# Generator THD

Many people don’t understand what Total Harmonic Distortion is or why it’s important, and they may not be aware of the other adverse effects of harmonic distortion.

The THD value is a critical factor in assessing the power quality of any generator model and the loads they are powering. Harmonics beyond acceptable limits can cause several problems, including equipment overheating, vibrations, noise, damage or malfunctioning of electronic equipment, interference with communication and control circuits, reduced system efficiency, and even fires.

The article below will give you critical insights and valuable information about harmonics, their generation, how they affect the systems, their acceptable limits, Generator THD, and much more.

## Harmonic Quantities

Let us introduce you to several basic terms related to the harmonics phenomena. If you already know these, skip to the next sections.

### What is Harmonics?

Electrical Energy is distributed on industrial AC power supply networks in a three-phase sinusoidal system. One of the desired characteristics of the system is the waveforms should always remain as close to a pure sine wave as possible.

In practice, the voltage and current waveforms differ considerably from the desired ones. The actual waveform carries many sine waves of different frequencies superimposed over the desired power frequency waveform. Such power with harmonics is also termed Dirty Power.

The power frequency waveform is also commonly referred to as the “fundamental frequency” or “fundamental component” or even simply as the “fundamental“.

### Harmonic Component

The other sinusoidal components of different frequencies, referred to above, distort the original waveform and are referred to as “harmonic components” or simply the harmonics of the fundamental.

One of the interesting characteristics of the harmonics is that they are a multiple of the fundamental frequency. The amplitude of any harmonic is usually denoted as a percentage of the amplitude of the fundamental.

### Harmonic Order

Also known as the harmonic number, it designates any harmonic by the ratio of its frequency fn and the fundamental f1.

Hence, the Harmonic Order n has a frequency fn = n x f1.

The harmonic order of the fundamental frequency f1 is 1. The harmonic order “n” is also known as the nth harmonic.

This means that for a 60 Hz system, the 3rd harmonic happens at 180 Hz, the 5th at 300 Hz, the 7th at 420 Hz, and so on.

### Frequency Spectrum

A frequency spectrum is a histogram that plots the amplitude of any network’s harmonic components as a function of harmonic order. A sample spectrum is shown below. The amplitudes generally decrease with an increase in harmonic number.

### Harmonic Distortion

The diagram below shows the fundamental waveform getting superimposed by a third harmonic. You can also see the resultant waveform as it appears on an oscilloscope. See the ripple effect caused by the superimposition. These ripples are the harmonic distortion of the fundamental.

#### Waveform

As you may already know from high school physics, the superimposition of two or more waves results in constructive or destructive interference. Constructive interference raises the amplitude, while destructive interference lowers it.

Most portable generators have two pole salient pole rotors. Due to this arrangement, all the even harmonic components cancel out, leaving only the odd ones in the circuit. The modern test equipment can carry accurate THD measurements considering harmonic frequencies up to 63rd.

The below diagram shows the fundamental and the third harmonic component in a power system. The blue is the fundamental waveform, and the red is the third harmonic. Note that its frequency is three times that of the fundamental voltage.

The red waveform in the below image shows the combined effect of the above two components on the produced voltage waveform. The blue wave is the desired or the fundamental waveform, while the red is the actual waveform with the 3rd harmonic.

As more harmonic components are added, the combined waveform will shift toward the square waveform shape. This is evident from the below-distorted waveform with odd harmonic components up to the ninth harmonic.

### The mathematical expression of the distorted wave

Fourier series is used to represent any periodic phenomena mathematically. The expression of the series is

where Y0 represents the amplitude of the DC component. Y0 is zero at a steady state in electrical power distribution. In fact, IEEE 519 does not allow harmonics of order 0 to exist in power systems.

Yn is the RMS value of the nth harmonic, and

Qn is the phase angle of the nth harmonic at t = 0.

You can neglect the orders above 50 as per the relevant standards.

### RMS Values of Quantities in Wave under Distortion

It is usual to express the voltage and current harmonics in terms of their RMS values because the heating effect produced in the related circuit depends on them. RMS values for all sinusoidal quantities are given by their maximum instantaneous values divided by the square root of 2.

When any distorted quantity is in a steady-state condition, the total energy dissipated by it is the sum of the dissipated energies by the individual harmonic components, i.e.

RI2t = R(I1)2t + R(I2)2t + R(I3)2t + …. + R(In)2t

or I2 = (I1)2 + (I2)2 + (I3)2 + …. + (In)2, if the resistance is constant.

From the above expression, the RMS current is the square root of the sum of squares of currents of different orders.

The measurement of RMS values for any distortion can be done by spectrum analysis or by using instruments designed to measure the true RMS quantities directly.

### Individual Harmonic Ratio

This measure is used to quantify the disturbances caused in the power supply network by the individual component. The harmonic ratio for any order n is the ratio of the RMS value of the nth component to that of the fundamental.

Hence it is equal to Vn / V1, where Vn is the RMS voltage of the nth component and V1 for the fundamental.

## Whats THD?

You must now be familiar with waveform distortion, harmonics, various quantities associated with this phenomenon, and their mathematical treatment. With this background, you will now be ready to understand and appreciate the core concepts behind total harmonic distortion, THD, and its causes & effects. THD is also known as the total harmonic factor and quantifies all the harmonics’ total thermal effects.

THD is the ratio of the two RMS values: Of all the harmonics present to that of the fundamental frequency. The RMS value of all the harmonics is the under root of the sum of the squares of the individual quantities.

If we replace the root mean square value of the fundamental with the total load current in the denominator in the ratio above, we get the Total Demand Distortion, TDD.

## Why & How are Harmonics Produced?

The distortion is introduced in the power system at the source and the load side.

### Source-related issues

A pure original sine wave is a theoretical concept and can be produced only by an ideal AC generator built with

• A perfectly distributed stator winding
• A field that creates an absolutely uniform magnetic field.

In practice, both these conditions cannot be achieved, and the output waveform from any working AC generator deviates from the perfect waveform.

#### Rotor pole Tip

In AVR generators, the shape of the waveform depends on the physical shape of the rotor pole head. A rotor with a square-shaped pole head will generate a square flux wave. This will induce a lot of harmonic frequencies in the stator winding.

Many manufacturers bevel the pole tips, leading to an increase in the air gap and hence a reduction in flux at these positions, resulting in a better waveform than the square wave.

The best flux waveform is achieved by rounding the pole face at a radius. The center of the rounding is different than the stator core. You can say that the waveform deviation factor largely depends on how much effort goes into shaping the pole heads, leading to increased costs.

The use of non-linear loads in modern times is ever-increasing. Non-linear loads are the biggest source of harmonics in any network. The most common types of non-linear loads include:

• Static converters with rectifier bridges that are made up of diodes and thyristors.
• Other power converters such as cyclo converters and dimmers.
• Lighting systems comprising of fluorescent lamps and discharge lamps. In such systems, the largest single harmonic is the third order, with a ratio exceeding 100% percent in certain cases. Waveform for Compact fluorescent lamp shown below.
• Arc furnaces
• Saturated reactors Current Waveform for Compact Fluorescent Lamp in blue Wtshymanski, CC BY-SA 3.0, via Wikimedia Commons

Usually, we keep focussing on the source side, but the harmonic currents generated by non-linear loads greatly impact the total harmonic distortion in the power systems. Let us understand how?

### Voltage Waveform Distortion

Harmonic currents flowing through any impedance in an electrical power distribution system will create harmonics of the same order. A 5th-order harmonic current will produce a 5th-order harmonic voltage. You may refer to the below diagram to understand the concept.

V1 is a sinusoidal voltage source that produces a clean sine wave of the fundamental voltage. This source is connected to a non-linear load Z1 through a circuit with impedance Z. The load Z1 will produce currents of multiple harmonic frequencies. Each of these currents will produce a voltage drop against the impedance Z.

Hence, the voltage waveform at the source terminals, which was undistorted earlier, becomes distorted now. Anything connected at the source terminals in parallel with this non-linear load will start experiencing voltage and current harmonics even if that load is linear. This point where both the loads are getting connected is often referred to as the Point of common coupling.

As the load impedance Z1 is higher than the network impedance Z, which in turn is higher than the source impedance Zs, the voltage distortion is maximum near the load and least near the source. To say the same reversely, even if the voltage distortion levels are low at the source, they can reach unacceptable levels at the load.

As seen by you above, the harmonic currents interact with the system impedance to cause the voltage drops. Hence the magnitude of voltage waveform distortion directly depends on the magnitude of the source impedance. The lower the source impedance, the less distortion is there.

### Is Generator THD Important?

The source impedance of any portable generator varies with time after a load change till the system is stable again. The generator with the lowest internal reactance to the change in the instantaneous current value for any given load will produce the lowest total harmonic distortion, THD.

You can understand this with the following logic. When you suddenly switch a relatively large load on a small generator, the voltage and frequency values fluctuate till the AVR and the frequency governor adjust to this load change. Hence, based on the design and size of the generator, it may have a much greater internal reactance to a sudden change in load. This is often referred to as the sub-transient reactance.

This is why the non-linear loads work fine on utility power and produce much higher total harmonic distortion on generators. Hence, the generators with comparatively large sub-transient reactance and high THD levels in the inherent power waveforms will magnify even the small amount of harmonics fed back by the load to produce a much higher total harmonic distortion in the voltage.

The matters are even worse if a large share of the generator’s capacity is taken up by non-linear loads.

## Other Adverse Effects of Harmonics

Different types of loads experience the different detrimental effects of the harmonics. These effects are classified into instantaneous effects and long-term effects. The long-term effects are due to heating. You can learn the details about these effects in the upcoming sections.

### Instantaneous Effects

The harmonic voltages can adversely impact the electronic equipment, cause vibrations & noise, and cause interference with communication and control circuits.

#### Impact on electronic equipment

The harmonic voltages can

1. Alter the switching conditions of the thyristors by shifting the zero crossing of the voltage wave, thereby causing the controllers to malfunction.
2. Cause errors in induction disc type of energy meters.
3. Ripple control receivers – the relays used by the utilities for central control can be disturbed if the harmonic frequency matches the control frequency of these relays.

#### Vibrations and Noise

1. The harmonic currents can produce large electrodynamic forces to cause vibrations and acoustical noise in transformers and reactors.
2. Harmonics can produce their own rotating fields in the rotating machines, resulting in pulsating mechanical torque and vibrations.

#### Interference with communication and control circuits

1. Harmonic currents in power distribution circuits cause disturbances in communication and control circuit lines running parallel to them. The impact depends on the parallel length, separation in two lines, and harmonic frequencies,

### Long-term effects

The long-term effects are caused by mechanical fatigue due to vibrations and heating. They include

1. Capacitor heating occurs due to losses caused by conduction and dielectric hysteresis, which in turn are proportional to the square of RMS current. High THD can cause heating and dielectric breakdown.
2. Heating in rotating machines: Harmonic distortion causes additional copper and iron losses in the stator and in the rotor. The losses are due to differences in the speed of the rotor and the harmonics-inducing rotating fields.
3. Heating in Transformers: There are additional losses in transformers caused by (1) hysteresis and eddy current in the magnetic circuit due to harmonic frequencies and (2) by the skin effect due to increasing the copper resistance with frequency. These losses result in additional heating of the transformer.
4. Heating of cables: Cables carrying harmonic currents get overheated due to (1) an increase in RMS current, (2) an increase in the core resistance due to pronounced skin effect at higher frequencies, (3) an increase in dielectric losses in the insulation of the cable with an increase in frequency, and (4) proximity effect.

Generally speaking, any electrical equipment (1) subjected to voltage harmonics or (2) passing the current harmonics will have increased energy losses leading to a temperature rise.

## Adverse effects On portable generators

Let us quickly make you aware of the impact of excessive total harmonic distortion, THD, on the performance of portable generators.

### Erratic AVR functioning

An Automatic Voltage Regulator (AVR) will sense the incorrect voltage at the stator terminals if the amount of THD-V is high and regulate the generator to the wrong levels.

The AVRs on the larger generator sets are designed for non-linear loads and use filters on the voltage sensors. They sense all the phases and carry out the true RMS calculation. The prohibitive costs of such a system do not allow the use of these sophisticated AVRs on portable generators.

### Erratic speed fluctuations

AC frequency governor can easily malfunction due to high total harmonic distortion. These governors obtain speed feedback signals by sensing the frequency of output voltage inside the AVR unit. These frequency measurements involve sensing zero crossing of the voltage waveforms.

High total harmonic distortion can cause problems in this scenario involving multiple zero crossings in one cycle leading to incorrect measurements and instability of the speed governing system.

### Limits the Continuous Load Ratings

The harmonics cause overheating of the stator and rotor windings. This, coupled with the instability due to erratic self-excitation at higher leading power factor loads, affects the generator’s continuous load ratings.

## Acceptable limits & recommendations

You may wonder, “How much THD is too much?” or “What is normal THD?“. We will present answers to all of your similar questions in this section.

The general permissible limits for Total Harmonic Distortion for different types of equipment are:

1. Cables: Core shielding voltage distortion = 10%
2. Sensitive Electronics: Voltage distortion = 5%, however, the individual harmonic percentage should be limited to 3%.
3. Synchronous machines: Stator current distortion = 1.3 to 1.4%.
4. Asynchronous machines: Stator current distortion = 1.5 to 3.5%
5. Capacitors: Current distortion = 83% with an overload of 30%. Overvoltages can be up to 10%.

### Limits as per the Standards

IEEE Std 519 has the recommended practices to guide you. The general opinion is that they are not very hard to comply with. The standard lays down the goals for designing electrical systems with linear and non-linear loads. The limits in the standard and the recommendations are not binding. All the limits are defined at the point of the common coupling (PCC) shown in the diagram below.

If the customer under consideration has his own transformer, the PCC is on the MV side.

If the customer under study is fed from the same LV transformer as other customers, the PCC is on the LV side.

A very frequently asked question is, “if all your loads are complying with IEEE 519, would your system comply with it”. The answer is that it is very difficult to ensure all your equipment, like LEDs, will use harmonic control. You can ensure load-side compliance for bigger equipment like VFDs, rectifiers, etc.

The standard makes the assumption that by limiting the non-linear current injections to the network by the users, you can keep the voltage distortion below acceptable limits. The limits indicated below apply only at the point of common coupling and not on any individual piece of equipment.

### Voltage Limits

The table for voltage limits is shown below. It is organized based on the voltage limits – LV, MV, and HV. It gives the line to neutral voltage limits at the PCC for individual harmonics and the total harmonic distortion percentage. The THD percentage has increased from 5% to 8% in 2014, as the loads are not affected at low THD levels of voltage.

IEE 519 – 2014 – Voltage Distortion Limits

### Current Limits

The table below shows the current limits as the percentage of load current. The table is organized based on the short-circuit current and load current ratio at the PCC, denoted as Isc / IL. It gives the recommended maximum value of percentage for each harmonic order. It also gives the limit for total demand distortion TDD.

The important points to note from the table are:

1. If the ratio Isc/IL is small, the limit on TDD is more stringent, as in this case, the current distortion will eventually cause voltage distortion at the PCC.
2. A high value of current THD will cause heating in your equipment.
3. The even harmonics value should be limited to 25% of the odd harmonics limits.
4. DC offset or harmonic of order zero is not allowed.
5. The limits for the power generation equipment are the same as that for the ISC/IL ratio of 20.

## Conclusion

After reading this article, we hope you understand harmonics better. If you still have any questions or want to know more about generator total harmonic distortion, please post your comments below, and we will do our best to answer them. Stay safe and keep generating!