Showing posts with label Transformer Losses. Show all posts
Showing posts with label Transformer Losses. Show all posts
POWER TRANSFORMER RATING, LOSSES AND EFFICIENCY BASIC INFORMATION
Power transformer capacity is rated in kilovolt-amperes (kVA). The output rating for a transformer is determined by the maximum current that the transformer can withstand without exceeding its stated temperature limits.
Power in an AC circuit depends on the power factor of the load and the current, so if any AC electrical equipment is rated in kilowatts, a power factor must be included to make its power rating meaningful. To avoid this, transformers and most AC machines are rated in kVA, a unit that is independent of power factor.
In addition to its kVA rating, the nameplates of transformers typically include the manufacturer’s type and serial number, the voltage ratings of both high- and low voltage windings, the rated frequency, and the impedance drop expressed as a percentage of rated voltage. Some nameplates also include an electrical connection diagram.
Power transformers are generally defined as those used to transform higher power levels than distribution transformers (usually over 500 kVA or more than 67 kV). The kVA terminal voltages and currents of power transformers, defined in ANSI C57.12.80, are all based on the rated winding voltages at no-load conditions.
However, the actual primary voltage in service must be higher than the rated value by the amount
of regulation if the transformer is to deliver the rated voltage to the load on the secondary.
TRANSFORMER LOSSES AND EFFICIENCY
The efficiency of all power transformers is high, but efficiency is highest for large transformers operating at 50 to 100 percent of full load. However, some losses are present in all transformers. They are classified as copper or I2R losses and core losses.
Copper losses, also called load losses, are proportional to the load being supplied by the transformer. These losses can be calculated for a given load if the resistances of both windings are known. As in generators and motors, the core loss is due to eddy-current induction loss and hysteresis (molecular friction) loss, caused by the changing polarity of the applied AC.
If the cores are laminated from low-loss silicon steel, both eddy-current and hysteresis losses will be reduced. Nevertheless, well-designed transformers in all frequency and power ranges typically have efficiencies of 90 percent or more.
CALCULATING TRANSFORMER LOSS OF LIFE BASIC AND TUTORIALS
Industry standards also address the loss of life of a transformer due to temperature and aging. The relation of insulation aging to time and temperature follows the well-known Arrhenius chemical reaction rate model.
The adaptation used in the IEEE standard [3] has the following form. Per unit life = Ae^[B/(θH 273)] where θH winding hot-spot temperature in °C, and A and B are constants.
The meaning of per unit life is illustrated as follows: If per unit life = 2, then the transformer would be expected to last twice the ‘‘normal’’ life. If per unit life = 0.5, then the transformer would be expected to last only half the ‘‘normal’’ life. Normal life for most transformers is considered to be around 30 to 40 years.
The constants A and B depend on the types of material used to insulate the windings. Since cellulose in the form of kraft paper is the most common insulation material, these constants have been worked out empirically:
Per unit life = 9.8 10 18e15000/(θH 273) (3.14.2)
The winding hot-spot design temperature to attain a normal life is 110°C. This is based on an assumed ambient temperature of 30° plus the 65°C average winding temperature gradient over ambient plus a 15°C allowance for the hotspot gradient over the average winding temperature.
Using θH = 110°C yields a per unit life = 1. The aging acceleration factor FAA is the ratio of the per unit life at the design temperature of 110°C divided by the per unit life at some operating temperature θH. The constant A then divides out:
FAA = e15000/383 15000/(θH 273) = e39.16 15000/(θH 273)
To calculate the equivalent aging of the transformer FEQA with a varying hot-spot temperature such as occurs for a cycling load or a seasonal ambient temperature, FAA is integrated over time and the integral is divided by the total time to obtain the average.
The per unit life and FAA are plotted vs. hot-spot temperature in the chart shown in Figure below.
The per unit life and the aging acceleration factor as a function of
the hot-spot temperature.
It should be stressed that most transformer failures are random events that occur for various reasons besides insulation loss of life. Therefore, the formula for per unit life cannot be used as a predictive model to determine when a given transformer will ultimately fail.
However, it is indeed certain that overloading a transformer will shorten its life, so it is a good practice from a reliability standpoint to keep the loading within the transformer’s thermal capability.
MEASUREMENT OF TRANSFORMER NO LOAD LOSSES BASIC INFORMATION
Measuring no-load losses of a transformer when subjected to
a sinusoidal voltage waveform can be achieved simply by using a wattmeter and a
voltmeter; refer to Figure 1. Transformers may be subjected to a distorted
sine-wave voltage.
In order to achieve the required measuring accuracy, the
instrumentation used should accurately respond to the power frequency harmonics
encountered in these measurements. Also, measured values need to be corrected to
account for the effect of the voltage harmonics on the magnetic flux in the
core and hence on both the hysteresis and eddy current loss components of iron
losses.
The hysteresis loss component is a function of the maximum
flux density in the core, practically independent of the waveform of the flux.
The maximum flux density corresponds to the average value of the voltage (not
the rms value), and, therefore, if the test voltage is adjusted to be the same
as the average value of the desired sine wave of the voltage the hysteresis
loss component will be equal to the desired sine wave value.
The average-voltage voltmeter method as illustrated in
Figure 1 utilizes an averagevoltage responding voltmeter based on a full-wave
rectification. These instruments are generally scaled to give the same
indication as a rms voltmeter on a sine-wave voltage.
The figure shows the necessary equipment and connections
when no instrument transformers are needed. As indicated in Figure 1, the
voltmeters should be connected across the winding, the ammeter nearest to the
supply, and wattmeter between the two; with its voltage coil on the winding
side of the current coil.
NOTE
‘F’ is a frequency meter
‘A’ is an ammeter
‘W’ is a wattmeter
‘V’ is a true rms voltmeter
‘AV’ is an average-responding, rmscalibrated voltmeter
The eddy-current loss component of the core loss varies
approximately with the square of the rms value of the core flux. When the test
voltage is held at rated voltage with the average-voltage voltmeter, the actual
rms value of the test voltage is generally not equal to the rated value.
The eddy-current loss in this case will be related to the
correct eddy-current loss at rated voltage by a factor k given in Equation 8.2,
Clause 8 of the IEEE Std. C57.12.90-1993 and C57.12.91-1979 Standard. This is
only correct for a reasonably distorted voltage wave.
THE NATURE OF TRANSFORMER LOSSES BASIC INFORMATION
Transformer losses are broadly classified as no-load and load losses. No load losses occur when the transformer is energized with its rated voltage at one set of terminals but the other sets of terminals are open circuited so that no through or load current flows.
In this case, full flux is present in the core and only the necessary exciting current flows in the windings. The losses are predominately core losses due to hysteresis and eddy currents produced by the time varying flux in the core steel.
Load losses occur when the output is connected to a load so that current flows through the transformer from input to output terminals. Although core losses also occur in this case, they are not considered part of the load losses.
When measuring load losses, the output terminals are shorted to ground and only a small impedance related voltage is necessary to produce the desired full load current. In this case, the core losses are small because of the small core flux and do not significantly add to the measured losses.
Load losses are in turn broadly classified as I2R losses due to Joule heating produced by current flow in the coils and as stray losses due to the stray flux as it encounters metal objects such as tank walls, clamps or bracing structures, and the coils themselves. Because the coil conductors are often stranded and transposed, the I2R losses are usually determined by the d.c. resistance of the windings.
The stray losses depend on the conductivity, permeability, and shape of the metal object encountered. These losses are primarily due to induced eddy currents in these objects.
Even though the object may be made of ferromagnetic material, such as the tank walls and clamps, their dimensions are such that hysteresis losses tend to be small relative to eddy current losses.
Although losses are usually a small fraction of the transformed power (<0.5% in large power transformers), they can produce localized heating which can compromise the operation of the transformer. Thus it is important to understand how these losses arise and to calculate them as accurately as possible so that, if necessary steps can be taken at the design stage to reduce them to a level which can be managed by the cooling system.
Other incentives, such as the cost which the customer attaches to the losses, can make it worthwhile to find ways of lowering the losses. Modern methods of analysis, such as finite element or boundary element methods, have facilitated the calculation of stray flux losses in complex geometries.
These methods are not yet routine in design because they require a fair amount of geometric input for each new geometry. They can, however, provide useful insights in cases where analytic methods are not available or are very crude. Occasionally a parametric study using such methods can extend their usefulness beyond a specialized geometry.
POWER TRANSFORMER SERIES IMPEDANCE AND REGULATION BASIC AND TUTORIALS
The series impedance of a transformer consists of a resistance that accounts for the load losses and a reactance that represents the leakage reactance. This impedance has a very low power factor, consisting almost entirely of leakage reactance with only a small resistance.
As discussed earlier, the transformer design engineer can control the leakage reactance by varying the spacing between the windings. Increasing the spacing ‘‘decouples’’ the windings and allows more leakage flux to circulate between the windings, increasing the leakage reactance.
While leakage reactance can be considered a transformer loss because it consumes reactive power, some leakage reactance is necessary to limit fault currents. On the other hand, excessive leakage reactance can cause problems with regulation.
Regulation is often defined as the drop in secondary voltage when a load is applied, but regulation is more correctly defined as the increase in secondary output voltage when the load is removed. The reason that regulation is defined this way is that transformers are considered to be ‘‘fully loaded’’ when the secondary output voltage is at the rated secondary voltage.
This requires the primary voltage to be greater than the rated primary voltage at full load.
Let Ep equal the primary voltage and let Es equal the secondary voltage when the transformer is fully loaded. Using per-unit values instead of primary and secondary voltage values, the per-unit secondary voltage will equal Ep with the load removed. Therefore, the definition of regulation can be expressed by the following equations.
Regulation = (Ep - Es)/ Es
Since Es = 1 by definition,
Regulation Ep - 1 (3.8.2)
Regulation depends on the power factor of the load. For a near-unity power
factor, the regulation is much smaller than the regulation for an inductive load
with a small lagging power factor.
Example 3.4
A three-phase 1500 KVA 12470Y-208Y transformer has a 4.7% impedance. Calculate the three-phase fault current at the secondary output with the primary connected to a 12,470 V infinite bus. Calculate the regulation for a power factor of 90% at full load.
The three-phase fault is a balanced fault, so the positive-sequence equivalent circuit applies. The full-load secondary current is calculated as follows:
I 1.732 500,000 VA per phase/208 V 4167 A per phase
The per-unit fault current is the primary voltage divided by the series impedance:
1/0.047 = 21.27 per unit
The secondary fault current is equal to the per-unit fault current times the fullload current:
If 21.27 per unit 4167 A per phase 88,632 A per phase To calculate regulation, the secondary voltage is 1∠0° per unit by definition.
Applying a 1 per unit load at a 90% lagging power factor, I 1.0∠ 25.8°. Since the series impedance is mainly inductive, the primary voltage at full load Ep can be calculated as follows:
Ep 1∠0° + 1.0∠ 25.8° X 0.047∠90°
1.02 + j0.042 = 1.021 per unit
Regulation = Ep - 1 = 0.021 = 2.1%
HIGH PERMEABILITY STEEL USED IN TRANSFORMER CORE BASIC INFORMATION
Use of cold-rolled grain-oriented steel as described above continued with only steady refinement and improvement in the production process until the late 1960s.
However, in 1965 the Japanese Nippon Steel Corporation announced a step-change in the quality of their electrical steel: high-permeability grainoriented silicon steel.
Production is simplified by the elimination of one of the coldrolling stages because of the introduction of around 0.025% of aluminium to the melt and the resulting use of aluminium nitride as a growth inhibitor.
The final product has a better orientation than cold-rolled grain-oriented steel (in this context, generally termed ‘conventional’ steel), with most grains aligned within 3° of the ideal, but the grain size, average 1 cm diameter, was very large compared to the 0.3 mm average diameter of conventional material.
At flux densities of 1.7 T and higher, its permeability was three times higher than that of the best conventional steel, and the stress sensitivity of loss and magnetostriction were lower because of the improved orientation and the presence of a high tensile stress introduced by the so-called stress coating.
The stress coating imparts a tensile stress to the material which helps to reduce eddy-current loss which would otherwise be high in a large-grain material.
The total loss is further offset by some reduction in hysteresis loss due to the improved coating. However, the low losses of high-permeability steels are mainly due to a reduction of 30 40% in hysteresis brought about by the improved grain orientation.
The Nippon Steel Corporation product became commercially available in 1968, and it was later followed by\ high-permeability materials based MnSe plus Sb (Kawasaki Steel, 1973) and Boron (Allegheny Ludlum Steel Corporation, 1975).
TRANSFORMER NO LOAD LOSSES BASICS AND TUTORIALS
TRANSFORMER NO LOAD LOSSES BASIC INFORMATION
What Are The Transformer No Load Losses?
Alternating magnetic flux produces both hysteresis losses and eddy-current losses in the steel. As we have seen, hysteresis losses depend on several factors including the frequency, the peak flux density, the type of core steel used, and the orientation of the flux with respect to the ‘‘grain’’ of the steel.
All of the above factors, except the frequency, are under the control of the transformer designer. Core losses are sometimes referred to as iron losses and are commonly referred to as no load losses, because core losses do not require load currents.
Decreasing the induced voltage per turn can reduce the peak flux density. This obviously involves increasing the numbers of turns in both the primary and secondary windings in order to maintain the same transformer turns ratio.
The disadvantage of adding more turns is that this increases the length of conductor and increases the conductor resistance. More cross sectional area is required in order to keep the resistance constant.
Doubling the number of turns requires about four times the volume of copper. Another way of reducing core losses is to use various types of low-loss core steels that are now available, including ‘‘amorphous’’ core materials, which have extremely low losses and superior magnetic properties.
Unfortunately, amorphous core materials have ceramic-like properties, so fabricating transformer cores with these materials is much more difficult than with laminated steel cores.
With grain-oriented steel, the direction of the core flux must be kept more or less parallel to the grain of the steel by mitering the corners of the laminations where the flux changes direction by 90°. Since the flux will cross the grain at about a 45° angle at the mitered edges, the hysteresis losses will increase somewhat in these places.
These additional localized core losses must be factored into the calculation of the total core losses. Building up the core with thin laminated strips controls eddy losses in the core, each strip having an oxide film applied to the surface.
The oxide film is extremely thin and it is more like a high-resistance film than true electrical insulation; but since the potential differences between adjacent laminations is quite small, the resistance of the oxide film is very effective in breaking up the eddy current paths.
During the manufacture of the core, the core cutting machine must not be allowed to get dull; otherwise, ‘‘burrs’’ will form along the edges of the laminations. Burrs are imperfections that form electrical bridges between the laminations and create paths for eddy currents and increased losses.
Sometimes the eddy currents near a burr can be large enough to cause localized overheating that can actually cause core damage. Core losses are approximately proportional to the square of the excitation voltage E applied to the transformer.
Therefore, placing an equivalent linear conductance Gm across the transformer terminals can approximate transformer core losses. The core losses are expressed by Wm = E^2Gm
What Are The Transformer No Load Losses?
Alternating magnetic flux produces both hysteresis losses and eddy-current losses in the steel. As we have seen, hysteresis losses depend on several factors including the frequency, the peak flux density, the type of core steel used, and the orientation of the flux with respect to the ‘‘grain’’ of the steel.
All of the above factors, except the frequency, are under the control of the transformer designer. Core losses are sometimes referred to as iron losses and are commonly referred to as no load losses, because core losses do not require load currents.
Decreasing the induced voltage per turn can reduce the peak flux density. This obviously involves increasing the numbers of turns in both the primary and secondary windings in order to maintain the same transformer turns ratio.
The disadvantage of adding more turns is that this increases the length of conductor and increases the conductor resistance. More cross sectional area is required in order to keep the resistance constant.
Doubling the number of turns requires about four times the volume of copper. Another way of reducing core losses is to use various types of low-loss core steels that are now available, including ‘‘amorphous’’ core materials, which have extremely low losses and superior magnetic properties.
Unfortunately, amorphous core materials have ceramic-like properties, so fabricating transformer cores with these materials is much more difficult than with laminated steel cores.
With grain-oriented steel, the direction of the core flux must be kept more or less parallel to the grain of the steel by mitering the corners of the laminations where the flux changes direction by 90°. Since the flux will cross the grain at about a 45° angle at the mitered edges, the hysteresis losses will increase somewhat in these places.
These additional localized core losses must be factored into the calculation of the total core losses. Building up the core with thin laminated strips controls eddy losses in the core, each strip having an oxide film applied to the surface.
The oxide film is extremely thin and it is more like a high-resistance film than true electrical insulation; but since the potential differences between adjacent laminations is quite small, the resistance of the oxide film is very effective in breaking up the eddy current paths.
During the manufacture of the core, the core cutting machine must not be allowed to get dull; otherwise, ‘‘burrs’’ will form along the edges of the laminations. Burrs are imperfections that form electrical bridges between the laminations and create paths for eddy currents and increased losses.
Sometimes the eddy currents near a burr can be large enough to cause localized overheating that can actually cause core damage. Core losses are approximately proportional to the square of the excitation voltage E applied to the transformer.
Therefore, placing an equivalent linear conductance Gm across the transformer terminals can approximate transformer core losses. The core losses are expressed by Wm = E^2Gm
TRANSFORMER HEATING BASICS AND TUTORIALS
TRANSFORMER HEATING BASIC INFORMATION
Why There Is Transformer Heating?
In a real transformer, some power is dissipated in the form of heat. A portion of these power losses occur in the conductor windings due to electrical resistance and are referred to as copper losses.
However, so-called iron losses from the transformer core are also important. The latter result from the rapid change of direction of the magnetic field, which means that the microscopic iron particles must continually realign themselves—technically, their magnetic moment—in the direction of the field (or flux).
Just as with the flow of charge, this realignment encounters friction on the microscopic level and therefore dissipates energy, which becomes tangible as heating of the material.
Taking account of both iron and copper losses, the efficiency (or ratio of electrical power out to electrical power in) of real transformers can be in the high 90% range. Still, even a small percentage of losses in a large transformer corresponds to a significant amount of heat that must be dealt with.
In the case of small transformers inside typical household adaptors for low-voltage d.c. appliances, we know that they are warm to the touch.
Yet they transfer such small quantities of power that the heat is easily dissipated into the ambient air (bothering only conservatio nminded analysts, who note the energy waste that could be avoided by unplugging all these adaptors when not in use).
By contrast, suppose a 10-MVA transformer at a distribution substation operates at an efficiency of 99%: A 1% loss here corresponds to a staggering 100 kW.
In general, smaller transformers like those on distribution poles are passively cooled by simply radiating heat away to their surroundings, sometimes assisted by radiator vanes that maximize the available surface area for removing the heat.
Large transformers like those at substations or power plants require the heat to be removed from the core and windings by active cooling, generally through circulating oil that simultaneously functions as an electrical insulator.
The capacity limit of a transformer is dictated by the rate of heat dissipation. Thus, as is true for power lines, the ability to load a transformer depends in part on ambient conditions including temperature, wind, and rain.
For example, if a transformer appears to be reaching its thermal limit on a hot day, one way to salvage the situation is to hose down its exterior with cold water—a procedure that is not “by the book,” but has been reported to work in emergencies.
When transformers are operated near their capacity limit, the key variable to monitor is the internal or oil temperature. This task is complicated by the problem that the temperature may not be uniform throughout the inside of the transformer, and damage can be done by just a local hot spot. Under extreme heat, the oil can break down, sustain an electric arc, or even burn, and a transformer may explode.
A cooling and insulating fluid for transformers has to meet criteria similar to those for other high-voltage equipment, such as circuit breakers and capacitors: it must conduct heat but not electricity; it must not be chemically reactive; and it must not be easily ionized, which would allow arcs to form.
Mineral oil meets these criteria fairly well, since the long, nonpolar molecules do not readily break apart under an electric field.
Another class of compounds that performs very well and has been in widespread use for transformers and other equipment is polychlorinated biphenyls, commonly known as PCBs.
Because PCBs and the dioxins that contaminate them were found to be carcinogenic and ecologically toxic and persistent, they are no longer manufactured in the United States; the installation of new PCB-containing utility equipment has been banned since 1977.
However, much of the extant hardware predates this phase-out and is therefore subject to careful maintenance and disposal procedures (somewhat analogous to asbestos in buildings).
Introduced in the 1960s, sulfur hexafluoride (SF6) is another very effective arcextinguishing fluid for high-voltage equipment. SF6 has the advantage of being reasonably nontoxic as well as chemically inert, and it has a superior ability to withstand electric fields without ionizing.
While the size of transformers and capacitors is constrained by other factors, circuit breakers can be made much smaller with SF6 than traditional oil-filled breakers.
However, it turns out that SF6 absorbs thermal infrared radiation and thus acts as a greenhouse gas when it escapes into the atmosphere; it is included among regulated substances in the Kyoto Protocol on global climate change.
SF6 in the atmosphere also appears to form another compound by the name of trifluoromethyl sulfur pentafluoride (SF5CF3), an even more potent greenhouse gas whose atmospheric concentration is rapidly increasing. This surprising and unfortunate characteristic may motivate future restriction of SF6 use.
Why There Is Transformer Heating?
In a real transformer, some power is dissipated in the form of heat. A portion of these power losses occur in the conductor windings due to electrical resistance and are referred to as copper losses.
However, so-called iron losses from the transformer core are also important. The latter result from the rapid change of direction of the magnetic field, which means that the microscopic iron particles must continually realign themselves—technically, their magnetic moment—in the direction of the field (or flux).
Just as with the flow of charge, this realignment encounters friction on the microscopic level and therefore dissipates energy, which becomes tangible as heating of the material.
Taking account of both iron and copper losses, the efficiency (or ratio of electrical power out to electrical power in) of real transformers can be in the high 90% range. Still, even a small percentage of losses in a large transformer corresponds to a significant amount of heat that must be dealt with.
In the case of small transformers inside typical household adaptors for low-voltage d.c. appliances, we know that they are warm to the touch.
Yet they transfer such small quantities of power that the heat is easily dissipated into the ambient air (bothering only conservatio nminded analysts, who note the energy waste that could be avoided by unplugging all these adaptors when not in use).
By contrast, suppose a 10-MVA transformer at a distribution substation operates at an efficiency of 99%: A 1% loss here corresponds to a staggering 100 kW.
In general, smaller transformers like those on distribution poles are passively cooled by simply radiating heat away to their surroundings, sometimes assisted by radiator vanes that maximize the available surface area for removing the heat.
Large transformers like those at substations or power plants require the heat to be removed from the core and windings by active cooling, generally through circulating oil that simultaneously functions as an electrical insulator.
The capacity limit of a transformer is dictated by the rate of heat dissipation. Thus, as is true for power lines, the ability to load a transformer depends in part on ambient conditions including temperature, wind, and rain.
For example, if a transformer appears to be reaching its thermal limit on a hot day, one way to salvage the situation is to hose down its exterior with cold water—a procedure that is not “by the book,” but has been reported to work in emergencies.
When transformers are operated near their capacity limit, the key variable to monitor is the internal or oil temperature. This task is complicated by the problem that the temperature may not be uniform throughout the inside of the transformer, and damage can be done by just a local hot spot. Under extreme heat, the oil can break down, sustain an electric arc, or even burn, and a transformer may explode.
A cooling and insulating fluid for transformers has to meet criteria similar to those for other high-voltage equipment, such as circuit breakers and capacitors: it must conduct heat but not electricity; it must not be chemically reactive; and it must not be easily ionized, which would allow arcs to form.
Mineral oil meets these criteria fairly well, since the long, nonpolar molecules do not readily break apart under an electric field.
Another class of compounds that performs very well and has been in widespread use for transformers and other equipment is polychlorinated biphenyls, commonly known as PCBs.
Because PCBs and the dioxins that contaminate them were found to be carcinogenic and ecologically toxic and persistent, they are no longer manufactured in the United States; the installation of new PCB-containing utility equipment has been banned since 1977.
However, much of the extant hardware predates this phase-out and is therefore subject to careful maintenance and disposal procedures (somewhat analogous to asbestos in buildings).
Introduced in the 1960s, sulfur hexafluoride (SF6) is another very effective arcextinguishing fluid for high-voltage equipment. SF6 has the advantage of being reasonably nontoxic as well as chemically inert, and it has a superior ability to withstand electric fields without ionizing.
While the size of transformers and capacitors is constrained by other factors, circuit breakers can be made much smaller with SF6 than traditional oil-filled breakers.
However, it turns out that SF6 absorbs thermal infrared radiation and thus acts as a greenhouse gas when it escapes into the atmosphere; it is included among regulated substances in the Kyoto Protocol on global climate change.
SF6 in the atmosphere also appears to form another compound by the name of trifluoromethyl sulfur pentafluoride (SF5CF3), an even more potent greenhouse gas whose atmospheric concentration is rapidly increasing. This surprising and unfortunate characteristic may motivate future restriction of SF6 use.
TRANSFORMER LOSSES DEFINITION BASIC AND TUTORIALS
TRANSFORMER LOSSES COMPONENTS TUTORIALS
What Are Transformer Losses Components?
Transformer Losses is a natural occurrence in the Power System Cycle. Below are the different components of the Transformer Losses.
No-Load Loss and Exciting Current
When alternating voltage is applied to a transformer winding, an alternating magnetic flux is induced in the core. The alternating flux produces hysteresis and eddy currents within the electrical steel, causing heat to be generated in the core. Heating of the core due to applied voltage is called no-load loss.
Other names are iron loss or core loss. The term “no-load” is descriptive because the core is heated regardless of the amount of load on the transformer. If the applied voltage is varied, the no-load loss is very roughly proportional to the square of the peak voltage, as long as the core is not taken into saturation.
The current that flows when a winding is energized is called the “exciting current” or “magnetizing current,” consisting of a real component and a reactive component. The real component delivers power for no-load losses in the core.
The reactive current delivers no power but represents energy momentarily stored in the winding inductance. Typically, the exciting current of a distribution transformer is less than 0.5% of the rated current of the winding that is being energized.
Load Loss
A transformer supplying load has current flowing in both the primary and secondary windings that will produce heat in those windings. Load loss is divided into two parts, I2R loss and stray losses.
I2R Loss
Each transformer winding has an electrical resistance that produces heat when load current flows. Resistance of a winding is measured by passing dc current through the winding to eliminate inductive effects.
Stray Losses
When alternating current is used to measure the losses in a winding, the result is always greater than the I2R measured with dc current. The difference between dc and ac losses in a winding is called “stray loss.”
One portion of stray loss is called “eddy loss” and is created by eddy currents circulating in the winding conductors. The other portion is generated outside of the windings, in frame members, tank walls, bushing flanges, etc.
Although these are due to eddy currents also, they are often referred to as “other strays.” The generation of stray losses is sometimes called “skin effect” because induced eddy currents tend to flow close to the surfaces of the conductors.
Stray losses are proportionally greater in larger transformers because their higher currents require larger conductors. Stray losses tend to be proportional to current frequency, so they can increase dramatically when loads with high-harmonic currents are served. The effects can be reduced by subdividing large conductors and by using stainless steel or other nonferrous materials for frame parts and bushing plates.
Harmonics and DC Effects
Rectifier and discharge-lighting loads cause currents to flow in the distribution transformer that are not pure power-frequency sine waves. Using Fourier analysis, distorted load currents can be resolved into components that are integer multiples of the power frequency and thus are referred to as harmonics. Distorted load currents are expected to be high in the 3rd, 5th, 7th, and sometimes the 11th and 13th harmonics, depending on the character of the load.
Odd-Ordered Harmonics
Load currents that contain the odd-numbered harmonics will increase both the eddy losses and other stray losses within a transformer. If the harmonics are substantial, then the transformer must be derated to prevent localized and general overheating.
ANSI standards suggest that any transformer with load current containing more than 5% total harmonic distortion should be loaded according to the appropriate ANSI guide (IEEE, 1998).
Even-Ordered Harmonics
Analysis of most harmonic currents will show very low amounts of even harmonics (2nd, 4th, 6th, etc.) Components that are even multiples of the fundamental frequency generally cause the waveform to be nonsymmetrical about the zero-current axis.
The current therefore has a zeroth harmonic or dc-offset component. The cause of a dc offset is usually found to be half-wave rectification due to a defective rectifier or other component. The effect of a significant dc current offset is to drive the transformer core into saturation on alternate half-cycles.
When the core saturates, exciting current can be extremely high, which can then burn out the primary winding in a very short time. Transformers that are experiencing dc-offset problems are usually noticed because of objectionably loud noise coming from the core structure.
Industry standards are not clear regarding the limits of dc offset on a transformer. A recommended value is a dc current no larger than the normal exciting current, which is usually 1% or less of a winding’s rated current (Galloway, 1993).
What Are Transformer Losses Components?
Transformer Losses is a natural occurrence in the Power System Cycle. Below are the different components of the Transformer Losses.
No-Load Loss and Exciting Current
When alternating voltage is applied to a transformer winding, an alternating magnetic flux is induced in the core. The alternating flux produces hysteresis and eddy currents within the electrical steel, causing heat to be generated in the core. Heating of the core due to applied voltage is called no-load loss.
Other names are iron loss or core loss. The term “no-load” is descriptive because the core is heated regardless of the amount of load on the transformer. If the applied voltage is varied, the no-load loss is very roughly proportional to the square of the peak voltage, as long as the core is not taken into saturation.
The current that flows when a winding is energized is called the “exciting current” or “magnetizing current,” consisting of a real component and a reactive component. The real component delivers power for no-load losses in the core.
The reactive current delivers no power but represents energy momentarily stored in the winding inductance. Typically, the exciting current of a distribution transformer is less than 0.5% of the rated current of the winding that is being energized.
Load Loss
A transformer supplying load has current flowing in both the primary and secondary windings that will produce heat in those windings. Load loss is divided into two parts, I2R loss and stray losses.
I2R Loss
Each transformer winding has an electrical resistance that produces heat when load current flows. Resistance of a winding is measured by passing dc current through the winding to eliminate inductive effects.
Stray Losses
When alternating current is used to measure the losses in a winding, the result is always greater than the I2R measured with dc current. The difference between dc and ac losses in a winding is called “stray loss.”
One portion of stray loss is called “eddy loss” and is created by eddy currents circulating in the winding conductors. The other portion is generated outside of the windings, in frame members, tank walls, bushing flanges, etc.
Although these are due to eddy currents also, they are often referred to as “other strays.” The generation of stray losses is sometimes called “skin effect” because induced eddy currents tend to flow close to the surfaces of the conductors.
Stray losses are proportionally greater in larger transformers because their higher currents require larger conductors. Stray losses tend to be proportional to current frequency, so they can increase dramatically when loads with high-harmonic currents are served. The effects can be reduced by subdividing large conductors and by using stainless steel or other nonferrous materials for frame parts and bushing plates.
Harmonics and DC Effects
Rectifier and discharge-lighting loads cause currents to flow in the distribution transformer that are not pure power-frequency sine waves. Using Fourier analysis, distorted load currents can be resolved into components that are integer multiples of the power frequency and thus are referred to as harmonics. Distorted load currents are expected to be high in the 3rd, 5th, 7th, and sometimes the 11th and 13th harmonics, depending on the character of the load.
Odd-Ordered Harmonics
Load currents that contain the odd-numbered harmonics will increase both the eddy losses and other stray losses within a transformer. If the harmonics are substantial, then the transformer must be derated to prevent localized and general overheating.
ANSI standards suggest that any transformer with load current containing more than 5% total harmonic distortion should be loaded according to the appropriate ANSI guide (IEEE, 1998).
Even-Ordered Harmonics
Analysis of most harmonic currents will show very low amounts of even harmonics (2nd, 4th, 6th, etc.) Components that are even multiples of the fundamental frequency generally cause the waveform to be nonsymmetrical about the zero-current axis.
The current therefore has a zeroth harmonic or dc-offset component. The cause of a dc offset is usually found to be half-wave rectification due to a defective rectifier or other component. The effect of a significant dc current offset is to drive the transformer core into saturation on alternate half-cycles.
When the core saturates, exciting current can be extremely high, which can then burn out the primary winding in a very short time. Transformers that are experiencing dc-offset problems are usually noticed because of objectionably loud noise coming from the core structure.
Industry standards are not clear regarding the limits of dc offset on a transformer. A recommended value is a dc current no larger than the normal exciting current, which is usually 1% or less of a winding’s rated current (Galloway, 1993).
POOR POWER QUALITY (PQ) EFFECTS ON TRANSFORMERS BASIC AND TUTORIALS
EFFECT OF POOR POWER QUALITY ON TRANSFORMERS BASIC INFORMATION
What Are The Effects Of Poor Power Quality To Transformers?
Presence of harmonic current increases the core losses, copper losses, and stray-flux losses in a transformer. These losses consist of ‘no load losses’ and ‘load losses’. No load loss is affected mainly by voltage harmonics, although the increase of this loss with harmonics is small. It consists of two components: hysteresis loss (due to non-linearity of the transformers) and eddy current loss (varies in proportion to the square of frequency).
The load losses of a transformer vary with the square of load current and increase sharply at high harmonic frequencies. They consist of three components:
• Resistive losses in the winding conductors and leads
• Eddy current losses in the winding conductors
• Eddy current losses in the tanks and structural steelwork
Eddy current losses are of large concern when harmonic current is present in the network. These losses increase approximately with the square of frequency. Total eddy current losses are normally about 10% of the losses at full load. Equation (1) gives total load losses (PT) of a transformer when harmonics are present in the network [Hulshorst & Groeman, 2002].
What Are The Effects Of Poor Power Quality To Transformers?
Presence of harmonic current increases the core losses, copper losses, and stray-flux losses in a transformer. These losses consist of ‘no load losses’ and ‘load losses’. No load loss is affected mainly by voltage harmonics, although the increase of this loss with harmonics is small. It consists of two components: hysteresis loss (due to non-linearity of the transformers) and eddy current loss (varies in proportion to the square of frequency).
The load losses of a transformer vary with the square of load current and increase sharply at high harmonic frequencies. They consist of three components:
• Resistive losses in the winding conductors and leads
• Eddy current losses in the winding conductors
• Eddy current losses in the tanks and structural steelwork
Eddy current losses are of large concern when harmonic current is present in the network. These losses increase approximately with the square of frequency. Total eddy current losses are normally about 10% of the losses at full load. Equation (1) gives total load losses (PT) of a transformer when harmonics are present in the network [Hulshorst & Groeman, 2002].
Where,
PCU = total copper loss
PWE = eddy current losses at 50Hz (full load)
PCE1 = additional eddy current losses at 50Hz (full load)
PSE1 = stray losses in construction parts at 50Hz (full load)
In = rms current (per unit) at harmonic ‘n’
IL = total rms value of the load current (per unit)
I1 = fundamental component of load current (per unit) at 50Hz frequency
n = harmonic number
Other concern is the presence of ‘triple-n’ harmonics. In a network, mainly the LV nonlinear loads produce harmonics. With a MV/LV transformer of Δ/Y configuration, ‘triple-n’ currents circulate in the closed delta winding. Only the ‘non triple-n’ harmonics pass to the upstream network.
When supplying non-linear loads, transformers are vulnerable to overheating. To minimize the risk of premature failure of transformers, they can either be de-rated or use as ‘K-rated’ transformer which are designed to operate with low losses at harmonic frequencies. Increased loading can cause overstressing of transformer and the chance of its premature failure.
This effect is usually expressed in terms of ‘loss of lifetime’. The hot-spot temperature is used for evaluation of a relative value for the rate of thermal ageing as shown in Fig. 4.
It is taken as unity for a hot-spot temperature of 98oC with the assumption of an ambient temperature of 20oC and hot-spot temperature rise of 78oC. Equation (2) shows the calculation of relative ageing rate (V) as a function of hot-spot temperature θh [Najdenkoski et al., 2007].
TRANSFORMER ZERO SEQUENCE IMPEDANCE BASICS AND TUTORIALS
ZERO SEQUENCE OF TRANSFORMERS BASIC INFORMATION
What Is The Zero Sequence of Transformers?
It is usual in performing system design calculations, particularly those involving unbalanced loadings and for system earth fault conditions, to use the principle of symmetrical components. This system is described and and ascribes positive, negative and zero-sequence impedance values to the components of the electrical system.
For a three-phase transformer, the positive and negative sequence impedance values are identical to that value described above, but the zero-sequence impedance varies considerably according to the construction of the transformer and the presence, or otherwise, of a delta winding.
The zero-sequence impedance of a star winding will be very high if no delta winding is present. The actual value will depend on whether there is a low reluctance return path for the third-harmonic flux.
For three-limb designs without a delta, where the return-flux path is through the air, the determining feature is usually the tank, and possibly the core support framework, where this flux creates a circulating current around the tank and/or core framework.
The impedance of such winding arrangements is likely to be in the order of 75 to 200% of the positive-sequence impedance between primary and secondary windings. For five-limb cores and three-phase banks of single-phase units, the zero-sequence impedance will be the magnetising impedance for the core configuration.
Should a delta winding exist, then the third harmonic flux will create a circulating current around the delta, and the zero-sequence impedance is determined by the leakage field between the star and the delta windings. Again the type of core will influence the magnitude of the impedance because of the effect it has on the leakage field between the windings.
Typical values for threelimb transformers having a winding configuration of core/tertiary/star LV/star HV are:
[Z0]LV approximately equal to 80 to 90% of positive-sequence impedance LV/tertiary
[Z0]HV approximately equal to 85 to 95% of positive-sequence impedance HV/tertiary
where Z0 = zero-sequence impedance.
Five-limb transformers have their zero-sequence impedances substantially equal to their positive-sequence impedance between the relative star and delta windings.
What Is The Zero Sequence of Transformers?
It is usual in performing system design calculations, particularly those involving unbalanced loadings and for system earth fault conditions, to use the principle of symmetrical components. This system is described and and ascribes positive, negative and zero-sequence impedance values to the components of the electrical system.
For a three-phase transformer, the positive and negative sequence impedance values are identical to that value described above, but the zero-sequence impedance varies considerably according to the construction of the transformer and the presence, or otherwise, of a delta winding.
The zero-sequence impedance of a star winding will be very high if no delta winding is present. The actual value will depend on whether there is a low reluctance return path for the third-harmonic flux.
For three-limb designs without a delta, where the return-flux path is through the air, the determining feature is usually the tank, and possibly the core support framework, where this flux creates a circulating current around the tank and/or core framework.
The impedance of such winding arrangements is likely to be in the order of 75 to 200% of the positive-sequence impedance between primary and secondary windings. For five-limb cores and three-phase banks of single-phase units, the zero-sequence impedance will be the magnetising impedance for the core configuration.
Should a delta winding exist, then the third harmonic flux will create a circulating current around the delta, and the zero-sequence impedance is determined by the leakage field between the star and the delta windings. Again the type of core will influence the magnitude of the impedance because of the effect it has on the leakage field between the windings.
Typical values for threelimb transformers having a winding configuration of core/tertiary/star LV/star HV are:
[Z0]LV approximately equal to 80 to 90% of positive-sequence impedance LV/tertiary
[Z0]HV approximately equal to 85 to 95% of positive-sequence impedance HV/tertiary
where Z0 = zero-sequence impedance.
Five-limb transformers have their zero-sequence impedances substantially equal to their positive-sequence impedance between the relative star and delta windings.
POWER TRANSFORMERS LOAD LOSSES BASICS AND TUTORIALS
LOAD LOSSES OF POWER TRANSFORMERS BASIC INFORMATION
What Are The Load Losses Of Power Transformers?
The term load losses represents the losses in the transformer that result from the flow of load current in the windings. Load losses are composed of the following elements:
• Resistance losses as the current flows through the resistance of the conductors and leads
• Eddy losses caused by the leakage field. These are a function of the second power of the leakage field density and the second power of the conductor dimensions normal to the field.
• Stray losses: The leakage field exists in parts of the core, steel structural members, and tank walls. Losses and heating result in these steel parts.
Again, the leakage field caused by flow of the load current in the windings is involved, and the eddy and stray losses can be appreciable in large transformers. In order to reduce load loss, it is not sufficient to reduce the winding resistance by increasing the cross-section of the conductor, as eddy losses in the conductor will increase faster than joule heating losses decrease.
When the current is too great for a single conductor to be used for the winding without excessive eddy loss, a number of strands must be used in parallel. Because the parallel components are joined at the ends of the coil, steps must be taken to circumvent the induction of different EMFs (electromotive force) in the strands due to different loops of strands linking with the leakage flux, which would involve circulating currents and further loss.
Different forms of conductor transposition have been devised for this purpose. Ideally, each conductor element should occupy every possible position in the array of strands such that all elements have the same resistance and the same induced EMF.
Conductor transposition, however, involves some sacrifice of winding space. If the winding depth is small, one transposition halfway through the winding is sufficient; or in the case of a two-layer winding, the transposition can be located at the junction of the layers.
Windings of greater depth need three or more transpositions. An example of a continuously transposed conductor (CTC) cable, shown in Figure 1.10, is widely used in the industry. CTC cables are manufactured using transposing machines and are usually paper-insulated as part of the transposing operation.
Stray losses can be a constraint on high-reactance designs. Losses can be controlled by using a combination of magnetic shunts and/or conducting shields to channel the flow of leakage flux external to the windings into low-loss paths.
What Are The Load Losses Of Power Transformers?
The term load losses represents the losses in the transformer that result from the flow of load current in the windings. Load losses are composed of the following elements:
• Resistance losses as the current flows through the resistance of the conductors and leads
• Eddy losses caused by the leakage field. These are a function of the second power of the leakage field density and the second power of the conductor dimensions normal to the field.
• Stray losses: The leakage field exists in parts of the core, steel structural members, and tank walls. Losses and heating result in these steel parts.
When the current is too great for a single conductor to be used for the winding without excessive eddy loss, a number of strands must be used in parallel. Because the parallel components are joined at the ends of the coil, steps must be taken to circumvent the induction of different EMFs (electromotive force) in the strands due to different loops of strands linking with the leakage flux, which would involve circulating currents and further loss.
Different forms of conductor transposition have been devised for this purpose. Ideally, each conductor element should occupy every possible position in the array of strands such that all elements have the same resistance and the same induced EMF.
Conductor transposition, however, involves some sacrifice of winding space. If the winding depth is small, one transposition halfway through the winding is sufficient; or in the case of a two-layer winding, the transposition can be located at the junction of the layers.
Windings of greater depth need three or more transpositions. An example of a continuously transposed conductor (CTC) cable, shown in Figure 1.10, is widely used in the industry. CTC cables are manufactured using transposing machines and are usually paper-insulated as part of the transposing operation.
Stray losses can be a constraint on high-reactance designs. Losses can be controlled by using a combination of magnetic shunts and/or conducting shields to channel the flow of leakage flux external to the windings into low-loss paths.
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