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Direct Current Transmission - Kimbark

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Page 1: Direct Current Transmission - Kimbark
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7 6 GENERAL ASPECTS OF DC TRANSMISSION

Present-day mereury-are valves for high-voltage transmission, known as excitrons, have, in addition to the anode and the mercury-pool cathode, an ignition electrode for starting the arc, one or more excitation electrodes for maintaining the are, and a control grid that prevents the are from reaching the anode until it is desired that the valve begin to conduct. There are also several grading electrodes placed between the control grid and the anode for obtaining a more uniform potential gradient than would otherwise existo The grading electrodes are kept at the desired potentials by connecting them to taps on an externaI resistance-capacitance potential divider the ends of which are connected to the anode and control grid. This system of grading elec­trodes, invented by U. Lamm in 1939, has considerably increased the peak inverse voltage that the valves can withstand.

Valves for HV dc transmission are invariably of single-phase eonstruction, in contrast to the polyphase valves with mercury-pool cathode formerly used extensively in low-voltage rectifiers for industrial and railway application.

The development of valves for HV de transmission has been carried out since World War 11 princípally by engineers in the U.S.S.R. and by the Swedish firm of Allmanna Svenska Elektriska Aktiebolaget (ASEA), with which Lamm is connected. A noteworthy feature of ASEA valves is the use of several, usually four, anodes in multiple on single-phase valves. The current ratings are 200 to 300 A per anode. Russian engineers have concentrated on single-anode valves, which so far appear to have been less successful than the ASEA valves.

About 1960, control electrodes were added to silicon diodes, giving silicon­controlled rectifiers (SCRs), also called thyristors. At present these are not capable of handling the highest voltages and powers required for HV dc transmission. Their ratings have increased, however, with surprising rapidity, and it seems certain that such valves will soon replace mercury-arc valves in HV dc use.

Experimental DC Transmission Projects and First Commercial Lines

The initiative in exploring the use of mercury-arc valves for dc transmission was taken by the General Electric Company. After two smaller experi­

2'mentsB1 . they proceeded in December 1936 to use direct current on a 17-mi (27-km) line between the Mechanicville hydroelectric pIant of the New York Power & Light Corporation and the General Electric factory in Schenectady.B1S The line carried 5.25 MW at 30 kV, 175 A. The converter at each end of the line had 12 hot-cathode glass-envelope thyratrons in 6 series pairs. The ac input at Mechanicville was at a frequency of 40 Hz, and the output at Schenectady was at 60 Hz. Thus was demonstrated a feature of dc transmission that has been important in several subsequent instalIations: frequency conversion.

1-1 HISTORICAL SKETCH

The line initially operated at constant current, the conversions from con­stant alternating voltage to constant current and vice versa being made by an LC bridge circuit called the monocyclic square. Constant-current operation was chosen because the hot-cathode tubes then used couId not withstand the high short-circuit currents expected to occur on a constant-voItage system. After the more rugged steel-envelope mercury-pool ignitron became available, however, the line was converted in 1940 to constant-voltage operation. The circuitry then used was basically the same as that of modern dc transmission systems, fauIt currents being limited by control of valve ignítíon. The operation of the line was discontinued in 1945 in the belief that nothing more would be learned by continuing it. Perhaps an additional belief was that there was no future in dc transmission.

Meanwhile, two 25/60-Hz frequency changers using controlled mercury­arc valves were installed in steel mills in the United States in 1943. The larger of these, rated at 20 MW, was installed at the Edgar Thompson plant of the

- Carnegie-Illinois Steel Company near Pittsburgh. The United States was inactive in the field of dc transmission, however, for nearly 20 years.

A demonstration of dc transmission using grid-controlled steel-tank mercury-arc conversion was given at Zurich, Switzerland, in 1939, at the Fifth Swiss National Exhibition.B4

,S Power of 0.5 MW at 50 kV, 10 A, was sent 19 mi (30 km) from Wettingen power plant near Baden to Zurich over a circuit of one conductor, partIy overhead and partIy in underground cable, with earth returno In 1946, Brown-Boyeri discontinued their work on HV dc transmission.

Two HV dc experiments were conducted in Germany during World War 11 at the instance of the German Secretariat for Aviation.B6,19 A 4OO-kV three-phase liDe from the AIps to the Ruhr had already been planned, but the Secretariat intervened in favor of a HV dc cable line, which, it felt, would be less vulnerable to air-raíd damage. The Siemens-Schuckertwerke A.G. began experiments in preparation for such a line. They transmitted 4 MW at 110 kV a distance of 3 mi (5 km) over an existing line from a station ia the Charlottenburg district of Berlin to one in the Moabit district. B'5 A second, larger experiment was to be the transmission of 60 MW by means of a 70-mi (11O-km) 4QO-kV dc cable from the Elbe (near Dessau) to Marienfelde (near Berlin).B6.9 This experiment was to be conducted jointly by Siemens and the A.E.G. The fortunes ofwar prevented completion ofthe project, and in 1945 such plant and pertinent documentsas survived were taken to the U.S.S.R. as reparations.

In Sweden, where the principal new hydroelectric sites are in the north and the principal loads are in the south, HV transmíssion is required; and, because of the development of valves by the Swedish firm of ASEA, interest was aroused in the possibility of a HV de transmissíon system as an alternative to

,

Page 14: Direct Current Transmission - Kimbark

8 9 GENERAL ASPECTS OF DC TRANSMISSION

ac. An experimental transmission between Mellerud and Trollhãttan (36 began operation in 1944. It aided further development ofvalves by permitting them to be tested under service conditions. The Swedish State Power Board decided to use alternating '-eurrent for the north-to-south transmission already mentioned. The resuIts of the MeIlerud-Trollhãttan transmission, however, encouraged the Board to proceed with HV dc transmission by sub­marine cable from the Swedish mainland to the island of Gotland, 96 km (60 mi) offshore.G This system, built by ASEA, began service in 1954 and may be considered the first commercial HV dc transmission system. The line transmits 20 MW at 100 kV through a single-conductor cable, with return path through the sea and earth. Each converter has two vaIve groups rated 50 kV, 200 A, 10 MW, the groups being in series on the dc side. Each valve has two anodes working in parallel.

Building the dc link was judged more economical than construeting additional thermal power plants on the island. The distance is far toa great for ac eable transmission.

Power fiow is normally from the mainland to Gotland but is sometimes in the opposite direetion. M uch of the time when power is delivered to Gotland, there are no generators in operation there, the only synchronous maehine being a condenser. Power is adjusted automatically to maintain rated frequency (50 Hz) in Gotland.

The link is still in operation (1970) and has a good performance recordo One of the mercury-arc valves was replaced by an air-cooled thyristoi' assem­bly, which also has performed well. Plans have been announced for doubling the voltage and power on the existing cable by the addition of a new thyristor valve group to each terminal, thereby doubling the voltage,

In the V.S.S.R., where even greater distances than in Sweden separate the potential hydroelectrie sites from the principal industrialload areas, the use of HV de transmission was considered necessary,B8 and an extensive program of research and development was undertaken, begun as a part of the 5-yr pIan of industrial development for 1946 to 1950.

An experimental line between Moscow and Kashira (112 km or 60 mi, 30 MW, ±Ioo kV) began operation in December 1950.Blo.II,13.16

It was basically an underground cable line, but at times sections of overhead Íine were put into the circuit. Both bipolar metallíc operation and monopolar, ground-return operation were tried. Practical ground electrodes were developed, and various kinds of valves and converter control were tested.

A Direct eurrent InstituteB12.14 was established in Leningrad, which since 1957 has published approximately one volume per year of articles on its researches.A3

A fuIl-scale 474-km (294-mi) overhead line between a hydroelectric plant at Volgograd, formerly called Stalingrad, and the Donets Basin was energized

1-2 CONSTITUTION OF EHV AC AND DC LlNKS

at reduced voltage and power in 1962 and, beginning in 1965, was operated at its full rating of ±400 kV, 900 A, 720 MW.' Other dc lines of lengths of 2000 to 2500 km and voltage of ± 750 kV are planned.Q6

1-2 CONSTITUTION OF EHV AC AND DC LlNKS

EHV transmission links, superposed on a lower-voltage ac network, or inter­eonnecting two such networks, or connecting distant generating plants to an ac network, are compared as to their principal components and the arrange­ments thereof, according to whether the line operates on ac or dc. The phrase "transmission link" denotes the transmission line proper together with its terminal and auxiliary equipment.

Figure la shows a single-eircuit three-phase ac line. In general, such a line in the categories already mentioned, one which might be competitive with a dc link, requires transformers at both ends- step-up transformers at the

__ sending end and step-down transformers at the receiving end-although in some cases they can be omitted at one or both ends. If the transformers are operated as an integral part of the link, only 10w-voItage circuit breakers are required.

Ac system

Ac system

(b) Inve~rter •Rectifier

De line~ Ac ~ system~)"I

:t l(c)

~~~ Ac

system systemr 1{ ~ ,\1 ) Ac

~(d) ~ Fig. 1. Constitution of ae and de EHV Iinks shown by single-Iine diagrams.

Page 15: Direct Current Transmission - Kimbark

11

--------------------------~... ­

10 GENERAL ASPECTS OF DC TRANSMISSION

Most long overhead ac tines require series compensation of part of the induetive reaetanee. In the figure, one bank of series capacitors for this pur­pose is shown at the middle of the tine.

Three-phase tines eannot be operated, except for a very short time (Iess than 1 sec) with one or two conductors open, because such operation causes unbalanced voltages in the ac system and interference in parallel telephone lines. Therefore three-pole switching is always used to clear permanent faults, although such a fauIt may involve only one conductor. This being so, two parallel three-phase circuits are required for reliable transmission (see Fig. Ih). Long two-cireuit ac links are usually sectionalized by means of intermediate switching stations for severa) reasons. Among these are (a) limiting the deerease in stability power Iimit attributable to switching out one circuit to clear a fault or for line maintenance, (b) Iimiting the overvoltage when a line is energized from one end, (c) providing a place for the connection of grounding transformers to limit the overvoltages of the unfaulted phases with respect to ground when one phase is faulted to ground, and (d) for con­nection of intermediate loads or generation. Intermediate generation raises the stability limit of the link. On many long EHV lines, shunt reactors are required for limiting the voltage, especially at light loads, but they may be required even at full load. These reactors are usually placed at intermediate switching stations and are so indicated in Figure Ih.

A representative single-circuit dc link is shown in Figure le. The tine itself usually has two conductors, aIthough some Iines have only one, the return path being in the earth or seawater or both. At both ends of the tines are converters, the components of which are transformers and groups of mercury­arc valves. The converter at the sending end is called a reetifier, and that at the receiving end an inverter. Either converter, however, can function as rectifier or inverter, permitting power to be transmitted in either direction. The ac line, of course, also has this reversibility.

Circuit breakers are installed only on the ac sides of the converters. These breakers are not used for clearing faults on the dc line or most misoperations ofthe valves, for these faults can be cleared more rapidly by grid controlof the valves. The breakers are required, however, for clearing faults in the transformers or for taking the whole dc link out of service. • Harmonic filters and shunt capacitors for supplying reactive power to the converters are connected to the ac sides of the converters. Large inductances ealled de .smoothing reaetors are connected in series with each pole of the dc line.

Some writers claim that a two-conductor dc tine provides the same re­liability as a two-circuit three-phase tine having six Une conductors, for either conduetor of lhe de line ean be used with ground return continuously or for Iímited periods, say, a few days per year.

-,

1-3 KINDS OF DC LINKS

~ If higher reliability is required of a dc tine than that provided by two con­ductors, three or four conductors may be provided. One pole of a four­conductor line is shown in Figure Id, with two converters per terminal. The bus-tie switches I are normally open. If a permanent fault occurred on the lower conductor, the converters connected to it would be controlled so as to bring the voltage and current on it to zero. Then switches 3 would be opened, isolating the faulted line. Next the converter voltages would be raised to equality with those of the respective adjacent converters, after which switches I would be closed. The capability of ali converters would then be usable, and the power normally carried by two conductors would then be carried by one. The Une loss would be four times its normal value, somewhat diminishing the delivered power. The whole switching operation would take about 0.3 sec, a time as short as that required for rapid reclosure on an ac line. Each pole would be switched independently of the other.

Comparison of the ac and dc links shows that (a) the dc line proper is ~~ simpler, having one or two conductors instead of three, but that (b), on the

other hand, the terminal equipment is more complex, having the groups of valves and some auxiliary equipment that the ac tine does not need.

1-3 KlNDS OF De LlNKS

Direet-current links are classified as shown in Figure 2. The rnonopolar link has one conductor, usually of negative polarity, and

ground or sea returno The bipolar Iink has two conductors-one positive, the other negative.

Each terminal has two converters of equal rated voltages in series on the dc side. The neutral points (junctions between converters) are grounded at one or both ends. If both neutrals are grounded, the two poles can operate inde­pendently. Norrnally they operate at equal current; then there is no ground current. In the event of a fault on one conductor, the other conductor with ground return can carry up to half of the rated load. •

The rated voltage of a bipolar link is expressed as ±100 kV, for example, pronounced plus and minus 100 kV.

The hornopolar Iink has two or more conductors ali having the same polar­ity, usually negative, and always operates with ground returno In the event of a fault on one conductor, the entire converter is available for connection to the remaining conductor or conductors, which, having some overload capability, can carry more than half of the rated power, and perhaps the whole rated power, at the expense of increased tine loss. In a bipolar scheme reconnection of the whole converter to one pole of the line is more complicated and is usually not feasible because of graded insulation. In this respect a homopolar line is preferable to a bipolar tine in cases where continuai ground current is

1

Page 16: Direct Current Transmission - Kimbark

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Page 17: Direct Current Transmission - Kimbark

14 15 GENERAL ASPECTS OF DC TRANSMISSION

different countries. Brief comments are made on these links, alI of which except Volgograd-Donbass were based wholly or mainly on ASEA techniq ues.

Engüsb Cbannel CrossingH

The next link to go in to service after Gotland was an interconnection between the ac systems of England (Central Electricity Generatíng Board) and France (Électricité de France) through two single-conductor submarine cables. The dístance (42 mi or 64 km) is shorter than that of the Gotland scheme, but the rated power (160 MW) is eight titnes as great. Each valve has four anodes, and each of two bridges (one per pole) is rated at 800 A, 100 kV, 80 MW. Like Gotland, the Channel Crossing scheme involves cross­ing water;'but, unlike Gotland, it does not use the sea as a return conductor. Because of concern with the effect of the direct current on ships' compasses in a channel having much shipping, two cables were laid close together, one operating at + 100 kV with respect to ground and the other at -100 kV. The midpoint (neutral) of the converters is grounded at one terminal only, so that ground current cannot flow except briefly in the event of a cable fault.

This link interconnects two large ac systems but has a small power rating compared with the capacity of either system. An ac link of this kind would have been feasible except that it would be difficult to controI. The British power system has no automatic load-frequency controI. Installation of such a control for the sake of the interconnection would have been very expensive. The dc link is an asynchronous tie between two systems of the same nominal frequency (50 Hz). Its power flow is readily controlled to a set value.

The purpose of the interconnection is to take advantage of time-zone and generation diversity. The direction of power flow varies. The French system has a considerable amount of hydroelectric generation; the British system has practically none. In seasons in which the supply of water to the hydro plants is ample, power can be exported to Great Britain. When water is scarce, power can be imported from there.

The Channellink was plagued by troubles in its first few years of operation. One of the transformers in the French terminal failed. The submarine cables were broken several times by trawlers, and they could not be repaired soon

• because of bad weather and rough seas. Since then the link has operated with very little trouble.

Volgograd-Donbass Line l

When built, this was the longest dc line. It usually carries power from a hydroelectric power plant on the Volga River at Volgograd to an industrial and mining district in the Donets Basin. For such an operation generators

1-4 HV DC PROJECTS FROM 1954 TO 1970

in the hydro plant may be disconnected from the ac bus and connected only to a valve group of the rectifier. For power flow in the opposite direction the inverter valve groups are connected to the ac bus.

It seems that the link did not offer any advantage in cost compared with an ac link, but it was built to gain experience in dc transmission for longer higher­power !ines that will be built in the future.

Each terminal has eight valve groups (four per pole), using single-anode valves of Russian design, with two valves in series in each armo

The year 1965 was called "the dc year" by the editor of Direct Current. Not only was the Volgograd-Donbass Iink brought up to its designed volt age and power, but also two additional dc transmission schemes (New Zealand and Konti-Skan) and a frequency changer at Sakuma, Japan, went into operation. A third transmission scheme (Sardinia) was expected to go into operation, but it was delayed until the following year.

~.--New Zealand LinkJ

To meet the growing demand for power on the North Island, either addi­tional steam-electric power plants would, have to be built there, or hydro­electric power plants would have to be built on the South Island, from which the power would be transmitted electrically to the North Island. Submarine cables 24 mi (39 km) long would be required across Cook Strait, which separates the two islands. The hydroelectric alternative was more economical and it was chosen. Direct-current transmission was selected as being more feasible than ac for this long water crossing. Three dc cables are used (one for each pole and a spare), but 11 ac cables would have been required (for three three-phase circuits and two spares), which would have occupied a wide belt of sea bed. The decision was made even before the English Channel scheme was in operation.

The transmission system includes, in addition to the submarine ca'bles, 335 mi (535 km) of overhead bipolar transmission line on the South Island and 25 mi (40 km) on the North Island. It extends from Benmore power plant on the South Island to Haywards Substation on the North Island, near the city of Wellington. The power rating of 600 MW is considerable com­pared with the aggregate generation on either island then (1400 MW on the North Island and less on the South Island) and slightly exceeds the rating of the Benmore plant. The cost of the dc-transmission scheme was about two­thirds of that of the ac-transmission scheme that was considered as an alternative.

Ground return is used in emergencies when one pole of a converter or the transmission circuit is faulted.

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16 17 GENERAL ASPECTS OF DC TRANSMISSION

The valves, manufaetured by ASEA, are rated at 1.2 kA, 125 kV, and have four anodes.

Konti-Skan LinkK

This is an intereonneetion between Sweden and Denmark and thus, through previously existing ae conneetions, between Germany and the rest of Western Europe and the Seandinavian eountries. It erosses the Kattegat by way of the island of Laesõ and has two eable seetions and overhead seetions on the island and at eaeh end.

The de scheme was eompared with an ae seheme having a shorter eabIe. The cost of the two schemes was approximateIy equal, but the de seheme presented two advantages over the ae:

I. The de line provides an asynehronous tie. The stabiIity Iimit of the ae seheme was estimated as 350 MW; the ultimate power eapability of the de link was 500 MW. The need for expensive Ioad-frequeney regulation is avoided.

2. The de seheme ean be built in two stages, and thus almost half of the investment ean be postponed. The first stage operates monopolarly with one submarine cable and sea return at a power eapability of 250 MW. In the second stage the line will be a bipolar, metallie cireuit for 500 MW, with sea return used only in emergencies.

Four-anode, l.l-kA, 125-kV valves are used.

Sakuma Frequency Cbanger

This station was put into operation in 1965, intereonneeting the 50- and 60-Hz systems of Japan. It ean transmit 300 MW in either direetion. There is no de transmission line, the de eireuits being eonfined to the station. With minor exceptions, the equipment and cireuits are like tho'se of a transmission seheme. The valves are similar to those of the New Zealand and Konti-Skan links.

Sardinian ScbemeL

In order to use large deposits of low-grade coaI on the Italian island of Sardinia, a thermal power pIant was built there, and a de link was built eon­neeting it, by way of the Freneh island of Corsiea, to the Italian mainland near La Spezia. This link consists mainly of submarine eable, with some overhead line on Corsiea and at the ends. A peculiarity of this seheme is that the line has two eonduetors ofthe same polarity, with sea returno The polarity is nega tive when power is transmitted from Sardinia to the mainland, whieh

1-4 HV DC PROJECTS FROM 1954 TO 1970

is the usual direetion, although the opposite direction holds when the Sardin­ian plant is shut down. Power ftow is regulated so as to keep eonstant fre­queney on the Sardinian ae system. The valves are similar to those of several other sehemes. are rated at 1.0 kA. 100 kV, and have four anodes.

Vancouver Island ScbemeM

This provides a de eonnection between the mainland of the Canadian province of British Columbia at Arnott, south of the mouth of the Fraser River, and Vancouver Island. It is being built in stages of 78 MWeach, with an expeeted final power of 312 MW. It erosses the Strait of Georgia by submarine eable and Salt Spring Island by overhead line. The four-anode valves are rated at 1.2 kA, 130 kV.

This is the first seheme in whieh a de link operates in parallel with an ae link.

..-;:--:-.­-Pacific Nortbwest-Pacific Soutbwest IntertiesN

The purpose of this seheme is to take advantage of seasonaI diversity in load and generation between the northwest area, eomprising the states of Washington and Oregon, and the southwest area, eomprising southern California and Arizona. The entire seheme inc1udes two 5OO-kV ae eireuits with a totallength of 905 mi (1450 km) from the CoIumbia River to the vicinity of Los Angeles and two ±4OO-kV bipolar de cireuits. The first de cireuit is from Celilo substation near The Danes, Oregon, to Sylmar sub­station, near Los Angeles. The second de eireuit is planned to be built from Celilo to Mead substation near Hoover Dam at BouIder City, Nevada. The power ratings of the ae lines are 1000 MW eaeh and those of the de lines 1440 MW eaeh. A third de line, the so-ealled "de eross tie," from SyImar to Mead, about 270 mi (430 km), has been diseussed, but there is no definite pIan for building it. •

Eaeh of the two de lines exceeds any previous de line in length and in power rating, although the rated voltage is equal to that of the Volgograd­Donbass line. The valve ratings are also greater, being 1.8 kA, 133 kV, 240 MW per group, with six anodes per vaIve.

The de lines operate in parallel with a 60-Hz ae system. Because of the great length of the ae lines, the stability of the ae system poses a eonsiderable problem, and it was necessary to use a high degree (average 65%) of series eompensation. A permanent bipoIar fau!t on a fully-Ioaded de line is ooe of the severest disturbaoces that the ae system must withstand, although the oeeurrenee of sueh a fault is believed to be very infrequent.

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18 19 GENERAL ASPECTS OF DC TRANSMISSION

KingsnorthO

The Central Eleetricity Generating Board of Great Britain is interested in the use of de links for reinforcing an ac system in areas of high load density without increasing the interrupting duty ofac cireuit breakers. A trial installa­tion of this kind is the transmission of power by underground dc eable from the Kingsnorth thermaI power pIant, situated on the south shore of the Thames Riverestuary, to two substations in London. This is a bipolar scheme having three cables: one for eaeh pole and a neutral cabIe. Eaeh pole goes to a different substation, with the result that, aIthough the whole seheme has three terminaIs, each pole has only two terminaIs. The Beddington substation is 37 mi (59 km) from Kingsnorth, and the Willesden substation is 14 mi (23 km) beyond Beddington. Whenever the loads of the two substations are unequal, there will be neutra I current. This current is not allowed to flow in the ground for fear of damage by electrolytic corrosion to some of the many buried metallic structures found in a metropolitan area.

The rating of this scheme is ±266 kV, 1.2 kA, 640 MW. There are four groups of valves at Kingsnorth and two groups at each substation, each group being rated at 133 kV, 1.2 kA, 160 MW.

Nelson River, Manitoba, SchemeP

The Nelson River has a potential hydroeleetric power development of about 6500 MW, including some diversion ofwater from other streams. It has been decided to develop this power and to transmit it to Winnipeg by direet current. Bipolar ±450-kV overhead dc lines were judged more economical than 5OO-kV ac lines. Ultimately there will be several such bipolar circuits as the development proceeds by stages. With two such lines, the transmission capacity will be 3240 MW.

In response to the invitation for bids on terminal equipment for the first stage, three proposals were received for thyristor converters and two for mereury-arc-vaIve eonverters. The proposal for mercury-arc equipment by the English Electric Company was accepted. Each vaIve group will operate at 1.8 kA, 150 kV, 270 MW. There will be three groups in series per pote.

Eel River (New Brunswick)

This station provides an asynehronous tie between the 60-Hz ac systems of Hydro Quebec and of New Brunswick. As at Sakuma, the dc circuits are confined to the station. In contrast to Sakuma, the nominal frequencies of the two ac systems are equaJ, although one ean drift with relation to the

1-5 LIMITATIONS AND ADVANTAGES OF AC AND DC TRANSMISSION

other. The distinctive feature of the Eel River station is that it is the fust large converter station designed to use thyristor valves initially and exclusively. The rating ofthe station is 320 MW, 80 kV dc, 230 kV ac.

1-5 LlMITATIONS AND ADV ANTAGES OF AC AND DC TRANSMISSION

Noting the universal use of alternating current for electric power trans­mission, as well as for generation, distribution, and use, one natural1y asks what limitations ae transmission has that have led to the use of dc transmis­sion in some projeets.

The limitations may beither technical-something cannot be done-or eeonomie-it can be done more cheaply some other way. In most practical cases the technical limitations are not reached, and economic limitations dietate the final ehoice of designo

,..,."....,- We are interested in limitations on the amount of transmitted power and -on the distance over which it can be transmitted. More exactly, we are inter­ested in the cheapest method by which a certain amount of power at a certain load factor can be transmitted reliably over a certain distance. The power depends on the current, volt age, power facto r, and number of conductors.

Current Limit

The temperature of a conductor must be limited in order to avoid damage to the conductor itself (permanently increased sag) or, in case of a cable, to the insulation in eontact with it. Hence the current in the conductor must be

in accordance with its duration and the ambient temperature. The limiting current is seldom reached on long overhead ac lines beca use of other limitations' being reached first, but on cables the current limit due to heating is important, as shown later.

The ac resistance of a conductor is somewhat higher than its do. resistánce because of skin effect, but the difference is not important in nonmagnetic conductors of the usual diameters at the usual power frequencies.

Voltage Limits

The normal working voltage and the overvoltages caused by switching surges and lightning must be limited to values that will not cause puncture or flashover of the insulation. On EHV overhead lines, switching surges, rather than lightning, have become the more serious transient overvoltages, and on ac lines attempts are made to limit them to peak values of two or three times normal crest voltage. Switching surges on dc lines are lower than this, say,

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20 GENERAL ASPECTS OF DC TRANSMISSION

1.7 times normal voltage. On overhead tines, the maximum working voltage or the minimum conductor size is limited also by loss and radio interference due to corona. In current ac practice, radio interference during foul weather (rain, snow, or fog) is usually the limiting factor. Here dc lines have a distinct advantage in that radio interference is slightly decreased by foul weather, whlle interference due to ac lines is greatly increased by foul weather. In cables, where the limiting ractor is usually the normal working voltage, the insulation will withstand a direct voltage higher than the crest of alternating voltage, which is already 1.4 times the rms value of the alternating voltage.

Reactive Power and Voltage Regulation

On long EHV ac overhead tines and on much shorter ac cables, the produc­tion and consumption of reactive power by the line itself constitutes a serious problem. On a line having series inductance L and shunt capacitance C per unit or length and operating voltage Y and current I, the line produces reactive power

Qc =coCY'"

and consumes reactive power

QL = coLI" (2)

per unit or length. The reactive power produced by the line equals that con­sumed by it, with no net production or consumption, ir

coCY" = coLI 2

hence ir

~ = (!:.)1/2 (3)I C Z.

In this case the load impedance has the value Z., known as the surge im­pedance of the tine. The surge impedance or an overhead line with single conductors is about 400 n, and with bundle conductors, about 300 n; that of cables is only 15 to 25 n.

• The power carried by the line so loaded is

V'" P = VI= (4)

n Z.

and is called the surge impedance loading (SIL) or natural load. It is inde­pendent or distance and depends mainly on the voltage. Typical values for three-phase overhead lines are as follows:

1-5 L1MITATlONS AND ADVANTAGES OF AC AND DC TRANSMISSION 21

voltage (kV) 132 230 345 500 700

surge impedance Ioading (MW) 43 130 300 830 1600

On a line carrying its natural load, the magnitude of voltage is the same everywhere, as shown in curve 2 in Figure 3, and the reactive power is zero

1.05 -----:.: '- I I 1. No load

1.00v E

0.95

o 10 20 30 Distance from sending end (elec deg)

Fig. 3. Voltage profiles of one-twelfth-wavelength low-Ioss line with equal terminal voltages E. Length at 60 Hz is 258 mi (416 km).

everywhere (curve 2 in Figure 4).

+0.5,1----,-----~----r_---,-----.----,

Q

P"

-0.51 I I I o 10 20 30

Distance from sending end (elec deg)

Fig. 4. Flow of reactive power Q on the line in Figure 3.

Most tines cannot be operated always at their natural loads, for the loads vary with time. The most economical load on an overhead line is usually greater than the naturalload. Ir the load is greater than the naturalload, net reactive power is consumed by the line and must be supplied from one or both ends. If equal voltages are maintained at both ends or the line, equaI amounts or reactive power are supplied from both ends (curve 3 in Figure 4),

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52 CONVERTER CIRCUITS

FuIl-wave Rectifier

This has two valves and one transformer with center-tapped secondary winding (Figure 3). The wave forms are shown in Figure 4. In Figure 4a, the line-to-neutral secondary voltages el and ez, having a phase difference of one-half period (180°), are plotted. The anode voltages of valves 1 and 2 with respect to neutral point N are equal to. e1 and.ez, respectively. The common cathode voltage of both valves, being equal to the higher of the anode voltages, consists ofthe positive half waves of e1 and ez . This curve, redrawn in Figure lb, represents also the instantaneous direct voltage va on the valve side of the smoothing reactor. The average direct voltage Vd is also shown. The difference Vd - Va, which appears across the reactor, is represented by the vertical shading in Figure lb. Its average value is zero, corresponding to equal positive and negative areas between the curve and the horizontal line.

When valve 2 is conducting, the full secondary voltage e1 - e"}. appears across valve 1; when valve 1 is conducting, ez - e1 appears across valve 2. Figure 4c shows the voltage v1 across valve 1. The valve currents, which are aiso the currents in the halves ofthe secondary winding, are shown in Figure 4d. They are rectangular pulses of height Ia and length 180°. The MMF of the entire secondary winding is porportional to i 1 - iz and has an average value of zero; in other words, there is no dc component of MMF, hence no tendency to saturate the core. The primary MMF must oppose the secondary MMF

(Ti, = ;1 - iz), so that the primary current i, has the form shown in Figure 4e.

Now let us compute the numerical values of the various circuit quantities. The filtered direct voltage Vais the average value of va, and the latter con­

sists of the positive halves of sine waves having crest value Em and frequency f =ro/21t. Let {1 = rot.

2f n!Z 2E ( ),,/2 2EVa = - Em cos{1d{1 = -'" sin (1 =~ = 0.637Em (I)

1t O 1t O 1t

1t Em = 2: Va = 1.571 Va (2)

The peak-to-peak ripple is Em = 1.571 Va, and its frequency is 2[, where f is the frequency of the ac source.

The peak inverse valve voltage is 2Em = 3.142Va• The transformer voltages are sinusoidal by assumption. The voltage

across each half of the secondary winding has crest value Em and rms value 0.707Em = 1.111 Va. The primary voltage has crest value TEm and rms value O.707TEm= 1.111 TVa, where Tis the transformer turns ratio.

The crest value of current in each valve and in each half of the secondary

ip Ia~ --i>~ T:l:l li' r L

j V! Deel

NA~tep

le2 ep - TEm sin wt 112-2-'~

'2

Fig. 3. Single-phase full-wave rectifier circuito

wIIr l!" '41' ~wt

rI 1 ~~~

I(c) I

: 111 I

I I I I·l I I

II '1 I

i lIaI I r- wt (d) II '2. II II I­

--I )" I I i1 ' ~-"'i

(.) ~ i'l l,,/T I r1Idf T ~wt

Fig.4. Wave forms of the circuit of Figure 3: (o) transformer secondary voltages e, and e~; (b) unfiltered and filtered direct voltages !Ia and Vd ; (c) voltage across valve 1, 11,; (d) valve currents or secondary currents i, and i 2 ; (e) primary current i p •

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222 MISOPERATION OF CONVERTERS

insuflicient to igniteanyofthe nonconducting valves. When the current in any valve decreases to zero, however, and is extinguished, a positive voltage appears instantly across the other valve on the same phase, igniting it; for example, when valve 2 extinguishes, valve 5 ignites, both of these valves being connected to phase c. Thus the three-phase short circuit is maintained except during extremely brief time intervals when there is a phase-to-phase short circuito

The dc components decay but usually too slowly to change the crest current significantly during the first cycle.

Maximum Crest Currents in DC Sbort Circuits

These are given below in the same manner as the arcback currents in Table I. They are less than the corresponding arcback currents.

Table 2. Crest Currents in DC Sbort Circuits

Type i//'3 i//.2 i/(E/X)

Controlled 0.87 1.00 1.23 Uncontrolled 2.00 2.31 2.83

6-5 COMMUTATION FAILURE

Causes

The commonest misoperation of an inverter is a failure of commutation. A true commutation failure is not due to any misoperation of a valve but to conditions in the ac or dc circuits outside ofthe bridge in which the failure occurs or to inadequate control of the time of ignition. Because of increased direct current, low alternating voltage (caused perhaps by an ac short cir­cuit), late ignition, or a combination of these, commutation is not completed before the alternating commutation EMF reverses. Thereafter the direct cur­rent is shifted back from the incoming valve to the valve that was expected to go out. [t is shown below that nearly alI inverter valve faults lead to results similar to those caused by a commutation failure.

Analysis

A failure of commutation from valve I to valve 3 is analyzed with refer­ence to the wave forms in Figure 19 and to the various simplified diagrams of an inverter bridge mentioned hereafter. The normal extinction angle is taken

6-5 COMMUTATlON FAILURE 223

as 15° and the ignition angle as 40°. For simplicity in computation, the is assumed to result from late firing of valve 3, with direct current and alter­nating voltage remaining unchanged, although in practice changes in the last two quantities are likely to be involved either as causes or effects. /s2 is assumed to be 10 kA and / d to be 2 kA.

(a)

(b)

(c) :W! ... wt

Instant

6 1Valves 2conducting 3

A 80° Normal commutation begins from valve 6 to valve 2. B 105° Commutation is completed. Valves I and 2 are still conducting. C 1450

Valve 3 fires 5° late, and commutation begins from valve 1 to valve 3.

Fig. 19. Wave forms of voltages and eurrents with failure of eommutation of an inverter: (a) phase EMP'S and de pole voItages wíth respeet to neutraJ of ae source; (b) direet voItage, and (c) valve eurrents. Valve I faíls to eommutate to valve 3.

NARRATIVE

PI. rol

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