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Power transmission
BENT SØRENSEN
CHAPTER
26
POWER TRANSMISSION
26.1 Normal conducting lines At present, electric current is transmitted in major utility grids, as well as distributed locally to each load site by means of conducting wires. Electricity use is dominated by alternating current (AC), as far as utility networks are concerned, and most transmission over distances up to a few hundred kilometres is by AC. For transmission over longer distances (e.g. by ocean cables), conversion to direct current (DC) before transmission and back to AC after transmission is common. Cables are either buried in the ground (with appropriate electric insulation) or are overhead lines suspended in the air between masts, without electrical insulation around the wires. Insulating connections are provided at the tower fastening points, but otherwise the low electric conductivity of air is counted on. This implies that the losses will comprise conduction losses depending on the instantaneous state of the air (the “weather situation”), in addition to the ohmic losses connected with the resistance R of the wire itself, Eheat = RI2, with I being the current. The leak current between the elevated wire and the ground depends on the potential difference as well as on the integrated resistivity, such that the larger the voltage, the further the wires must be placed from the ground. Averaged over different meteorological conditions, the losses in a standard AC overhead transmission line (138−400 kV, at an elevation of some 15−40 m) are currently a little under 1% per 100 km of transmission (Hammond et al., 1973), but the overall transmission losses of utility networks, including the finely branched distribution networks in the load areas, may for many older, existing grids amount to some 12−15% of the power production, for a grid extending over a land area of about 104 km2 (Blegaa et al., 1976). Losses are down to 5−6% for the best systems installed at present and are expected to decrease further to the level of 2−3% in the future, when the currently best technologies penetrate further (Kuemmel et al., 228
26. POWER TRANSMISSION 1997). This loss is calculated relative to the total production of electricity at the power plants attached to the common grid, and thus includes certain inplant and transformer losses. The numbers also represent annual averages for a power utility system occasionally exchanging power with other utility systems through interconnecting transmission lines, which may involve transmission distances much longer than the linear extent of the load area being serviced by the single utility system in question. The trend is to replace overhead lines by underground cables, primarily for visual and environmental reasons. This has already happened for the distribution lines in most of Europe and is increasingly also being required for transmission lines. In Japan and the United States, overhead lines are still common. Underground transmission and distribution lines range from simple coaxial cables to more sophisticated constructions insulated by a compressed gas. Several trans-ocean cables (up to 1000 km) have been installed in the Scandinavian region in order to bring the potentially large surpluses of hydropower production to the European continent. The losses through these high-voltage (up to 1000 kV) DC lines are under 0.4% per 100 km, to which should be added the 1−2% transmission loss occurring at the thyristor converters on shore that transform AC into DC and vice versa (Ch. 19 in IPCC, 1996b). The cost of these low-loss lines is currently approaching that of conventional AC underwater cables (about 2 euro kW−1 km−1; Meibom et al., 1999; Wizelius, 1998). One factor influencing the performance of underground transmission lines is the slowness of heat transport in most soils. In order to maintain the temperature within the limits required by the materials used, active cooling of the cable could be introduced, particularly if large amounts of power have to be transmitted. For example, the cable may be cooled to 77 K (liquid nitrogen temperature) by means of refrigerators spaced at intervals of about 10 km (cf. Hammond et al., 1973). This allows increased amounts of power to be transmitted in a given cable, but the overall losses are hardly reduced, since the reduced resistance in the conductors is probably outweighed by the energy spent on cooling. According to (3.1), the cooling efficiency is limited by a Carnot value of around 0.35, i.e. more than three units of work have to be supplied in order to remove one unit of heat at 77 K. Off-shore issues The power from an off-shore wind farm is transmitted to an on-shore distribution hub by means of one or more undersea cables, the latter providing redundancy that in the case of large farms adds security against cable disruption or similar failures. Current off-shore wind farms use AC cables of up to 150 kV (Eltra, 2003). New installations use cables carrying all three leads plus control wiring. In the interest of loss minimisation for larger inVII. ENERGY TRANSMISSION
229
BENT SØRENSEN stallations, it is expected that future systems may accept the higher cost of DC−AC conversion (on shore, the need for AC−DC conversion at sea depends on the generator type used), similar to the technology presently in use for many undersea cable connections between national grids (e.g. between Denmark and Norway or Sweden). Recent development of voltage sourcebased high voltage direct current control systems to replace the earlier thyristor-based technology promises better means of regulation of the interface of the DC link to the on-shore AC system (Ackermann, 2002).
26.2 Superconducting lines For DC transmission, the ohmic losses may be completely eliminated by use of superconducting lines. A number of elements, alloys and compounds become superconducting when cooled to a sufficiently low temperature. Physically, the onset of superconductivity is associated with the sudden appearance of an energy gap between the “ground state”, i.e. the overall state of the electrons, and any excited electron state (similar to the situation illustrated in Fig. 14.3, but for the entire system rather than for individual electrons). A current, i.e. a collective displacement (flow) of electrons, will not be able to excite the system away from the “ground state” unless the interaction is strong enough to overcome the energy gap. This implies that no mechanism is available for the transfer of energy from the current to other degrees of freedom, and thus the current will not lose any energy, which is equivalent to stating that the resistance is zero. In order that the electron system remains in the ground state, the thermal energy spread must be smaller than the energy needed to cross the energy gap. This is the reason why superconductivity occurs only below a certain temperature, which may be quite low (e.g. 9 K for niobium, 18 K for niobium−tin, Nb3Sn). However, there are other mechanisms that in more complex compounds can prevent instability, thereby explaining the findings in recent years of materials that exhibit superconductivity at temperatures approaching ambient (Pines, 1994; Demler and Zhang, 1998). For AC transmission, a superconducting line will not be loss-free, owing to excitations caused by the time variations of the electromagnetic field (cf. Hein, 1974), but the losses will be much smaller than for normal lines. It is estimated that the amount of power that can be transmitted through a single cable is in the gigawatt range. This figure is based on suggested designs, including the required refrigeration and thermal insulation components within overall dimensions of about 0.5 m (cable diameter). The power required for cooling, i.e. to compensate for heat flow into the cable, must be considered in order to calculate the total power losses in transmission. For transmission over longer distances it may, in any case, be an advantage to use direct current, despite the losses in the AC−DC and DC−AC con230
26. POWER TRANSMISSION versions (a few per cent as discussed above). Future intercontinental transmission using superconducting lines has been discussed, notably by Nielsen and Sørensen (1996), Sørensen and Meibom (2000), and Sørensen (2004). Motivation for such thoughts is of course the location of some very promising renewable energy sites far from the areas of load. Examples would be solar installations in the Sahara or other desert areas, or wind power installations at isolated rocky coastlines of northern Norway or in Siberian highlands. Finally, radiant transmission of electrical energy may be mentioned. The technique for transmitting radiation and re-collecting the energy (or some part of it) is well developed for wavelengths near or above visible light. Examples are laser beams (stimulated atomic emission) and microwave beams (produced by accelerating charges in suitable antennas), ranging from the infrared to the wavelengths used for radio and other data transmission (e.g. between satellites and ground-based receivers). Large-scale transmission of energy in the form of microwave radiation has been proposed in connection with satellite solar power generation, but is not currently considered practical. Short distance transmission of signals, e.g. between computers and peripheral units, do involve only minute transfers of energy and is already in widespread use.
VII. ENERGY TRANSMISSION
231
CHAPTER
26
POWER TRANSMISSION
26.1 Normal conducting lines At present, electric current is transmitted in major utility grids, as well as distributed locally to each load site by means of conducting wires. Electricity use is dominated by alternating current (AC), as far as utility networks are concerned, and most transmission over distances up to a few hundred kilometres is by AC. For transmission over longer distances (e.g. by ocean cables), conversion to direct current (DC) before transmission and back to AC after transmission is common. Cables are either buried in the ground (with appropriate electric insulation) or are overhead lines suspended in the air between masts, without electrical insulation around the wires. Insulating connections are provided at the tower fastening points, but otherwise the low electric conductivity of air is counted on. This implies that the losses will comprise conduction losses depending on the instantaneous state of the air (the “weather situation”), in addition to the ohmic losses connected with the resistance R of the wire itself, Eheat = RI2, with I being the current. The leak current between the elevated wire and the ground depends on the potential difference as well as on the integrated resistivity, such that the larger the voltage, the further the wires must be placed from the ground. Averaged over different meteorological conditions, the losses in a standard AC overhead transmission line (138−400 kV, at an elevation of some 15−40 m) are currently a little under 1% per 100 km of transmission (Hammond et al., 1973), but the overall transmission losses of utility networks, including the finely branched distribution networks in the load areas, may for many older, existing grids amount to some 12−15% of the power production, for a grid extending over a land area of about 104 km2 (Blegaa et al., 1976). Losses are down to 5−6% for the best systems installed at present and are expected to decrease further to the level of 2−3% in the future, when the currently best technologies penetrate further (Kuemmel et al., 228
26. POWER TRANSMISSION 1997). This loss is calculated relative to the total production of electricity at the power plants attached to the common grid, and thus includes certain inplant and transformer losses. The numbers also represent annual averages for a power utility system occasionally exchanging power with other utility systems through interconnecting transmission lines, which may involve transmission distances much longer than the linear extent of the load area being serviced by the single utility system in question. The trend is to replace overhead lines by underground cables, primarily for visual and environmental reasons. This has already happened for the distribution lines in most of Europe and is increasingly also being required for transmission lines. In Japan and the United States, overhead lines are still common. Underground transmission and distribution lines range from simple coaxial cables to more sophisticated constructions insulated by a compressed gas. Several trans-ocean cables (up to 1000 km) have been installed in the Scandinavian region in order to bring the potentially large surpluses of hydropower production to the European continent. The losses through these high-voltage (up to 1000 kV) DC lines are under 0.4% per 100 km, to which should be added the 1−2% transmission loss occurring at the thyristor converters on shore that transform AC into DC and vice versa (Ch. 19 in IPCC, 1996b). The cost of these low-loss lines is currently approaching that of conventional AC underwater cables (about 2 euro kW−1 km−1; Meibom et al., 1999; Wizelius, 1998). One factor influencing the performance of underground transmission lines is the slowness of heat transport in most soils. In order to maintain the temperature within the limits required by the materials used, active cooling of the cable could be introduced, particularly if large amounts of power have to be transmitted. For example, the cable may be cooled to 77 K (liquid nitrogen temperature) by means of refrigerators spaced at intervals of about 10 km (cf. Hammond et al., 1973). This allows increased amounts of power to be transmitted in a given cable, but the overall losses are hardly reduced, since the reduced resistance in the conductors is probably outweighed by the energy spent on cooling. According to (3.1), the cooling efficiency is limited by a Carnot value of around 0.35, i.e. more than three units of work have to be supplied in order to remove one unit of heat at 77 K. Off-shore issues The power from an off-shore wind farm is transmitted to an on-shore distribution hub by means of one or more undersea cables, the latter providing redundancy that in the case of large farms adds security against cable disruption or similar failures. Current off-shore wind farms use AC cables of up to 150 kV (Eltra, 2003). New installations use cables carrying all three leads plus control wiring. In the interest of loss minimisation for larger inVII. ENERGY TRANSMISSION
229
BENT SØRENSEN stallations, it is expected that future systems may accept the higher cost of DC−AC conversion (on shore, the need for AC−DC conversion at sea depends on the generator type used), similar to the technology presently in use for many undersea cable connections between national grids (e.g. between Denmark and Norway or Sweden). Recent development of voltage sourcebased high voltage direct current control systems to replace the earlier thyristor-based technology promises better means of regulation of the interface of the DC link to the on-shore AC system (Ackermann, 2002).
26.2 Superconducting lines For DC transmission, the ohmic losses may be completely eliminated by use of superconducting lines. A number of elements, alloys and compounds become superconducting when cooled to a sufficiently low temperature. Physically, the onset of superconductivity is associated with the sudden appearance of an energy gap between the “ground state”, i.e. the overall state of the electrons, and any excited electron state (similar to the situation illustrated in Fig. 14.3, but for the entire system rather than for individual electrons). A current, i.e. a collective displacement (flow) of electrons, will not be able to excite the system away from the “ground state” unless the interaction is strong enough to overcome the energy gap. This implies that no mechanism is available for the transfer of energy from the current to other degrees of freedom, and thus the current will not lose any energy, which is equivalent to stating that the resistance is zero. In order that the electron system remains in the ground state, the thermal energy spread must be smaller than the energy needed to cross the energy gap. This is the reason why superconductivity occurs only below a certain temperature, which may be quite low (e.g. 9 K for niobium, 18 K for niobium−tin, Nb3Sn). However, there are other mechanisms that in more complex compounds can prevent instability, thereby explaining the findings in recent years of materials that exhibit superconductivity at temperatures approaching ambient (Pines, 1994; Demler and Zhang, 1998). For AC transmission, a superconducting line will not be loss-free, owing to excitations caused by the time variations of the electromagnetic field (cf. Hein, 1974), but the losses will be much smaller than for normal lines. It is estimated that the amount of power that can be transmitted through a single cable is in the gigawatt range. This figure is based on suggested designs, including the required refrigeration and thermal insulation components within overall dimensions of about 0.5 m (cable diameter). The power required for cooling, i.e. to compensate for heat flow into the cable, must be considered in order to calculate the total power losses in transmission. For transmission over longer distances it may, in any case, be an advantage to use direct current, despite the losses in the AC−DC and DC−AC con230
26. POWER TRANSMISSION versions (a few per cent as discussed above). Future intercontinental transmission using superconducting lines has been discussed, notably by Nielsen and Sørensen (1996), Sørensen and Meibom (2000), and Sørensen (2004). Motivation for such thoughts is of course the location of some very promising renewable energy sites far from the areas of load. Examples would be solar installations in the Sahara or other desert areas, or wind power installations at isolated rocky coastlines of northern Norway or in Siberian highlands. Finally, radiant transmission of electrical energy may be mentioned. The technique for transmitting radiation and re-collecting the energy (or some part of it) is well developed for wavelengths near or above visible light. Examples are laser beams (stimulated atomic emission) and microwave beams (produced by accelerating charges in suitable antennas), ranging from the infrared to the wavelengths used for radio and other data transmission (e.g. between satellites and ground-based receivers). Large-scale transmission of energy in the form of microwave radiation has been proposed in connection with satellite solar power generation, but is not currently considered practical. Short distance transmission of signals, e.g. between computers and peripheral units, do involve only minute transfers of energy and is already in widespread use.
VII. ENERGY TRANSMISSION
231