RLC CCTs To Simulate Damping

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RLC CCTs To Simulate Damping

• FI of branch or V across the CCT
• ?V across a comp. or I in CCT

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Typical Differential Eq. of RLC

• The Parallel RLC Eq(1)
• The Series RLC Eq(2)

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Load Switching

• Switch on off loads most Freq.
• RL, Low P.F. when Inductive
• High P.F. when Resistive
• C_loadbus role in After sw. off. Transient
• V0 Vs (at instant I ceases)
• C charged to V0, disch., In RL, Damp Os. Dis.
• A damped cosine wave of Fig. 4.6
• As P.F. improve, Transient decrease

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The RL Load and Switching off
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Arc Furnace Example

• Low voltage High Curent
• Fed by step down furn. Transformer
• Low P.F. freq. switching
• Cap.s connected to HV bus impr. P.F.
• Delta Wye Connections
• ExampleWye connection,Transf.60Hz
• 13.8 KV,20 MVA Y/Y solid Gr
• P.F. at Full Load0.6,C corr. P.F.to 1.0
• Transient?, sw.off fully loaded Transf.

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Eq. CCTs Discussion

• Schematic Eq.
• Iload20000/(13.8v3)836.7 A (rms)
• Z13.8/(v3x836)
• 9.522 O
• fcos-?0.653.
• RTRL9.52cosf5.7
• XTXL9.52sinf7.6
• L20.2 mH

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Discussion Furn. Ex. continued

• openIs(0)0,
• requiredIc(0)-I(0)
• Ic-I836.7sinF669.4A (rms)
• Ic is at peak since Vc0, and
• Ic(t0)669.4v2946.67A (text result should
  be corrected)
• Vc(0)0
• Xc13.8/(v3x669.4)11.9O (please correct text
  book results)
• C222.6 µF

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Discussion of Transient Resp.

• for I, the current
• d?I/dt?1/Ts dI/dt1/T?0
• i(s)(s?s/Ts1/T?)(s1/Ts)I(0)I(0)
• Transient of series RLC CCT
• L dI/dtIRVc
• LI(0)I(0)RVc(0)0
• I(0)-I(0)R/L-I(0)/Ts
• i(s)s/(s?s/Ts1/T?) . I(0)-?Fig4.6

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Discussion Continued

• Z0vL/Cv20.2/0.22289.52 O
• ?Z0/R9.52/5.7131.6664
• I, starts with 946.67 A, swing to ve
• peak of 0.105 half cycle later.
• -.06X946.67 after another half cycle
• (these values should be corrected in
  the text book)
• For Vc
• d?Vc/dt?1/Ts dVc/dt Vc/T?0
• vc(s)(s?s/Ts1/T?)(s1/Ts)Vc(0)Vc(0)
• Vc(0)0, Vc(0)-I(0)/c
• vc(s)1/(s?s/Ts1/T?) . I(0)/c

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Transformer Terminal Voltage

• Fig 4.4 ? ?1.66 peak reaches 65
• undamped-I(0)/CT-I(0)Z0
• The first voltage peak
• 0.65x946.67x9.525.85 KV
• (please correct the value in the
  text book)
• The time scale is TvLC 2.121 ms
• Reaches peak in 1.4T2.97 ms
• Fast Transient and Corona Damping
• Always higher freq. Damped quicker

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Abnoraml Switching

• Normal 2 pu
• Abnormal mag. Far beyond this
• 1-current suppression
• 2- Capacitor Bank switching off
• 3-Other Restriking Phenomena
• 4-Transformer Mangnetizing Inrush
• 5-Ferroresonance

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Current Suppression

• N.,I ceases, arc current, periodic Zero
• Abn., arc suppression force current 0
• Current Chopping
• trapped mag. Energy ? Abn. Voltage
• Ex sw. off Transformer magnetizing current
• Energy stored½LmI0?
• Lm very large

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Cur. Chop.

• ½ CV?1/2 LmI0?? VI0 vLm/C
• I0 Instant. current chopped
• i.e. 1000KVA, 13.8 KV Transformer
• 1- magnetizing current1.5 A (rms)
• 2-LmV/?Im13800/(v3x377x1.5)14 H
• eff.Cap.?type of wind.ins(1000-7000PF)
• If C5000 PF, Z0v14/5x10-952915O
• If C.B. chops I_peak, can be 2.5 A,
  V(peak)132KV Abnormal for 13.8 KV

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Cur. Chop. Discussion

• Not So High
• 1- damping,
• 2- fraction of Energy
• release
• shaded arealt 30 stored energy
• I0v(0.3Lm/C)
• 55 V (transient)
• Dis. Transf. most
• vulnerable

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Continued

• Air cored reactors (core of significant air-gap)
• 1-All energy recoverable
• 2-If as shunt compensator, protected by
  L.A.
• Formal Evaluation of RLC CCT
• 1- ICIRIL0, sub. Diff.
• 2- d?V/dt?1/RCdV/dtV/LmC0
• 3-v(s)(s?s/RC1/LmC)(s1/RC)V
  (0)V0
• V(0)-Ic(0)/c-I0/C
• V(s)sV(0)/(s?s/RC1/Lmc)V(0)/Rc x
  1/(s?s/RC1/Lmc) I0/c(s?s/RC1/LmC)
• Transforms of Fig4.4 Fig 4.6
• first two normal Transient terms without chop

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continued

• Chopping of Magnetizing current of a 13.8 kV

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The response with cur. Chop.

• 1st term Fig4.6, puV(0)
• 2nd term fig4.4,puTVc(0)/Tp Vc(0)/?
• ?-? I0/cs?s/Tp1/T?TI0/C 2?/(v4??-1) .
• exp(-t/2?) sinv(4??-1) t/2?
• ? TI0/CZ0I0 peak Amp. Chopping Term (exclude
  damp.)

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The response with cur. Chop.

• Practical Ex Shown in Figure ?
• 1-chop only 0.5-0.6 A (I to zero) TRV 20KV
• 2- chop occur instantaneously
• 3- in practice I declines on a measurable time
• 4-TRV and time-to-chop/period H.F. Osc.
  Figure ?
• 5-TRV max if tc0, TRV reduce as tcgtT/4
  

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Discussion on CB performance

• small contact sep. dielectric fails
• Successive attempts raise Higher Voltages until
  isolation
• TRV of Cur.Chop. Limited by reignitions (Fig)
• G. Practice a cable between C.B. and Transformer
  drastic reduction in TRV
• 100 ft of 15 KV cable (100PF/ft)
  Transformer(3000PF eff. Cap.) TRV halved
• Motors No risk Noload inductance very small
  compare to transformer

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Semiconductor DevicesCurrent Suppression

• Gen. OVs to destroy them
• end half cycle of diode conduction
• 1-carriers remained at junction region
• allow current to flow reverses
• 2- then sweeps the carriers returns device to
  Block stateI collapses fast
• inductive CCT Eng. Transf. to C,large V

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Current Suppresssion Silicon Diode

• CCT and Current
• H.F. Osc. LC
• Protection
• 1-snubber cap. In P.
• 2-additional series R

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Capacitance Switching Off

• Disconnect C /unload Transmission lines
• Concerns reignite/restrike in opening
• Chance low, Cap. Sw. frequent
• Cap fully charged
• Half Cycle VCB2 Vp

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Capacitance Switching off
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Discussion Cap. Sw. Off

• In fact VcgtVsys Ferranti Rise
• Vsource_side decrease to Vsys
• There is a ?V change (however,exist in weak
  systems)
• Discon. a C.B. in lower side of step down
  Transformer
• supplying an unloaded cable
• Current in Cap. Sw. is freq. small and it is
• possible to disconnect it In first zero
• -- with small contact sep., 2 V appear across
  contacts
• --- increased possibility of restrike (small
  separation)
• Oscillating to new voltage with f01/2?vLC
• I(restrike)2Vp/vL/C sin?0t
• Transient peak of 3 Vp

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Capacitance Switching with a Restrike at
Peak of Voltage
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Capacitor Switching continued

• A 13.8 KV, 5000KVAR, 3ph bank,NGr
• Source Gr, inductance1 mH
• Restrike at Vp
• 1- c5/(377x13.8?)69.64µF
• 2- Zv1000/69.643.789O
• 3-Ip2v2x13.8/(v3x3.789)5.947 KA
• 4-f0603 Hz

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Multiple Restrikes During Capacitance Switching