VFD Cable Length, Peak Voltage and dv/dt Filter Selection

Cable reflections and peak voltage

For a single differential-mode edge, $\Gamma_m=(Z_m-Z_c)/(Z_m+Z_c)$ and the one-way delay is $t_d=L/v$. The source is stiff, with reflection coefficient approximately −1. The retained von Jouanne three-transit engineering approximation is

It reaches its plateau at $L=v t_r/3$; it is not the exact finite-ramp reflection sum. See von Jouanne et al. (1996), DOI 10.1109/2943.532149, and von Jouanne and Enjeti (1997), DOI 10.1109/28.633789, Sections II–III. Their filter study DOI 10.1109/28.511650 supports slowing the cable-input edge.

Two distinct timing markers are retained: full-ramp $L_{2,full}=v t_{r,full}/2$ and vendor-style $L_{vendor}=v(0.8t_{r,full})/2$. MTE's 2004 technical information, attached PDF p.14, defines a 10–90% time and uses 100 m/µs for its examples. MTE Series A manual Rev.006 (2011), PDF p.32, repeats its critical-length examples. These markers must not be confused with the three-transit approximation's saturation length.

For nonzero cable, the initial-edge slew bound is $D=(1+\Gamma_m)V_{dc}/t_r$; at zero length use $V_{dc}/t_r$. A reactor or dv/dt filter substitutes its verified cable-input transition time, without implying a generic improvement from percent impedance. Ideal sine mode uses $V_{pk}=\sqrt2 V_{LL,rms}$ and $D=2\pi fV_{pk}$ with explicit frequency conversion.

RPDIV voltage and rise-time coverage

Assume symmetric positive and negative operating peaks, so $U_{pp}=2V_{pk}$. Enter terminal-equivalent repetitive inception voltage for the complete winding, or a supplier-validated conversion to those same terminals. No turn-to-turn voltage division is inferred. With reserve ratio $k_{PD}$, allowable peak-to-peak stress is $U_{PD}/k_{PD}$ and the reserved headroom is $U_{PD}/k_{PD}-U_{pp}$. The raw margin $U_{PD}-U_{pp}$ remains a calculation step.

A slew bound limits how quickly a transition can cross 10–90% of its final bus step. Therefore $t_{10–90}\ge0.8V_{dc}/D$. The reported value is this conservative floor, not a reconstruction of the terminal waveform. If that floor is at least the entered qualification minimum, and carrier frequency is within its qualified maximum, the entered rise/frequency envelope covers this screening. Otherwise voltage reserve alone gives no PD-free conclusion. The supplier must confirm that the RPDIV envelope covers all slower transitions, overshoot duration, polarity, duty and service environment. RPDIV is not a generic function of rise time; see Yang et al., DOI 10.1049/hve2.12375. Sine mode leaves these impulse-only margins unavailable.

Required phase-to-phase insulation category

The bus-relative ratio $r=V_{pk}/V_{dc}$ is retained only as a waveform overshoot band. It does not determine a motor's insulation rating.

The required phase-to-phase IVIC instead uses $q=U_{pp}/U_N=2V_{pk}/U_N$. Select the lowest class whose normalized peak-to-peak operating allowance covers this demand. The allowances are implemented from OEMER General Catalogue GC012024 Rev.1.0, section A p.25 (attached PDF p.26); no standards table is reproduced. Siemens SINAMICS S120 Chassis-2, edition 08/2025, printed p.129 (PDF p.131), independently gives a 1180 V peak allowance for a 400 V class C motor.

This published-envelope screen requires a terminal 10–90% rise-time floor of at least 0.3 µs, a two-level Type I application and rated voltage above 300 V through 690 V. These are this calculator's supported application boundaries, not a claim that the standard excludes other ratings. A faster edge, a voltage outside this scope, an unavailable qualification basis or stress above class D withholds the required-category verdict. Obtain a supplier-specific qualification for such cases. No generic increase in withstand is inferred for a slower edge.

The result specifies only the required phase-to-phase category, not the complete motor IVIC declaration. Phase-ground and turn insulation need separate assessment. Follow IEC 60034-18-41:2014+A1:2019 (edition 1.1; 2020 corrigendum) and IEC TS 60034-25:2022 (edition 4.0); check against the standard in force.

Candidate PWM filter target

Use $V_a=\min(V_{lim},U_{PD}/(2k_{PD}))$. If the long-line plateau exceeds $V_a>V_{dc}$, the voltage constraint requires $t_{r,V}=3\Gamma_m t_d/(V_a/V_{dc}-1)$; otherwise it adds no requirement. A limit below the bus is infeasible; equality is feasible only with zero cable or matched impedances. The slew constraint requires $t_{r,D}=gV_{dc}/D_{lim}$ and rise-time qualification requires $t_{r,PD}=g t_{PD}/0.8$, where $g=1+\Gamma_m$ for a finite cable and 1 at zero length. The candidate target is the maximum of these and the original drive rise time. It is unavailable if the voltage allowance is infeasible, carrier frequency exceeds qualification, or the required edge cannot fit within half a carrier period. This half-period check is a necessary timing condition, not a minimum-pulse-width guarantee for a particular PWM modulator. In sine mode it remains a comparison with a PWM-preserving alternative, not a sine-filter requirement.

Electrical endurance sensitivity

Implement the separable, normalized inverse-power model

Yang et al. (2024), DOI 10.1049/hve2.12375, supports inverse-power voltage and slew-rate acceleration. The separable multiplication and frequency exponent are explicit modelling assumptions, not that paper's fitted motor model. A constant damage-per-pulse assumption gives $n_f=1$ at a fixed pulse pattern. Default $n_V=8$, $n_f=1$, $n_D=1$ and the reference stress values are illustrative sensitivity choices. No universal motor exponent is claimed. Setting $n_D=0$ removes the additional slew factor. Because slew also changes with voltage, a joint calibration must avoid double-counting those effects.

Relative mode is explicitly an illustrative sensitivity calculation, restricted to valid carrier timing but not interpreted as life across a PD transition. Reference stress and exponents can be opened with “Edit reference and exponents”. It deliberately supplies no hours.

Calibrated mode requires confirmation of matched test data, tested minimum and maximum peak voltage, terminal slew and carrier frequency, a declared PD regime, and reference terminal rise time. Both the reference and evaluated waveform must lie within all supplied stress ranges and the same PD regime. PD-free means peak-to-peak stress strictly below the entered RPDIV; PD-active means strictly above it. Equality is outside both regimes. Reference rise time must be covered by the RPDIV qualification, and the entire calibration frequency range must be within its qualified maximum. The entered RPDIV must cover the full tested waveform domain at the same environment.

Missing test confirmation, an unspecified PD regime, a reference outside its domain or an evaluated point outside its domain produces an intentional gap. Calibrated hours and normalized life are withheld there. The selected/unfiltered comparison requires both cases to qualify; a PD-active unfiltered case cannot be compared with a PD-free filtered case using one calibration. Hours equal the qualified reference endurance multiplied by the bounded life ratio, at the same failure percentile. The PD-active option describes laboratory electrical endurance; it does not permit PD operation of a Type I motor.

Ideal sine output has no transferable PWM endurance calibration, so selected impulse life remains unavailable. The unfiltered comparison and edge-speed sweep are explicitly PWM scenarios.

The life charts plot $\log_{10}(H/H_0)$: 0 means reference life, +1 means ten times, and −1 means one tenth. Length uses about 200 points plus exact voltage knees; the edge sweep uses 81 logarithmic points. Its upper cable-input rise time is the smaller of 10 µs and 0.499 carrier periods, so every point fits strictly within half a period. Calibrated curves and their reference trace leave invalid samples as gaps.

Animation follows an incident sharp front between the drawn cable interfaces. A nonzero motor reflection adds the return trip and the negative source reflection. A matched termination ends after the incident trip; zero cable length and ideal sine output show no PWM fronts. Heavy sweeps do not depend on the play input.

• One two-level voltage-source drive, uniform cable and motor; a settled initial state and one differential-mode step equal to the entered DC bus.
• Constant real surge impedances with $Z_m\ge Z_c$, a stiff source and lossless propagation. Input defaults are illustrative application values.
• Equivalent full 0–100% linear input ramps; a linear 10–90% time is 0.8 of the full transition. The terminal rise-time floor uses 10–90% of the final bus step, not of the overshoot peak.
• Symmetric operating peaks for the peak-to-peak insulation envelope. Actual positive and negative terminal peaks must be measured when the waveform or duty is asymmetric.
• RPDIV data already refer to the whole winding at the same line terminals and cover the service temperature, pressure, polarity, pulse pattern and overshoot duration. The 2400 V default and 1.2 reserve are illustrative, not a motor rating or an IEC test requirement.
• Reactor and dv/dt filter times are guaranteed or measured cable-input performance, including local ringing. A single time cannot describe arbitrary filter resonance.
• Relative endurance uses illustrative adjustable power factors. Calibrated endurance requires matched winding data, a common failure percentile, constant pulse pattern and environment, tested stress ranges and one declared PD regime; the RPDIV must be applicable across that test domain.
• Ideal sine mode is a pure differential-mode sinusoid, without residual PWM.

This is a preliminary cable, output-treatment and winding-insulation screen. An entered margin or required phase-to-phase category does not qualify a complete motor. Obtain the motor maker's full IVIC declaration and a repetitive-impulse PD-free operating envelope. Type I systems under IEC 60034-18-41 are intended to remain PD-free; exceeding RPDIV is a reason to change filtering or insulation, not permission to consume a calculated life. Type II PD-resistant systems need their own qualification under IEC 60034-18-42 and are not covered by this Type I category screen.

The single-edge peak is capped at $(1+\Gamma_m)V_{dc}\le2V_{dc}$ only in this approximation. Finite-ramp cancellation can produce substantially lower peaks and non-monotonic exact waveforms. Barzkar and Ghassemi (2022), DOI 10.3390/vehicles4030040, PDF pp.4–7, shows this sensitivity. Interacting PWM pulses, polarity reversal, regeneration, resonance and multilevel switching can produce different or higher stresses. The symmetric peak-to-peak envelope is not a simulation of a direct polarity reversal.

A positive RPDIV voltage margin applies only within the entered qualified waveform envelope. A rise-time floor below its minimum is an unresolved coverage check, not a prediction that PD necessarily occurs. Raw twisted-pair, turn-to-turn, phase-ground or 50/60 Hz PDIV cannot be compared directly with this line-terminal stress. The actual winding voltage distribution and PD inception must come from the motor supplier or applicable tests.

The life model is an electrical endurance sensitivity, not total motor service life or remaining life. Relative-mode default coefficients are illustrative; numerical improvement ratios may be very large and are not product claims. Calibrated hours, comparisons and curve samples are automatically withheld outside the entered peak-voltage, frequency and slew ranges or across the declared PD regime, including when the reference fails those checks. The same pulse width, temperature, pressure, waveform, insulation construction and life percentile must also hold; these remain the test-data supplier's responsibility. Switching frequency is a proxy for pulse repetition only at the same PWM pattern. Arafat et al. (2026), DOI 10.1049/hve2.70174, reports non-monotonic endurance above about 100 kHz, so the inverse-frequency assumption must not be extended into that regime. Interactions, heating, space-charge effects and statistical uncertainty require separate treatment.

The roughly 201-point length grid and 81-point carrier-limited edge grid keep browser evaluation short. Linear chart chords approximate the nonlinear life curves between samples; the voltage knees are retained exactly. The life discontinuity at exactly zero cable follows the conservative finite-cable slew bound and should not be interpreted as an actual endurance jump in a short lead.

Final reactor, dv/dt filter and sine filter selection needs supplier checks for current, overload, cable capacitance, maximum length, voltage drop, losses, cooling, carrier/output frequency and drive control. No component L/C sizing or installation approval follows from the rise-time target. Common-mode voltage, bearing currents, winding turn stresses, EMC, thermal ageing and branched or parallel-motor cables are outside the model. Drive and installation work belongs to a qualified person.