Control Scheme for Wide-Bandgap Motor Inverters with an Observer-Based Active Damped Sine Wave Filter

Transcription

1 PCIM Europe June 28 Nuremberg Germany Control Scheme for Wie-Bangap Motor Inverters with an Observer-Base Active Dampe Sine Wave Filter F. Maislinger an H. Ertl TU-Wien Institute of Energy Systems an Electrical Drives A-4 Vienna Austria franz.maislinger@tuwien.ac.at G. Stojcic C. Lagler an F. Holzner B&R Inustrial Automation GmbH A-542 Eggelsberg Austria Abstract This paper presents an effective metho for the active amping of a two-stage sine wave LC output filter for wie-bangap motor inverters avoiing any sensing of filter voltages/currents. The metho is base on a linear observer moel which is use for estimating the filter capacitor currents require for implementing the active amping. The motor currents are controlle using a conventional PI-type controller with aitional feeback base on the estimate filter capacitor currents. Using the propose metho the inverter s stanar output current sensing can be use also in case of active filter amping avoiing any aitional measurement channels an issipative losses which appear in case of passive filter amping. The paper reports the operating principle an analyzes the stability region an robustness of the total system by simulations. Finally the propose scheme is teste by implementation of a laboratory inverter prototype base on GaN- MOSFETs at a switching frequency of khz.. Introuction Toay silicon (Si) base insulate gate bipolar transistors (Si-IGBTs) operating in pulse with moulation (PWM) moe at switching frequencies up to 2 khz are commonly use for the implementation of motor inverters in the kw omain. During the past few years however wie-bangap switching evices like GaN- an SiC MOSFETs have consierably emerge also in inverter applications base on 6 V GaN evices. The wie bangap associate with the high critical electrical fiel of GaN an the high electron mobility principle (HEMT) has le to very impressive new power transistors []. The low semiconuctor capacitances of GaN as well as avances in packaging technologies facilitate very high switching spee resulting in substantially lower switching losses in comparison to silicon (Si) base IGBTs. Low switching- an also low on-state losses of GaN MOSFETs now enable motor inverters operating at high switching frequencies with high efficiency rates [2]. GaN power stage p n C DC Active-ampe filter 3x L L L 2 R C C 2 Filter capacitor currents gaine by observer 3-phase motor R M L M Measure currents Fig. : Basic concept of the propose motor inverter with GaN power stage an actively ampe symmetrical twostage filter for a 3-phase motor loa. The very fast switching in the nanosecon range at 4 V DC-link voltage however creates some crucial issues for motor applications using stanar 3- phase / two level inverters. Transient overvoltages at the motor terminals cause by the high u/t rates of more than 5 kv/μs may impair wining isolation an reuce the lifetime of motors [3]. Furthermore aitional loa currents ue to cable capacitances an motor voltage ringing limit the maximum cable length an increase switching losses of the inverter. The high switching spee of GaN MOSFETs on the other han facilitates switching frequencies of khz an above which make an output filter possible that can be irectly implemente into the inverter. This LC filter substantially suppresses most of the switching frequency harmonics to obtain sinusoiallike inverter output voltages. Consequently as reporte in [2] by avoiing high frequency motor an cable losses the total system efficiency is expecte to be increase. Furthermore it seems to be possible to avoi shiele motor cables resulting in a ISBN

2 PCIM Europe June 28 Nuremberg Germany cost an application benefit. A schematic outline of the propose inverter system is epicte in Fig.. Here to achieve a sufficient switching noise suppression but also rather high control banwith as being necessary for servo rives at least a twostage LC sine wave filter is require [4]. The filter is esigne such that the noise level at the inverter s output comply with common inustrial stanars. In this paper the stanar IEC/EN 55 class-a is consiere. Nevertheless the LC filter resonances have to be ampe for actual implementations an for proper control loop esign. For this frequently issipative components are use leaing however to aitional losses ecreasing the system efficiency. As an improvement in [5] e.g. the filter resonances are ampe by a hybri structure consisting of a single-stage LC filter with a resonance tank in parallel to the LC stage capacitor in connection with a igital notch filter. The resonance tank (LCR series circuit) is tune to the switching frequency the amping resistor acts for the tank as well as for the main LC stage. Nevertheless the amping resistor leas to aitional issipative losses an so a trae-off has to be taken between the occurring output voltage overshoot an the filter losses. To effectively avoi filter amping losses an active amping concept by capacitor current feeback is propose in [6]. The sense filter capacitor current is multiplie by a coefficient k an fe back to the PWM stage with negative sign. This emulates a kin of ohmic but not issipative amping resistor resulting into a well ampe system if k is properly matche to the filter parameters L an C. However this approach requires knowlege of the inner filter state variables consequently leaing to aitional sensing channels which are often not available or only by aitional costs. In this paper to obtain high inverter efficiencies but avoiing the mentione aitional sensing channels the propose concept in [6] is extene by an observer moel which estimates the require capacitor filter currents for active amping. The following section shows the observer-base active amping concept as well as a corresponing esign for a conventional PI controller. Furthermore the influence of parameter variations on the system stability is also iscusse. 2. Control Scheme For the analysis of the motor current control applying the propose observer-base active amping a single-phase equivalent circuit of the inverter an the two-stage LC output filter as shown in Fig. 2 is use. Here it is assume that the GaN power stage block acts as a transfer function of gain ν =. The motor loa is specifie by a L M R M element in combination with a voltage source representing the inuce motor voltage. ν = L L L 2 R i u i C C 2 - PI u a - i C k GaN power stage î C Observer moel i M u i i M R M L M Fig. 2: Propose close-loop control using a PI-type controller for motor current control employing aitional feeback of the observe filter capacitor current î C. The LC filter resonance frequencies have to be well between the maximum electrical motor operation frequency f el an the inverter switching frequency f s i.e. f el << f res << f s. To achieve a sufficient attenuation of the switching noise but also a rather high current control banwith the corresponing filter parameters are specifie in [6] an liste in Table. In contrast to passive amping schemes which reuce the system efficiency ue to aitional issipative losses the resonance of the first filter-stage now is attenuate by a feeback of the filter capacitor current i C. Using an aequate feeback parameter k which can be approximate by (L + L M ) L k =2ξ ξ=.9 () C L M the feeback acts like an ohmic resistor resulting in a well ampe ynamic of the controlle plant. However instea of an aitional current measurement for i C the filter capacitor current is estimate ISBN

3 PCIM Europe June 28 Nuremberg Germany by a linear observer moel which maps the ifferential equations of the ynamic system. It has to be note that the secon LC filter-stage still uses a small issipative amper R L (parallel branch to L 2 ). This is because the resonance frequency efine by the parameters L 2 C 2 is about 3-times higher as for the first stage an the banwith limit of the igital PWM an control of the brige leg is not sufficient for a very effective amping of L 2 C 2. The losses in R however are almost negligible. Tab. : Parameter settings of implemente system. Part Parameter value unit Inverter U DC 4 V C DC 2 μf f s khz Sine-Filter L 2 μh R mω C 2.5 μf L 2 25 μh R 2 3 mω C μf L 33 μh R 5.6 Ω Motor L M 4.4 mh R M.48 Ω I M 6 A U M 4 V 2p n M 3 min Controller T s μs T I.476 ms V I 5.4e4 VA k 2. VA Observer k OB [].5 k OB [2-5] k OB [6] Observer Moel In the following a linear observer moel corresponing to the ynamic plant of the inverter is implemente. Fig. 2 shows the ynamic plant of a singlephase system with two input quantities: The voltage u i escribes the input value of the system whereas the internal inuce voltage acts as an external isturbance to the system an oes not affect its stability. Nevertheless its knowlege is necessary for the observer moel. Both variables can be combine to the vector u =[u i ] T. For controlling the motor current i M is measure an therefore is u i i L -i C u C sl +R sc sl 2+R i M G(s) sl M +R M - u C2 sl +R sc 2 i L2 Fig. 3: Plant ynamic moel incluing two-stage filter an a R M L M path as motor loa. The parameters R an R 2 take into account the ohmic copper losses of the two inuctors. known for the observer esign. From the resulting system ifferential equations t i L(t) = R i L u C + u i L (2a) t u C(t) = i L i L2 i C (2b) t i L2(t) = R 2i L2 + u C u C2 L 2 (2c) t u C2(t) = i L2 + i i M C 2 (2) t i (t) = R i + u C u C2 L (2e) an t i M(t) = R Mi M + u C2 (2f) L M a state space moel in the continuous time omain can be obtaine in the form ẋ = Ax + Bu y = c T x i - (3a) (3b) with x =[i L u C i L2 u C2 i i M ] T (corresponing to the six state variables) the output vector c = [ ] T as well as the matrices R L L C C C L A = 2 R 2 L 2 L 2 C 2 C 2 C 2 L L R L L M R M LM (4a) ISBN

4 PCIM Europe June 28 Nuremberg Germany an B = [ [ ] ] T b b 2 = L. (4b) L M By using the Popov-Belevitch-Hautus (PBH) eigenvector test [7] it can be seen that the obtaine system is completely observable if the conition L 2 R L R 2 is vali. It has to be note that a numerical calculation of the complete observability in a Matlab calculation has faile cause of numerical inaccuracies inuce by the chosen parameters liste in Table. However if the conition is not met the eigenvalues of the occurring null ynamic of the investigate system must be consiere which correspons for linear systems to the zeros of G(s) = c T (se A) b. Here the zero of G(s) has a negative eigenvalue which implicates an exponentially stable null ynamic. Thus in both cases an observer for estimating the filter capacitor current i C can be moelle. For a igital implementation the observer can be written in a iscrete form as ˆx k+ = Φˆx k + Γu k + k OB (ŷ k y k ) ] [ [ŷk c ŷ k = = T ] ˆx k ŷ 2k (5a) (5b) where ŷ 2k conforms to î C an k to a iscrete time step of length T s =/f s. The iscrete matrices Φ =exp(at s ) Γ = Ts exp(aτ)τb can be obtaine by the zero-orer hol iscretization of A an B with a sampling perio T s. In orer to obtain a stable error system e k+ = ˆx k+ x k+ = ( Φ + k OB c T ) e k (6) with e k = ˆx k x k the values of k OB are chosen in a form that the error ynamic matrix (Φ + k OB c T ) becomes exponentially stable for which Ackermann s formula can be use [8]. Inserting (5b) an (6) in (5a) leas to the resulting observer moel [ ] uk ˆx k+ = A OBˆx k + B OB (7a) y k ŷ k = C OBˆx k (7b) with A OB = Φ + k OB c T B OB = [Γ k OB ] an C OB appropriate to (5b). The filter current î C obtaine from the observer now acts as an approximation of the actual current in the capacitor C an in case of sufficient small parameter variations it can be use for the propose active amping concept Current Control For controlling the motor currents a close-loop control concept using a conventional PI-type controller with a transfer function ( R(z) =V I T I + T ) s + T sv I 2 z (8) in the complex z-omain with the controller parameters V I an T I employing aitional feeback of the observe capacitor currents is propose. For calculating the controller parameters it is assume that the filter capacitor current require for the active amping concept is available as a measure value. Therefore the transfer function G(s) is ivie into two parts which can be moelle by G z (z) = z z G z2 (z) = z Z z ( Z s ( s i C (s) u i (s) i M (s) i C (s) ) (9a) ) (9b) for a igital implementation in the z-omain (Fig. 4). Hence in iscrete time omain the transfer function of the actively ampe system leas to G(z) = z U DC G z (z) +k z U DC G z (z) G z2(z) () where the inverter is moelle as a linear U DC gain with a sample elay z to account for PWM transport elay [9]. The active amping parameter k has to be chosen that a well ampe behaviour occurs. As mentione above in continuous time i u i - R(z) - z U DC k G z i C G z2 G(z) Fig. 4: Propose close-loop control concept in z- omain without observer. i M ISBN

5 PCIM Europe June 28 Nuremberg Germany (a) Mag. in B 5 (b) Phase in G(q) k < 3 G(q) T ry (q) 2 2 Frequency in khz T ry (q) Fig. 5: Boe plot of ynamic plant an of the close-loop transfer function for ifferent active amping parameters k =...3 (gray) as well as for k = 2 V A (blue) (a) magnitue (b) phase. omain k can be calculate by () however in a igital implementation a phase shift introuce by the sampling process an the processing elay can estabilize a esign that is stable in continuous time omain []. The influence of ifferent active amping parameters k on the transfer function of the iscrete ynamic plant is illustrate in Fig. 5. For this by applying a bilinear Tustin transformation with pre-warping [] G(z) is rewritten as G(q) for a sampling time of T s = μs where the expression z = +qt s/2 () qt s /2 maps the unit circle of the complex z-plane to the complex axis in the q-plane with the new frequency parameter q = 2ω/T s. As epicte in the blue curves of Fig. 5 a well ampe system behaviour can be obtaine with an active amping parameter k = 2 V A. Now it is possible to calculate the close-loop transfer function of the iscrete system as T ry (q) = R(q)G(q) +R(q)G(q) (2) using a PI controller R(q) =V I ( + qt I ) /q. As can be seen in Fig. 5 the transfer function for a well ampe system only has one intersection with the B-line. Thus a frequency response metho can Magnitue in A % t in ms Fig. 6: Current step-responses of the close-loop control for ifferent active amping parameters (gray) for k = 2 V A (blue) as well as of the implemente moel in Matlab/Simulink (ashe) for nominal filter parameters. be use to etermine the controller parameters V I an T I. These values epen on the rise time the esire overshoot an the motor inuctance. Here the chosen characteristics of the step response with 2 % overshoot an a rise time of.2mslea to the controller parameters V I = 5.4kVA an T I =.48 ms. Fig. 5 epicts the obtaine close-loop transfer function for ifferent active amping parameters k. As can be seen for k < 3VA unstable close-loop functions occur. The resulting motor current step responses for the propose control scheme are illustrate in Fig. 6. Here only active amping parameter values corresponing to a stable system behaviour are consiere. Furthermore the propose control concept by using the observer for estimation of the filter capacitor current is implemente in Matlab/Simulink an teste with the obtaine controller an active amping parameters. A single-phase equivalent circuit of the moel is shown in Fig. 7 where a zero-orer-hol part is use to switch the iscrete system input u i on the continuous ynamic plant G(s). For nominal filter- an motor- values the obtaine step response correspons to the esire behaviour ( see Fig. 6 - ashe curve) Influence of Parametric Variation This section iscusses the effects of parametric variations on the previously esigne close-loop system with observer-base active ampe filter. Component tolerances of the use filter capacitors C an C 2 as well as saturation effects of the inuctors L L 2 an L M can affect the system stability. ISBN

6 PCIM Europe June 28 Nuremberg Germany i iscrete - R(z) - z U DC Controller Processing ea time k î C u i Observer moel Active amping part ZOH i Mk continuous i M (t) G(s) Plant T s Sampler Fig. 7: Propose close-loop control concept of a single phase moel implemente in Matlab/Simulink. 3. Experimental Results In orer to verify the propose control an observerbase active amping concept a 2kW/4 V laboratory prototype has been implemente. Filter- an motor parameters as well as esign specifications are given in Table. Filter inuctor first stage DC-link capacitor bank Heat sink FPGA Due to the passive amping of the secon filterstage the varying parameters are constraine to L C an L M. To perform the analysis the active amping- as well as the controller parameters are calculate for the nominal values of the two-stage filter as liste in Table. For the simulation the Matlab/Simulink moel illustrate in Fig. 7 is use. Then each of the filter parameters is varie in a range of 5 % to +5 % for motor inuctances.4l Mnom L M.4L Mnom. Fig. 8 epicts the lower stability limit for ifferent values of L M. As inicate for the nominal motor inuctance the system has a stable behaviour for a parametric variation of 2 % in L an C. At 6 % reuce motor inuctance the allowe eviation of the filter parameters however is only %. Furthermore for L M =.6L Mnom an L =.5L nom the conition L M > L is no longer satisfie so the mismatch of active amping increases the overshoot an the whole system becomes unstable. By increasing the motor inuctance the robustness of the system can be increase slightly however larger values of L M reuce the close-loop system ynamic. L/Lnom % 4 % +2 % L Mnom unstable omain 2 % stable omain for L M = 6 % C /C nom Fig. 8: Lower stability limit for ifferent values of motor inuctance L M. The region above the ifferent curves inicates the stable omain. Control boar Power boar WBG boar Fig. 9: Laboratory prototype consisting of power- WBGan control-boar. Power-boar imensions: 2 mm x 25 mm. As illustrate in Fig. 9 the prototype mainly consists of three PCB boars: A GaN transistor carrier- (WBG) a basic power- an a control-boar. A separate WBG-boar place uner the heat sink is use to test ifferent wie bangap transistors an Gate rivers. Here the half-briges (forme by 2 GaN-HEMTs GS6658T) are controlle by Si82394 isolator/rivers which feature fully isolation 4Aoutput current capability an inclue also programmable interlock elay ajuste to 5 ns. It has to be remarke that high switching frequencies reuce the inverter/filter volume on the one han but on the other han the switching losses are increase. Accoringly the cooling system volume increases compensating the filter volume savings. Besie this fact the efficiency is also reuce. Consequently as a compromise for high inverter efficiency an low volume the switching frequency of the GaN power stage is set to khz. A stanar motion control-boar is taken from B&R Inustrial Automation GmbH. It inclues an embee system where the iscusse current controlas well as the observer-base active amping con- ISBN

7 PCIM Europe June 28 Nuremberg Germany u Mu u Mu i Mu i Mu i Mv i Mw i Mv i Mw Fig. : Measure motor currents i Mu i Mv i Mw an motor voltage u Mu for an external loa of 2.5Nm at a motor operating frequency of f el = 25 Hz. Fig. : Measure motor currents i Mu i Mv i Mw an motor voltage u Mu for a spee increase from stanstill to 3 min within 6 ms. cept is implemente for each motor phase. A controller sampling time of T s = μs is use in singleege sampling moe PWM transport elay an current oversampling lea to a processing ea time of μs. The approach of the propose linear observer moel is necessary to enable a fast an reliable calculation of the require state variables within one sampling perio. It shall be note that a measurement of the filter capacitor current woul a an aitional sampling elay impairing ynamic behaviour an stability. The two-stage filter measurement circuits for currents an temperature as well as the DC-link electrolytic capacitor bank are all place on the main power-boar. To reuce noise impacts the require motor phase current measurements are realize by shunts in combination with a ACPL-798J secon orer sigma elta moulator which oversamples the analog input signal into a high-spee ata stream. As shown in Sec. 2.3 for the observer-base active amping scheme chokes with a sufficient linear behaviour with respect to the current as well as with a relatively high saturation current limit to meet the emans for servo motor applications are necessary. Hence toroial power cores (L : Kool-Mμmax μ r = mm 57 turns L 2 : Senust μ r =6 2.3mm 2 turns) are use for the inuctors of the filter-stages. The coils are forme as single layer winings to minimize proximity effects hence stanar copper wire is sufficient. To obtain a rather small filter volume ceramic capacitors are use for the implemente two-stage filter which easily can hanle the switching frequency current ripple. However the capacitance of most ceramic capacitors in this voltage omain shows a very pronounce nonlinear behaviour epening on the DC-bias voltage an this may influence the controllability of the inverter system. Fortunately aequate CG ielectric capacitors are recently available (Kemet KC-link 22 nf 5 V) showing a capacitance being almost inepenent of DC-bias voltage an therefore are use for the first filter-stage. For the secon filter-stage stanar ceramic capacitors (Arcshiel X7R 5 V) are use for saving cost. It has been observe that their voltage epenency oes not have severe impact on the output voltage quality an system stability. In Fig. the motor phase currents as well as the motor voltage u Mu in a stationary operating point for an electrical frequency of 25 Hz an a mechanical loa of 2.5Nm are shown. Due to the twostage filter both the motor- currents as well as the motor/cable voltage show the expecte sinusoial shape with a rather small ripple. In Fig. the occurring motor- currents an voltage for a spee increase from stanstill to 3 min within a time ISBN

8 PCIM Europe June 28 Nuremberg Germany range of 6 ms are epicte. Here small current an voltage istortions can be observe inuce by the high currents to bypass the starting torque of the permanent magnet synchronous machine (PM- SM). In particular for high currents the nonlinearity of the motor inuctance as well as of the filter inuctor result in a mismatch of the observer-base active amping scheme. In orer to emonstrate the stable behaviour of the propose metho the system is further teste by a step change in loa torque. For this purpose the PMSM fe by the laboratory prototype is mechanically couple to a secon PMSM whose phases are terminate by a 3-phase power resistor as illustrate in Fig. 2. In Fig. 3 the measure motor- as well as the observe filter capacitor current of one phase are illustrate for a step change in loa of half nominal torque. As can be seen the controlle motor current shows the esire sinusoial shape an after a time of 3 ms the resulting rop of the rotational spee n is fully compensate. GaN power stage p n L C PMSM Observer-base active ampe filter Mechanically couple motors PMSM 3 x R L Power resistor Fig. 2: Couple motors for testing step changes in loa. n i Mu î C Step change in loa Fig. 3: Measure motor current i Mu an observe filter current î Cu for a step change in loa of half nominal torque at a rotational spee of 8 min. controller. Furthermore an analysis of the influence on filter parameter variations which show the theoretical limits for a stable close-loop controlle system is performe. An implemente laboratory prototype feeing a mechanically couple 3-phase PMSM is use for testing the propose control concept. The measure motor- currents an voltages show a stable behaviour for step changes in loa as well as the expecte almost noise-free sinusoial shape. 4. Conclusion In this work a control scheme for a 3-phase wiebangap inverter operating at 4 V DC-link voltage at a PWM frequency of khz with an observer-base actively ampe sine wave output filter is analyze. In orer to obtain high system efficiencies the resonance of the first filter-stage is ampe actively by feeback of the filter capacitor current avoiing aitional losses cause by issipative amping. Instea of aitional current sensing channels a linear observer moel is propose an esigne for estimating the capacitor currents neee for active amping. The paper escribes the applie close-loop control scheme for a purely igital implementation using a conventional PI-type 5. References [] A. Liow J. Stryom M. e Rooij an Davi Reusch. GaN Transistors for Efficient Power Conversion. John Wiley & sons El Seguno California 2 n eition 25. [2] K. Shirabe an M.M. Swamy. Avantages of high frequency PWM in AC motor rive applications. Energy Conversion Congress an Exposition (ECCE) September [3] P. Nussbaumer C. Zoeller T.M. Wolbank an M.A. Vogelsberger. Transient istribution of voltages in inuction machine stator winings resulting from switching of power electronics. Inustrial Electronics Society IECON 23 - ISBN

9 PCIM Europe June 28 Nuremberg Germany 39th Annual Conference of the IEEE pages [4] P. Cortes D.O. Boillat H. Ertl an J.W.Kolar. Comparative evaluation of multi-loop control schemes for a high banwith AC power source with a two-stage LC output filter. Proceeings of the International Conference on Renewable Energy Research an Applications (ICRERA 22) November [5] F. Stubenrauch N. Seliger an D. Schitt- Lansieel. Design an performance of a 2kHz GaN motor inverter with sine wave filter. International Exhibition an Conference for Power Electronics Intelligent Motion Renewable Energy an Energy Management PCIM Europe 27 May [6] F. Maislinger H. Ertl G. Stojcic C. Lagler an F. Holzner. Design of a khz wie bangap-inverter for motor applications with active ampe sine wave filter. International Conference on Power Electronics Machines an Drives (PEMD 28) April [7] B. K. Ghosh an J. Rosenthal. A generalize Popov-Belevitch-Hautus test of observability. IEEE Transactions on Automatic Control 4 January 995. [8] J. Ackermann. Parameter space esign of robust control systems. IEEE Transactions on Automatic Control 25:58 72 December 98. [9] S.G. Parker B.P. McGrath an D.G. Holmes. Regions of active amping control for LCL filters. IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS VOL. 5 pages January 24. [] J. Dannehl F. Fuchs S. Hansen an P. Thorgersen. Investigation of active amping approaches for PI-base current control of griconnecte pulse with moulation converters with LCL filters. IEEE Trans. In. Appl. 46:59 57 August 2. [] K.J. Astrom an B. Wittenmark. Computer- Controlle Systems: Theory an Design. Prentice Hall 2 n eition 99. ISBN