The panel or meter shows a higher voltage at the unloaded end of a 60 Hz line, and the first suspicion is a VFD-style reflected-wave problem. Start with the waveform. A steady power-frequency voltage rise, a short switching surge, and a fast PWM pulse are three different faults. Treating them alike leads to filters, reactors, and terminations that do not address the cause.
Identify the waveform first
Measure the voltage at the connected end and the remote end. Record the steady 60 Hz value, then capture any fast event with an instrument, probe, and connection method suited to the expected voltage and edge rate.
| Observed symptom | Likely mechanism |
|---|---|
| Remote-end RMS voltage rises steadily when the line is lightly loaded or open | Distributed shunt capacitance supplies reactive current through the line inductance, raising the open-end voltage. |
| Brief remote-end voltage peak during switching | A traveling surge meets an impedance discontinuity and reflects. |
| Repeated peaks associated with VFD output pulses | Fast PWM edges make the motor cable electrically long even though the same cable is short at 60 Hz. |
| Voltage magnitude varies slowly across many cycles | System or electromechanical oscillation, not an individual reflected 60 Hz wave. |
If the reading is a stable 60 Hz rise, continue with electrical length. If it is a fast transient, inspect the switching source, surge path, cable, and termination instead. Installing a VFD output filter on a circuit that only has steady power-frequency voltage rise wastes time.
Calculate the line electrical length
Use the dimensionless propagation factor:
K = 2*pi*f*sqrt(L*C)*length
Use inductance L and capacitance C per unit length, line length in the matching unit, and frequency f. When K is much smaller than 1, a lumped pi circuit normally captures the power-frequency behavior. As K approaches 1, solve the distributed line equations or apply correction factors derived from them.
For a representative two-bundle 345 kV overhead line with L = 9.83x10^-7 H/m, C = 11.59x10^-12 F/m, and resistance treated as approximately zero, the stated results are:
- 50 km:
K = 0.063 - 100 km:
K = 0.127 - 300 km:
K = 0.382
Those values show why even hundreds of kilometres can occupy only a fraction of a 60 Hz wavelength. Pronounced standing-wave behavior belongs to much greater electrical lengths; about 1250 km was identified as the scale at which wave effects become material for the stated case.
A household appliance branch circuit is far shorter electrically at 60 Hz. Its ordinary voltage drop, conductor impedance, connections, and load current deserve attention before power-frequency reflections. Fast switching disturbances are separate because their high-frequency content has a much shorter wavelength.
Check whether the remote end is open
Disconnecting or reducing the load removes the remote termination but leaves the line capacitance connected. The capacitance generates reactive current. That current flows through the series inductance toward the energized end and creates a voltage difference, so the open end can sit above the connected-end voltage.
A simplified open-end relationship from the pi representation is:
Vopen_end = Vconnected_end * (Zc / (Zc + ZL))
Zc represents the shunt capacitive impedance and ZL the series inductive impedance. Their reactive signs oppose each other. Under the stated operating condition, the denominator can be smaller in magnitude than Zc, producing a ratio greater than 1. This is not an automatic two-times voltage rise.
- Measure both endpoint voltages under the same source condition.
- Record whether the remote end is open, lightly loaded, or normally loaded.
- Repeat the reading after applying the intended load, where operating rules permit it.
- If the voltage rise collapses with load, move to the capacitance and reactive-current check.
- If sharp peaks remain, return to transient capture; the steady-state pi model is not the complete diagnosis.
Measure charging current and reactive behavior
Cable requires attention at shorter physical lengths because its capacitance per unit length can be much higher. For the theoretical cable values L = 9.83x10^-7 H/m, C = 190x10^-12 F/m, and resistance treated as approximately zero, the stated factors are:
- 10 km:
K = 0.052 - 50 km:
K = 0.258 - 100 km:
K = 0.515 - 200 km:
K = 1.030
Start by reading the actual cable capacitance from its datasheet or test record. Calculate the charging current at the operating frequency, then compare it with measured no-load current and equipment limits. High charging current can constrain usable cable length and change the receiving-end voltage substantially as load changes, even before a dramatic standing-wave pattern becomes the main issue.
Do not reuse overhead-line capacitance for a cable calculation. Do not select compensation from length alone. The source impedance, line inductance, distributed capacitance, connected load, and switching state all change the voltage profile.
Separate surges and system oscillations
A small steady open-end rise does not rule out a much larger switching surge. An impedance discontinuity can reflect a transient, and an open termination is the limiting reflection case. Capture the event at both ends and compare its timing with breaker, contactor, converter, or load switching.
Also check the time scale. A slow brightening-and-dimming pattern near 1 Hz belongs to electromechanical interaction or power-system resonance, not a 60 Hz wave bouncing on a branch circuit. Review disturbance records, generator or motor behavior, and system oscillation channels instead of fitting a transmission-line termination.
These checks prevent two common errors: calling every endpoint voltage increase a reflected-wave doubling, and calling every slow voltage swing a transmission-line reflection.
Apply the model and verify the result
- Classify the measurement as steady 60 Hz voltage, switching transient, repeated PWM pulse, or slow modulation.
- Collect the actual line length and per-unit-length
L,C, and resistance data. - Calculate
K. Use a pi model only while the result is well below 1; move to a distributed model as electrical length becomes material. - Model the real termination state. Include the open, light-load, and normal-load cases that operators can create.
- For a steady rise, compare predicted and measured connected-end voltage, open-end voltage, and charging current.
- For a transient, capture peak magnitude and event timing at both ends, then analyze the switching source and impedance discontinuity.
- Repeat the measurements after the corrective change. Verify both the endpoint voltage and current; a lower voltage with excessive charging current is not a complete fix.
Reject the model if endpoint readings, load state, and charging current cannot be reconciled. Recheck units first: mixing inductance or capacitance per metre with length in kilometres corrupts K immediately.
FAQ
What happens if the far end is open at 60 Hz?
The line capacitance drives reactive current through the series inductance, so the open-end voltage can exceed the connected-end voltage. Calculate K and compare simultaneous endpoint readings before treating the rise as a traveling-wave fault.
What happens if cable capacitance is high?
Charging current rises and the receiving-end voltage becomes more sensitive to loading. Use the cable's actual C value; the theoretical case reaches K = 0.515 at 100 km and K = 1.030 at 200 km.
When should I stop testing and escalate to official support?
Stop when the measured endpoint voltage or transient exceeds equipment limits, switching cannot be performed safely, or a distributed model still cannot reproduce the measured voltage and charging current. Escalate with waveform captures, endpoint readings, line data, load state, switching sequence, and the K calculation to the utility, system operator, or equipment manufacturer's official support channel.