Sub‐synchronous oscillation in PMSGs based wind farms caused by amplification effect of GSC controller and PLL to harmonics
2018; Institution of Engineering and Technology; Volume: 12; Issue: 7 Linguagem: Inglês
10.1049/iet-rpg.2017.0740
ISSN1752-1424
Autores Tópico(s)Islanding Detection in Power Systems
ResumoIET Renewable Power GenerationVolume 12, Issue 7 p. 844-850 Research ArticleFree Access Sub-synchronous oscillation in PMSGs based wind farms caused by amplification effect of GSC controller and PLL to harmonics Yanhui Xu, Corresponding Author Yanhui Xu xuyanhui23@sohu.com School of Electrical and Electronic Engineering, North China Electric Power University, Beijing, 102206 People's Republic of ChinaSearch for more papers by this authorYuping Cao, Yuping Cao School of Electrical and Electronic Engineering, North China Electric Power University, Beijing, 102206 People's Republic of ChinaSearch for more papers by this author Yanhui Xu, Corresponding Author Yanhui Xu xuyanhui23@sohu.com School of Electrical and Electronic Engineering, North China Electric Power University, Beijing, 102206 People's Republic of ChinaSearch for more papers by this authorYuping Cao, Yuping Cao School of Electrical and Electronic Engineering, North China Electric Power University, Beijing, 102206 People's Republic of ChinaSearch for more papers by this author First published: 12 April 2018 https://doi.org/10.1049/iet-rpg.2017.0740Citations: 19AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract Sub-synchronous oscillation (SSO) caused by direct-drive permanent magnet synchronous generators (PMSGs) occurs frequently in Xinjiang Uygur Autonomous Region, China. As a new type of SSO, the mechanism of power oscillation triggered by PMSGs has not been clarified yet. In this study, a small-signal analysis method was used to investigate the response process of the grid-side converter (GSC) controller and a phase-locked loop (PLL) to harmonics. Components with the same frequency of input disturbance signal and an output signal which generated by response process of controller superpose at the outlet of PMSGs could be amplified by positive feedback. Amplified harmonics will cause sustained power oscillation in sub-synchronous frequency. A criterion for judging dangerous frequencies of SSO was deduced based on phase relation between input and output signals, and the form of output signal was predicted under the condition of certain parameters setting. The theoretical analysis is then validated by the simulation results and the on-site data measured by the phasor measurement unit. Furthermore, the impacts of GSC and PLL parameters on SSO were discussed. This study provides the theoretical basis for SSO mechanism and judgement method in practical engineering. Nomenclature u GSC's voltage v equivalent grid voltage s Laplace operator θ feedback angle of PLL θc angle of GSC's frame Ut0 amplitude of grid-side voltage C capacitor in converter's DC link L, Lg equivalent inductance of GSC and grid Kpp, Kip parameters of PLL's PI controller Kip, Kii parameters of GSC's PI controller Superscripts ^ value on the αβ-axis Subscripts ref reference value αβ reference frame of GSC dq global synchronous coordinates of the system 0 steady-state value 1 Introduction Wind power, as a clean and renewable energy, has developed rapidly in recent years. With the increase of wind power installed capacity, the related sub-synchronous oscillation (SSO) problem becomes more and more prominent. The most commonly variable speed constant frequency wind turbine generators (WTGs) can be divided into doubly fed induction generator (DFIG) [1, 2] and direct-drive permanent magnet synchronous generator (PMSG) [3, 4]. Large-scale application of DFIG was relatively earlier, so the relevant SSO research was carried out more in-depth. The first reported SSO incident of WTGs [5-10] produced by sub-synchronous control interaction took place in TX, the USA in October 2009. The cause of the oscillation is the interaction between the control system of DFIG and series capacitor, which lead numerous DFIGs dropped out and crowbar circuits damaged [5, 6]. The results of the previous researches focus on DFIG SSO show that the converter controller has significant impacts on system stability at sub-synchronous frequency [11-15]. Then, the impacts of fully controlled voltage-source converters (VSCs) on SSO are widely studied by scholars [9, 14]. Alawasa et al. [16, 17] and Joseph et al. [18] point out that the interaction between AC networks and general VSCs on certain conditions can induce negative damping at sub-synchronous frequencies, which would make system under instability. Works in [19, 20] reveal that phase-locked loops (PLLs) coupled with adjacent VSCs could lead the system under the risk of oscillations. The series/parallel resonant circuits are used in [21] to indicate the possibility of oscillations in grid-connected VSC system. The study of the PMSGs based SSO can be divided into two stages: the stage of pure theoretical analysis and the stage of the research associated with actual oscillation issues. On the basis of the study of VSCs, [16, 22, 23] show that PMSGs could induce negative damping and trigger SSO. However, in other papers, different conclusions are drawn. Larsen [24] and Ma et al. [25] mentioned that due to its special grid-connected structure, PMSGs are immune to the oscillatory mode associated with grid-side converter (GSC) controller. Alawasa et al. [16] propose that the positive damping provided by PMSGs can prevent SSO. The above discussion has not reached an agreement, especially for the absence of support of engineering example and the theory can only be verified by computer models. On 1st July 2015, Xinjiang of China, a serious SSO incident was observed in a large PMSGs based wind farm, which made the PMSG SSO a research hotspot [26-29]. There are two features of this accident: first, unlike the structure of the DFIG-based wind farm integration, there was no series capacitor between the power system and PMSG-based wind farm when the oscillation occurred [27]. So as a new type of SSO, its mechanism is unclear. Second, from the recorded data of wind field, during the oscillation, the bus voltage at the PMSGs outlet contains complex and regular harmonic components [29], which is different from the previous SSO problem of WTGs. Until recently, there are few papers particularly discussing the impact of PMSG on SSO based on real oscillatory issues. In [26, 27], the transfer function, eigenvalue value analysis, impedance model analysis and electromagnetic transient simulation are used to reveal the mechanism of SSO. Liu et al. [27] advance the negative-resistance effect to explain the reason of oscillation by equivalent RLC (resistance-inductance-capacitance) circuit. Bi et al. [29] analyses the cause of a specific spectrum of harmonics and the frequency transformation relationship between input and output signals by small-signal analysis method. However, the simulation results in existing references are not entirely consistent with the measured data. Moreover, the investigation of response characteristics of PMSG to sub-synchronous frequency components has not been effectively linked with the mechanism. So, one of the present tasks is to propose a mechanism that can explain the process of oscillation and engineering phenomena simultaneously. In this paper, a small-signal analysis method is used to study the harmonic response process of PMSG control system and derive the analytic expressions for the output signal of GSC. By considering controller of GSC and PLL, the phase relationships of harmonics are revealed and a criterion for judging the SSO issue induced by PMSG based on positive feedback effect is proposed. The theoretical analysis is verified by both simulation results and on-site recorded data monitored by phasor measurement units (PMUs). The influence of controller parameters on the characteristics of SSO is also discussed, and the corresponding simulation is also used as theoretical verification. The organisation of this paper is organised as follows. Section 2 concisely introduces SSO accident observed in renewable energy collection zone in Xinjiang, China. In Section 3, the GSC and PLL models are introduced, and small-signal model of the system by considering the dynamic characteristics of the controller of GSC and PLL is proposed. Section 4 presents the response characteristics of the control system to the input sub-synchronous frequency component. Moreover, based on phase relation, a criterion to judge the existence of oscillation caused by positive feedback effect of harmonics is provided. In Section 5, the theoretical analysis is confirmed by the simulation and the field measured data, and the factors influencing the oscillation are analysed. Section 6 makes the conclusion. 2 SSO issue in Xinijang large-scale wind power integration project The part of a network diagram of the renewable energy collection zone in Xinjiang, China is shown in Fig. 1a, provided by Xinjiang State Grid. The process of the above-mentioned incident occurred in the Xinjiang power grid can be summarised into three steps. First, the PMSGs based wind farm generated sustained oscillation, and then associated sub/super-synchronous frequency harmonics transmitted to other units in the adjacent grid through the network. Second, three 600 MW thermal generators, whose shaft torsional frequencies were complementary to some of the harmonics, were tripped by shafting torsional oscillation. Finally, Tianzhong line commutated converter (LCC)-high-voltage DC (HVDC) was forced to operate in a low-voltage state and the frequency of the northwestern power grid decreased from 50.05 to 49.91 Hz, because of the insufficient power supply. Since 1st July 2015, this kind of SSO has been frequently observed in Xinjiang, threatening the security of the power system seriously. Fig. 1Open in figure viewerPowerPoint SSO in Xinjiang grid on 1st July 2015 (a) Part of network diagram of the renewable energy collection zone in Xinjiang, China, (b) Frequency spectrum analysis of harmonics monitored in the voltage in PCC Fig. 1b shows sub/super-synchronous components monitored in the voltage at the point of common coupling (PCC) node when oscillation occurs. The SSO was measured by the PMU located at the point of common coupling of the PMSGs based wind farms, and multiple frequency components were detected as 19.4, 29.6, 39.8, 60.2, 70.4, 80.6, 90.8 Hz and so on. At the terminal of thermal generators and the interconnected transmission lines, multiple sub/super-synchronous frequency components were detected, whose distribution was same as the PCC node. The frequencies of the 19.4 and 29.6 Hz components were complementary to the frequencies of two torsional modes of the thermal-generator shaft (30.6 and 20.4 Hz). The generation of these harmonics is closely related to the control system of PMSG. 3 Study system modelling This paper mainly studies the mechanism of oscillation generation, which corresponds to the first stage of SSO process described in Section 2. When oscillation is occurring, the multiple frequency components were not detected in the LCC-HVDC line that the LCC-HVDC was not participating in the SSO formation process [27]. Oscillation modes dominated by shafting mechanical parts of PMSG and the machine-side converter (MSC) are isolated from GSC by back-to-back converters, so they do not involve in the following discussion [26-29]. Fig. 2 shows a typical system model of PMSG integration. Assume that the transmission network operates in three-phase symmetry state, so the influence of the zero-sequence component on the circuit can be neglected. Fig. 2Open in figure viewerPowerPoint Typical block diagram of PMSG 3.1 Control system of GSC Fig. 3a shows the control system of GSC. The dynamic process of the voltage outer loop of the control system can be ignored, for it has a larger time constant than the inner current control loop [15, 29]. The mathematical equation of small-signal model of the control system can be obtained from Fig. 3a, which can be expressed in matrix form as (1) Fig. 3Open in figure viewerPowerPoint Control system (a) Control block diagram of GSC, (b) Control block diagram of PLL In the above equations, Gαβ(s) denotes the transfer function of the control system on the αβ-axis. 3.2 PLL and small-signal model Fig. 3b shows the typical structure of PLL. The proportional–integral-based PLL is given by (2) θc is chosen as θc = −uq/Ut0, where Ut0 is amplitude of grid-side voltage in a steady state. Ut0 = Ud0 = 1 can be approximately obtained under the control model in Fig. 3a, by adopting voltage-oriented control strategy in GSC. So θ can be linearised as (3) Taking the linearisation of (1) into (4), yields (4) The relationship between dq reference frame and αβ reference frame is shown in Fig. 4, and the conversion relationship of the electrical quantities between two reference frames is (5) Fig. 4Open in figure viewerPowerPoint Spatial relation between the dq-axis and the αβ-axis By considering (1) and (5), under the small disturbance, the equation of control system in the dq-axis is (6) where Gdq(s) = TGαβ(s)T−1. Equation (6) represents the dynamic characteristics of small disturbance of PMSG to the grid-side harmonics under the combined action of the PLL and the current control loop. 4 Formation process and criterion of PMSGs based SSO 4.1 Response characteristics of PMSG to the sub-synchronous frequency components Suppose that a disturbance current is introduced from the PCC node to the PMSG, which is a three-phase symmetrical sine wave with an amplitude of δ and a frequency of ωs. In the following derivation, it is found that the initial phase of the disturbance current does not affect the reaction of the control system so that the initial phase of the disturbance current can be assumed to be zero without loss of generality. A-phase current is (7) Ignoring the resistance of the network, the A-phase voltage fluctuation caused by (7) is (8) After the disturbance is introduced into GSC, the voltage and current fluctuations will be induced in DC link. Disturbance in DC side will be further introduced into the MSC. However, since converters on both sides are isolated by back-to-back structure, only necessary to analyse the dynamic process of GSC. Transforms (7) and (8) in the dq-axis are (9) (10) As shown in Appendix 2 of Section 10, substituting Δuq in (10) into (4) can get Δθ as (11) Bring (11) and (9) into (6), as shown in Appendix 3 of Section 11, the reference voltages in the dq frame are (12) Transform (12) into three coordinate system as (13) Values of K1, K2, γ1 and γ2 are shown in Appendix 4 of Section 12. 4.2 Amplification effect of control loop to harmonics The ωs component and the original perturbation will stack at the outlet of PMSG. When the phase angle difference between two sine waves with same frequency has the relationship as shown in Fig. 5, the positive feedback will generate amplification effect between harmonics and cause sustained power oscillation. Fig. 5Open in figure viewerPowerPoint Schematic diagram of positive feedback between harmonics The phase angle between Δua and Δuas is given by (14) Substituting (14) into (15), the criterion of instability can be expressed as (15) If the value of Q is positive at a certain frequency, the system SSO will occur by amplification effect. When oscillation is occurring, (13) will be the new disturbance input of PMSG. According to the procedure of (8)–(14), by iterative calculation the voltage at the outlet of PMSG can be expressed as (16) That is, when oscillation occurs, in addition to the oscillatory component, components with a frequency of k(ω0–ωs) ± ω0 are also generated in the outlet of PMSG. 5 Simulation validation and influencing factors of SSO 5.1 Analysis based on criterion Q and simulation verification On the basis of as shown in Fig. 2, using the control system shown in Fig. 3, parameters shown in Table 1, a simulation is built in MATLAB/Simulink. Fig. 6 shows the curve of Q changing with frequency according to (15). As shown in Fig. 6, two peaks appear at the frequencies 29.6 and 70.4 Hz, where the values of Q are both positive, which corresponds to the oscillation frequency. According to (16), besides 29.6/70.4 Hz harmonics are produced, harmonics of other frequencies also exist. The frequencies of those harmonic components in the spectrum analysis window (0−100 Hz) are 9.2, 19.4, 29.6, 39.8, 60.2, 70.4, 80.6 and 90. 8 Hz [k(50−29.6) ± 50 Hz]. Table 1. Parameters of system Symbol Value Sb, MVA 6 × 1.5 Vt, V 575 Udc_ref, V 1175 Lg, mH 0.8 L, mH 1 C, mF 1.2 Kpp 50 Kip 15,000 Kpi 20 Kii 40 Kpdc 5 Kidc 20 Fig. 6Open in figure viewerPowerPoint Curve of Q varying with frequency Fig. 7a displays the waveforms of active and reactive powers at the outlet of PMSG, and the spectrum analysis result of AB-inter-phase voltage is shown in Fig. 7b. To facilitate observation, 50 Hz component is filtered out in the spectrum analysis result. As shown in Fig. 7b, the frequencies of 29.6 and 70.4 Hz with the largest amplitude are distributed symmetrically. Other obvious components are basically consistent with the theoretical result above. Fig. 7Open in figure viewerPowerPoint Simulation result (a) Power oscillation waveform, (b) Spectrum analysis of voltage in PMSG outlet The theoretical result can also be verified by the compare with field measured data as shown in Fig. 1b. Note that the harmonics near 80 Hz in Fig. 1b are non-stationary signals caused by other reasons which only maintained for few seconds. Moreover, some filter devices for low-frequency oscillation were installed, due to the grid of Xinjinag area and a grid of Henan are connected asynchronously, so 9.2 Hz component does not appear. The distributions of frequencies and amplitudes of other harmonics in Fig. 7b are essentially consistent with Fig. 2b. 5.2 Impact of controller parameters on the SSO The above results showed that GSC controller and PLL are associated with SSO characteristic closely. To reduce the risk of SSO by adjusting the controller parameters, it is necessary to analyse the influence of the controller parameters on the oscillation characteristics. Moreover, the corresponding simulation results can further prove the theory. 5.2.1 Impact of PLL's controller parameters Fig. 8 shows the influence of PLL proportional gain Kpp on the SSO characteristics of PMSG. As shown in Fig. 8, with the decrease of Kpp, the amplitudes of the peaks of criterion Q decreases so as the amplitude of each harmonic component of spectrum analysis. Therefore, the intensity of SSO also reduces. Fig. 8Open in figure viewerPowerPoint Q varying with frequency and the spectrum analysis results under different Kpp (a) Kpp = 50, (b) Kpp = 5, (c) Kpp = 1 Fig. 9 shows the influence of PLL integral gain Kip on the SSO characteristics of PMSG. As shown in Fig. 9, with the decrease of Kip, the frequencies of the two peaks of criterion Q are closer to the power frequency and the amplitudes of each harmonic component decrease slightly in spectrum analysis. Fig. 9Open in figure viewerPowerPoint Q varying with frequency and the spectrum analysis results under different Kip (a) Kip = 50, (b) Kip = 5, (c) Kip = 1 5.2.2 Impact of GSC's controller parameters Fig. 10 shows the influence of current inner loop proportional gain Kpi on the SSO characteristics of PMSG. As shown in Fig. 10, with the decrease of Kpi, the whole value of criterion Q increases, so the intensity of SSO increases. Fig. 10Open in figure viewerPowerPoint Q varying with frequency and the spectrum analysis results under different Kpi (a) Kpi = 20, (b) Kpi = 2, (c) Kpi = 0.2 In addition, changing the current inner loop integral gain Kii, almost have no impact on the characteristics of the SSO. 6 Conclusion To investigate the emerging SSO issue occurred in Xinjiang, China, this paper studies the mechanism of SSO by analysing small-signal dynamic characteristic of GSC. The results show that the amplification effect of GSC controller and PLL to harmonics may lead the system to sustained oscillation. A criterion (Q) for evaluating the existence of SSO is obtained, according to analytic expression between the input and output signals' phase relation. Time-domain simulation and field data collected from an actual SSO incident are used to examine this mechanism and discuss impact of controller parameters on the SSO characteristics. The analysis process is based on the transfer function of the control system, so the method of this paper can be applied in WTGs with different structures. Research indicates that: (i) when Q > 0 under a certain frequency ωs, the oscillation will occur at this frequency by the amplification effect. (ii) Besides ωs and (2ω0−ωs) components corresponding to the oscillation frequencies with peak amplitude, k(ωs−ω0) ± ω0 components are generated together when oscillating. (iii) The proportional gain of PLL (Kpp), integrator gain of PLL (Kip) and inner loop proportional gain of GSC (Kpi) have considerable influence on the characteristics of SSO. With the decrease of Kpp, the amplitude of harmonics and intensity of SSO decreases. The work in this paper provides a theoretical basis for the future engineering application. 7 Acknowledgments This work was supported by the National Natural Science Foundation of China (NSFC) under Grant no. 51677066 and the Fundamental Research Funds for the Central Universities under Grant nos. 2018MS007 and 2018ZD01. 9 Appendix 1 Basic mathematical formulas used in later calculations 10 Appendix 2 Suppose that: Substituting Δuq in (10) into (4), we have (17) Solving the above equation can get 11 Appendix 3 (18) where 12 Appendix 4 (19) Solving (19), we have 8 References 1Mitra, A., Chatterjee, D.: 'Active power control of DFIG-based wind farm for improvement of transient stability of power systems', IEEE Trans. Power Syst., 2016, 31, (1), pp. 82– 93 2Zhang, Y., Xu, D.: ' Direct power control of doubly fed induction generator based on extended power theory under unbalanced grid condition'. IEEE Third Int. Future Energy Electronics Conf. ECCE Asia (IFEEC 2017 – ECCE Asia), Kaohsiung, 2017, pp. 992– 996 3Kuschke, M., Strunz, K.: 'Energy-efficient dynamic drive control for wind power conversion with PMSG: modeling and application of transfer function analysis', IEEE J. Emerg. Sel. Top. Circuits Syst., 2014, 2, (1), pp. 35– 46 4Wang, Y., Meng, J., Zhang, X., et al: 'Control of PMSG-based wind turbines for system inertial response and power oscillation damping', IEEE Trans. Sustain. Energy, 2015, 6, (2), pp. 565– 574 5Mishra, Y., Mishra, S., Li, F., et al: ' Small signal stability analysis of a DFIG based wind power system with tuned damping controller under super/sub-synchronous mode of operation'. IEEE Power & Energy Society General Meeting, Calgary, AB, 2009, pp. 1– 8 6Nath, R., Grande-Moran, C.: ' Study of sub-synchronous control interaction due to the interconnection of wind farms to a series compensated transmission system'. PES T&D 2012, Orlando, FL, 2012, pp. 1– 6 7Irwin, G.D., Isaacs, A., Woodford, D.: ' Simulation requirements for analysis and mitigation of SSCI phenomena in wind farms'. PES T&D 2012, Orlando, FL, 2012, pp. 1– 4 8Ghofrani, M., Arabali, A., Etezadi-Amoli, M.: ' Modeling and simulation of a DFIG-based wind-power system for stability analysis'. IEEE Power and Energy Society General Meeting, San Diego, CA, 2012, pp. 1– 8 9Badrzadeh, B., Sahni, M., Zhou, Y., et al: ' General methodology for analysis of sub-synchronous interaction in wind power plants'. IEEE Power & Energy Society General Meeting, Vancouver, BC, 2013, p. 1 10Suriyaarachchi, D.H.R., Annakkage, U.D., Karawita, C., et al: 'A procedure to study sub-synchronous interactions in wind integrated power systems', IEEE Trans. Power Syst., 2013, 28, (1), pp. 377– 384 11Mohammadpour, H.A., Shin, Y.J., Santi, E.: ' SSR analysis of a DFIG-based wind farm interfaced with a gate-controlled series capacitor'. IEEE Applied Power Electronics Conf. Exposition – APEC 2014, Fort Worth, TX, 2014, pp. 3110– 3117 12Mohammadpour, H.A., Santi, E.: ' Sub-synchronous resonance analysis in DFIG-based wind farms: definitions and problem identification – part I'. IEEE Energy Conversion Congress and Exposition (ECCE), Pittsburgh, PA, 2014, pp. 812– 819 13Wu, M., Xie, L., Cheng, L., et al: 'A study on the impact of wind farm spatial distribution on power system sub-synchronous oscillations', IEEE Trans. Power Syst., 2016, 31, (3), pp. 2154– 2162 14Leon, A.E., Solsona, J.A.: 'Sub-synchronous interaction damping control for DFIG wind turbines', IEEE Trans. Power Syst., 2015, 30, (1), pp. 419– 428 15Hu, J., Wang, B., Wang, W., et al: 'Small signal dynamics of DFIG-based wind turbines during riding through symmetrical faults in weak AC grid', IEEE Trans. Energy Convers., 2017, 32, (2), pp. 720– 730 16Alawasa, K.M., Mohamed, Y.A.R.I., Xu, W.: 'Active mitigation of subsynchronous interactions between PWM voltage-source converters and power networks', IEEE Trans. Power Electron., 2014, 29, (1), pp. 121– 134 17Alawasa, K.M., Mohamed, Y.A.R.I., Xu, W.: ' New approach to damp subsynchronous resonance by reshaping the output impedance of voltage-sourced converters'. IEEE Power & Energy Society General Meeting, Vancouver, BC, 2013, pp. 1– 5 18Joseph, T., Ugalde-Loo, C.E., Liang, J.: ' Subsynchronous oscillatory stability analysis of an AC/DC transmission system'. IEEE Eindhoven PowerTech, Eindhoven, 2015, pp. 1– 6 19Liu, Z., Liu, J., Bao, W., et al: 'Infinity-norm of impedance-based stability criterion for three-phase AC distributed power systems with constant power loads', IEEE Trans. Power Electron., 2015, 30, (6), pp. 3030– 3043 20Wen, B., Boroyevich, D., Burgos, R., et al: 'Analysis of D–Q small-signal impedance of grid-tied inverters', IEEE Trans. Power Electron., 2016, 31, (1), pp. 675– 687 21Wang, X., Blaabjerg, F., Liserre, M., et al: 'An active damper for stabilizing power-electronics-based AC systems', IEEE Trans. Power Electron., 2014, 29, (7), pp. 3318– 3329 22Alawasa, K.M., Mohamed, Y.A.R.I., Xu, W.: 'Modeling, analysis, and suppression of the impact of full-scale wind-power converters on subsynchronous damping', IEEE J. Syst., 2013, 7, (4), pp. 700– 712 23Hsu, P., Muljadi, E.: ' Damping control for permanent magnet synchronous generators and its application in a multi-turbine system'. Australasian Universities Power Engineering Conf. (AUPEC), Perth, WA, 2014, pp. 1– 6 24Larsen, E.V.: ' Wind generators and series-compensated AC transmission lines'. IEEE Power and Energy Society General Meeting, San Diego, CA, 2012, pp. 1– 4 25Ma, H.T., Brogan, P.B., Jensen, K.H., et al: ' Sub-synchronous control interaction studies between full-converter wind turbines and series-compensated AC transmission lines'. IEEE Power and Energy Society General Meeting, San Diego, CA, 2012, pp. 1– 5 26Xiao, X., Luo, C., Zhang, J., et al: 'Analysis of frequently over-threshold subsynchronous oscillation and its suppression by subsynchronous oscillation dynamic suppressor', IET Gener., Transm. Distrib., 2016, 10, (9), pp. 2127– 2137 27Liu, H., Xie, X., He, J., et al: 'Subsynchronous interaction between direct-drive PMSG based wind farms and weak AC networks', IEEE Trans. Power Syst., 2017, 32, (6), pp. 4708– 4720 28Feng, G., Qifei, H., Zhiguo, H., et al: ' The research of sub-synchronous oscillation in PMSG wind farm'. IEEE PES Asia-Pacific Power and Energy Engineering Conf. (APPEEC), Xi'an, 2016, pp. 1883– 1887 29Bi, T., Li, J., Zhang, P., et al: 'Study on response characteristics of grid-side converter controller of PMSG to sub-synchronous frequency component', IET Renew. Power Gener., 2017, 11, (7), pp. 966– 972 Citing Literature Volume12, Issue7May 2018Pages 844-850 FiguresReferencesRelatedInformation
Referência(s)