# Regulating the behaviour of DC motors with in-series excitation, with the constant power hyperbole

When the starting period of the motors has been exceeded (section A-B in Figures 16 and 18), we must deal with controlling the motor in order to fit its behaviour to the constant power hyperbole.

The Electromotive Force "E" induced in the rotor by the stator is proportional to the magnetic flow "0" and the angular velocity of the rotor's rotation "m", (Karnopp, 2005):

E = Kt O w

Where "Ki" is a constant associated with the stator winding.

From the above equation we can calculate the angular velocity "o": Also, from equation (22), we can obtain the following expression for the value of the Electromotive Force "E": From this it may be deduced that a given voltage can increase the motor's rotational speed by reducing the flux "0" of the stator. As we also know, this flux depends on the current flowing through the stator, because as we are dealing with in-series excitation, it is the same as that flowing through the rotor. To change the current in the stator (and, therefore, the induced flux), without changing that of the rotor, an assembly is used like the one in Figure 20, where a rheostat is installed in parallel to the stator. As the resistance of the rheostat gradually decreases, the part of the current flowing through the stator becomes less and as a result, the flux "0" decreases.

The control of direct current motors, based on reducing the current passing through the stator, is called "Shunting" the motors. This term was used in section 4.1., (Figure 15), when dealing with the starting of DC motors with independent excitation. Fig. 20. Shunting DC motors with in-series excitation.

The shunting "a" of a motor is defined as:

a = '-y • 100 (29)

By shunting the motor, its characteristic curves move towards the right, the bigger the move, the greater the shunting percentage. This can be seen in Figure 21, where the shunting curves are shown, continuing the behaviour simulation of the DC motor with inseries excitation carried out in Section 4.2, once the starting period had been completed (section A-B").

It is not possible to totally decrease the current in the stator as it depends on how the motor is constructed. It can usually only be shunted up to 55%, because with higher values switching problems arise in the motor. Fig. 21. Torque curves on shunting the DC motor with in-series excitation.