Power Systems Modelling and Fault Analysis

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1 Power Systems Modelling and Fault Analysis Theory and Practice Nasser D. Tleis BSc, MSc, PhD, CEng, FIEE AMSTERDAM BOSTON HEIDELBERG LONDON NEW YORK OXFORD PARIS SAN DIEGO SAN FRANCISCO SINGAPORE SYDNEY TOKYO ELSEVIER Newnes is an imprintof Elsevier NCWIIGS %

2 List of Electrical Symbols Foreword Preface Biography xvü xix xxi xxiv 1 Introduction to power System faults General Structure of power Systems Need for power System fault analysis General Health and safety considerations Design, Operation and protection of power Systems Design of power System equipment Characteristics of power System faults Nature of faults Types of faults Causes of faults Characterisation of faults Terminology of short-circuit current waveform and current interruption Effects of short-circuit currents on equipment Thermal effects Mechanical effects Per-unit analysis of power Systems General Single-phase Systems Change of base quantities Three-phase Systems Mutually coupled Systems having different operating voltages Examples 25

3 viii Contents Theory of symmetrical components and connection of phase sequence networks during faults General Symmetrical components of a three-phase power System Balanced three-phase voltage and current phasors Symmetrical components of unbalanced voltage or current phasors Apparent power in symmetrical component terms Definition of phase sequence component networks Sequence components of unbalanced three-phase impedances Sequence components of balanced three-phase impedances Advantages of symmetrical components frame of reference Examples Analysis of balanced and unbalanced faults in the sequence reference frame General Balanced three-phase to earth short-circuit faults Balanced three-phase clear of earth short-circuit faults Unbalanced one-phase to earth short-circuit faults Unbalanced phase-to-phase or two-phase short-circuit faults Unbalanced two-phase to earth short-circuit faults Unbalanced one-phase open-circuit faults Unbalanced two-phase open-circuit faults Example Fault analysis and choice of reference frame General One-phase to earth short-circuit faults Two-phase to earth short-circuit faults Analysis of simultaneous faults General Simultaneous short-circuit faults at the same location Cross-country faults or simultaneous faults at different locations Simultaneous open-circuit and short-circuit faults at the same location Simultaneous faults caused by broken and fallen to earth conductors Simultaneous short-circuit and open-circuit faults on distribution transformers 69 Further reading 73

4 ix 3 Modelling of multi-conductor overhead lines and cables General Phase and sequence modelling of three-phase overhead lines Background Overview of the calculation of overhead line Parameters Untransposed single-circuit three-phase lines with and without earth wires Transposition of single-circuit three-phase lines Untransposed double-circuit lines with earth wires Transposition of double-circuit overhead lines Untransposed and transposed multiple-circuit lines Examples Phase and sequence modelling of three-phase cables Background Cable sheath bonding and earthing arrangements Overview of the calculation of cable parameters Series phase and sequence impedance matrices of single-circuit cables Shunt phase and sequence susceptance matrices of single-circuit cables Three-phase double-circuit cables Examples Sequence n modeis of single-circuit and double-circuit overhead lines and cables Background Sequence jt modeis of single-circuit overhead lines and cables SequenceTT modeis of double-circuit overhead lines Sequence Tt modeis of double-circuit cables Sequence n modeis of three-circuit overhead lines Three-phase modelling of overhead lines and cables (phase frame of reference) Background Single-circuit overhead lines and cables Double-circuit overhead lines and cables Computer calculations and measurements of overhead line and cable parameters Computer calculations of overhead line and cable parameters Measurement of overhead line parameters Measurement of cable parameters 193

5 x Contents 3.8 Practical aspects of phase and sequence parameters of overhead lines and cables Overhead lines Cables 197 Further reading Modelling of transformers, static power plant and static load General Sequence modelling of transformers Background Single-phase two-winding transformers Three-phase two-winding transformers Three-phase three-winding transformers Three-phase autotransformers with and without tertiary windings Three-phase earthing or zig-zag transformers Single-phase traction transformers connected to three-phase Systems Variation of transformer's PPS leakage impedance with tap position Practical aspects of ZPS impedances of transformers Measurement of sequence impedances of three-phase transformers Examples Sequence modelling of QBs and PS transformers Background PPS, NPS and ZPS modelling of QBs and PSs Measurement of QB and PS sequence impedances Sequence modelling of series and shunt reactors and capacitors Background Modelling of series reactors Modelling of shunt reactors and capacitors Modelling of series capacitors Sequence modelling of static variable compensators Background PPS, NPS and ZPS modelling Sequence modelling of static power System load Background PPS, NPS and ZPS modelling Three-phase modelling of static power plant and load in the phase frame of reference Background Three-phase modelling of reactors and capacitors Three-phase modelling of transformers 287

6 xi Three-phase modelling of QBs and PSs Three-phase modelling of static load 299 Further reading Modelling of ac rotating machines General Overview of synchronous machine modelling in the phase frame of reference Synchronous machine modelling in the dqo frame of reference Transformation from phase ryb to dqo frame of reference Machine dqo equations in per unit Machine Operator reactance analysis Machine parameters: subtransient and transient reactances and time constants Synchronous machine behaviour under short-circuit faults and modelling in the sequence reference frame Synchronous machine sequence equivalent circuits Three-phase short-circuit faults Unbalanced two-phase (phase-to-phase) short-circuit faults Unbalanced single-phase to earth short-circuit faults Unbalanced two-phase to earth short-circuit faults Modelling the effect of initial machine loading Effect of AVRs on short-circuit currents Modelling of synchronous motors/compensators/ condensers Examples Determination of synchronous machines parameters from measurements Measurement of PPS reactances, PPS resistance and d-axis short-circuit time constants Measurement of NPS impedance Measurement of ZPS impedance Example Modelling of induction motors in the phase frame of reference General Overview of induction motor modelling in the phase frame of reference Modelling of induction motors in the dq frame of reference Transformation to dq axes Complex form of induction motor equations Operator reactance and parameters of a single-winding rotor 363

7 xii Contents Operator reactance and parameters of double-cage or deep-bar rotor Induction motor behaviour under short-circuit faults and modelling in the sequence reference frame Three-phase short-circuit faults Unbalanced single-phase to earth short-circuit faults Modelling the effect of initial motor loading Determination of motor's electrical parameters from tests Examples Modelling of wind turbine generators in short-circuit analysis Types of wind turbine generator technologies Modelling of fixed speed induction generators Modelling of small speed ränge wound rotor induction generators Modelling of doubly fed induction generators Modelling of series converter-connected generators 393 Further reading 396 Short-circuit analysis techniques in ac power Systems General Application of Thevenin's and superposition's theorems to the Simulation of short-circuit and open-circuit faults Simulation of short-circuit faults Simulation of open-circuit faults Fixed impedance short-circuit analysis techniques Background Passive short-circuit analysis techniques The ac short-circuit analysis techniques Estimation of de short-circuit current component Variation with time Estimation of ac short-circuit current component Variation with time Time domain short-circuit analysis techniques in large-scale power Systems Analysis of the time Variation of ac and de short-circuit current components Single short-circuit source connected by a radial network Parallel independent short-circuit sources connected by radial networks Multiple short-circuit sources in interconnected networks 412

8 xiii 6.6 Fixed impedance short-circuit analysis of large-scale power Systems Background General analysis of balanced three-phase short-circuit faults General analysis of unbalanced short-circuit faults General analysis of open-circuit faults Three-phase short-circuit analysis of large-scale power Systems in the phase frame of reference Background Three-phase modeis of synchronous and induction machines Three-phase analysis of ac current in the phase frame of reference Three-phase analysis and estimation of X/R ratio of fault current Example 448 Further reading 450 International Standards for short-circuit analysis in ac power Systems General International Electro-technical Commission Standard Background Analysis technique and voltage source at the short-circuit location Impedance correction factors Asynchronous motors and static Converter drives Calculated short-circuit currents Example UK Engineering Recommendation ER G7/ Background Representation of machines and passive load Analysis technique Calculated short-circuit currents Implementation of ER G7/4 in the UK American IEEE C Standard Background Representation of System and equipment Analysis technique Calculated short-circuit currents Example calculations using IEC 60909, UK ER G7/4 and IEEEC

9 7.6 IEC and IEEE C circuit-breaker Standards Short-circuit ratings Assessment of circuit-breakers short-circuit duties against ratings 481 Further reading 483 Network equivalents and practical short-circuit current assessments in large-scale ac power Systems General Power System equivalents for large-scale System studies Theory of static network reduction Need for power System equivalents Mathematical derivation of power System equivalents Representation of power Systems in large-scale studies Representation of power generating stations Representation of transmission, distribution and industrial networks Practical analysis to maximise short-circuit current predictions Superposition analysis and initial ac loadflow operating conditions Effect of mutual coupling between overhead line circuits Severity of fault types and substation configuration Uncertainties in short-circuit current calculations: precision versus accuracy Probabilistic short-circuit analysis Background Probabilistic analysis of ac short-circuit current component Probabilistic analysis of de short-circuit current component Example Risk assessment and safety considerations Background Relevant UK legislation Theory of quantified risk assessment Methodology of quantified risk assessment 518 Further reading 519 Control and limitation of high short-circuit currents General Limitation of short-circuit currents in power System Operation Background Re-certification of existing plant short-circuit rating 521

10 xv Substation Splitting and use of circuit-breaker autoclosing Network Splitting and reduced System parallelism Sequential disconnection of healthy then faulted equipment Increasing short-circuit fault clearance time De-loading circuits Last resort generation disconnection Example ^ Limitation of short-circuit currents in power System design and planning Background Opening of unloaded delta-connected transformer tertiary windings Specifying higher leakage impedance for new transformers Upgrading to higher nominal System voltage levels Uprating and replacement of switchgear and other substation equipment Wholesale replacement of switchgear and other substation equipment Use of short-circuit fault current limiters Examples Types of short-circuit fault current limiters Background Earthing resistor or reactor connected to transformer neutral Pyrotechnic-based fault current limiters Permanently inserted current limiting series reactor Series resonant current limiters usingabypass switch Limiters using magnetically coupled circuits Saturable reactor limiters Passive damped resonant limiter Solid State limiters using power electronic switches Superconducting fault current limiters The ideal fault current limiter Applications of fault current limiters Examples 546 Further reading An introduction to the analysis of short-circuit earth return current, rise of earth potential and electrical interference Background Electric shock and tolerance of the human body to ac currents Step, touch, mesh and transferred potentials 551

11 xvi Contents Electrical resistance of the human body Effects of ac current on the human body Substation earth electrode System Functions of substation earth electrode System Equivaient resistance to remote earth Overhead line earthing network Overhead line earth wire and towers earthing network Equivaient earthing network impedance of an infinite overhead line Analysis of earth fault ZPS current distribution in overhead line earth wire, towers and in earth Cable earthing system impedance Overall substation earthing System and its equivaient impedance Effect of System earthing methods on earth fault current magnitude Screening factors for overhead lines Screening factors for cables General Single-phase cable with metallic sheath Three-phase cable with metallic sheaths Analysis of earth return currents for short-circuits in substations Analysis of earth return currents for short circuits on overhead line towers Calculation of rise of earth potential Examples Electrical interference from overhead power lines to metal pipelines Background Electrostatic or capacitive coupling from power lines to pipelines Electromagnetic or inductive coupling from power lines to pipelines Resistive or conductive coupling from power Systems to pipelines Examples 595 Further reading 603 Appendices 605 A. 1 Theory and analysis of distributed multi-conductor lines and cables 605 A.2 Typical data of power system equipment 608 A.2.1 General 608 A.2.2 Data 609 Index 619

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