Copper losses

from Wikipedia, the free encyclopedia

As copper losses or losses of coils is referred to in all the coils in transformers , electric motors , generators and electrical magnets occurring current heat loss . The losses are mainly caused by the ohmic resistance of the copper winding.

Basics

The copper losses occur with direct current as well as with alternating current . The losses are load-dependent, they increase quadratically with the current strength and can be calculated according to the formula:

can be calculated, where stands for the strength of the coil current and for the winding resistance.

The copper losses are determined by the wire used, the winding technology used, the temperature and the current strength or voltage. In addition to the losses caused by alternating fields in the iron core , the iron losses , the copper losses form the essential part of the power loss of electromagnetic energy converters.

Transformers

In the case of transformers, copper losses include all losses that are caused by the load current in the respective coils. Although the windings of transformers can also be made of aluminum, the term copper losses has established itself and is mainly used. As can be seen from the formula for electricity heat losses (copper power loss), copper losses are heavily dependent on the load. In the case of transformers with several windings, the total copper losses correspond to the sum of the respective individual winding losses. The transformer heats up due to the copper losses, which leads to an increase in the specific resistance of the windings. As a result, the copper losses are higher and the voltage on the secondary side drops more strongly when the transformer is loaded than when the transformer is cold.

The copper losses, or load losses, for network transformers are:

  • almost 0 percent when idling
  • at half load about 0.1 to 0.5 percent
  • at full load about 0.5 to 2.0 percent

In the construction of today's power transformers for network operation, a loss ratio of iron power loss: copper power loss at the nominal operating point is specified at 0.17 to 0.25. The maximum efficiency of the transformer lies in the operating point at which the copper losses are just as great as the iron losses. i.e. about half of the rated output. In the case of transformers in switched-mode power supplies, the skin effect also influences the copper losses.

Electric motors

In the case of electric motors, copper losses include all losses that are caused by the load current in the windings through which it flows. Permanent magnet motors only have one winding; in the DC machine this is in the armature , in the electrically commutated machine it is in the stator . In the case of a fully developed electrically excited DC machine , these are the armature windings, the reversing pole windings , the excitation winding and the compensation winding . With synchronous machines the stator winding and the excitation winding , with asynchronous machines the stator winding and the rotor winding. With three-phase asynchronous motors, the winding losses in the rotor are directly dependent on the slip . Since when the motor is switched on at the moment when the rotor is not yet rotating, the slip is equal to one, the entire power induced in the rotor is converted into heat. Since the starting current in three-phase asynchronous motors is a multiple of the rated current, the current heat losses are also a multiple of the rated motor power. If the mains voltage is too low, the motor speed will decrease if the load remains the same, thus increasing the slip. This leads to an increase in power consumption and thus an increase in copper losses.

At high frequencies, additionally enters the motor windings current crowding on. In the stator windings, this effect is usually small and can be neglected due to the low field strength in the slots and the equal distribution of the total current of the windings enforced by the series connection of the windings. The situation is different in the rotor bars: Here the conductors are connected in parallel throughout the entire slot. At higher frequencies, such as those occurring when the motor is starting up, the upper layers of the rotor winding or the rotor bars can almost completely compensate for the stator field and the lower layers do not carry any current. This displacement of current leads to a higher AC resistance. This higher resistance leads to higher losses, but also to a higher torque during start-up and is therefore desirable in larger asynchronous machines because the frequency in the rotor is so low at the nominal operating point that the current displacement effect does not occur.

Loss reduction

There are several ways to reduce copper losses. The ohmic resistance of the windings of transformers can be reduced by reducing the number of turns (and, given the winding space, also increasing the wire cross-section). However, this cannot be varied as desired, since the main inductance is proportional to the square of the number of turns and the copper losses increase accordingly when idling. However, this method is common practice for coils and transformers used at higher frequencies. From a certain frequency, high-frequency litz wires are used instead of solid wires for the coils . This reduces the skin effect. However, above a certain frequency limit, the use of HF braids does not make sense; this frequency limit depends on the wire radius. Above this frequency, the external proximity effect causes losses that are proportional to the number of wires. Either a solid wire or a smaller wire radius must be used here. When designing such transformers or coils for the HF range, a compromise between copper losses and proximity losses is sought.

In motors, the copper losses at a given load cannot be influenced by varying the wire cross-section and number of turns, since the total flow determines the torque, regardless of how many conductors it is distributed over. The copper losses in the stator can be optimized through a minimal conductor length and an optimal fill factor. Once these steps, which are self-evident, have been taken, they can only be reduced by increasing the size of the stator slots. Copper losses in the rotor of an asynchronous machine are reduced by larger rotor bars, copper instead of aluminum and better-sized short-circuit rings. With a given motor volume, however, there are limits to the enlargement of the area for the windings, since the copper area shares its space with the iron carrying flux, which can only conduct magnetic flux to a limited extent due to its saturation . Machines optimized with regard to copper losses therefore have a low overload capacity. This problem does not exist in iron-free air coil machines; the winding height directly reduces the air gap induction usually excited by permanent magnets , which ultimately results in an optimal winding thickness with regard to copper losses. In contrast to the grooved motor, which is optimized with regard to copper losses, full optimization in air-coil machines does not result in any saturation effects and therefore no reduced overload capacity.

literature

  • Jens Lassen la Cour, E. Arnold (ed.): The alternating current technology. Second volume. The transformers. Published by Julius Springer, Berlin 1904.

Individual evidence

  1. ^ A b c d e Paul Vaske, Johann Heinrich Riggert: Electrical machines and converters. Part 2. Calculation of electrical machines. 8th, revised edition. BG Teubner, Stuttgart 1974, ISBN 3-519-16402-7 .
  2. ^ A b Günter Springer: Electrical engineering. 18th edition. Verlag Europa-Lehrmittel, Wuppertal 1989, ISBN 3-8085-3018-9 .
  3. ↑ Panos Konstantin: Practical book energy industry. Energy conversion, transport and procurement in the liberalized market. Springer Verlag, Berlin / Heidelberg 2007, ISBN 978-3-540-35377-5 , p. 191.
  4. ↑ Herbert Kyser: The electric power transmission . Volume I: The Motors - Converters and Transformers. Springer Verlag, Berlin Heidelberg 1912, pp. 201-202.
  5. ↑ G. Schindler: Magnetic components and assemblies. Basics, areas of application, background and history. ( online , accessed May 17, 2011; PDF; 7.6 MB)
  6. ↑ Karl-Heinz Locher, Hans Müller, Thomas Harriehausen, Dieter Schwarzenau: Moeller Fundamentals of Electrical Engineering . Springer-Verlag, 2011, ISBN 978-3-8348-0898-1 , pp. 401 .
  7. ↑ Calculation of core and winding losses of inductive components for switched-mode power supplies . ( online , accessed May 18, 2011; PDF; 2.5 MB)
  8. ^ Richard Rühlmann: Basics of alternating current technology. Published by Oskar Leiner, Leipzig 1897.
  9. ^ Hans-Rudolf Niederberger: Electrical engineering transformers . ( online , accessed June 13, 2016)
  10. ^ TU Dresden: Transformer . ( online , accessed June 16, 2016).
  11. ↑ G. Schenke: Transformers. ( online ( Memento of the original from September 16, 2011 in the Internet Archive ) Info: The archive link was automatically inserted and not yet checked. Please check the original and archive link according to the instructions and then remove this note. (PDF; 332 kB) FB Technik, accessed on May 17, 2011). @1@ 2Template: Webachiv / IABot / www.technik-emden.de
  12. ↑ a b M. Albach, M. Döbrönti, H. Roßmann: Winding losses in coils and transformers made of HF litz wire . In: electronics industry . No. 10 , 2010, p. 32-34 .
  13. ↑ Rockwell Automation: Basics for Practical Three- Phase Induction Motors . ( online , accessed May 17, 2011; PDF; 1.4 MB).
  14. ^ Markus Hüging, Josef Kruse, Nico Nordendorf: Qualifications in electrical engineering, industrial engineering. 1st edition. Bildungsverlag EINS, 2005, ISBN 3-427-50015-2 .
  15. ↑ University of Tübingen: TR transformer . ( accessed online on May 18, 2011; PDF; 167 kB).
  16. ^ Arndt Josef Kelleter: Increasing the utilization of small electrical machines . Dissertation . Technical University of Munich, Munich 2010.