UNIT - II CONTROLLED RECTIFIERS (Line Coutated AC to DC converters) INTRODUCTION TO CONTROLLED RECTIFIERS Controlled rectifiers are line coutated ac to power converters which are used to convert a fixed voltage, fixed frequency ac power supply into variable output voltage. AC Input oltage Line Coutated Converter + DC Output () - Type of input: Fixed voltage, fixed frequency ac power supply. Type of output: ariable output voltage The input supply fed to a controlled rectifier is ac supply at a fixed rs voltage and at a fixed frequency. We can obtain variable output voltage by using controlled rectifiers. By eploying phase controlled thyristors in the controlled rectifier circuits we can obtain variable output voltage and variable (average) output current by varying the trigger angle (phase angle) at which the thyristors are triggered. We obtain a uni-directional and pulsating load current wavefor, which has a specific average value. The thyristors are forward biased during the positive half cycle of input supply and can be turned ON by applying suitable gate trigger pulses at the thyristor gate leads. The thyristor current and the load current begin to flow once the thyristors are triggered (turned ON) say at t. The load current flows when the thyristors conduct fro t to. The output voltage across the load follows the input supply voltage through the conducting thyristor. At t, when the load current falls to zero, the thyristors turn off due to AC line (natural) coutation. In soe bridge controlled rectifier circuits the conducting thyristor turns off, when the other thyristor is (other group of thyristors are) turned ON. The thyristor reains reverse biased during the negative half cycle of input supply. The type of coutation used in controlled rectifier circuits is referred to AC line coutation or Natural coutation or AC phase coutation. When the input ac supply voltage reverses and becoes negative during the negative half cycle, the thyristor becoes reverse biased and hence turns off. There are several types of power converters which use ac line coutation. These are referred to as line coutated converters. Different types of line coutated converters are Phase controlled rectifiers which are AC to DC converters. AC to AC converters o AC voltage controllers, which convert input ac voltage into variable ac output voltage at the sae frequency. o Cyclo converters, which give low output frequencies.
All these power converters operate fro ac power supply at a fixed rs input supply voltage and at a fixed input supply frequency. Hence they use ac line coutation for turning off the thyristors after they have been triggered ON by the gating signals. DIFFERENCES BETWEEN DIODE RECTIFIERS AND PHASE CONTROLLED RECTIFIERS The diode rectifiers are referred to as uncontrolled rectifiers which ake use of power seiconductor diodes to carry the load current. The diode rectifiers give a fixed output voltage (fixed average output voltage) and each diode rectifying eleent conducts for one half cycle duration (T/ seconds), that is the diode conduction angle = 8 or radians. A single phase half wave diode rectifier gives (under ideal conditions) an average output voltage O and single phase full wave diode rectifier gives (under ideal conditions) an average output voltage O, where is axiu value of the available ac supply voltage. Thus we note that we can not control (we can not vary) the output voltage or the average load current in a diode rectifier circuit. In a phase controlled rectifier circuit we use a high current and a high power thyristor device (silicon controlled rectifier; SCR) for conversion of ac input power into output power. Phase controlled rectifier circuits are used to provide a variable voltage output and a variable (average) load current. We can control (we can vary) the average value ( value) of the output load voltage (and hence the average load current) by varying the thyristor trigger angle. We can control the thyristor conduction angle fro 8 to by varying the trigger angle fro to 8, where thyristor conduction angle APPLICATIONS OF PHASE CONTROLLED RECTIFIERS DC otor control in steel ills, paper and textile ills eploying otor drives. AC fed traction syste using traction otor. Electro-cheical and electro-etallurgical processes. Magnet power supplies. Reactor controls. Portable hand tool drives. ariable speed industrial drives. Battery charges. High voltage DC transission. Uninterruptible power supply systes (UPS). Soe years back ac to power conversion was achieved using otor generator sets, ercury arc rectifiers, and thyratorn tubes. The odern ac to power converters are designed using high power, high current thyristors and presently ost of the ac- power converters are thyristorised power converters. The thyristor devices are phase controlled to obtain a variable output voltage across the output load terinals. The phase controlled thyristor converter uses ac line coutation (natural coutation) for coutating (turning off) the thyristors that have been turned ON. The phase controlled converters are siple and less expensive and are widely used in industrial applications for industrial drives. These converters are classified as two quadrant
converters if the output voltage can be ade either positive or negative for a given polarity of output load current. There are also single quadrant ac- converters where the output voltage is only positive and cannot be ade negative for a given polarity of output current. Of course single quadrant converters can also be designed to provide only negative output voltage. The two quadrant converter operation can be achieved by using fully controlled bridge converter circuit and for single quadrant operation we use a half controlled bridge converter. CLASSIFICATION OF PHASE CONTROLLED RECTIFIERS The phase controlled rectifiers can be classified based on the type of input power supply as Single Phase Controlled Rectifiers which operate fro single phase ac input power supply. Three Phase Controlled Rectifiers which operate fro three phase ac input power supply. DIFFERENT TYPES OF SINGLE PHASE CONTROLLED RECTIFIERS Single Phase Controlled Rectifiers are further subdivided into different types Half wave controlled rectifier which uses a single thyristor device (which provides output control only in one half cycle of input ac supply, and it provides low output). Full wave controlled rectifiers (which provide higher output) o Full wave controlled rectifier using a center tapped transforer (which requires two thyristors). o Full wave bridge controlled rectifiers (which do not require a center tapped transforer) Single phase sei-converter (half controlled bridge converter, using two SCR s and two diodes, to provide single quadrant operation). Single phase full converter (fully controlled bridge converter which requires four SCR s, to provide two quadrant operation). Three Phase Controlled Rectifiers are of different types Three phase half wave controlled rectifiers. Three phase full wave controlled rectiriers. o Sei converter (half controlled bridge converter). o Full converter (fully controlled bridge converter). PRINCIPLE OF PHASE CONTROLLED RECTIFIER OPERATION The basic principle of operation of a phase controlled rectifier circuit is explained with reference to a single phase half wave phase controlled rectifier circuit with a resistive load shown in the figure. 3
RR L Load Resistance Fig.: Single Phase Half-Wave Thyristor Converter with a Resistive Load A single phase half wave thyristor converter which is used for ac- power conversion is shown in the above figure. The input ac supply is obtained fro a ain supply transforer to provide the desired ac supply voltage to the thyristor converter depending on the output voltage required. vp represents the priary input ac supply voltage. vs represents the secondary ac supply voltage which is the output of the transforer secondary. During the positive half cycle of input supply when the upper end of the transforer secondary is at a positive potential with respect to the lower end, the thyristor anode is positive with respect to its cathode and the thyristor is in a forward biased state. The thyristor is triggered at a delay angle of t, by applying a suitable gate trigger pulse to the gate lead of thyristor. When the thyristor is triggered at a delay angle of t, the thyristor conducts and assuing an ideal thyristor, the thyristor behaves as a closed switch and the input supply voltage appears across the load when the thyristor conducts fro t to radians. Output voltage vo vs, when the thyristor conducts fro t to. For a purely resistive load, the load current (output current) that flows when the T thyristor is on, is given by the expression vo io, for t RL The output load current wavefor is siilar to the output load voltage wavefor during the thyristor conduction tie fro to. The output current and the output voltage wavefor are in phase for a resistive load. The load current increases as the input supply voltage increases and the axiu load current flows at t, when the input supply voltage is at its axiu value. The axiu value (peak value) of the load current is calculated as io ax I. R L Note that when the thyristor conducts ( T is on) during t to, the thyristor current i, the load current i T O through R and the source current i L S flowing through the transforer secondary winding are all one and the sae. Hence we can write 4 i O
I vo sint is it io ; for t R R is the axiu (peak) value of the load current that flows through the transforer secondary winding, through T and through the load resistor R at the instant t L, when the input supply voltage reaches its axiu value. When the input supply voltage decreases the load current decreases. When the supply voltage falls to zero at t, the thyristor and the load current also falls to zero at t. Thus the thyristor naturally turns off when the current flowing through it falls to zero at t. During the negative half cycle of input supply when the supply voltage reverses and becoes negative during t to radians, the anode of thyristor is at a negative potential with respect to its cathode and as a result the thyristor is reverse biased and hence it reains cut-off (in the reverse blocking ode). The thyristor cannot conduct during its reverse biased state between t to. An ideal thyristor under reverse biased condition behaves as an open switch and hence the load current and load voltage are zero during t to. The axiu or peak reverse voltage that appears across the thyristor anode and cathode terinals is. The trigger angle (delay angle or the phase angle ) is easured fro the beginning of each positive half cycle to the tie instant when the gate trigger pulse is applied. The thyristor conduction angle is fro to, hence the conduction angle. The axiu conduction angle is radians (8 ) when the trigger angle. Fig: Quadrant Diagra The wavefors shows the input ac supply voltage across the secondary winding of the transforer which is represented as v S, the output voltage across the load, the output (load) current, and the thyristor voltage wavefor that appears across the anode and cathode terinals. 5
Fig: Wavefors of single phase half-wave controlled rectifier with resistive load EQUATIONS vs sin t the ac supply voltage across the transforer secondary. ax. (peak) value of input ac supply voltage across transforer secondary. S RMS value of input ac supply voltage across transforer secondary. v O vl the output voltage across the load ; io il output (load) current. When the thyristor is triggered at t (an ideal thyristor behaves as a closed switch) and hence the output voltage follows the input supply voltage. v v t ; for t to, when the thyristor is on. O L sin 6
i O vo il = Load current for t to, when the thyristor is on. R TO DERIE AN EXPRESSION FOR THE AERAGE (DC) OUTPUT OLTAGE ACROSS THE LOAD If is the peak input supply voltage, the average output voltage can be found fro vo. d O t t d t O sin. t d t O sin. t d t O sin. cost O cos cos O ; cos cos ; O The axiu average () output voltage is obtained when and the axiu output voltage ax d. The average output voltage can be varied by varying the trigger angle fro to a axiu of 8 radians. We can plot the control characteristic, which is a plot of output voltage versus the trigger angle by using the equation for. O S 7
CONTROL CHARACTERISTIC OF SINGLE PHASE HALF WAE PHASE CONTROLLED RECTIFIER WITH RESISTIE LOAD The average output voltage is given by the expression cos O We can obtain the control characteristic by plotting the expression for the output voltage as a function of trigger angle Trigger angle in degrees O % d %.933 93.3 % 3 d 6 d 9 d.75 75 %.5 5 %.5 d 5 % 5.6698 d 6.69 % 8 d d d d d d d ax O() d.6 d. d 6 8 Trigger angle Fig.: Control characteristic Noralizing the output voltage with respect to n O( ) ax d in degrees d, the noralized output voltage 8
n n cos n d cos n d TO DERIE AN EXPRESSION FOR THE RMS ALUE OF OUTPUT OLTAGE OF A SINGLE PHASE HALF WAE CONTROLLED RECTIFIER WITH RESISTIE LOAD The rs output voltage is given by vo. d O RMS t Output voltage vo sin t ; for t to sin. O RMS t d t cos t By substituting sin t, we get Hence we get, cos t. d O RMS t cos t. d O RMS t 4 d t t d t O RMS 4 cos. sin t t O RMS O RMS sin sin sin O RMS ; sin 9
O RMS sin PERFORMANCE PARAMETERS OF PHASE CONTROLLED RECTIFIERS Output power (average or output power delivered to the load) Where P I O O O ; i.e., P I I O O I average or value of output (load) voltage. average or value of output (load) current. Output ac power P I O ac O RMS O RMS Efficiency of Rectification (Rectification Ratio) P Efficiency P ; The output voltage can be considered as being coposed of two coponents The coponent = DC or average value of output voltage. The ac coponent or the ripple coponent RMS value of all the ac ripple coponents. The total RMS value of output voltage is given by O O ac O PO % Efficiency P ac O ac r rs Therefore For Factor (FF) O RMS O r rs ac r rs O RMS O which is a easure of the shape of the output voltage is given by FF O RMS O RMS output load voltage DC output load voltage The Ripple Factor (RF) which is a easure of the ac ripple content in the output voltage wavefor. The output voltage ripple factor defined for the output voltage wavefor is given by r rs ac rv RF O
Therefore O RMS O ORMS rv O O rv FF Current Ripple Factor defined for the output (load) current wavefor is given by Where I ri I r rs O I I ac I I I I r rs O RMS O ac Soe ties the peak to peak output ripple voltage is also considered to express the peak to peak output ripple voltage as The peak to peak ac ripple load current is the difference between the axiu and the iniu values of the output load current. Transforer Utilization Factor (TUF) peak to peak ac ripple output voltage r pp I I I ax in r pp O O Where S I S TUF PO I S S RMS value of transforer secondary output voltage (RMS supply voltage at the secondary) RMS value of transforer secondary current (RMS line or supply current).
vs i S Supply voltage at the transforer secondary side. Input supply current (transforer secondary winding current). is Fundaental coponent of the input supply current. IP Peak value of the input supply current. Phase angle difference between (sine wave coponents) the fundaental coponents of input supply current and the input supply voltage. Displaceent angle (phase angle) For an RL load Displaceent angle = Load ipedance angle Displaceent Factor (DF) or Fundaental Power Factor Haronic Factor (HF) or Total Haronic Distortion Factor (THD) The haronic factor is a easure of the distortion in the output wavefor and is also referred to as the total haronic distortion (THD) Where L R DF I S Cos tan for an RL load S S S IS IS I I I HF RMS value of input supply current. IS RMS value of fundaental coponent of the input supply current. Input Power Factor (PF) S IS IS PF cos cos I I S S S
The Crest Factor (CF) IS peak Peak input supply current CF I RMS input supply current For an Ideal Controlled Rectifier FF ; which eans that O RMS O. Efficiency % ; which eans that P P O Oac. S ac ; so that RF r v ; Ripple factor = (ripple free converter). r rs TUF ; which eans that P SI S HF THD ; which eans that IS IS PF DPF ; which eans that SINGLE PHASE HALF WAE CONTROLLED RECTIFIER WITH AN RL LOAD In this section we will discuss the operation and perforance of a single phase half wave controlled rectifier with RL load. In practice ost of the loads are of RL type. For exaple if we consider a single phase controlled rectifier controlling the speed of a otor, the load which is the otor winding is an RL type of load, where R represents the otor winding resistance and L represents the otor winding inductance. O A single phase half wave controlled rectifier circuit with an RL load using a thyristor ( T is an SCR) is shown in the figure below. T The thyristor T is forward biased during the positive half cycle of input supply. Let us assue that T is triggered at t, 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 3
voltage when T is ON. The load current flows through the thyristor T and through the load i O in the downward direction. This load current pulse flowing through T can be considered as the positive current pulse. Due to the inductance in the load, the load current i O flowing through T would not fall to zero at t, when the input supply voltage starts to becoe negative. A phase shift appears between the load voltage and the load current wavefors, due to the load inductance. The thyristor T will continue to conduct the load current until all the inductive energy stored in the load inductor L is copletely utilized and the load current through T falls to zero at t, where is referred to as the Extinction angle, (the value of t ) at which the load current falls to zero. The extinction angle 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 t to. The conduction angle of T is, which depends on the delay angle and the load ipedance angle. The wavefors of the input supply voltage, the gate trigger pulse of T, the thyristor current, the load current and the load voltage wavefors appear as shown in the figure below. i i i O S Fig.: Input supply voltage & Thyristor current wavefors is the extinction angle which depends upon the load inductance value. 4
Fig.: Output (load) voltage wavefor of a single phase half wave controlled rectifier with RL load Fro to, the thyristor reains cut-off as it is reverse biased and behaves as an open switch. The thyristor current and the load current are zero and the output voltage also reains at zero during the non conduction tie interval between to. In the next cycle the thyristor is triggered again at a phase angle of, and the sae operation repeats. TO DERIE AN EXPRESSION FOR THE OUTPUT (INDUCTIE LOAD) CURRENT, DURING t to WHEN THYRISTOR T CONDUCTS Considering sinusoidal input supply voltage we can write the expression for the supply voltage as v sin S t = instantaneous value of the input supply voltage. Let us assue that the thyristor is triggered by applying the gating signal to T at T t. The load current which flows through the thyristor T during t to can be found fro the equation dio L RiO sin t dt ; The solution of the above differential equation gives the general expression for the output load current which is of the for Z t io sin t A e ; Where S = axiu or peak value of input supply voltage. Z R L = Load ipedance. L tan R = Load ipedance angle (power factor angle of load). 5
L R = Load circuit tie constant. Therefore the general expression for the output load current is given by the equation R t L io sin t A e ; Z The value of the constant A can be deterined fro the initial condition. i.e. initial value of load current io, at t. Hence fro the equation for i equating i O O to zero and substituting t, we get i O sin A e Z R t L Therefore Ae R t Z L sin A e R t L Z sin A R t Z L e sin R t By substituting t, we get the value of constant A as L A e sin Z A R Z L e sin Substituting the value of constant A fro the above equation into the expression for i O, we obtain R R t L L io sin t e e sin ; Z Z R t R io t e e Z Z L L sin sin Z Z R io t e t L sin sin 6
Therefore we obtain the final expression for the inductive load current of a single phase half wave controlled rectifier with RL load as io sin t sin e Z R t L ; Where t. The above expression also represents the thyristor current tie interval of thyristor T fro t to. i T, during the conduction TO CALCULATE EXTINCTION ANGLE The extinction angle, which is the value of t at which the load current falls to zero and T is turned off can be estiated by using the condition that io, at t By using the above expression for the output load current, we can write i O i O sin sin Z e R L As, we can write Z Therefore we obtain the expression R L sin sin e sin sin L The extinction angle can be deterined fro this transcendental equation by using the iterative ethod of solution (trial and error ethod). After is calculated, we can deterine the thyristor conduction angle. is the extinction angle which depends upon the load inductance value. Conduction angle increases as is decreased for a specific value of. Conduction angle ; for a purely resistive load or for an RL load when the load inductance L is negligible the extinction angle e R and the conduction angle Equations v sin t Input supply voltage s v v sin t Output load voltage for t to, O L 7
when the thyristor conducts ( T is on). T Expression for the load current (thyristor current): for t to io sin t sin e Z R t L ; Where t. Extinction angle can be calculated using the equation sin sin e R L TO DERIE AN EXPRESSION FOR AERAGE (DC) LOAD OLTAGE v d t O L O. L vo. d t vo. d t vo. d O t ; v for t to & for t to ; O L vo. d t ; vo sin t for t to O L sin t. d O t t O L cos cos cos O L cos cos Note: During the period t to, we can see fro the output load voltage wavefor that the instantaneous output voltage is negative and this reduces the average or the output voltage when copared to a purely resistive load. Average DC Load Current O I I cos cos O L Avg R R L L SINGLE PHASE HALF WAE CONTROLLED RECTIFIER WITH RL LOAD AND FREE WHEELING DIODE 8
T i + + s ~ FWD R L Fig. : Single Phase Half Wave Controlled Rectifier with RL Load and Free Wheeling Diode (FWD) With a RL load it was observed that the average output voltage reduces. This disadvantage can be overcoe by connecting a diode across the load as shown in figure. The diode is called as a Free Wheeling Diode (FWD). The wavefors are shown below. s Supply voltage t i G Gate pulses - t i O Load current t= t O Load voltage t At t, the source voltage vs falls to zero and as vs becoes negative, the free wheeling diode is forward biased. The stored energy in the inductance aintains the load current flow through R, L, and the FWD. Also, as soon as the FWD is forward biased, at t, the SCR becoes reverse biased, the current through it becoes zero and the SCR turns off. During the period t to, the load current flows through FWD (free wheeling load current) and decreases exponentially towards zero at t. 9
Also during this free wheeling tie period the load is shorted by the conducting FWD and the load voltage is alost zero, if the forward voltage drop across the conducting FWD is neglected. Thus there is no negative region in the load voltage wave for. This iproves the average output voltage. The average output voltage cos, which is the sae as that of a purely resistive load. The output voltage across the load appears siilar to the output voltage of a purely resistive load. The following points are to be noted. If the inductance value is not very large, the energy stored in the inductance is able to aintain the load current only upto t, where, well before the next gate pulse and the load current tends to becoe discontinuous. During the conduction period to, the load current is carried by the SCR and during the free wheeling period to, the load current is carried by the free wheeling diode. The value of depends on the value of R and L and the forward resistance of the FWD. Generally. If the value of the inductance is very large, the load current does not decrease to zero during the free wheeling tie interval and the load current wavefor appears as shown in the figure. i t t t 3 t 4 SCR FWD SCR FWD t Fig. : Wavefor of Load Current in Single Phase Half Wave Controlled Rectifier with a Large Inductance and FWD During the periods t, t3,... the SCR carries the load current and during the periods t, t,... the FWD carries the load current. 4 It is to be noted that The load current becoes continuous and the load current does not fall to zero for large value of load inductance. The ripple in the load current wavefor (the aount of variation in the output load current) decreases.
SINGLE PHASE HALF WAE CONTROLLED RECTIFIER WITH A GENERAL LOAD A general load consists of R, L and a DC source E in the load circuit + ~ v S i O + R L E v O In the half wave controlled rectifier circuit shown in the figure, the load circuit consists of a source E in addition to resistance and inductance. When the thyristor is in the cut-off state, the current in the circuit is zero and the cathode will be at a voltage equal to the voltage in the load circuit i.e. the cathode potential will be equal to E. The thyristor will be forward biased for anode supply voltage greater than the load voltage. When the supply voltage is less than the voltage E in the circuit the thyristor is reverse biased and hence the thyristor cannot conduct for supply voltage less than the load circuit voltage. The value of t at which the supply voltage increases and becoes equal to the load circuit voltage can be calculated by using the equation sin t E. If we assue the value of t is equal to then we can write sin E. Therefore is calculated as E sin. For trigger angle, the thyristor conducts only fro t to. For trigger angle, the thyristor conducts fro t to. The wavefors appear as shown in the figure
v O Load voltage E t i O I Load current t Equations v sin t Input supply voltage. S v sin t Output load voltage for t to O v E for t to & for t to O Expression for the Load Current When the thyristor is triggered at a delay angle of, the equation for the circuit can be written as dio sin t io R L +E ; t dt The general expression for the output load current can be written as t E io sin t Ae Z R Where Z R L = Load Ipedance L R tan Load ipedance angle L R Load circuit tie constant The general expression for the output load current can be written as Z E R R t L io sin t Ae
To find the value of the constant A apply the initial condition at t, load current i. Equating the general expression for the load current to zero at t, we get O i O E sin Ae Z R We obtain the value of constant A as R L E A R Z sin e R L Substituting the value of the constant A in the expression for the load current, we get the coplete expression for the output load current as E E io sin t sin e Z R R Z R L t The Extinction angle can be calculated fro the final condition that the output current i at t. By using the above expression we get, O i O E E sin sin Z R R Z R L e To derive an expression for the average or load voltage v d t O O. vo. d t vo. d t vo. d O t v sin t Output load voltage for t to O v E for t to & for t to O E. d t sin t E. d O t E t t E t O cos E E O cos cos 3
E O cos cos E cos cos O Conduction angle of thyristor RMS Output oltage can be calculated by using the expression vo. d O RMS t DISADANTAGES OF SINGLE PHASE HALF WAE CONTROLLED RECTIFIERS Single phase half wave controlled rectifier gives Low output voltage. Low output power and lower efficiency. Higher ripple voltage & ripple current. Higher ripple factor. Low transforer utilization factor. The input supply current wavefor has a coponent which can result in saturation of the transforer core. Single phase half wave controlled rectifiers are rarely used in practice as they give low output and low output power. They are only of theoretical interest. The above disadvantages of a single phase half wave controlled rectifier can be over coe by using a full wave controlled rectifier circuit. Most of the practical converter circuits use full wave controlled rectifiers. SINGLE PHASE FULL WAE CONTROLLED RECTIFIERS Single phase full wave controlled rectifier circuit cobines two half wave controlled rectifiers in one single circuit so as to provide two pulse output across the load. Both the half cycles of the input supply are utilized and converted into a uni-directional output current through the load so as to produce a two pulse output wavefor. Hence a full wave controlled rectifier circuit is also referred to as a two pulse converter. Single phase full wave controlled rectifiers are of various types Single phase full wave controlled rectifier using a center tapped transforer (two pulse converter with id point configuration). Single phase full wave bridge controlled rectifier Half controlled bridge converter (sei converter). Fully controlled bridge converter (full converter). SINGLE PHASE FULL WAE CONTROLLED RECTIFIER USING A CENTER TAPPED TRANSFORMER 4
A + i S T AC Supply O v S R v O L i O FWD v S B T = Supply oltage across the upper half of the transforer secondary winding v v t S sin AO vbo v sin AO t secondary winding. supply voltage across the lower half of the transforer This type of full wave controlled rectifier requires a center tapped transforer and two thyristors T and T. The input supply is fed through the ains supply transforer, the priary side of the transforer is connected to the ac line voltage which is available (norally the priary supply voltage is 3 RMS ac supply voltage at 5Hz supply frequency in India). The secondary side of the transforer has three lines and the center point of the transforer (center line) is used as the reference point to easure the input and output voltages. The upper half of the secondary winding and the thyristor along with the load act as a half wave controlled rectifier, the lower half of the secondary winding and the thyristor with the coon load act as the second half wave controlled rectifier so as to produce a full wave load voltage wavefor. There are two types of operations possible. Discontinuous load current operation, which occurs for a purely resistive load or an RL load with low inductance value. Continuous load current operation which occurs for an RL type of load with large load inductance. T T Discontinuous Load Current Operation (for low value of load inductance) Generally the load current is discontinuous when the load is purely resistive or when the RL load has a low value of inductance. During the positive half cycle of input supply, when the upper line of the secondary winding is at a positive potential with respect to the center point O the thyristor is forward biased and it is triggered at a delay angle of. The load current flows through the thyristor T T 5
, through the load and through the upper part of the secondary winding, during the period to, when the thyristor T conducts. The output voltage across the load follows the input supply voltage that appears across the upper part of the secondary winding fro t to. The load current through the thyristor T decreases and drops to zero at t, where for RL type of load and the thyristor T naturally turns off at t. v O t i O ( ) ( ) t Fig.: Wavefor for Discontinuous Load Current Operation without FWD During the negative half cycle of the input supply the voltage at the supply line A becoes negative whereas the voltage at line B (at the lower side of the secondary winding) becoes positive with respect to the center point O. The thyristor is forward biased during the negative half cycle and it is triggered at a delay angle of the thyristor T T. The current flows through, through the load, and through the lower part of the secondary winding when conducts during the negative half cycle the load is connected to the lower half of the T secondary winding when conducts. For purely resistive loads when L =, the extinction angle. The load current falls to zero at t, when the input supply voltage falls to zero at t. The load current and the load voltage wavefors are in phase and there is no phase shift between the load voltage and the load current wavefor in the case of a purely resistive load. For low values of load inductance the load current would be discontinuous and the extinction angle but. For large values of load inductance the load current would be continuous and does not fall to zero. The thyristor conducts fro to, until the next thyristor T is T T triggered. When is triggered at t, the thyristor T will be reverse biased and hence turns off. T T 6
TO DERIE AN EXPRESSION FOR THE DC OUTPUT OLTAGE OF A SINGLE PHASE FULL WAE CONTROLLED RECTIFIER WITH RL LOAD (WITHOUT FREE WHEELING DIODE (FWD)) The average or output voltage of a full-wave controlled rectifier can be calculated by finding the average value of the output voltage wavefor over one output cycle (i.e., T radians) and note that the output pulse repetition tie is seconds where T represents the input supply tie period and T ; where f = input supply frequency. f Assuing the load inductance to be sall so that, we obtain discontinuous load current operation. The load current flows through T for t to, where is the trigger angle of thyristor T and is the extinction angle where the load current through T falls to zero at t. Therefore the average or output voltage can be obtained by using the expression v d t O O. t v d t O. O t sin. O t d t When the load inductance is sall and negligible that is L, the extinction angle radians. Hence the average or output voltage for resistive load is obtained as cos cos O ; cos cos ; for resistive load, when L cos O t cos cos O Therefore cos cos O, for discontinuous load current operation,. cos O O 7
THE EFFECT OF LOAD INDUCTANCE Due to the presence of load inductance the output voltage reverses and becoes negative during the tie period t to. This reduces the output voltage. To prevent this reduction of output voltage due to the negative region in the output load voltage wavefor, we can connect a free wheeling diode across the load. The output voltage wavefor and the output voltage obtained would be the sae as that for a full wave controlled rectifier with resistive load. When the Free wheeling diode (FWD) is connected across the load When T is triggered at t, during the positive half cycle of the input supply the FWD is reverse biased during the tie period t to. FWD reains reverse biased and cut-off fro t to. The load current flows through the conducting thyristor T, through the RL load and through upper half of the transforer secondary winding during the tie period to. At t, when the input supply voltage across the upper half of the secondary winding reverses and becoes negative the FWD turns-on. The load current continues to flow through the FWD fro t to. v O t i O ( ) ( ) t Fig.: Wavefor for Discontinuous Load Current Operation with FWD EXPRESSION FOR THE DC OUTPUT OLTAGE OF A SINGLE PHASE FULL WAE CONTROLLED RECTIFIER WITH RL LOAD AND FWD v d t O Thyristor T is triggered at t. T conducts fro t to Output voltage. O O t v sin t ; for t to 8
FWD conducts fro t to and v during discontinuous load current O Therefore t d t O sin. cos t O cos cos ; cos O Therefore O cos The DC output voltage is sae as the DC output voltage of a single phase full wave controlled rectifier with resistive load. Note that the output voltage of a single phase full wave controlled rectifier is two ties the output voltage of a half wave controlled rectifier. CONTROL CHARACTERISTICS OF A SINGLE PHASE FULL WAE CONTROLLED RECTIFIER WITH R LOAD OR RL LOAD WITH FWD The control characteristic can be obtained by plotting the output voltage versus the trigger angle. The average or output voltage of a single phase full wave controlled rectifier circuit with R load or RL load with FWD is calculated by using the equation cos O can be varied by varying the trigger angle fro to 8. (i.e., the range of trigger angle is fro to radians). Maxiu output voltage is obtained when ax cos Therefore ax for a single phase full wave controlled rectifier. Noralizing the output voltage with respect to its axiu value, we can write the noralized output voltage as n n ax d 9
Therefore n n cos n cos cos n cos d d Trigger angle in degrees O Noralized output voltage n d.63669 3.593974.933 6.47746.75 9.38398.5.9549.5 5.464.6698 8 O() d.6 d. d 6 8 Trigger angle Fig.: Control characteristic of a single phase full wave controlled rectifier with R load or RL load with FWD CONTINUOUS LOAD CURRENT OPERATION (WITHOUT FWD) For large values of load inductance the load current flows continuously without decreasing and falling to zero and there is always a load current flowing at any point of tie. This type of operation is referred to as continuous current operation. Generally the load current is continuous for large load inductance and for low trigger angles. The load current is discontinuous for low values of load inductance and for large values of trigger angles. The wavefors for continuous current operation are as shown. 3 in degrees
v O t i O T ON T ON T ON ( ) ( ) t Fig.: Load voltage and load current wavefor of a single phase full wave controlled rectifier with RL load & without FWD for continuous load current operation In the case of continuous current operation the thyristor which is triggered at a delay angle of, conducts fro t to. Output voltage follows the input supply voltage across the upper half of the transforer secondary winding v v t. The next thyristor is triggered at t, during the negative half cycle input supply. As soon as is triggered at t, the thyristor T will be reverse biased and turns off due to natural coutation (ac line coutation). The load current flows through T the thyristor fro t to. Output voltage across the load follows the input supply voltage across the lower half of the transforer secondary winding v v sint. O BO operation. T T T Each thyristor conducts for in the case of continuous current TO DERIE AN EXPRESSION FOR THE AERAGE OR DC OUTPUT OLTAGE OF SINGLE PHASE FULL WAE CONTROLLED RECTIFIER WITH LARGE LOAD INDUCTANCE ASSUMING CONTINUOUS LOAD CURRENT OPERATION. v d t O. O t radians 8 sin. O t d t T O AO sin 3
cos t O cos cos O ; cos cos O cos cos cos O The above equation can be plotted to obtain the control characteristic of a single phase full wave controlled rectifier with RL load assuing continuous load current operation. Noralizing the output voltage with respect to its axiu value, the noralized output voltage is given by n cos n cos ax Therefore cos n n Trigger angle in degrees d O.866.5 -.5 d 5 -.866 d 8 d 3 d 6 d 9 d Rearks Maxiu output voltage ax d 3
O() d.6 d. d -. d 3 6 9 5 8 -.6 d - d Trigger angle in degrees Fig.: Control Characteristic We notice fro the control characteristic that by varying the trigger angle we can vary the output voltage across the load. Thus it is possible to control the output voltage by changing the trigger angle. For trigger angle in the range of to 9 degrees ie.., 9, is positive and the circuit operates as a controlled rectifier to convert ac supply voltage into output power which is fed to the load. For trigger angle 9,cos becoes negative and as a result the average output voltage becoes negative, but the load current flows in the sae positive direction. Hence the output power becoes negative. This eans that the power flows fro the load circuit to the input ac source. This is referred to as line coutated inverter operation. During the inverter ode operation for 9 the load energy can be fed back fro the load circuit to the input ac source. TO DERIE AN EXPRESSION FOR RMS OUTPUT OLTAGE The rs value of the output voltage is calculated by using the equation vo. d O RMS t sin t. d O RMS t sin t. d O RMS t 33
34 Therefore ; The rs output voltage is sae as the input rs supply voltage. SINGLE PHASE SEMICONERTERS cos. O RMS t d t cos. O RMS d t t d t sin O RMS t t sin sin O RMS sin cos cos sin sin O RMS sin sin O RMS O RMS O RMS
D D D D Errata: Consider diode as in the figure and diode as Single phase sei-converter circuit is a full wave half controlled bridge converter which uses two thyristors and two diodes connected in the for of a full wave bridge configuration. The two thyristors are controlled power switches which are turned on one after the other by applying suitable gating signals (gate trigger pulses). The two diodes are uncontrolled power switches which turn-on and conduct one after the other as and when they are forward biased. The circuit diagra of a single phase sei-converter (half controlled bridge converter) is shown in the above figure with highly inductive load and a source in the load circuit. When the load inductance is large the load current flows continuously and we can consider the continuous load current operation assuing constant load current, with negligible current ripple (i.e., constant and ripple free load current operation). The ac supply to the seiconverter is norally fed through a ains supply transforer having suitable turns ratio. The transforer is suitably designed to supply the required ac supply voltage (secondary output voltage) to the converter. During the positive half cycle of input ac supply voltage, when the transforer secondary output line A is positive with respect to the line B the thyristor and the diode are both forward biased. The thyristor T is triggered at t ; by applying D an appropriate gate trigger signal to the gate of. The current in the circuit flows through the secondary line A, through T, through the load in the downward direction, through diode D back to the secondary line B. T and D conduct together fro t to and the load is connected to the input ac supply. The output load voltage follows the input supply voltage (the secondary output voltage of the transforer) during the period t to. At t, the input supply voltage decreases to zero and becoes negative during the period t to. The free wheeling diode D across the load becoes forward biased and conducts during the period t to. T T 35
Fig:. Wavefors of single phase sei-converter for RLE load and constant load current for > 9 The load current is transferred fro and D to the FWD. and D are turned T off. The load current continues to flow through the FWD D T. The load current free wheels (flows continuously) through the FWD during the free wheeling tie period to. During the negative half cycle of input supply voltage the secondary line A becoes negative with respect to line B. The thyristor T and the diode D are both forward biased. T is triggered at t, during the negative half cycle. The FWD is reverse biased and D 36
turns-off as soon as is triggered. The load current continues to flow through and during the period t T T to TO DERIE AN EXPRESSION FOR THE AERAGE OR DC OUTPUT OLTAGE OF A SINGLE PHASE SEMI-CONERTER The average output voltage can be found fro sin t. d t D cos t cos cos ; cos Therefore cos can be varied fro to by varying fro to. The axiu average output voltage is ax d Noralizing the average output voltage with respect to its axiu value n n.5 cos d The output control characteristic can be plotted by using the expression for 37
TO DERIE AN EXPRESSION FOR THE RMS OUTPUT OLTAGE OF A SINGLE PHASE SEMI-CONERTER The rs output voltage is found fro sin t. d O RMS t cos t. d O RMS t O RMS sin SINGLE PHASE FULL CONERTER (FULLY CONTROLLED BRIDGE CONERTER) The circuit diagra of a single phase fully controlled bridge converter is shown in the figure with a highly inductive load and a source in the load circuit so that the load current is continuous and ripple free (constant load current operation). The fully controlled bridge converter consists of four thyristors T, T, T3 and T4 connected in the for of full wave bridge configuration as shown in the figure. Each thyristor is controlled and turned on by its gating signal and naturally turns off when a reverse voltage appears across it. During the positive half cycle when the upper line of the transforer secondary winding is at a positive potential with respect to the lower end the thyristors and T are forward biased during the tie interval t to. The thyristors and T are triggered siultaneously t ;, the load is connected to the input supply through the conducting thyristors and T. The output voltage across the load follows the input supply voltage and hence output voltage T T v sint. Due to the inductive load and T will continue to conduct beyond t, even though the input voltage becoes O T T 38
negative. and conduct together during the tie period to, for a tie duration T T of radians (conduction angle of each thyristor = 8 ) During the negative half cycle of input supply voltage for t to the thyristors and are forward biased. and are triggered at t. As soon as the T3 T4 T3 4 thyristors T3 and T4 are triggered a reverse voltage appears across the thyristors T and T T T and they naturally turn-off and the load current is transferred fro and T to the thyristors T3 and T4. The output voltage across the load follows the supply voltage and vo sint during the tie period t to. In the next positive half cycle when T and T are triggered, T3 and T4 are reverse biased and they turn-off. The figure shows the wavefors of the input supply voltage, the output load voltage, the constant load current with negligible ripple and the input supply current. During the tie period t to, the input supply voltage v and the input supply i S current are both positive and the power flows fro the supply to the load. The converter operates in the rectification ode during t to. S 39
During the tie period t to, the input supply voltage vs is negative and the input supply current i S is positive and there will be reverse power flow fro the load circuit to the input supply. The converter operates in the inversion ode during the tie period t to and the load energy is fed back to the input source. The single phase full converter is extensively used in industrial applications up to about 5kW of output power. Depending on the value of trigger angle, the average output voltage ay be either positive or negative and two quadrant operation is possible. TO DERIE AN EXPRESSION FOR THE AERAGE (DC) OUTPUT OLTAGE The average () output voltage can be deterined by using the expression vo. d t ; O The output voltage wavefor consists of two output pulses during the input supply tie period between & radians. In the continuous load current operation of a single phase full converter (assuing constant load current) each thyristor conduct for radians (8 ) after it is triggered. When thyristors and T are triggered at t and T conduct fro to and the output voltage follows the input supply voltage. Therefore output voltage vo sint ; for t to Hence the average or output voltage can be calculated as T T sin t. d O t sin t. d O t sin t. d O t cos t O cos cos O ; cos cos Therefore cos O 4
The output voltage can be varied fro a axiu value of for to a iniu value of for radians 8 The axiu average output voltage is calculated for a trigger angle and is obtained as ax d cos Therefore ax d The noralized average output voltage is given by O n n ax d n cos n cos Therefore n n cos constant load current operation. ; for a single phase full converter assuing continuous and CONTROL CHARACTERISTIC OF SINGLE PHASE FULL CONERTER The output control characteristic can be obtained by plotting the average or output voltage versus the trigger angle For a single phase full converter the average output voltage is given by the equation cos O Trigger angle in degrees d O.866.5 -.5 d 5 -.866 d 8 d 3 d 6 d 9 d Rearks Maxiu output voltage ax d 4
O() d.6 d. d -. d 3 6 9 5 8 -.6 d - d Trigger angle in degrees Fig.: Control Characteristic We notice fro the control characteristic that by varying the trigger angle we can vary the output voltage across the load. Thus it is possible to control the output voltage by changing the trigger angle. For trigger angle in the range of to 9 degrees ie.., 9, is positive and the average load current I is also positive. The P average or output power is positive, hence the circuit operates as a controlled rectifier to convert ac supply voltage into output power which is fed to the load. For trigger angle 9,cos becoes negative and as a result the average output voltage becoes negative, but the load current flows in the sae positive direction i.e., I is positive. Hence the output power becoes negative. This eans that the power flows fro the load circuit to the input ac source. This is referred to as line coutated inverter operation. During the inverter ode operation for 9 the load energy can be fed back fro the load circuit to the input ac source TWO QUADRANT OPERATION OF A SINGLE PHASE FULL CONERTER The above figure shows the two regions of single phase full converter operation in the versus plane. In the first quadrant when the trigger angle is less than 9 I, and I are both positive and the converter operates as a controlled rectifier and converts the ac input power into output power. The power flows fro the input source to the load circuit. This is the noral controlled rectifier operation where is positive. When the trigger angle is increased above 9, becoes negative but I is positive and the average output power ( output power) P P becoes negative and the power flows 4
fro the load circuit to the input source. The operation occurs in the fourth quadrant where is negative and I is positive. The converter operates as a line coutated inverter. TO DERIE AN EXPRESSION FOR THE RMS ALUE OF THE OUTPUT OLTAGE The rs value of the output voltage is calculated as vo. d O RMS t The single phase full converter gives two output voltage pulses during the input supply tie period and hence the single phase full converter is referred to as a two pulse converter. The rs output voltage can be calculated as vo. d O RMS t sin t. d O RMS t sin t. d O RMS t cos t. d O RMS t d t cos t. d O RMS t t O RMS O RMS sin t sin sin O RMS sin sin ; sin sin sin sin O RMS 43