Analysis of ACDC Systems and Short Circuits
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Transcript of Analysis of ACDC Systems and Short Circuits
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Chapter 3
Analysis of AC/DC Systems and short circuits
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Contents
• Limitations of EHV AC Transmission• Introduction of HVDC Transmission• Principle Application • Advantages and Modeling of HVDC Lines in Load Flow
Analysis• Effect of Short Circuits • Various Types of Faults • Symmetrical Components• Sequence Networks • Balance and Unbalanced Fault Analysis
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Limitations of EHV AC Transmission
• Power transmission
DC AC DC
End of second world war – 345Kv and 400Kv 1965, 735Kv is commissioned in Canada Mostly the trend is for 800Kv 1200Kv and research is going for 1500Kv
Why?Transformers
and induction
motors
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Trends in EHV ac installation
ABB deliveries of auto transformers and generator step up transformers
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Shift in Trend
• UHV plans in most countries have been postponed – 1000KV lines in Russia, Italy and USA
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Problems faced by EHV ac
• Increased current density • Use of bundled conductors • High surface voltage gradient on conductors • Corona problems: audible noise, radio interference, corona
energy loss, carrier interference and TV interference • High electrostatic field under the line • Switching surge over voltages • Increased short circuit currents • Use of gap-less metal oxide arresters• Shunt reactor compensation and use of series capacitors
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Introduction of HVDC Transmission
• 1950, 200Kv DC link , Moscow to Kasira 116Km• 500Kv and above 1979• Brazil 600Kv lines • There is an increase in trend of using HVDC and since
2000, an increase in high capacity projects• Anticipations • For >1000Km transmission, 800Kv solutions
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Trend in use of HVDC
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Comparison in use of HVDC and EHV ac
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Design aspects of TL
• Electrical aspects – Power transmission capacity • Voltage level and number of parallel circuits
– Emergency loading capacity – Reactive power compensation for ac lines – Power loss • Operational • Should be optimized with voltage level
– Overvoltage levels, air clearance and environmental conditions and selection of insulators • Insulation performance • Effect on tower height
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Design aspects …
– Corona performance • Design of conductor bundles
• Mechanical factors – Mechanical loading – Design of conductor bundles and climatic
condition
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Comparison of EHV ac TL and HVDC TL
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Power TX capacity
• Reactive power consumption of line inductance
• Reactive power generation of line capacitance • Surge impedance – Geometrical configuration of lines
– SIL for 230KV is 150MW and for 765KV is 2000MW
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Reactive power consumption vs SIL at different levels of compensation
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TX limits of HVDC and EHV ac
• For EHV ac transmission capacity is limited by – Reactive power consumption – Emergency loading capacity depends on reactive
constraints and allowable temperature • For HVDC – Max. allowable conductor temp. both for normal
and emergency – Emergency loading is further dependent on
number of redundant lines
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Comparison of number of lines to TX 8-12GW
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Effect of weather and altitude on loss
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Comparison of loss as function of line length for EHV ac and HVDC
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Cost comparison
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Cost comparison
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Principle Application
• HVDC substation – Converter transformer – Converter valves – Control electronics – Filters – Switching circuits
• HVDC transmission line – Bipolar lines
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HVDC substation
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Modelling of HVDC Lines in Load Flow Analysis
• AC-DC load flow – Analysis of load flow condition of combined
system – Variables • Vector of angles • all voltage at AC buses• Vector of DC variables
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Problem formulation
• Real power mismatch at converter terminal
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Problem formulation contd…
• Injected powers
Where is a vector of DC variables• The equations derived from ac system are
then
x
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• From the dc system condition
• Where k runs from 1 to number of converters present
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General ac-dc system
• For a general ac-dc system
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D.C. system model
• Assumptions for selection of variables
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Converter variables
• Balanced condition – Converter bridges operate identically if attached
to same ac bus bar
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Converter variables contd…
• Single phase equivalent circuit
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Derivation of equations
• For the above system models
• Fundamental current and dc current are related as
• Is and Ip are related as
1
2
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Derivation of equations contd…
• Dc voltage and ac source are related as
• Dc current and voltage relation
• Real power equation
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Derivation of equation contd…
• Transformer is lossless
• Fundamental current flow across transformer
• Combining 1,2,3 and 4
3
4
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Final DC model summary
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• The power relations
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Inverter operation
• During inversion– Extinction angle is control variable
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Generalized flow chart for equation solution
• Iteration equations
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AC-DC load flow
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Revision of symmetrical and unsymmetrical faults
• Faults in power system – Symmetrical or balanced faults – Unsymmetrical or unbalanced faults
• Single line to ground • Line to line fault • Double line to ground fault
• Proper relay setting and coordination – Three phase fault- phase relays – Line to ground fault- ground relays
• Rating of protective switch gear
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Symmetrical components
• Consider the following current vectors
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Mathematical relations between symmetrical components
• If we have the positive, negative and zero sequence currents of phase a, then the
• Where
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Symmetrical components relation
• Given any three currents in a TL, the symmetrical components can be found from
• Example: find the symmetrical components when a system has
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Example 2: Find the symmetrical components of SLG fault
• Fault condition
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Effect of Short Circuits
• Short circuit current flows on the faulted line • Line current flow on lines without fault
becomes zero • System symmetry is disturbed • Zero sequence currents – Over heating of motor windings
• Negative sequence currents – Generate torque in opposite directions
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Computing fault current, bus voltage and line currents
• Thevenin’s equivalent circuit method
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Formulating the sequence impedance matrix
• Draw backs of Thevenin’s method – not applicable for large networks
• N bus system
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Formulating sequence impedance
• Balanced fault at bus k with fault impedance zf• Pre fault voltage is obtained from PF• After fault, Thevenin’s equivalent network
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• Bus voltage change is
• The bus voltages are then
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• From power flow, current entering a bus is
• For the Thevenin’s equivalent network
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• In matrix form
• Solving for change in bus voltage
• Bus voltage during fault
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• In matrix form
• For the kth equation
• From the Thevenin’s equivalent circuit
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• Using in above equation
• For any other element
• Substituting the fault current Ik(F)
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• Fault current between line i and j is then
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Sequence Networks
• Consider a line under SLG fault
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Sequence networks contd…
• The SLG can be substituted with a current source
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Using superposition
• The individual sequence networks can be drawn
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Sequence networks of SLG
• Negative sequence network
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Sequence networks of SLG fault contd…
• Zero sequence network
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Sequence networks
• Taking note of
• Hence Vag is the voltage across the series connection of the three networks
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Sequence network of SLG