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2. Das Deutsche Kupferinstitut, die Auskunfts- und Beratungsstelle fr die Anwendung von Kupfer und seinen Legierungen, informiert und bert:. HandelHandwerkIndustrieForschungHochschulenKnstlerStudentenPrivatpersonen. MittelsPostTelefonTelefaxE-MailWeb-SeiteOnline-Datenbankoder persn
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1. 1 Aufbau, Auswahl und Betrieb von Verteil-Transformatoren Stefan Fassbinder
Deutsches Kupferinstitut
Am Bonneshof 5
D-40474 Düsseldorf
Tel.: +49 211 4796-323
Fax: +49 211 4796-310
sfassbinder@kupferinstitut.de
www.kupferinstitut.de The German Copper Institute, DKI, welcomes you to this presentation “Design, selection and operation of distribution transformers”. It is written by Stefan Fassbinder, DKI’s Technical Director and is narrated by Jonathan Manson on behalf of the European Copper Institute. It is one of a series of Webcasts presented by the Leonardo Energy Academy that is dedicated to building a library of materials addressing contemporary electrical energy issues. Full details of this library and how to subscribe free to it are given at the end of this presentation.The German Copper Institute, DKI, welcomes you to this presentation “Design, selection and operation of distribution transformers”. It is written by Stefan Fassbinder, DKI’s Technical Director and is narrated by Jonathan Manson on behalf of the European Copper Institute. It is one of a series of Webcasts presented by the Leonardo Energy Academy that is dedicated to building a library of materials addressing contemporary electrical energy issues. Full details of this library and how to subscribe free to it are given at the end of this presentation.
2. 2 Das Deutsche Kupferinstitut, die Auskunfts- und Beratungsstelle für die Anwendung von Kupfer und seinen Legierungen, informiert und berät: Handel
Handwerk
Industrie
Forschung
Hochschulen
Künstler
Studenten
Privatpersonen Mittels
Post
Telefon
Telefax
E-Mail
Web-Seite
Online-Datenbank
oder persönlich Who are DKI? DKI is the German Copper Institute, the central information and advisory service in Germany dealing with all aspects of the production, use and purchase of copper and copper alloys. DKI is open to anyone and everyone. The Institute is supported by its members – two copper fabricators and around 45 companies all of which are semi-manufacturers. Only just recently DKI recruited our first member company from within the electrical engineering sector.Who are DKI? DKI is the German Copper Institute, the central information and advisory service in Germany dealing with all aspects of the production, use and purchase of copper and copper alloys. DKI is open to anyone and everyone. The Institute is supported by its members – two copper fabricators and around 45 companies all of which are semi-manufacturers. Only just recently DKI recruited our first member company from within the electrical engineering sector.
3. 3 1. Grundlagen: Gigantomanie oder ökonomische Notwendigkeit? Warum so große Kraftwerks-Einheiten, dass man so große Transformatoren braucht? Why is electrical energy still largely generated by huge power facilities far away from the end-user is a frequently raised question nowadays, especially by the green and ecological communities. But that’s not all – why build up a transmission system that requires, among other things, transformers weighing around 550 tons that require a dedicated 32-axle railway carriage to transport them? Why is the electricity not generated right at the point of need, thus reducing transmission losses and facilitating use of sustainable energy delivered in small quantities dispersed across a wide area. So why is this centralized approach still followed? Is it a severe case of “gigantomania”? Well, not really, it is more to do with a cost issue imposed by a law of physics…Why is electrical energy still largely generated by huge power facilities far away from the end-user is a frequently raised question nowadays, especially by the green and ecological communities. But that’s not all – why build up a transmission system that requires, among other things, transformers weighing around 550 tons that require a dedicated 32-axle railway carriage to transport them? Why is the electricity not generated right at the point of need, thus reducing transmission losses and facilitating use of sustainable energy delivered in small quantities dispersed across a wide area. So why is this centralized approach still followed? Is it a severe case of “gigantomania”? Well, not really, it is more to do with a cost issue imposed by a law of physics…
4. 4 Dieser Trafo wiegt 300t und leistet 600MVA... ...und dieser hier wiegt 300g und müsste also 600VA leisten! Tatsächlich bringt er es nur auf 6VA! …which says that the relative energy intensity in large plant is higher than in small plant. To be precise, when the power generating or throughput rating of a plant or components is increased by a certain factor, the material requirements only increase by same factor to the power of 3 by 4. As we are dealing with transformers in this presentation, let’s take his example of a 600 MVA bulk supply point transformer which weighs in at an overall weight of 300 tons. So you would expect the small transformer on the right with its mass of about 300 grams to perform some 600 VA – but unfortunately it barely manages more than 6 VA! However, the prices for the small transformers, using the high-class materials with extra low losses that are built into big transformers would very well correlate in a roughly linear way. The transformer on the left comes at a price of perhaps 8 million Euros, and the one on the right, also fitted with grain-oriented steel, may cost some 8 Euros. So to replace the big transformer with 100 million of these small ones, in theory at least, would drive up the cost from 8 million Euros to 800 million Euros.
A similar relationship applies right across the whole range of electrical equipment as it does for synchronous generators. As an example, an exponent of 4 by 5 is given for asynchronous motors.…which says that the relative energy intensity in large plant is higher than in small plant. To be precise, when the power generating or throughput rating of a plant or components is increased by a certain factor, the material requirements only increase by same factor to the power of 3 by 4. As we are dealing with transformers in this presentation, let’s take his example of a 600 MVA bulk supply point transformer which weighs in at an overall weight of 300 tons. So you would expect the small transformer on the right with its mass of about 300 grams to perform some 600 VA – but unfortunately it barely manages more than 6 VA! However, the prices for the small transformers, using the high-class materials with extra low losses that are built into big transformers would very well correlate in a roughly linear way. The transformer on the left comes at a price of perhaps 8 million Euros, and the one on the right, also fitted with grain-oriented steel, may cost some 8 Euros. So to replace the big transformer with 100 million of these small ones, in theory at least, would drive up the cost from 8 million Euros to 800 million Euros.
A similar relationship applies right across the whole range of electrical equipment as it does for synchronous generators. As an example, an exponent of 4 by 5 is given for asynchronous motors.
5. 5 Den Zusammen-hang be-schreibt eine empirische Formel Ein Gesetz der Physik: Größere Energiedichte in größerer Anlage This transformer example shows this empirically as well as theoretically; based on the ratios of the conductor cross sections, we can calculate the core cross sections, the resulting voltages per turn and subsequently the numbers of turns needed.
Moreover, while the energy density increases in bigger plant, the relative loss level decreases, so the bigger units are even more efficient. The big transformer you just saw may have an efficiency of 99.5%, while the small one, thanks to the uncommonly high quality steel, may reach 80%. So this difference by far outweighs the losses in an electricity grid, which are as low as 4.6% in Germany and no higher than 12% in any of the 25 EU member states, measuring from the power plant down to the low voltage customer.This transformer example shows this empirically as well as theoretically; based on the ratios of the conductor cross sections, we can calculate the core cross sections, the resulting voltages per turn and subsequently the numbers of turns needed.
Moreover, while the energy density increases in bigger plant, the relative loss level decreases, so the bigger units are even more efficient. The big transformer you just saw may have an efficiency of 99.5%, while the small one, thanks to the uncommonly high quality steel, may reach 80%. So this difference by far outweighs the losses in an electricity grid, which are as low as 4.6% in Germany and no higher than 12% in any of the 25 EU member states, measuring from the power plant down to the low voltage customer.
6. 6 Struktur des öffentlichen Netzes To build an efficient power supply system requires the use of a wide range of transformers, from the huge utility ones down to the far smaller distribution transformers we want to deal with here!To build an efficient power supply system requires the use of a wide range of transformers, from the huge utility ones down to the far smaller distribution transformers we want to deal with here!
7. 7 2. Aufbau hier eines Verteil-Transformators Let us start at the centre or the design of the core of a transformer. A stack of core laminations by nature has a square or rectangular cross section and the use of laminated cores to reduce losses is essential as the current in the primary winding would otherwise induce huge eddy currents in a solid core. Put another way, the core would just act as a short-circuit winding. Which brings us back to the core and another essential design feature – the use of round windings, because, if they started “rectangular”, they would be round anyway after the first short-circuit. This is due to the repelling magnetic forces between the input and output windings, which are proportional to the product of their currents and thereby proportional to the square of either current, since the input and output currents are always approximately proportional to each other. So these forces are insignificant for the normal operating currents, but they are a crucial design factor for the transformer’s capability to survive a short-circuit – the greater these currents and subsequently the forces are the bigger the transformer is. With small transformers these are not an issue, and their bobbins are therefore rectangular. Some distribution transformer manufacturers take a compromise approach and use elliptic windings for smaller sizes, round ones only for the middle and upper segments.
To save space, the core is made up of laminations with different widths, forming different rectangles in a way so that the total core cross section approximates the round shape of the windings.
The high voltage winding is usually on the outside. The space between the low voltage and the high voltage winding has 3 different tasks:
1. It provides the necessary insulation between input and output side,
2. it provides cooling ducts,
3. it forms the main stray channel, which is the part of the magnetic field that is not shared between both of the windings. It is used by the high voltage winding only and thereby creates some inductive reactance, which is independent of the iron and therefore totally linear. This “stray channel” is good as it limits the current in the case of a short-circuit. This is important not only for the individual transformer but also for the behaviour of the whole grid, of which the transformer is a component and to whose short-circuit impedance the transformer contributes the greatest part.Let us start at the centre or the design of the core of a transformer. A stack of core laminations by nature has a square or rectangular cross section and the use of laminated cores to reduce losses is essential as the current in the primary winding would otherwise induce huge eddy currents in a solid core. Put another way, the core would just act as a short-circuit winding. Which brings us back to the core and another essential design feature – the use of round windings, because, if they started “rectangular”, they would be round anyway after the first short-circuit. This is due to the repelling magnetic forces between the input and output windings, which are proportional to the product of their currents and thereby proportional to the square of either current, since the input and output currents are always approximately proportional to each other. So these forces are insignificant for the normal operating currents, but they are a crucial design factor for the transformer’s capability to survive a short-circuit – the greater these currents and subsequently the forces are the bigger the transformer is. With small transformers these are not an issue, and their bobbins are therefore rectangular. Some distribution transformer manufacturers take a compromise approach and use elliptic windings for smaller sizes, round ones only for the middle and upper segments.
To save space, the core is made up of laminations with different widths, forming different rectangles in a way so that the total core cross section approximates the round shape of the windings.
The high voltage winding is usually on the outside. The space between the low voltage and the high voltage winding has 3 different tasks:
1. It provides the necessary insulation between input and output side,
2. it provides cooling ducts,
3. it forms the main stray channel, which is the part of the magnetic field that is not shared between both of the windings. It is used by the high voltage winding only and thereby creates some inductive reactance, which is independent of the iron and therefore totally linear. This “stray channel” is good as it limits the current in the case of a short-circuit. This is important not only for the individual transformer but also for the behaviour of the whole grid, of which the transformer is a component and to whose short-circuit impedance the transformer contributes the greatest part.
8. 8 On account of the magnetic forces under short-circuit conditions, the whole so-called active part of a transformer, the assembly of core and windings has to be fitted solidly. Adequate bolts ensure that the yoke spanning bars horizontally compress the yokes and vertically span the windings. The method of yoke lamination spanning shown here is the advanced approach, using bow-shaped pieces of steel. A cheaper method would be to punch both the laminations and yoke spanning bars in the middle and fit another bolt in there but this creates additional eddy current losses. The use of niro steel, which amazingly is not ferro-magnetic, can cut these losses, but in return it will not even partially replace the iron punched out, compared to some degree with bolts of conventional steel.On account of the magnetic forces under short-circuit conditions, the whole so-called active part of a transformer, the assembly of core and windings has to be fitted solidly. Adequate bolts ensure that the yoke spanning bars horizontally compress the yokes and vertically span the windings. The method of yoke lamination spanning shown here is the advanced approach, using bow-shaped pieces of steel. A cheaper method would be to punch both the laminations and yoke spanning bars in the middle and fit another bolt in there but this creates additional eddy current losses. The use of niro steel, which amazingly is not ferro-magnetic, can cut these losses, but in return it will not even partially replace the iron punched out, compared to some degree with bolts of conventional steel.
9. 9 In order to keep the effective air gaps in the core as small as possible, the laminations are stacked interweaved, 4 by 4 or, with most of the manufacturers, 2 by 2. This is what this looks like in theory and in practice.In order to keep the effective air gaps in the core as small as possible, the laminations are stacked interweaved, 4 by 4 or, with most of the manufacturers, 2 by 2. This is what this looks like in theory and in practice.
10. 10 3. Betriebs-Verhalten Ersatzschaltbild des Transformators:
Alle Werte werden auf eine Seite umgerechnet, hier auf die Sekundärseite. Achtung:
Verschiedene Lasten wirken sich verschieden aus! The equivalent circuit of a transformer can be used to help interpret the transformer’s operating behaviour. It assumes that both input and output windings have equal numbers of turns. Since this is not normally the case, the dimensions of one side are mathematically converted to the other side by means of the number of turns ratio. This way the behaviour becomes calculable from the referenced side, here the secondary. The equivalent circuit also helps to understand the different effects of different loads upon the transformer. The transformer ratings refer to resistive load but also inductive load may occur. As a rule, the load will be a mix out of these two, while capacitive load is possible as well. Sometimes a transformer is used exclusively to feed a capacitor bank, because reactive power compensation of a large electricity customer may have to be carried out at medium voltage level, where metering and counting takes place. But it is sometimes cheaper to use low voltage capacitors plus a transformer than medium voltage capacitors. We will soon see what can happen in these circumstances!
To avoid resonances, especially when harmonic frequencies are incurred, capacitor banks should be, and often are, detuned. This means that the capacitors are connected in series with an inductance dimensioned in such a way that at mains frequency it takes away only a fraction of the capacitor’s reactive power rating but at harmonic frequencies, it makes the serial reactance appear inductive.The equivalent circuit of a transformer can be used to help interpret the transformer’s operating behaviour. It assumes that both input and output windings have equal numbers of turns. Since this is not normally the case, the dimensions of one side are mathematically converted to the other side by means of the number of turns ratio. This way the behaviour becomes calculable from the referenced side, here the secondary. The equivalent circuit also helps to understand the different effects of different loads upon the transformer. The transformer ratings refer to resistive load but also inductive load may occur. As a rule, the load will be a mix out of these two, while capacitive load is possible as well. Sometimes a transformer is used exclusively to feed a capacitor bank, because reactive power compensation of a large electricity customer may have to be carried out at medium voltage level, where metering and counting takes place. But it is sometimes cheaper to use low voltage capacitors plus a transformer than medium voltage capacitors. We will soon see what can happen in these circumstances!
To avoid resonances, especially when harmonic frequencies are incurred, capacitor banks should be, and often are, detuned. This means that the capacitors are connected in series with an inductance dimensioned in such a way that at mains frequency it takes away only a fraction of the capacitor’s reactive power rating but at harmonic frequencies, it makes the serial reactance appear inductive.
11. 11 Kurzschluss-Spannung – was ist das überhaupt? Man legt an die Eingangs- seite so viel Spannung an, bis auf der Ausgangsseite im Kurzschluss der Nennstrom fließt. A student of electrical engineering who hears the phrase “short-circuit voltage” for the first time may well think his professor has finally totally flipped. This same professor may have taught that a short-circuit is by general definition a state where the voltage is zero. Well, in the case of transformers, a special definition applies. Here short-circuit voltage means the voltage across the input terminals while the short-circuit is located across the output terminals. The voltage level across the input terminals that is required to drive exactly the rated current in the shorted output winding is defined as the short-circuit voltage. It is sometimes given as an absolute figure in volts but more commonly in relative terms as a percentage of the rated voltage. It forms a very useful dimension to give an estimate of what happens in the system under fault conditions. With distribution transformers the rated levels of 4% for smaller and 6% for bigger units are common.
The rating plate, however, usually gives the actual “tension court-circuit” or “kortsluitspanning” amplitude measured during final commissioning test.A student of electrical engineering who hears the phrase “short-circuit voltage” for the first time may well think his professor has finally totally flipped. This same professor may have taught that a short-circuit is by general definition a state where the voltage is zero. Well, in the case of transformers, a special definition applies. Here short-circuit voltage means the voltage across the input terminals while the short-circuit is located across the output terminals. The voltage level across the input terminals that is required to drive exactly the rated current in the shorted output winding is defined as the short-circuit voltage. It is sometimes given as an absolute figure in volts but more commonly in relative terms as a percentage of the rated voltage. It forms a very useful dimension to give an estimate of what happens in the system under fault conditions. With distribution transformers the rated levels of 4% for smaller and 6% for bigger units are common.
The rating plate, however, usually gives the actual “tension court-circuit” or “kortsluitspanning” amplitude measured during final commissioning test.
12. 12 Kurzschluss-Leistung – was ist das überhaupt? Die gibt‘s eigentlich gar nicht. Man multipliziert die Leerlaufspannung mit dem Kurzschluss-Strom. The next question to be asked in this context is: What really is short-circuit power? – Well, it doesn't really exist. It is calculated by multiplying the no-load voltage by the short-circuit current. Before you finally decide that your professor of electrical engineering is indeed certifiable, be assured that all experts are aware of the obvious conflict that the states of no-load and short-circuit exclude one another from simultaneous occurrence, but still the obtained figure is quite a useful dimension to assess what happens in the case of a short-circuit.The next question to be asked in this context is: What really is short-circuit power? – Well, it doesn't really exist. It is calculated by multiplying the no-load voltage by the short-circuit current. Before you finally decide that your professor of electrical engineering is indeed certifiable, be assured that all experts are aware of the obvious conflict that the states of no-load and short-circuit exclude one another from simultaneous occurrence, but still the obtained figure is quite a useful dimension to assess what happens in the case of a short-circuit.
13. 13 R-Last (Nennlast) L-Last We have already briefly touched upon the fact that the phase angle of the load makes a crucial difference for the transformer’s behaviour. This is best described by Kapp’s triangle, which stands for the vector adding of the resistive and inductive voltage drops in a transformer. As a rule, the inductive component is greater. It is evident that, if a distribution transformer has an efficiency of, say, 98.5%, then the ohmic voltage drop in it cannot be any greater than 1.5%!
What you see here are the voltages in and across the transformer, all of them referenced to the low voltage side, with the input and output voltages both equalling 400 volts and the numbers of turns being the same. The green arrow represents the input voltage U1, or the converted input voltage U1’, respectively. Let us assume its magnitude is 100% of the rating and its phase angle is zero, to serve as the reference voltage. The black arrow represents the output voltage, that results from subtracting Kapp’s triangle or the sum of the active and reactive voltage drops in the transformer from the input voltage. Incidentally, voltage drops in a transformer compared to input and output are normally quite small, just a few percent, so let us have a look at a magnification of Kapp’s triangle.
Here it is. We have assumed that the short-circuit voltage is 6% and the resistive drop in the windings is 1% of the rated voltage at rated load, which applies to a 1000 kVA transformer of medium efficiency. Since the load is active but the major part of the internal drop is reactive, the total internal drop fortunately has only little impact upon the magnitude of the output voltage. If this were not the case, a short-circuit voltage of 6% would mean a voltage regulation of 6% between no load and full load for just one transformer! And there are several transformers involved in the supply chain, not to mention cables and switchgear.
Things look different with inductive loads. The voltage drop across the load now adds practically linearly to the internal drop. Kapp’s triangle has now turned round by 90 degrees against the reference input voltage.
But life starts to get really exciting when capacitive load is applied to the transformer. Kapp’s triangle now also turns round by 90 degrees, but into the other direction! This means a turn of 180 degrees against the previous case of inductive load or, in other words, an inversion of signs. So the voltage drops inside the transformer and across the load now no longer accumulate up but subtract from each other. The voltage across the output bushings of the transformer is now higher under load than it is without load! This effect will be all the clearer, the less significant the influence of the ohmic drop across the windings becomes, or, speaking in Kapp’s terms, the shorter the blue line becomes compared to the red one. Let us see in a moment how far this could theoretically take us, confirming that we kept our input voltage fixed as the reference. Let’s summarize so far:
- Voltage regulation across the load is insignificant with ohmic load between zero and the rated current, around 1%.
- Voltage regulation across the load is significant with inductive load, approximately as high as the short-circuit voltage at rated current amplitude.
- Voltage drop in the transformer becomes negative with capacitive load. Output voltage exceeds rating (by about the short-circuit voltage at rated current amplitude)!We have already briefly touched upon the fact that the phase angle of the load makes a crucial difference for the transformer’s behaviour. This is best described by Kapp’s triangle, which stands for the vector adding of the resistive and inductive voltage drops in a transformer. As a rule, the inductive component is greater. It is evident that, if a distribution transformer has an efficiency of, say, 98.5%, then the ohmic voltage drop in it cannot be any greater than 1.5%!
What you see here are the voltages in and across the transformer, all of them referenced to the low voltage side, with the input and output voltages both equalling 400 volts and the numbers of turns being the same. The green arrow represents the input voltage U1, or the converted input voltage U1’, respectively. Let us assume its magnitude is 100% of the rating and its phase angle is zero, to serve as the reference voltage. The black arrow represents the output voltage, that results from subtracting Kapp’s triangle or the sum of the active and reactive voltage drops in the transformer from the input voltage. Incidentally, voltage drops in a transformer compared to input and output are normally quite small, just a few percent, so let us have a look at a magnification of Kapp’s triangle.
Here it is. We have assumed that the short-circuit voltage is 6% and the resistive drop in the windings is 1% of the rated voltage at rated load, which applies to a 1000 kVA transformer of medium efficiency. Since the load is active but the major part of the internal drop is reactive, the total internal drop fortunately has only little impact upon the magnitude of the output voltage. If this were not the case, a short-circuit voltage of 6% would mean a voltage regulation of 6% between no load and full load for just one transformer! And there are several transformers involved in the supply chain, not to mention cables and switchgear.
Things look different with inductive loads. The voltage drop across the load now adds practically linearly to the internal drop. Kapp’s triangle has now turned round by 90 degrees against the reference input voltage.
But life starts to get really exciting when capacitive load is applied to the transformer. Kapp’s triangle now also turns round by 90 degrees, but into the other direction! This means a turn of 180 degrees against the previous case of inductive load or, in other words, an inversion of signs. So the voltage drops inside the transformer and across the load now no longer accumulate up but subtract from each other. The voltage across the output bushings of the transformer is now higher under load than it is without load! This effect will be all the clearer, the less significant the influence of the ohmic drop across the windings becomes, or, speaking in Kapp’s terms, the shorter the blue line becomes compared to the red one. Let us see in a moment how far this could theoretically take us, confirming that we kept our input voltage fixed as the reference. Let’s summarize so far:
- Voltage regulation across the load is insignificant with ohmic load between zero and the rated current, around 1%.
- Voltage regulation across the load is significant with inductive load, approximately as high as the short-circuit voltage at rated current amplitude.
- Voltage drop in the transformer becomes negative with capacitive load. Output voltage exceeds rating (by about the short-circuit voltage at rated current amplitude)!
14. 14 Theoretische Herleitung des Laststroms Now let us stick to the 1000 kVA transformer with a short-circuit voltage of 6%. Then the short-circuit current will be 100% by 6% or about 16.7 times the rated current.
This is the critical threshold, as the transformer is designed to just about withstand such a current amplitude for only a very few seconds. The resistive drop in the windings is about 1% of the rated voltage at rated load – and hence some 16.7% of the rated voltage in the case of a short-circuit. But let us now edge our way from the point of rated current to the point of short-circuit current by gradually enhancing the admittance of the load, which is the inverse of its impedance. In this diagram the expected current is plotted against this admittance, which, when reaching infinity, would mean a zero impedance load, that is, a short-circuit. We are using relative terms when we are referring to the rated admittance magnitude; this is obtained by dividing the transformer’s rated output voltage by its rated output current. It is a value that we use as unity. This means that around the value of 16.7 on the abscissa we would expect equal impedance magnitudes in the load and in the transformer; “half a short-circuit”, so to speak, with half the no-load voltage across a load in which half the short-circuit current would flow. Well, actually reality sometimes does not match up to expectations, as here the phase angle is not that of the rated load.
With an inductive load we are still nearly correct with this assumption, as the blue curve shows, as the voltage drops across the load and across the transformer’s internal impedance have similar phase angles. The current is about 8.3 times the nominal, proportionally to the 16.7 times we would expect for a “full” short-circuit.
With a resistive load of 16.7, at “half a short-circuit”, where internal and load impedances are of equal amplitudes, the load voltage is already higher than half the no-load output voltage, as the green line shows. The current is already around 11 times the nominal.
But now let us apply a capacitive load. By definition, its phase angle is -90°, while that of the transformer’s stray reactance is +90°. This means that these have inverse polarities, and their amplitudes subtract from each other instead of accumulating. If our example transformer has a short-circuit voltage of 6%, composed of 5.9% inductive drop and 1% resistive drop perpendicular to each other, as seen in the previous slide, then the load reactance will be reduced by these 5.9%. This increases the load current, and the voltage drop across the load goes up accordingly, since the capacitive load is a linear component. This again drives up the current and lets us finally land around 7% overcurrent in both the transformer and the load and 7% overvoltage across their terminals. This is so, although we have been at the point all the time where the amplitude of the load admittance G equals the nominal, and we would have expected to encounter both rated current and voltage, as the rated load admittance is by definition the quotient of rated current by rated voltage. Now this self-enhancing effect would accelerate as we increase the load current by increasing the load admittance. Finally, at the peak of the red curve, the inductive reactance inside the transformer and the capacitive reactance attached to the transformer as a load, are of equal amplitudes but opposite signs. So they cancel each other out, and the current would only be further limited by the ohmic resistance in the windings, which is small at just 1/6th of the transformer’s whole inner impedance! So while the current under a true short circuit would be limited to 16.7 times the rated output current, the “load” current would rise right up to 100 times the rated output current with such a “load”!
Of course nobody will ever connect such a weird load to any transformer. It might occur feeding a static Var compensator with a rating of 1670 kvar via a transformer of 100 kVA. Whilst highly unlikely, if it were the case then a lot more things would happen immediately! After all, the voltage across both the transformer’s secondary windings and the capacitors would be 6 times the rating, and the current through them would be 6 times the capacitors’ rated current and 6 times the transformer’s short-circuit current! So the contemplation of the theoretical model helps to understand the coherences; in practice we would cause an almighty and instantaneous explosion. So let us now have a look at that relevant practical section of the diagram:Now let us stick to the 1000 kVA transformer with a short-circuit voltage of 6%. Then the short-circuit current will be 100% by 6% or about 16.7 times the rated current.
This is the critical threshold, as the transformer is designed to just about withstand such a current amplitude for only a very few seconds. The resistive drop in the windings is about 1% of the rated voltage at rated load – and hence some 16.7% of the rated voltage in the case of a short-circuit. But let us now edge our way from the point of rated current to the point of short-circuit current by gradually enhancing the admittance of the load, which is the inverse of its impedance. In this diagram the expected current is plotted against this admittance, which, when reaching infinity, would mean a zero impedance load, that is, a short-circuit. We are using relative terms when we are referring to the rated admittance magnitude; this is obtained by dividing the transformer’s rated output voltage by its rated output current. It is a value that we use as unity. This means that around the value of 16.7 on the abscissa we would expect equal impedance magnitudes in the load and in the transformer; “half a short-circuit”, so to speak, with half the no-load voltage across a load in which half the short-circuit current would flow. Well, actually reality sometimes does not match up to expectations, as here the phase angle is not that of the rated load.
With an inductive load we are still nearly correct with this assumption, as the blue curve shows, as the voltage drops across the load and across the transformer’s internal impedance have similar phase angles. The current is about 8.3 times the nominal, proportionally to the 16.7 times we would expect for a “full” short-circuit.
With a resistive load of 16.7, at “half a short-circuit”, where internal and load impedances are of equal amplitudes, the load voltage is already higher than half the no-load output voltage, as the green line shows. The current is already around 11 times the nominal.
But now let us apply a capacitive load. By definition, its phase angle is -90°, while that of the transformer’s stray reactance is +90°. This means that these have inverse polarities, and their amplitudes subtract from each other instead of accumulating. If our example transformer has a short-circuit voltage of 6%, composed of 5.9% inductive drop and 1% resistive drop perpendicular to each other, as seen in the previous slide, then the load reactance will be reduced by these 5.9%. This increases the load current, and the voltage drop across the load goes up accordingly, since the capacitive load is a linear component. This again drives up the current and lets us finally land around 7% overcurrent in both the transformer and the load and 7% overvoltage across their terminals. This is so, although we have been at the point all the time where the amplitude of the load admittance G equals the nominal, and we would have expected to encounter both rated current and voltage, as the rated load admittance is by definition the quotient of rated current by rated voltage. Now this self-enhancing effect would accelerate as we increase the load current by increasing the load admittance. Finally, at the peak of the red curve, the inductive reactance inside the transformer and the capacitive reactance attached to the transformer as a load, are of equal amplitudes but opposite signs. So they cancel each other out, and the current would only be further limited by the ohmic resistance in the windings, which is small at just 1/6th of the transformer’s whole inner impedance! So while the current under a true short circuit would be limited to 16.7 times the rated output current, the “load” current would rise right up to 100 times the rated output current with such a “load”!
Of course nobody will ever connect such a weird load to any transformer. It might occur feeding a static Var compensator with a rating of 1670 kvar via a transformer of 100 kVA. Whilst highly unlikely, if it were the case then a lot more things would happen immediately! After all, the voltage across both the transformer’s secondary windings and the capacitors would be 6 times the rating, and the current through them would be 6 times the capacitors’ rated current and 6 times the transformer’s short-circuit current! So the contemplation of the theoretical model helps to understand the coherences; in practice we would cause an almighty and instantaneous explosion. So let us now have a look at that relevant practical section of the diagram:
15. 15 Ausschnitt des real vor-kommenden Betriebs-Bereichs Now this small excerpt of the previous chart just summarizes what has been said before:
When a distribution transformer has a short-circuit voltage of 6%, then with an inductive load the voltage regulation between no load and rated current will be an approximate 6% drop.
When the load is resistive, which the ratings refer to, the drop is barely any more than 1%.
With a purely capacitive load, the voltage across the output bushings will increase by some 6% from zero to rated current and even 7% from zero to rated load admittance. After all, it will always be a fixed capacitive admittance, or reactance, respectively, which is connected. So a 7% overcurrent and overvoltage of both the transformer and the load is the rule when a compensator dimensioned for the transformer’s rated output voltage is connected.
Indeed system designers and planners are not always totally aware of these coherences, but specialists for compensation or for transformer design are. It happened to a manufacturer, not of compensators but only of reactive power regulation equipment, that they were requested to install the control for a centralized static Var compensator at a customer’s power entrance point (the PCC – point of common coupling). Since medium voltage capacitors are expensive, it appeared to be cheaper to install a dedicated 1600 kVA transformer solely for the 1400 kvar compensator and use low voltage capacitors. This done, the phase-to-neutral output voltage of the transformer rose from 230 volts to 255 volts when the load was connected. Fortunately, in this case the problem could be solved by connecting the input terminals to the 10.5 kilovolt taps, although the medium voltage was only around 10 kV, and everything was in balance again. But, the morals of this case are:
Had there not been a specialist involved, probably nobody would have measured the voltage under load, and the overvoltage would not have been detected until the transformer would probably have fallen victim to a premature failure on account of excess heat.
And even under normal load conditions as achieved by the final configuration, it is doubtful whether this solution was really still any more economical after some years of paying about 1% of the reactive power as active transformer losses.
Furthermore it remains to be considered why utilities want their customers to compensate: mainly because reactive power causes extra losses in the system. But this applies to the customer’s installation just as it does to the utility’s grid, so the central Var compensator takes this avoidable extra burden off the grid, but still leaves it circulating across the customer’s premises, causing losses there, but now paid for by the customer! So splitting the 1400 kvar into several smaller units and pitching these closer to the inductive loads might have been more costly to install but would certainly have been more effective. But this is a different topic. We are now talking about transformers, not about compensators.Now this small excerpt of the previous chart just summarizes what has been said before:
When a distribution transformer has a short-circuit voltage of 6%, then with an inductive load the voltage regulation between no load and rated current will be an approximate 6% drop.
When the load is resistive, which the ratings refer to, the drop is barely any more than 1%.
With a purely capacitive load, the voltage across the output bushings will increase by some 6% from zero to rated current and even 7% from zero to rated load admittance. After all, it will always be a fixed capacitive admittance, or reactance, respectively, which is connected. So a 7% overcurrent and overvoltage of both the transformer and the load is the rule when a compensator dimensioned for the transformer’s rated output voltage is connected.
Indeed system designers and planners are not always totally aware of these coherences, but specialists for compensation or for transformer design are. It happened to a manufacturer, not of compensators but only of reactive power regulation equipment, that they were requested to install the control for a centralized static Var compensator at a customer’s power entrance point (the PCC – point of common coupling). Since medium voltage capacitors are expensive, it appeared to be cheaper to install a dedicated 1600 kVA transformer solely for the 1400 kvar compensator and use low voltage capacitors. This done, the phase-to-neutral output voltage of the transformer rose from 230 volts to 255 volts when the load was connected. Fortunately, in this case the problem could be solved by connecting the input terminals to the 10.5 kilovolt taps, although the medium voltage was only around 10 kV, and everything was in balance again. But, the morals of this case are:
Had there not been a specialist involved, probably nobody would have measured the voltage under load, and the overvoltage would not have been detected until the transformer would probably have fallen victim to a premature failure on account of excess heat.
And even under normal load conditions as achieved by the final configuration, it is doubtful whether this solution was really still any more economical after some years of paying about 1% of the reactive power as active transformer losses.
Furthermore it remains to be considered why utilities want their customers to compensate: mainly because reactive power causes extra losses in the system. But this applies to the customer’s installation just as it does to the utility’s grid, so the central Var compensator takes this avoidable extra burden off the grid, but still leaves it circulating across the customer’s premises, causing losses there, but now paid for by the customer! So splitting the 1400 kvar into several smaller units and pitching these closer to the inductive loads might have been more costly to install but would certainly have been more effective. But this is a different topic. We are now talking about transformers, not about compensators.
16. 16 Leerlaufstrom eines Transformators 16kV / 420V, 630kVA, hier von der Unter-spannungsseite her erregt! It is often said that the magnetisation currents of transformers also contribute to the harmonic distortion of the currents in the power system. Indeed these no-load currents of a 630 kVA transformer do look very distorted, but if you consider that this transformer was excited from the 400 volts side for this test, then you become aware that the current amplitudes are only around 1/1000th of the rated current. This puts them into the correct context.
These are the dimensions in the equivalent circuit, here quantified for this transformer and referenced to the output voltage. Note that the equivalent circuit cannot represent the non-linearity of the no-load impedance, described here in terms of the so-called iron resistance RFe, representing the losses, and the so-called main reactance Xm! But it becomes evident that their magnitudes are around 1000 times larger than the load impedance, and the currents through them are therefore negligible – at least from the viewpoint of power quality, not from the viewpoint of losses, as we will see!
Since the no-load loss of such a transformer is also around 1/1000th of the rated throughput, it must be concluded that it has hardly any magnetising current intake at all. But this is a very good example from Switzerland. We have seen other transformers, from Poland for example, with considerably higher no-load currents.
It is also often said that transformers reduce the power factor within the whole system. After what we have just seen, this can only refer to a loaded transformer. Indeed, the stray impedance X1s’ plus X2s of a distribution transformer will add 4%, or 6%, respectively, of inductive reactive power to the active power throughput when the transformer is fully loaded. At lower load the shares of reactive current and reactive voltage drop inside the transformer both drop proportionally, so the absolute reactive power magnitude drops by the square of the current. This is inevitable and remains to be considered when talking about compensating the entire system.It is often said that the magnetisation currents of transformers also contribute to the harmonic distortion of the currents in the power system. Indeed these no-load currents of a 630 kVA transformer do look very distorted, but if you consider that this transformer was excited from the 400 volts side for this test, then you become aware that the current amplitudes are only around 1/1000th of the rated current. This puts them into the correct context.
These are the dimensions in the equivalent circuit, here quantified for this transformer and referenced to the output voltage. Note that the equivalent circuit cannot represent the non-linearity of the no-load impedance, described here in terms of the so-called iron resistance RFe, representing the losses, and the so-called main reactance Xm! But it becomes evident that their magnitudes are around 1000 times larger than the load impedance, and the currents through them are therefore negligible – at least from the viewpoint of power quality, not from the viewpoint of losses, as we will see!
Since the no-load loss of such a transformer is also around 1/1000th of the rated throughput, it must be concluded that it has hardly any magnetising current intake at all. But this is a very good example from Switzerland. We have seen other transformers, from Poland for example, with considerably higher no-load currents.
It is also often said that transformers reduce the power factor within the whole system. After what we have just seen, this can only refer to a loaded transformer. Indeed, the stray impedance X1s’ plus X2s of a distribution transformer will add 4%, or 6%, respectively, of inductive reactive power to the active power throughput when the transformer is fully loaded. At lower load the shares of reactive current and reactive voltage drop inside the transformer both drop proportionally, so the absolute reactive power magnitude drops by the square of the current. This is inevitable and remains to be considered when talking about compensating the entire system.
17. 17 Schaltgruppen Ist der Sternpunkt belastbar? In principle all three-phase devices can be designed for star or delta wiring. With transformers, the star configuration provides the advantage that two different single-phase voltages can be tapped, even without any taps on the windings themselves. The delta configuration offers other advantages. In a transformer these advantages can be combined by wiring one side in delta and the other in star.In principle all three-phase devices can be designed for star or delta wiring. With transformers, the star configuration provides the advantage that two different single-phase voltages can be tapped, even without any taps on the windings themselves. The delta configuration offers other advantages. In a transformer these advantages can be combined by wiring one side in delta and the other in star.
18. 18 Schaltgruppen Ist der Sternpunkt belastbar? For instance, the delta-star-configuration provides the option to create a system with a star point out of one which has none. But can the star point also be loaded to, for example, carry substantial amounts of current far above the level needed for metering and monitoring purposes but rather for the purpose of driving loads without causing any substantial unbalance? Not necessarily as if the input winding is star configured and its star point is not connected, then the output star point is not loadable. When the input winding is connected in delta, it then cannot have a star point at all and the output star point is perfectly loadable. How can this be?For instance, the delta-star-configuration provides the option to create a system with a star point out of one which has none. But can the star point also be loaded to, for example, carry substantial amounts of current far above the level needed for metering and monitoring purposes but rather for the purpose of driving loads without causing any substantial unbalance? Not necessarily as if the input winding is star configured and its star point is not connected, then the output star point is not loadable. When the input winding is connected in delta, it then cannot have a star point at all and the output star point is perfectly loadable. How can this be?
19. 19 Schaltgruppen Ist der Sternpunkt belastbar? When a single-phase AC load is connected to the output, then this load is fed from the voltage between both ends of one winding. This creates a magnetic flux in this winding, which requires a counter flux on the same leg to offset it. This counter flux requires the ends of the input winding on that leg to be also directly connected to a single phase, or two-phase, voltage on the input side. The delta configuration provides this, but an open star point on the input side does not. With a loaded star point on the output side, the equivalent circuit would resemble something like this diagram shown here: The counter flux on this leg is missing, so that the load lies more or less in series with the main reactance and the iron resistance of another leg. Now the load impedance was 400 Milliohms in the previous example, while the parallel connection of the main reactance with the iron resistance yields something around 400 Ohms. So the voltage across the load will collapse to near zero, while the voltage across the terminals of the unloaded legs will increase approximately by a factor of square root 3. Imagine these legs were not totally unloaded and if they were feeding some very slight loads, these would be destroyed.
More than that: The overvoltage would over-excite the unloaded legs and operate the transformer in a most unhealthy state with excess core loss. The non-linearity of the parallel connection out of main reactance and iron resistance would certainly yield a substantial drop of their combined impedance and therefore improve the situation of the underfed great load and to an extent the overfed small loads, but only at the expense of surplus core heat and most likely some terrible noise.When a single-phase AC load is connected to the output, then this load is fed from the voltage between both ends of one winding. This creates a magnetic flux in this winding, which requires a counter flux on the same leg to offset it. This counter flux requires the ends of the input winding on that leg to be also directly connected to a single phase, or two-phase, voltage on the input side. The delta configuration provides this, but an open star point on the input side does not. With a loaded star point on the output side, the equivalent circuit would resemble something like this diagram shown here: The counter flux on this leg is missing, so that the load lies more or less in series with the main reactance and the iron resistance of another leg. Now the load impedance was 400 Milliohms in the previous example, while the parallel connection of the main reactance with the iron resistance yields something around 400 Ohms. So the voltage across the load will collapse to near zero, while the voltage across the terminals of the unloaded legs will increase approximately by a factor of square root 3. Imagine these legs were not totally unloaded and if they were feeding some very slight loads, these would be destroyed.
More than that: The overvoltage would over-excite the unloaded legs and operate the transformer in a most unhealthy state with excess core loss. The non-linearity of the parallel connection out of main reactance and iron resistance would certainly yield a substantial drop of their combined impedance and therefore improve the situation of the underfed great load and to an extent the overfed small loads, but only at the expense of surplus core heat and most likely some terrible noise.
20. 20 Bedingungen für Parallel-Betrieb: Gleiche Spannungen der parallel zu betreibenden Wicklungen.
Gleiche Nenn-Kurzschlussspannungen.
Gleiche Schaltgruppen-Kennziffern.
Wenn eingangsseitig nicht parallel gefahren wird: Gleiche Phasenlagen der speisenden Netze sicherstellen.
Wenn eingangsseitig nicht parallel gefahren wird: Ungefähr gleiche Kurzschlussleistungen der speisenden Netze sicherstellen.
Größenverhältnis parallel zu betreibender Einheiten maximal 3:1. So we need to see when can transformers be operated in parallel? There are a number of conditions that need to be fulfilled:
Of course the voltages of the windings or taps, respectively, which are to operate in parallel, need to be equal.
The transformers need to have equal short-circuit voltage ratings.
The vector group figures need to be equal. This does not by necessity mean that the vector groups have to be equal, only the phase shifts between the input and output windings has to be the same. Theoretically a transformer wired Dzn6 can be operated parallel with one wired Yzn6, but in practice this will hardly ever be done and is not recommended. Although transformers of these vector groups will behave identically under balanced linear three-phase loads, if the short-circuit voltages are equal, their behaviours are likely to differ when the star point becomes loaded, as happens in most cases of non-linear or unbalanced loads.
If a parallel operation means that only the output windings are paralleled and the input sides are not fed from the same grid make sure the feeding grids are in phase with each other!
If this is the case you still have to make sure that the feeding grids have approximately equal short-circuit powers.
The ratio of power ratings of units to be paralleled should be no greater than 3:1.
Why is this? Well, the short-circuit impedance of a smaller transformer has a greater resistive and a smaller reactive share. This leads to an uneven distribution of the full load across the transformers that are set up in parallel. If the load is inductive, the voltage drop in the bigger transformer will be greater, and in the smaller one it will be smaller. If the load is resistive, it will be the other way round. A rule of thumb says that the rated powers of transformers with output windings paralleled should not exceed a ratio of 1 by 3. If you remember Kapp’s triangle, the contribution of a load current to the internal voltage drop inside the transformer will always be greatest when the load current vector has the same orientation as the vector of the overall internal voltage drop (the brown one in the pictures).
By the way, this decision should never ever arise anyway, since it makes little sense to supplement a 1000 kVA transformer with a little 100 kVA assistant if the load exceeds the 1000 kVA by just 10%. It would then be much more reasonable to install a second 1000 kVA unit, as we will see right now:So we need to see when can transformers be operated in parallel? There are a number of conditions that need to be fulfilled:
Of course the voltages of the windings or taps, respectively, which are to operate in parallel, need to be equal.
The transformers need to have equal short-circuit voltage ratings.
The vector group figures need to be equal. This does not by necessity mean that the vector groups have to be equal, only the phase shifts between the input and output windings has to be the same. Theoretically a transformer wired Dzn6 can be operated parallel with one wired Yzn6, but in practice this will hardly ever be done and is not recommended. Although transformers of these vector groups will behave identically under balanced linear three-phase loads, if the short-circuit voltages are equal, their behaviours are likely to differ when the star point becomes loaded, as happens in most cases of non-linear or unbalanced loads.
If a parallel operation means that only the output windings are paralleled and the input sides are not fed from the same grid make sure the feeding grids are in phase with each other!
If this is the case you still have to make sure that the feeding grids have approximately equal short-circuit powers.
The ratio of power ratings of units to be paralleled should be no greater than 3:1.
Why is this? Well, the short-circuit impedance of a smaller transformer has a greater resistive and a smaller reactive share. This leads to an uneven distribution of the full load across the transformers that are set up in parallel. If the load is inductive, the voltage drop in the bigger transformer will be greater, and in the smaller one it will be smaller. If the load is resistive, it will be the other way round. A rule of thumb says that the rated powers of transformers with output windings paralleled should not exceed a ratio of 1 by 3. If you remember Kapp’s triangle, the contribution of a load current to the internal voltage drop inside the transformer will always be greatest when the load current vector has the same orientation as the vector of the overall internal voltage drop (the brown one in the pictures).
By the way, this decision should never ever arise anyway, since it makes little sense to supplement a 1000 kVA transformer with a little 100 kVA assistant if the load exceeds the 1000 kVA by just 10%. It would then be much more reasonable to install a second 1000 kVA unit, as we will see right now:
21. 21 4. Wirkungsgrad Entwicklung des Dynamobleches There has been a steady increase in magnetic steel quality during all of the past century, as you see, with a substantial dip in 1975, when amorphous iron was invented. We will come back to this peculiar material later.
As you also see, the ratings for the magnetic flux densities for the different materials may differ. This did not happen in order to cause confusion and to put a block in the way of achieving the desired 1 in 1 comparability of the individual materials, but it is due to the different states of magnetizability. The values given are the maximum useable ones, where the magnetisation enters a state of saturation. This adds to the difficulty of optimizing the trade-off between load loss and no-load loss in a transformer. As the no-load loss, or iron loss, increases by the square of the flux density, this loss can substantially be reduced by using less than these maxima. But alas, this requires more turns on each winding, and this means to use longer and thinner wires, which leads to a rapid increase of the load loss or copper loss.
A second trade-off, interlinking with this one, is the ratio of copper to steel quantity. As a very rough rule of thumb, transformer manufacturers say that a ratio of copper weight by core weight of 1 by 2 would provide the lowest production cost, but this minimum is one of a very flat curve, so in the end the trade-off is more one of operating behaviour rather than material costs. The most important operational parameter here is the ratio of load loss by no-load loss. Now assuming a manufacturer has made a decision for a fixed magnetic flux density in the core and a fixed current density in the copper, then a transformer with more steel will also have more core loss, and one with more copper will have more copper loss! So the decision will usually be to build, for example, a generator transformer, which runs at full load all of its service life, with a very thick core in order to be able to use the smallest possible number of turns and, subsequently, the thickest possible wire for the windings. With distribution transformers it is vice versa: They are only slightly loaded for nearly all of their lives and fully loaded, if ever, for only short periods. The decision here will require a different ratio of copper to magnetic steel quantities.There has been a steady increase in magnetic steel quality during all of the past century, as you see, with a substantial dip in 1975, when amorphous iron was invented. We will come back to this peculiar material later.
As you also see, the ratings for the magnetic flux densities for the different materials may differ. This did not happen in order to cause confusion and to put a block in the way of achieving the desired 1 in 1 comparability of the individual materials, but it is due to the different states of magnetizability. The values given are the maximum useable ones, where the magnetisation enters a state of saturation. This adds to the difficulty of optimizing the trade-off between load loss and no-load loss in a transformer. As the no-load loss, or iron loss, increases by the square of the flux density, this loss can substantially be reduced by using less than these maxima. But alas, this requires more turns on each winding, and this means to use longer and thinner wires, which leads to a rapid increase of the load loss or copper loss.
A second trade-off, interlinking with this one, is the ratio of copper to steel quantity. As a very rough rule of thumb, transformer manufacturers say that a ratio of copper weight by core weight of 1 by 2 would provide the lowest production cost, but this minimum is one of a very flat curve, so in the end the trade-off is more one of operating behaviour rather than material costs. The most important operational parameter here is the ratio of load loss by no-load loss. Now assuming a manufacturer has made a decision for a fixed magnetic flux density in the core and a fixed current density in the copper, then a transformer with more steel will also have more core loss, and one with more copper will have more copper loss! So the decision will usually be to build, for example, a generator transformer, which runs at full load all of its service life, with a very thick core in order to be able to use the smallest possible number of turns and, subsequently, the thickest possible wire for the windings. With distribution transformers it is vice versa: They are only slightly loaded for nearly all of their lives and fully loaded, if ever, for only short periods. The decision here will require a different ratio of copper to magnetic steel quantities.
22. 22 Einteilung der Klassen nach dem bisherigen HD 428 While big transformers for power plants and substations are individually designed according to customers’ demands and the loss levels individually negotiated, distribution transformers are purchased off the shelf. To facilitate this, the loss levels, next to the rest of the technical properties, are standardised. So far, you can select among 3 load loss levels and 3 no-load loss levels, which you can combine as you like. List C provides the lowest load losses and list C’ the lowest no-load levels. The highest no-load losses are in category A’, while, surprisingly, the highest load loss levels are found in the centre category B’. This is an error which happened during compilation of the final document, which had been accomplished after long and partly contentious discussions, and was not noticed in time. Later on, nobody felt really motivated to correct it.
But it was recently considered whether to introduce a fourth category DD’ with even lower loss levels. The Swiss utilities provided evidence that the standardised levels were not really challenging any more, and they have been ordering and using even better transformers for many years.While big transformers for power plants and substations are individually designed according to customers’ demands and the loss levels individually negotiated, distribution transformers are purchased off the shelf. To facilitate this, the loss levels, next to the rest of the technical properties, are standardised. So far, you can select among 3 load loss levels and 3 no-load loss levels, which you can combine as you like. List C provides the lowest load losses and list C’ the lowest no-load levels. The highest no-load losses are in category A’, while, surprisingly, the highest load loss levels are found in the centre category B’. This is an error which happened during compilation of the final document, which had been accomplished after long and partly contentious discussions, and was not noticed in time. Later on, nobody felt really motivated to correct it.
But it was recently considered whether to introduce a fourth category DD’ with even lower loss levels. The Swiss utilities provided evidence that the standardised levels were not really challenging any more, and they have been ordering and using even better transformers for many years.
23. 23 Einteilung der Klassen nach dem zukünftigen HD 428 Finally, instead of adding one category, the total harmonisation document was revised and will probably be released soon in the format displayed here or very similar to this. As you see, we will then have 4 categories of load losses and even 5 of no-load losses. Maximum noise levels were allocated to the no-load loss levels, and the sequence was inversed. “A” is now the best class. This has the disadvantage that it cannot easily be expanded upward, to even better values, but it was intended to adapt it to most of the other classification schemes around, most of which use “A” as the best category.Finally, instead of adding one category, the total harmonisation document was revised and will probably be released soon in the format displayed here or very similar to this. As you see, we will then have 4 categories of load losses and even 5 of no-load losses. Maximum noise levels were allocated to the no-load loss levels, and the sequence was inversed. “A” is now the best class. This has the disadvantage that it cannot easily be expanded upward, to even better values, but it was intended to adapt it to most of the other classification schemes around, most of which use “A” as the best category.
24. 24 Now, more than ever, you have the choice: You can, for instance, combine the best class of no-load loss with the poorest class of load loss, and you will get a transformer that has its optimum efficiency at only 24% of rated load, for a load profile where high load rarely occurs. If you do it the other way round and combine the best class of load loss with the poorest class of no-load loss, the maximum efficiency still occurs below half load.
Of course you can also select the best category of either, but it depends on the application whether this will ever pay back. Please also see the presentation by our colleague Walter Hulshorst about how to dimension and select a transformer with lowest life cycle costs.
But what will pay back in most cases is what we already mentioned when we discussed parallel operation: Use 2 transformers where only 1 is needed to carry the load! They will be running at half load most of the time then and therefore close to the point of optimal efficiency. Moreover, you have reserves enough to bridge the gap, should one transformer fail, which rarely ever happens but is quite embarrassing if it happens. But make sure your system is adequately designed and protected to cope with the duplicate short-circuit current! In many cases it may be advisable to split the system into several parts, individually fed by 1 transformer each, which can be coupled to provide for the possibility of 1 transformer failing.Now, more than ever, you have the choice: You can, for instance, combine the best class of no-load loss with the poorest class of load loss, and you will get a transformer that has its optimum efficiency at only 24% of rated load, for a load profile where high load rarely occurs. If you do it the other way round and combine the best class of load loss with the poorest class of no-load loss, the maximum efficiency still occurs below half load.
Of course you can also select the best category of either, but it depends on the application whether this will ever pay back. Please also see the presentation by our colleague Walter Hulshorst about how to dimension and select a transformer with lowest life cycle costs.
But what will pay back in most cases is what we already mentioned when we discussed parallel operation: Use 2 transformers where only 1 is needed to carry the load! They will be running at half load most of the time then and therefore close to the point of optimal efficiency. Moreover, you have reserves enough to bridge the gap, should one transformer fail, which rarely ever happens but is quite embarrassing if it happens. But make sure your system is adequately designed and protected to cope with the duplicate short-circuit current! In many cases it may be advisable to split the system into several parts, individually fed by 1 transformer each, which can be coupled to provide for the possibility of 1 transformer failing.
25. 25
26. 26
27. 27 Amorphes Eisen könnte die Leerlauf-Verluste auf einen Bruchteil senken Jedoch:
größer
teurer
lauter Now back to the amorphous steel. As you have seen in this table before, it could cut the no-load losses down to a fraction. Unfortunately it has a few disadvantages that have so far hampered its more universal use, which was ground to a halt at the start of electricity market liberalisation:
Since it is magnetisable only up to around 1.3 T, while common grain-oriented magnetic steel sheets are usable up to 1.75 T, it requires more turns of wire and thereby makes the transformer bigger, heavier and more expensive. Also the noise levels are about 12 dB higher than those of equivalent transformers, but this need not always be an issue. In many situations noise may be totally irrelevant, and the extremely low no-load losses would provide payback periods of 2 to 5 years. So a combination of increasing fuel prices and the present inversion of the initial price drop that took place immediately after the electricity markets opened up, should provide scope for a revival of this excellent technique, especially in situations where the average loading is low, as in the case of distribution transformers.Now back to the amorphous steel. As you have seen in this table before, it could cut the no-load losses down to a fraction. Unfortunately it has a few disadvantages that have so far hampered its more universal use, which was ground to a halt at the start of electricity market liberalisation:
Since it is magnetisable only up to around 1.3 T, while common grain-oriented magnetic steel sheets are usable up to 1.75 T, it requires more turns of wire and thereby makes the transformer bigger, heavier and more expensive. Also the noise levels are about 12 dB higher than those of equivalent transformers, but this need not always be an issue. In many situations noise may be totally irrelevant, and the extremely low no-load losses would provide payback periods of 2 to 5 years. So a combination of increasing fuel prices and the present inversion of the initial price drop that took place immediately after the electricity markets opened up, should provide scope for a revival of this excellent technique, especially in situations where the average loading is low, as in the case of distribution transformers.
28. 28 Der Ersatz alter Transformatoren lohnt also aus verschiedenen Gründen 1958 1998
(Rauscher & Stoecklin) (ABB Sécheron SA) It has already been mentioned that, although the principle has always remained the same, a century of steady development has lead to a lot of detail improvement in transformer technology. This refers to more than just the losses but also to properties like noise levels and dimensions.
Now fortunately transformers have no mechanical moving parts and therefore hardly wear out – or should we rather say unfortunately? A transformer’s life lasts about 20 to 40 years, after which the mechanical and electrical strengths are diminished. The next short-circuit will destroy it mechanically because of the magnetic forces, or the next lightning strike will cause a flashover in the insulant. But in locations where neither a short-circuit nor a lightning strike ever occurs for 20 years, a transformer may very well remain in operation for 60 years. Now is this really a good message? Not really, as a Swiss study discovered. After all, it would be more economical to replace these ancient transformers with modern low-loss models than to refurbish them or just leave them in operation until they fail.It has already been mentioned that, although the principle has always remained the same, a century of steady development has lead to a lot of detail improvement in transformer technology. This refers to more than just the losses but also to properties like noise levels and dimensions.
Now fortunately transformers have no mechanical moving parts and therefore hardly wear out – or should we rather say unfortunately? A transformer’s life lasts about 20 to 40 years, after which the mechanical and electrical strengths are diminished. The next short-circuit will destroy it mechanically because of the magnetic forces, or the next lightning strike will cause a flashover in the insulant. But in locations where neither a short-circuit nor a lightning strike ever occurs for 20 years, a transformer may very well remain in operation for 60 years. Now is this really a good message? Not really, as a Swiss study discovered. After all, it would be more economical to replace these ancient transformers with modern low-loss models than to refurbish them or just leave them in operation until they fail.
29. 29 Leerlauf-Verlust eines 400-kVA-Verteiltransformators 16 kV / 400 V Wirkungsgrad-Verbesserung This becomes evident when you have another look at the tremendous reduction of no-load losses and also when viewing the lower but still significant development of the load losses.This becomes evident when you have another look at the tremendous reduction of no-load losses and also when viewing the lower but still significant development of the load losses.
30. 30 5. Überlast durch Übellast Scheinleistung, Spannung und Strom eingehalten, Echt-Effektivwerte ver-wendet – und doch zu heiß geworden? We have now seen how a transformer interacts with its environment, especially its load. We studied the transformer’s impact upon the load and vice versa, single- and multiphase loads, balanced and unbalanced, and their effect upon the voltage, current and losses of a transformer. But these loads were all linear. Now since the widespread proliferation of non-linear loads has begun, there are new styles of mutual influence, be they of healthy or detrimental nature. Because non-linear loads are a synonym for sources of harmonic frequencies, which are higher than the transformer’s rated operating frequency, these effects have a lot to do with the leakage reactance, which rises linearly to the frequency. Let us have a look what can happen:
In the upper figure we have a relatively clean power system and a transformer that is powering a smallish load – a compact energy saver lamp. The lamp has a power rating of 11 watts and – so far – an apparent power intake of 20 VA. However, if the same transformer is made to carry its rated current by powering a load that consists purely of lamps of this type, the power supply characteristics will change as shown in the lower figure. While there is less relative distortion of the current profile and the apparent power drops to 15 VA, the distortion of the line voltage is substantially larger.
Even though the harmonic spectrum of the current is attenuated, it still has an effect on the transformer! Unfortunately, this experiment is rather complicated to set up in the laboratory whilst being practically impossible to perform in the field. For this reason, the measurements shown below were made using only one energy saver lamp and the resistance and the leakage reactance of the transformer windings were simulated. This nevertheless produces the same conditions as those when, for example, a 15 kVA transformer powers 1000 of such 15-VA lamps (and nothing else). Extrapolating from the single-lamp simulation to the 1000-lamp configuration then simply involves multiplying the measured current values by 1000, i.e. reading A for mA and (inversely in this case) µH for mH.
In the simulation, the transformer carried its rated current and should therefore exhibit the rated temperature rise. However in reality, eddy-current losses arise in components made of ferromagnetic materials and, most importantly, in the conductors themselves. These losses grow with the square of the current and with the square of the frequency. This quadratic dependence makes sense when one considers the fact that the stray magnetic fields of the load current induce what one might call an “eddy voltage” that drives the eddy currents perpendicular to the actual current direction. As this “eddy voltage” is proportional to the rate of change of current, so too is the (ohmic) eddy current. The eddy-current power loss, which is computed as voltage times current, is therefore proportional to the square of the rate of current change.We have now seen how a transformer interacts with its environment, especially its load. We studied the transformer’s impact upon the load and vice versa, single- and multiphase loads, balanced and unbalanced, and their effect upon the voltage, current and losses of a transformer. But these loads were all linear. Now since the widespread proliferation of non-linear loads has begun, there are new styles of mutual influence, be they of healthy or detrimental nature. Because non-linear loads are a synonym for sources of harmonic frequencies, which are higher than the transformer’s rated operating frequency, these effects have a lot to do with the leakage reactance, which rises linearly to the frequency. Let us have a look what can happen:
In the upper figure we have a relatively clean power system and a transformer that is powering a smallish load – a compact energy saver lamp. The lamp has a power rating of 11 watts and – so far – an apparent power intake of 20 VA. However, if the same transformer is made to carry its rated current by powering a load that consists purely of lamps of this type, the power supply characteristics will change as shown in the lower figure. While there is less relative distortion of the current profile and the apparent power drops to 15 VA, the distortion of the line voltage is substantially larger.
Even though the harmonic spectrum of the current is attenuated, it still has an effect on the transformer! Unfortunately, this experiment is rather complicated to set up in the laboratory whilst being practically impossible to perform in the field. For this reason, the measurements shown below were made using only one energy saver lamp and the resistance and the leakage reactance of the transformer windings were simulated. This nevertheless produces the same conditions as those when, for example, a 15 kVA transformer powers 1000 of such 15-VA lamps (and nothing else). Extrapolating from the single-lamp simulation to the 1000-lamp configuration then simply involves multiplying the measured current values by 1000, i.e. reading A for mA and (inversely in this case) µH for mH.
In the simulation, the transformer carried its rated current and should therefore exhibit the rated temperature rise. However in reality, eddy-current losses arise in components made of ferromagnetic materials and, most importantly, in the conductors themselves. These losses grow with the square of the current and with the square of the frequency. This quadratic dependence makes sense when one considers the fact that the stray magnetic fields of the load current induce what one might call an “eddy voltage” that drives the eddy currents perpendicular to the actual current direction. As this “eddy voltage” is proportional to the rate of change of current, so too is the (ohmic) eddy current. The eddy-current power loss, which is computed as voltage times current, is therefore proportional to the square of the rate of current change.
31. 31 Die Verlustleistung eines Transformators ist: Die wahre Verlustleistung eines Transformators ist: This is how we learned to quantify a transformer’s losses: The steel loss is constant, and the copper loss increases by the square of the load current. Now it is justified to assume that the input voltage equals the rating and that the steel or no-load losses therefore are constant. But a transformer’s current rating always refers to ohmic load and rated frequency, while the load current today may as well look quite different. To be precise, the formula then looks as shown here, for if the load current includes any higher frequencies, the additional losses caused by these increase by the square of the current and by the square of the frequency!This is how we learned to quantify a transformer’s losses: The steel loss is constant, and the copper loss increases by the square of the load current. Now it is justified to assume that the input voltage equals the rating and that the steel or no-load losses therefore are constant. But a transformer’s current rating always refers to ohmic load and rated frequency, while the load current today may as well look quite different. To be precise, the formula then looks as shown here, for if the load current includes any higher frequencies, the additional losses caused by these increase by the square of the current and by the square of the frequency!
32. 32 »Zusätzliche Zusatzverluste« in Transformatoren Therefore let’s now try and quantify this effect by taking a look at a simplified example. Nothing could be easier. After all the harmonisation document HD 428 provides two very plain and simple formulae for this purpose. The only catch with these equations is that you’ve got to enter numbers that are simply not normally available. In such a situation it’s probably best to calculate a made-up extreme example, since there may hardly be any worse polluters around than such 1000 lamp load, and then use the results to compute an adequate safety factor for practical applications:
Typically, about 5 to 10% of load losses in a transformer are due to eddy-current losses – assuming a 50 hertz sinusoidal current. Here in our worst case scenario, the losses are 10%. The table lists the voltages and currents associated with the various component harmonics as measured at the output of the transformer. The table can be understood as shown here:
With our 1000-lamp “rated load”, the fundamental frequency of the load current generates eddy-current losses that are 5.6% of the copper loss we have under the rated operating conditions. The third and fifth harmonics, though smaller in magnitude than the fundamental, generate eddy-current losses that are 29.5% and 24.5% respectively of the copper losses. If one adds all these eddy-current losses up to the 51st harmonic, it becomes apparent that when powering this particular load, the eddy-current losses are not 10% but 81.4% of the copper losses. Thus, if one measures the true rms rated current, the additional power loss in the transformer due to eddy currents is eight times greater than the value specified for a 50 hertz operation.Therefore let’s now try and quantify this effect by taking a look at a simplified example. Nothing could be easier. After all the harmonisation document HD 428 provides two very plain and simple formulae for this purpose. The only catch with these equations is that you’ve got to enter numbers that are simply not normally available. In such a situation it’s probably best to calculate a made-up extreme example, since there may hardly be any worse polluters around than such 1000 lamp load, and then use the results to compute an adequate safety factor for practical applications:
Typically, about 5 to 10% of load losses in a transformer are due to eddy-current losses – assuming a 50 hertz sinusoidal current. Here in our worst case scenario, the losses are 10%. The table lists the voltages and currents associated with the various component harmonics as measured at the output of the transformer. The table can be understood as shown here:
With our 1000-lamp “rated load”, the fundamental frequency of the load current generates eddy-current losses that are 5.6% of the copper loss we have under the rated operating conditions. The third and fifth harmonics, though smaller in magnitude than the fundamental, generate eddy-current losses that are 29.5% and 24.5% respectively of the copper losses. If one adds all these eddy-current losses up to the 51st harmonic, it becomes apparent that when powering this particular load, the eddy-current losses are not 10% but 81.4% of the copper losses. Thus, if one measures the true rms rated current, the additional power loss in the transformer due to eddy currents is eight times greater than the value specified for a 50 hertz operation.
33. 33 Der Trafo schützt sich in gewissem Maße selbst... Denken Sie immer daran!
Bestünde der Einfluss des Transformators auf die Last nicht, dann wäre der Einfluss der Last auf den Trafo fast 9 Mal so groß! If we had simply just extrapolated from one compact fluorescent lamp, with the transformer’s influence being negligible, to the case with 1000 lamps, we would have calculated the influence of the load upon the transformer without taking the influence of the transformer upon the load into account. Then the “supplementary additional losses” would have turned out nearly 9 times as high as they really are, about 700% of the rating instead of around 80%! Fortunately this is not so, although it remains to be considered that even at 80%, this is 8 times greater than was associated with a pure 50 hertz sine wave. But note that this substantial reduction of influence from the load upon the transformer, effected by the transformer itself, comes at the price of an increased distortion of the voltage across the transformer’s output bushings.
Well, this brings us to the end of our transformer session. For more harmonic issues please see our 3 presentations on this topic!If we had simply just extrapolated from one compact fluorescent lamp, with the transformer’s influence being negligible, to the case with 1000 lamps, we would have calculated the influence of the load upon the transformer without taking the influence of the transformer upon the load into account. Then the “supplementary additional losses” would have turned out nearly 9 times as high as they really are, about 700% of the rating instead of around 80%! Fortunately this is not so, although it remains to be considered that even at 80%, this is 8 times greater than was associated with a pure 50 hertz sine wave. But note that this substantial reduction of influence from the load upon the transformer, effected by the transformer itself, comes at the price of an increased distortion of the voltage across the transformer’s output bushings.
Well, this brings us to the end of our transformer session. For more harmonic issues please see our 3 presentations on this topic!
34. Auch hierfür gibt es ein Werkzeug: Den K-Faktor-Rechner von www.cda.org.uk
35. 35 Deutsche Leonardo Schriften 1.1 Leitfaden Netzqualität – Einführung
1.2 Selbsthilfe-Leitfaden zur Beurteilung der Netzqualität
2.1 Kosten schlechter Netzqualität
3.1 Oberschwingungen – Ursachen und Auswirkungen
3.2.2 Echt effektiv – die einzig wahre Messung
3.3.1 Passive Filter
3.3.3 Aktive Filter
3.5.1 Auslegung des Neutralleiters in oberschwingungsreichen Anlagen
4.1 Ausfallsicherheit, Zuverlässigkeit und Redundanz
4.3.1 Verbesserung der Ausfallsicherheit durch Notstrom-Versorgung
4.5.1 Ausfallsichere und zuverlässige Stromversorgung eines modernen Bürogebäudes
5.1 Spannungseinbrüche – Einführung
5.1.3 Einführung in die Unsymmetrie
5.2.1 Vorbeugende Wartung – der Schlüssel zur Netzqualität
5.3.2 Maßnahmen gegen Spannungseinbrüche
5.5.1 Vom Umgang mit Spannungseinbrüchen – eine Fallstudie
6.1 Erdung mit System
6.3.1 »Erdungssysteme – Grundlagen der Berechnung und Auslegung
36. 36 förderte im Rahmen ihres LEONARDO-Programms durch sach- kundige Partner 3 Jahre lang mit insgesamt 3 Millionen Euro die Erstellung der Internet-Seite zu allen Fragen der Netzqualität! Gehen Sie von Zeit zu Zeit auf www.lpqi.org und sehen Sie die Leonardo Power Quality Initiative wachsen!
Wir wollen in 11 Sprachen Lehrmittel zur Minderung von EMV-Problemen entwickeln und verfügbar machen!
Wir wenden uns an alle Elektro-Praktiker: Ingenieure, Handwerker, Gebäudetechniker, Architektur- und Planungsbüros sowie Auszubildende und Ausbilder.
Wir sind bisher 86 Partner aus Europa, Nord- und Südamerika, darunter Unternehmen, Institute, Hochschulen und 5 nationale Kupfer-Institute. Teilnahme und Beiträge weiterer Partner aus Industrie und Hochschulen sind jederzeit möglich und von den bisherigen Projektpartnern erwünscht.
Auf Grund dieses überragenden Erfolgs wurde das Projekt um 3 Themenbereiche erweitert. Informieren Sie sich jetzt auch auf den Gebieten Nachhaltigkeit, dezentrale Energie-Erzeugung und betreutes Wohnen: www.leonardo-energy.org
Klicken Sie rein! Die Europäische Union Now you may have been wondering what was the significance of the Leonardo logo that you have been seeing throughout this presentation. The European Union has invested a total of 3 million Euros from their Leonardo programme framework to establish the Leonardo Power Quality Initiative European website that deals with all aspects of power quality and is supported by over 90 relevant and enthusiastic partners! The programme is continually growing as you will see from visiting www.lpqi.org. Our objective is to develop and provide vocational training material on the mitigation of power quality problems in 11 languages! We are targeting all electrical experts working in the field: Engineers, designers, building maintenance technicians, architectural and planning consultants as well as trainers and trainees. To date the partners supporting the programme come from Europe, North and South America, among them commercial companies, institutes, universities and 11 national copper centres. Participation and contributions of further partners from industry and academics is possible at any time and welcomed by the existing project partners.
We would like to point out that in December 2004 the first ever Leonardo award was issued by the EU, and LPQI won 1 out of 3 prizes for the best 3 projects of the year. As this was awarded in the context of about 4000 projects that are supported every year, we are naturally very proud of this achievement. And as it is an on-going programme. This is a further reason why we urge you to have a look at the website by clicking this link.
Thank you for listening to this presentation on metering – we look forward to any feed back you wish to make to the addresses shown here.
Mr Stefan Fassbinder
Deutsches Kupferinstitut
sfassbinder@kupferinstitut.de
Tel. +49 (0)211 47963-23
Or visit the Leonardo Power Quality Initiative at http://www.lpqi.orgNow you may have been wondering what was the significance of the Leonardo logo that you have been seeing throughout this presentation. The European Union has invested a total of 3 million Euros from their Leonardo programme framework to establish the Leonardo Power Quality Initiative European website that deals with all aspects of power quality and is supported by over 90 relevant and enthusiastic partners! The programme is continually growing as you will see from visiting www.lpqi.org. Our objective is to develop and provide vocational training material on the mitigation of power quality problems in 11 languages! We are targeting all electrical experts working in the field: Engineers, designers, building maintenance technicians, architectural and planning consultants as well as trainers and trainees. To date the partners supporting the programme come from Europe, North and South America, among them commercial companies, institutes, universities and 11 national copper centres. Participation and contributions of further partners from industry and academics is possible at any time and welcomed by the existing project partners.
We would like to point out that in December 2004 the first ever Leonardo award was issued by the EU, and LPQI won 1 out of 3 prizes for the best 3 projects of the year. As this was awarded in the context of about 4000 projects that are supported every year, we are naturally very proud of this achievement. And as it is an on-going programme. This is a further reason why we urge you to have a look at the website by clicking this link.
Thank you for listening to this presentation on metering – we look forward to any feed back you wish to make to the addresses shown here.
Mr Stefan Fassbinder
Deutsches Kupferinstitut
sfassbinder@kupferinstitut.de
Tel. +49 (0)211 47963-23
Or visit the Leonardo Power Quality Initiative at http://www.lpqi.org
