Rapid simulation of permanent magnet drives

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(1)Rapid Simulation of Permanent Magnet Drives Praveen Kumar1 Peter van Duijsen2 - Pavol Bauer3 1. ElmoCad, Germany, www.elmocad.de Simulation Research, The Netherlands, www.caspoc.com 3 Delft University of Technology, The Netherlands, www.tudelft.nl 2. Abstract: For designing an electrical drive a Rapid Application Development (RAD) tool during the design phase of an electrical machine in order to perform fast prototyping, speeds up the development. Using the RAD tool various prototypes of machines can be designed and the prototype of the design can be verified in simulating the complete electrical drive including power electronics, control and mechanical load Keywords: Simulation, Modeling, Brushless PMSM, rapid prototyping, Power Electronics, Smartfem, Caspoc.. 1 Introduction The industry and especially the automotive industry is faced with continuously increasing demand for shorter development time to market. This requires fast prototyping tools for the design of electrical machines, power electronics and electrical drives. The tools should predict the overall drive performance fast and accurate. Since there is a contradiction between the last two requirements to be fulfilled in one tool, a combination of tools has to be created. From a users standpoint a single tool would be preferred. Therefore an integration of simulation tools is required where each tool is designed for a specific task, but together form a single user interface. A fast prototyping tool for electrical drives should at least combine analytical/numerical fast prototyping of electrical machines, fast power electronics simulation without convergence problems, but capable of simulating the complete drive with all non-linear components and synthesis of embedded C-code for digital controller design.. 2 Integration of Simulation tools The entire model of the mechatronic system should ideally include all influences of the above-described components. However there is a. difference in the modeling techniques that will not allow us to integrate all models into one single model. For example the Finite Element analysis is mathematically different from system analysis which in turn is different from nonlinear circuit analysis[10]. Use is made of the multilevel modeling technique, where circuit modeling is combined with block-diagram system modeling and control in terms of a computer program. The more detailed models, required for the electrical machine and the mechanical system, are analyzed in Finite Elements. The results from the Finite Elements have to be included in the entire model. There are in principle two methods, Parameter exchange or Co-Simulation. Both methods will be described in the following section.. 3 Parameter exchange or Co-Simulation Parameter/Data exchange Parameter/Data exchange is a method where the first tool is used to design or analyze a component and use the resulting parameters/data from that analysis in a model in the second tool[4]. Depending on the results from the second tool, the user can make modifications in the model in the first tool and repeat the analysis in the first and in the second tool.. Figure 1: Parameter/data exchange Co-simulation If all models in a system are such of complexity that they cannot be described by a set of parameters for an equivalent model, cosimulation is required..

(2) Also if the mathematical models of the components form one implicit set of equations that has to be solved 'in one go' instead of a sequential simulation, co-simulation is required.. Co-simulation is required for, for example, the following applications: Design of an electromagnetic plunger where eddy currents influence the magnetic field distribution. The eddy currents can be calculated in a transient FEM analysis, but the driving coil voltage from the power electronics is dependent on the position of the anchor or the current drawn from the source or measured in the varying inductance. Design of a drive application where the mechanical load is modeled as a multi body kinetic model and the control of the electrical drive and its power electronics are modeled in a circuit simulator.. Figure 2: Co-Simulation A co-simulation is usually performed in the time domain and the results are waveforms from various observation points, like voltage, current speed, torque, power, pressure, etc. Since all tools have to run at the same time, the tool that requires the most calculation times determines the total simulation time. For example, in a co-simulation of a transient FEM analysis of an electrical machine together with a circuit simulation of a power converter, the FEM analysis requires far more calculation time than the circuit simulation. To choose for one of the two methods there is a very simple rule. If a simulation in one tool requires considerable more calculation effort, the parameter exchange has to be chosen. The only exception to this rule is, if co-simulation is required due to the implicit nature of the mathematical model, or if the total simulation time is within practical limits. Parameter exchange is common in, for example, the following applications: Design of an electrical machine in a FEM program and calculation of the tables storing the rotor-position dependent inductance and machine constants to calculate torque and back-emf. Design of the thermal behavior of a system where an equivalent thermal circuit is calculated in a FEM program. The resulting thermal circuit is coupled to the semiconductor models in the circuit simulator to calculate the transient thermal response caused by the losses in the semiconductors.. 4 Permanent Magnet Motor Design Since the emergence of new high field permanent magnet materials, brushless DC motors (BLDC) and permanent magnet synchronous machines (PMSM) have become increasingly attractive in a wide range of applications. They have smaller volume compared with equivalent wound field machines, operate at higher speed, dissipate heat better, require less maintenance, and are more efficient and reliable than conventional motors. Many researchers have made efforts to improve motor performance in terms of efficiency, maximum torque, back EMF, power/ weight ratio, and minimum losses in iron, coils, friction, and windings. A prerequisite to achieve optimal design of a motor is fast and reliable simulation tool. Caspoc and SmartFEM are developed to achieve reliable results and increase the speed in the predevelopment phase. The main features of a combined BLDCM/PMSM design tool are: • Pre-programmed stator and rotor topologies for PM motors, thus reducing the burden of drawing the geometry in any CAD programme • Coupling to Power electronics and Electrical drives simulator CASPOC for detailed electrical drive simulation • Uses FEMAG for FEM simulation, hence accurate results of simulation, especially for cogging torque and torque ripple calculations • Linear and non-linear FEM simulation • Flexible winding editor with automatic winding generation.

(3) • • • • •. Different phase connections (Star/Delta) Unbalanced windings, i.e. different coils can have different number of turns User defined magnetisation of permanent magnets User friendly pre-processing and postprocessing Three phase and single phase motor can be simulated. cogging torque and back-emf of the machine can be calculated directly, as shown in the figures below.. 5 Geometry of the motor The geometry is entered in SmartFEM, which is a simulation tool based on FEM and is suited for simulation of PM motors. It has predefined topologies of stator and rotor that a user can select. The user can select out of 20 different rotor topologies for the inner rotor and 4 stator topologies. One rotor and stator topology is shown below. Figure 4: Cogging torque. Figure 5: Induced back emf for each phase. Figure 3: PMSM with Spoke magnet design The advantage to the predefined topologies is that by varying the geometric input parameters the shape of the topologies can be changed with ease. In the above figure a spoke design for a specific set of input parameters is shown. The possibility to rapidly change the geometric configuration of the motor by varying the input parameters a user can compare the results of various variants. The RAD tool also aids the user in defining the winding schemes based on specified number of slots and poles, if the pole slot combination allows balanced winding . It has a winding editor where a user can define distributed or concentrated windings. In the Rad tool tool. Exact modelling is important to correctly calculate the winding inductance Ld and Lq depending on the saturation level. This can only be done in FEM due to the high-non-linear character of the material and the magnetic circuit that is evolving from the saturation in the material. Not all of the material is used for the flux lines and some parts of the material are highly saturated and thereby limiting the performance. There is a difference in Ld and Lq when is comes to saturation. This influences the performance of the total drive, since the field oriented controller is designed for a specific set of Ld, Lq and the associated time constants. The magnetic field distribution in the motor is shown in Fig.6. From the figure it can be seen that the teeth 1 and 3 are having a very high flux density (approximately 2 Tesla) that may result in saturation..

(4) inductance of the motor. The inductance of the motor will hence be a function of the rotor position and currents in the turns of the coil as high values of current may further add to the saturation in parts of the motor.. 6 Complete Electrical Drive simulation. Figure 6: Field distribution in a PMSM In Fig.7 it can be seen that most of the flux lines pass through the teeth 1 and 3. In order to avoid the saturation the width of the teeth has to be increased. High flux densities in any part of the machine result in higher iron losses (eddy current and hysteresis losses).. After a first initial protyping in Smartfem, the machine is included in the electrical drive simulation in Caspoc, where the performance of the machine in combination with power electronics, control and mechancial load is tested. Previous machine design tools only gave machine performance for simplified control schemes. In this new approach, the entire electrical drive is simulated and therefore more details on the performance of the electrical machine are obtained. The machine parameters and tabulated data are imported in Caspoc by supplying the Objectname for the machine in Caspoc. In the figure below the machine is connected to the power electronics model.. Figure 8: Coupling of the machine data to the machine model in the drive simulation.. 7 Fast loss predicting models. Figure 7: Field lines in a PMSM The fig.6 also shows that the steel sections above and on the edges of the magnet are also saturated. This is desired to force the flux to pass through the air-gap otherwise the flux will circulate within the rotor iron resulting in very small air-gap field and hence very small back emf. The configuration of the motor shows that neither the geometric air-gap is constant nor the magnetic air-gap is constant due to saturation in certain sectors of the motor. The combination of these effects viz., asymmetric geometry and saturation will have a consideration effect on the. To predict the losses in a drive system, the simulation has to run for many cycles. With the ever-increasing switching frequency, the total simulation time would be too long for a simulation employing dynamic Mosfet, IGBT or GTO models. Therefore the ideal switch model, with conduction and switching losses modeled are used to calculate the losses in the inverter.. Figure 9: Modules for the Mosfet, GTO and IGBT with loss prediction.

(5) The figure above shows the modules for the fast loss prediction models. Besides the electrical nodes, each module has a thermal node that can be connected to a thermal model. In case of a Mosfet, the transconductance and drain-source on-resistance are dependent on the temperature. In the fast loss prediction modules also a forward voltage drop for the mosfet is included in the model, although mostly the temperature dependent drain-source onresistance is the design parameter of interest. For the IGBT, both VCEon and RCeon are temperature dependent. The switching losses are given in the manufacturer data-sheet and are specified for 25˚ Celsius and 125˚ Celsius. The junction temperature has to be calculated during the simulation and is used to adapt the parameters for the semiconductors. Using the fast loss prediction model enables the prediction of the system behavior and prediction of the losses of the component. In an IGBT, the temperature dependent VCEon and RCeon model the conduction losses. The switching losses are calculated from the data-sheet parameters Eon and Eoff. The temperature on the heat sink is dependent on the losses. The losses are temperature dependent because VCEon and RCeon are temperature dependent.. The preset value of the current on the direct axis is set to 0. The speed controller PILIM3 controls the preset value on the quadrature axis. The speed controller is build from one PI controller that has as input the error signal between the measured and preset angular speed and the output is the required stator current on the quadrature axis. The controlled stator voltage in the DQ frame is transformed into the real stator voltage (VRSOLL, VSSOLL, VTSOLL) that is input to the pulse width modulator.. Figure 10: Complete electrical drive simulation in Caspoc with prototype of PMSM included. 8 Field Oriented Control The Permanent Magnet Synchronous Machine (PMSM) is used in this vector controlled application. An inverter is connected to the PMSM. The model for the PMSM is a dq model of the synchronous machine with permanent magnet excitation. The torque produced by the PMSM is connected to a mechanical drive train, being a rotating mass with to bearings. The inertia of the rotating mass is 0.05 [kgm2] and the total friction of the bearings is 0.5 [Nms/Rad]. A sensor measures the angular speed of the shaft and using the INTMOD block, the position of the shaft is calculated with a modulus of 2*π. The stator currents are measured using current sensors in the PMSM. From these currents i1, i2, i3, the stator currents in the DQ frame IDIST and IQIST are derived, using the position of the shaft THETA. The measured values of the stator current in the DQ frame are compared with the set values in the DQ frame and the resulting and the resulting vector (IDS, IQS) is controls the required stator voltage In the DQ frame VDSOLL and VQSOLL using two PI controllers.. 9 Exporting Embedded control C-Code From the control in the block diagram the C code can be exported and used in a DSP or microcontroller, see the figure below.. Figure 11: Export of Embedded C-Code for DSP or Micro-Controller After exporting the C code, the C code can be viewed directly from Caspoc or included into.

(6) your main embedded C project, see the figure below.. Figure 12: Exported C-Code from the vector control The exported code is optimized for execution speed and not used block names are optimized, to condense the exported C code, see figure below.. Figure 13: Optimization of exported C-Code. Conclusion Existing machine design tools are able to predict electrical machine behavior to some extend. However the coupling to power electronics, mechanical loads and control is not achieved in full detail. In this paper the complete model is shown where electrical machine prototype is fully included in the electrical drive simulation. Here all details of the electrical drive interact with the model of the electrical machine. Therefore a more detailed performance of the electrical machine prototype can be calculated. References [1] Bauer, P., and Duijsen P.J. van, "Challenges and Advances in Simulation," Proceedings of PESC '2005 Conference, Recife (Brazil), 2005. [2] SmartFem, Users Manual 2006, www.elmocad.de [3] Ansys/Workbench, Ansys Corp., www.ansys.com [4] Caspoc 2005, Simulation Research, www.caspoc.com [5] Otto J., Killat U., van Duijsen P.J., Energy Based Model Synthesis for Electrical Actuators and Sensors, PCIM 2002 Nürnberg.. [6] P.Bauer, D.Owsianik: Integrated Computers Aided Design of a Flyback Converter, Power Electronics, Power Electronics Journal, April 2002 [7] P.J. Van Duijsen, P. Bauer,D. Gospodaric: simulation based Optimization of Electrical Drives, PCIM 04, Nurnberg, May 25-27, ISBN 3-928643-39-8, pp.922-927 [8] P.J. Van Duijsen, P. Bauer, U. Killat, Thermal Simulation of Power Electronics, PCIM 04, Nurnberg, May 25-27, ISBN 3928643-39-8, pp.881-886 [9] P.Bauer, P.Korondi, P.J.van Duijsen : Integrated Control and circuit Simulation for a Motion Control System, EPE 2003 Toulouse; 2-4 september 2003, ISBN 9075815-07-7 [10] P.Bauer, P.J.van Duijsen: Integrated Simulation of Embedded Controls in Power Electronics, PCIM 2002 , Nurnberg, Proceedings Intelligent Motion, ISBN 3928643-31-2.

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