## 53 Dc Machines

The torque in electric machines is produced utilizing one of two basic principles of electromagnetic theory: by Lorentz force principle, where torque is produced by the mutual interaction of two orthogonal magnetomotive forces (mmf); and by reluctance principle, where the rotor produces torque while moving toward the minimum reluctance position in a varying reluctance path. The DC and AC machines, including the permanent magnet machines, work on the first principle, while the switched reluctance machines work on the latter principle.

The DC machines have two sets of windings, one in the rotor and the other in the stator, which establish the two fluxes; hence, the mmfs that interact with each other produce the torque. The orthogonality of the two mmfs, which is essential for maximum torque production, is maintained by a set of mechanical components called commutators and brushes. The winding in the rotor is called the armature winding, while the winding in the stationary part of the machine is called the field winding. The armature and the field windings are supplied with DC currents. The armature windings carry the bulk of the current, while the field windings carry a small field excitation current. The armature and the field currents in the respective windings establish the armature and field mmfs. The magnitude of the mmfs is the product of the number of turns in the windings and the current. Depending on the number of supply sources and the type of connection between the armature and field windings, there can be several types of DC machines. When the armature and field windings are supplied from independently controlled DC sources, then it is known as a separately excited DC machine. The separately excited DC machine offers the maximum flexibility of torque and speed control through independent control of the armature and field currents. The DC shunt machine has a similar parallel configuration of armature and field windings as in the separately excited motor, except that the same DC source supplies both armature and field windings. In shunt motors, simplicity in the power supply is compromised for reduced flexibility in control. In another type of DC machine, known as the series DC machine, the armature and the series windings are connected in series, and the machine is supplied from a single source. Because the armature and the field windings carry the same current, the field is wound with a few turns of heavy gauge wire to deliver the same mmf or ampereturns as in the separately excited machine. The greatest advantage of the series machine is the high starting torque that helps achieve rapid acceleration. However, control flexibility is lost due to the series connection of armature and field windings.

Positive attributes of DC machines are as follows:

• Ease of control due to linearity

• Capability for independent torque and flux control

• Established manufacturing technology

Disadvantages ofDC machines include the following:

• Brush wear that leads to high maintenance

• Low maximum speed

• EMI due to commutator action

• Low power-to-weight ratio

• Low efficiency

The separately excited DC motor used in an EV or HEV has two separate DC/DC converters supplying the armature and field windings from the same energy source, as shown in Figure 5.2. The DC/DC converters process the fixed supply voltage of the energy source to deliver a variable DC to the armature and field circuits. The power rating of the converter supplying the armature windings is much larger than that of the converter supplying the field winding. Control inputs to the converter circuits are the desired torque and speed of the motor. Control outputs of the converters are the voltages applied to the armature and field circuits of the DC motor.

Independent armature voltage and field current control, possible in separately excited DC machines or motors, offer the possibility of additional performance optimization in addition to meeting the torque-speed requirements of the machine. The indices used for measuring performance in motor drives include efficiency, torque per ampere, torque ripple, response time, etc. The weights on the individual performance indices depend on the application and the design requirements. The most critical performance index for EV and hybrid vehicle applications is efficiency. The analysis to follow on DC motors, based on separately excited DC motors, is intended to set forth the premise for performance analysis of DC drives in the next chapter.

The armature equivalent circuit of a DC motor is shown in Figure 5.3. The circuit consists of the armature winding resistance RA, the self-inductance of armature winding LAA and the back-emf eA. The variables shown in the figure are as follows:

Va=armature voltage /A=armature current re=developed motor torque

,„=shaft speed ;:=armature linking flux (primarily from field current)

Applying KVL around the armature circuit, the voltage balance equation is dt A

dt A

eA is known as the back-emf, and K is a machine constant that depends on the machine construction, number of windings, and core material properties. The field equivalent circuit of the DC motor is shown in Figure 5.4. The field circuit consists of the field winding resistance RF and the self-inductance of the field winding LFF. The voltage applied to the field is VF. The field circuit equation is

The resistances of the field windings in separately excited and shunt DC motors are high, because there are a lot of turns in the winding. The transient response in the field circuit is, thus, much faster than the armature circuit. The field voltage is also typically not adjusted frequently, and for all practical purposes, a simple resistor fed from a DC source characterizes the electrical unit of the field circuit. The field current establishes the mutual flux or field flux, which is responsible for torque

FIGURE 5.5 Typical DC motor magnetization characteristic. production in the machine. The field flux is a nonlinear function of field current and can be described by

The electromagnetic properties of the machine core materials are defined by the following relationship:

where B is the magnetic flux density in Tesla or weber/m2, H is the magnetic field intensity in ampereturn/m, and |i is the permeability of the material. The permeability, in turn, is given by |i=^0^r, where ^o=4px10-7 H/m is the permeability of free space, and |ir is the relative permeability. The relative permeability of air is one. The B-H relationship of magnetic materials is nonlinear and is difficult to describe by a mathematical function. Likewise, the field circuit of DC machines is characterized by nonlinear electromagnetic properties of the core, which is made of ferromagnetic materials. The properties of core materials are often described graphically in terms of the B-H characteristics, as shown in Figure 5.5. Nonlinearity in the characteristics is due to the saturation of flux for higher currents and hysteresis effects. When an external magnetization force is applied through the currents in the windings, the magnetic dipole moments tend to align to orient in a certain direction. This dipole orientation establishes a large magnetic flux, which would not exist without the external magnetization force applied on the core. The magnetic dipole

moments relax toward their random orientation upon removal of the applied magnetic force, but few dipole moments retain their orientation in the direction of the previously existing magnetization force. The retention of direction phenomenon of the dipole moments is known as magnetic hysteresis. Hysteresis causes magnetic flux density B to be a multivalued function that depends on the direction of magnetization. The magnetic effect that remains in the core after the complete removal of magnetization force is known as the residual magnetism (denoted by Br in Figure 5.5). The direction of the residual flux, as mentioned previously, depends on the direction of field current change. The B-H characteristics can also be interpreted as the V characteristics, because B is proportional to and H is proportional to iF for a given motor. Saturation in the characteristics reflects the fact that no more magnetic dipole moments remain to be oriented once sufficient magnetization force has been applied and the flux has reached the maximum or saturation level.

The energy required to cause change in magnetic orientations is wasted in the core material and is referred to as hysteresis loss. The area of the hysteresis loop in magnetization characteristics is proportional to hysteresis loss.

For most applications, it is sufficient to show the magnetic properties of core materials through a single-valued, yet nonlinear, function, which is known as the DC magnetization curve. The magnetization curve of a DC machine is typically shown as a curve of open-circuit-induced voltage E0 vs. field current iF at a particular speed. The open-circuit-induced voltage is nothing but the back-emf eA, which is linearly proportional to the flux at a constant speed (refer to Figure 5.3 and Equation 5.3). Therefore, the shape of this characteristic, shown in Figure 5.6, is similar to that of the magnetic characteri sti c s of the core materi al.

The torque-speed relationship of a DC motor can be derived from Equations 5.2 and 5.3 and is given by

The torque-speed characteristic is shown in Figure 5.7. The positive torque axis represents the motoring characteristic, while the negative torque region represents the generating characteristic. The speed-torque characteristic is adjusted through the armature voltage or the field current. For a given speed and torque (i.e., a point (T*, m*) in the —Jplane), there are an infinite number of corresponding armature

FIGURE 5.7 Speed-torque characteristics of a DC motor.

FIGURE 5.7 Speed-torque characteristics of a DC motor.

voltages and field currents, as shown in Figure 5.8 a, that would satisfy Equation 5.4. A smart control design will optimize one or more performance indices and operate the motor on the optimized characteristic curve. To follow up on the concept, let us assume that the controller can set the field current and the armature voltage, and we are interested in minimizing the loss in the machine. The driver input commands set the desired torque and speed (T*, m*) of the machine. Inserting the operating point in the armature voltage equation, we have

Equation 5.5 gives all possible combinations of armature voltage and field flux that will give the same operating point (T*, m*). The possible combinations are shown graphically in Figure 5.8b. The optimization algorithm will select the right combination of l\i and $ that will minimize losses. The loss in DC machines is minimized when armature circuit dependent losses equal the field circuit dependent losses.! Knowing the machine parameters, Va and commands can be set such that the armature circuit losses equal the field circuit losses to minimize the overall loss, hence, maximizing efficiency.

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