## INTRODUCTION

**Three phase half controlled bridge converters** & **fully controlled bridge converters** are used extensively in industrial applications up to about 15kW of output power. The **Three phase controlled rectifiers** provide a maximum dc output of

v_{dc(max)}=2v_{m / ∏}

The output ripple frequency is equal to the twice the ac supply frequency. The **single phase full wave controlled** rectifiers provide two output pulses during every input supply cycle and hence are referred to as two pulse converters.

**Three phase converters** are **3-phase controlled rectifiers** which are used to convert ac input power supply into dc output power across the load.

Features of **3-phase controlled rectifiers** are

- Operate from 3 phase ac supply voltage.
- They provide higher dc output voltage and higher dc output power.
- Higher output voltage ripple frequency.
- Filtering requirements are simplified for smoothing out load voltage and load current

**Three phase controlled rectifiers** are extensively used in high power variable speed industrial dc drives.

Three **single phase half-wave converters** are connected together to form a **three phase half-wave converter** as shown in the figure.

## THREE PHASE SUPPLY VOLTAGE EQUATIONS

We define three line neutral voltages (3 phase voltages) as follows

The **3-PHASE HALF WAVE CONVERTER** combines three **single phase half wave controlled rectifiers** in one single circuit feeding a common load. The thyristor T_{1} in series with one of the supply phase windings *'a-n'* acts as one half wave controlled rectifier. The second thyristor T_{2} in series with the supply phase winding *'b-n'* acts as the second half wave controlled rectifier. The third thyristor T_{3} in series with the supply phase winding acts as the third half wave controlled rectifier.

The 3-phase input supply is applied through the star connected supply transformer as shown in the figure. The common neutral point of the supply is connected to one end of the load while the other end of the load connected to the common cathode point.

When the thyristor T_{1} is triggered at ω*t*=(∏/6 + α)=(30° + α) , the phase voltage V_{an} appears across the load when T_{1} conducts. The load current flows through the supply phase winding *'a-n'* and through thyristor T_{1} as long as T_{1} conducts.

When thyristor T_{2} is triggered at ω*t*=(5∏/6α), T_{1} becomes reverse biased and turns-off. The load current flows through the thyristor and through the supply phase winding *'b-n'* . When T_{2} conducts the phase voltage *v*_{bn} appears across the load until the thyristor T_{3} is triggered .

When the thyristor T_{3} is triggered at ω*t*=(3∏/2 + α)=(270°+α) , T_{2} is reversed biased and hence T_{2} turns-off. The phase voltage V_{an} appears across the load when T_{3} conducts.

When T_{1} is triggered again at the beginning of the next input cycle the thyristor T_{3} turns off as it is reverse biased naturally as soon as T_{1} is triggered. The figure shows the 3-phase input supply voltages, the output voltage which appears across the load, and the load current assuming a constant and ripple free load current for a highly inductive load and the current through the thyristor *T*_{1}.

For a purely resistive load where the load inductance ‘L = 0’ and the trigger angle α >(∏/6) , the load current appears as discontinuous load current and each thyristor is naturally commutated when the polarity of the corresponding phase supply voltage reverses. The frequency of output ripple frequency for a **3-PHASE HALF WAVE CONVERTER** is *f*_{s}, where *f*_{s} is the input supply frequency. 3

The **3-PHASE HALF WAVE CONVERTER** is not normally used in practical converter systems because of the disadvantage that the supply current waveforms contain dc components (i.e., the supply current waveforms have an average or dc value).

**TO DERIVE AN EXPRESSION FOR THE AVERAGE OUTPUT VOLTAGE OF A ****3-PHASE HALF WAVE CONVERTER** FOR CONTINUOUS LOAD CURRENT

The reference phase voltage is *v*_{RN}=v_{an}=V_{m}sinωt. The trigger angle is measured from the cross over points of the 3-phase supply voltage waveforms. When the phase supply voltage *V*_{an} begins its positive half cycle at ω*t*=0 , the first cross over point appears at ω*t*=(∏/6)*radians* 30°.

The trigger angle α for the thyristor *T*_{1} is measured from the cross over point at . The thyristor *T*_{1} is forward biased during the period ω*t*=30° to 150° , when the phase supply voltage *v*_{an} has higher amplitude than the other phase supply voltages. Hence *T*_{1} can be triggered between 30° to 150°. When the thyristor *T*_{1} is triggered at a trigger angle α, the average or dc output voltage for continuous load current is calculated using the equation

Note from the trigonometric relationship

The maximum average or dc output voltage is obtained at a delay angle α = 0 and is given by

*V*_{dx(max>=vdm=3√3Vm/2∏}

V_{m }Is the peak phase voltage.

And the normalized average output voltage is

TO DERIVE AN EXPRESSION FOR THE RMS VALUE OF THE OUTPUT VOLTAGE OF A **3-PHASE HALF WAVE CONVERTER** FOR CONTINUOUS LOAD CURRENT

The rms value of output voltage is found by using the equation

**Three phase half wave controlled rectifier** output voltage waveforms for different trigger angles with RL load

**Three phase half wave controlled rectifier** output voltage waveforms for different trigger angles with R load

TO DERIVE AN EXPRESSION FOR THE AVERAGE OR DC OUTPUT VOLTAGE OF A **3 PHASE HALF WAVE CONVERTER** WITH RESISTIVE LOAD OR RL LOAD WITH FWD.

In the case of a **three-phase half wave controlled** rectifier with resistive load, the thyristor *T*_{1} is triggered at ω*t=(30°+α)* and *T*_{1} conducts up to ω*t=180°=&pron; * radians. When the phase supply voltage decreases to zero at , the load current falls to zero and the thyristor *T*_{1} turns off. Thus *T*_{1} conducts from *ωt=(30° + α) to (180°). *

Hence the average dc output voltage for a 3-pulse converter (3-phase half wave controlled rectifier) is calculated by using the equation

**three phase full converter** is a fully controlled bridge controlled rectifier using six thyristors connected in the form of a full wave bridge configuration. All the six thyristors are controlled switches which are turned on at a appropriate times by applying suitable gate trigger signals.

The**three phase full converter** is extensively used in industrial power applications upto about 120kW output power level, where two quadrant operations is required. The figure shows a **three phase full converter** with highly inductive load. This circuit is also known as three phase full wave bridge or as a six pulse converter.

The thyristors are triggered at an interval of (∏/3) radians (i.e. at an interval of 30°). The frequency of output ripple voltage is 6*f*_{s} and the filtering requirement is less than that of **three phase semi and half wave converters**.

At ω*t=(∏/6 +α) *, thyristor is already conducting when the thyristor is turned on by applying the gating signal to the gate of . During the time period ω*t=(∏/6 +α)* to (∏/2 +α), thyristors and conduct together and the line to line supply voltage appears across the load.

At ω*t=(∏/2 +α)*, the thyristor *T*_{2} is triggered and *T*_{6} is reverse biased immediately and *T*_{6} turns off due to natural commutation. During the time period ω*t=(∏/ +α) to (5∏/6 +α)*, thyristor *T*_{1} and *T*_{2} conduct together and the line to line supply voltage appears across the load.

The thyristors are numbered in the circuit diagram corresponding to the order in which they are triggered. The trigger sequence (firing sequence) of the thyristors is 12, 23, 34, 45, 56, 61, 12, 23, and so on. The figure shows the waveforms of three phase input supply voltages, output voltage, the thyristor current through *T*_{1} and *T*_{4}, the supply current through the line ‘a’.

We define three line neutral voltages (3 phase voltages) as follows

To derive an expression for the average output voltage of **three phase full converter** with highly inductive load assuming continuous and constant load current

The output load voltage consists of 6 voltage pulses over a period of 2∏ radians, hence the average output voltage is calculated as