Gyuláné Vincze, Gergely György Balázs

Budapest University of Technology and Economics Department of Electric Power Engineering

**Table of Contents**

The conventional electric vehicles are driven by rotating machines. Among the uncontrolled electric rotating machines the series wound commutator motors have the most suitable *M-ω* mechanical characteristic curve for the tractive requirements. This justifies that almost exclusively series wound commutator motors were applied in electric vehicle drives for long decades. Nowadays several vehicles are still driven by such motor.

Interesting feature of the series wound commutator motor that it can be operated from DC and single phase AC network with relatively few changes. The *M-ω* mechanical characteristic curve of the motor is similar at both supplies. The *AC commutator motors* are much more sensitive and more disposed for brush sparking than the *DC motors*. On the other hand at the beginning of the electrification the lossless change of the single phase supplying voltage could be achieved by split transformer, while there was not any device for changing the DC voltage with no-loss. Therefore at the beginning of the electrification in several countries the single phase commutator motor driven technologies were preferred and low-frequency AC railway electrification systems were selected to improve the motors operation. The single phase commutator motors are not applied since long time ago (this lecture is not dealing with these), however nowadays in some countries the low-frequency (16 2/3Hz, 15Hz or 25Hz) rail systems are still remaining.

Until recently the series wound DC motors were most commonly used in vehicle drives. The magnetic flux of the series wound machine is generated by such excitation coil which *I*
_{g} current is proportional to the *I* armature current: *I*
_{g}
*=cI*. The *c *factor represents the degree of the field weakening that can be in *c*
_{min}
* ≤ c ≤*1 range. The value of *c*
_{min} is depending on the machine, it is determined by the habit of the brush sparking. Common solution that the field weakening can be varied with some ratios and it is made by an *R*
_{s} shunt resistor connected in parallel with the excitation coil (Fig.4.1.a). If the resistance of the excitation coil is *R*
_{g}, then the degree of the field weakening is *I*
_{g}
*=IR*
_{s}
*/(R*
_{g}
*+R*
_{s}
*)=cI*. If there is no field weakening, then *R*
_{s}
*=∞*, *I*
_{g}
*=I*, *c=*1*.*

In traction the compound wound DC motors are relatively frequently used also, the one of the excitation coils current is *I*
_{g1}
*=I*, while the *I*
_{g2} current of the other excitation coil is independent of the armature current (Fig.4.1.b). In the compound wound DC motor the ϕ flux is generated by the *I*
_{g1}
*N*
_{s}
*+I*
_{g2}
*N*
_{k} resultant excitation, where the number of turns of the series excitation coil is *N*
_{s}, and the number of turns of the separated excitation coil is *N*
_{k}. Fig.4.1 does not presents, but the DC motors can be separately excited, where the series excitation coil is missing, or permanent magnet excited. The latter motor types are applied in soma vehicles generally in low power vehicles, in cars. The basic voltage, torque and speed equations of the DC commutator motors are:

4-1

The left column shows the transient equations valid for time functions. The right column contains the quantities described with the operating point values and valid at steady-state. The lower case letters represent the transient values, while the capital letters represent the operating point values. In the equations the meaning of the quantities and parameters are: the terminal voltage: *u,*
*U*, the internal voltage: *u*
_{b}
*,*
*U*
_{b} (internal induced voltage), the armature resistance: *R*, the armature inductance: *L*, the magnetic flux of the motor: ϕ, the machine constant: *k*, the motor torque: *m, M*, load torque of the motor: *m*
_{t}
*, M*
_{t}, moment of inertia to be accelerated: *θ*.

The ϕ magnetic flux of the machine is a non-linear, saturation-like function of the *I*
_{g}
*=cI* excitation current. Fig.4.2. represents (in per unit system) the characteristic curves of a series wound machine that has an assumed magnetization curve. The armature current range is 0<*I’*<2, i.e. it is varied between zero and twice the nominal value (*I*
_{n}).

The per unit quantity of the armature resistance is: *R’*=0,05 (*R’=R/R*
_{n}, where *R*
_{n}
*=U*
_{n}
*/I*
_{n}), the per unit quantity of the torque is: *M’=k*
*ϕ*
*I/(k*
*ϕ*
_{n}
*I*
_{n}
*)=*
*ϕ*
*’*
* I’*. The calculation of the speed is based on equations (4.1): *ω=(U-IR)/k*
*ϕ*
*,* with per unit quantities: *ω’=(U’-I’R’)/*
*ϕ*
*’*
*.*

Fig.4.2.a shows the flux and torque which are the function of the armature current. The two upper curves (*I*
_{g}
*=I)* are valid for the mode without field weakening, the lower curves (*I*
_{g}
*=0,5I* and *I*
_{g}
*=0,35I)* are valid for field weakening mode. Fig.4.2.b represents the *M-ω* mechanical characteristic curves of motor mode (*M*>0, *ω*>0) that approximates well the ideal traction requirements which is presented in Fig.2.5. The lower four curves represent the mode without field weakening (*I*
_{g}
*=I*), where the maximum torque can be achieved, the speed can be varied by the motor terminal voltage within the upper boundary curve, marked with *U’*=1 (the *U* voltage cannot be increased above the nominal value). The range limited by the previous boundary curve can be extended by applying field weakening that is presented by the two curves: *I*
_{g}
*=0,5I* and *I*
_{g}
*=0,35I*. The loadability of the motor (*M*
_{max}) is decreasing in field weakening mode, but its speed can be increased. This effect is utilized in traction, the traction characteristic curve of the V43 locomotive (Fig.1.5) is an example for this.

Based on the previous description, it ensures that the torque and the speed of the series wound DC motor can be controlled by varying terminal voltage and field weakening. There are several solutions for varying the terminal voltage (Fig.4.3):

In most of the solutions continuously variable voltage is generated by electronic converters with DC/DC converter (vehicle examples in Chapter 4.2.2) or with AC/DC converter (Chapter 4.2.4), but in some vehicles only step-like, discrete voltage values can be selected (vehicle example in Chapter 4.2.3). The variation of the field weakening can be continuous (examples in Chapter 4.2.2.) or discrete (vehicle examples in Chapter 4.2.3).

In older vehicles instead of the electronic converters, step-like series resistor variation is used (4.3.c), the motor voltage can be varied with these resistors according to the expression *U*
_{mot}
*=U*
_{T}
*–IR*
_{e}, where *U*
_{T} is the supply voltage. To reduce the loss (*I*
^{2}
*R*
_{e}) of the series resistor (*R*
_{e}), the driving technique of these vehicles is controlled, so that the series resistors are in the circuit for a short period only (at acceleration). In multi-motor driven vehicles the series-parallel connection commbinations are also applied in combination with the resistance varying. In two-motor drive e.g. the supply voltage can be halved by connecting the motors in series (Chapter 4.2.1).

For backward running the polarity of the armature or the excitation circuit of the series wound motor should be reversed. In Fig.4.4 the E switches are closed at forward operation while the H switches are closed at backward operation, and the selection is performed at standstill.

During braking, the kinetic energy of the motor and the vehicle can be reduced in two ways: recuperate the energy back to the electric network, or convert into heat (dissipate). The recuperating braking is equivalent to the generator mode of the electric machine. The dissipation brake can be electrical or mechanical based on friction. The electric solution is the resistive electrical brake, when the kinetic energy is converted into heat.

Compared to the advantages of the series wound motor from the feasible traction characteristic (Fig.4.2.b), the braking mode is relatively difficult to achieve. For braking, the *M=k*
*ϕ*
*I* torque direction of the traction motor can only be reversed by the changing of the *I* armature current direction or the *I*
_{g} excitation current direction (flux direction). Therefore the armature or the excitation circuit reversing switch (Fig.4.4) should be also applied in braking mode. The function of the *E* and *H* switches changes to driving and braking switch. The reversing of the *E* driving mode switch to *H/F* braking mode switch is possible only in no-current state. At series wound machine it means that before the switching the motor is de-excited because of *I=*0, *I*
_{g}
*=*0 current, i.e. the flux is reduced to the remanent value (ϕ_{rem}). After the switching, the internal voltage of the still rotating machine is excited-up by this remanent flux, i.e. reaches the U_{b}=kϕω operating voltage required for the formation of the brake current. Only such braking mode switch is operable, that helps this exciting-up process. Fig.4.5 represents an example for such braking circuit, where after the switching the direction of *I*
_{g}
*,*
* *
*ϕ*
* *and U_{b} remain unchanged, also at reversed direction *I*
_{fék} braking current compared to *I* direction. The braking current is generated by U_{b} through the resultant resistance of the circuit. (Beside the *R*
_{fék} braking resistance the armature and the excitation circuit resistances are negligible.)

After changeover switching the stabile operating point is set to such brake current where *I*
_{fék}
*R*
_{fék}
*=*U_{b}=kϕω* *(where* *
*ϕ*
* *is generated by *I*
_{g}
*=I*
_{fék} current). The energy converted into heat is: .

Chapter 4.2.2 presents vehicles that are capable for regenerative braking. The vehicle example of chapter 4.2.1 represents the solution for circle-connected or cross-connected resistive braking mode (Fig.4.10).

For traction purpose the series wound machines are the most commonly used from the DC machines. Sometimes the compound wound machines (Fig.4.1.b) are applied to eliminate the disadvantages of the series excitation. The ϕ flux of the machine is generated by the *I*
_{g1}
*N*
_{s}
*+I*
_{g2}
*N*
_{k} resultant excitation, which is the sum of the *I*
_{g1}
*N*
_{s}
*=IN*
_{s} series excitation and the *I*
_{g2}
*N*
_{k} separate excitation.

The compound excitation can be utilized well if *I*
_{g2}
* *is continuously controllable. The following purposes can be reached by controlling the separate excitation current (*I*
_{g2}):

The previous excitation boost can be applied also with series excitation coil, it is called pre-excitation (for example in Chapter 4.2.1).

For traction purpose the “purely” separately excited DC machine is generally applied in low-power vehicles. In these drives separate controllers are built in for controlling *I *armature current and *I*
_{g} excitation current (vehicle example in Chapter 4.2.5). Two ranges can be distinguished for *I*
_{g} control:

Fig.4.6.b presents simulation results of the mechanical characteristic curves in per units that can be achieved by the previously described excitation control.

If Fig.4.6.b is compared toFig.4.2.b, it can be observed that the *M-ω* boundary characteristic curves of the separately and series excited motors are similar, but there are some differences:

The steep characteristic curves can cause problems in cases, when a vehicle is driven by two or more electrically parallel connected motors at the same time, and these motors are forced to approximately the same speed because of their mechanical connection on the wheels. The terminal voltages of the motors are the same because of the parallel connection, but their characteristic curves can be slightly different. Because of the steep *M-ω* characteristic curve, at same speed the torque distribution of the motors may vary much more than at series motor. Moreover the unequal load can cause unequal warming of the parallel connected motors. Fig.4.7.a presents this phenomenon for the two motors (motor *1* and *2*) (slightly enlarged effect).

Unequal load distribution can also happen in case of same motor characteristic curves, if the speeds of the parallel connected motors are not exactly the same e.g. because of wheel wear. Such difference is higher if the characteristic curve – belongs to the same terminal voltage - is steeper. It can be seen in Fig.4.7.b.

In low power electric car drives *permanent magnet DC machine* can be applied because of its simplicity. The field weakening (can be seen in Fig.4.6.a) cannot be achieved by this type of machine, i.e. the motor can only operate in *ω≤ω*
_{on} range.