 ¼ 4 cosðxt 120Þ sinðxt 120Þ 1 54 uq 5 uc u0 cosðxt þ 120Þ sinðxt þ 120Þ 1 where ‘u’ can be voltage, current or flux. The modeling equations of AFPMG have been developed by assuming that the rotor flux completely acts along d-axis and there is no flux along q-axis. Flux linkages along d and q axes are given by 118 S.S. Laxminarayan et al. / Sustainable Energy Technologies and Assessments 19 (2017) 114–124 Fig. 4. MATLAB/Simulink model of Horizontal Axis Wind Turbine. wd ¼ Ld id þ wf ð27Þ wq ¼ Lq iq ð28Þ where Ld and Lq are inductances along d and q axes respectively, id and iq are the stator currents along d and q axes respectively. wf is the permanent magnet flux linkage given by wf ¼ Ke pP ð29Þ Pe ¼ 3 ðxe Lq iq id xe Ld id iq þ xe wf iq Þ 2 or, Pe ¼ 3 xe ½wf iq ðLd Lq Þid iq 2 ð38Þ The electromagnetic torque developed is given by Te ¼ Pe xm ¼ P 3 ½w iq ðLd Lq Þid iq 2 2 f ð39Þ where Ke is the induced emf constant of the AFPMG and P is the number of poles. The voltage equations along d and q axes are given by The MATLAB/Simulink model of the AFPMG developed based on the above modeling equations has been shown in Figs. 5–7. vd ¼ rd id þ pwd xe wq ð30Þ Model of drive train vq ¼ rq iq þ p wq þ xe wd ð31Þ where rd and rq are the resistances of the stator in d and q axes, xe is the angular electrical speed and p represents d=dt. Substituting the values of wd and wq from Eq. (27) and (28), we get vd ¼ rd id Ld pid þ xe Lq iq ð32Þ vq ¼ rq iq Lq piq xe Ld id þ xe wf ð33Þ Rearranging Eqs. (30) and (31), the current equations can be obtained as did 1 ¼ ½rd id þ xe Lq iq vd dt Ld ð34Þ diq 1 ¼ ½rq iq xe Ld id þ xe wf vq dt Lq ð35Þ The drive train represents the mechanical connection between the wind turbine and generator and its mathematical expression is given by the Swing equation. It characterizes the behaviour of rotor of the generator with respect to the input mechanical torque and output electromagnetic torque. The wind turbine and AFPMG are coupled directly through a shaft and therefore a simple lumped mass model has been considered [7,13] and the differential equation which represent the drive train is given by J dxm ¼ T m T e Kx m dt where J is the moment of inertia of rotor mass, xm is the angular velocity of turbine shaft (angular mechanical speed), Tm is the mechanical torque developed by turbine, Te is the electromagnetic torque developed by generator and K is the friction coefficient. The MATLAB/Simulink model of the drive train has been shown in Fig. 8. The relation between electrical rotating speed and mechanical speed is given by xe ¼ xm P 2 ð36Þ The electromagnetic power generated by the AFPMG is given by Pe ¼ 3 ðed id þ eq iq Þ 2 ð37Þ where ed and eq are induced emfs in d and q axes given by ed ¼ xe Lq iq and eq ¼ xe Ld id þ xe wf Substituting the expressions for ed and eq in Eq. (35) ð40Þ Fig. 5. MATLAB/Simulink model of AFPMG – Computation of vd . S.S. Laxminarayan et al. / Sustainable Energy Technologies and Assessments 19 (2017) 114–124 119 the current wind speed and the controller generates a iq control signal which is given as feedback to the AFPMG block for torque and voltage build up. The speed controller is designed in such a way that system settles down at the appropriate operating point with respect to available wind speed. The d-axis component of current is set to zero to maximise the torque development at the rated flux and minimize the losses. The MATLAB/Simulink model of the speed controller is shown in Fig. 9. Pitch controller Fig. 6. MATLAB/Simulink model of AFPMG – Computation of vq . Speed controller The wind speed being a highly variable input, it becomes necessary that the speed of the rotation of the generator and in turn the speed of the turbine has to be adjusted so that the system speed is brought to the optimal value where maximum power extraction from the wind and hence maximum power generation by the AFPMG would be possible. Field oriented vector control approach is one of the methods by which this is achieved, where the qaxis component of the stator current is the controlling factor [12,26,28]. It is clear from Eq. (37) that electromagnetic torque is dependent on q-axis current, hence if iq is controlled, then Te can be controlled. By controlling toque, the shaft speed xm , can be controlled as seen from Eq. (38). A speed controller incorporating the elements of this control approach has been adopted in this paper with a purpose to simulate the effect of both maximum power point tracking operation and loading effect on the AFPMG. It is designed based on a forcing function given by iq ¼ A Dx ð1 e t=Tc Þ As the wind speed increases, the speed of rotation of the wind turbine will naturally increase, causing the generator to run at speeds higher than its nominal speed and generate overvoltage. To prevent this and to keep the power within the designed limits, the turbine torque needs to be controlled when the generator speed exceeds its limit. From Eq. (23), it is clear that pitch angle of the turbine blades (b) can be adjusted to control the power coef- ð41Þ where A is a constant, Dx is the speed error, i.e., the difference between actual speed and reference speed, Tc is the time constant. A is chosen as 80 and Tc is chosen as 300 to minimize fluctuations and ensure smooth settling. Reference speed is generated based on Fig. 9. MATLAB/Simulink model of Speed Controller. Fig. 7. MATLAB/Simulink model of AFPMG – Computation of Te and Pe . Fig. 8. MATLAB/Simulink model of Drive Train. 120 S.S. Laxminarayan et al. / Sustainable Energy Technologies and Assessments 19 (2017) 114–124 ficient and in turn, control the turbine power output and torque. For the wind speeds lower than or equal to the nominal speed, the pitch angle of the blades is kept at 0° to extract as much power as possible from the wind. During this period, the action of speed controller alone takes care of the optimal speed at which the system operates. As wind speed exceeds the limit corresponding to the nominal speed of the generator, pitch controller is activated and the pitch angle is increased progressively to limit the speed and to keep the output power on or below the rated value. b is usually varied between 0° and 24° for pitch control in this mode. Once the wind speed reaches the cut-off limit, the pitch angle is set to 90° so that the wind turbine comes to a halt in order to avoid mechanical failure. The pitch angle is calculated based on an error signal which is the difference between the electromagnetic power and the rated power (reference signal) [26–28]. It employs a proportional (P) controller to process the error signal. This methodology for pitch control has been implemented using MATLAB/Simulink platform as shown in Fig. 10. A selector switch is used to select the state of operation according to the wind speed control input. The rate of change pitch angle is limited to 3° per second to minimize stress on the blades and disturbances in the speed of rotation. The MATLAB/Simulink model of the complete system is shown in Fig. 11. Table 2 Parameters used for Simulation. Parameter Symbol Value Unit Rotor Diameter of Wind Turbine Air density Number of poles in AFPMG d-Axis component of stator resistance q-Axis component of stator resistance d-Axis component of stator inductance q-Axis component of stator inductance Permanent magnet flux linkage Power Reference Moment of Inertia Friction coefficient D Rho P Rd Rq Ld Lq Psi Pref J K 4 1.225 10 5 5 0.247 0.066 1.6 2000 4 0.16 m kg/m3 – Fig. 10. MATLAB/Simulink model of Pitch Controller. Fig. 11. Complete MATLAB/Simulink model of the AFPMG based wind generator. X X H H Wb-turns VA kg m2 Nm/rad S.S. Laxminarayan et al. / Sustainable Energy Technologies and Assessments 19 (2017) 114–124 Parameters used for simulation The parameters used for the simulation of wind turbine driven 3 phase, 240 V, 25 Hz, 5 rps AFPMG with a rated power of 2000 VA and electromagnetic torque of 66 Nm is listed in Table 2 along with their corresponding symbols used in the MATLAB/ Simulink blocks. The cut-in and cut-off wind speed of the pitch 121 variable three bladed HAWT is designed to be 4 m/s and 15 m/ s respectively. Results and discussion The operation of the complete system has been simulated for various wind conditions, comprising of constant wind speed, a Fig. 12. Variation of a) Mechanical Speed ðxm Þ, b) frequency ðfÞ, c) Electromagnetic Torque ðTe Þ and d) Electromagnetic Power ðPe Þ for various constant wind speeds ðUw Þ. Fig. 13. Variation of a) Mechanical Torque ðTm Þ, b) Mechanical Power ðPm Þ, c) q-axis current (iq ), d) frequency ðfÞ for nominal wind speed of 8.5 m/s. 122 S.S. Laxminarayan et al. / Sustainable Energy Technologies and Assessments 19 (2017) 114–124 rapidly varying wind speed and high wind speed input, to evaluate the dynamic behaviour of the wind generator. Constant wind speed response Fig. 12 shows the values of mechanical speed, electromagnetic power, electromagnetic torque and frequency for constant wind speeds of 6, 7, 8 and 8.5 m/s. It can be observed that for these wind speeds, the speed controller assists the system to settle down at the suitable speed and the operation of the turbine and AFPMG is such that the maximum possible power is generated at each wind speed. Also, it is clear that the generator operates at its rated values i.e., power of 2000 VA and voltage of 240 V at speed of 5 rps (i.e., 31.4 rad/s or 300 rpm) when the wind speed is 8.5 m/s which is the nominal wind speed. The mechanical torque, mechanical power, q-axis current and the frequency at the nominal wind speed of 8.5 m/s have been shown in Fig. 13. The d and q-axes components of stator voltages and the three phase voltage output for this wind speeds have been shown in Fig. 14. For the three phase output voltage, a section has been expanded and shown to elucidate the balanced three phase nature of the three phase voltages. ative steps of wind speeds. The variations in electromagnetic power and the three phase output voltage of the generator with respect to the random wind pattern has also been shown in the figure. It can be seen that the generator is able to quickly adapt to the changing wind conditions and the transients are quite short in nature. High wind speed response As discussed previously, at wind speeds higher than the nominal value, the pitch control is activated. In order to clearly demonstrate the action of pitch controller, a three stepped wind pattern has been chosen with speeds 8.5 m/s, 10 m/s and 11 m/s as shown in the Fig. 16. The variation of the pitch angle, angular mechanical speed and electromagnetic power with respect to the change in wind speed also has been shown the figure. For the first 20 s, the wind speed remains at 8.5 m/s which is the rated wind speed. During this time pitch angle is set to 0° to extract maximum power from the wind. For the next 10 s, the wind speed increases to 10 m/s and then the pitch controller is activated. It is seen that Variable wind speed response To understand the dynamic response of the generator, its operation has been simulated for a rapidly varying wind pattern as shown in Fig. 15. This wind pattern includes both positive and neg- Fig. 14. a) d and q axis voltages ðVd ; Vq Þ, b) Three phase output voltage ðVa ; Vb ; Vc Þ for wind speed of 8.5 m/s. Fig. 15. Variation of a) Wind speed ðUw Þ, b) Electromagnetic Power ðPe Þ, c) Three phase output voltage ðVa ; Vb ; Vc Þ with respect to time. 123 S.S. Laxminarayan et al. / Sustainable Energy Technologies and Assessments 19 (2017) 114–124 Fig. 16. Variation of a) Wind Speed ðUw Þ, b) Pitch angle ðbÞ, c) Angular Speed ðxm Þ, d) Electromagnetic Power ðPe Þ at high wind speed conditions. the pitch angle increases to 2.8° due to which the turbine is prevented from further acceleration and the mechanical speed remains well within the rated speed. The power generated by the AFPMG also remains close to the rated power. Again for the next 10 s, when the wind speed increases to 11 m/s, the pitch angle becomes 7.2°. Similar effects can be seen on the speed and power during this time as well. The output voltage would also remain limited at the rated value during active pitch operation. Evidently, the pitch controller is successfully able to control the power of the AFPMG at high wind speed conditions. Table 3 Validation Chart. Wind Speed Parameter Calculated Result Simulated Result 7 m/s Tip Speed Ratio Angular Mechanical Speed Power Coefficient Turbine Power Angular Electrical Speed Frequency Electromagnetic Power q-Axis current Per phase output voltage 8 28 rad/s or 267.5 rpm 0.47 1240 W 140 rad/s 8.1 28.35 rad/s or 270.85 rpm 0.46 1213 W 141.75 rad/s 22.3 Hz 1142 VA 22.57 Hz 1173.7 VA 3.4 A 208 V 3.45 212.4 V Tip Speed Ratio Angular Mechanical Speed Power Coefficient Turbine Power Angular Electrical Speed Frequency Electromagnetic Power q-Axis current Per phase output voltage 7.4 31.4 rad/s or 300 rpm 0.462 2183 W 157 rad/s 7.45 31.66 rad/s or 302.4 rpm 0.463 2188.2 158.6 rad/s 25 Hz 2000 VA 25.25 Hz 2036.4 VA 5.3 A 240 V 5.35 A 242 V Validation of the model The simulation results presented above prove that the proposed model satisfactorily captures the real-time behaviour of the wind generator and mimics the system dynamics. The results of simulation have been verified against calculated results to further establish the validity of the developed model. It is to be noted that the only independent input to the whole system is wind speed, hence validation has been performed for two wind speeds, i.e. rated speed of 8.5 m/s and another token wind speed of 7 m/s. The expected results have been calculated using the formulae associated with the various components of the system whereas the simulated results have been obtained from the simulations of the MATLAB/Simulink model (also illustrated using the graphs and plots given above). Tip speed ratio for the particular wind speed has been estimated from the wind turbine characteristic plots. Comparison of simulation results with theoretical results have been shown in Table 3. The design data for the 2000 VA, 240 V AFPMG was fed to the model and, in turn, from the simulation results it has been shown that the model is able to successfully reproduce the generator output for its entire operational speed range. The validation chart shows that the simulated results match the estimated results with acceptable tolerance which validates the model. Conclusion An AFPMG has been designed considering SSDR structure with NS-SN pole configuration, suitable for variable speed wind energy systems and its basic design equations have been presented. This 8.5 m/s configuration has been found to have structural and functional advantages including zero iron losses, lighter weight and compact structure. The design output for the AFPMG rated at 2000 VA, 240 V, 10 pole, 3 phase 25 Hz, 5 rps is also listed. The mathematical model of the direct driven AFPMG along with the models developed for the HAWT, drive train, speed controller and pitch controller have also been presented. The detailed MATLAB/Simulink model implemented for each component has also been given. Simulations were carried out on the model for various wind conditions and the corresponding behaviour and response of the wind generator was analysed. It has been observed that the wind generator responds quickly to the varying wind conditions adapting to the optimal operating speed as per the available wind speed and performs satisfactorily in all cases. The action of pitch controller and 124 S.S. Laxminarayan et al. / Sustainable Energy Technologies and Assessments 19 (2017) 114–124 its effect on power control at high wind speeds has also been successfully demonstrated. From the simulation analysis, it can be safely concluded that AFPMG with SSDR (NS-SN) configuration is one of the best options for variable speed wind energy conversion systems. Acknowledgements I am deeply obliged to my co-authors for their valuable support in the research work and preparation of this paper. 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