Lecture-21

6.3 Principle of On-Off Control Technique (Integral Cycle Control)

The basic principle of on-off control technique is explained with reference to a single phase full

wave ac voltage controller circuit shown below. The thyristor switches T1 and T2 are turned on by

applying appropriate gate trigger pulses to connect the input ac supply to the load for ‘n’ number of

input cycles during the time interval tON . The thyristor switches T1 and T2 are turned off by blocking the

gate trigger pulses for ‘m’ number of input cycles during the time intervaltOFF . The ac controller ON time

tON usually consists of an integral number of input cycles.

Fig 6.3: Power Factor

Thyristors are turned ON precisely at the zero voltage crossings of the input supply. The thyristor T1 is

turned on at the beginning of each positive half cycle by applying the gate trigger pulses to T1 as shown,

during the ON time tON . The load current flows in the positive direction, which is the downward direction

as shown in the circuit diagram when T1 conducts. The thyristor T2 is turned on at the beginning of each

negative half cycle, by applying gating signal to the gate of T2 , during tON . The load current flows in the

reverse direction, which is the upward direction when T2 conducts. Thus we obtain a bi-directional load

current flow (alternating load current flow) in a ac voltage controller circuit, by triggering the thyristors

alternately.

This type of control is used in applications which have high mechanical inertia and high thermal

time constant (Industrial heating and speed control of ac motors). Due to zero voltage and zero current

switching of Thyristors, the harmonics generated by switching actions are reduced.

(i) To derive an expression for the rms value of output voltage, for on-off control method.

Output RMS voltage V

O RMS

Substituting for

VO RMS

2 2

0

1 .

ON t

m O t

V Sin t d t T

2 2

0 .

ON t m

RMS O O

V t d t Sin V

T

2 1 2

2

Cos Sin

2

0

1 2

2

ON t m

O

V Cos t d t

T

VO RMS

VO RMS

VO RMS

Now tON = an integral number of input cycles; Hence tON T,2T,3T,4T,5T,..... &

tON 2 ,4 ,6 ,8 ,10 ,......

Where T is the input supply time period (T = input cycle time period). Thus we note that sin2 t

2

0 0 2 .

2

ON ON t t m

O

V d t Cos t d t

T

2

0 0

2

2 2

ON ON t t m

O

V Sin t t

T

2 sin2 sin0 0

2 2 m ON

ON O

V t t

T

0 ON

2

2 2

m ON m ON O RMS

O O

V t V t V

T T

ON ON S i RMS O RMS

O O

t t V V V

T T

Where 2

m S RMS i

V V V = RMS value of input supply voltage;

ON ON

OFF ON O

t t n nT k

m T t t nT mT n duty cycle (d ). =

S S O RMS n

V V k V m n

Performance Parameters of Ac Voltage Controllers

Duty Cycle

RMS Load Current

V V

IO RMS ; For a resistive load Z RL .

Z R L

Output AC (Load) Power

PO IO2 RMS RL

RMS Output (Load) Voltage 1

2 2 2 2

0 sin .

2 m O RMS

n d V V t t

m n

2

m S O RMS i RMS

V n V V k k V

m n

S RMS i RMS O k V k V V

Where S i RMS V V = RMS value of input supply voltage.

ON ON

OFF ON O

t t nT k

n T T t t m

Where, n

k m n

= duty cycle (d ).

O RMS O RMS

Input Power Factor

The input supply current is same as the load current Iin

Hence, RMS supply current = RMS load current; Iin RMS.

The Average Current of Thyristor IT Avg

output load power

input supply volt amperes O O

S S

P P PF

VA V I

2 L O RMS

RMS RMS in i

R I PF

V I ;

S RMS in I I RMS input supply current.

2 L RMS RMS i O RMS O

i RMS i RMS in RMS i RMS

k I R V V k PF

V I V V

n k PF

m n

0 . sin

2 m T Avg

n t I d t I

m n

0 2 3 t

I m

n m i T

Waveform of Thyristor Current

O L I I

O RMS I

RMS Current of Thyristor IT RMS