# Nonlinear Electromagnetic Field and Its Harmonic Problems

## Harmonic Problems in Power Systems and Power Supply Transformers

### Nonlinear Electromagnetic Field

A nonlinear load, such as electric machines is, by definition, a device that naturally produces a non-sinusoidal current when energized by a sinusoidal voltage source. Nonlinear loads have high impedance during part of the voltage waveform, and when the voltage is at or near the peak, the impedance is suddenly reduced. Figure 2.1 illustrates characteristics of magnetic impedance associated with a B-H curve and permeability, and excitation current corresponding to a sinusoidal voltage excitation associated with a hysteresis B-H curve.

Current harmonics, as shown in Figure 2.1(b), are a problem because they cause increased losses in customer and utility power system components [1]. Single-phase nonlinear loads like magnetic component based devices, motors and transformers, and electronic devices and SMPS-based equipment (such as personal computers, electronic ballasts for fluorescent lights and other electronic equipment) generate odd harmonics (i.e. 3rd, 5th, 7th, 9th, etc.), as shown in Figure 2.2. When harmonic frequencies are prevalent, electrical power panels and transformers become mechanically resonant to the magnetic fields generated by higher frequency harmonics. When this happens, the

*Harmonic Balance Finite Element Method: Applications in Nonlinear Electromagnetics and Power Systems,* First Edition. Junwei Lu, Xiaojun Zhao and Sotoshi Yamada.

© 2016 John Wiley & Sons Singapore Pte. Ltd. Published 2016 by John Wiley & Sons Singapore Pte. Ltd. Companion website: www.wiley.com/go/lu/HBFEM

Figure 2.1 (a) Characteristics of magnetic impedance associated with a B-H curve and

permeability. (b) Excitation current corresponding to a sinusoidal voltage excitation associated with a hysteresis B-H curve

Figure 2.2 Excitation current corresponding to a sinusoidal voltage excitation

power panel or transformer vibrates and emits a buzzing sound for the different harmonic frequencies. Harmonic frequencies from the 3rd to the 25th are the most common range of frequencies measured in electrical distribution systems [2, 3].

Current distortion affects the power system and distribution equipment, and it may, directly or indirectly, cause the destruction of loads or loss of product. From a direct perspective, current distortion may cause transformers to overheat and fail, even though they are not fully loaded. Conductors and conduit systems can also overheat, leading to open circuits and down time.

Voltage distortion directly affects loads. Distorted voltage can cause motors to overheat and vibrate excessively. It can also cause damage to the motor shaft. Even nonlinear loads are prey to voltage distortion. Equipment ranging from computers to electronically ballasted fluorescent lights may be damaged by voltage distortion.

As the current distortion is conducted through the normal system wiring, it creates voltage distortion according to Ohm’s Law. While current distortion travels only along the power path of the nonlinear load, voltage distortion affects all loads connected to that particular bus or phase. Each harmonic current in a facility’s electrical distribution system will cause a voltage to exist at the same harmonic when the harmonic current flows into impedance, which results in voltage harmonics appearing at the load bus. For example, a 3rd harmonic current will produce a 3rd harmonic voltage, a 9th harmonic current will produce a 9th harmonic voltage, and so on. Another indirect problem introduced by current distortion is called resonance. Certain current harmonics may excite resonant frequencies in the system, and this resonance can cause extremely high harmonic voltages, possibly damaging sensitive electronic equipment.