Chapter 1
Power System Harmonics

The electrical power systems should be designed not only for the sinusoidal currents and voltages but also for nonlinear and electronically switched loads. There has been an increase in such loads in the recent times, and these can introduce harmonic pollution, distort current and voltage waveforms, create resonances, increase the system losses, and reduce the useful life of the electrical equipment. Harmonics are one of the major problems of ensuring a certain power quality. This requires a careful analysis of harmonic generation and their measurements and the study of the deleterious effects, harmonic controls, and limitation to acceptable levels. Interest in harmonic analysis dates back to the early 1990s in connection with high voltage DC (HVDC) systems and static var compensators (SVC; Reference [1]). The analytical and harmonic limitation technology has progressed much during this period (see Reference [2] for a historical overview of the harmonics in power systems).

DC power is required for a number of applications from small amount of power for computers, video equipment, battery chargers, UPS (uninterrptible power supplies) systems to large chunks of power for electrolysis, DC drives, and the like. A greater percentage of office and commercial building loads are electronic in nature, which have DC as the internal operating voltage. Fuel and solar cells and batteries can be directly connected to a DC system, and the double conversion of power from DC to AC and then from AC to DC can be avoided. A case study conducted by Department of Electrical Power Engineering, Chalmers University of Technology, Gothenburg, Sweden is presented in [3]. This compares reliability, voltage drops, cable sizing, grounding and safety: AC verses DC distribution system. In Reference [4], DC shipboard distribution system envisaged by US Navy is discussed. Two steam turbine synchronous generators are connected to 7000 V DC bus through rectifiers, and DC loads are served through DC-DC converters. However, this is not a general trend, bulk and consumer power distribution systems are AC; and we will not be discussing industrial or commercial DC distribution systems in this book, except that HVDC converter interactions with respect to harmonics and DC filters are of interest and discussed in the appropriate chapters.

Harmonics in power systems originate due to varied operations, for example, ferroresonance, magnetic saturation, subsynchronous resonance, and nonlinear and electronically switched loads. Harmonic emission from nonlinear loads predominates.

1.1 Nonlinear Loads

To distinguish between linear and nonlinear loads, we may say that linear time-invariant loads are characterized so that an application of a sinusoidal voltage results in a sinusoidal flow of current. These loads display constant steady-state impedance during the applied sinusoidal voltage. Incandescent lighting is an example of such a load. The electrical motors not supplied through electronic converters also approximately meet this definition. The current or voltage waveforms will be almost sinusoidal, and their phase angles displaced depending on power factor of the electrical circuit. Transformers and rotating machines, under normal loading conditions, approximately meet this definition. Yet, it should be recognized that flux wave in the air gap of a rotating machine is not sinusoidal. Tooth ripples and slotting in rotating machines produce forward and reverse rotating harmonics. Magnetic circuits can saturate and generate harmonics. Saturation in a transformer on abnormally high voltage produces harmonics, as the relationship between magnetic flux density and the magnetic field intensity in a magnetic material (the transformer core) is not linear. Yet, the harmonics emissions from these sources are relatively small (Chapter 3).

In a nonlinear device, the application of a sinusoidal voltage does not result in a sinusoidal flow of current. These loads do not exhibit constant impedance during the entire cycle of applied sinusoidal voltage. Nonlinearity is not the same as the frequency dependence of impedance, that is, the reactance of a reactor changes in proportion to the applied frequency, but it is linear at each applied frequency if we neglect saturation and fringing. However, nonlinear loads draw a current that may even be discontinuous or flow in pulses for a part of the sinusoidal voltage cycle.

Mathematically, linearity implies two conditions:

• Homogeneity
• Superposition

Consider the state of a system defined in the state equation form:

If is the solution to this differential equation with initial conditions at and input , :

then homogeneity implies that

where is a scalar constant. This means that with input is equal to times with input for any scalar .

Superposition implies that

That is, with inputs is equal to the sum of with input and with input .Thus, linearity is superimposition plus homogeneity.

1.2 Increases in Nonlinear Loads

Nonlinear loads are continuously on the increase. It is estimated that, during the next 10 years, more than 60% of the loads on utility systems will be nonlinear. Also much of the electronic load growth involves residential sector and household appliances. Concerns for harmonics originate from meeting a certain power quality, which leads to the related issues of (1) effects on the operation of electrical equipment, (2) harmonic analysis, and (3) harmonic control. A growing number of consumer loads are sensitive to poor power quality, and it is estimated that power quality problems cost US industry tens of billion of dollars per year. Although the expanded use of consumer automation equipment and power electronics is leading to higher productivity, these heavy loads are a source of electrical noise and harmonics and are less tolerant to poor power quality. For example, adjustable speed drives (ASDs) are less tolerant to voltage sags and swells as compared to an induction motor; and a voltage dip of 10% of certain time duration may precipitate ASD shutdown. These generate line harmonics and a source containing harmonics impacts their operation, leading to further generation of harmonics. This implies that the nonlinear loads which are a source of generation of harmonics are themselves relatively less tolerant to the poor power quality that originates from harmonic emission from these loads.

Some examples of nonlinear loads are as follows:

• ASD systems
• Cycloconverters
• Arc furnaces
• Rolling mills
• Switching mode power supplies
• Computers, copy machines, television sets, and home appliances
• Pulse burst modulation
• Static var compensators (SVCs)
• Thyristor-controlled reactors (TCRs)
• HVDC transmission, harmonics originate in converters
• Electric traction, chopper circuits
• Wind and solar power generation
• Battery charging and fuel cells
• Slip frequency recovery schemes of induction motors
• Fluorescent lighting and electronic ballasts
• Electrical vehicle charging systems
• Silicon-controlled rectifier (SCR) heating, induction heating, and arc welding.

The harmonics are also generated in conventional power equipment, such as transformer and motors. Saturation and switching of transformers generate harmonics. The harmonic generation is discussed in Chapters 3-5. The application of capacitor banks for power factor corrections and reactive power support can cause resonance and further distortions of waveforms (Chapter 9). Earlier rotating synchronous condensers have been replaced with modern shunt capacitors or SVCs (Chapter 4).

1.3 Effects of Harmonics

Harmonics cause distortions of the voltage and current waveforms, which have adverse effects on electrical equipment. The estimation of harmonics from nonlinear loads is the first step in a harmonic analysis, and this may not be straightforward. There is an interaction between the harmonic producing equipment, which can have varied topologies, and the electrical system. Over the course of years, much attention has been focused on the analysis and control of harmonics, and standards have been established for permissible harmonic current and voltage distortions (Chapter 10). The effects of harmonics are discussed in Chapter 8.

1.4 Distorted Waveforms

Harmonic emissions can have varied amplitudes and frequencies. The most common harmonics in power systems are sinusoidal components of a periodic waveform, which have frequencies that can be resolved into some multiples of the fundamental frequency. Fourier analysis is the mathematical tool employed for such analysis, and Chapter 2 provides an overview.

The components in a Fourier series that are not an integral multiple of the power frequency are called noninteger harmonics (Chapter 5).

The distortion produced by nonlinear loads can be resolved into a number of categories:

• A distorted waveform having a Fourier series with fundamental frequency equal to power system frequency and a periodic steady state exists. This is the most common case in harmonic studies. The waveform shown in Fig. 1.1 is synthesized from the harmonics shown in Table 1.1. The waveform in Fig. 1.1 is symmetrical about the x-axis and can be described by the...