Recommended articles：

Global Energy Interconnection
Volume 1, Issue 3, Aug 2018, Pages 366375
Simulation and analysis of UHV half wavelength and DC hybrid transmission system
Keywords
Abstract
The scenarios of a half wavelength transmission line (HWTL) connected to the original DC asynchronous interconnection system are established based on the quasisteady state model of HWTL, which include single or double loops of single channel and multichannel scenarios with different starting and landing points. Firstly, the steady state power flow characters of multiscenario 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.
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 ultralong distance and large capacity transmission are mainly separated into ultrahigh 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) ultralong distance threephase AC transmission technology [14].Compared with the traditional AC transmission mode,HWTL has the advantages of ultralong distance, large capacity transmission, and so on. It also does not need to install reactive power compensation devices and add intermediate switch stations [56].
There is no HWTL commercially operated in the world.But some researches of HWTL have been presented in[79]. The economics of several alternative solutions for pointtopoint 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.
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 Quasisteady model of UHV halfwavelength is proposed in section 2 and steady state power flow characters of multiscenario 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 Quasisteady model of UHV halfwavelength
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:
The uniform transmission line can be regarded as a twoport network, and it is assumed that the parameter matrix of the twoport transmission is T. The expression is as follows:
According to the theory of twoport networks, the twoport network of the line can be transformed into the equivalent model and the equivalent impedance and admittance are as follows.
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 πtype 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=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),
3 Steady state power flow characters of multiscenario transmission scheme
3.1 Classification of the hybrid system
Multiscenario scheme for connecting the original DC asynchronous network system to HWTL is established based on the quasisteady state model of HWTL including single/double loop of single channel and multichannel,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 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.
Fig.1 Different scenarios of the hybrid system
Fig.2 Voltage distribution characters of HWTL under varying HWTL 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 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 multichannel situation, that is, the starting points and landing points of two HWTLs are different.
Fig.3 Voltage distribution characters of HWTL under different load power factor
Fig.4 Voltage distribution characters of HWTL under varying DC power
Fig.5 Voltage distribution characters of HWTL under different load power factor
Fig.6 Voltage distribution characters of HWTL under varying HWTL power
The voltage distribution characters of multichannel 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 10601070 kV, and the voltage range of the first terminal of line 2 is 11101120 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 multichannel 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.
Fig.7 Voltage distribution characters of HWTL under varying DC power
The voltage distribution characters of multichannel 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 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.
Fig.8 DC line power variation
Contrast charts between commutation failure and no commutation failure after fault of HWTLL are shown in Fig.810. 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 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, halfwavelength 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.
Fig.9 Voltage variation of HWTL
Fig.10 Bus voltage in converter station
4.2 Simulation and analysis of power transfer capability of HWTL under DC blocking
The original DC asynchronous network system is established, which is connected with the single channel single circuit HWTL based on the quasisteady 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 stepup transformer, and the receiving end is connected with the bus through the 1050/525 kV stepdown transformer. The rated powers of two DC lines are 6000 MW and 4000 MW, respectively.The PSDBPA software is used to calculate the power flow and the 10section 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.
Fig.11 HWTL and multi DC parallel scenes
Fig.12 Transient operation characters of DC line 2 with unipolar blocking
Fig.13 Transient operation characters of DC line 1 with unipolar blocking
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 locked DC power is 4500 MW, and the system is in constant amplitude oscillation. So it is incritical stable state.
Fig.14 Midpoint voltage of HWTL
(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 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 03347.8 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.
Fig.15 Transient operation characters of DC line 1 and 2 with unipolar blocking
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 multichannel scenarios, and the longer the landing point distance is, the more serious the imbalance of power distribution is.
(3) In the multiDC parallel situations built in this paper, the transfer power that HWTL can withstand is 03347.8 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.
Acknowledgements
This work was supported by the State Grid Science and Technology Project (XTB1720160010001).
References

[1]
Prabhakara FS, Parthasarathy K, Ramachandra HN (1969)Analysis of natural halfwavelength power transmission lines.IEEE Transactions on Power Apparatus and Systems, 88(12):17871794 [百度学术]

[2]
Prabhakara FS, Parthasarathy K, Ramachandra HN (1969)Performance of tuned halfwavelength power transmission lines. IEEE Transactions on Power Apparatus and Systems,88(12): 17951800 [百度学术]

[3]
Iliceto F, Cinieri E (1988) Analysis of halfwave length transmission lines with simulation of corona losses. IEEE Transactions on Power Delivery, 3(4): 20812091 [百度学术]

[4]
Gatta FM, Iliceto F (1992) Analysis of some operation problems of halfwave length power transmission lines. In: AFRICON '92 Proceedings, 3rd AFRICON Conference: 5964 [百度学术]

[5]
Hubert FJ, Gent MR (1965) Halfwavelength power transmission lines. IEEE Spectrum: 8792 [百度学术]

[6]
Maria C. Tavares, Carlos M. Portela (2008) Halfwave length line energization case testproposition of a real test. In: 2008 International Conference on High Voltage Engineering and Application, Chongqing, China: 261264 [百度学术]

[7]
Milana Lima dos Santos, José Antonio Jardini, Ronaldo Pedro Casolari et al (2014) Power transmission over long distances:economic comparison between HVDC and halfwavelength line.IEEE Transactions on Power Delivery, 29(2): 502209 [百度学术]

[8]
Aredes M, Robson F. S. Dias (2011) A shunt FACTS device for tapping and power flow control in halfwavelength transmission lines. In: 2011 AsiaPacific Power and Energy Engineering Conference: 16 [百度学术]

[9]
Leandro C. Ferreira Gomes, Luiz C. P. da Silva, Maria C. Tavares (2014) Halfwavelength 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: 415420 [百度学术]

[10]
Zhao Q, Wang S, Qin X, et al (2017) Voltage and reactive power control of ultrahigh voltage halfwavelength and DC hybrid system based on steady state charcteristics. Automation of Electric Power Systems, 41(22) [百度学术]

[11]
Liu Y, Tian H, Liu Z et al (2018) Aspects of ultrahigh voltage halfwavelenght power transmission technology. Global Energy Interconnection, 1(1): 96102 [百度学术]
Fund Information
supported by the State Grid Science and Technology Project (XTB1720160010001)；
supported by the State Grid Science and Technology Project (XTB1720160010001)；