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1 Abstract--In this paper, the requirement and difficulties of large-capacity and long-distance power transmission under the background of national development strategy “transmission of electric power from the western to the eastern region” in China is analyzed. The compact transmission lines designed and constructed by China and FACTS technologies used to improve the power transmission stability and capacity in China are introduced. The preliminary study on the integrated technology predominance of compact transmission line and FACTS to enhance the transmission capability is carried out. Based on these investigations, the concept “flexible compact AC transmission system” is propounded. The inclusion and extension of this concept is analyzed: the complex and new questions of optimum- cooperating two technologies. Considering the long-distance transmission capability per unit corridor width, the flexible compact AC transmission system is a high efficient power transmission mode. It is applicable to EHV and UHV AC power transmission, and has a good developing and operating prospect. Index Terms—AC power transmission, transmission capability, compact transmission line, FACTS, large-capacity and long-distance power transmission. I. INTRODUCTION INCE the people used electric power, the techniques of power transmission have progressed step by step with the development of human civilizations. China is now building a well-off society, and the strong power supply is one of the reliable guarantees to attain the economic advance objective. The most obvious feature of the Chinese electric power industry is the extreme unbalance between the distribution of primary energy resource and that of power load. China is a country with the vast territory. The exploitable capability of hydropower is about 395 GW, and about two-thirds of the hydropower distributes in the southwest of China. With about 1000 billion tons of coal resources reserved, about two-thirds This work was supported by the Special Fund of the National Priority Basic Research of China (2004CB217906) Xuzheng Chai is with the Department of Electrical Engineering, State Key Lab of Power Systems, Tsinghua University, Beijing, 100084, China (e-mail: [email protected]). Xidong Liang is with the Department of Electrical Engineering, State Key Lab of Power Systems, Tsinghua University, Beijing, 100084, China (e-mail: [email protected]). Rong Zeng is with the Department of Electrical Engineering, State Key Lab of Power Systems, Tsinghua University, Beijing, 100084, China (e-mail: [email protected]). of them distributes in the northwest of China. However, two- thirds of the load centers concentrate at the east area, such as Beijing, Shanghai and Guangdong province. The distance between the load centers and the resource bases is about 500~2000 km. Obviously, it is imperative to transmit huge electric power from the hydro and coal bases to the remote load centers through long distance transmission. Therefore, large-capability and long-distance power transmission in China is an objective requirement. It will face two main difficulties when the conventional EHV and UHV AC power transmission is applied to large- capability and long-distance conditions in China. Firstly, it is necessary to keep power system networks synchronizing operation. The stability limitations decrease the transmission capability continuously in accordance with the transmission lines become longer and longer for the long-distance power transmission demand. So improving the stability of AC power transmission system become very important to realize the large-capability and long-distance power transmission. Secondly, China has a big population and lack of tillable field, and economization on land is very important. Conventional EHV and UHV AC transmission lines need a wide corridor, when they pass through forest and city, a large amount of trees and houses will fall and bulk power stations lack outgoing line corridors, too. Accordingly, enhancing the transmission capability per unit corridor width under the long-distance stable transmission is the aim of correlative studies. HVDC and UHVDC are also large-capability and long- distance power transmission mode. But the DC is more adapt to transmit than distribute electric power. Multi-point HVDC power transmission is quite expensive, and economical constraint limits its development. The Chinese “transmission of electric power from the western to the eastern region” will make the transmission lines pass through the wide west and central regions. With the develop-the-west strategy carried out in China, more and more factories will transfer from east to centric and west regions, and more centric and west regions are developing. These regions would have huge electric power demands in the future. Hence a large quantity of HVDC and UHVDC transmission systems applied to transmit electric power from west to east in China isn’t the best choice. Although the UHV AC and UHVDC power transmission projects have been studied and designed [1, 2] , integrating new Flexible Compact AC Transmission System ——a New Mode for Large-capacity and Long-distance Power Transmission Xuzheng Chai, Xidong Liang, Member, IEEE, Rong Zeng, Member, IEEE S 1-4244-0493-2/06/$20.00 ©2006 IEEE.

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Abstract--In this paper, the requirement and difficulties of

large-capacity and long-distance power transmission under the background of national development strategy “transmission of electric power from the western to the eastern region” in China is analyzed. The compact transmission lines designed and constructed by China and FACTS technologies used to improve the power transmission stability and capacity in China are introduced. The preliminary study on the integrated technology predominance of compact transmission line and FACTS to enhance the transmission capability is carried out. Based on these investigations, the concept “flexible compact AC transmission system” is propounded. The inclusion and extension of this concept is analyzed: the complex and new questions of optimum-cooperating two technologies. Considering the long-distance transmission capability per unit corridor width, the flexible compact AC transmission system is a high efficient power transmission mode. It is applicable to EHV and UHV AC power transmission, and has a good developing and operating prospect.

Index Terms—AC power transmission, transmission capability, compact transmission line, FACTS, large-capacity and long-distance power transmission.

I. INTRODUCTION INCE the people used electric power, the techniques of power transmission have progressed step by step with the

development of human civilizations. China is now building a well-off society, and the strong power supply is one of the reliable guarantees to attain the economic advance objective. The most obvious feature of the Chinese electric power industry is the extreme unbalance between the distribution of primary energy resource and that of power load. China is a country with the vast territory. The exploitable capability of hydropower is about 395 GW, and about two-thirds of the hydropower distributes in the southwest of China. With about 1000 billion tons of coal resources reserved, about two-thirds

This work was supported by the Special Fund of the National Priority Basic Research of China (2004CB217906)

Xuzheng Chai is with the Department of Electrical Engineering, State Key Lab of Power Systems, Tsinghua University, Beijing, 100084, China (e-mail: [email protected]).

Xidong Liang is with the Department of Electrical Engineering, State Key Lab of Power Systems, Tsinghua University, Beijing, 100084, China (e-mail: [email protected]).

Rong Zeng is with the Department of Electrical Engineering, State Key Lab of Power Systems, Tsinghua University, Beijing, 100084, China (e-mail: [email protected]).

of them distributes in the northwest of China. However, two-thirds of the load centers concentrate at the east area, such as Beijing, Shanghai and Guangdong province. The distance between the load centers and the resource bases is about 500~2000 km. Obviously, it is imperative to transmit huge electric power from the hydro and coal bases to the remote load centers through long distance transmission. Therefore, large-capability and long-distance power transmission in China is an objective requirement.

It will face two main difficulties when the conventional EHV and UHV AC power transmission is applied to large-capability and long-distance conditions in China. Firstly, it is necessary to keep power system networks synchronizing operation. The stability limitations decrease the transmission capability continuously in accordance with the transmission lines become longer and longer for the long-distance power transmission demand. So improving the stability of AC power transmission system become very important to realize the large-capability and long-distance power transmission. Secondly, China has a big population and lack of tillable field, and economization on land is very important. Conventional EHV and UHV AC transmission lines need a wide corridor, when they pass through forest and city, a large amount of trees and houses will fall and bulk power stations lack outgoing line corridors, too. Accordingly, enhancing the transmission capability per unit corridor width under the long-distance stable transmission is the aim of correlative studies.

HVDC and UHVDC are also large-capability and long-distance power transmission mode. But the DC is more adapt to transmit than distribute electric power. Multi-point HVDC power transmission is quite expensive, and economical constraint limits its development. The Chinese “transmission of electric power from the western to the eastern region” will make the transmission lines pass through the wide west and central regions. With the develop-the-west strategy carried out in China, more and more factories will transfer from east to centric and west regions, and more centric and west regions are developing. These regions would have huge electric power demands in the future. Hence a large quantity of HVDC and UHVDC transmission systems applied to transmit electric power from west to east in China isn’t the best choice.

Although the UHV AC and UHVDC power transmission projects have been studied and designed [1, 2], integrating new

Flexible Compact AC Transmission System ——a New Mode for Large-capacity and

Long-distance Power Transmission Xuzheng Chai, Xidong Liang, Member, IEEE, Rong Zeng, Member, IEEE

S

1-4244-0493-2/06/$20.00 ©2006 IEEE.

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technologies to solve the requirements of large-capability and long-distance power transmission in China still evoke many researchers’ great interests.

The compact transmission lines have been designed and constructed with different towers and conductor configurations in many countries, such as USA, Russia, Brazil, Italy, China etc. There are operating compact transmission lines even to thousands kilometers in some countries. The Brazilian North-South interconnection, a single-circuit 500 kV compact transmission line, 1020 km long, was energized in the beginning of 1999[3]. Based on the principle of AC power transmission, compact conductor configuration can utilize the conductors fully, which makes the surge impedance loading (SIL) increase significantly and the right-of-way decrease obviously. The proposed and tested high surge-impedance-loading compact transmission line even has the surge impedance loading of 1880 MW and the right-of-way width of 18 meters [4] in Brazil.

China has made a point of designing and using the compact transmission lines. Fig. 1 shows the Operating 500 kV single-circuit compact transmission line and double-circuit compact transmission lines on the same tower in china, which designed and constructed by Chinese researchers and Power Grid Corporations [5]. In China, the Operating 500 kV single-circuit compact transmission line has the surge impedance loading of 1309.6 MW and the right-of-way width of 16 meters, and double-circuit compact transmission lines has the surge impedance loading of 2×1312.3 MW and the right-of-way width of 31 meters [6, 7]. However, the right-of-way width of 500 kV conventional transmission line with horizontal three phases conductors configuration is about 48 meters. The right-of-way width is the horizontal distance of electric field intensity above 4kV/m on the ground up 1 m according to the Chinese national standard.

Fig. 1. Operating 500 kV single-circuit compact transmission line and double-circuit compact transmission lines on the same tower in china

In order to improve the stability and transmission capability, more and more FACTS devices (such as TCSC, SVC and STACOM ect.) have been installed in the power transmission systems in China. Owing to the excellent effect in improving transmission system stability and capacity, the TCSC (including FSC and TCSC ordinarily) has been used in large-capability and long-distance power transmission. The Tian-

Ping 500 kV TCSC system [8] (5% TCSC segment and 35% FSC segment) and Cheng-Bi 220 kV TCSC system [9] (50% TCSC) have been operating. Many SVC and STACOM have been applied in power transmission system. The main aim of them is keep voltage stability and Var balance. Although they could offer damping for transient stability, the action isn’t very efficient.

To the combination of compact transmission line and FACTS technologies, whether it is a new mode or choice for large-capability and long-distance power transmission? The integrated effect will be preliminary studied in this paper. The possible main questions will be analyzed. Based on these investigations, the concept “flexible compact AC transmission system” is propounded. Considering the long-distance transmission capability per unit corridor width, the flexible compact AC transmission system is a high efficient power transmission mode. It is applicable to EHV and UHV AC power transmission, and has a good developing and operating prospect.

II. CALCULATION AND SIMULATION OF TRANSMISSION SYSTEM INTEGRATED COMPACT TRANSMISSION LINE WITH FACTS

TECHNOLOGIES The transmission capability of power transmission system

with combined compact transmission line and FACTS technologies is evaluated through the calculation and simulation under steady-state stability and transient stability.

A. Transmission Capability under Steady State Stability The power-carrying capability of the transmission system

is generally evaluated by line loadability curve (St. Clair curve)

[10, 11], which expressed in per unit of surge impedance load, SIL. In the calculation of line loadability curve, the thermal rating of conductors, line voltage drop and steady state stability are the actual restrictive conditions. The extensive simulations and analyses have revealed that the thermal limitation, line-voltage-drop limitation and steady-state-stability limitation are the main controlling factors for loadability of short, moderate and long lines respectively.

The conventional calculation method of power-carrying capability (loadability expressed with actual value) curve adopts the voltage drop between sending-end bus voltage and receiving-end bus voltage [10, 11] or between sending-end system equivalent voltage and receiving-end bus voltage [12] as the line voltage drop criterion (5%). The voltage distributions of actual operating AC transmission line are variable. When the transmission line carries the load above SIL, the reactive power will be transmitted from both ends to the medial, and some medial point will appear the maximum voltage. When the transmission line carries the load below SIL, the reactive power will be transmitted from the medial to both ends, and the voltage of both ends will be higher than the other points in the transmission line. In fact, the sending-end bus voltage and receiving-end bus voltage have been prescribed concretely according to relevant guide to power system voltage and reactive power techniques in China: When the transmission

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line carries the load below SIL, the installed shunt reactors in both ends will keep the line voltage in the required level; When the transmission line carries the load above SIL, the generator excitation and reactive compensation equipments will keep the line voltage in the required level. So according to the guide to power system voltage and reactive power techniques in China, the sending-end bus voltage scopes within 100%~110% of rated voltage and receiving-end bus voltage scopes within 95%~105% of rated voltage are adopted as the line voltage required level in the calculation of power-carrying capability curve.

The mathematical model of AC transmission system is shown in Fig. 2.

Fig. 2. Mathematical model of AC transmission system

In the calculation of power-carrying capability curve, considering the main point-to-network transmission condition in China, the sending-end and receiving-end short-circuit currents are set at 15 kA and 50 kA respectively. The sending-end and receiving-end system equivalent voltage Es and Er are specified as 1.05 and 1 per unit in the present case based on the case of load flow. The limitation criterion of sending-end bus voltage scopes and receiving-end bus voltage scopes are 100%~110% of rated voltage and 95%~105% of rated voltage respectively. In accordance with the steady state stability criterion of Transmission Line Reference Book 345 kV and Above by EPRI, the steady-state stability margin 30% is taken, corresponding phase angle differenceδ= 44° across the system terminals. Full details are given in [13]. The Fig. 3 is power-carrying capability curve under the above condition.

Fig. 3. Power-carrying capability of different AC power transmission mode

According to this figure, it could be summarized that: the

transmission capability of 750 kV conventional transmission line and integrated 500 kV compact transmission line with 50% series compensation(concluding TCSC and FSC) is equivalent on the whole at the distance between 600 and 1000 km; At the 1000 km transmission distance, the transmission capability per unit corridor width of integrated 500 kV compact transmission line with 50% series compensation is 116.9 MW/m, however, the transmission capability per unit corridor width of conventional 500 kV transmission line with horizontal three phases conductors configuration is only 17.2 MW/m. According to the power-carrying capability curve, the integrated compact transmission line with series compensation technologies reveal great superiority in the transmission capability per unit corridor width.

B. Transmission Capability under Transient Stability The actual transmitted power of the operating power

transmission system depends on its transient stability. The characteristics of terminal systems and transmission line with accessory equipments will make the transient stability of power transmission systems widely different. It is necessary to investigate the transmission capability of the integrated compact transmission line with FACTS technologies under transient stability limitation.

The energy function (lyapunov) method has been used to determine the transient stability margin to develop control strategies for improving transient stability. The analysis followed uses a structure preserving energy mode of a post-fault power system, which retains the topology of the system. Consider a power transmission system with Ng generators, Nb buses (excluding generator internal buses), and Nl transmission lines (including transient reactance branch of generators), the energy function defined as [14] [15]:

20

0 0

212

1

12

1 1

(1)

( )

( )

g

b lSVCi iLi i i

i ii i

N

i i mi ii

N Nv vQ b VLi i i i seriesV Vv v

i l

v M P

P dV dV Q

ω δ

θ

=

= =

= − +

+ − +

∑ ∑∫ ∫

%%

%

where iω% and iδ% are the angular speed and rotor angle of ith generator with respect to the center of inertia (COI) reference frame respectively. Mi and Pmi are the moment of inertia and mechanical power input of ith generator respectively. Pli and Qli are the real power load and active power load at ith bus respectively. iθ% is the phase angle of voltage at ith bus. Qseries is the reactive power loss in series branches. It is supposed that the TCSCs are installed in lines between ith bus and jth bus, and SVCs are installed in ith bus. TCSC is modeled as a series combination of a fixed capacitance reactance 0

TCSCijX ,

and a controlled part TCSCijuX , hence the applied series

compensation capacitance reactance is0

TCSC TCSC TCSCij ij ijuX X X= + .

The SVC is modeled as a parallel combination of fixed shunt

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susceptance 0SVCib and a controlled part SVC

iub . Only fixed part of TCSC and SVC are operating before system fault.

The introduction of FACTS equipments doesn’t alter the original value of energy function (1) at the post-fault system. However, they will alter the trend and speed of energy function change [16]. When TCSC and SVC change the transmission line reactance and susceptance according to the control strategy, the real power and active power of any bus will keep balance and sum to zero. The trend and speed of energy function change is evaluated by the time derivative of energy function:

0

1 1 1

2 21 12 2 ( )( )

1 1(2)

( )g b b

i

i

b l TCSCiju

TCSC TCSCLij ij Lij ij

g

N N NV

i i gi mi i i i iVi i i

N NXSVC d d

iu i seriesdt dtX X X Xi l N

v M P P P Q

b V V

ω δ θ= = =

− −= = +

= + − + + +

∑ ∑ ∑

∑ ∑

&& && % %%&

where LijX is the reactance of power transmission line,

and 2 2 2 22 cos( ) [ ]series i j i j i j Lij TCSC TCSCV V V VV X I Vθ θ= + − − = −% % .

According to the energy balance of generator, real power balance and active power balance of any bus, the three items ahead in formula (2) are zero. And so:

0

2 21 12 2 ( )( )

1 1(3)

b l TCSCiju

TCSC TCSCLij ij Lij ij

g

N NXSVC d d

iu i seriesdt dtX X X Xi l N

v b V V− −

= = +

= −∑ ∑&

The energy function describes total energy of the post-fault system, and the v& describes the rate of system energy function change. The system energy function must be a positive definite function. If the v& is negative, the system energy will decrease continuously till the balance point of system new steady. The formula (3) is deduced and gotten by amending the process and conclusion of reference [17].

Therefore, the control law for TCSC: 2

min max, 0,TCSC TCSC TCSC TCSCdiju TCSC series TCSC ijdtX K V K X X X= > < <

The control law for SVC: 2

min max, 0,SVC SVC SVC SVCdiu SVC i SVC idtb K V K b b b= − > < <

The deduction and analysis of reference [18] could validate the correctness of the control law for SVC in this paper, which adopt the bang-bang control for transient steady stability.

For TCSC,2 sind

series ij ijdt V K dθ θ≈ % % , K>0, and so the

control law for TCSC with bang-bang control is

max

min

sin 0, ( )

sin 0, ( )

TCSC TCSCij ij

TCSC TCSCij ij thyristor blocked

d X X TCSC forced compensation

d X X TCSC

θ θ

θ θ

⎧ ≥ =⎪⎨

< =⎪⎩

When the TCSC works in forced compensation state, the capacitance reactance is twice of normal operation and even more.

CEPRI-7 buses system is typical point-to-network power transmission system [19], and the simulation has been

performed with its parameters of sending-end and receiving-end system. The simulation uses the BPA software (Chinese 3.0 version). The transmission capability of several EHV power transmission modes under transient steady stability limitation have been simulated and analyzed.

Fig. 4 shows the test system. The transmission line is 1000 km long between the sending-end bus B1-500 and the receiving-end bus B4-500, which is divided into three sections averagely.

Fig. 4. Test system of a typical point-to-network power transmission

A three-phase fault occurs at bus B1-500 side of one of transmission line between bus B1-500 and bus B2-500. The fault is cleared after 0.1 s by opening the faulted line. When the system comes into post-fault condition, the TCSC begins to operate in forced compensation state, and its capacitance reactance is twice of normal operation. The operating time in forced compensation state is 25 circles (0.5 s). The controlled part of SVC will be put into system according to the control law of BPA software, which is in accordance with the conclusion in this paper.

The table I is the simulation results. It is assumed that all SC (include FSC and TCSC) are installed in the three-section transmission line averagely. TCSC is installed in faulted section and its parallel section, and FSC is installed in other sections.

TABLE I

TRANSIENT STABILITY TRANSFER CAPABILITY OF DIFFERENT AC POWER TRANSMISSION MODE

In this case, the transient stability of 500 kV compact

transmission line with 33%FSC and 17% TCSC is quiet well, when it transfer power 1459MW. The Fig. 5 shows its sending-end generator angle variation curve, and when the sending-end and receiving-end capacity are 3999 MW and

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9999 MW respectively. Under the transient stability limitation, the transmission capability per unit corridor width of integrated 500 kV compact transmission line with 33% FSC and 17%TCSC is 91.2 MW/m, however, the transmission capability per unit corridor width of conventional 500 kV transmission line with horizontal three phase conductors configuration is only 13.75 MW/m. According to the preliminary analysis and simulation, the integrated compact transmission line with TCSC reveals great superiority in the transmission capability per unit corridor width under transient stability, too.

Fig. 5. Angle variation of the test system in transient stability

III. FLEXIBLE COMPACT AC TRANSMISSION SYSTEM The compact transmission lines have been widely designed,

constructed and applied according technical code of different countries. Although these compact transmission lines have different voltage classes, different conductor configurations and different tower structures [4, 5, 20, 21], they possess some common technical characteristics: Compact configuration of three phase conductors make

the right-of-way of power transmission line decrease obviously.

Compact configuration of three phase conductors and optimum number and arrangement of subconductors per phase make the line capacitance increase evidently and line inductance decrease appropriately.

The increase of line capacitance and decrease of line inductance make the surge impedance diminish and surge impedance loading capability enhance prominently.

From the case of Chinese compact transmission line whose parameters are used in the above calculations and simulations, concrete structure and data comparison with conventional transmission line of horizontal conductor configuration will reveal these features clearly.

Fig. 6. Comparison of conductor configuration and tower

The Fig. 6 is the comparison of conductor configuration and tower between Chinese 500 kV compact transmission line with invert-delta three phase conductors configuration (Chang-Fang line[22]) and conventional 500 kV transmission line with horizontal three phase conductors configuration (No.2 Chang-An line[5]). According to the relative technical report [22], some typical power frequency parameters of compact and conventional transmission line are in table II.

TABLE II

SOME TYPICAL POWER FREQUENCY PARAMETERS OF COMPACT AND CONVENTIONAL TRANSMISSION LINE

The flexible compact transmission system is the AC power

transmission mode of integrated compact transmission line with FACTS technologies for large-capability and long-distance power transmission. It should be the optimum combination of the compact transmission line (include different types of compact line in other countries) with various necessary FACTS equipments. The preliminary investigation shows that the combination of compact transmission line and FACTS technologies could improve the capability and efficiency of large-capability and long-distance power transmission obviously. In this paper, the concept of flexible compact transmission system is proposed. It is applicable to long-distance EHV and UHV AC power transmission, at the same time the common question must be analyzed and solved when this AC power transmission mode is performed optimally. All these aspects come from the characteristics and joint actions of compact transmission line and FACTS equipments, and the requirements of integrative optimal operation, such as:

A. Integrative FACTS Equipments Scheme and Control Law with Compact Transmission Line

It is very important to keep the flexible compact AC transmission system for large-capability and long-distance power transmission security and stability. Based on the parameters characteristics and network structure of system, the integrative FACTS equipments scheme and control law of should be gotten by suitable mathematic optimization method

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and control theory. For the steady state stability, transient stability and voltage stability of whole power transmission system, all kinds of FACTS equipments, such as TCSC, STACOM, SVC, SSSC etc, should be chose to exploit their particular advantages.

B. Electromagnetic Transient Characteristics and Protective Scheme of Flexible Compact AC Transmission System

The parameters of compact transmission line are quite different from the conventional transmission line, and the electromagnetic transient characteristics also have its own particularity. When the FACTS devices are installed in the long-distance compact transmission line, the electromagnetic transient characteristics will be more complex. It is necessary to research the complex characteristics for the overvoltage protection and insulation coordination of power transmission devices and FACTS devices.

C. Relay Protection and Fault Location of Flexible Compact AC Transmission System

When the compact transmission line and some FACTS equipments are adopted, the features of AC transmission system maybe are quite different from ordinary system. Some relay protections and fault locations perhaps would be failed and wrong, especially when the FACTS equipments act.

IV. CONCLUSION Based on the preliminary investigation, this paper proposes

a new large-capability and long-distance power transmission mode: flexible compact transmission system. Calculation and simulation show its high efficiency. Some complex and new questions only are presented in this paper, and the further study should be aimed at these questions in concrete practical application. Considering the long-distance transmission capability per unit corridor width, the flexible compact AC transmission system has a good developing and operating prospect.

V. REFERENCES [1] Yinbiao Shu, "Development of Ultra high voltage transmission

technology in China," in Proc. 2005 the XIVth International Symposium on High Voltage Engineering, pp. 1.

[2] Licheng Li, "Technical characteristics and engineering application of UHVDC power transmission," in Proc. 2005 the XIVth International Symposium on High Voltage Engineering, pp. 272.

[3] C. Gama, “Brazilian North-South Interconnection control-application and operating experience with a TCSC “in Proc. 1999 IEEE Power Engineering Society Summer Meeting Conf., pp. 1103-1108.

[4] P. C. V. Esmeraldo, C. P. R. Gabaglia, and G. N. Aleksandrov et al, "A proposed design for the new Furnas 500 kV transmission lines-the High Surge Impedance Loading Line," IEEE Trans. Power Delivery, vol. 14, pp. 278-286, Jan. 1999.

[5] Weigang Huang, "Study on conductor configuration of 500 kV Chang-Fang compact line," IEEE Trans. Power Delivery, vol. 18, pp. 1002-1008, July. 2003.

[6] Technical code for design of 500 kV compact overhead transmission line, State Grid Corporation Standard Q/GDW 110-2003, Jan. 2003.

[7] Yinbiao Shu, Chenghua Zhao, "Study and implementation of 500 kV compact power transmission line with double circuit on a same tower in China, " Power System Technology, vol.26, pp. 49-51, Oct. 2002.

[8] Jiming Lin, Baoshu Peng, and Qiang Guo et al, "Tian-Ping TCSC in China Southern Grid," International Electric Power for China, vol. 8, pp. 48-51, Oct. 2004.

[9] Jianbo Guo, Shouyuan Wu, and Guofu Li et al, "Study on domestic-manufactured demo project of 220kV TCSC for power transmission from Cheng County to Bikou in Gansu province, " Power System Technology, vol.29, pp. 12-17, Oct. 2005.

[10] S. N. Tiwari, A. S. Binsaroor, "An investigation into loadability characteristics of EHV high phase order," IEEE Trans on Power Systems, vol. 10, pp. 1264-1270, Nov. 1995.

[11] J. J. LaForest, Transmission line reference book 345kV and above (second edition) California: Electric Power Research Institute, 1982.

[12] R. D. Dunlop, R. Gutman, P. P. Marchenko, "Analytical development of loadability characteristics for EHV and UHV transmission line," IEEE Trans on Power Apparatus and System, vol. PAS-98, pp. 606-613, March.1979.

[13] Xuzheng Chai, Xidong Liang, Rong Zeng, "An improved calculation method for Power-Transmitting Capability Curve of AC transmission line," Power System Technology (in Chinese), to be published.

[14] M. A. Pai, Energy Function Analysis for Power System Stability Boston: Kluwer, 1989

[15] K. N. Shubhanga, A. M. Kulkarni, "Application of Structure Preserving Energy Margin Sensitivity to Determine the Effectiveness of Shunt and Series FACTS Devices,” IEEE Transaction on power system, vol.17, pp. 730-738, Aug. 2002.

[16] M. Ghandhari, G. Andersson, I. Hiskens, et al, "Control Lyapunov functions for controllable series devices,” IEEE Transaction on power system, vol.16, pp. 689-694, Nov. 2001.

[17] M. Noroozian, M. Ghandhari, G. Andersson, et al, "A robust control strategy for shunt and series reactive compensators to damp electromechanical oscillations,” IEEE Transaction on power delivery, vol.16, pp. 812-817, Oct. 2001.

[18] M. H. Haque, "Improvement of first swing stability limit by utilizing full benefit of shunt FACTS devices," IEEE Transaction on power system, vol. 19, pp. 1894-1902, Nov. 2004.

[19] CEPRI. PSASP program basic data book Beijing: CEPRI, 2001. (In Chinese).

[20] R. de la Rosa, M. Ochoa, J. L. Bonilla, et al, “Contributions to lightning research for transmission line compaction,” IEEE Transaction on power delivery, vol.3, pp. 716-723, April. 1988.

[21] T. J. F. Ordon, K. E. Lindsey, “Considerations in the design of three phase compact transmission lines,” in Proc. 1995 IEEE Seventh International Conference on Transmission and Distribution Construction and Live Line Maintenance, pp.108-114

[22] Zuping Zhang, Gesong Chen, Jiming Lin, et al, "Study on the system operation characteristics of 500 kV Chang-Fang compact transmission line," CEPRI, and North China Electric Power Group Co., Tech. Rep.X9714, April. 1997.

VI. BIOGRAPHIES

Xuzheng Chai was born in Henan Province, China, in 1978. He received B.S. degree in electrical engineering from Zhengzhou University of Technology in 2000. He received M.S. degree in electrical engineering from Wuhan University in 2003. Now he is a Ph.D. candidate in Tsinghua University. His major research fields are electromagnetic transient analysis, compact transmission line and FACTS.

Xidong Liang (M’00) received Ph.D. degree from the Department of electrical engineering, Tsinghua University in July 1991. Now he is a professor and the Head of the Department of electrical engineering, Tsinghua University. His major research fields are outdoor insulation and power transmission line.

Rong Zeng (M’02) was born in Shanxi Province, China, in 1971. He received B.Sc., M. Eng., and Ph.D. degree from the Department of electrical engineering, Tsinghua University, Beijing, respectively, in 1995, 1997, and 1999.

Now he is an Associate Professor Department of electrical engineering, Tsinghua University. His research interests include high voltage technology, grounding technology, and power transmission technology.