As far as I know the magnetic force is responsible for the motor rotation. So, horsepower of the motor is mostly related to magnetic flux on the coils (windings). Also magnetic flux is directly related to inductance (Number of turns) and the current flow on the coil. Am I right so far?
That is not quite right. Energy is force X distance. Power is the rate of energy transfer or conversion, force x distance / time. The power delivered by a motor is torque X speed. Torque is force multiplied by the radius at which the force is applied.
1- What is magnetizing reactance of the winding?
The magnetizing reactance is the part of the stator reactance that produces useful magnetic flux. Due to limitations of the geometry of the motor structure, less than 100% of the winding flux actually contributes to producing torque and transferring energy to the rotor. Therefore the winding is shown in the equivalent circuit as two components. X1 is just an impedance to the flow of current that does not directly contribute to the function of the motor. The flux in Xm is the flux that produces torque.
2- Why do we want high power factor?
High power factor means the minimum current to deliver a given power to the load.
3- How can I calculate the horsepower and the efficiency of my motor?
You completely analyze the equivalent circuit. The mechanical power developed in the rotor is the power in R2x(1-s)/s. In the rotor circuit, R2/s is comprised of two parts, R2, the rotor resistance, and R2x(1-s)/s the representation of the mechanism of conversion of electrical power to mechanical power.
You also need to consider that some of the power developed in the rotor is lost to friction and windage rather than delivered to an external load.
Note that you have asked at least four questions. A complete answer would require a chapter in a text book assuming that you have mastered the prerequisites for the course.
For instance, is this the equivalent circuit model for stator?
That is the equivalent model of one phase of the entire motor. The stator part consists of Rs, Xs and Xm. Wr and Rr are the rotor components. Note that it has been simplified to remove the effect of the stator:rotor turns ratio. However you can assume that the rotor parameters given are the values referred to the stator circuit. Referral to the stator means that the stator frequency can be used to calculate both Xs and Xr. The speed of the rotor is the mechanical speed.
The stator current is calculated by dividing the phase voltage by the equivalent complex impedance of the entire circuit shown.
The speed of the stator magnetic field in radians per second is 4xPixf/poles. The speed of the rotor (mechanical speed) is the speed of the stator magnetic field minus the slip. The speed of the rotor magnetic field is the same as the speed of the stator magnetic field. In the other problem, I believe that the stator omega is the frequency of the power and the mechanical speed is the speed of the magnetic field.
To further explain the concept:
Conceptually, the mechanical structure must always be kept in mind. In analyzing motor performance, "no-load" is assumed to be operation with nothing connected to the shaft. Except for that special condition the speed of the rotor = speed of load. The torque developed in the rotor = torque of load plus mechanical losses in the motor consisting of bearing friction and aerodynamic drag on the rotor (windage). In this problem, mechanical losses seem to be considered to be part of the load or considered to be negligible. Stator speed = field speed = synchronous speed.
It appears that iron losses have been considered as negligible in this problem. In the equivalent circuit, iron losses (hysteresis and eddy-current losses) would be represented as a resistor in parallel with Xm. That is a rather large loss to neglect, but I it is probably necessary to neglect it in order to construct the problem the way is is constructed.
Motor & Load Torque vs Speed
This problem defines load torque demand, the torque required to drive the load at a given speed. The load torque demand is proportional to speed squared. That would be typical for a fan. Information is provided to define the motor torque capability as a function of speed. The steady-state operating speed and torque for a motor driving a load is the intersection of the motor torque capability curve and the load torque demand curve. If the actual operating speed is above or below the normal operating point as it is when the motor is initially energized, the excess motor torque capability is applied to accelerating the motor and load inertia to the normal operating speed.
Best Answer
If you know the resistance and inductance of the windings, you can calculate the impedance angles from Zm = Rm + jXm and Za = Ra + jXa - jXc. Main winding angle = arctan (Xm/Rm) and aux winding angle = arctan (Ra/(Xa-Xc)). These angles will only be true for the instant the motor is energized. Once the rotor begins to rotate, the rotor characteristics and load must be taken into account.