Essay: Harmonic currents and their effect on distribution transformers

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Literature review
Introduction
This project examines harmonic currents and their effect on distribution transformers. Details of transformer losses associated with harmonic currents will be discussed. Data from a residential distribution transformer will be used to illustrate the amount of harmonic current present.
Harmonic currents have existed in electrical power systems for many years, but have increased dramatically in recent years due to a large increase in the amount of electronic devices which create these currents.
Harmonic current is a non linear load which does not oppose the applied voltage with constant impedance. The result is a non-sinusoidal current waveform that does not conform to the waveform of the applied voltage (Sankaran, 1995).
Harmonic currents cause many problems in distribution systems such as overheating of neutrals, over heating of transformers and power quality issues. Distribution transformers supply various types of residential and industrial loads. The non-linearity of their loads can inject high frequency harmonics into the current. Almost 50% of the transformer lifetime reduction is caused by the heat tensions which are produced by non-linear loads (Shafiee, 2012).
The following topics were reviewed in order to facilitate background information for the reader and to ascertain the best course of action for this project.
Distribution Transformers
1.2.1 History of Distribution Transformers
In 1831 Michael Faraday discovered electromagnetic induction, from which he established what became known as Faraday’s law of electromagnetic induction:
1) A changing magnetic flux induces an emf in a conductor; 2) The emf induced is proportional to the rate of change of magnetic flux.
The apparatus used in Faraday’s experiments contained all the basic elements of a transformer but it took more than 50 years before three Hungarian engineers of the Ganz factory in Budapest, constructed the first transformers and built the first transformer system with parallel distribution.
Figure 1 The first Transformer (Harnden, 2001).
By transforming electrical power to a high voltage, low current form and back again, the transformer greatly reduces energy losses and so enables the economic transmission of power over long distances. Energy losses are proportional to the current squared, but higher voltages can transmit the same power with less current. It has shaped the electricity supply industry, permitting generation to be located remotely from points of demand.
Although the transformer is one of the simplest electrical machines, the transformer is also one of the most efficient, with large units achieving performances of up to 99.75% (Lebedev, 2007).
Figure 2 A basic Transformer (Lebedev, 2007).
1.2.2 Modern-day Transformers
Transformers come in all range of sizes, from a thumbnail sized coupling transformer hidden inside a stage microphone, to huge gigaVA rated units used to interconnect portions of national power grids.
Due to the rapid growth in electric power, transformers have continued to evolve. While the essential features have stayed the same, some of its components have been changed to improve its efficiency. Significant improvements have been made in reducing core losses by increasing permeability, saturation and resistivity while decreasing hysteresis losses (Lebedev, 2007).
Insulation and cooling have also made significant advances due to the combination of circulating oil used and a variety of oil impregnated cellulose materials that became standard.
The overall size of the transformer has been reduced mainly due to the progress in heat removal. Transformers used to be insulated with oil which relied on natural convection to circulate the coolant, but now, many units have fan-cooled external radiators through which the oil circulates by convection or pumping.
Modern day transformers can operate at 765 kV and at more than a million kVA, with a lifespan of generally 25-40 years (Coltman, 2002).
Figure 3 Modern day transformer (Coltman, 2002)
Nearly all power transformers today are three-phase units. These normally have the primary windings connected as a delta arrangement with each phase of the incoming supply connected to two windings. Since the secondary loads on the transformer are rarely balanced between phases, it is normal for secondary windings to be connected in a star configuration with each phase of the load connected to a single winding, and for the other ends of the three windings to be connected together and brought out as a neutral connection. The capacity of a power transformer is defined by the full load power in kVA that it can produce. For three-phase transformers, this is expressed as:
S = Uph?? Iph ?? 10’3 ‘??3 Where S is the full load power (kVA), Uph is the secondary (no-load) voltage (V) and Iph is the rated output current (A) (CIBSE, 2004).
Figure 4 Diagrammatic representation of a delta-star transformer (CIBSE, 2004).
1.2.3 AC Power
With AC power, high voltage can be used to send electricity down a long wire. AC becomes more practical because once you send power to the intended destination; you can use a transformer to change the voltage down to a safer level. The power is stepped down and up several times before it reaches the consumer.
By the early 1900’s ac power systems had been universally adopted and the transformer had assumed a key role in electrical transmission and distribution (Harnden, 2001).
1.2.4 Transformer losses
Even an unloaded transformer has losses. Energy is lost when magnetising current takes the core through alternating cycles of flux at the system frequency; this is known as a no load loss or core loss. Alternating fluxes also generate alternating forces in the core which creates noise. Core losses are constant in a transformer as they do not depend on load current (Hulshorst, 2002).
Core losses consist of hysteresis losses and eddy current losses. Hysteresis losses are due to the magnetising and demagnetising of the core. The rate of these losses is dependent on the core material and the frequency. Eddy current losses are electric currents induced within conductors by magnetic fields which cause the core to heat up. The induced currents eddy back and forth along core. These currents can be limited by the core being made of thin laminations covered in an insulating varnish between each lamination.
Cooper losses or variable losses are due to the resistance of the windings. This is caused by the amount of energy lost by the current being pushed through the transformer windings. Cooper losses vary with the load and are proportional to the square of the current.
1.2.5 Transformer types
There are two basic types of transformers categorised by their winding and core configuration as seen below in figure 5, shell type and core type (Heathcoat, 2011).
Figure 5 Shell and core type transformers (Heathcoat, 2011)
In the shell type transformer the flux return paths of the core are external and enclose the windings. Due to the improved magnetic shielding that the shell type provides it is suitable for supplying power at low voltage and high current.
As can be seen in figure 5, the core type transformer on the right has its limbs surrounded by the main windings, these represents a three phase three limb arrangement. Having the top and bottom yokes equal in cross section to the wound limbs, no separate flux return path is needed. This means that for a balanced three phase system, the fluxes will add up to zero at all times. Core type transformers are the most common type used today.
The majority of transformers are oil filled using mineral oil complying with the international standard IEC 60296 which covers fluids for electrotechnical applications ‘ Unused Mineral Insulating oils for Transformers and Switchgear. The oil works as both an insulator and a cooling medium to dissipate the heat created in transformers (Heathcoat, 2011).
1.2.6 All Day Efficiency of Transformers
Transformers operate at maximum efficiency when the iron losses are equal to the copper losses. As the load of the transformer is always changing, so is the transformers efficiency. In order to obtain an indicator of the actual transformer performance an all-day efficiency equation is used, this measures the energy in and energy out of a transformer over a 24 hour period.
The formula used to calculate all day efficiency is;
Efficiency = Output in kWh for 24 hours/ Output in kWh for 24 hours
Generally, transformers have their highest efficiency when not fully loaded as its copper losses in the windings are lower than at full load. A figure of between 94 and 96% is expected for most distribution transformers.
Harmonics
1.3.1 What are Harmonics?
Due to the increasing amount of electronic devices used today which have non sinusoidal power supplies, distribution transformers are being subjected to excessive internal heating. Current waveforms from non-linear loads appear distorted; the non-linear waveform is the result of adding harmonic components to the fundamental current. The distorted current waveform produces additional heating in the transformer core and coils. This heat, along with the normal heat from the transformer under load, leads to insulation damage and reduction in transformer lifespan (Massey, 1993).
1.3.1 Triple n harmonics
The triple harmonics (3rd, 9th, 15th, etc.) are the major cause of heat because the phase currents add in the neutral conductor. The magnitude of the harmonic current produced by the triples can be double that of the phase current. This causes the neutral conductor to overheat because neutral conductors were historically designed for the same current as the phase conductors.
Distribution transformers are generally connected using delta-star connections to reduce harmonic effects. These triple harmonics are trapped, and circulate on the delta primary of the transformer, thus harmonic content is reduced as it is reflected back to source. The circulating harmonic currents create heat in delta winding due to their higher frequencies (Hulshorst, 2002).
1.3.3 K factor and Factor K
There are several methods used to estimate the harmonic content. The most common of these is the k-factor used in United States and the factor-k used in Europe.
K-factor is a weighting of the harmonic load currents according to their effects on transformer heating, as derived from ANSI/IEEE C57.110. A K-factor of 1.0 indicates a linear load (no harmonics). The higher the K-factor, the greater the harmonic heating effects.
The RMS load current could be much higher than the kVA rating of the load would indicate. Hence, a transformer rated for the expected load will have insufficient capacity. Once the k-factor is found, a transformer with a higher k-rating can be installed. The formula below is used (Hasan, 2007).
Ih= Harmonic current of hth harmonic frequency number (harmonic order)
Irms= Total rms current
h= harmonic number
Factor-k is used in Europe as defined in BS 7821 part 4 as
e= eddy current loss at fundamental frequency divided by loss due to a D.C. current equal to the R.M.S. value of the sinusoidal current.
In= magnitude of nth harmonic current
I1= magnitude of the fundamental current
q= Exponent constant dependent on type of winding and frequency
= 1.7 for round/rectangular section or 1.5 for foil type low voltage winding.
I= R.M.S. value of the current including all harmonics
The objective is to estimate the total losses at 100% current, when that current contains harmonics (Hulshorst, 2002).
Electricity in residential sector
According to SEAI, electricity accounts for a quarter of all energy used in Ireland and after transport is the second largest energy sector. Energy usage is mainly for appliances such as washing machines, cookers and tumble dryers, but there has been a large increase in recent years in the use of different entertainment devices i.e. laptops, large TV’s etc (SEAI, 2011).
1.4.1 Current energy usage and trends
As can be seen from figure 6, hot water and heating still account for about one third of all energy used in the home. When compared to similar data compiled for SEAI, Electricity End Use 2006, the biggest change is the increase of small appliances which is at 19% in 2011 report.
The increase of small appliances is quite considerable and very relevant to this particular project as these small appliances would be laptops, iPods and other electronic devices which can cause harmonic currents. Although most homes built in the last few years will have more energy saving features, they are also more likely to have a significant amount of electronic devices installed (SEAI, 2013).
Figure 6 Residential Electricity Applications in Ireland (SEAI, 2013).
1.4.2 Targets and future predictions
Demand for electricity is likely to increase in the home due to the increasing demand for electrical devices. The government has introduced different measures to reduce electricity consumption in the home. The building energy rating (BER) certificate, which is an energy rating for a building, should lead to homes being better insulated. Smart metering has also been introduced to increase energy efficiency.
These measures have achieved some success, but have a long way to go if Ireland’s electricity usage is to be cut by much more. The electricity usage for the country as whole is well down from 2006 figures but that is mainly due to the downturn in the economy (SEAI, 2011).
According to Eirgrid, which manages Ireland’s transmission network, electricity demand will increase by 2020. This is due to several factors, including the increase in electronic devices used in the home, increased population growth and the expected increase in electrical vehicle numbers. The forecast set out in Figure 7 appear quite large at the moment, considering the current economic climate (Eirgrid, 2010).
Figure 7 All Ireland Electricity demand forecast 2010-2020 (Eirgrid, 2010)
Advances in the development of electric vehicles, along with policy incentives, are expected to see a wider uptake of this technology in the transport sector in future years. However, large penetrations of EVs could lead to adverse effects on power system networks, especially at the residential distribution network level. These effects could include excessive voltage drop and thermal loading of network components (Richardson, 2011).
Current harmonic standards
All harmonic and distortion limits are covered in IEC/TR3 61000 (harmonics) which is a planning standard and in line with other European networks. These standards are set by the international electrotechnical commission, which is an international standards organization that prepares and publishes International Standards for all electrical, electronic and other related technologies (Ging, 2013).
The main reasons for these standards are to limit harmonic emissions from electronic devices in order to protect other loads and components of the power system. There are several difficulties in setting the relevant limits for individual equipment before this equipment is installed in the power system, as well as establishing the share of financial responsibility between equipment manufacturer, user, and electric power supplier (Blooming, 2006).
Odd Harmonic Distortion limit
3rd ‘ 9th < 4.0%
11th ‘ 15th < 2.0%
17th ‘ 21th < 1.5%
23rd ‘ 33rd < 0.6%
Above the 33rd < 0.3%
* For conditions lasting more than one hour. (Shorter periods increase limit by 50%).
* Even numbered harmonics are limited to 25% of the odd numbered ones.
Figure 8 Current harmonic limits (Wang, 2011)
Previous studies on current harmonics
There have been a number of previous studies done on this topic and on other issues related to current harmonics and distribution transformers.
1.6.1 Effect of harmonic distortion
The effect of current distortion on power systems can be serious because the current doesn’t deliver any power and its presence simply uses up the system capacity and reduces the number of loads that can be powered. Harmonic currents can cause equipment malfunction, overheating of neutral buses and increase heat losses in transformers and wiring.
Transformer impedance is frequency dependant, so it increases with the harmonic number. The impedance at the 5th harmonic is five times that of the fundamental frequency. Each amp of 5th harmonic current causes five times as much heating as an amp of fundamental current (Blooming, 2006).
1.6.2 Effect of current harmonic on transformer losses
There are three effects that the increased heating of the transformer can cause when the load current includes harmonic current.
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 increase conductor losses.
Eddy current losses – These are induced currents in the transformer caused by the magnetic fluxes. These induced currents flow in the windings, in the core, and in the other connecting 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 current. Therefore, this becomes a very important component of transformer losses for harmonic heating.
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 of this will depend on the thickness of the core laminations and the quality of the core steel (Szabados, 1981).
1.6.3 Aging of transformer
The aging factor of a distribution transformer is dependent on the total harmonic distortion of the current, which with the increase in electronic devices present in homes will threaten the safe operation of distribution transformers.
The financial consequences and the impact on grid reliability of non linear loads will have major consequences in the future if the necessary steps are not taken to reduce current harmonics (Singh, 2010).
Conclusion
Harmonic currents have been present in electrical systems for many years. Due to the increased demand in recent years for portable electrical devices which have harmonic content, the harmful effects on distribution transformer are only going to increase.
Transformers operate at maximum efficiency when the iron losses are equal to the copper losses. As the load of the transformer is always changing, so is the transformers efficiency. Transformers have their highest efficiency when not fully loaded as its copper losses in the windings are lower than at full load.
Triple n harmonics cause heat in transformer due to phase current adding together in neutral conductor, which causes neutral conductor to overheat if it is not oversized. The magnitude of the harmonic current produced by the triples can be double that of the phase current. Distribution transformers are generally connected using delta-star connections to reduce harmonic effects. These triple harmonics are trapped, and circulate on the delta primary of the transformer, thus harmonic content is reduced as it is reflected back to source.
To estimate the harmonic content of a transformer, factor K calculation is used. The objective is to estimate the total losses at 100% current, when that current contains harmonics. Transformers are subject to excessive internal heating as a consequence of harmonic currents being present. This heat along with the normal heat from a transformer under load conditions leads to insulation damage and a reduction in lifespan of transformer.
Methodology
Figure 9 Flowchart of Project
Introduction
This chapter will cover the detailed explanation of methodology that is used in this project. A flowchart as seen in figure 10 was created to show the multiple steps involved in the data analysis process. Each graph produced for this report details important information about transformer derived from the data. All calculation methods were found through research of related topics in journals, books and online resources.
Analysis Technique
At the start of this project when discussing the purpose and objective of the project with my supervisor it was decided to use Microsoft Excel and Matlab for all the calculations needed throughout this project. This decision was made mainly due to Microsoft Excel’s calculation flexibility for large amounts of data and Matlab’s range of easy to use functions to reduce a large amount of data into a manageable and easy to understand graphs.
This project was approached with the idea of comparing two separate days of transformer information. During this project I have had regular meetings with my supervisor, in order to put together suitable Matlab scripts to carry out relevant calculations and graphs. It was decided that given the transformer information the following calculations would be carried out: Line current, phase current, line voltage, phase voltage, all day efficiency, factor k, true RMS current, total harmonic distortion and percentage harmonic content.
Detailed transformer data contained in excel spreadsheets for a two week period was obtained for a substation in Goatstown Co. Dublin. The excel spreadsheets detailed readings taken from a transformer at an interval of every thirty seconds. This was used to show the differences between a weekday and a weekend day. There are many different calculations which can be carried out on this data such as the true RMS current of each phase, comparison of the fundamental currents, comparison of 3rd, 5th 7th and 11th harmonic, as well as the all-day efficiency of the transformer.
Sunday 7th of November 2010 and Monday 8th of November 2010 were the two days chosen for comparison purposes to show the contrast between a weekend day and a normal weekday. Matlab and excel was used to calculate and graph all the data detailed in the excel spreadsheets. All calculations and script functions will be explained in detail in next section. The complete script and any excel calculations can be found in appendix and also in attached Matlab and excel files.
Figure 10 Flowchart of analysis technique
Transformer data
Transformer Data
Power rating 400 kVA
Line voltage 400 Volts
Phase voltage 230 Volts
Iron losses 930 Watts
Copper losses 6000 Watts
Line current 577 Amps
Phase current 577 Amps
Figure 11 Table of transformer data
Power calculations
As the transformer is a star connected load, line current is equal to phase current and therefore phase voltage = (Line voltage)/(Phase voltage*’3)
As can be seen in figure 11 with the power rating of transformer given as 400 kVA and the line voltage as 400 volts, the phase voltage, line current and phase current could then be found.
All-day efficiency of transformer
With the line and phase current and line and phase voltage calculations complete, and the figures for the load losses and the no load losses known, the all day efficiency of the transformer for both days could then be found.
All day efficiency of transformer is a measure of (Energy out)/(Energy in) for a 24 hour period.
Maximum efficiency of transformer = (Power out)/( Power out+no load losses+load losses)
Factor K
In excel the factor K formula as seen below was used to find the % de-rating of the transformer of each phase for both days of data. This data for then inputted into Matlab script which applied a smoothing filter in order to show a more readable graph.
e= eddy current loss at fundamental frequency divided by loss due to a D.C. current equal to the R.M.S. value of the sinusoidal current.
In= magnitude of nth harmonic current, I1= magnitude of the fundamental current
q= Exponent constant dependent on type of winding and frequency
= 1.7 for round/rectangular section or 1.5 for foil type low voltage winding.
I= R.M.S. value of the current including all harmonics
The objective is to estimate the total losses at 100% current, when that current contains harmonics (Hulshorst, 2002).
True RMS current
The true RMS current for each phase was calculated in excel using the formula below. A smoothing filter was also applied in Matlab in order to make graph easier to understand.
I1= Fundamental current, I2= First harmonic current value, I3= Next harmonic current value etc…
The current wave form is distorted from the shape of a sine wave when a non linear load draws current from the transformer. An example of a distorted waveform would be a square or saw tooth waveform.
The distorted waveform is actually a summation of the fundamental frequency sine wave and a variety of harmonics. Harmonics are pure sine waves themselves but each has a frequency that oscillates at a multiple of 50Hz (i.e. 3rd harmonic = 3 x 50 = 150Hz, 5th harmonic = 5 x 50 = 250Hz).
To find the total RMS value of any distorted wave, you have to take “the square root of the sum of the squares” of the RMS value of the fundamental and the series of harmonics.
The fundamental current and all the harmonics present are squared, added together and then the square root of this figure is found to find the true rms current.
Total harmonic distortion
Total harmonic distortion is the square root of the sum of all harmonic components squared, divided by the RMS value of the fundamental current and it is expressed as a percentage.
Harmonic limits
Graphs of each harmonic number for each phase were made to show the change in harmonic content over each 24 hour period. This was calculated using the formula below. The fundamental current of each phase was also graphed to show how they varied over time.
Harmonic percentage = (Harmonic current)/(Fundamental current)*100
Conclusion
The analyses of project data was done using both Matlab and excel formats in order to create appropriate graphs to show the effect of harmonic currents on the transformer in question. This enabled transformer data for separate days to be compared as well as calculations to be made.
Matlab script was created in order to import data from excel spreadsheet and then perform calculations on data which could be stored in Matlab workspace. A lot of script had to be created in order to carry out calculations. Hundreds of lines of script were written for first day of data which could then be easily applied to second day of data.
Excel was used for a number of transformer calculations as it was simple to input calculation formulas into excel, thus creating a new set of values for data. This set of data was then imported into Matlab, using script previously generated and graphs of values plotted.
Data analysis
Comparison of fundamental current
Figure 12 Fundamental Current Comparisons (Monday)
Figure 13 Fundamental Current Comparisons (Sunday)
A smoothing filter is applied when data is imported into Matlab which gives an average value over a set interval in order to provide a graph which is easy to interpret; this explains how none of the phases of fundamental current actually touch the maximum value. The maximum fundamental current is 122 amps for Monday compared to 126 amps for Sunday for the R phase. All of phases reach their peak value between 5-7 pm, which is time of maximum demand on distribution transformer.
There is only a slight difference between both of days. Sunday is more balanced with several small peaks from morning to early evening, whereas Monday follows the general system demand curve of early morning peak, flatting out during the day until peaking in early evening again. There are small variations between each of the phases, with the R phase carrying the largest amount of current most of the time. It must be remembered that it is only the fundamental frequency which provides real power to customers.
Comparison of 3rd Harmonic current
Figure 14 Comparison of 3rd Harmonic Current (Monday)
Figure 15 Comparison of 3rd Harmonic Current (Sunday)
The harmonic content present on Monday is steady during the day, but then rises quite high during night time periods. Each of the phases is relatively balanced, with the T phase generally carrying the most harmonic current on average. There is more variance between phases on the plot of Sunday harmonic content. The harmonic content is steadier during the 24 hour period with smaller peaks until early evening, when the T phase reaches is maximum value. All the values were well within recommended limits.
These harmonics are called zero sequence or triple-n harmonics, which include the harmonic numbers 3, 9, 15, 21, etc. These harmonics do not develop usable torque, but produce additional losses in the equipment and add current onto neutral conductor.
Comparison of 5th Harmonic current
Figure 16 Comparison of 5th Harmonic Current (Monday)
Figure 17 Comparison of 5th Harmonic Current (Sunday)
The harmonic content for the 5th harmonic is above the recommended limits for the T phase for long periods during Sunday, with the S phase all rising above limit for a short period also. Monday is quite different with the harmonic content only being above its limit for a short period between midnight and early morning. The 5th harmonic is a negative sequence harmonics similar to the 2nd, 8th, 11th, 14th etc., which develop magnetic fields and currents that rotate in the opposite direction to the positive frequency set that would have a detrimental effect on transformer.
Comparison of 7th Harmonic current
Figure 18 Comparison of 7th Harmonic Current (Monday)
Figure 19 Comparison of 7th Harmonic Current (Sunday)
There was a large amount of the 7th harmonic current present in the data for both days. The T phase was above the recommended limits during most of the period between midnight and 6 am, with the R and T phase also rising above the limit for a time during Monday. For a large period of Sunday the T phase is well above the harmonic limit, while the R phase is also above the limit for a period.
Positive sequence harmonics are the harmonic numbers 1, 4, 7, 10, 13, etc. these harmonics produce magnetic fields and currents rotating in the same direction as the fundamental frequency harmonic.
Comparison of 11th Harmonic current
Figure 20 Comparison of 11th Harmonic Current (Monday)
Figure 21 Comparison of 11th Harmonic Current (Sunday)
There is a relatively low amount of the 11th harmonic current present for both days, with each of the phases producing at peak well below limit for this harmonic. The 11th harmonic is a negative sequence harmonic which develops magnetic fields and currents that rotate in the opposite direction to the positive frequency set that would have a detrimental effect on transformer.
Comparison of Daily efficiencies
Figure 22 Comparisons of Daily Efficiencies (Monday)
Figure 23 Comparisons of Daily Efficiencies (Sunday)
With the core loss and load losses calculated for each 24 hour period the all day efficiency could be calculated. The efficiency is the ratio of the useful power output to the power input, the power input being equal to the useful power output plus the power losses. The efficiency of each phase is quite high for both sets of data, with the lowest value for efficiency being just over 86% for early Monday morning.
The transformer load may vary considerably during each day of data and depends not only on the size and type of transformer but also on the load cycle. There will be periods when the transformer carries its rated load and periods when it only carries a small load.
Comparison of Mean and all-day efficiencies
Figure 24 Comparisons of Mean and All-day Efficiencies (Monday)
Figure 25 Comparisons of Mean and All-day Efficiencies (Sunday)
There is very little difference between the average efficiency of the transformer on each of the days of data. As the load peaks the transformer reaches its maximum value for efficiency on both days. Sunday would have a low load when compared to a week-day. The transformer is carrying its optimum load on Sunday evening; this can be seen with average efficiency reaching 98%.
Distribution transformers are designed for maximum efficiency at half load, therefore transformer will be most efficient between 40%-80%. During night-time most of the load demand reduces down which means there would be a lower load on the transformer.
Comparison of True RMS current
Figure 26 Comparisons of True RMS Current (Sunday)
Figure 27 Comparisons of True RMS Current (Monday)
When different frequencies of current are present in each phase, a root mean square calculation is required to obtain an effective or mean value for current flowing in each phase. As AC is changing from positive to negative during each cycle if an average value was taken, it would be zero amps so another method is required. A summation of all the currents squared in each phase is used, and then the square root of this value found for the RMS value. The RMS current contains fundamental and harmonic current.
The RMS value for both days of data is higher than the fundamental current by about 10% on average, with the R phase at over 130 amps for Sunday data compared to an averaged peak value fundamental current of 100 amps. This would indicate that there is a large amount of harmonic current present in this phase. Both the R and S phases follow the pattern of a normal daily load curve, whereas the T phase is significantly lower at all times which indicates harmonic distortion present.
Comparison of % Harmonic distortion
Figure 28 Comparisons of % Harmonic Distortion (Sunday)
Figure 29 Comparisons of % Harmonic Distortion (Monday)
Harmonic distortion is the RMS value of harmonic current with the fundamental current left out of calculation. Nonlinear loads cause the current to be distorted. The effect of current distortion on loads is low as current is path dependant. Therefore, harmonic currents only flow into equipment that caused them and do not interfere with other equipment. The effect of current distortion on power systems can be serious, due to the increased current flowing in the distribution system. The term total harmonic distortion is a measure of how badly the waveform is distorted.
For both the R and S phase there is significant harmonic pollution with the level varying between 10% and 40% on average during both days of data. This amount of harmonic distortion would result in a risk of temperature rise in cables. The T phase has a major amount of harmonic pollution present, with values reaching over 70% at times which would result in malfunctions of system being very possible.
Comparison of Factor K for day
Figure 30 Factor K (Sunday)
Figure 31 Factor K (Monday)
The eddy current losses rise with the square of the current in the conductor and the square of its frequency. As harmonic current is present, eddy current losses will increase in transformer, increasing operating temperature of transformer which will reduce lifespan of transformer. Transformers that supply power to equipment with harmonics present must be rated to take these increased eddy currents into account. The rated capacity of transformer must be reduced or derated based on amount of harmonic current and the rated eddy current loss. The average value of factor k for each of the phases is 99%, which means the transformer capacity only needs to be derated slightly.
Conclusion
Each phase of fundamental current varies during both days of data, with the R phase carrying the most current on average reaching a peak value in the early evening period of both days.
The amount of 3rd and 11th harmonic content was quite limited for each of the phases indicting that neither of these would have a significant adverse effect on transformer. There was a large amount of 5th and 7th harmonic content on both days, with the T phase on Sunday being well above recommended limits for long periods. Even though some of this current will cancel each other out due to the 5th and 7th harmonics being negative and positive sequences, such high levels of harmonic content are a concern.
The daily efficiencies of each of the phases vary with the load on transformer. When the transformer is at low load between midnight and early morning the efficiency of each phase is at its lowest. When the transformer is at mid to peak load in early evening the efficiency rises to its highest value for each of the phases.
There is an increase of about 10% between the RMS value of the current for each of the phases and the fundamental current values. This is due to the large amount of harmonic content in 5th and 7th harmonic, increasing the current flowing in system. This will have the negative effect of increased transformer and neutral conductor heating and possible insulation damage.
There is a large amount of harmonic distortion present on both days of data analysed. Of particular concern are the distortion levels of the T phase, which is quite high on both days. On Sunday the harmonic distortion level is high for a long period of time in early morning and early evening, when it is expected that a large number of devices which produces a high level of harmonic distortion when connected to a distribution system would be used. This high level of distortion is reducing the efficiency of the transformer by increasing line and transformer losses.
The factor K of each of the transformer phases was an average of 99%, which is means transformer, only requires a small derating. The T phase of transformer is the one with the largest amount of harmonic distortion and as a result has the most effect on transformer derating.
The harmonic content of the T phase is likely to be as a result of a large amount of harmonic producing devices being present in the homes that this phase supplies. There is a relatively low amount of harmonic content being produced from both the R and S phase by comparison. If each of the phases had an equal amount of harmonic content between them, harmonic distortion levels would be greatly reduced.

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