Influence of the earth connections of the PWM drive on the voltage constraints endured by the motor insulation

3.1 Equivalent circuit structure and hypothesis

The voltage stress analysis is made with an equivalent circuit that considers all the connections of the whole drive. The standard 50/60 Hz grid has its own earthing system, which imposes a ground wire connected to all the metallic frames accessible by users to the Earth’s conductive surface [31,32,33]. For widespread cases, the neutral point of the grid transformer is connected to a specific earth terminal and the grid ground wires to other earth terminals. Differential circuit breakers provide the protection of users when insulation faults occur.

Figure 6 shows the general circuit of the whole drive assuming an unsaturated induction machine. The voltage pulses are created by the IGBTs legs that make intermittent connections of the motor phases to the + or the − of the DC bus depending on the PWM pattern. The DC bus capacitance provides constant voltage. Each phase-to-phase voltage pulses has a constant magnitude because of the high value of the DC bus capacitance. The gate command of the two IGBTs of an inverter leg is made with a deadtime between the OFF and the ON command for avoiding any short-circuit of the DC bus during simultaneous commands. Despite this deadtime, the free-wheel diode offers a path to the phase current. This deadtime must be considered for studying the EMC of the inverter and the accuracy of the actual pulse width when compared with the command one. Considering the diodes, the three outputs of the inverter are always connected to the + or – pole of the DC bus. Consequently, the deadtimes do not significantly change the shape of the voltage pulse imposed on the input of the cable used to connect the motor.

Figure 6

Whole drive connected to the AC grid with its earthing system. The ground wire offers a path to the common-mode current resulting from the insulated gate bipolar transistor (IGBT) switchings and the complex coupling in the motor. The common-mode current flows through to the grid earth terminals and the phase wires of the grid cable.

The phase-to-phase voltages can take only three values + E B , − E B , or 0 , depending on the IGBT states as it can be seen on the experimental curves in Figure 2. The neutral point of the machine (N) is not connected anywhere; the voltage between this point and the motor frame connected to the ground (V _NG) depends on the electrical environment of the whole drive:

• the common-mode capacitance existing between the winding copper wire and the motor frame;

• the capacitances between the IGBT chips and the inverter heatsink, which is also connected to the ground wire;

• the HF equivalent circuit of the machine windings;

• the HF equivalent circuit of the connections, including the grounding system;

• the fast-fronted imposed by the IGBT legs to the phase-to-phase voltage (differential mode).

A global equivalent circuit is considered for studying the voltage stresses in the motor windings at the time scale of the oscillations observed on the Ph-to-N and N-to-G voltages. The whole drive acts as a perturbation source connected to the 4-conductor grid cable. The common-mode currents mainly due to the capacitances exist between the motor windings and its frame connected to the ground wire of the cables. The common-mode current loop is schematized in Figure 6 in green. This current comes from the voltage pulses imposed between phases A, B, and C by the inverter and the complex couplings between differential and common modes. Therefore, the ground connection circuit of the grid must be considered because it is a major part of the common-mode current loop.

Figure 7 shows the details of the inverter DC bus feeding system. The grid transformer is represented by 3 voltage sources e 1 ( t ) , e 2 ( t ) , and e 3 ( t ) , which form a perfect 3-phase balanced sine system ( e 1 ( t ) + e 2 ( t ) + e 3 ( t ) = 0 at any time) and the grid transformer leakage inductance λ . The neutral point of the grid transformer is connected to an earth terminal G T . The point G G represents the general grounding system of the grid, which is very often another ground terminal. The common-mode current flows through the earth between the two earth terminals and in two-phase wires of the grid cable because two diodes of the PD3 rectifier are at the ON state at any time.

Figure 7

DC bus feeding circuit of the industrial converter connected to the AC grid with a 4-wire standard cable.

The high value of the filtering capacitance C F creates a short-circuit for the high frequency (HF) differential mode currents coming from the inverter; the voltage E B can be supposed constant. The equivalent circuit shown in Figure 8 is obtained by splitting the DC source E B in two equal parts for creating a middle point O. The inverter parasitic common-mode capacitance C I represents the capacitances between the IGBT chips and the heatsink. The equivalent impedance Z OGI , between the middle point O and the inverter frame G I , depends on the equivalent circuit of the feeding cable and the earth resistance R G defined between the two earth terminals G G and G T . The IGBT leg common-mode capacitance of an IGBT leg is measured with the impedance analyzer connected between the heatsink and the three screws of the module connected together. The result is 85 pF per IGBT module; therefore, C I = 255 pF .

Figure 8

Equivalent circuit of the DC bus connected to the grid.

The three inverter legs can be modeled by the 3 voltage sources v _AO, v _BO, and v _CO presented in Figure 9. Each source imposes the voltage pulse defined by the PWM pattern presented in Figure 10 drawn for a ratio of 96 between the PWM switching frequency and the motor one (switching frequency of 4.8 kHz). When the command signal of the leg X (X = A, B, or C) is “1,” the upper IGBT is ON; the lower one is OFF; v XO = + E B / 2 . When the command is “ 0 ” v XO = − E B / 2 . At a large timescale, the three voltage sources v _AO, v _BO, and v _CO are made of many pulses defined by the PWM pattern. They are used as excitation sources for the equivalent circuit that simulates with SPICE, using the “Piece-Wise Linear” function. Each pulse is defined by four points (low value, high value, rise time, and fall time). A Matlab script has been developed for writting automatically the spice netlist.

Figure 9

Equivalent circuit of the PWM voltage source of the inverter fed by the industrial grid.

Figure 10

Elaboration of the PWM command of the inverter.

Figure 11 shows the equivalent circuit of the motor, which is supposed to operate in linear conditions; R P , L S , R S , and C S represent the HF behavior of the phase windings; they are associated with the phase resistance and inductance R and L. The parameters are determined with the experimental data. The phase resistance R is measured in DC ( R = 0.35 Ω ). The other parameters are estimated from the impedance spectrum of the phase windings presented in Figure 12. The impedance spectrum is measured with a HP4294 impedance analyzer connected to another machine, which has the same reference than the motor of the testing bench. The second motor is placed on an insulated plate because the impedance analyzer cannot operate in differential mode and the motor frame cannot be connected to ground. The impedance analyzer is used with short wires when the motor coupling connections are removed. Figure 13 can be helpful for interpreting this impedance spectrum. The 3-phase machine is made of six 34-turn coils per phase placed in the 36 stator slots. Each coil is made with a class 2 enameled wire and placed in two stator slots previously protected by polymer sheets (in white). This protection is mainly aimed at protecting the enameled wire from the remaining burrs of the magnetic core during the automatic winding process; it also reinforces the slot insulation. The thickness of this layer ( 250 μm) is large when compared with the insulation layer of the class 2 enameled wire of this diameter ( 40 μm ) . This picture shows that the turn-to-turn capacitance between adjacent turns in the slots and in the end-windings has a larger influence on the HF behavior a of coil than the copper–iron capacitance of the wires in contact with the slot insulation thicker layer.

Figure 11

Equivalent circuit of the motor winding.

Figure 12

Impedance spectrums of the motor phases of an identical motor insulated from ground and impedance computed with the RLC equivalent circuit.

Figure 13

Picture of a random winding of the experimental machine at the end of stator slots.

The parameters R P , L S , R S , C S , and L are computed from the specific points highlighted in the experimental impedance spectrum. The phase inductance L is calculated from the low-frequency point; R P is obtained from the parallel resonance point, this resistance includes the damping effect due to iron losses at the parallel resonance frequency. L S , R S , and C S are obtained from the main series resonance point by identification. Results are R P = 2.9 kΩ , L S = 2.8 μH , R S = 12 Ω , C S = 720 pF , and L = 3.2 mH . Calculation details are presented in [27]. This figure also shows an inductive behavior up to 100 kHz. Let us keep in mind that these parameters are obtained by identification; they do not represent directly the physical elements on the six coils of a phase but only the global behavior of a phase in a frequency range limited to the main series resonance.

The mutual inductance between two phases M = − 1.5 mH is measured at 50 Hz using a standard method. Let us remind that a perfect coupling between two identical stator coils of inductance L shifted by an electrical angle α is L cos ( α ) , which is − 0.5 L for a perfect 3-phase motor with coils shifted by α = 2 π 3 and 4 π 3 . The mutual inductances are implemented in the spice netlist using the coupling factor between the two inductances defined by (1).

The electromotive force of each phase e X ( t ) ( X = A , B or C ) are sine functions of time at the fundamental frequency (50 Hz); they correspond to the voltages induced by the rotating field supposed to have a sine spatial distribution along the machine airgap. The magnitudes and phase lag depend on the motor operating point they are computed with the complex equation (2) where V X ̲ is the fundamental voltage imposed by the inverter and I X ̲ is the corresponding phase current. ℒ = L − M is the three-phase inductance of the machine. The magnitude and the phase lag of the current is imposed by the motor operating point. The tests were made at no load ( I = 7 A RMS cos φ 0 = 0.2 ). This relation supposes a classical PWM command without any zero-sequence component at 50 Hz. Equation (3) is implemented in the SPICE netlist for phase A; the expressions are similar for phases B and C but with an additional phase lag of − 2 π / 3 and − 4 π / 3 .

The winding common-mode capacitance of each phase C CM = 22 nF is measured connecting the impedance analyzer between a phase and the frame of the second motor, posed on an insulated plate when the coupling connections are removed.

3.2 simplifications required for interpreting the N-to-G transient voltages

The measurements made on the industrial drive show a natural frequency at 56 kHz. Therefore, several simplifications can be made as follows:

• The series resonance of a motor phase at 3.5 MHz is out of the scope of the analysis; the corresponding components of the equivalent circuit can be removed ( L S , R S , C S ).

• The propagation time in the cable connecting the motor to the inverter can be neglected.

• At 56 kHz, the wavelength in a standard cable insulated with polyethylene is 3.6 km; for cable lengths under a quarter of the wavelength (900 m), the propagation effects can be neglected. The grid cable can be considered as an inductive circuit.

With these simplifications, the equivalent circuit used for simulating the neutral-to-ground voltage of the machine is shown in Figure 14. The experimental room is situated at about 120 m of the grid transformer taking the configuration of the distribution grid into account, distribution cable between the main distribution cabinet is a 5 × 25 mm 2 cable, which length is more or less 150 m, with a Neutral and a Ground wire. The specific data for this cable are as follows: 0. 0.45 mH/km and 440 mΩ/km . The neutral wire is not used in these experiments. The low-voltage grid earthing specifications are defined in the IEC 60364 standard [29]; the part 5.54 relative to the earthing arrangements defines only a maximum value of 100 Ω for the ground resistance. For the specific grid structure of the laboratory grid, the ground resistance can be estimated to R G ≈ 10 Ω .

Figure 14

Equivalent circuit for simulation N-to-G voltage of the machine.

3.3 Simulation results

Figure 15 shows the transient of the motor currents. It can be seen that the steady-state is reached in the third period; simulation results of voltage spikes must be taken in a short time window after t = 60 ms.

Figure 15

Transient state of the motor currents.

Figure 16 shows the simulation results in a short time window where one of the voltage sources remains constant as it is made for experimental results shown in Figure 5. This simulation shows a natural frequency of 47 kHz which is close to the 56 kHz of the measurements. The Ph-to-N voltage spikes are also similar.

Figure 16

Ph-to-N and N-to-G voltages simulated in a short time window where v AO = C te = + E B 2 .

4.1 Simulation results from interpretation

For interpreting the simulation results, a simulation is made without any common-mode capacitance ( C CM = 0 ). Results are shown in Figure 17. It can be seen that, with a zero common-mode capacitance, the motor Ph-to-N voltage is a perfect 5-level PWM waveform without any spike. Therefore, the slot capacitances existing between the motor frame have a major importance for estimating the voltage stress endures by the motor coils and their turn-to-turn insulation.

Figure 17

Ideal Ph-to-N voltage obtained without any common-mode capacitances with the same grounding connections.

Table 1 presents a synthesis of simulations made for several combinations of the grid cable lengths and the ground resistance. These values must be compared with the ideal case (Figure 17), where the maximum Ph-to-N voltage is 386 V. The first case corresponds to the case of an industrial grid with a ground wire connected to the transformer neutral point. This case is described in the IEC 60364 standard, which is used for ensuring user safety without any differential breaker when a direct contact occurs between a phase and a grounded frame. This grid architecture corresponds to the worst case because the damping factor of the oscillations excited by the PWM pulse fronts is very low. The most favorable case is obtained when the ground resistance has the highest possible value defined by the IEC 60364 standard. A better solution is possible for the insulated neutral point grid configuration, but this case is very rare.

A possible solution consists of adding a wire in the cable between the motor neutral point N and the DC bus middle point O. This middle point is easy to materialize by splitting the DC bus filtering capacitance C F into two equal parts connected in series. Additional resistances are required for stabilizing the DC value of the middle point potential because a slow drift that depends on capacitance leakage currents may occur. Figure 18 shows the corresponding simulation results. This figure also shows a strong reduction of the voltage pulses magnitude applied to the motor winding.

Figure 18

Ph-to-N simulated voltage for an additional O–N connection.

With such a reduction, the peak voltage stress endured by a motor phase is much under the value of the PDIV measured on a twisted pair, which is more or less 800 V _RMS (1,130 V _Peak) for a standard class 2 enameled wire [10]. Even in the most unfavorable case, where the first turn of the first coil is adjacent to the last one, the motor can be a guarantee as PD free, considering the addition of the shorter spikes due to the differential mode fast transient widely studied in many publications [17,18,19].

This solution is very effective from the insulation point of view, but it has a drawback considering the zero-sequence current that may flow in the additional wire of the connection cable. This problem can be overcome using a specific PWM pattern that can control the zero-sequence voltage of the inverter [34]. Standard PWM industrial drive is designed for a 3-wire connection of the motor, without any neutral wire, which corresponds to a quasi-infinite zero-sequence impedance. The proposed additional wire between the motor Neutral ant the DC bus middle point requires a specific design of the PWM pattern that can control the zero-sequence current flowing in a low impedance. However, solutions exist and are described in the scientific literature [35,36]. They are more complex and require a higher switching frequency.