Title: Implementation of reactive power‐based MRAS for sensorless speed control of brushless doubly fed reluctance motor drive
Abstract: IET Power ElectronicsVolume 11, Issue 1 p. 192-201 Research ArticleFree Access Implementation of reactive power-based MRAS for sensorless speed control of brushless doubly fed reluctance motor drive Karuna Kiran, Karuna Kiran Department of Electrical Engineering, Indian Institute of Technology (Indian School of Mines), Dhanbad, IndiaSearch for more papers by this authorSukanta Das, Corresponding Author Sukanta Das [email protected] Department of Electrical Engineering, Indian Institute of Technology (Indian School of Mines), Dhanbad, IndiaSearch for more papers by this author Karuna Kiran, Karuna Kiran Department of Electrical Engineering, Indian Institute of Technology (Indian School of Mines), Dhanbad, IndiaSearch for more papers by this authorSukanta Das, Corresponding Author Sukanta Das [email protected] Department of Electrical Engineering, Indian Institute of Technology (Indian School of Mines), Dhanbad, IndiaSearch for more papers by this author First published: 01 January 2018 https://doi.org/10.1049/iet-pel.2017.0104Citations: 16AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract The present work introduces the concept of classical reactive power (Q)-based model reference adaptive system (MRAS) for the speed estimation and control of low-cost BDFR motor drive. The reasons behind such choice for this drive's control are: (i) MRAS-based controllers can inherently take care of the machine parameter variations which had been a challenging issue with the other available sensorless speed estimation strategies and (ii) the employment of Q as a functional candidate inevitably makes the formulation immune to the variations in stator resistance. The experimental assessment, in this respect, confirms these claims. Furthermore, the analytical validation of Popov's hyperstability criteria on the proposed controller, confirms the drive's overall stability within the investigated speed control range. The speed control performance is examined in MATLAB/Simulink. The simulation results are further validated by a real-time implementation using dSPACE-1103-based 1.6 kW BDFR machine prototype. Nomenclature d–q primary and secondary currents (A) d–q primary and secondary voltages (V) d–q primary and secondary winding fluxes (Wb) primary and secondary winding resistances (Ω) primary and secondary winding self-inductances (H) mutual flux (Wb) and inductance (H) electromagnetic and load torque (Nm) number of rotor poles, primary and secondary pole pairs primary and secondary supply angular frequencies (rad/s) rotor electrical and mechanical angular speed (rad/s). Herein after denoted as speed (rad/s) leakage factor error signal time derivative operation rotor, primary and secondary reference frame positions Subscripts primary/secondary-phase quantities Superscripts rotating and stationary reference frame quantity *, ^ reference/command and estimated quantities 1 Introduction In recent years, brushless doubly fed reluctance machines (BDFRMs) have shown better suitability for the applications such as wind power generation [1, 2] and pump-type appliances [3, 4] to meet narrow variable speed requirement. Greater robustness, simple but efficient speed control strategies, lower capital investment and maintenance cost than the other slip-power recovery machines [5] [such as BDF inductance machines (BDFIMs)] are the major grounds behind their growing popularity. A detailed comparative study between BDFIM and BDFRM is available in [6]. The stator of BDFRM consists of two electrically and magnetically isolated three-phase windings: primary and secondary. The electromagnetic (EM) torque production in the machine depends on the magnetic coupling between the windings through a position-dependent highly salient cageless reluctance rotor with its number of poles equal to the total number of stator pole pairs [7, 8]. The primary winding of BDFRM is usually fed from the grid, whereas the secondary winding is powered by a fractionally rated variable-voltage-variable-frequency converter for bi-directional power flow between the grid and the machine under subsynchronous, synchronous and supersynchronous speeds [3, 9, 10]. Various methodologies such as scalar control [3, 11], vector or field-oriented control (VC/FOC) [3, 9-12], direct torque (DTC) and secondary flux [11, 13] or primary reactive power [14, 15] control, direct power control [16] and variable structure control [2] have been addressed in the literature to achieve different control objectives of BDFRM-based drives. A comparative and progressive work with respect to these control strategies is also available in [11, 12]. However, the execution of these closed-loop controls relies on the rotor position/speed feedback. Moreover, a limited number of research efforts are put forward for the sensorless speed control of such drives [11-13, 17]. Except for a very recent work based on sensorless FOC of BDFRM [12], the remaining works are primarily concerned with the DTC-based strategies. In addition, model reference adaptive system (MRAS)-based control techniques have been overlooked yet for this machine. The MRAS-based approaches are simple in formulation and implementation; and inherently take the machine parameter variations into account with minimum computational effort [18]. Since, MRAS-based control techniques have been used satisfactorily in the other AC drives, these techniques are also resourceful for BDFRM drive as well. Depending on the functional candidate used for the formulation of the error, a number of MRASs based on either rotor flux [19, 20] or back electromotive force [21] or reactive power [22-24] or active power or EM torque [25] or [26] are developed for induction machines (IMs). A detailed review of different MRAS-based controllers for IM drive is presented in [27]. Hence, the present work intends to introduce the MRAS-based new approach for sensorless speed control of BDRFM (as motor) drive employing secondary-side reactive power as the functional candidate under primary field orientation. The reference model of the proposed MRAS is formulated with secondary winding instantaneous reactive power, whereas the adaptive model is expressed in the form of its steady-state value. Since, the formulation of the proposed scheme does not involve secondary flux evaluation, drift and saturation-related challenges associated with the integrator operation and resistance drop effects are eliminated naturally. Consequently, a satisfactory performance around the synchronous speed at the low-secondary frequency region has been achieved. The Popov's hyperstability tests on the controller also confirm the drive's overall stability. The proposed controller's immunity in terms of the sensitivity on the estimated speed against secondary transient inductance variation is also confirmed experimentally. All the simulation studies, in this respect, are done in MATLAB/Simulink. The proposed scheme is experimentally validated by a dSPACE-1103-based BDFRM laboratory prototype. The investigations approve the promising potential of Q-MRAS to work under a significant variation (± 25%) of speed around the synchronous speed maintaining the drive's stability. The outline of this paper is as follows: Section 2 presents the basic equations governing the machine modelling and sensorless control procedure under primary field orientation satisfying the maximum torque per inverter ampere (MTPIA) strategy in brief. Section 3 elaborates the formulation of the proposed Q-MRAS speed estimator for BDFRM drive. A detailed stability analysis of the drive, in this regard, is presented in Section 4. Sections 5 and 6 present the MATLAB/Simulink studies and relevant experimental validation with a dSPACE-1103-based BDFRM laboratory prototype, respectively. Finally, Section 7 concludes this present work. 2 Mathematical illustration of BDFRM The following sub-sections present the basic equations governing the machine modelling andsensorless control procedure under primary field orientation satisfying the MTPIAstrategy in brief. 2.1 Dynamic model of BDFRM Assuming motoring convention, d and q components of primary and secondary voltages and fluxes of BDFRM in dp − qp and ds − qs reference frames rotating at and , respectively are represented as below equation [8] (Fig.1a): (1a) (1b) (1c) (1d)where (2a) (2b) (2c) (2d)Moreover, the inter-relations of angular speed, angular position and pole number for EM torque production are given by Betz and Jovanovic [8]. Rotor speed (3a)Rotor position (3b)Rotor number of poles (3c)EM torque (3d) 2.2 Sensorless control under primary field orientation Fig. 1a demonstrates the position of the primary flux vector in the stationary reference frame aligned with the dp-axis of primary reference frame rotating at under primary field orientation [10]. Fig. 1Open in figure viewerPowerPoint BDFRM control under primary field orientation (a) Phasor diagram, (b) Schematic diagram of BDFRM drive with Q-MRAS-based speed estimator The primary flux in stationary reference frame can be estimated by using the primary-phase measurements as (4)To address the DC offset-related problems due to pure integration, several approaches have been adopted in the literature [28]. In the present work, the DC offset compensation in (4) is accomplished by a conventional three-phase phase-locked loop (PLL) while estimating [29]. In PLL, the output of the phase detector is a measure of the phase difference between the input signal (with offset and noise) and the signal of voltage-controlled oscillator (VCO). This difference voltage, i.e. the control voltage (filtered by an adaptive cut-off-based loop filter) on the VCO changes the frequency in a direction that reduces the phase difference between the input signal and the local oscillator. Furthermore, the loop filter (in PLL) with its characteristic smaller bandwidth ensures DC offset compensation. The thus obtained is used for estimating by (3b). Furthermore, under primary field orientation (Fig. 1a), the quadrature component of primary flux vanishes; resulting in the following modified expressions of (2a), (2b) and (3d), respectively: (5a) (5b) (6)Using (5), secondary d–q currents employed as the control feedback in Fig. 1b are estimated as (7a) (7b)Fig. 1b shows a schematic diagram of BDFRM drive with Q-MRAS speed estimator under primary field orientation. In the proposed control scheme, q-component of secondary current reference is directly obtained using a speed proportional–integral (PI) controller because of a linear relationship between and (6). This modification upholds effectively the parameter mismatch by appropriately tuning the current controller gains. 2.3 Maximum TPIA MTPIA scheme allows minimum inverter loading and higher machine efficiency by reducing secondary winding copper and switching losses for a given load torque. This control objective would be satisfied if the secondary current is only torque producing [10], i.e. (8) 3 Formulation of Q-MRAS MRAS is an adaptive control approach for online rotor speed/position estimation applicable for wide-speed range operation of drives. The objective of the present work is to design an adaptive controller that ensures the resemblance of the behaviour of the controlled plant (adaptive model, dependent on the quantity to be estimated) with that of a desirable model (reference model, free from the quantity to be estimated) despite the uncertainties in the plant parameters and operating conditions. A basic structural block diagram of the proposed Q-MRAS speed estimator with relevant equations of the reference and adaptive models monitored by an adaptation mechanism is depicted in Fig. 2a. The reference model in the proposed control scheme is formulated by employing instantaneous reactive power of the secondary winding as (9)where and are given by (7) and the reference voltage signals are generated by the PI controllers in the control scheme (Fig. 1b) as (10a) (10b)where is the transfer function of speed PI controller and is the transfer function of current PI controllers. Fig. 2Open in figure viewerPowerPoint Q-MRAS scheme for speed estimation of BDFRM drive (a) Structural diagram of Q-MRAS, (b) Modified structure of Q-MRAS for the stability analysis, (c) Closed-loop representation of Q-MRAS-based speed estimator The model formulation in the proposed scheme is done in the respective rotating reference frames. are used because the actual secondary voltage signals approach the respective reference values at the steady state. These not only eliminate the need of external secondary current and voltage sensors but also improve the speed estimation quality because of the superior quality of reference voltage signals. Moreover, the ripple-free primary current further ensures good quality of as well. Substituting (1c)–(1d) into (9), the new expression of reactive power can be developed as (11)In steady state, the derivative terms vanish. Substituting (2c)–(2d) into (11), an approximate expression for Q is established as (12)Substituting (7b) into (12) (13)Equation (13) contains the rotor speed term and is more sophisticated than (11)–(12) because the secondary flux computation and derivative operations are eliminated. Additionally, the absence of derivative terms at steady state eliminates the effect of computational noise. Hence, (13) is preferred as the adaptive model. As per the MRAS-based control principle, the error signal generated by comparing the two models (9) and (13) is fed to the adaptive mechanism for the convergence of the estimated quantity to that of the reference value (Fig. 2a). Therefore, the reactive power error signal is obtained as (14a) (14b)The adaptive mechanism of MRAS plays a significant role in deciding the convergence of the functional candidate (Q) obtained by the adaptive model with the reference model and the overall stability of the system [30]. 4 Stability study of the proposed scheme To investigate the stability of the proposed controller, Popov's criteria [31, 32] followed by time-domain analysis using root loci are examined in the following sub-sections. 4.1 Overall stability analysis using Popov's hyperstability criteria To perform the overall stability, the structure of the proposed Q-MRAS (Fig. 2a) is reconfigured as Fig. 2b, where the error generation block is split into linear time-invariant feedforward and non-linear time-varying feedback blocks distinctly. To satisfy the hyperstability, the stability of each block is assessed independently. Strict positive realness (SPR) of the feedforward path transfer function ensures the stability of the feedforward path. This is confirmed by incorporating a compensator 'D' in the feedforward path. This error manipulator ('D') confirms the SPR property by setting the sign of . Furthermore, the stability of the feedback path is ensured by confirming the Popov's integral inequality criterion as follows. The modified error (14) can be expressed as (Fig. 2b) (15)Comparing (14) and (15) (16a) (16b)Again, from Fig. 2b (17) (18a) (18b)where is the transfer function of the PI controller of the adaptation mechanism and is the output of block 'D'. Again (18c)The Popov's integral inequality criterion for the stability of non-linear feedback block (Fig. 2b) is expressed as (19)where is a positive real constant. Using (17), (18a) and (18b) (20)Hence (21a)where (21b)Now, substituting (18b) and (21a) on the left-hand side of (19) and further simplifying, the integral inequality relation becomes (22)The derived inequality (22) satisfies the Popov's integral inequality criterion (19) for the adaptive feedback mechanism (Figs. 2a and b) as well. Therefore, the stability of the complete system is confirmed. 4.2 Verification of stability using root locus The time-invariant dynamic equations as described in Section 2 are used for the stability analysis of the proposed drive system. The state-space model of the BDFRM in terms of the primary and secondary currents and voltages can be expressed as (23a) (23b)where , , , , , , and . Using (10) (24a) (24b)Using the small signal analysis with respect to an operating point, , (23) can be represented as (25a)Subsequently (25b)and (25c)where ( vary over 1–4). For a small perturbation in speed (as ), the changes in A (23a) and u (24a) are obtained as (26a) (26b)Substituting B (23a), C (23b), (26a) and (26b) into (25c) and rearranging, following relations can be obtained: (27)where (28a) (28b) (28c) (28d) (28e) (28f)Now, using (14) and (27), the small signal error with respect to (w.r.t.) the change in the speed can be expressed as (29)where (30a) (30b) (30c)Using (29), the closed-loop transfer function of Q-MRAS-based speed estimator (Fig. 2c) can be obtained as (31)To reaffirm the stability of the drive, root loci are drawn at the two operating points as mentioned in Figs. 3a and b captions. The poles and loci lie completely in the left half of the s-plane, thereby depicting the stability of the drive at these operating points. Fig. 3Open in figure viewerPowerPoint Stability and sensitivity analyses (a) Root locus for the drive system at supersynchronous speed , (b) Root locus for the drive system at subsynchronous speed , (c) Speed profile for variation w.r.t. nominal value by −5.5%, (d) Speed profile for variation w.r.t. nominal value + 5.5% 4.3 Sensitivity analysis Incorrect measurement of machine parameters may lead to the erroneous performance of the proposed speed estimator, and hence their impact on the estimated speed is explored hereunder experimentally. Under constant primary flux operation of BDFRM drive, the variations in the primary inductance and the magnetising inductance are not significant. In addition, the formulation of Q-MRAS [(9) and (13)] is inherently independent of stator resistance terms; hence, the speed estimation is quite insensitive against the variations in these parameters. However, the adaptive model (13) of the Q-MRAS may be influenced by the change in secondary transient inductance . Therefore, the quantitative eccentricity in the speed profile due to the mismatch of in the controller to that of the nominal value is analysed in this section [33]. Figs. 3c and d depict that the oscillations in the estimated and actual speeds are amplified slightly for the variation in by ± 5.5%. Moreover, the magnitude of oscillation in Fig. 3c is more than that in Fig. 3d. Table 1 shows the global mean error corresponding to the different variations in . Hence, the experimental results reveal that the variation in even by ± 5.5% do not impose much threat to the controller performance while estimating the speed. Table 1. Global mean error in speed estimation with the variation in secondary transient inductance Transient inductance Global mean error in speed, rad/s 0.189 0.08 0.194 0.068 0.20 (nominal) 0.05 0.205 0.06 0.211 0.65 5 Simulation results The BDFRM drive with the adopted control criteria (Section 2) and newly introduced speed estimation technique (Section 3) as demonstrated by Fig. 1b is simulated in MATLAB/Simulink. The motor drive's performance at half of the rated load torque (∼8 Nm) with speed variations of ± 25% around the synchronous speed (78.5 rad/s) is investigated. The parameters and the rating of the motor used for the study are given in the Appendix. A few simulation results are presented in this section. The performance of the proposed drive system for the speed-riding through supersynchronous–synchronous–subsynchronous and vice versa involving entire speed control range is depicted in Figs. 4 and 5. As depicted in Fig. 4a, a trapezoidal speed command with ± 19.5 rad/s (i.e. ± 25% of synchronous speed) speed range around the synchronous speed (78.5 rad/s) is considered. The estimated and the actual speeds follow the reference speed maintaining smooth transitions and operations within this defined range. The estimation error in the rotor speed as depicted in Fig. 4b is about 0.05 rad/s which sometimes surges upto 2 rad/s during transient which is quite acceptable in practical applications. Fig. 4c shows the superimposed estimated and measured rotor positions confirming accurate primary field orientation. It is important to mention here that the shaft encoder is used for the instrumentation purpose only but not in the control process. The absolute position error estimates corresponding to Fig. 4c have been portrayed in Fig. 4d. The estimates are small and within an acceptable range with the mean estimation error of 3° which exceeds occasionally beyond 10° during the transitory periods only. The decoupled nature of primary and secondary d–q current components are shown in Figs. 5a and b, respectively. The constant d-axis primary and secondary currents validate the correctness of primary field orientation (as described in Section 2). In addition, the zero d-component of the secondary current (Fig. 5b) demonstrates the successful validation of the MTPIA condition (8). The positive active components of currents ipq and isq (Figs. 5a–b) confirm that the power is being transported from the grid. Moreover, the q-axis current components maintain constant values as determined by the constant load torque magnitude, except during the transient (acceleration/deceleration). Fig. 5c reveals the zero-frequency DC nature of the secondary-phase currents during synchronous speed and the phase sequence reversal during the ride through from the supersynchronous to the subsynchronous speed. The phase sequence reversal is also supported by the secondary frame position estimates as depicted in Fig. 5d. Fig. 4Open in figure viewerPowerPoint Simulation results for 8 Nm load torque (a) Reference, estimated and actual speeds, (b) Speed estimation error, (c) Rotor position estimation, (d) Absolute rotor position errors Fig. 5Open in figure viewerPowerPoint Simulation results for 8 Nm load torque (a) d and q Axes primary currents, (b) d and q Axes secondary currents, (c) Secondary three-phase currents displaying phase sequence reversal from supersynchronous to subsynchronous speed, (d) Secondary frame position demonstrating phase sequence reversal from supersynchronous to subsynchronous speed 6 Experimental verifications Fig. 6 shows the dSPACE-1103-based 6/2 pole BDFRM prototype. The simulation results as obtained in the previous section are experimentally validated by a real-time implementation and are demonstrated in Figs. 7 and 8. The proposed estimation algorithm is executed successfully with 8 kHz sampling frequency using MATLAB/Simulink interface. The primary windings are directly fed from 415 V, 50 Hz mains, whereas the secondary windings are supplied through an space vector pulse-width modulation inverter (about 30% of its rating) operating with a switching frequency of 2.5 kHz. The machine is started and run with half of the full load torque. During start-up, secondary windings are shorted to avoid the inverter overcurrent and eliminate inrush current as in the case of wound rotor IMs. As the motor gains about 30% of synchronous speed, the control mechanism is enabled. It is evident that only two sensors (for primary voltage and current measurements) are sufficient to execute the proposed control scheme. The speed control performance of the proposed estimator is quite satisfactory at synchronous, supersynchronous and subsynchronous speeds including transitions from one operating point to the other (Fig. 7a). Fig. 7b shows that the error between the actual and estimated speeds is within an acceptable limit. Figs. 7c and d demonstrate rotor positions (actual and estimated) and position error, respectively. Figs. 8a and b confirm the satisfactory fulfilment of primary field orientation and MTPIA conditions, respectively. The q components of currents, in this case, are higher than those of the corresponding simulation results to account for the machine core losses. Fig. 8c demonstrates the phase reversal during the transition from the supersynchronous to subsynchronous speed and Fig. 8d shows the corresponding secondary position estimate. All these results satisfactorily validate the simulation results as obtained in Figs. 4 and 5. Similarly, Figs. 9 and 10 describe satisfactory performance of the drive system in generating mode under torque disturbance condition as well. Fig. 6Open in figure viewerPowerPoint Experimental setup of BDFRM prototype Fig. 7Open in figure viewerPowerPoint Experimental results for 8 Nm load torque (a) Reference, estimated and actual speeds, (b) Speed estimation error, (c) Rotor position estimation, (d) Absolute rotor position errors Fig. 8Open in figure viewerPowerPoint Experimental results for 8 Nm load torque (a)d and q Axes primary currents, (b)d and q Axes secondary currents, (c) Secondary three-phase currentsdisplaying phase sequence reversal from supersynchronous tosubsynchronous, (d) Secondary frame position demonstratingphase sequence reversal from supersynchronous to subsynchronousspeed Fig. 9Open in figure viewerPowerPoint Experimental results for −8 Nm load torque under disturbance (a) Reference, estimated and actual speeds, (b) Speed estimation error, (c) Rotor position estimation, (d) Absolute rotor position errors Fig. 10Open in figure viewerPowerPoint Experimental results for −8 Nm load torque under disturbance (a)d and q Axes primary currents, (b)d and q Axes secondary currents, (c) Secondary three-phase currentsdisplaying phase sequence reversal from supersynchronous tosubsynchronous, (d) EM and load torque 7 Conclusion In the present work, the main idea, design aspects and experimental verification of a versatile online rotor speed estimation technique, MRAS, utilising secondary-side reactive power have been introduced for encoder-less primary field-oriented BDFRM drive. The mathematical formulation of the Q-MRAS is done in rotating frame, thereby eliminating the need of extra frame conversions. Computer simulations in MATLAB/Simulink, real-time experimentations, associated sensitivity and stability analysis confirm the reliability of the speed estimator in controlling the speed of BDFRM drive in the range ± 25% around the synchronous speed. In fact, the speed variation under investigation is adequate for the target applications. The key advantages of the proposed MRAS-based sensorless speed estimation techniques are: Stable operation for the entire speed control range including low-secondary frequency region down to the synchronous speed. Amenable interface with the hardware platform as neither the injection of additional signals nor any special inverter switching strategies are required unlike many other sensorless schemes. Robust estimator performance because of the selection of reactive power as the functional candidate for the generation of the error signal for the adaptation mechanism. The reference model is independent from machine parameters. Moreover, the adaptive model is free from differentiation operator, thereby making the scheme immune to noise. The formulation is also independent of the temperature-dependent stator resistance variations. Since, the sensors are employed only for the measurement of constant and inverter switching ripple-free grid voltages and currents; hence, estimation quality is improved. Owing to the less number of transducers and low filtering requirements, the cost in implementation is optimised. This, otherwise, makes the drive more reliable and robust. 8 Acknowledgments Science and Engineering Research Board (Department of Science and Technology), GOI for providing financial grant under Young Scientist Scheme (YSS/2015/001670). 10 Appendix. Machine parameters and ratings Rated shaft power: 1.6 kW; current rating: 3 A/2.3 A; voltage rating: 415 V/415 V; nominal frequency of primary supply: 50 Hz; number of rotor poles, primary and secondary winding pole pairs: 4, 6 and 2, respectively; synchronous speed: 78.5 rad/s; primary and secondary winding resistances: 10.2 and 12.8 Ω, respectively; primary and secondary winding self and mutual inductances: 0.30, 0.54 and 0.25 H; and rotor inertia: 0.035 kg m2. 9 References 1Song W.K., and Dorrell D.G.: ' Implementation of improved direct torque control method of brushless doubly-fed reluctance machines for wind turbine'. IEEE Int. Conf. Industrial Technology (ICIT), 2014, Busan, February—March 2014 2Valenciaga F., and Puleston P.: 'Variable structure control of a wind energy conversion system based on a brushless doubly fed reluctance generator', IEEE Trans. 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Publication Year: 2018
Publication Date: 2018-01-01
Language: en
Type: article
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