BG Fernandes Department of Electrical Engineering II T - Power ...

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Harmonic Oscillator . ⎡ ⎤ ⎢ x ⎥ ⎢ . ⎥ ⎣y⎦ = ⎡ 0 ω⎤⎡x⎤ ⎢ ⎥⎢ ⎥ ⎣-ω 0⎦⎣y⎦ • Has Eigen values at S = • If x(0) = 0 and y(0) =1 ± jω x( t) = sinωt y( t) = cosωt x& = ω y y& = − ω x Application of Power Electronics in Power Systems B. G. Fernandes 128/454
* x ∫ ω xt () x y n + 1 − Δ t n +1 − Δ t y x n n = = − ω y xω * y −ω ∫ y() t x n = x + ωyΔt + 1 n y n = y − ωxΔt + 1 n Application of Power Electronics in Power Systems B. G. Fernandes 129/454
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EE 660 Application of Power Electro
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Books for Reference • T. J. E. Mi
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• Consumption of Electricity are
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• Thermal limit (depends on ambie
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• Voltage profile along the line
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• To control V R & ↑ power tran
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• High ‘V’ & high KVar source
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• What sort of PWM technique to u
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V = V = V = m S R V It can be shown
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Provide • Series capacitive compe
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• Is it possible to change the ph
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• Injecting V in series with line
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• Definite amount of power that s
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• To control the power flow & to
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• Most of the loads are Non-linea
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Current drawn by the load fed from
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Effect of harmonics: A. In the Rota
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Conclusions • Load compensator +
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Notation of quality of supply • H
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Ideal compensator • Correct the p
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Voltage regulation • Which is the
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I L = P L − V jQ L ΔV = ( R + jX
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Vary Q S => ΔV rotates till E = V
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• Approximate relationship for vo
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• If short circuit resistance of
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I a = V R ab Vca − jX VL∠0 V∠
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I b = I c ∠120 ⎛ ⎜ ⎝ 3 2X
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Contd.. • Using passive reactive
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Comments • Branch currents of Δ
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Application of Power Electronics in
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• May not be possible • Most of
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• Can be shown that if V < C1 V S
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• M => Magnitude of sine wave (no
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Review • Linear lagging load can
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Contd.. • If space vector PWM is
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⇒ (n-1) harmonics are eliminated
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• Assume that there are 5 switchi
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• Non-linear transcendental equat
Page 77 and 78: How to calculate Ref. Var ? i = I m
Page 79 and 80: Controlled current SLCVC • Compen
Page 81 and 82: Control strategy -I Application of
Page 83 and 84: Review • In harmonic elimination
Page 85 and 86: Contd.. Controlled current SLCVC
Page 87 and 88: • i S * is in phase with v S •
Page 89 and 90: • If Inverter i S * is changed in
Page 91 and 92: • Use two compensators & connect
Page 93 and 94: • Main compensator ⇒ Voltage co
Page 95 and 96: i Cm1 = V S −VCm 1∠ −δ Z∠
Page 97 and 98: • Var calculator determines V * d
Page 99 and 100: Contd.. • For high power applicat
Page 101 and 102: [A] [v'] = [z] [A] [i'] [v'] = [A]
Page 103 and 104: Vector representation of instantane
Page 105 and 106: [ C] t = ⎡ ⎢ ⎢− ⎢ ⎣−
Page 107 and 108: ⎡v ⎢ ⎢ v ⎢⎣ v a b c ⎤
Page 109 and 110: e e i i α β α β = = V V S S cos
Page 111 and 112: Application of Power Electronics in
Page 113 and 114: e . q i * = β α C 3 2 + ( 2 2 ) e
Page 115 and 116: • Frequency of e α , i α , e β
Page 117 and 118: Review Instantaneous real power P =
Page 119 and 120: Contd.. Application of Power Electr
Page 121 and 122: Change of reference frame q S d S d
Page 123 and 124: • Let us assume that v S is along
Page 125 and 126: • AC filtering ⇒ phase shift
Page 127: • Information about system freque
Page 131 and 132: e α = e a − 1 2 e b − 1 2 e c
Page 133 and 134: e d e d = = = e e s e s α cos( θ
Page 135 and 136: Review • In synchronous rotating
Page 137 and 138: To change MI using harmonic elimina
Page 141 and 142: • 3φ sinusoids which are in phas
Page 143 and 144: • This voltage waveform can be us
Page 145 and 146: 1 1 • = = Switching frequency T T
Page 147 and 148: • Assume that over one cycle V re
Page 149 and 150: Rule to be followed • A term in t
Page 151 and 152: S 4 , S 3 ON for DT S : di L = V s
Page 153 and 154: Aim • i s and V s should be in ph
Page 155 and 156: Contd.. • Generate reset pulse at
Page 157 and 158: 1φ AC-DC Control technique (1 −
Page 159 and 160: Alternate Approach DC-DC Converter
Page 161 and 162: • Information regarding V s shoul
Page 165 and 166: Inverter topology for high power ap
Page 167 and 168: • Number of pulse should be high
Page 169 and 170: Switches ON V AX S1, S2 V dc S2, S3
Page 173 and 174: Review • In one cycle control ‘
Page 175 and 176: Contd.. • At any time 2-devices (
Page 177 and 178: 4-level inverter • Number of swit
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S2, S3, S4 ON : ⇒ V AX = 2V dc /3
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• ‘V’ rating of D B = 2V dc /
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Voltage space vectors for 3 level i
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( NNP ) ⇒ ( 001 ) ⇒ ( PPN ) ⇒
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C B A O O N O N O N O O C B A O N N
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V q ∴V S = = 3 2 V 2 dC ⎡V ⎢
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OOP : V AO = V dC /2, V BO = V CO =
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OPO : V AO = V CO = 0, V BO = V dC
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Medium voltage vectors ONP : V AO =
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NPO : V AO = 0, V BO = V dC /2 , V
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Contd.. • No. of medium voltage v
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Voltage control • Space vector PW
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• Unbalances has no effect on loa
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• Passive elements Load compensat
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Shunt Compensation : • Inject cur
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Mid point voltage regulator • Two
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• Reactive power supplied by the
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• Shunt compensator can increase
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Review Mid-point shunt compensation
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Summary • Compensator must remain
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Variable impedance type S.V.C 1. Th
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• ‘i’ is continuous when α =
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2. Thyristor switched capacitor (TS
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3. Fixed Capacitor, Thyristor contr
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• At α = π/2, Q L = Q L(max)
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Control • ‘Q’ is controlled b
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Operating V-I region Application of
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Contd.. T.S.C • Thyristors are tr
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Advantages • Since voltage profil
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Series compensation • Injects vol
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X eff = ( X − X ) L C = ( 1− K
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Q Q se sh = tan ⎛ ⎜ ⎝ 2 δ ma
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Approaches to controllable series c
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• Amplitude of the fundamental V
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(b). Impedance compensation mode: V
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Review GTO controlled series capaci
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Contd.. • Control ‘i’ in ‘L
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Voltage compensating mode : • Rea
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• In FCTCR continuously varying c
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V 2 1 I1 ⎜ Sin X ⎝ π π ⎛
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• If X L (α) < X C , There are t
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• ‘V C ’ gets distorted • I
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• If X TCR = 1.5X C ⇒ Capacitiv
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Modes of operation By pass mode :
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Static Synchronous Series Compensat
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• Voltage across ‘L’ ⇒ V (
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Contd.. • For both region X L < X
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Control range: • Voltage compensa
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• Compensation for both reactive
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• If V S = V R =V Per phase power
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⇒ Reactive VA associated with the
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Voltage & phase angle regulators Vo
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Power flow control : • Optimal lo
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• Basic idea is to keep the trans
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UPFC : • Able to control simultan
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• Independently control the react
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Case1 : Control capabilities ρ = 0
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U.P.F.C : Review • Two VSI connec
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Using UPFC • Active power flow an
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⇒ A common DC-link voltage is reg
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= Ve ⎧V ⎨ ⎩ ( Cosδ 2 − jSi
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• ‘ρ’ can vary from 0 to 2π
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⇒ Shunt current is controlled ind
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FACTS installments in India • TSC
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HVDC • Long distance transmission
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Back to Back : • Chandrapur - Ram
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• ‘P’ through link can not be
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• If alternator-2 generates 1000
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• One conductor (generally -ve)
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• Each terminal has two converter
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Components of HVDC transmission Bi-
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Smoothing Reactor : Large value of
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Reactive power support : • Both c
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• If α 1 is trigger angle for br
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⇒T 1 is turned off at ωt= 30+ (3
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At ωt = 210 o V a = Sin210 = −1
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At ωt = 330 o V a −1 2, V = 1 =
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At ωt = 300 o V − 3 2, V = 0 V =
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Vdc = 2.34V ph. Cosα =1.35V LL .Co
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Contd.. • As α 1 ↑ (AC-DC conv
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Phase relationship between phase V
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As α↑: • V dc ↓ • Displace
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Boundary conditions : At ωt = α,
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∴V 0 = V pn −V mn V = − 2 cn
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Representation of inverter mode of
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Converter α ⇒ delay angle μ ⇒
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V dco = [cos + cos γ ] − − −
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12-pulse converter • Series conne
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V d ⎛ 3 = VdoCosα − Id . B.
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• 24/36 harmonic filter ⇒ 2*80
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Direct current : • Nominal I ⇒
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Basic control : • DC voltage or I
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Basis for selection of control : Fo
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• Denominator is very small • A
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• P.F should be as high as possib
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• γ ⇒ necessary to maintain a
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I d = V dcor Cosα −V R + R + cr
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• Maintains adequate commutation
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• As taps are changed, CEA regula
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Basic control : • DC voltage or I
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Basis for selection of control : Fo
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• Rectifier control ⇒ To preven
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Control of HVDC system Application
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• Quantities forming the co-ordin
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• Rectifier characteristics can b
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• Constant current characteristic
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• After some time, tap changer ch
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• Therefore rectifier characteris
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• At normal voltage , characteris
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• In order to avoid the problem,
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• When inverter is on current con
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When does change over take place ?
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Review Rectifier characteristics Co
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• ‘e’ is -ve, ‘K’ is +ve
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• Due to line fault or during low
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Inverter side : • I d can be ↑
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Mode stabilization : • Intersecti
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• ‘V’ profile is flat • Con
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• V dcoi Cosβ remains constant
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Current limit Maximum current limit
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Voltage depend current-order limit
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• VDCOL characteristics could be
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Contd.. But I ref(R) > I ref(I) I r
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Contd.. Mode stabilization : • In
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Voltage depend current-order limit
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• VDCOL characteristics could be
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Significant aspects of basic contro
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• If there is a ↓ in AC voltage
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⇒ Achieved using by pass valve an
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• For energization of blocked bri
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• Instead use VSI • ‘I’ cou
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• ‘V’ can not reverse, but
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BG Fernandes Department of Electrical Engineering II T - Power ...

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