# Harmonics in Power System: generation and hazards of Harmonics.

The root cause of harmonic generation in power systems is non-linear loads. When the current flows through the load, it does not have a linear relationship with the applied voltage, and a non-sinusoidal current is formed, thereby generating harmonics. The harmonic frequency is an integer multiple of the fundamental frequency. According to the analysis principle of the mathematician Fourier (M. Fourier), any repeated waveform can be decomposed into a sine wave component containing the fundamental frequency and a series of harmonics multiples of the fundamental.

Harmonics are sine waves, each with a different frequency, amplitude, and phase angle. Harmonics can be divided into even and odd harmonics. The 3rd, 5th, and 7th are odd harmonics, while 2, 1, 4, 6, and 8 are even harmonics. For example, when the fundamental wave is 50Hz, the 2nd harmonic is 100Hz, and the 3rd harmonic is 150Hz. Generally speaking, odd harmonics cause more harm than even harmonics. In a balanced three-phase system, due to the symmetry, even harmonics have been suppressed, and only odd harmonics exist. For three-phase rectified loads, the harmonic currents that appear are 6n±1 harmonics, such as 5th, 7th, 11th, 13th, 17th, 19th, etc. The frequency converter mainly produces 5th and 7th harmonics.

The term “harmonic” originates from acoustics. Mathematical analysis of harmonics was well established in the 18th and 19th centuries. The harmonic analysis method proposed by Fourier et al. is still used today. The problem of harmonics in power systems was noticed as early as the 1920s and 1930s. At that time in Germany, the voltage and current waveforms were distorted due to the use of static mercury arcs. The 1945 JCRead paper on converter harmonic converters was an early case paper on harmonic research. In the 1950s and 1960s, many papers were written about the problem of harmonics in power systems caused by converters. This was because of the growth of HVDC transmission technology. Since the 1970s, due to the development of power electronic technology, the application of various power electronic devices in power systems, industries, transportation, and households has become increasingly common, and the harm caused by harmonics has become increasingly severe. Every country in the world has paid full attention to the harmonic problem. Many academic conferences on harmonic issues have been held, and many academic organizations have formulated standards and regulations to limit harmonics in power systems and electrical equipment. The significance and morality of harmonic research are because the harm of harmonics is severe. Harmonics reduces the efficiency of the production, transmission, and utilization of electrical energy, overheats electrical equipment, generates vibration and noise, and causes insulation aging, shortened service life, and even failure or burnout. Harmonics can cause local parallel or series resonance in the power system, amplify the harmonic content, and cause capacitors and other equipment to burn. Harmonics can also cause the malfunction of relay protection and automatic devices, causing confusion in electric energy measurement. For the outside of the power system, harmonics can cause severe interference to communication equipment and electronic equipment.

The definition of power supply system harmonics is decomposing the periodic non-sinusoidal electricity by the Fourier series. In addition to obtaining the same component as the fundamental frequency of the grid, a series of components greater than the fundamental frequency of the grid are obtained. This part of the electricity is called harmonics. The harmonic order is the ratio of the harmonic frequency to the fundamental frequency (n=fn/f1). Sometimes there are non-integer harmonics in the power grid, called non-harmonics or fractional harmonics. Harmonics is actually a disturbance quantity that “pollutes” the grid. The field of electrical technology mainly studies the occurrence, transmission, measurement, harm, and suppression of harmonics, and its frequency range is generally 2≤n≤40.

## How are harmonics created?

Power grid harmonics come from three aspects:

The quality of the power generation source is not high to generate harmonics. It is difficult for the generator to achieve absolute symmetry in manufacturing three-phase windings, and it is difficult to achieve absolute uniformity of the iron core and other reasons. The power generation source also produces some harmonics, but generally very few.

The second issue is the generation of harmonics in the transmission and distribution system; the primary source of harmonics in the transmission and distribution system is power transformers. When designing the transformer, the working magnetic density is chosen. This is because the saturation of the transformer core, the nonlinearity of the magnetization curve, and the consideration of economy all play a role in this choice. On the near-saturation section of the magnetization curve, the magnetizing current has a sharp peak waveform, thus containing odd harmonics. Its size is related to the magnetic circuit’s structural form and the iron core’s saturation degree. The higher the saturation degree of the iron core, the farther the transformer operating point deviates from the linearity and the greater the harmonic current. The third harmonic current can reach 0.5% of the rated current.

The third is the harmonics generated by electrical equipment; Thyristor rectifier equipment. Since thyristor rectification has been increasingly widely used in many aspects such as electric locomotives, aluminum electrolytic cells, charging devices, switching power supplies, etc., it has caused many harmonics to the power grid. If the rectifier is a single-phase rectifier circuit, it contains odd-order harmonic currents when connected to inductive loads, of which the content of the 3rd harmonic can reach 30% of the fundamental wave; when connected to capacitive loads, it contains odd-order harmonic voltages. Its harmonic content increases with the increase of capacitance value. If the rectifier is a three-phase fully-controlled bridge 6-pulse rectifier, the primary side of the transformer and the power supply line contains 5th and above odd harmonic currents; if it is a 12-pulse rectifier, there are also 11th and above odd harmonic currents. Statistics show that the harmonics generated by the rectifier account for nearly 40% of the harmonics, which is a more comprehensive source of harmonics.

## Frequency conversion device:

Fans, water pumps, elevators, and other types of equipment utilize frequency conversion devices in some capacity. The utilization of phase control has contributed to the complexity of the harmonic components. It features integer harmonics and fractional harmonics in addition to those two types. The introduction of variable frequency speed regulation has increased the number of harmonics introduced into the power grid.

Electric arc furnace, calcium carbide furnace. When heating the raw material, it is difficult for the three-phase electrodes of the electric furnace to simultaneously contact the uneven charge. As a result, the combustion is unstable, the load on the three-phase transformer is unbalanced, and a harmonic current is generated. This current is then injected into the power grid through the delta connection coil of the transformer. Among them, it is mainly the 27th harmonic, which can reach an average of 8% and 20% of the fundamental wave and 45% at most..

Gas discharge type electric light source. Fluorescent, high-pressure mercury, sodium, and metal halide lamps are gas discharge electric light sources. Analysis and measurement of the volt-ampere characteristics of this type of electric light source show that its nonlinearity is severe. Some of them also have negative volt-ampere characteristics, which will cause odd harmonic currents to the power grid.

Household appliances. TVs, video recorders, computers, dimming lamps, temperature-adjusting cookers, etc., have deep odd-order harmonics due to their voltage-regulating and rectifying devices. In washing machines, electric fans, air conditioners, and other equipment with windings, the waveform can also be changed due to changes in unbalanced current. Although these household appliances are small in power, they are huge in number and are also one of the primary sources of harmonics.

## Harmonic Suppression:

Harmonic pollution from power electronics and other harmonic sources can be fixed by installing a device that cancels out harmonics. This works for a wide range of harmonic sources. The power electronic device is modified, so no harmonics are generated, and the power factor can be controlled to 1. Of course, this only applies to the power electronic device as the primary harmonic source.

The traditional method of installing harmonic compensation devices uses LC-tuned filters. This method can compensate for both harmonics and reactive power and has a simple structure, so it has been used all the time. The main disadvantage of this method is that the compensation characteristics are affected by the grid impedance and operating state. It is easy to generate parallel resonance with the system, resulting in harmonic amplification, overloading, or even burning the LC filter. In addition, it can only compensate for fixed frequency harmonics, and the compensation effect is not ideal.

## Reactive power compensation

It is easy for people to understand active power, but it is not easy to deeply understand reactive power. In sinusoidal circuits, the concept of reactive power is clear, but when harmonics are included, there is no generally accepted definition of reactive power. However, the importance of the concept of reactive power and the understanding of the importance of reactive power compensation are consistent. Reactive power compensation should include fundamental wave reactive power and reactive harmonic power.

Reactive power is significant to the operation of the power supply system and the load. The impedance of the power system network elements is mainly inductive. So, in a general sense, to send active power, there needs to be a difference in phase between the voltages at the sending end and the receiving end, which can be done over a fairly wide range. The voltages at both ends must have an amplitude value to send reactive power. Poor, this can only be achieved in a very narrow range. Not only do most network elements consume reactive power, but most loads also consume reactive power. The reactive power required by network elements and loads must be obtained from somewhere in the network. Obviously, it is unreasonable and usually impossible for these reactive powers to be provided by generators and transmitted over long distances. A reasonable method should be to generate reactive power where reactive power needs to be consumed, which is reactive power compensation.

The main functions of reactive power compensation are as follows:

(1) Improve the power factor of the power supply system and load, reduce equipment capacity, and reduce power loss.

(2) Stabilize the voltage of the receiving end and the power grid to improve the quality of the power supply. Setting dynamic reactive power compensation devices at suitable locations in long-distance transmission lines can also improve the transmission system’s stability and transmission capacity.

(3) In the case of unbalanced three-phase loads such as electrified railways, the active and reactive loads of the three-phase can be balanced by appropriate reactive armatures.

## Generation of harmonics and reactive power

In industrial and domestic electrical loads, resistive and inductive loads occupy a large proportion. Asynchronous motors, transformers, fluorescent lamps, etc., are all typical resistive and inductive loads. The reactive power consumed by asynchronous motors and transformers occupies a high proportion of the reactive power provided by the power system. Reactors and overhead lines in the power system also consume some reactive power. A resistive load must absorb reactive power to work correctly, determined by its nature.

Non-linear devices such as power electronic devices also consume reactive power, especially various phase-controlled devices. Such as phase-controlled rectifiers, phase-controlled AC power adjustment circuits, and cyclic converters, the fundamental current lags behind the grid voltage during operation. It consumes a large amount of reactive power. In addition, these devices also generate a large number of harmonic currents, and the harmonic sources all consume reactive power. The fundamental wave current phase of the diode rectifier circuit is roughly the same as the grid voltage phase, so basically, no fundamental wave reactive power is consumed. But it also generates a lot of harmonic currents and consumes reactive power.

In the past 30 years, the application of power electronic devices has become more and more common, which also makes power electronic devices a more significant source of harmonics. In various power electronic devices, the rectifier device accounts for a large proportion. Most commonly used rectifier circuits use thyristor phase-controlled or diode rectifier circuits, among which three-phase bridge rectifier circuits and single-phase bridge rectifier circuits are more common. Harmonic pollution and power factor lag from rectifier circuits with resistive, inductive loads are well known. The diode rectifier circuit using capacitor filtering on the DC side is also a severe source of harmonic pollution. The phase of the fundamental component of the input current of this circuit is roughly the same as the phase of the supply voltage, so the fundamental power factor is close to 1. However, the harmonic components of the input current are substantial, causing severe pollution to the power grid and making the total power factor very low. In addition, electronic devices such as phase-controlled AC power adjustment circuits and cyclic converters also generate a large amount of harmonic current on the input side.

## Influence of Reactive Power

(1) The increase of reactive power will increase current and apparent power, thereby increasing the capacity of generators, transformers, and other electrical equipment and conductors.

. At the same time, the size and specifications of starting and control equipment and measuring instruments of power users should also be increased.

(2) The increase of reactive power increases the total current, thus increasing the loss of equipment and lines, which is obvious.

(3) The voltage drop of the line and the transformer will increase. The voltage will fluctuate violently if it impacts the reactive power load, reducing the power supply quality.

## Hazards of Harmonics

An ideal utility grid should provide a single, fixed frequency with a specified voltage amplitude. The appearance of harmonic current and harmonic voltage pollutes the public power grid. The environment in which the electrical equipment is used deteriorates and affects the surrounding power and electronic equipment. Before applying harmonics and their hazards, people had researched and thoroughly understood them, but harmonic pollution had not attracted enough attention then. In the past 30 or 40 years, the rapid development of various power electronic devices has made the harmonic pollution of the public power grid more serious. Various faults and accidents caused by harmonics have also occurred. The harm of harmonics to the utility grid and other systems is roughly in the following aspects.

(1) Harmonics causes additional harmonic losses to the components in the public power grid, reducing the efficiency of power generation, transmission, and electrical equipment. When many 3rd harmonics flow through the neutral line, the line will overheat or even cause a fire.

(2) Harmonics affects the regular operation of various electrical equipment. The influence of harmonics on the motor causes additional losses and produces mechanical vibration, noise, and overvoltage, which will cause severe local overheating of the transformer. Harmonics make capacitors, cables, and other equipment overheat, aging insulation, shorten life, and even damage.

(3) Harmonics will cause local parallel resonance and series resonance in the public power grid, thereby amplifying the harmonics, which significantly increases the harm of the above (1) and (2), and even cause serious accidents.

(4) Harmonics will cause malfunction of relay protection and automatic devices and will make the measurement of electrical measuring instruments inaccurate.

(5) Harmonics will interfere with the adjacent communication system. The light ones will generate noise and reduce the communication quality; the heavy ones will lead to the loss of residence and make the communication system unable to work.