2.2.Dc transmission systems
KHBO Renaat De Craemer, Joan Peuteman
1: Historical evolution from AC-grids to DC-grids
Although in the early years of electricity production a lot of electrical grids were DC-grids, nowadays the great majority of the electrical grids are AC-grids. This switch from DC-grids to AC-grids has a number of technical reasons.
Due to the need for a commutator, it is very difficult to build DC-generators generating high voltages. Especially when generating higher voltages (of 24 kV for instance), it is easier to construct alternators (AC-generators).
An additional advantage arises when considering electrical motors. In general, constructing AC-motors (like the three phase induction motor) is easier and cheaper than constructing DC-motors. Moreover, a lot of AC-motors require less maintenance.
When using AC, it is possible to use transformers. Due to these transformers, a generated voltage level can be transformed to a higher voltage level of 70 kV, 220 kV or even 380kV. These transformers have a long life expectancy (more than 30 years) and they have a high efficiency (even more than 99.9%). Transformers have a straightforward construction and they require almost no maintenance (no moving parts).
When using a high voltage grid to inject power into a medium or a low voltage grid, transformers can be used to transform the voltage level to a lower level (for instance from 380 kV to 70 kV or from 11 kV to 400 V).
By using transformers, it is possible to supply power at a low voltage level of 230 V and/or 400 V to a customer (reducing the risks related with electricity) and to use high voltage grids to transport large amounts of power over larger distances (reducing the losses in the grid).
It is easier to interrupt AC-currents since these currents have two zero-crossings in one single period whereas a DC-current has no zero-crossings. When opening an electrical contact, the zero-crossing can be used to extinct the arc and it is sufficient to prevent re-ignition of the arc.
When considering AC voltages, the insulation level
of cables, appliances and machines must withstand the peak value and
not only the RMS value. This peak value equals 
or 1.41 of the RMS value.
2: HVDC-grids as an emerging technology
Although all these technical aspects explain why nowadays the large majority of the grids are AC-grids, it is wrong to conclude that using DC to transport electrical energy is old-fashioned and the use of DC only has disadvantages. Using DC, can be an emerging and useful technological challenge.
When transporting electrical energy, it is possible to compare the energy losses between a single phase AC-grid, a three phase AC-grid and a DC-grid. The Joule losses in a three phase grid are only 75% of the Joule losses in a similar single phase grid (insulation which withstands the same voltage level and the same amount of copper is used) transporting the same amount of power. This explains why three phase grids instead of single phase grids are used when transporting electrical energy.
When comparing the Joule losses of a DC-grid and a three phase AC-grid. The Joule losses in a DC-grid are only 67% of the Joule losses in a similar three phase AC-grid. This explains why DC-grids are sometimes used when transporting large amount of electrical energy over large distances (more than 750 km).
2.1: Investment costs related with HVDC-grids
A disadvantage related with the use of DC-grids to transport electrical energy is the lack of transformers allowing increasing or decreasing of the voltage level. In practice, the situation visualized in Figure 1 combines the use of DC-grids and AC-grids.
Figure 1: Basic structure of a HVDC-grid
Starting from a classical three phase AC-grid, the voltage level is increased using a transformer. A very high AC-voltage is obtained which will be rectified giving a very high DC-voltage (originally mercury-vapor rectifiers were used, nowadays semiconductor rectifiers are used). The very high DC-voltage will be used to transport the electrical energy over a long distance (HVDC: High Voltage Direct Current). At the other side of the DC-grid, an inverter converts this DC-voltage back to an AC-voltage. Using a transformer, the AC-voltage level is decreased and the power is injected into a classical three phase AC-grid.
It is not only possible to transport active power from the left side to the right side. In case the left power electronic converter does not operate as a rectifier but as an inverter and in case the right power electronic converter does not operate as an inverter but as a rectifier, active power is transported from the right side to the left side.
This is an emerging technology since it is not obvious to construct a rectifier and an inverter dealing with such high voltages. Such a rectifier and inverter require a considerable investment. This investment can only be justified when the energy is transported over a very long distance and the transported power is sufficiently large (for instance 2000 MW). Indeed, when preconceiving the energy losses, less copper (or aluminum) is required when using a HVDC-grid instead of a three phase AC-grid. However, only for sufficiently long distances the reduced use of copper is able to justify the installation cost of the rectifier and the inverter.
This situation is visualized in Figure 2 (information provided by ABB). The DC terminal cost is much higher than that of the AC terminal but the DC line cost is lower implying a lower total investment when the distance is sufficiently large.
Figure 2: Comparison investment of a HVDC grid and an AC grid
2.2: Applications of HVDC-grids
HVDC-grids are used to transport large powers over
large distances. For instance, a HVDC-grid in Brazil transports power
of the Itaipu hydroelectric power plant to the region of Sao Paulo.
This installation contains two 
bipoles having a total rated power of 6300 MW and transporting the
power over a distance of 780 km.
Using HVDC-grids, it is also possible to connect two AC-grids having a different frequency. For instance in Japan, the eastern and northern parts of Honshu and Hokkaido have a grid frequency of 50 Hz whereas the western Honshu, Shikoku, Kyushu and Okinawa operate at 60 Hz. The boundary between these two regions contains four back-to-back HVDC-substations operating as frequency converters (in case the rectifier and the inverter which are visualized in Figure 1 are located in the same station, a back-to-back HVDC-system is obtained). For instance the Higashi-Shimizu frequency converter operates with a DC voltage of 125 kV and has a maximum power of 300 MW.
Moreover, DC-grids also allow interconnect grids having the same rated frequencies but which are not synchronized with each other. For instance, there is a DC-cable interconnecting the British grid and the continental European grid. This HVDC Cross-Channel is a 2000 MW system and has a total length of 73 km containing 46 km submarine cables (an operating voltage of 270 kV).
2.3: DC-grids and renewable energy generation
HVDC allows transporting large amount of electrical energy over large distances. This is useful to transport the energy of large remotely located hydroelectric power stations (for instance the Three Gorges Dam in China, the Itaipu dam in Brasil) to the industrialized world.
More recently and focused to the transportation of powers which are not that extremely high, is the use of HVDC light (http://www.abb.com/hvdc) which is used to transport the energy coming from onshore and offshore wind turbine parks.
When considering the Thornton Bank (offshore wind turbine park) in Belgium, a three phase AC-grid having a voltage level of 150 kV is used to transport the power to land. For instance the Gotland project in Sweden (onshore wind energy) uses the HVDC light technology to transport the generated power.
3: Low voltage DC-grids
Due to the rise of distributed generation (the use of small scale renewable energy sources which inject their power in the low voltage distribution grid) and the importance of a reliable power supply for an increasing number of loads, mainly in the academic world there is a growing interest for the use of low voltage DC distribution grids.
Due to a number of technical evolutions, the importance of the old disadvantages related with the use of DC-grids (which stimulated the rise of AC-grids about a century ago) have mainly disappeared when considering low voltage applications.
The power of a lot of distributed renewable energy sources is injected into the grid using a power electronic converter. For instance in the case of photovoltaic panels generating a DC voltage, it is possible to use of DC-AC-converter in the case of an AC-grid. However, by using a DC-DC-converter it is also possible to inject the power of the photovoltaic panels into a DC-grid. Sometimes, it is even possible to inject the power of photovoltaic panels into the DC-grid without any power electronic converter in the case of a DC-grid with an appropriate voltage level.
In general, no power will be generated using a traditional rotating DC-generator. In the case of a wind turbine or a generator driven by a combustion engine, an AC-voltage will be generated which will be converted into DC using an AC-DC-converter.
Due to the rise of power electronics, a DC-AC-converter can be used to supply for instance induction machines or permanent magnet synchronous motors (PMSM). The use of a DC-grid does not anymore imply the need to use DC-motors having a commutator and carbon brushes.
Power electronic DC-DC-converters can be used to connect two DC-busses having different voltage levels which compensate the lack of transformers.
Using semiconductor devices, it is also possible to interrupt a DC-current although there are no zero-crossings of the current. Also in the case of fault currents, circuit breakers can be used to interrupt overload currents or short circuit currents [Sannino, Gregory] .
3.1: Advantages when using low voltage DC grids
The rise of small scale renewable energy resources (photovoltaic panels, micro wind turbines, small scale CHP installations, …) increases the need to store energy. Especially when working in island mode, the storage capacity is important in order to maintain the power balance. In case the generated power is larger than the consumed power, the excess of power is stored using for instance batteries of fuel cells. In the case the generated power is smaller than the consumed power, the batteries of fuel cells provide the additionally required power. Since batteries and fuel cells are DC-sources, the use of a DC-grid instead of an AC-grid can be useful in order the decrease the number of power electronic converters.
Figure 3: Photovoltaic panels mounted on the roof of a private household
The importance of energy storage devices is growing since the number of sensitive loads is increasing. In industry, in commercial premises, in service businesses and also in residential complexes the number of for instance power sensitive computers and communication devices is increasing. In order to obtain a reliable power supply, UPS systems (Uninterruptible Power Supply) are needed. The batteries and other storage devices (fuel cells, ultra capacitors) which are crucial in these UPS systems generally provide a DC voltage which stimulates the use of local DC-grids.
When using photovoltaic panels, loaded batteries, fuel cells, etc. to supply power, they generate a DC-voltage which is commonly converted into an AC-voltage in order to obtain a 50 Hz or a 60 Hz grid. Internally, a lot of loads do not need an AC-voltage but a DC-voltage implying they are commonly equipped with a transformer in combination with a rectifier or a rectifier in combination with a DC-DC-converter. By using a DC-grid instead of an AC-grid, a lot of converters can be eliminated. Since power electronic converters require an investment, account for power losses (especially giving a low efficiency when the load is low) and account for EMC-related problems, reducing the number of converters is useful.
3.2: The structure of AC and DC local grids
Figure 4 compares the structure of a local low voltage AC-grid (part (a) on the left) with the structure of a local low voltage DC grid (part (b) on the right) indicating the structure of the DC grid is more straightforward.
Figure 4: Comparison between AC-grid and DC-grid (source: Sannino)
The AC-grid in Figure 4 requires DC-AC-converters to inject the powers of solar panels and fuel cells. Natural gas micro turbines generally rotate at a very high speed and produce energy at a high frequency implying a two-stage frequency converter is needed. Notice also the connection between the local AC-grid and the public AC-grid.
Some loads of the AC-grid are fed without the use of a converter, but a lot of loads need a converter. For instance, digital electronic equipment needs a limited DC-voltage which is obtained by cascading two converters i.e. an AC-DC-converter (a rectifier) and a DC-DC-converter. Sensitive loads are fed by a DC-voltage while using an UPS system. The second converter in the UPS system can also be a DC-AC-converter in case the sensitive load requires an AC-voltage.
By choosing an appropriate voltage level and using a DC-grid, solar panels and fuel cells can be able to inject their power without the need for a power electronic converter. The same remark applies for batteries. A micro turbine only needs one single AC-DC-converter. Sensitive loads can be fed by the DC-grid without the need for converters or separate UPS-systems. Only one large battery is sufficient to obtain the UPS-property for all the sensitive loads. The digital electronic equipment is fed by one single step-down DC-DC-converter (instead of two cascaded converters). Some loads are fed by the DC-grid without the need for converters. If there are AC-loads (for instance induction motors), they need a DC-AC-converter which is not needed in the case of an AC-grid. When connecting with the public AC-grid also an additional converter is needed. However in general, less converters are needed which accounts for less power losses in these converters.
A similar comparison between an AC-grid and a DC-grid is visualized in Figure 5 and Figure 6. Figure 5 visualizes a local AC-grid which needs a larger number of converters than the local DC-grid visualized in Figure 6.
Figure 5: Structure of a local AC-grid
Figure 6: Structure of a local DC-grid
4: The DC-voltage level
When realizing a local DC-voltage grid, an appropriate choice of the voltage level is important. When using a higher voltage level, the current will be lower in order to supply the same required power. This implies the voltage drops decrease and also the power losses in the grid conductors decrease. On the other hand, using a higher voltage level has implications concerning safety issues and the number of power electronic converters which are needed.
In order to allow standardization, not all voltage levels are possible. In reality the standardized voltages of 326 VDC, 230 VDC, 120 VDC, 48 VDC, 24 VDC, 12 VDC and finally 6 VDC can be taken into consideration.
Many electronic appliances use a DC voltage which is obtained by rectifying the 230 VAC grid voltage using a diode rectifier. The rectified voltage level equals 326 VDC which is the peak value of the 230 VAC grid voltage. By supplying directly with 326 VDC, the same appliances can be used by simply removing the input rectifier.
When using 230 VDC, the RMS value is the same in comparison with the traditional 230 VAC grid voltage. This is useful when feeding resistance equipment like heating resistors or incandescent lamps (in the case they are still used). In such situations, no changes to the resistor appliances are needed.
By using a 120 VDC voltage level, no protection against indirect contacts (contacts with exposed conductive parts which have become live under fault conditions) is required. This makes the system simpler due to the absence of grounding.
By using a 48 VDC voltage level, even no protection against direct contacts (contacts with live parts) is needed. This normalized voltage is also used to supply a lot of communication devices implying a lot of devices adapted to a 48 VDC supply are available on the market which is an important advantage.
Also 24 VDC, 12 VDC and 6 VDC are existing standardized voltage levels which are safe to be used. They are useful when considering small power systems (for instance in a car or to supply pay and display machines) but when considering the powers used in a domestic or a similar situation, they are not useful. Due to the low voltage level, the required currents are too high implying the voltage drops and the copper losses are also too high.
5: Voltage drops and power losses in local AC and DC-grids
A practical application of a distribution system has been realized in the Department of Electric Power Engineering at the Chalmers University of Technology in Gothenburg (Sweden) [Sannino]. The electric diagram of the system is visualized in Figure 7. The system includes 15 offices with a total of 26 people. Mainly typical office loads like computers and lighting are fed. There is also a copy room with a printer, a fax and a copy machine. There is also a lunchroom equipped with a refrigerator, a cooker, an exhaust fan, a dishwasher, a coffee machine, two microwave ovens and a water boiler.
Figure 7: Electric diagram of the low voltage grid at Chalmers university
In Figure 7, the majority of the loads are single phase loads (230 VAC). Only the high power three-phase loads of the kitchen (like the coffee machine and the cooker) are fed by a three-phase grid (having a 400 VAC line-to-line voltage level). Using this three phase grid instead of a single phase supply reduces the voltage drops and the copper losses.
By replacing the AC-grid of Figure 7 by a DC-grid where either 326 VDC, 230 VDC, 120 VDC or 48 VDC voltage levels are considered, it is possible to compare the properties of the AC-grid and the DC-grids. Also the three phase connections feeding the high power loads are replaced by a DC-connection.
Figure 7 and Figure 8 give an overview of all the loads with their consumed active powers and their cosφ. This allows calculate the consumed active and reactive currents in the AC-grid. Figure 7 also visualizes the lengths of the conductors and when the cross sections of these conductors are known, the voltage drops and the copper losses in the AC-grid can be calculated. Information about the cross sections of the cables is given in Figure 9 (the numbers of the feeders are indicated in Figure 7).
Figure 8: Overview of load power consumption and power factor
One “office unit” consists of a computer with a monitor (consuming 180 W) and a table lamp (consuming 30 W). The total power consumed by the system is almost 30 kW. Notice the impedance Z in Figure 7 between the substation transformer and the switchgear. This impedance (0.443 + j0.07 Ω/km at 20°C) represents 20 m of 70 mm2 cables implying a maximum current of 145 A.
The cable between the substation transformer and the switchgear can be considered in AC and DC. When considering DC, the rectifier is placed immediately after the transformer. If the DC cable between transformer/rectifier and switchgear accounts for a voltage drop which is too high, it is also possible to place the rectifier at the switchgear and still use the AC-connection between the transformer and the switchgear.
Figure 9: Load and feeder data of the grid visualized in Figure 7
5.1: Calculating the voltage drops and the copper losses
Consider a single-phase AC-grid having a voltage level E (in the present application, E = 230 V) and a load consuming an active power P and a reactive power Q = P tgφ. The resistance of the cable is given by R (at 80°C) and its reactance is given by X (for instance based on a specific reactance x = 0.1 Ω/km). The voltage drop ΔV is calculated by
and the power losses ΔP are
Consider a three phase voltage having a
phase-to-ground voltage E (E equals 230 V and the line-to-line
voltage equals 
).
The load consumes a three phase active power P and a three phase
reactive power Q = P tgφ (the three-phase load is assumed to be a
symmetrical load). In case the cable has a resistance R and an
inductance X, the voltage drop ΔV is
and the power losses ΔP are as follows
Consider a DC-grid implying only active power P and no reactive power Q is consumed. The power P of the DC-load is assumed to be equal to the active power of the AC-load. The voltage drop ΔV and the power losses ΔP are calculated
and
in case 
is the DC-grid voltage.
5.2: Simulation results
Figure 10 shows the calculated voltage drops and the calculated power losses (copper losses) when the AC-grid is used to supply all the loads. The voltage drops and the power losses are expressed as percent values. In case of the single-phase parts, the voltage drop is referred to the line-to ground rated voltage E. In case of the three-phase parts, the voltage drop is referred to the line-to-line rated voltage. Power losses are referred to the total load power for each feeder. For the cable, the power losses are referred to the system total power.
Columns 5 and 6 show the results (voltage drops and power losses) for the individual feeders. Columns 7 and 8 show the results (voltage drops and power losses) from the substation i.e. the cable connection between the transformer and the switchgear is included.
In Figure 10 (and also in the figures giving similar results when considering the DC-grid), some cells are highlighted. This indicates the feeder either exceeds the allowed 5% limit for the voltage drop or exceeds the maximum current (exceeding the maximum current implies an excessive heating of the cable decreasing the life expectancy of the insulation material). In the case of a cable section of 1.5 mm2, a maximum current of 14 A is allowed. In the case of a cable section of 2.5 mm2, a maximum current of 20 A is allowed. With cable section of 70 mm2, a maximum current of 145 A is allowed.
Figure 10: Voltage drop and power losses for the AC-supply
Notice in Figure 10 the maximum allowed voltage drop and the maximum allowed current are never exceeded. This situation can be compared with the situation visualized in Figure 11 where a DC voltage level of 326 V is used. Also in Figure 11, the maximum allowed voltage drop is never exceeded. Feeder 4 requires a current of 14.417 A but since a cable section of 2.5 mm2 is used, no problem occurs. The cable requires a current of 91.681 A but since a cable section of 70 mm2 is used, no problem occurs. In Figure 11 with 326 VDC, the maximum allowed current is never exceeded.
By decreasing the voltage level with factor , the required current increases with a the same factor . This increases the absolute voltage drop with factor , but it doubles the relative voltage drop. The increase of the current also doubles the power losses in the conductors. Indeed, when comparing the results in Figure 12 with the results in Figure 11, it is obvious that
The relative voltage drops double.
The power losses double.
The currents increase with factor .
Figure 11: Voltage drop and power losses for the DC-supply (326 VDC)
When considering the results in Figure 12, the maximum allowed current is slightly exceeded in feeder 4 (20.435 A in a 2.5 mm2 cable allowing 20 A). The maximum allowed voltage drop of 5% is never obtained.
The power losses visualized in Figure 12 in the case of 230 VDC are in general slightly lower than the corresponding losses in the case of 230 VAC (Figure 10) (when excluding the three phase loads fed by a three-phase cable). Indeed, in the case of an AC-grid some loads consume reactive current which increases the copper losses. The lower the power factor, the higher the copper losses (this is for instance the case when considering the dish washer fed by feeder 19).
The results of Figure 11 and Figure 12 show a DC-grid with voltage levels of 326 VDC or 230 VDC can be used and the cables used in the existing AC-grid can be used. By reducing the voltage level to 120 VDC, the voltage drops increase and the copper losses increase as visualized in Figure 13.
When using 120 VDC, the maximum allowed current is exceeded in feeder 3, feeder 4, feeder 22 and the 70 mm2 cable. Notice also in quite a lot of feeders, the voltage drop exceeds the maximum allowed 5% limit. Feeder 3 and feeder 4 are three-phase cables where changing into DC gives significantly larger voltage drops. Feeders 7, 9 and 13 are quite long cables (80 m, 40 m and 30 m) implying quite large voltage drops.
When considering the 120 VDC system, it is useful to place the rectifier at the switchgear and not immediately after the transformer in order to reduce the voltage drop across the 70 mm2 cable. It is also useful to realize a voltage control system in order to maintain a constant voltage at the DC-side.
Figure 12: Voltage drop and power losses for the DC-supply (230 VDC)
When reducing the DC voltage level to 48 VDC (see Figure 14), a further increase of the required currents is obtained. This implies in the great majority of the feeders the maximum allowed current is exceeded. Similarly, in almost all feeders the allowed voltage drop of 5% is exceeded. A limited voltage of 48 VDC can only be used in the cases when:
The consumed powers are lower.
The lengths of the cables are smaller.
The cables have cross-sections which are sufficiently large i.e. the existing conductors must be replaced.
Low DC-voltages like 48 VDC, 24 VDC or even 6 VDC are standardized but they are only applicable in case the distances are sufficiently short and/or the consumed powers are sufficiently low.
Figure 13: Voltage drop and power losses for the DC-supply (120 VDC)
6: Maximum voltage drop and maximum current limitations
Depending on the voltage level and the feeder length, the maximum power which can be fed can be limited by
the maximum allowed current,
the voltage drop limitation.
The most restrictive of these two conditions is dominant. The cable section S determines the maximum allowed current Imax which limits the heat dissipation and the temperature in the cable in order to avoid a decreased life expectancy of the cable insulation. In the case of a voltage level VDC, the maximum power
does not depend on the cable length as visualized in Figure 15 and Figure 16. This independent Pmax1 of cable length increases as the cable section S increases and as the voltage level VDC increases.
Figure 14: Voltage drop and power losses for the DC-supply (48 VDC)
The maximum power than can be supplied without exceeding the 5% voltage drop is given by
where ρ is the specific resistance at 80°C and L is the cable length. In the case of a longer cable, the maximum power Pmax2 decreases. The actual power which can be supplied is the minimum of Pmax1 and Pmax2. In the case of smaller cable lengths, Pmax1 is dominant. If cable lengths are larger , Pmax2 is dominant as visualized in Figure 15 and Figure 16.
Figure 15 visualizes Pmax in the case of a DC-grid with a cross-section S = 1.5 mm2 and a cross-section S = 2.5 mm2. The thin line is valid when the rated voltage equals 326 VDC. The thick line is valid when the rated voltage equals 230 VDC. Figure 16 visualizes Pmax when DC-grid is with a cross-section S = 1.5 mm2 and a cross-section S = 2.5 mm2. The thin line is valid when the rated voltage equals 120 VDC. The thick line is valid when the rated voltage equals 48 VDC.
Figure 15: Pmax in case of 326 VDC and 230 VDC
Figure 16: Pmax in case of 120 VDC and 48 VDC
7: Protection of low-voltage DC-systems
Since a DC-current has no natural zero crossings, interrupting a DC-current is more difficult than interrupting an AC-current. This observation is valid in the case of a normal load current, an overload current and short circuit current. Due to this reason dedicated DC-contactors, DC circuit breakers and DC-fuses exist .
In a low-voltage DC-system, it is also possible to use AC circuit breakers provided that the ratings are adjusted by proper correction factors which are provided by the manufacturers.
A thermal-magnetic circuit breaker [Sannino, Gregory] allows the protection against overload currents using the thermal part of the current-time-characteristic. The tripping time is the same for AC and for DC applications since the bimetal sensor reacts to the RMS value of the current which is the same for AC and DC.
When protecting against short circuit currents, the circuit breakers opens as fast as possible. Tripping occurs due to the electromagnetic force which is proportional with the square of the instantaneous value of the current.
Based on catalogs from Siemens or ABB [Sannino], information about the rated voltages, rated currents and also the breaking capacity is available. When considering the project visualized in Figure 7 at Chalmers University of Technology, a sufficient breaking capacity was obtained. For instance a more effective arc interruption can be obtained by mounting poles in series (especially for voltages higher than 250 VDC).
8: Conclusion
Due to the existing dominance of AC-grids, they will not disappear very fast. However, the rise of distributed renewable energy sources and the need of a reliable power supply for an increasing number of sensitive loads will probably encourage the installation of local DC-grids. The competition between AC-grids and DC-grids has a growing attention of the academic world and the situation differs from the situation at the age of Edison and Tesla.
References
Agustoni A., Brenna M. and Tironi E., “High Quality DC local distribution network with photovoltaic generation and storage systems”, 7th Electrical Power Quality and Utilisation Conference (EPQU ‘03), September 17-19, 2003, Cracow, Poland, pp. 623-632.
Brenna M., Tironi E. and Ubezio G. “Proposal of a Local DC Distribution Network with Distributed Energy Resources”, 11th International Conference on Harmonics and Quality of Power ICHQP, 2004, pp. 397-402.
Ciezki J.G. and Ashton R.W., “Optimal Design of a Soft-Switched DC-DC Converter For a Prototype DC Distribution System”, 35th Annual IEEE Power Electronics Specialists Conference, Aachen, Germany, 2004, pp. 1731-1736.
Gregory G.D., “Applying low-voltage circuit breakers in direct current”, IEEE Transactions on Industry Applications, vol. 31, pp. 650-657, July/Augustus 1995.
Karlsson P. and Svensson, “DC bus Voltage Control for a Distributed Power System”, IEEE Transactions on Power Electronics, vol. 18, pp. 1405-1412, November 2003.
Nilsson D. and Sannino A., “Efficiency analysis of low- and medium-voltage DC distribution systems”, IEEE Power Engineering Society General Meeting, PES 2004, vol. 2, pp. 2315-2321.
Sannino A., Postiglione G. and Bollen M.H.J., “Feasibility of a DC Network for Commercial Facilities”, IEEE Transactions on Industry Applications, vol. 39, pp. 1499-1507, September/October 2003.
Electricity losses caused by corona discharge in the overhead lines and the construction-material methods reduce them
The overhead high voltage electricity losses occur. Part of these losses can not be avoided. This applies to energy loss associated the emitted of wires with a small but non-zero thermal resistance in accordance with the Joule's law.
The second source of losses associated with the occurrence of the wires so-called of corona discharge, which is one embodiment of a partial discharge of the gases. As it is known, in the air located in the electric field at the field intensity value is reached approximately:
,
V·m-1,
(1)
takes place its ionization, which decreases the resistivity of the air, and thus results in increased current flow. The high voltage current flows in the direction of wire-ground, causing the losses of electric energy. It results in the conclusion that the use of appropriate construction wires can reduce losses caused by corona discharge, and thus to a more efficient use of energy fuels used in power plants to produce electricity and reduce greenhouse gas emissions generated during combustion.
To explain ways to reduce losses caused by corona discharge first analyze the phenomenon. When the value of the electric field intensity on the surface of the cylindrical wire exceeds the initial value E0 corona discharge, electrons being in small amounts in the air are accelerated to the energy field, greater than the ionization energy of the gas molecules (nitrogen and oxygen) contained in the air. After the collision an electron from a neutral molecule reaches its ionization and the formation of a second free electron. After their further accelerated in the constantly interact with loads of electric field and collisions with molecules very quickly created an avalanche of electrons, and hence, an increase in the concentration of electrons. This phenomenon is illustrated in figure 1.
Fig. 1. Electron avalanche formation under the influence of a uniform electric field,
λ - free path of the electron.
It should be emphasized that the process-ionization ion does not participate in further avalanche ionization. It is related to the large difference in the masses of ions and electrons, and thus, accelerated ion can not knock an electron from a neutral particle.
The increase in carrier concentration takes place as a result of the so-called collision ionization, which takes place in the following manner. For the ionization of neutral particles of air the ionization energy Wj is necessary. The first electron avalanche which starts the process is usually stamped by cosmic rays from the neutral particle. Within one second cubic centimeter of air under the influence of cosmic rays produced only about 10 pairs of ion-electron. The free electron is accelerated in an electric field. After traveling free path λ is obtained of the electric field energy:
, (2)
where: λ – free path, which overcomes the electron between two successive collisions with neutral particle of air, e – electron charge, E – electric field intensity.
After passing by electron free path λ comes to its collision with the neutral particle. When the electron energy, obtained from the electric field is:
,
(3)
comes only to the excitation of the particle. With the increase in the value of the field intensity above E0 - the formula (1), there is the opposite situation and comes to knock an electron from a neutral molecule, that is, to its ionization. In the air, instead of one, there are two free electrons. The limit of electric field intensity, which corresponds to the transition to the collision ionization, and to a corona discharge means, we can calculate with the condition of W = Wj, having formulas (2) and (3):
. (4)
From the kinetic theory of gases known that air particle may be with approximation replaced by the balls of the same cross-sectional area equal to S, and its content per unit volume in N. Then, the mean free path is described by the formula:
(5)
Substitute this value into the formula for the initial field intensity corona discharge (4):
(6)
In the above formula all parameters, except for N are fixed. The value of N we get from the equation of state of one mole of an ideal gas after its transformation. First divide the equation of state of one mole of an ideal gas by the Avogadro constant N0 = 1,380·1023 J/(cząst·K):
(7)
We get:
, (8)
because:
,
where: k – Boltzmann constant is :
(9)
Substituting the result of (9) to the formula on the initial field intensity corona discharge (6) yields:
(10)
As you can see from the formula (10), the initial field intensity corona discharge is not constant. It depends on the weather conditions. The increase in atmospheric pressure causes the gas is compressed and reduced mean free path λ, and hence, the need to increase the initial field intensity corona discharge. The increase in air temperature result lowers E0. It turns out that other atmospheric conditions such as fog, rain, snow also affect the value of the initial field intensity corona discharge.
In this technique, instead of equation (10) apply a formula, in which to the calculation of changes in the value of the initial field intensity corona discharge, caused by changes in atmospheric pressure and temperature are taken into account changes in these parameters compared to normal pressure, amounting p0 = 1013 hPa, and the fiducial temperature T0 = 20ºC:
(11)
Therefore, formula (10) is transformed to:
(12)
where: E0N – initial field intensity corona discharge under normal conditions (p0 = 1013 hPa, fiducial temperature T0 = 20ºC).
The formation of electron avalanches dramatically increases the concentration of electrons. This results in accordance with the Ohm's law in differential form a sharp increase in current density:
,
[Am-2] (13)
where: j – current density, e – electron charge, n – density of electrons, μ – electron mobility.
The same increase in the concentration of ions has practically no effect on the current density, because the mass of ions is much greater than the electron. This means that the mobility of ions is much smaller than the electron.
Transmission of electrical energy from the power plant where it was produced, for large distances used are the high voltage lines. The transmission takes place only in the three-phase lines. In figure 2a we can see the distribution strength of the electric field lines for the case of three-phase high voltage lines having in each of the phases of a single wire they are used a cylindrical-shaped wires. Radius wire is r, the distance wire from the surface of the ground A.
a)
|
|
b)
|
Fig. 2. The distribution strength of the electric field lines (a) and the distribution of the electric field in the direction of the ground (b) for a single wire of radius r, located at a distance A from the surface of the ground. In the figure marked the formation of corona discharge zone.
The amplitude of electric field in a direction from the surface of the wire to ground is described with the formula:
,
[Vm-1] (14)
where: r – radius wire, U – rms phase voltage, A – distance from the wire to the ground, x – the distance from the cable surface toward the surface of the ground.
Electric field intensity distribution depending on the distance from the surface wire towards the ground, calculated from formula (4) is shown in Figure 2b.
As it can be seen from figure 2b, near to the wire surface there is an area containing the field intensity value higher than the initial value of the intensity corona discharge EM > E0. In this area for the air ionization and the formation of electron avalanches causing corona discharge and loss of electricity will be reached. This phenomenon is called a corona discharge. In the area corona discharge formed electromagnetic emissions starting from visible light and radio waves to the range. In this area there are also sound phenomena. This area is often called the crown.
The first and most obvious way to eliminate corona discharge and loss of electricity caused by corona discharge in the high-voltage power lines results from the analysis of the equation (14). This is the increase wire radius r to a value at which the field intensity at the wire surface is aligned with the initial value E0 of the corona discharge intensity. Calculations using formula (14) provide for a line of 220 kV wire radius r = 12 mm. This value is acceptable from the point of view of materials used for the manufacture of wires. Power line carrier wire is twisted with several thin layers of single aluminum wires. In the middle of wire several conductors of steel are placed serving to improve the mechanical strength of the wire. Wire size for power line carrier is shown in figure 4.
a) |
b) |
|
|
Fig. 3. View (a) and cross section (b) wire of the steel and aluminum to overhead power lines: the number of aluminum wires – 54, steel – 7, cross section aluminum wires – 519,5 mm2, steel (core) – 67,35 mm2.
Cross section area of all the aluminum conductors is selected on the basis of the value current intensity transmitted by the given line and is limited with the mechanical strength of the wire and other parameters of the overhead line. For the overhead line 400 kV for which radius at which there is no corona discharge, it should be increased to r = 25 mm. This is not acceptable because of the large mass and the price of such wire.
In order to reduce the corona discharge without increasing weight the wire apply so-called group of wires, consisting of two or more wires, the total cross section of which is equal to that of a single wire, intended for conducting a current of the intensity designed power line carrier. This means that the line beam is used, each of n wires of which has a cross sectional area of n times smaller than in the case of a single wire. The radius of each wire of the bundle consisting of n wires is
(15)
where: r1 – radius of a single wire.
The examples of group of conductors are shown in figure 4. For the number of wires in the bundle n = 2 the distance between them is a. For n > 2 wires are placed at the vertices of a regular polygon. For n = 3 is the triangle, n = 4 – a square. The distance between adjacent wires in the bundle is usually a = 0.40 m. This arrangement of the conductors of the electric field reduces the intensity on the surface.
The radius of a replacement wire in the bundle is:
, (16)
where: r1 – radius of a single wire; a – the spacing between adjacent wires; n – number of wires in a bundle.
The radius of the circle described on the vertices of a regular polygon:
(17)
In order to prevent approaching of the wires in the bundle under the influence of wind special insulation spacers are used.
a) |
b) |
|
|
|
|
c) |
d) |
|
|
Fig. 4. Single wire and examples of group of wires for n = 2, 3, 4.
Formula (17) shows that by increasing the number of wires in the bundle, and a constant value of the distance between adjacent wires and the increase in the number n increases the radius Rn of the circle described at the vertices of a regular polygon, in which the individual wires are arranged, thereby reducing the field strength electrical wires on the surface. By suitable selection of the number n and spacing between the conductors can be effectively reduced field intensity and eliminate phenomenon the corona discharge under normal conditions. Corona discharge phenomenon can occur in rain or fog even in a selected wires system.
When corona discharge occurs under the conditions of absence of rainfall, the condition should be satisfied:
(18)
where: Uf – phase voltage line, UU – voltage the occurrence of corona discharge.
Voltage UU can be calculated from the semi empirical formula Peek `a, which was developed on the basis of the results of studies corona discharge:
, (19)
where: ma – factor depending on the state of the weather, the sunny weather ma = 1, rain or fog ma = 0.8, mp – coefficient depending on the state of the surface conductors, the new wires mp = 1, old mp = 0.93 – 0.98; δ – relative density of air, formula (11); rz – radius of wire replacement, formula (16); a – the distance between the wires in a bundle.
Peek on the basis of measurements has also developed a semi empirical formula for the power loss during the corona discharge:
(20)
where: f – mains frequency, UU – voltage corona discharge, formula (19), Uf – rms phase voltage, rz – radius of wire replacement, formula (16), a – the distance between the wires in a bundle; δ – relative density of air, formula (11).
It follows that by using a group of wires without increasing of their weight we can effectively reduce electricity losses in overhead lines due to the occurrence of the phenomenon of corona discharge in power lines, and thus reducing fuel consumption and greenhouse gas emissions at power plants for the production of electricity.
Literature
R. Resnik, D. Halliday, K.S. Krane: Physics (volume 1), 1992.
G.S. Kuchynski (Editor): High Voltages Technology, Sankt-Petersburg, 2003.
Tele-Fonika Kable Sp. z o.o. S.K.A. catalog – Electroenergy cables and wires (Kable i przewody elektroenergetyczne), http://www.tfkable.com/sites/default/files/karty-katalogowe/afl-8_525_wg_pse-ts.pr525.nn_pl_2008w1_en_50182_mt02-2012.pdf
Reduction of electric energy losses, fuel consumption and greenhouse gases emission by reactive power compensation in electric receivers
In electric network, powered by alternating voltage with frequency 50 Hz, devices and electric receivers, which have got inductances or capacities in their circuits, besides consuming active electric energy consume also reactive energy. In the receiver the active component of energy evolves in different type of energy, for the production of which this device was designed.
Mostly it is mechanical energy, into which the electric energy is transformed by means of electric engines in various types of devices. It could be vehicles, powered by electric energy, such as locomotives on the railways, trams, trolley buses, trains of metro lines. Electrical engines are used in industry for drivers to machine tools, pumps, fans, conveyors and many other machines.
Another often used type of energy is thermal energy, into which electric energy can be easily transformed.
Another widely utilized energy type, into which electric energy is transformed, is light energy and electromagnetic energy from different frequency ranges, which is used in television, radio and medicine.
In electric receivers containing inductance (it can be a coil in electric engine), besides intensity current active component, intensity current reactive component occurs, phase-shifted by an angle 90º in respect to active component, which is presented in figure 1.
In receivers or network elements, which have got capacity like cables lines, phase shift of intensity current reactive component occurs in opposite direction, it means by an angle -90º, which is presented in figure 2.
Fig. 1. Components of electric current for circuit contains induction: IP – active current, IQ – reactive current
Fig. 2. Components of electric current for circuit contains capacity: IP – active current, IQ – reactive current
Two intensity current components – active and reactive – correspond to power components: active power and reactive power. Active electric energy could be changed into other form of energy used in industry device.
Active power consumed by device from network powered by three-phase voltage is presented with the formula:
(1)
where, U – chase voltage, IP – intensity current active.
Reactive electric energy cannot be changed into other form of energy or effective work and occurs only in alternating current circuits, however it is necessary for operation of electric devices (it is needed to induce variable magnetic fields of engines, magnetization of transformer cores and charging of capacity of open-wire transmission lines and underground lines). Reactive energy flows between sources (power station) and alternating current receivers and is received by only perfect coils and capacitors, and consumption by other receivers is limited and is formulated by the value of the power factor cosφ.
Active and reactive power can be graphically presented as a triangle of power (fig. 3). It follows that, apparent power is a vector sum of active and reactive power. Resulting from this triangle cosφ is the ratio of active to apparent power, and tgφ is a ratio of reactive to active power.
Fig. 3. Triangle of power.
In receivers inductive reactive power connected with induction elements, for example engines, induction furnaces, and capacitive reactive power connected with capacitors or long live cable sections are distinguished.
Reactive power is presented with the formula:
(2)
The unit of reactive power is var: [Q] = 1 var
Geometric sum of active and reactive power is called as apparent power:
(3)
The ratio of active power to apparent power is called as power factor:
(4)
At supplies by sinusoidal voltage and current, power factor is equal to the cosine of phase angle between current and voltage at given point in the network and that is why often defined as:
(5)
Power factor cosφ is a generally accepted indicator of energy management and electric energy parameter receivers, although more useful in balancing energy is the ratio of the active and passive devices tgφ.
(6)
Rated power factor cosφ is the power factor of the receiver electric energy at the rated operating conditions. It is given in the catalogues.
The rms value of the power factor at the change of the reactive power and apparent power, active power at a constant is in figure 3.
Fig. 4. Dependence consumption reactive power and apparent power at consumption active power in depending on the power factor
Figure 4 shows that the reduction of the power factor cosφ receiver electrical leads to an increase in the value of reactive power and apparent power, needed for the proper functioning of the device. This is particularly important in factories with electric motors that need to provide them with the reactive power.
Reactive power can be produced at a power station and then sent to a power line to a receiver. It results in the increased consumption and increased greenhouse gas emissions from power station. The second adverse effect of the production of reactive power in power station is the increased losses of electricity in power lines carrier supplying electricity to customers. This can be explained by means of figure 1. When current flows from the power station it has in-phase component and reactive component, the resultant current intensity is higher than that of the in-phase component. This means that the energy loss in the conversion of heat, occurring in the wires of the power line from the power station to the recipient, called the Joule heat and will increase in:
(7)
where: R – wire resistance.
Active power losses in the power system components depend on the load and increase at the reducing the power factor receivers. Can be expressed by the formula:
(8)
They are inversely proportional to the square of the power factor.
Active power losses, which cause flowing in the power grid reactive power cause a decrease in the efficiency of the transmission system. There is also a reduction in the production capacity of active power generators and thus to the need for devices with higher current rated. Power of the electric generator is limited by the current flowing in the armature windings but turbine is selected to the active power of the electric generator and therefore to its rated power factor. If the generator working at cosφ at less than the rated then the thermal load field frame limits the use of the active power generator. Low power factor also affects the decrease in the apparent power issued by the generator as a result of the growth impact of the armature.
In the transmission lines the increased voltage drops are formed. The relative voltage drop element of the power grid with a resistance R and reactance Q transmitting active power P and reactive power Q can be calculated by means of the formula:
(9)
It can be seen a linear dependence voltage drop tg
and the ratio X/R, which is a constant
value for a given power grid element. The increase in voltage drops
with decreasing power factor adversely affects the operation of
receivers and difficult to adjust the tension.
From the above considerations it is obvious that the improvement of the power factor is of great importance for both economic and ecological aspects.
Electricity suppliers compensate their losses by imposing limits to energy consumers of reactive power. Exceeding these limits is associated with incurring additional fees.
In order to improve the negative effects of the demand receivers for reactive power different methods of compensation are applied and can be divided into:
natural methods of reactive power factor correction
the methods to improve the power factor using compensatory devices.
The main way to improve the power factor of the recipients should be natural ways that do not require the installation of additional equipment for the production of reactive power. Such methods rely on the proper selection and operation of reception equipment, mainly by eliminating idling and at low loads.
Only after exhausting all the possibilities offered by natural ways for further improvement of cosφ it can be realized by the installation for electricity consumers of reactive power sources, i.e. the use of reactive power compensation.
Reactive power compensation is based on its production at the place it is required. You will not need to send it from the manufacturer to the customer. This reduces the current in the power grid, and, hence, reduces the voltage drop and power loss in transmission lines. However, the load variation during the day may result in certain time intervals for power grid over-compensation. It is important that the correct choice of power compensation equipment is primarily the capacitors.
Artificially compensating reactive power devices use the effect of reactive power generation by energy capacitors. The principle of operation of such compensation consists in that the phase shift current flowing by the capacitor is opposite to the induction current, which results from fig. 1 and 2. When a phase shift caused by the element inductors occurs in the receiver, capacitors should be joined to the electric circuit with a capacity providing voltage resonance in the electric circuit. During the resonance voltage phase angle φ = 0. The condition of resonance voltage is:
(10)
where: f – mains frequency; L – inductance receiver; C – capacity capacitor compensation reactive power.
Power capacitors produced as a unit for reactive power compensation have many positive attributes like those:
very low active power losses for compensation of 1 kvar reactive power (0.003 – 0.005 kW/kvar);
the ability to create a capacitor bank with arbitrary powers;
small size and thus small space requirement, easy installation and maintenance;
the ability to install anywhere on your network and virtually at any rated voltage;
construction of capacitor units with different voltages and power ratings;
Capacitors, however, are not devoid of some unfavourable characteristics such as:
the possibility of overloads and surges when turning on the battery and the occurrence of surge during the shutdown;
sensitivity to the presence of higher harmonics in the supply voltage;
As it can be seen from formula (10) in order to obtain the reactive power compensation the appropriate capacitance value should be selected. Due to the placement of capacitors we have to deal with compensation individual, group, central and mixed.
Compensation individual is to place the capacitor directly at the receiver. This does not require the use of additional control devices because the capacitor switched on and off the same adapter like the receiver. This solution is used in the case of light sources such as fluorescent lamps.
In the case of electric motors the degree of compensation is chosen so that at any time no over-compensation exists. Reactive power compensated by capacitors should compensate the reactive power at no-load running, that is, the value of cosφ = (0.9 – 0.95) at full load.
Compensation group is to connect the capacitor bank switching to the power rails so that the compensation was a subject to a group of receivers powered by with the switchgear.
Compensation central is to install capacitor banks in the transformer station or switching center.
Both to compensation central and compensation group is used automatic control. Control system by measuring the voltage and current supply, such as:
tension between the measured phases [V];
phase current measurement [A];
the frequency of the mains voltage [Hz];
apparent power [kVA];
active power [kWh];
reactive power [kVar];
the odd harmonic currents (1. -19.) w %;
harmonic current distortion factor THDI w %;
the odd harmonic voltage (1 .-19.) w %;
harmonic voltage distortion factor THDU w %;
the number of attached individual degrees.
Based on the analysis of measurement results, the reactive power regulator can choose the number of attached capacitors and their capacity so that the condition of reactive power compensation (10) has been met, but it was not over-compensated.
To conclude that the technology of reactive power compensation using a capacitor bank and modern reactive power regulator allows you:
reduction in demand for fuels used in power plants to produce electricity;
reduction in greenhouse gas emissions from the production of electricity;
reducing the losses in electricity transmission lines;
to improve working conditions and reliability of electric generators.
Literature
R. Resnik, D. Halliday, K.S. Krane: Physics (volume 1), 1992.
G.S. Kuchynski (Editor): High Voltages Technology, Sankt-Petersburg, 2003.