When a power system includes nonlinear (time-varying or time-invariant) loads, even if the power supply operates at a main frequency of 50Hz, the nonlinear loads can generate sinusoidal voltages or currents at frequencies different from the main frequency. These different frequency sinusoidal voltages or currents are referred to as electrical harmonics when expanded into the Fourier series.
The definition of harmonics in a power supply system involves decomposing a periodic non-sinusoidal quantity using the Fourier series. Besides obtaining components with the same frequency as the mains, a series of components with frequencies higher than the mains frequency are also obtained. These components are called harmonics. The ratio of the harmonic frequency to the fundamental frequency (n=fn/f1) is known as the harmonic order. Sometimes, non-integer multiples of harmonics exist in the grid, referred to as non-harmonics or fractional harmonics. Harmonics essentially act as interference, causing “pollution” in the grid. The field of electrical engineering mainly studies the generation, transmission, measurement, hazards, and suppression of harmonics, generally within the frequency range of 2 ≤ n ≤ 40.
1. Hazards to Power Distribution Lines
Impact on Line Stability
Power distribution systems usually employ electromagnetic relays, induction relays, or transistor relays for detection and protection, ensuring the safety of lines and equipment in the event of faults. However, electromagnetic and induction relays can malfunction if the harmonic content exceeds 10%, leading to ineffective protection. Although transistor relays have many advantages, they utilize rectifying sampling circuits, making them susceptible to harmonic interference, causing false or missed operations. Thus, harmonics pose a serious threat to the stability and safety of the power distribution system.
Impact on Power Quality
Harmonics in the power system can cause voltage and current waveforms to distort. For instance, in residential distribution systems, loads such as fluorescent lights, dimmers, and computers generate substantial odd harmonics, especially the third harmonic, which can reach up to 40%. In three-phase distribution lines, third-order harmonic currents in the phase lines can add up in the neutral line, causing the neutral current to exceed the phase current. Moreover, harmonic voltage and current of the same frequency produce active and reactive power of the same harmonic order, lowering grid voltage and wasting grid capacity.
2. Hazards to Power Equipment
Impact on Power Transformers
Harmonics increase the copper losses in transformers, including resistance losses, eddy current losses in conductors, and stray losses caused by leakage flux outside the conductors. Harmonics also increase the iron losses, primarily by increasing hysteresis losses in the core. The worse the voltage waveform distortion, the greater the hysteresis losses. Consequently, the actual usable capacity of the transformer must be reduced, or the rated capacity of the transformer should account for the harmonic content in the grid. Additionally, harmonics can increase transformer noise. The vibration noise of the transformer, mainly caused by the magnetostrictive effect of the core, increases with higher harmonic orders, contributing to mixed noise frequencies around 1kHz and sometimes producing metallic sounds.
Impact on Power Cables
Higher harmonic orders increase frequency, and the skin effect becomes more pronounced with larger conductor cross-sectional areas, leading to increased AC resistance of the conductor and reduced allowable current through the cable. Furthermore, the cable, system bus impedance, and line inductance resistance can resonate with capacitors to improve power factor and system capacitance, causing resonances at certain inductance and capacitance values.
Impact on Electrical Equipment (Motors)
Harmonics impact asynchronous motors mainly by increasing additional losses and reducing efficiency, which can lead to motor overheating in severe cases. In particular, negative sequence harmonics generate negative sequence rotating magnetic fields in the motor, creating a torque opposite to the motor’s rotation, reducing its output. Additionally, harmonic currents in the motor can cause mechanical vibrations and significant noise if the frequencies approach the natural frequencies of certain motor parts.