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.
The starting current and starting torque can be calculated from the per-phase equivalent circuit. The circle diagram is an aid for that calculation. You need to use the data from the no-load and blocked-rotor tests. However the DC resistance is also required and should be measured. You should be able to find the procedure for calculating the equivalent circuit component values in a text book or lecture notes that can be found on the internet. The procedure for calculating torque from the equivalent circuit can also be found.
The rated motor speed and current should be marked on the name plate. The rated torque can be calculated from the rated speed and power. With the rated torque and current, you can use the given percentage values to calculate starting torque and current.
The energy meter is not very useful beyond performing the no-load and blocked-rotor tests.
You should find the procedures mentioned above, work on the solution, then ask for assistance with any parts that you don't understand. The full solution can not be provided here as the answer to a single question.
Best Answer
The RPM is determined by the frequency and does not directly effect the current. The current is more closely related to torque. Some useful relationships are:
Motor speed RPM = 120 X Frequency (Hz) / Number of motor poles (4 poles for the Tesla I think)
Input power to the motor, Watts = Volts X Amps X Square Root of 3 X Power Factor
Horsepower output = Torque (Ft-Lbs) X RPM / 5252
Input Power X Efficiency = Output Power
1 Horsepower = 746 Watts
The Tesla motor is very efficient, 0.95 or higher
For constant torque operation, the voltage applied to the motor is proportional to frequency.
The Tesla motor can provide constant torque up to some frequency limit. Above that, the voltage does not increase any more (or perhaps it increases at a slower rate). That allows the motor to provide constant power.
Re. Test Data
It appears that the voltage and current for the test data are battery voltage and current. The power at the battery is just watts = voltage X current. The inverter is between the battery and the motor. The Tesla inverter efficiency is also quite high, perhaps 0.95 or higher.