CONTROL AND PERFORMANCE OF A NINE PHASE SYNCHRONOUS RELUCTANCE DRIVE

Transcription

1 CONTRO AN PERFORMANCE OF A NINE PHASE SYNCHRONOUS REUCTANCE RIVE Abstract C.E. Coates*,. Platt** an V.J. Gosbell ** * epartment of Electrical an Computer Engineering Uniersity of Newcastle ** epartment of Electrical, Computer an Telecommunications Engineering Uniersity of Wollongong This paper eals with the control aspects of a nine-phase synchronous reluctance motor. Increasing the number of phases aboe three allows the stator MMF s to be shape so that the motor prouces significantly greater torue / RMS ampere. Generalize - oltage an torue euations are gien for the motor. Two methos of fiel-oriente control are consiere. The first is base on a simple hysteresis strategy in the stator current plane. The secon attempts to fin the optimal inerter-switching configuration in the transforme - harmonic current planes. Simulation results for both controllers are presente. A kw experimental rie base on the hysteresis controller is escribe an its performance characteristics etaile.. INTROUCTION The synchronous reluctance motor (SynRM) oes not naturally prouce sinusoial flux waes in its air-gap. The rotor saliency of the SynRM prouces a suare air-gap flux ensity istribution. If a suare current istribution interacts with this flux the SynRM generates its maximum torue per ampere. The suare current machine also exhibits lower copper losses in comparison to a similarly rate sinusoial current machine. These ieas are supporte by recent work showing that the aition of a thir harmonic space component to the MMF istribution effectiely raises the torue per rms ampere of the motor [4, ]. A esign moel has been propose which assumes the SynRM is excite by an ieal suare stator current istribution []. In the esign moel, irect axis excitation exists as a rectangular block of current oer the rotor pole eges. uarature axis excitation exists as another rectangular block of current oer the rotor pole face. Machines esigne by this metho reuire non-sinusoial winings of more than three phases to approximate the ieal current istribution of the esign moel. An experimental nine-phase, four-pole kw motor has been esigne an built base on the esign moel. This paper escribes the eelopment an implementation of a suitable spee controller for this motor.. GENERAIZE EUATIONS To moel an control the experimental motor s performance reuires the etermination of appropriate oltage an torue euations. The key to obtaining these expressions is the formation of a stator inuctance matrix. Traitionally, approximations are mae to the stator wining istribution an air-gap length as functions of angular isplacement aroun the stator. These expressions are then use to etermine the inuctance alues incluing the necessary harmonic components [6,8]. An alternatie approach is to approximate the air-gap flux ensity istribution an hence etermine flux linkages []. This metho significantly simplifies the necessary calculations. It can be use to show the mutual inuctance between two fully pitche, concentrate stator coils (separate by β raians) as a function of rotor position, α, is, M ab 4 ( α) ( ) 4 + ( n ( o ) + ) cos( n(α + β )) n n ( o ) cos( nβ ) n () an are the inuctances seen when the axis of a stator phase wining is aligne with the rotor irect an uarature axes respectiely. The stator inuctance matrix, (α), can be forme gien the specific imensions of the nine-phase machine. The matrix is symmetrical an a transformation matrix, T(α), can be foun such that the orthogonal transformation, T(α)(α)T T (α), yiels a iagonal matrix whose iagonal elements are,

2 These elements correspon to the funamental, thir, fifth an seenth harmonic, irect an uarature components of stator inuctance. The transformation matrix can also be applie to the stator oltage euation to etermine the - oltage euations in harmonic component form. These euations are; + i + ω () i rsi + ωi () i rsi + + ωi (4) i rsi + 6 ωi () i rsi + + ωi (6) i rsi + ωi () i rsi + + 4ωi (8) i rsi + 4 ωi (9) rsi i 6 Note that the stator wining of the experimental SynRM is star connecte with no neutral. As such there are only eight inepenent stator phase currents an no zero seuence component. Only eight transforme ariables are reuire to escribe the system. The corresponing - torue expression can be etermine by consiering the change in system coenergy with respect to rotor position. The torue euation is, T ( e + ( ) i i ) i + 6( ) i i i + 4( ) i i (). CONTRO STRATEGY Fiel-oriente control inoles separately controlling the irect an uarature axis excitations in the motor. ifferent strategies can be use to achiee such goals as maximum torue, maximum rate of change of torue an maximum power factor []. Here a constant current in the inuctie axis type controller is implemente. Figure shows a simplifie block iagram of this controller. irect axis excitation is hel at a constant alue to maintain machine flux. uarature axis excitation is arie to control the motor torue. The control methos presente here are essentially means to implement the current controller block in Figure. They take the irect an uarature axis excitation alues an etermine the appropriate inerter switching configuration in any gien control cycle. ω ref ω f/b Constant PI Spee Controller i,ref i,ref Current Controller State ariables S Inerter/ SynRM Figure Simplifie block iagram of SynRM spee controller Two strategies are consiere. The first is base on a simple hysteresis strategy in the stator current plane. The secon attempts to fin the optimal inerterswitching configuration in the transforme - harmonic planes.. Stator Current Controller The stator current controller splits the stator wining into two sections similar to the original esign moel. Phase winings locate oer the rotor pole eges carry irect axis current. The winings locate oer the rotor pole face carry uarature axis current. By knowing the rotor position an its imensions the appropriate phase current references can be generate. A similar strategy has been use in a fiel regulate reluctance machine []. Howeer, in this instance the iniiual phase winings were isolate an each supplie by a separate full brige inerter. Here the winings will be star connecte an supplie from a nine-phase oltage source inerter eliminating half of the power switches reuire in the comparable fiel regulate machine. Generating the stator current reference is complicate by two practical constraints. First, stator current is not

3 continuously istribute but is concentrate in the stator slots. Step changes in the stator current can only be mae at a slot opening. As the rotor moes iniiual phase winings at either ege of the rotor pole face must make a transition from supplying purely irect axis excitation to purely uarature axis excitation or ice ersa. Thus, the current reference is not suare but is instea trapezoial. Further, the stator phase wining is star connecte. The iniiual phase currents must sum to zero. To ai in achieing this reuirement ajacent phase winings on the stator hae their connection polarities reerse. Gien the kw machine imensions, typically one phase supplies the irect axis excitation, while the other eight phases supply uarature excitation. The eight uarature current phases will coneniently sum to zero. A fraction of the current reference from the ninth phase, that supplies irect axis excitation, must be subtracte from each of the other eight phases so that all nine phase currents sum to zero. improements oer the stator current controller. Stator currents an oltages are consiere as transforme ariables in the - harmonic planes. Thus, any one phase wining s contribution to both irect axis or uarature axis excitation is recognize rather than the simplifie esignation of the stator current controller. A current reference is generate as a ector in the harmonic planes where oltage ectors can be applie, ia the inerter, to control its position. The current reference is generate from the harmonic components of the ieal, esign moel current istribution. These components are foun by performing a Fourier series ecomposition. Figure shows the current reference ectors for the transforme frame controller thus forme. Effectiely, the reference becomes a set of stationary ectors in the rotor current plane whose lengths hae a simple proportional relationship to what is esignate irect an uarature axis current in the esign moel. Figure shows a typical current reference for one stator phase of the kw machine. The current reference is plotte against rotor position. Compensation for both stator slotting effects an the stator wining connection are inclue in the current reference. For comparison, the ieal current reference assume by the esign moel is also shown. I REF I.98 I.8 I Funamental.6 I. I r Harmonic I ieal. I.6 I θ.6 I th Harmonic.4 I th Harmonic Figure SynRM current reference in transforme rotor current plane. Figure Typical phase current reference ersus rotor position The stator current controller reas rotor position an generates the appropriate current references for the nine motor phases. Iniiual phase winings are then switche to either the positie or negatie inerter bus epening on the phase current relationship to the reference.. Transforme Frame Controller Selecting the optimal inerter switching configuration in the transforme - current planes offers potential Selecting the optimal inerter switching configuration, or oltage ector, to be applie uring a control cycle is a significant problem. In a three phase inuction motor rie this is euialent to the familiar choice from 8 ( istinct) two imensional oltage ectors. For the nine-phase rie this becomes a choice from 9 ( istinct) eight imensional oltage ectors. The choice is further complicate by the ifferent inuctances seen in the irect an uarature axes as well as the ifferent harmonic planes. In an inuction motor rie the choice can be mae by calculating the ieal oltage ector, ieal, an comparing it to the

4 possible oltage ectors. in (s) (where s enotes the inerter switching configuration). The optimal oltage ector is foun by minimizing the error, in (s) ieal. This metho works where all inuctances are eual because the error in the current plane is proportional to the error in the oltage plane. For the SynRM, it has been shown that the inuctance associate with each irect an uarature harmonic component is ifferent. To correctly relate oltage error to current error the iniiual components must be scale. The scaling function for oltage error is, ( in ( s) ieal ) ( in 9 ( s) 9 ieal ) () To implement the transforme frame controller the motor phase currents, spee an position are rea. The currents are transforme to the corresponing ector in the - harmonic planes. The oltage reuire to maintain the current reference at its esire alue is calculate using the generalize oltage euations. The inerter switching configuration is then etermine by choosing the best oltage ector on the basis of scale oltage error.. Simulation Results Initial testing an comparison of the two controllers was one by simulation in MATAB / Simulink. Figure 4 shows the step torue response for both controllers. Both simulations were carrie out assuming a khz control cycle. The transforme frame controller can be seen to offer faster response as well as better torue regulation. Although the transforme frame controller offers significantly improe performance it still presents some ifficulty to implement. The calculation oerhea for the oltage ector selection process is uite large. Most significantly, the controller is reuire to transform the motor currents an select the best oltage ector within a control cycle. These functions coul not be implemente in software with sufficient spee. A potential solution is to o the current transformation in harware an use symmetries amongst the oltage ectors to reuce the number of ectors reuire in the comparison. ue to these ifficulties only the stator current controller has been implemente in the experimental rie. Torue (Nm) Torue (Nm) - - Stator Current Controller Time (s) Transforme Frame Controller Time (s) Figure 4 Step torue response of (a) stator current controller an (b) transforme frame controller 4. RIVE HARWARE Figure shows an oeriew of the harware use to implement the stator current controller on the experimental SynRM. The power circuit is that of a typical oltage source inerter. A ioe rectifier an C filter conert the ac mains to a c bus oltage. A nine leg inerter then conerts the c bus oltage to the nine phase supply reuire by the SynRM. ynamic braking is inclue to limit the bus oltage uring eceleration of the rie. The rie is controlle by an Innoatie Integration AC64 SP car. This car contains a 6MHz TMSC processor along with appropriate support peripherals. Interfacing circuitry between the controller an power circuit can be logically iie into gate rie, current sensing an shaft encoer interface circuitry. The gate rie circuitry proies isolation between the controller an power circuit as well as harware base anti-shoot through protection. Current sensing is performe using Hall effect eices in eight of the motor phases. These are rea through

5 INVERTER POWER CIRCUIT Motor Phase Supply C ink Power Supply ynamic Brake Circuit Inerter Encoer CONTROER INTERFACE CIRCUIT Gate rie Circuit Current Sensing Circuit Shaft Encoer Interface SP CONTROER Figure Block iagram of rie system harware khz A/ conerters on the AC64 car. Position an spee feeback are obtaine from a three channel, pulse per reolution optical encoer. Two channels in uarature rie a counter an proie up/own logic corresponing to forwar/reerse irection. The thir channel proies a synchronization pulse once per reolution.. RESUTS The stator current controller was implemente in the rie. Figure 6 shows the current in one phase of the SynRM as measure ersus rotor position. The irect axis excitation is set to A. This correspons to half the current reuire to fully flux the experimental machine. uarature axis excitation is set by the spee loop to the alue necessary to maintain the spee of the unloae motor. The irect an uarature components of current can be clearly recognize along with the ajustments mae for stator slotting an the wining connection. Figure shows the step spee response of the rie. Both Figure 6 an represent interim results obtaine uring commissioning of the system harware. In each instance the experimental machine is operating with only half of its rate irect axis excitation. While these results o not inicate the performance limits of the rie they o emonstrate the feasibility of the system. Current (A) Measure Phase Current Rotor Position (egrees) Figure 6 Measure current in SynRM uner stator current control. Spee (rpm) Step Response of Spee oop Time (s) Figure Step response of spee loop

6 6. CONCUSIONS Two methos of implementing fiel-oriente control on a nine-phase SynRM hae been inestigate. The transforme frame controller operates on transforme oltage an current ariables achieing superior performance. Howeer, the computational reuirement makes it ifficult to implement solely in software. Suggestions hae been mae on means to implement the controller but these remain unerifie. The stator current controller proies a much simpler means to implement fiel-oriente control. While its performance oes not match that of the transforme frame controller it has been possible to emonstrate goo current an spee regulation.. REFERENCES [] RE Betz, Theoretical Aspects of Control of Synchronous Reluctance Machines, IEE Proceeings B, Volume 9, Number 4, pages -4, July 99. [] CE Coates, Platt an BSP Perera, esign Optimization of an Axially aminate Synchronous Reluctance Motor", Conference Recor of IEEE IAS Annual Meeting 99, Volume, pages 9-8. [] CE Coates, Platt an VJ Gosbell, Generalize Euations for a Nine Phase Synchronous Reluctance Motor, Australian Uniersities Power Engineering Conference 96, Volume, pages [4] JS HSu (Htsui), SP iou an HH Wooson, Peake-MMF Smooth Torue Reluctance Motors, IEEE Transactions on Energy Conersion, Volume, Number, pages 4-9, March 99. [] J aw, A Chertok an TA ipo, esign an Performance of Fiel Regulate Reluctance Machine, IEEE Transactions on Inustry Applications, Volume, Number, pages 8-9, September / October 994. [6] PJ awrenson, an A Agu, Theory an Performance of Polyphase Reluctance Machines, Proceeings of IEE, Volume, Number 8, pages 4-44, August 964. [] HA Toliyat, MM Rahimian an TA ipo, A Fie Phase Reluctance Motor with High Specific Torue, IEEE Transactions on Inustry Applications, Volume 8, Number, pages 69-66, May / June 99. [8] HA Toliyat, MM Rahimian an TA ipo, Moelling of a Fie Phase Synchronous Reluctance Machine Incluing Thir Harmonic of Air-Gap MMF, Conference Recor of IEEE IAS Annual Meeting 99, Volume, pages -.