# Three-phase alternating current motors

The third type of motor, which is becoming more and more used in railway traction is the asynchronous three-phase alternating current (hereafter AC) motor. This type of motor has the advantage of not having a collector and therefore maintenance is greatly reduced.

Figure 12 shows the equivalent electrical circuit for each of the three-phase motor phases (Esperilla et al, 2007). The resistance "Re" and the winding "Le" represent the behaviour of the stator circuit. The Resistance "R'r" and the winding "L'r", reduced to the stator circuit, represent the behaviour of the rotor circuit. The resistance "Rp" and the winding "Lp" represent the losses due to hysteresis produced in the air-gap and the losses due to magnetic flux produced in the stator and the rotor. Finally, the resistance "R'C" is the equivalent load resistance that models the effect of the mechanical energy produced by each motor phase, where "s" is the slip existing between the rotational velocities of the magnetic field generated by the stator and the rotor. The electrical potential dissipated through the resistance "R'C" is equivalent to the potential generated by the electric motor in each of its phases. Fig. 12. Equivalent circuit of an asynchronous three-phase AC motor. Fig. 13. Bond-Graph of the asynchronous three-phase motor.

Figure 13 illustrates the complete Bond-Graph model of the asynchronous three-phase AC motor. Each of the horizontal branches of the Bond-Graph models each of the phases of the motor, starting out from the equivalent circuit shown in Figure 4. The three phases are subjected to an alternating current "U", 120° out of phase using the Metatransformer ports shown to the left. The mechanical power generated by each phase is modelled by the "MGY" ports shown to the left. This rotational mechanical power is added to the "1" junction shown on the extreme right of the Bond Graph, so that it can be applied to the motor shaft modelled by the Inertial port "I" with parameter "J". The friction losses are also taken into account, and these are represented in the resistance port "R" with parameter "p".