Gyuláné Vincze, Gergely György Balázs

Budapest University of Technology and Economics Department of Electric Power Engineering

**Table of Contents**

The synchronous motor is known for a long time ago, but only in the recent decades has provided an opportunity to apply it in intelligent drive systems as in vehicle drive systems. The breakthrough has been reached by high quality permanent magnet rotor motors and inverter fed current vector control synchronized to the rotor flux. This control is similar to the field oriented control of the induction motors, but it can be easily applied, because the rotor flux of the permanent magnet synchronous motor is approximately constant. Complicated calculations and machine model ate not required, the rotor flux vector position can be definitely determined in every time instant by measuring the rotor angle.

The synchronous motor drive - provided with current vector control synchronized to the rotor flux - has at least as good dynamical properties as the field oriented controlled induction motor drive system. However the permanent magnet synchronous motor is much more sensitive, expensive and can be produced with smaller power than the induction motor. The expansion of the synchronous motor power can be reached only with separately electromagnetic excitation.

There are two possible solutions for the air gap flux density spatial distribution of the permanent magnet synchronous motor. Accordingly sinusoidal and rectangular field machines can be distinguished. The optimal (joint) current vector control of the two motor types is different. For traction the *sinusoidal field permanent magnet rotor motor drive system* is favorable, which speed range can be increased by field weakening mode. The *rectangular field permanent magnet rotor motor drive system* is applied only in low power electric vehicles, e.g. in cars.

The rotor pole flux vector is the main parameter for the current control of the *sinusoidal field permanent magnet synchronous drives* that is defined according to Fig.6.1.a in x-y stationary coordinate system:

The magnitude of Ψ_{p} is approximately constant, and its direction can be identified with the rotor phase angle (α).

The synchronous motor drive control is based on the vector current control fixed to the direction of the pole flux. The main purpose of this control can be represented with Park vectors in *d-q* coordinate system, fixed to pole flux (Fig.6.1.b and c).

The torque of the current controlled permanent magnet synchronous machine is defined by the *i*
_{q} current component and the ϑ_{p} torque angle, because the torque can be calculated as follows (*p** is the number of the pole pairs):

6-1

Minimal stator current belongs to a given torque if the *d* component of the current is zero (*i*
_{d}=0), i.e. the torque angle is ϑ_{p}±90°, that can be seen in Fig.6.1.b. This is the energy efficient “normal mode” of the motor that possess the optimal torque transmission condition. Positive torque can be created with ϑ_{p}>0 negative can be created with ϑ_{p}<0 torque angle.

The field weakening mode differs from the optimal, and it is fulfilled in ϑ_{p}>90° and ϑ_{p} <(-90°) range as in Fig.6.1.c. The torque transmission deteriorates in field weakening mode, but the motor speed range can be expanded, that is important at traction.

*Negotiation of the sinusoidal field permanent magnet rotor sy*
*n*
*chronous motor *

For the negotiation of the cylindrical rotor sinusoidal field permanent magnet motor, the most adequate and simplest equivalent circuits can be seen on Fig.6.2 (*L*
_{d} synchronous inductance). Fig.6.2.a is valid for fluxes.

The equivalent circuits of Fig.6.2.b are represented with quantities valid in stationary *x-y* coordinate system. According to these, the transient equations of the synchronous motors - valid for instantaneous values and written by Park vectors - are as follows:

Voltage equation:

Flux equation:

6‑2

Fig.6.3. presents the current vector and the *M-ω* boundary characteristics of the current controlled permanent magnet synchronous motor, where three mode ranges can be distinguished.

Fig.6.3 presents only the motor mode range valid for *M*>0 torque. In *M*<0 braking mode range the curves are similar to the motor mode range, but these are mirrored to the horizontal axis.

*Energy efficient, normal mode *

In Fig.6.3 the normal mode is represented by the I marked range. The main characteristic is that the torque angle is *J*
_{p}=±90°, and *i*
_{d}=0. A given torque can be produced by minimal current, i.e. minimal copper loss, and in this case a given current can be produced maximum torque. The *M*
_{max }torque is determined by *I*
_{qmax}
*=I*
_{max}, by considering the short-term permitted *I*
_{max}
*/I*
_{n} current overload. The energy efficient normal mode is sustainable until the voltage required for the control is *U≤U*
_{max}, where generally *U*
_{max}
*≈U*
_{n}. The dashed line shows the reachable speed range in this mode. The reachable maximum no-load speed is: *ω*
_{üj}.

*Field weakening range*

So the dashed line represents the speed that can be reached by the motor with *J*
_{p}=±90° torque angle and maximum (nominal) voltage. While more voltage is not available, field weakening must be applied to further increase the speed. The field weakening concerns for the stator flux and does not perform the demagnetization of the rotor permanent magnets. According to Fig.6.4.b the stator flux magnitude can be reduced by the *d* current component. The vector diagrams are concerning for fundamental values, it is represented by index *1*.

Fig.6.4 a and b figures are concerning for an operating point with same speed and same torque (I_{1q} is equal). Based on the comparison of the two figures, the previous statement is turned out that more resultant current vector is required in field weakening mode than in normal mode for producing the same torque. On the other hand for the same speed with field weakening – by applying *I*
_{1d} current component with opposite direction to – smaller *U*
_{i1}
^{*} voltage magnitude would be required. Consequently if the *U*
_{i1}
^{*} voltage magnitude would reach the maximum (nominal) voltage, the speed would be increased with *U*
_{max}
*/U*
_{i1}
^{*} ratio. The speed increasing rate is approximately 2…2,5*ω*
_{üj}, depending on the motor parameters, and can be characterized with *II* and *III* ranges of Fig.6.3. In *II* range the torque is limited by *I*
_{qmax} current component, as a consequence of the overcurrent protection of the resultant current vector magnitude *I*
_{max} (in Fig.6.3.a the cycle arc with *I*
_{max}). In *III* range the magnitude of the reachable torque is determined by the limitation of the field weakening component (*i*
_{d}).

Fig.6.4 also presents a disadvantage of the permanent magnet synchronous motor vehicle drive. Compared to the nominal speed, the field weakening mode allows the significant increasing of the speed. If the electric control is interrupted at such a high speed, the *U*
_{p}
*=ωΨ*
_{p}
*>>U*
_{max} voltage can get out to the synchronous motor terminals that can cause inverter failure. It should be definitely avoided.

*Inverter solutions for synchronous motor drives*

Such inverters can be applied for sinusoidal field synchronous motor drive control that can fulfill the previously described current vector control. Principally there are two types of synchronous motor drives:

voltage source inverter fed synchronous motor drive,

current source inverter fed synchronous motor drive.

Nowadays almost the voltage source inverter solutions are used. The current source inverter fed synchronous motor drives were used for traction in the past by some manufacturers therefore these are briefly discussed.

Fig.6.5 presents a possible construction for voltage source inverter fed sinusoidal field synchronous motor driven vehicle.

In normal mode the prescribed value for the current d component is: *i*
_{dref}=0 that changes only if the motor voltage reaches the maximum value. In this case the field weakening mode starts. The reference signal of the current q component (*i*
_{qref}) is defined by required tractive force (torque) or the output of the vehicle speed controller, according which control method was selected. The cross compensation (dashed line) is implemented to eliminate the cross-effect of the *d-q* components

The development of the thyristor technique allowed to build high power voltage source inverter fed synchronous motor driven vehicles. It can be realized only by excitation current controlled, separately excited, slip-ring synchronous motor. Fig.6.6 presents an example, was used at the French Railways.

This construction is similar to the current source inverter fed drive system that can be seen in Fig.5.15. The current of the DC link is controlled by the line-side converter and the *L* inductance is smoothing it. There is a great difference in the operation of the motor-side thyristor bridge. At current source inverter fed synchronous motor the motor-side thyristor bridge operates with natural commutation, commutating capacitor is not required for the commutation. The operation is similar to the network commutation current converters, but the role of the three phase network is fulfilled by stator of the synchronous machine. The synchronous machine is over-excitable through the slip-rings that create the possibility for the natural commutation. Similarly to the current source inverter fed induction motor drive (Fig.5.15.) electrically the conducting states replace each other with 60° that causes torque ripples at both solutions. According to the locomotive in Fig.6.6 the torque ripples can be reduced by two stator coils shifted with 30° to each other. The auxiliary thyristors of the DC link is required for low speed operation, when the inducted voltage – that is proportional to speed - is not large enough for the natural commutation, and the current conduction states should be varied.

Over the years the voltage source inverters suitable for pulse width modulation control and the field oriented controlled induction motor drives obscured the importance of the current source inverter fed synchronous motor drives.