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Simulation and analysis of UHV half wavelength and DC hybrid transmission system
Vol. 1 No. 3 Aug. 2018 DOI: 10.14171/j.2096-5117.gei.2018.03.008
Global Energy Interconnection www.geidco.org Full-length article
Simulation and analysis of UHV half wavelength and DC hybrid transmission system Qianyu Zhao1, Shouxiang Wang1, Xiaohui Qin2, Seyedamirabbas Mousavian3, Lei Wu4 1. Tianjin University, Key Laboratory of Smart Grid of Ministry of Education, Nankai District, Tianjin 300072, P. R. China 2. China Electric Power Research Institute, Haidian District, Beijing 100192, P. R. China
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3. School of Business, Clarkson University, Potsdam, NY, USA 4. Department of Electrical and Computer Engineering, Clarkson University, Potsdam, NY, USA
Abstract: The scenarios of a half wavelength transmission line (HWTL) connected to the original DC asynchronous interconnection system are established based on the quasi-steady state model of HWTL, which include single or double loops of single channel and multi-channel scenarios with different starting and landing points. Firstly, the steady state power flow characters of multi-scenario transmission schemes are studied. The voltage distribution characters of HWTL are analyzed when its transmission power and power factor vary, and the influence of the DC power variation on voltage of HWTL is discussed. Then the transient characters of HWDHTS are explored. The DC commutation failure caused by the fault of HWTL is simulated and the power transfer capacity of HWTL while DC blocking is calculated in this paper. Keywords: UHV half-wavelength AC power transmission line, UHV DC system, Steady state characters, Transient stability.
1 Introduction The global energy interconnection is a strategic concept for the effective allocation of energy in the global context. One of the necessary premises for the realization of the energy Internet is the long distance, large capacity, low loss transmission technology. The transmission modes that can meet the demand of ultra-long distance and large capacity transmission are mainly separated into ultra-high voltage (UHV) AC/DC transmission technology and HWTL technology. The UHV AC/DC transmission technology has been applied in China. The HWTL technology refers to the electric power transmission of a distance approaching 1 power frequency half wave, namely 3000 km (50 Hz) ultraReceived: 20 November 2017/ Accepted: 12 December 2017/ Published: 25 August 2018 Qianyu Zhao [email protected]
Seyedamirabbas Mousavian [email protected]
Shouxiang Wang [email protected]
Lei Wu [email protected]
Xiaohui Qin [email protected] Open access under CC BY-NC-ND license. 366
long distance three-phase AC transmission technology [1-4]. Compared with the traditional AC transmission mode, HWTL has the advantages of ultra-long distance, large capacity transmission, and so on. It also does not need to install reactive power compensation devices and add intermediate switch stations [5-6]. There is no HWTL commercially operated in the world. But some researches of HWTL have been presented in [7-9]. The economics of several alternative solutions for point-to-point HWTL are evaluated in [7]. [8] introduces a shunt FACTS device for tapping and realizing power flow control in HWTL. Three HWTL corridors are studied in [9] for the interconnection of Belo Monte Power Plant, located in the state of Para, to the Brazilian interconnected system through Assis Substation, in the state of Sao Paulo, with a total distance of 2664 km. The references mentioned above considered neither the different situations of networks to networks, nor the steady state operation and transient characters of HWTL after the transmission of HWTL connected to the original DC asynchronous network system.
Qianyu Zhao et al. Simulation and analysis of UHV half wavelength and DC hybrid transmission system
In this paper, the steady state operating characters of different situations of networks to networks as well as the simulation and analysis of transient characters of HWTL are studied, after considering the original transmission network connected to the original DC asynchronous network. The rest of the paper is organized as follows. The Quasi-steady model of UHV half-wavelength is proposed in section 2 and steady state power flow characters of multi-scenario transmission scheme are analyzed in section 3. Transient characters of the hybrid system including simulation and analysis of DC commutation failure as well as simulation of power transfer capability of HWTL under DC blocking are discussed in section 4. Finally, conclusions are drawn in section 5.
2 Quasi-steady model of UHV half-wavelength Voltage and current equations at the xkM position from the receiving end of HWTL are obtained if the line has no loss and the voltage and current of the transmission line terminal are known as: U = U cos αx − jI Z sin αx x 2 2 c U2 I x = j Z sin αx − I 2 cos αx c •
(1)
•
where U 2 and I 2 are the terminal voltage and current of • HWTL, respectively. The direction of outflow of I 2 is positive. And α = ω L0 C0 , which is the line transmission constant. Z c = L0 C0 is line wave impedance. L0 and C0 are inductance and capacity value of unit length of the line, respectively. The uniform transmission line can be regarded as a twoport network, and it is assumed that the parameter matrix of the two-port transmission is T. The expression is as follows:
cos αx Z c sin αx T = sin αx cos αx Z c
(2)
According to the theory of two-port networks, the two-port network of the line can be transformed into the equivalent model and the equivalent impedance and admittance are as follows.
Z eq = jZ c sin αx (3) cos αx − 1 Yeq = jZ sin αx c The above π type equivalent model and parameters are
strictly equivalent in power frequency steady state and can be easily used in power flow calculation. If the transmission line is simulated approximately with series of multiple π type segments, the final HWTL can be equivalent to a cascade of two ports, namely, the equivalent T array of the HWTL, which is the n order casecade of the piecewise T matrix and then the equivalent parameters of the HWTL can be transformed. It is shown in the formula (1) that the terminal voltage of HWTL is proportional to the current of the receiving terminal, and the midpoint current is proportional to the magnitude of the receiving terminal voltage. When αx = π, that is the HWTL length, and the voltage at the end of the head and the end are the same, but the phase is opposite. Although the voltage at the two ends of lossless HWTL is not affected by transmission power, but the closer to the middle of the line, the voltage changes are more seriously affected by the power. The limiting transmission power of HWTL is shown in formula (4),
Pm =
U1U 2 Pn = Z c sin αx sin αx
(4)
U1 and U2 are the voltages at both ends of the circuit, and Pn is the natural power. The power limit of the line is the natural power when αx = π 2 and the theoretical limit value of HWTL can be infinite when αx = π(i.e. HW length).
3 S teady state power flow characters of multi-scenario transmission scheme 3.1 Classification of the hybrid system Multi-scenario scheme for connecting the original DC asynchronous network system to HWTL is established based on the quasi-steady state model of HWTL including single/double loop of single channel and multi-channel, which are all for network to network. Specific scenarios are shown in Fig. 1. This section studies the steady state operation characters of the above scenarios transmission schemes including voltage distribution characters of HWTL with different power supplies, and load power factors, and influences of DC transmitted power variations on voltages of HWTL.
3.2 Steady state operation characters of single loop or double loops of single channel The voltage distribution characters of single loop or double loops of single channel with varying power of HWTL are shown in Fig. 2. The figure shows the transmission power of double scenes is two times as much as that of single scene transmission, and the voltage 367
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distribution character of HWTL itself is similar to that of point to network, that is, the middle voltage of the line rises when the transmission power is greater than the natural power, and that of the line decreases when the transmission power is less than the natural power. The voltage distribution characters of single loop or double loops of single channel with varying power factor of HWTL are shown in Fig. 3. From the figure, the voltage is approximately sinusoidal when the capacitive reactive power load is connected to the end of HWTL (i.e. the power factor is negative), and the greater the power factor, the greater the voltage fluctuation along the line. The voltage is negative in the sine curve. The voltage along the line is negative sinusoidal when the inductive reactive
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power load is connected to the end of HWTL (i.e. the power factor is positive), and the greater the power factor, the greater the voltage fluctuation along the line. The voltage distribution characters of single loop or double loops of single channel with varying DC power are shown in Fig. 4. The figure shows the characteristic of voltage distribution of HWTL is similar to that of HWTL with varying power when the DC power varies. However, the half wave line voltage is highly coupled with the DC power, and the HWTL is affected by the DC power control. When the DC transmission power is reduced, the excess power will be transmitted through HWTL, which increases the power of HWTL, and affects the voltage distribution characters. Otherwise, the power of HWTL decreases and results in the reduction of the midpoint voltage when the DC transmission power increases. Therefore, the voltage of HWTL must be controlled within a certain range by controlling the change of DC transmission power.
3.3 Steady state operation characters of multichannel with different starting and landing points In multi-channel situation, that is, the starting points and landing points of two HWTLs are different.
Qianyu Zhao et al. Simulation and analysis of UHV half wavelength and DC hybrid transmission system
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The voltage distribution characters of multi-channel with varying power of HWTL are shown in Fig. 5. From the diagram, the first terminal voltages of the two HWTLs are different. The range of the first terminal voltage of line 1 is 1060-1070 kV, and the voltage range of the first terminal of line 2 is 1110-1120 kV, which is slightly higher than that of line 1. The transmission powers of the two half wavelength lines are not the same when the load power changes. While the transmission power of the half wavelength line 1 is 4076.3 MW, the transmission power of the line 2 is 4170.5 MW; while the transmission power of the half wavelength line 1 is 5718.8 MW, the transmission power of the line 2 is 5583.3 MW. The voltage distribution characters of multi-channel with varying power factor of HWTL are shown in Fig. 6. From the figure, the voltage is roughly sinusoidal when the capacitive reactive power load is connected to the end of HWTL (i.e. the power factor is negative), and the greater the power factor, the greater the voltage fluctuation along the line. The voltage is negative in the sine curve. The voltage along the line is negative sinusoidal when the inductive reactive power load is connected to the end of HWTL (i.e. the power factor is positive), and the greater the power factor, the greater the voltage fluctuation along the line. 370
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The voltage distribution characters of multi-channel with varying DC power are shown in Fig. 7. The change rule is similar to single loop or double loops of single channel. From the diagram, the first terminal voltage of line 2 is higher than the first terminal voltage of line 1, the overall trend is higher than the line 1, and the first terminal voltages of the two lines are higher than the terminal voltages. The power of DC line increases from 5600 MW to 6800 MW, and the transmission power of half wavelength line decreases with the increase of DC power. When the DC line power is less than 5600 MW or higher than 6800 MW, the system does not converge. When the DC
Qianyu Zhao et al. Simulation and analysis of UHV half wavelength and DC hybrid transmission system
power is 5200 MW, the system can still converge while the power of the DC receiving end is reduced, while the power of the half wavelength line is not changed. The power of the half wavelength line changes in multichannel scenarios, and the farther the landing point is, the more serious the imbalance of power distribution is.
4 Transient characters of the hybrid system 4.1 Commutation failure caused by fault of HWTL The first and the second ends of HWTL have single phase short circuit fault in 0.2s and recover in 0.3s. Then the single line short circuit fault occurs in 0.3s and restores in 1.3s. Contrast charts between commutation failure and no commutation failure after fault of HWTLL are shown in Fig. 8-10. The failure of HWTL leads to commutation failure of the DC line, and it occurs in 1.32s. Recovering from commutation failure in 1.38s from Fig. 8, the power
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fluctuation time of DC line during commutation failure is longer than that without commutation failure. Meanwhile, midpoint voltage of HWTL fluctuates in a long time, at a relatively high value during the commutation failure. The commutation failure recovery period which is shown in Fig. 9, and in this period the bus voltage is low in converter station as shown in Fig. 10. Therefore, much reactive power is needed in the process of DC commutation failure and recovery. There are three reasons for the failure of commutation caused by the fault of HWTL. First, half-wavelength failure leads to a sudden drop of DC voltage and the inverter control system does not have enough time to function. Second, the DC transmission power is close to the rated power before the failure, which leaves a small margin for the extinction angle. Third, the fault occurs near the bus of the converter station. Although the halfwavelength and the DC lines are geographically far apart, the electrical distance between the two is relatively short.
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Fig. 9 Voltage variation of HWTL 371
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The original DC asynchronous network system is established, which is connected with the single channel single circuit HWTL based on the quasi-steady state model as shown in Fig. 11. The rated voltage of the ring network node is 500 kV, the HWTL is connected with the sending end bus through the 525/1050 kV step-up transformer, and the receiving end is connected with the bus through the 1050/525 kV step-down transformer. The rated powers of two DC lines are 6000 MW and 4000 MW, respectively. The PSD-BPA software is used to calculate the power flow and the 10-section model is adopted for the HWTL. 4.2.1 Unipolar blocking of the second DC line The DC line 2 has unipolar locking, with the locking DC power of 2000 MW. Half of the filter is removed, and the system remains stable. Fig. 12 shows that when
the DC line suffers unipolar blocking, the first power of HWTL from the original 4652.2 MW to the current 6380 MW, as HWTL bears the transfer of 1727.8 MW, and the midpoint voltage of HWTL increases from 1.0 p.u to 1.42 p.u.
4.2 Simulation and analysis of power transfer capability of HWTL under DC blocking
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Fig. 12 Transient operation characters of DC line 2 with unipolar blocking 372
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Qianyu Zhao et al. Simulation and analysis of UHV half wavelength and DC hybrid transmission system
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4.2.2 Unipolar blocking of the first DC line The DC line 1 has unipolar locking, with the locking DC power of 3000 MW. Half of the filter is removed, and the system remains stable. Fig. 13 shows that when the DC line suffers unipolar blocking, the first power of HWTL increases from the original 4652.2 MW to the current 7420 MW, and HWTL bears the transfer of 2767.8 MW, and the midpoint voltage of HWTL increases from 1.0 p.u to 1.68 p.u. But high voltages situation is not permitted in engineering practice, so the power of blocking can be transferred to other DC lines or HWTL, so that the voltage and power of the transmission line are controlled in the allowed range. 4.2.3 Bipolar blocking of the second DC line The DC line 2 has bipolar locking, with the locking DC power of 4000 MW and all of the filter is removed, and the system remains stable. It is shown that the system is in the state of critical stability due to the equal amplitude oscillation of the system. 4.2.4 Bipolar blocking of the first DC line The DC line 1 has bipolar locking, as the locking DC power is 6000 MW, and the system is unstable. Changing transmission power of the first DC line 1, then the corresponding DC blocking is carried out. The transmission power of the DC line 1 is reduced from 2*3000 MW to 2*2500 MW, that is to say, 1000 MW output power of the DC line to the end is removed, and 1000 MW of the load by the end of the DC line is removed. (1) The DC line 2 has unipolar locking, as the locking DC power is 2000 MW and the system remains stable. (2) The DC line 1 has unipolar locking, as the locking DC power is 2500 MW and the system remains stable. (3) The DC line 1 and 2 are simultaneously locked at the same time, and each half of the filter is removed. The total
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locked DC power is 4500 MW, and the system is in constant amplitude oscillation. So it is incritical stable state. (4) The DC line 2 has bipolar locking, the locking DC power is 4000 MW and the system is in the critical stable state. (5) The DC line 1 has bipolar locking, as the locking DC power is 5000 MW and the system is unstable. Changing transmission power of the first DC line 1, then the corresponding DC blocking is carried out. The transmission power of the DC line 1 is reduced from 2×3000 MW to 2×1500 MW, that is to say, 3000 MW output power of the DC line to the end is removed, and 3000 MW of the load by the end of the DC line is removed. (1) The DC line 2 has unipolar locking, as the locking DC power is 2000 MW and the system remains stable. (2) The DC line 1 has unipolar locking, as the locking DC power is 1500 MW and the system remains stable. (3) The DC line 1 and 2 are simultaneously locked at the same time, and each half of the filter is removed. The total locked DC power is 3500 MW, and the system is 373
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stable. Fig. 15 shows that when the DC line suffers unipolar blocking, the first power of HWTL decreases from the original 4652.2 MW to the current 8000 MW, and HWTL bears the transfer of 3347.8 MW. The midpoint voltage of HWTL increases from 1.0 p.u to 1.81 p.u. In summary, the transfer power that HWTL can withstand is 0-3347.8 MW. The system is stable when the power cut off by DC line is less than 3500 MW and the system transits from the critical stability to instability when the power at above 4000 MW. The first end of HWLL
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5 Conclusions (1) The steady state power flow characters of the single channel single/double loop network are similar to the characters of the voltage distribution of HWTL. However, the voltage state of HWTL is highly coupled with the DC power. Half wavelength line state is affected by DC power control. (2) The power of HWTL changes in multi-channel scenarios, and the longer the landing point distance is, the more serious the imbalance of power distribution is. 374
Acknowledgements This work was supported by the State Grid Science and Technology Project (XTB17201600100-01).
References
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(3) In the multi-DC parallel situations built in this paper, the transfer power that HWTL can withstand is 0-3347.8 MW. The system is stable when the power cut off by DC line is less than 3500 MW and the system transits from the critical stability to instability when the power is above 4000 MW.
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Qianyu Zhao et al. Simulation and analysis of UHV half wavelength and DC hybrid transmission system
Biographies Qianyu Zhao received her bachelor in Electrical Engineering from Tianjin Polytechnic University in 2012 and master degrees in Control Science and Engineering from Tianjin Polytechnic University in 2015. She is currently working on her Ph.D. degree at Electrical Engineering in Tianjin University. Her research interest is power system stability. Shouxiang Wang received his bachelor and master degrees in Electrical Engineering from Shandong University of Technology, in 1995 and 1998 respectively. He received his Ph.D. degree in Electrical Engineering from Tianjin University in 2001. His research interests include distributed generation, micro grid and smart distribution system.
Seyedamirabbas Mousavian received his Ph.D. degree in Industrial and Systems Engineering from Auburn University. He is currently working as an assistant professor. his research interests include smart grid, cyberphysical systems security, cyber-physical systems investment, power systems operations and planning, electric vehicles, and operations research. Lei Wu, associate professor, his research interests include power systems operation and planning, energy economics, and community resilience micro grid. (Editor Chenyang Liu)
Xiaohui Qin received his Ph.D. degree in North China Electric Power University in 2008. His research interests include power system planning and simulation, advanced applications of WAMS.
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Simulation and analysis of UHV half wavelength and DC hybrid transmission system Qianyu Zhao1, Shouxiang Wang1, Xiaohui Qin2, Seyedamirabbas Mousavian3, Lei Wu4 1. Tianjin University, Key Laboratory of Smart Grid of Ministry of Education, Nankai District, Tianjin 300072, P. R. China 2. China Electric Power Research Institute, Haidian District, Beijing 100192, P. R. China
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3. School of Business, Clarkson University, Potsdam, NY, USA 4. Department of Electrical and Computer Engineering, Clarkson University, Potsdam, NY, USA
Abstract: The scenarios of a half wavelength transmission line (HWTL) connected to the original DC asynchronous interconnection system are established based on the quasi-steady state model of HWTL, which include single or double loops of single channel and multi-channel scenarios with different starting and landing points. Firstly, the steady state power flow characters of multi-scenario transmission schemes are studied. The voltage distribution characters of HWTL are analyzed when its transmission power and power factor vary, and the influence of the DC power variation on voltage of HWTL is discussed. Then the transient characters of HWDHTS are explored. The DC commutation failure caused by the fault of HWTL is simulated and the power transfer capacity of HWTL while DC blocking is calculated in this paper. Keywords: UHV half-wavelength AC power transmission line, UHV DC system, Steady state characters, Transient stability.
1 Introduction The global energy interconnection is a strategic concept for the effective allocation of energy in the global context. One of the necessary premises for the realization of the energy Internet is the long distance, large capacity, low loss transmission technology. The transmission modes that can meet the demand of ultra-long distance and large capacity transmission are mainly separated into ultra-high voltage (UHV) AC/DC transmission technology and HWTL technology. The UHV AC/DC transmission technology has been applied in China. The HWTL technology refers to the electric power transmission of a distance approaching 1 power frequency half wave, namely 3000 km (50 Hz) ultraReceived: 20 November 2017/ Accepted: 12 December 2017/ Published: 25 August 2018 Qianyu Zhao [email protected]
Seyedamirabbas Mousavian [email protected]
Shouxiang Wang [email protected]
Lei Wu [email protected]
Xiaohui Qin [email protected] Open access under CC BY-NC-ND license. 366
long distance three-phase AC transmission technology [1-4]. Compared with the traditional AC transmission mode, HWTL has the advantages of ultra-long distance, large capacity transmission, and so on. It also does not need to install reactive power compensation devices and add intermediate switch stations [5-6]. There is no HWTL commercially operated in the world. But some researches of HWTL have been presented in [7-9]. The economics of several alternative solutions for point-to-point HWTL are evaluated in [7]. [8] introduces a shunt FACTS device for tapping and realizing power flow control in HWTL. Three HWTL corridors are studied in [9] for the interconnection of Belo Monte Power Plant, located in the state of Para, to the Brazilian interconnected system through Assis Substation, in the state of Sao Paulo, with a total distance of 2664 km. The references mentioned above considered neither the different situations of networks to networks, nor the steady state operation and transient characters of HWTL after the transmission of HWTL connected to the original DC asynchronous network system.
Qianyu Zhao et al. Simulation and analysis of UHV half wavelength and DC hybrid transmission system
In this paper, the steady state operating characters of different situations of networks to networks as well as the simulation and analysis of transient characters of HWTL are studied, after considering the original transmission network connected to the original DC asynchronous network. The rest of the paper is organized as follows. The Quasi-steady model of UHV half-wavelength is proposed in section 2 and steady state power flow characters of multi-scenario transmission scheme are analyzed in section 3. Transient characters of the hybrid system including simulation and analysis of DC commutation failure as well as simulation of power transfer capability of HWTL under DC blocking are discussed in section 4. Finally, conclusions are drawn in section 5.
2 Quasi-steady model of UHV half-wavelength Voltage and current equations at the xkM position from the receiving end of HWTL are obtained if the line has no loss and the voltage and current of the transmission line terminal are known as: U = U cos αx − jI Z sin αx x 2 2 c U2 I x = j Z sin αx − I 2 cos αx c •
(1)
•
where U 2 and I 2 are the terminal voltage and current of • HWTL, respectively. The direction of outflow of I 2 is positive. And α = ω L0 C0 , which is the line transmission constant. Z c = L0 C0 is line wave impedance. L0 and C0 are inductance and capacity value of unit length of the line, respectively. The uniform transmission line can be regarded as a twoport network, and it is assumed that the parameter matrix of the two-port transmission is T. The expression is as follows:
cos αx Z c sin αx T = sin αx cos αx Z c
(2)
According to the theory of two-port networks, the two-port network of the line can be transformed into the equivalent model and the equivalent impedance and admittance are as follows.
Z eq = jZ c sin αx (3) cos αx − 1 Yeq = jZ sin αx c The above π type equivalent model and parameters are
strictly equivalent in power frequency steady state and can be easily used in power flow calculation. If the transmission line is simulated approximately with series of multiple π type segments, the final HWTL can be equivalent to a cascade of two ports, namely, the equivalent T array of the HWTL, which is the n order casecade of the piecewise T matrix and then the equivalent parameters of the HWTL can be transformed. It is shown in the formula (1) that the terminal voltage of HWTL is proportional to the current of the receiving terminal, and the midpoint current is proportional to the magnitude of the receiving terminal voltage. When αx = π, that is the HWTL length, and the voltage at the end of the head and the end are the same, but the phase is opposite. Although the voltage at the two ends of lossless HWTL is not affected by transmission power, but the closer to the middle of the line, the voltage changes are more seriously affected by the power. The limiting transmission power of HWTL is shown in formula (4),
Pm =
U1U 2 Pn = Z c sin αx sin αx
(4)
U1 and U2 are the voltages at both ends of the circuit, and Pn is the natural power. The power limit of the line is the natural power when αx = π 2 and the theoretical limit value of HWTL can be infinite when αx = π(i.e. HW length).
3 S teady state power flow characters of multi-scenario transmission scheme 3.1 Classification of the hybrid system Multi-scenario scheme for connecting the original DC asynchronous network system to HWTL is established based on the quasi-steady state model of HWTL including single/double loop of single channel and multi-channel, which are all for network to network. Specific scenarios are shown in Fig. 1. This section studies the steady state operation characters of the above scenarios transmission schemes including voltage distribution characters of HWTL with different power supplies, and load power factors, and influences of DC transmitted power variations on voltages of HWTL.
3.2 Steady state operation characters of single loop or double loops of single channel The voltage distribution characters of single loop or double loops of single channel with varying power of HWTL are shown in Fig. 2. The figure shows the transmission power of double scenes is two times as much as that of single scene transmission, and the voltage 367
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distribution character of HWTL itself is similar to that of point to network, that is, the middle voltage of the line rises when the transmission power is greater than the natural power, and that of the line decreases when the transmission power is less than the natural power. The voltage distribution characters of single loop or double loops of single channel with varying power factor of HWTL are shown in Fig. 3. From the figure, the voltage is approximately sinusoidal when the capacitive reactive power load is connected to the end of HWTL (i.e. the power factor is negative), and the greater the power factor, the greater the voltage fluctuation along the line. The voltage is negative in the sine curve. The voltage along the line is negative sinusoidal when the inductive reactive
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power load is connected to the end of HWTL (i.e. the power factor is positive), and the greater the power factor, the greater the voltage fluctuation along the line. The voltage distribution characters of single loop or double loops of single channel with varying DC power are shown in Fig. 4. The figure shows the characteristic of voltage distribution of HWTL is similar to that of HWTL with varying power when the DC power varies. However, the half wave line voltage is highly coupled with the DC power, and the HWTL is affected by the DC power control. When the DC transmission power is reduced, the excess power will be transmitted through HWTL, which increases the power of HWTL, and affects the voltage distribution characters. Otherwise, the power of HWTL decreases and results in the reduction of the midpoint voltage when the DC transmission power increases. Therefore, the voltage of HWTL must be controlled within a certain range by controlling the change of DC transmission power.
3.3 Steady state operation characters of multichannel with different starting and landing points In multi-channel situation, that is, the starting points and landing points of two HWTLs are different.
Qianyu Zhao et al. Simulation and analysis of UHV half wavelength and DC hybrid transmission system
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Fig. 5 Voltage distribution characters of HWTL under different load power factor 369
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Fig. 6 Voltage distribution characters of HWTL under varying HWTL power
The voltage distribution characters of multi-channel with varying power of HWTL are shown in Fig. 5. From the diagram, the first terminal voltages of the two HWTLs are different. The range of the first terminal voltage of line 1 is 1060-1070 kV, and the voltage range of the first terminal of line 2 is 1110-1120 kV, which is slightly higher than that of line 1. The transmission powers of the two half wavelength lines are not the same when the load power changes. While the transmission power of the half wavelength line 1 is 4076.3 MW, the transmission power of the line 2 is 4170.5 MW; while the transmission power of the half wavelength line 1 is 5718.8 MW, the transmission power of the line 2 is 5583.3 MW. The voltage distribution characters of multi-channel with varying power factor of HWTL are shown in Fig. 6. From the figure, the voltage is roughly sinusoidal when the capacitive reactive power load is connected to the end of HWTL (i.e. the power factor is negative), and the greater the power factor, the greater the voltage fluctuation along the line. The voltage is negative in the sine curve. The voltage along the line is negative sinusoidal when the inductive reactive power load is connected to the end of HWTL (i.e. the power factor is positive), and the greater the power factor, the greater the voltage fluctuation along the line. 370
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The voltage distribution characters of multi-channel with varying DC power are shown in Fig. 7. The change rule is similar to single loop or double loops of single channel. From the diagram, the first terminal voltage of line 2 is higher than the first terminal voltage of line 1, the overall trend is higher than the line 1, and the first terminal voltages of the two lines are higher than the terminal voltages. The power of DC line increases from 5600 MW to 6800 MW, and the transmission power of half wavelength line decreases with the increase of DC power. When the DC line power is less than 5600 MW or higher than 6800 MW, the system does not converge. When the DC
Qianyu Zhao et al. Simulation and analysis of UHV half wavelength and DC hybrid transmission system
power is 5200 MW, the system can still converge while the power of the DC receiving end is reduced, while the power of the half wavelength line is not changed. The power of the half wavelength line changes in multichannel scenarios, and the farther the landing point is, the more serious the imbalance of power distribution is.
4 Transient characters of the hybrid system 4.1 Commutation failure caused by fault of HWTL The first and the second ends of HWTL have single phase short circuit fault in 0.2s and recover in 0.3s. Then the single line short circuit fault occurs in 0.3s and restores in 1.3s. Contrast charts between commutation failure and no commutation failure after fault of HWTLL are shown in Fig. 8-10. The failure of HWTL leads to commutation failure of the DC line, and it occurs in 1.32s. Recovering from commutation failure in 1.38s from Fig. 8, the power
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fluctuation time of DC line during commutation failure is longer than that without commutation failure. Meanwhile, midpoint voltage of HWTL fluctuates in a long time, at a relatively high value during the commutation failure. The commutation failure recovery period which is shown in Fig. 9, and in this period the bus voltage is low in converter station as shown in Fig. 10. Therefore, much reactive power is needed in the process of DC commutation failure and recovery. There are three reasons for the failure of commutation caused by the fault of HWTL. First, half-wavelength failure leads to a sudden drop of DC voltage and the inverter control system does not have enough time to function. Second, the DC transmission power is close to the rated power before the failure, which leaves a small margin for the extinction angle. Third, the fault occurs near the bus of the converter station. Although the halfwavelength and the DC lines are geographically far apart, the electrical distance between the two is relatively short.
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Fig. 9 Voltage variation of HWTL 371
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The original DC asynchronous network system is established, which is connected with the single channel single circuit HWTL based on the quasi-steady state model as shown in Fig. 11. The rated voltage of the ring network node is 500 kV, the HWTL is connected with the sending end bus through the 525/1050 kV step-up transformer, and the receiving end is connected with the bus through the 1050/525 kV step-down transformer. The rated powers of two DC lines are 6000 MW and 4000 MW, respectively. The PSD-BPA software is used to calculate the power flow and the 10-section model is adopted for the HWTL. 4.2.1 Unipolar blocking of the second DC line The DC line 2 has unipolar locking, with the locking DC power of 2000 MW. Half of the filter is removed, and the system remains stable. Fig. 12 shows that when
the DC line suffers unipolar blocking, the first power of HWTL from the original 4652.2 MW to the current 6380 MW, as HWTL bears the transfer of 1727.8 MW, and the midpoint voltage of HWTL increases from 1.0 p.u to 1.42 p.u.
4.2 Simulation and analysis of power transfer capability of HWTL under DC blocking
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Fig. 12 Transient operation characters of DC line 2 with unipolar blocking 372
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Qianyu Zhao et al. Simulation and analysis of UHV half wavelength and DC hybrid transmission system
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4.2.2 Unipolar blocking of the first DC line The DC line 1 has unipolar locking, with the locking DC power of 3000 MW. Half of the filter is removed, and the system remains stable. Fig. 13 shows that when the DC line suffers unipolar blocking, the first power of HWTL increases from the original 4652.2 MW to the current 7420 MW, and HWTL bears the transfer of 2767.8 MW, and the midpoint voltage of HWTL increases from 1.0 p.u to 1.68 p.u. But high voltages situation is not permitted in engineering practice, so the power of blocking can be transferred to other DC lines or HWTL, so that the voltage and power of the transmission line are controlled in the allowed range. 4.2.3 Bipolar blocking of the second DC line The DC line 2 has bipolar locking, with the locking DC power of 4000 MW and all of the filter is removed, and the system remains stable. It is shown that the system is in the state of critical stability due to the equal amplitude oscillation of the system. 4.2.4 Bipolar blocking of the first DC line The DC line 1 has bipolar locking, as the locking DC power is 6000 MW, and the system is unstable. Changing transmission power of the first DC line 1, then the corresponding DC blocking is carried out. The transmission power of the DC line 1 is reduced from 2*3000 MW to 2*2500 MW, that is to say, 1000 MW output power of the DC line to the end is removed, and 1000 MW of the load by the end of the DC line is removed. (1) The DC line 2 has unipolar locking, as the locking DC power is 2000 MW and the system remains stable. (2) The DC line 1 has unipolar locking, as the locking DC power is 2500 MW and the system remains stable. (3) The DC line 1 and 2 are simultaneously locked at the same time, and each half of the filter is removed. The total
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locked DC power is 4500 MW, and the system is in constant amplitude oscillation. So it is incritical stable state. (4) The DC line 2 has bipolar locking, the locking DC power is 4000 MW and the system is in the critical stable state. (5) The DC line 1 has bipolar locking, as the locking DC power is 5000 MW and the system is unstable. Changing transmission power of the first DC line 1, then the corresponding DC blocking is carried out. The transmission power of the DC line 1 is reduced from 2×3000 MW to 2×1500 MW, that is to say, 3000 MW output power of the DC line to the end is removed, and 3000 MW of the load by the end of the DC line is removed. (1) The DC line 2 has unipolar locking, as the locking DC power is 2000 MW and the system remains stable. (2) The DC line 1 has unipolar locking, as the locking DC power is 1500 MW and the system remains stable. (3) The DC line 1 and 2 are simultaneously locked at the same time, and each half of the filter is removed. The total locked DC power is 3500 MW, and the system is 373
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stable. Fig. 15 shows that when the DC line suffers unipolar blocking, the first power of HWTL decreases from the original 4652.2 MW to the current 8000 MW, and HWTL bears the transfer of 3347.8 MW. The midpoint voltage of HWTL increases from 1.0 p.u to 1.81 p.u. In summary, the transfer power that HWTL can withstand is 0-3347.8 MW. The system is stable when the power cut off by DC line is less than 3500 MW and the system transits from the critical stability to instability when the power at above 4000 MW. The first end of HWLL
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5 Conclusions (1) The steady state power flow characters of the single channel single/double loop network are similar to the characters of the voltage distribution of HWTL. However, the voltage state of HWTL is highly coupled with the DC power. Half wavelength line state is affected by DC power control. (2) The power of HWTL changes in multi-channel scenarios, and the longer the landing point distance is, the more serious the imbalance of power distribution is. 374
Acknowledgements This work was supported by the State Grid Science and Technology Project (XTB17201600100-01).
References
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(3) In the multi-DC parallel situations built in this paper, the transfer power that HWTL can withstand is 0-3347.8 MW. The system is stable when the power cut off by DC line is less than 3500 MW and the system transits from the critical stability to instability when the power is above 4000 MW.
[1] Prabhakara FS, Parthasarathy K, Ramachandra HN (1969) Analysis of natural half-wave-length power transmission lines. IEEE Transactions on Power Apparatus and Systems, 88(12): 1787-1794 [2] Prabhakara FS, Parthasarathy K, Ramachandra HN (1969) Performance of tuned half-wave-length power transmission lines. IEEE Transactions on Power Apparatus and Systems, 88(12): 1795-1800 [3] Iliceto F, Cinieri E (1988) Analysis of half-wave length transmission lines with simulation of corona losses. IEEE Transactions on Power Delivery, 3(4): 2081-2091 [4] Gatta FM, Iliceto F (1992) Analysis of some operation problems of half-wave length power transmission lines. In: AFRICON '92 Proceedings, 3rd AFRICON Conference: 59-64 [5] Hubert FJ, Gent MR (1965) Half-wavelength power transmission lines. IEEE Spectrum: 87-92 [6] Maria C. Tavares, Carlos M. Portela (2008) Half-wave length line energization case test-proposition of a real test. In: 2008 International Conference on High Voltage Engineering and Application, Chongqing, China: 261-264 [7] Milana Lima dos Santos, José Antonio Jardini, Ronaldo Pedro Casolari et al (2014) Power transmission over long distances: economic comparison between HVDC and half-wavelength line. IEEE Transactions on Power Delivery, 29(2): 502-209 [8] Aredes M, Robson F. S. Dias (2011) A shunt FACTS device for tapping and power flow control in half-wavelength transmission lines. In: 2011 Asia-Pacific Power and Energy Engineering Conference: 1-6 [9] Leandro C. Ferreira Gomes, Luiz C. P. da Silva, Maria C. Tavares (2014) Half-wavelength transmission lines for connecting power plants in Amazon Region to the Brazilian system. In: 2014 Eighth International Conference on Innovative Mobile and Internet Services in Ubiquitous Computing: 415-420 [10] Zhao Q, Wang S, Qin X, et al (2017) Voltage and reactive power control of ultra-high voltage half-wavelength and DC hybrid system based on steady state charcteristics. Automation of Electric Power Systems, 41(22) [11] Liu Y, Tian H, Liu Z et al (2018) Aspects of ultra-high voltage half-wavelenght power transmission technology. Global Energy Interconnection, 1(1): 96-102
Qianyu Zhao et al. Simulation and analysis of UHV half wavelength and DC hybrid transmission system
Biographies Qianyu Zhao received her bachelor in Electrical Engineering from Tianjin Polytechnic University in 2012 and master degrees in Control Science and Engineering from Tianjin Polytechnic University in 2015. She is currently working on her Ph.D. degree at Electrical Engineering in Tianjin University. Her research interest is power system stability. Shouxiang Wang received his bachelor and master degrees in Electrical Engineering from Shandong University of Technology, in 1995 and 1998 respectively. He received his Ph.D. degree in Electrical Engineering from Tianjin University in 2001. His research interests include distributed generation, micro grid and smart distribution system.
Seyedamirabbas Mousavian received his Ph.D. degree in Industrial and Systems Engineering from Auburn University. He is currently working as an assistant professor. his research interests include smart grid, cyberphysical systems security, cyber-physical systems investment, power systems operations and planning, electric vehicles, and operations research. Lei Wu, associate professor, his research interests include power systems operation and planning, energy economics, and community resilience micro grid. (Editor Chenyang Liu)
Xiaohui Qin received his Ph.D. degree in North China Electric Power University in 2008. His research interests include power system planning and simulation, advanced applications of WAMS.
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