# Introduction to Harmonics – Effect of Harmonics on Power System

**What are Harmonics and How to Filter and Eliminate it.**

**Introduction to Harmonics**

The quality of electrical power supply is an important issue both for utility companies and users, but that quality may affected by **electromagnetic disturbances**.

Among these *disturbances* it must be highlighted **harmonics** that happens in all *voltage levels* and whose *study, calculation of acceptable values and correction methods* are defined in *IEC*^{[1]}* Standard 61000-2-4: **Electromagnetic compatibility (EMC)*^{[2]}* – Environment – Compatibility levels in industrial* *plants for low-frequency conducted disturbances*.

**What are Harmonics?**

Alternators produce *alternated voltages* (**V**) and *currents* (**I**) with a **sinusoidal wave form** and a *frequency* (**f**) of **50 Hz **or **60 Hz** (this frequency, the **first harmonic**, is usually designated by **industrial frequency** or** fundamental**), what can be observed in Figure 1.

Figure 1 – Sinusoidal alternated voltage

However, due to some **equipments characteristics**, which are installed in the network, *voltages and/or currents* with *different frequencies*, **odd integral multiples** **of industrial frequency**, may be induced in the network, the *harmonics*, i. e.: *3th harmonic *– **150 Hz** or **180 Hz**; *5th harmonic* – **250 Hz** or **300 Hz**; *7th harmonic* – **350 Hz **or **420 Hz**; etc.

We can say then that **harmonics** are **continuous (steady-state) disturbances** or** distortions** on the *electrical network and are a ***completely different subject or problem*** from line spikes, surges, sags, impulses, etc., *which are categorized as* transient disturbances*.

Figure 2 shows examples of 1st harmonic, 3th harmonic and 5th harmonic.

Figure 2 – Fundamental, 3th harmonic and 5th harmonic waves

The presence of *harmonics* gives origin to a **distorted wave** of *voltage* (or *current*) that may be observed in Figure 3, taking into account that all *complex waveforms* can be resolved into a **series of sinusoidal waves of various frequencies**, therefore any *complex waveform* is the **sum** of a number of **harmonics** of **lesser or greater value**.

**Fourier series**^{[3]} expresses the *instantaneous value* of that *sum* – **u(t)** – by the equation:**Where**:

*t*is the time [**s**]**ω = 2πf**[**s**]^{-1}*T*is the period [s]*f*is the fundamental frequency [_{0}**Hz**]*s(t)*is a periodic function integrable in the interval**[0, T]**

Figure 3 – Harmonic distortion

Usually **3th harmonic** is the *most harmful*, but in certain conditions, **5th and 7th harmonics** *cannot be overlooked*.

**Harmonic Distortion**

According to *IEC Standard 61000-2-4* **harmonic distortion** is characterized by the parameter **THD** – *Total Harmonic Distortion* – calculated by the equation:

Where **Q _{1}** represents the

**rms value**of the

*voltage*or of the

*current*at

**industrial frequency**and

**Q**the

_{i}*harmonic wave*of order

*“*

**i**

*”*(

*2nd harmonic*–

**i=2**;

*3th harmonic*

**i=3**; etc.) of the voltage or of the current.

The same IEC Standard defines also the following parameters:

**TDC**(*Total Harmonic Content*), which**rms value**is calculated by the equation:

Where **Q _{1}** represents the

**rms value**of the

*voltage*or of the

*current*at

**industrial frequency**and

**Q**the

**rms value**of the

*voltage*or of the

*current*.

**TDR**(*Total Harmonic Ratio*) – relation between the**rms value**of**TDC**and the**rms value**of the*voltage*or of the*current*at**industrial frequency**(**Q**), which is calculated by the equation:_{1}

Usually calculations are made for the **voltage**, *considering minimum three-phase short-circuit power* (**S” _{K}**) of the network and

*maximum values*(in

**Ω**) of

*short-circuit impedance*in the points where

*THD*is calculated (

**Z**

_{K}; R_{K}; X_{K}^{[4]}); a

*specific software*is required to do these calculations.

The above referred *IEC Standard* defines **3 classes **for *electromagnetic environment*^{[5]}:

**Class 1**: This class applies to protected supplies and has compatibility levels lower than those on public networks. It relates to the use of equipment very sensitive to disturbances in the power supply, for instance electrical instrumentation in laboratories, some automation and protection equipment, some computers, etc.**Class 2**: This class applies generally to**PCC**^{[6]}and to**IPC**^{[7]}in the environments of industrial and other non-public power supplies. The compatibility levels of this class are generally identical to those of public networks. Therefore, components designed for supply from public networks may be used in this class of industrial environment.**Class 3**: This class applies only to**IPC**in industrial environments. It has higher compatibility levels than those of class 2 for some disturbance phenomena. For instance, this class should be considered when any of the following conditions are met:*a major part of the load is fed through converters; welding machines are present; large motors are frequently started; loads vary rapidly.*

*Harmonic* **compatibility** **levels**^{[8]} (**U _{h} [%]**) for

**odd frequencies**

*multiples*of

**3**are indicated in Table 1and for

**odd frequencies**

*not multiples*of

**3**are indicated in Table 2.

Table 1 – Levels of harmonic compatibility for odd frequencies multiples of 3

Table 2 – Levels of harmonic compatibility for odd frequencies multiples of 3

*Compatibility levels* of **THD** for each of the classes are:

- Class 1 –
**5%**. - Class 2 –
**8%**. - Class 3 –
**10%**.

**Sources and Effects of Harmonics**

**Harmonics are a permanent source of problems in electrical equipments and systems.**

The following *types of loads* (**non-linear loads** ^{[9]}) are the main sources of harmonics:

- Power electronic equipment (example: rectifiers – namely those used in
**electrical traction systems**– and static converters). - Arcing equipment (example: arc furnaces,
**AC**or**DC, arcing welding machines**). - Saturable devices (example: off-load current wave absorbed by a transformer with an insufficiently large power rating).

To minimize **harmonics generation** *rectifier units* are preferably **six-pulse** and these type of units for *electrical traction systems* typically *generate current harmonics* of **5th, 7th, 17th and 19th order**, resulting from *diodes unbalancing* and from *network impedance*.

Although of a **lower magnitude**, *under normal working conditions of equipments and of network*, it must be taken into account the **risk of resonance** for those *frequencies*.

**Switching operations** of *capacitor banks* and *power transformers* with a **permanent overload** are also an *important harmonics source*.

*Power transformers* for *voltages* **above 60 kV** with **star-star connection** (**Yy**) are equally a *harmonic source*. To compensate those *harmonics,* the referred *power transformers ***must have a tertiary winding, delta connected**.

Apart from the **distortion of voltage wave**, *harmonics* are an origin of *erroneous operation* of control and protection systems*, *due to **electromagnetic interferences***, *increase* skin effect* ^{[10]}*, *cause *mechanical oscillation and vibrations* of electrical machines, namely power transformers and rotating machines, *decrease power factor *(**cos Φ**), conduce to *premature ageing of insulation materials*, leading to the **lost of their dielectric characteristics**, origin *overheating and losses increasing*, namely power transformers and cables, and **decrease useful life of equipments**.

*Harmonics*, which are the cause of *voltage wave distortion*, circulating in **non-linear loads**, like *motors*, when subjected to a **variable magnetic flux**, *induce circulating currents* (**Foucault currents**) in conducting materials, what **decrease torque**.

In **unbalanced systems**, *harmonics* may cause a *neutral current* **higher** than the *vectorial sum of phase currents at fundamental frequency*, leading to an **overload in the neutral conductor**.

*Skin effect* **increases** *conductors’ resistance* and therefore **voltage drop and losses by Joule effect**. This issue is particularly **sensitive** in *overhead lines* with a *voltage ***above 150 kV** and a *length *of **800 km and above**. Common solution to solve this problem is to use **DC** *overhead lines*, in which *skin effect ***does not exists**.

*Mechanical oscillation and vibrations* of rotating electrical machines may origin **shaft misalignment** and **destruction of stator, rotor and bearings**.

**Losses increase** in power transformers, happens in **iron losses**, due to **Foucault currents** and **hysteresis**^{[11]}, which are *proportional to the frequency* and in **copper losses**, due to **skin effect**.

**Harmonics Compensation & Types of Filters**

When *capacitor banks *are used for *power factor correction*, a **significant harmonics component flows into the capacitor bank**; in these situations is necessary to **temporarily switch-off** the *capacitor bank* to allow an **accurate location of harmonics sources**.

In such an installation it is **crucial **to verify if there is **any risk of harmonic resonance** caused by the **specific capacitor bank harmonics**. This is the **first step** to define the *correct solution* for **harmonic compensation**.

Once confirmed the existence of *harmonics* and that *THD value* **exceeds the limit** defined by *IEC Standard 61000-2-4 *and/or *established by the utility company* it is **mandatory** proceed to **harmonic compensation**; the solution to be implemented depends on the *installation characteristics*.

The simplest solution, used in *low voltage* (**V ≤ 1 kV**) installations, is the use of **copper coils** (see Figure 4) that *act* as **high frequency filter**, *limit the starting current of rectifiers* and **restrain mutual interference**.

Figure 4 – Reactance for harmonic compensation

The inductance (**L**) of each phase is calculated by the equation:Where:

*ΔV*_{L}**i**s the internal voltage drop of the reactance [**%**]*V*is phase-to-phase voltage of the network [_{n}**V**]*f*is the industrial frequency of the network [_{n}**Hz**]*I*is the current [_{n}**A**]

In *networks and installations* with a **strong electrical pollution** (*higher harmonics level*), where **G _{h}/S_{n} > 60%** (

**G**is the

_{h}**apparent power**of all

**non-linear loads**responsible for

*harmonics production*and

**S**is the

_{n}**apparent power**of all

*upstream transformers*

*connected to the same bus bar where loads are connected*) is recommended to install

**harmonics filters**, like the one shown in Figure 5).

Figure 5 – Harmonics filter

*Harmonics compensation* may be **centralized**, with *harmonic filters* connected in the *main incoming switchboard*, or **de-centralized or local**, installing the *harmonic filters* **close to the equipments** that are the *main sources of harmonics*. Both solutions are shown in Figure 6.

Figure 6 – Location of harmonic filters

Harmonic filters are classified into three categories:

**Passive filters**

These are constituted by **LC series association circuits**, *tuned for each one of the frequencies* that they are *designed to compensate*, usually **5th, 7th and 11th harmonics**. Their main characteristics are:

- There is no limit to harmonic to current to be eliminated.
- They perform power factor correction.
- They risk amplifying harmonics when there are network modifications.
- There is an overload risk, caused by external electromagnetic pollution.

**Active filters**

These are constituted by **electronic and micro-processed units**, controlling *harmonics* within a **range between 2nd to 50th orders**; for *each range of frequency* it is generated a *current*, which **has a phase shift of 180° and the same value** of the *harmonic current to be compensated*.

This type of filters is well adapted to *modifications of the network, of the loads and of the harmonic range*, being particularly suitable for *de-centralized or local compensation*.

**Hybrid filters**

These are a *combination of active and passive filters*, controlling *harmonics* within a **range between 2nd to 25th orders**, doing also** power factor correction**.

Good to know:

**Good to know:**

^{[1]} **IEC**: International Electrotechnical Comission.

^{[2]}** Electromagnetic compatibility** is defined as the capability of electrical equipments to worker properly in a “electromagnetic environment” without introducing any type of electromagnetic disturbances in other equipments and systems that may exist in that environment.

^{[3]} **Fourier series** are *converging trigonometric series* used to represent the *sum of sinusoidal functions*.

^{[4]} If the values of **R _{K}** e

**X**of the

_{K }*network*it is usual to consider, as an approximation,

**R**and the equation

_{K}/X_{K}= 0.1**Z _{K} = √(R_{K}^{2}+X_{K}^{2}).**

^{[5]} The definition of the classes is a transcription of *IEC Standard 61000-2-4*.

^{[6]} **PCC**: Point on a public power supply network, electrically nearest to a particular load, at which other loads are, or could be, connected.

^{[7]} **IPC**: Point on a network inside a system or an installation, electrically nearest to a particular load, at which other loads are, or could be, connected.

^{[8]} **Compatibility level** defines the specified *electromagnetic disturbance level* used as a reference level in a specified environment for coordination in the setting of emission and immunity limits.

^{[9]} A *load* is said **non-linear** if its *impedance* **vary** with *applied voltage*.

^{[10]} **Skin effect** is a phenomenon that can be characterized by the repulsion of electromagnetic current lines, which consequence is a tendency for AC current to flow only at the surface of conductors.

^{[11]} **Hysteresis** is the by which, when **magnetic field** is applied to a **ferromagnetic material**, as the *core of the transformers*, the material stays **permanently magnetized**, even if the magnetic field is not present.