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IEEE Press Editorial Board
Ekram Hossain, Editor in Chief

To those who have not been given the chance to get the education they wanted.

When people of similar frequencies come together, output is not a simple sum of individual work, but exponential. In science we term this phenomenon as resonance. Output at this stage is beyond any logical limit.

Ravindra Shukla

1.1 Electromagnetic emission frequency bands defined by PQ and EMC related standards.

1.2 Characteristic emission spectra of typical power electronic converters commonly used in contemporary applications.

1.3 General configuration of grid-connected ASD and EMC-related naming convention.

1.4 Fundamental CM currents loops in ASD.

2.1 Transistor switching losses for different shapes of voltage and current waveforms.

2.2 Typical simplified transistor's switching trajectories.

2.3 Parameters of rectangular waveform.

2.4 Linear envelope approximation of sinc function.

2.5 Continuous spectrum envelope of single rectangular pulse (upper characteristic) and line spectrum of rectangular pulse train.

2.6 Normalized envelope of rectangular waveform with different duty cycles.

2.7 Exemplary spectrum envelopes of typical rectangular simplified switching waveform, occurring in power electronic converter: pulse repetition frequency , switched voltage and different duty cycles , and 0.5% obtained for different switch-on times 50, 5, and , respectively.

2.8 Trapezoidal approximation of switching waveforms: —switched DC voltage; T—switching period; —voltage pulse duration; —voltage rise time; —voltage fall time.

2.9 Trapezoidal waveform represented as a convolution of two ideally rectangular waveforms.

2.10 Simplified linear spectrum envelope of trapezoidal waveform with rise time equal to fall time.

2.11 Examples of voltage spectra calculated using formula (2.10).

2.12 Analysis of spectrum envelop of trapezoidal waveform with different rise time and fall time.

2.13 Transistor switching waveform approximation by a number of trapezoidal segments.

2.14 S-shaped voltage waveform as an example of higher order voltage transition.

2.15 Simplified linearized spectra envelope of the S-shaped waveform.

2.16 Switching voltage waveform at output terminals of full-bridge DC--AC inverter supplied by DC bus voltage originated from grid-powered diode rectifier.

2.17 Spectrum of experimentally obtained voltage waveform presented in Figure 2.16 calculated using FFT method with graphically estimated linear asymptotes.

2.18 Transistor switching voltage waveform with ringing effects.

2.19 Spectral characteristic of voltage waveform presented in Figure 2.18.

3.1 Inverter's transistor switching states in correlation with output voltage vector.

3.2 All possible state changes in three-phase bridge controlled according to the strategy of only one converter's leg transition.

3.3 Graphical representation of carrier-based PWM sinusoidal modulation pattern for output vector located in sector .

3.4 Three-phase bridge transitions used during one modulation period.

3.5 Example of inverter output current loop reconfiguration during commutation process.

3.6 Example of converter's output voltage repolarization during commutation process.

3.7 Common and differential mode voltage components in AC motor.

3.8 Common and differential mode current components in AC motor.

3.9 Simplified representation of DM currents distribution at motor side of frequency converter.

3.10 Simplified representation of CM currents distribution at motor side of frequency converter.

3.11 Simplified representation of CM-to-DM voltages conversion in ASD.

3.12 Simplified representation of DM-to-CM voltages conversion in ASD.

3.13 CM voltage components resulting from voltage and impedance asymmetries occurring in three-phase power system.

3.14 Instantaneous asymmetry of line-side and motor-side currents of frequency converter in ASD.

3.15 DM currents distribution at converter's output side during active vectors switching.

3.16 CM currents distribution at converter's output side during active vectors switching.

3.17 Low- and high-frequency components of output currents of frequency converter.

3.18 Example of experimentally obtained three-phase voltages at terminals of AC motor fed by frequency converter.

3.19 Converters output voltage switching times during modulation of negative output currents (upper characteristic) and during modulation of positive output currents (lower characteristic).

3.20 Converter's output current distribution at the beginning of slow commutation process and lumped representation of CM and DM parasitic capacitances of motor cable and motor windings.

3.21 Converter's output voltage and current waveforms during slow and fast commutation processes.

3.22 DM parasitic current loops during slow commutation process after switching-off of the transistor .

3.23 CM parasitic current loops during slow commutation process after switching-off the transistor .

3.24 Distribution of converter's output currents after slow commutation process.

3.25 Measurement setup for HF current components at converter's output side.

3.26 Example of CM and DM currents distribution at converter's output side during fast type commutation.

4.1 Internal and external coupling paths between motor side and grid side of frequency converter.

4.2 Transistor-to-ground capacitances distribution in relation to converter's output terminals and DC bus.

4.3 Simplified representation of CM current couplings in DC bus.

4.4 Correlation of a phase input current and the input CM current of FC for low load of the ASD with no continuous DC current in the rectifier output.

4.5 DC bus voltages: positive bus bar —upper waveform; negative bus bar —lower waveform.

4.6 Calculated DC bus voltage components: differential mode —upper waveform; common mode —lower waveform.

4.7 Coupling paths of CM currents generated at the motor side toward the power grid.

4.8 Simplified representation of output-side CM current loops with exposed midpoint of DC bus voltage parasitically connected to ground via capacitances and .

4.9 Input and output CM currents of converter's correlated with DC bus voltages referenced to ground.

4.10 PWM-related DC bus voltage ripples during nonconducting state of the rectifier—left side (A) and during conducting state—right side (B).

4.11 Grid-side CM currents propagation paths in loaded phases.

4.12 Input-side CM current waveform during single pulse of line current of the rectifier operating in noncontinuous current mode.

4.13 Grid-side CM currents propagation paths in nonconducting phase.

5.1 Voltage and current waveforms at one of the converter's output terminals.

5.2 Converter's current subcomponents at one of the output terminals.

5.3 Different levels of complexity of circuit models used for analysis of iron core inductors. (a) With equivalent circuit-lumped components connected to inductor's terminals only. (b) With distributed equivalent parasitic capacitances correlated with winding's layers. (c) With parasitic capacitances distributed to each winding's turn.

5.4 Impedance characteristics of an inductor calculated with the use of circuit models of different complexity: model a—parasitic capacitances represented by 3 equivalent capacitances (Figure 5.3a) and model c—by 30 equivalent capacitances (Figure 5.3c).

5.5 Insertion loss of the inductor calculated based on circuit models of different complexity: model a—parasitic capacitances represented by 3 equivalent capacitances (Figure 5.3a) and model c—by 30 equivalent capacitances (Figure 5.3c).

5.6 Characteristic subranges of frequencies essential for generation of conducted emission in ASDs.

5.7 General schematic of conducted emission generation and propagation in ASD.

5.8 Output voltage , CM current , and motor current waveform during typical commutation process at converters output terminal.

5.9 Single-circuit representation of the generation loop of the output CM current transients.

5.10 Unbalancing of CM impedances of DC buses by reconnecting CM impedance of FC load .

5.11 Capacitive representation of coupling impedances in loop of single CM current transient generation during commutation process at one of FC terminals.

5.12 CM voltage ripples at FC DC bus during fast and slow voltage switching correlated to CM current transients.

5.13 Variations of magnitudes of CM current transients during one period of the motor operating current.

5.14 Absolute values of CM currents magnitudes during one-sixth of the motor operating current period.

5.15 Comparison of CM currents magnitudes generated during fast and slow switchings of the converter's output voltage.

5.16 Increased CM current transient magnitudes due to simultaneous fast voltage switchings in two outputs of FC.

5.17 Correlation of the overall CM current measured at the FC output side with CM current transients generated in each individual phase during one period of the controlled output frequency.

5.18 Comparison of the overall CM current measured at the FC output side with CM current transients generated in each phase individually.

5.19 Incomplete switchings of voltage at FC outputs during short switching-on sequences.

5.20 Remote type of a CM current transient generated in other two phases , , by CM current transient in the commutated phase .

5.21 Secondary CM current transients generated in other two phases , , by CM current transient in the commutated phase .

5.22 Characteristic subintervals during the period of controlled motor current meaningful for generated overall CM currents of FC.

6.1 Representation of a component with two terminals for DM signals analysis as one-port network (a) and for CM signals as two-port network (b).

6.2 Broadband circuit model and general theoretical DM impedance characteristic of capacitors.

6.3 Exemplary impedance–frequency characteristics of different types of capacitors used in power electronic applications: aluminum electrolytic capacitor (AEC), metalized polypropylene film capacitors (MKP).

6.4 Exemplary impedance–frequency characteristics of type X and Y capacitors commonly used for filtering of conducted emission at the grid side of power electronic converters.

6.5 One-port broadband circuit model and general theoretical impedance frequency characteristic of inductors.

6.6 Bode plot of impedance-frequency characteristics of evaluated exemplary inductor.

6.7 Frequency characteristics of equivalent impedance and resistance of the evaluated inductor.

6.8 Frequency dependence of the evaluated inductor's inductance and equivalent parasitic capacitance.

6.9 Realization of frequency-dependent inductance and resistance using the first Foster circuit model.

6.10 Sample of three-sectional circuit model of inductor's frequency dependent equivalent inductance and resistance.

6.11 Graphical representation of simplified method of modeling frequency-dependent inductances.

6.12 Characteristic resonance frequencies originated by distributed partial parasitic capacitances in the frequency range above the inductor's main self-resonance .

6.13 General concept of distribution of winding's partial parasitic capacitances.

6.14 Changes of equivalent parasitic capacitance and associated quality factor versus frequency.

6.15 Circuit model of distributed parasitic capacitances of an inductor—the First Cauer topology.

6.16 Simplified theoretical characteristic of input impedance of LC ladder circuit.

6.17 Topology and parameters of the developed ladder circuit model of inductor's DM impedance taking into account variable inductance and the most expressive internal parasitic resonances.

6.18 Modeled and experimental DM impedance–frequency characteristics of the evaluated inductor.

6.19 Ladder circuit model of dielectric losses increasing with frequency associated to parasitic capacitances.

6.20 Inductive and capacitive current components of the evaluated inductor–relative comparison.

6.21 Test setups for measurement of inductor's CM and DM impedances.

6.22 Comparison of CM and DM impedances of the evaluated inductor.

6.23 Test setups for measurement of unbalance of inductor's CM capacitances.

6.24 Inductor's impedance characteristics seen from both winding ends A and B used for estimation of unbalance of inductor's ground capacitances.

6.25 An example of two-port circuit model of the developed inductor with extracted parameters, relevant for analysis of CM currents propagation.

6.26 Simplified flat view of stator windings diagram of three phase AC motor with different categories of parasitic capacitive couplings between windings indicated.

6.27 Lumped representation of parasitic capacitances of AC motor windings referenced to the motor terminals.

6.28 Test setup for measurement of DM and CM impedance characteristic of AC motor windings.

6.29 DM impedance characteristics of windings of AC motors of different rated power.

6.30 CM impedance characteristics of windings of AC motors of different rated power.

6.31 Reduced representation of lumped parasitic capacitances of AC motor windings connected into star topology.

6.32 DM impedance characteristics measured for different phases of AC motor windings.

6.33 CM impedance characteristics measured for different phases of AC motor windings.

6.34 Comparison of DM and CM impedance characteristic of AC motor windings.

6.35 Changes of equivalent parasitic capacitances of AC motor windings with frequency.

6.36 Distributed representation of CM and DM parasitic capacitances of AC motor windings configured in star connection.

6.37 One-port representation of distributed parasitic capacitances of AC motor windings.

6.38 CM currents distribution in an LC ladder circuit model of AC motor windings.

6.39 Theoretical CM impedance characteristic of AC motor windings represented by the LC ladder circuit model.

6.40 Parameters of the ladder circuit model determined for 7.5 kW AC motor.

6.41 Comparison of CM impedance characteristics of 7.5 kW AC motor windings–measured and calculated using the developed ladder circuit model.

6.42 Geometry of transmission line formed by a single wire over the ground.

6.43 Per-unit parameters of single wire over grounded conducting plane: inductance , capacitance , and characteristic impedance .

6.44 Ladder representation of equally distributed parasitic capacitances and inductances of a wire.

6.45 Simplified impedance characteristic of a wire with the matched impedance at far end.

6.46 Simplified representation of oscillations of the wire impedance above characteristic transition frequency due to the wire resonances correlated to the wire length.

6.47 Simplified theoretical impedance characteristic of the power cable taking into account the effect of HF losses.

6.48 (a) Reflection coefficients presented on the complex plane as circles. (b) The impedance grid useful for graphically solving a impedance matching problem.

6.49 Smith chart representation of the complex reflection coefficient for differently unmatched lossy wires, for selected termination impedances; (a), (b), (c).

6.50 Equivalent parasitic capacitances of a three wire shielded cable with typical internal structure.

6.51 Test setups for measurement of CM and DM impedance characteristics of the motor cable.

6.52 DM and CM impedance characteristics of the tested cable in open- and short-circuit testing configurations.

6.53 Lossy TL circuit model of three-wire-shielded power cable characterized by per-unit parameters: resistances , inductances , DM and CM capacitances and , and conductances .

6.54 Graphical estimation of characteristic impedance of a cable for CM components of transferred signals.

6.55 Characteristic impedances of the cable calculated for CM and DM signal components based on the impedance characteristics measured in open- and short-circuit configuration.

6.56 CM and DM impedance characteristics of a cable–resonances resulting from the electrical length of a cable and impedances mismatch.

6.57 TL model of motor cable simplified to single wire representation adequate for analysis of single voltage transient generated during the FC output bridge commutation.

6.58 Experimentally identified parameters of a single wire TL model of the tested motor cable.

6.59 Comparison of the measured and modeled impedance characteristics of the tested motor cable.

7.1 Common mode currents' loops in ASD with shielded motor cable.

7.2 Simplified graphical estimation of the CM impedance characteristic of the motor with the feeding cable based on CM impedance characteristics of the motor and the cable.

7.3 Single-wire broadband circuit model of the complete load of FC designed for CM currents analysis in frequency domain.

7.4 CM impedance characteristics of motor with feeding cables of different lengths in comparison to CM impedance of same motor windings.

7.5 Comparison of calculated CM impedances of the motor and the motor with feeding cables of different lengths connected.

7.6 Comparison of measured CM impedances: of the motor windings, 100 m-long motor feeding cable, and the motor windings with feeding cable.

7.7 Signal reflections at the motor feeding cable ends.

7.8 Reflection characteristic at winding terminals of the evaluated AC motor.

7.9 Smith chart representation of complex reflection coefficient at terminals of the evaluated motor.

7.10 Influence of a matching network on reflection characteristics of FC load. (a) Without matching. (b) With an RC matching network.

7.11 Influence of impedance mismatch at the motor terminals on generated CM currents at the output side of FC and in the motor windings.

7.12 The rate of change of CM impedance of the FC load caused by the motor cable: measurement data for the evaluated motor and 100 m-long feeding cable.

7.13 Simulation results of the motor feeding cable influence on CM currents generated at the FC output for different cable lengths 10, 30, 100, and 300 m.

7.14 Measured CM currents at FC output for short (1 m) and long (100 m) motor feeding cables.

7.15 Characteristic frequency subranges associated with motor cable influence on CM currents generated at the output side of FC.

7.16 Transfer of CM currents generated at the FC output via 100 m-long feeding cable toward motor windings .

7.17 The influence of motor feeding cables of different lengths on CM currents magnitudes at motor terminals simulation results.

7.18 CM currents measured at motor's terminal for short (1 m) and long (100 m) feeding cables.

7.19 Correlation between CM currents generated at the output side of FC and injected into the power grid by the ASD with 100 m-long motor cable (upper graph) and transfer characteristics of CM currents generated at the output side of FC towards the grid side (lower graph): experimental results.

7.20 Comparison of CM currents injected into the power grid by the same ASD setup with short and long motor feeding cables (upper graph) and correlation between influence of the motor feeding cable on CM currents magnitudes at the output and grid sides of the ASD (lower graph): experimental results.

6.1 Categories of lumped parasitic capacitances of AC motor windings

6.2 Matrix of lumped parasitic capacitances of AC motor windings referenced to motor terminals

6.3 Short cable lengths estimated for characteristic frequencies associated to frequency range of conducted emission

6.4 Identified per unit parameters of the tested cable - 100m long, 3x2.5mm2, with braided shield