Deceber 9, INGE PHAE FU WAE AC OTAGE CONTROER (AC REGUATOR ingle phase full wave ac voltage controller circuit using two CRs or a single triac is generally used in ost of the ac control applications. The ac power flow to the load can be controlled in both the half cycles by varying the trigger angle ' '. The RM value of load voltage can be varied by varying the trigger angle ' '. The input supply current is alternating in the case of a full wave ac voltage controller and due to the syetrical nature of the input supply current wavefor there is no dc coponent of input supply current i.e., the average value of the input supply current is zero. A single phase full wave ac voltage controller with a resistive load is shown in the figure below. It is possible to control the ac power flow to the load in both the half cycles by adjusting the trigger angle ' '. Hence the full wave ac voltage controller is also referred to as to a bi-directional controller. Fig.: ingle phase full wave ac voltage controller (Bi-directional Controller using CRs The thyristor T is forward biased during the positive half cycle of the input supply voltage. The thyristor T is triggered at a delay angle of ' ' ( radians. Considering the ON thyristor T as an ideal closed switch the input supply voltage appears across the load resistor R and the output voltage v O v during ωt to radians. The load current flows through the ON thyristor T and through the load resistor R in the downward direction during the conduction tie of T fro ωt to radians. At ωt, when the input voltage falls to zero the thyristor current (which is flowing through the load resistor R falls to zero and hence T naturally turns off. No current flows in the circuit during ωt +. to AC OTAGE CONTROER Page
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
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
Deceber 9, d( ωt cos ωtd. ( ωt + d( ωt cos ωtd. ( ωt + + sinωt sinωt + 4 ( ωt ( ωt + + 4 + + ( ( ( sin sin ( sin 4 sin ( sin sin 4 + ( ( ( ( + + 4 sin sin ( + ( ( + sin sin ( + + 4 sin sin.cos cos.sin 4 + + + 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
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
Deceber 9, Where RM value of input supply voltage Trigger angle in degrees Trigger angle in radians.985477 3 ; ( 6 6 6 ; ( 3 6 9 ; ( 3 6 ; ( 4 3 6 5 5 ; ( 5 6 6 8 ;( 6.896938.77.445.698 6 ORM % % 98.54% 89.69% 7.7% 44.% 6.98% O(RM.6. 6 8 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
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
Deceber 9, INGE PHAE FU WAE AC OTAGE CONTROER UING A INGE THYRITOR D D 3 + T AC upply D 4 D R - A single phase full wave ac controller can also be ipleented with one thyristor and four diodes connected in a full wave bridge configuration as shown in the above figure. The four diodes act as a bridge full wave rectifier. The voltage across the thyristor T and current through thyristor T are always unidirectional. When T is triggered at ωt, during the positive half cycle (, the load current flows through D, T, diode D and through the load. With a resistive load, the thyristor current (flowing through the ON thyristor T, the load current falls to zero at ωt, when the input supply voltage decreases to zero at ωt, the thyristor naturally turns OFF. In the negative half cycle, diodes D3& D 4 are forward biased during ωt to radians. When T is triggered at ωt ( +, the load current flows in the opposite direction (upward direction through the load, through D 3, T and D 4. Thus D 3, D4 and T conduct together during the negative half cycle to supply the load power. When the input supply voltage becoes zero at ωt, the thyristor current (load current falls to zero at ωt and the thyristor T naturally turns OFF. The wavefors and the expression for the RM output voltage are the sae as discussed earlier for the single phase full wave ac controller. But however if there is a large inductance in the load circuit, thyristor T ay not be turned OFF at the zero crossing points, in every half cycle of input voltage and this ay result in a loss of output control. This would require detection of the zero crossing of the load current wavefor in order to ensure guaranteed turn off of the conducting thyristor before triggering the thyristor in the next half cycle, so that we gain control on the output voltage. In this full wave ac controller circuit using a single thyristor, as there are three power devices conducting together at the sae tie there is ore conduction voltage drop and an increase in the ON state conduction losses and hence efficiency is also reduced. The diode bridge rectifier and thyristor (or a power transistor act together as a bidirectional switch which is coercially available as a single device odule and it has AC OTAGE CONTROER Page 8
Deceber 9, relatively low ON state conduction loss. It can be used for bidirectional load current control and for controlling the RM output voltage. INGE PHAE FU WAE AC OTAGE CONTROER (BIDIRECTIONA CONTROER WITH R OAD In this section we will discuss the operation and perforance of a single phase full wave ac voltage controller with R load. In practice ost of the loads are of R type. For exaple if we consider a single phase full wave ac voltage controller controlling the speed of a single phase ac induction otor, the load which is the induction otor winding is an R type of load, where R represents the otor winding resistance and represents the otor winding inductance. A single phase full wave ac voltage controller circuit (bidirectional controller with an R load using two thyristors T and T ( T and T are two CRs connected in parallel is shown in the figure below. In place of two thyristors a single Triac can be used to ipleent a full wave ac controller, if a suitable Traic is available for the desired RM load current and the RM output voltage ratings. Fig: ingle phase full wave ac voltage controller with R load The thyristor T is forward biased during the positive half cycle of input supply. et us assue that T is triggered at ωt, by applying a suitable gate trigger pulse to T during the positive half cycle of input supply. The output voltage across the load follows the input supply voltage when T is ON. The load current i O flows through the thyristor T and through the load in the downward direction. This load current pulse flowing through T can be considered as the positive current pulse. Due to the inductance AC OTAGE CONTROER Page 9
Deceber 9, in the load, the load current i O flowing through T would not fall to zero at the input supply voltage starts to becoe negative. ωt, when The thyristor T will continue to conduct the load current until all the inductive energy stored in the load inductor is copletely utilized and the load current through T falls to zero at ωt β, where β is referred to as the Extinction angle, (the value of ω t at which the load current falls to zero. The extinction angle β is easured fro the point of the beginning of the positive half cycle of input supply to the point where the load current falls to zero. The thyristor T conducts fro ωt to β. The conduction angle of T is δ ( β, which depends on the delay angle and the load ipedance angle φ. The wavefors of the input supply voltage, the gate trigger pulses of T and T, the thyristor current, the load current and the load voltage wavefors appear as shown in the figure below. Fig.: Input supply voltage & Thyristor current wavefors β is the extinction angle which depends upon the load inductance value. AC OTAGE CONTROER Page
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
Deceber 9, Fig.: Wavefors of Input supply voltage, oad Current, oad oltage and Thyristor oltage across T Note The RM value of the output voltage and the load current ay be varied by varying the trigger angle. This circuit, AC RM voltage controller can be used to regulate the RM voltage across the terinals of an ac otor (induction otor. It can be used to control the teperature of a furnace by varying the RM output voltage. For very large load inductance the CR ay fail to coutate, after it is triggered and the load voltage will be a full sine wave (siilar to the applied input supply voltage and the output control will be lost as long as the gating signals are applied to the thyristors T and T. The load current wavefor will appear as a full continuous sine wave and the load current wavefor lags behind the output sine wave by the load power factor angle φ. TO DERIE AN EXPREION FOR THE OUTPUT (INDUCTIE OAD CURRENT, DURING ωt to β WHEN THYRITOR T CONDUCT Considering sinusoidal input supply voltage we can write the expression for the supply voltage as v sin ωt instantaneous value of the input supply voltage. et us assue that the thyristor T is triggered by applying the gating signal to T at ωt. The load current which flows through the thyristor T during ωt to β can be found fro the equation dio + RiO sinωt dt ; The solution of the above differential equation gives the general expression for the output load current which is of the for AC OTAGE CONTROER Page
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
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
Deceber 9, For δ β + > β the load current wavefor appears as a discontinuous current wavefor as shown in the figure. The output load current reains at zero during ωt β +. This is referred to as < radians, i.e., for ( < radians, for to discontinuous load current operation which occurs for β < ( +. When the trigger angle is decreased and ade equal to the load ipedance angle φ i.e., when φ sin β φ, we obtain fro the expression for ( β φ ; Therefore sin β φ radians. Extinction angle β ( + φ ( + ; for the case when φ Conduction angle δ β radians 8 ; for the case when φ Each thyristor conducts for 8 ( radians. T conducts fro ωt φ to ( + φ and provides a positive load current. T conducts fro ( + φ to ( + φ and provides a negative load current. Hence we obtain a continuous load current and the output voltage wavefor appears as a continuous sine wave identical to the input supply voltage wavefor for trigger angle φ and the control on the output is lost. v O v Ov φ 3 ωt φ φ φ i O I φ ωt Fig.: Output voltage and output current wavefors for a single phase full wave ac voltage controller with R load for φ Thus we observe that for trigger angle φ, the load current tends to flow continuously and we have continuous load current operation, without any break in the load current wavefor and we obtain output voltage wavefor which is a continuous sinusoidal wavefor identical to the input supply voltage wavefor. We loose the control on the output voltage for φ as the output voltage becoes equal to the input supply voltage and thus we obtain AC OTAGE CONTROER Page 5
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
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
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
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
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 45. 4. 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