Chapter 3

Analysis of AC/DC Systems and short circuits

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

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

Trends in EHV ac installation

ABB deliveries of auto transformers and generator step up transformers

Shift in Trend

• UHV plans in most countries have been postponed – 1000KV lines in Russia, Italy and USA

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

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

Trend in use of HVDC

Comparison in use of HVDC and EHV ac

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

Design aspects …

– Corona performance • Design of conductor bundles

• Mechanical factors – Mechanical loading – Design of conductor bundles and climatic

condition

Comparison of EHV ac TL and HVDC TL

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

Reactive power consumption vs SIL at different levels of compensation

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

Comparison of number of lines to TX 8-12GW

Effect of weather and altitude on loss

Comparison of loss as function of line length for EHV ac and HVDC

Cost comparison

Cost comparison

Principle Application

• HVDC substation – Converter transformer – Converter valves – Control electronics – Filters – Switching circuits

• HVDC transmission line – Bipolar lines

HVDC substation

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

Problem formulation

• Real power mismatch at converter terminal

Problem formulation contd…

• Injected powers

Where is a vector of DC variables• The equations derived from ac system are

then

x

• From the dc system condition

• Where k runs from 1 to number of converters present

General ac-dc system

• For a general ac-dc system

D.C. system model

• Assumptions for selection of variables

Converter variables

• Balanced condition – Converter bridges operate identically if attached

to same ac bus bar

Converter variables contd…

• Single phase equivalent circuit

Derivation of equations

• For the above system models

• Fundamental current and dc current are related as

• Is and Ip are related as

1

2

Derivation of equations contd…

• Dc voltage and ac source are related as

• Dc current and voltage relation

• Real power equation

Derivation of equation contd…

• Transformer is lossless

• Fundamental current flow across transformer

• Combining 1,2,3 and 4

3

4

Final DC model summary

• The power relations

Inverter operation

• During inversion– Extinction angle is control variable

Generalized flow chart for equation solution

• Iteration equations

AC-DC load flow

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

Symmetrical components

• Consider the following current vectors

Mathematical relations between symmetrical components

• If we have the positive, negative and zero sequence currents of phase a, then the

• Where

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

Example 2: Find the symmetrical components of SLG fault

• Fault condition

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

Computing fault current, bus voltage and line currents

• Thevenin’s equivalent circuit method

Formulating the sequence impedance matrix

• Draw backs of Thevenin’s method – not applicable for large networks

• N bus system

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

• Bus voltage change is

• The bus voltages are then

• From power flow, current entering a bus is

• For the Thevenin’s equivalent network

• In matrix form

• Solving for change in bus voltage

• Bus voltage during fault

• In matrix form

• For the kth equation

• From the Thevenin’s equivalent circuit

• Using in above equation

• For any other element

• Substituting the fault current Ik(F)

• Fault current between line i and j is then

Sequence Networks

• Consider a line under SLG fault

Sequence networks contd…

• The SLG can be substituted with a current source

Using superposition

• The individual sequence networks can be drawn

Sequence networks of SLG

• Negative sequence network

Sequence networks of SLG fault contd…

• Zero sequence network

Sequence networks

• Taking note of

• Hence Vag is the voltage across the series connection of the three networks

Sequence network of SLG