**DC Motor Control through Converters**:

DC motor control is conveniently and efficiently achieved by phase-controlled converters wherein the ac input voltage is converted to a controlled dc output. The commutation process, the transfer of currentĀ from one thyristor to the other, in these converters is the inexpensive **natural** or **line commutation**. As, an incoming thyristor is turned-on, it reverse-biases the outgoing thyristor, turning it off. No additional commutation circuitry is therefore required. The power conversion efficiency in these converters is above 95% because of relatively low losses in thyristors. These converters are used in the speed control of fractional-kW dc motors as well as in large motors employed in variable-speed reversing drives for rolling mills with motor ratings as large as several MWs.

In certain types of converters (**semi-converters**) a diode known as a, **free-wheeling diode** is connected across motor terminals to allow for dissipation of energy stored in motor inductance and to provide for continuity of motor current when the thyristors are blocked. It also provides protection against transient overvoltages.

**Single Phase Half wave Converter:**

Figure 11.14 shows a single-phase half-wave converter for controlling a separately excited DC Motor. It requires a single thyristor and a free-wheeling diode. In this circuit the motor current is always discontinuous, resulting in poor motor performance. This type of converter is employed only for motors below 400 W. It will not be described in detail here; these easily follow from the description of waveforms (voltage and current) for the semi-converter.

**Semi-Converter feeding a Separately excited DC Motor:**

This is a one-quadrant converter (Fig. 11.15a) which gives voltage and current of one polarity at dc terminals. It therefore does not provide for regenerative braking, i.e. power flow from DC Motor Control to the ac supply. Where regeneration is not required, this converter is used for reasons for economy.

Figure 11.15(b) gives the circuitry of a semi-converter feeding a separately excited DC Motor Control. The armature resistance R_{a} and inductance L_{a} are shown lumped in series with an armature-induced emf e_{a} while the armature terminal voltage is v_{a}. It has two thyristors, two diodes and a free-wheeling diode (connected across motor terminals). It will be assumed that in steady-state operation the armature current is continuous over the whole range of operation. Typical steady-state voltage and current waveforms are shown in Fig. 11.16. The thyristor Th_{1} is fired at angle Ī±Ā and Th_{2}Ā at angle Ļ + Ī±Ā with respect to the supply voltage Ī½ and the process is repeated continuously.

Under steady conditions, as Th_{1} is fired (Ļt = Ī±), Th_{1} and D_{2} conduct and the motor is connected to the supply, i.e. Ī½_{a} = Ī½. At ĻtĀ **= **Ļ,Ā Ī½_{a} tends to become negative as the input voltage polarity changes. This causes D_{FW}, the free-wheeling diode, to become forward-biased and the armature current flowing through Th_{1}D_{2} is transferred to D_{Fw}, which means that Th_{1}Ā commutates (naturally). The motor terminals are shorted through D_{Fw} for the free-wheeling period Ļ < Ļt < Ļ + Ī± providing for continuity of the armature current during this period when the motor remains disconnected from the supply. At Ļt = Ļ + Ī±, Th_{2}Ā is fired and Th_{2}D_{1} conduct, causing D_{FW} to become reverse-biased and therefore open-circuited. The motor is once again connected positively to the supply for the next period of Ļ + Ī±Ā < Ļt < 2Ļ. This process repeats continuously.

Various voltage and current waveforms of a separately excited DC Motor Control fed through a semi-converter are shown in Fig. 11.16. Though the voltage across motor terminals (Fig. 11.16(c)) contains harmonics over and above a steady dc value, it is rightly assumed here that the motor does not respond to these harmonics and therefore runs at constant speed (n) and has constant induced emf (e_{a}). As Th_{1} fires at Ļt = Ī±, the motor current is given by

up to the point P shown in Fig. 11.16(a); Ī½ > e_{a} so that the motor current increases. So does the motor emf e_{a}. During this period, apart from the energy being delivered to the load, energy is also being stored in motor inductance (L_{a}). Beyond the point P, Ī½ < e_{a} and the motor current begins to decrease. This also implies the reversal of voltage across the motor inductance which now feeds energy into the system. During the free-wheeling period (Ļ < Ļt < Ļ + Ī±), the diode continues to be forward-biased by the reversal of the inductive voltage. During this period a part of the energy stored in motor inductance is consumed to feed the mechanical load. The motor current, speed and emf, therefore, all reduce. This process then repeats over the next period (Ļ + Ī± < Ļt < 2Ļ + Ī± ) via Th_{2}D_{1} and later through D_{FW}. The current drawn from the supply shown in Fig. 11.16(d) is that part of the armature current which flows over the periods (Ī±, Ļ), (Ļ + Ī±, 2Ļ), …Ā when the motor is connected to the supply. It is not necessary to use the free-wheeling diode. In its absence at Ļt Ā = Ļ, D_{1} becomes forward-biased so that free-wheeling takes place through Th_{1}D_{1}Ā till Th_{2} is fired. At Ļt = 2Ļ free-wheeling takes place through Th_{2}D_{2} and so on.

It should be observed from Fig. 11.16(d) that the fundamental of the current drawn from the mains lags the voltage by an angle Ī¦_{1}Ā (< Ī± ).

**Discontinuous Armature Current:**

The armature current becomes discontinuous for large values of the firing angle, high speed and low values of torque. The motor performance deteriorates with discontinuous armature current. The ratio of peak to average and rms to average armature current increases. It is, therefore, desirable to operate the motor in the continuous current mode. To achieve this, an external armature circuit choke may be used, which decreases the rate of current decay during the free-wheeling operation.

The voltage and current waveforms for semi-converter with discontinuous current are shown in Fig. 11.17. The motor is connected to supply through Th_{1}D_{2} for the period Ī± < Ļt < Ļ. Beyond Ļ, the motor is shorted through the free-wheeling diode D_{FW}. The armature current decays to zero at angle Ī² (extinction angle) Ļ + Ī±, i.e. before the thyristor Th_{2} is fired, thereby making the armature current discontinuous. During Ī±Ā to Ļ, the conduction period through Th_{1}D_{2}, the motor terminal voltage is the same as the input voltage. During ĻĀ to Ī²Ā the motor terminal voltage is zero as motor terminals are shorted by the free-wheeling diode. From Ī²Ā to ĻĀ + Ī±, the motor coasts and so its terminal voltage is the same as its induced emf.

**Full-Converter feeding a Separately Excited DC Motor:**

A full-converter is a two-quadrant converter (see Fig. 11.18(a)) in which the voltage Ā polarity of the output can reverse, but the current remains unidirectional because of the unidirectional thyristors. A full-converter employs four thyristors but no free-wheeling diode is required. A full-converter feeding a separately excited DC Motor Control is shown in Fig. 11.18. The voltage and current waveforms are shown in Fig. 11.19 with the assumption that the armature current i_{a}Ā is almost constant. Thyristors Th_{1} Th_{3} conduct for the interval Ī±Ā < ĻtĀ < Ļ + Ī±Ā and connect the motor to supply. At ĻĀ + Ī±, thyristors Th_{2}Th_{4} are triggered. Immediately the supply voltage appears in reverse-bias across Th_{1} Th_{3} and turns them off. This is **natural** or **line commutation**. The motor current is transferred from Th_{1} Th_{3} to Th_{2}Th_{4}. Since there is no period when the motor is disconnected from supply, no free-wheeling is necessary. During Ī±Ā to ĻĀ , energy flows from the supply to motor (both Ī½ and i are positive and so are v_{a} and i_{a}).

However, during Ā ĻĀ toĀ Ļ + Ī±, some of the motor energy is fed back to the supply (v and i have opposite polarity and so are v_{a} and i_{a} which means reversal of power flow). Observe that the fundamental of the current drawn from the mains lags the voltage by angle Ī¦_{1}Ā = Ī±.

The voltage and current waveforms for Ī±Ā > 90Ā° are shown in Fig. 11.20. The average motor terminal voltage is now negative. If the motor terminals are reversed, it will act as a generator feeding power back to the ac supply. This is the **inversion operation** of the converter and is used in regenerative braking of the motor. One point needs to be noted here. During the conduction period of either Th_{1}Th_{3} or Th_{2}Th_{4} as the supply voltage becomes negative, the armature current begins to reduce, causing the inductance polarity to reverse so that the conducting thyristors continue to be forward-biased.

The voltage and current waveforms for the case of discontinuous armature current can be found as in the case of the semi-converter. (see Fig. 11.20).

**Torque-Speed Characteristics:**

It will be assumed here that the armature current is continuous. For a semiconverter with free-wheeling diode action, the armature circuit equations are

For a full-converter, the armature circuit equation is

Let Ī½ = ā2 V sin Ļt . The average motor terminal voltages are: With a semi-converter,

With a full-converter,

Figure 11.21 gives the variation of the motor terminal voltage as a function of the firing angle for both the semi-converter and full-converter. In the case of the full-converter inversion operation occurs for 90Ā° < Ī±Ā < 180Ā°.

The motor equations for average values are

and

Substituting for I_{a}Ā from Eq. (11.8) and V_{a}Ā from Eqs (11.5) or (11.6) in Eq. (11.9), the speed-torque characteristics are given as follows:

With a semi-converter,

With a full-converter

The first term in Eqs. (11.10) and (11.11) represents the theoretical no-load speed while the second term represents speed drop caused by armature resistance. The theoretical no-load speed can be varied by the firing angle Ī±.

In the case of discontinuous current, the average voltage at motor terminals depends upon the angle Ī² (extinction angle) which itself is dependent on the average motor speed n, average motor current I_{a} and firing angle Ī±. The analytical treatment of this case is beyond the scope of this book.

**Dual-Converter:**

The dual-converter can operate in all the four quadrants as shown in Fig. 11.22(a). Its circuit is shown in Fig. 11.22(b). It is indeed two full-converters converting to dcĀ in either direction. The dual converter provides virtually instantaneous reversal of voltage at dc terminals.

**Control of DC Series Motor:**

Semi-converters and full-converters are also employed for control of a dc series motor. The total circuit inductance is high because of the series field, as a consequence of which the armature current is mostly continuous. The governing motor equations differ as the flux/pole is now proportional to the armature current. The treatment otherwise is similar to that of a separately excited DC Motor Control and will not be pursued here for want of space.