Single-Phase Drives for Controlling DC Motors

The single phase ac is converted into dc by a controlled rectifier or converter and the dc is supplied to the dc motor. By varying the firing angle the voltage applied to the motor can be varied and thus the speed of the motor can be controlled.

Single phase drives can be further classified as: 1. Single Phase Half-Wave Converter Drives 2. Single Phase Semi-Converter Drives 3. Single Phase Full-Converter Drives 4. Single Phase Dual Converter Drives.

1. Single Phase Half-Wave Converter Drives:

Figure 3.3 (a) shows a single phase half-wave converter for controlling a separately excited dc motor. It needs a single thyristor and a freewheeling diode (D_FW). Freewheeling diode, also sometimes known as bypass diode or commutating diode is used to improve the wave-shape of load current and power factor. Freewheeling diode is connected across the motor terminals to allow for dissipation of energy stored in the motor inductance and to provide for continuity of motor current when the thyristors are blocked. It also provides protection against transient over-voltages.

Separate converters are employed for the armature and field circuits. It is desirable that the supply to the field winding is provided through a semi-converter or full converter. If half-wave converter is used for supply to field circuit, the high ripple content in the field circuit would cause increase in the iron losses of the machine. It is one quadrant drive, as illustrated in Fig. 3.3 (b).

Because of inductance of the field and armature, the thyristor would not turn off at ωt = π. Therefore it is desirable to have freewheeling diode (D_FW), as shown.

Average value of voltage applied across armature is given by-

Where, α_a is the firing angle of converter in the armature circuit.

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In this circuit the motor current is always discontinuous, resulting in poor performance. This type of drive is used only for small dc motors of rating up to 500 W or so.

2. Single Phase Semi-Converter Drives:

Figure 3.4 (a) shows the circuit of a semi-converter feeding a separately excited dc motor. Both armature and field circuits are supplied from single phase ac supply through semi-converters. Because of inductance in the armature and field circuits, freewheeling diodes are required in both the circuits.

The voltages applied to the armature and fields are:

where α_a and α_f are the firing angles of converters in the armature and field circuits respectively.

This is also a one quadrant drive [Fig. 3.4 (b)] which provides voltage and current of one polarity at dc terminals. It, therefore, does not provide for regenerative braking, i.e., power flow from dc motor to the ac supply. Where regeneration is not required, this converter is used for reasons of economy. This drive is used for motors up to 15 kW rating.

Typical steady-state voltage and current waveforms are illustrated in Fig. 3.5. The thyristor TH₁ is fired at angle α_awhile TH₂ at angle π + α_a with respect to supply voltage v and process is repeated continuously.

Under steady conditions, as thyristor TH₁ is fired (ωt = α_a), TH_] and diode D₂ conduct and the motor gets supply, i.e., v_a. At ωt = π, v_a tends to become negative as the input voltage reverses in polarity. This makes freewheeling diode to become forward biased and armature current flowing through TH₂D₁ is transferred to D_FW for the freewheeling period π < ωt < π + α_aproviding for continuity of the armature current during this period when the motor remains disconnected from the supply. At ωt = π + α_a, the thyristor TH₂ is fired and TH₂D, conduct, causing to become reverse biased, and therefore, open circuited. The motor is once again connected positively to the supply for the next period of π + α_a < ωt < 2π. This process repeats continuously.

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Different voltage and current waveforms of a separately excited dc motor supplied through a semi-converter are illustrated in Fig. 3.5. Though the voltage across motor terminals [Fig. 3.5 (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 thus runs at constant speed of n rps and has constant induced back emf e_b. As TH₁ fires at ωt = α_a, the motor current is given as

assuming R_a negligibly small up to the point P illustrated in Fig. 3.5 (a) ; v > e_b so that the motor current increases. So does the motor back emf e_b. During this period, apart from energy being delivered to the load, energy is also being stored in the motor armature inductance L_a. Beyond the point P, voltage v becomes lesser than induced back emf e_band the motor current starts to drop. This also implies the reversal of voltage across motor armature inductance which now feeds energy into the system. During the freewheeling period (π < ωt < π + α_a), the diode continues to be forward biased by the reversal of the inductive voltage.

During this period a part of the energy stored in armature inductance is consumed in supplying the mechanical load. The motor current, speed, and emf, therefore, all decrease. This process then repeats over the next period (π + α_a < ωt < 2π + α_a) through TH₂D₁, and later through D_FW. The current drawn from the supply shown in Fig. 3.5 (d) is that part of the armature current which flows over the periods (α_a, π), (π + α_a, 2π), when the motor is connected to the supply. It is not necessary to employ the freewheeling diode. In its absence at ωt = π, diode D₁ becomes forward biased so that freewheeling occurs through TH₁D₁ till TH₂ is fired. At ωt = 2π freewheeling occurs through TH₂D₂ and so on.

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Discontinuous Armature Current:

The armature current becomes discontinuous for large values of the firing angle, high speed and low values of torque. Discontinuous armature current results in deterioration of motor performance. The ratio of peak to average and rms to average value of armature current increases. Thus it is desirable to operate the motor in the continuous current mode. This can be achieved by using an external armature circuit choke, which reduces the rate of decay of current during the freewheeling operation.

The voltage and current waveforms for semi-converter with discontinuous current are illustrated in Fig. 3.6. The motor is connected to the supply through TH₁ and D₂ for the period α_a < ωt < π. Beyond π, the motor is shorted through the freewheeling diode D_FW. The armature current falls to zero at angle β (extinction angle) < π + α_a i.e., before the thyristor TH₂ is fired, thereby making the armature current discontinuous.

During α_a to π, the conduction period through TH₁ and D₂, the motor terminal voltage is the same as the input voltage. During n to P, the motor terminal voltage is zero, motor terminals being shorted by the freewheeling diode D_FW. From β to π + α_a, the motor coasts and, therefore, its terminal voltage is the same as its induced emf. It should be noted here that the fundamental of the current drawn from the mains lags behind the voltage by an angle φ, (< α_a).

Torque-Speed Characteristics:

The emf induced in armature conductors of a motor, known as back emf, is given by-

E_b = k_e φN …(3.5)

where K_e is emf constant and is equal to PZ/60A.

In a separately excited dc motor, the field winding is excited from a separate source. So voltage applied to the armature is given by-

V_a = E_{b +} l_aR_a …(3.6)

where I_a is armature current in amperes and R_a is the armature resistance in ohms.

Thus, from Eqs. (3.5) and (3.6), we have-

Back emf, E_b = V – I_a R_a = k_e N φ

Since field is excited separately, field current I_f and flux φ are constant. Moreover voltage drop in armature, I_aR_a is negligible. So motor speed N is constant if voltage applied to the armature is constant, and speed varies directly in proportion to the applied voltage i.e., N ∝ V_a.

Electromagnetic torque developed in a dc motor is given by-

The first term of RHS of Eq. (3.12) represents the theoretical speed and the second term represents the speed drop due to voltage drop in armature circuit.

The theoretical no-load speed can be controlled by varying the firing angle α_a.

3. Single Phase Full-Converter Drives:

The circuit diagram is illustrated in Fig. 3.7 (a). A full-converter needs four thyristors but no freewheeling diode. Full converters are employed for both the armature and field supply. As illustrated in Fig. 3.7 (b), two quadrant operation is possible. The converter in the armature circuit provides + V_a or – V_a thus allowing operation in first and fourth quadrants.

Current remains unidirectional because of the unidirectional thyristors. When operating in the fourth quadrant regenerative braking is possible and motor feeds back energy to the source. If α_a and α_f are the firing angles for the converters used in the armature and field circuits, the armature voltage V_a and field voltage V_f are given as-

This drive is also employed for motors of rating up to 15 kW.

The voltage and current waveforms are illustrated in Fig. 3.8; armature current i_a being assumed to be almost constant. During the time interval α_a < ωt < π + α_a, thyristors TH₁ and TH₃ conduct and connect the motor to supply. At π + α_a, thyristors TH₂ and TH₄ are triggered. Immediately the supply voltage appears in reverse bias across thyristors TH₁ and TH₃ and turns them off. This is natural or line commutation. The motor current is transferred from thyristors TH₁ and TH₃ to thyristors TH₁ and TH₄.

During the time interval α_a to π energy is supplied to the motor (both v and i are positive and, therefore, are v_aand i_a). But during time interval π to π + α_a, some of the motor energy is fed back to the supply (v and i and so the v_a and i_a being of opposite polarity). The noteworthy point is that the fundamental of the current drawn from the supply mains lags behind the applied voltage by angle ɸ₁ = α_a.

The voltage and current waveforms for α_a > 90° are illustrated in Fig. 3.9. The average motor terminal voltage is now negative. On reversing of the motor terminals, it will operate as a generator supplying power back to the ac supply. This is the inversion operation of the converter and is employed in regenerative braking of the motor. The noteworthy point here is that during the conduction period of either TH₁ TH₃ or TH₂TH₄ as the supply voltage becomes negative, the armature current begins to drop, causing the inductance polarity to reverse and thus conducting thyristors continue to be forward biased.

From Eqs. (3.11) and (3.13) we have-

In the case of discontinuous current, the average voltage at motor terminals depends upon the extinction angle β which itself depends on the average motor speed N, average armature current l_a and firing angle α_a. We need not to go in its analytical treatment.

4. Single Phase Dual Converter Drives:

The circuit diagram is illustrated in Fig. 3.10 (a). In this drive, the armature is supplied from two full converters while the field is supplied from another full converter. Converter 1 provides operation in the first and fourth quadrants while converter 2 provides operation in second and third quadrants. Thus it is a four quadrant drive and allows all four modes of operation, i.e., forward motoring, forward regenerative braking, reverse motoring and reverse regenerative braking. When converter 1 is operating, a positive voltage V_a is applied to the armature. When converter 2 is operating a negative voltage -V_a is applied to the armature. It is employed for motors of rating up to 15 kW. If α_a1 is the firing angle of converter 1, the armature voltage V_ais given as-