Penetrating power characteristics of half-wavelength AC transmission in point-to-grid system
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Abstract
With the concept of global energy interconnection being proposed, half-wavelength alternating current transmission (HWACT) technology becomes of more interest. HWACT lines can be adopted to establish a point-to-grid system, in which the penetrating power (PP) is produced between receiving terminals, having a significant effect on the power flow distribution. In order to investigate this phenomenon, the PP characteristics of the HWACT system are researched in this paper. First, the mathematical relationship between the transmission power and terminal bus voltages of a single HWACT line is derived using the equations of a distributed parameter model. The research indicates that the relationship between power and terminal voltages shows “reverse characteristics” opposite to those of regular short transmission lines. Then, the concept and definition of PP in a point-to-grid system with two receiving terminals are proposed, and the corresponding relationship between PP and the terminal bus voltages is derived. Simulations are carried out to validate the theory under different conditions, so that the accuracy and adaptiveness of the theoretical analysis can be proved. In addition, the results demonstrate that selecting the location for a HWACT system has demanding requirements in order to control the value of PP.
Keywords
Half-wavelength alternating current transmission (HWACT) Ultra-high voltage Synchronous power grids Penetrating power (PP)1 Introduction
Half-wavelength alternating current transmission (HWACT) refers to a kind of AC transmission technology whose transmission distance is equal to a half of the wavelength under the fundamental frequency [1]. With the concept of global energy interconnection being proposed, HWACT technology becomes of more interest. In 2015, the State Grid Corporation of China (SGCC) launched a series of research projects on HWACT technology in order to seek alternatives for long-distance power transmission besides high voltage direct current (HVDC) transmission.
The equivalent reactance of a HWACT line is theoretically equal to zero. This can largely reduce the electrical distance between both ends of the line [2, 3]. Because of this, HWACT is suitable for long-distance and high-capacity transmission [4, 5, 6, 7, 8]. For the traditional line, the resistance is far less than the reactance. Thus, the active power is strongly correlated with the phase angle of the node voltage whereas the reactive power is strongly related to the amplitude of the node voltage [9, 10, 11, 12, 13, 14]. As the length of the line reaches the half-wavelength, the power-voltage characteristic becomes different. Under the assumption that the line is lossless, the voltage amplitudes of both ends are equal and the phase angle difference is 180 degrees for the HWACT line [1, 2, 3, 15]. This indicates that the terminal voltages are not related to the transmission power. However, further investigation is required to verify the correctness of this conclusion. The power-voltage characteristics also determine the overvoltage on the HWACT line. These could be serious when the transmission power is high [3, 16]. If the power factor is equal to 1, the overvoltage at the midpoint of the line is roughly equal to the ratio of the active power to the natural power [1, 2, 3, 17, 18].
HWACT technology can also be used to enhance synchronous power grids. Reference [19] proposes the concept of building stereoscopic power grids using multiple HWACT lines. The HWACT lines share a common sending end and connect to different terminals in one power grid. The single point-double terminals (SPDT) system has been built in [19] and it is supposed to be the most typical system reflecting the networking capability of HWACT. The simulations demonstrate that the stability of the power grid can be enhanced effectively because the HWACT lines shorten the electrical distances between the terminals, changing the grids into a stereoscopic structure from a plane structure. Since it is a relatively new field, there are no more relevant references except [19]. Thus, some new features of the SPDT system are not yet completely clear. The power flow distribution on the HWACT lines is one of the key issues which need further study. The situation of the power flow distribution is quite complex in the SPDT system compared with that of a single line. Thus, it is necessary to study the power flow distribution characteristics of the SPDT system in depth.
Aiming at the above-mentioned problems, this paper derives and validates the power-voltage characteristics as well as the power distribution of the HWACT system. According to the equations of the distributed parameter model, the power-voltage characteristics of a single HWACT line are derived. The “reverse characteristics” of the HWACT line are found, opposite to those of regular short transmission lines. Then, the concept and definition of the penetrating power (PP) in a SPDT system is proposed. The corresponding relationship among PP, the terminal bus voltages and the supplied power can be obtained based on the principles and characteristics of PP. The research indicates that the relationship between PP and terminal voltages also shows “reverse characteristics”. The simulations are carried out to validate the theoretical analysis under different conditions. The results indicate that demanding requirements should be made for the precision control of a HWACT system.
2 Power-voltage characteristics of a single HWACT line
Since the resistance is much smaller than the reactance per unit length, the imaginary part of the wave impedance Z_{ s } is very small. Thus, if the value of U_{2} is determined, the real part of \(\dot {U}_{1}\) is related to the active power whereas the imaginary part is related to the reactive power.
Since the coefficients of P, Q are small, the real part of (9) is much larger than the imaginary part when P, Q are in a normal range. Thus, the amplitude of \(\dot {U}_{1}\) has a higher correlation with the active power whereas the phase angle is more related to the reactive power. This feature shows “reverse characteristics” which is opposite to those of regular short transmission lines. Based on the previous derivation, it can be inferred that Z_{ s }sinh(γl) is the equivalent series impedance of π circuit of the line. If βl = π, the equivalent reactance of Z_{ s }sinh(γl) is equal to zero in theory, so the coefficients of P and Q only reflect the effect of the equivalent resistance.
As shown in Figs. 2 and 3, if P remains unchanged and Q ranges from − 50 to 50 p.u. (− 5000-5000 Mvar), the value of U_{1} ranges from 1.0012 to 1.0026 p.u., and the maximum variation of the voltage amplitude is about 0.0014 p.u. In this case, the value of angle changes from 177° to 183°, and the maximum variation of the phase angle is about 6°. According to the same figures, if Q remains unchanged and P changes in the same interval, the maximum variation of the voltage amplitude is approximately 0.1 p.u. (from 0.95 to 1.05 p.u.), while the phase angle remains 180°. The results verify the previous discussion to some extent. However, it also indicates that the inference from the hypothesis of the lossless line (the voltage amplitude of each terminal is equal and the phase angle difference is 180°) is not strictly correct. As for the HWACT line, the resistance cannot be ignored in some circumstances because it has impact on “reverse characteristics” opposite to those of regular short transmission lines.
3 Power-voltage characteristics of SPDT system
This shows that the active component of PP is only linearly related to the square error of voltage amplitude between the terminal points if there is no power being sent. On the other hand, the reactive component of PP is determined by both the voltage amplitude and the phase difference.
The above analysis indicates that the PP between the terminal points can be controlled by adjusting the voltage amplitude and phase angle of each terminal. In addition, the active and reactive power can be decoupled. Ideally, the value of PP should be controlled at zero to guarantee the maximum transmission power. The active PP can be controlled by arranging the amount of reactive power compensation at the terminal point properly. This contributes to adjusting the voltage amplitude. As for the reactive PP, the phase angle can be controlled by adjusting the unit operation mode at the adjacent areas of terminal points.
4 Simulation verification
In order to verify the theoretical analysis of the characteristics of a single HWACT line and SPDT system, PSD-BPA [20] is used to simulate the load flow distribution in a power grid. The HWACT line is modeled by 20 π sections connecting with each other [18]. The line length is set as 2938.3 km.
4.1 Simulation of single HWACT line
Comparison of theory and simulation results for single HWACT line
P (p.u.) | Q (p.u.) | Theory result | Simulation result | ||
---|---|---|---|---|---|
U_{1} (p.u.) | φ_{1} (°) | U_{1} (p.u.) | φ_{1} (°) | ||
− 50 | 0 | 1.0545 | 180.00 | 1.0567 | 179.92 |
− 45 | 0 | 1.0492 | 180.00 | 1.0512 | 179.92 |
− 40 | 0 | 1.0439 | 180.00 | 1.0456 | 179.93 |
− 35 | 0 | 1.0385 | 180.00 | 1.0401 | 179.94 |
− 30 | 0 | 1.0332 | 180.00 | 1.0345 | 179.95 |
− 40 | − 10 | 1.0439 | 179.41 | 1.0454 | 179.32 |
− 40 | − 5 | 1.0439 | 179.71 | 1.0455 | 179.63 |
− 40 | 5 | 1.0439 | 180.29 | 1.0458 | 180.24 |
− 40 | 10 | 1.0439 | 180.59 | 1.0460 | 180.54 |
According to Table 1, if the reactive power remains unchanged and the active power is adjusted step-by-step, the terminal voltage mainly displays amplitude variation. However, if the reactive power is adjusted with the invariability of active power, the terminal voltage is changed mainly in phase angle. The amplitude errors between the theoretical and simulation results are in the 10^{-3} order of magnitude, and the phase angle errors are in the 10^{-2} order of magnitude. It can be seen that the theoretical and simulation results have high similarity. Thus, the correctness of the theory can be verified.
4.2 SPTD system
Comparison of theory and simulation results for SPTD system
U_{2} (p.u.) | U_{1} (p.u.) | φ_{12} (°) | Theory result | Simulation result | ||
---|---|---|---|---|---|---|
P_{ cr } (p.u.) | Q_{ cr } (p.u.) | P_{ cr } (p.u.) | Q_{ cr } (p.u.) | |||
1.0124 | 0.9960 | − 3.216 | 7.70 | − 26.46 | 8.49 | − 26.37 |
1.0129 | 1.0023 | − 3.382 | 5.00 | − 28.02 | 5.82 | − 28.00 |
1.0086 | 1.0052 | − 3.626 | 1.60 | − 29.99 | 2.42 | − 30.09 |
1.0058 | 1.0064 | − 3.761 | − 0.24 | − 31.06 | 0.66 | − 31.22 |
1.0032 | 1.0074 | − 3.896 | − 1.98 | − 32.12 | − 1.06 | − 32.33 |
1.0107 | 0.9993 | − 2.789 | 5.34 | − 22.99 | 6.02 | − 22.94 |
1.0078 | 1.0045 | − 2.084 | 1.54 | − 17.22 | 2.04 | − 17.24 |
1.0059 | 1.0076 | − 1.603 | − 0.80 | − 13.26 | − 0.42 | − 13.33 |
1.0030 | 1.0134 | − 0.777 | − 4.91 | − 6.45 | − 4.72 | − 6.61 |
As can be seen in Table 2, the PP will change over a wide range if the value of the terminal voltages is adjusted. The simulation results have shown satisfactory agreement with theory. The maximum errors of the active and reactive PP are 0.92 p.u. (92 MW), 0.21 p.u. (21 Mvar), respectively.
According to Figs. 9 and 10, the PP shows great variation with the voltage amplitude and the phase angle at terminals. That is, a little voltage difference can lead to a large PP. It can be seen that the active power is more correlated with the amplitude of the bus voltage whereas the reactive power is more related to the phase angle.
5 Conclusion
In this paper, the “reverse characteristics” of the HWACT line and the concept of PP have been proposed.
1) The HWACT line shows “reverse characteristics” opposite to those of regular short transmission lines. The active power is more correlated with the amplitude of the bus voltage whereas the reactive power is more related to the phase angle. From this perspective, HWACT is similar to DC transmission. Thus, the resistance should not be ignored in the calculation and analysis of the HWACT line.
2) The power flow distribution of the SPTD system is analyzed. This helps reveal the characteristics of the PP on the HWACT line. PP is much more related to terminal voltages than the supplied power. The active PP is linearly related to the square error of amplitudes of the terminal voltages whereas the reactive PP is highly determined by the phase angle difference of the terminal voltages. Little difference of the voltage amplitude and phase angle will lead to a large PP. Thus we can infer that different control methods should be adopted in the HWACT system. In addition, the accuracy and reliability of the control is demanding, and the terminal locations of the HWACT lines need to be selected carefully.
3) This paper provides a preliminary study on the related problems of the HWACT system. This should be helpful for the application of HWACT technology. In future work, control methods for the HWACT system as well as the characteristics of the mixed HWACT system (such as the grid-to-grid system in which two independent power grids are connected by several HWACT lines) will be further researched.
Notes
Acknowledgements
This work was supported by National Natural Science Foundation of China (No. 51307109) and State Grid Corporation of China (No. XT71-16-001). The authors would also thank for the technique support of China Electric Power Research Institute.
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