Harmonic distortion affects power systems in three main ways: it increases equipment heating, increases voltage and insulation stress, and can disturb the operation of connected equipment. These effects are not always visible immediately — a system may run for some time with distortion present, but the long-term result can be overheating, accelerated insulation ageing, capacitor failures, transformer derating, nuisance tripping, metering errors or malfunction of sensitive electronics.
Section 2
Why harmonics increase heating
The most common effect of harmonics is additional heating. Harmonic currents raise the RMS current and so increase losses in conductors, windings, cores and insulation. The RMS value of a distorted current is:
\[ I_{rms}=\sqrt{I_1^2+\sum_{h=2}^{\infty}I_h^2} \]
- \(I_{rms}\)
- total RMS current
- \(I_1\)
- fundamental current
- \(I_h\)
- current at harmonic order \(h\)
With the current distortion \(THD_I=\dfrac{\sqrt{\sum_{h\ge2}I_h^2}}{I_1}\), this can be written as:
\[ I_{rms}=I_1\sqrt{1+THD_I^2} \]
- \(THD_I\)
- current total harmonic distortion (as a fraction)
so harmonics raise the total RMS current even when the fundamental load current is unchanged. Ignoring skin and proximity effects, copper loss is approximately:
\[ P_{cu}=R\sum_{h=1}^{\infty}I_h^2 = R I_1^2\left(1+THD_I^2\right) \]
- \(P_{cu}\)
- copper (conductor) loss
- \(R\)
- conductor resistance (assumed constant)
In practice, resistance rises with frequency through skin and proximity effects, so a more realistic expression uses an effective AC resistance per order:
\[ P_{cu}=\sum_{h=1}^{\infty}R_h I_h^2 \]
- \(R_h\)
- effective AC resistance at harmonic order \(h\)
- \(I_h\)
- current at harmonic order \(h\)
This matters for transformers, cables, busbars, generators and motors: even a harmonic current smaller than the fundamental can cause significant heating, because effective resistance and stray losses grow with frequency.
Section 3
Core losses and magnetic equipment
Harmonics also raise iron losses in transformers, motors and generators. Iron loss has two parts — hysteresis and eddy-current. Hysteresis loss follows approximately:
\[ P_h \propto f\,B_m^{\,n} \]
- \(P_h\)
- hysteresis loss
- \(f\)
- frequency
- \(B_m\)
- maximum flux density
- \(n\)
- Steinmetz exponent (typically about 1.6)
and eddy-current loss follows approximately:
\[ P_e \propto f^{2}\,B_m^{2} \]
- \(P_e\)
- eddy-current loss
- \(f\)
- frequency
- \(B_m\)
- maximum flux density
Eddy-current loss rises with the square of frequency, far faster than hysteresis loss, so high-order harmonics can be especially important even when their flux magnitude is small. Since \(f_h=h f_0\), frequency-dependent losses grow with harmonic order — another reason harmonic heating cannot be judged from THD alone; the individual spectrum matters. Conceptually the total iron loss is \(P_{iron}=P_{hyst}+P_{eddy}\). In detailed studies, manufacturers may need to confirm acceptable harmonic loading, since actual losses depend on construction, core material, winding design, cooling and temperature limits.
Section 4
Dielectric and insulation stress
Harmonics increase dielectric losses in capacitors, cables and insulation. In an ideal capacitor the current leads the voltage by exactly \(90^\circ\); in a real dielectric there is a small loss angle \(\delta\), and the dielectric loss is:
\[ P_d \approx \omega C V^2 \tan\delta \]
- \(P_d\)
- dielectric loss
- \(\omega\)
- angular frequency
- \(C\)
- capacitance
- \(V\)
- applied voltage
- \(\tan\delta\)
- dielectric loss tangent
At harmonic order \(h\), with \(\omega_h=h\omega_0\) and \(\tan\delta\) roughly constant:
\[ P_{d,h} \approx h\,\omega_0 C V_h^2 \tan\delta \]
- \(P_{d,h}\)
- dielectric loss at harmonic order \(h\)
- \(V_h\)
- harmonic voltage at order \(h\)
- \(\omega_0\)
- fundamental angular frequency
so dielectric loss grows with frequency and with the square of the harmonic voltage. Harmonics can also raise the peak voltage; insulation is stressed by peaks, not only by RMS. A distorted waveform may have a higher crest factor than a sine wave:
\[ CF_V=\frac{V_{peak}}{V_{rms}} \qquad (\text{pure sine: } CF_V=\sqrt{2}) \]
- \(CF_V\)
- voltage crest factor
- \(V_{peak},V_{rms}\)
- peak and RMS voltage
If harmonics raise the peak, insulation stress increases — important for cables, capacitors, transformers, surge arresters, power-electronic equipment and sensitive insulation.
Section 5
Capacitor banks: the most harmonic-sensitive equipment
Capacitor banks are strongly affected by harmonics because capacitive reactance falls with frequency, \(X_C(h)=\dfrac{X_C}{h}\), so a capacitor becomes a lower-impedance path at higher orders and tends to attract harmonic current. The harmonic current through a capacitor is:
\[ I_{C,h}=\frac{V_h}{X_C(h)}=h\,\frac{V_h}{X_C} \]
- \(I_{C,h}\)
- capacitor current at harmonic order \(h\)
- \(V_h\)
- harmonic voltage at order \(h\)
- \(X_C\)
- capacitor reactance at the fundamental frequency
so, for the same harmonic voltage, higher orders drive higher capacitor current. The total RMS current and the harmonic reactive loading are:
\[ I_{C,rms}=\sqrt{\sum_{h=1}^{\infty}I_{C,h}^2} \qquad Q_C=\sum_{h=1}^{\infty} h\left(\frac{V_h}{V_1}\right)^2 Q_{C1} \]
- \(I_{C,rms}\)
- total RMS capacitor current
- \(Q_{C1}\)
- capacitor reactive power at the fundamental
- \(V_1\)
- fundamental voltage
Table 1 — Why capacitor banks are vulnerable to harmonics.
| Harmonic Effect | Practical Consequence |
|---|
| Harmonic current absorption | Fuse operation, overheating, reduced life |
| Dielectric loss increase | Internal heating and insulation ageing |
| Voltage crest increase | Higher dielectric stress |
| Parallel resonance with source inductance | Voltage amplification and possible failure |
| Series resonance with filters or reactors | High harmonic current in a tuned path |
The most important risk is resonance. A capacitor against the system inductance forms a resonant circuit whose approximate resonant order is:
\[ h_r=\sqrt{\frac{X_C}{X_S}}=\sqrt{\frac{\mathrm{SCC}}{Q_C}} \]
- \(h_r\)
- resonant harmonic order
- \(X_S\)
- system reactance at the bus
- \(\mathrm{SCC}\)
- short-circuit capacity at the capacitor bus
- \(Q_C\)
- capacitor bank rating
Table 2 — How capacitor size and system strength move resonance.
| Change | Effect |
|---|
| Larger capacitor bank | Resonance moves to a lower harmonic order |
| Smaller capacitor bank | Resonance moves to a higher harmonic order |
| Stronger system | Resonance moves to a higher harmonic order |
| Weaker system | Resonance moves to a lower harmonic order |
This is critical because common converter harmonics are low-order — the 5th, 7th, 11th and 13th. If a bank shifts resonance close to one of these, voltage distortion and capacitor current can rise sharply. The amplification can be expressed conceptually as:
\[ A_f=\frac{Z_c}{R_s}, \qquad Z_c=\sqrt{\frac{L}{C}}=\sqrt{X_S X_C} \]
- \(A_f\)
- amplification factor at resonance
- \(Z_c\)
- characteristic (surge) impedance of the resonant circuit
- \(R_s\)
- system damping resistance
Low resistance means low damping and high amplification. A capacitor bank should therefore be assessed not only for fundamental reactive power, but for harmonic current, voltage distortion, resonance, dielectric stress and operating scenarios.
Section 7
Cables, busbars and neutral conductors
Harmonics increase heating in cables and busbars by raising RMS current and because effective resistance rises with frequency:
\[ P=\sum_{h=1}^{\infty}R_h I_h^2 \]
- \(P\)
- conductor loss
- \(R_h\)
- effective AC resistance at order \(h\) (incl. skin and proximity effects)
- \(I_h\)
- current at harmonic order \(h\)
Neutral conductors need special attention in low-voltage systems with many single-phase nonlinear loads. Triplen harmonics — especially the 3rd — are zero-sequence: balanced fundamental phase currents cancel in the neutral, but triplen currents add:
\[ I_{N,3} \approx 3\,I_{3,\text{phase}} \]
- \(I_{N,3}\)
- 3rd-harmonic neutral current
- \(I_{3,\text{phase}}\)
- 3rd-harmonic current per phase
so the neutral current can exceed the phase current even with balanced phase loads. This is especially important for:
Table 4 — Installations prone to triplen neutral current.
| Installation Type | Reason |
|---|
| Offices and commercial buildings | Many single-phase switched-mode power supplies |
| Data centres | High density of electronic loads |
| LED lighting installations | Electronic drivers |
| EV charging installations | Power-electronic converters |
| Industrial panels | Mixed single-phase nonlinear loads |
Neutral sizing, thermal assessment, harmonic filtering and load balancing should therefore be considered.
Section 8
Rotating machines and generators
Rotating machines are affected by harmonic currents and voltages through extra losses, heating, torque pulsation and vibration. Positive-sequence harmonics produce a field rotating with the fundamental; negative-sequence harmonics produce a field rotating against it. These fields interact with the rotor and cause heating and torque pulsation. The sequence follows the order:
Table 5 — Harmonic sequence by order, with examples.
| Harmonic Order | Sequence | Example Orders |
|---|
| \(h=3n+1\) | Positive sequence | 7th, 13th |
| \(h=3n-1\) | Negative sequence | 5th, 11th |
| \(h=3n\) | Zero sequence | 3rd, 9th |
Negative-sequence currents are particularly important for generators and motors because they induce rotor currents at frequencies that can cause severe heating. For generators, the negative-sequence withstand is often given as an \(I_2^2 t\) thermal capability:
\[ I_2^{2}\,t = K \]
- \(I_2\)
- negative-sequence current
- \(t\)
- duration
- \(K\)
- machine-dependent thermal constant (from the manufacturer or standard)
Harmonics also produce pulsating torques, which can cause vibration, noise, mechanical stress and interaction with shaft torsional modes — if a harmonic torque frequency is near a mechanical natural frequency, torsional resonance may occur. The practical risks are:
Table 6 — Practical harmonic risks for rotating machines.
| Risk | Explanation |
|---|
| Additional copper loss | Harmonic RMS current increases stator heating |
| Rotor heating | Negative-sequence components induce rotor currents |
| Iron loss increase | Harmonic flux increases core losses |
| Torque pulsation | Harmonic fields interact with the fundamental |
| Vibration and noise | Pulsating electromagnetic torque |
| Shaft stress | Possible torsional interaction |
| Reduced efficiency | Additional electrical and mechanical losses |
For generators and large motors the harmonic withstand should not be assumed — manufacturer confirmation is often required, especially with converter loads, HVDC, large drives or unbalanced harmonic conditions.
Section 9
Protection, metering, control and communication
Many protection and control devices measure RMS values, peaks, zero crossings, phase angles or frequency components — all of which distortion can change. Protection may be affected in several ways:
Table 7 — Possible harmonic effects on protection.
| Equipment | Possible Harmonic Effect |
|---|
| Overcurrent relays | Incorrect RMS or peak response depending on measurement method |
| Earth-fault relays | Sensitivity to zero-sequence and triplen harmonics |
| Distance relays | Incorrect impedance estimation under distorted voltage/current |
| Differential relays | Harmonic restraint or blocking may be affected |
| Circuit breakers | Interruption affected by waveform distortion and recovery voltage |
| Voltage relays | False operation from distorted RMS or peak voltage |
Metering also responds differently to non-sinusoidal waveforms: true-RMS meters generally perform better than average-responding meters, but accuracy still depends on bandwidth, crest-factor capability and harmonic content. Electronic controls, synchronising and timing circuits rely on clean voltage zero crossings, which distortion can shift — causing timing errors. Sensitive equipment can experience:
Table 8 — Effects on sensitive equipment.
| Effect | Example |
|---|
| Maloperation | Incorrect control triggering |
| Nuisance tripping | Protection or electronic controls operate incorrectly |
| Communication interference | Harmonic coupling into signal circuits |
| Data errors | Sensitive electronics affected by a distorted supply |
| Reduced life | Thermal or dielectric stress in components |
Harmonic currents can also couple inductively into communication circuits — historically a telephone-interference concern where power and signal circuits run close together. The effect depends on the harmonic magnitude \(I_h\) and order \(h\), the circuit geometry and separation, screening and the soil return path; higher-frequency harmonics tend to couple more strongly, and weighted indices (telephone interference factors) are used where relevant. Interference is therefore not governed by total current distortion alone.
Section 11
Practical design and mitigation
Table 10 — Main harmonic mitigation options.
| Mitigation Method | Purpose |
|---|
| Detuned capacitor banks | Prevent resonance at characteristic harmonic orders |
| Passive harmonic filters | Provide low-impedance paths for selected harmonics |
| Active harmonic filters | Inject compensating harmonic currents |
| Multi-pulse converters | Reduce lower-order characteristic harmonics |
| Phase-shifting transformers | Cancel selected harmonic orders |
| Line reactors or DC chokes | Smooth converter current and reduce harmonic magnitude |
| Transformer derating | Reduce thermal loading under harmonic current |
| Oversized neutrals | Manage triplen harmonic current |
| Separation and screening | Reduce communication interference |
| Operating restrictions | Avoid resonance-prone switching combinations |
A detuned capacitor bank is often used instead of a plain bank where nonlinear loads are present: a series reactor shifts the bank tuning frequency below the dominant harmonic order — usually below the 5th in many industrial systems — reducing the risk of parallel resonance with the supply and limiting the harmonic current absorbed by the capacitor. The design must be checked carefully, because a filter or detuned bank is itself a frequency-dependent device: it can solve one resonance problem and create another if not correctly designed.
Key message
Harmonics affect power systems mainly by increasing losses, heating, voltage peaks, insulation stress and operational disturbance. Capacitors are vulnerable because their impedance falls with frequency and they can resonate with system inductance; transformers because winding eddy and stray losses rise strongly with order; cables and neutrals through higher RMS current, skin/proximity effects and triplen summation; machines through heating, negative-sequence effects and torque pulsation; and protection, metering, control and communication because harmonics distort the quantities they rely on. The central conclusion is that harmonic distortion is both an emission problem and an equipment-duty problem: a system can meet the PCC voltage limit yet still overstress internal equipment. For design, keep \(V_h=Z_h I_h\) in mind — the source sets the current, the network sets how much voltage distortion results, and the equipment sets how much can be tolerated. Good harmonic engineering combines source control, network frequency-response assessment, equipment-duty verification and appropriate mitigation.
