Harmonics @ Discussion

❖ Harmonics refer to voltage or current waveforms that have

frequencies that are integer multiples of the fundamental frequency
of the power system. In electrical power systems, the fundamental
frequency is typically 50 Hz (India, Europe) or 60 Hz (USA, Canada).
❖ If the fundamental frequency is f, harmonics are given by:
h = nf
where:
▪ h = Harmonic frequency
▪ n = Harmonic order (integer: 2, 3, 4, …)
▪ F = Fundamental frequency
For example, in a 50 Hz system, the harmonics are:
▪ 2nd harmonic = 100 Hz
▪ 3rd harmonic = 150 Hz
▪ 5th harmonic = 250 Hz, and so on.
 Types of Harmonics @ Discussion
1) Even Harmonics (2nd, 4th, 6th, …) - Less common, but can occur
due to asymmetry in circuits.
2) Odd Harmonics (3rd, 5th, 7th, …)- More common in power systems.
3) Triplen Harmonics (3rd, 9th, 15th, …) - These harmonics, multiples
of 3, add up in the neutral conductor and can cause overheating.
4) Interharmonics - Frequencies that are non-integer multiples of the
fundamental (e.g., 75 Hz in a 50 Hz system).
5) Subharmonics - Frequencies below the fundamental frequency (e.g.,
25 Hz in a 50 Hz system).
❖ Harmonic distortion is the presence of unwanted frequency components in
a power system. These unwanted components are integer multiples of the
fundamental frequency (usually 50 or 60 Hz) and can significantly impact
the performance and reliability of the power system. There are several
causes of harmonic distortion in power systems, which can be broadly
categorized as follows: Non-linear Loads, Power Electronic Devices,
Magnetic Saturation, Resonance, Faults, and Asymmetrical Conditions.
 Causes of Harmonic Distortion @ Discussion
▪ Non-linear Loads: The primary cause of harmonic distortion is the presence of
non-linear loads. These loads draw current in a non-sinusoidal manner,
causing the current waveform to be distorted. Examples of non-linear loads
include power electronic devices such as rectifiers, inverters, adjustable
speed drives, and electronic equipment like computers, fluorescent lights,
and LED lamps. The switching operations in these devices generate harmonics,
which can then propagate through the power system.
▪ Power Electronic Devices: As mentioned above, power electronic devices like
inverters and converters are significant sources of harmonics. The rapid
switching operations in these devices can generate high-frequency harmonics
that can propagate throughout the system. In addition, the control algorithms
used in these devices can introduce interharmonics, which are non-integer
multiples of the fundamental frequency.
▪ Magnetic Saturation: Magnetic saturation in transformers and other inductive
devices can also lead to harmonic distortion. When a transformer becomes
saturated, its magnetizing current becomes non-linear, leading to the generation
of harmonics. This phenomenon is more likely to occur during high-load
conditions or when the transformer is subjected to an overvoltage.
 Causes of Harmonic Distortion @ Discussion
▪ Resonance: Resonance can occur in power systems when the system's
natural frequency aligns with one or more harmonic frequencies. This
can cause harmonic amplification, significantly increasing the
harmonic distortion levels. Resonance can occur due to the interaction
between the system's inductive and capacitive components, such as
transformers, capacitor banks, and transmission lines.
▪ Faults and Asymmetrical Conditions: Faults, such as short-circuits,
or asymmetrical conditions, such as unbalanced loads, can also cause
harmonic distortion. These situations can result in non-sinusoidal
currents and voltages, generating harmonics.
❖ Different types of harmonic distortion, namely voltage and current
harmonics, each have unique impacts on power quality and the operation
of electrical equipment.
❖ The presence and impact of harmonic distortion are measured using
various harmonic indices. The most common measurements include Total
Harmonic Distortion (THD) and Individual Harmonic Distortion (IHD).
 Generation of Harmonics by Converters
❖ Converters transform AC to DC (rectifier) and DC to AC (inverter).
However, due to their nonlinear switching operation, they introduce
harmonics into both the AC and DC sides of the system.
❖ Converters, generate harmonics due to the non-sinusoidal nature of
their operation, leading to distortion in the current and voltage
waveforms.
❑ Causes of Harmonic Generation
▪ Switching Devices: The rapid switching on and off of power
electronic components like thyristors, IGBTs, and MOSFETs in
converters creates non-linear current waveforms.
▪ Non-Linear Loads: Converters themselves, along with other non-
linear loads (like rectifiers, inverters, and variable frequency drives),
draw non-sinusoidal currents, leading to harmonic generation.
▪ Saturation: Saturation of magnetic components in transformers and
inductors can also introduce harmonics.
 Generation of Harmonics by Converters @ Continuation
❖ HVDC converters are typically thyristor-based line-commutated
converters (LCC) or voltage source converters (VSC).
a) Line-Commutated Converters (LCC) Harmonics: LCCs use
thyristors, which switch on and off in synchronization with the AC
voltage waveform. The conversion process introduces characteristic
harmonics and non-characteristic harmonics.
1) Characteristic Harmonics: These harmonics follow a
predictable pattern and are given by the formula:
h = np ± 1
where:
▪ h = harmonic order
▪ n = integer (1, 2, 3, …)
▪ p = pulse number of the converter (typically 6 or 12 in HVDC
systems)
 Generation of Harmonics by Converters @ Continuation
For a 6-pulse converter, the characteristic harmonics are:
▪ AC side: 5th,7th,11th,13th,...
▪ DC side: 6th, 12th, 18th,...
For a 12-pulse converter (using phase-shifting transformers to cancel
harmonics)
▪ AC side: 11th,13th, 23rd, 25th,...
▪ DC side: 12th, 24th, 36th,...
These harmonics arise because the converter switches in discrete steps,
creating a non-sinusoidal waveform.
(ii) Non-Characteristic Harmonics
These occur due to asymmetries, such as:
▪ Voltage unbalance in AC supply, Unequal transformer
impedance, Control system imperfections
▪ Non-characteristic harmonics may include even harmonics
(e.g., 2nd, 4th) and subharmonics.
 Generation of Harmonics by Converters @ Continuation
(b) Voltage Source Converters (VSC) Harmonics: VSC-based HVDC
uses IGBTs or MOSFETs, operating with Pulse Width Modulation
(PWM). Harmonics generated in VSCs differ from those generated in
LCCs.
1) Switching Frequency Harmonics: VSCs switch at high frequencies
(kHz range), creating harmonics around the switching frequency and
its multiples.
2) Low-Frequency Harmonics: Unbalanced operation or DC voltage
ripple can introduce low-frequency harmonics (2nd, 3rd order).
3) Interharmonics: Unlike LCCs, VSCs can generate interharmonics,
which are non-integer multiples of the fundamental frequency.
❖ Harmonic generation in HVDC converters is primarily due to switching
behavior and non-linearity in conversion. LCCs mainly produce low-order
harmonics, while VSCs introduce high-frequency harmonics and
interharmonics. Advanced filtering techniques, improved modulation
strategies, and phase-shifting transformers are used to mitigate these harmonics.
 Impact of Converter Harmonics
Harmonics generated by converters can cause
▪ Power quality issues (voltage waveform distortion)
▪ Equipment heating and losses (transformers, cables, capacitors)
▪ Electromagnetic interference (EMI)
▪ Malfunction of protection systems
▪ Increased stress on insulation in HVDC cables and transformers
❖ Power Quality Issues: Harmonics can cause voltage distortion,
overheating of equipment, and reduced efficiency.
❖ Equipment Damage: High levels of harmonics can damage sensitive
equipment and disrupt the operation of power systems.
 Harmonics Mitigation Techniques
To minimize the adverse effects of harmonics in HVDC systems, various
techniques are employed:
▪ Passive and Active Harmonic Filters
▪ Multi-Pulse Converters (e.g., 12-pulse, 24-pulse)
▪ Tuned Filter Banks
▪ HVDC Modulation and Control Adjustments
▪ Use of PWM Converters in Modern HVDC Systems
▪ Filters: Harmonic filters can be used to reduce the level of harmonics
in the power system.
▪ Active Power Filters: These filters can actively compensate for
harmonics by injecting counter-harmonics into the power system.
▪ Improved Converter Design: Using advanced converter topologies
and control techniques can help reduce harmonic generation.
 Harmonic Mitigation in Converters
To reduce harmonic distortion, the following techniques are used:
a) For LCC-Based HVDC
▪ Use of 12-pulse or higher-pulse converters
▪ AC and DC harmonic filters (passive filters tuned to eliminate
characteristic harmonics)
▪ Synchronous condensers for reactive power support and harmonic
damping
▪ Phase-shifting transformers to cancel harmonics at the fundamental
frequency
b) For VSC-Based HVDC
▪ Higher switching frequency to shift harmonics away from
fundamental frequency
▪ Active harmonic filters
▪ Modulation techniques like Space Vector PWM (SVPWM) to
reduce lower-order harmonics
 Sources of Harmonics in HVDC Systems
Harmonics in High Voltage Direct Current (HVDC) systems primarily
originate from the conversion process and associated components. The
major sources include:
1) Converters (Rectifiers & Inverters)
▪ HVDC systems use thyristor-based or IGBT-based converters,
which introduce non-sinusoidal currents.
▪ The switching action of these converters generates characteristic
and non-characteristic harmonics.
2) Transformer Magnetization Non-Linearity
▪ Converter transformers operate under non-sinusoidal conditions,
causing magnetization harmonics.
3) AC & DC Filters
▪ Improper design or resonance effects in filters can introduce
additional harmonic components.
 Sources of Harmonics in HVDC Systems @ Continuation
4) DC Side Components
▪ Smoothing reactors, capacitors, and cables may exhibit non-linear
behaviors that contribute to harmonic distortion.
5) Commutation Process
▪ Commutation overlaps in thyristor-based converters lead to
voltage dips and harmonic distortions.
6) Control System Interactions
▪ HVDC control systems, including current and voltage regulators,
can contribute to low-frequency harmonics due to their dynamic
response.
 Adverse Effects of Harmonics in HVDC Systems
The presence of harmonics can cause several operational and reliability issues,
including:
1) Power Quality Degradation: Harmonics lead to voltage and current waveform
distortion, affecting the quality of the power supply.
2) Increased Losses: Additional losses occur in transformers, generators, and
transmission lines, reducing system efficiency.
3) Equipment Overheating: Transformers, capacitors, and cables experience
increased thermal stress, leading to insulation degradation and reduced lifespan.
4) Electromagnetic Interference (EMI): Harmonics can interfere with
communication and control signals, causing malfunctions in sensitive
equipment.
5) Resonance Issues: Harmonics can excite network resonances, leading to over-
voltages and equipment failures.
6) Protective Relay Malfunction: Relays may misoperate due to distorted
waveforms, leading to false tripping or failure to detect faults.
7) Increased Audible Noise: Harmonic components can cause transformers and
rotating machines to produce additional noise.
 Characteristics of Harmonics on DC-Side
❖ Harmonics on the DC side of an HVDC system are primarily caused
by the operation of converters (rectifiers and inverters). These
harmonics arise due to the switching behavior of thyristors or IGBTs,
leading to non-sinusoidal DC waveforms.
❖ Nature of DC Side Harmonics
Unlike the AC side, where harmonics are present in the form of
voltage and current distortions at multiple frequencies, the DC side
harmonics mainly appear as:
▪ Ripple in DC voltage and current
▪ Pulsating components superimposed on the DC signal
▪ Even-order harmonics (unlike the AC side, where odd-order
harmonics dominate)
▪ DC side harmonics in HVDC systems are multiples of the pulse number (p) and
cause ripple effects in voltage and current. Effective filtering, higher-pulse
converters, and optimized control strategies are necessary to mitigate these
harmonics and ensure smooth DC transmission.
 Characteristics of Harmonics on DC-Side @ Continuation
The dominant harmonic orders on the DC side of an HVDC system
follow the general formula,
h = np
where:
▪ h = Harmonic order
▪ n = Integer (1, 2, 3, …)
▪ p = Pulse number of the converter (6 for a 6-pulse, 12 for a 12-
pulse, etc.)
For different converter configurations:
▪ 6-Pulse Converter: DC side harmonics are 6th, 12th, 18th, …
▪ 12-Pulse Converter: DC side harmonics are 12th, 24th, 36th, …
These harmonics are noticeable as voltage and current ripples on the
DC side.
Ripple is the unwanted, fluctuating AC component that remains in the
DC output after the AC voltage is converted to DC.
 Characteristics of Harmonics on DC-Side @ Continuation
❖ In an HVDC system, harmonics on the DC side primarily arise due to the
operation of power electronic converters, particularly line-commutated
converters (LCC) and voltage source converters (VSC).
❖ The switching of thyristors or IGBTs introduces ripple in the DC voltage and
current, leading to the presence of harmonic components.
❖ The characteristic harmonics on the DC side follow the formula h= np, where
p is the pulse number of the converter (e.g., 6 for a 6-pulse, 12 for a 12-pulse
system), and n is an integer. This means a 6-pulse converter produces
harmonics at the 6th, 12th, 18th, and higher multiples, while a 12-pulse
converter generates harmonics at the 12th, 24th, 36th, and so on.
❖ Unlike the AC side, where odd harmonics dominate, the DC side mainly
exhibits even-order harmonics. These harmonics result in current and voltage
ripples, causing increased losses, heating in DC cables, and stress on
insulation. Additionally, harmonics can induce resonance effects, interfering
with control and protection systems.
❖ To mitigate these effects, DC smoothing reactors, passive filters, and higher-
pulse converters are used to suppress harmonic components and improve
power quality in HVDC transmission.
 Characteristics of Current Harmonics
❖ In HVDC systems current harmonics are unwanted frequency
components that arise due to the conversion processes between AC and
DC. These harmonics are primarily generated by the non-linear nature of
converter operation and are characterized by specific harmonic orders,
primarily of the form h = np ± 1 on the AC side and h = np on the DC
side, where 'n' is an integer and 'p' is the pulse number. These harmonics
can be categorized into characteristic and non-characteristic types.
❖ Characteristic Harmonics: These harmonics occur at predictable
frequencies determined by the converter's pulse number. For instance, a
12-pulse converter typically generates AC-side harmonics at orders
12n±1 (e.g., 11th, 13th, 23rd, 25th) and DC-side harmonics at orders 12n
(e.g., 12th, 24th). These harmonics result from the normal operation of
the converters and are inherent to the conversion process.
❖ Non-Characteristic Harmonics: These harmonics arise due to system
imbalances, such as unequal AC voltages, transformer mismatches, or control
system imperfections. They can include even-order harmonics and other
unexpected frequencies, potentially causing additional operational issues.
 Characteristic Variation of Harmonic Currents with
Variation of Firing Angle and Overlap Angle
❖ In HVDC systems, the variation of harmonic currents is influenced
by changes in the firing angle (α) and the overlap angle (μ), both of
which affect the converter's operation and the resulting harmonic
spectrum.
❑ Effect of Firing Angle (α) on Harmonic Currents
The firing angle (α) determines the point at which the thyristors are
triggered in each AC cycle. As α increases,
▪ The average DC voltage decreases, leading to higher harmonic
distortion.
▪ The harmonic content of the AC current changes, with lower-order
harmonics (like 5th and 7th) increasing in magnitude at moderate α,
and higher-order harmonics becoming dominant at larger α.
▪ When α approaches 90° (inverter mode) or above 120°, the system
operates under extreme conditions, leading to increased reactive
power demand and higher harmonic generation.
Characteristic Variation of Harmonic Currents with Variation of Firing Angle and
Overlap Angle @ Continuation
❑ Effect of Overlap Angle (μ) on Harmonic Currents
The overlap angle (μ) is caused by the inductance in the AC system,
leading to a period where both incoming and outgoing thyristors conduct
simultaneously. As μ increases,
▪ The DC voltage further decreases, as more time is spent in
overlapping conduction.
▪ The harmonic spectrum of AC current is altered, with increased
even-order harmonics and an overall widening of harmonic
distortion.
▪ Higher μ increases the current ripple on the DC side, causing
additional heating and power losses.
Overall Impact
Both α and μ affect the harmonic content and power quality of HVDC systems. A
larger α worsens lower-order harmonics, while an increasing μ affects higher-order
harmonics and ripple. Proper control strategies, such as optimized pulse patterns,
harmonic filters, and reactive power compensation, are essential to mitigate their
negative effects.
 Effect of Control Mode on Harmonics
❖ Different HVDC control modes significantly impact harmonic
generation. Line-commutated converters (LCC), for example, generate
non-characteristic harmonics, while Voltage Source Converters (VSC)
can be designed to mitigate harmonics through various control
strategies.
1) Constant Current Control Mode
In this mode, the converter regulates the DC current (𝑰𝒅 ) to a set value.
The firing angle α is adjusted to maintain this current despite variations
in the AC system.
Impact on Harmonics:
▪ Since the 𝐼𝑑 is nearly constant, the harmonic content remains stable
under normal conditions.
▪ If AC voltage fluctuations occur, firing angle variations can increase
certain harmonic components.
▪ Low-frequency harmonics (e.g., 5th, 7th, 11th, 13th) dominate,
especially in line-commutated converters (LCCs).
 Effect of Control Mode on Harmonics @ Continuation
2) Constant Voltage Control Mode
Here, the DC voltage (𝑽𝒅 ) is regulated while allowing 𝐼𝑑 to vary based
on system conditions. This is often used at the inverter station in bipolar
HVDC links.
Impact on Harmonics
▪ Voltage variations can cause DC-side ripple, affecting the harmonic
content of AC currents.
▪ Sudden changes in voltage can excite higher-order harmonics (e.g.,
23rd, 25th).
▪ In voltage-sourced converters (VSC-HVDC), harmonics are shifted
to higher frequencies due to pulse-width modulation (PWM).
 Effect of Control Mode on Harmonics @ Continuation
3) Power Factor Control Mode
Some HVDC systems control reactive power (Q) or maintain a fixed power
factor. This affects the firing angle (α\alphaα) dynamically.
Impact on Harmonics:
▪ Rapid changes in power factor correction can lead to harmonic
instability.
▪ Increased firing angle variations cause greater harmonic distortion in
the AC network.
▪ Filters may need to be adaptive to compensate for varying harmonic
conditions.
4) Advanced Control Techniques & Harmonics Mitigation
To reduce harmonics, HVDC systems employ:
▪ Pulse-Width Modulation (PWM) in VSCs, which shifts harmonics to
higher frequencies, making them easier to filter.
▪ Higher pulse-number converters (e.g., 12-pulse, 24-pulse), which
minimize lower-order harmonics.
▪ Active filters that dynamically adjust to control variations and harmonic
distortions.
 Effect of Control Mode on Harmonics @ Continuation
▪ Current control mode stabilizes harmonics but can still produce low-
order harmonics.
▪ Voltage control mode introduces higher-order harmonics,
particularly during transients.
▪ Power factor control can cause dynamic harmonic variations,
requiring advanced filtering.
▪ Modern control techniques (PWM, active filtering, multi-pulse
converters) help mitigate harmonic distortion.
 Non-Characteristic Harmonics in HVDC Systems
❖ Non-characteristic harmonics are undesired harmonic components
that do not follow the expected harmonic orders of an HVDC
converter. Unlike characteristic harmonics, which are predictable and
depend on the converter pulse number, non-characteristic harmonics
arise due to system imbalances, control errors, and asymmetries in
operation.
❖ They introduce additional harmonic components beyond the expected
characteristic harmonics, leading to power losses, equipment
degradation, and power quality issues. Advanced filtering
techniques, improved control methods, and higher pulse-number
converters are essential to mitigate their impact.
❖ Ideal HVDC Systems: Ideally, a 12-pulse HVDC converter (a common type)
generates only characteristic harmonics (11th, 13th, 17th, etc.) on the AC side.
❖ Non-Ideal Conditions: However, in real-world scenarios, various factors can lead
to the generation of non-characteristic harmonics (harmonics that are not multiples
of the fundamental frequency minus or plus 1).
 Causes of Non-Characteristic Harmonics in HVDC Systems
Non-characteristic harmonics in HVDC systems primarily arise due to
the following factors:
❖ Unbalanced AC Supply Voltages: Voltage asymmetry in the three-
phase AC supply introduces even harmonics and interharmonics.
❖ Unequal Transformer Impedances: Differences in transformer
winding resistance and reactance cause distortions in the current
waveforms.
❖ Control System Imperfections: Variations in the firing angle
(α\alphaα) and overlap angle (μ\muμ) due to delayed or incorrect
triggering of thyristors lead to additional harmonic components.
❖ Commutation Overlap Variations: If commutation overlap
fluctuates due to system impedance changes, unexpected harmonics
appear.
❖ DC Line Disturbances: Sudden load changes, faults, or switching
events can introduce non-characteristic harmonics into the DC and AC
sides.
 Harmonic Orders in Non-Characteristic Harmonics
❖ In a six-pulse converter, characteristic harmonics follow the order:
h = 6n±1 n=1,2,3,…
However, non-characteristic harmonics can introduce even
harmonics (e.g., 2nd, 4th, 6th, etc.) and non-integer harmonics
(interharmonics).
❖ In a twelve-pulse converter, characteristic harmonics are at:
h=12n±1
However, due to asymmetries, harmonics like 3rd, 9th, or fractional
harmonics may appear.

❖ Examples of Non-Characteristic Harmonics;

▪ Triple Harmonics: The 3rd, 6th, 9th, 12th harmonics, etc.
▪ Harmonics at frequencies other than the expected characteristic
harmonics.
 Effects of Non-Characteristic Harmonics
❖ Increased Power Losses: Additional harmonic components lead to
heating in cables, transformers, and converters.
❖ Electromagnetic Interference (EMI): These harmonics can interfere
with communication lines and sensitive electronics. Non-characteristic
harmonics can interact with the system's impedance, leading to
resonance and potentially causing equipment damage.
❖ Reduced Equipment Life: Higher harmonic distortion stresses
insulation and accelerates wear and tear. Means that prolonged
exposure to harmonics can lead to equipment failure.
❖ Voltage Distortion: Non-characteristic harmonics contribute to THD
(Total Harmonic Distortion), degrading power quality.
❖ Power Quality Problems: Non-characteristic harmonics can lead to
voltage distortion, increased losses, and other power quality issues.
 Mitigation of Non-Characteristic Harmonics
To suppress non-characteristic harmonics, HVDC systems employ,
❖ Active and Passive Filters: Filters tuned to specific non-
characteristic harmonics eliminate unwanted frequency components.
❖ Improved Converter Firing Control: Digital controllers with
precise synchronization reduce firing angle errors.
❖ Balanced AC System Design: Proper transformer design and voltage
regulation help minimize asymmetries.
❖ Higher Pulse-Number Converters: Using 12-pulse, 24-pulse, or
multi-level converters minimizes the effect of non-characteristic
harmonics.
❖ Damped High-Pass (DHP) Filters: DHP filters can be used to
suppress resonance at non-characteristic harmonics.
❖ Retrofitting: Retrofitting existing systems with additional filters or
modifying existing filters can be an effective way to mitigate non-
characteristic harmonics.