# Impact of PWM Voltage Waveforms in High-Speed Drives: A Survey on High-Frequency Motor Models and Partial Discharge Phenomenon

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## Abstract

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## 1. Introduction

## 2. Partial Dicharges

## 3. Overview of the PWM Voltage Waveform Affecting the Insulation

#### 3.1. Microscopic Effects

#### 3.1.1. Effect of the Voltage Pulse Polarity

#### 3.1.2. Effect of Rise Time

#### 3.1.3. Effect of the Frequency

#### 3.2. Macroscopic Effects

## 4. Selection of the HF Motor Model

- Series connection of the stator/rotor resistance R and the leakage inductance ${L}_{d}$ to describe the low-frequency behaviour, which can be obtained by the locked rotor test with a fundamental frequency. However, the suggested value of the leakage inductance to be used in the HF motor model is not the one obtained by the locked rotor test but is calculated and estimated on the basis of the high-frequency impedance measurements.
- Resistance ${R}_{e}$ to account for eddy currents inside the magnetic core and the frame, estimated from the high-frequency impedance measurements.
- Capacitance ${C}_{t}$ representing the turn-to-turn distributed capacitive coupling, calculated and estimated according to the high frequency impedance measurement. Usually a very small value, which is much smaller than the winding to ground distributed capacitive coupling.

- The parameter C
_{g}represents the winding-to-ground capacitance. The parameter R_{g}is added in the circuit to represent the dissipative effects that are present in the motor frame resistance. - The circuit formed by the parameters ${R}_{t}$, ${L}_{t}$, and ${C}_{t}$ is the part of the network responsible to capture the second resonance in the frequency response, which is related to the winding turn-to-turn capacitance.
- The parameter ${R}_{e}$ is responsible to account for the losses introduced by the eddy current inside the magnetic core.
- To estimate the parameters of the high-frequency part of the model, it is suggested to replace the motor $dq$ model by a lumped-inductance, which represents the leakage inductance of the machine winding.

- Stator resistance ${R}_{s}$, obtained from the manufacturer’s tests.
- Core loss resistance ${R}_{core}$, which together with ${L}_{m}$ have an effect on rounding the reflected wave ringing wave shape. The value of ${R}_{core}$ is estimated.
- Rotor resistance ${R}_{r}$, rotor inductance ${L}_{rl}$, and slip s determined by using the manufacturer T-equivalent circuit values.
- Magnetizing inductance ${L}_{m}$ and IEEE Standard 112 fundamental frequency circuit value has been used.
- Stator Leakage Inductance ${L}_{ls}$ and IEEE Standard 112 fundamental frequency circuit value has also been used for the determination of its value.
- Stator First Turn Leakage Inductance $\eta {L}_{ls}$: one of the critical parameters in defining the DM motor high-frequency impedance, predicting the antiresonance point and setting the correct EMI leakage current to the ground in the CM circuit. It accounts for the fact that only a fraction of the total stator leakage inductance is attributed to the high-frequency antiresonance point, in particular the first few turns. It is estimated according to winding data and machine geometry.
- Stator-frame capacitance ${C}_{sf-effective}$: effective stator-to-frame capacitance of the first slot per phase, calculated from the machine geometry.
- Stator Turn-to-Turn Winding Capacitance ${C}_{sw}$: this parameter can be determined in different ways, for example by the heuristic method as a function of ${C}_{sf-effective}$.
- Stator initial frame-to-ground damping resistance $\mu {R}_{s}$: this component is the AC resistance of the fractional part of the total stator resistance ${R}_{s}$ associated with $\eta {L}_{ls}$. It affects the peak CM current as well as the damping of oscillations in the CM current to the ground, and, as it needs further research, it was not accounted for this analysis.

- ${R}_{g1}$ and ${C}_{g1}$ represent the parasitic resistance and capacitance between the stator winding and the motor frame, respectively.
- ${R}_{g2}$ and ${C}_{g2}$ represent the parasitic resistance and capacitance between the stator neutral and the motor frame, respectively.
- ${L}_{d}$ represents the stator winding leakage inductance.
- ${R}_{e}$ represents the high-frequency iron loss of the stator winding.
- ${L}_{t}$ and ${C}_{t}$ are introduced to capture the second resonance in the motor impedance characteristic, caused by the skin effect and interturn capacitance of the stator windings.

#### Comparison of Dynamic Behaviour of Different HF Motor Models

## 5. Conclusions and Suggestion for Future Work

- The connection of the PDs and steep PWM pulses coming from the modern power electronics devices working at higher switching frequencies, such as GaN and SiC devices, both as two-level and multi-level inverters.
- The definition of the critical cable lengths, PD occurance probabilities, critical pulse amplitudes, etc. for the drives supplied by WBG-based inverters.
- The guidelines for PD alleviation for the high-frequency inverters and high-speed drives application.
- The possible improvement in the insulation system of the machine, considering the effects of the high-switching frequency operation of the inverters: new dielectric materials have to be designed to resist the problems related to HF effects.
- Creation of the new standards and guidelines on the motor overvoltages considering the increasing usage of the WBG-based inverters.
- Development of the overvoltage mitigation techniques for WBG-based inverters.
- The improvement of the monitoring and prediction techniques for WBG-based high-speed drives: additional research needs to be carried out to improve current monitoring techniques in order to accurately diagnose the state of degradation of the electrical machine in order to prevent and reduce process downtime caused by unexpected motor failures and its cost.
- Further analysis and investigation on the electrical ageing of complex systems, e.g., more accurate analysis of macroscopic quantities.
- Developments of a simple but accurate models of HF motor, which can accurately model the interturn insulation and spot the presice location of the PD which and can be integrated in the prediction and monitoring techniques.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## References

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**Figure 5.**Schematic of a variable frequency drive highlighting the inverter, cable, and motor impedances.

**Figure 7.**Relationship between partial discharge and breakdown behavior of typical turn insulations; figure extrapolated from experimental data of the work conducted by Kaufhold et al. [41].

**Figure 8.**Average number of surges to failure of Type I crossed pair specimens subjected to square wave voltage having different rise times and frequencies; figure extrapolated from experimental data of the work conducted by Wang et al. [62].

**Figure 9.**Relationship between lifetime values and different voltage frequencies; figure extrapolated from experimental data of the work conducted by Wang et al. [62].

**Figure 11.**Three-terminal HF equivalent circuit of the coil proposed in [69].

**Figure 12.**HF phase circuit proposed in [71].

**Figure 13.**HF phase circuit proposed in [75].

**Figure 14.**HF phase circuit proposed in [76].

**Figure 15.**HF phase circuit proposed in [78].

**Figure 16.**HF phase circuit proposed in [79].

**Figure 17.**HF phase circuit proposed in [80].

**Figure 18.**HF phase circuit proposed in [81].

**Figure 21.**Comparison between the experimental voltage at motor terminals and voltages of different HF models for 32 kHz switching frequency and 30 m long lead (

**a**) the whole waveform and (

**b**) zoom indicated in (

**a**).

**Table 1.**Influence of the features of machine terminal voltage on components of Type I insulation systems.

Insulation Component | Fundamental Frequency | Impulse Voltage Repetition Rate | Peak/Peak Impulse Voltage (Fundamental Frequency) | Peak/Peak Impulse Voltage (Impulse Frequency) | Jump Voltage | Rise Time |
---|---|---|---|---|---|---|

Turn to turn insulation | ∘ | ∘ | ∘ | ∘ | • | • |

Main wall insulation | ∘ | ∘ | • | • | ∘ | ∘ |

Phase/phase insulation | ∘ | ∘ | • | • | ∘ | ∘ |

Stress Category | Overshoot OF (${\mathit{U}}_{\mathbf{peak}}$/${\mathit{U}}_{\mathit{d}\mathit{c}}$) | Rise Time ($\mathsf{\mu}$s) | Overvoltage (kV/$\mathsf{\mu}$s) |
---|---|---|---|

IEC Std. | |||

A—Benign | OF ≤ 1.1 | 0.2 ± 0.1 * | max 11${U}_{dc}$ |

B—Moderate | 1.1 ≤ OF ≤ 1.5 | 0.2 ± 0.1 * | max 15${U}_{dc}$ |

C—Severe | 1.5 ≤ OF ≤ 2 | 0.2 ± 0.1 * | max 20${U}_{dc}$ |

D—Extreme | 2 ≤ OF ≤ 2.5 | 0.2 ± 0.1 * | max 25${U}_{dc}$ |

NEMA Std. | |||

PD-free voltage | OF ≤ 1.39 | 0.1 | 13.9${U}_{dc}$ |

withstand voltage | OF ≤ 1.93 | 0.1 | 19.3${U}_{dc}$ |

Model | [70] | [71] | [75] | [76] | [78] | [79] | [80] | [81] | [82] |
---|---|---|---|---|---|---|---|---|---|

Number of comp./phase | 14 | 6 | 9 | 11 | 9 | 9 | 19 | 17 | 27 |

Frequency range | 10 kHz–2 MHz | 1 kHz–1 MHz | 1 kHz–1 MHz | 10 Hz–10 MHz | up to 30 MHz | 100 Hz–10 MHz | 150 kHz–30 MHz | 1kHz–13 MHz | 10 kHz–1 MHz |

Y-winding connection | x | x | x | x | - | x | x | x | x |

Δ-winding connection | x | possible | x | x | - | - | - | x | - |

Physical meaning | x | x | x | x | - | x | x | x | x |

Inter-turn effects | x | x | x | x | - | x | x | x | x |

Equations for parameters calculation | - | x | x | x | x | x | - | x | x |

Model accuracy | discrepancies reported | x | x | except CM current | non for simpler model | x | x | x | x |

Motor Parameter | Unit | Value |

Output power | kW | 0.37 |

Full load speed | rev/min | 1370 |

Rated voltage (Y/$\Delta $) | V | 230/400 |

Rated current (Y/$\Delta $) | A | 1.93/1.11 |

Locked rotor current | p.u. | 3.6 |

Full load torque | Nm | 2.58 |

Insulation class (temp. rise) | -K | F(80) |

Cable Parameter | Unit | Value |

${R}_{cable}$ | m$\mathsf{\Omega}$/m | 195.87 |

${L}_{cable}$ | $\mathsf{\mu}$H/m | 0.63 |

${C}_{cable}$ | pF/m | 63.33 |

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## Share and Cite

**MDPI and ACS Style**

D’Amato, D.; Loncarski, J.; Monopoli, V.G.; Cupertino, F.; Di Noia, L.P.; Del Pizzo, A. Impact of PWM Voltage Waveforms in High-Speed Drives: A Survey on High-Frequency Motor Models and Partial Discharge Phenomenon. *Energies* **2022**, *15*, 1406.
https://doi.org/10.3390/en15041406

**AMA Style**

D’Amato D, Loncarski J, Monopoli VG, Cupertino F, Di Noia LP, Del Pizzo A. Impact of PWM Voltage Waveforms in High-Speed Drives: A Survey on High-Frequency Motor Models and Partial Discharge Phenomenon. *Energies*. 2022; 15(4):1406.
https://doi.org/10.3390/en15041406

**Chicago/Turabian Style**

D’Amato, Davide, Jelena Loncarski, Vito Giuseppe Monopoli, Francesco Cupertino, Luigi Pio Di Noia, and Andrea Del Pizzo. 2022. "Impact of PWM Voltage Waveforms in High-Speed Drives: A Survey on High-Frequency Motor Models and Partial Discharge Phenomenon" *Energies* 15, no. 4: 1406.
https://doi.org/10.3390/en15041406