# SINGLE PHASE FULL WAVE AC VOLTAGE CONTROLLER (AC REGULATOR)

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2 Deceber 9, The thyristor T is forward biased during the negative cycle of input supply and when thyristor T is triggered at a delay angle ( +, the output voltage follows the negative halfcycle of input fro ωt ( + to. When T is ON, the load current flows in the reverse direction (upward direction through T during ωt ( + to radians. The tie interval (spacing between the gate trigger pulses of T and T is kept at radians or 8. At ωt the input supply voltage falls to zero and hence the load current also falls to zero and thyristor T turn off naturally. Instead of using two CR s in parallel, a Triac can be used for full wave ac voltage control. Fig.: ingle phase full wave ac voltage controller (Bi-directional Controller using TRIAC Fig: Wavefors of single phase full wave ac voltage controller AC OTAGE CONTROER Page

3 Deceber 9, EQUATION Input supply voltage v sinωt sinωt; Output voltage across the load resistor R ; vo v sinωt ; for ωt to and ωt ( + to Output load current vo sinωt io Isinωt ; R R for ωt to and ωt ( + to TO DERIE AN EXPREION FOR THE RM AUE OF OUTPUT (OAD OTAGE The RM value of output voltage (load voltage can be found using the expression ORM v d t ; ( ω RM For a full wave ac voltage controller, we can see that the two half cycles of output voltage wavefors are syetrical and the output pulse tie period (or output pulse repetition tie is radians. Hence we can also calculate the RM output voltage by using the expression given below. RM sin ωtd. ωt RM. ( ω v d t ; v v sinωt; For ωt to O and to ωt + Hence, ( sin t d( t ( sin t RM ω ω ω d( ωt + + sin ωtd. ( ωt sin ωtd. ( ωt + + cosωt cosωt d( ωt d( ωt + + AC OTAGE CONTROER Page 3

4 Deceber 9, d( ωt cos ωtd. ( ωt + d( ωt cos ωtd. ( ωt + + sinωt sinωt + 4 ( ωt ( ωt ( ( ( sin sin ( sin 4 sin ( sin sin 4 + ( ( ( ( sin sin ( + ( ( + sin sin ( sin sin.cos cos.sin sin & cos Therefore, ( ( ( 4 sin sin + + RM sin 4 + ( sin RM 4 + Taking the square root, we get ( sin RM + ( sin RM + AC OTAGE CONTROER Page 4

5 Deceber 9, ( sin RM + sin + ( RM sin + ( RM sin + i ( RM ( RM sin + ( RM Maxiu RM voltage will be applied to the load when, in that case the full sine wave appears across the load. RM load voltage will be the sae as the RM supply voltage. When is increased the RM load voltage decreases. sin + RM ( RM + ( RM i( RM The output control characteristic for a single phase full wave ac voltage controller with resistive load can be obtained by plotting the equation for ORM CONTRO CHARACTERITIC OF INGE PHAE FU-WAE AC OTAGE CONTROER WITH REITIE OAD The control characteristic is the plot of RM output voltage ORM versus the trigger angle ; which can be obtained by using the expression for the RM output voltage of a full-wave ac controller with resistive load. sin + ( ORM ; AC OTAGE CONTROER Page 5

6 Deceber 9, Where RM value of input supply voltage Trigger angle in degrees Trigger angle in radians ; ( ; ( ; ( 3 6 ; ( ; ( ;( ORM % % 98.54% 89.69% 7.7% 44.% 6.98% O(RM Trigger angle in degrees We can notice fro the figure, that we obtain a uch better output control characteristic by using a single phase full wave ac voltage controller. The RM output voltage can be varied fro a axiu of % at to a iniu of at 8. Thus we get a full range output voltage control by using a single phase full wave ac voltage controller. Need For Isolation In the single phase full wave ac voltage controller circuit using two CRs or Thyristors T and T in parallel, the gating circuits (gate trigger pulse generating circuits of Thyristors T and T ust be isolated. Figure shows a pulse transforer with two separate windings to provide isolation between the gating signals of T and T. AC OTAGE CONTROER Page 6

7 Deceber 9, Gate Trigger Pulse Generator G K G K Fig.: Pulse Transforer INGE PHAE FU-WAE AC OTAGE CONTROER WITH COMMON CATHODE It is possible to design a single phase full wave ac controller with a coon cathode configuration by having a coon cathode point for T and T & by adding two diodes in a full wave ac controller circuit as shown in the figure below Fig.: ingle phase full wave ac controller with coon cathode (Bidirectional controller in coon cathode configuration Thyristor T and diode D are forward biased during the positive half cycle of input supply. When thyristor T is triggered at a delay angle, Thyristor T and diode D conduct together fro ωt to during the positive half cycle. The thyristor T and diode D are forward biased during the negative half cycle of input supply, when trigged at a delay angle, thyristor T and diode D conduct together during the negative half cycle fro ωt ( + to. In this circuit as there is one single coon cathode point, routing of the gate trigger pulses to the thyristor gates of T and T is sipler and only one isolation circuit is required. But due to the need of two power diodes the costs of the devices increase. As there are two power devices conducting at the sae tie the voltage drop across the ON devices increases and the ON state conducting losses of devices increase and hence the efficiency decreases. AC OTAGE CONTROER Page 7

11 Deceber 9, Fig.: Gating ignals Wavefors of single phase full wave ac voltage controller with R load for > φ. Discontinuous load current operation occurs for φ β < + ; i.e., ( β <, conduction angle <. > and AC OTAGE CONTROER Page

13 Deceber 9, + ; t τ io sin ( ωt φ Ae Where axiu or peak value of input supply voltage. ( ω R + oad ipedance. ω φ tan R oad ipedance angle (power factor angle of load. τ oad circuit tie constant. R Therefore the general expression for the output load current is given by the equation R t io sin ( ωt φ + Ae ; The value of the constant A can be deterined fro the initial condition. i.e. initial value of load current i O, at ωt. Hence fro the equation for i O equating i O to zero and substituting ωt, we get i O sin( φ + Ae R t sin Therefore Ae ( φ A sin R t e A + R t ( φ e sin ( φ A R( ωt ω e sin ( φ R t By substituting ωt, we get the value of constant A as R( ω e sin ( φ A AC OTAGE CONTROER Page 3

14 Deceber 9, ubstituting the value of constant A fro the above equation into the expression for i O, we obtain R R( t ω io sin ( ωt φ + e e sin ( φ ; R( ωt R( io t e e + ω ω sin ( ω φ sin ( φ + R io t e ω t ω sin ( ω φ sin ( φ Therefore we obtain the final expression for the inductive load current of a single phase full wave ac voltage controller with R load as io sin ( ωt φ sin ( φ e R ( ω t ω ; Where ωt β. The above expression also represents the thyristor current i T, during the conduction tie interval of thyristor T fro ωt to β. To Calculate Extinction Angle β The extinction angle β, which is the value of ω t at which the load current i O falls to zero and T is turned off can be estiated by using the condition that i O, at ωt β By using the above expression for the output load current, we can write As i O sin sin ( β φ ( φ e R ( β ω we can write ( β φ ( φ Therefore we obtain the expression R ( β ω sin sin e sin ( β φ sin ( φ e R ( β ω The extinction angle β can be deterined fro this transcendental equation by using the iterative ethod of solution (trial and error ethod. After β is calculated, we can deterine the thyristor conduction angle δ β. β is the extinction angle which depends upon the load inductance value. Conduction angle δ increases as is decreased for a known value of β. AC OTAGE CONTROER Page 4

16 Deceber 9, Hence, ORM ; for φ RM output voltage RM input supply voltage for φ TO DERIE AN EXPREION FOR RM OUTPUT OTAGE ORM OF A INGE PHAE FU-WAE AC OTAGE CONTROER WITH R OAD. When > O, the load current and load voltage wavefors becoe discontinuous as shown in the figure above. β sin td. ORM ω ( ωt Output vo sinωt, for ωt to β, when T is ON. ( ωt β cos ORM d( ωt β β d t td t ORM ( ω cos ω. ( ω β sin ωt ( ωt ORM ( β ORM β sinβ sin + sin sin β + ( β ORM AC OTAGE CONTROER Page 6

17 Deceber 9, sin sin β + ( β ORM The RM output voltage across the load can be varied by changing the trigger angle. For a purely resistive load, therefore load power factor angle φ. ω φ tan ; R Extinction angle β radians 8 PERFORMANCE PARAMETER OF A INGE PHAE FU WAE AC OTAGE CONTROER WITH REITIE OAD sin + RM Output oltage ( input supply voltage. ORM ; RM IORM ORM RM value of load current. R I IORM RM value of input supply current. Output load power Input Power Factor P I R O ORM I R I R PO ORM ORM PF I I ORM Average Thyristor Current, ORM sin PF ( + i T I ( + 3 ωt AC OTAGE CONTROER Page 7

18 Deceber 9, Fig.: Thyristor Current Wavefor I i d t I td t T Avg T ( ω sin ω. ( ω I I I sin ωtd. ( ωt cosωt T Avg I I I T Avg Maxiu Average Thyristor Current, for, I IT( Avg RM Thyristor Current [ cos + cos ] [ + cos ] I I sin td. T RM ω ( ωt I I sin + ( T RM Maxiu RM Thyristor Current, for, I I T( RM In the case of a single phase full wave ac voltage controller circuit using a Triac with resistive load, the average thyristor current I. Because the Triac conducts in T Avg both the half cycles and the thyristor current is alternating and we obtain a syetrical thyristor current wavefor which gives an average value of zero on integration. PERFORMANCE PARAMETER OF A INGE PHAE FU WAE AC OTAGE CONTROER WITH R- OAD The Expression for the Output (oad Current The expression for the output (load current which flows through the thyristor, during ωt to β is given by R ( ω t ω io it sin ( ωt φ sin ( φ e ; for ωt β Where, Maxiu or peak value of input ac supply voltage. ( ω R + oad ipedance. AC OTAGE CONTROER Page 8

19 Deceber 9, ω φ tan R oad ipedance angle (load power factor angle. Thyristor trigger angle Delay angle. β Extinction angle of thyristor, (value of current falls to zero. β is calculated by solving the equation sin ( β φ sin ( φ e R ( β ω ω t at which the thyristor (load Thyristor Conduction Angle δ ( β Maxiu thyristor conduction angle δ ( β radians 8 for φ. RM Output oltage sin sin β + ( β ORM The Average Thyristor Current β I T Avg it d( ωt β R ( ω t ω I sin ( t sin T Avg ω φ ( φ e d( ωt β β R ( ω t ω I sin ( t. d( t sin T Avg ω φ ω ( φ e d( ωt Maxiu value of I T( Avg occur at. The thyristors should be rated for I axiu IT( Avg, where I. RM Thyristor Current I T( RM β I T RM it d( ωt Maxiu value of I T( RM occurs at. Thyristors should be rated for I axiu IT( RM AC OTAGE CONTROER Page 9

20 Deceber 9, When a Triac is used in a single phase full wave ac voltage controller with R I type of load, then I and axiu I T Avg T( RM PROBEM. A single phase full wave ac voltage controller supplies an R load. The input supply voltage is 3, RM at 5Hz. The load has H, R Ω, the delay angle of thyristors T and T are equal, where. Deterine 3 a. Conduction angle of the thyristor T. b. RM output voltage. c. The input power factor. Coent on the type of operation.. A single phase full wave controller has an input voltage of (RM and a load resistance of 6 oh. The firing angle of thyristor is. Find a. RM output voltage b. Power output c. Input power factor d. Average and RM thyristor current. 3. A single phase half wave ac regulator using one CR in anti-parallel with a diode feeds kw, 3 heater. Find load power for a firing angle of Find the RM and average current flowing through the heater shown in figure. The delay angle of both the CRs is 45. CR + i o -φ ac CR kw, heater AC OTAGE CONTROER Page

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