The behaviour of a DC motor with in-series excitation is similar to that of a DC motor with independent excitation, but there is one very important difference: the current flowing in the rotor and the stator is the same (see Figure 10). Following a similar procedure to that in the preceding section, we will now find the behaviour equations for the DC motor with in-series excitation. The following equation considers a total fall in the voltage in the motor according to the intensity of the current:
U = E + Rrl = K l u + RrI (22)
From which we can find the value of the current intensity flowing through the motor "I", according to the operational voltage and the already known parameters of the motor, "K" and "Rr":
By entering into equation (13), the equation for the motor torque "t" can be found according to the angular velocity, "co", since the current intensity flowing through the rotor and the stator is the same:
t = K K ,2=K <24>
By analysing equations (23) and (24), similar conclusions can be drawn as from the case of the DC motor with independent excitation:
1. During starting when "co « 0", the current intensity "I" is very high since "I « U/Rr", as the ohmic resistance of the rotor circuit "Rr" is very small.
2. The motor torque "t" during starting is also very high and gradually decreases as the angular velocity of the motor " " increases.
3. Consequently, during starting, the current intensity needs to be limited to avoid the circuits burning out and to limit the motor torque, thereby preventing the adhesion limits being exceeded in the wheel-rail contact.
In the example of the DC motor with in-series excitation, the above is achieved by inserting resistances in series with the motor, as can be seen in Figure 17. At the beginning of starting the maximum number of starting resistances "Ri = R1 + R2 + R3" are connected to produce the maximum reduction of current intensity "I" and therefore, the maximum reduction of the motor torque "t". As the locomotive gathers greater speed, the intensity "I" and the motor torque "t" gradually decrease. Then it is necessary to increase the motor torque to recover traction capability during starting. By means of the connections A, B and C, the resistances are successively bridged, and, therefore, cease to function and the starting resistance "Ri" gradually decreases in value. So, in a controlled manner, the current intensity "I" and the motor torque "t" again increase and the locomotive recovers its traction capability (see "real operational curve" in Figure 18).
The operation of a DC motor with in-series excitation has been simulated using the BondGraph model shown in Figure 11, with variable starting resistances. For this simulation, since the starting resistances are placed in series with the motor, they are taken into account by adding them to the rotor resistance "Rr, through the Resistance port "R:Rr", (see Figure 11). The motor under consideration has a power of 1200 kW and in the simulation was working under zero load. Figure 18 shows the results obtained for the motor torque according to the rotational speed of the motor for different values of the starting resistances "Ri" and comparing the results to the theoretical torque corresponding to the constant power hyperbole, as well as to the maximum continuous torque.
Fig. 17. Resistances in series with the motor in starting mode.
Fig. 18. Simulation results of a DC motor with in-series excitation for different values of the starting resistances "Ri".
Fig. 19. Starting diagram of a locomotive with two traction motors.
Locomotives usually have several motors and starting can also be controlled by combining the incorporation of resistances in series, "Ri", of each motor with the motors being connected in series. Figure 19 shows a schematic outline of the electrical connection of a locomotive that has two traction motors. Both have resistances in series for the starting, and in addition, switches A and B are installed so as to be able to connect both motors in series or in parallel. When the motors are connected in series, the voltage in them is half the nominal voltage, and, as a result the intensity flowing through them is also half, reducing the starting torque "t" to half. In this way, the resistances "Ri" during the starting of each motor can be less, resulting in fewer energy losses during starting. Initially, when the train is gathering speed, the starting resistances "Ri" are gradually reduced. At a given instant, the in-series connection of the motors is switched to in-parallel and the starting resistances "Ri" are slightly increased. Finally, when the train reaches a determined speed the process is concluded by cancelling the starting resistances "Ri".