A PROJECT REPORT ON STUDY OF AC TO DC CONVERTER USING MATLAB SIMULINK SUBMITTED IN THE PARTIAL FULFILLMENT OF THE AWARD OF DEGREE OF
BACHELOR OF TECHNOLOGY IN
ELECTRICAL AND ELECTRONICS ENGINEERING
UNDER THE GUIDANCE OF:MR. ASIF JAMIL ANSARI SENIOR PROFESSOR EEED, INTEGRAL UNIVERSITY LUCKNOW
SUBMITTED BY:1. PRAN PRANAV AV TRIP TRIPAT ATHI HI 2. ZAINAB 3. TE TEJA JASV SVIN INII 4. PREE PREETI TI SING SINGH H 5. ABHI ABHISH SHEK EK NIGA NIGAM M
INTEGRAL UNIVERSITY, LUCKNOW Kursi Road, Lucknow-226026, Uttar Pradesh (INDIA) Phone: 022 2890812, 2890730, 3296117, 6451039 Fax No.: 0522-2890809
Web: www.integraluniversity.ac.in
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CERTIFICATE
This is to certify that the project work entitled ‘Study of AC to DC Converters using MATLAB’, which is being submitted by Pranav Tripathi, Zainab, Abhishek Nigam, Preeti Singh and Tejasvini Gupta in partial fulfillment fulfillment of award award of degree degree of Bachelor of Technology in Electrical and Electronics Engineering from integral university, is carried out under my supervision and guidance.
epartment allick
Under the guidance of: -
Head of
Mr. Asif Jamil Ansari
Mr. M.A.
Senior Professor EEED, Integral University Lucknow
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Department of Electrical and Electronics Integral University, Lucknow
ACKNOWLEDGEMENT
I would first of all thanks Mr.Asif Jamil Ansari who helped me to select such an important topic for my project work in which I received nice exposure of my field and a innovation to do something in this field. It was very exciting along with interesting and amazing facts. I wish to express our sincere thanks to Mr. M A Mallick, Head of Department. Department. I also express express sincere thanks to the Integral Integral University, Lucknow for providing us with all the necessary facilities for completing the project work. I would also like to thank all the faculty and staff members of CAD lab who extended their full cooperation for completion of this work. Lastly and most importantly, we wish to thank all our friends for being the surrogate family during the years we stayed here and for their moral support.
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INDEX Chapter
NAME OF CHAPTER
Pg. No.
No. 1. 2. 2.( 2.(i)
Introduction 5-7 Half Wave Controlled Rectifiers 8Sing Si ngle le Pha Phase Half alf Wave Th Thyyristo istorr Cir Circui cuit with
2.( 2.(ii) 2.(i 2.(iii ii))
R-load 1-Φ 1-Φ Hal Halff Wa Wave Th Thyyrist istor Cir Circui cuit wit withh RL RL llooad 1-Φ 1-Φ Hal Halff Wav Wavee Thy Thyri rist stor or Circ Circui uitt wit withh RLRL-lo load ad
2.(iv)
& Freewheeling Diode Single Phase Half Wave Circuit with RLE-
3. 3.(i)
load Full Wave Controlled Converters Single Ph Phase Fu Full Wa Wave Mi Mid Po Point Co Converters
3.( 3.(ii)
(M-2 Connection) Sing Si ngle le pha phase full ull wave wave bri bridge dge conve onverrter ter
3.(iv) 3.(iv) 3.(v) 4. 5.
(B-2 Connection) Line-Commutated Inverter Single-phase semiconverter Single-phase Full Converter Drives Three Phase Converters Simulation Design and Analysis
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CHAPTER 1 INTRODUCTION
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INTRODUCTION
Many Industrial applications need controllable DC power. Examples of such applications are:1. Steel Steel rolling rolling mills, mills, paper mills, mills, printing printing presses presses and textil textilee mills employing DC motor drives. 2. Tracti Traction on syst system emss workin workingg on DC. DC. 3.
Electromechanical Electromechanical and Electrometallurgical Electrometallurgical processes.
4. Magn Magnet et Powe Powerr sup suppl plie iess 5. Port Portab able le han handd tool tool driv drives es 6. High High Volt Voltage age DC transm transmiss ission ion Earlier, dc power was obtained from motor-generator (MG) sets or ac power was converted to dc by means of mercury-arc rectifiers rectifiers or thyratrons. thyratrons. The advent of thyristors thyristors has changed the the art of ac to dc conversion. Presently, phase controlled ac to dc converters employing thyristors are extensively used for changing constant ac input to controlled dc output voltage. In an industry where there is a provision for modernization, mercury arc rectifiers rectifiers and thyratrons are being replaced by thyristors. In phase controlled rectifiers, a thyristor is turned off as ac supply reverse biases it, provided anide current has fallen to a level below the holding current. The turning-off, or commutation,
of a thyristor by supply
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voltage itself is called as natural
or line commutation. In industrial applications, rectifier circuits make user of more than one SCR. In such circuits, when an incoming SCR is turned on by triggering, it immediately reverse biases the outgoing SCR and turns it off. As phase controlled rectifiers rectifiers need no commutation circuitry, these are simple, less expensive and are therefore widely used in industries where controlled dc power is required. In the study of thyristor systems, SCRs and Diodes are assumed to be ideal switches which means that (i)
there is no voltage drop across them.
(ii) ii)
no rever verse curr urrent exis xists unde underr reve everse volt voltag agee conditions.
(iii)
holding cu current is is ze zero.
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CHAPTER 2 HALF WAVE CONTROLLED RECTIFIERS
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HALF WAVE
CONTROLLED
RECTIFIERS PRINCIPLE OF PHASE CONTROL 2.(i). Single Phase Half Wave Thyristor Circuit with R-load
The simplest form of controlled rectifier circuits consists of a single thyristor feeding dc power to a resistive load R as shown in fig. 2.(i). The source voltage is v s=V m sin ω t , Fig.2.(i). An SCR can conduct only when anode voltage is positive and a gating signal is applied. As such, a thyristor blocks the flow of load current io until it is triggered. At some delay angle α , a positive gate signal applied between gate and cathode turns on the SCR. Immediately, full supply voltage is applied to the load as vo, as in Fig. 2.(i). At the instant of delay angle α , vo rises from zero to Vm sin α as shown. For resistive load, current io is in phase with vo. Firing angle of a thyristor is measured from the instant it would start conducting if it were replaced by a diode. In Fig. 2.(i), if thyristor is replaced by diode, it would begin conduction at ω t = 0, 2π , 4π etc ; firing angle is therefore measured from these instants. A firing angle may thus be defined as the angle between the instant thyristor would conduct if it were a diode and the instant it is triggered.
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A firing angle may thus be defined as follows: A firing angle is measured from from the angle that gives gives the largest average output voltage, or the highest load voltage. If thyristor in Fig. 2.(i) is fired at ω t = 0, 2π , 4π etc, the average load voltage is the highest; the firing angle should thus be measured from these instants. A firing angle may thus be defined as
the angle measured from the instant
that gives the largest average output voltage to the instant it is triggered. A firing angle may also be defined as the angle measured from the instant SCR gets forward biased to the instant it is triggered. Once the SCR is on, load current flows, until it is turned-off by reversal of voltage at ω t = 0, π , 3π , 5π etc. At these angles of π , 3π , 5π etc., load current falls to zero and soon after the supply voltage reverse biases the SCR, the device is therefore turned-off. turned-off. It isc seen from Fig.2.(i) that by varying the firing angle α , the phase relationship between the start of the load current and the supply voltage can be controlled, hence term phase control is used for these methods of controlling the load currents. A single phase half wave circuit is one which produces only one pulse of load current during one
cycle of source voltage. As the
circuit shown in Fig. 2.1 produces only one load current pulse for
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one cycle of sinusoidal source voltage, this circuit represents represents a single-phase half-wave thyristor circuit. In Fig.2.(i), thyristor conducts from ω t = α to π , (2π +α ) to 3π and so on. Over the firing angle delay α , load voltage vo = 0 but during conduction angle ( π -α ), vo = vs. . As firing angle is increased from zero to π , the average load voltage decreases from the largest value to zero. The variation of voltage across thyristor is also shown as v T in Fig. 2.(i). Thyristor remains on from ω t = α toπ , (2π +α ) to 3π and so on. During these intervals v T = 0 (strictly speaking 1 to 1.5V). It is off from ω t = π to (π +α ) , 3π to (4π + α ) etc. During these off intervals v T has the waveshape of supply voltage vs. It may be observed that v s = vo + vT. As the thyristor is reverse biased for π radians, the circuit turn off time is given bytc = (π /ω ) sec where ω = 2π f and f is the supply frequency in Hz.
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Fig.2.(i). The circuit turn off time t c must be more than the SCR turn off time tq as specified by the manufacturers. manufacturers. Average voltage Vo across load R in Fig. 6.1 for the single – phase half wave circuit in terms of firing angle α is given byVo = (1/2π ) α ∫ π Vm sin ω t d (ω t) = (Vm/2
) (1+ cos
)
The maximum value of average output voltage Vo occurs at α = 0o.
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Vom = (Vm/2π ) (1+ cos 0o)
⇒ Vom = (Vm/2π ) .2 ⇒ Vom = (Vm/π ) Also, Vo = (Vom /2) (1+ cos α ) Average load current, I o = Vo/R = (Vm/ 2π R) (1+ cos α ) In some types of loads, one may be interested in RMS value of load voltage Vor . Examples of such loads are electric heating and incandescent lamps. Rms voltage Vor in such cases is given byVor = [(1/2π )α ∫ π V2m sin2 ω t d (ω t) ]1/2
⇒ Vor = (Vm/2√ π )[(π -α )+ ((sin 2α )/2)]1/2 The value of rms current I or is Ior = (Vor /R) /R) Power delivered to resistive load
current)
= (rms load voltage) (rms load
= Vor Ior = (V2or /R) /R) = I2or R
Input voltamperes = (rms source voltage) (total rms line
current)
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= Vs Ior = ((√2
V2s )/( 2R √ π )) [(π -α )+ ((sin
2α )/2)]1/2
Input power factor = (Power delivered to load)/ (input VA) = ( Vor Ior )/( )/( Vs Ior ) = (Vor )/( )/( Vs) Input pf = pf = (1/√2 π
) [(π -α )+ ((sin 2α )/2)]1/2
____________________________________________________________________________
2.(ii). 1-Φ Half Wave Thyristor Circuit with RL load
A single-phase half-wave thyristor thyristor circuit with RL load is shown in Fig. 2.(ii). At wt=α, thyristor is turned on by gating signal (not shown). The load voltage V o at once becomes equal to source voltage V s as shown. But the inductance L forces the load, or output, current io to rise gradually. After some time, io reaches maximum value and then begins to decrease. At wt=α, V o is zero but io is not because of the load inductance L. After wt=π, SCR is subjected to regverse anode voltage but is will not be turned off as load current io is not less than the holding current. At some angle β>π, io reduces to zero and SCR is turned off as it is already reverse biased. After wt=β, V o =0 and io =0 and io =0. At wt=2π+α. SCR is triggered again. V o is applied to the load and load current develops as before.
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turned off as it is already reverse biased. After wt=β, V o =0and io = o. At wt=2π+α, SCR is triggered again V o is applied to the load and
load current develops as before. Angle β is called the extinction angle and (β-α)=γ is called the conduction angle.
The wave form of voltage V T T across thyristor T in Fig. 2.(ii). reveals that when wt =α, =α, V T T = V m sin α; from wt =α =α to β, V T T =0 and at wt =β, =β, V T T = V m sinβ. As β>π, V T T is negative at wt =β. =β. Thyristor is
therefore reverse biased from wt =β =β to 2π. Thus, circuit turn-off time t c=2π-β/w sec. for
satisfactory satisfactory commutation, t c should be more than
t q the thyristor turn-off time.
Fig.2.(ii)
The voltage equation for
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the circuit of Fig.2.(ii), when T is
on, is Vm sin wt= Rio+ L dio/dt
The load current io consists of two components, one steadystate component is and the other transient component i t. Here is is given by is = Vm /(√R 2+X2 sin (wt -φ )) where φ = tan-1(X/R) and X=wL. Here φ is the angle by which rms current I s lags V s The transient component is can be obtained from force-free equation. Rit+L dit/dt =0 Its solution gives,
it = Ae-(R/L)t
io = is+ it = [V m/( z z sin (wt -φ
))]+ A –(R/L)t ………………..(1)
where, Z=√ R 2+X2 Constant A can be obtained from the boundary condition at wt =α. =α.
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At this time t = α/w, io = 0. Thus, from Eq. (1), 0=V m/Z sin (α-φ ) + Ae-Ra/Lw A= (-V m /Z) sin (α-φ ) eRα/wL Substitution of A in Eq. (1) gives
io = V m /Z sin (wt-φ
) – V m /Z sin (α-φ ) exp. {-R/wL (wt-α)} …....
(2) for It is also seen from the waveform of io in fig. 2(ii) that when wt=β, load current io =0 Substituting this in Eq. (2) gives
sin (β-φ )= sin(α-φ ). exp {-R/wL(β-α) }
This transcendental equation can be solved to obtain the value of extinction angle β. In case β is known, average load voltage V o is given by V o = (1/2π)
[α∫ β Vm sin wt d (wt)] = V /[2π (cosα-cosβ)] m
Average load current, I o= V m /2πR (cosα-cosβ) 2 β 1/2 Rms load voltage, V or or = [1/2π α ∫ V 2 sin wt.d(wt)}
= V m /2√π
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[(β-α)-1/2 {sin 2β-sin2α } ] 1/2
_______________________________________________________
2.(iii). 1-Φ Half WaveThyristor Circuit with RL-load & Freewheeling Diode
A single-phase half wave thyristor circuit with RL-load and freewheeling freewheeling diode is shown in Fig. 2 (iii). Line voltage is shown at the top of Fig. 2 (iii). At ω t = α , thyristor is turned on by the gating signal ( not shown). shown). The load voltage at once becomes becomes equal to source voltage vs as shown. But inductor L forces the load or output current io to rise gradually. After some time, i o reaches the maximum value and begins to decrease. At ω t = π , vo is zero but io is not because of the load inductance L. After ω t = π , SCR is subjected to reverse anode voltage and it will turn off thyristor. At the same time FD is forward biased through the conducting SCR. As a result, load current i o is immediately transferred transferred from SCR to FD. The waveform of load current i o is improved by connecting a freewheeling freewheeling (or flywheeling) flywheeling) diode across load. A freewheeling freewheeling diode is also called as by-pass or commutating diode. Voltage drop
across FD is taken almost zero.
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So load voltage vo is therefore
zero during freewheeling period. SCR is reverse biased from ω t =
π to ω t = 2π . Therefore circuit turn off time istc = (π /ω ) sec
The source current i s and thyristor currents i T have same waveforms. Operation Operation of circuit is divided in two modes. In first mode, called conduction mode, SCR conducts from α to π , (2π +
α ) to 3π and so on and FD is reverse biased. The duration of this mode is for [( π -α )/ω ] sec. Let the load current at the beginning of mode 1 be Io. The expression for current i o in mode 1 can be obtained as follows: Mode 1:-
t
Vm sin ω t = Rio + L(dio/dt) Its solution isio = [(Vm/Z)(sin (ω t-φ )] + A e ((-R/L)t) At ω t = α , io = Io i.e. at t = ( α /ω ), io = Io A = [Io – (Vm/Z)( sin (α -φ )) ] e(R α /Lω )
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io=(Vm/Z)(sin (ω t-φ )+[Io – (Vm/Z)( sin (α -φ )) ]exp{(-R/L)(t]exp{(-R/L)(t(α /ω )}
Fig.2.(iii).
Mode 2:-
t (2
+
)
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This mode is called freewheeling freewheeling mode, extends from π to 2π , 3π to 4π …. As shown by voltage waveform vT in Fig. 6.3 (b). As the load current is assumed continuous, FD conducts from π to (2π +α ), 3π to (4π +α )… Let the current at the beginning of mode 2 be Io1 as shown. As load current is passing through FD, the voltage equation for mode 2 is 0 = Rio + L(dio/dt)
Its solution is –
io = A e((-R/L)t)
At ω t = π , io = Io1 It gives
A = Io1 e((-R π /ω L)) Io = Io1 exp [(-R/L) (t-( π /ω ))]
Average load voltage V o = (1/2π ) α ∫ π Vm sin ω t d (ω t)
⇒V o = (Vm/2
) (1+ cos
)
Average load current, I o = V o/R = (Vm/ 2π R) (1+ cos α ) Load current is contributed by SCR from α to π , (2π + α ) to 3π and so on and by FD conducts from 0 to α , π to (2π +α ), 3π to (4π +α ) and so on. Thus the wave shape of iT is identical to io for ω t = α to π , (2π + α ) to 3π and so on. Similarly, the
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wave shape of FD current i fd is
identical with io for ω t = 0 to α ,
π to (2π +α ), 3π to (4π +α ) and so on. Load consumes power p 1from source for α to π (both vo and io are positive) whereas energy stored in inductance L is returned to the source as power p 2 for π to β (vo is negative and io is positive). As a result, net power consumed bythe load is difference of these two powers p1 and p2. Load absorbs power for α to π , but for π to (2π +α ), energy stored in L is delivered to load resistance R through
the FD. As a consequence, power delivered to load, for the same firing angle, is more when FD is used. As volt-ampere input is almost the same in both fig. , the input pf = (power delivered delivered to load/ input volt-ampere) with the use of FD is improved. Thus the advantages of using freewheeling freewheeling diode are(i)
input pf is improved
(ii)
load cu current wa waveform is is im improved
(iii)
load performance is is be better
(iv) (iv)
as ener energy gy stor stored ed in indu induct ctor or L is is tra trans nsfe ferr rred ed to R dur durin ingg the freewheeling period, overall converter efficiency improves.
Supply current i s taken
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from the source is unidirectional
and is in the form of dc pulses. Single phase half wave converter thus introduces a dc component into the line. This is undesirable as it leads to saturation of the supply transformer and difficulties (harmonics etc...). __________________________________________________
2.(iv). Single Phase Half Wave Circuit with RLE-load
A single phase half controlled converter with RLE load is shown in Fig. 2(iv). The counter emf E in the load may be due to a battery or a dc motor. The minimum value of firing angle is obtained from the relation V m sin ω t = E. This is shown to occur at an angle
θ 1 in Fig. 2. (iv) where θ 1 = sin-1(E/Vm) In case thyristor T is fired at an angle α <θ 1, then E > Vs, SCR is reverse biased and therefore it will not turn on. Similarly, maximum value of firing angle is θ 2 = (π -θ 1), Fig.2.(iv). During the interval
load current i o is zero, load
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voltage vo = E and during the
time io is not zero, vo follows vs curve. For the circuit of Fig. 6.4(a) and with SCR T on, KVL gives the voltage differential differential equation asVm sin ω t = Rio + L(dio/dt)+ E
Fig. 2.(iv).
The solution of this
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equation is made up of two
components:- steady state current component i s and the transient current component it. Let, is= is1 + is2 where is1 is the steady state current due to ac source voltage acting alone and i s2 is that due to counter emf E acting alone. is1 = (Vm /Z) sin (ω t-φ ) If only E were present, then steady state current i s2 would be given byis2 = - (E/R) The transient current i t = A e-(R/L)t
Thus total current io = is1 + is2 + it
⇒ io = (Vm /Z) sin (ω t-φ ) - (E/R) + A e -(R/L)t At ω t =α , io= 0, i.e. at t = ( α /ω ), io = 0. This gives
A = [(E/R)-(Vm/Z) ( sin (α -φ ))] e(R α /Lω )
io = (Vm /Z) = [ (sin (ω t-φ ))-( sin ( α -φ ))exp{(-R/ω L) (ω t-α )}](E/R) [ 1- exp{(-R/ ω L) (ω t-α )}] This equation is applicable for α ≤ ω t≤ β . The extinction angle β depends upon load emf E, firing angle α and the load impedance
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angleφ . Average voltage across
inductance L is zero. Average
load current can be given asIo= (1/2π R) α ∫ β [(Vm sin ω t) – E] d ( ω t)
⇒ Io= (1/2π R) [(Vm (cos α -cos β ) – E(β -α )] Here conduction angle γ =β -α . Putting β = γ +α gives Io= (1/2π R) [(Vm (cos α -cos γ +α ) – E(γ )] Vo = E + IoR
⇒Vo = (1/2π )[ α ∫ β (Vm sin ω t) d (ω t)+ E(2π +α -β )] ⇒Vo = (1/2π )[ (Vm(cos α - cos β ) + E(2π +α -β )]
CHAPTER 3
27
FULL WAVE CONTROLLED RECTIFIERS
Full Wave Controlled Converters
There is large variety of SCR controlled converters (or rectifiers). rectifiers). They can be classified in different ways. According to number of supply phases on input side, ac to dc converters can be1. Single Single phase phase conve convert rters ers 2. Three Three phase phase conv convert erter erss
According to number of load
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current pulses per cycle of source
voltage, ac to dc converters can be1. A Half Half controlled controlled converters converters produces produces only one pulse so called as single pulse rectifier. rectifier. 2. A Full controll controlled ed converter converter produces produces two pulses pulses so called called as two-pulse rectifier. rectifier. There are two basic configurations of two pulse rectifier. One configuration uses an input transformer with two windings for each input phase winding. This is called as mid-point converter. Second configuration uses SCRs in the form of a bridge circuit. Single phase two pule bridge converter converter using 4 SCRs and a three phase six-pulse bridge converter is shown in figure.
(1-φ fully-controlled fully-controlled rectifier) rectifier) (3- φ fully-controlled rectifier)
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(1-φ 2-pulse mid point converter) (3- φ 6-pulse mid point converter)
(1-φ 2-pulse bridge converter)
(3-φ 6-pulse bridge
converter)
Single Phase Full Wave Converters
In single phase two-pulse
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(or full wave) converters, voltage
at the output terminals can be controlled by adjusting firing angle delay of the thyristors. Mid-point or Bridge type circuits may be used for ac to dc conversion. 3.(i). Single Phase Full Wave Mid Point Converters (M-2 Connection)
The circuit diagram of a single phase full wave converter using a centre-tapped transformer transformer is shown in Fig. 3.8 (a). When terminal a is positive with respect to n, terminal is positive with respect to b. Therefore, van =vnb or van =-v bn as n is the mid-point of secondary winding. Assume that load current is continuous and turns ratio from primary to each secondary is unity. Thyristors T! and T2 are forward biased during positive and negative half cycles respectably ; these are therefore triggered accordingly. Suppose T2 is already conducting. After WT=0, v an is positive, T! is therefore forward biased and when triggered at delay angle α, T1 gets turned on. At this firing angle α, supply voltage 2V n sin α reverse biases T2, this SCR is therefore turned off. Here T1 is called the incoming thyristor and T2 the out going thyristor.
As the incoming SCR is triggered, Ac supply voltage applies reverse bias across the outgoing thyistors and turns it off. Load
current is also transfer from
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outgoing SCR to incoming SCR.
This process of SCR turned off by natural reversal of AV supply voltage is called natural or line commutation.
Fig. 3.(i).
From the equivalent circuit of figure 6.8 (b) it is seen that if
32
van = Vm sin wt then
v bn = -vnb = -Vm sin wt
and
vab = van + vnb = 2Vm sin wt
when wt=α, T1 is triggered. SCR T2 is subjected to a reverse voltage vab = 2Vm sin α as stated before, current is transferred transferred from T2 to T1 and as a result T2 is turned off. The magnitude of reverse voltage across T2 can also be obtained by applying KBL to the loop efghe of the equivalent circuit of fig.3.(i) at the instant T1 is triggered. Thus vt2-v bn + van –vt1 = 0 vt2 = v bn-van+vt1 with T1 conducting, vt1=0. therefore the voltage across T2, at the instant wt=α is given by vt2 =-Vm sin α – Vm sin α = -2 Vm sin α this shows that SCR T2 is reverse biased by voltage 2V m sin α and it is therefore turned off at wt = α . thyristor T1 conducts from α to π + α. After wt = π T1 is reversed biased but it will continue conducting as the forward forward biased SCR T2 is is not get gated. At wt = π + α , T2 is
triggered, T1 is reversed biased by voltage of magnitude 2vm sin α, current is transferred from T1 to T2, T1 is therefore turned off.
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At wt = α , T2 is turned off and it remain reverse biased from wt =α to π, this can be seen from fig.3.(i). the turned of time provided by this circuit to SCR T2 is there fore given by tc = [(π-α)/ ω ] sec…………………….(3.1) Thyristor T1 is turned off at wt = π + α and fig.3.(i). reveals reveals that T1 is subjected to a reverse voltage from wt = π +α to wt= 2π. Therefore this circuit provides a turn of time to thyristor T1 as tc = [2π-(π+α)/ ω ] = [(π-α)/ ω ] which is the the same provided to thyristor T2 ; Eq(1) It is seen from voltage waveform v0, Fig.3.(i), that average value of output voltage is given by Vo= 1/π ∫αα+π Vm sin wt . d (wt) = [ (2Vm/π) . cos α] The circuit turn off time t c eq.(1), as provided by this circuit of Fig.3(i), a must be greater than SCR turn off time t q as given in the specification specification sheet. In case t c < tq , commutation failure will occur and the whole secondary winding will be short circuited. During commutation failure, if the rate of rise of fault current is high, the incoming SCR may be damaged in case protective elements do not clear the fault. Figure. 3.(i) reveals that each SCR is subjected to a peak voltage of 2V m.
34
The following following observations can be made made from the above above studies studies I. When commut commutatio ationn of an SCR SCR is desire desired, d, is it must must be rever reverse se baised and the incoming SCR must be forward biased. II. When incomi incoming ng SCR is gated gated on, curren currentt is transf transferd erd from from outgoing SCR to incoming SCR. III. III. The circui circuitt turn off off time time must must be greater greater than SCR SCR turn turn off time. It is seen from above that thyrister commutation achieved by means of natural reversal of line voltage, called line or natural commutation, is simple, it is therefore employed employed in all phasecontrolled rectifiers, Ac voltage controllers and cycloconverters. _______________________________________________________ 3.(ii). Single phase full wave bridge converter (B-2 Connection)
A single phase full converter bridge using four SCRs is shown in fig.3.(ii).The fig.3.(ii).The load is assumed to be of RLE type, where e is the load circuit emf. Voltage E may be due to a battery in the load circuit or may be generated emf of a dc motor. Thyristor pair T1,T2is simultaneously triggered triggered & π radians later ,pair T3,T4 is gated together.When a is positive with respect to b, supply voltage waveform is shown as v ab in fig.3.(ii). When b is positive with respect to a, supply voltage waveform is shown dotted as v ba. Obviously, vab=-v ba. The current directions & voltage polarities shown in fig.3.(ii), are treated as positive.
Load current or output current i o
35
is assumed continous over the
working range; this means that load is always connected to the ac voltage sources through the thyristors .Between wt=0 & wt=π; T1,T2 are forward baised through already conduting SCRs T3 & T4 and block the forward voltage. For continuous current thyristors T3 ,T4 conduct aftr wt=0 even though these are reverse biased. When forward biased SCRs T1,T2 are triggered at wt=π, they get turned on. As a result supply voltage V m sin α immediately appears across thyristors T3,T4 as a reveres bias , these are therefore turned off by natural, or line , commutation. At the same time, load current io flowing through T3,T4 is transferred to T1,T2 at wt=α. Note that when T1,T2 are gated at wt=α, these SCRs will get turned on only if Vm sin α> E. Thyristors T1,T2 conduct from wt=α to π+α. In other words, T1,T2 conduct for π radian. Likewise, waveform of current i t1 through T1 (or it2 through T2) is shown to flow π radians in fig.3. (ii). At wt=π+α, forward biased SCRs T3,T4 are triggered. The supply voltage turns off T1,T2 by natural commutation & the load current is transferred from T3,T4 . Voltage across thyristors thyristors T1, T2 is shown as uT1=uT2 and that across T3, T4 as uT3=uT4. Maximum reverse voltage across, T1, T2, T3 or T4 is Vm, and at the instant of triggering with firing angle α, each SCR is subjected to a reverse voltage of Vm sin α. Source current is treated as positive in the arrow direction . Under this assumption, source current is shown positive when T1, T2 are conducting and negative when T3, T4 are conducting, Fig.3.(ii).
36
Fig.3.(ii)
During α to π, both v s and is are positive, power therefore flows from ac source to load During the interval π to (π + α), is negative
37
but is positive, positive, the load therefore returns some of its energy to the supply system, But the net power flow is from ac source to dc load because (π – α)>α om Fig. 6.10 (b. The load terminal voltage, or full-converter output voltage, vo is shown in Fig.3.(ii). The average value of output voltage Vo is given by Vo = (1/π)α ∫ π+α Vmsin(wt).d(wt) = [(2Vm/π ) cos α]
…(3.2)
rms value of output voltage for single-phase M-2, or B-2, controlled converter can also be obtained as under. Vor = √[(1/π) α ∫ π+α Vm2 sin(2wt) d (wt) = (Vm2/2π ) [wt-{1/2 sin (2 wt)|} π+αα] = Vm2/2 =V2s Vor = Vs _______________________________________________________
3.(iii). Line-Commutated Inverter
Eq. (3.2) shows that if α > 90 o,
38
vo is negative. This is illustrated
in Fig.3. (iii)., where α is shown greater than 90 o. In this figure, average terminal voltage V o is negative, If the load circuit emf E is reversed, this source E will feed power back to ac supply. This operation of full converter is known as inverter operation of the converter. The full converter with firing angle delay greater than 90o is called line-commutated inverter. Such an operation is used
in the regenerative braking mode of a dc motor in which case then E is counter emf of the de motor. During 0 to α, ac source voltage v s is positive but ac source current is is negative, power therefore flows from dc source to ac source. From α to π, both V s and is are positive, power therefore, flows from ac source to dc source. But the net power flow is from dc source to ac source, because (π – α) < α in Fig.3. (iii). In converter operation, the average value of output voltage V o must be greater than load circuit emf E. During inverter operation, load circuit emf when inverted to ac must be more than ac supply voltage. In other words, de source voltage E must be more than inverter voltage Vo, only then power would flow from de source to ac supply system. But in both converter and inverter modes, thyristors must be forward biased and current current through SCRs must flows in the same in the same direction as these are unidirectional devices. This is the reason output current io is shown positive in
Fig.3. (iii). As before, source
39
current is is positive when T1,
T2 are conducting.
Fig.3. (iii).
The variation of voltage
40
across thyristors thyristors T1, T2 T3 or T4
reveals that circuit turn-off time for both converter and inverter operations is given by tc = [(π-α)/ω ] sec As both the types of phase-controlled phase-controlled converter have been studied, the advantages of single-phase bridge converter over single phase mid-point converter can now be stated: (i)
SCRs are subjected to a peak inverse voltage of 2 Vm in mid-point converter an V m in full converter. Thus for the same voltage and current ratings of SCRs, Power handled by mid-point configuration is about half of that handled by bridge configuration.
(ii)
In mid-point converter, each secondary should be able to supply the load power. As such the transformer transformer rating in mid-point converter is double the load rating. This, however, is not the case in single-phase bridge converter.
41
(iv). Single-phase
semiconverter
A single-phase semiconverter bridge with two thyristors and three diodes is shown in fig.3. (iv). The semiconverter are T1, T2; the two diodes are D1, D2; the third diode connected across load is freewheeling freewheeling diode FD. The load is of RLE Type as for the full converter bridge. Various voltage and current waveforms for this converter are shown in Fig.3. (iv), where load current is assumed continuous over the working range. After wt = 0, thyristor T1 is forward biased only when source voltage Vm sinα > E. With T1 on, load gets connected to source through T1 and d1. For the period wt = α to π, load current i o flows through RLE, D1, source and T1 and the load terminal voltage v o is the same wave shape as the ac source v s. Soon after wt = π, load voltage vo tends to reverse as the ac source voltage changes polarity. Just as vo tends to reverse (at wt = π+), FD gets forward biased and starts conducting. The load, or output, current io, is transferred transferred from T1, D1 to FD. As SCR T1 is reverse biased at wt = π+ through FD, T1 is turned off at wt = π+. The waveform of current i T1 through thyristor T1 is shown in Fig.3. (iv). It flows α to π, (2π+α) to 3π and so on for an interval of (π-α) radians. The load terminals are short circuited through FD, therefore load, or output, voltage v o is zero during π(π+a). After wt=π, during the negative half cycle, T2 will be forward forward biased only when source voltage more than than E.
At wt = (π+α), source
42
voltage exceeds E, T2 is
therefore triggered. triggered. Soon after (π+α), FD is reverse biased and is therefore turned off; load current now shift form FD to T2, D2. At wt = 2π, FD is again forward biased and output current i o is transferred transferred from T2, D2 to FD as explained explained before. The source current is in positive from α to π when T1, D1 conduct and is negative from (π + α) to 2π when T2, D2 conduct, see Fig.3.(iv). During the interval α to π, T1 and D1 conduct and ac source delivers energy to the load circuit. This energy is partially stored in inductance L, partially stored as electric energy in load-circuit emf E and Partially dissipated as heat in r. During the freewheeling period π to (π + α), energy stored in inductance is recovered and is partially dissipated in R and partially added to the energy stored in load emf E. No energy is fed back to the source during freewheeling freewheeling period. For semiconverter, semiconverter, the average average output voltage Vo, from from Fig.3. (iv), is given by Vo = (1/π) α∫ π Vm sin wt. d(wt) = (Vm/π) (1+cos α) ….(3.3) and rms value of output voltage is Vor = √[(1/π) α∫ π Vm2 sin(2wt) d (wt) = (Vm2/2π ) [ wt-{sin2wt/2} π α] = (Vs/π) [(π-α)+(sin2α)/2] [(π-α)+(sin2α)/2] = Vs [(1/π) {(π-α) + (sin 2α)/2}] 1/2
43
Fig.3. (iv)
The variation of voltage across across T1 and T2 is also depicted in Fig.3. (iv). It is seen from these waveforms that circuitturn off time for the semiconverter is tc=π-α/w sec _______________________________________________________
44
3.(v). Single-phase Full
Converter Drives
Two full converters, one feeding the armature circuit and other feeding the field circuit of a separately-excited de motor, are shown in Fig.3.(v). This scheme offers two-quadrant drive, Fig.3.(v) and its use is limited to about 15 kW. For regenerative braking of the motor, the power must flow from motor to the ac source and this is feasible only if motor counter emf is reversed because then e aia would be negative. Note that direction of current cannot be reversed as SCRs are unidirectional devices. So, for regenerative regenerative breaking, the polarity of ea must be reversed which is possible by reversing the direction of motor field current by making delay angle of full converter 2 more than 90o . In order that current in field winding can be reversed, the field winding must be energised through single-phase full converter as in Fig.3.(v).
45
Fig.3.(v).
For the armature converter 1, V o= Vt = 2 Vm /π cos α For 0<α>π
46
……(3.4)
For the field converter converter 2, Vf = (2 Vm /π) cos α1 for 0< α1>π .. ...(3.5)
From the waveforms waveforms in Fig.3.(v), it is seen seen that rms value of source current,
I sr =√ =√ I a 2 . π/π = I α
rms value of thyristor current,
I Tr I α 2 . π/2π]1/2 = I α/ Tr = [ I α/ √2 …..(3.6)
From Eq. (3.4), input supply pf= V t . I α / Vs . I sr = 2 Vm /π cosα. Iα . /2/ Vm . I a
= 2√2/π cos α
…..(3.7)
It is seen from Eq.3.7 that pf depends on the firing angle α only under the assumptions of constants armature current. _______________________________________________________
47
CHAPTER 4 THREE PHASE
CONVERTERS
48
THREE PHASE
CONVERTERS
If all the diodes of fig.3.39 are replaced by thyristors , a three phase full converter bridges as shown in fig.4.(i) is obtained. The three phase input supply is connected to terminals A,B,C & the load RLE is connected across the output terminals of converter as shown. As in a single phase converter full converter, thyristor power circuit of fig.6.26 works as a three phase ac to dc converter for firing angle delay 0o < α < 180 o . A three phase full converter is therefore preferred preferred where regeneration of power is required. The numbering of SCRs in Fig. 6.26 is 1, 3, 5 for the positive group and 4(=1+3), 6(=3+3), 2(=5+3-6) for the negative group. This numbering scheme is adopted here as it agrees with the sequence of gating of the six thyristors in a 3-phase full converter.
49
Fig. 4.(i).
For α=0o; T1, T2,…..T6
50
behave like diodes. This is
shown in fig.4.(i). The sequence of conduction of SCRs T1 to T6 is also indicated in this figure. Note that for α=0 o, T1 is triggered at wt = π/6, T2 at 90 o, T3 at 150o and so on. The load voltage has, therefore, the waveform as shown in Fig.4.( i). For α = 60 o, the conduction
sequence of thyristors T1 to T6 is shown in fig.4.( i). Here T1 is triggered at wt=30 o + 60o = 90o , T2 at 90 + 60= 150o and so on. If the conduction interval of various thyristors T1, T2, …… T6 is shown first, then it becomes easier to draw the voltage and current waveforms. Note that each SCR conducts for 120 o, when T1 is triggered, reverse biased thyristor thyristor T5 is turned on. T6 is already conducting. As T1 is connected to A and T6 to B, voltage V abab appears across load. It varies form 1.4 V m to zero as shown. Here V mp mp is the maximum value value of phase voltage. voltage. When T2 is turned on,T6 is commutated from the negative group. T1 is already conducting. As T1 and T2 are connected to A and C respectively, respectively, voltage V acac appears across load. Its value varies from 1.5 V mp mp to zero as shown. This sequence of triggering is continued for other SCRs. Note that positive group of SCRs are fired at an interval of 120o. Similarly, negative group of SCRs are fired with an interval of 120o amongst them. But SCRs from both the groups are fired at an interval of 60o. This means that commutation occurs every 60o
alternatively in upper and lower
51
group of SCRs. Each SCR from
both groups conducts for 120 o . At any time, two for SCRs, one from the positive group and the other from negative group, must conduct ABC phase sequence together for the source to energise the load. For ABC
of the three-phase supply, thyristors conduct in pairs; T1 and T2, T2 and T3, T3 and T4 and so on.
CHAPTER 5 SIMULATION DESIGN AND ANALYSIS
52
2.(i). Single Phase Half Wave Thyristor Circuit with R-load
Source voltage Vs = 100V Load resistance R = 100 Ω Firing angle α = 450
53
54
2.(ii). Single Phase Half Wave Thyristor Circuit with RL-without FD
Source voltage Vs = 100V Load resistance R = 100 Ω and inductance L = 0.01H Firing angle α = 450
55
56
2.(iii). Single Phase Half Wave Thyristor Circuit with RL- FD load
Source voltage Vs = 100V
57
Load resistance R = 100 Ω and Firing angle α = 450
inductance L = 0.01H
58
2.(iv). Single Phase Half Wave Thyristor Circuit with RLE load
Source voltage Vs = 100V Load resistance R = 100 Ω and inductance L = 0.01H Back emf E = 50V Firing angle α = 450
59
60
3.(i). Single Phase Full Wave Mid Point Converters (M-2 Connection)
Source Vs1 = 100V
Vs1 = 100V
61
Load resistance R = 100 Ω and Back emf E = 50V Firing angle α = 450
inductance L = 0.01H
62
3.(ii). Single phase full wave bridge converter (B-2 Connection)
63
64
3.(iii). Line-Commutated Inverter
65
66
(iv). Single-phase semiconverter
67
68
3.(v). Single-phase Full Converter Drives in continuous mode of operation
69
70
3.(vi). Single-phase Full Converter Drives in discontinuous mode of operation
71
72
4.(i).THREE PHASE CONVERTERS
73
74
REFERENCES
75
