Harmonic Effects on Induction Motors: Network Pollution, Variable Frequency Drive Stress, and Mitigation

Introduction

The induction motor is the workhorse of industrial power systems — converting electrical energy to mechanical work across every sector from mining to food processing, from water treatment to manufacturing. It is also among the most sensitive loads to power quality degradation, and among the most common sources of unexpected maintenance cost when operated outside the conditions it was designed for.

Harmonics affect induction motors in two fundamentally different ways, depending on whether the motor is connected to the network or to the output of a variable frequency drive. A motor connected to a distorted supply network — one shared with 6-pulse rectifier loads, arc furnaces, or other non-linear equipment — is subjected to harmonic voltages at its terminals that drive harmonic currents through its windings. A motor fed directly from the output of a PWM variable frequency drive faces a completely different problem: the high-frequency switching of the inverter creates common mode voltages, bearing currents, insulation stress, and torsional pulsations that have no equivalent in supply-side harmonic distortion.

The physics, the failure modes, the applicable standards, and the mitigation strategies are different in each case. Confusing the two leads to incorrect diagnosis, inappropriate remedies, and continued failures. This article treats both scenarios with equal rigour, using a single 100 HP (75 kW) motor as the thread connecting the two practical examples.

01 How Supply Harmonics Enter the Motor

When harmonic voltages are present at the motor terminals, harmonic currents flow through the stator impedance according to:

Where $V_h$ is the harmonic voltage at order $h$, $R_1$ and $R_2’$ are the stator and referred rotor resistances, and $X_1$, $X_2’$ are the leakage reactances at fundamental frequency. Since leakage reactance increases linearly with frequency, harmonic impedance rises with harmonic order — higher-order harmonics drive proportionally less current for the same voltage distortion.

Each harmonic current flowing in the three-phase stator winding produces its own rotating magnetic field in the air gap. The rotational direction and speed of each harmonic field depends on its sequence classification — one of the most important concepts for understanding motor behaviour under harmonic distortion.

Harmonic sequence classification

For a balanced three-phase system, harmonic orders follow a repeating sequence pattern:

Positive-sequence harmonics (7th, 13th, 19th…) produce rotating fields in the same direction as the fundamental — forward rotating. They add to the fundamental torque but also contribute to additional rotor losses due to the high slip at harmonic frequency.

Negative-sequence harmonics (5th, 11th, 17th…) produce fields rotating in the opposite direction to the fundamental. This is the critical mechanism: the rotor, spinning at near-synchronous speed in the forward direction, sees these backward-rotating fields at nearly twice synchronous frequency. The result is a braking torque component and intense rotor heating — energy dissipated as heat with no useful mechanical output. In a motor with significant 5th harmonic content on its supply, this mechanism is responsible for the majority of harmonic-related temperature rise.

Zero-sequence harmonics (3rd, 9th, 15th…) are balanced in all three phases simultaneously. In a delta-connected or isolated-neutral stator winding, they circulate internally and do not appear as line currents. In a star-connected winding with a connected neutral, they circulate in the neutral conductor. For most industrial motors with isolated neutral or delta windings, triplen harmonics contribute negligible additional loss.

Figure 1 — Harmonic rotating fields in the motor air gap

Harmonic currents in the motor — two industrial scenarios

When harmonic voltages are present at the motor terminals, harmonic currents flow through the stator and rotor according to the motor’s harmonic impedance at each frequency. The motor is a victim load — it responds to whatever harmonic voltage the network presents at its terminals. The magnitude of those voltages depends on the network harmonic environment, which IEC standards describe through compatibility levels.

Before presenting the calculations, an important distinction must be made about what compatibility levels actually represent. Compatibility levels are system planning objectives — the levels the utility designs to ensure that harmonic voltages at any point in the public network remain below these values under normal operating conditions. They are not measurements at motor terminals, and they do not describe the harmonic environment inside an industrial facility. Inside a plant, actual harmonic voltages at individual motor terminals depend on the internal network impedance, the concentration and mix of non-linear loads on shared busbars, and whether resonance conditions exist between capacitor banks and transformer or cable impedances. In a poorly coordinated industrial installation — particularly in mining or smelting where large drives share a common MV bus — harmonic voltages at motor terminals can exceed the IEC compatibility levels because the internal network is the customer’s responsibility, not the utility’s. The IEC 61000-2-4 Class 2 and Class 3 levels used below are the correct reference for equipment specification and worst-case screening when measured data is not available. Where measurements exist, they always take precedence.

Two environments are relevant for industrial motor installations. IEC 61000-2-4 defines compatibility levels for industrial and non-public networks — Class 2 for general industrial environments (most plant installations), and Class 3 for dedicated or heavy industry supplies where large non-linear loads such as arc furnaces, mine hoists, and large drives dominate the network:

These are compatibility levels — the worst-case harmonic voltages the utility plans for at the point of common coupling (PCC). A motor connected anywhere on the network downstream of the PCC may see up to these levels at its terminals. For engineering calculations without measured data, these levels represent the correct worst-case reference.

Practical example — 100 HP (75 kW) direct-on-line motor, two industrial network environments

The motor in this example is connected direct-on-line to the industrial network — it is not fed from a VFD. The network is shared with 6-pulse rectifier loads and other non-linear equipment that generate the harmonic voltages tabulated above. Using representative parameters for a 100 HP (75 kW), 4-pole, 400V, IE3 motor (R₁ = 0.08 Ω, R₂ = 0.06 Ω, X₁ = 0.15 Ω, X₂ = 0.12 Ω at 50 Hz, I₁ = 140 A — actual values vary by manufacturer and design) and IEC 61000-2-4 compatibility levels as terminal voltage input:

* Values marked with ~ calculated using representative parameters for a 100 HP (75 kW) IE3 motor. Actual values depend on specific motor design — use manufacturer equivalent circuit data for precise calculations per IEC/TS 60034-2-3 [2].
† Thermal equivalent overcurrent calculated on total copper loss basis: $I_{equiv} = I_1 \times \sqrt{P_{add}/P_{cu,fund}}$ where $P_{cu,fund} \approx 8{,}200\,\text{W}$ for this motor. Harmonic rotor copper losses calculated using harmonic slip $s_h = (h \pm 1)/h$ and skin-effect corrected rotor resistance $R_2(h) = R_2(1)\cdot\sqrt{h}$. Since $s_h \approx 1$, rotor copper loss equals air gap power: $P_{r,h} = 3I_h^2 R_2(h)$.

02 Harmonic Slip and Rotor Losses

The slip experienced by the rotor with respect to each harmonic rotating field is fundamentally different from the near-zero slip seen at fundamental frequency. For a motor running at fractional slip $s$ at the fundamental, the slip at harmonic order $h$ is:

Where $h$ is the harmonic order, $s$ is the rated slip at fundamental frequency (typically 0.02–0.04 for IE3 motors), and the upper sign (−) applies to positive-sequence harmonics, the lower sign (+) to negative-sequence harmonics. Since $s \ll h$ for all practical harmonic orders, the simplified forms are used:

For the dominant harmonics from a 6-pulse VFD network:

The critical insight from this table is that for all harmonic orders, $s_h \approx 1$. The rotor is essentially at standstill with respect to every harmonic rotating field. This has a profound consequence: the equivalent circuit of the motor at harmonic frequency resembles a transformer at short-circuit, with rotor copper loss determined almost entirely by rotor resistance at that frequency.

Why negative sequence harmonics drive more current

For the same harmonic voltage magnitude at the motor terminals, a negative-sequence harmonic drives more current than a positive-sequence harmonic of comparable order. The reason lies in the rotor branch impedance of the equivalent circuit. At harmonic order $h$ the rotor branch resistance referred to the stator is $R_2/s_h$. For negative-sequence harmonics, $s_h > 1$, so $R_2/s_h < R_2$ — the rotor branch resistance is reduced. For positive-sequence harmonics, $s_h < 1$, so $R_2/s_h > R_2$ — the rotor branch resistance is increased.

At the same terminal voltage of 6% of $V_1$, the h5 negative-sequence harmonic drives approximately 40% more current than h7 positive-sequence at equal voltage (varies with motor leakage reactance). Leakage reactance dominates the impedance at harmonic frequencies ($hX \approx 27 \times R_2/s_h$), so the primary driver of this difference is the lower harmonic order of h5 — lower order means lower leakage reactance and lower total impedance. But the sequence effect on rotor branch resistance is a real secondary contribution that always pushes negative-sequence current higher than positive-sequence at comparable harmonic orders.

This compounds the three other reasons h5 is more damaging than h7: its IEC compatibility voltage limit is higher (6% vs 5%), its harmonic order is lower giving higher current for the same voltage, and its braking torque converts all rotor loss to heat with zero mechanical output. The sequence effect on rotor impedance adds a fourth mechanism working in the same direction.

The 6f₁ torque pulsation — electromagnetic origin and six reinforcing sources

When multiple harmonic fields are simultaneously present in the motor air gap, their cross-product interactions produce pulsating torque components at beat frequencies. This mechanism is well established in the literature — the interaction of the 5th and 7th harmonic fields with the fundamental produces a pulsating torque at $6f_1$, and the interaction of h11 and h13 with the fundamental each produce pulsation at $12f_1$ [6][13]. What is less commonly presented is the complete enumeration: for a motor on a 6-pulse polluted network, there are six independent harmonic pair interactions that all produce torque pulsation at exactly $6f_1$ simultaneously:

Where $\omega_1$ and $\omega_2$ are the angular velocities of the two harmonic rotating fields (rad/s), equal to $\pm h \cdot \omega_1^{fund}$ where the sign is positive for positive-sequence harmonics and negative for negative-sequence harmonics. The absolute value ensures the beat frequency is always positive regardless of field rotation direction.

The pattern is consistent: every harmonic pair that differs by exactly 6 orders always produces a $6f_1$ beat — regardless of sequence. This is a direct mathematical consequence of the 6-pulse harmonic structure where characteristic harmonics follow $h = 6k \pm 1$, making adjacent harmonics always 6 orders apart.

All six interactions produce pulsation at exactly $6f_1$ — 300 Hz on a 50 Hz system, 360 Hz on a 60 Hz system. They reinforce each other in phase. This mathematical structure is not a coincidence: it is a direct consequence of the 6-pulse harmonic pattern $h = 6k \pm 1$, in which adjacent harmonics always differ by 6. The ‘6’ in 6-pulse rectifier and the $6f_1$ torque pulsation frequency share the same mathematical origin — the 6 commutation events per fundamental cycle of the converter.

Crucially, the fundamental field itself contributes: the interaction of h1 with h5 produces $6f_1$, and the interaction of h1 with h7 also produces $6f_1$. This means that even with very effective harmonic filtering, as long as any trace of h5 or h7 remains at the motor terminals, the fundamental — which is always present at full amplitude — will interact with it to maintain a $6f_1$ torque pulsation. Complete elimination of $6f_1$ pulsation requires a true sine wave at the motor terminals.

The 6f₁ rotor bar current — h5 and h7 both produce current at the same frequency (300 Hz / 360 Hz)

As shown in the harmonic slip analysis, the frequency of the current induced in the rotor bars by each harmonic field is $s_h \times h \times f_1$. For h5 and h7 this gives a remarkable result:

Both the 5th and 7th harmonic stator fields induce rotor bar currents at exactly $6f_1$. These two rotor currents are nearly in phase and add together — the combined rotor heating from the h5/h7 pair is greater than the sum of independent contributions. This is both a thermal effect (increased rotor copper loss) and a mechanical effect (reinforced $6f_1$ torque pulsation).

Propagation to direct-on-line motors from network pollution

An important and underappreciated consequence: the $6f_1$ torque pulsation affects every direct-on-line motor on the shared network — not just motors electrically close to the harmonic source. A direct-on-line pump motor sharing a busbar with a 6-pulse VFD driving a conveyor experiences $6f_1$ torque pulsation because the VFD rectifier’s harmonic injection creates h5 and h7 voltage distortion at the common bus, and those harmonic voltages drive harmonic currents in the pump motor’s stator. The pump motor has nothing to do with the conveyor VFD — it is simply connected to the same network. The 6-pulse converter’s mechanical signature propagates through the network voltage and reappears as shaft torque ripple in every directly connected motor downstream. This is why flow variation in a process pump can sometimes be traced to a VFD on a completely different piece of equipment sharing the same MV bus.

Inertia filtering — why 2f₁ (100 Hz / 120 Hz) matters more than 6f₁ (300 Hz / 360 Hz) for process quality

At $6f_1$ — 300 Hz on a 50 Hz system, 360 Hz on a 60 Hz system — the motor’s rotational inertia provides significant attenuation of shaft speed variation. The mechanical low-pass filter effect of the rotor-load inertia means that while the electromagnetic torque pulsation is real and measurable, the resulting shaft speed ripple is much smaller than the torque ripple amplitude would suggest. As the literature notes, when supply frequency is not very low, the frequency of torque pulsations can be partially filtered by motor inertia [6].

The The h5–h7 interaction produces a beat frequency at:

The $2f_1$ pulsation — 100 Hz on a 50 Hz system, 120 Hz on a 60 Hz system — is at a frequency low enough that motor inertia provides little attenuation. It transmits directly to shaft speed variation and to the driven load. For process quality purposes, the $2f_1$ pulsation is more significant than the $6f_1$ pulsation precisely because it is below the mechanical cutoff frequency of the motor-load system.

The complete pulsation spectrum from 6-pulse network harmonics on a 50 Hz system:

Higher beat frequencies — $18f_1$ (900 Hz), $24f_1$, $30f_1$, $36f_1$ — also exist mathematically from higher-order harmonic pair interactions, but are effectively eliminated by rotor inertia before reaching the shaft. The mechanical low-pass filter characteristic of the rotor-load system provides increasing attenuation with frequency. At 900 Hz the shaft speed ripple is negligible for any practical industrial load. For process quality assessment, only $2f_1$ and $6f_1$ require engineering attention. The $12f_1$ row is included for completeness but is relevant only for very sensitive, low-inertia processes at high line speeds.

Rotor skin effect — the amplifying mechanism

Since $s_h \approx 1$, the frequency of the current induced in the rotor bars by the $h$-th harmonic is approximately $h \times f_1$. At $5f_1$ — 250 Hz on a 50 Hz system, 300 Hz on a 60 Hz system — the skin effect in rotor bars becomes highly significant. Current is pushed toward the outer surface of the bar, effectively reducing the conducting cross-section and increasing rotor resistance.

The skin effect correction factor $K_R(h)$ for a rectangular rotor bar of depth $d$ is governed by the bar depth parameter:

Where $d$ is the rotor bar depth (m), $\mu_0 = 4\pi \times 10^{-7}\,\text{H/m}$ is the permeability of free space, $\sigma$ is the electrical conductivity of the bar material (approximately $3.5 \times 10^7\,\text{S/m}$ for aluminium, $5.8 \times 10^7\,\text{S/m}$ for copper), $h$ is the harmonic order, and $f_1$ is the supply frequency. The parameter $\xi_h$ represents the ratio of bar depth to skin depth at harmonic frequency $hf_1$ — as $\xi_h$ increases, current is progressively confined to the bar surface.

Where $K_R(h)$ is the ratio of rotor bar AC resistance at harmonic frequency $hf_1$ to its DC resistance — always $\geq 1$. At low frequency ($\xi_h \ll 1$), $K_R \to 1$ (no skin effect). At high frequency ($\xi_h \gg 1$), $K_R \to \xi_h$ (resistance proportional to frequency). For a typical industrial motor rotor bar at h5 (250 Hz on a 50 Hz system, 300 Hz on a 60 Hz system), $\xi_h$ is in the range 1.5–3.0, giving $K_R(5) \approx 2.5$–$4.0$. The exact value depends on bar geometry and must be measured per IEC/TS 60034-2-3 [2] for precise calculations.

For the simpler $\sqrt{h}$ approximation — adequate for first-order engineering estimates:

For typical IE3 industrial motors, the measured values of $K_R(h)$ from short-circuit tests at harmonic frequencies are significantly higher than the $\sqrt{h}$ approximation suggests — particularly for deep-bar and double-cage designs. Published data indicates $K_R(5) \approx 2.5$–$4.0$ and $K_R(7) \approx 3.0$–$5.0$ depending on bar geometry. The $\sqrt{h}$ approximation gives $K_R(5) = 2.24$ and $K_R(7) = 2.65$ — conservative but useful for screening calculations.

Rotor copper loss at harmonic frequency

With $s_h \approx 1$, the rotor copper loss at harmonic order $h$ is approximately:

Where $P_{r,h}$ is the three-phase rotor copper loss (W) at harmonic order $h$, $I_h$ is the RMS harmonic current per phase (A) referred to the stator, $R_2(h) = R_2(1) \cdot K_R(h)$ is the rotor resistance at harmonic frequency, and $R_2(1)$ is the rotor resistance at fundamental frequency referred to the stator. The factor of 3 accounts for all three phases. Since $s_h \approx 1$, the air gap power and rotor copper loss are approximately equal at harmonic frequencies — unlike at fundamental frequency where rotor copper loss equals slip times air gap power.

Stator copper loss at harmonic $h$ adds a secondary contribution:

Where $R_1(h) \approx R_1(1) \cdot \sqrt{h}$ is the stator winding AC resistance at harmonic frequency, using the $\sqrt{h}$ skin effect approximation. Stator skin effect is secondary to rotor skin effect at supply harmonic frequencies because the stator leakage reactance $hX_1$ dominates the stator impedance — but at PWM switching frequencies (Part 2), stator skin effect becomes significant and must be accounted for separately.

Core loss at harmonic frequency follows the Steinmetz relationship. Eddy current losses increase as $h^2$ and hysteresis losses as $h^{1.6}$, making higher-order harmonics progressively more damaging per unit of flux — though the lower harmonic voltage magnitude at higher orders moderates this effect in practice. The total additional harmonic loss above fundamental is the sum over all harmonic orders present:

Figure 2 — Interactive: Rotor impedance and loss at harmonic frequencies

03 K-Factor: Quantifying the Harmonic Derating Requirement

The K-factor is the standard engineering metric for quantifying the additional rotor heating effect of a harmonic current spectrum, relative to a purely sinusoidal supply. It was developed jointly by NEMA and IEEE and is defined in NEMA MG1 Part 31 and used in conjunction with IEEE 112:

Where $I_h$ is the RMS harmonic current at order $h$, expressed in per unit of the fundamental current $I_1$. The $h^2$ weighting reflects the increased rotor copper loss at harmonic frequencies due to skin effect — it is an approximation of the $K_R(h)$ factor discussed in Section 2, calibrated for the average of NEMA design B motor bar geometries.

A motor with K-factor rating of $K_x$ is designed to carry its full rated load while supplying a current waveform with K-factor up to $K_x$ without exceeding its rated temperature rise. A standard motor has an implied K-factor of 1.0 — rated for sinusoidal supply only.

Practical example — K-factor calculation

Consider a 100 HP (75 kW), 4-pole, 400V, 50 Hz, IE3 motor connected to a network shared with 6-pulse VFD loads. Using the practical harmonic spectrum from Article 1 at full VFD load:

A K-factor of 2.74 means this motor requires a K-4 rated motor (the next standard rating above 2.74) to operate without exceeding rated temperature rise on this network. Standard K-factor ratings are K-1, K-4, K-7, K-13, K-20. The 6-pulse VFD network without line reactors typically demands K-4 to K-7 depending on the proportion of VFD load and network impedance.

Figure 3 — Interactive K-factor calculator

04 Derating for Supply Harmonics

When the supply harmonic content exceeds the level a standard motor was designed for, two approaches are available: derate the motor’s output (operate it at less than nameplate power) or specify a motor with sufficient K-factor rating to carry full load without exceeding temperature limits.

IEC 60034-17 derating method

IEC 60034-17 [3] provides derating curves for squirrel-cage induction motors as a function of the harmonic voltage factor (HVF), defined as:

The HVF normalises each harmonic voltage by its order — reflecting the fact that higher-order harmonic currents are attenuated by leakage reactance. For our 100 HP (75 kW) practical example, with a network THD_V of 8% dominated by 5th and 7th harmonics (V₅ = 6%, V₇ = 4%, V₁₁ = 2%), the HVF is approximately 0.015 p.u. IEC 60034-17 derating curves indicate approximately 3–7% derating for a standard K-1 motor at this distortion level — the precise value depends on motor design parameters and should be read from the standard’s curves using the actual measured HVF.

NEMA MG1 approach

NEMA MG1 Part 30 and Part 31 [4] address harmonic derating through K-factor ratings. A standard general-purpose motor (K-1) should be derated when the supply current K-factor exceeds 1.0. For K-4 rated motors, full rated output is available up to a supply K-factor of 4.0. The NEMA approach is more directly related to the loss mechanism than the HVF method and is generally preferred for North American applications.

Practical example — 100 HP (75 kW) on polluted network

Network conditions: THD_V = 8%, dominant 5th and 7th harmonic, K-factor of supply current = 2.74 (calculated in Section 3).

05 Variable Frequency Drive Technologies — Motor Stress Profile

The motor does not distinguish between inverter topologies — it responds to the voltage waveform presented at its terminals. But different VFD technologies produce fundamentally different waveforms, with very different consequences for common mode voltage, bearing currents, insulation stress, and harmonic losses. Understanding the drive technology is the essential first step in assessing motor stress.

Five main topologies are in industrial use today, spanning from the widely deployed standard IGBT inverter to emerging wide-bandgap semiconductor designs:

Standard 2-level IGBT PWM

The dominant industrial topology. Six IGBT switches chop the DC bus voltage into a pulse-width modulated output. Switching frequencies of 2–16 kHz, voltage rise times of 100–500 ns, and common mode voltage of $\pm V_{DC}/2$ [7]. Well understood, extensively standardised under IEC TS 60034-25 [1] and NEMA MG1 Part 31 [4]. All subsequent sections of Part 2 describe this topology as the baseline unless stated otherwise.

Soft switching inverters

Resonant-link and quasi-resonant topologies ensure switching transitions occur at zero voltage or zero current, dramatically reducing dv/dt. Bearing current generation and insulation stress are significantly lower than hard-switching IGBT designs. The trade-off is increased circuit complexity, higher cost, and reduced robustness. Soft switching inverters have not achieved wide industrial adoption despite their motor-health advantages.

Multi-level inverters — NPC and flying capacitor

Instead of switching the full DC bus voltage in one step, multi-level inverters divide each transition into smaller voltage steps. A 3-level NPC inverter produces voltage steps of $V_{DC}/2$ rather than the full $V_{DC}$ of a 2-level inverter, reducing both dv/dt and peak common mode voltage to $\pm V_{DC}/6$ — a three-fold reduction. Multi-level topologies are standard in medium-voltage drives (2.3–11 kV) and increasingly available for high-power low-voltage applications. They represent the best available solution for bearing current reduction without output filtering.

Active Front End (AFE) drives

Replacing the standard diode bridge rectifier with an IGBT-based active rectifier allows the supply-side current to be nearly sinusoidal — eliminating the supply harmonics that affect motors in Part 1. AFE drives are the correct solution when IEEE 519 [14] compliance on the supply side is the primary concern. However, the AFE rectifier uses PWM switching which generates its own high-frequency common mode currents on the supply side. The motor-side inverter is unchanged from a standard drive — bearing currents, insulation stress, and PWM losses at the motor are identical to a standard IGBT drive.

SiC and GaN wide-bandgap inverters

Silicon Carbide (SiC) and Gallium Nitride (GaN) semiconductors allow switching frequencies of 50–200 kHz with switching losses far below silicon IGBTs. Higher switching frequency improves current waveform quality and reduces torque ripple. However, the faster switching produces dramatically higher dv/dt — voltage rise times of 10–50 ns compared to 100–500 ns for silicon IGBTs. This creates more severe bearing currents and insulation stress, not less. Cable length limits for SiC inverters can be as short as 3 metres without output filtering. SiC drives are advancing rapidly in electric vehicle and aerospace applications and are beginning to appear in industrial installations.

06 Common Mode Voltage — The Root Cause

When a motor is fed from a PWM variable frequency drive, it is subjected to a harmonic environment that has no equivalent in direct-on-line operation or supply-side harmonic distortion. The origin of this environment is the common mode voltage — a parasitic voltage between the motor windings and the motor frame that arises directly from the PWM switching process.

Origin of common mode voltage

In a three-phase IGBT inverter, each output phase is switched between the positive and negative DC bus rails. At any instant, the three phase voltages $v_a$, $v_b$, $v_c$ relative to the DC bus midpoint rarely sum to zero — the switches are in different states and the DC midpoint is electrically floating. The common mode voltage $V_{cm}$ is defined as the average of the three phase voltages relative to ground:

For a standard 2-level IGBT inverter with DC bus voltage $V_{DC}$, the common mode voltage can take values of $\pm V_{DC}/6$, $\pm V_{DC}/2$ depending on the switching state, switching at the carrier frequency (typically 2–16 kHz). On a 400V system, $V_{DC} \approx 565\,\text{V}$, giving peak common mode voltages of 94 V to 283 V — switching thousands of times per second. On a 480V system, peak values reach 300–400 V.

This high-frequency, high-amplitude voltage oscillation is present between the motor star point and the motor frame ground. In a direct-on-line motor, $V_{cm}$ is essentially zero — the star point is at a stable low-frequency potential and the frame is grounded. The common mode voltage is entirely a consequence of PWM switching.

The motor as a capacitance network at kHz frequencies

At supply frequency (50–60 Hz), the motor behaves as an inductive load. At switching frequencies of 2–16 kHz, the inductive reactances are very high but the parasitic capacitances — between windings, between stator and rotor, between rotor and frame, and across the bearing lubricant film — become dominant conduction paths. Four parasitic capacitances determine the distribution of common mode current:

The common mode voltage drives displacement currents through this capacitive network. The largest path — stator winding to frame through $C_{sf}$ — carries most of the common mode current directly to ground. A smaller fraction passes through $C_{sr}$ to the rotor, where it charges the rotor-to-frame capacitance $C_{rf}$ and raises the shaft voltage. When the shaft voltage exceeds the dielectric strength of the bearing lubricant film, the stored charge discharges through the bearing — initiating the bearing damage mechanisms described in Section 6.

Figure 4 — Common mode voltage circuit and parasitic capacitance paths

07 Bearing Current Mechanisms

The common mode voltage described in Section 5 drives current through the motor via four distinct mechanisms, each with its own physical path, damage pattern, frame size dependency, and mitigation [8][9]. Understanding which mechanism dominates in a given application is essential to selecting the correct — and cost-effective — solution.

Mechanism 1 — Capacitive discharge current

The stator-to-rotor capacitance $C_{sr}$ forms a voltage divider with $C_{rf}$ and $C_b$. The shaft voltage is:

Where $V_{shaft}$ is the resulting shaft-to-frame voltage (V), $V_{cm}$ is the common mode voltage at the motor star point (V), $C_{sr}$ is the stator-to-rotor capacitance across the air gap, $C_{rf}$ is the rotor-to-frame capacitance, and $C_b$ is the bearing capacitance through the lubricant film. Since $C_{sr} \ll C_{rf}$ in most motors, $V_{shaft}$ is typically 5–30% of $V_{cm}$ — but this fraction can be significantly higher in smaller motors with thin air gaps.

This capacitive current flows at switching frequency through the stator-air gap-rotor-bearing-frame path. The magnitude is generally small — $C_{sr}$ is small compared to $C_{sf}$ — and alone rarely causes bearing damage. It is, however, the source of shaft voltage that enables the more damaging mechanisms that follow.

Mechanism 2 — EDM (Electric Discharge Machining) bearing current

The rotor-to-frame capacitance $C_{rf}$ charges progressively with each switching event. When the voltage across $C_{rf}$ — which appears across the bearing lubricant film — exceeds the dielectric breakdown strength of the lubricant (typically 5–30 V depending on film thickness and lubricant condition), the stored charge discharges as a micro-arc through the bearing. Each discharge is essentially a miniature EDM event: a microscopic pit is eroded from the bearing race or rolling element surface.

Over thousands of switching events per second and millions of operating hours, the accumulated pitting produces the characteristic fluting pattern — evenly spaced circumferential grooves on the bearing inner race, spaced at intervals corresponding to the switching frequency and rotor rotation rate. Fluting damage is the most commonly observed bearing failure mode in VFD-driven motors and produces a characteristic high-pitched whine that changes pitch with motor speed.

EDM bearing current occurs in motors of any frame size and is the dominant mechanism in motors below approximately 100 kW (IEC frame 315). It is mitigated by providing an alternative low-impedance path for the bearing current — typically a shaft grounding ring (AEGIS SGR type) that continuously diverts current away from the bearing.

Mechanism 3 — Circulating high-frequency bearing current

In motors above approximately 100 kW (IEC frame 315 and above), a second and more destructive mechanism emerges. The common mode current flowing through $C_{sf}$ is not uniformly distributed around the stator circumference — the asymmetric winding layout and slot distribution create a net high-frequency magnetic flux along the rotor axis. By Faraday’s law, this axial flux induces a circulating current in the loop:

Drive-end bearing → shaft → non-drive-end bearing → stator frame → back to drive-end bearing

This circulating current flows at switching frequency and can reach amplitudes of several amperes — significantly higher than the capacitive discharge mechanism. Unlike EDM currents which discharge in microsecond pulses, circulating bearing current flows continuously at switching frequency, producing severe Joule heating and rapid lubricant degradation in addition to electrolytic corrosion of the bearing surfaces.

The mitigation is an insulated bearing on the non-drive end (NDE) — breaking the circulating current loop by eliminating one conducting path. A ceramic-coated bearing or hybrid ceramic bearing (ceramic rolling elements in a steel race) is used. Insulating only one bearing is generally sufficient — insulating both creates difficulties with shaft alignment and thermal management.

Mechanism 4 — Rotor ground current

When the motor cable shield is not properly terminated — or when a single-conductor cable is used — the common mode return current has no low-impedance path back to the inverter. The current instead returns via the motor shaft, bearing, and motor frame to the distribution ground, and from there back to the drive cabinet. This rotor ground current can be large (hundreds of milliamperes to several amperes) and affects not only motor bearings but also bearings in any coupled equipment — gearboxes, pumps, fans — that share the same shaft.

The mitigation is correct cable installation: a shielded cable with the shield terminated at both the drive and motor end with 360° clamps, not pigtail connections. A common mode choke on the output cable further reduces rotor ground current in difficult installations.

08 PWM Harmonic Losses in the Motor

Beyond bearing currents, the PWM waveform imposes additional losses in the motor that are absent from direct-on-line operation. These losses differ fundamentally from the supply-harmonic losses discussed in Part 1, both in their frequency range and in the dominant loss mechanism.

Why PWM harmonics are different from supply harmonics [10]

Supply harmonics (5th, 7th, 11th…) appear as harmonic voltages at 250, 350, 550 Hz on a 50 Hz system. PWM switching harmonics appear at the carrier frequency and its sidebands — typically 2–16 kHz and multiples thereof. At these frequencies, the motor’s leakage inductance is very high, attenuating the harmonic current effectively. The motor current waveform on a VFD output is therefore nearly sinusoidal despite the highly distorted voltage.

However, the voltage is not filtered. The full PWM voltage — with its fast-switching edges, reflected wave transients, and high dv/dt — is applied directly to the stator insulation. The additional losses at switching frequency, while not large enough to affect torque production, are sufficient to meaningfully increase motor temperature rise — typically 5–15°C above direct-on-line operation at the same load.

Additional losses from PWM operation

IEC/TS 60034-2-3 [2] identifies and quantifies the additional losses in converter-fed motors through a structured loss separation procedure. The main contributors are:

The total additional loss from PWM operation — typically 15–40% above direct-on-line — manifests as an increase in motor temperature rise. For a motor with a rated temperature rise of 80°C (Class F insulation, Class B rise), a 20% increase in losses produces approximately 16°C of additional temperature rise, consuming a significant portion of the available insulation life margin.

Switching frequency has a non-trivial effect: lower switching frequencies (2–4 kHz) produce higher harmonic current ripple and higher rotor copper loss. Higher switching frequencies (8–16 kHz) reduce current ripple but increase core loss and stator copper loss through skin effect. An optimum switching frequency exists for minimum total motor loss, typically in the 4–8 kHz range for most industrial motors.

09 Torsional Pulsations, Shaft Stress, and Product Quality

Among all the harmonic effects on VFD-driven motors, torsional pulsations are the least understood and the most consequential for production operations. An engineer investigating a bearing failure will measure shaft voltage. An engineer investigating a process quality problem rarely thinks to analyse motor torque ripple — yet the connection is direct, measurable, and in many cases the root cause of otherwise unexplained product variability.

Origin of torque pulsations — direct-on-line motor on polluted network

When two harmonic rotating fields of different orders are simultaneously present in the motor air gap, their interaction produces a pulsating torque component at the beat frequency between them. For the dominant 5th and 7th harmonics from a 6-pulse rectifier network:

The $2f_1$ torque pulsation — 100 Hz on a 50 Hz system, 120 Hz on a 60 Hz system — is twice the supply frequency. It appears regardless of motor speed and is always present when both 5th and 7th harmonic currents flow simultaneously on the network. Additional pulsation frequencies arise from other harmonic pair interactions:

On a VFD-fed motor, additional torsional pulsations arise from the PWM switching pattern itself. At lower switching frequencies (2–4 kHz), the current ripple is sufficient to produce torque ripple at the switching frequency and its sidebands — this is the source of the characteristic acoustic noise of VFD-driven motors and contributes to mechanical vibration transmitted through the shaft to the load and bearings.

Subsynchronous resonance and forbidden speed bands

In variable-speed operation, the mechanical system has natural resonant frequencies determined by the rotor inertia, shaft stiffness, coupling compliance, and load inertia. When the VFD output frequency is such that a harmonic torque pulsation coincides with a mechanical resonant frequency of the shaft system — even transiently during acceleration or deceleration — the resulting resonant excitation can be severe:

Torsional pulsations and bearing fatigue

Even below resonance, sustained torque pulsations at $2f_1$ (100 Hz / 120 Hz) and $12f_1$ (600 Hz / 720 Hz) impose cyclic radial and axial loading on the bearings. Rolling element bearings are rated for a static and dynamic load in one direction — the L10 bearing life calculation assumes a constant or slowly varying load. A $2f_1$ oscillating radial load (100 Hz / 120 Hz) superimposed on the static load accelerates bearing fatigue by increasing the peak dynamic load on each cycle. The L10 bearing life is proportional to the cube of the load ratio $(C/P)^3$ — a modest oscillating component has limited impact at high static loads, but as the oscillating amplitude approaches the static load magnitude, the effective peak load increases sharply and bearing life degrades rapidly. In light-load applications — where the motor is heavily derated and the static bearing load is low — the oscillating component from torque pulsations can become the dominant loading, making bearing life the critical design constraint.

Product quality consequences

The shaft torque pulsation of a running motor is transmitted directly to whatever the motor drives. In most industrial processes, the shaft is the primary means by which electrical energy is converted to process work — and any variation in shaft speed or torque appears immediately in the process output. The following applications are particularly sensitive:

Pumps and flow systems

A centrifugal pump driven through a motor with 100 Hz torque pulsation produces flow ripple at the same frequency. In dosing and metering applications — chemical injection, pharmaceutical filling, food and beverage proportioning — this flow ripple translates directly to dose weight variation. A filling machine running at 60 containers per minute that experiences 1% flow ripple at 100 Hz will show a systematic weight variation pattern in the filled containers that correlates with the drive switching pattern. The variation may be within specification individually but shows up immediately in statistical process control as non-random variation — failing Cpk requirements while all individual measurements pass specification.

Conveyors and web-fed processes

In continuous web processes — paper, film, foil, textile — the conveyor or nip roll motor drives at a controlled speed that determines coating weight, calender gap thickness, or print register. Speed ripple from torque pulsations at $2f_1$ (100 Hz / 120 Hz) produces a periodic variation in material velocity that appears in the product as a regular pattern of thickness variation, coating weight fluctuation, or print misregister at a spatial wavelength determined by the web speed and the pulsation frequency. At a web speed of 200 m/min (3.3 m/s), a 100 Hz (50 Hz system) speed ripple produces variations spaced 33 mm apart — clearly visible in the product and frequently the cause of customer complaints attributed to the product rather than the drive system.

Compressors

Torque pulsations in a compressor drive produce discharge pressure oscillations at $2f_1$ (100 Hz / 120 Hz). In process gas applications — particularly where compressed gas feeds a downstream reactor, separator, or analyser — these pressure oscillations interfere with process instrumentation, cause false trips on pressure differential switches, and in severe cases couple with acoustic resonances in the pipe system, amplifying to damaging pressure wave amplitudes. In reciprocating compressors, the interaction between inherent pressure pulsation from the compression cycle and electrically-induced torque pulsations can produce shaft fatigue loading not anticipated in the original mechanical design.

Mixers and extruders

In polymer extrusion and mixing, the screw speed determines residence time, shear rate, and energy input per unit volume of product. Speed variation from torque pulsations produces variation in melt temperature, viscosity at the die, and pressure at the screw tip — all of which affect product dimensions, surface finish, and mechanical properties. In food mixing applications, speed ripple affects blend uniformity and emulsification efficiency. These effects are process-specific and may be very sensitive to small speed variations — a 0.1% speed ripple that would be mechanically negligible can be process-critical in a high-value pharmaceutical or specialty polymer application.

Winding machines

In film, foil, paper, and wire winding, the winding tension is controlled by a combination of torque control and speed feedback. Torque pulsations directly modulate the winding tension at $2f_1$ (100 Hz / 120 Hz), producing variation in roll density and wound-in tension that appears as layer-to-layer stress variation in the finished roll. In film and foil winding, this tension variation causes blocking (layers sticking together) in high-stress zones and loose winding in low-stress zones — both of which produce defect rates in subsequent converting operations. In wire winding, tension variation causes dimensional variation in the wound coil that affects its electrical characteristics.

Figure 5 — Interactive: Torque pulsation spectrum and product quality impact

10 Mitigation Summary and Specification Guide

Effective mitigation of harmonic effects on induction motors is fundamentally an electromagnetic compatibility (EMC) challenge — the motor must coexist with the power conversion equipment driving it or sharing its network. Each mechanism requires a solution applied at a different point in the system: matching the solution to the specific mechanism is the first requirement. Over-engineering wastes capital; under-engineering produces repeated failures. The following guide covers both scenarios from this article.

Part 1 mitigation — Supply-side harmonics

For a detailed treatment of passive and active filter solutions, see Article 2 in this series.

Part 2 mitigation — VFD bearing currents and insulation

Torsional pulsation and product quality mitigation

Inverter-duty motor specification checklist — 100 HP (75 kW) practical example

The two scenarios treated in this article — a direct-on-line motor on a polluted network, and a motor supplied by a variable frequency drive — require fundamentally different assessment methods, different standards, and different mitigation strategies. Applying the wrong approach to either scenario produces incorrect diagnosis and ineffective remedies. The engineering checklist above brings both scenarios together into a single specification framework for the 100 HP (75 kW) reference motor that runs throughout this article.

Harmonic distortion on industrial networks is not a static condition — it evolves as loads change, new equipment is commissioned, and network impedances shift. The mitigation solutions specified today must be verified periodically against the harmonic environment that actually exists. Power quality measurement per IEC 61000-4-7 [15] is the only reliable basis for that verification. A future article in this series will address measurement methodology, instrument selection, and the interpretation of harmonic survey data for motor condition assessment.

References

1. IEC TS 60034-25:2022, Rotating Electrical Machines — Part 25: AC Electrical Machines Used in Power Drive Systems — Application Guide, IEC, 2022.
2. IEC/TS 60034-2-3:2013, Rotating Electrical Machines — Part 2-3: Specific Test Methods for Determining Losses and Efficiency of Converter-Fed AC Motors, IEC, 2013.
3. IEC 60034-17:2006, Rotating Electrical Machines — Part 17: Cage Induction Motors When Fed from Converters — Application Guide, IEC, 2006.
4. NEMA MG1-2021, Motors and Generators, Part 30 and Part 31, NEMA, 2021.
5. IEEE Std 112-2017, IEEE Standard Test Procedure for Polyphase Induction Motors and Generators, IEEE, 2017.
6. Boldea, I., Nasar, S.A., The Induction Machine Handbook, 2nd ed., CRC Press, 2010.
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8. ABB Drives, Technical Guide No. 5 — Bearing Currents in Modern AC Drive Systems, ABB, 2011.
9. Muetze, A., Binder, A., “Practical Rules for Assessment of Inverter-Induced Bearing Currents in Inverter-Fed AC Motors up to 500 kW,” IEEE Transactions on Industrial Electronics, vol. 54, no. 3, pp. 1614–1622, 2007.
10. Skibinski, G., Kerkman, R., Schlegel, D., “EMI Emissions of Modern PWM AC Drives,” IEEE Industry Applications Magazine, vol. 5, no. 6, pp. 47–81, 1999.
11. Zawirski, K. et al., “Derating of Squirrel-Cage Induction Motors Due to High Harmonics in Supply Voltage,” Energies, vol. 16, no. 18, 6604, 2023.
12. Bollen, M.H.J. et al., “Supraharmonics (2 to 150 kHz) and Multi-Level Converters,” CIGRE/CIRED/IEEE C4.24 Working Group, 2014.
13. Dugan, R.C., McGranaghan, M.F., Santoso, S., Beaty, H.W., Electrical Power Systems Quality, 3rd ed., McGraw-Hill, 2012.
14. IEEE Std 519-2022, IEEE Standard for Harmonic Control in Electric Power Systems, IEEE, 2022.
15. IEC 61000-4-7:2002+A1:2008, Electromagnetic Compatibility — Testing and Measurement Techniques — General Guide on Harmonics and Interharmonics Measurements, IEC, 2008.