Power Quality in Power Systems, Electrical Machines, and Power-Electronic Drives

Front Cover
Power Quality in Power Systems, Electrical Machines, and Power-Electronic Drives
Copyright
Contents
Preface
	1. Past and future electric energy systems
	2. Renewable hybrid energy system developments
		Key features
	References
Acknowledgments
	References
The climate dilemma
	References
Summary overview of chapters
Chapter 1: Introduction to power quality
	1.1. Definition of power quality
	1.2. Causes of disturbances in power systems
		1.2.1. Unpredictable events
		1.2.2. The electric utility
		1.2.3. The customer
		1.2.4. Manufacturing regulations
	1.3. Classification of power quality issues
		1.3.1. Transients
		1.3.2. Short-duration voltage variations
		1.3.3. Long-duration voltage variations
		1.3.4. Voltage imbalance
		1.3.5. Waveform distortion
		1.3.6. Voltage fluctuation and flicker
		1.3.7. Power-frequency variations
	1.4. Formulations and measures used for power quality
		1.4.1. Harmonics
			1.4.1.1. Triplen harmonics
			1.4.1.2. Subharmonics
			1.4.1.3. Interharmonics
			1.4.1.4. Characteristic and uncharacteristic harmonics
			1.4.1.5. Positive-, negative-, and zero-sequence harmonics [48]
			1.4.1.6. Time and spatial (space) harmonics
		1.4.2. The average value of a nonsinusoidal waveform
		1.4.3. The rms value of a nonsinusoidal waveform
		1.4.4. Form factor (FF)
		1.4.5. Ripple factor (RF)
		1.4.6. Harmonic factor (HFh)
		1.4.7. Lowest order harmonic (LOH)
		1.4.8. Total harmonic distortion (THD)
		1.4.9. Total interharmonic distortion (TIHD)
		1.4.10. Total subharmonic distortion (TSHD)
		1.4.11. Total demand distortion (TDD)
		1.4.12. Telephone influence factor (TIF)
		1.4.13. C-message weights
		1.4.14. V . T and I . T products
		1.4.15. Telephone form factor (TFF)
		1.4.16. Distortion index (DIN)
		1.4.17. Distortion power (D)
		1.4.18. Application Example 1.1: Calculation of input/output currents and voltages of a three-phase thyristor rectifier
		1.4.19. Application Example 1.2: Calculation of input/output currents and voltages of a three-phase rectifier with one se ...
		1.4.20. Application Example 1.3: Calculation of input currents of a brushless DC motor in full-on mode (three-phase perma ...
		1.4.21. Application Example 1.4: Calculation of the efficiency of a polymer electrolyte membrane (PEM) fuel cell used as  ...
		1.4.22. Application Example 1.5: Calculation of the currents of a wind-power plant PWM inverter feeding power into the po ...
	1.5. Effects of poor power quality on power system devices
	1.6. Standards and guidelines referring to power quality
		1.6.1. IEC 61000 series of standards for power quality
		1.6.2. IEEE-519 standard
	1.7. Harmonic modeling philosophies
		1.7.1. Time-domain simulation
		1.7.2. Harmonic-domain simulation
		1.7.3. Iterative simulation techniques
		1.7.4. Modeling harmonic sources
	1.8. Power quality improvement techniques
		1.8.1. High power quality equipment design
		1.8.2. Harmonic cancellation
		1.8.3. Dedicated line or transformer
			1.8.3.1. Application Example 1.6: Interharmonic reduction by dedicated transformer
		1.8.4. Optimal placement and sizing of capacitor banks
		1.8.5. Derating of power system devices
		1.8.6. Harmonic filters, APLCs, and UPQCs
			1.8.6.1. Application example 1.7: Hand calculation of harmonics produced by 12-pulse converters
			1.8.6.2. Application Example 1.8: Filter design to meet IEEE-519 requirements
			1.8.6.3. Application Example 1.9: Several users on a single distribution feeder
	1.9. Summary
	1.10. Problems
	References
	Additional bibliography
Chapter 2: Harmonic models of transformers
	2.1. Sinusoidal (linear) modeling of transformers
	2.2. Harmonic losses in transformers
		2.2.1. Skin effect
		2.2.2. Proximity effect
		2.2.3. Magnetic iron-core (hysteresis and eddy-current) losses
			2.2.3.1. Application Example 2.1: Relation between voltages and flux linkages for 0 phase shift between fundamental and h ...
			2.2.3.2. Application Example 2.2: Relation between voltages and flux linkages for 180 phase shift between fundamental and ...
		2.2.4. Loss measurement
			2.2.4.1. Indirect loss measurement
			2.2.4.2. Direct loss measurement
			2.2.4.3. Application Example 2.3: Application of the direct-loss measurement technique to a single-phase transformer
	2.3. Derating of single-phase transformers
		2.3.1. Derating of transformers determined from direct-loss measurements
		2.3.2. Derating of transformers determined from the K-factor
		2.3.3. Derating of transformers determined from the FHL-factor
			2.3.3.1. Application Example 2.4: Sensitivity of K- and FHL-factors and derating of 25 kVA single-phase pole transformer  ...
			2.3.3.2. Application Example 2.5: K- and FHL-factors and their application to derating of 25 kVA single-phase pole transf ...
	2.4. Nonlinear harmonic models of transformers
		2.4.1. The general harmonic model of transformers
		2.4.2. Nonlinear harmonic modeling of transformer magnetic core
			2.4.2.1. Time-domain transformer core modeling by multisegment hysteresis loop
			2.4.2.2. Frequency- and time-domain transformer core modeling by saturation curve and harmonic core-loss resistances
			2.4.2.3. Time-domain transformer coil modeling by saturation curve and a constant core-loss resistance
			2.4.2.4. Frequency-domain transformer coil modeling by harmonic current sources
			2.4.2.5. Frequency-domain transformer coil modeling by describing functions
		2.4.3. Time-domain simulation of power transformers
			2.4.3.1. State-space formulation
			2.4.3.2. Transformer steady-state solution from the time-domain simulation
		2.4.4. Frequency-domain simulation of power transformers
		2.4.5. Combined frequency- and time-domain simulation of power transformers
		2.4.6. Numerical (finite-difference, finite-element) simulation of power transformers
	2.5. Ferroresonance of power transformers
		2.5.1. System conditions susceptible (contributive, conducive) to ferroresonance
		2.5.2. Transformer connections and single-phase (pole) switching at no load
			2.5.2.1. Application Example 2.6: Susceptibility of transformers to ferroresonance
		2.5.3. Ways to avoid ferroresonance
			2.5.3.1. Application Example 2.7: Calculation of ferroresonant currents within transformers
	2.6. Effects of solar-geomagnetic disturbances on power systems and transformers
		2.6.1. Application Example 2.8: Calculation of magnetic field strength H
		2.6.2. Solar origins of geomagnetic storms
		2.6.3. Sunspot cycles and geomagnetic-disturbance cycles
		2.6.4. Earth-surface potential (ESP) and geomagnetically induced current (GIC)
		2.6.5. Power system effects of GIC
		2.6.6. System model for calculation of GIC
		2.6.7. Mitigation techniques for GIC
		2.6.8. Conclusions regarding GIC
	2.7. Grounding
		2.7.1. System grounding
			2.7.1.1. Factors influencing choice of grounded or ungrounded system
				Definitions
				Service continuity
				Grounded systems
				Multiple faults to ground
				Safety
				Power system overvoltages
				Lightning
				Switching surges
			2.7.1.2. Application Example 2.9: Propagation of a surge through a distribution feeder with an insulator flashover
			2.7.1.3. Application Example 2.10: Lightning arrester operation
		2.7.2. Equipment grounding
		2.7.3. Static grounding
		2.7.4. Connection to earth
		2.7.5. Calculation of magnetic forces
	2.8. Measurement of derating of three-phase transformers
		2.8.1. Approach
			2.8.1.1. Three-phase transformers in Delta-Delta or Y-Y ungrounded connection
			2.8.1.2. Three-phase transformers in Delta-Y connection
			2.8.1.3. Accuracy requirements for instruments
			2.8.1.4. Comparison of directly measured losses with results of no-load and short-circuit tests
		2.8.2. A 4.5 kVA three-phase transformer Bank #1 feeding full-wave rectifier
		2.8.3. A 4.5 kVA three-phase transformer Bank #2 supplying power to six-step inverter
		2.8.4. A 15 kVA three-phase transformer supplying power to resonant rectifier
		2.8.5. A 15 kVA three-phase transformer bank absorbing power from a PWM inverter
		2.8.6. Discussion of results and conclusions
			2.8.6.1. Discussion of results
			2.8.6.2. Comparison with existing techniques
	2.9. Summary
	2.10. Problems
	References
	Additional Bibliography
Chapter 3: Modeling and analysis of induction machines
	3.1. Complete sinusoidal equivalent circuit of a three-phase induction machine
		3.1.1. Application Example 3.1: Steady-state operation of induction motor at undervoltage
		3.1.2. Application Example 3.2: Steady-state operation of induction motor at overvoltage
		3.1.3. Application Example 3.3: Steady-state operation of induction motor at undervoltage and under-frequency
	3.2. Magnetic fields of three-phase machines for the calculation of inductive machine parameters
	3.3. Steady-state stability of a three-phase induction machine
		3.3.1. Application Example 3.4: Unstable and stable steady-state operation of induction machines
		3.3.2. Application Example 3.5: Stable steady-state operation of induction machines
		3.3.3. Resolving mismatch of wind-turbine and variable-speed generator torque-speed characteristics
	3.4. Spatial (space) harmonics of a three-phase induction machine
	3.5. Time harmonics of a three-phase induction machine
	3.6. Fundamental and harmonic torques of an induction machine
		3.6.1. The fundamental slip of an induction machine
		3.6.2. The harmonic slip of an induction machine
		3.6.3. The reflected harmonic slip of an induction machine
		3.6.4. Reflected harmonic slip of an induction machine in terms of fundamental slip
		3.6.5. Reflected harmonic slip of an induction machine in terms of harmonic slip
	3.7. Measurement results for three- and single-phase induction machines
		3.7.1. Measurement of nonlinear circuit parameters of single-phase induction motors
			Stator impedance
			Rotor impedance
			Magnetizing impedance
			Iron-core resistance
			Turns ratio between the turns of the main- and auxiliary-phase windings
			3.7.1.1. Measurement of current and voltage harmonics
			3.7.1.2. Measurement of flux-density harmonics in stator teeth and yoke (back iron)
				Measurement via computer sampling
		3.7.2. Application Example 3.6: Measurement of harmonics within yoke (back iron) and tooth flux densities of single-phase ...
			3.7.2.1. Data of motor R333MC
			3.7.2.2. Discussion of results and conclusions
	3.8. Inter- and subharmonic torques of three-phase induction machines
		3.8.1. Subharmonic torques in a voltage-source-fed induction motor
		3.8.2. Subharmonic torques in a current-source-fed induction motor
		3.8.3. Application Example 3.7: Computation of forward-rotating subharmonic torque in a voltage-source-fed induction motor
		3.8.4. Application Example 3.8: Rationale for limiting harmonic torques in an induction machine
		3.8.5. Application Example 3.9: Computation of forward-rotating subharmonic torque in current-source-fed induction motor
	3.9. Interaction of space and time harmonics of three-phase induction machines
		3.9.1. Application Example 3.10: Computation of rotating mmf with time and space harmonics
		3.9.2. Application Example 3.11: Computation of rotating mmf with even space harmonics
		3.9.3. Application Example 3.12: Computation of rotating mmf with noninteger space harmonics
	3.10. Conclusions concerning induction machine harmonics
	3.11. Voltage-stress winding failures of AC motors fed by variable-frequency, voltage- and current-source PWM inverters
		3.11.1. Application Example 3.13: Calculation of winding stress due to PMW voltage-source inverters
		3.11.2. Application Example 3.14: Calculation of winding stress due to PMW current-source inverters
	3.12. Nonlinear harmonic models of three-phase induction machines
		3.12.1. Conventional harmonic model of an induction motor
		3.12.2. Modified conventional harmonic model of an induction motor
		3.12.3. Simplified conventional harmonic model of an induction motor
		3.12.4. Spectral-based harmonic model of an induction machine with time and space harmonics
	3.13. Static and dynamic rotor eccentricity of three-phase induction machines
	3.14. Operation of three-phase machines within a single-phase power system
	3.15. Classification of three-phase induction machines
	3.16. Summary
	3.17. Problems
	References
	Additional bibliography
Chapter 4: Modeling and analysis of synchronous machines
	4.1. Sinusoidal state-space modeling of a synchronous machine in the time domain
		4.1.1. Electrical equations of a synchronous machine
		4.1.2. Mechanical equations of synchronous machine
		4.1.3. Magnetic saturation of synchronous machine
		4.1.4. Sinusoidal model of a synchronous machine in dq0 coordinates
	4.2. Steady-state, transient, and subtransient operation
		4.2.1. Definition of transient and subtransient reactances as a function of leakage and mutual reactances
		4.2.2. Phasor diagrams for round-rotor synchronous machines
			4.2.2.1. Consumer (motor) reference frame
			4.2.2.2. Generator reference frame
			4.2.2.3. Similarities between synchronous machines and pulse-width-modulated (PWM) current-controlled, voltage-source inv ...
			4.2.2.4. Phasor diagram of a salient-pole synchronous machine
		4.2.3. Application Example 4.1: Steady-state analysis of a nonsalient-pole (round-rotor) synchronous machine
		4.2.4. Application Example 4.2: Calculation of the synchronous reactance XS of a cylindrical-rotor (round-rotor, nonsalie ...
		4.2.5. Application Example 4.3: dq0 modeling of a salient-pole synchronous machine
		4.2.6. Application Example 4.4: Calculation of the amortisseur (damper winding) bar losses of a synchronous machine durin ...
		4.2.7. Application Example 4.5: Measured voltage ripple of a 30kVA permanent-magnet synchronous machine, designed for a d ...
		4.2.8. Application Example 4.6: Calculation of synchronous reactances Xd and Xq from measured data based on phasor diagram
		4.2.9. Application Example 4.7: Design of a low-speed 20kW permanent-magnet generator for a wind-power plant
		4.2.10. Application Example 4.8: Design of a 10kW wind-power plant based on a synchronous machine
		4.2.11. Synchronous machines supplying nonlinear loads
		4.2.12. Switched-reluctance machine
		4.2.13. Some design guidelines for synchronous machines
			4.2.13.1. Maximum flux densities
			4.2.13.2. Recommended current densities
			4.2.13.3. Relation between induced Ephase and terminal Vphase voltages
			4.2.13.4. Iron-core stacking factor and copper-fill factor
		4.2.14. Winding forces during normal operation and faults
			4.2.14.1. Theoretical basis
	4.3. Harmonic modeling of a synchronous machine
		4.3.1. Model of a synchronous machine as applied to harmonic power flow
			4.3.1.1. Definition of positive-, negative-, and zero-sequence impedances/reactances
			4.3.1.2. Relations between positive-, negative-, and zero-sequence reactances and the synchronous, transient, and subtran ...
		4.3.2. Synchronous machine harmonic model based on transient inductances
			4.3.2.1. Application Example 4.9: Measured current spectrum of a synchronous machine
		4.3.3. Synchronous machine model with harmonic parameters
			4.3.3.1. Application Example 4.10: Harmonic modeling of a 24-bus power system with asymmetry in transmission lines
			4.3.3.2. Application Example 4.11: Harmonic modeling of a 24-bus power system with a nonlinear static VAr compensator (SVC)
		4.3.4. Synchronous machine harmonic model with imbalance and saturation effects
			4.3.4.1. Synchronous machine harmonic model based on dq0 coordinates
			4.3.4.2. Synchronous machine harmonic model based on abc coordinates
			4.3.4.3. Computation of synchronous machine injected harmonic currents [Inl(h)]
				Injected harmonic current due to frequency conversion [If(h)]
				Total injected harmonic current [Inl(h)]
			4.3.4.4. Application Example 4.12: Effect of frequency conversion on synchronous machine negative-sequence impedance
			4.3.4.5. Application Example 4.13: Effect of imbalance on power quality of synchronous machines
			4.3.4.6. Application Example 4.14: Effect of Delta connection on power quality of synchronous machines
			4.3.4.7. Application Example 4.15: Effect of saturation on power quality of synchronous machines
			4.3.4.8. Application Example 4.16: Impact of nonlinear loads on power quality of synchronous machines
		4.3.5. Static- and dynamic-rotor eccentricities generating current and voltage harmonics
		4.3.6. Shaft flux and bearing currents
		4.3.7. Conclusions
	4.4. Discretization errors of numerical solutions
	4.5. Operating point-dependent reactances under saturated magnetic field conditions
	4.6. Summary
	4.7. Problems
	References
	Additional bibliography
Chapter 5: Performance of power-electronic drives with respect to speed and torque
	5.1. Closed-form and numerical-solution techniques for variable-speed, variable-torque drives, and review of circuit appr ...
		5.1.1. Performance of ideal and nonideal storage elements
			5.1.1.1. Nonideal equivalent circuits of batteries and PEM fuel cell
			5.1.1.2. Nonideal battery parameters
			5.1.1.3. Performance of batteries under low temperature conditions
		5.1.2. Numerical solution approaches
			5.1.2.1. Discretization errors of numerical methods
			5.1.2.2. Operating-point-dependent equivalent circuits of synchronous machines
			5.1.2.3. Operating-point-dependent equivalent circuits of induction (asynchronous) machines
			5.1.2.4. Operating-point-dependent equivalent circuits of permanent-magnet machines
			5.1.2.5. Six-step and current-controlled, pulse-width-modulated, voltage-source inverters, and the choice of the modulati ...
		5.1.3. Energy considerations
			5.1.3.1. The influence of wave-shaping inductance Lw with resistance Rw
			5.1.3.2. Recovering of braking energy
			5.1.3.3. Energy savings based on heat pumps
			5.1.3.4. Renewable power plants
			5.1.3.5. Need for nuclear plants
			5.1.3.6. Figure of merit, low and high-speed operation of electric automobiles
			5.1.3.7. CFW [26,27] at high-speed operation
			5.1.3.8. Manufacturing of electric energy within interconnected and smart power systems
			5.1.3.9. Synchrophasors for monitoring and control of interconnected smart power system
	5.2. Three-phase distribution system supplying energy to lithium-ion batteries via rectifiers
		5.2.1. Application Example 5.1: Delta-wye, three-phase transformer supplying diode-bridge rectifier in series with one th ...
			5.2.1.1. Conclusions
		5.2.2. Application Example 5.2: Delta-wye, three-phase transformer supplying one MOSFET in series with diode-bridge recti ...
			5.2.2.1. Conclusion
		5.2.3. Application Example 5.3: Delta-wye, three-phase transformer supplying half-controlled thyristor bridge with LfCf o ...
			5.2.3.1. Conclusions
		5.2.4. Application Example 5.4: Current-controlled discharging a lithium-ion to support three-phase distribution systems  ...
			5.2.4.1. Electric automobiles face a few important problems
			5.2.4.2. Alternative storage methods
			5.2.4.3. Conclusion
		5.2.5. Application Example 5.5: Single-phase transformer supplying diode bridge in series with MOSFET with two filters Lf ...
			5.2.5.1. Conclusions
	5.3. Three-phase permanent-magnet generator supplying energy to lead-acid battery via rectifier
		5.3.1. Application Example 5.6: MOSFET switch in series with diode-bridge rectifier and two filters Lf1Cf1, Lf2Cf2 supply ...
			5.3.1.1. Conclusions
	5.4. Speed and torque control of drives consisting of three-phase induction machine connected to current-controlled, volt ...
		5.4.1. Application Example 5.7: Three-phase IM operating regimes are analyzed when supplied by either a lithium-ion or a  ...
	5.5. Speed and torque control of brushless-DC machine or permanent-magnet machine fed/supplied by inverter for either mot ...
		5.5.1. Application Example 5.8: Brushless DC motor-inverter performance for rated speed and rated torque supplied by idea ...
			5.5.1.1. Conclusions
		5.5.2. Application Example 5.9: Brushless DC motor-inverter performance at low speed corresponding to fstart1=6Hz and fst ...
			5.5.2.1. Conclusion
		5.5.3. Application Example 5.10: Brushless DC motor-inverter performance for high speed corresponding to f2=1500Hz employ ...
	5.6. Control of speed and torque for three-phase synchronous motor/machine fed/supplied by either lithium-ion battery or  ...
		5.6.1. Application Example 5.11: Synchronous motor-inverter performance for rated operation supplied by lithium-ion battery
	5.7. Performance issues with batteries, fuel cells, and combustion engines
	5.8. Summary
	References
Chapter 6: Interaction of harmonics with capacitors
	6.1. Application of capacitors to power-factor correction
		6.1.1. Definition of displacement power factor
		6.1.2. Total power factor in the presence of harmonics
		6.1.3. Application Example 6.1: Computation of displacement power factor (DPF) and total harmonic distortion (THD) for a  ...
		6.1.4. Benefits of power-factor correction
	6.2. Application of capacitors to reactive power compensation
	6.3. Application of capacitors to harmonic filtering
		6.3.1. Application Example 6.2: Design of a tuned harmonic filter
	6.4. Power quality problems associated with capacitors
		6.4.1. Transients associated with capacitor switching
		6.4.2. Harmonic resonances
			6.4.2.1. Parallel resonance
			6.4.2.2. Series resonance
			6.4.2.3. Capacitor bank behaves as a harmonic source
		6.4.3. Application Example 6.3: Harmonic resonance in a distorted industrial power system with nonlinear loads
		6.4.4. Application Example 6.4: Parallel resonance caused by capacitors
		6.4.5. Application Example 6.5: Series resonance caused by capacitors
		6.4.6. Application Example 6.6: Protecting capacitors by virtual harmonic resistors
			6.4.6.1. Suggested solutions to resonance problems
	6.5. Frequency and capacitance scanning
		6.5.1.1. Frequency scan
		6.5.1.2. Capacitance scan
		6.5.2. Application Example 6.7: Frequency and capacitance scanning [9]
	6.6. Harmonic constraints for capacitors
		6.6.1. Harmonic voltage constraint for capacitors
		6.6.2. Harmonic current constraint for capacitors
		6.6.3. Harmonic reactive-power constraint for capacitors
		6.6.4. Permissible operating region for capacitors in the presence of harmonics
			6.6.4.1. Safe operating region for the capacitor voltage
			6.6.4.2. Safe operating region for the capacitor current
			6.6.4.3. Safe operating region for the capacitor reactive power
			6.6.4.4. Feasible operating region for the capacitor reactive power
		6.6.5. Application Example 6.8: Harmonic limits for capacitors when used in a three-phase system
	6.7. Equivalent circuits of capacitors
		6.7.1. Application Example 6.9: Harmonic losses of capacitors
	6.8. Summary
	6.9. Problems
	References
Chapter 7: Lifetime reduction of transformers and induction machines
	7.1. Rationale for relying on the worst-case conditions
	7.2. Elevated temperature rise due to voltage harmonics
	7.3. Weighted-harmonic factors
		7.3.1. Weighted-harmonic factor for single-phase transformers
		7.3.2. Measured temperature increases of transformers
			7.3.2.1. Single-phase transformers
			7.3.2.2. Three-phase transformers
		7.3.3. Weighted-harmonic factor for three-phase induction machines
		7.3.4. Calculated harmonic losses and measured temperature increases of induction machines
			7.3.4.1. Single-phase induction motors
			7.3.4.2. Three-phase induction motors
	7.4. Exponents of weighted-harmonic factors
		7.4.1. Determination of factor k
		7.4.2. Determination of factor
	7.5. Additional losses or temperature rises versus weighted-harmonic factors
		7.5.1. Application Example 7.1: Temperature rise of a single-phase transformer due to single harmonic voltage
		7.5.2. Application Example 7.2: Temperature rise of a single-phase induction motor due to single harmonic voltage
	7.6. Arrhenius plots
		7.6.1. Thermal aging
	7.7. Reaction rate equation
	7.8. Decrease of lifetime due to an additional temperature rise
		7.8.1. Application Example 7.3: Aging of a single-phase induction motor with E=0.74eV due to a single harmonic voltage
		7.8.2. Application Example 7.4: Aging of a single-phase induction motor with E=0.51eV due to a single harmonic voltage
	7.9. Reduction of lifetime of components with activation energy E=1.1eV due to harmonics of the terminal voltage within r ...
		7.9.1. Conclusion
	7.10. Possible limits for harmonic voltages
		7.10.1. Application Example 7.5: Estimation of lifetime reduction for given single-phase and three-phase voltage spectra  ...
		7.10.2. Application Example 7.6: Estimation of lifetime reduction for given single-phase and three-phase voltage spectra  ...
	7.11. Probabilistic and time-varying nature of harmonics
	7.12. The cost of harmonics
	7.13. Temperature as a function of time
		7.13.1. Application Example 7.7: Temperature increase of rotating machine with a step load
	7.14. Various operating modes of rotating machines
		7.14.1. Steady-state operation
		7.14.2. Short-term operation
		7.14.3. Steady state with short-term operation
		7.14.4. Intermittent operation
		7.14.5. Steady state with intermittent operation
		7.14.6. Application Example 7.8: Steady state with superimposed periodic intermittent operation with irregular load steps
		7.14.7. Reduction of vibrations and torque pulsations in electric machines
		7.14.8. Application Example 7.9: Reduction of harmonic torques of a piston-compressor drive with synchronous motor as pri ...
		7.14.9. Calculation of steady-state temperature rise DeltaT of electric apparatus based on thermal networks
			7.14.9.1. Heat flow related to conduction
			7.14.9.2. Heat flow related to radiation and convection
		7.14.10. Application Example 7.10: Temperature-rise equations for a totally enclosed fan-cooled 100hp motor
		7.14.11. Application Example 7.11: Temperature-rise equations for a drip-proof 5hp motor
	7.15. Summary
	7.16. Problems
	References
Chapter 8: Power system modeling under nonsinusoidal operating conditions
	8.1. Overview of a modern power system
		8.1.1. Generation with storage plants
		8.1.2. Single and three-phase transformers
		8.1.3. Transmission and subtransmission lines
		8.1.4. Distribution system
		8.1.5. Linear and nonlinear loads, including energy storage plants
		8.1.6. Renewable energy generation plants
		8.1.7. Control and dispatch centers
	8.2. Power system matrices
		8.2.1. Bus admittance matrix
			8.2.1.1. Application Example 8.1: A simple power system configuration
			8.2.1.2. Application Example 8.2: Construction of bus admittance matrix
			8.2.1.3. Application Example 8.3: Building of nonsingular bus admittance matrix
			8.2.1.4. Application Example 8.4: Building of singular bus admittance matrix
		8.2.2. Triangular factorization
			8.2.2.1. Application Example 8.5: Matrix multiplication
			8.2.2.2. Application Example 8.6: Triangular factorization
		8.2.3. Jacobian matrix
			8.2.3.1. Application Example 8.7: Jacobian matrices
	8.3. Fundamental power flow
		8.3.1. Fundamental bus admittance matrix
		8.3.2. Newton-Raphson power flow formulation
		8.3.3. Fundamental Jacobian entry formulas
		8.3.4. Newton-Raphson power flow algorithm
		8.3.5. Application Example 8.8: Computation of fundamental admittance matrix
		8.3.6. Application Example 8.9: Evaluation of fundamental mismatch vector
		8.3.7. Application Example 8.10: Evaluation of fundamental Jacobian matrix
		8.3.8. Application Example 8.11: Calculation of the inverse of Jacobian matrix
		8.3.9. Application Example 8.12: Inversion of a 3x3 matrix
		8.3.10. Application Example 8.13: Computation of the correction voltage vector
	8.4. Newton-based harmonic power flow
		8.4.1. Harmonic bus admittance matrix and power definitions
		8.4.2. Modeling of nonlinear and linear loads at harmonic frequencies
		8.4.3. The harmonic power flow algorithm (assembly of equations)
		8.4.4. Formulation of Newton-Raphson approach for harmonic power flow
		8.4.5. Harmonic Jacobian entry formulas related to line currents
		8.4.6. Newton-based harmonic power flow algorithm
		8.4.7. Application Example 8.14: Computation of harmonic admittance matrix
		8.4.8. Application Example 8.15: Computation of nonlinear load harmonic currents
		8.4.9. Application Example 8.16: Evaluation of harmonic mismatch vector
		8.4.10. Application Example 8.17: Evaluation of fundamental and harmonic Jacobian submatrices
		8.4.11. Application Example 8.18: Computation of the correction bus vector and convergence of harmonic power flow
	8.5. Classification of harmonic power flow techniques
		8.5.1. Decoupled harmonic power flow
		8.5.2. Fast harmonic power flow
		8.5.3. Modified fast decoupled harmonic power flow
		8.5.4. Fuzzy harmonic power flow
		8.5.5. Probabilistic harmonic power flow
		8.5.6. Modular harmonic power flow
		8.5.7. Application Example 8.19: Accuracy of decoupled harmonic power flow
	8.6. Summary
	8.7. Problems
	References
Chapter 9: Impact of poor power quality on reliability, relaying, and security
	9.1. Reliability indices
		9.1.1. Application Example 9.1: Calculation of reliability indices
	9.2. Degradation of reliability and security due to poor power quality
		9.2.1. Single-time and nonperiodic events
		9.2.2. Harmonics and interharmonics affecting overcurrent and under-frequency relay operation [32]
			9.2.2.1. Under-frequency relays
			9.2.2.2. Overcurrent relays
		9.2.3. Power-line communication
		9.2.4. Electromagnetic field (EMF) generation and corona effects in transmission lines
			9.2.4.1. Generation of EMFs
				Electric field strength E
			9.2.4.2. Application Example 9.2: Lateral profile of electric field at ground level below a three-phase transmission line
				Magnetic field strength H
			9.2.4.3. Application Example 9.3: Lateral profile of magnetic field at ground level under a three-phase transmission line
			9.2.4.4. Mechanism of corona
			9.2.4.5. Factors reducing the effects of EMFs
				Active shielding or cancellation/compensation of EMFs
				Passive shielding/mitigation using bypassing networks
			9.2.4.6. Factors influencing generation of corona
			9.2.4.7. Application Example 9.4: Onset of corona in a transmission line
			9.2.4.8. Negative effects of EMFs [50,51] and corona
				Biological effects of electric fields E on people and animals
				Suggested biological effects of magnetic fields H and B on people and animals
				Effects of corona
			9.2.4.9. Solutions for the minimization of EMFs, corona, and other environmental concerns in newly designed transmission  ...
				EMFs
				Visual impact
				Audible noise, radio interference (RI), and television interference (TVI) caused by corona
				Ozone (O3) and NOx generation
				Impact of physical location of transmission lines
			9.2.4.10. Economic considerations
			9.2.4.11. No-cost/low-cost EMF mitigation hearings of PUC of California [52]
			9.2.4.12. Summary and conclusions
		9.2.5. Distributed-, cogeneration, and frequency/voltage control
			9.2.5.1. Application Example 9.5: Frequency control of an interconnected power system broken into two areas: The first on ...
			9.2.5.2. Application Example 9.6: Frequency control of an interconnected power system broken into two areas: The first on ...
	9.3. Tools for detecting poor power quality
		9.3.1. Sensors
		9.3.2. Application Example 9.7: Detection of harmonic power flow direction at point of common coupling (PCC)
		9.3.3. Maximum error analysis
			9.3.3.1. Review of existing methods
			9.3.3.2. Approach
			9.3.3.3. Accuracy requirements for instruments
			9.3.3.4. Application Example 9.8: Conventional approach PLoss=Pin-Pout
		9.3.4. Application Example 9.9: New approach pcu=i2(v1-v2) and pfe=v1(i1-i2)
		9.3.5. Application Example 9.10: Back-to-back approach of two transformers measured with CTs and PTs
		9.3.6. Application Example 9.11: Three-phase transformer with DC bias current
		9.3.7. Discussion of results and conclusions
		9.3.8. Uncertainty analysis [102]
		9.3.9. SCADA and National Instrument LabVIEW software [103]
	9.4. Tools for improving reliability and security
		9.4.1. Fast interrupting switches and fault-current limiters
			9.4.1.1. Fast interrupting switches (FIS)
			9.4.1.2. Fault-current limiters (FCLs)
		9.4.2. Application Example 9.12: Insertion of a fault current limiter (FCL) in the power system
		9.4.3. Intentional islanding, interconnected, redundant, and self-healing power systems
		9.4.4. Definition of problem
		9.4.5. Solution approach
			9.4.5.1. What can be done to prepare the power system prior to an emergency?
			9.4.5.2. What should be done during the failure?
			9.4.5.3. What will be done after the failure has occurred?
			9.4.5.4. What strategies for efficiency improvements and maintaining regulatory constraints must be addressed?
			9.4.5.5. Reliability
			9.4.5.6. Demand-side management programs
		9.4.6. Voltage regulation, ride-through capabilities of load components; CBEMA, ITIC tolerance curves, and SEMI F47 standard
			9.4.6.1. Voltage regulation VR
			9.4.6.2. Voltage-tolerance CBEMA and ITIC curves
			9.4.6.3. SEMI F47 standard
		9.4.7. Application Example 9.13: Ride-through capability of computers and semiconductor manufacturing equipment
		9.4.8. Backup, emergency, or standby power systems (diesel-generator set, batteries, flywheels, fuel cells, and supercapa ...
		9.4.9. Automatic disconnect of distributed generators in case of failure of central power station(s)
	9.5. Load shedding and load management
	9.6. Energy-storage methods
	9.7. Matching the operation of intermittent renewable power plants with energy storage
		9.7.1. Application Example 9.14: Peak-power tracker [56] for photovoltaic power plants
	9.8. Summary
	9.9. Problems
	References
	Additional bibliography
Chapter 10: The roles of filters in power systems and unified power quality conditioners
	10.1. Types of nonlinear loads
	10.2. Classification of filters employed in power systems
	10.3. Passive filters as used in power systems
		10.3.1. Filter transfer function
			10.3.1.1. Impedance transfer functions
			10.3.1.2. Current-divider transfer functions
			10.3.1.3. Voltage-divider transfer functions
		10.3.2. Common types of passive filters for power quality improvement
			10.3.2.1. First-order, high-pass filter
			10.3.2.2. First-order damped high-pass filter
			10.3.2.3. Second-order band-pass filter
			10.3.2.4. Second-order damped band-pass filter
			10.3.2.5. Composite filter
		10.3.3. Classification of passive power filters
		10.3.4. Potentials and limitations of passive power filters
		10.3.5. Application Example 10.1: Hybrid passive filter design to improve the power quality of the IEEE 30-bus distributi ...
	10.4. Active filters
		10.4.1. Classification of active power filters based on topology and supply system
		10.4.2. Classification of active power filters based on power rating
	10.5. Hybrid power filters
		10.5.1. Classification of hybrid filters
	10.6. Block diagram of active filters
	10.7. Control of filters
		10.7.1. Derivation of reference signal using waveform compensation
			10.7.1.1. Waveform compensation using time-domain filtering
			10.7.1.2. Waveform compensation using frequency-domain filtering
			10.7.1.3. Other methods for waveform compensation
		10.7.2. Derivation of compensated signals using instantaneous power compensation
			10.7.2.1. Application Example 10.2: Instantaneous power for sinusoidal supply voltages and distorted load currents
			10.7.2.2. Application Example 10.3: Instantaneous power consumed by a resistive load subjected to distorted supply voltages
			10.7.2.3. Application Example 10.4: Supply current distortion caused by active filters with instantaneous power-based con ...
		10.7.3. Derivation of compensating signals using impedance synthesis
			10.7.3.1. Impedance-based blocking
			10.7.3.2. Impedance-based compensation
		10.7.4. DC bus energy balance
		10.7.5. Generation of compensation signal using reference-following techniques
		10.7.6. Application Example 10.5: Hybrid of passive and active power filters for harmonic mitigation of six-pulse and twe ...
	10.8. Compensation devices at fundamental and harmonic frequencies
		10.8.1. Conventional compensation devices
		10.8.2. Flexible AC transmission systems (FACTS)
			10.8.2.1. Shunt FACTS controllers
			10.8.2.2. Series FACTS controllers
			10.8.2.3. Combined shunt-series FACTS controllers
			10.8.2.4. FACTS controllers with storage
			10.8.2.5. Development of FACTS controllers
		10.8.3. Custom power devices
		10.8.4. Active power line conditioner (APLC)
		10.8.5. Remark regarding compensation devices
	10.9. Unified power quality conditioner (UPQC)
		10.9.1. UPQC structure
		10.9.2. Operation of the UPQC
			10.9.2.1. Operation of the UPQC with unbalanced and distorted system voltage and load current
			10.9.2.2. Operation of UPQC with unbalanced system voltages and load currents
	10.10. The UPQC control system
		10.10.1. Pattern of reference signals
	10.11. UPQC control using the Park (dqo) transformation
		10.11.1. General theory of the Park (dq0) transformation
		10.11.2. Control of series converter based on the dq0 transformation
		10.11.3. Control of shunt converter relying on the dq0 transformation
		10.11.4. Control of DC link voltage using the dq0 transformation
	10.12. UPQC control based on the instantaneous real and imaginary power theory
		10.12.1. Theory of instantaneous real and imaginary power
			10.12.1.1. Application Example 10.6: The αβ0 transformation for three-phase sinusoidal system supplying a linear load
			10.12.1.2. Application Example 10.7: The αβ0 transformation for three-phase sinusoidal system supplying a nonlinear load
			10.12.1.3. Application Example 10.8: The αβ0 transformation for unbalanced three-phase, four-wire system supplying a line ...
		10.12.2. UPQC control system based on instantaneous real and imaginary powers
			10.12.2.1. Phase-lock loop (PLL) circuit
			10.12.2.2. Positive-sequence voltage detector
			10.12.2.3. Control of shunt converter using instantaneous power theory
			10.12.2.4. Control of DC voltage using instantaneous power theory
			10.12.2.5. Control of series converter using instantaneous power theory
	10.13. Performance of the UPQC
		10.13.1. Application Example 10.9: Dynamic behavior of UPQC for current compensation
		10.13.2. Application Example 10.10: UPQC compensation of voltage harmonics
		10.13.3. Application Example 10.11: UPQC compensation of voltage imbalance
		10.13.4. Application Example 10.12: Dynamic performance of UPQC for sudden voltage variation
		10.13.5. Application Example 10.13: Damping of harmonic oscillations using a UPQC
		10.13.6. Application Example 10.14: UPQC compensation of flicker
	10.14. Summary
	References
Chapter 11: Optimal placement and sizing of shunt capacitor banks in the presence of harmonics
	11.1. Reactive power compensation
		11.1.1. Benefits of reactive power compensation
			11.1.1.1. Improved voltage profile
			11.1.1.2. Reduced power system losses
			11.1.1.3. Released power system capacity
			11.1.1.4. Increased plant ratings
			11.1.1.5. Capital deferment
		11.1.2. Drawbacks of reactive power compensation
			11.1.2.1. Resonance
			11.1.2.2. Harmonic resonance
			11.1.2.3. Magnification of capacitor-switching transients
			11.1.2.4. Overvoltages
	11.2. Common types of distribution shunt capacitor banks
		11.2.1. Open-rack shunt capacitor bank
			11.2.1.1. Internally fused open-rack capacitor bank
			11.2.1.2. Externally fused open-rack capacitor bank
			11.2.1.3. Fuseless open-rack capacitor bank
		11.2.2. Pole-mounted capacitor bank
		11.2.3. Modular capacitor bank
		11.2.4. Enclosed fixed capacitor bank
		11.2.5. Enclosed switched capacitor bank
	11.3. Classification of capacitor allocation techniques for sinusoidal operating conditions
		11.3.1. Analytical methods
			11.3.1.1. Drawbacks of analytical methods
		11.3.2. Numerical programming methods
			11.3.2.1. Drawbacks of numerical programming methods
		11.3.3. Heuristic methods
			11.3.3.1. Drawbacks of heuristic methods
		11.3.4. Artificial intelligence-based (AI-based) methods
			Drawbacks of AI-based methods
			11.3.4.1. Genetic algorithms
				Genetic representation
				Structure of chromosomes
				Initialization
				Evaluation (fitness) function
				Genetic operators
				Genetic parameters
				Convergence criterion
				Flowchart of genetic algorithm for capacitor placement and sizing
				Drawbacks of genetic algorithms
			11.3.4.2. Expert systems
			11.3.4.3. Simulated annealing
			11.3.4.4. Artificial neural networks
				Drawbacks of artificial neural networks
			11.3.4.5. Fuzzy set theory
				Fuzzy logic and fuzzy inference system
				Fuzzy sets
				Membership function
				Fuzzy logic operators
				Fuzzy if-then rules
				Implication
				Fuzzy inference
				Defuzzification
				Fuzzy expert system for capacitor placement and sizing
				Drawbacks of fuzzy set theory
		11.3.5. Graph search algorithm
			11.3.5.1. Drawbacks of graph search algorithm
		11.3.6. Particle swarm algorithm
			11.3.6.1. Drawbacks of particle swarm algorithm
		11.3.7. Tabu search algorithm
			11.3.7.1. Drawbacks of tabu search algorithm
		11.3.8. Sequential quadratic programming
			11.3.8.1. Drawbacks of sequential quadratic programming
		11.3.9. Application Example 11.1: Fuzzy capacitor placement in an 11kV, 34-bus distribution system with lateral branches  ...
		11.3.10. Application Example 11.2: Genetically optimized placement of capacitor banks in an 11kV, 34-bus distribution sys ...
	11.4. Optimal placement and sizing of shunt capacitor banks in the presence of harmonics
		11.4.1. Reformulation of the capacitor allocation problem to account for harmonics
			11.4.1.1. System model at fundamental and harmonic frequencies
			11.4.1.2. Constraints
			11.4.1.3. Objective function (cost index)
		11.4.2. Application of maximum sensitivities selection for the capacitor allocation problem
			11.4.2.1. Sensitivity functions for MSS
			11.4.2.2. The MSS algorithm
			11.4.2.3. Convergence of the MSS algorithm
		11.4.3. Application of local variation for the capacitor allocation problem
		11.4.4. A hybrid MSS-LV algorithm for the capacitor allocation problem
		11.4.5. Application Example 11.3: Optimal placement and sizing of capacitor banks in the distorted 18-bus IEEE distributi ...
		11.4.6. Fuzzy approach for the optimal placement and sizing of capacitor banks in the presence of harmonics
			11.4.6.1. Sensitivity of objective function and THDv
				Sensitivity of objective function
				Sensitivity of THDv
			11.4.6.2. Fuzzy implementation
				Fuzzification of sensitivities
				Fuzzification of objective function and constraints
				Fuzzy combination of membership functions
				Alpha-cut process
				Analysis
			11.4.6.3. Solution methodology
		11.4.7. Application Example 11.4: Optimal placement and sizing of capacitor banks in the distorted 18-bus IEEE distributi ...
		11.4.8. Optimal placement, replacement, and sizing of capacitor banks in distorted distribution networks by genetic algor ...
			11.4.8.1. Genetic algorithm
				Structure of chromosomes
				Fitness functions
				Genetic operators
				Convergence criterion
			11.4.8.2. Solution methodology
		11.4.9. Application Example 11.5: Optimal placement and sizing of capacitor banks in the 6-bus IEEE distorted system
		11.4.10. Application Example 11.6: Optimal placement and sizing of capacitor banks in the 18-bus IEEE distorted system
			11.4.10.1. Computing time
		11.4.11. Genetically optimized fuzzy placement and sizing of capacitor banks in distorted distribution networks
			11.4.11.1. Solution method
				Structure of chromosomes
				Fuzzy fitness (suitability) functions
				Suitability of THDv (STHDv)
				Suitability of voltage (SV)
					Cost index (cost)
					Fitness (suitability) of a chromosome (Schrom)
				Genetic operators
			11.4.11.2. Solution methodology
		11.4.12. Application Example 11.7: Genetically optimized fuzzy placement and sizing of capacitor banks in the 18-bus IEEE ...
			11.4.12.1. Analysis and convergence criterion of the GA-FL algorithm
		11.4.13. Application Example 11.8: Genetically optimized fuzzy placement and sizing of capacitor banks in the 123-bus IEE ...
			11.4.13.1. Analysis and convergence criterion
	11.5. Summary
	References
Chapter 12: Power quality solutions for renewable energy systems
	12.1. Energy conservation and efficiency
		12.1.1. Future plans for implementation of renewable energy sources: Europe
		12.1.2. Application example 12.1: Efficient residence in Germany where photovoltaic (PV) generation exceeds total energy  ...
		12.1.3. Application Example 12.2: Energy conservation within residences
		12.1.4. Tiered energy rates
		12.1.5. Solutions to power quality problems
	12.2. Photovoltaic and thermal solar (power) systems
		12.2.1. System integrated mode
		12.2.2. Stand-alone mode
		12.2.3. Solutions to power quality problems of photovoltaic and thermal solar systems
		12.2.4. Custom power devices
			12.2.4.1. Pulse-width-modulated (PWM) rectifier
			12.2.4.2. Current-controlled PWM inverter
		12.2.5. Operation at maximum power point
		12.2.6. Safety considerations
		12.2.7. Solutions to power quality problems of custom power devices with switching action
	12.3. Horizontal and vertical-axes wind power (WP) plants
		12.3.1. Mechanical and electronic gears
		12.3.2. Basic principle of (V.p)/f and (V/f.N) control of electronic gear [79,80]
			12.3.2.1. Starting and motoring operation
			12.3.2.2. Generator operation
			12.3.2.3. Experimental verification [84]
			12.3.2.4. Optimization of torque production during start-up
			12.3.2.5. The need for current snubbers
			12.3.2.6. Generator operation
			12.3.2.7. Conclusions with respect to electronic gears
			12.3.2.8. Solutions to power quality problems of wind power plants with mechanical gears
		12.3.3. Influence of tower on energy production and flicker
		12.3.4. Constant-speed wind power (WP) plants
		12.3.5. Variable-speed wind power plants
		12.3.6. Operation of wind farms
		12.3.7. Control of wind power systems
		12.3.8. Maximum power extraction from horizontal-axis wind turbine
		12.3.9. Vertical-axis wind turbines
		12.3.10. Solutions to power quality problems of wind power plants
		12.3.11. Short- and long-term energy storage systems
		12.3.12. Role and design of short-term and long-term storage plants [144]
		12.3.13. Storage devices for short-term and long-term plants
		12.3.14. Hydro-storage or pump-storage plants
			12.3.14.1. Application Example 12.3: Design of a 250MW pumped-storage, hydro-power plant [1]
		12.3.15. Flywheel storage
			12.3.15.1. Application Example 12.4: Design of a 10MWh flywheel short-term storage power plant [1]
		12.3.16. Battery storage
			12.3.16.1. Application Example 12.5: Design a 10MWh battery short-term storage plant
		12.3.17. Compressed-air storage
			12.3.17.1. Application Example 12.6: Design of a 100MW compressed-air storage facility
			12.3.17.2. Solutions to power quality problems of compressed-air storage
		12.3.18. Hydrogen generation and storage
			12.3.18.1. Application Example 12.7: Production of hydrogen based on electrolysis and its application with respect to ele ...
		12.3.19. Fuel cells
			12.3.19.1. Application Example 12.8: Calculation of the efficiency of a polymer electrolyte membrane (PEM) fuel cell used ...
			12.3.19.2. Solutions to power quality problems of fuel cells
		12.3.20. Molten salt storage
		12.3.21. Solutions to power quality problems of molten salt storage
	12.4. Complementary control of renewable plants with energy storage plants [144]
		12.4.1. Energy efficiency and reliability increases based on distributed generation of interconnected power system and is ...
		12.4.2. Distributed power plants
		12.4.3. Review of current methods and issues of present-day frequency and voltage control
		12.4.4. Control or frequency/load control of an isolated power plant with one generator only
			12.4.4.1. Application Example 12.9: Angular frequency change for a positive (acceptance) and a negative (rejection) load  ...
		12.4.5. Load/frequency control with droop characteristics of an interconnected power system broken into two areas each ha ...
			12.4.5.1. Application Example 12.10: Instability with identical droop characteristics and stability with different droop  ...
		12.4.6. Complementary operation of renewable plants with short-term and long-term storage plants analyzed with either Mat ...
			12.4.6.1. Application example 12.11: Operation of natural-gas fired and long-term storage plants with two renewable sourc ...
		12.4.7. Power quality issues due to renewable sources
		12.4.8. Control of voltage and reactive power
			12.4.8.1. Transition from central power station to distributed energy sources
		12.4.9. Frequency variations due to charging and discharging of storage plants of grid with renewable sources
			12.4.9.1. Simplified grid
			12.4.9.2. Limits on stability of transmission
			12.4.9.3. Nonconstant power output of renewable sources
		12.4.10. Reduced life time of storage plants
		12.4.11. Solutions to power quality problems due to renewable plants with energy storage systems
	12.5. AC transmission lines vs DC lines
		12.5.1. Solutions to power quality problems of high-voltage AC transmission lines
	12.6. Fast-charging stations for electric cars
	12.7. Off-shore renewable plants
	12.8. Metering
		12.8.1. Net metering
		12.8.2. Virtual net metering
		12.8.3. Feed-in tariff
	12.9. Other renewable energy plants
	12.10. Production of automotive fuel from wind, water, and CO2
	12.11. Water efficiency
	12.12. Village with 2600 inhabitants achieves energy independence
	12.13. Reduction of lifetime as a function of temperature
		12.13.1. Application Example 12.12: Aging/reduction of generation of photovoltaic power plant with mainly south orientation
		12.13.2. Application Example 12.13: Aging/reduction of generation of photovoltaic power plant with mainly west orientation
			12.13.2.1. Conclusion
	12.14. Paralleling of two power systems
	12.15. The TEXAS synchrophasor network
	12.16. Summary
	12.17. Problems
	References
Glossary of symbols, abbreviations, and acronyms
	A
Appendices
	Appendix 1: Sampling techniques
		A1.1 What criterion is used to select the sampling rate (see line 500 of two-channel program (Chapter 2, reference 81))?
		A1.2 What criterion is used to select the total number of conversions (line 850 of the two-channel program (Chapter 2, refe ...
		A1.3 Why are the two-channel program dimension and the array for the channel number not used for the five-channel program ( ...
		A1.4 What is the criterion for selecting the multiplying factor in Step 9 (0.0048828120.004883) for the two- and five-chann ...
		A1.5 Why is in Step 9 of the two-channel program (line 1254) the array DA(n+10) or DA(733), and in the five-channel program ...
	Appendix 2: Program list for Fourier analysis (Chapter 2, reference 81)
		A2.1 Fourier analysis program list
		A2.2 Output of the Fourier analysis program
	Appendix 3: Equipment for tests
		A3.1 The 9kVA three-phase transformer bank
		A3.2 The 4.5kVA three-phase transformer bank #1
		A3.3 The 4.5kVA three-phase transformer bank #2
		A3.4 The 15kVA three-phase transformer bank
		A3.5 Three-phase diode bridge
		A3.6 Half-controlled three-phase six-step inverter
		A3.7 Controlled three-phase resonant rectifier (Chapter 2, reference 12)
		A3.8 Controlled three-phase PWM inverter (Chapter 2, reference 12)
	Appendix 4: Measurement error of powers
		A4.1 Measurement error of powers
		A4.2 Nameplate data of measured transformers
Index
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