Line commutated converters (LCCs) are converters where the operating mode is determined by the ac supply. They allow the following forms of power conversion: ac to dc, ac to ac, dc to ac.

Controlled rectifiers convert an ac voltage from the supply to controlled dc voltage. They can be designed to permit energy to flow in reverse - from the dc side to the ac side. In such a case the rectifier acts as a line commutated inverter and converts dc voltage to ac voltage.

Cycloconverters and ac voltage controllers are ac to ac converters. They directly control the r.m.s. value or the frequency of the ac voltage.

Many applications (battery charger, dc-motor drives) need variable dc voltage. Controlled rectifiers perform this ac to controlled-dc conversion. To obtain the controlling effect of diode rectifiers, the unidirectional device (diode) is replaced by a thyristor. However, the thyristor needs to be switched on and off.

Switching off is easily achieved during the negative half-cycle of the ac line voltage (natural line-commutation). Switching on requires additional control circuitry to produce trigger pulses for the thyristors. The pulses are applied at variable delay with respect to the instant of natural (diode) conduction. A control signal u_c determines this phase shifting of the gate pulses.

Controlled half-wave rectifiers have the same circuit topology as diode half-wave rectifiers. There are three rectifier types: single-phase, two-phase and three-phase.

In a diode rectifier the diode switches on when its anode voltage becomes positive with respect to the cathode. This is the so-called instant of natural conduction or commutation.

In thyristor rectifiers the thyristor is switched on under control. It needs a trigger pulse with positive biasing. The controlled half-waves of the ac supply voltage are applied to the load. Thus, the rectified dc voltage is smoothly controlled by appropriate choice of the triggering instant.

The ac voltage has a sine-wave form and can be expressed by the equation:

u = U_msin (ωt) = U_msin (2πft), where u is the instantaneous voltage [V], U_m is the peak value of the sinusoidal voltage [V], f is the frequency [Hz], and t is time [sec].

It is more convenient to specify points on the sine wave in terms of an angle expressed in degrees or radians:

u = U_msin (Θ), where Θ is the instantaneous angle [rad].

The angle for one complete cycle of a sine wave is 360° or 2π radians.

A single-phase half wave controlled rectifier is the simplest case. If no gate pulse is applied, the thyristor never turns on and the output voltage is zero.

When the control circuit is on, the trigger pulse is applied to the thyristor gate during the positive half-wave of the supplied ac voltage. After switching on, the thyristor-rectified dc voltage u_d follows the ac voltage as shown in the figure. During the negative half wave it is zero.

The switching on of the thyristor may be phase shifted with respect to the moment of natural conduction. The sign of the phase shift is given by α - control angle (trigger angle, delay angle). It may be seen that increasing α reduces the dc voltage.

A two-phase half-wave controlled rectifier is shown in the illustration. Using thyristors instead of diodes allows the dc voltage to be controlled. When the control circuit is off, the rectified voltage is zero - no current flows through the load.

During the positive half-wave of voltage u_2a, after turning on the thyristor Th₁, current flows from an ac voltage source u_2a, via the thyristor and a load. For an interval 0 - α the output voltage is zero. For the interval α - π it matches the positive half wave of the voltage u_2a.

Thyristor Th₂ operates in the same manner during the positive half-wave of the line voltage u_2b. The output voltage is a sequence of positive voltage segments.

When both thyristors are off, the voltage across the load is zero. The voltage u _T1 follows the ac supply voltage u _2a. When thyristor Th₁ is on, the voltage u _T1 is zero (ideal thyristor). When the thyristor Th₂ is on, it acts like a closed switch. So the cathode of Th₁ is connected to the lower point of the secondary transformer winding. Then the voltage across the thyristor Th₁ equals the line-to-line voltage, u_T1 = u_2a - u_2b = 2.u_2a. The maximum reverse voltage across the thyristor is U_Rmax = 2.U_2m.

Each thyristor conducts for half a cycle. Thyristor current matches the shape of the voltage across the load. The average thyristor current is I_Tav = I_d /2.

To smooth the dc current an inductor L is included in the load circuit. The rectifier operates with a resistive-inductive load. This alters all the waveforms as shown in the illustration. It is assumed that the inductance is infinite.

The thyristor Th₁ is turned on by a gate pulse with controlled delay during the positive half-wave. Current flows from the ac source u_2a through Th₁, L, R_L. The inductor accumulates energy. At the beginning of the negative half-wave Th₁ ought to turn off but, due to the stored energy, the thyristor Th₁ continues conducting. A negative voltage segment is allowed through and the average value of the dc voltage decreases. Thyristor Th₁ conducts till thyristor Th₂ turns on.

An inductor L connected in series with the load R_L smoothes the dc current. It is assumed the inductance is infinite. Then the load current i_d is constant and never falls to zero. This mode of operation is known as continuous conduction. The average current value I_d depends on the load resistance R_L and the control angle α. The current i_d is produced alternately from ac sources u_2a and u_2b due to controlled triggering of thyristors Th₁ and Th₂. Hence, the secondary currents are phase-shifted with respect to the secondary voltages by the control angle α.

The primary current i₁ has a rectangular form and is phase-shifted with respect to the primary voltage u ₁ by the control angle α. In this case the power factor for cosφ = cosα is not very good.

The rectifier shown in the illustration is widely used in practice. Thyristor Th₁ is turned on with controlled delay during the positive half-wave. A current flows from ac source u_2a through Th₁, L, R_L. The inductor accumulates energy. At the beginning of negative half-wave Th₁ turns off. Energy stored in the inductor dissipates through the load and through diode D, which is known as a freewheeling diode. The same happens when thyristor Th₂ is on. The rectified voltage u _d has no negative parts.

The voltage waveforms and control characteristic of the rectifier with a freewheeling diode, are equivalent to the case with resistive loading, in spite of the inductance being added to the load.

Current i _d is produced alternatively from ac sources u _2a and u _2b due to controlled triggering of thyristors Th₁ and Th₂. A recovery diode D limits the on-state interval of the thyristors. The current continues to flow in the freewheeling circuit (R_L-L- D).

The average thyristor current I_Tav is reduced at the expense of diode current as shown in the illustration.

The primary current i₁ has a modified rectangular shape. Its phase shift with respect to the primary voltage u ₁ is reduced as compared to the rectifier without a freewheeling diode. The power factor cosφ = cos(α/2) is better.

A three-phase rectifier resembles three single-phase rectifiers. A thyristor with a more positive anode is able to conduct if a gate pulse is applied. With no trigger pulses the voltage u_d is zero.

To control the rectified voltage the trigger pulse is delayed with respect to the instant of a natural commutation. When the control angle is α ≤ α_cr, a segment of the line voltage u_2a is applied to the load when thyristor Th₁ turns on. If Th₂ is turned on u_2b is applied to the load.

When α > α_cr, each thyristor conducts till the end of the corresponding positive half-wave of the line voltage. Then it turns off due to the negative voltage applied. Since the next thyristor is not yet switched on, the rectified voltage u_d is zero for the interval from α_cr to α.

Increasing the phase control angle α delays the switching on of the thyristor. A smaller region of the positive half-waves of ac supply voltages u_2a, u_2b or u_2c is applied to the load. Varying the delay angle α from 0 to (5π/6) causes the average value of the rectified voltage U_d to reduce from its nominal value down to zero.

When α ≤ α_cr, the rectifier is in its continuous mode of operation – the current is not interrupted. When α > α_cr, the rectified voltage and load current become zero for a certain time-interval – discontinuous mode of operation.

The average rectified voltage U_d is given by two expressions - for α ≤ α_cr and for α > α_cr .

When the thyristor Th₁ is on, the voltage u_T1 is zero (in the case of an ideal thyristor).

If α ≤ α_cr, one of the thyristors is on all the time. Th₁ switches off when Th₂ is turned on. The cathode of Th₁ is connected to the line voltage u_2b. Hence, the voltage across Th₁ is the line-to-line voltage, u_T1 = u_2a - u_2b. When the thyristor Th₃ acts as a closed switch, the voltage across Th₁ is u_T1 = u_2a - u_2c. The maximum reverse voltage across the thyristor is U_Rmax.

When α > α_cr, the rectified voltage becomes zero for certain interval. Hence, for interval α_cr to α, the voltage u_T1 matches the ac supply voltage u_2a.

The inductor connected in series to the load smoothes the load current. It is assumed the inductance is infinite.

When α ≤ α_cr, the rectified voltage u_d has the same waveform as with a resistive load.

If the thyristor Th₁ is turned on, a current flows from the ac voltage supply u_2a through the load. Due to the energy stored in the inductor L, when α > α_cr, the current continues to flow in a positive direction although the ac voltage is negative. The on-state thyristor interval is extended till the next thyristor switches on. The rectified voltage consists of negative segments.

The rectifier is in continuous mode of operation.

The inductor connected in series with the load changes the output voltage waveform of the rectifier. Part of negative half-wave of the secondary ac supply voltage appears in the rectified voltage. This reduces the output dc voltage rapidly more than in the case with resistive load.

Varying the control angle α from 0 to (π/2) causes the average value of the rectified voltage U_d to be reduced from its nominal value down to zero.

It is important to remember that in all controlled rectifiers with R-L loads (and very large inductance) the control characteristic has the same shape, as shown in the illustration.

If an infinite inductance is included in the load circuit, the load current i_d will be smoothed very well. In theory it would display no ripple. One of thyristors is always in its on condition, the load current i_d never falls to zero and remains continuous.

Increasing the phase control angle α increases the delay before thyristor turns on. Thus the rectified voltage and average current value I_d are reduced.

From the other side this increases the phase shift of the primary ac supply current with respect to the ac voltage. Hence, as in a two-phase rectifier, the power factor is reduced.

The circuit shown in the illustration is used to improve the controlled rectifier power factor. When thyristor Th₁ is turned on with controlled delay angle α, during the positive half-wave a current flows from the ac source u_2a through the load. The inductor accumulates energy.

If α > α_cr, each thyristor conducts till the end of the corresponding positive half-wave of the ac voltage. Stored inductor energy dissipates through the load and freewheeling diode D.

The voltage waveforms and the control characteristic of the rectifier with freewheeling diode, are equivalent to the case with resistive loading in spite of the inductance being added to the load.

The load current i_d is continuous and flows alternately through the thyristors and the diode.

A controlled bridge rectifier is full wave rectifier and has the same circuit topology as the diode bridge rectifier. A transformer, if one is used, consists of only one secondary winding. To smooth ripple in the rectified voltage, an inductor is used as a filter. Trigger pulses for switching on the thyristor on are generated by a specially designed control circuit. With no gate pulses, thyristors are turned off and no current flows through the circuit.

In standard operation all devices in the bridge rectifier are thyristors. Such a configuration is known as a fully controlled circuit. If only half the devices are thyristors and others are diodes, the bridge rectifier is known as a semi-controlled circuit.

A fully controlled bridge rectifier is shown in the illustration. When the control circuit is off the rectified voltage is zero - no current flows through the load.

If the thyristors are turned on at the instant of natural commutation (control angle α=0) the rectified voltage has the same shape as for an uncontrolled bridge rectifier.

With control angle α>0, during the positive half wave of ac secondary voltage u₂, a current flows via Th₁ and Th₃ after they turn on. Hence, for time interval (0 to α) the output voltage is zero. For the time interval (α to π) it matches the positive half wave of the voltage u₂.

During negative half wave thyristors Th₂ and Th₄ operate in the same manner.

When all the thyristors are off, the load voltage is zero. Each thyristor behaves as a very large resistance. Then the voltage u_T1 across it matches the half-wave of the ac supply voltage u₂. When thyristor Th₁ (and Th₃) is on, the voltage u_T1 is zero (ideal thyristor).

When thyristors Th₂ and Th₄ are on, Th₂ acts as a closed switch. So the cathode of Th₁ is connected to the lower point of the secondary transformer winding. Then the voltage across thyristor Th₁ is the line voltage u₂.

To smooth the dc current an inductor L is included in the load circuit. It alters all the waveforms as shown in the illustration. It is assumed the inductance is infinitely large.

A gate pulse to thyristors Th₁ and Th₃ turns them on during the positive half-wave of the ac voltage u₂. Current flows from the ac source u₂ through Th₁, L, R_L, Th₃. The inductor accumulates energy. At the beginning of the negative half-wave Th₁ and Th₃ ought to turn off. Due to the energy stored, however, thyristors Th₁ and Th₃ continue conducting beyond the zero crossover of the ac voltage u₂. A negative voltage segment is transferred to the rectified dc voltage.

This thyristor pair conducts till the next pair, Th₂ and Th₄ turn on.

A fully controlled rectifier circuit with resistive-inductive loading and large angles of control has a significantly reduced power factor - the component of reactive power is much greater than the real power. To improve this, a freewheeling diode D is included in the circuit.

The thyristor pairs are turned on alternately with controlled delay. Current flows from the ac source u₂ through the load. The inductor accumulates energy. At the beginning of every half-wave the thyristors turn off and energy stored in the inductor dissipates through the load and the diode D.

The voltage waveforms and control characteristic of the bridge rectifier with freewheeling diode are equivalent to the case with resistive loading, in spite of the inductance being added to the load.

The circuit shown in the illustration consists of two thyristors and two diodes. It is known as a semi-controlled rectifier and operates with resistive-inductive loading in the same way as a rectifier with a freewheeling diode.

When thyristor Th₁ is turned on, a current flows from the ac source u₂ through Th₁, L, R_L, D₁. At the beginning of the negative half-wave D₂ starts conducting instead of D₁. The load current continues flowing through Th₁, D₂, L, R_L. The load is isolated from the ac source. No negative voltage transients are produced. Due to the energy stored the thyristor, Th₁ continues conducting till Th₂ turns on. The conducting pairs are then Th₂, D₂ and Th₂, D₁.

The circuit consists of two thyristors and two diodes connected as shown in the illustration. This is the alternative way of constructing a semi-controlled rectifier.

When the thyristor Th₁ is turned on, current flows from the ac source u₂ through Th₁, L, R_L, D₁. At the beginning of negative half-wave D₁ and D₂ conduct due to the energy stored in the inductor. When the thyristor Th₂ is turned on, the load current flows from the ac source through Th₂, D₂, L, R_L.

For the mode of operation explained here answer the questions included with the illustration.

The fully controlled three-phase bridge rectifier consists of 6 thyristors. The circuit shown in the illustration utilizes secondary voltage sources u_2a, u_2b and u_2c in Y (wye) connection.

If the control angle is α=0, the rectifier operates like a diode rectifier. For correct operation trigger pulses must be applied simultaneously to two thyristors in designated sequence. Hence, pairs of trigger pulses are applied to every thyristor.

When Th₆ and Th₁ are turned on (colored region) with controlled delay, the load current flows from the ac source u_2a through Th₁, load, Th₆ and u_2b. A segment of the line-to-line voltage u_2ab is applied to the load.

The average value of a rectified voltage U_d is dependent on the control angle α. For a pure resistive load, the control characteristic is given by two expressions for continuous and discontinuous modes of operation. The discontinuous mode of operation emerges when α> α_cr = 60°.

The dc voltage becomes U_d = 0 (with resistive load) when the control angle reaches α=120°.

With inductive load and α > α_cr the shape of rectified voltage includes negative voltage segments. Due to the energy stored in the inductor, the control characteristic changes. At a control angle of 90°, the average value of the dc voltage would be 0V.

The semi-controlled three-phase bridge rectifier consists of 3 thyristors and 3 diodes.

If the control angle is α=0, the rectifier operates as a diode rectifier. When α is increased, the thyristors are turned on later with respect to the instant of a natural commutation. The diodes commutate without delay. Hence, when pairs Th₁-D₆, Th₃-D₂, Th₅-D₄ conduct, a controlled segment of the corresponding line-to-line voltage is applied to the load. When pairs Th₁-D₂, Th₃-D₄, Th₅-D₆ conduct, the line-to line voltage is applied to the load with no delay.

With control angle α> α_cr= 60°, only pairs Th₁- D₂, Th₃- D₄, Th₅- D₆ may conduct. The rectified voltage has a ripple frequency half of that in the fully controlled circuit.

The semi-controlled three-phase bridge rectifier has equivalent control characteristics for pure resistive or resistive-inductive load. The maximal control angle is α=180°.

The expression for the average value of dc voltage U_d is shown in the illustration.

In the rectifier-mode of operation an ac voltage is converted to a dc voltage. Energy is consumed from the ac mains supply.

In certain circumstances it is possible to reverse the power conversion from dc to ac using the same rectifier circuit. This is only possible with thyristor rectifiers. The important requirement is the presence of an energy source in the load - for example a dc motor or battery.

The relationship between the source and the load is demonstrated by a very simple circuit. With a passive resistive load the current flows in the direction shown. Inside the source (battery) the current flows from - to + and in the external circuit from + to -.

A dc motor is an active load. It contains a dc voltage source E_a. When a dc machine is in the motor-mode the battery is a source and the motor is a load.

If the dc motor is forced to run quickly due to an external force it produces a higher internal voltage E_a >U_B. The current changes its direction of flow. Hence, the dc motor becomes a source and the battery becomes a load.

In the simple rectifier shown in the illustration, it is assumed that the load consists of a voltage source U_dc. During the positive half-wave, when the thyristor is turned on, a current flows in the direction shown. Thus, the ac voltage source delivers energy to the load.

If the polarity of U_dc is changed, the current could be forced to flow in the same direction during the negative half-cycle. Hence, the "ac source" becomes a consumer and receives energy.

The same rectifier circuit operates in so-called inverter mode. Inverter mode is obtained by reversing the thyristor. If the thyristor is turned on at the instant t₀, the current flows through the ac source in reverse direction. The current should be cancelled out well before t₂ to ensure time for the thyristor to turn off reliably.

When the bridge circuit is operating in rectifier mode, the output voltage u_d is positive. The control angle is 0 ≤ α ≤ π/2. Thyristor pair Th₁, Th₃ conducts during the positive half-wave of the secondary voltage u₂.

The same bridge rectifier could operate in inverter mode if an energy source is included in the load circuit. An additional voltage source permits thyristor pair Th₁, Th₃ to conduct during the negative half-wave of the ac supply voltage u₂. The current flows from + U_dc through Th₃, ac source u₂ (down-up), Th₁, L, R_L, -U_dc. The load energy is transferred to the mains. The output voltage is negative. The control angle varies from π/2 ≤ α < π.

A lot of practical dc drive applications allow for reversing the direction of rotation.

This can be implemented using so-called four-quadrant control based on two rectifiers operating back-to back. The "+ rectifier" produces a positive output voltage for clock-wise running of a dc motor. To force the motor to stop a "- rectifier" is used in inverter mode. In this mode the energy of the rotating motor is transferred to the mains.

In the same way the "- rectifier" produces a negative voltage for counter-clockwise running and the "+ rectifier" is used in inverter mode to stop the rotation quickly.

AC to AC converters are based on thyristors connected in anti-parallel or on triacs. They produce an ac output voltage with a controlled r.m.s. value. Two modes of operation are possible.

An ac power controller produces smoothly variable ac voltage by transferring a segment of each half wave of the sinusoidal ac supply voltage to its output. This mode of operation is used to vary brightness or to control the speed or the power of domestic appliances.

An ac multi-cycle control is used for temperature control and regulation of electric heating equipment. The converter is used to switch of the supply voltage to the load on and off for whole periods.

The ac power controller shown in the above illustration is composed of two thyristors connected in anti-parallel so that current can flow in both directions.

The thyristors may be turned on by applying trigger pulses. Th₁ is on during the positive half-wave. The load current then flows through it. During the negative half-wave current flows from the ac voltage source through thyristor Th₂. Due to the delay in the trigger pulses a regulated segment of the ac supply voltage, symmetrical for the positive and negative half-cycles, is applied to the load.

The waveform of the thyristor voltage u_T is shown in the illustration. Its maximum value is U_m.

A simple cycloconverter is shown in the illustration. It consists of three thyristor groups.

Thyristors Th₁, Th₂, Th₃ and Th₁ are triggered in sequence by trigger pulses. As a result the circuit behaves like a 3-pulse rectifier and its output is positive with respect to the neutral point.

In the similar way thyristors Th₂, Th₄, Th₆ and Th₂ again are then triggered. The output voltage becomes negative with respect to the neutral. For the time-interval T_LOW the cycloconverter produces a single-phase low-frequency ac voltage as shown in the illustration. The output frequency is one third of the ac supply frequency.