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]]>Harmonics are sinusoidal voltages or currents having frequencies that are integer multiples of the frequency at which the supply system is designed to operate.

Harmonics as pure tones making up a composite tone in music. A pure tone is a musical sound of a single frequency, and a combination of many pure tones makes up a composite sound. Sound waves are electromagnetic waves travelling through space as a periodic function of time. Can the principle behind pure music tones apply to other functions or quantities that are time dependent?

In the early 1800s, French mathematician, Jean Baptiste Fourier formulated that a periodic non-sinusoidal function of a fundamental frequency f may be expressed as the sum of sinusoidal functions of frequencies which are multiples of the fundamental frequency. In our discussions here, we are mainly concerned with periodic functions of voltage and current due to their importance in the field of power quality. In other applications, the periodic function might refer to radiofrequency transmission, heat flow through a medium, vibrations of a mechanical structure, or the motions of a pendulum in a clock.

**A sinusoidal voltage or current function that is dependent on time t may be represented by the following expressions: **

Voltage function,

v(t) = V sin (ωt) …(4.1)

Current function,

i(t) = I sin (ωt ± θ) …(4.2)

where, ω = 2πf is known as the angular velocity of the periodic waveform and 0 is the difference in phase angle between the voltage and the current waveforms referred to as a common axis. The sign of phase angle θ is positive if the current leads the voltage and negative if the current lags the voltage.

Figure 4.1 contains voltage and current waveforms expressed by Eqs. (4.1) and (4.2) and which by definition are pure sinusoids.

For the periodic non-sinusoidal waveform shown in Fig. 4.2, the simplified Fourier expression states-

V (t) = V_{0} + V_{1} sin(ωt) + V_{2} sin(2 ωt) + V_{3} sin(3 ωt) + … + Vn sin( n ωt) + V_{n+1} sin (( n + 1) ωt) +………….. (4.3)

The Fourier expression is an infinite series. In this equation, V_{0 }represents the constant or the DC component of the waveform.

V_{1}, V_{2}, V_{3}, … , V_{n} are the peak values of the successive terms of the expression. The terms are known as the harmonics of the periodic waveform. The fundamental (or first harmonic) frequency has a frequency of f, the second harmonic has a frequency of 2 x f, the third harmonic has a frequency of 3 x f, and the nth harmonic has a frequency of n x f. If the fundamental frequency is 60 Hz (as in the U.S.), the second harmonic frequency is 120 Hz, and the third harmonic frequency is 180 Hz.

The significance of harmonic frequencies can be seen in Fig. 4.3. The second harmonic undergoes two complete cycles during one cycle of the fundamental frequency, and the third harmonic traverses three complete cycles during one cycle of the fundamental frequency.

V_{1}, V_{2}, and V_{3} are the peak values of the harmonic components that comprise the composite waveform, which also has a frequency of f.

The ability to express a non-sinusoidal waveform as a sum of sinusoidal waves allows us to use the more common mathematical expressions and formulas to solve power system problems. In order to find the effect of a non-sinusoidal voltage or current on a piece of equipment, we only need to determine the effect of the individual harmonics and then vectorially sum the results to derive the net effect. Figure 4.4 illustrates how individual harmonics that are sinusoidal can be added to form a non-sinusoidal waveform.

The Fourier expression in Eq. (4.3) has been simplified to clarify the concept behind harmonic frequency components in a nonlinear periodic function. For the purist, the following more precise expression is offered. For a periodic voltage wave with fundamental frequency of-

ω = 2πf,

v(t) = V_{0} + ∑(a_{k} cos kωt + b_{k} sin k ωr) (for k- 1 to ∞)…(4.4)

Where a_{k} and b_{k} are the coefficients of the individual harmonic terms or components. Under certain conditions, the cosine or sine terms can vanish, giving us a simpler expression. If the function is an even function, meaning f (-t) = f(t), then the sine terms vanish from the expression. If the function is odd, with f (- t) = – f(t) then the cosine terms disappear.

For our analysis, we will use the simplified expression involving sine terms only. It should be noted that having both sine and cosine terms affects only the displacement angle of the harmonic components and the shape of the nonlinear wave and does not alter the principle behind application of the Fourier series. The coefficients of the harmonic terms of a function-

f(t) contained in Eq. (4.4) are determined by- Coefficient

The coefficients represent the peak values of the individual harmonic frequency terms of the nonlinear periodic function represented by f (t).

Harmonic number (h) refers to the individual frequency elements that comprise a composite waveform. For example, h = 3 refers to the third harmonic component with a frequency equal to third times the fundamental frequency. If the fundamental frequency is 60 Hz, then the 3^{rd} (third) harmonic frequency is 3 x 60, or 180 Hz. The harmonic number 6 is a component with a frequency of 360 Hz.

Dealing with harmonic numbers and not with harmonic frequencies is done for two reasons. The fundamental frequency varies among individual countries and applications. The fundamental frequency in the U.S. is 60 Hz, whereas in Europe and many Asian countries it is 50 Hz. Also, some applications use frequencies other than 50 or 60 Hz; for example, 400 Hz is a common frequency in the aerospace industry, while some AC systems for electric traction use 25 Hz as the frequency.

The inverter part of an AC adjustable speed drive can operate at any frequency between zero and its full rated maximum frequency, and the fundamental frequency then becomes the frequency at which the motor is operating. The use of harmonic numbers allows us to simplify how we express harmonics. The second reason for using harmonic numbers is the simplification realized in performing mathematical operations involving harmonics.

**Odd and Even Order Harmonics:**

As their names imply, odd harmonics have odd numbers (e.g., 3, 5, 7, 9, 11), and even harmonics have even numbers (e.g., 2, 4, 6, 8, 10). Harmonic number 1 is assigned to the fundamental frequency component of the periodic wave. Harmonic number 0 represents the constant or DC component of the waveform. The DC component is the net difference between the positive and negative halves of one complete waveform cycle.

Figure 4.5 shows a periodic waveform with net DC content. The DC component of a waveform has undesirable effects, particularly on transformers, due to the phenomenon of core saturation. Saturation of the core is caused by operating the core at magnetic field levels above the knee of the magnetization curve. Transformers are designed to operate below the knee portion of the curve.

When DC voltages or currents are applied to the transformer winding, large DC magnetic fields are set up in the transformer core. The sum of the AC and the DC magnetic fields can shift the transformer operation into regions past the knee of the saturation curve. Operation in the saturation region places large excitation power requirements on the power system. The transformer losses are substantially increased, causing excessive temperature rise. Core vibration becomes more pronounced as a result of operation in the saturation region.

We usually look at harmonics as integers, but some applications produce harmonic voltages and currents that are not integers. Electric arc furnaces are examples of loads that generate non-integer harmonics. Arc welders can also generate non-integer harmonics. In both cases, once the arc stabilizes, the non-integer harmonics mostly disappear, leaving only the integer harmonics.

The majority of nonlinear loads produce harmonics that are odd multiples of the fundamental frequency. Certain conditions need to exist for production of even harmonics. Uneven current draw between the positive and negative halves of one cycle of operation can generate even harmonics. The uneven operation may be due to the nature of the application or could indicate problems with the load circuitry. Transformer magnetizing currents contain appreciable levels of even harmonic components and so do arc furnaces during startup. Sub-harmonics have frequencies below the fundamental frequency and are rare in power systems.

When sub-harmonics are present, the underlying cause is resonance between the harmonic currents or voltages with the power system capacitance and inductance. Sub-harmonics may be generated when a system is highly inductive (such as an arc furnace during startup) or if the power system also contains large capacitor banks for power factor correction or filtering. Such conditions produce slow oscillations that are relatively un-damped, resulting in voltage sags and light flicker.

A pure sinusoidal waveform with zero harmonic distortion is a hypothetical quantity and not a practical one. The voltage waveform, even at the point of generation, contains a small amount of distortion due to non-uniformity in the excitation magnetic field and discrete spatial distribution of coils around the generator stator slots. The distortion at the point of generation is usually very low, typically less than 1.0%.

The generated voltage is transmitted many hundreds of miles, transformed to several levels, and ultimately distributed to the power user. The user equipment generates currents that are rich in harmonic frequency components, especially in large commercial or industrial installations. As harmonic currents travel to the power source, the current distortion results in additional voltage distortion due to impedance voltages associated with the various power distribution equipment, such as transmission and distribution lines, transformers, cables, buses, and so on.

Figure 4.9 illustrates how current distortion is transformed into voltage distortion. Not all voltage distortion, however, is due to the flow of distorted current through the power system impedance. For instance, static uninterruptible power source (UPS) systems can generate appreciable voltage distortion due to the nature of their operation. Normal AC voltage is converted to DC and then reconverted to AC in the inverter section of the UPS. Unless waveform shaping circuitry is provided, the voltage waveforms generated in UPS units tend to be distorted.

As nonlinear loads are propagated into the power system, voltage distortions are introduced which become greater moving from the source to the load because of the circuit impedances. Current distortions for the most part are caused by loads. Even loads that are linear will generate nonlinear currents if the supply voltage waveform is significantly distorted.

When several power users share a common power line, the voltage distortion produced by harmonic current injection of one user can affect the other users. This is why standards are being issued that will limit the amount of harmonic currents that individual power users can feed into the source.

The major causes of current distortion are nonlinear loads due to adjustable speed drives, fluorescent lighting, rectifier banks, computer and data-processing loads, arc furnaces, and so on. One can easily visualize an environment where a wide spectrum of harmonic frequencies are generated and transmitted to other loads or other power users, thereby producing undesirable results throughout the system.

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]]>In power system studies involving harmonics, this relationship is important. In a balanced three-phase electrical system, the voltages and currents have a positional relationship as shown in Fig. 4.6. The three voltages are 120° apart and so are the three currents.

The normal phase rotation or sequence is a-b-c, which is counterclockwise and designated as the positive-phase sequence. For harmonic analyses, these relationships are still applicable, but the fundamental components of voltages and currents are used as reference. All other harmonics use the fundamental frequency as the reference. The fundamental frequencies have a positive-phase sequence. The angle between the fundamental voltage and the fundamental current is the displacement power factor angle.

So how do the harmonics fit into this space-time picture? For a clearer understanding, let us look only at the current harmonic phasors. We can further simplify the picture by limiting the discussion to odd harmonics only, which under normal and balanced conditions are the most prevalent. The following relationships are true for the fundamental frequency current components in a three-phase power system-

i_{a1 }= I_{a1} sin ωt… (4.7)

i_{b1} = I_{b1} sin (ωt – 120°)… (4.8)

i_{c1} = I_{c1 }sin (ωt – 240°) … (4.9)

The negative displacement angles indicate that the fundamental phasors i_{b1} and i_{c1} trail the i_{a1} phasor by the indicated angle. Figure 4.7(a) shows the fundamental current phasors.

**The expressions for the third harmonic currents are:**

i_{a3} = I_{a3} sin 3ωt…(4.10)

i_{b3} = I_{b3} sin 3 (ωt – 120°) = I_{b3} sin (3ωt – 360°)

= I_{b3} sin 3ωt …(4.11)

i_{c3} = I_{c3} sin 3(ωt – 240°) = I_{c3} sin (3ωt – 720°)

= I_{c3} sin 3ωt …(4.12)

The expressions for the third harmonics show that they are in phase and have zero displacement angle between them. Figure 4.7(b) shows the third harmonic phasors. The third harmonic currents are known as zero sequence harmonics due to the zero displacement angle between the three phasors.

**The expressions for the fifth harmonic currents are: **

i_{a5} = I_{a5} sin 5ωt…(4.13)

i_{b5} = I_{b5} sin 5(ωt – 120°) = I_{b5} sin (5ωt – 600°)

= I_{b5} sin (5ωt – 240°)…(4.14)

i_{c5} = I_{c5} sin 5(ωt – 240°)

i_{c5} = i_{c5} sin 5(ωt – 240°) = I_{c5} sin (5ωt – 1200°)

= I_{c5} sin (5ωt – 120°) …(4.15)

Figure 4.7(c) shows the fifth harmonic phasors. Note that the phase sequence of the fifth harmonic currents is clockwise and opposite to that of the fundamental. The fifth harmonics are negative sequence harmonics.

**Similarly the expressions for the seventh harmonic currents are: **

i_{a7} = I_{a7} sin 7ωt…(4.16)

i_{b7} = I_{b7} sin 7(ωt – 120°) = I_{b7} sin (7ωt – 840°)

= I_{b7} sin (7ωt – 120°)…(4.17)

i_{c7} = I_{c7} sin 7(ωt – 240°) = I_{c7} sin (7ωt – 1680°)

= I_{c7} sin (7ωt – 240°) …(4.18)

Figure 4.7(d) shows the seventh harmonic current phasors. The seventh harmonics have the same phase sequence as the fundamental and are positive sequence harmonics.

The expressions shown so far for harmonics have zero phase shifts with respect to the fundamental. It is not uncommon for the harmonics to have a phase-angle shift with respect to the fundamental. Figure 4.8 depicts a fifth harmonic current waveform with and without phase shift from the fundamental.

**Expressions for the fifth harmonics with a phase-shift angle of 0 degrees are: **

i_{a5} = I_{a5} sin 5 (ωt – θ) …(4.19)

i_{b5} = I_{b5} sin 5 (ωt – 120°- θ) …(4.20)

i_{c5} = I_{c5} sin 5 (ωt – 240°- θ) …(4.21)

While the phase-shift angle has the effect of altering the shape of the composite waveform, the phase sequence order of the harmonics is not affected.

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]]>**Harmonics can affect transformers primarily in two ways:**

1. Voltage harmonics produce additional losses in the transformer core as the higher frequency harmonic voltages set up hysteresis loops, which superimpose on the fundamental loop. Each loop represents higher magnetization power requirements and higher core losses.

2. A second and a more serious effect of harmonics is due to harmonic frequency currents in the transformer windings. The harmonic currents increase the net RMS current flowing in the transformer windings which results in additional I_{2}R losses. Winding eddy current losses are also increased. Winding eddy currents are circulating currents induced in the conductors by the leakage magnetic flux. Eddy current concentrations are higher at the ends of the windings due to the crowding effect of the leakage magnetic field at the coil extremities. The winding eddy current losses increase as the square of the harmonic current and the square of the frequency of the current.

Thus, the eddy loss (EC) is proportional to I_{h}^{2} x h^{2}, where I_{h} is the RMS value of the harmonic current of order h, and h is the harmonic frequency order or number. Eddy currents due to harmonics can significantly increase the transformer winding temperature. Transformers that are required to supply large nonlinear loads must be derated to handle the harmonics. This derating factor is based on the percentage of the harmonic currents in the load and the rated winding eddy current losses. One method by which transformers may be rated for suitability to handle harmonic loads is by k factor ratings. The k factor is equal to the sum of the square of the harmonic frequency currents (expressed as a ratio of the total RMS current) multiplied by the square of the harmonic frequency numbers-

k = I_{1}^{2} (1)^{2} + I_{2}^{2} (2)^{2} + I_{3}^{2} (3)^{2} + I_{4}^{2} (4)^{2} +… + I_{n}^{2} (n)^{2} ….(4.23)

where,

I_{1} is the ratio between the fundamental current and the total RMS current.

I_{2} is the ratio between the second harmonic current and the total RMS current.

I_{3} is the ratio between the third harmonic current and the total RMS current.

Equation (4.23) can be rewritten as-

**There are three effects that result in increased transformer heating when the load current includes harmonic components: **

**1. RMS Current:**

If the transformer is sized only for the kVA requirements of the load, harmonic currents may result in the transformer rms current being higher than its capacity. The increased total rms current results in increased conductor losses.

**2. Eddy Current Losses:**

These are induced currents in a transformer caused by the magnetic fluxes. These induced currents flow in the windings, in the core, and in other conducting bodies subjected to the magnetic field of the transformer and cause additional heating. This component of the transformer losses increases with the square of the frequency of the current causing the eddy currents. Therefore, this becomes a very important component of transformer losses for harmonic heating.

**3. Core Losses:**

The increase in core losses in the presence of harmonics will be dependent on the effect of the harmonics on the applied voltage and the design of the transformer core. Increasing the voltage distortion may increase the eddy currents in the core laminations.

The net impact that this will have depends on the thickness of the core laminations and the quality of the core steel. The increase in these losses due to harmonics is generally not as critical as the previous two.

Application of distorted voltage to a motor results in additional losses in the magnetic core of the motor. Hysteresis and eddy current losses in the core increase as higher frequency harmonic voltages are impressed on the motor windings. Hysteresis losses increase with frequency and eddy current losses increase as the square of the frequency. Also, harmonic currents produce additional I_{2}R losses in the motor windings which must be accounted for.

Another effect, and perhaps a more serious one, is torsional oscillations due to harmonics. Two of the more prominent harmonics found in a typical power system are the fifth and seventh harmonics. The fifth harmonic is a negative sequence harmonic, and the resulting magnetic field revolves in a direction opposite to that of the fundamental field at a speed five times the fundamental. The seventh harmonic is a positive sequence harmonic with a resulting magnetic field revolving in the same direction as the fundamental field at a speed seven times the fundamental.

The net effect is a magnetic field that revolves at a relative speed of six times the speed of the rotor. This induces currents in the rotor bars at a frequency of six times the fundamental frequency. The resulting interaction between the magnetic fields and the rotor-induced currents produces torsional oscillations of the motor shaft. If the frequency of the oscillation coincides with the natural frequency of the motor rotating members, severe damage to the motor can result. Excessive vibration and noise in a motor operating in a harmonic environment should be investigated to prevent failures.

Motors intended for operation in a severe harmonic environment must be specially designed for the application. Motor manufacturers provide motors for operation with ASD units. If the harmonic levels become excessive, filters may be applied at the motor terminals to keep the harmonic currents from the motor windings. Large motors supplied from ASDs are usually provided with harmonic filters to prevent motor damage due to harmonics.

Capacitor banks are commonly found in commercial and industrial power systems to correct for low power factor conditions. Capacitor banks are designed to operate at a maximum voltage of 110% of their rated voltages and at 135% of their rated kVARS.

1. When large levels of voltage and current harmonics are present, the ratings are quite often exceeded, resulting in failures. Because the reactance of a capacitor bank is inversely proportional to frequency, harmonic currents can find their way into a capacitor bank.

2. The capacitor bank acts as a sink, absorbing stray harmonic currents and causing overloads and subsequent failure of the bank.

3. A more serious condition with potential for substantial damage occurs due to a phenomenon called harmonic resonance. Resonance conditions are created when the inductive and capacitive reactance become equal at one of the harmonic frequencies.

The two types of resonances are series and parallel. In general, series resonance produces voltage amplification and parallel resonance results in current multiplication.

In a harmonic-rich environment, both series and parallel resonance may be present. If a high level of harmonic voltage or current corresponding to the resonance frequency exists in a power system, considerable damage to the capacitor bank as well as other power system devices can result.

Current flowing in a cable produces I_{2}R losses. When the load current contains harmonic content, additional losses are introduced. To compound the problem, the effective resistance of the cable increases with frequency because of the phenomenon known as skin effect. Skin effect is due to unequal flux linkage across the cross section of the conductor which causes AC currents to flow only on the outer periphery of the conductor.

This has the effect of increasing the resistance of the conductor for AC currents. The higher the frequency of the current, the greater the tendency of the current to crowd at the outer periphery of the conductor and the greater the effective resistance for that frequency.

The capacity of a cable to carry nonlinear loads may be determined as follows. The skin effect factor is calculated first. The skin effect factor depends on the skin depth, which is an indicator of the penetration of the current in a conductor. Skin depth (δ) is inversely proportional to the square root of the frequency: δ = SI√f, where S is a proportionality constant based on the physical characteristics of the cable and its magnetic permeability and f is the frequency of the current.

If R_{dc} is the DC resistance of the cable, then the AC resistance at frequency f, (R_{f}) = K x R_{dc}.

The value of K is determined from Table according to the value of X which is calculated as-

X = 0.0636 …(4.25)

Where, 0.0636 is a constant for copper conductors, f is the frequency, µ is the magnetic permeability of the conductor material, and R_{dc} is the DC resistance per mile of the conductor. The magnetic permeability of a nonmagnetic material such as copper is approximately equal to 1.0.

Harmonic currents influence the operation of protective devices. Fuses and motor thermal overload devices are prone to nuisance operation when subjected to nonlinear currents. This factor should be given due consideration when sizing protective devices for use in a harmonic environment. Electromechanical relays are also affected by harmonics. Depending on the design, an electromechanical relay may operate faster or slower than the expected times for operation at the fundamental frequency alone.

Such factors should be carefully considered prior to placing the relays in service.

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]]>The relative size of the load with respect to the source is defined as the short circuit ratio (SCR), at the point of common coupling (PCC), which is where the consumer’s load connects to other loads in the power system. The consumer’s size is defined by the total fundamental frequency current in the load, IL, which includes all linear and nonlinear loads. The size of the supply system is defined by the level of short-circuit current, ISC, at the PCC.

**These two currents define the SCR: **

A high ratio means that the load is relatively small and that current limits will not be as strict as limits that pertain to a low ratio. This is demonstrated in 1, which lists recommended, maximum current distortion levels as a function of SCR and harmonic order. The table also identifies total harmonic distortion levels. All of the current distortion values are given in terms relative to the maximum demand load current. The total distortion is in terms of total demand distortion (TDD) instead of the more common THD term.

Table 4.1 shows ocomponents as well as total harmonic distortion. For example, a consumer with an SCR between 50 and 100 has a recommended limit of 12.0% for TDD, while for individual odd harmonic components with orders less than 11, the limit on each is 10%. It is important to note that the individual harmonic current components do not add up directly so that all characteristic harmonics cannot be at their individual maximum limit without exceeding the TDD.

**Table 4.1. IEEE 519 Current distortion limits** f**or conditions lasting more than one hour ****(Shorter periods increase limit by 50 %)**

Harmonic current limits for non-linear load at the point-of-common-coupling with other loads, for voltages 120-69,000 volts.

Maximum odd harmonic current distortion in % of fundamental harmonic order.

Harmonic current limits for non-linear load at the point-of-common-coupling with other loads, for voltages > 69,000 – 161,000 volts.

Maximum odd harmonic current distortion in % of fundamental harmonic order.

Harmonic current limits for non-linear load at the point-of-common-coupling with other loads, for voltages > 161,000 volts.

Maximum odd harmonic current distortion in % of fundamental harmonic order.

Even harmonics are limited to 25% of the odd harmonic limits above.

*A11 power generation equipment is limited to these values of current distortion, regardless of actual ISC/1L.

Where ISC = Maximum short circuit current at point-of-common-coupling.

And IL = Maximum demand load current (fundamental frequency) at point of common coupling.

TDD = Total demand distortion (RSS) in % of maximum demand.

It is important to note that Table 4.1 shows limits for odd harmonics only. IEEE 519 addresses even harmonics by limiting them to 25% of the limits for the odd orders within the same range. Even harmonics result in an asymmetrical current wave (dissimilar positive and negative wave shapes) which may contain a dc component that will saturate magnetic cores.

**Guidelines for Utilities: **

The second set of criteria established by IEEE 519 is to voltage distortion limits. This governor the amount of voltage distortion that is acceptable in the utility supply voltage at the PCC with a consumer. The harmonic voltage limits recommended are based on levels that are low enough to ensure that consumers’ equipment will operate satisfactorily. Table 4.2 lists the harmonic voltage distortion limits from IEEE 519.

**Table 4.2. Voltage distortion limits from IEEE 519**

**(For conditions lasting more than one hour. Shorter periods increase limit by 50%) **

Note- High voltage systems can have up to 2.0% THD where the cause is a high voltage DC terminal which will attenuate by the time it is tapped for a user.

As for current, limits are imposed on individual components and on total distortion from all harmonic voltages combined (THD). What is different in this table, however, is that three different limits are shown. They represent three voltage classes, up to 69 kV, 69 to 161 kV, and equal to or greater than 161 kV. Note that the limits decrease as voltage increases, the same as for current limits.

Again only odd harmonic limits are shown in the table. The generation of even harmonics is more restricted since the resulting dc offset can cause saturation in motors and transformers. Negative sequence current can cause heating in generators. Individual even harmonic-voltage is limited to 25% of the odd harmonic limits, the same limit as currents.

Often utility feeders supply more than one consumer. The voltage distortion limits shown in the table should not be exceeded as long as all consumers conform to the current injection limits. Any consumer who degrades the voltage at the PCC should take steps to correct the problem. However, the problem of voltage distortion is one for the entire community of consumers and the utility. Very large consumers may look for a compromise with the utility over resolution of a specific problem, and both may contribute to its solution.

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]]>The use of electronic power devices is steadily increasing. It is estimated that more than 70% of the loading of a facility by year 2010 will be due to nonlinear loads, thus demand is increasing for product manufacturers to produce devices that generate lower distortion. The importance of equipment design in minimizing harmonic current production has taken on greater importance, as reflected by technological improvements in fluorescent lamp ballasts, adjustable speed drives, battery chargers, and uninterruptible power source (UPS) units.

Computers and similar data-processing devices contain switching mode power supplies that generate a substantial amount of harmonic currents. Designing power supplies for electronic equipment adds considerably to the cost of the units and can also make the equipment heavier. At this time, when computer prices are extremely competitive, attempts to engineer power supplies that draw low harmonic currents are not a priority.

Adjustable speed drive (ASD) technology is evolving steadily, with greater emphasis being placed on a reduction in harmonic currents. Older generation ASDs using current source inverter (CSI) and voltage source inverter (VSI) technologies produced considerable harmonic frequency currents.

**The significant harmonic frequency currents generated in power conversion equipment can be stated as: **

n = k q ± 1

where, n is the significant harmonic frequency, k is any positive integer (1, 2, 3, etc.), and q is the pulse number of the power conversion equipment which is the number of power pulses that are in one complete sequence of power conversion. For example, a three-phase full wave bridge rectifier has six power pulses and therefore has a pulse number of 6.

**With six-pulse-power conversion equipment, the following significant harmonics may be generated: **

For k = 1, n = (1 x 6) ± 1 = 5^{th} and 7^{th} harmonics.

For k = 2, n = (2 x 6) ± 1 = 11^{th} and 13^{th} harmonics.

With six-pulse-power conversion equipment, harmonics below the 5^{th} harmonic are insignificant. Also, as the harmonic number increases, the individual harmonic distortions become lower due to increasing impedance presented to higher frequency components by the power system inductive reactance. So, typically, for six-pulse-power conversion equipment, the 5^{th} harmonic current would be the highest, the 7^{th} would be lower than the 5^{th}, the 11^{th} would be lower than the 7^{th}, and so on, as- We can deduce that, when using 12-pulse-power conversion equipment, harmonics below the 11^{th} harmonic can be made insignificant. The total harmonic distortion is also considerably reduced. Twelve-pulse-power conversion equipment costs more than six-pulse-power equipment. Where harmonic currents are the primary concern, 24-pulse-power conversion equipment may be considered.

Transformer connections employing phase shift are sometimes used to effect cancellation of harmonic currents in a power system. Triplen harmonic (3^{rd}, 9^{th}, 15^{th}, etc.) currents are a set of currents that can be effectively trapped using a special transformer configuration called the zig-zag connection. In power systems, triplen harmonics add in the neutral circuit, as these currents are in phase. Using a zig-zag connection, the triplens can be effectively kept away from the source. Figure 4.18 illustrates’ how this is accomplished.

The transformer phase-shifting principle is also used to achieve cancellation of the 5^{th} and the 7^{th} harmonic currents. Using a ∆ – ∆ and a ∆ – Y transformer to supply harmonic producing loads in parallel as shown in Fig. 4.19, the 5^{th} and the 7^{th} harmonics are cancelled at the point of common connection.

This is due to the 30° phase shift between the two transformer connections. As the result of this, the source does not see any significant amount of the 5^{th} and 7^{th }harmonics. If the nonlinear loads supplied by the two transformers are identical, then maximum harmonic current cancellation takes place; otherwise, some 5^{th} and 7^{th }harmonic currents would still be present. Other phase-shifting methods may be used to cancel higher harmonics if they are found to be a problem. Some transformer manufacturers offer multiple phase-shifting connections in a single package which saves cost and space compared to using individual transformers.

Nonlinear loads produce harmonic currents that can travel to other locations in the power system and eventually back to the source. Harmonic currents can produce a variety of effects that are harmful to the power system. Harmonic currents are a result of the characteristics of particular loads. As long as we choose to employ those loads, we must deal with the reality that harmonic currents will exist to a degree dependent upon the loads. One means of ensuring that harmonic currents produced by a nonlinear current source will not unduly interfere with the rest of the power system is to filter out the harmonics. Application of harmonic filters helps to accomplish this. Harmonic filters are broadly classified into passive and active filters.

Passive filters, as the name implies, use passive components such as resistors, inductors, and capacitors. A combination of passive components is tuned to the harmonic frequency that is to be filtered. Figure 4.20 is a typical series-tuned filter. Here the values of the inductor and the capacitor are chosen to present a low impedance to the harmonic frequency that is to be filtered out. Due to the lower impedance of the filter in comparison to the impedance of the source, the harmonic frequency current will circulate between the load and the filter.

This keeps the harmonic current of the desired frequency away from the source and other loads in the power system. If other harmonic frequencies are to be filtered out, additional tuned filters are applied in parallel. Applications such as arc furnaces require multiple harmonic filters, as they generate large quantities of harmonic currents at several frequencies.

Applying harmonic filters requires careful consideration. Series-tuned filters appear to be of low impedance to harmonic currents but they also form a parallel resonance circuit with the source impedance. In some instances, a situation can be created that is worse than the condition being corrected. It is imperative that computer simulations of the entire power system be performed prior to applying harmonic filters.

As a first step in the computer simulation, the power system is modelled to indicate the locations of the harmonic sources, then hypothetical harmonic filters are placed in the model and the response of the power system to the filter is examined. If unacceptable results are obtained, the location and values of the filter parameters are changed until the results are satisfactory. When applying harmonic filters, the units are almost never tuned to the exact harmonic frequency. For example, the 5^{th} harmonic frequency may be designed for resonance at the 4.7^{th} harmonic frequency.

By not creating a resonance circuit at precisely the 5^{th} harmonic frequency, we can minimize the possibility of the filter resonating with other loads or the source, thus forming a parallel resonance circuit at the 5^{th} harmonic. The 4.7^{th} harmonic filter would still be effective in filtering out the 5^{th} harmonic currents. This is evident from the series-tuned frequency vs. impedance curve shown in Fig. 4.20. Sometimes, tuned filters are configured to provide power factor correction for a facility as well as harmonic current filtering.

In such cases the filter would be designed to carry the resonant harmonic frequency current and also the normal frequency current at the fundamental frequency. In either case, a power system harmonic study is paramount to ensure that no ill effects would be produced by the application of the power factor correction/filter circuit. Active filters use active conditioning to compensate for harmonic currents in a power system.

Figure 4.21 shows an active filter applied in a harmonic environment. The filter samples the distorted current and, using power electronic switching devices, draws a current from the source of such magnitude, frequency composition, and phase shift to cancel the harmonics in the load. The result is that the current drawn from the source is free of harmonics.

An advantage of active filters over passive filters is that the active filters can respond to changing load and harmonic conditions, whereas passive filters are fixed in their harmonic response. Application of passive filters requires careful analysis. Active filters have no serious ill effects associated with them. However, active filters are expensive and not suited for application in small facilities.

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]]>**When a problem occurs, the basic options for controlling harmonics are: **

1. Reduce the harmonic currents produced by the load.

2. Add filters to either siphon the harmonic currents off the system, block the currents from entering the system, or supply the harmonic currents locally.

3. Modify the frequency response of the system by filters, inductors, or capacitors.

There is often little that can be done with existing load equipment to significantly reduce the amount of harmonic current it is producing unless it is being misoperated. While an overexcited transformer can be brought back into normal operation by lowering the applied voltage to the correct range, arcing devices and most electronic power converters are locked into their designed characteristics. PWM drives that charge the dc bus capacitor directly from the line without any intentional impedance are one exception to this.

Adding a line reactor or transformer in series will significantly reduce harmonics, as well as provide transient protection benefits. Transformer connections can be employed to reduce harmonic currents in three-phase systems. Phase-shifting half of the 6-pulse power converters in a plant load by 30° can approximate the benefits of 12-pulse loads by dramatically reducing the fifth and seventh harmonics. Delta- connected transformers can block the flow of zero-sequence harmonics (typically triplens) from the line. Zig-zag and grounding transformers can shunt the triplens off the line.

Purchasing specifications can go a long way toward preventing harmonic problems by penalizing bids from vendors with high harmonic content. This is particularly important for such loads as high-efficiency lighting.

The shunt filter works by short-circuiting harmonic currents as close to the source of distortion as practical. This keeps the currents out of the supply system. This is the most common type of filtering applied because of economics and because it also tends to correct the load power factor as well as remove the harmonic current.

Another approach is to apply a series filter that blocks the harmonic currents. This is a parallel-tuned circuit that offers a high impedance to the harmonic current. It is not often used because it is difficult to insulate and the load voltage is much distorted. One common application is in the neutral of a grounded-wye capacitor to block the flow of triplen harmonics while still retaining a good ground at fundamental frequency. Active filters work by electronically supplying the harmonic component of the current into a non-linear load.

**There are a number of methods to modify adverse system responses to harmonics: **

1. Add a shunt filter.

2. Add a reactor to detune the system.

3. Change the capacitor size.

4. Move a capacitor to a point on the system with a different short-circuit impedance or higher losses.

5. Remove the capacitor and simply accept the higher losses, lower voltage, and power factor penalty. If technically feasible, this is occasionally the best economic choice.

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]]>**Harmonic studies are often performed when:**

1. Finding a solution to an existing harmonic problem

2. Installing large capacitor banks on utility distribution systems or industrial power systems

3. Installing large nonlinear devices or loads

4. Designing a harmonic filter

5. Converting a power factor capacitor bank to a harmonic filter.

Harmonic studies provide a means to evaluate various possible solutions and their effectiveness under a wide range of conditions before implementing a final solution. In this article, methods for carrying out harmonic studies are presented.

**The ideal procedure for performing a power systems harmonics study can be summarized as follows: **

1. Determine the objectives of the study. This is important to keep the investigation on track. For example, the objective might be to identify what is causing an existing problem and solve it. Another might be to determine if a new plant expansion containing equipment such as adjustable-speed drives and capacitors is likely to have problems.

2. If the system is complex, make a pre-measurement computer simulation based on the best information available. Measurements are expensive in terms of labor, equipment, and possible disruption to plant operations. It will generally be economical to have a good idea what to look for and where to look before beginning the measurements.

3. Make measurements of the existing harmonic conditions, characterizing sources of harmonic currents and system bus voltage distortion.

4. Calibrate the computer model using the measurements.

5. Study the new circuit condition or existing problem.

6. Develop solutions (filter, etc.) and investigate possible adverse system interactions. Also, check the sensitivity of the results to important variables.

7. After the installation of proposed solutions, perform monitoring to verily the correct operation of the system. Admittedly, it is not always possible to perform each of these steps ideally.

The most often omitted steps are one, or both, measurement steps due to the cost of engineering time, travel, and equipment charges. An experienced analyst may be able to solve a problem without measurements, but it is strongly recommended that the initial measurements be made if at all possible because there are many unpleasant surprises lurking in the shadows of harmonics analysis.

There are two fundamental issues that need to be considered in developing a system model for harmonic simulation studies. The first issue is the extent of the system model to be included in the simulation. Secondly, one must decide whether the model should be represented as a single- phase equivalent or a full three-phase model. As an example of model extent, suppose a utility plans to install a large capacitor bank on a distribution feeder and would like to evaluate the frequency response associated with the bank. Representing the entire distribution system is usually not practical because it would be time-consuming to develop the model and it would strain computational resources to run simulations.

One approach would be to start developing a model one or two buses back from the bus of interest and include everything in between. Another approach would be to start with a small simple circuit that accurately represents the phenomena and add more of the system details to determine the impact on the solution result.

At the point when adding more system details does not change the analysis results, the physical system is sufficiently represented by the simulation model. In modelling distribution systems for harmonic studies, it is usually sufficient to represent the upstream transmission system with a short circuit equivalent at the high-voltage side of the substation transformer.

The leakage impedance of the transformer dominates the short-circuit equivalent and effectively isolates the transmission and distribution for many studies. However, if there is a capacitor bank near the high-voltage side of the transformer, part of the transmission system must be modelled to include the capacitor bank.

The combination of the transformer and the capacitor bank may behave as a filter for some frequency as seen from the low-voltage side of the transformer. Distribution system components downstream from the substation transformer (or at the low-voltage side) such as feeder lines, capacitor banks, key service transformers, and end-user capacitor banks must be represented. Since the feeder capacitor banks dominate the system capacitance, it is usually acceptable to neglect capacitance from overhead feeder lines. However, if there is a significant amount of UD cable, cable capacitance should be represented, especially if the study is concerned with higher-order harmonics.

The analyst must then decide if the model should be represented as a complete three-phase model or a single-phase equivalent. A single-phase equivalent model is generally simpler and less complicated to develop compared to a three-phase model. However, it is often inadequate to analyze unbalanced phenomena or systems with numerous single-phase loads. Fortunately, there is a rule that permits the simplified positive sequence modelling for many three- phase industrial loads.

Determining the response of the system to positive-sequence harmonics is straightforward since both utility and industrial power engineers are accustomed to doing such modelling in their load flow and voltage drop analyses. The rule may be simply stated- When there is a delta winding in a transformer anywhere in series with the harmonic source and the power system, only the positive-sequence circuit need be represented to determine the system response. It is impossible for zero- sequence harmonics to be present; they are blocked.

Figure 7.3 illustrates this principle, showing what models apply to different parts of the system. Both the positive- and negative-sequence networks are generally assumed to have the same response to harmonics. Sometimes measurements will show triplen harmonics in the upstream from a delta winding. One normally assumes these harmonics are zero sequence. They may be, depending on what other sources are in system.

However, they can also be due to unbalanced harmonic sources, one example of which would be an arc furnace. Only the triplens that are in phase are zero sequence and are blocked by the delta winding. Therefore, it is common to include triplen harmonics when performing analysis using a positive-sequence model.

The symmetrical component technique fails to yield an advantage when analyzing four-wire utility distribution feeders with numerous single-phase loads. Both the positive- and zero sequence networks come into play. It is generally impractical to consider analyzing the system, manually, and most computer programs capable of accurately modelling these systems simply set up the coupled three-phase equations and solve them directly.

Fortunately, some computer tools now make it almost as easy to develop a three-phase model as to make a single-phase equivalent. It takes no more time to solve the complete three-phase model than to solve the sequence networks because they would have to be coupled also. Not only does the symmetrical component technique fail to yield an advantage in this case, but analysts often make errors and inadvertently violate the assumptions of the method.

It is not generally recommended that harmonic analysis of unbalanced circuits be done using symmetrical components. It should be attempted only by those who are absolutely certain of their understanding of the method and its assumptions.

Most harmonic flow analysis on power systems is performed using steady-state, linear circuit solution techniques. Harmonic sources, which are nonlinear elements, are generally considered to be injection sources into the linear network models. They can be represented as current injection sources or voltage sources. For most harmonic flow studies, it is suitable to treat harmonic sources as simple sources of harmonic currents.

This is illustrated in Fig. 7.4 where an electronic power converter is replaced with a current source in the equivalent circuit. The voltage distortion at the service bus is generally relatively low, less than 5 percent. Therefore, the current distortion for many nonlinear devices is relatively constant and independent of distortion in the supply system.

Values of injected current should be determined by measurement. In the absence of measurements and published data, it is common to assume that the harmonic content is inversely proportional to the harmonic number. That is, the fifth-harmonic current is one-fifth, or 20 percent, of the fundamental, etc. This is derived from the Fourier series for a square wave, which is at the foundation of many nonlinear devices.

However, it does not apply very well to the newer technology PWM drives and switch-mode power supplies, which have a much higher harmonic content. When the system is near resonance, a simple current source model will give an excessively high prediction of voltage distortion. The model tries to inject a constant current into a high impedance, which is not a valid representation of reality.

The harmonic current will not remain constant at a high voltage distortion. Often, this is inconsequential because the most important thing is to know that the system cannot be successfully operated in resonance, which is readily observable from the simple model. Once the resonance is eliminated by, for example, adding a filter, the model will give a realistic answer.

For the cases where a more accurate answer is required during resonant conditions, a more sophisticated model must be used. For many power system devices, a Thevenin or Norton equivalent is adequate.

The additional impedance moderates the response of the parallel resonant circuit. A Thevenin equivalent is obtained in a straightforward manner for many nonlinear loads. For example, an arc furnace is well represented by a square-wave voltage of peak magnitude approximately 50 percent of the nominal ac system voltage. The series impedance is simply the short-circuit impedance of the furnace transformer and leads (the lead impedance is the larger of the two).

Unfortunately, it is difficult to determine clear-cut equivalent impedances for many nonlinear devices. In these cases, a detailed simulation of the internals of the harmonic-producing load is necessary. This can be done with computer programs that iterate on the solution or through detailed time- domain analysis.

Fortunately, it is seldom essential to obtain such great accuracy during resonant conditions and analysis do not often have to take these measures. However, modelling arcing devices with a Thevenin model is recommended regardless of need.

The characteristics of such programs and the heritage of some popular analysis tools are described here.

First, it should be noted that one circuit appears frequently in simple industrial systems that does lend itself to manual calculations (Fig. 7.6). It is basically a one-bus circuit with one capacitor.

**Two things may be done relatively easily: **

1. Determine the resonant frequency. If the resonant frequency is near a potentially damaging harmonic, either the capacitor must be changed or a filter designed.

2. Determine an estimate of the voltage distortion due to the current.

Given that the resonant frequency is not near a significant harmonic and that projected voltage distortion is low, the application will probably operate successfully. Unfortunately, not all practical cases can be represented with such a simple circuit. In fact, adding just one more bus with a capacitor to the simple circuit in Fig. 7.6 makes the problem a real challenge to even the most skilled analysts. However, a computer can perform the chore in milliseconds. To use the computer tools commonly available, the analyst must describe the circuit configuration, loads, and the sources to the program.

**Data that must be collected include: **

i. Line and transformer impedances

ii. Transformer connections

iii. Capacitor values and locations (critical)

iv. Harmonic spectra for nonlinear loads

v. Power source voltages.

These values are entered into the program, which automatically adjusts impedances for frequency and computes the harmonic flow throughout the system.

**Capabilities for Harmonics Analysis Programs:**

**Acceptable computer software for harmonics analysis of power systems should have the following characteristics: **

1. It should be capable of handling large networks of at least several hundred nodes!

2. It should be capable of handling multiphase models of arbitrary structure. Not all circuits, particularly those on utility distribution feeders, are amenable to accurate solution by balanced, positive sequence models.

3. It should also be capable of modelling systems with positive sequence models. When there can be no zero-sequence harmonics, there’s no need to build a full three-phase model.

4. It should be able to perform a frequency scan at small intervals of frequency (e.g., 10 Hz) to develop the system frequency-response characteristics necessary to identify resonances.

5. It should be able to perform simultaneous solution of numerous harmonic sources to estimate the actual current and voltage distortion.

6. It should have built-in models of common harmonic sources.

7. It should allow both current source and voltage source models of harmonic sources.

8. It should be able to automatically adjust phase angles of the sources based on the fundamental frequency phase angles.

9. It should be able to model any transformer connection.

10. It should be able to display the results in a meaningful and user-friendly manner.

The most common type of computer analysis of power systems performed today is some form of power flow calculation. Most power engineers have some experience with this class of tool. Other common computer tools include short-circuit programs and, at least for transmission systems, dynamics (transient stability) programs. Harmonics and electromagnetic transients tools have traditionally been in the domain of specialists due to the modelling complexities.

While power flow tools are familiar, their formulation is generally unsuitable for harmonics analysis. Of the tools in common usage, the circuit model in short-circuit programs is closer to what is needed for harmonic flow analysis in networks. In fact, prior to the advent of special power systems harmonic analysis tools, many analysis would use short-circuit programs to compute harmonic distortion, manually adjusting the impedances for frequency.

This is an interesting learning experience for the student, but not one that the practitioner will want to repeat often. Of course, one could also perform the analysis in the time domain using electromagnetic transients programs, but this generally is more time-consuming and is excessive for most problems. Today, most power system harmonics analysis is performed in the sinusoidal steady state using computer programs specially developed for the purpose.

It is encouraging to see many vendors of power system analysis software providing some harmonics analysis capabilities in their packages, although the main application in the package may be a power flow program. It is useful to see how this has evolved. Unlike power flow algorithms, few of the developers have written technical papers documenting their efforts. Therefore, it is difficult to trace the history of harmonics analysis in power systems through the literature.

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]]>The primary objective of the standards is to provide a common ground for all involved parties to work together to ensure compatibility between end-use equipment and the system equipment is applied. An example of compatibility (or lack of compatibility) between end-use equipment and the system equipment is the fast-clock problem. The end-use equipment is the clock with voltage zero-crossing detection technology, while the system yields a voltage distorted with harmonics between 30^{th }and 35^{th}. This illustrates a mismatch of compatibility that causes misoperation of the end-use equipment.

This article focuses on standards governing harmonic limits, including IEEE 519-1992, IEC 61000-2-2, IEC 61000-3-2, IEC 61000-3-4, IEC 61000-3-6, NRS 048-02 and EN 50160.

It should be emphasized that the philosophy behind this standard seeks to limit the harmonic injection from individual customers so that they do not create unacceptable voltage distortion under normal system characteristics and to limit the overall harmonic distortion in the voltage supplied by the utility.

The voltage and current distortion limits should be used as system design values for the worst case of normal operating conditions lasting more than 1 h. For shorter periods, such as during start-ups, the limits may be exceeded by 50 percent. This standard divides the responsibility for limiting harmonics between both end users and the utility. End users will be responsible for limiting the harmonic current injections, while the utility will be primarily responsible for limiting voltage distortion in the supply system.

The harmonic current and voltage limits are applied at the PCC. This is the point where other customers share the same bus or where new customers may be connected in the future. The standard seeks a fair approach to allocating a harmonic limit quota for each customer.

The standard allocates current injection limits based on the size of the load with respect to the size of the power system, which is defined by its short-circuit capacity. The short-circuit ratio is defined as the ratio of the maximum short-circuit current at the PCC to the maximum demand load current (fundamental frequency component) at the PCC as well. The basis for limiting harmonic injections from individual customers is to avoid unacceptable levels of voltage distortions. Thus the current limits are developed so that the total harmonic injections from an individual customer do not exceed the maximum voltage distortion shown in Table 7.3.

Table 7.3 shows harmonic current limits for various system voltages. Smaller loads (typically larger short-circuit ratio values) are allowed a higher percentage of harmonic currents than larger loads with smaller short-circuit ratio values. Larger loads have to meet more stringent limits since they occupy a larger portion of system load capacity. The current limits take into account the diversity of harmonic currents in which some harmonics tend to cancel out while others are additive.

The harmonic current limits at the PCC are developed to limit individual voltage distortion and voltage THD to the values. Since voltage distortion is dependent on the system impedance, the key to controlling voltage distortion is to control the impedance. The two main conditions that result in high impedance are when the system is too weak to supply the load adequately or the system is in resonance.

The latter is more common. Therefore, keeping the voltage distortion low usually means keeping the system out of resonance. Occasionally, new transformers and lines will have to be added to increase the system strength. IEEE Standard 519-1992 represents a consensus of guidelines and recommended practices by the utilities and their customers in minimizing and controlling the impact of harmonics generated by nonlinear loads.

IEC 61000-2-2 defines compatibility levels for low-frequency conducted disturbances and signalling in public low-voltage power supply systems such as 50- or 60-Hz single- and three-phase systems with nominal voltage up 240 and 415 V, respectively. Compatibility levels are defined empirically such that they reduce the number of complaints of mis-operation to an acceptable level. These levels are not rigid and can be exceeded in a few exceptional conditions. Compatibility levels for individual harmonic voltages in the low-voltage network are shown in Table 7.4. They are given in percentage of the fundamental voltage.

Both IEC 61000-3-2 and 61000-3-4 define limits for harmonic current emission from equipment drawing input current of up to and including 16 A per phase and larger than 16 A per phase, respectively. These standards are aimed at limiting harmonic emissions from equipment connected to the low-voltage public network so that compliance with the limits ensures that the voltage in the public network satisfies the compatibility limits defined in IEC 61000-2-2.

The IEC 61000-3-2 is an outgrowth from IEC 555-2 (EN 60555-2).

**The standard classifies equipment into four categories: **

i. Class A- Balanced three-phase equipment and all other equipment not belonging to classes B, C, and D

ii. Class B- Portable tools

iii. Class C- Lighting equipment including dimming devices

iv. Class D- Equipment having an input current with a “special waveshape” and an active input power of less than 600 W

Figure 7.19 can be used for classifying equipment in IEC 61000-3-2. It should be noted that equipment in classes B and C and provisionally motor-driven equipment are not considered class D equipment regardless of their input current waveshapes.

Maximum permissible harmonic currents for classes A, B, C, and D are given in actual amperage measured at the input current of the equipment. Note that harmonic current limits for class B equipment are 150 percent of those in class A.

Note that harmonic current limits for class D equipment are specified in absolute numbers and in values relative to active power. The limits only apply to equipment operating at input power up to 600 W. IEC 61000-3-4 limits emissions from equipment drawing input current larger than 16 A and up to 75 A. Connections of this type of equipment do not require consent from the utility. Harmonic current limits based on this standard are shown in Table 7.5.

IEC 61000-3-6 specifies limits of harmonic current emission for equipment connected to medium-voltage (MV) and high-voltage (HV) supply systems. In the context of the standard, MV and HV refer to voltages between 1 and 35 kV, and between 35 and 230 kV, respectively. A voltage higher than 230 kV is considered extra high voltage (EHV), while a voltage less than 1 kV is considered low voltage (LV). The standard argues that emission limits for individual equipment connected to the MV and HV systems should be evaluated on the voltage distortion basis.

This is to ensure that harmonic current injections from harmonic-producing equipment do not result in excess voltage distortion levels. The standard provides compatibility levels and planning levels for harmonic voltages in the LV and MV systems. The compatibility level refers to a level where the compatibility between the equipment and its environment is achieved.

The compatibility level is usually established empirically so that a piece of equipment is compatible with its environment most of the time. Compatibility levels are generally based on the 95 percent probability level, i.e., 95 percent of the time, the compatibility can be achieved. Planning levels are design criteria or levels specified by the utility company. Planning levels are more stringent than compatibility levels. Thus, their levels are lower than the compatibility levels.

The IEC 61000-3-6 provides Evaluation guidelines to determine admissibility of equipment connected to MV and HV systems.

**There are three stages for evaluating equipment admissibility: **

i. Stage 1- Simplified evaluation of disturbance emission

ii. Stage 2- Emission limits relative to actual network characteristics

iii. Stage 3- Acceptance of higher emission levels on an exceptional and precarious basis.

In stage 1, equipment can be connected to MV or HV systems without conducting harmonic studies as long as its size is considered small in relation to the system short-circuit capacity. For small appliances, manufacturers are responsible for limiting their harmonic emissions. If the equipment does meet stage 1 criteria, the harmonic characteristics of the equipment should be evaluated in detail along with the available system absorption capacity.

Upon evaluation, individual equipment will be allocated with appropriate system absorption capacity according to its size. Thus, if the system absorption capacity has been fully allocated to all equipment, and this equipment injects its harmonic currents up to its limits, the system voltage distortion should be within its planning levels.

If equipment does not meet stage 2 criteria, it may be allowed to be connected to the system if the end user and utility agree to make special arrangement to facilitate such a connection.

The Quality of Supply Standard, NRS 048, is the South African standard for dealing with the quality of electricity supply and has been implemented since July 1, 1997. This standard requires electricity suppliers to measure and report their quality of supply to the National Electricity Regulator.

The NRS 048 is divided into five parts. It is, perhaps, the most thorough standard dealing with all aspects of quality of supply. It covers the minimum standards of quality of supply (QOS), measurement and reporting of QOS, application and implementation guidelines for QOS, and instrumentation for voltage quality monitoring and recording. Part 2 of NRS 048 sets minimum standards for the quality of the electrical product supplied by South African utilities to end users.

The minimum standards include limits for voltage harmonics and inter-harmonics, voltage flicker, voltage unbalance, voltage dips, voltage regulation, and frequency. NRS 048-02 adopts IEC 61000-2-2 harmonic voltage limits as its compatibility standards for LV and MV systems. For South African systems, the nominal voltage for LV systems is less than 1 kV, while the nominal voltage for MV systems ranges between 1 and 44 kV. NRS 048 has not established limits for harmonic voltages for HV systems yet. However, it adopts IEC 61000-3-6 planning levels for harmonic voltages for HV and EHV systems as its recommended planning limits for HV systems (the nominal voltage is between 200 and 400 kV).

EN 50160 is a European standard for dealing with supply quality requirements for European utilities. The standard defines specific levels of voltage characteristics that must be met by utilities and methods for evaluating compliance. EN 50160 was approved by the European.

Committee for Electrotechnical Standardization (CENELEC) in 1994. EN 50160 specifies voltage characteristics at the customer’s supply terminals or in public LV and MV electricity distribution systems under normal operating conditions. In other words, EN 50160 confines itself to voltage characteristics at the PCC and does not specify requirements for power quality within the supply system or within customer facilities.

Harmonic voltage limits for EN 50160 are given in percentage of the fundamental voltage. The limits apply to systems supplied at both LV and MV levels, i.e., from a nominal 230 V up to 35 kV. Medium voltage is between 1 and 35 kV. The total harmonic distortion of the supply voltage including all harmonics up to order 40 should not exceed 8 percent. Values for higher-order harmonics are not specified since they are too small to use as a practical measure to establish a meaningful reference value. Note that limits in EN 50160 are nearly identical to the IEC 61000-3-6 compatibility levels for harmonic voltages for its corresponding LV and M V systems, except for the absence of higher-order harmonic limits in EN 50160.

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