Investigation on Overvoltage Distribution in Stator Windings of Permanent Magnet Synchronous Wind Turbines

Abstract

The PWM voltage pulses output by the inverter reaches the stator winding of the wind turbine generator through the cable. Due to the impedance mismatch between the motor and the cable, the voltage at the motor end rises under the action of the circuit wave process; on the other hand, electromagnetic oscillation occurs within the motor winding. Higher overvoltage is generated under the combined effect of both, which greatly accelerates the aging and breakdown of the insulation layer of the permanent magnet synchronous wind turbine. In this paper, a three-dimensional electromagnetic model of the permanent magnet synchronous wind turbine generator is established. The distribution circuit parameters of the stator winding of the permanent magnet machine are calculated using the finite element method, and its circuit model is based. The voltage distribution of the stator winding under different PWM excitations is investigated by simulation software, and the effects of the time of the rising edge and the pulse width of the PWM pulse on the stator winding voltage to ground and the turn-to-turn voltage distribution are studied. The results show that the effect of the rising edge time is larger when the rising edge time is shorter, the maximum voltage to ground occurs in the first coil, and the amplitude can be up to 1.5 times of the output voltage. When the rising edge time is longer, the maximum voltage to ground occurs in the end coil, and the amplitude is slightly higher than the output voltage. The trend of turn-to-turn voltage variation is similar for different rising edges; only the maximum turn-to-turn voltage amplitude is different. Pulse width has a small effect on overvoltage and only occurs when the pulse width is less than 10 μs. The research results of this paper are of great significance in revealing the aging and breakdown mechanism of the generator stator insulation, as well as the insulation coordination and design.

1. Introduction

In 2023, 116.6 GW of new wind power capacity was added to the power grid worldwide, 50% more than in 2022, bringing total installed wind capacity to 1021 GW, a growth of 13% compared with last year [1]. For countries with large wind resources, such as China, Vietnam, and India, developing wind power is an effective way to solve the energy problem [2,3,4]. Wind turbines are the core components that convert wind energy into electricity, among which permanent magnet synchronous generators have become the main type of wind power generation due to their high power density, simple structure, and high reliability [5].

With the rapid development and extensive application of permanent magnet synchronous generators, the requirements for their insulation structure and materials are higher [6,7,8]. Research shows that 37% of the reasons are due to the damage of the stator winding insulation of the generator [9]. D. Hyypio [10] believes that the inverter switch generates a steep voltage wave due to the impedance mismatch between the cable and the stator winding. This causes the high-frequency pulse waves to undergo reflection processes between the cable and the stator winding and between the conductors of the stator winding, further causing the voltage wave to be unevenly distributed in the stator winding, which in turn generates a large reflected voltage wave through the long cables. Actual measurements of motor terminal voltages by C. Hudon, R. Kerkman et al. [11,12] have shown that the amplitude of the overvoltage can reach two to three times the amplitude of the power supply output pulse voltage. With further research, many scholars have found that this overvoltage can lead to partial discharges, thus damaging the insulation material [13]. With the challenges of maintenance and the high operating costs of wind turbines [14], studying the voltage distribution characteristics of wind turbine stator winding insulation under PWM pulse voltage is of great significance for improving the insulation protection level of the motor and reducing maintenance and operating costs.

Early motors used power-frequency voltage wave theory to design insulation, but it was soon discovered that under the action of PWM inverters, the insulation life was much less than the design expectation [15,16]. To study the influence of PWM pulse voltage on the insulation of stator windings, scholars have conducted much research on the overvoltage distribution of stator windings through simulation and experimental tests. M. K. Busch et al. proposed a high-frequency pulse voltage discharge model different from AC sinewave discharge, indicating that traditional sinewave power sources are not suitable for high-frequency conditions [17]. Wang Peng et al. designed a continuous high-voltage square wave test system to simulate partial discharge under the action of high-frequency PWM power sources and later discovered the relationship between surface charge of insulation film under high-frequency square wave pulse voltage and discharge [18]. Finally, through the comparison of sinewaves and square waves, it was found that the partial discharge amplitude between turns under square waves is about 10 times that of sinewaves, and the lifespan is reduced to 1/3 of sinewaves [19,20].

With the deepening of the research, some scholars have proposed that the amplitude of overvoltage and the frequency of oscillation are related to the rising edge time, pulse width, cable length, and other factors [21]. Skibinski et al. [22,23] studied the cable length, spike overvoltage amplitude, and high-frequency oscillation of the relationship between the cable length. With the growth of the cable length, the overvoltage amplitude increases, the oscillation frequency decreases; when the cable length reaches or exceeds a certain critical length, the motor end of the overvoltage amplitude generated by the motor is approximated to be 2 times the rated voltage. Research [24,25] on over-voltage and high-frequency oscillation suppression methods has been studied, and by adding reactors at both ends of the cable or converter output series reactor, the motor terminal voltage characteristics can be improved. Currently, research has made great strides in terms of the effects caused by cable length, but very limited research has been carried out on the effects of other factors on PWM power. Meanwhile, most of the previous studies have focused on the turn-to-turn voltages and obtained the corresponding results [26]. However, there are few studies on the variations and patterns of the voltage of their coils to ground.

Based on the above research, this paper uses simulation software to investigate the voltage distribution of each turn conductor in the stator winding coil under the action of PWM pulse waves with different rise times and pulse widths, obtaining the changing laws of the conductor-to-ground voltages for each turn conductor. We consider the distribution of voltage to ground while studying the turn-to-turn voltage distribution, and determine where the maximum voltage occurs, providing a basis for the subsequent improvement of the insulation structure.

2. Research on the Simulation Model and Distributed Parameters of Permanent Magnet Machine Stator Winding

2.1. Establishment of Equivalent Circuit Model for Stator Winding

This article conducts simulation calculation and analysis on a 6 MW permanent magnet synchronous wind turbine generator. The stator winding structure of the permanent magnet wind turbine generator consists of six parallel branches, each branch consisting of 4 coils in series, with each coil connected by five turns of conductors. The equivalent circuit is shown in Figure 1.

Each box in Figure 1 represents an equivalent coil. The circuit diagram of a single coil is shown in Figure 2:

The equivalent circuit model of the stator winding of a permanent magnet synchronous wind turbine generator is shown in Figure 2. In the diagram, C_g1–C_g5 represent the ground capacitances of the first to fifth conductor turns, C₁₂–C₄₅ represent the inter-turn capacitances between the first and second conductor turns to the fourth and fifth conductor turns, R₁–R₅ represent the equivalent resistances of the first to fifth conductor turns, and L₁–L₅ represent the equivalent inductances of the first to fifth conductor turns.

2.2. Establishment of the Stator Winding Electromagnetic Model

The rated voltage of the permanent magnet synchronous generator is 1380 V. Permanent magnet motors mainly include stator core, rotor core, stator slots, magnetic poles (N-pole, S-pole), conductor ends, and individual insulation. Among them, the stator and rotor models of permanent magnet wind turbine are shown in Figure 3.

As shown in Figure 3, the dark gray part represents the permanent magnet wind turbine (PMWT) stator core model, which consists of 288 slots, and the silver-white part represents the PMWT rotor model, which consists of 12 pairs (24) of magnetic poles, with the red color representing the N-pole and the blue color representing the S-pole.

The slot insulation and conductor-to-conductor insulation of the stator are both made of polyimide, and the interlayer insulation uses polyester fiber. Each coil of the stator has 5 conductors, and the distribution of the conductors is shown in Figure 4.

The three-dimensional finite element simulation model of the permanent magnet wind turbine built in ANSYS.Electronics.Suite.2023.R2 is finally shown in Figure 5.

2.3. Calculation of Stator Winding Distribution Parameters

2.3.1. Calculation of the Distribution Inductance of the Permanent Magnet Machine Stator Winding Using Finite Element Method

The method for obtaining the distributed inductance is to choose the static magnetic field solver in Ansys EM. The approach to solving the static magnetic field within the solution domain is to use the finite element method to partition the solution domain, perform element analysis on each element, and finally obtain the inductance values between each conductor.

Based on the established three-dimensional model and corresponding boundary conditions, it is necessary to determine the boundary conditions and current excitation sources during the solution process.

$${\displaystyle \frac{{\partial }^2{\phi }_m}{\partial x^2}}\overrightarrow{e_x}+{\displaystyle \frac{{\partial }^2{\phi }_m}{\partial y^2}}\overrightarrow{e_y}+{\displaystyle \frac{{\partial }^2{\phi }_m}{\partial z^2}}\overrightarrow{e_z}=0$$

(1)

$$H=-({\displaystyle \frac{\partial {\phi }_m}{\partial x}}\overrightarrow{e_x}+{\displaystyle \frac{\partial {\phi }_m}{\partial y}}\overrightarrow{e_y}+{\displaystyle \frac{\partial {\phi }_m}{\partial z}}\overrightarrow{e_z})$$

(2)

$${\displaystyle \oint \overrightarrow{H}·dl=\overrightarrow{I}}$$

(3)

$$\left\{\begin{array}{c}{I}_1={\displaystyle \frac{({\phi }_1-{\phi }_0)}{L_{10}}}+{\displaystyle \frac{({\phi }_1-{\phi }_2)}{L_{12}}}+\cdots +{\displaystyle \frac{({\phi }_1-{\phi }_k)}{L_{1k}}}+\cdots +{\displaystyle \frac{({\phi }_1-{\phi }_n)}{L_{1n}}}\\ ⋮\\ I_k={\displaystyle \frac{({\phi }_k-{\phi }_1)}{L_{k1}}}+{\displaystyle \frac{({\phi }_k-{\phi }_2)}{L_{k2}}}+\cdots +{\displaystyle \frac{({\phi }_k-{\phi }_0)}{L_{k0}}}+\cdots +{\displaystyle \frac{({\phi }_k-{\phi }_n)}{L_{kn}}}\\ ⋮\\ I_n={\displaystyle \frac{({\phi }_n-{\phi }_1)}{L_{n1}}}+{\displaystyle \frac{({\phi }_n-{\phi }_2)}{L_{n2}}}+\cdots +{\displaystyle \frac{({\phi }_n-{\phi }_k)}{L_{nk}}}+\cdots +{\displaystyle \frac{({\phi }_n-{\phi }_0)}{L_{n0}}}\end{array}\right.$$

(4)

I_t represents the current source excitation of the nth. Conductor H represents the magnetic field intensity, φ_m represents the magnetic potential function, e_x represents the unit vector along the x direction, and L_n0 represents the self-inductance of the n^th. Conductor and L_nk represent the mutual inductance between the n^th and k^th conductors.

The final calculation result is shown in

Table 1. Distributed Inductance of Permanent Magnet Wind Turbine Generators.

Inductance/μH	1st Conductor	2nd Conductor	3rd Conductor	4th Conductor	5th Conductor
1st conductor	16.0	15.4	14.9	14.3	13.8
2nd conductor	15.4	15.9	15.4	14.8	14.3
3rd conductor	14.9	15.4	15.9	15.4	14.8
4th conductor	14.3	14.8	15.4	15.8	15.4
5th conductor	13.8	14.3	14.8	15.4	15.8

Note: The diagonal in Table 1 represents the self-inductance of each turn conductor, while the others represent the mutual inductance between different conductors.

:

2.3.2. Calculation of the Distribution Capacitance of the Permanent Magnet Machine Stator Winding Using Finite Element Method

Unlike in the case of inductance-distributed parameters, when calculating capacitance-distributed parameters, the solution domain is the electrostatic field. At this time, the boundary conditions are different and the excitation source is:

$${\displaystyle \frac{{\partial }^2\phi }{\partial x^2}}\overrightarrow{e_x}+{\displaystyle \frac{{\partial }^2\phi }{\partial y^2}}\overrightarrow{e_y}+{\displaystyle \frac{{\partial }^2\phi }{\partial z^2}}\overrightarrow{e_z}=0$$

(5)

$$E=-({\displaystyle \frac{\partial \phi }{\partial x}}\overrightarrow{e_x}+{\displaystyle \frac{\partial \phi }{\partial y}}\overrightarrow{e_y}+{\displaystyle \frac{\partial \phi }{\partial z}}\overrightarrow{e_z})$$

(6)

$$\underset{\partial V}{\iint }E\cdot \mathrm{d}S={\displaystyle \frac{1}{{\epsilon }_0}}\sum _{q_{i}inV}{q}_i$$

(7)

$$\left\{\begin{array}{c}{q}_1=C_{10}({\phi }_1-{\phi }_0)+C_{12}({\phi }_1-{\phi }_2)+\cdots +C_{1k}({\phi }_1-{\phi }_k)+\cdots +C_{1n}({\phi }_1-{\phi }_n)\\ ⋮\\ q_k=C_{k1}({\phi }_k-{\phi }_1)+C_{k2}({\phi }_k-{\phi }_2)+\cdots +C_{k0}({\phi }_k-{\phi }_0)+\cdots +C_{kn}({\phi }_k-{\phi }_n)\\ ⋮\\ q_n=C_{n1}({\phi }_n-{\phi }_1)+C_{n2}({\phi }_n-{\phi }_2)+\cdots +C_{nk}({\phi }_n-{\phi }_k)+\cdots +C_{n0}({\phi }_n-{\phi }_0)\end{array}\right.$$

(8)

In the above formula, E represents the voltage source excitation, φ represents the electric potential function, e_x represents the unit vector along the x direction, ε₀ is the vacuum permittivity, q_i represents the charge on the n^th conductor, C_n0 represents the capacitance to ground of the n^th conductor, and C_nk represents the mutual capacitance between the n^th and k^th conductors.

The capacitance parameters to the ground of each turn of the conductor were obtained through simulation calculations, as shown in

Table 2. Ground capacitance of permanent magnet wind turbine generator.

Capacitance to Ground	Capacitance Value/pF
C1	496.3
C2	587.7
C3	620.4
C4	587.8
C5	492.2

Note: C1–C5 in the table represent the ground capacitance of the first coil conductor, the ground capacitance of the second coil conductor, the ground capacitance of the third coil conductor, the ground capacitance of the fourth coil conductor, and the ground capacitance of the fifth coil conductor, respectively.

.

The distribution parameters of inter-turn capacitance between adjacent conductors are shown in

Table 3. Turn-to-turn capacitance of permanent magnet wind generators.

Capacitance	Capacitance Value/pF
C1–2	1046.2
C2–3	1013.6
C3–4	978.8
C4–5	938.4

Note: C1–2 and C4–5 in the table represent the inter-turn capacitance between the first and second turns of the coil, between the second and third turns of the coil, between the third and fourth turns of the coil, and between the fourth and fifth turns of the coil, respectively.

.

2.3.3. Calculation of Equivalent Resistance of Permanent Magnet Machine Stator Windings

The equivalent winding resistance is calculated using the following Formula (9) considering the skin effect and proximity effect [27].

$$R={\displaystyle \frac{2l_{\mathrm{d}}}{\alpha \delta \sigma }}$$

(9)

In the above equation, R represents the resistance of the winding conductor, l_d is the length of the conductor, α is the circumference of the conductor cross-section, δ is the skin depth, σ is the electrical conductivity of copper. The calculated equivalent resistance of a single-turn coil is 0.26 Ω.

3. Research the Wave Process in the Winding under the Action of PWM Pulses

The waveform output at the wind turbine frequency converter end is a unipolar pulse wave with a sharp rising edge and a wide frequency band, as shown in Figure 6.

3.1. Study on the Influence of PWM Pulse Rising Edge on Overvoltage

Setting the PWM pulse output voltage to 2.8 kV, pulse width to 20 μs, and with a cable length of 4 m, the influence of different rising edge pulse voltage signals on the ground voltage and inter-turn voltage distribution characteristics of the winding is studied.

3.1.1. Study on the Influence of Rise Time on Ground-to-Ground Overvoltage

The voltage pulse wave in the winding undergoes reflection and superposition in the winding due to the mismatch of the stator winding coils and the distributed parameters in the cable when the rising edge is small. Since the equivalent frequency of the short rising edge is relatively high, the equivalent impedance of the end coil of the motor is relatively large, which has a more obvious effect on the input voltage impedance, resulting in a large voltage at the end. Figure 7 illustrates the terminal voltage distribution characteristics of the permanent magnet machine under different rising edges.

Voltage distribution characteristics of motor terminals under different rising edges, as shown in Figure 7.

From Figure 7, it can be seen that under different pulse rising edges, the voltage distribution between the stator winding terminals and the ground of different coil first-turn conductors is as follows. The abscissa in the figure represents the first-turn conductors in coils 1 to 5, where coils 1 to 4 show higher ground voltage on the first-turn and fifth-turn conductors under different rising edges. When the rising edge time is short, i.e., 0.1 μs and 0.2 μs, the maximum ground voltage of the entire stator winding is located at the first-turn conductor of coil 1, reaching up to 4.2 kV, which is 1.5 times the input voltage. The voltage on the fifth-turn conductor in coils 2, 3, and 4 is higher than that on the first-turn conductor, and, as the rising edge time increases, the highest voltage starts to shift towards the middle and back. For example, at rising edge times of 1 μs and 2 μs, the ground voltage on the first-turn conductor of coil 1 is 2.9 kV and 2.9 kV, respectively, with the voltage at the terminal close to the input voltage and lower in magnitude. On the other hand, the voltage on the last-turn conductor in coil 4 is 3.6 kV and 3.5 kV, respectively, which are 1.3 times and 1.2 times the input voltage, respectively, and the highest voltage is concentrated in the middle and back.

Figure 8 shows the evolution of the maximum grounding voltage of each conductor in the 4 coils inside the permanent magnet machine stator winding under different rising edge times of the pulse.

In Figure 8, it can be seen that the voltage distribution of the stator winding end of the motor and the ground voltage distribution of different coil starting conductors on the rising edges of different pulses. As the rising edge increases, the voltage at the end of the permanent magnet wind turbine generator stator winding gradually decreases. When the rising edge is steeper, the voltage reaches up to 1.5 times the power output voltage, that is, 4.2 kV. With the increase of the rising edge, there is a critical value of the rising edge. Before the critical value, the end overvoltage changes more obviously, and after the critical value, as the rising edge increases, the decrease of the end overvoltage is not obvious.

3.1.2. Study on the Influence of Rise Time on Turn-to-Turn Overvoltage

The distribution of the maximum voltage between adjacent conductors in the stator winding of a permanent magnet synchronous wind generator with 4 coils inside at different rising edge times of the PWM input pulses is shown in Figure 9.

Figure 9 shows the distribution characteristics of maximum inter-conductors voltage on different rising edges of windings.

The distribution of the inter-turn’s voltage between adjacent conductors in the stator windings of the motor under different pulse-rising edges can be seen in Figure 9. In the figure, 1-1-2, 1-2-3~4-3-4, and 4-4-5 represent the inter-turn numbers of adjacent conductors in coils 1, 2, 3, and 4 respectively. It can be seen that as the rising edge increases, the overall inter-turn voltage between conductors in the permanent magnet wind turbine generator stator windings gradually decreases. When the input pulse rising edge is relatively small, the first-turn conductor bears the maximum inter-turn voltage, which is also the highest for the first-turn conductor in different coils. Under different rising edges, when the rising edge time is short, the inter-turn potential difference borne by the conductors between the ends of the coils is larger. At 0.1 μs and 0.2 μs, the maximum inter-turn potential difference is concentrated between the 1st and 2nd conductors in coil 1, reaching up to 998 V, about 30 times the average winding voltage. As the rising edge increases, the distribution of the inter-turn voltage becomes more uniform. For example, under a rising edge time of 1 μs, the maximum voltage borne by the conductor is 263 V, located between the 2nd and 3rd conductors in the first end coil 1, about 8.8 times the average winding voltage. Under a rising edge time of 2 μs, the maximum voltage borne by the conductor is 163 V, located between the first and second conductors in the first end coil 1, about 5.5 times the average winding voltage.

3.2. Research on the Impact of PWM Pulse Width on Overvoltage

The width of the PWM pulse also has a certain impact on the overvoltage distribution of the stator winding of the permanent magnet synchronous generator. Ignoring the influence of other conditions, for the permanent magnet wind turbine generator input PWM pulse, its rising edge is set to 2 μs, pulse amplitude is set to 2800 V, cable length is set to 4m, and the pulse widths are set to 5 μs, 10 μs, 20 μs, and 40 μs, respectively. Study the influence of input pulse width on the overvoltage distribution.

3.2.1. The Impact of Pulse Width on the Overvoltage to Earth

Due to setting the same rising edge pulses, the overvoltage waveforms caused by the rising edges are completely identical. To investigate the effect of pulse width on overvoltage, the overvoltage generated by the first falling edge was selected for study. Figure 10 below shows the voltage to the ground of each turn conductor in the four coils generated by the falling edge with different pulse widths.

The distribution characteristics of winding-to-ground voltage at different pulse widths are shown in Figure 10.

Figure 10 shows the distribution of the maximum ground voltages of different conductors in the motor windings generated by the pulse falling edge under different pulse widths. As shown in the figure, the overall change is relatively small with the increase of the pulse width. The ground voltages of different conductors in the motor windings follow the following rule: with the increase of the pulse width, the overvoltage generated by the falling edge shows a trend of first increasing and then stabilizing. The reason for the increase is that the overvoltage generated by the rising edge in the process of voltage wave transmission in the stator winding is superimposed with the reflected overvoltage, hence showing an increasing trend. However, with the increase of the pulse width, the overvoltage generated by the rising edge has decayed to a very small level, and the overvoltage generated by the rising and falling edges do not affect each other. At this point, the overvoltage generated by the falling edge is consistent with the waveform of the overvoltage generated by the rising edge. Under a pulse width of 40 μs, the maximum magnitude of the ground voltage generated by the falling edge reaches 771 V and is located at the end coil.

3.2.2. The Impact of Pulse Width on the the Turn-to-Turn Overvoltage

Figure 11 shows the characteristics of maximum inter-turn voltage distribution of the winding at different pulse widths.

From Figure 11, the distribution of the inter-turn voltage between adjacent conductors of the stator winding under different pulse widths of the motor can be seen. In the same figure, 1-1-2, 1-2-3~4-3-4, and 4-4-5 respectively represent the inter-turn voltages between adjacent conductors 1-2, 2-3, 3-4, and 4-5 in coils 1, 2, 3, and 4. The black curve labeled in the figure represents the distribution of the inter-turn overvoltage generated by the rising edge of the pulse. It can be seen that with the increase of the pulse width, the inter-turn voltage of the stator winding shows a trend of first increasing and then stabilizing. The inter-turn overvoltage at the rising edge of the pulse is the same under different pulse widths, with a maximum value of 263.7, which is approximately 8.8 times the average voltage of the winding, located between conductors 2-3 in coil 1 of the stator winding. The inter-turn voltage between the conductors of the motor stator winding generated by the falling edge of the pulse gradually approaches the inter-turn voltage generated by the rising edge of the pulse. When the pulse width is 10 μs or more, the distribution pattern and amplitude of the waveform generated by the falling edge (black) are quite similar to those generated by the rising edge. The maximum inter-turn voltage appears when the pulse width is around 10 μs, reaching approximately 257 V.

4. Comparison of Simulation and Real Measurement for Verification

To further verify the validity of the model, the actual motor voltage is measured in this paper. In the actual measurement, the output amplitude of the oscilloscope is 2 V after passing through the voltage divider, so the simulation input voltage is set to 2 V as well. A comparison of the results obtained for the 0.1 μs rising edge case is shown in Figure 12 and Figure 13:

It can be seen that the rising phase of both waveforms consists of two steps, with the first starting to appear around 2.5 μs and the second starting to rise around 5 μs.

It can be seen that the voltage between coil 1 and coil 2 peaks first, followed by the voltage between coil 2 and coil 3. The voltage between coil 3 and coil 4 and the width of the voltage between coil 1 and coil 2 are about 2 μs, and then begin to decay. In 10 μs a trend of decay is shown, in which the highest voltage occurs in the first 2 μs.

In order to verify the simulation results under the effect of pulse width, the rising edge time is set to 1 μs and the pulse width is 5 μs, and the comparison of the results is shown in Figure 14 and Figure 15.

It can be seen that the measured and simulated waveforms are relatively similar, 5 μs to reach the falling edge of the pulse at this point in the waveform begins to decline and then ends at about 20 μs. The voltage size is coil 4, coil 3, coil 2, coil 1 in order.

Relative to the voltage to ground, the measured and simulated waveforms between the coils are overall similar, again first the voltage between coil 1 and coil 2 peaks first, followed by the voltage between coil 2 and coil 3, and the voltage between coil 3 and coil 4.

The above measured results show that the simulation model exists this validity and rationality.

5. Conclusions

This paper mainly investigates the effects of the rising edge and pulse width of PWM pulses on the ground voltage and inter-turn voltage distribution at the end of the stator winding coils of the permanent magnet machine. An equivalent circuit model of the stator winding of the permanent magnet machine is built using simulation software. By changing the rising edge and pulse width of the input PWM pulses, the distribution characteristics of the ground voltage and inter-turn voltage at the end of the stator winding coils are studied. The conclusions obtained are as follows:

(1) As the rising edge increases, the ground voltage of each turn of the conductor shows a gradually decreasing trend, and the position of the maximum ground voltage will move from the motor end towards the rear. Under a rising edge of 0.1 μs, the maximum ground voltage reaches 4.2 kV, appearing at the motor end, which is 1.5 times the input voltage; under a rising edge of 2 μs, the maximum ground voltage is 3.5 kV, appearing at the middle to rear part of the motor, which is 1.3 times the input voltage. Therefore, when using the method of increasing the rising edge to reduce overvoltage, the insulation condition at the mid-to-rear part of the motor should be considered. With the increase of the rising edge, the maximum turn-to-turn voltage in the motor stator winding decreases significantly. Under a rising edge of 0.1 μs, the highest turn-to-turn voltage can reach 998 V, occurring between conductors 1 and 2 in coil 1, about 30 times the average winding voltage; under a rising edge of 2 μs, the highest turn-to-turn voltage can reach 163 V, located between conductors 1 and 2 in coil 1, about 5.5 times the average winding voltage. At the same time, the distribution of turn-to-turn voltage will become more uniform.

(2) Pulse width plays a certain role in improving the ground voltage of the stator winding. With the increase of pulse width, if the overvoltage generated by the rising edge before the falling edge arrives has completely decayed, the overvoltage generated by the rising and falling edges is the same for the inter-turn voltage as well. Under different pulse widths, the maximum ground voltage is concentrated at the end coil of the stator winding, while the maximum inter-turn voltage is concentrated between conductors 2-3 in the first end coil of the stator winding.