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Impedance: a weak source turns bad current into bad voltage

Reactive, harmonic and unbalanced current pays a toll in the source impedance. On a generator or an inverter, that toll is bad voltage. We change the current through the impedance, not the impedance itself.

Impedance is the property of a supply that turns current into voltage drop. A transformer has a nameplate impedance. A cable has resistance and reactance per foot. A utility service has a short-circuit strength. Together they set how far the bus voltage moves when the loads draw current, and how much of each harmonic current becomes harmonic voltage.

On a stiff source, one with low impedance, a distorted current makes little distorted voltage, so the current goes unnoticed. On a weak one, such as a generator or a long feeder, every ampere of it shows in the voltage.

What impedance does

Current the controller supplies beside the loads never flows through the source impedance, so it causes no drop across it. The controller changes the current through the source impedance, not the impedance itself. On a stiff utility source the change in voltage is small 14.

  • Generators. Ships, remote plants and standby sets. On a 12% to 20% impedance generator set, the same current makes up to about four times the voltage distortion of a utility transformer 5.
  • Capacitor banks. Panels with existing correction. The Army’s facilities manual lists what follows a bank resonance: blown fuses, failed capacitors and tripped relays 11.
  • Weak interconnections. Inverter microgrids and long feeders. IEEE 519 tightens the harmonic current limit as the source gets weaker. It falls from 20% total demand distortion on a stiff bus to 5% on a weak one 9.
  • At the panel. Correction beside the loads. The controller supplies reactive, harmonic and unbalanced current locally, so those currents cause no drop across the source impedance 13.

Conductor and winding loss is a sum over frequencies: the current at each frequency, squared, times the resistance at that frequency 1. Skin and proximity effects raise the resistance with frequency. In a cable it rises roughly as the square root of the harmonic order, the multiple of the supply frequency a harmonic sits at 2. In a transformer winding, the eddy-current share of the loss rises as the square of the order. That is the basis of the K-factor 3.

Resistance rises with the harmonic orderTwo panels. In the first, resistance rises with the harmonic order as the square root of the order, the way a cable behaves. In the second it rises as the square of the order, the way a transformer winding behaves.Resistance rises with the harmonic orderTwo relations, two panels. Neither axis carries a scale.A cableResistance15723Harmonic orderabout the square rootof the orderA transformer windingResistance15723Harmonic orderthe square of the order:the basis of the K-factorCable: Journal of Physics Conference Series 2527 (2023). Transformer winding: a leading maker’sK-factor paper, quoting IEEE C57.110-2018.Resistance rises with the harmonic orderTwo relations, no scaleA cableResistance15723Harmonic orderabout the square rootof the orderA transformer windingResistance15723Harmonic orderthe square of the order:the basis of the K-factorCable: Journal of Physics Conference Series 2527(2023). Transformer winding: a leading maker’sK-factor paper, quoting IEEE C57.110-2018.
The shapes are drawn without a scale. On a single axis the winding curve would bury the cable curve. The page makes no claim about their relative size.

The bus is the common connection at the panel that every load hangs from. Its voltage is the source voltage minus the load current times the source impedance 4. Two impedances set that number. The load impedance decides how much current is drawn, and the source impedance decides how much voltage that current costs.

Reactive current lowers the fundamental voltage, harmonic current makes harmonic voltage at each order and unbalanced current makes unbalanced voltage. Each effect grows with the impedance.

An illustrative trace of one load current into two sources, not a capture. The Green Grid’s table puts a generator set at 12% to 20% impedance and a utility transformer at 5% to 7% 5. The two states drawn are 15% and 5%. Two harmonics ride on the load current: a 22% fifth and a 13% seventh, and each meets a reactance that rises with its own order.

What it costs

The weak source pays most. A generator set’s typical impedance of 12% to 20% is up to about four times a utility transformer’s 5% to 7% 5. A leading generator maker’s application note says the alternator’s reactance sets the distortion for a given current 6. We found no published figure in dollars for what a weak source costs a facility.

A laboratory test of a data center UPS shows the exchange directly: the same disturbance appears as less current and more voltage as the source gets weaker. When the grid impedance was raised, the UPS switching emission near 28 kHz fell 61% in current and rose 28% in voltage 7.

An interconnection with a short-circuit ratio below 3 is classed as weak 8. Microgrids, ships and remote plants live there.

How the industry has dealt with it

The design answer has been a smaller impedance, or less current through it. That means a lower-impedance transformer and shorter, fatter feeders. It also means capacitor banks and filters near the loads, so reactive and harmonic currents circulate locally.

A K-rated transformer does not lower the harmonic current. It tolerates the heat the current makes 3. A tuned passive filter presents a low impedance at one order and moves the resonance to another.

The capacitor bank creates a resonance of its own with the source reactance at the order sqrt(S_sc / Q). S_sc is the short-circuit power and Q the bank rating. In one leading maker’s worked example, a 350 kvar bank on a 630 kVA transformer resonates at the 5.5th harmonic 10.

More of the sources are now inverters. A grid-following inverter injects current but needs a voltage to follow. A grid-forming inverter holds the voltage within its current limit 12.

The transformer, feeder, bank and filter above are each sized once, for the load study of the day. The correction below is digital and follows the current as it changes.

How Software-Defined Electricity handles it

The controller connects to the panel bus through its own breaker, beside the loads and not in series with them. It supplies the reactive, harmonic and negative-sequence currents locally, in under 5 microseconds 13, so those currents drop out of the upstream sum. Negative-sequence current is the unbalanced part of a three-phase current. Locally means beside the loads at the panel, so the controller’s current never passes through the source impedance and causes no drop across it. The controller holds source and load impedance matched for maximum power transfer: impedance matching 13,16.

The upstream loss falls at each frequency, weighted by the resistance there. The plant’s own voltage drop falls by the removed current times its upstream impedance, within the controller’s rating 13,1.

On a stiff utility source, that share is small. A field assessment on a 120 V panel recorded 119.53 V uncorrected and 119.52 V corrected 14. A generator can have up to about four times the impedance. There the same correction moves the harmonic voltage up to about four times further 5. The controller is an active full-bridge converter, not a capacitor bank, so the bank resonance above does not arise from it 13.

An illustrative trace, not a capture. A facility at 0.85 power factor pushes 18% more current through the same source impedance than the work needs 16. The corrected trace is the working current alone.

Where it matters

This matters most on weak sources. A ship runs on generators, and a microgrid runs on inverters. A network coming back in a blackstart has no stiff grid behind it. Each of those pages carries what was measured on a bus like it.

The weak source belongs to two of the three directions this site calls Opportunity Pillars. Generation is where the source is a generator or an inverter rather than a stiff grid. Delivery is where a long feeder’s impedance is the source the load sees.

What to measure

Measure the source impedance at the bus on the day. Do not take it from the nameplate. A motor start or a load-bank step changes the current by a known amount. The half-cycle root-mean-square (rms) voltage change divided by the current change is the impedance 1,15. A low power factor step, such as a motor start, reads mostly the source reactance 1. Read the harmonic voltage at the panel before and after correction on the same load.

The share of the voltage drop and distortion that arrives from the utility side stays. The branch circuits downstream still carry the full current at the full impedance.

Where each instrument reads and where the corrector sitsWhere each instrument reads and where the corrector sits. The corrector removes the load-driven share of the voltage drop and nothing else.Where each instrument reads and where the corrector sitsUtility sourceSource impedance Z_s(transformer, feeder)Revenue meter15 min, kVARhClass A analyzer, PCC200 ms, 3 s, 10 minSource carries the loads’ active current only, within ratingPanel busDrive (6-pulse):harmonicsMotor (line-fed):reactiveSingle-phase loads:unbalance, triplensUPS (double conversion):its own ride-throughSDE shunt corrector: inparallel, never in the powerpath. Supplies I_q, I_hthrough the 23rd order,I_minus, I_zero, withinrating and inside the band.dedicated breakerVoltage at the panel has two sharesV_panel = V_utility minus I_loads × Z_sUtility-deliveredshare: stays.Distortion, unbalance andsags arriving from upstreamof Z_s.Load-drivenshare: removed.The corrected loads’reactive, harmonic andunbalanced current timesthe plant’s own Z_s.Illustrative topology. The corrector sits in parallel through its own breaker: never in series, never on a drive output andnever upstream of the UPS. Operating band ±15% V, ±0.5% Hz.Where each instrument reads and where the corrector sitsUtility sourceSource impedance Z_s(transformer, feeder)Revenue meter15 min, kVARhClass A analyzer, PCC200 ms, 3 s, 10 minPanel busSource carries the loads’ active current only, within ratingDrive (6-pulse): harmonicsMotor (line-fed): reactiveSingle-phase loads: unbalance, triplensUPS (double conversion): its own ride-throughSDE shunt corrector: in parallel, never in the power path.Supplies I_q, I_h through the 23rd order, I_minus, I_zero,within rating and inside the band.dedicatedbreakerVoltage at the panel has two sharesV_panel = V_utility minus I_loads × Z_sUtility-deliveredshare: stays.Distortion, unbalance and sagsarriving from upstream of Z_s.Load-drivenshare: removed.The corrected loads’ reactive,harmonic and unbalancedcurrent times the plant’s ownZ_s.Illustrative topology. The corrector sits in parallel through its own breaker:never in series, never on a drive output and never upstream of the UPS.Operating band ±15% V, ±0.5% Hz.
The corrector removes the load-driven share of the voltage drop and nothing else. The stated operating band is the product document’s 13.

Start by measuring the impedance at one bus before specifying a filter.

Frequently asked questions

What is impedance matching in a power distribution system?

Impedance matching is the condition of maximum power transfer, source impedance matched to load impedance, and the 3DFS controller holds that match continuously 13,16. Impedance is the property of a supply that turns current into voltage drop. The controller, beside the loads, supplies the reactive, harmonic and unbalanced currents locally, within its rating, so they do not pass through the source impedance 13. On a stiff utility source the change in voltage is small 14.

Why does a generator show more voltage distortion than a utility transformer?

Because the same current meets more impedance. The bus voltage is the source voltage minus the load current times the source impedance 4. A generator set’s typical impedance of 12% to 20% is up to about four times a utility transformer’s 5% to 7% 5. A laboratory test of a data center UPS shows the exchange: when the grid impedance was raised, the UPS switching emission near 28 kHz fell 61% in current and rose 28% in voltage 7.

How is source impedance measured at a bus?

At the bus, on the day, with a known current step. Do not take the impedance from the nameplate. A motor start or a load-bank step changes the current by a known amount, and the half-cycle root-mean-square voltage change divided by the current change is the impedance 1,15. Read the harmonic voltage at the panel before and after correction on the same load. An interconnection with a short-circuit ratio below 3 is classed as weak 8.

Sources
  1. Rule review for this series: loss as the sum over orders, the two-share rule, impedance from a step. First-party derivation.
  2. Research on Energy Efficiency Loss of Typical Distribution Network, Journal of Physics: Conference Series 2527 (2023) 012079, Eq. (6) and (7).
  3. A leading maker’s K-factor technical paper 1TQC194900E0001 (2023), quoting IEEE C57.110-2018 and UL 1561.
  4. Huang et al., Applied Sciences 2021, 11(9), 4288, Eq. (1) to (3). https://doi.org/10.3390/app11094288
  5. The Green Grid, White Paper 55, Table 3, p. 15, and p. 24.
  6. A leading maker’s generator application note AGN 025, Non Linear Loads, pp. 4-6.
  7. Sutaria and Rönnberg, IEEE Access 2023, 11, 36823, Section IV.A.1. https://doi.org/10.1109/ACCESS.2023.3266092
  8. Li et al., Electronics 2025, 14(11), 2203, Section 1. Lei and Zhao, Frontiers in Energy Research 2024, 12, 1413910.
  9. IEEE 519-2022, Table 2.
  10. A leading maker’s Electrical Installation Guide, Risk of resonance due to power-system harmonics. https://www.electrical-installation.org/enwiki/Risk_of_resonance_due_to_power-system_harmonics
  11. U.S. Army, TM 5-689 (2006), paragraphs 5-4 a(2) and 5-4 b.
  12. Shi, Bai and Wang, Nature Communications 2026, 17, 8498. https://doi.org/10.1038/s41467-026-76692-0
  13. 3DFS, VectorQ Technical Overview (current revision), Technical Specifications table, pp. 9 and 12 (p. 12, impedance matching as maximum power transfer). First-party.
  14. 3DFS, electrical network analysis of server racks at a data center, Assessment 1 overview sheet. First-party.
  15. IEC 61000-4-30:2025, clauses 3 and 4.4.
  16. 3DFS, Power Quality Impact White Paper, System Losses: 0.85 power factor needs 18% more current than unity. P. 7, impedance matching as maximum power transfer. First-party.

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