Using 3-Level Inverters to Reduce Bearing Damage

Pumps & Systems, June 2008

A look at how 3-level inverters can help reduce electrical damage to bearings.

PWM inverters introduce motor shaft voltages and bearing currents. The bearing damage in inverter-driven motors is mainly caused by the shaft voltage and bearing currents created by the common-mode voltage and its sharp edges [1]. All inverters generate common-mode voltages relative to the power source ground that cause coupling currents through the parasitic capacitances inside the motor. The main source of bearing currents is the capacitance-coupling currents that return via the motor bearings back to the ground. 

This paper describes the common-mode voltage in inverter-driven AC machines and compares them in 2-level and 3-level inverters. The relationship among common-mode voltage, motor shaft voltage and bearing currents are discussed using parasitic capacitances and its mathematical representation inside the motor. Test results of shaft voltage and bearing currents are presented to prove that 3-level technology has advantages over the 2-level inverter with regard to shaft voltage and bearing currents, which result in reduced bearing damage.

Common-Mode Voltage in Inverter-Driven Machines

Common-Mode Voltage

In a three-phase AC system, the common-mode voltage can be defined as the voltage difference between the power source ground and the neutral point of a three-phase load. If the load is an AC motor, the neutral point of the load means the stator neutral of the motor. It is important to define the common-mode voltage in mathematical terms in order to compare its characteristics among different types of source and load combinations.

In a three-phase AC system, the phase to ground voltage can be written as the sum of the voltage from phase to the neutral point of the load and the neutral point of the load to system ground. As per the definition, the common mode voltage is the voltage across the neutral point of the load and the system ground. Since in a balanced system, the sum of all three phase-to-neutral voltages is zero, the voltage from neutral to ground (common-mode voltage) can be defined in terms of phase to ground voltage as shown in Equation 1.

In Equation 1, it is assumed that the load is balanced so that the sum of all three phase-to-neutral voltages is zero (åV_a,b,c-N = 0). If the source is also assumed to be balanced and ideal, then the sum of all three phase-to-ground voltages is zero (åV_a,b,c-G = 0). Under such an ideal case, for a balanced AC motor driven by a balanced three-phase AC source, from Equation 1, the common mode voltage V_N-G  will be zero. However, in the case of an inverter-driven AC machine, a common-mode voltage exists because the voltage source inverter does not constitute an ideal balanced source. Figure 1 shows a typical 2-level voltage source inverter-fed AC machine.

In an inverter-driven system, the common mode voltage  (V_com or V_N-G) can also be defined as the voltage across the stator neutral (N) and the DC bus midpoint (M) because from a high-frequency viewpoint, the DC bus midpoint (M) is same as the electrical ground (G) of the system. Using this definition, the common-mode voltage can be redefined as in Equation 2. This definition would then be valid for 3-level inverters as well.

In Equation 2, it should be noted that the source voltage nomenclature has been changed from V_a,b,c-G  to V_u,v,w-M  to reflect the source as the voltage source inverter.

The common mode current (i_com)  is defined as the instantaneous sum-total of all the currents flowing through the output conductors. Stray capacitances of the motor cable and inside the motor are the paths of this current, and a source of EMI noise problems.

2-level Inverter

2-level voltage source inverters have eight different switching states for the six inverter-switches, and the voltages across the output terminals and the DC bus mid-point (V_U-M, V_V-M and V_W-M)  can be either +E/2 or -E/2 according to the inverter switching states. The three output legs could 1) all be connected to the positive or negative rail of the DC bus; 2) two legs can be connected to the positive rail and one leg to the negative rail or vice versa. Given these constraints and Equation 2, the inverter output neutral with respect to the DC bus midpoint will have a voltage of ±E/2 for condition 1) and a voltage of ±E/6 for condition 2). Figure 2 shows an example of the switching states and the common-mode voltage waveform.

During a PWM cycle, the change in voltage from -E/2 to -E/6 constitutes a change of E/3. When the level changes from -E/6 to +E/6, the change in voltage is again E/3. Since this change in voltage is proportional to the DC bus voltage and has a frequency equal to the inverter carrier frequency, the change in the common-mode voltage level is steep and typically occurs in hundreds of nanoseconds.

Figure 2. 2-level inverter switching states and the corresponding common-mode voltage

Since the motor windings are fed from PWM pulses having fast rising and falling common mode voltage edges, there exists a leakage current from each phase to ground due to the existence of various parasitic capacitances that include cable capacitance formed between the power leads and ground and other capacitances between the stator winding to the grounded frame. This leakage current that flows only during the step change in the common mode voltage is called common mode current.

Motor Shaft Voltage and Common-Mode Voltage

Parasitic Capacitances Inside the Motor

Figure 3 shows the various parasitic capacitances in an AC motor that become relevant when the motor is driven by a PWM voltage source inverter. The high dv/dt of the common mode voltage applied across the stator and grounded frame of the motor causes pulsed currents to flow through the parasitic capacitances shown in Figure 3. The parasitic capacitances shown are:

• Stator to Frame Capacitance (C_SF): The primary capacitance formed between the stator winding and the grounded frame, it is perhaps the largest single parasitic capacitance in the motor. Most of the common mode current due to the high dv/dt of the common mode voltage flows through this path.
• Stator to Rotor Capacitance (C_SR): This capacitance is formed in between the stator winding and the rotor frame. The value of this capacitance is small but is the principal path that charges the rotor body to which the motor shaft is physically connected. Hence, the value of this capacitance is important in evaluating the magnitude of the shaft voltage.
• Rotor to Frame Capacitance (C_RF): The rotor to frame capacitance completes the charging path that started from the stator winding to the rotor surface. The value of this capacitance is typically about ten times that of the stator winding to rotor surface capacitance (CSR). Since the voltage across a capacitor is inversely proportional to its capacitance value, most applied common mode voltage appears across CSR and only a small voltage is developed across CRF or the rotor to frame structure. This voltage is called the "shaft voltage." The rotor to frame capacitance is vital in establishing the shaft voltage.
• Shaft to Frame Capacitance or Bearing Capacitance (C_B): When the motor is rotated at or above a certain speed, the balls in a ball-bearing or rollers in a roller-bearing of the motor float up and occupy the space in between the inner and outer race of the bearing. An insulating film is formed by the lubricant medium in which the ball or roller is floating. The value of this capacitance depends on the shaft speed, type of lubricant used, the surface area of the ball or roller in the bearing, the temperature of the lubricant and the mechanical load on the shaft. This parasitic capacitance is transient and is formed only when the motor rotates, so it is shown to be variable in Figure 3. The value of this capacitance is important because its characteristics determine bearing current and dictate the life of the bearing.

All of the above parasitic capacitances are depicted in an electrical model shown in Figure 3(a) and its physical presence shown in Figure 3(b).

Relationship Between Motor Shaft Voltage and Common-Mode Voltage

Figure 4 shows typical common-mode voltage and shaft voltage in a two-level inverter. As show in Figure 4, the shaft voltage (V_SH) has the same shape as the stator common-mode voltage (V_com) because as mentioned earlier, the shaft voltage is formed as a result of the common mode voltage and the capacitive voltage divider circuit shown in Figure 3.  V_SH can be obtained from Equation 3.

As mentioned earlier, the ratio V_SH / V_com is typically 1:10 because the value of C_RF  is much larger than that of C_SR. The exact ratio depends on the size of the motor. From Equation 3, it is also interesting to note that at standstill and low speeds, the inner race and outer race of the bearing are in physical contact via the balls or rollers in the bearing that results in a value of infinity for C_B, resulting in zero shaft voltage.

[[{"type":"media","view_mode":"media_original","fid":"559","attributes":{"alt":"fig-4-common-mode-voltage.jpg","class":"media-image","id":"2","typeof":"foaf:Image"}}]]Bearing Currents and Its Generation Mechanisms

The common-mode voltage, and its associated dv/dt, generate bearing currents. Due to the various physical paths shown in Figure 3, different mechanisms can be assigned to the generation of different types of bearing currents. As shown in Figure 5, bearing currents can be summarized into four different currents according to their generation mechanism:

1)      Capacitive Bearing Currents (i₁): High common-mode voltage dv/dt in the stator windings causes pulse currents to flow to the rotor through the stray capacitance between the stator winding and the rotor surface (C_SR). These currents get distributed to two different paths. The first path is the return path formed by the capacitance between the rotor and the frame C_RF, and the second path is formed by the capacitance in between the inner race of the bearing and the outer race of the bearing, C_B. Since C_SR is much smaller than the parallel combination of C_RF and C_B, the amplitude of i1 is small compared to the total common-mode current (iSF).

However, the consistent flow of this current through the bearing capacitance causes heat in the lubricating medium and its exact influence on bearing failure is still being researched. Note that the portion of the current that flows through the bearing is dependent on the speed and mechanical load on the shaft. At low speeds, the bearing could be represented by a short circuit resulting in relatively higher value of i1 to flow through it. Since this current flows through the metallic parts in the bearing, its influence on the insulating film is considered negligible.

2)      Electric Discharge Machining (EDM) Bearing Currents (i₂): Due to the common-mode voltage, an electric charge is stored in the capacitance (C_RF) formed across the rotor body and the grounded stator frame. The voltage across C_RF is practically the voltage across the shaft as seen from Figures 3(a) and (b). The voltage across this capacitor can keep building up and eventually reach such a level that causes the insulation of the lubricating film to breakdown. This dielectric breakdown results in the charge stored across C_RF to discharge through the insulating film of the bearing, creating EDM bearing current. Since the capacitance of C_RF is relatively higher than C_SR, the energy stored in C_RF can be sufficiently large to cause bearing damage.

EDM currents are not generated if the motor shaft is grounded or the rotating speed is low enough for the ball bearing assembly to contact the stator frame. EDM current does not flow at every edge of the common mode voltage. The instant at which it flows depends on when the insulation film undergoes a dielectric breakdown, which could be arbitrary.

3)      Common Mode Current Flow Through Shaft Due to Poor Grounding (i₃): If the motor frame is poorly grounded and the motor shaft is connected to a mechanical load with much lower ground impedance, the common mode current that flows at every edge of the common mode voltage through the capacitor  C_SR and charges up the rotor structure now finds a way to flow through the shaft into an external ground that has a lower impedance. This is exactly what happens when an external grounding brush kit is used to ground the rotating shaft. The current bypasses the bearing and makes its way safely into a lower impedance ground through the shaft or the load structure connected to the shaft.

4)      Circulating Bearing Currents (i₄): The shaft voltage, due to asymmetry in the magnetic field from one end of the rotor to the other end of the rotor, is prevalent in long axial machines. This asymmetry induces a shaft voltage across the length of the rotor and is basically an electromagnetic induction phenomenon opposed to the capacitive coupled phenomenon discussed above. This phenomenon is observed only in long axial machines that are used for large horsepower applications typically greater than 110-kW [2]. Yet another distinction is that the induced voltage is of very low frequency and depends on the fundamental excitation of the motor. The circulating current flows along the axis of the rotor, through the bearings, circulates through the stator frame and returns back from the other bearing end. This current is generally not significant in small power AC machines less than 110kW [3].

Bearing Current Reduction

Here are some approaches that prevent bearing current damage of AC machines:

• External Passive/Active Common-Mode Filters: Common-mode noise filters are a good solution to cancel common-mode noise of the system, but typical common-mode noise filters consist of magnetically coupled three-phase inductor and capacitor components. These filters are bulky and expensive; in addition, filters reduce efficiency, and can cause voltage oscillation if parameters of the passive components are not tuned properly.
• Motor Shaft Ground Brushes or Insulated Bearings: The grounding of the motor shaft by connecting a brush between the motor shaft and the motor frame is an effective way to shunt the current path that normally would flow through the motor bearing. However, regular maintenance is required due to limited lifetime of the brush. Insulated bearings such as ceramic bearings can also prevent bearing current problems, but require the replacement of the existing bearings in the motor.
• Multi-Level Inverter Technologies: Reducing the amplitude and voltage transition step of the common-mode voltage can reduce bearing currents. One way of achieving this is to use a multi-level inverter topology. Progress in inverter technology has made it possible to introduce a 3-level inverter to the general purpose-inverter market [1]. The advantages of a 3-level inverter are discussed in the next section.

Features and Advantages of the 3-Level Inverter

General Features

Figure 6 shows a typical neutral-point clamped 3-level inverter. In order to determine the common-mode voltage in a three-level inverter, it is important to understand the various switching combinations in a 3-level inverter. In contrast to a 2-level inverter, a 3-level inverter has four switches (IGBTs) per phase, totaling twelve switches (IGBTs) for all three phases. According to the switching signals, each output phase voltage with respect to the DC bus midpoint can have three distinct levels, i.e., E/2, 0, and -E/2. Consequently, this arrangement is called a 3-level inverter.

Figure 7 shows various switching states and common-mode voltage waveforms among 27 different switching states of the 3-level inverter. By comparing the common-mode voltage of a 3-level inverter to that of a 2-level inverter as shown in Figure 2, it is clear that in a 2-level inverter the difference in voltage level from one state to the other is always ±E/3.

In the case of a 3-level inverter, the voltage level is generally ±E/6; this means that the transition level of the common-mode voltage in a 3-level inverter is typically one-half that of the 2-level inverter. In a 3-level inverter, the amplitude of the common-mode voltage can be lower than a 2-level inverter in the high voltage region. In fact, the maximum and minimum values of the common-mode voltage in a 3-level inverter at higher voltage (i.e. at higher speed) reaches only ±E/3 as shown in Figure 7(b), while the common-mode voltage reaches ±E/2 in the case of a traditional 2-level inverter as shown in Figure 2. The lower transition level of the 3-level inverter also results in a lower common-mode current compared to the 2-level inverter, an important advantage of the 3-level inverter over the traditional 2-level inverter.

Reduced Bearing Current and Increased Bearing Life with the G7 3-Level Inverter

The steep voltage transient in the shaft voltage causes current to flow through the bearing insulation, which leads to the breakdown of the bearing grease insulation and discharge of the shaft voltage. Since the change of the common-mode voltage is smaller in the 3-level inverter, this provides a significant advantage over the 2-level inverter with regard to shaft voltage and bearing currents. Figure 8 shows the comparative test results of the shaft voltage and bearing current for the 2-level and 3-level inverters. In these tests, insulation material was inserted in between the bearing and the housing so that the current through the bearing could be observed. Figure 8 shows that the bearing current of the 3-level inverter in Figure 8(b) is significantly smaller than a 2-level inverter in Figure 8(a).

Actual longevity tests were conducted to verify the superiority of the 3-level inverter. The tests simulated extreme conditions including temperature, types of grease and motor speed. The results of the bearing life test are shown in Figure 9. Note that during normal operation the normal bearing life would be longer than that shown here. Figure 9 clearly proves that the use of a drive with a 3-level inverter topology can yield a significantly longer bearing life.

 

 

 

 

 

 

 

References

• H.P. Krug, T. Kume, M. Swamy, "Neutral-point clamped three-level general purpose inverter - features, benefits and applications," IEEE Power Electronics Specialists Conference, pp. 323 - 328, 2004.
• J. Erdman, R. Kerkman, D. Schlegel, and G. Skibinski, "Effect of PWM inverters in AC Motor Bearing Currents and Shaft Voltages," IEEE APEC Conference, Dallas, TX, 1995, CD-ROM.
• A. Muetze, A. Binder, "Experimental evaluation of mitigation techniques for bearing currents in inverter-supplied drive-systems - investigations on induction motors up to 500 kW," IEEE International Electric Machines and Drives Conference, pp.1859 - 1865, vol.3, 2003.

USE OF TECHNICAL INFORMATION

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