1

Non Conventional Transmission Line with FACTS inElectromagnetic Transient ProgramsRobson F. S. Dias, Antonio C. S. Lima, Carlos Portela, Maurıcio Aredes

Abstract—This work presents some procedures tosimulate, in an electromagnetic transient program, anon conventional transmission line, that, in the pre-sented example, has 12 conductors per phase, in trans-mission trunks with an electric length, at power fre-quency, a little longer than half wavelength (λ/2

+). Thiskind of line is indicated to bulk power transmissionover very long distances. Although it is not a basicallypoint-to-point transmission system, in a sense similar toHVDC transmission systems, and allows e.g. to connecteach“terminal”to a few substations a few hundred kilo-meters apart, it has some constraints and limitationsin power received or supplied at intermediate pointsand in line operation in separate parts. To overcomethis drawback a FACTS device is proposed to drain,or inject, energy from the line without changing itselectrical characteristic. The paper also presents somesimulation results about FACTS device draining energyfrom the line.

Keywords—EHV Transmission Lines, UHV Trans-mission Lines, Power Transmission Lines, FATCS.

I. Introduction

One of the many upcoming challenge of the PowerIndustry lies in the transmission of bulk energy over verylong distances and/or interconnect large power systemsseparated by large distances. In many regions throughoutthe world there are possible candidates for a bulk energytransmission over long distances such as Brazil, Russiaor even continents like Africa and Europe. In those sitesthere are large electric generation potential locate beyondtwo thousand kilometers from the main load centers. Forinstance, in the Amazon Basin, in North Region of Brazil,the hydroelectric potencial is above 100 GW [1], althoughthe actual used potencial is less than 1% there is a plan toincrease the generation up to 18 GW in the next 10 years.In this particular example, the main load centers are lo-cated in the Southern Region of Brazil with a distance over2500 km. Another example is located in Southern Africa,an interconnection from Inga in the Democratic Republic

This work was supported in part by “Fundacao de Amparao aPesquisa Carlos Chagas”, FAPERJ, Rio de Janeiro, Brazil and in partby“Conselho Nacional de Desenvolvimento Cientıfico e Tecnologico”,CNPq, Brasılia, Brazil.R. F. S. Dias, A. C. S. Lima, C. Portela and M. Aredes are with theUniversidade Federal do Rio de Janeiro, Department of ElectricalEngineering, P.O. Box. 68504, 21945-970, Rio de Janeiro, RJ, Brazil,(email:dias@coe.ufrj.br, acsl@dee.ufrj.br, portelac@ism.com.br, are-des@ufrj.br).

Paper submitted to the International Conference on Power SystemsTransients (IPST2009) in Kyoto, Japan June 3-6, 2009

of Congo to Omega in South Africa and from Kwanzain Angola to Pegasus in South Africa. The objective isto transmit 4 GW over three thousand kilometers [2]. Asimilar challenge exists in Russia where the main sourceof energy are concentrated in the Asian part, whereas theload centers are located in the European part. In thiscase the length of the circuit may exceed three thousandkilometers. With respect of power interconnection thereis the tie between Russia and Germany [3], [4] and theinterconnections in Northeast Asia that will tie Russia,China, Mongolia, South Korea and Japan [5] [6]. Theformer is an east-west European power link of 4 GW andcircuit length of around 1700 km.

For the challenge of bulk power transmission over verylong distances the HVDC transmission system is usuallythe solution. However, this work shows an option for bulkpower transmission, that is an ac transmission system withan equivalent electrical length (at power frequency) a littlelonger than the half wavelength, i.e. λ/2 ≈ 2500 km (for60Hz) or ≈ 3000 km (for 50Hz). It uses a non conventionalac overhead circuit lines and ties systems that are afew thousand kilometers apart. This solution can be ascompetitive as a HVDC system of same circuit length. Bynon conventional ac transmission system we mean a circuitoptimized with robust criteria, with solutions possiblydifferent of “usual”, e.g. in what concerns phase bundlearrangement, choice of conductors, mechanical structures,operation criteria; for instance, the example line is ade-quate for a transmission, in a single circuit, at a very largedistance, of 8 GW, for 1000 kV voltage level [7]–[9].

As the main goal of the non conventional ac system isfor very long distance transmission, above 2500 km, inthe remaining of this work we call the longer than halfwavelength transmission line by λ/2 + symbol, to remem-ber that the electrical length is a little longer than halfwavelength. It is important to note that such a line cannotoperate with an equivalente electrical angle of exactly π(half-wavelength) as this is a singular point and a stableoperating point can only be achieved for an electricallength higher than π.

The λ/2 + transmission ties two electrical subsystemswidely apart, i.e. with a distance of a few thousandskilometers. Thus it shares some similarities with a HVDCtransmission systems, although a λ/2 + system may have afew substations near the line extremities without any extraequipment. It means that a λ/2 + line is not essentially apoint-to-point transmission system.

In Section II are presented some conceptions about λ/2 +

2

line, some characteristics and its representation in an EMTtype of program. The line modeling is validated against aFrequency Domain Transient Program and results for theline energization is presented. Section III presents the basicstructure of the proposed series and shunt HVAC tap. Thelast Section presents simulation results of some test casesof a HVAC tap inserted along the λ/2 + line. Although,there are some issues about line operation in function lineloading, e.g.terminal line voltage reduction for minimizingtransmission losses, the results presented are valid for anyother line operation point.

II. Very Long Non Conventional TransmissionLines

Very long transmission line has many aspects that arequite different from what would be expected by simpleextrapolation of medium distance transmission line (a fewhundred kilometers). For instance [10]:

• It does not need large amount of reactive compensa-tion. It is only needed the compensation required toadjust the electrical length of the line to a little morethan half wave length. That decreases (in comparisonwith “usual” large distance AC transmission trunks)the cost of ac transmission per unit length.

• For several (normal) switching operations the tran-sients are moderate, therefore not imposing a greatstress in breakers or other switching equipment andto equipment connected to the transmission trunk.

• For single-phase faults, it is possible to have an highprobability of success opening faulted phases at bothline terminals and reclosing, after a relatively shorttime, during which it is assured an high probability orsecondary arc interruption. The typical solution, usedat traditional transmission systems of a few hundredkilometers, based e.g., in neutral reactors of shuntcompensation reactors, is not applicable, but othertypes of solutions may be used, to very large distancetransmission systems.

To explain some basic aspects of very long transmissionline consider an ideal line with total length `, longitudinalreactance per unit length X and shunt admittance perunit length Y , both for non-homopolar condition, at powerfrequency f . The electrical length of the line is defined by:

Θ =√X Y ` or Θ =

ω

ν` , (1)

being ω = 2π f , and ν the phase velocity. For a linewithout series or shunt compensation and at the powerfrequency, ν is close to the speed of light, typically around96% to 99% [11].

The characteristic impedance, (Zc), and the character-istic power,(Pc), are given by (2).

Zc =

√X

Yand Pc =

U20

Zc, (2)

for a reference (line) voltage U0.

For the power frequency, the reactive compensation canbe “included” in the total series impedance and shuntadmittance of the circuit as shown in (3),

X = ξseX0 and Y = ξsh Y0 , (3)

being ξse = (1− ηse) and ξsh = (1− ηsh), where ηse isthe level of series compensation and ηsh is the level ofshunt compensation, and X0 and Y0 the uncompensatedseries impedance and shunt admittance per unit length,respectively.

The electric line length, the characteristic impedanceand characteristic power are affected by the reactive com-pensation, respectively as show in (4).

Θ =√ξse ξsh Θ0

Zc =

√ξseξsh

Zc0

Pc =

√ξshξse

Pc0

(4)

For very long transmission distance, conventional ac sys-tems use a large amount of reactive power compensation,both series and shunt. The compensation is needed toreduce the electrical length to much less than a quarter ofwavelength which increases substantially the overall costof the transmission system. Furthermore, a high level ofcompensation introduces additional resonances which maycause severe switching overvoltages and related problems.For extra long distances (2000 km to 3000 km) thislimitation may be overcome with an equivalent electricallength slightly longer than half wavelength, λ/2 +, (π rad≈ 2500km @ 60Hz or ≈ 3000km @ 50Hz) [10]. Aλ/2 + line has the advantage that it requires little, if any,reactive power compensation. Thus it has the same costper kilometer as a short line. The main drawback remainsin the fact that the transmitted (active) power power (P1)should not exceed the characteristic power of the line (i.e.−Pc ≤ P1 ≤ Pc) to avoid overvoltages along the line.

Figure 1: Ideal λ/2 + system

To illustrate a little further the basic characteristics of aλ/2 + line consider the system shown in Fig. 1. Fig. 2 showsthe voltage profile and Fig. 3 shows the current along theline for several loading on an ideal line with 1.1π rad elec-trical length. These figures indicate that there are regionsalong the line where one may find an almost constant

3

current or an almost constant voltage for a reasonablerange of operation conditions.

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 H´ ΠL0.

0.5

1.

1.5

2.

2.5

Electrical Length HradL

Vol

tage

Hp.u.

L

2.0

1.5

P = 1.0 ´ Pc

0.5

0

Figure 2: Voltage profile along an ideal line.

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 H´ ΠL0.

0.5

1.

1.5

2.

2.5

Electrical Length HradL

Cur

rent

Hp.u.

L

2.0

1.5

P = 1.0 ´ Pc

0.5

0

Figure 3: Current profile along an ideal line.

A λ/2 + line should be designed for a large capacity ofpower transmission so an optimization of line geometry isof paramount importance. This optimization can improvethe right of way utilization with a minimum cost. Nev-ertheless, there are several criteria that might be takeninto account for reach the minimum total cost (losses,installations, equipment and operational costs). Some pa-rameters have a direct correlation with the total cost,for instance, voltage level, number of phases, conductortype, geometric configuration of the bundle, ground wires,insulating distances, tower profile, foundation type, lineroute, tower location, tower grounding, circuit breaker,overvoltages limiters, switching overvoltages, environmen-tal issues among others.

All of those parameters have an intrinsic effect on trans-mission cost and among each other. The great numberof parameters presents a limitation to establish a globaloptimization procedure. Although a global optimizationis very hard to reach, partial optimization can be usedinstead, as it tend to optimize some of the parameters andkeep the final cost to reasonable levels. It is important topoint out that as a transmission system is in fact a physicalsystem, the minimum cost may not be the best solution.

There are several procedures to optimize transmissionline. The applied optimization procedure in this workis based on [12]–[15]. This results in an unconventionalbundle arrangements as shown in Fig. 4. For a nominalvoltage of 1000 kV, the line presents a characteristic powerequal to 8 GW.

-20 -15 -10 -5 0 5 10 15 2040

45

50

55

60

Horizontal Distance HmL

Hei

ghtHm

L

Figure 4: Line spacing and bundle arrangement near thetower.

A. Transmission Line ModelingTwo parallel 2700 kilometer (≈ 1.1π rad) λ/2 + lines

were simulated in electromagnetic transient programPSCAD/EMTDC using a phase-domain model. Dueto non conventional bundle arrangement each phase-conductor has to be implemented indenpendently and yetfully coupled line, using a single Line Tower Universal(LTU), as if each phase has a tower, i.e., the line model isequivalent to 3 circuits in the same right of way.

The lines were considered distant from each other sothat the magnetic coupling could be considered negligible.In addition, due to very long line length some transpositioncycles are necessary. It was considered 9 cycles of 300 kmin each line.

In order to verify the adequacy of the implementedmodel in PSCAD/EMTDC, a comparison with a Fre-quency Domain Program build in Mathematica using theNumerical Laplace Transform was carried out. It wassimulated the energization from an infinite bus bar. Fig. 5shows the open circuit response at the receiving end (phasea). There is a good agreement between the results.

MathematicaPSCAD

0 20 40 60 80 100 120 140 160 180 200-3

-2

-1

0

1

2

3

Time HmsL

Vol

tage

Hp.u.

L

Figure 5: Open circuit output voltage.

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B. Line Energization

For the energization tests consider a λ/2 + line with alength `=2700 km and the bundle arrangement shownabove. Fig. 7 shows the voltage at the receiving end ofthe line for an cosine input where phase a is closed at themaximum voltage. There are no surge arresters at the re-ceiving end of the line. For this case, the maximum voltageexceeds 2.0 pu. Unlike conventional (medium length) lineswere the dominant switching frequencies lie in the range ofa few kHz, for a λ/2 + line the frequencies are much lower.For instance assuming an ideal λ/2 + line, the frequenciesfor the open circuit voltage foc are given by

foc ≈n c

4 `= 28 · n (Hz) (5)

where c is the speed of light and n is the harmonic number.The low order harmonics cause a modulation at the outputvoltage and should be avoided to allow an efficient and fastenergization. The high frequency components are absentof the output voltage as they are damped along the line.

One possibility to mitigate the transients is to use acontrollable switching (point-on-wave closing) with a clos-ing resistor. The point-on-wave closing allows the breakerat the sending end to close near zero voltage for oneof the phases while the resistor reduces the line inputvoltage during the energization. The output voltage forsimultaneously switching is shown in Fig. 8. The closingresistor improves the transient damping as can be seen inFig. 9.

100 101 102 10310-8

10-6

10-4

10-2

100

102

Frequency HHzL

Vol

tage

Hp.u.

L

U2 c

U2 b

U2 a

Figure 6: Open circuit output voltage frequency response.

III. HVAC Tap

Several alternatives are usually considered in the studiesfor the interconnection of two distant subsystems. A λ/2 +

system can be a feasible solution to high bulk powertransmission over extra long distances. However similarto HVDC transmission a λ/2 + system is essentially apoint-to-point connection. To overcome this limitation,a HVAC Tap can be inserted in the main power lineto supply additional loads throughout the circuit length.Although a HVAC Tap may seem an overkill, it should

0 10 20 30 40 50 60 70 80 90 100-3

-2

-1

0

1

2

3

4

Time HmsL

Vol

tage

Hp.u.

L

u2 a u2 b u2 c

Figure 7: Line energization – phase to ground voltage atreceiving end line terminal.

be noticed that a transformer connected to any point inline to drain power from the main circuit, may affectsthe performance of the whole system. To overcome thislimitation a HVAC tap is proposed. The tap is based on apower electronics converter and provides a multi-terminalbi-directional power flow capability. A HVAC tap can beused to connect local loads or generation to a λ/2 + line.

0 10 20 30 40 50 60 70 80 90 100-2

-1

0

1

2

Time HmsL

Vol

tage

Hp.u.

L

u2 a u2 b u2 c

Figure 8: Details of the line output voltage withsimultaneously switching – point-on-wave plus closing

resistor.

0 100 200 300 400 500 600 700 800 900 1000-2.5

-1.5

-0.5

0.5

1.5

2.5

Time HmsL

Vol

tage

Hp.u.

L

u2 c

u2 b

u2 a

Figure 9: Output voltage with controllable switching –point-on-wave plus closing resistor.

5

Fig. 10 depicts the general topologies for series andshunt taps. It can be seen that one key difference inpower circuits is the connection of the transformer. Theremaining circuit is essentially the same: both types con-sist of two NPC converters [16] linked by DC capacitorsin back-to-back configuration. The interface between theconverter and the transmission line is done by a connectiontransformer.

The series taps can be seen as controlled voltage sourcesthat produce a desired power injection (or drain) under theactual line currents. Shunt taps are the dual circuit, i.e. acontrolled current source under the actual line voltages.Therefore, for an efficient/effective tap shunt taps shouldbe connected near the line sending (or receiving) end andseries tap are more suitable to be connected midway alongthe line, independently of line voltage operation.

IV. Test Cases

The single-line diagram for the simulated system isshown in Fig. 12. It is based on the power transmissionfrom the Madeira River either/or Belo Monte complexboth in the Amazon Basin to the main load centers inBrazil in the northeast or southeast [17], [18]. The circuitlength for this configuration may exceed 2500 km and thegeneration is over 17 GW, see Fig 11.

(a) Series Tap

(b) Shunt Tap

Figure 10: HVAC Tap connection.

The test system has two λ/2 + circuit operating at1000kV. Each overhead line circuit has a characteristicpower of 8 GW. The circuit length is 2700 km. Thegeneration is represented by an infinite bus, the load centeris represented by an equivalent electrical circuit at powerfrequency. The HVAC tap connects a local system withgeneration and load to the main transmission path. Theconverter series (or shunt) are controlled using the in-stantaneous active and reactive power theory (pq-theory)

Figure 11: Distances from Madeira river complex to mainload centers.

developed in [19]. The controller demands measurementsof the line actual voltage and current to transform thosedata to αβ frame using Clarke’s transformation.

A a time-step of 10µs was considered in all tests and thetotal simulation time was 5 s. A snapshot of the system(without the converters) at t = 1 s was used to initializeall the tests. The chain of effects is as following:

• t1 = 1.4 s ⇒ The first converter of the HVAC Tapis connected to the power line to charge the dc-linkcapacitors.

• t2 = 1.7 s ⇒ The second converter of the HVAC Tapwhich was blocked is now connected to the dc-link, thepower order is null, i.e. the HVAC Tap is now fullyconnected but without any power drain Pref = 0.

• t3 = 2.0 s ⇒ The HVAC Tap starts to drain 1 GWfrom one of the λ/2 + overhead lines. The load reactivepower is supplied by the Local Generation.

• t4 = 3.0 s ⇒ Now the HVAC Tap starts to inject1 GW in the main transmission system, i.e., there isa total power flow inversion.

• t5 = 4 s ⇒ the reference power of the HVAC Tap ischanged to Pref = 0.5 GW.

The same chain of events was considered for the seriesand shunt HVAC tap. Fig. 13 depicts the variation ofinstantaneous reactive and active power at the connectionof HVAC Tap and the Local Generation at 230 kV. A seriesHVAC Tap was used in this test. The power consumptionat the load remains unaffected independently of the powersupply source. At first, the Local Generation is responsiblefor the load (PG > 0), then the HVAC Tap supplies theload (Ptap > 0) and finally both the HVAC Tap andthe Local Generation share the power demand. It shouldbe pointed out that although not shown here, identicalresults for the instantaneous active and reactive power areobtained in the case of a shunt HVAC Tap.

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Figure 12: Single Line Diagram of the simulated system.

PLG

PTap

PLoad

0 1 2 3 4 5-1.

0

1.

2.

Time HsL

Act

ive

Pow

erHGW

L

(a) Active Power

QLG

QTap

QLoad

0 1 2 3 4 5-200

0

200

400

600

Time HsL

Rea

ctiv

ePo

wer

HMva

rL

(b) Reactive Power

Figure 13: Interchange of power between HVAC tap andlocal system (in Fig. 12).

In the following figures itap stands for the HVAC tapcurrent and utap is the voltage across the HVAC tapterminals. For a series tap, utap = UP1−UP2. Fig. V showsthe waveforms for HVAC Tap connected halfway across thetransmission line. At this particular point, the current inthe λ/2 + line is essentially constant, thus the power flowthrough the tap heavily depends on the HVAC tap voltage.No significant overvoltage was found. Fig. 15 depicts utapand itap during the power flow inversion, as it can be seen,no overvoltages or overcurrents occurred. Fig. 16 shows therms values for UP1 and UP2 obtained using measurementsfrom all phases. The shunt HVAC tap was connected at450 km from the Generation bus. Fig. 17 shows itap andutap. Again, no severe overvoltage or overcurrents werefound during the tap operation. Fig. 18 shows itap and utapduring the power flow inversion. It is worth to mention,that the performance of the shunt HVAC tap is dual to its

series counterpart.

V. Conclusion

0 1 2 3 4 5-300

-200

-100

0

100

200

300

-12.

-8.

-4.

0

4.

8.

12.

Time HsL

Vol

tage

HkVL

Cur

rent

HkAL

utapitap

Figure 14: Voltage and current waveforms at tapterminals.

This work presents some aspects of an alternative forbulk ac power transmission over very large distances. Itis based on a non conventional ac overhead line with anelectrical length a little higher than half wave length (atpower frequency), called here λ/2 +.

As example, we considered a 2700 km three-phase linewith transmission capacity 8 GW, at 1000 kV. This ex-ample transmission system is of the type of transmissionsystems adequate for power transmission from the AmazonBasin (in which there important hydro-electric resourcesnot yet used) to main electricity consumer regions ofBrazil.

2.9 2.95 3. 3.05 3.1 3.15 3.2-300

-200

-100

0

100

200

300

-12

-8

-4

0

4

8

12

Time HmsL

Vol

tage

HkVL

Cur

rent

HkAL

utapitap

Figure 15: Voltage and current at tap terminals– (detail).

Although the considered alternative is not a basicallypoint-to-point transmission system, in a sense similar toHVDC transmission systems, and allows e.g. to connecteach “terminal” to a few substations a few hundred kilo-meters apart, it has some constraints and limitations inpower received or supplied at intermediate points and inline operation in separate parts. As a solution to overcomethis limitation, this work presents a HVAC tap, that usesa back-to-back self-commutated converters and can beconnected in series or shunt with a λ/2 + line. The HVACtap is used to connect the “main” power circuit to asubsystem with a 1 GW load.

7

0 1 2 3 4 5400

500

600

700

800

Time HsL

Vol

tage

HkVL

UP1UP2

Figure 16: Voltage at tap terminals.

0 1 2 3 4 5-1500

-1000

-500

0

500

1000

1500

-3.

-2.

-1.

0

1.

2.

3.

Time HsL

Vol

tage

HkVL

Cur

rent

HkAL

utap itap

Figure 17: Voltage and current waveforms at shunt tapterminals.

2.9 2.95 3. 3.05 3.1 3.15 3.2-1500

-1000

-500

0

500

1000

1500

-3.

-2.

-1.

0

1.

2.

3.

Time HmsL

Vol

tage

HkVL

Cur

rent

HkAL

utapitap

Figure 18: Voltage and current waveforms at shunt tapterminals.

The test indicated that the HVAC tap can inject ordrain power from the λ/2 + line without affecting theperformance of the bulk power transmission.

It is important to notice that many studies have beendone to overcome these challenges of electric power trans-mission at very large distances, and most of them havepointed to the HVDC transmission systems as the mostattractive solution. Nevertheless, almost all of such studieshave been done without regard to non-conventional actransmission lines and transmission trunks with an electri-cal length a little higher than half-wave length (at powerfrequency). This alternative was careful studied, e.g. in ref-erences indicated in this article. The obtained results showthat such alternative has many interesting characteristicsand, in several conditions, may have significant economical

and technical advantages, e.g. in comparison with HVDC,for transmission at very large distances.

References

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