Online Adaptive Compensation Scheme for Dead-Time and Inverter Nonlinearity in PMSM Drive

14th IFAC Conference on Programmable Devices and Embedded 14th IFAC Conference on Programmable Devices and Embedded Systems 14th IFAC IFAC Conference on Programmable Devices Devices and and Embedded Embedded 14th Systems Conference on Programmable Available online at www.sciencedirect.com October 5-7, 2016. Brno, Czech Republic Systems Systems October 5-7, 2016. Brno, Czech Republic October October 5-7, 5-7, 2016. 2016. Brno, Brno, Czech Czech Republic Republic

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Online Adaptive Compensation Scheme for Online Online Adaptive Adaptive Compensation Compensation Scheme Scheme for for Dead-Time and Inverter Nonlinearity in Dead-Time and Inverter Nonlinearity in Dead-Time and Inverter Nonlinearity in PMSM Drive PMSM PMSM Drive Drive Ludek Buchta ∗∗ Ludek Buchta ∗∗ Ludek Ludek Buchta Buchta ∗ ∗ Faculty of Electrical Engineering and Communication, Technicka Faculty of Electrical Engineering and Communication, ∗ ∗ Faculty of Electrical Electrical Engineering and [email protected]). Communication, Technicka Technicka 3058/10, Czech Republic (e-mail: FacultyBrno, of Engineering and Communication, Technicka 3058/10, Brno, Czech Republic (e-mail: [email protected]). 3058/10, 3058/10, Brno, Brno, Czech Czech Republic Republic (e-mail: (e-mail: [email protected]). [email protected]).

Abstract: The paper focuses on a novel online dead-time compensation strategy for vector Abstract: The paper focuses on a novel online dead-time compensation strategy for vector Abstract: The on online dead-time compensation strategy for vector controlled permanent-magnet proposed approach composed Abstract: The paper paper focuses focusessynchronous on aa novel novel motor online(PMSM). dead-timeThe compensation strategyis for vector controlled permanent-magnet synchronous motor (PMSM). The proposed approach is composed controlled permanent-magnet synchronous motor (PMSM). The proposed approach is composed of two parts. The first adaptive parameter-independent part is based on the monitoring of controlled permanent-magnet synchronous motor (PMSM). The proposed approach is composed of The adaptive parameter-independent part is the of of two two parts. parts. The first first adaptive parameter-independent part is based based ison ondefined the monitoring monitoring of harmonic distortion in the d-axisparameter-independent current. Consequently, part the criterion as the sum of two parts. The first adaptive is based on the monitoring of harmonic distortion in the d-axis current. Consequently, the criterion is defined as the sum harmonic distortion in the d-axis current. Consequently, the criterion is defined as the sum twocurrent. zero-crossing points ofthe thecriterion phase currents. This criterion of squareddistortion id currentinbetween harmonic the d-axis Consequently, is defined as the sum of squared id current between two zero-crossing points of the phase currents. This criterion current between two zero-crossing points of currents. This criterion of squared is PI controller output is slowly which used to of minimized squared iidd by current betweenand twothe zero-crossing pointstime-varying of the the phase phasevoltage, currents. Thisis criterion is minimized by PI controller and the output is slowly time-varying voltage, which is used to is minimized by PI controller and the output is slowly time-varying voltage, which is to calculate the compensation voltages. This approach is extended by observer of persistent voltage is minimized by PI controller and the output is slowly time-varying voltage, which is used used to calculate the compensation voltages. This approach is extended by observer of persistent voltage calculate the thethat compensation voltages. Thisofapproach approach is extended by observer observer ofproposed persistent voltage disturbance is based on the model PMSM. is The effectiveness of theof approach calculate compensation voltages. This extended by persistent voltage disturbance that is based on the model of PMSM. The effectiveness of the proposed approach disturbance that based on of is verified through simulations and experiments. disturbance that is isthe based on the the model model of PMSM. PMSM. The The effectiveness effectiveness of of the the proposed proposed approach approach is verified through the simulations and experiments. is verified through the simulations and experiments. is verified through the simulations and experiments. © 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Keywords: Dead-time compensation; voltage disturbance observer; voltage distortion; Keywords: Dead-time compensation; voltage disturbance observer; voltage distortion; Keywords: Dead-time compensation; voltage disturbance permanent-magnet synchronous motor (PMSM); Keywords: Dead-time compensation; voltage disturbance observer; observer; voltage voltage distortion; distortion; permanent-magnet synchronous motor (PMSM); permanent-magnet permanent-magnet synchronous synchronous motor motor (PMSM); (PMSM); 1. INTRODUCTION (Hao and Junzheng (2011)) or (Zhao et al. (2015)). In (Lee 1. INTRODUCTION INTRODUCTION (Hao and (2011)) et (2015)). In (Lee 1. (HaoAhn and Junzheng Junzheng (2011)) or or (Zhao (Zhao et al. al. is (2015)). In (Lee and (2014)), compensation method based In on(Lee the 1. INTRODUCTION (Hao and Junzheng (2011)) or (Zhao et al. (2015)). and Ahn (2014)), compensation method is based on the and Ahn (2014)), compensation method is based on the complex calculation and analysis method of switching voltages in Industrial drives are frequently controlled by the pulse- and Ahn (2014)), compensation is based on the complex calculation and analysis of switching voltages in Industrial drives are frequently controlled by the pulsecomplex calculation and analysis of switching voltages in Industrial drives are frequently controlled by the pulseeach switching interval according to the equivalent circuit. width modulated (PWM) voltagecontrolled source inverters (VSI). complex calculation and analysis of switching voltages in Industrial drives are frequently by the pulseeach switching interval according to the equivalent circuit. width modulated (PWM) voltage source inverters (VSI). each switching interval according to the equivalent circuit. width modulated (PWM) voltage source inverters (VSI). The compensation approach in (Dafang et al. (2014)) Unfortunately, these PWM inverters produce voltage diseach switching interval according to the equivalent circuit. width modulated (PWM) voltage source inverters (VSI). compensation approach in et Unfortunately, these these PWM PWM inverters inverters produce produce voltage voltage disdis- The The compensation approach in (Dafang (Dafang et al. al. (2014)) (2014)) Unfortunately, is based on feedforward strategies and reconstruction of tortion caused these by undesirable non-linear characteristics. compensation approach in (Dafang et al. (2014)) Unfortunately, PWM inverters produce voltage dis- The is based on feedforward strategies and reconstruction of tortion caused caused by by undesirable undesirable non-linear characteristics. is based on feedforward strategies and reconstruction of tortion non-linear characteristics. thebased phaseoncurrents. Another methods are based on a deThe most significant non-linearity is dead-time. It is nec- is feedforward strategies and reconstruction of tortion caused by undesirable non-linear characteristics. the phase currents. Another methods are based on a deThe most significant non-linearity is dead-time. It is necthe phase currents. Another methods are based on a deThe most significant non-linearity is dead-time. It is nectailed nonlinear physical model of the power converter, essarily inserted in the gate signals of switches to prevent the phase currents. Another methods are based on a deThe most significant non-linearity is dead-time. It is necnonlinear physical model of the power converter, essarily inserted inserted in in the the gate gate signals signals of of switches switches to to prevent prevent tailed tailed physical of power converter, essarily a nonlinear model is presented in (Bedetti al. (2014)). The short circuit of the DCgate link signals caused of byswitches simultaneous con- such tailed nonlinear physical model model of the theet power converter, essarily inserted in the to prevent such a model is presented in (Bedetti et al. (2014)). The short circuit of the DC link caused by simultaneous consuch a a model model is presented presented in (Bedetti (Bedetti et etare al.derived (2014)).based The short circuit of the DC link caused equations of the voltage compensation duction of both power switches in by thesimultaneous same leg of conthe such is in al. (2014)). The short circuit of the DC link caused by simultaneous conof the voltage compensation are derived based duction of of both both power power switches switches in in the the same same leg leg of of the the equations equations of the voltage compensation are derived based duction on the model. The quality of compensation depends on VSI. Unfortunately, during the dead-time period, both equations of the voltage compensation are derived based duction of both power switches in the same leg of the the model. The quality of compensation depends on VSI. Unfortunately, Unfortunately, during during the the dead-time dead-time period, period, both both on on the model. The quality of compensation depends on VSI. precision estimation of the inverter parameters, which switches cease conduct and the the dead-time phase current can both flow the on the model. The quality of compensation depends on VSI. Unfortunately, during period, the precision estimation of the inverter parameters, which switches cease conduct and the phase current can flow the precision estimation of the inverter parameters, which switches cease conduct and the phase current can flow can be problematic. Effects of inverter snubber and paraonly through free wheeling diodes. In this case, the control the precision estimation of the inverter parameters, which switches cease conduct and the phase current can flow can be problematic. Effects of inverter snubber and paraonly through through free free wheeling wheeling diodes. diodes. In In this this case, case, the the control control sitic can be be problematic. Effects of inverter inverter snubber and paraparaonly capacitance during switching of power elements are of switches lost. The output dependent on can problematic. Effects of snubber and only throughis wheeling diodes.voltage In this is case, the control capacitance during switching of power elements are of switches switches isfree lost. The output output voltage is dependent on sitic capacitance elements are of is lost. The voltage is dependent not considered induring most switching papers. Itof ispower assumed that the the directionisoflost. the The phaseoutput current. Although dead-timeon is sitic sitic capacitance during switching of power elements are of switches voltage is dependent on not considered in most papers. It is assumed that the the direction of the phase current. Although dead-time is not considered in most papers. It is assumed that the the direction of the phase current. Although dead-time is transition from turn-on to turn-off state or conversely is very short it causes distortion of the output voltage of not considered in most papers. It is assumed that the the direction of the phase current. Although dead-time is from turn-on to turn-off state or conversely is very short short it it causes causes distortion distortion of of the the output output voltage voltage of of transition transition from turn-on to turn-off state or conversely is very infinitely fast. Papers (Zhang and Xu (2014); Morohoshi the VSI. This behavior complicates application of conventransition from turn-on to turn-off state or conversely is very short it behavior causes distortion of the output of voltage of infinitely fast. Papers (Zhang and Xu (2014); Morohoshi the VSI. This complicates application conveninfinitely fast. Papers (Zhang and Xu (2014); Morohoshi the VSI. This behavior complicates of convenet al. (2013)) describe in detailand methods considering partional and innovative approaches in application drive control because infinitely fast. Papers (Zhang Xu (2014); Morohoshi the VSI. This behavior complicates application of convenal. (2013)) describe in detail methods considering partional and and innovative innovative approaches approaches in in drive drive control control because because et al. (2013)) tional asitic the resulting output voltage disagrees with the required et al. capacitance. (2013)) describe describe in in detail detail methods methods considering considering parpartional and innovative approaches in drive control because et asitic capacitance. the resulting output voltage disagrees with the required asitic capacitance. the resulting output voltage disagrees with the required calculated voltage (Kim and Park (2007)). Therefore it is asitic capacitance. the resulting output voltage disagrees with the required calculated voltage voltage (Kim (Kim and and Park Park (2007)). (2007)). Therefore Therefore it it is is In this paper, a novel online compensation strategy for calculated necessary to compensate undesirable characteristics this paper, a novel online compensation strategy for calculated voltage (Kim and Park (2007)). Thereforeof itthe is In In this a online compensation for dead-time effects reduction nonlinearitystrategy compensanecessary to compensate undesirable characteristics of the In this paper, paper, a novel novel onlineand compensation strategy for necessary compensate undesirable characteristics of the VSI. The to dead-time problem has already been described dead-time effects reduction and nonlinearity compensanecessary to compensate undesirable characteristics of the dead-time effects reduction and nonlinearity compensation of the VSI is presented. The proposed approach is VSI. The dead-time problem has already been described dead-time effects reduction and nonlinearity compensaVSI. The dead-time problem has already been described in theThe several papersproblem and various possible been solutions have tion is presented. The approach is VSI. dead-time has already described tion of of the theofVSI VSI is presented. The proposed proposed approach is composed two parts whose application leads to effective in the several papers and various possible solutions have tion of the VSI is presented. The proposed approach is in the several papers and various possible solutions have been suggested. composed of two parts whose application leads to effective in the several papers and various possible solutions have composed of two parts whose application leads to effective compensation. The first adaptive parameter-independent been suggested. composed of two parts whose application leads to effective been suggested. compensation. The first adaptive parameter-independent been suggested. compensation. The first adaptive is based on monitoring of harmonic distortion In most cases, the strategies of dead-time compensation part compensation. Thethe first adaptive parameter-independent parameter-independent part is based on the monitoring of harmonic distortion In most cases, the strategies of dead-time compensation part is based on the monitoring of distortion In most cases, the strategies of dead-time compensation in the d-axis current which is caused by the occurrence are based on an average value of the lost voltages over an part is d-axis based current on the which monitoring of harmonic harmonic distortion In most cases, the strategies of dead-time compensation in the is caused by are based on an average value of the lost voltages over an in 6th the d-axis d-axis current which is is caused caused by the the occurrence occurrence are based on an average of the lost voltages over an of harmonics. Consequently, the criterion is defined entire PWM cycle, whichvalue is added to the reference voltage in the current which by the occurrence are based on an average value of the lost voltages over an of 6th harmonics. Consequently, the criterion is defined entire PWM cycle, which is added to the reference voltage Consequently, the entire PWM cycle, which to reference voltage as 6th the harmonics. sum of squared id currents between is twodefined zeroaccording to the direction ofadded the phase current (Attaianese of 6th harmonics. Consequently, the criterion criterion is defined entire PWM cycle, which is is added to the the reference voltage of as the sum of squared i currents between two zeroaccording to the direction of the phase current (Attaianese d the sum of squared iidd currents two zeroaccording to the direction of the phase current (Attaianese crossing points of the phase currents.between This criterion is et al. (2014);Lee et al. (2012)). These methods are depen- as currents between two zeroas the sum of squared according to the direction of the phase current (Attaianese crossing points of the phase currents. This criterion is et al. (2014);Lee et al. (2012)). These methods are depencrossing points of the phase currents. This criterion is et al. (2014);Lee et al. (2012)). These methods are depenminimized and the compensation voltages are calculated. dent on accurate polarity detection of the phase currents points of the phase currents. This criterion is et al. on (2014);Lee et al. (2012)). Theseofmethods arecurrents depen- crossing minimized and the compensation voltages are calculated. dent accurate polarity detection the phase minimized and the compensation voltages are calculated. calculated. dent on accurate polarity detection the phase currents The secondand partthe contains the observer of persistent voltage around the zero-crossing points. Thisof issue is discussed in minimized compensation voltages are dent on accurate polarity detection of the phase currents The second part contains the observer of persistent voltage around the zero-crossing points. This issue is discussed in second of persistent around the zero-crossing points. This issue in disturbance thatcontains is basedthe on observer the model PMSM, voltage known The second part part contains the observer of of persistent voltage aroundwork the was zero-crossing points. issue is is discussed discussed in The  supported by grant This No. FEKT-S-14-2429 - The disturbance that is based on the model of PMSM, known  This disturbance that is based on the model of PMSM, known machine parameters and easily measurable variables. The This work was supported by grant No. FEKT-S-14-2429 The  This work disturbance that is based on the model of PMSM, known was supported by grant No. FEKT-S-14-2429 The research of new control methods, measurement procedures and  machine parameters and easily measurable variables. The This work was supported by grant No. FEKT-S-14-2429 The machine parameters and easily measurable variables. The research of new control methods, measurement procedures and validity of the proposed approach is verified by simulations machine parameters andapproach easily measurable variables. The research new measurement intelligent in methods, automation”, which wasprocedures funded by and the validity of the proposed is verified by simulations research of ofinstruments new control control measurement intelligent instruments in methods, automation”, which wasprocedures funded by and the validity ofbythe the proposed approach is is verified verified by by simulations simulations and alsoof real experiments. validity proposed approach intelligent instruments in automation”, which was funded by the Internal Grant Agency of Brno University of Technology. intelligent instruments in automation”, which was funded by the and also by real experiments. Internal Grant Agency of Brno University of Technology. and Internal and also also by by real real experiments. experiments. Internal Grant Grant Agency Agency of of Brno Brno University University of of Technology. Technology. Copyright 2016 IFAC 43 Hosting by Elsevier Ltd. All rights reserved. 2405-8963 © 2016, IFAC (International Federation of Automatic Control) Copyright © 2016 IFAC 43 Copyright 2016 IFAC 43 Peer review© of International Federation of Automatic Copyright ©under 2016 responsibility IFAC 43 Control. 10.1016/j.ifacol.2016.12.008

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equation (4) may be considered as the approximation of the real disturbance voltages. It is very difficult to estimate compensation voltages by the off-line method based on the aforementioned equation. This approach does not allow to achieve adequate compensation under all conditions. The described issue is solved by designing the new adaptive compensation method. 3.1 Parameter-Independent Adaptive Method The precise estimate of the trajectory of time-varying periodical signal is very difficult task for the estimator. Therefore, the only voltage Vdead is chosen as the estimation parameter in this method. Vdead can be considered as a slowly time-varying parameter. A prerequisite for the application of adaptive methods is the steady state of the system. Steady state is reached when the measured speed does not deviate from reference value according to the following conditions. (5) |ωr − ωref | ≤ 0.05 |ωref | If this condition is sufficiently satisfied, the estimation of Vdead will be initiated. First, the size of criterion Cid must be calculated. It is assumed that d-component of the current in the synchronous frame should be zero during the steady state in the ideal case. But the dead-time effect causes occurrence of parasitic harmonic components (the deformation of d-component of the current is shown in Fig. 5(b)) where the 6th harmonic is dominant. The information about dominance can be used for evaluation. The period of ripple Tid6 of the d-axis current corresponds to 1/6 of the period Tiabc of the phase currents in the stationary reference frame. The size of the criteria Cid is defined as the quadratic criterion of the id current between two zero-crossing points of the phase currents. N  Cid = id (k)2 wd (6)

Fig. 1. Switching patterns and phase voltage. 2. ANALYSIS OF DEAD-TIME EFFECTS The dead-time effect causes distortion of the inverter output voltage which leads to deformation of the phase currents and ripple of the dq-axes currents, torque pulsation and effectiveness reduction of vector control algorithm. The analytical analysis of these distortions is dealt with in many papers (Sam-Young Kim et al. (2010)), where voltage distortion is expressed as disturbance voltage in the synchronous frame depending on the electrical rotor position (Bolognani et al. (2008)). Switching patterns and the relationship between the anticipated and actual output voltages according to the direction of the phase current is shown in Fig. 1. SHi and SLi are upper and lower ideal gating signal. The gating signals SH and SL are supplemented by dead-time for a practical application. The ideal phase output voltage is represented by the voltage waveform Vai . Subsequently, the waveforms of the phase voltage Va are supplemented by the dead-time and switching delay as turn-on/-off time of the switching elements. The average voltage error over one PWM period of the output voltage can be expressed as Tdead ΔVa = VDC sign(ia ) = Vdead ∙ sign(ia ) (1) TP W M  1 ia > 0 (2) sign(ia ) = −1 ia < 0 where Tdead represents the dead-time compensation time, TP W M is the PWM switching period and VDC is the DC link voltage. Tdead is equal to (3) Tdead = (Td + ton − tof f ) where ton and tof f are rise/fall-time of the switching elements. The magnitude of the voltage error due to the nonlinear switching is indicated by parametr Vdead . The amplitude of the output voltage Va is affected by the voltage drops Vsat and Vd of switching elements and diodes respectively. Voltage error Vdead can be extended by the voltage drops as follows Tdead (VDC − Vsat + Vd ) + 0.5(Vsat + Vd ) (4) Vdead = TP W M The equation (4) is conventionally used for compensating nonlinearities of the VSI as it is described in (Kim and Park (2007)).

k=1

Thereafter the sign of the criterion must be determined. Once coordinates of minimum and maximum of id current during the period Tid6 are determined, the slope kslope of id is obtained and the resulting criterion can be determined as follows: Cid,sgn = sign(kslope )Cid (7) idmin − idmax kslope = (8) indexmin − indexmax The resulting criterion Cids,sgn is applied to the input of the proportional-integral (PI) controller as control error. The criterion is minimized by PI controller and voltage Vˆdead is given as   1 ∙ (−Cids,sgn ) Vˆdead = kp 1 + ki (9) p where kp and ki are the PI controller gains and p is the differentiation operator. Resulting compensation voltages Vˆdα and Vˆdβ in the stationary reference frame are obtained by substituting the estimated voltage Vˆdead into the equation (10).     Vˆdead 2 sign(i Vˆdα √ a ) − sign(ib ) − sign(ic ) = (10) 3(sign(ib ) − sign(ic )) 3 Vˆdβ

3. PROPOSED COMPENSATION STRATEGY It is normally assumed that the values of Vd , Vsat , ton and tof f are constant in many papers but these parameters vary with the operating conditions. Therefore, the

These compensation voltages are dependent on the polarity detection of phase currents. The problem can occur during polarity detection around zero-crossing points

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of phase currents. Incorrect polarity detection of the phase current may cause erroneous dead-time compensation which is undesirable. Furthermore, the proposed method cannot be used in a speed range near zero, because intersections with zero-value of phase current cannot be accurately determined. Consequently the time of period Tid6 cannot be defined and criterion cannot be calculated. For these reasons, second part of the proposed compensation strategy is used which is the observer of the voltage disturbance.

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3.2 Voltage Disturbance Observer The observer of the voltage disturbance is based on the mathematical model of PMSM in stationary reference frame. It assumes the equality of inductances Ld and Lq . The model which contains anticipated disturbance voltages can be specified as follows  ∗    vα Rs + Ls p iα 0 = vβ∗ 0 Rs +Ls p iβ  (11) − sin θe Vdis,α + ωe λm + cos θe Vdis,β where vα∗ and vβ∗ are the reference voltages, iα and iβ are the αβ-axis currents. ωe and θe represent electrical rotor angular velocity and rotor electrical position. λm is the rotor flux linkage. Rs and Ls are the stator resistance and inductance (In this case, the inductance is L +L calculated as follows Ls = d 2 q ). Vdis,α and Vdis,β are the disturbance voltages caused by dead-time effects. If the sampling frequency is sufficiently high, the following difference equation can be derived from equation (11)   Δiα  ∗     R i + L s α s vα − sin θe Vdis,α   T s Δiβ  + ωe λm cos θe + Vdis,β vβ∗ =  Rs iβ + Ls Ts (12) where Δ operator represents the increment of variable during one sampling period Ts . Consequently, it is possible to obtain increments of the voltage Δvα and Δvβ from the stator variables as  follows.  ∗   (v − R i )T − L Δi Δvα = (vα∗ − Rs iα )Ts − Ls Δiα (13) Δvβ s β s s β β

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Substituting increments Δvα and Δvβ from (13) to the difference equation, the equation (14) is obtained. Subsequently, overall disturbance voltages Vdis,α and Vdis,β can be directly expressed by (15).     (−ωe λm sinθe + Vdis,α )Ts Δvα = (14) Δvβ (ωe λm cosθe + Vdis,β )Ts       Vdis,α Vˆ fˆ = ˆdα + ˆdα (15) Vdis,β Vdβ fdβ

Fig. 2. Simulation results of the proposed compensation method during estimation of Vdead . (a) Current id and start of the estimation. (b) Velocity. (c) Trend of criterion Cid,sign . (d) Estimation of Vˆdead . (e) Estimation of disturbance voltages Vˆdα and Vˆdβ . (f) Trend of residual disturbance voltages fˆdα and fˆdβ . (g) Stator phase currents.

Estimated voltages fˆdα and fˆdβ should be zero in the ideal case because the nonlinearity of inverter should be

compensated by adaptive method. However, the estimate of voltages Vˆdα and Vˆdβ and polarity detection of the phase currents are not entirely accurate in practice. Thus, the voltage error of estimate (10) corresponds to the estimated voltages in equation (16). The estimation error of the compensation voltages depends on the accuracy of the motor parameters such as Rs , Ls and λm . The observer of the voltage disturbance includes the numerical approximation of derivative which can cause problems if

The estimates of Vˆdα and Vˆdβ are subtracted from the expected disturbance voltages which are given by adaptive method (10). Consequently, the outputs of the estimator are the estimates of residual disturbance voltages fˆdα and fˆdβ , which are given by the following equation.         1 Δvα −sinθe Vˆdα fˆdα λ = ω + − (16) e m cosθe Ts Δvβ Vˆdβ fˆdβ

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Fig. 3. Block diagram of the vector control of the PMSM with proposed compensation strategy

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the measured current is noisy. Therefore, the output of the observer must be filtered by the first order LPF. The resulting compensation voltages are obtained by merging the compensation voltages from both parts.

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Fig. 5. Simulation results without and with proposed compensation. (a, d) Stator phase currents. (b, e) daxes currents. (c, f) q-axes currents.

4. SIMULATION RESULTS The verification of the proposed compensation strategy is carried out on the model of the real system in the MATLAB/Simulink 2015b. The simplified block diagram of the vector control of the PMSM drive is shown in Fig.(3). The simulation model has the same parameters and control algorithm as the real system. The dead-time Td = 0.5μs, the further specification of the inverter and PMSM are as follows: TP W M = 62.5μs, VDC = 20V , Rs = 0.55Ω, Ld = 220μH, Lq = 250μH and PMSM has three pole pairs.

tor speed of 50 rad/s without load. Harmonic distortion HD of phase current is calculated to demonstrate the effectiveness of proposed compensation method (HD =  2 + I 2 /I , where I , I , I , I I52 + I72 + I11 5 7 11 13 represent 13 1 the dominant odd harmonics and I1 denotes the magnitude of the first harmonic of the phase current). It is evident that the voltage error significantly deforms the progress of the phase currents without dead-time compensation. It is reflected by the occurrence of the parasitic odd harmonics in the spectrum of the phase current as it is shown in Fig. 4(a). 5th, 7th, 11th and 13th harmonic components are dominant in accordance with the theoretical assumptions. The deformation is also visible in ripples of the dq-currents as it is obvious from Fig. 5(b)-(c) and spectrums of the currents in Fig 4(b)(c). These negative effects cause torque pulsations and generally reduce the effectiveness of the vector control algorithm.

The process of dead-time compensation by the proposed method is shown in Fig. 2. It is evident from waveforms of the phase currents in Fig. 2 (g) that the compensation is implemented from the beginning of the simulation experiment. The Dead-time is suppressed before estimation of the voltage Vˆdead due to estimation of disturbance voltages fˆdα and fˆdβ whose waveform is shown in Fig. 2(f). The estimation of Vˆdead is started when the condition (5) was satisfied and a-phase current passed through zero as it is shown in Fig. 2(a), where the red pulses indicate zerocrossing of the phase currents. The size of criterion Cid,sgn is always calculated between two pulses. The criterion is minimized by PI controller whose output is the voltage Vˆdead as it is shown in Fig. 2(d). The speed of the Vˆdead estimation is affected by the parameters settings of PI controller, but primarily it is given by frequency of phase currents. Because the frequency indicates the rate of change in the criterion Cid,sgn . Trends of compensation voltages Vˆdα , Vˆdβ rise slowly, whereas trends of residual disturbance voltages fˆdα , fˆdβ converge to zero as it is shown in Fig. 2(e) and Fig. 2(f) respectively. Unfortunately, it is not possible to compensate the dead-time effect by only voltages Vˆdα and Vˆdβ because the high-frequency noise contained in the id current complicates polarity detection of criterion Cid . Therefore, the persistent dead-time effect is still compensated by estimated voltages fˆdα and fˆdβ .

Voltage error caused by dead-time effects and its negative consequences is suppressed due to the proposed compensation strategy as is evident from results in Fig. 5(c)-(d) and Fig. 4(a)-(c). The deformation of phase current around zero crossing-point is reduced. Furthermore, the dominant odd harmonics of phase currents, 6th and 12th harmonic in dq-currents are suppressed, as is shown in comparison of the current spectra in Fig. 4. The resulting harmonic distortion HD of the a-phase current decreased from 5.35% to 0.11% due to the proposed compensation scheme. 5. EXPERIMENTAL RESULTS The proposed approach has been applied on an industrial drive to confirm the correctness of the theoretical approach and to show the effectiveness of the proposed compensation strategy. The PMSM motor is connected to the power stage and dSpace control platform DS1103. The compensation strategy and vector control algorithm is implemented in the control platform. The verifications of the proposed dead-time compensation strategy are carried out at rotor speed of 50 rad/s in the steady state without

The validity of the proposed approach is verified by comparing results that are obtained by proposed compensation and without compensation during steady state as it is shown in Fig. 5. The simulations are carried out at ro46

2016 IFAC PDES October 5-7, 2016. Brno, Czech Republic

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by the zero current clamping phenomenon. Further, the proposed approach is equipped with the observer of voltage disturbance based on PMSM model. The disturbance estimator is not affected by this phenomenon but depends on the accuracy of the model parameters. The very effective method of dead-time compensation is obtained by merging both approaches as it is proved by the results of simulations and experiments. The proposed solution does not require any additional hardware.

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REFERENCES

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Attaianese, C., D’Arpino, M., Monaco, M.D., and Tomasso, G. (2014). Recursive dead time compensation techniques for PV system power converters. Bedetti, N., Calligaro, S., and Petrella, R. (2014). Accurate modeling, compensation and self-commissioning of inverter voltage distortion for high-performance motor drives. In 2014 IEEE Applied Power Electronics Conference and Exposition - APEC 2014, 1550–1557. IEEE. Bolognani, S., Peretti, L., and Zigliotto, M. (2008). Repetitive-Control-Based Self-Commissioning Procedure for Inverter Nonidealities Compensation. IEEE Transactions on Industry Applications, (5), 1587–1596. Dafang, W., Bowen, Y., Cheng, Z., Chuanwei, Z., and Ji, Q. (2014). A Feedback-Type Phase Voltage Compensation Strategy Based on Phase Current Reconstruction for ACIM Drives. IEEE Transactions on Power Electronics, 29(9), 5031–5043. Hao, W. and Junzheng, W. (2011). A novel dead-time compensation in vector controlled PMSM system. IEEE Proceedings of the 30th Control Conference, 3478–3483. Kim, S.Y. and Park, S.Y. (2007). Compensation of DeadTime Effects Based on Adaptive Harmonic Filtering in the Vector-Controlled AC Motor Drives. IEEE Transactions on Industrial Electronics, 1768–1777. Lee, D.H. and Ahn, J.W. (2014). A Simple and Direct Dead-Time Effect Compensation Scheme in PWM-VSI. IEEE Transactions on Industry Applications, PP(99). Lee, D.H., Kim, H.m., and Ahn, J.W. (2012). A direct compensation scheme of the dead-time effect in PWMVSI. In 2012 IEEE Industry Applications Society Annual Meeting, 1–6. IEEE. Morohoshi, T., Hoshi, N., and Haruna, J. (2013). Deadtime compensation of adjustable dead-time controlled three-phase resonant snubber inverter for induction motor drive application. In 2013 International Conference on Electrical Machines and Systems (ICEMS), 1766– 1770. IEEE. Sam-Young Kim, Wootaik Lee, Min-Sik Rho, and SeungYub Park (2010). Effective Dead-Time Compensation Using a Simple Vectorial Disturbance Estimator in PMSM Drives. IEEE Transactions on Industrial Electronics, 57(5), 1609–1614. Zhang, Z. and Xu, L. (2014). Dead-Time Compensation of Inverters Considering Snubber and Parasitic Capacitance. IEEE Transactions on Power Electronics, 29(6), 3179–3187. Zhao, Y., Qiao, W., and Wu, L. (2015). Dead-Time Effect Analysis and Compensation for a Sliding-Mode Position Observer-Based Sensorless IPMSM Control System. IEEE Transactions on Industry Applications, 51(3), 2528–2535.

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Fig. 6. Experimental results of the proposed dead-time compensation method. (a) Estimation of disturbance voltages Vˆdα and Vˆdβ . (b) Trend of residual disturbance voltages fˆdα and fˆdβ . (c) Estimation of Vˆdead . load. Other parameters are the same as in the simulation experiments. Its results are compared with the standard compensation and uncompensated state as it is shown in Fig. (7). The steady state of the proposed compensation is illustrated in Fig. 6. This figure shows the waveform of the estimated voltage Vˆdead from which compensation voltages Vˆdα and Vˆdβ are obtained. These voltages are summed with the estimates fˆdα and fˆdβ which are obtained from (16) and suppress persistent dead-time effect. Subsequently, the output voltage distortion of the VSI is compensated. Due to the ripple and deformation of phase current around zero crossing-point is suppressed as it is shown in Fig. 7(g). The ripple of the dq-current is also reduced (Fig. 7(h)(i)). The fast Fourier transform (FFT) results in Fig. 8 show the difference on magnitude of the harmonic components of the dq-currents and a-phase current with proposed/standard compensation and without compensation. In cases of compensations, the magnitude of dominant parasitic odd harmonics of a-phase current and the dominant 6th and 12th harmonics in dq-axis current are significantly reduced. But the newly proposed compensation achieves significantly better results as evidenced by decline in the index of harmonic distortion HD (uncompensated HD = 3.61%). In the case of standard compensation HD is 1.79% and in the case of the proposed method HD index value is decreased to 0.77%. 6. CONCLUSION In this paper, a simple online adaptive compensation method of dead-time effects and inverter nonlinearity is presented. The output of the adaptive method is slowly time-varying voltage, which is used to compensate the output voltage distortion. The advantage of the proposed method is its independence on parameters of the VSI, but the effectiveness of the compensation may be affected 48