I would like to ask how higher harmonics are generated?

Higher harmonics are generated by nonlinear loads; when current flows through a load that does not have a linear relationship with the applied voltage, a non-sinusoidal current is formed. Any periodic waveform can be decomposed into a sine wave at the fundamental frequency and sine waves at many harmonic frequencies. The harmonic frequency is an integer multiple of the fundamental frequency; for example, if the fundamental frequency is 50 Hz, the second harmonic is 100 Hz, the third harmonic is 150 Hz, and so on, with higher-order harmonics being generated in this manner. The general solution is to add a filter.

1 Reasons for harmonic generation In power supply systems, harmonics are primarily caused by two factors: (1) the widespread use of thyristor rectifiers and voltage regulation devices, the common use of thyristors in numerous household appliances, and the increase in various nonlinear loads, all of which lead to waveform distortion. (2) Change in the design philosophy of the equipment. In the past, there was a tendency to adopt designs that operated below rated conditions or with a large margin of safety. Now, for competitive reasons, there is a tendency to use designs for electrical equipment that are optimized for critical conditions. For example, some designs aim to save materials by operating the magnetic material in the deeply saturated region of its magnetization curve; however, operating in such regions causes severe distortion of the excitation material’s waveform. 2 The hazards of harmonics to power systems: The pollution caused by harmonics in power systems is becoming increasingly severe. The injection of harmonic sources leads to an increase in harmonic currents and voltages in the power grid, and these hazards affect the entire network, impacting various electrical devices to varying degrees. The hazard analysis for specific equipment is as follows: (1) Alternator. Synchronous motors and induction motors experience additional heat losses in their stator windings and rotor windings. In addition to the copper loss I2nR caused by harmonic currents, additional losses arise due to the skin effect of currents, which leads to increased heat loss in the rotor. In large turbogenerators, if harmonic oscillations occur multiple times and the harmonic current exceeds 25% of the rated current, local overheating of the rotor may occur due to the reasons mentioned above, leading to damage. For transformers, the core experiences heat losses, particularly significant eddy current losses. Harmonic currents exist in the transformer windings, which induce magnetic flux in the core and result in core losses. (2) Harmonic currents in overhead lines cause thermal losses, and larger components of higher-order harmonics can significantly delay the extinction of the stray supply current, leading to the failure of single-phase reclosing. Harmonic currents in the cable cause heat loss, leading to increased dielectric loss and temperature rise in the cable. (3) Harmonic currents in power capacitors cause additional dielectric losses, accelerating the insulation aging of these capacitors. Resonance in the system’s harmonic voltages or currents can cause overvoltage and overcurrent, leading to damage to the insulation of electrical equipment as well as noise and vibration. (4) Electronic computers will become distorted due to harmonic interference ； The functions of industrial electronic equipment are impaired when they are damaged. (5) It causes interference with relay protection devices, automatic control systems, and computers, leading to erroneous operations and errors in electricity metering. (6) The flow of harmonic currents in high-voltage overhead lines not only increases line losses but also causes interference to adjacent communication lines. 3 Measures to Suppress Harmonics in Power Systems To keep the interference (pollution) caused by harmonics on power systems within acceptable levels, China and other countries have issued the \"Interim Provisions on Harmonic Management in Power Systems\" as well as IEC standards, which specify the maximum values of harmonics that can be generated by various harmonic sources. The main measures for suppressing harmonics in power systems are: (1) Connecting a set of reactors in series in the compensation capacitor circuit. Before Xc is applied and ignoring the resistance, the harmonic voltage at the In bus due to the harmonic source is: Un = Xsn • In ； After connecting a compensation capacitor in parallel, the input harmonic reactance of the harmonic source becomes: at this point, the harmonic voltage, as well as the harmonic currents injected into the system, are Un, Isn > In. In other words, the parallel capacitor causes the harmonics in the system to be amplified. If for a certain harmonic Xsn-Xcn=0, that is, a harmonic occurs, then both the harmonic current and voltage tend to infinity. To get rid of this resonance point, a reactor is usually connected in series with the capacitor branch; the value of its inductive reactance is chosen so that, under any possible harmonics, the total reactance of the capacitor circuit is inductive rather than capacitive, thereby eliminating the possibility of harmonic generation. (2) Install a single-tuned filter and a high-pass filter composed of capacitors, inductors, and resistors. A single-tuned filter is a filter designed for a specific harmonic order, while a high-pass filter is a filter used to absorb certain higher harmonic orders. The type of filters to be installed, the number of such filters, and their tuning frequencies (filter orders) can be determined through specific calculations. Since electric locomotives are high-power single-phase rectifiers, they suffer from harmonic problems. According to empirical data, the harmonic content in the current of the Shaoshan-1 type locomotives is roughly as shown in Table 1. There are many factors that affect the harmonic currents injected by electric locomotives into the power system, and the catenary is one of such factors. In the diagram, Zsn represents the harmonic impedance of the power system; the total length of the power supply arm is L, and there is only one electric locomotive on this arm, located at a distance l from the substation. Let the nth harmonic impedance and admittance per unit length of the contact network be Zn and Yn, respectively. Then its nth harmonic characteristic impedance Zcn and propagation constant γn can be determined. It can be seen that a typical contact network acts as an amplifier for the harmonic currents generated by the locomotive, with this amplifying effect being greatest when the locomotive is at the end of the power supply section (i.e., when l = L). To address the harmonic problem of traction locomotives, a common approach is to install filters for the 3rd, 5th, and 7th harmonics in the traction substation. Some newly put into service electric locomotives in recent years have adopted on-board multistage filters, which achieve very good results in filtering out the 3rd and 5th harmonics. (3) Increasing the number of rectification phases: High-order harmonic currents are closely related to the number of rectification phases; that is, as the number of phases increases, the lowest order of the high-order harmonics rises, resulting in a smaller amplitude of the harmonic currents. Most thyristor rectifier units are 6-phase; to reduce high-order harmonic currents, 12-phase or 36-phase versions can be used instead. When 12-phase rectification is used, the higher harmonic currents account for only about 1% of the total current, thus **reducing** their harmful effects. (4) When two or more rectifier transformers are powered from the same busbar, the primary windings of these transformers can be connected in a Y configuration and a Δ configuration alternately. This allows the 5th and 7th harmonics to cancel each other out, so that only the effects of the 11th and 13th harmonics need to be considered. Due to their high frequencies, their amplitude values are small, thereby reducing their harmful impact. 4 Conclusions (1) The occurrence of harmonics affects the environment of the entire power system; for example, harmonic noise can degrade the quality of communications, cause control and protection devices to malfunction, and lead to overloading of electrical equipment and systems, thereby posing a threat to the proper operation of the power system. (2) The management of harmonics usually involves establishing limits on the voltage harmonic content at the user’s common connection point; that is, relevant standards are set, appropriate measures are taken to exercise strict control, and the power system environment is purified. (3) When measuring harmonics, attention must be paid to the accuracy of PT and CT; otherwise, significant errors will occur. Using the voltage division on the CT’s secondary side to measure the system’s harmonic voltage offers the advantages of accuracy and convenience. It has been widely applied in the harmonic voltage testing of ultra-high voltage systems.

The main sources of harmonics in factory power supply are devices such as rectifiers, frequency converters, and soft starters.

As an example to illustrate the mechanism of harmonic generation, consider how harmonics are produced during the frequency conversion process using nonlinear components such as thyristors. The main circuit of an inverter generally adopts an AC-DC-AC topology. The external 380V 50HZ mains power supply is rectified into a DC voltage signal through a three-phase bridge with uncontrolled rectification; this DC signal is then filtered by capacitors, and an alternating current signal with a variable frequency is generated using high-power transistor switching elements. In the rectification circuit, the waveform of the input current is an irregular rectangular wave. This rectangular waveform can be decomposed into the fundamental wave and various harmonics using Fourier series. The 5th harmonic of the input current can account for up to 20%, while the 7th harmonic can account for up to 12%. High levels of input harmonics can interfere with the power supply system. In the inverter output circuit, the output current signal is a pulse waveform modulated by a pulse-width modulation carrier signal. For GTR high-power inverter components, the frequency of this pulse-width modulation carrier is 2–3 KHZ, whereas for IGBT high-power inverter components, the maximum frequency can reach 15 KHZ. The current signal in the output circuit can also be broken down into the fundamental sine wave and various harmonics; it is the higher-order harmonics that cause interference with the load. It can also radiate into space via cables, interfering with nearby electrical devices.

To address the issue of harmonics and eliminate harmonic interference, two aspects can be considered: conduction and radiation. The first way to address conduction is to filter out or isolate the high-frequency currents that cause conduction in the circuit ； The latter involves shielding the radiation source or the interfered circuit. Strategies that can be used to eliminate harmonics: 1. Increase the internal impedance of the power supply for the inverter; 2. Install reactors; 3. Operate the transformer in multiple phases; 4. Adjust the carrier frequency ratio of the inverter; 5. Use specialized filters; 6. Employ multi-pulse thyristor rectifier circuits. As for the hazards, many have already been mentioned above – I agree!

Harmonics are primarily generated by the chopper and rectifier operations in various power electronic devices. Fourier series can be used for analysis, but it’s actually not necessary to do so as it’s quite complex; generally, it’s sufficient to know how to avoid them

Learning together*, thanks for the detailed materials on the third floor!