Harmonics
What it does
Some loads do not draw a pure sine-wave current. Examples: variable speed drives, rectifiers, LED lighting and PV inverters. These non-linear loads draw current at multiples of the fundamental frequency. These multiples are the harmonic orders. For example, on a 50 Hz system, the 5th harmonic is 250 Hz.
The harmonic currents flow through the network impedance. They cause voltage distortion at each bus — not only at the bus where the load is connected.
Phasor runs two related calculations:
- Frequency scan. Phasor sweeps the driving-point impedance at each selected bus, across the harmonic orders. It plots the impedance magnitude against frequency. Each peak is a parallel resonance. A parallel resonance occurs where a capacitor bank and the upstream inductance make a tank circuit. At a resonance, a small harmonic current makes a large harmonic voltage. The frequency scan explains why a network distorts. It needs no harmonic source data.
- Harmonic voltage penetration. Phasor injects the harmonic current spectrum of each non-linear load. It solves the network at each order. The result is the voltage distortion at each bus.
When you supply the source spectra, the results include:
- Individual harmonic voltage — the magnitude of one order, as a percentage of the solved fundamental voltage.
- Voltage THD — the total harmonic distortion: the RMS of the calculated harmonic voltage components, relative to the fundamental.
- Source current evidence — the Norton current magnitude and phase that Phasor used at each supplied order.
How to run a harmonic study
- Start from a converged fundamental case. The base is a persisted, converged NR or FDLF study case. The scan uses the passive network of that scenario and its solved fundamental voltage. This makes the result reproducible.
- Run the frequency scan first. If a resonance is near an order that your loads inject, that is the finding. No amount of spectrum data changes it.
- Enter load spectra only from traceable data. Use manufacturer data or measured spectra. Phasor supplies no invented default spectrum. The reason: if you assume a six-pulse spectrum where a twelve-pulse drive is installed, the calculated 5th and 7th harmonics are much too high.
- Solve the penetration case. Read the voltage distortion for each bus.
- Assess the evidence in the project context. Phasor calculates the scan, the harmonic voltages and the voltage THD. Phasor does not give an IEEE 519 or IEC 61000-3-6 compliance verdict. That assessment is yours.
- Test the mitigation in the model. Options: detuned reactors on the capacitor banks, passive filters, or a different converter topology. Then run the frequency scan again. A filter that removes one resonance can make a new resonance at a different order.
Inputs and outputs
Inputs
| Input | Notes |
|---|---|
| Fundamental case | A persisted, converged, balanced NR or FDLF study case. |
| Monitor nodes | One to sixteen energized network nodes. A slack node is not permitted. |
| Harmonic sources | Optional: a current spectrum per order, with magnitude and phase angle. |
| Passive network | Branch resistance stays constant. Reactance scales with the order. Charging and shunt susceptance scale with the order. |
| Scan range | The orders to sweep, and the step size within an order. |
Outputs
| Output | Notes |
|---|---|
| Driving-point impedance | Magnitude and angle against frequency, for each monitored bus. |
| Resonance candidates | The strict local maxima, ranked, with order, frequency and impedance magnitude. |
| Harmonic voltage | For each order: the magnitude, the percentage of the fundamental, and the phase angle. |
| Voltage THD | The THD and the dominant calculated order, for each bus. |
| Source currents | The explicit Norton currents that the penetration solve used. |
Notes
Phase angles have a large effect. Harmonic currents from different sources can partly cancel each other. If you add the magnitudes and ignore the angles, the result is conservative. Sometimes it is so conservative that it fails an installation that would pass.
This is a positive-sequence planning model. These effects are outside the current calculation: transformer harmonic-sequence propagation, skin and proximity correction curves, distributed line models, converter controls, and interharmonic modulation.
A frequency scan is low-cost insight
You can run a frequency scan with no harmonic source in the model. The scan tells you if the network has a resonance that waits for a source. It is the fastest useful harmonic result from a model that you already built for power flow.