PERFORMANCE OF SENSORLESS CONTROL OF PERMANENT MAGNET SYNCHRONOUS GENERATOR IN WIND TURBINE SYSTEM*

Transcription

1 Vol. 1(6), No. 2, 2016 POWER ELECTRONICS AND DRIVES DOI: /PED PERFORMANCE OF SENSORLESS CONTROL OF PERMANENT MAGNET SYNCHRONOUS GENERATOR IN WIND TURBINE SYSTEM OTR GAJEWSKI, KRZYSZTOF EŃKOWSKI Department of Electrical Machines, Dries and Measurements, Wrocław Uniersity of Science and Technology, ul. Smoluchowskiego 19, Wrocław, Poland, Abstract: The paper presents a sensorless control of permanent magnet synchronous generator (PMSG) in a ariable-speed wind energy conersion system. The system of wind turbine consists of PMSG and back-to-back power conerter. The back-to-back conerter system is composed of machine side conerter (MSC) and grid side conerter (GSC). In the control of MSC and GSC the methods of ector control hae been applied. For operation of MSC the method of Rotor Field Oriented Control (RFOC) with MPPT algorithm has been used. For estimation of angular rotor position and angular speed the flux linkage estimator with synchronous frame phase locked loop (SF-PLL) has been used. In the control of GSC the method of Voltage Oriented Control (VOC) has been considered. Simulation studies hae been carried out in order to ealuate the system of sensorless strategy. The results of simulation studies demonstrate the high efficiency and high accuracy of the sensorless control system considered. Keywords: wind turbine, PMSG, power conerters, sensorless algorithm, simulation studies 1. INTRODUCTION The number of application of wind energy conersion systems with permanent magnet synchronous generators (PMSGs) has increased rapidly in recent years [2], [10]. The wind turbine is one of the most important elements in wind energy conersion system. The wind turbine is responsible for conersion of the wind energy into mechanical rotational energy. Nowadays the total aerage power rating of installed wind turbines and generators has grown rapidly. To reduce the high maintenance cost of gearbox, a direct drien wind turbine system with low speed, multipole PMSG is a profitable technology [6], [9]. Reduction of cost and increasing reliability are the results of application of wind turbine systems without gearbox. Manuscript receied: March 0, 2016; accepted: May 18, 2016.

2 166 P. GAJEWSKI, K. EŃKOWSKI In order to conert electrical energy produced by the PMSG generator the power conerters should be applied. The conerter systems enable the control of speed and electromagnetic torque of the generator and allow the power flow to the AC grid to be adjusted. Different designs and combinations of power conerters lead to a wide ariety of wind energy conersion systems (WECS) [] [5]. The application of full capacity power conerter system allows the performance of the wind energy conersion system to be enhanced. With the use of this type of power conerter systems, the generator is completely decoupled from the grid and can be operated in full speed range. For conentional ector control of PMSG, the sensors of rotor position and angular speed are required. The information of generator rotor position makes it possible to orient correctly the stator current ector to the flux ector of permanent magnets. Howeer, these sensors are undesirable due to the cost, big size, maintenance and poor reliability [4]. For these reasons there are different ways to manage of this problem. In this paper, a sensorless control method based on stator and rotor flux linkage estimators is presented. Additionally, for design of angular rotor position and speed of PMSG the application of synchronous frame phase locked loop (SF-PLL) is considered. In the literature, usually the sensorless methods of control hae been mainly restricted to the control of motors, but not for generators with power electronic conerters, applied in wind energy systems. The application of sensorless control methods and systems should significantly improe the reliability and the cost of wind turbine systems [10]. 2. MODEL OF PERMANENT MAGNET SYNCHRONOUS GENERATOR The dynamic equations of three-phase PMSG can be expressed in synchronously rotating reference frame. The d-axis is aligned with the direction of the rotor flux ector and the q-axis is 90 ahead. The mathematical equations of the PMSG in frame can be described as follows [2], [], [5], [10] sd R s i i sd sd sd p e, (1) sd L i, (2) d sd q PM L i, (), (4) e np m where sd, components of the stator oltage ector in d and q axis; i sd, i components of the stator current ector in d and q axis, R s stator resistance; ψ sd, ψ direct

3 Performance of sensorless control of permanent magnet synchronous generator and quadrature ector components of the stator flux linkages; L d, L q direct and quadrature stator inductances; ψ PM flux linkage established by the permanent magnets; n p number of pole pairs of PMSG; p = d/dt differential operator; ω e, ω m electrical and mechanical angular speed of the PMSG. The electromagnetic torque of generator can be expressed as follows Te np [ PMi ( Ld Lq ) isdi ]. (5) 2 For a non-salient pole machine the stator direct and quadrature inductances L d and L q are approximately equal and L s = L d = L q. In this case, the equation of electromagnetic torque can be described in the following form Te np PMi. (6) 2 Equation (6) shows that the generator torque can be controlled by the quadrature component i of stator current ector. The equation of mechanical motion of the wind turbine system is gien as d Tt Te J m B f m (7) dt where T t mechanical torque of wind turbine, J the total inertia of the system, B f coefficient of iscous friction.. CONTROL OF BACK-TO-BACK CONVERTER SYSTEM The deeloped configuration and control circuits of direct drien WECS with PMSG are presented in Fig. 1. This configuration consists of a wind turbine, a PMSG generator, a back-to-back conerter system and a grid filter. The conerter system is composed of the Machine Side Conerter (MSC) and Grid Side Conerter (GSC). The PMSG is directly coupled to the wind turbine and connected to the MSC. The GSC is connected to the AC grid through the grid filter. In the control systems of both conerters, a ector control method has been applied. In the control system of the MSC the Rotor Field Oriented Control (RFOC) with sensorless method has been used. Additionally, in order to obtain the maximum power from the wind turbine, the optimal tip speed ratio MPPT algorithm has been included. In the control system of the GSC the Voltage Oriented Control (VOC) with control of instantaneous reactie and actie power has been applied. The control scheme of MSC consists of three control loops. The outer control loop regulates the angular generator speed ω m to follow the reference alue ω opt, which is

4 168 P. GAJEWSKI, K. EŃKOWSKI obtained by MPPT algorithm. In the control system the estimated alue of angular generator speed ω mest is used by application of sensorless control method. Machine Side Conerter (MSC) Grid Side Conerter (GSC) PMSG isa isb isc C d i i ga gb igc L g, R g ga gb gc ga gb gc s s is i s Sensorless Algorithm (Fig.2) mest est est abc αβ i sd αβ i L i e d s s L i e sd q est PM i SV PWM s s αβ αβ sd gd i sd i gd SV PWM g i gq g g gq igd i gd igq abc igq glgigq L i g g PLL gd g abc gd gq mest opt i i sd 0 dc dc 2 gd q g Fig. 1. The scheme of ariable speed wind turbine control system with direct-drien PMSG generator and back-to-back conerter system In order to obtain the MPPT condition at any wind speed the rotational speed of the wind turbine rotor should be regulated to the their optimal alue ω opt. The reference speed ω ref should be equal to ω opt and can be determined from the general equation of the mechanical output power of the wind turbine 2 w p P 0.5 R C (, ) (8) t where ρ air density; R radius of the turbine blade; w wind speed; C p power coefficient of the wind turbine; tip speed ratio; β blade pitch angle. This equation of wind turbine power (8) can be expressed as a function of the rotational speed ω m of wind turbine 5 C p (, ) 0.5 R m Pt. (9) In order to fulfil the MPPT algorithm should be replaced by opt, and C p (, β) = C pmax ( opt, β). After this operation the following expression is obtained

5 Performance of sensorless control of permanent magnet synchronous generator opt 5 topt /( 0,5 R C p max( opt, )) PMPPT / Kopt P (10) where K opt coefficient of wind turbine, P MPPT maximum wind turbine mechanical power at the wind speed considered. The MPPT algorithm can be achieed by keeping the optimal alue of tip speed ratio opt and the maximum alue of power coefficient C pmax. This condition allows the maximum mechanical power to be produced by wind turbine at wide range of wind speeds. To regulate the stator current ector components i, i sd the two inner control loops hae been used. In the RFOC strategy the reference alue of stator current ector component i sd is set to zero. This condition allows the torque per ampere ratio of PMSG to be maximized [9], [10]. The reference alue of stator current ector components i sd and i are compared with the measured stator current ector components i sd, i. The error signals are sent to two controllers. The required reference components of oltage ector of MSC sd and obtained from controllers are then transformed to the --system. The required switching signals for MSC are generated through Space Vector PWM modulation block (SV-PWM). Additionally, the decoupled circuits hae been applied to obtain high performance of the RFOC method considered. The control system of GSC is based on grid oltage ector orientation control (VOC). The angle position θ g of the grid oltage ector is obtained from the PLL (Phase Locked Loop) block. In the control system of GSC the three control loops with controllers hae been used. The outer control loop is responsible for keeping the constant alue of the dc-link oltage between MSC and GSC conerter. The output alue from this controller determines the reference alue of grid current ector component i gd. In order to obtain the operation of the unity power factor, the instantaneous reactie power is controlled directly by i gq and is set to zero alue. Then, the reference alues of grid current ector components i gd and i gq are compared with the measured and transformed grid phase currents i gd and i gq. The decoupled terms hae been applied in order to obtain high performances of VOC control system. The output alues from both controllers determine the reference alues of oltages gd and gq for the GSC. These reference oltages are then transformed to the --system and are sent to the block of SV-PWM. 4. SENSORLESS SPEED CONTROL OF PMSG SYSTEM The elimination of speed sensor or encoder makes it possible to reduce the costs and possibility of failure of the wind turbine system. The information of rotor position of PMSG generator is required to perform the control with rotor flux orientation [1], [2], [4], [7], [9].

6 170 P. GAJEWSKI, K. EŃKOWSKI The use of sensorless ector control is attractie for wind turbine applications with PMSG generators. The application of sensorless algorithm for estimation of rotor position and angular rotor speed allows reliability to be increased and maintenance requirements to be reduced. In this paper, the synchronous frame phase locked loop (SF-PLL) control technique has been used to obtain the rotor position and rotor speed. This technique is based on calculation of the components of the stator and rotor flux ectors. The oltage equations of PMSG obtained in -axis system can be rewritten in stationary - reference frame s s d R s i s s, (11) dt d R s i s s, (12) dt where sα, sβ components of stator oltage ector in - system, ψ sα, ψ sβ components of stator flux ector in - system, i sα, i sβ components of stator current ector in - system. Based on the mathematical model of PMSG the components of stator and rotor flux ector can be calculated as s ( s Rsis ) dt, (1) s ( s Rsis ) dt, (14) r r L i, (15) s s s s L i, (16) where ψ rα, ψ rβ rotor flux linkages in α and β axes. According to the practice the components of stator oltage ector sα, sβ hae been replaced in equations (1), (14) by their reference alues sα, sβ. The angle of the rotor flux ector e is also an electrical angle of rotor position of PMSG, which is required by the Rotor Field Oriented Control. The applied block scheme of flux linkage estimation (SF-PLL) of angular rotor position est and angular rotor speed ω est is presented in Fig. 2 [1], [2], [4], [8]. The presented block consists of oltage model for stator and rotor flux ector estimation and the SF-PLL block for estimation of angular rotor speed and position [2], [6], [8]. The basic scheme of the SF-PLL system is a feedback system with -controller tracking the angle position of rotor flux ector. The inputs of SF-PLL block are the rotor flux ector components in - system. The outputs of SF-PLL block are s s

7 Performance of sensorless control of permanent magnet synchronous generator the estimated angular position est of rotor flux ector and estimated angular rotor speed ω est of the rotor flux ector. The component of rotor flux ector ψ rq is forced to zero, so the SF-PLL system is synchronized with ψ rd component of rotor flux ector. Flux linkage estimation SF PLL (Synchronous Frame Phase Locked Loop) block 0 1/pb mest s s i s R S LPF LPF s s r r αβ est rq rd est est i s R S L S L S Fig. 2. The scheme of block estimation of angular rotor position θ e and angular rotor speed ω est The application of the integrators usually causes the limits of the effectieness of the oltage model and contributes to inaccuracy of estimation. For this reason, in the control system the integrator blocks hae been replaced by equialent low-pass filter blocks (LPF) of first order []. The integrator blocks in the oltage model may also cause problems due to unknown initial rotor position and sensitiity to influence of drifts [2], [6]. 5. SIMULATIONS RESULTS The control strategy of proposed wind energy conersion system has been tested by digital simulation in MATLAB/Simulink in order to ealuate the behaior of the proposed sensorless ector control. Digital simulation studies were made for the system with wind energy conersion system data and parameters which are presented in Tables 1 and 2. Table 1. Data and parameters of wind turbine Parameter Value Rated power P t 20 kw Rotor radius R 4.4 m Power coefficient C pmax 0.48 Air density kg/m

8 172 P. GAJEWSKI, K. EŃKOWSKI Table 2. Data and parameters of PMSG PMSG parameter Value Rated power; P N 20 kw Stator resistance; R s Stator -axis inductance; L d, L q 4.48 mh Number of pole pairs; n p 18 Rated speed; n N 211 rpm Stator rated phase current; I sn 5.1 A Total moment of inertia; J 1.8 kgm 2 Permanent magnet flux, PM 0.92 Wb Fig.. Waeforms of: (a) wind speed w ; (b) reference speed ω opt and estimated speed ω mest of PMSG; (c) measured e and estimated est rotor angle position; (d) error of measured speed ω m. and estimated speed ω mest ; (e) tip speed ratio ; (f) power coefficient C p of wind turbine The waeforms of simulation results are presented in Figs. and 4. Figure a shows the wind speed ariation for the period of a 10 s simulation. Figure b contains the estimated ω mest and reference ω opt alue of angular speed of PMSG. The estimated speed is obtained by the SR-PLL block. From this figure, it can be stated that control strategy based on the sensorless algorithm ensures high control accuracy and fast responses at wide ranges of speeds. Figure c shows the measured e and estimated rotor position est of PMSG. This figure confirms the high accuracy of the control strategy considered. The waeform errors of the measured and estimated angular speed of

9 Performance of sensorless control of permanent magnet synchronous generator PMSG are presented in Fig. d. It can be noticed that the errors between reference and estimated speed are close to zero. The waeforms of tip speed ratio and power coefficient are presented in Fig. e, f. From these waeforms, it can be noticed that the alues of tip speed ratio and power coefficient are kept at reference and maximum alues according to the operation of the MPPT algorithm. Figure 4a presents the waeforms of the stator current ector components i sd, i caused by the ariation of wind speed. The component i sd of the stator current ector is kept at zero alues in order to maximize the torque per ampere ratio [8]. The responses of the component i of the stator current ector hae similar waeforms as the ariations of the wind speeds. The waeforms of electromagnetic torque T e of PMSG and mechanical torque T t of wind turbine are shown in Fig. 4b. The responses of PMSG electromagnetic torque T e hae similar behaior as mechanical torque T t of wind turbine. This is caused by high accuracy and fast responses of control strategy. Figure 4c presents the waeform of the oltage dc in dc link. The instantaneous alues of oltage dc are quite constant across the wide range of ariations of wind speeds. The waeforms of instantaneous actie and reactie power p g, q g deliered to the AC grid are presented in Fig. 4d. From this figure it is clear that the reactie power is set to zero in order to perform the condition of unity power factor. The changes of instantaneous actie power deliered to the AC grid are in accordance with changes of the wind speeds. a) 20 i sd b) isd, i [A] i t [s] Te,Tt [Nm] T t T e t [s] c) 750 d) dc [V] 700 dc=690v t [s] pg, qg [W, ar]1 x q g p g t [s] Fig. 4. Waeforms of: (a) stator current ector components i sd, i sd ; (b) electromagnetic torque T e of PMSG and mechanical torque T t of wind turbine; (c) dc link oltage dc ; (d) instantaneous actie and reactie grid power p g, q g 6. CONCLUSIONS This paper has presented a wind energy conersion system with direct-drien PMSG. For estimation of angular rotor speed and rotor position the sensorless ector

10 174 P. GAJEWSKI, K. EŃKOWSKI control of PMSG using a flux linkage with SR-PLL has been used. The simulation results demonstrate the high accuracy of proposed sensorless control strategy. The application of sensorless control based on ector control has many adantages including higher reliability, simplicity and ease of implementation. Additionally, the application of ector control with MPPT algorithm allows conersion of the maximum power obtained from the wind turbine. The simulation results demonstrate that the tip speed ratio and power coefficient of wind turbine are kept at reference and maximum alues. The use of VOC for GSC makes it possible to perform the unity power factor. So, the instantaneous reactie power is kept at zero alue and the instantaneous actie power is only deliered to AC grid. The presented simulation results of the back-to-back wind energy conersion system with PMSG demonstrate high accuracy and fast responses of the ector control method considered. REFERENCES [1] BURGOS R.P., KSHIRSAGAR P., LIDOZZI A., JANG J., WANG F., BOROYEVICH D., RODRIGUEZ P., SUL SEUNG K., Design and Ealuation of a PLL-Based Position Controller for Sensorless Vector Control of Permanent-Magnet Synchronous Machines, 2nd Annual Conference on IEEE Industrial Electronics IECON, Paris, France, 2006, [2] DIAZ S.A., SILVA C., JULIET J., MIRANDA H., Indirect sensorless speed control of a PMSG for wind application, IEEE International Electric Machines and Dries Conference, IEMDC 09, [] ERRAMI Y., MAAROUFI M., OUASSAID M., Modeling and control strategy of PMSG based ariable speed wind energy conersion system, International Conference on Multimedia Computing and Systems (ICMCS), 2011, 1 6. [4] FAN S., WANG P., WEN C., A new sensorless control strategy used in direct-drie PMSG wind power system, 2nd IEEE International Symposium on Power Electronics for Distributed Generation Systems (PEDG), 2010, [5] GAJEWSKI P., EŃKOWSKI K., Control of a Variable Speed Wind Turbine System with PMSG Generator, Maszyny Elektryczne Zeszyty Problemowe, /2015 (107), [6] MOUSSA M.F., GABER M., ATTAR El., Vector control drie of permanent magnet motor without a shaft encoder, 12th International Middle-East Power System Conference, MEPCON 2008, [7] QIAO W., YANG X., GONG X., Wind Speed and Rotor Position Sensorless Control for Direct-Drie PMSG Wind Turbines, IEEE Transactions on Industrial Applications, 2012, 48, 1, 11. [8] RIZO M., RODRÍGUEZ A., BUENO F., RODRÍGUEZ J., Robustness analysis of Wind Turbines based on PMSG with sensorless ector control, IEEE Industrial Electronics 6th Annual Conference Society, IECON 2010, [9] SILVA C., ASHER M., SUMMER M., Hybrid rotor position obserer for wide speed-range sensorless PM motor dries including zero speed, IEEE Transactions on Industrial Electronics, 2006, 5, [10] WU B., LANG Y., ZARGARI N., KOURO S., Power Conersion and Control of Wind Energy, John Wiley & Sons, Inc., 2011.