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

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i + = i I 1 3 0 di 1 di = − 3 dt dt V ba = 2L c di dt 3 V Sinωt = 2L m 3 c di dt 3 ∴i 3 = − 3V m Cosωt + 2ωL c K Application of Power Electronics in Power Systems B. G. Fernandes 350/454
Boundary conditions : At ωt = α, i = I i = −I , i 0 , = 1 0 2 0 3 = α+μ, i 0 i = I 1 = , i2 = −I0, 3 0 ∴i 3 = 3V 2ωL m c ( Cosα − Cosωt) At ωt = α+μ, i 3 = I0 ∴ I 0 = 3V 2ωL m c ( Cosα − Cos( α + μ) ) Application of Power Electronics in Power Systems B. G. Fernandes 351/454
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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
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How to calculate Ref. Var ? i = I m
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Controlled current SLCVC • Compen
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Control strategy -I Application of
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Review • In harmonic elimination
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Contd.. Controlled current SLCVC
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• i S * is in phase with v S •
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• If Inverter i S * is changed in
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• Use two compensators & connect
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• Main compensator ⇒ Voltage co
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i Cm1 = V S −VCm 1∠ −δ Z∠
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• Var calculator determines V * d
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Contd.. • For high power applicat
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[A] [v'] = [z] [A] [i'] [v'] = [A]
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Vector representation of instantane
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[ C] t = ⎡ ⎢ ⎢− ⎢ ⎣−
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⎡v ⎢ ⎢ v ⎢⎣ v a b c ⎤
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e e i i α β α β = = V V S S cos
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e . q i * = β α C 3 2 + ( 2 2 ) e
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• Frequency of e α , i α , e β
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Review Instantaneous real power P =
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Contd.. Application of Power Electr
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Change of reference frame q S d S d
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• Let us assume that v S is along
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• AC filtering ⇒ phase shift
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• Information about system freque
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* x ∫ ω xt () x y n + 1 − Δ t
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e α = e a − 1 2 e b − 1 2 e c
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e d e d = = = e e s e s α cos( θ
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Review • In synchronous rotating
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To change MI using harmonic elimina
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• 3φ sinusoids which are in phas
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• This voltage waveform can be us
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1 1 • = = Switching frequency T T
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• Assume that over one cycle V re
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Rule to be followed • A term in t
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S 4 , S 3 ON for DT S : di L = V s
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Aim • i s and V s should be in ph
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Contd.. • Generate reset pulse at
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1φ AC-DC Control technique (1 −
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Alternate Approach DC-DC Converter
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• Information regarding V s shoul
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Inverter topology for high power ap
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• Number of pulse should be high
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Switches ON V AX S1, S2 V dc S2, S3
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Review • In one cycle control ‘
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Contd.. • At any time 2-devices (
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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
Page 299 and 300: U.P.F.C : Review • Two VSI connec
Page 301 and 302: Using UPFC • Active power flow an
Page 303 and 304: ⇒ A common DC-link voltage is reg
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Page 307 and 308: • ‘ρ’ can vary from 0 to 2π
Page 309 and 310: ⇒ Shunt current is controlled ind
Page 311 and 312: FACTS installments in India • TSC
Page 313 and 314: HVDC • Long distance transmission
Page 315 and 316: Back to Back : • Chandrapur - Ram
Page 317 and 318: • ‘P’ through link can not be
Page 319 and 320: • If alternator-2 generates 1000
Page 321 and 322: Application of Power Electronics in
Page 323 and 324: • One conductor (generally -ve)
Page 325 and 326: • Each terminal has two converter
Page 327 and 328: Components of HVDC transmission Bi-
Page 329 and 330: Smoothing Reactor : Large value of
Page 331 and 332: Reactive power support : • Both c
Page 333 and 334: • If α 1 is trigger angle for br
Page 335 and 336: ⇒T 1 is turned off at ωt= 30+ (3
Page 337 and 338: At ωt = 210 o V a = Sin210 = −1
Page 339 and 340: At ωt = 330 o V a −1 2, V = 1 =
Page 341 and 342: At ωt = 300 o V − 3 2, V = 0 V =
Page 343 and 344: Vdc = 2.34V ph. Cosα =1.35V LL .Co
Page 345 and 346: Contd.. • As α 1 ↑ (AC-DC conv
Page 347 and 348: Phase relationship between phase V
Page 349: As α↑: • V dc ↓ • Displace
Page 353 and 354: ∴V 0 = V pn −V mn V = − 2 cn
Page 355 and 356: Representation of inverter mode of
Page 357 and 358: Converter α ⇒ delay angle μ ⇒
Page 359 and 360: V dco = [cos + cos γ ] − − −
Page 361 and 362: 12-pulse converter • Series conne
Page 363 and 364: Application of Power Electronics in
Page 365 and 366: V d ⎛ 3 = VdoCosα − Id . B.
Page 367 and 368: • 24/36 harmonic filter ⇒ 2*80
Page 369 and 370: Direct current : • Nominal I ⇒
Page 371 and 372: Basic control : • DC voltage or I
Page 373 and 374: Basis for selection of control : Fo
Page 375 and 376: • Denominator is very small • A
Page 377 and 378: • P.F should be as high as possib
Page 379 and 380: • γ ⇒ necessary to maintain a
Page 381 and 382: I d = V dcor Cosα −V R + R + cr
Page 383 and 384: • Maintains adequate commutation
Page 385 and 386: • As taps are changed, CEA regula
Page 387 and 388: Basic control : • DC voltage or I
Page 389 and 390: Basis for selection of control : Fo
Page 391 and 392: • Rectifier control ⇒ To preven
Page 393 and 394: Control of HVDC system Application
Page 395 and 396: • Quantities forming the co-ordin
Page 397 and 398: • Rectifier characteristics can b
Page 399 and 400: • 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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