Transient reactive power characteristics of HVDC during commutation failure and impact of HVDC control parameters

The 6th International Conference on Renewable Power Generation (RPG) 19 20 October 2017 Transient reactive power characteristics of HVDC during commutation failure and impact of HVDC control parameters Jingzhe Tu 1, Yan Pan 2, Jian Zhang 1, Bing Zeng 1, Junchuan Jia 1, Jun Yi 1 1 China Electric Power Research Institute, Beijing, People s Republic of China 2 C-EPRI Electric Power Engineering Co. Ltd, Beijing, People s Republic of China E-mail: tujingzhe@epri.sgcc.com.cn Published in The Journal of Engineering; Received on 9th October 2017; Accepted on 1st November 2017 Abstract: HVDC commutation failure and recovery, the reactive power exchanged between HVDC and AC systems will change largely, showing the external characteristic of large capacity reactive impact load, so it is quite necessary to carry out studies on this problem. In this study, first, the HVDC sending-side and receiving-side reactive power equations in steady state and transient process are given. Second, the HVDC sending-side and receiving-side reactive power characteristics during commutation failure and recovery are analysed. Finally, the impact of the HVDC control system parameters is studied. All the contents are verified by simulation of the HVDC equivalent case system. 1 Introduction As the HVDC transmission projects are being continually commissioned, the strong DC and weak AC characteristic of the power system is becoming gradually apparent. HVDC has an advantage in large capacity and long distance, but will also bring security and stability problems. The converters on the sending side and receiving side both consume a large amount of reactive power in operation, usually, the reactive power consumed by the rectifier and inverter is 30 50 and 40 60% of the active power, respectively [1 3]. Commutation failure is one of the most common contingencies in HVDC [4 6], which has a great impact on the stability of the sending-side and receiving-side AC systems [7 10]. During HVDC commutation failure and recovery, the reactive power consumed by converters and supplied by AC filters has a transient process. So the reactive power exchanged between HVDC and the sending-side/ receiving-side AC system will change largely, showing the external characteristic of large capacity reactive impact load which is harmful to the system. So far, there have been several papers studying the HVDC reactive power characteristic and its impact on system, mainly in two aspects: (i) HVDC reactive power characteristic in steady state and under small disturbances Zheng et al. [11, 12] analyse the dynamic reactive power trajectory characteristic of the rectifier and inverter, respectively. Xin et al. [13] propose an index of the multi-infeed HVDC generalised short-circuit ratio, which can precisely measure the supporting of the receiving-side AC system to the HVDCs. (ii) Impact of HVDC control on reactive power characteristic the authors of [14, 15] study the impact of a control mode of the rectifier and inverter on commutation failure, respectively. On the base of that Yang et al. [16] furtherly studies the overshoot problem during HVDC commutation failure. It can be seen that most studies are mainly concerned about local problems using simulation, but lacking integrated studies on HVDC transient reactive power characteristic during commutation failure and recovery. Therefore, it is quite necessary to carry out studies on this problem. In this paper, first, the differential-algebraic equations describing the HVDC sending-side and receiving-side reactive power characteristics in steady state and transient process are given. Second, the HVDC reactive power characteristic of the sending side and receiving side during commutation failures and recovery is analysed. Finally, on the base of those, the impact of the HVDC control system parameters on transient reactive power characteristic is studied. All the contents are verified by simulation of the HVDC equivalent case system. 2 HVDC reactive power equations in steady state and transient process 2.1 Steady state According to the HVDC quasi-steady state model [1, 2], the reactive power exchanged between HVDC and AC system (positive if absorbing reactive power from AC system, negative if sending reactive power to AC system) is shown as U r0 = 3 2 Nr T p r U r, U i0 = 3 2 Ni T p i U i (1) U dr = U r0 cos a 3 p N r X cr I d, U di = U i0 cos g 3 p N i X ci I d (2) U dr U di = R d I d (3) ( w r = arccos U ) ( dr, w U i = arccos U ) di r0 U i0 (4) P r = 2U dr I d, P i = 2U di I d (5) Q r = P r tan w r U 2 r B r, Q i = P i tan w i U 2 i B i (6) where U r0, U i0 denote the DC open-circuit voltage (subscript r, i denote the rectifier side and inverter side, the same hereinafter), N r, N i denote the number of 6-pulse converters (normally EHVDC with 2, UHVDC with 4), T r, T i denote the tap ratio of converter transformers, U r, U i denote the converter bus AC voltage, U dr, U di denote the DC voltage, a denotes the rectifier ignition angle, g denotes the inverter extinction angle, X cr, X ci denote the commutation reactance, I d denotes the DC current, R d denotes the

DC line resistance, w r, w i denote the power factor angle, P r, P i denote the DC active power, B r, B i denote the AC filter susceptance, Q r, Q i denote the reactive power exchanged between HVDC and AC system. Therefore, the reactive power exchanged between HVDC and AC system in steady state can be calculated by solving the algebraic equations shown in (1) (6), easy for a theoretical calculation. 2.2 Transient process Contingencies of HVDC itself or the sending-side/receiving-side AC system, will both make HVDC enter into a transient process [3]. In HVDC transient process, the main variables are the rectifier ignition angle a, the inverter ignition angle b (the extinction angle g), and the DC current I d. In which, a, b (g) are decided by the differential-algebraic equations of HVDC control system, I d is decided by differential equations of HVDC transmission line. 2.2.1 HVDC control system: The HVDC control system used in practical HVDC projects in China can be divided into ABB technology and Siemens technology, the main differences lie in the inverter-side control mode, but the HVDC transient regulation characteristics of the two are similar during commutation failure [15]. In this paper, ABB technology is taken as an example, the main structure of an ABB HVDC control system can be seen in Fig. 1. The ABB HVDC control system mainly includes three levels: the main control, the pole control, and the ignition control. The pole control mainly includes the DC current controller, the DC voltage controller, and the extinction angle controller. These three fundamental controllers all have independent proportional integral (PI) regulators, and the coordination method of magnitude limit, in turn, is applied. In the transient process after contingencies, according to the set logic, the HVDC control system will rapidly output the rectifier and inverter ignition angle a, b, g [17]. Because the HVDC control system is very complicated, in order to simplify analysis and illustration, the differential-algebraic equations describing the transient process of the HVDC control system are shown as dx r dt = f r (x r, U r, I d, a), dx i dt = f i (x i, U i, I d, g) (7) 0 = g r (x r, U r, I d, a), 0 = g i (x i, U i, I d, g) (8) where f r ( ) f i ( ) denote the state equation of rectifier and inverter HVDC control, g r ( ), g i ( ) denote the corresponding output equation, x r, x i denote the state variables of HVDC control system. It should be noted that the ABB inverter extinction angle control (AMAX) is a predictive open-loop control, so its Fig. 1 Main structure of ABB HVDC control system differential-algebraic equation will degenerate to the algebraic equation: 0 = g i (x i, U i, I d, g). 2.2.2 HVDC transmission line: The differential equation of HVDC transmission line is shown as U dr U di = (L r + L i + L d ) di d dt + R d I d (9) where L r L i denote the reactance of smooth reactor, L d denotes the reactance of HVDC transmission line. In the transient calculation, (3) should be replaced by (9). Therefore, in the transient process, the reactive power exchanged between HVDC and AC system can be calculated by solving the differential-algebraic equations shown in (1) (9). Normally, the numerical integration method with the help of power system simulation software is needed. 3 HVDC receiving-side transient reactive power characteristic during commutation failure and recovery 3.1 HVDC receiving-side transient reactive power characteristic during commutation failure Under different short-circuit fault locations resulting in HVDC commutation failure, the reactive power absorbed by HVDC from the receiving-side AC system changes greatly, which can be divided into the following two conditions. 3.1.1 Fault near to the inverter: The short-circuit fault near to the inverter will result in HVDC commutation failure, the inverter bus AC voltage will drop to a low level (will drop to 0 after a fault on the inverter bus). The commutation failure prediction (CFPREV) will operate to decrease the inverter ignition angle, making the inverter DC voltage drop to nearly 0 (U i0 0 in (2)). Although the DC current will have a transient process of rapid increase (U di 0 in (9)), the reactive power consumed by the inverter during commutation failure is nearly 0 (P i tan w i 0 in (6)). The inverter bus AC voltage is very low during commutation failure, making the reactive power supplied by AC filters is nearly 0 (Ui 2 B i 0 in (6)). Therefore, during commutation failure, HVDC will absorb nearly 0 reactive power from the receiving-side AC system (the reactive power consumed by the inverter minus the reactive power supplied by AC filters) under nearby fault. 3.1.2 Fault distant from the inverter: The short-circuit fault distant from the inverter can also result in commutation failure, the inverter bus AC voltage will still remain at a high level (with enough voltage drop to cause commutation failure). CEPREV will operate to decrease the inverter ignition angle, and the inverter DC voltage can still remain above 0 (U i0. 0 in (2)). So the rapid increase of DC current during commutation failure (U di. 0 in (9)), will make the inverter consume a large amount of reactive power (P i tan w i very large in (6)). Although the inverter bus AC voltage can still remain during commutation failure, the reactive power supplied by AC filters is still much smaller than the reactive power consumed by the inverter (Ui 2 B i a little bit small in (6)). Therefore, during commutation failure, HVDC will absorb a large amount of reactive power from the receiving-side AC system under remote fault. 3.2 HVDC receiving-side transient reactive power characteristic during recovery Under different strength conditions of the receiving-side AC system, the relative recovery speed of the AC voltage and the DC power is different, the HVDC receiving-side transient reactive power characteristic varies, which can be divided into the following two conditions.

3.2.1 Strong receiving-side AC system: If the receiving-side AC system infeed by HVDC is strong (the effective short-circuit ratio ESCR. 3), the recovery speed of the AC voltage is normally faster than that of the DC power (measured by the time from fault cleared to AC voltage/dc power recovered to 90% of the prefault steady-state value). After fault cleared, the AC voltage will rapidly recover to the steady-state value. Because the voltagedependent current order limit (VDCOL) restricting current increase has a time delay, the DC power recovery has some time lag. After fault cleared and before DC power recovered, the reactive power supplied by AC filters is much larger than the reactive power consumed by the inverter (P i, steady state value and U i steady state value in (6)), HVDC will send a large amount of reactive power to the receiving-side AC system. After HVDC recovered to the rated power, because of the overshoot effect of the PI controller [16], the DC power will continually increase exceeding the rated value and then decrease. During the short period after HVDC recovered, the reactive power consumed by the inverter will be larger than the reactive power supplied by AC filters (P i. steady state value and U i steady state value in (6)), HVDC will absorb some reactive power from the receiving-side AC system. Therefore, during commutation failure recovery, HVDC will firstly send a large amount of reactive power to the receiving-side AC system and then absorb some reactive power from the receiving-side AC system under strong system conditions. 3.2.2 Weak receiving-side AC system: If the receiving-side AC system infeed by HVDC is weak (ESCR, 3), the recovery speed of the AC voltage may be slower than that of the DC power. The receiving-side AC system lacks dynamic reactive power support because of small short-circuit capacity, the AC voltage recovery after fault cleared is slow, making the reactive power supplied by AC filters is small. If HVDC has already got rid of the restriction of VDCOL making the DC power recover normally at that time, the reactive power consumed by the inverter may be always larger than the reactive power supplied by AC filters (P i steady state value and U i, steady state value in (6)). Therefore, during commutation failure recovery, HVDC may continually absorb some reactive power from the receiving-side AC system under weak system conditions. 3.3 Case system analysis 3.3.1 Comparison of electromagnetic simulation and electromechanical simulation: Simulations are performed on the detailed electromagnetic model and the simplified electromechanical model [17] of a practical UHVDC applying the electromagnetic program PSCAD and the electromechanical program PSD-BPA, respectively (fault clearance time is 0.1 s). During HVDC commutation failure and recovery, the electromagnetic and electromechanical caparison curves of the reactive power exchanged between HVDC and the receiving-side AC system (positive if absorbing reactive power from AC system, negative if sending reactive power to AC system) are shown in Figs. 2 and 3. It can be seen from Figs. 2 and 3, the simulation results of the simplified electromechanical model are almost the same as the detailed electromagnetic model, which can precisely reflect the HVDC receiving-side transient reactive power characteristic during commutation failure and recovery. Therefore, the electromechanical program of PSD-BPA is used as the simulation tool in the following case system analysis. 3.3.2 HVDC receiving-side transient reactive power characteristic simulation (nearby fault): Simulation analysis is performed on the HVDC equivalent case system (ideal power source with series impedance) applying PSD-BPA. During HVDC commutation failure Fig. 2 Comparison curves of the reactive power exchanged with the receiving-side AC system (nearby fault) Fig. 3 Comparison curves of the reactive power exchanged with the receiving-side AC system (remote fault) resulted by inverter nearby fault, the simulation curves of reactive power consumed by HVDC, reactive power supplied by AC filters, and reactive power exchanged with the receiving-side AC system are shown in Fig. 4. It can be seen from Fig. 4, during HVDC commutation failure resulted by nearby fault, the reactive power consumed by HVDC is nearly 0, the reactive power supplied by AC filters is also nearly 0, so the reactive power absorbed by HVDC from the receiving-side AC system is nearly 0. After fault cleared and HVDC entered into recovery process, the reactive power supplied by AC filters instantly increases from 0 to 3600 Mvar (strong receiving-side system), and after a time delay of 40 ms, the reactive power absorbed by HVDC increases from 0 to 4600 Mvar in 50 ms, then gradually recovers to the steady-state value 3500 Mvar. Therefore, the reactive power absorbed by HVDC from the receiving-side AC system reaches the maximum value 1400 Mvar in 90 ms after fault cleared. 3.3.3 HVDC receiving-side transient reactive power characteristic simulation (remote fault): During HVDC commutation failure Fig. 4 Reactive power curves of the HVDC receiving side (nearby fault)

rectifier (Ur 2 B r not vary a lot in (6)). Therefore, during commutation failure, HVDC will absorb large amount of reactive power from the sending-side AC system in the stage of current increase. Fig. 5 Reactive power curves of the HVDC receiving side (remote fault) resulted by inverter remote fault, the simulation curves of reactive power consumed by HVDC, reactive power supplied by AC filters, and reactive power exchanged with the receiving-side AC system are shown in Fig. 5. It can be seen from Fig. 5, during HVDC commutation failure resulted by remote fault, the reactive power consumed by HVDC first increases to the maximum value 4200 Mvar in 30 ms and then decreases, the reactive power supplied by AC filters is kept at 1200 Mvar, so the reactive power absorbed by HVDC from the receiving-side AC system reaches the maximum value 3000 Mvar in 30 ms after fault. After the fault cleared and HVDC entered into the recovery process, which is almost the same as the nearby fault, the reactive power absorbed by HVDC from the receivingside AC system reaches the maximum value 1400 Mvar in 90 ms after fault cleared. Therefore, the simulation results show that, the threat of commutation failure on the receiving-side AC system is mainly the voltage instability resulted by large amount of reactive power absorbed by HVDC. 4 HVDC sending-side transient reactive power characteristic during commutation failure and recovery HVDC commutation failure is caused by incomplete recovery of the inverter thyristors blocking capability, so the rectifier will not have commutation failure [1 3, 18]. However, the HVDC control of the two sides is coupled with each other, so HVDC commutation failure of the receiving side will also result in transient reactive power variation of the sending side. 4.1 HVDC sending-side transient reactive power characteristic during commutation failure After HVDC commutation failure, the control system will decrease the DC current order, making the DC current have the transient process of firstly increase and then decrease, which can be divided into the following two stages. 4.1.2 DC current decrease stage: As the rectifier ignition angle continually increases, the DC current will reach the maximum value and then rapidly decrease, finally reaching the VDCOL restricted minimum value (U dr decrease rapidly in (9)). As the DC current rapidly decreases to the minimum value, the reactive power consumed by the rectifier will also rapidly decrease to nearly 0 (P r tan w r very small in (6)). But the reactive power supplied by AC filters still does not vary a lot due to small fluctuations of bus voltage, much larger than the reactive power consumed by the rectifier (U 2 r B r not vary a lot in (6)). Therefore, during commutation failure, HVDC will send large amount of reactive power to the sending-side AC system in the stage of current decrease. 4.2 HVDC sending-side transient reactive power characteristic during recovery As the same as the HVDC receiving side, after the DC power recovered to the rated value, the overshoot effect of the PI controller will make the reactive power consumed by the rectifier be larger than the reactive power supplied by AC filters in a short period. Therefore, during commutation failure recovery, HVDC will absorb some reactive power from the sending-side AC system. 4.3 Case system analysis 4.3.1 Comparison of electromagnetic simulation and electromechanical simulation: During HVDC commutation failure and recovery, the electromagnetic and electromechanical caparison curves of the reactive power exchanged with the sending-side AC system are shown in Fig. 6. It can be seen in Fig. 6, the simulation results of the simplified electromechanical model are almost the same as the detailed electromagnetic model, which can precisely reflect the HVDC sendingside transient reactive power characteristic during commutation failure and recovery. Therefore, the electromechanical program of PSD-BPA is used as the simulation tool in the following case system analysis. 4.3.2 HVDC sending-side transient reactive power characteristic simulation: Simulation analysis is performed on the HVDC equivalent case system. During HVDC commutation failure, the simulation curves of reactive power consumed by HVDC, reactive power supplied by AC filters, and reactive power exchanged with the sending-side AC system are shown in Fig. 7. It can be seen from Fig. 7, during HVDC commutation failure, the reactive power consumed by HVDC increases from 3600 Mvar to the maximum value 11,600 Mvar in 30 ms, then gradually decreases to the minimum value 0 in 50 ms. The reactive 4.1.1 DC current increase stage: After HVDC commutation failure and before fault cleared, the inverter DC voltage remains at a low level. Under the function of VDCOL, the DC current order will be restricted at the minimum value (0 0.3 p.u.). In order to decrease the DC current to the VDCOL restricted minimum value after commutation failure, the function of current control (CCA) will rapidly increase the rectifier ignition angle to above 90. Because the control system has some time delay, at the early stage of the ignition angle increase, the DC current will still increase continually (U di very small in (9)). Because both of the DC current and the rectifier ignition angle increase rapidly, the rectifier will consume large amount of reactive power (P r tan w r very large in (6)). However, the reactive power supplied by AC filters does not vary a lot due to small fluctuations of bus voltage, much smaller than the reactive power consumed by the Fig. 6 Comparison curves of the reactive power exchanged with the sending-side AC system

Table 1 Maximum output reactive power of the HVDC sending side under different VDCOL parameters U dhigh Q I omin Q T U dtdn Q 0.6 3490 0.245 4670 0.005 3850 0.7 3590 0.345 3590 0.015 3590 0.8 3660 0.445 3460 0.025 3300 Table 2 Maximum input reactive power of the HVDC receiving side under different VDCOL parameters Fig. 7 Reactive power curves of the HVDC sending side power supplied by AC filters fluctuates in the range of 2400 3400 Mvar. Therefore, the reactive power sent by HVDC to the sending-side AC system reaches the maximum value 3600 Mvar in 80 ms after a fault. HVDC will enter the recovery process after fault cleared, which is almost the same as the receiving side. Therefore, the simulation results show that the threat of commutation failure on the sending-side AC system is mainly the transient overvoltage resulted by a large amount of reactive power sent by HVDC. 5 Impact of control parameters on HVDC sending-side and receiving-side reactive power characteristics 5.1 VDCOL parameters VDCOL is normally installed both on the HVDC rectifier side and the inverter side [19]. When the DC voltage drops resulted by AC/ DC contingencies, VDCOL will limit the DC current order of the main control. The VDCOL characteristic curves under different parameters are shown in Fig. 8. In which, U dlow denotes the VDCOL start voltage, U dhigh the denotes VDCOL quit voltage, I omin denotes the VDCOL minimum current order. It can be seen from Figs. 8b d, increasing U dlow, increasing U dhigh, and decreasing I omin of the inverter-side VDCOL, can decrease the reactive power absorbed by HVDC from the receivingside AC system during commutation failure and recovery. U dhigh Q I omin Q T U dtup Q 0.6 1990 0.245 1300 0.02 1860 0.7 1450 0.345 1450 0.03 1450 0.8 1000 0.445 1590 0.04 1040 Decreasing U dlow, decreasing U dhigh, and increasing I omin of the rectifier-side VDCOL, can decrease the reactive power sent by HVDC to the sending-side AC system during commutation failure. Moreover, increasing the voltage drop filtering time constant T U dtdn of the rectifier-side VDCOL can decrease the reactive power sent by HVDC to the sending-side AC system during commutation failure. Increasing the voltage rise filtering time constant T U dtup of the inverter-side VDCOL can decrease the reactive power absorbed by HVDC from the receiving-side AC system HVDC commutation failure recovery. The simulation results are shown in Tables 1 and 2. 5.2 CFPREV parameters CFPREV is normally installed on the HVDC inverter-side applying ABB technology [20]. When the inverter bus voltage drop exceeding the threshold is detected, CFPREV will operate and rapidly decrease the inverter ignition angle, in order to increase the commutation margin. In CFPREV, increasing the commutation failure prediction gain G cf and the angle reduce the time constant T dn cf, will increase the reactive power absorbed by HVDC from the receiving-side AC system. The simulation results are shown in Table 3. 5.3 CCA parameters CCA is one of the basic controllers in HVDC pole control system [21]. In the steady state, the rectifier current controller will take effect, but in the transient process after fault, the inverter will also take over to control the DC current in some period. In CCA, increasing the DC current filtering time constant T I dt and the gain constant Gain of constant current control will accelerate the DC current reduce speed after reaching the maximum value during commutation failure, and increase the reactive power sent by HVDC to the sending-side AC system. The simulation results are shown in Table 4. Table 3 Maximum input reactive power of the HVDC receiving side under different CFPREV parameters Fig. 8 VDCOL characteristic curves under different parameters a Basic characteristic bu dlow variation c U dhigh variation di omin variation G cf Q T dn cf Q 0.05 1370 0.01 1360 0.15 1450 0.02 1450 0.25 1500 0.03 1520

Table 4 Maximum output reactive power of the HVDC sending side under different CCA parameters T I dt Q Gain Q 0.0001 3300 28 3300 0.0011 3590 30 3580 0.0021 3990 32 3870 6 Conclusions (a) During commutation failure, HVDC will absorb nearly 0 reactive power from the receiving-side AC system under nearby fault and will absorb a large amount of reactive power from the receiving-side AC system under remote fault. (b) During commutation failure recovery, HVDC will firstly send a large amount of reactive power to the receiving-side AC system, then absorb some reactive power from the receiving-side AC system under the condition of the strong system, and will continually absorb some reactive power from the receiving-side AC system under the condition of the weak system. (c) During commutation failure, HVDC will absorb a large amount of reactive power from the sending-side AC system at the stage of DC current increase and will send large amount of reactive power to the sending-side AC system at the stage of DC current decrease. (d) Optimising important control parameters setting such as VDCOL, CFPREV, CCA and so on, can decrease the maximum reactive power exchanged between HVDC and the sending-side and receiving-side AC systems during the process of commutation failure. Studies such as the impact of reactive power impact on system stability and HVDC control parameters optimisation to improve system stability level will be conducted in the future. 7 References [1] Kimbark E.W.: Direct current transmission (Wiley-Inter science, New York, 1971) [2] Kundur P.: Power system stability and control (McGraw-Hill, New York, 1994) [3] Arrillaga J., Smith B.: AC-DC power system analysis (IET, London, 1998) [4] Zhou C., Xu Z.: Study on commutation failure of multi-infeed HVDC system. Proc. of 2002 Int. Conf. Power System Technology, 2002, pp. 2462 2466 [5] Wang Y., Li X., Wen C., ET AL.: Impact of AC system strength on commutation failure at HVDC inverter station. Proc. of 2012 Asia-Pacific Power and Energy Engineering Conf., 2012, pp. 1 4 [6] Rahimi E., Gole A.M., Davies J.B., ET AL.: Commutation failure analysis in multi-infeed HVDC systems, IEEE Trans. Power Deliv., 2011, 26, (1), pp. 378 384 [7] Aik D.L.H., Andersson G.: Voltage stability analysis of multi-infeed HVDC systems, IEEE Trans. Power Deliv., 1997, 12, (3), pp. 1309 1318 [8] Wang J., Zhao C., Hu J., ET AL.: The analysis and simulation of commutation failure and protection strategies. Proc. of the 4th Int. Conf. Electric Utility Deregulation and Restructuring and Power Technologies, 2011, pp. 504 508 [9] Xia C., Suo M., Xi L.: Analysis on commutation failure caused by AC faults in multi-infeed HVDC systems. Proc. of 2012 IEEE Power Engineering and Automation Conf., 2012, pp. 1 4 [10] He J., Li M., Yi J., ET AL.: Research on dynamic characteristics and countermeasures of AC-DC hybrid power system with large scale HVDC transmission. Proc. of 2014 Int. Conf. Power System Technology, 2014, pp. 799 805 [11] Zheng C., Tang Y., Ma S., ET AL.: Study on the dynamic reactive power characteristic of HVDC rectifier stations and optimization measure, Proc. CSEE, 2014, 34, (28), pp. 4886 4896 [12] Wang H., Zheng C., Ren J., ET AL.: Dynamic reactive power trajectory of HVDC inverter station and its optimization measures, Power Syst. Technol., 2015, 39, (5), pp. 1254 1260 [13] Xin H., Zhang F., Yu Y., ET AL.: Generalized short circuit ratio for multi-infeed DC systems: definition and theoretical analysis, Proc. CSEE, 2016, 36, (3), pp. 633 647 [14] Chen S., Rong J., Bi G., ET AL.: Study of the effect of rectifier side control modes on UHVDC commutation failure, Electr. Power, 2015, 48, (7), pp. 1 7 [15] Li Y., Lu Y., Liu X., ET AL.: Influence of inverter control strategy on commutation failure and recovery characteristic optimization, Electr. Power Constr., 2015, 36, (9), pp. 112 116 [16] Yang H., Zhu L., Cai Z., ET AL.: Influence of HVDC control on HVDC reactive power dynamic characteristic, Power Syst. Technol., 2014, 38, (10), pp. 2631 2637 [17] Wan L., Ding H., Liu W.: Simulation model of control system for HVDC power transmission based on actual project, Power Syst. Technol., 2013, 37, (3), pp. 629 634 [18] Arrillaga J.: High voltage direct current transmission (IET, London, 1998) [19] Zhou B., Du Z., Luo D., ET AL.: VDCOL parameters design of multiinfeed HVDC based on a simplified model of DC P-Q coupling recovery. Proc. of 2014 IEEE PES Asia-Pacific Power and Energy Engineering Conf., 2014, pp. 1 7 [20] Wei Z., Yuan Y., Lei X., ET AL.: Direct-current predictive control strategy for inhibiting commutation failure in HVDC converter, IEEE Trans. Power Syst., 2014, 29, (5), pp. 2409 2417 [21] Xie G., Wang M.: Parameter optimization for current controller in HVDC control system. Proc. of 2010 Int. Conf. Power System Technology, 2010, pp. 1 5