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https://designers-guide.org/forum/YaBB.pl Modeling >> Behavioral Models >> How can I model a 3-phase bldc motor in Verilog-A https://designers-guide.org/forum/YaBB.pl?num=1126427071 Message started by Neo on Sep 11th, 2005, 1:24am |
Title: How can I model a 3-phase bldc motor in Verilog-A Post by Neo on Sep 11th, 2005, 1:24am Dear all Who can teach me to model a 3-phase brushless dc motor ??? Thx. a lot :) |
Title: Re: How can I model a 3-phase bldc motor in Verilo Post by Jess Chen on Sep 12th, 2005, 11:10am Before developing a behavioral model, you must clearly identify the purpose and constraints of the model. How much accuracy do you want and how long are you willing to wait for it? The most accurate way to model the motor is to model each of the three phases individually and use detailed models of the drive electronics. However, the switching frequency of the drive system will probably tax your patience. There is also the trigonometric operations on the shaft angle. Since the shaft spins at a high rate compared to the time constants of interest, the shaft rotation also slows the simulation. In any motor model, an ideal transformer converts winding current to shaft torque in one direction while converting shaft velocity to back emf in the other. Each winding has such a transformer and the turns ratio depends dynamically on shaft angle. The shaft angle comes from integrating shaft velocity. One way to think of this system is as a PLL. The shaft converts speed to positiion the same way a VCO converts frequency to phase. The first simplification (i.e. way to reduce run time), in my opinion, is to use state space averaged models for the power electronics. The next level of simplification is to assume unilateral signal flow from the drive to the winding. In other words, if you are controlling winding current, you may be able to neglect the effects of the winding impedance and back emf. If after using state space averaged models for the power electronics your patience is still taxed, you can perform two transformations on the motor variables to remove the trigonometric functions of shaft angle in the ideal transformers that convert current to torque. The first transformation is from 3-phase motor to an equivalent 2-phase motor. The second transformation converts stator variables to rotor variables. In the rotor reference frame, the transformer turns ratios are constant; they no longer depend on trigonometric functions of shaft angle. This model is particularly simple if you treat the power electronics as ideal current sources. As you look upstream in the power electronics, you must eventually assume power comes from an ideal source. The further away from the shaft you make that assumption, the more accurate your model. You can use the aforementioned transformation to the rotor reference frame and still include mechanical loading on the power electronics through the back emf by also transforming the drive electronics to the rotor reference frame. The overall model runs fast because state space averaging removes the switching frequency and the rotor-referenced variables remove dependencies on shaft angle. The down side is that all of the inductors and capacitors in one phase of the drive electronics are coupled through controlled sources to their counterparts in the other phase. If you are interested, I can dig up a paper for you. |
Title: Re: How can I model a 3-phase bldc motor in Verilo Post by Jess Chen on Sep 12th, 2005, 6:19pm Please note that I've edited my response slightly. |
Title: Re: How can I model a 3-phase bldc motor in Verilo Post by sheldon on Sep 17th, 2005, 12:56am Jess, How good are the models with trignometric approximations at capturing start-up effects? The start-up effects I am referring to are the effect of backlash, the angle between stator and rotor, in-rush current in the stator inductors, etc. on start-up. Also are the transforms you refer to the physical --> abc --> dq0 transforms? Also any insights into how much effort should go into modeling the non-idealities of the stator inductors and the air gap flux? For example, would you expect the the stator inductor to saturate during start-up? Does the air gap flux saturate during start-up? Best Regards, Sheldon |
Title: Re: How can I model a 3-phase bldc motor in Verilo Post by Jess Chen on Sep 19th, 2005, 12:33am Sheldon, I'm not sure I know what you mean by trigonometric approximations. I assume you are talking about the transformation to rotor coordinates. I am indeed referring to the abc to qd0 transformation, but please note that I spoke of two transformations. The first is from abc stator variables to stator qd0 variables. The second is from qd0 stator variables to qd0 rotor variables. The first transformation reduces the number of effective windings. The second removes shaft angle from the dynamics. I have used the second transformation primarily for stability analysis. I wanted a model that SPICE would linearize about a true DC quantity. Angular velocity is a DC quantity whereas angle is not. You could probably combine the two transformations into one. I have not modeled backlash with a rotor reference frame model but I think it is possible. One would probably have to detect when the velocity drops to zero and then integrate velocity to determine when the gears re-engage. If you are willing to neglect ripple at the harmonics of shaft speed, the rotor reference frame model should simulate the inrush current fairly accurately. I assume the angle between stator and rotor you refer to is the torque angle. Neglecting harmonic ripple, the rotor reference frame model accounts for torque angle dynamics. As for saturation, I believe the air gap should prevent it. However, I don't see why it would be any harder to model for a motor than it would be for a power supply, once you have the basic motor model down. You would have to make sure the saturation levels are transformed to two phase variables just as the inductances and three-phase variables are. Regardless of the application, the rotor reference frame model is complex enough that I would spot check it against a stator reference frame model with transient simulations. -Jess |
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