Induction Motors

This book like most, if not all, on induction motors deals with equivalent circuit models. A proficiency in circuit theory at the level of Alexander/Sadiku and electromagnetics at the level of Kraus is required. Heavy use is made of phasors, linear algebraic solution, Norton-Thevenin, etc. Unfortunately, like most others, it stops short of providing any detailed approach to the prediction of the performance of a motor under load or even why the motor works at all. This is a criticism of this class of books and not this particular book. It was clear that he was only concerned with circuit models and using circuit theory concepts like power factor to analyze possible performance characteristics. He does an exemplary job on finding space current vectors in the appendices and in section 5.3 on transients he adjoins circuit model equations with a torque equation (An Approach!! Others none at all.) which is why I gave 5 stars and also inspires my hopefully satisfying example. I'll outline a crude but effective model of motor which shows that when a circuit model is coupled with a load or torque equation, an ordinary differential equation describing the angular motion of the rotor results-means it works! The equation is nonlinear, so Runge-Kutta numerical solution is needed. Nonlinearity is traced to the feedback nature of the induction motor effect. Once solution is found, torque and speed curves can be plotted.We start with a circular conductor loop. This loop is the rotor which has axis of rotation about a diameter. About this same diameter a uniform(constant magnitude) magnetic field vector, perpendicular to the diameter and at its center, say, rotates at constant angular speed about the diameter. This vector is of course representative of a field of parallel vectors and this rotating effect is achieved through the stator by ac circuit theory means (easy). The conductor loop has a self inductance and a resistance and is free to rotate about the axis diameter. Faraday's law tells you that a voltage is induced in the loop by a time changing magnetic flux. What matters in calculating the flux is the projection of the magnetic field vector on the unit normal vector to the plane of the loop (dot product). To this end what is important is the angle between the magnetic field vector and the normal. Luckily we can deal with this angle exclusively since the magnetic field rotates at constant angular speed and we can subtract it out at the end to get loop motion. We assume in general a different angular velocity for the rotor of which the angle takes account. Anyway, set up the flux. Use Faraday's law to get the voltage which is a product of the sine of our angle and the derivative of our angle. Equate this voltage to the sum of resistance voltage drop and inductance voltage drop in the loop. This is a first order differential equation for the rotor current relating it to our angle. Assuming current flowing in the loop, it has a magnetic moment parallel (or anti-) to the normal with magnitude which is the product of current and loop area. The magnetic torque on the loop is given by the vector cross product of the magnetic moment and the magnetic field vector which gives a constant multiplied by the product of the rotor current and the sine of our angle. We can introduce a viscous torque like a fan which depends on the time derivative of the rotor angle or our angle. Use Newton's law with this and the magnetic torque on one side of equation and product of loop moment of inertia and loop angular acceleration (same as acceleration of our angle)on other side. This equation gives us the loop current in terms of our angle and its derivatives. Putting this into our voltage equation gives the sought after differential equation and proof that the rotor moves.An excellent and more introductory text to bundle with this and the other mentioned books is Chapman's book Electric Machinery Fundamentals which is more elementary but much more detailed and pedagogical.