Sub‐synchronous oscillation analysis of complicated power grid incorporating wind farms with different types
2017; Institution of Engineering and Technology; Volume: 2017; Issue: 13 Linguagem: Inglês
10.1049/joe.2017.0637
ISSN2051-3305
AutoresFan Yang, Libao Shi, Yixin Ni,
Tópico(s)Microgrid Control and Optimization
ResumoThe Journal of EngineeringVolume 2017, Issue 13 p. 1777-1782 ArticleOpen Access Sub-synchronous oscillation analysis of complicated power grid incorporating wind farms with different types Fan Yang, Fan Yang National Key Laboratory of Power Systems in Shenzhen, Graduate School at Shenzhen, Tsinghua University, Shenzhen, People's Republic of ChinaSearch for more papers by this authorLibao Shi, Corresponding Author Libao Shi shilb@sz.tsinghua.edu.cn National Key Laboratory of Power Systems in Shenzhen, Graduate School at Shenzhen, Tsinghua University, Shenzhen, People's Republic of ChinaSearch for more papers by this authorYixin Ni, Yixin Ni National Key Laboratory of Power Systems in Shenzhen, Graduate School at Shenzhen, Tsinghua University, Shenzhen, People's Republic of ChinaSearch for more papers by this author Fan Yang, Fan Yang National Key Laboratory of Power Systems in Shenzhen, Graduate School at Shenzhen, Tsinghua University, Shenzhen, People's Republic of ChinaSearch for more papers by this authorLibao Shi, Corresponding Author Libao Shi shilb@sz.tsinghua.edu.cn National Key Laboratory of Power Systems in Shenzhen, Graduate School at Shenzhen, Tsinghua University, Shenzhen, People's Republic of ChinaSearch for more papers by this authorYixin Ni, Yixin Ni National Key Laboratory of Power Systems in Shenzhen, Graduate School at Shenzhen, Tsinghua University, Shenzhen, People's Republic of ChinaSearch for more papers by this author First published: 12 December 2017 https://doi.org/10.1049/joe.2017.0637Citations: 5AboutSectionsPDF 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 A complicated test system with integration of doubly-fed induction generator (DFIG)-based and permanent magnet synchronous generator (PMSG)-based wind farms is built up in this study to explore and exploit the interactions between DFIG unit and PMSG unit on the issue of sub-synchronous oscillation (SSO). With detailed modelling of wind farm units, transmission lines and loads, the SSO modes are elaborately analysed through eigenvalue analysis and participation factor methods. The level and position of series compensated lines are discussed leading to some useful comments and suggestions. Besides, the power outputs of the two wind farm types are compared to investigate their potential influences on the oscillation, and the most influential proportional–integral parameters producing the potential risks of oscillation are chosen out. 1 Introduction With the increasing demand of energy and severe deterioration of environment, the development of renewable energy resources has been set great expectations to alleviate the current disparities, which inevitably leads to the stability troubles of power systems, such as sub-synchronous oscillation (SSO) problems. The first observed SSO issue related to wind farms is in 1993, which is even more complex and frequent in these years, such as the wind farm accident of large scale off-net occurred in the north China in 2012 and the sub-synchronous power oscillation spread to thermal power units in western China in 2015. Therefore, more and more researchers have made great efforts on the settlement of this issue. It is discussed in [1] about sub-synchronous phenomena as related to wind turbine generators in the vicinity of series compensated transmission systems, meanwhile, some basic methods and options are also discussed. Bengtsson et al. [2] offers a summary of the sub-synchronous control interaction (SSCI) phenomenon, then simulations of type 3 wind turbine model in PSCAD/EMTDC provide some recommendations for power system development. Besides, a SSCI damping controller is also designed to help mitigate the problem. As presented in [3], a time-invariant model of the doubly-fed induction generator (DFIG) unit is linearised to observe all sub-synchronous modes, which also points out the control parameters to which the sub-synchronous modes are highly sensitive. Shi et al. [4] discusses a complicated thermal power system with a wind farm integration. Besides, the torsional vibration modes and the transmission lines relative modes are analysed to study the potential risk of SSO. Leon [5] builds up an actual test system derived from Argentinian power system, in which multiple DFIG type wind farms are connected, and a type of supplementary damping control is designed to enhance the operating range. Actually, the cutting edge research achievements in this aspect are mostly related to single wind farm type, or even single wind farm, regardless of interactions among various types of wind farms. It is imperative to make deeper and more comprehensive studies on SSO issue of complicated power system incorporating multiple wind farms with different types. In this paper, a complicated test system with multiple wind farms of permanent magnet synchronous generator (PMSG) and DFIG types is constructed. Based on the eigenvalue analysis, the influences of wind farm types, positions and interactions between wind farms pertinent to SSO problem are investigated. Besides, the role of series compensated lines playing in SSO is also discussed. Some interesting conclusions are drawn. 2 System modelling In this paper, the test system consists of one DFIG-type wind farm and one PMSG-type wind farm combining with nine transmission lines. 2.1 Test system The test system is built up as follows. From Fig. 1, it can be seen that the output of bus2 is contributed by DFIG-type wind farm, while the output of bus3 is injected by PMSG-type wind farm. Also, the series compensated capacitors can be constructed in any of nine transmission lines. Fig. 1Open in figure viewerPowerPoint Single diagram of test system incorporating DFIG-based and PMSG-based wind farms 2.2 Modelling of wind farms and shaft system In this paper, both types of wind farms are operating under rated wind speed, and for simplicity, the DFIG-type wind farm can be regarded as a cluster of multiple 2 MW DFIG units, while the PMSG-type wind farm is equivalent to a macro-wind turbine generator consisting of multiple 1.5 MW PMSG units. In our work, the two-mass mechanical model is adopted to describe the shaft system of both types of wind farms involving wind turbines and generator blocks. 2.3 Modelling of DFIG unit The detailed modelling of DFIG unit is expressed in Fig. 2 which can be covered as five parts varying from wind turbine shaft system, asynchronous generator, rotor-side converter (RSC), DC link and grid-side converter (GSC). For the control of RSC, the stator voltage oriented control (SVOC) strategy is applied. In this condition, the direction of stator voltage is fixed to the d -axis of synchronous coordinate system, then vd s = v s and vq s = 0. Meanwhile, in order to keep GSC working at unit power factor, the given reactive power of GSC is set to be 0, whose detailed modelling can be given as follows: (1) (2) where is state vector, is input vector, is input vector of voltage of DFIG unit and the DFIG unit is connected to bus k. Fig. 2Open in figure viewerPowerPoint Modelling of DFIG unit 2.4 Modelling of PMSG unit The modelling of PMSG unit can be sorted as five parts consisting of wind turbine shaft system, synchronous generator, generator-side converter (GESC), DC link and GSC. Among them, the SVOC control strategy is applied in GESC, and the GSC side adopts the grid voltage-oriented control (GVOC) strategy to keep the voltage stable. The corresponding system structure is shown in Fig. 3. Fig. 3Open in figure viewerPowerPoint Modelling of PMSG unit The detailed derivation can be formed as (3) (4) where is state vector, is input vector, is input vector of voltage of PMSG unit and the PMSG unit is connected to bus k. 2.5 Modelling of parallel bus As the parallel bus combines with several transmission lines, whose parallel capacitors can be centralised to the parallel bus, in this way, the state equation can be listed as (5) where is the voltage state vector of parallel bus j, is the current increment of parallel bus j. 2.6 Modelling of transmission lines and load In this paper, the transmission lines can be divided into two types which are series compensated lines and normal lines, whose modelling are given as (6) where is the state vector of transmission line I (connected by parallel bus j and f). Also the state vectors differ in the two types of lines. Besides, the load in this paper adopts the constant impedance model whose state equation can be listed as (set load j connected to parallel bus k as an example) below: (7) where is the state vector of load j, is the relative vector of parallel bus k. 3 Eigenvalue analysis for solution of SSO After the modelling of system, all equations can be ranked, and the elimination of input vector such as the load current and the parallel bus current can be achieved through Kirchhoff's current law, in this way, the final state equations SA can be obtained. Among them, the relative state vectors of DFIG unit are The relative state vectors of PMSG unit are As for transmission line, if the constructed lines are with series compensated capacitors, the state vectors can be formed in four-dimension as given in the following: while the normal lines only consist of two-dimension state vectors which are expressed as . Meanwhile, the state vectors of inductive load I are the magnitudes of currents as , and which of capacitive load I are . In this paper, one DFIG unit, one PMSG unit, three parallel buses, seven transmission lines and six loads combine a 62-dimension state matrix (if not taking series compensated lines into consideration). 4 Case study 4.1 Basic analysis In this section, the SSO modes are calculated and given in Table 1 (series compensated level of line 1 is set to be 0.1). Table 1. Sub-synchronous modes Mode Eigenvalue Frequency Damping ratio Real Imaginary mode 1 −0.0013 0.0093 0.5564 0.1389 mode 2 −0.0014 0.0163 0.9775 0.0857 mode 3 −1.3734 0.0667 4.0004 0.9988 mode 4 −3.2767 0.2412 14.4735 0.9973 mode 5 −0.0911 0.3808 22.8495 0.2325 mode 6 −4.7326 0.8731 52.3879 0.9834 mode 7 −0.0135 0.8901 53.4063 0.0151 mode 8 −0.1739 0.9999 59.9983 0.1713 From Table 1, the mode 1 is the torsional vibration mode of PMSG unit, while the mode 2 is which of DFIG unit, whose participation factors are given in Fig. 4. Fig. 4Open in figure viewerPowerPoint Participation factors of mode 1 and mode 2 From Fig. 4, the conditions of both mode 1 and mode 2 are determined by the design of shaft system, which are hardly influenced by other factors. Also, the existing researches have pointed out that the risk of this oscillation shows lower danger for the stiffness of wind turbine shaft, which will not be discussed in detail in this paper. Mode 5 is mostly influenced by the PMSG unit, whose participation factors are given in Fig. 5. Fig. 5Open in figure viewerPowerPoint Participation factors of mode 5 It can be found from Fig. 5 that the most powerful participation factors are Δv dc and Δx 5 . Modes 3, 4, 6, 7 are mainly influenced by the DFIG unit and power grid, whose participation factors are shown in Fig. 6. Fig. 6Open in figure viewerPowerPoint Participation factors of modes 3, 4, 6 and 7 a Related to DFIG units b Distribution of all factors From Fig. 6 a, Δid s, Δid r should be paid great attentions when exploring the DFIG relative modes, especially, mode 3 also shows greater influenced by Δx 1 and Δx 4 while the participation factors of Δiq s, Δiq r in mode 7 are also over 0.1. From the influenced modes, it can be inferred that the DFIG unit plays a stronger role in the SSO than PMSG unit due to the reason of decoupling of PMSG unit from power grid. Besides, mode 4 will disappear in some typical series compensated lines, and the detailed simulation results will be discussed in the following sections. 4.2 Series compensated lines In this part, each transmission line will be constructed with series compensated capacitors successively where the series compensated level is set varying from 0.1 to 0.95. The change of frequency and damping ratio of PMSG relative to mode 5 are given in Fig. 7. Fig. 7Open in figure viewerPowerPoint Frequency and damping ratio changes of mode 5 a Frequency b Damping ratio Apart from line 5 and line 9, the frequency experiences a slight increase in compensating other lines, and the damping ratio of mode 3 increases about 0.3 when increasing the series compensated level of line 3, similar condition happens to line 2, combining with the topology of system, line 3 and line 2 are the paths of PMSG unit to infinite bus. Besides, the distributions of main participation factors show little change to the series compensated level change. Then regarding modes 3, 4, 6 and 7 relevant to DFIG unit, it can be seen that the mode 7 shows more sensitive to the change of series compensated level, whose frequency and damping ratio changes are shown in Fig. 8. Fig. 8Open in figure viewerPowerPoint Frequency and damping ratio change of mode 7 a Frequency b Damping ratio It can be discovered that only the series compensated capacitors set in line 1 decreases the oscillation frequency while other lines lead to the opposite phenomenon. As for the damping ratio, when series compensated capacitors are set near the infinite bus (as line 1) and connective lines (as line 5 and line 9), the damping ratio increases with the increase of series compensated level, comparing to the decrease of other lines, it is a better choice to set the series compensated capacitor near the infinite bus and connective lines. Moreover, the construction of other series compensated lines will lead to the damping ratio decrease to negative which denotes the instability of SSO modes. 4.3 Output of units In this part, the outputs of the two units will be changed to observe the influences of SSO modes. In this way, the series compensated capacitor is set in line 1 as 0.1. First, changing the output of PMSG unit from 0.1 to 1.0, the damping ratio and frequency changes of mode 5 are given in Fig. 9. Fig. 9Open in figure viewerPowerPoint Frequency, damping ratio and participation factor changes of PMSG relative modes a Frequency b Damping ratio c Participation factor change of mode 5 d Participation factor change of new mode It can be discovered that at a smaller output of PMSG unit, a new mode which is influenced by Δiq s, Δx 1, Δx 2, Δx 3, Δx 4 appears, with the continuing increase of output of PMSG unit, and its frequency drops with a damping ratio increase and finally disappears after the PMSG output is over 0.4. As for mode 5, it has a concave decrease of damping ratio. In this way, it can be concluded that the output of PMSG unit should be set at a suitable range. The changes of DFIG relative modes are given in Fig. 10. Fig. 10Open in figure viewerPowerPoint Frequency and damping ratio change of DFIG relative modes a Frequency b Damping ratio Apparently, these modes are not so much influenced by the change of PMSG output. Also, it is worth mentioning that the mode 4 only appears when the PMSG output is over 0.4, and the mode 7 has a slight decrease, for the sake of security, the output of PMSG should be suit causally. Then changing the output of DFIG unit from 0.2 to 2.0, the changes of PMSG relative mode 5 are shown in Fig. 11. Fig. 11Open in figure viewerPowerPoint Frequency, damping ratio and participation factors change of PMSG relative mode a Frequency and damping ratio change b Participation factor change It can be found that the frequency of mode 5 experiences a slight decrease with the increase of DFIG unit output, and the damping ratio has an increase, which denotes a better stability. It is remarkable that the participation factors Δv dc and Δx 5 of mode 5 are faced with a slight decrease with the increase of DFIG unit output. As for DFIG relative modes, the corresponding simulation results are shown in Fig. 12. Fig. 12Open in figure viewerPowerPoint Frequency and damping ratio change of DFIG relative modes a Frequency b Damping ratio c Change of mode 7 It can be seen that the damping ratios of all modes increase to some extent with increase of DFIG unit output, in this way, the output of DFIG unit should be chosen at a suitable range. Besides, some modes only appear at some special range of output, although the damping ratios of them are over 0.9. Similar to the PMSG output change condition, the modes 5 shows poor reaction to the output change of DFIG unit. 4.4 Proportional–integral (PI) parameters In this part, the PI parameters of units are changed to observe their influences of the unit relative modes. First of all, changing the PI parameters of DFIG units from 0.9 times of its initial value to 1.3 times, the simulation results can be obtained from Fig. 13 (for consideration of stability, only damping ratio change is discussed). Fig. 13Open in figure viewerPowerPoint Damping ratio change of DFIG relative modes a Mode 7 b Mode 6 c Mode 3 d Mode 4 It can be discovered that the kp 3 play a more important role in mode 7, and similar condition happens to mode 6. As mode 7 is under weak damping condition, the selection of kp 3 of DFIG unit should be taken great care. Besides, the rest modes may disappear at sometimes under strong damping condition, and the damping ratio of mode 5 changes little. It is also verified that the PMSG relative modes show poor relativity to DFIG parameters. Then changing the PI parameters of PMSG unit from 0.9 times to 1.3 times, the PMSG relative modes are shown in Fig. 14. Fig. 14Open in figure viewerPowerPoint Damping ratio change of PMSG relative mode In this way, the kp 5 plays a more special role in the change of damping ratio of mode 5, and the more the kp 5 increases, the stronger damping ratio of mode 5 is. Not surprisingly, the DFIG relative modes keep calm to the change of PI parameters. In this way, the kp 3 parameter of DFIG should be chosen carefully for the sub-synchronous stability. 5 Conclusion This paper builds up a test system with derivation of relative mathematical model, in this way interaction of PMSG-type wind farm and DFIG-type wind farm to the SSO problem can be discussed through eigenvalue analysis methods [6]. It can be discovered that the interaction of PMSG-type wind farm and DFIG-type wind farm is not so strong as which of two DFIG-type wind farms, as DFIG (PMSG) relative modes are not so sensitive to the change of PMSG (DFIG) wind farm. Besides, position and level of series compensated capacitor can strongly influence the SSO of system which should be carefully determined. 6 Acknowledgment This work was supported in part by the National Natural Science Foundation of China (51777103). 8 Appendix Some basic parameters applied in the test system can be found in Tables 2 and 3. Table 2. Parameters of DFIG unit Shaft system H t, s 4.29 H g, s 0.9 K tg, p.u. 0.15 D tg, p.u. 1.5 D t, p.u. 0.1 D g, p.u. 0.1 Impedance parameters X m, p.u. 3.95279 X s, p.u. 0.09231 X gG, p.u. 0.3 R gG, p.u. 0 R s, p.u. 0.00488 R r, p.u. 0.00549 PI parameters Kp 1 9.2299 Ki 1 11.9062 Kp 2 2.5874 Ki 2 21.4573 Kp 3 3.2611 Ki 3 0.1170 Kp 4 9.4446 Ki 4 12.9021 Kp 5 14.5211 Ki 5 26.0787 Table 3. Parameters of PMSG unit Shaft system H t, s 2.52 H g, s 0.45 K tg, p.u. 0.0726 D tg, p.u. 1.5 D t, p.u. 0 D g, p.u. 0 Impedance parameters Xd, p.u. 0.7 Xq, p.u. 1.11 X gG, p.u. 0.0002 R gG, p.u. 0 R s, p.u. 0.017 PI parameters Kp 1 0.0278 Ki 1 0.4160 Kp 2 4.5753 Ki 2 6.2860 Kp 3 3.1806 Ki 3 3.8099 Kp 4 6.2022 Ki 4 4.1891 Kp 5 4.9016 Ki 5 5.7479 Kp 6 6.2298 Ki 6 0.2330 Kp 7 1.3037 Ki 7 0.6136 7 References 1Irwin G.D., Jindal A.K., Isaacs A.L.: 'Sub-synchronous control interactions between type 3 wind turbines and series compensated AC transmission systems'. Power and Energy Society General Meeting, 2011, pp. 1 – 6 2Bengtsson T., Roxenborg S., Saha M.M. et al.: 'Case studies and experiences with sub-synchronous resonance (SSR) detection technique'. Power Systems Computation Conf. (PSCC), 2016, pp. 1 – 6 3Ali M.T., Ghandhari M., Harnefors L.: 'Effect of control parameters on infliction of sub-synchronous control interaction in DFIGs'. IEEE Int. Conf. Power and Renewable Energy (ICPRE), 2016, pp. 72 – 78 4Shi L., Su J., Yao L.: 'Sub-synchronous resonance analysis of complex power system incorporating wind power', IET Renew. Power Gener., 2016, 11, (3), pp. 305 – 312 (doi: https://doi.org/10.1049/iet-rpg.2016.0289) 5Leon A.E.: 'Integration of DFIG-based wind farms into series-compensated transmission systems', IEEE Trans. Sustain. Energy, 2016, 7, (2), pp. 451 – 460 (doi: https://doi.org/10.1109/TSTE.2015.2498312) 6Yang F., Shi L.: 'Sub-synchronous oscillation analysis of transmission system with multiple wind farms'. IEEE PES General Meeting, 2017 Citing Literature Volume2017, Issue132017Pages 1777-1782 FiguresReferencesRelatedInformation
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