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Power Quality Harmonics Audit (Practical Guide)

Five Steps for Succesful Power Quality Audit

Purpose of Harmonics Analysis?

Generally, the following are the objectives of performing harmonics measurement & analysis:

Power Quality Analysis

Doing harmonics audit for electric power systems allows us to:

  • Identify proliferation & impure components (harmonics, THD, swell, dips) in the power systems
  • Check current & voltage distortion in the system
  • Identify / pin-point harmonic distortion components damaging the system
  • Measure the extent & spread of distortion  
  • Measure the value / percentage of distortion
  • Measure the duration of harmonic distortion effect
  • Work out mitigation solution on the basis of analysis report

The following illustration shows a typical measurement of harmonics (THD) from a power quality analyzer:

Identify Heat Losses

One of the major issues of harmonics in power losses is in the form of heat which affect considerably electrical equipment. Thus harmonics audit allows us to:

  • Check whether electrical equipment like transformers , motors, generators, cables are overheated
  • Monitor & measure the duration of distortion effect on the machines & equipment
  • Work out energy savings due to mitigation

The following illustrations represent thermal images identifying overheated areas in a transformer and a motor due to harmonics!

Heat-losses-harmonics-analysis

Note: Clients requirements and any specific issue/problem/event in the power system defines the primary and secondary nature of the above objectives 

Step 1: Collection of Plant Information and Data

Once the purpose of the harmonics audit is clear, the next step is to collect basic preliminary information & data about the plant from the client. The best is to prepare a questionnaire about the plant and send it to the client.

The questionnaire should include the followings:

  1. Type of Plant (details about its’ batch, process, manufacturing and final product)
  2. SLD (Single Line Diagram of complete power system)
  3. Details of Load including motors, lighting, Variable Speed Drives, Rectifiers, Voltage Regulators, Heaters, Computers, IT Equipment etc.
  4. Details of Power Sources (utility, generators, turbines, renewable power sources etc.)
  5. Details of Earthing / Grounding system (number & location of earth pits; type of earthing system ; grounding conductor network inside & outside the plant; recent record of earth testing) 
  6. Data / Record / Information of Power Quality from the already installed Network Analyzers & energy meters, if any.
  7. Details / history of any specific issue/problem/event in the power system

Step 2: Preliminary Analysis of Collected Data and Strategy Preparation for Actual Harmonics Analysis (Audit)

This part of the activity has significant importance in setting the direction of the harmonics measurement procedure. A thorough & conclusive work on the data collected/received from the client identifies the problem & its causes.

This sets the course of actual harmonics audit in the plant. That is why it is said that accurate preliminary analysis means half of the job is done!

The preliminary analysis covers the following activities:

  1. Study of Data
  2. Making a simulation of the existing power system
  3. Identification of Potential Harmonics Areas & its probable causes

The work plan should consider the following points for a successful Harmonics audit:

  • How many loads to be analyzed
  • Planning of sequence & duration of sessions for conducting measurement in various load areas, sub-station, power house and utility
  • Making customized templates for final harmonics measurement

Step 3: Arrangement of Testing & Measurment Equipment for Harmonics Analysis

For a successful harmonic analysis, the team should be fully equipped with testing instruments & meters. All the below equipment must be available during the course of the audit, as complex problems in the power system require parallel testing by multiple instruments.

1. Power Analyzer / Data Logger

  • Flexible CTs are recommended for easy & safe measurements. For larger loads, CTs with multiple settings are suggested (see figure below)
  • If an analyzer is not available, one can get rental equipment as well
Power Analyzer with iFlex CTs (Fluke)

2. Thermal Imaging Camera with high-resolution features

  • It is used as supportive equipment with power analyzer to exactly pin-point the fault and the extent of damage (overheating effect) by harmonics.
thermal imaging of a motor
Thermal imaging of a motor (Fluke)

3. Temperature Gun

  • It is also used as supportive equipment with power analyzer to exactly pin-point the fault

4. Grounding/Earthing Tester

  • It is used as a supportive equipment to check the health of earthing. A weak or faulty earthing can lead to floating neutral which adds up third harmonics in an un-balanced power system and can contribute to noise & vibrations caused by the harmonics.

5. Set of spare batteries (as a power backup)

6. Spare memory card (in case Analyzer memory gets filled with data)

7. Safety tools including electrical safety gloves, double-insulated tools, safety helmets, safety shoes, etc.

Step 4:  ON-SITE Harmonics Measurements

Harmonics’ measurement will be carried out as per the strategy worked out in the preliminary analysis of the collected data (step 2). The harmonic audit is conducted in stages in different locations & load areas of the complete plant and accordingly, the procedural methodology is adapted in this regard.

DETAILS OF AREAS & LOAD TO BE MEASURED:

  1. SUB-STATION (UTILITY SUPPLY)
    • Transformers (LV side)
    • Main outgoing feeders in the LT Panels
    • PFI Panels
    • Main outgoing feeders in bus-coupler panels
    • Main outgoing feeders of sync supply, if any
  2. POWER HOUSE (GENERATORS, TURBINES, SOLAR POWER ETC.)
    • Outgoing feeders of all individual power sources
    • Each outgoing feeder of the PDBs and DBs in the allied equipment like cooling towers, pumps etc. 
  3. PDBs (POWER DISTRIBUTION BOARDS) & DBs (DISTRIBUTION BOARDS) IN THE PLANT’s PROCESS & MANUFACTURING AREAS
    • Each outgoing feeder of the PDBs and DBs
    • Ideally, measurement shall be taken in all PDBs & DBs. However, in case of more than one similar rating of machines and fewer small loads up to 3 KW, measurements can be taken randomly (keeping in view the preliminary report and discussions with the client).
  4. UTILITYY AREA
    1. Each outgoing feeder of the PDBs and DBs
    2. In case of more than one similar rating of machines and fewer small loads up to 3 KW, measurements can be taken randomly (keeping in view the preliminary report and discussions with the client)

MEAUREMENT METHODOLOGY

This is a normal methodology for a standard plant. However, depending on the type of plant process, findings of preliminary report/analysis, and subsequent discussions with the plant staff, the methodology can be revised.

  1. Minimum of 30-minutes data logging of harmonics distortion (THD) in the sub-station and power house areas.
  2. In case the THD is high (i-e THD I is > 10% and THD V is > 5%) individual spectrum of the highest most harmonic order shall be measured as well. This practice shall be followed in all load locations.
  3. Data logging of 30-minutes to 24-hours duration shall be done in the PDBs and DBs of plant area & utility (data logging duration can vary in accordance with the plant type and client’s requirements). The following illustration shows data logging being carried out on a motor load.
Data logging being carried out on a motor load (Fluke)
  1. Thermal Imaging & Temperature measurement of bus-bars/busways, breaker terminals, fuses and main cables shall be done in parallel during the activity of harmonics data measurement in sub-stations and power house (* in case of abnormal results of thermal imaging, duration of data-logging can be extended).
  2. Thermal Imaging & Temperature measurement of breakers terminals & main cables in PDBs & DBs in plant area and utility. The following image shows thermal imaging on breaker terminals & cables.
Thermal imaging on breaker terminals & cables (Fluke)
  1. Thermal Imaging of motors, pumps, drives & allied machinery in the plant area.
  2. Grounding / Earthing testing of all earth pits.
  3. In the case where identification of heat losses is part of the agenda of harmonics analysis for energy savings, all of the above exercise will be supplemented with extended duration and multiple sessions of data logging on each feeder, scheduling it according to the process & batch of the plant.
  4. Make sure to transfer the data from the power analyzer memory to the computer system at the end of the day. This will keep enough space in the analyzer for the next day data logging
  5. Make sure to write down the name, number & location of each reading!

Step 5:   Report Preparation

The report can be prepared and written based on observations and data analysis by following these tips:

  • Transfer measured data from analyzer to the computer system
  • Give proper names to the files
  • Covert data to graphs & waveforms. Highlight THD and order of maximum harmonic distortion.
Bar Graph of orders of harmonic in a Ring section of Textile Spinning Unit
Bar Graph of orders of harmonic in a Ring section of Textile Spinning Unit
  • On the basis of the results, highlight load areas & load where distortion is high & abnormal.
  • Identify causes of distortion. Supplement it with the record of thermal images & temperature measurements.
  • For harmonics mitigation / reduction solution, it is recommended to refer the case to the suppliers of mitigation equipment.
The individual spectrum of 5th order of harmonic in a Ring section of Textile Spinning Unit
  • Whether the client goes for mitigation solution or not, always suggest to the client to install network analyzers and monitor power quality & energy consumption through the software.
Highlight Harmonic distortion of a motor (Fluke)

We reached the end of Today’s tutorial, If you liked it please consider sharing it!

Conclusion

In this article, we considered power quality audit, precisely harmonics analysis, and identifying anomalies in electrical power systems. The audit has been summarized in 5 steps with a lot of tips and advice to provide successful and professional reports to clients!

Shunt Filter Design: Short Guide

Description, working principle and design with illustrative example

What are harmonics?

According to the Fourier Theorem, a periodical waveform could be reduced to its Fourier components as sinusoidal waveforms with different frequencies and amplitudes.

In the case of a pure sinusoidal waveform, there will be no harmonics other than the first harmonic of the waveform itself. Abrupt changes in a voltage or current waveform indicate a high harmonic content in the waveform.

Especially in parts of the waveform, where these abrupt changes take place, there will be a constructive addition of the amplitudes of the harmonics. Harmonics will be described as integer multiples of the frequency of the first harmonic.

Example:

A waveform with a fundamental frequency of 50Hz could have a second harmonic with 100Hz and a third harmonic with 150Hz. With different amplitudes of every harmonic, the total voltage could assume changing waveforms.

To make it more concrete the practical consequences of harmonics will be explained in the following subsection!

How are harmonics generated?

Injection of Harmonics into the transmission system is caused by different factors.

The most prevalent factor could be defined as static power converters which represent the largest nonlinear loads in the transmission system.

The fast-switching action of these converters results in a distorted voltage waveform of the transmission system by drawing rapidly changing currents.

The measurement of the distortion in a waveform caused by harmonics will be expressed by the total harmonic distortion THD, which in general will cover harmonics until the 50th harmonic in terms of their percentage contribution.

In the following subsection problems related to the harmonics are mentioned.

Negative effects of harmonics on grid components

The most prominent degrading effect of harmonics could be summarized as losses resulting from heat and vibration. Especially components like transformers, generators, and motors of the grid suffer from iron losses, eddy current losses, and hysteresis losses.

Other than additional losses, harmonics also cause the malfunction of circuit breakers and fuses. A non-linear load might require a higher RMS current for the same amount of power, which results in more heating of the trip mechanism in fuses and circuit breakers. This might result in a false breaking of the circuit breaker, even though the amount of power delivered is the same.

There are additional harmful effects of harmonics, which will not be covered in this article (read this for more details!).

In this article, we presented different solutions to reduce harmonics in electrical systems. In the sequel, shunt filters as a solution for harmonics reduction will be explained.

Shunt Filters description

Attenuation of harmonics will be required by the majority of non-linear equipment in the grid. There are different approaches to solve this issue. Power equipment might come as an all-in-one package, including own harmonic mitigation, or it might be necessary to include a discrete mitigation mechanism.

Figure 1: Shunt Filter Diagram

The above figure illustrates a shunt filter structure that operates as a notch filter tuned for certain harmonic filterings such as 3rd, 5th, or 11th harmonics.

Working Principle of Shunt Filters

The working principle is simple!

At a designed filter resonance frequency f_R, the amplitude of the impedance of the filter goes to zero, providing a short circuit path for harmonic currents.

Shunt filters could be arranged as single tuned or multiple tuned filters. Multiple tuned filters provide attenuation for multiple frequencies by compromising the amount of attenuation in comparison to the single tuned type.

The resonance frequency could be calculated as follows.

\displaystyle f_R=\frac{1}{2\pi \sqrt{L_sC_s}}

It should be noted that there is also the ESR of the capacitor and the resistance of the inductance which together influence the quality factor of the filter.

The impedance of inductance at a given frequency f is given as follows:

X_L=j\omega L

and the impedance of a capacitor is:

\displaystyle X_C=-\frac{j}{\omega C_s}

It is trivial to see that, at a certain frequency namely f_R the sum of the impedances goes to zero. This means that the only limiting factor for the current will be the resistance resulting from the line, capacitor, and inductor.

If the total contribution of resistances is neglected, the whole harmonic current will be flowing through the path of the “trapping” filter, hindering any pass of the current of the harmonic frequency to any other consumer on the line.

Design Steps of a Shunt Filter

According to the IEEE Std 141-1993 there are 4 steps to a design of a shunt filter. Those consider the:

  • maximum voltage rating of the filter capacitor,
  • total RMS current of the filter inductance, and
  • series resistance value required to have a desired quality factor.

The steps are listed below:

  1. Choice of capacitance to improve the power factor.
  2. Selection of a reactor to tune the filter.
  3. Calculation of the peak voltage across the capacitor and the total RMS current through the reactor.
  4. Choice of off-the-shelf components.

Application example

A shunt filter will be designed for a system with the following characteristics:

  • a line to neutral voltage of 230 Vrms
  • a load of 1187 kVA per phase having a lagging power factor of 0.539.
  • It is assumed, that the power factor should be upgraded to a value of 0.95.

1. Calculate filter capacitance

Firstly, the required capacitance will be calculated:

\displaystyle S=(640+1000i)\text{VA}=1187.2\angle{57.38^{\circ}}\text{VA}

To improve the power factor, the capacitor should provide a reactive power of 326 VAR.

\displaystyle 326\text{VAR}=\frac{230V^2}{X_C} \implies C=19.675\mu F

2. Calculate filter inductance

By choosing the reactance, the filter can be tuned to the desired frequency. In this example the desired frequency is 150Hz.

\displaystyle 150\text{Hz}=\frac{1}{2\pi \sqrt{LC}} \implies L=57.34 \text{mH}

3. Capacitor voltage constraint

The peak voltage can be calculated separately for 1st and 3rd harmonics. To accommodate the possibility of a worst-case condition, it will be assumed that the 3rd harmonic will be constitutive to the 1st causing a voltage increase. The calculation is as follows.

\displaystyle I_1=\frac{V_{L-N}}{\sqrt{(X_X-X_L)^2+R^2}}=\frac{230V}{144 \Omega} =1.59A

\displaystyle I_3=\frac{1}{3}\frac{640 W}{230V}=0.92A

V_C=I_1X_C+I_3X_{C_3}=1.59*162+0.92*54=307.26V

A standard capacitor with 240 V 1kVAR would suffice in this example. The per-unit voltage would be determined as:

\displaystyle V_{pu}=\frac{307.26}{240}=1.28pu

The reactor should be chosen according to its total RMS current, which could be calculated as follows:

\displaystyle I_{rms}=\sqrt{I_1^2+I_3^2}=1.83A

4. Simulation & Validation

A further assessment of the special condition is required to implement safety factors that are responsible to accommodate other load conditions the filter will undergo.

Figure 2: Simulated circuit diagram

The above-calculated example was simulated using LT Spice. The load condition was simulated using phase-shifted current sources in series with resistive loads, fig. 2. To emphasize the effect of the filter, a switch is added to the circuit, which will be triggered after the first second.

The result is represented in fig. 3; where:

  • Before the switching action, the phase shift and current magnitude could be read as 57.35° and 1.2 Arms.
  • After the filter is connected, the RMS current decreases to 1 Arms. There is a remaining 26.46° phase shift due to imperfect power factor correction.
Figure 3: Waveforms of line voltage and current

That’s all for today’s tutorial!

Conclusion

In this article, we considered the problem of harmonics reduction using passive filters. We considered the shunt filter topology, we describe it and highlight it in different design steps. To complete the tutorial, we added an application example with simulations!

Harmonics Analysis in Matlab: Full guide

Fast Fourier Transform (FFT) Analysis in MATLAB/Simulink

In this tutorial, we will present a harmonics analysis of a simple circuit in Matlab/Simulink using FFT (Fast Fourier Transform).

FFT converts a time-domain waveform to a frequency domain and by this transformation, all signal frequency components can be obtained easily.

This means that different harmonics of a current or voltage waveform can be derived using this technique. let’s get into the details!

Figure 1 shows the circuit implemented in Simulink which consists of a rectifier with a resistive load. The system has the following elements:

  • Three-phase source created by “AC Voltage Source” block,
  • a three-phase full-bridge diode-based rectifier which is created by “Universal Bridge” block ,
  • A resistive load which forms with the rectifier a non-linear load.
Harmonic analysis Simulink MATLAB FFT
The simulated circuit in MATLAB/Simulink

Parameters:

  • The source RMS voltage is 220V/phase in this circuit, and
  • The load resistance is 150 Ohm.
  • The sampling time in this simulation is Ts=1μs which is enough for this simulation.

Harmonics analysis of load current

In this example, we would like to check harmonic content in phase A current. The latter should be firstly measured and saved for analysis.

Current is measured by the block “current measurement” and it is visualized and saved using the “scope” block as shown above.

Running the above Simulink file for 0.1s, we get the following input current:

Rectifier Harmonic Analysis

It is evident that the signal is not purely sinusoidal, and harmonics are available in this signal. Now, the harmonics and their values should be derived. There are two ways for this purpose that are discussed in this tutorial. The methods are:

  1. FFT analysis using powergui block
  2. Exporting signal values to workspace and use FFT script

The input current harmonics in a three-phase full-bridge rectifier is 6k±1 where k=0, 1, 2, etc.

Therefore, it can be expected that the mentioned harmonics would be available in the FFT results.

FFT analysis using powergui block: Method 1

Step 1: save signal in “structure with time” format

Firstly, the current signal should be saved for FFT analysis. This can be achieved by the mean of “scope” block or to “Workspace” block.

  • Double click on the scope block > then click on configuration properties (scope settings), we get the following window:
  • The signal would be named and saved by going to “Logging” (“history“) tab.
  • You can specify the Variable name in the corresponding field, in this case, we choose “Input_Current
  • The “Format” field is for defining the saved signal format in the workspace, which can be:
    • Structure with time
    • Structure
    • Array
    • Dataset

As shown in the above illustration, theStructure With Time” format is chosen which is required for powergui FFT tool.

Step 2: open FFT tool

To start the analysis, the FFT Analysis must be selected in powergui block according to the following figure.

FFT analysis powergui Matlab Simulink
  • Double click on “FFT Analysis” yields the following window:

Step 3: choose signal and set FFT settings

Powergui FFT analysis tool MAtlab Simulink

We distinguish four main parts:

  • Available signals: which is related to choosing a waveform. As can be seen, the variable name of “Input_Current” is available in “Name” field. The “Display” field also lets the user see the entire signal or the FFT window in Signal part.
  • Signal part: it plots the chosen signal entirely or part of it (FFT window).
  • FFT analysis: in this part, harmonics analysis is displayed according to the parameters chosen in FFT settings.
  • FFT settings: is the most important part of FFT Analysis.
    • Start time field: allows us to choose at which time we would like to analyse the signal, generally we start after the transient state and analyse it it in steady state. There is no transient part, so the starting time can be at the beginning of the signal (0 s).
    • Number of cycles: as it names states, it corresponds of how many cycles we would like to analyze. We can go for one cycle for FFT calculation.
    • Fundamental frequency: in this case study, the frequency is 50 Hz, and the signal is periodical.
    • The “Max frequency” field, the user can use the highest frequency that is necessary. In this study, 20th harmonic or 1000 Hz is enough. For noisy signals, high-order harmonics are available, and, in some cases, the user wants to derive high-frequency components.
    • For the result presentation, there are six choices that users can select based on the report that is needed
Display style FFT Matlab Simulink

Step 4: Display results

As an example, “Bar (relative to fundamental)” has been chosen, and the bar chart is available below after clicking on the Display button.

6 pulse rectifier FFT analysis powergui Matlab Simulink
  • It is clear that the harmonic magnitudes decrease regarding higher-order harmonics.
  • Moreover, the above rule 6k±1 harmonics are available in the input current of a three-phase full-bridge rectifier circuit (1st harmonic, 5th harmonic, 7th harmonic, 11th harmonic, 17th harmonic and 17h harmonic).

The above is also confirmed by choosing List instead of Bar:

FFT analysis in Matlab Workspace: Method 2

In the previous section, a powergui block was used for the FFT analysis, and different harmonics were presented.

“powergui” is not the only method to find the harmonics of a signal. Harmonics can be obtained by writing codes in an m-file environment as follows.

Step 1: save signal in “array” format

First, the signal must be saved to the workspace in an “Array” format as shown in the next figure. In this array, time and signal magnitude have been saved, and these parameters must be separated for signal processing.

Save-current-for-harmonic-analysis-using-FFT-simulink

Step 2: use FFT script to analyse your signal

The harmonic values can be calculated by writing a short script for FFT analysis. In this script, the FFT function should be used to derive the values of the harmonics of the input current.

As can be seen in the following script,

  • the sampling time and frequency are defined firstly.
  • Then, time and signal magnitude are saved in two variables, namely “time” and “mag”.
  • At the final step, the FFT function is used to determine the harmonic values based on the fundamental harmonic.
Ts = 1e-6;  %Sampling Time
Fs = 1/Ts;  %Sampling Frequency
F1 = 50;    %Fundamental Frequency
%Simulated Signal Data
time = Input_Current(:,1);
mag = Input_Current(:,2);
subplot(2,1,1)
plot(time,mag)
%FFT Calculation
L = length(mag);
Y = fft(mag,L);
Yabs = abs(Y);
f = 0:(1/time(end))/F1:(Fs/2-(1/time(end)))/F1; % Frequency based on Nyquist Theorem
Ymax = max(Yabs);  %Fundamental Magnitude
subplot(2,1,2)
bar(f,Yabs(1:length(f))/Ymax)   %Plotting bar chart
xlim([0,20])    %X-axis Limitation

Compiling this code, we get the harmonic orders and their values, which are similar to the previous results of the FFT analysis.

FFT script file harmonic analysis rectifier matlab simulink

Harmonics content of rectifier supplying a resistive laod

From above, the harmonic content of the electrical circuit corresponding to a rectifier feeding a resistive load is reported in the following table:

Harmonic orderHarmonic %
1st harmonic (fundamental frequency)Used as a reference
5th harmonic (250Hz)22.57%
7th harmonic (350Hz)11.29%
11th harmonic (550Hz)9.03%
13th harmonic (650Hz)6.45%
17th harmonic (850Hz)5.64%
19th harmonic (950Hz)4.52%

Conclusion

All in all, MATLAB suggests various methods for harmonics study, and users can check the FFT results in Simulink or m-file. Having the discretized signal in the workspace environment would be a great feature. The users can apply various signal processing approaches by writing different scripts and plotting them in an appropriate shape.  

5th Harmonics Explained

Definition, causes, measurment and solutions

What is 5th harmonic?

In the ideal case, voltages and currents in AC power systems are pure sine waves with 50 Hz frequency (or 60Hz).

However, voltages (or currents) in the actual power system have additional components, called harmonics, whose frequencies are integral multiples of the power system frequency. Harmonics are multiples of the fundamental frequency and can therefore be expressed as 1f, 2f, 3f, 4f, 5f, etc.

Figure1 is a plot of harmonics (up to 50th order) measured from a power analyzer for an AC Power System of a beverages plant. The yellow bar represents the 5th harmonics.

 Figure 1: Harmonic content measured in AC power system of a Blow Moulding line of a beverages plant

Usually, power analyzers available in the market measure harmonics up to 50th order.

What is the frequency of 5th harmonic?

From above, you may conclude that the 5th harmonic for a 50 Hz power system is 250 Hz. The following illustration shows one cycle of a sinusoid with a peak amplitude of 1.00 (labeled as the fundamental). The other two waveforms shown in the figure are the third harmonic and the fifth harmonic.

5th harmonic explained

Note that the third harmonic completes three cycles during the one cycle of the fundamental and the fifth harmonic completes five cycles.

The 5th harmonic component is added to the fundamental one which yields a distorted signal as shown below:

Fifth Harmonic waveform

What causes 5th order harmonic?

Harmonics are generated due to non-linear loads as explained here. Most of the time, fifth order harmonics are present in distorted signals caused by non-linear loads such as:

  • Variable Frequency Drives (VFDs)
  • Power electronic converters such as rectifiers
  • LED lighting
  • Arcing devices
  • Uninterrupted Power Supplies (UPS)
  • Electric vehicle chargers, etc

Is 5th harmonic a negtaive or positive sequence?

To answer this question, we should define what we mean by positive and negative sequences.

In a balanced three-phase system, we have phase A is at 0 degrees, phase B is shifted by 120 degrees, and phase C by 240 degrees as shown below:

Three Phase System
  • If harmonics of a given order respect the same shifting: Harmonic of phase A, then harmonic of phase B, and after that harmonic of phase C, we say that the harmonic in question is a positive sequence.

The following image shows the 7th harmonic of each phase where they respect the same order: Harmonic of phase A, then harmonic of phase B, and after that harmonic of phase C (yellow, pink, and cyan). This means that the 7th harmonic is a positive sequence.

Positive sequence 7th harmonic

What about the 5th harmonic? is it a positive or a negative sequence? short answer: 5th harmonic is a negative sequence!

Indeed, the 5th harmonic is a negative sequence as shown in the following image where 3 phase harmonics do not respect the order: Harmonic of phase A, then harmonic of phase C, and after that harmonic of phase B (yellow, cyan, and pink).

How do you measure 5th order harmonic?

As we mentioned above, harmonics are measured by a Power Quality Analyzer which can measure up to 50th order of harmonics. It should be noted that some analyzers have the provision to measure harmonics up to 99th order.

Measurement is done in THD (total harmonic distortion) and in an individual order where the THD graph displays the contribution of the 5th harmonic to the total distortion in the power system.

How to eliminate 5th order harmonic?

Many solutions can be adopted to reduce or eliminate the 5th harmonic in the power system. To cite a few:

  • Using passive harmonic filters
  • Using active power filters
  • Using reactors for local loads
  • Adding isolation transformers
  • Using 12 pulse drive rectifiers instead of 6 pulse drive version.

Conclusion

In this short article, we highlighted the 5th harmonic in power systems. This includes its definition, why it is considered as a negative sequence, its causes, and how it can be measured. In the end, we presented some solutions to reduce (or even cancel) the 5th harmonic.

Further reading

Electrical Harmonics

A detailed understanding of harmonics in electrical power systems

What are harmonics?

Harmonics are a distortion of the electrical voltage (or current) waveform, generally due to nonlinear loads such as: switched power converters, TVs, computers, and battery chargers.

A harmonic is defined as a sinusoidal component of a periodic wave or quantity having a frequency that is an integral multiple of the fundamental frequency (IEEE 141-1993).

To clarify this definition, consider the following example of a distorted current waveform:

distorted current illustrative example

This periodic signal corresponds to a sum of sine waves with different frequencies and amplitudes:

Sine wave 1:

The first sine function frequency is equal to 50Hz, which corresponds to the fundamental frequency. It is called 1st harmonic!

Distorted Current first harmonic

The above sine wave function is defined by the following expression:

Equation Harmonic 1

Sine wave 2:

The second sine function frequency is equal to 250Hz, which corresponds to a 5 multiple of the fundamental frequency. It is called the 5th harmonic!

Distorted Current fifth harmonic

The 5th harmonic is defined by the following expression of a sine wave function:

Equation Harmonic 5

Sine wave 3:

The third sine function frequency is equal to 350Hz, which corresponds to a 7 multiple of the fundamental frequency. It is called the 7th harmonic!

Distorted Current 7th harmonic

The 7th harmonic with 7*50Hz frequency and 6 Amps amplitude is defined by:

Equation Harmonic 7

Sine wave 4:

The fourth sine function frequency is equal to 550Hz, which corresponds to an 11 multiple of the fundamental frequency. It is called the 11th harmonic!

Distorted Current 11th harmonic

In this case, we have a sine wave with 11*50=550 Hz frequency and smaller amplitude (5 Amps). This harmonic is defined by the following expression:

Equation Harmonic 11

Taking the sum of the above 4 harmonics, we get an approximated version of the distorted current, check the following image:

Distorted current compared to the sum of its four harmonics

In summary and in simple terms:

A harmonic of a voltage waveform (or current) is a sinusoidal wave whose frequency is integer multiple of the fundamental frequency.

From above, you may ask how I can get the harmonics of a distorted signal?

Short answer: by applying Fast Fourier Transform (FFT) to the distorted signal.

Let’s talk about this later and now we move to the origin of electrical harmonics!

What causes electrical harmonics

As we mentioned above, Harmonics are mainly caused by non-linear loads. But what do we mean by non-linear loads? what is the difference between linear and non-linear ones?

1. Linear loads

For this class of loads, If we apply a sinusoidal voltage, it draws a sinusoidal current proportional to the applied voltage. Examples of linear loads include:

  • Resistive loads such as heaters,
  • Capacitive loads,
  • Inductive loads such as inductive motors and transformers,

or any combination thereof.

2. Non linear loads

Contrary to linear loads, when we apply a sinusoidal voltage to a non-linear load, the current it draws does not have the same waveform as the supply voltage. It draws currents in abrupt short pulses which distort the current waveforms. Examples of non-linear loads include:

  • Switched power converters,
  • Variable frequency drives (VFDs),
  • Arcing devices
  • High-voltage dc transmission stations
  • Computers, TVs, etc

Harmonics effects

In this part, we will highlight the effect of harmonics on electrical equipment and power network in general.

Electrical systemMain Effects
1. Power system\
– Losses due to heating
– Voltage distortions
/
2. Motors and generators\
– Increased heating due to iron and copper losses
– Higher audible noise
– Mechanical oscillations
– Temperature rise on the stator and in the rotor
/
3. Power cables\
– Voltage stress and corona
– Insulation failure
– Additional heating
/
4. Transformers\
– Increase of copper, Iron, and stray flux losses
– Higher audible noise
– Parasitic heating
/
5. Telephone interference\
– Noises
/

Harmonics analysis

Harmonic percentage can be calculated with respect to the 1st harmonic (corresponding to the fundamental frequency) or with respect to all harmonics.

1. Single harmonic percentage

Let’s consider the above example:

  • The distorted current has the amplitude 65.5A, 1st harmonic has 60A amplitude, 5th harmonic has 12A amplitude, 7th harmonic has 6A amplitude, and 11th harmonic has 5A amplitude.
  • With respect to all harmonics, we divide each harmonic’s amplitude by the amplitude of the distorted current, 65.5A in this case.
  • With respect to the 1st harmonic, we divide each harmonic’s amplitude by 60A

The following table reports different harmonics percentages with respect to total harmonics (column 2) as well as with respect to 1st harmonic (column 1)

HarmonicsTotal harmonics1st harmonics
1st harmonic91.6%100%
5th harmonic18.32%20%
7th harmonic09.16%10%
11th harmonic07.63%8.33%



Harmonics spectrum
  • It should be noted that we can also use RMS in the above calculations instead of amplitude. This also applies to distorted voltage signals.

2. Total Harmonic Distortion (THD)

Total harmonic distortion can be calculated with respect the 1st harmonic by taking the square root of the sum of all squared single harmonic percentages.

From the above example, assume the distorted current has only 1+3 harmonics, we have:

This image has an empty alt attribute; its file name is Total-distortion-harmonic-1024x377.webp

Total harmonic distortion (THD) can be used to troubleshoot symptoms of harmonics.

Further reading: Harmonics Analysis in Matlab: Full guide

Power factor

The power factor, cos(Φ), is defined as the ratio of real power to apparent power. It is an indicator about how effectively power is used by the load.

In the case of harmonics presence, this parameter is no longer equal to cos(Φ).

1. What is relation between power factor and harmonics?

Assuming that the most distorted signal is current, and a nearly sinusoidal voltage at the fundamental frequency. Hence, the power factor is given by the following approximated expression:

Power factor harmonics

where: cos (Φ1) corresponds to the power factor of the 1st harmonic current and voltage.

2. Does harmonics affect power factor?

The answer to this question is YES, from the previous equation, High THD yields to a low power factor which means that harmonics affects negatively the power factor of electrical installations.

On the other side, THD =0 means the power factor is the same as cos (Φ1), the power factor of the 1st harmonic current and voltage.

How can we reduce harmonics in electrical system?

Harmonics in electrical power systems can be reduced using different methods, such as:

These solutions will be considered with more details in the coming tutorials!

Conclusion

This tutorial is an introduction to harmonics and it is followed by a set of tutorials that address each part with more details!

What You Need to Know About Third Harmonic

Definition, causes, and effects!

Harmonics are an important concept in power systems, which significantly impacts power quality. In this post, we will address only third harmonics and for a general case, check this article.

Let’s get into the details!

What is 3rd harmonic and what is its frequency?

In AC three-phase systems, each phase has a periodic current/voltage wave with a specific fundamental frequency with 120 degrees phase angle difference between phases. There are two common fundamental frequencies in power systems, including 50Hz and 60Hz. For simplification, 50Hz frequency is considered as the fundamental frequency, but all subjects can be extended to other frequencies.

So what is 3rd harmonic frequency? As the harmonics are the integral multiple of the fundamental frequency, the third harmonic frequency is three times greater than the fundamental frequency which means that the third harmonic frequency would be 150Hz (3×50 Hz), check the above illustration. It is worth noting that the frequency of the third harmonic in the 60 Hz system is 180 Hz.

What causes 3rd harmonics?

In symmetrical three-phase systems, there are no harmonics, and all waves are purely sinusoidal with the fundamental frequency. However, some types of electric loads create disturbances in electric systems, and waves with non-fundamental frequencies are added to the original one. Therefore, the system is no longer pure sinusoidal.

Electric Vehicle (EV) Charger: Photo by dcbel on Unsplash

In fact, non-linear loads are the main cause of distortion and produce harmful third harmonics in energy systems. A wide range of non-linear loads is available in each system due to advances in power electronics. Nowadays, there are many power electronics devices such as:

  • power converters,
  • switching power supplies,
  • inverters, and transistors in the systems,

known as non-linear loads.

Non linear load example

Apart from power electronic devices, electric motors and non-ideal transformers can be the main sources of the third harmonics.

In distribution systems, having a balanced power system is challenging because there are many consumers who use different types of single-phase electric loads. Therefore, the distribution may be unbalanced, and, in this situation, the third harmonics are shown up in voltages and currents.

Asymmetrical short-circuit faults like phase to ground faults act as a huge non-linear load and make the system unbalanced. Thus, third harmonics would also be available in fault conditions.

Why 3rd harmonic is dangerous?

In power systems, the presence of odd harmonics is more probable than even ones. Moreover, higher-order harmonic magnitudes are relatively low in general, and in most cases, they are filtered in the system. It means that low-order odd harmonics can be more harmful because their magnitudes are considerable.

Generally, as the harmonic magnitudes decrease in higher-order harmonics, the third harmonic in the system would be the dominant harmonic component, which distorts the voltage or current waveform.

In the third harmonic, all phases have the same phase angle, and the instantaneous sum of the currents in the three phases taken at any moment will not be zero (phases cannot cancel out each other).

The current harmonics can flow in the entire system and devices, which may reduce their efficiencies and performance significantly.

Moreover, the third harmonic currents in the three-phase system are not eliminated in the neutral conductor, and in this situation, the neutral conductor will draw a cumulative third harmonic current which is too dangerous because it may lead to maloperation of electric apparatus and protection systems.

The problem gets more concerning once the neutral conductor/cable size is lower than phase one because when it becomes overloaded by third-order harmonic, substantial losses (heat) are produced in the neutral. As the overheating results from overloading losses, the neutral cable insulation can deteriorate, or its conductor may be deformed due to the high temperature.

Moreover, the neutral point can be loosened if its connection is not well. All these consequences are probable when a neutral path is available, and designers must be aware of the mentioned issues when designing neutral conductors.

However, the third harmonic can be a problem when the system does not have a ground path for the current third harmonic. If the current third harmonic cannot find a way to the ground, the current will be sinusoidal, but the peak voltage will go up significantly, which is undesirable and may lead to damage.

Effect of 3rd harmonics (power system, transformer, generator, induction motor)

To be more specific, the third harmonic has detrimental effects on generators, transformers, and induction motors which are available in each electric system. These effects can be somehow similar. For instance;

  • The third harmonic in a grounded generator with a resistor may create continuous heating (without fault) of the earthing resistor and malfunction the protection system.
  • About induction motors, the winding connection configuration is important because, in delta connection, the current third harmonic circulates in the delta and does not reflect at the source side. This harmonic increases the current RMS value, and more copper and core losses will be generated. Owing to an increase in losses, the motor output de-rating should be considered to prevent any damages. It means that the output will be decreased to follow the allowable temperature rise, and efficiency will be reduced due to losses. 
  • These impacts are also in transformers as third harmonic can increase core and copper losses, and core saturation may decrease the transformer efficiency and reduce the transformer operating power. In star-star connection, the third harmonic current is either towards the neutral point or away from it, and this harmonic will flow through the line. However, in the star-delta connection, the third harmonic will be trapped in the delta, and there is no path for flowing the harmonic.

In most cases, the third harmonic is dominant among Triplen harmonics (third, ninth, etc.), and other harmonics can be neglected. Thus, as mentioned before, the current third harmonic is accumulated in the neutral conductor, and it can be measured easily. The measured neutral current would be three times greater than the phase third harmonic currents and I3N=3×I3p.

Conclusion

To sum up this article, it is worth noting that the solution for the third harmonic in the power system is using a delta connection in the transformer. In this way, the current third harmonic will be rotated in the delta connection, and it never shows up in line currents.

Apart from that, to reduce the risk of the third harmonic in grounded star connection, the neutral conductor size should be three times one phase conductor’s size to decrease the risk of overloading and overheating.