## Power System Harmonics and distortion limits

### Power System Harmonics

Power system harmonics; Power quality; Total demand distortion; Total harmonic distortion; Total rated current distortion

## Introduction

Harmonics are the presence of multiple frequencies in the fundamental frequency of voltage or current or both. Due to this, a fundamental frequency of 50 Hz is superimposed by multiple frequencies like 100 Hz, 150 Hz, 250 Hz etc. resulting in deviating from ideal sinusoidal characteristics.
Harmonics are classified into two types:

• Voltage harmonics and
• Current harmonics.

The generation of harmonics in voltage is called voltage harmonic distortion and the generation of harmonics in current is called current harmonic distortion.

• Voltage harmonics are produced by the nonlinear load as in an arc furnace and
• Current harmonics are mainly generated by power converters.

Compared to voltage harmonic distortions, current harmonic distortions affect the power system due to the deployment of large numbers of power electronics-based static power converters.

### Voltage harmonics

Loads draw nonlinear voltage and current characteristics when sinusoidal voltage is applied across the terminals. Due to nonlinear characteristics, voltage is changed from ideal sinusoidal and injecting the voltage harmonics into the supplied voltage. These loads are called voltage harmonic sources or loads. Harmonics injected by these loads are called voltage harmonics.

The loads that generate voltage harmonics are:

• Arc furnace
• Arc welding

### Current harmonics

Loads draw nonlinear voltage and current characteristics when sinusoidal voltage is applied across the terminals. Due to nonlinear characteristics, current drawn by the loads from the voltage is not sinusoidal, which results in the supply voltage
changing from sinusoidal and injecting the current harmonics into the system.
These loads are called current harmonic sources or loads. Harmonics injected by these loads are called current harmonics. The major sources of generation of current harmonics are due to the employment of power electronics-based loads.

The loads generating current harmonics in industrial system applications are:

1. Solid-state rectifiers and battery chargers
2. Variable frequency drives (VFDs)
3. Uninterruptible power supply (UPS) systems
4. Frequency changers or cycloconverters
5. AC voltage regulators

etc.
The loads generating current harmonics in commercial system applications are:

1. Switched mode power supplies (SMPSs)
2. Light-emitting diodes (LEDs) and compact fluorescent lamps (CFLs)
3. Electronic ballasts
4. UPS systems
5. VFDs
6. Voltage stabilizers
7. Solid-state rectifiers and battery chargers

etc.
Compared to commercial and industrial systems, current harmonics are generated from residential systems that are smaller in magnitude and higher by number of devices connected to the system.

Rectifier circuits are used to convert AC supply into DC supply. They have power electronic devices like a diode, insulated-gate bipolar transistor (IGBT), metaloxide–semiconductor field-effect transistor (MOSFET), etc., for conversion.

Basedon the number of phases, rectifiers are classified into

• single-phase rectifiers and
• three-phase rectifiers

## Single-phase rectifiers

The single-phase rectifiers are used for various applications like UPS systems, SMPSs in computers, LEDs, battery chargers, etc. Either diode-based (uncon- trolled) or IGBT/MOSFET-based (controlled) rectifiers are widely used in these applications.
The instantaneous phase to neutral voltage wave shape is shown in Fig. 2.1 and the instantaneous current wave shape is shown in Fig. 2.2. From Figs. 2.1 and 2.2, when a sinusoidal voltage is supplied to a nonlinear load (rectifier part of a UPS system), it draws a distorted current wave shape from sinusoidal supply voltage.
The corresponding current harmonic spectrum in % and absolute ampere for Fig. 2.2 is shown in Figs. 2.3 and 2.4 respectively.

## Three-phase rectifiers  Three-phase rectifiers are used for various low-power and high-power applications
like UPS systems, VFDs, cycloconverters, AC voltage regulators, etc.

Most of these rectifiers are controlled by IGBTs, MOSFETs, or silicon-controlled rectifiers
(SCRs). The SCR-based rectifiers are classified based on the number of pulses used for conversion, which are:

• Six-pulse rectifier
• 12-pulse rectifier
• 18-pulse rectifier
• 24-pulse rectifier
Mostly, six-pulse and 12-pulse rectifiers are used in various applications due to economics, product size, and other constraints. The current harmonic content for an ideal current wave is fundamental current divided by harmonic order:

## Six-pulse rectifier

Six-pulse rectifiers are used in drives, UPS systems, cycloconverters, etc., for both lower and higher power applications. They generate fifth and seventh order harmonics in a higher magnitude. A typical six-pulse rectifier-generated current harmonic spectrum in % for the R phase is shown in Fig. 2.5.
From Fig. 2.5, the major harmonic orders are seventh, fifth, 11th, and 13th. Other harmonic orders are also present but have less percentages compared to these four orders.

Example 2.5: A three-phase, 415 V, 5 kW VFD is operating at 3.6 kW.
The current drawn by the rectifier circuit in VFD is 5.7 A per phase, operating at a 0.9
lag power factor.

The instantaneous voltage of the R phase to neutral is shown in Fig. 2.6 and the
instantaneous R phase current is shown in Fig. 2.7.

The corresponding current harmonic spectrum of the R phase in % for Fig. 2.7
is shown in Fig. 2.8 and the current harmonic spectrum in absolute ampere is
shown in Fig. 2.9.

## Twelve-pulse rectifier

Twelve-pulse rectifiers are used in VFDs, UPS systems, etc. and in higher-power applications because of economics. For the same rating, a 12-pulse system rectifier costs 40%–60% more than a six-pulse rectifier. It generates 11th and 13th order harmonics in a higher magnitude. A typical 12-pulse rectifier-generated current har- monic spectrum in % is shown in Fig. 2.10.
From Fig. 2.10, the major harmonic order produced by a 12-pulse converter is 11th and 13th in a higher magnitude as compared to fifth and seventh order.

Example 2.6: A three-phase, 415 V, 160 kVA UPS system is monitored for 10
min between 18:02:22 and 18:12:47 h.

The current drawn by the rectifier circuit of the UPS system is 56 A per phase at 0.75 lag power factor.

The instantaneous voltage of phase to neutral is shown in
Fig. 2.11 and the instantaneous current is shown in Fig. 2.12.

The corresponding current harmonic spectrum in % for Fig. 2.12 is shown in Fig. 2.13 and

The current harmonic spectrum in absolute ampere is shown in Fig. 2.14.

From Figs. 2.13 and 2.14, THD is 10% and absolute harmonic current is 5.6 A.

## Point of common coupling  The point of common coupling (PCC) is a common point or location where multiple customers and their equipment are connected to a utility power grid.

IEEE standard 519-2014 defines PCC as the point on a public power supply system
electrically nearest to a particular load at which other loads could be connected.
The PCC is a point located upstream of the considered plant electrical installation.

Example 2.7:

A paper plant has a connected load of 10 MVA and receives power from a 110 kV grid supply.

The electrical distribution of the industrial system is shown in Fig. 2.16.
The PCC for this paper plant is 110 kV. In most cases, a metering point or
billing point is considered as the PCC.

Example 2.8:

Two industrial plants have connected loads of 10 and 15 MVA, respectively, and receive power from a 110 kV grid supply. The electrical distribution of the industrial system is shown in Fig. 2.17.

The IEEE standard 519-2014 recommended harmonic limits both voltage harmonic distortion and current harmonic distortion at the PCC only.

These limits should not be applied anywhere within the customer’s locations, individual feeders, or equipment.

## Source-side harmonics

Ideally, power sources should be sinusoidal in nature and free from harmonics.
However, in a practical system, power sources no longer have sinusoidal characteristics and the minimal amount of harmonic content is the presence in the power source. Harmonics from the utility power supply can affect customer equipment.
quality of the power supply.  PCC is a common interconnection point for different customers connected to the same utility power supply. If current harmonic injections by customer loads are not limited, the power quality at the PCC will be affected.

These current harmonic distortions at the PCC also affect the power quality of different customers connected to the same PCC, i.e., current harmonics injected by one customer affect the voltage quality at the PCC.

Harmonic current is injected from customer 1 to the PCC as shown in Fig. 2.18 and this affects the voltage at the PCC.

The distorted voltage at the PCC affects other customers connected to the same PCC by supplying a distorted voltage supply, i.e., distorted voltage is supplied to customer 2 connected to the same PCC.

Even if customer 2 loads are linear, they will draw the non-sinusoidal current from the voltage because of supply voltage distortion. Fig. 2.19 shows the distorted voltage at customer 2 connected loads.

## Evaluation of harmonics in the system

Generally, harmonics in the system are evaluated using THD for both voltage harmonic distortion and current harmonic distortion. IEEE Std 519-2014, using the total demand distortion (TDD) for evaluation of current harmonic distortion at the PCC, and IEEE Std 1547-2018, introduced new terminology for the evaluation of current harmonics called total rated harmonic distortion (TRD) .

## Total harmonic distortion  THD is the ratio of the square root of the sum of all harmonic components except
fundamental to the fundamental component. The term THD is used to find the
percentage of distortion from its fundamental wave shape.

IEEE standard 519-2014 defines THD as the ratio of the root mean square of the harmonic content, considering harmonic components up to the 50th order and specifically excluding interharmonics, expressed as a percentage of the fundamental. Harmonic components of order greater than 50 may be included when necessary.

Voltage THD is the ratio of the square root of the sum of all voltage harmonic components except the fundamental voltage component to the fundamental voltage component.

The expression for voltage harmonic distortion is shown in Eq. (2.3):

## Total demand distortion TDD is the ratio of the square root of the sum of all current harmonic components
except fundamental current to the fundamental current of maximum demand.
IEEE standard 519-2014 defines TDD as the ratio of the root mean square of the harmonic content, considering harmonic components up to the 50th order and
specifically excluding interharmonics, expressed as a percentage of the maximum
demand current.

Harmonic components of order greater than 50 may be included when necessary.

## Total rated current distortion   TRD is introduced by IEEE standard 1547-2018. The evaluation of harmonics by TRD is different from THD and TDD in IEEE standard 519.

The definition of TRD as per IEEE standard 1547-2018 is the total root sum square of the current distortion components, including both harmonics and interharmonics created by the distributed energy resources (DER) unit to DER rated current capacity in percentage. The expression for calculating TRD is given in Eq. (2.9):

Example 2.17: An SLD of a 10 MVA rated solar photovoltaic system as a DER unit connected to a 10 MVA transformer is shown in Fig. 2.29.
The rated current of the DER unit of 10 MVA at the PCC (33 kV) is 174.95 A.

Case 1: DER delivering a rated power of 10 MVA
The power analyzer connected at the PCC measures the fundamental current (I 1)
and RMS current (I RMS ), including harmonic and interharmonic components, as follows:
I 1 is 174.8 A
I RMS is 175.4 A
The TRD can be calculated as per Eq. (2.9): TRD value at the RPA is 8.28%.

Case 2: DER delivering 75% of rated power—7.5 MVA
The power analyzer connected at the PCC measures the fundamental current (I 1) and RMS current (I RMS ), including harmonic and interharmonic components, as follows:
I 1 is 130.5 A
I RMS is 131.5 A
The TRD can be calculated as per Eq. (2.9): TRD value at the RPA is 9.25%.
Case 3: DER delivering 25% of rated power—2.5 MVA The power analyzer connected at the PCC measures the fundamental current (I1) and RMS current (IRMS), including harmonic and interharmonic components, as follows: I1 is 42 A IRMS is 44 A The TRD can be calculated as per Eq. (2.9): TRD value at the RPA is 7.49%.

## Voltage Distortion Limits

The recommended voltage distortion limits (see Table 11-1) are concerned with the following indice: THD: Total (RSS) harmonic voltage in percent of nominal fundamental frequency voltage.The limits listed in Table 11-1 should be used as system design values for the “worst case” for normal operation (conditions lasting longer than one hour). For shorter periods, during start-ups or unusual conditions, the limits may be exceeded by 50%.

## Current Distortion Limits

Ideally, the harmonic distortion caused by single consumer should be limited to an acceptable level at any point in the system; and the entire system should be operated without substantial harmonic distortion anywhere in the system. The harmonic distortion limits recommended here establish the maximum allowable current distortion for a consumer. The
recommended current distortion limits are concerned with the following indices:
TDD: Total demand distortion (RSS), harmonic current distortion in %of maximum demand load current (15 or 30 min demand)
The limits listed in Tables 10-3 and 10-4 should be used as system design values for the “worst case” for normal operation (conditions lasting longer than one hour). For shorter periods, during start-ups or unusual conditions, the limits may be exceeded by 50%.
These tables are applicable to six-pulse rectifiers and general distortion situations. However, when phase shift transformers or converters with pulse numbers (q) higher than six are used, the limits for the characteristic harmonic orders are increased by a factor equal to provided that the amplitudes of the non characteristic harmonic orders are less than 25% of the limits specified in the tables. See 13.1 for an example.

Table 10-3 lists the harmonic current limits based on the size of the load with respect to the size of the power system to which the load is connected. The ratio Isc/IL is the ratio of the short-circuit available at the point of common coupling (PCC), to the maximum fundamental load current. It is recommended that the load current, IL, be calculated as the average current of the maximum demand for the preceding 12 months. Thus, as the size of the user load
decreases with respect to the size of the system, the percentage of harmonic current that the user is allowed to inject into the utility system increases. This protects other users on the same feeder as well as the utility, which is required to furnish a certain quality of voltage to its customers.

## harmonics measurement

Measurements of current and voltage harmonics are essential for the reliable distribution of electric energy. The following are a few reasons that highlight the importance of measurements:

## General

1. Monitoring existing values of harmonics and checking against recommended or admissible levels.
2. Testing equipment that generates harmonies.
3. Diagnosing and troubleshooting situations in which the equipment performance is unacceptable to the utility
or to the user.
4. Observing existing background levels and tracking the trends in time of voltage and current harmonics (daily, monthly, seasonal patterns).
5. Measuring for verification of simulation studies that include harmonic load flow.
6. Measuring harmonic currents and harmonic voltages with their respective phase angle. Such measurements can be made with and without apart of the nonlinear loads connected and can help determine the harmonic driving point impedance and given location.
The techniques used for harmonics measurements differ from those used tor ordinary power system measurement the frequency bandwidth of the ordinary measurements of voltage, current, and power can be accomplished with attention to narrow band of frequencies near the distribution frequency. Substantially wider bandwidths (up to 3kHz) are required in the study of power system harmonics.

## 1. Osilloscope

The display of the waveform on the oscilloscope gives immediate qualitative information on the degree and type of distortion. Sometimes cases of resonances are identifiable through the visible distortion that is present in the current
and voltage waveform.

## 2. Spectrum Analyzers

These instruments display the power distribution of a signal as a function of frequency. A certain range of frequencies is scanned, and all the components, harmonics, and interharmonics of the analyzed signal are displayed. The display format may be a CRI or a chart recorder.

## 3. Harmonic Analyzers or Wave Analyzers

These instruments measure the amplitude (and in more complex units, the phase angle) of a periodic function. These instruments provide the line spectrum of an observed signal. The output can be recorded, or it can be monitored with analog or digital meters.

## 4. Distortion Analyzers

These instruments indicate to the harmonic distortion (THD) directly.

## 5. Digital Harmonics Measuring Equipment

Digital analysis can be performed with two basic techniques:

• By means of digital filter. This method is similar to analog filtering. Dual-channel digital signal analyzers include digital filtering. In the setup for a particular measurement, the frequency range to be measured sets up the digital filters for that range. Also, the bandwidth is varied to optimize the capture of smaller harmonics in the presence of a very large fundamental.
• The Fast Fourier Transform technique. These are real-time, very fast methods of performing a spectrum
analysis that permit the evaluation of a large number of functions. Multichannel analog-digital conversion and micro or mini computers are used for real-time data acquisition.

When the waveform is recorded with suitable bandwidth using either analog or digital techniques on-line, the Fast Fourier Transform (FFT) calculation of harmonic components, the conversion to engineering units, the calculation of statistics, and the plotting and printing of results can be performed off-line in the laboratory using suitable facilities.

## Requirements for Instrument Response

For accurate harmonics mcasurements. the following important reguirements must be met

## 1. Accuracy

The instrument must perform the measurement of a constant (steady-state) harmonic component with an error compatible with the permissible limits. It is reasonable to use an instrument with an uncertainty no larger than %5 of the permissible limit. For example, assume a 480 V, three-phase system in which the 11th harmonic should be les than 0.70%. The line-neutral 11th harmonic, V11, is less than 1.94 V. This indicates that the instrument should have na uncertainty of less than =(0.05) (1.94)= =0.097 V.

## 2. Selectivity

The selectivity of the instrument is an indication of its ability to separate harmonic components of different frequencies. One practical way to ensure good selectivity is to define requirements for minimum attenuation of an injected frequency, while the instrument is set (tuned) at a frequency fh = 50 Hz.

## 3. Averaging or Snapshot

If the measured harmonics vary in time, it is necessary to “smooth out” rapidly fluctuating components over a period of time. Two factors become important in this case: dynamic response and bandwidth.

• Dynamic Response
• If, for example an average over a period of 3S is desirable, them the response to the output meter should be identical to a first order low-pass filter with a time constant of 1.5 ±0.15s.
• Bandwidth
• The bandwidth of the instrument will strongly affect the reading, especially when harmonics are fluctuating. It is recommended that instruments with a constant bandwidth for the entire range of frequencies be used. The bandwidth should be 3±0.5 Hz between the -3 dB points with a minimum attenuation of 40 dB at a frequency of fh + 15 Hz. In situations in which interharmonics and transients are present, a larger bandwidth will cause large positive errors.