Power Electronics Overview & Applications
Power Electronics Overview & Applications
on
“Unit-I”
                             Presented by
                           Dr. Vadthya Jagan,
                     M. Tech & Ph. D (IIT Roorkee),
                           Associate Professor,
           Department of Electrical and Electronics Engineering,
                 Vignana Bharathi Institute of Technology.
2-Nov-21                                                           1
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Contents…..
✓   Concept of Power Electronics
    ✓      Scope and Applications
                                             Prepared by: Dr. Vadthya Jagan – M. Tech & Ph. D (I.I.T Roorkee)
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 (c) Industrial
      Pumps, Compressors, Blowers and fans, Machine tools (robots), Arc furnaces,
      induction furnaces, Lighting, Industrial lasers, Induction heating, Welding.
                     Source: Power Electronics – Ned Mohan, T. M. Undeland, W. P. Robbins
                                              Prepared by: Dr. Vadthya Jagan – M. Tech & Ph. D (I.I.T Roorkee)
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                                     Quiz-1
1. Electronic Devices (BJT, MOSFET, Diode, and IGBT) will
operate at
              (a) Low Power and High Frequency
              (b) Low Power and Low Frequency
              (c) High Power and Low Frequency
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(c) DC to AC Converters
     (d) AC to AC Converters
              (i) AC Voltage Controllers
              (ii) Cycloconverter
     (e) Static Switches
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                          Applications:
                          1. Electric traction,
                          2. Battery charging,
                          3. Electroplating,
                          4. Electrochemical processing
                          5. Power supplies,
                          6. Welding and
                          7. Uninterruptible power supply (UPS) systems.
          2-Nov-21                Department of Electrical and Electronics Engineering                                12
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                                            PEC
VDC                                                                                       V0
                           Fixed DC                               Variable DC                                            V0,avg
            VDC                                                                                    ton       toff
                       (Constant voltage)             (Variation in magnitude of voltage)
                                                                                               0                            t
  0               t                                                                                      T
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          VDC
                           Fixed DC
                                                                   Variable AC
                       (Constant voltage)                                                       0                   wt
                                                         (Variation in voltage magnitude)
  0             t
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                             Applications:
                             1. Aerospace
                             2. Slow-speed large ac drives like rotary kiln,
                             3. Induction heating etc..
             (e) Static Switches: The power semiconductor devices can operate as static
             switches or contactors. Static switches possess many advantages over mechanical
             and electromechanical circuit breakers. Depending upon the input supply, the
             static switches are called ac static switches or dc static switches.
             2-Nov-21              Department of Electrical and Electronics Engineering                                     17
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                                      Quiz-2
3. Commutation can be defined, as the process of
              (a) Making the SCR ON
              (b) Making the SCR OFF
              (c) Making the SCR ON and OFF
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                        Power Electronic
       Source                                        Motor                         Load
                          Converter
                             Control                              Sensing
                              Unit                                 Unit
                                     Input
                                   commond
            Fig.1.1: Block diagram of a typical power electronic system.
                                             Source: Power Electronics – Dr. P. S. Bimbhra
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                                     Quiz-3
5. Power-electronic equipment has very high efficiency, because
              (a) The devices always operate in active region
              (b) The devices never operate in active region
               (c) The devices traverse active region at high speed and stay at the two
               states, ON and OFF
              (d) Cooling is very efficient.                           (1)
(4)
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    Uncontrolled Switches
                                      Diode
                              A               IA     K
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         Signal Diode
                                                           Diode
     A                         K
                                                 A                    IA    K
               P    N
                                             .
                                                                                                          IA
                                                           VAK
                (a)                     IA                 (b)                   Forward voltage drop, VAK
                                                                                                                     Forward Conduction
                                                                                                                           State
                                                                                            Reverse
                                                                                        leakage current
                                                                                  VBR
                                                     VAK                    -VAK
                        -VAK                                                                               o                      VAK
                                        o                                                                      Cut-in voltage
                                                                                       Reverse Blocking
                                                                                            State
                               (d)       -                                                  (c)
                                        IA                                                            -IA
Fig. 1.2: signal diode (a) structure (b) circuit symbol (c) practical V-I characteristics (d) ideal characteristics
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                      IA               .
                                                Drift
                                                                                  (b)                     IA
                                               region
                                                                                Forward voltage drop, VAK
                                                 (a)                                                                 Forward Conduction
                                                                                                                           State
                                                                                            Reverse
                             VAK                                                        leakage current
  -VAK                                                                           VBR
                     o
                                                                           -VAK                                                   VAK
                                                                                                           o
                                                                                                               Cut-in voltage
                                                                                        Reverse Blocking
                                                                                             State
                      -
                     IA
                                                                                                                  (c)
                    (d)                                                                                -IA
Fig. 1.3: Power diode (a) structure (b) circuit symbol (c) practical V-I characteristics (d) ideal characteristics
                                                                Prepared by: Dr. Vadthya Jagan – M. Tech & Ph. D (I.I.T Roorkee)
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                                     Diode                   0                   π      2π           3π             4π   wt
                                 A           K
                                                  I0                   V0
                                      VD                    V0
                                                                            I0
                                                            I0
230V, 50Hz
  1-Φ ACAC
               Vac         Vin
                                             R Load    V0                                                 V0(avg)
  Supply                                                     0                   π      2π           3π             4π   wt
                                                            VD
                     1:1
                 Transformer
                                                             0                   π      2π           3π             4π   wt
                                                                 (1-2)V Drop
                           (a)
                                                                                          (b)
Fig. 1.4: Single-phase half wave rectifier (a) circuit diagram with R load (b) waveforms.
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                                     Quiz-4
7. The manufacturer provided the details on the data sheet as
voltage rating as 100V, current rating as 80A and switching time
as 0.2µs
    (a) General purpose diode,                            (b) Schottky diode,
    (c) Fast recovery diode,                              (d) Signal diode.
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Diode as a Switch
Diode Conductor
  A                    IA     K               A           IA              K
                                    .                                                     Low Resistance
                                                   ON – Short Circuited
              VAK
   Forward Biased Condition                         VAK = 1 to 2V
              Diode                                   Insulator
  A                     IA     K             A                            K
                                                       IA = 0
                                                                                         High Resistance
                                                  OFF – Open Circuited
              VAK
      Reverse Biased Condition                        VAK = Finate
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                                            P                                                       P
                               .                    J1                                                      J1
                                            N                                         N             N
VAK             SCR                                                                                         J2
                                                    J2
                                            P                                         P             P
                                     G              J3                       G                              J3
      G    IA                               N                                         N
K K
Fig. 1.5: SCR (a) circuit symbol (b) structure (c) interconnection of two transistors
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            P                                                                                  P
                    J1 – Forward biased .                                                              J1 – Reverse biased
            N                                                                                  N
Open                                                                               Open
                    J2 – Reverse biased                                                                J2 – Forward biased
            P                                                                                  P
                                                         A
   G                J3 – Forward biased                                               G                J3 – Reverse biased
            N                                                                                  N
                                                     P
                                                             J1 – Forward biased                   K
                K                                    N
                                            Closed
Forward blocking state                                       J2 – Reverse biased    Reverse blocking state
                                                     P
    – OFF State                                G             J3 – Forward biased        – OFF State
High resistance                                      N
                                                                                       High resistance
                                                         K
                                Forward conducting state – ON State                   Low resistance
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                           Load
                                                                                      Forward voltage drop, VT
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                     P                                                                                            IG2>IG1>IG
                             J1 – Reverse biased                     Reverse       IL                      IG2
                     N                                                                                           IG1 I =0
          Open                                                   leakage current                                      G
                             J2 – Forward biased                                   IH                                          VAK
                                                   -VAK VBR
                     P
               G             J3 – Reverse biased                                        o                 VAK2 VAK1 VBO
                     N                                OP
                                                                                                                       VAK2<VAK1<VB0
                                                              Reverse Blocking State          Forward Blocking State
                                                                                            Forward
                                                                                        leakage current
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                      P                                                                                             IG2>IG1>IG
                              J1 – Forward biased                      Reverse       IL                      IG2
                      N                                                                                            IG1 I =0
           Open                                                    leakage current                                      G
                               J2 – Reverse biased                                   IH                                          VAK
                                                     -VAK VBR
                      P
                G              J3 – Forward biased                                        o                 VAK2 VAK1 VBO
                      N
                                                        OP
                                                                                                                         VAK2<VAK1<VB0
                                                                Reverse Blocking State          Forward Blocking State
                                                                                              Forward
                                                                                          leakage current
-IA
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                                                                                                                                            IG3>IG2>IG1>IG
                                                                                                    Reverse       IL                 IG3   IG2   IG1
                                                                                                leakage current                                          IG=0
                             VAK1                                                                                 IH
                                                                                  -VAK VBR                                                                       VAK
                             VAK2                                                                                      o             VAK3 VAK2 VAK1 VBO
                                                                                     OP
                                                                                             Reverse Blocking State
                                                                                                                                                       VAK3<VAK2<VAK1<VB0
                                                                                                                             Forward Blocking State
                             VAK3                                Finger voltage                                            Forward
                                                                                                                       leakage current
                                o         a          IG2
                                               IG1         IG3
                                IG=0          Gate current
-IA
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                      (b)            -                                                       (a)
                                    IA                                                -IA
                   Fig. 1.7: (a) practical V-I characteristics (b) ideal V-I characteristics
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                                        Quiz-5
10. When a thyristor is reverse biased, the number of blocked
p-n junction is
    (a) 1,                     (b) 2,
    (c) 3,                      (d) 4.
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SCR as a Switch
            SCR
                   GClosed
                                                   Conductor
A                    IA K
                                                                       K
                                           A           IA                         Low Resistance
                                    .
             VAK                                ON – Short Circuited
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                                      Quiz-7
16. The most efficient gate-triggering signal for SCR is
 (a)    a steady dc level,                 (b) a short duration pulse ,
 (c) a high-frequency pulse train ,       (d) a low-frequency pulse train.
17. Once SCR starts conducting a forward current, its gate loses
control over
 (a) anode circuit voltage only,             (b) anode circuit current only,
 (c) anode circuit voltage and current, (d) anode circuit voltage, current and time.
18. In a thyristor
 (a) Latching current IL is associated with turn-off process and holding current IH
       with turn-on process,
 (b) both IL and IH are associated with turn-off process
 (c) IH is associated with turn-off process and IL with turn-on process,
 (d) both IL and IH are associated with turn-on process.
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                                                                             0
    Applications:                                                         V0          V0
                                                                                           I0
                                                                                                                                wt
                                                                          I0
    1.Phase-controlled rectifiers,                                                                               V0(avg)
                                                                            0                   π   2π      3π             4π   wt
    2.Line commutated inverters,
                                                                          VT
    3.AC voltage controllers, and
                                                                            0                   π   2π      3π             4π   wt
    4.Step-down cycloconverter.                                                  (1-2)V Drop
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                                               RL                                    C   RL
                       (a)                                   (b)
Fig. 1.8: Class-A commutation (a) load in series with capacitor (b) load in parallel with capacitor
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 = w =    −                                       R   1                                       4L
                                                           <                                 R<
           2 L   CL                                2 L   CL                                    C
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VDC = VL + VC + VRload
                                                                                                                         d
                              VDC = VL + VC                         VC = VDC − VL                    VC = VDC − L           i (t )
                                                                                                                         dt
                                           R 
                                         −         VDC                                                R 
                                                                                                       −      
                         VC = VDC + Le     2L  w
                                                                                       VC = VDC  1 + e  2 L  w 
                                                      L                                                          
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                  K        G
                                                             K
                                           C                                       C
 VDC                                             VDC
                      i0                                            i0
                          RL                                         RL
                                                                          Charging current of capacitor, IC
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                   Operating Principle:
      Mode 2: (T – ON)     .                                 Mode 3: (T – ON)
            A                                                                 A
                  T -ON     L                                                      T -ON         L
            K                                                                 K
                            C                                                                     C
VDC                                                            VDC
                 i0                                                               i0
                  RL                                                               RL
                     SCR carries two currents:
                     1) Discharging capacitor current, ID                               Net current= IL-IC
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RL R RL R
                              C                                               C
              VDC                                      VDC                                          V =0
                                                                                                      C
A A A A
TM TA TM - OFF TA - OFF
K G K G K K
                             (a)                                            (b)
      Fig. 1.11: Circuit configuration of (a) class-C commutation (b) circuit during Mode-0
                                                      Source: Power Electronics – Dr. M. D. Singh
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        K                 K        2) Load current, IL
                                                                                                              V = −V
                                           V =V
                                                                                                               C         DC
                   (a)
                                           C   DC
                                                                                                    (b)
Fig. 1.12: Equivalent circuits of class-C commutation in (a) Mode-1 and (b) Mode-2.
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        VDC = VRload + VC                       .
                                                                                                                 RL                   R
                                1
        VDC = RL i (t ) +          i(t )dt                                                                                C
                                C
                                                                                             VDC
Applying the Laplace Transform to the above equation                                                       A                   A
     VDC                 1                            VDC                  1 
         = RL I ( S ) +    I (S )                         = I ( S )  RL +                            TM - OFF                     TA - ON
      S                 CS                             S                  CS 
Apply inverse Laplace Transform to the above equation
                                                                                                           K                   K
                V
        i (t ) = DC et /( R C )
                            L
                                              (1)
                 RL
             When TM is conducting, the capacitor is charged to dc supply voltage VDC
through R. Now, when TA is triggered, a voltage twice the supply voltage is applied to
                                                                                                           2VDC t /( R C )
the RLC series circuit. So the current through this circuit is                                  i (t ) =       e       L
                                                                                                                                    (2)
                                                                                                            RL
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                              0 = VDC (1 − 2e                                      0 = 1 − 2e                                 1 = 2e                                0.5 = e
                                                                                                         toff /( RL C )
At t= toff, VC = 0
                                                   toff /( RL C )                                                                      toff /( RL C )                         toff /( RL C )
                                                                    )                                                                                                                          (5)
                                                                                                                                                             toff
 Apply logarithmic on both sides                                                        toff = 0.6931RL C                                 C = 1.44
                                                                                                                                                             RL
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                        Numerical Problems
Problem 1.1: For the class-C commutation, the dc source voltage VDC = 120V and
the current through Rload and R is 20A. The turn-off time of both the SCRs is 60µs.
Calculate, the value of commutating
                           .        capacitance C for successful commutation.
                                         60*10−6
                                C = 1.44                                             RL                   R
                                            6
                                                                                           C
                                                                        VDC
                                   C = 14.4  F                                  A                 A
TM TA
K G K G
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                       Numerical Problems
Problem 1.2: For class-C commutation, the dc voltage Edc = 220V and the
current through R1 and R2 is 25A. The turn-off time of both the SCRs is
50μsec. Calculate the value
                       .
                            of commutating capacitor C for successful
commutation. Ans: 8.18μF
                                                toff
                                     C = 1.44
                                                RL
                                           50*10−6
                                  C = 1.44
                                             8.8
C = 8.18*10−6
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                         (a)                                                     (b)
     Fig. 1.13: Configuration of (a) class-D commutation circuit and (b) circuit during Mode-0
                                                   Source: Power Electronics – Dr. M. D. Singh
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              T
                          Mode 1: (TA – ON)
                     M -OFF
                                                                                                    TM -OFF
                A             K
                                                                                                A              K
        C
                                                                                     C          VC = VDC
                    TA - ON
                                                                                                    TA - OFF
VDC     K       A             K          RL                                                     A
                                                                              VDC     K                        K        RL
        D - OFF
                                                                                     D - OFF
        A             L
                                                 VC = VDC                             A               L
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                                                                                   VDC    K     A            K          RL
                                                  C
                             iC ( peak ) = VDC                                                D - ON
                                                  L
                                                                                          A            L
                                                      2
                                    V 
                              L  C  DC 
                                     I L max 
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VDC VDC
                             PULSE       EP                                                     PULSE
                                                                                                            EP
                          TRANSFORMER                                                        TRANSFORMER
                 RL                                                               RL
                (a)                                                                    (b)
          Fig. 1.16: Configuration of (a) class-E commutation circuit and (b) circuit during Mode-0
                                                        Source: Power Electronics – Dr. M. D. Singh
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                                                    Quiz-8
19. Commutation is a ……………… process of thyristor
 (a)   turn – ON,                                  (b) turn – OFF,
 (c) Both turn ON and OFF,                         (d) None of these.
20. Which commutation technique is used in a phase-controlled
rectifier
 (a) Line commutation,                                (b) Load commutation,
 (c) Resonant pulse commutation, (d) Forced commutation.
21. In a complementary commutation, main thyristor TM can be
turned OFF by
 (a) Making use of auxiliary thyristor TA, (b) Making use of capacitor, C
 (c) Making use of diode, D,                  (d) Bringing the current below the holding current IH.
22. For successful commutation of class-D, the equation for C is
                  toff                      RL                                                 iL *VDC
 (a)   C = 1.44          , (b)   C = 1.44               (c) C = iL * tOFF   ,   (d)       C=
                  RL                        toff                   VDC                            tOFF
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(i) If power circuit has more than one SCR, the firing circuit should
    produce gating pulses
                     .    for each SCR at the desired instant for
    proper operation of the power circuit. These pulses must be
    periodic in nature and the sequence of firing must correspond
    with the type of thyristorised power controller.
(ii) The control signal generated by a firing circuit may not be able to
    turn-on an SCR It is therefore common to feed the voltage pulses
    to a driver circuit and then to gate-cathode circuit. A driver circuit
    consists of a pulse amplifier and a pulse transformer.
                                              Source: Power Electronics – Dr. P. S. Bhimbra
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                                                   Quiz-9
23. Most efficient and reliable triggering method is
 (a)   forward voltage triggering,                                   (b) dv/dt triggering,
 (c) Gate Triggering,                                                (d) Thermal triggering.
24. The function of R1 in case of R-firing circuit is to
 (a) Limit the gate current,                           (b) limit the load current,
 (c) None of these, (d) both (a) and (b).
25. In a complementary commutation, main thyristor TM can be
turned OFF by
 (a) Making use of auxiliary thyristor TA, (b) Making use of capacitor, C
 (c) Making use of diode, D,                  (d) Bringing the current below the holding current IH.
26. For successful commutation of class-D, the equation for C is
                  toff                      RL                                             iL *VDC
 (a)   C = 1.44          , (b)   C = 1.44           (c) C = iL * tOFF   ,   (d)       C=
                  RL                        toff               VDC                            tOFF
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                                                                                                                                                                                                            T1            R ED
 ED is the voltage drop across the first SCR, T1, ED = I1 R
 E1 is the voltage drop across the
                                .  remaining (ns-1) SCRs                                                                                                                                           Ibmax            I2
                                                                                                                                                                                                            T2           R
 Ibmin is the minimum leakage current of the SCR T1,
 Ibmax is the leakage current through the remaining SCRs, T2 to Tns,                                                                                                                                                          ES
 I           +I =I                        +I                      I −I =I
                                                                  1       2    b max
                                                                                       −I          b min
                                                                                                                       I − I = I
                                                                                                                       1           2            b
                                                                                                                                                                    I = I
                                                                                                                                                                        b           b max
                                                                                                                                                                                             −I   b min
                                                                                                                                                                                                            T3            R
     b min           1        b max               2
String voltage, E = E + (n − 1) E             S           D           s          1
                                                                                                       E = RI
                                                                                                           1                   2
                                                                                                                                               I = I − I
                                                                                                                                               2            1               b
                         E = I R + (n − 1) I R
                          S           1               s               2
                                                                                     E = I R + (n − 1)( I − I ) R
                                                                                       S               1                   s               1            b
E = I R + n I R − I n R − I R + I R
  S          1                s   1                   b       s           1            b
                                                                                                                       E = n I R − I n R + I R
                                                                                                                           S           s   1                    b   s                b
                                                                                                                                                                                                            Tns           R
                                                                                  nE −E                                                E = n E − I R (n − 1)
I R(n − 1) = n E − E                                                         R=
                                                                                                                                           S        s       D                   b        s
                                                                                           s       D           S
                                                                                                                                                                                                                K
      b          s                        s       D           S
                                                                                 (n − 1) I                                                Source: Power Electronics – Dr. P. S. Bimbhra
                                                                                               s                   b
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E = E + n E − n E − E + E
     S             D           s   E = n E − n E + E
                                   D             s       max           D                 max                  S               s       D      s         max         max
                                                    Q R
E = n E − E (n − 1) E (n − 1) = n E − E E =
                                                                   D                                                                                                     D
                                                                            T        R                                                                       max                         ns
 S             s       D           max           s                     max       s                        s       D               S              max
                                                      C C
 Q                           Q   ( n − 1)
       (n − 1) = n E − E
           max           C=                                                                         max           s
  C
                           s   nE −E         s
                                              Source: Power Electronics – K
                                                     D         S
                                                                          Dr. P. S. Bimbhra     s     D                   S
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Thyristor Ratings
                           (a)                                                         (b)
Fig. 1.25: Thyristor (a) anode voltages during blocking state and (b) V-I characteristics of a SCR with gate open.
Some subscripts are associated with voltage ratings for convenience in identifying them.
First subscript letter indicates the direction or the state : D - forward-blocking region; R –reverse-
blocking region.
Second subscript letter denotes the operating values: W - working value; R - repetitive value ; S -
surge or non-repetitive value.
Third subscript letter: M - indicates the maximum or peak value.
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                                                                                    P
                                                                                            J1 – Forward biased
                                    .                                              N
                                                                                            J2– Reverse biased
                                                                    Open            P
                                                                           G                J3 – Forward biased
                                                                                   N
                                                                                        K
i.   VDWM – Peak working forward blocking voltage: It specifies the maximum forward-blocking
     voltage that a thyristor can withstand during its working. VDWM equal to the maximum value of
     the sine voltage wave.
ii. VDRM – Peak repetitive forward blocking voltage: It refers to the peak transient voltage that a
     thyristor can withstand repeatedly or periodically in its forward-blocking mode. Voltage VDRM is
     encountered when a thyristor is commutated or turned-off.
iii. VDSM – Peak surge (non-repetitive) forward blocking voltage: It refers to the peak value of the
     forward surge voltage that does not repeat. Its value is about 130% of VDRM, but VDSM is less than
     forward breakover voltage VBO.
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                                                                                    P
                                                                                            J1 – Forward biased
                                   .                                               N
                                                                                            J2– Reverse biased
                                                                    Open            P
                                                                           G                J3 – Forward biased
                                                                                   N
                                                                                        K
iv. VRWM – Peak working reverse blocking voltage: It specifies the maximum reverse-blocking
    voltage that a thyristor can withstand during its working. VDWM equal to the negative maximum
    value of the sine voltage wave.
v. VRRM – Peak repetitive reverse blocking voltage: It refers to the peak reverse transient voltage
    that may occur repeatedly or periodically. Voltage VRRM is encountered when a thyristor is
    commutated or turned-off.
vi. VRSM – Peak surge (non-repetitive) reverse blocking voltage: It refers to the peak value of the
    reverse surge voltage that does not repeat. Its value is about 130% of VRRM, but VRSM is less than
    forward breakover voltage VBR.
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                                                 .
Fig. 1.26. Average on-state power dissipation Pavg as a
 function of ITAV for (a ) rectangular wave and (b) half
                     wave sinusoid.
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 Thyristor Protection
Reliable operation of a thyristor demands that its specified ratings are not exceeded. In
practice, a thyristor may be subjected to over voltages or over currents. During SCR turn-on,
di/dt may be prohibitively large. There may be false triggering of SCR by high value of dv/dt.
A spurious signal across gate-cathode
                             .        terminals may lead to unwanted turn-on. SCRs are
very delicate devices, their protection against abnormal operating conditions is, therefore,
essential.
Fig. 1.28. Thyristor protection circuit. Source: Power Electronics – Dr. P. S. Bimbhra
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                                                                       EE501PE: POWER ELECTRONICS
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                                                                              EE501PE: POWER ELECTRONICS
                                                                                                                  di
                                                                                         VDC = ( RS + RL )i + L                        (1)
                                                                                                                  dt
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                                                                             EE501PE: POWER ELECTRONICS
                                                                                  di VDC − ( t / )
                                                                                     =   e              (3)
                                                                                  dt   L
                                    di      VDC
                                                         L=
                                                                  VDC
 At t = 0; i= imax from eq(3)        =                         di 
                                                                                  Voltage across SCR is Va = RS*i
                                    dt  max  L
                                                                 
                                                                 dt  max
    dVa      di          dVa        di 
        = RS                                                    dVa                                        L      dV 
                               = RS  
                                                                            VDC
     dt      dt                                                     = RS                      RS =             * a 
                         dt  max    dt  max                 dt  max    L                              VDC     dt  max
                                                        L
                                              RS = 2
                                                        CS
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                                                               EE501PE: POWER ELECTRONICS
 (d) Gate Protection: Gate circuit should also be protected against over voltages
 and over currents. Over voltages across the gate circuit can cause false triggering of
 the SCR. Overcurrent may raise junction temperature beyond specified limit leading
 to its damage. Protection against over-voltages is achieved by connecting a zener
 diode ZD across the gate circuit. A resistor R2 connected in series with the gate
 circuit provides protection against over currents.
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