Abstract
Line commutated converter based high-voltage direct-current (LCC-HVDC) transmissions are prone to harmonic oscillation under weak grids. Impedance modeling is an effective method for assessing interaction stability. Firstly, this paper proposes an improved calculation method for the DC voltage and AC currents of commutation stations to address the complex linearization of the commutation process and constructs an overall harmonic state-space (HSS) model of an LCC-HVDC. Based on the HSS model, the closed-loop AC impedances on the LCC-HVDC sending and receiving ends are then derived and verified. The impedance characteristics of the LCC-HVDC are then analyzed to provide a physical explanation for the harmonic oscillation of the system. The effects of the grid strength and control parameters on system stability are also analyzed. To improve the impedance characteristics and operating stability of the LCC-HVDC system, a virtual impedance based stability enhancement control is proposed, and a parameter design method is considered to ensure satisfactory phase margins at both the sending and receiving ends. Finally, simulation results are presented to verify the validity of the impedance model and virtual impedance based stability enhancement control.
4, 2023.
α, μ, γ Firing, commutation, and extinction angles
Δx, x Perturbation and steady-state terms
θpll, θ1, φ Phase-locked loop (PLL) output phase, commutation voltage phase, and initial phase
ωp, ω1 Perturbation and fundamental angular frequencies
Γ Toeplitz transform
Cr1, Ci1 Shunt capacitor banks of sending end and receiving end
fp, f1 Perturbation and fundamental frequencies
ic AC current of commutation stations
idc DC line current of commutation stations
idcrm, vdcim Outputs of DC current and voltage filters
ig, vg Grid current and voltage
ilr1, ili1 Inductance currents of transmission line
ilr2, ilr3, ili2, ili3 Inductance currents of AC filters
it1yy, it2yy, vt2yy Primary current, secondary current, and secondary voltage of a Y/Y transformer
it1yd, it2yd, vt2yd Primary current, secondary current, and secondary voltage of a Y/D transformer
Idcref, Vdcref DC current and voltage reference
kt Line commutated converter (LCC) commutation transformer ratio
kpi, kii Proportional and integral gains of DC current controller
kpp, kip Proportional and integral gains of PLL
kpv, kiv Proportional and integral gains of DC voltage controller
Ld DC smoothing inductance
Lt Equivalent leakage reactance at the primary side of commutation transformer
Rd, Cd DC line resistance and capacitance
Rr1, Rr2 Transmission line resistances at sending end
Ri1, Ri2, Ri3 Transmission line resistances at receiving end
Lr1, Li1, Lgi Transmission line inductances
Rr3, Lr2, Cr2 Resistance, inductance, and capacitance of AC filter 1
Rr4, Rr5, Lr3, Resistances, inductance, and capacitances of Cr3, Cr4 AC filter 2
Ri4, Li2, Ci2 Resistance, inductance, and capacitance of AC filter 3
Ri5, Ri6, Li3, Resistances, inductance, and capacitances of
Ci3, Ci4 AC filter 4
Ti, Tv Time constants of DC current and voltage filters
vcr2, vcr3, vcr4 Capacitance voltages of AC filters 1and 2
vci2, vci3, vci4 Capacitance voltages of AC filters 3 and 4
vpcc Commutation bus voltage
vdc, vdc1 DC voltages of 12-pulse and 6-pulse commutation stations
vdcl DC line capacitance voltage
xidc, xvdc Integral outputs of DC current and voltage controllers
xpll, v Integral outputs and q-axis voltage of PLL controllers
Zgr, Zgi Grid impedances at sending and receiving ends
ZLCCp, ZLCCn Positive- and negative-sequence impedances of line commutated converter based high-voltage direct-current (LCC-HVDC)
d, q d- and q-axis components in the dq reference frame
k Three phases of a, b, and c
n Harmonic truncation order
Perturbation at frequency
r, i Signals at sending and receiving ends
LINE commutated converter based high-voltage direct-current (LCC-HVDC) transmissions are extensively used in power systems to realize long-distance and bulk-power transmissions [
In recent years, small-signal models and stability analysis of LCC-HVDC transmissions have been reported [
Harmonic state-space (HSS) modeling is a feasible method to build the model with multiple-harmonic and frequency-coupling dynamics [
LCC-HVDC system impedance modeling has three main obstacles: ① the commutation process of the LCC-HVDC system is difficult to linearize under small-signal perturbation; ② many characteristic harmonics occur during steady-state operation, which results in intricate frequency coupling behavior; and ③ numerous state variables of the LCC-HVDC system hinder the derivation of the impedance model. To solve these problems, this paper presents an improved calculation method for the DC voltage and AC current of commutation stations to address the complex linearization of the commutation process. Closed-loop AC impedance models at the LCC-HVDC sending and receiving ends are then derived based on the HSS model considering characteristic harmonics. Finally, virtual impedance based stability control for LCC-HVDC systems is proposed to improve impedance characteristics and operating stability.
The remainder of this paper is organized as follows. Section II presents LCC-HVDC model in time domain. Section III describes LCC-HVDC closed-loop impedance based on HSS. Section IV explains the verification and analysis. The virtual impedance based stability control for LCC-HVDC system is then proposed in Section V. Section VI presents simulation verification. Section VII draws the conclusions.

Fig. 1 Topology of a monopolar 12-pulse LCC-HVDC system.

Fig. 2 Topology of an LCC connected to a commutation bus through a Y/Y transformer.
For the AC current calculation, the dq-frame current model that considers the commutation process proposed in [
(1) |
Note that the perturbation response of DC voltage and line currents of the 12-pulse converter’s is twice that of the 6-pulse converter [
(2) |
where , , , and are expressed by (SA1)-(SA7) in Supplementary Material A, respectively; and the overline represents the steady-state terms.
For the DC voltage calculation, this paper adopts the neutral-point voltages of the bridge arms and the corresponding switching functions. As shown in

Fig. 3 Voltage and switching function waveforms when neutral-point voltages of bridge arms are used.
Accordingly, the switching function model of the phase-a voltage can be expressed by (3). The switching functions of phase-b voltage and phase-c voltage can be obtained by lagging and leading phases a , respectively. Thus, of the converter fed by the Y/Y transformer can be calculated using (4). The DC voltage and AC current of the converter fed by the Y/D transformer are calculated using the same method.
(3) |
(4) |
To calculate the neutral-point voltages of the bridge arms, the commutation transformer model is derived. The magnetic saturation of the transformer can be neglected under normal operation, and the simplified equivalent model can be adopted. Thus, if we use the Y/Y transformer as an example, the relationship between the voltage and current of the transformer primary and secondary windings can be expressed as:
(5) |
When (5) is substituted into (4), the linearized expression of the DC voltage can be expressed as:
(6) |
When a balanced three-phase system without a neutral connection is considered, no zero-sequence signal exists at the AC side. It is assumed that the positive/negative-sequence small-signal voltage perturbations and at fp are imposed on the sending-end and receiving-end AC systems, respectively. Let us use phase a as an example, where (t) is omitted for a simpler representation. According to Kirchhoff Laws and the linearization around periodic steady-state operating points of variables, the state-space equations in the time domain of a sending-end AC system, receiving-end AC filter, and DC line can be obtained as:
(7) |
where ; ; ; ; ; ; and the coefficient matrixes AsrT, AsiT, and AdcT are expressed by (SA8)-(SA10) in Supplementary Material A, respectively.

Fig. 4 Control scheme of LCC-HVDC system under normal operation.
(8) |
where ; ; ; ; and AcrT and AciT are expressed by (SA10) in Supplementary Material A.
We next convert the time-domain model of the LCC-HVDC system into an LTI model and derive the overall HSS model. In addition, to facilitate small-signal analysis, the closed-loop AC impedance model of the LCC-HVDC sending and receiving ends is further derived.
To obtain an HSS model of the LCC-HVDC system, its linearized time-varying periodical (LTP) model should be converted to an LTI model in the frequency domain. According to the HSS modeling method [
(9) |
Regarding the product of and steady-state component b(t), the results are expressed as a convolution operation in the frequency domain as:
(10) |
where the operator indicates the Toeplitz transform .
When the differential of in the time domain is used in the frequency domain, the diagonal matrix is multiplied by the vector composed of the Fourier coefficient:
(11) |
where .
To simplify the HSS model expression of (12), the following principles are applied [
(12) |
(13) |
where is expressed by (SA11) in Supplementary Material A; and the other coefficient matrices are addressed in the same manner.
Based on the frequency model of the Park and inverse Park transformations derived in [
(14) |
(15) |
where and are the transformation matrices expressed by (SA12) in Supplementary Material A.
Therefore, when (14) is substituted into (2) and HSS theory is applied, the LTP model of the AC currents of the rectifier and inverter stations can be converted to the LTI model as:
(16) |
where , , and are expressed by (SA13) in Supplementary Material A.
To obtain , the voltage switching function svyy(t) should first be shifted to the frequency domain. This paper applies the frequency-domain modeling method of switching function through double-Fourier series analysis [
(17) |
where is the complex Fourier coefficient of svyy(t) at frequency , which can be obtained by integrating svyy(t) over the unit area. The calculation result is:
(18) |
where is the Bessel function of the first order.
For , the steady-state components of svyy can be expressed in the frequency domain by (19). When the high-order perturbation components, i.e., , are omitted, the linearized model of can be obtained in the frequency domain by (20).
(19) |
(20) |
where is expressed by (SA14) in Supplementary Material A.
When (19) and (20) are substituted into (6) and HSS theory is applied, the DC voltages of the LTP model of the rectifier and inverter stations can be converted to the LTI model as:
(21) |
where ; ; and .
The overall HSS model of the LCC-HVDC system is obtained by combining (12), (13), (15), (16), and (21), which is illustrated as a block diagram, as shown in

Fig. 5 Block diagram of overall HSS model of LCC-HVDC.
According to
(22) |
where Yfi, Ygi, and YLi are expressed by (SA15) and (SA16) in Supplementary Material A.
Then, because contains only the perturbation at , the current response can be solved by (22). Consequently, the closed-loop impedance of the LCC-HVDC receiving end can be obtained as:
(23) |
Similarly, when is set to be zero, the closed-loop impedance of the LCC-HVDC sending end can be solved by the overall HSS model as:
(24) |
Note that the imposed perturbation voltage or will produce infinite AC current responses at frequency , , , , etc. In addition, the coupling current perturbations will flow across the grid impedance and cause the corresponding voltage perturbations and induce the LCC-HVDC system to affect the current at [
To validate the precision of the LCC-HVDC sending- and receiving-end impedance model, the CIGRE benchmark model in PSCAD is used, where the system parameters are shown in
System | Parameter | Value |
---|---|---|
Sending-end system | Rated power | 1000 MW |
Line-to-line RMS voltage | 382.87 kV | |
Rr1, Rr2, Lr1 | 3.737 Ω, 2160.633 Ω, 0.151 H | |
Cr1 | 3.342 μF | |
Rr3, Lr2, Cr2 | 83.32 Ω, 0.0136 H, 6.685 μF | |
Rr4, Rr5, Lr3, Cr3, Cr4 | 261.87 Ω, 29.76 Ω, 0.1364 H, 6.685 μF, 74.28 μF | |
ktr | 345/213.46 | |
Ltr | 0.113 H | |
Ti, kpi, kii |
0.0012 s, 5.495×1 | |
kppr, kipr |
2.84×1 | |
Receiving-end system | Line-to-line RMS voltage | 215.05 kV |
Ri1, Ri2, Ri3, Li1, Lgi | 0.7406 Ω, 24.81 Ω, 0.7406 Ω, 36.5 mH, 36.5 mH | |
Ci1 | 7.522 μF | |
Ri4, Li2, Ci2 | 37.03 Ω, 0.0061 H, 15.04 μF | |
Ri5, Ri6, Li3, Ci3, Ci4 | 116.38 Ω, 13.23 Ω, 0.0606 H, 15.04 μF, 167.2 μF | |
kti | 230/209.23 | |
Lti | 0.0512 H | |
Ti, kpv, kiv |
0.02 s, 1.845×1 | |
kppi, kipi |
4.26×1 | |
DC line | Idcref | 2 kA |
Ld | 0.5968 H | |
Rd, Cd | 2.5 Ω, 26 μF |
Because the main harmonic orders of the LCC-HVDC system are the

Fig. 6 Frequency response of established impedance models and measured results of LCC-HVDC. (a) Sending end. (b) Receiving end.

Fig. 7 Frequency response of impedance models derived from switching function without considering commutation process. (a) Sending end. (b) Receiving end.
In addition,
According to [

Fig. 8 Frequency response of positive-sequence impedance of LCC-HVDC sending end. (a) Changing with kpi. (b) Changing with SESCR.

Fig. 9 Frequency response of positive-sequence impedance of LCC-HVDC receiving end. (a) Changing with kpv. (b) Changing with RESCR.

Fig. 10 Effects of DC line parameters on LCC-HVDC positive-sequence impedance characteristics. (a) Sending-end impedance with the increase of Rd. (b) Receiving-end impedance with the increase of Rd. (c) Sending-end impedance with the increase of Cdr. (d) Receiving-end impedance with the increase of Ld.
The above stability analysis shows that an increase in kpi reduces the phase of the LCC-HVDC sending-end impedance to approximately 120 Hz, whereas an increase in of the rectifier station increases the phase of the LCC-HVDC sending-end system in this frequency band. In addition, the decrease in or RESCR reduces the PM of the LCC-HVDC receiving-end impedance to approximately 70 Hz, whereas an increase in Ld of the inverter station increases the phase of the LCC-HVDC receiving-end system in this frequency band. Therefore, the small-signal stability of the LCC-HVDC sending- and receiving-end systems can be improved by increasing and of the DC line, respectively. However, adding capacitors and flat-wave reactors in practical projects increases the construction cost and operation loss of the system. Accordingly, a virtual impedance based stability control is proposed in this paper, and the principle of parameter design is further discussed.
According to the stability analysis and control method of the LCC-HVDC system, parallel virtual capacitance Cv and series virtual inductance Lv are introduced in the rectifier and inverter station controls, respectively, as shown in
(25) |

Fig. 11 Proposed virtual impedance based stability control.
After the virtual impedance control is introduced, the input vectors and in (13) can be re-expressed as and , respectively. Therefore, the proposed stability control can reshape the LCC-HVDC impedance characteristics by and .
To assign proper values for Cv and Lv, the effects of different Cv and Lv on the positive-sequence impedance characteristics of the LCC-HVDC must first be analyzed, as shown in

Fig. 12 Frequency responses of positive-sequence impedance of LCC-HVDC system. (a) Sending-end impedance with and the increase of Cv. (b) Receiving-end impedance with and the increase of Cv. (c) Sending-end impedance with and the increase of Lv. (d) Receiving-end impedance with and the increase of Cv.

Fig. 13 Effects of Cv and Lv on PMs of ZLCCrp(s) and ZLCCip(s).
To further verify the above theoretical analyses and stability control, an LCC-HVDC system simulation is performed in PSCAD. The system parameters are the same as those of the stability analysis listed in

Fig. 14 Simulation waveforms under different parameters. (a) Decreased kpi. (b) Increased SESCR. (c) Decreased kpv. (d) Decreased RESCR.

Fig. 15 FFT analysis of oscillation waveforms. (a) kpi is increased by twice. (b) kpv is decreased by four times. (c) RESCR is reduced to 2.0.

Fig. 16 Simulation waveforms with proposed stability control. (a) Normal operation. (b) kpi is increased by twice. (c) RESCR is reduced to 2.0. (d) kpv is decreased by four times.
This paper proposes an improved calculation method for the DC voltage and AC current of an LCC-HVDC commutation station to avoid the complex linearization of the commutation process. The paper also establishes an overall HSS model of the LCC-HVDC. To facilitate small-signal stability analysis and impedance measurements of the LCC-HVDC, closed-loop AC impedances of the LCC-HVDC sending and receiving ends are derived based on the HSS model. The positive-sequence impedance of the LCC-HVDC receiving end shows negative-resistive and capacitive characteristics, i.e., phase angle ranges from -180° to -90°, at 56-65 Hz, which easily led to the oscillation between the LCC-HVDC system and the weak receiving-end grid. In addition, the larger the proportional gain of the DC current controller or the smaller the proportional gain of the DC voltage controller, the more unstable the system is. Finally, a virtual impedance based stability control and parameter design method is proposed and verified to improve impedance characteristics and suppress the oscillation of the LCC-HVDC system.
References
R. Zhu, X. Zhou, H. Xia et al., “A commutation failure prediction and mitigation method,” Journal of Modern Power Systems and Clean Energy, vol. 10, no. 3, pp. 779-787, May 2022. [Baidu Scholar]
D. Shu, X. Xie, H. Rao et al., “Sub- and super-synchronous interactions between STATCOMs and weak AC/DC transmissions with series compensations,” IEEE Transactions on Power Electronics, vol. 33, no. 9, pp. 7424-7437, Sept. 2018. [Baidu Scholar]
C. Luo, Q. Guo, Y. Hu et al., “Analysis and countermeasures of harmonic instability in a practical HVDC system with fixed series compensation and STATCOM,” in Proceedings of IEEE 2021 4th CIEEC, Wuhan, China, May 2021, pp. 1-6. [Baidu Scholar]
M. Zhang, X. Yuan, and J. Hu, “Mechanism analysis of subsynchronous torsional interaction with PMSG-based WTs and LCC-HVDC,” IEEE Journal of Emerging and Selected Topics in Power Electronics, vol. 9, no. 2, pp. 1708-1724, Apr. 2021. [Baidu Scholar]
W. Du, Z. Zhen, and H. Wang, “The subsynchronous oscillations caused by an LCC HVDC line in a power system under the condition of near strong modal resonance,” IEEE Transactions on Power Delivery, vol. 34, no. 1, pp. 231-240, Feb. 2019. [Baidu Scholar]
Y. Ma, L. Tong, D. Zhu et al., “Analysis of small-signal stability for LCC-HVDC system integrated to weak sending-end system,” in Proceedings of IEEE 2020 4th International Conference on HVDC, Xi’an, China, Nov. 2020, pp. 698-704. [Baidu Scholar]
X. Lin, H. Li, W. Wei et al., “Impact of characteristic harmonics on the small-signal stability of LCC-HVDC station,” in Proceedings of IEEE 2020 4th International Conference on HVDC, Xi’an, China, Nov. 2020, pp. 705-711. [Baidu Scholar]
A. Zheng, C. Guo, P. Cui et al., “Comparative study on small-signal stability of LCC-HVDC system with different control strategies at the inverter station,” IEEE Access, vol. 7, pp. 34946-34953, Jan. 2019. [Baidu Scholar]
J. Sun, “Small-signal methods for AC distributed power systems: a review,” IEEE Transactions on Power Electronics, vol. 24, no. 11, pp. 2545-2554, Nov. 2009. [Baidu Scholar]
V. Salis, A. Costabeber, S. M. Cox et al., “Stability assessment of power-converter-based AC systems by LTP theory: eigenvalue analysis and harmonic impedance estimation,” IEEE Journal of Emerging and Selected Topics in Power Electronics, vol. 5, no. 4, pp. 1513-1525, Dec. 2017. [Baidu Scholar]
X. Wang and F. Blaabjerg, “Harmonic stability in power electronic-based power systems: concept, modeling, and analysis,” IEEE Transactions on Smart Grid, vol. 10, no. 3, pp. 2858-2870, May 2019. [Baidu Scholar]
J. Sun, “Impedance-based stability criterion for grid-connected inverters,” IEEE Transactions on Power Electronics, vol. 26, no. 11, pp. 3075-3078, Mar. 2011. [Baidu Scholar]
H. Xu, F. Nie, Z. Wang et al., “Impedance modeling and stability factor assessment of grid-connected converters based on linear active disturbance rejection control,” Journal of Modern Power Systems and Clean Energy, vol. 9, no. 6, pp. 1327-1338, Nov. 2021. [Baidu Scholar]
A. Rygg, M. Molinas, C. Zhang et al., “On the equivalence and impact on stability of impedance modelling of power electronic converters in different domains,” IEEE Journal of Emerging and Selected Topics in Power Electronics, vol. 5, no. 4, pp. 1444-1454, Dec. 2017. [Baidu Scholar]
H. Liu and J. Sun, “Analytical mapping of harmonics and impedance through phase-controlled converters,” in Proceedings of IEEE 13th COMPEL Workshop, Kyoto, Japan, Jul. 2012, pp. 1-8. [Baidu Scholar]
H. Liu and J. Sun, “DC terminal impedance modeling of LCC-based HVDC converters,” in Proceedings of 14th IEEE Workshop on Control Model and Power Electronics, Salt Lake City, USA, Jun. 2013, pp. 1-9. [Baidu Scholar]
H. Liu and J. Sun, “Small-signal stability analysis of offshore wind farms with LCC HVDC,” in Proceedings of IEEE Grenoble PowerTech, Grenoble, France, Jun. 2013, pp. 1-8. [Baidu Scholar]
Y. Qi, H. Zhao, S. Fan et al., “Small signal frequency-domain model of a LCC-HVDC converter based on an infinite series-converter approach,” IEEE Transactions on Power Delivery, vol. 34, no. 1, pp. 95-106, Feb. 2019. [Baidu Scholar]
X. Chen, J. Ma, S. Wang et al., “An accurate impedance model of line commutated converter with variable commutation overlap,” IEEE Transactions on Power Delivery, vol. 37, no. 1, pp. 562-572, Feb. 2022. [Baidu Scholar]
M. Daryabak, S. Filizadeh, J. Jatskevich et al., “Modeling of LCC-HVDC systems using dynamic phasors,” IEEE Transactions on Power Delivery, vol. 29, no. 4, pp. 1989-1998, Aug. 2014. [Baidu Scholar]
J. Kwon, X. Wang, F. Blaabjerg et al., “Harmonic interaction analysis in a grid-connected converter using harmonic state-space (HSS) modeling,” IEEE Transactions on Power Electronics, vol. 32, no. 9, pp. 6823-6835, Sept. 2017. [Baidu Scholar]
X. Yue, X. Wang, and F. Blaabjerg, “Review of small-signal modeling methods including frequency-coupling dynamics of power converters,” IEEE Transactions on Power Electronics, vol. 34, no. 4, pp. 3313-3328, Apr. 2019. [Baidu Scholar]
J. Lyu, X. Zhang, J. Huang et al., “Comparison of harmonic linearization and harmonic state space methods for impedance modeling of modular multilevel converter,” in Proceedings of IEEE IPEC-Niigata 2018-ECCE Asia, Niigata, Japan, May 2018, pp. 1004-1009. [Baidu Scholar]
J. Kwon, X. Wang, F. Blaabjerg et al., “Linearized modeling methods of AC-DC converters for an accurate frequency response,” IEEE Journal of Emerging and Selected Topics in Power Electronics, vol. 5, no. 4, pp. 1526-1541, Dec. 2017. [Baidu Scholar]
C. Zhang, M. Molinas, S. Føyen et al., “Harmonic-domain SISO equivalent impedance modeling and stability analysis of a single-phase grid-connected VSC,” IEEE Transactions on Power Electronics, vol. 35, no. 9, pp. 9772-9785, Sept. 2020. [Baidu Scholar]
Z. Xu, B. Li, L. Han et al., “A complete HSS-based impedance model of MMC considering grid impedance coupling,” IEEE Transactions on Power Electronics, vol. 35, no. 12, pp. 12929-12948, Dec. 2020. [Baidu Scholar]
L. Fan, P. Zhou, S. Wang et al., “Harmonic state space modeling of LCC-HVDC system with consideration of harmonic dynamics,” in Proceedings of IEEE 3rd CIEEC, Beijing, China, Sept. 2019, pp. 2076-2081. [Baidu Scholar]
K. Sano, T. Kikuma, T. Nakajima et al., “A suppression method of harmonic instability in line-commutated converters applying active harmonic filters,” in Proceedings of IEEE IPEC–Niigata 2018–ECCE Asia, Niigata, Japan, May 2018, pp. 3299-3303. [Baidu Scholar]
B. Fang, Y. Jiao, L. Dong et al., “Using virtual synchronous generator control based energy storage to enhance the stability of sending terminal in LCC-HVDC system,” in Proceedings of IEEE 2020 4th International Conference on HVDC, Xi’an, China, Nov. 2020, pp. 304-309. [Baidu Scholar]
G. Li, Y. Chen, A. Luo et al., “Wideband harmonic voltage feedforward control strategy of STATCOM for mitigating sub-synchronous resonance in wind farm connected to weak grid and LCC HVDC,” IEEE Journal of Emerging and Selected Topics in Power Electronics, vol. 9, no. 4, pp. 4546-4557, Aug. 2021. [Baidu Scholar]
Z. Bing and J. Sun, “Frequency-domain modeling of multipulse converters by double-fourier series method,” IEEE Transactions on Power Electronics, vol. 26, pp. 3804-3809, Dec. 2011. [Baidu Scholar]
Y. Liao and X. Wang, “Impedance-based stability analysis for interconnected converter systems with open-loop RHP poles,” IEEE Transactions on Power Electronics, vol. 35, no. 4, pp. 4388-4397, Apr. 2020. [Baidu Scholar]
Y. Liu, L. Hong, X. Zhou et al., “HSS-based impedance modeling and oscillation suppression strategy for SDBC-STATCOM in LCC-HVDC receiving grid,” in Proceedings of IEEE CIYCEE, Chengdu, China, Dec. 2021, pp. 1-7. [Baidu Scholar]