Файл: Metodichka_Kuzmenko_dlya_elektrikov.doc

An ideal step-down transformer showing flux in the core

If a time-varying voltage is applied to the primary winding of turns, a current will flow in it producing a magnetomotive force (MMF). Just as an electromotive force (EMF) drives current around an electric circuit, so MMF tries to drive magnetic flux through a magnetic circuit. The primary MMF produces a varying magnetic flux in the core, and, with an open circuit secondary winding, induces a back electromotive force (EMF) in opposition to . In accordance with Faraday's law of induction, the voltage induced across the primary winding is proportional to the rate of change of flux:

     and     

where

• v_P and v_S are the voltages across the primary winding and secondary winding,

• N_P and N_S are the numbers of turns in the primary winding and secondary winding,

dΦ_P / dt and dΦ_S / dt are the derivatives of the flux with respect to time of the primary and secondary windings.

In the hypothetical ideal transformer, the primary and secondary windings are perfectly coupled, or equivalently, . Substituting and solving for the voltages shows that:

where

• v_p and v_s are voltages across primary and secondary,

• N_p and N_s are the numbers of turns in the primary and secondary, respectively.

Hence in an ideal transformer, the ratio of the primary and secondary voltages is equal to the ratio of the number of turns in their windings, or alternatively, the voltage per turn is the same for both windings. The ratio of the currents in the primary and secondary circuits is inversely proportional to the turns ratio.

The EMF in the secondary winding will cause current to flow in a secondary circuit. The MMF produced by current in the secondary winding opposes the MMF of the primary winding and so tends to cancel the flux in the core. Since the reduced flux reduces the EMF induced in the primary winding, increased current flows in the primary circuit. The resulting increase in MMF due to the primary current offsets the effect of the opposing secondary MMF. In this way, the electrical energy fed into the primary winding is delivered to the secondary winding. In addition, the flux density will always stay the same as long as the primary voltage is steady.

For example, suppose a power of 50 watts is supplied to a resistive load from a transformer with a turns ratio of 25:2.

• P = EI (power = electromotive force × current)

50 W = 2 V × 25 A in the primary circuit if the load is a resistive load. (See note 1)

• Now with transformer change:

50 W = 25 V × 2 A in the secondary circuit.

Since a direct current by definition does not change, it produces a steady MMF and so steady flux in the core; this quantity does not change and so cannot induce a voltage in the secondary winding. In a practical transformer, direct current applied to the winding will create only heat.

4. Math the following English words with the Ukrainian ones.

transformer - сердечник

transfer - пристрій

induce - міжз’єднання

magnetic coupling - електрична мережа живлення

unit - індукувати

interconnection - протиелектрорушійна сила

primary winding - первинна обмотка

power grid - магнітна взаємодія

electro magnetic induction - активне навантаження

coupling transformer - магнітне коло

resistive load - електромагнітна індукція

magnetic circuit - трансформатор зв’язку

core - трансформатор

back electro motive force - передавати.

5. Find English equivalents to the words:

Подавати, зв’язувати, створювати, вторинна обмотка, взаємоіндукція, вторинна обмотка, взаємоіндукція, коефіцієнт трансформації по напрузі, густота потоку, середньоквадратичний, площа поперечного розтину, максимум, частота, обернено пропорціональній, вирішувати, магніторушійна сила, електрорушійна сила.

6. Translate the word combinations from the text:

Time-varying magnetic flux; thumbnail-sized coupling transformer; inversely proportional; magnetic flux density; peak magnetic flux density.

7. Answer the questions to the text.

1. What is a transformer?

2. What does a transformer comprise?

3. What does a changing voltage applied to one winding create in the core?

4. What does a time- varying magnetic flux induce in the other windings?

5. What sizes do transformers have?

6. What magneto-motive force does the core require to sustain a magnetic flux in an ideal transformer?

7. What does a magnetic flux linking the primary winding do?

8. Has the ideal transformer resistance in its coils?

9. What is mutual induction?

10. What will current produce in the primary winding if a time-varying voltage is applied to it?

11. What produces a back electromotive force?

12. What does Faraday’s low of induction state?

13. What is the ratio of the primary and secondary voltages equal to?

14. What is inversely proportional to the turns ratio?

15. What will the EMF in the secondary winding cause?

16. What is produced by current in the secondary winding?

17. What tends to cancel the flux in the core ?

18. How the electrical energy fed into the primary winding is delivered to the secondary winding?

19. How long will the flux density stay the same?

20. What kind of current produces a steady MMF and so steady flux in the core?

21. Can steady MMF induce a voltage in the secondary winding?

22. What relationship is given by the universal e m f equation?

Text B

Operation at different frequencies

1. Read and memorize the words and word-combinations

operation – робота

compact – компактний

saturation – насичення

property – властивість

losses – втрати

skin-effect – поверхневий ефект, скін-ефект

increase – збільшуватись

designed voltage – розрахована напруга

intended – призначений

reduce – зменшувати

magnetising current – намагнічуючий струм

applied voltage – прикладена напруга

excessive – надмірний

level – рівень

assessment – визначення, оцінка

equip – обладнувати

protection – захист

over-excitation protection – захист від перезбудження

"volts per hertz" – відношення напруги до частоти

protection relay – реле захисту

overvoltage – перенапруга

higher-than-rated frequency – частота вища номінальної;

load – навантаження.

2. Be sure that you know these words

adapt – впроваджувати, пристосовувати

application – застосування

fraction – частина

volt-ampere – вольт-ампер

power supply – джерело живлення

impedance matching – узгодження повного опору

circuit – коло (ланцюг), схема

circuit isolation – розв’язка кола (ланцюга)

range – діапазон

power frequency – частота мережі

audio frequency – звукова частота

ratio frequency – радіочастота

cooling – охолодження

distribution – розподіл

rectifier – випрямляч

arc furnace – дугова піч

amplifier output – вихід підсилювача

step-up transformer – підвищуючий трансформатор

step-down transformer – знижуючий трансформатор

isolating transformer – розв’язуючий трансформатор

coil – катушка, обмотка, виток

equal – однаковий, рівний

compensate – компенсувати

variable transformer – регулюючий трансформатор напруги.

3. Read and translate the text.

The equation shows that the EMF of a transformer at a given flux density increases with frequency. By operating at higher frequencies, transformers can be physically more compact without reaching saturation, and a given core is able to transfer more power. However, other properties of the transformer, such as losses within the core and skin-effect, also increase with frequency. Generally, operation of a transformer at its designed voltage but at a higher frequency than intended will lead to reduced magnetising (no load primary) current. At a frequency lower than the design value, with the rated voltage applied, the magnetising current may increase to an excessive level.

Operation of a power transformer at other than its design frequency may require assessment of voltages, losses, and cooling to establish if safe operation is practical. For example, transformers at hydroelectric generating stations may be equipped with over-excitation protection, so-called "volts per hertz" protection relays, to protect the transformer from overvoltage at higher-than-rated frequency which may occur if a generator loses its connected load.

Classifications. Transformers are adapted to numerous engineering applications and may be classified in many ways:

• By power level (from fraction of a volt-ampere(VA) to over a thousand MVA),

• By application (power supply, impedance matching, circuit isolation),

• By frequency range (power, audio, radio frequency(RF))

• By voltage class (a few volts to about 750 kilovolts)

• By cooling type (air cooled, oil filled, fan cooled, water cooled, etc.)

• By purpose (distribution, rectifier, arc furnace, amplifier output, etc.).

• By ratio of the number of turns in the coils

• Step-up. The secondary has more turns than the primary.

• Step-down. The secondary has fewer turns than the primary.

• Isolating. Intended to transform from one voltage to the same voltage. The two coils have approximately equal numbers of turns, although often there is a slight difference in the number of turns, in order to compensate for losses (otherwise the output voltage would be a little less than, rather than the same as, the input voltage).

• Variable. The primary and secondary have an adjustable number of turns, which can be selected without reconnecting the transformer.

4. Find Ukrainian equivalents to the words:

saturation, skin-effect, over-excitation protection, impedance matching, circuit isolation, rectifier, amplifier output, step-up transformer, step-down transformer, isolating transformer, variable transformer, power frequency.

5. Point out English equivalents to the words:

розрахована напруга, надмірний, відношення напруги до частоти, реле захисту, намагнічуючий струм, призначений, прикладена напруга, джерело живлення, компенсувати, звукова частота, радіочастота.

6. Translate the word combinations from the text.

Rated voltage applied, hydroelectric power station, higher-than-rated frequency.

7. Give the classification of transformers according to engineering applications. Discuss it.

8. Speak on the classification of the transformers by ratio of the number of the coils.

Text C

Limitations

1. Read and memorize the words and word-combination.

limitation – обмеження

convert – перетворювати

vice versa – навпаки

dissipate – розсіюватись

copper loss – втрати в міді, втрати в обмотці

attributable – властивий

iron loss – втрати у сердечнику

plug-in – вставний

power brick – блок живлення

proximity effect – вплив близкості зворотного (сусіднього) провода

additional – додатковий

eddy currents – вихрові струми

induce – індукувати

circulate – циркулювати

cause – викликати, заставляти

resistance – опір

resistive – резестивний

silicon – кремній

aging – старіння

hysteresis losses – гістерезисні втрати, втрати на гістерезис

reverse – змінювати напрямок на зворотний

magnetostriction – магнітострикція

expand – розширювати(сь)

contract – взаємодіяти

buzzing – дзижчання

friction – тертя

susceptible – чутливий.

2. Make sure that you know these words and word combinations.

mechanical losses – втрати на механічні процеси

fluctuate – коливатись

incite – збуджувати

vibration – коливання

humming – гул

consume – споживати

stray losses – паразитні втрати

intercept – перехоплювати

leakage flux – потік розсіювання

support structure – несуча конструкція

cooling – охолодження

cooling fan – охолоджуючий вентилятор

oil pump – масляний насос

water-cooled heat exchanger – теплообмінник з водяним охолодженням

load-dependent (load-losses) – втрати у трансформаторі під навантаженням

no-load loss – втрати у режимі холостого ходу

dominate – впливати

eddy current losses – втрати на вихрові струми

contribute – сприяти.

3. Read and translate the text.

Transformers alone cannot do the following:

• Convert DC to AC or vice versa

• Change the voltage or current of DC

• Change the AC supply frequency.

However, transformers are components of the systems that perform all these functions.

Energy losses An ideal transformer would have no losses, and would therefore be 100% efficient. In practice, energy is dissipated due both to the resistance of the windings known as copper loss or I²R loss, and to magnetic effects primarily attributable to the core (known as iron loss). Transformers are, in general, highly efficient: large power transformers (over 50 MVA) may attain an efficiency as high as 99.75%. Small transformers, such as a plug-in "power brick" used to power small consumer electronics, may be less than 85% efficient.

Transformer losses:

• Winding resistance. Current flowing through the windings causes resistive heating of the conductors (I² R loss). At higher frequencies, skin effect and proximity effect create additional winding resistance and losses.

• Eddy currents. Induced eddy currents circulate within the core, causing resistive heating. Silicon is added to the steel to help in controlling eddy currents. Adding silicon also has the advantage of stopping aging of the electrical steel that was a problem years ago.

• Hysteresis losses. Each time the magnetic field is reversed, a small amount of energy is lost to hysteresis within the magnetic core. The amount of hysteresis is a function of the particular core material.

• Magnetostriction. Magnetic flux in the core causes it to physically expand and contract slightly with the alternating magnetic field (producing a buzzing sound), an effect known as magnetostriction. This in turn causes losses due to frictional heating in susceptible ferromagnetic cores.

• Mechanical losses. In addition to magnetostriction, the alternating magnetic field causes fluctuating electromagnetic forces between the primary and secondary windings. These incite vibrations within nearby metalwork, creating a familiar humming or buzzing noise, and consuming a small amount of power.

• Stray losses. Not all the magnetic field produced by the primary is intercepted by the secondary. A portion of the leakage flux may induce eddy currents within nearby conductive objects, such as the transformer's support structure, and be converted to heat.

• Cooling system. Large power transformers may be equipped with cooling fans, oil pumps or water-cooled heat exchangers designed to remove the heat caused by copper and iron losses. The power used to operate the cooling system is typically considered part of the losses of the transformer.

Losses may be either load-dependent('load-losses') or independent of it ('no-load loss'). Winding resistance dominates load-losses, whereas hysteresis and eddy currents losses contribute to over 99% of the no-load loss.

4. Find the equivalents to the following.

iron losses – втрати в обмотці

energy losses – паразитні втрати

winding resistance losses – втрати на охолоджувальну систему

eddy current losses – втрати на магнітострикцію

hysteresis losses – втрати на механічні процеси

magnetostriction losses – втрати на вихрові струми

mechanical losses – втрати на гістерезис

stray losses – втрати енергії

cooling system losses – активні втрати

copper loss – втрати у сердечнику

5. Find English equivalents to the words:

потік розсіювання, збуджувати, несуча конструкція, перехоплювати, коливання, споживати, вплив близькості сусіднього провода, розсіюватись, перетворювати, змінювати напрямок на зворотній, індукувати, коливатись, споживати, опір, навпаки, вставний.

6. Translate the word combinations.

Highly efficient, resistive heating, large power transformers, frictional heating, alternating magnetic field, fluctuating electromagnetic forces, transformer's support structure, water-cooled heat exchanger; load – dependent losses; no – load loss.

7. Answer the questions.

1. What cannot transformers do alone?

2. What kinds of losses are attributable to transformers?

8. Are you agree with the statements?

1. Fluctuating electromagnetic forces between the primary and secondary windings doesn’t incite vibrations within nearby metalwork.

2. Small power transformers may be equipped with cooling fans, oil pumps or water-cooled heat exchangers.

9. Speak on all kinds of losses.

Text D

Construction

1. Listen to the words and word combinations from the text. Pay attention to their meaning.

lamination – пластина

E-shaped – Ш-образний стрижень

C-core – U образний стрижень

piece – частина

laminated – слоїстий, шихтований, пластинчатий

stack – складати

interleave – прошаровувати

gap – проміжок

press together – зпресовувати, прошаровувати

reduce – зменшувати

width – ширина

insulation – ізоляція

area – площа

effective – діючий, результативний

capacitor – конденсатор

gradually – поступово

wedging – розклинювання

increase – збільшуватись (сь)

overlap – накладання, перекривання

grain – структура

remanence – залишкова магнітна індукція, залишкова намагніченість

strip – стрічка, штаба

rectangular – прямокутний

thickness – товщина

remove – знімати, виймати, усувати

bond – з’єднувати.

2. Read and memorise the words and word combinations

grind – шліфувати

smooth – рівний, гладкий

fit – підганяти, приладжувати

tight – щільний

halve – половина

strap – скоба

triangular – трикутний

cross-section – поперечний розтин

due to – завдяки

toroidal – тороїдальний

bending – вигин, викривлення

retain – зберігати

static – статичний

reapply – подавати, прикладати знову

residual – залишковий

inrush current – пробійний струм

cycle – цикл

alternating current – змінний струм

overcurrent protection – захист від надструмів

fuse – плавкий запобіжник

power transmission line – лінія електропередачі

geomagnetic – геомагнітний

disturbance – збурення

false operation – помилкове спрацьовування

protection device – захисний пристрій

operating frequency – робоча частота

ferrite – ферит

VHF band – діапазон дуже високих частот.

3. Read and translate the text.

Cores

A typical laminated core is made from E-shaped and I-shaped pieces, leading to the name "EI transformer". In the EI transformer, the laminations are stacked in what is known as an interleaved fashion. Due to this interleaving a second gap in parallel (in an analogy to electronic circuits) to the gap between E and I is formed between the E-pieces. The E-pieces are pressed together to reduce the gap width to that of the insulation. The gap area is very large, so that the effective gap width is very small (in analogy to a capacitor). For this to work the flux has to gradually flow from one E to the other. That means that on one end all flux is only on every second E. That means saturation occurs at half the flux density. Using a longer E and wedging it with two small Is will increase the overlap and additionally make the grains more parallel to the flux (think of a wooden frame for a window). If an air gap is needed (which is unlikely considering the low remanence available for steel), all the E's are stacked on one side, and all the I's on the other creating a gap.

The cut core or C-core is made by winding a silicon steel strip around a rectangular form. After the required thickness is achieved, it is removed from the form and the laminations are bonded together. It is then cut in two forming two C shapes. The faces of the cuts are then ground smooth so they fit very tight with a very small gap to reduce losses. The core is then assembled by placing the two C halves together, and holding them closed by a steel strap. Usually two C-cores are used to shorten the return path for the magnetic flux resulting in a form similar to the EI. More cores would necessitate a triangular cross-section. Like toroidal cores, they have the advantage, that the flux is always in the oriented parallel the grains. Due to the bending of the core, some area is lost for a rectangular winging.

A steel core's remanence means that it retains a static magnetic field when power is removed. When power is then reapplied, the residual field will cause a high inrush current until the effect of the remanent magnetism is reduced, usually after a few cycles of the applied alternating current. Overcurrent protection devices such as fuses must be selected to allow this harmless inrush to pass. On transformers connected to long overhead power transmission lines, induced currents due to geomagnetic disturbances during solar storms can cause saturation of the core, and false operation of transformer protection devices.

Steel cores develop a larger hysteresis loss due to eddy currents as the operating frequency is increased. Ferrite, or thinner steel laminations for the core are typically used for frequencies above 1kHz. The thinner steel laminations serve to reduce the eddy currents. Some types of very thin steel laminations can operate at up to 10 kHz or higher. Ferrite is used in higher frequency applications, extending to the VHF band and beyond.

4. Find the equivalents to the folloving English words:

lamination – - перекривання

remanence – - помилкове спрацьовування

interleave – - залишковий

overlap – - плавкий запобіжник

inrush current – - робоча частота

overcurrent protection – - залишкова магнітна індукція

residual – - прошаровувати

operating frequency – - захист від надструмів

fuse – - пластина

false operation – - пробійний струм.

5. Point out English equivalents to the words:

проміжок, слоїстий (шихтований), розклинювати, площа, зпресовувати, прямокутний, шліфувати, підганяти, поперечний розтин, трикутний, скоба, зберігати, тороїдальний, ізоляція.

6. Translate the word combinations.

Typical laminated core; E-shaped and I-shaped pieces; triangular cross-section; static magnetic field; remanent magnetism; overcurrent protection device; power transmission line; long overhead power transmission line; transformer protection device; VHF band; effective gap width.

7. Answer the questions.

1. What shape of pieces has a typical laminated core?

2. What fashion are the laminations stacked in?

3. How is a second gap formed between the E-pieces of the core?

4. Why are the E-pieces pressed together?

5. Is the effective gap width very large or very small?

6. What has the flux to do in order to work?

7. When does a saturation occur?

8. What will increase the overlap?

9. How can an air gap be created in that case?

10. In which way is the C-core made?

8. Read the passage about steel cores. Retell it.

Text E

Windings

1. Listen to the words and word combinations from the text and memorize them.

magnet wire – обмоточний провід (дріт)

coating – покриття

varnish – лак

synthetic – синтетичний

enamel – емаль

strip conductors – штабовий провідник (стрічковий)

heavy current – великий струм

strand – жила, скручувати

multiple-stranded conductor – багатожильний провід

power frequency – частота мережі

non-uniform – нерівномірний, неоднорідний

distribution – розподіл

arrange – розміщати

transposition – переміщення

equalize – вирівнювати

flexible – гнучкий

solid – твердий

winding – виток

external – зовнішній

connection – з’єднання, сполучення

tap – відгалуження, відвід

intermediate – проміжний

adjustment – регулювання

tap changer – перемикач вихідних обмоток трансформатора

on-load tap changer – перемикач вихідних обмоток трансформатора під напругою