Combined Application of SEDC and GTSDC for SSR ... - IEEE Xplore

IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 31, NO. 1, JANUARY 2016

769

Combined Application of SEDC and GTSDC for SSR Mitigation and Its Field Tests Xiaorong Xie, Senior Member, IEEE, Liang Wang, and Yingduo Han, Senior Member, IEEE

Abstract—The subsynchronous resonance (SSR) problem may become more serious with the continuous evolvement of a series-compensated power system. Consequently, the existing SSR mitigation scheme might no longer keep the system stable. This issue has been encountered by Shangdu Power Plant, where the deployed supplementary excitation damping controllers (SEDCs) that well stabilized the system before cannot maintain torsional stability after the recent change occurred in the power system. Therefore, a combined mitigation scheme of SEDC and generator terminal subsynchronous damping controller (GTSDC) is proposed in this paper to regain system stability. SEDC provides electrical damping by modulating the excitation voltage at the rotor side. Meanwhile, GTSDC can damp SSR via injecting super-synchronous and subsynchronous currents into the generator stator. Field tests have proven the effectiveness of this combined scheme in addressing the deteriorated SSR issue. Eigenvalue analysis indicates that the combined scheme can provide enough positive damping for the system under any operating condition. Thanks to the low investment of SEDC and the flexibility of GTSDC, this combined scheme provides an economical and scalable solution for SSR mitigation, especially when the target system changes constantly. Index Terms—Field test, fixed series capacitor (FSC), generator terminal subsynchronous damping controller (GTSDC), subsynchronous resonance (SSR), supplementary excitation damping controller (SEDC).

I. INTRODUCTION

S

INCE the first report of shaft failure due to subsynchronous resonance (SSR) at Mohave Power Plant in Arizona, USA, in the early 1970s [1], various countermeasures have been proposed [2]. Many of them had been put into practical use, such as blocking filters at Navajo [3] and Tuoketuo [4], supplementary excitation damping controllers (SEDC) at Navajo [3] and Shangdu [5], dynamic stabilizer at San Juan [6], NGH SSR damper at Lugo [7], and thyristor controlled series capacitor at Slatt [8]. It is well recognized that, if there is a potential risk of SSR in a practical system, a comprehensive technological and Manuscript received October 18, 2014; revised December 14, 2014; accepted January 14, 2015. Date of publication February 05, 2015; date of current version December 18, 2015. This work was supported in part by the National Natural Science Foundation of China under Grant 51322701. Paper no. TPWRS-014402014. X. Xie and Y. Han are with the State Key Laboratory of Power System, Department of Electrical Engineering, Tsinghua University, Beijing 100084, China (e-mail: [email protected]; [email protected]). L. Wang is with the School of Automation, Beijing Institute of Technology, Beijing, 100081, China (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TPWRS.2015.2393892

economical comparison should be conducted to find a solution with good balance between damping effect and investment cost to address the problem. With the development of society, power systems need change to meet the steadily increasing load. This condition could hardly be taken into full consideration in advance during the design of the initial SSR countermeasure. Therefore, if the topology and/or parameters of a power system with fixed series capacitors (FSCs) is undergoing major change, the characteristics of a countermeasure to SSR should be re-evaluated. Nowadays, power systems change fast in China due to the rapid increase of load. Many new generators and transmission corridors are being constructed. Once the torsional stability is worsened, in particular, if the existing SSR countermeasures cannot provide sufficient positive damping, additional countermeasures should be adopted. Preferably, the existing devices should be enclosed into the new solution to save cost and maximize the damping performance. The SSR problem and its SEDC-based solution of Shangdu Power Plant (SPP) have been well documented in [5]. In 2007, after the completion of its first- and second- phase construction projects, SPP had four 600-MW steam turbine-generators in service. It is connected to the North China Power Grid through 500-kV transmission lines, part of which is compensated by FSCs. To solve the SSR problem caused by FSC, a scheme using SEDC and torsional stress relay (TSR) was adopted after undergoing deep technological and economic analyses. Then, field tests were carried out in 2008 and 2009, verifying that SEDC and TSR can effectively address the SSR issue [5]. Hence, the corresponding control and protection devices as well as FSCs were put into commercial operation in 2009. However, at the end of 2011, two more generators were added to the plant and a new transmission corridor was put into operation. Then, the electrical tie between SPP and the main grid was strengthened, and the range of total equivalent compensation degree (TECD, defined as the percentage of the capacitance over the total line reactance) was increased. As a result, the SSR problem became more serious and the existing SEDCs can no longer reach the original objective even after their parameters are elaborately adjusted. A combined scheme with generator terminal subsynchronous damping controller (GTSDC) and SEDC is proposed to increase the system damping and to minimize project cost. As discussed in [5], SEDC could generate damping torque via the modulation of excitation voltage at rotor side. The recently added GTSDCs produce positive damping via generating complimentary super-synchronous and subsynchronous currents at the stator side. Both field tests and model analyses have verified the effectiveness of this combined scheme.

0885-8950 © 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

770


TABLE I TORSIONAL FREQUENCIES OF UNITS 5 AND 6

Fig. 1. Single-line diagram of the Shangdu series-compensated system.

The remainder of this paper is organized as follows. Section II describes the evolvement of the target system and its new SSR characteristics. Section III elaborates the combined control-scheme of SEDC and GTSDC. The applications of this control scheme and its field test results will be discussed in Section IV. The performances of this scheme under all possible operating conditions are further investigated through model analysis in Section V. Section VI draws the conclusions. II. EVOLVEMENT OF THE SERIES-COMPENSATED SYSTEM AND ITS SSR CHARACTERISTICS A. The Shangdu System and Its Evolvement SPP is located in the Inner Mongolia Autonomous Region, about 300 kilometers north of Beijing city. After the construction of its first- and second-phase projects, the plant had four 600-MW steam turbine-generators in service. They were connected to the North China Power Grid through double-circuit 500-kV transmission lines. The solid line in Fig. 1 illustrates the one-line diagram of the equivalent transmission system. To improve the transmission capability and system stability, FSCs are added to the lines between SPP and Chengde Substation. The compensation degree is 45%. SEDC and TSR were adopted to mitigate SSR caused by FSC and to protect the generator units. The effectiveness of this scheme had been proved by extensive analyses and field tests conducted in 2008 and 2009. Only when one Shangdu-Chengde line suffers three-phase short-circuit fault near the plant does TSR need to trip a generator to avoid shaft damage. Hence, the series capacitors as well as the corresponding control and protection devices were put into commercial operation in 2009 [5]. SEDC and TSR are characterized by low cost, small land occupation, and low operational power consumption. Reference [5] gives detailed information about this scheme. At the end of 2011, another two 660-MW generators, Nos. 5 and 6, were put into operation to meet the continuously increasing power load of North China. To transmit the increased electric power, a new 500-kV transmission corridor had been constructed and started operation at the end of 2012. The change of whole system is illustrated with dotted lines in Fig. 1. As a result, the electrical connection between SPP and the power grid was strengthened and TECD was increased. Higher TECD led to a further deterioration of the SSR problem. As discussed in [9], higher TECD tends to increase the critical gain and lower the effective gain of SEDC. As a result, the control ability of SEDC,

indicated by stabilizing ability index (SAI), decrease dramatically considering the fixed hard limit of the exciter. Under certain operating conditions or disturbances, SAI even becomes negative, which means that SEDCs can no longer stabilize SSR effectively under these situations [9]. B. SSR Characteristics The recently added two generators (Nos. 5 and 6) are almost the same. Their natural torsional frequencies are listed in Table I. They are higher than those of generator Nos. 1–4. In particular, for the most risky torsional mode 2, the frequencies of Nos. 5 and 6 are about 1.5 Hz higher than Nos. 1–4. All generators are equipped with SEDCs and TSRs. Eigenvalue analysis has been carried out on this changed system. Considering the combination of different generators, transmission lines and three typical loading conditions (i.e., 40%, 75%, and full load), there are 8316 different operating conditions. The analysis results are presented in Fig. 2. Taking time-domain simulation results into consideration as well, the characteristics of SSR in the changed Shangdu system can be summarized as follows. 1) Torsional frequencies of generator Nos. 1–4 are very close to each other. Hence, there is strong coupling among the same torsional modes of these generators. The situation is similar for Nos. 5 and 6. There are comparatively large frequency difference between Nos. 1–4 and Nos. 5–6. Hence, the coupling between these two groups is relatively weak. 2) Mode 1 is always stable under any conditions. However, there are negative or weak damping conditions for modes 2 and 3. In other words, multimodal SSR exists under some conditions. 3) Since the control ability of SEDC is limited by the capacity of the exciter, fault on the system would cause even worse SSR. Hence, the occurrence probability of unstable modes 2 and 3 is increased. This may result in more generators to be tripped by TSR, which would endanger the stability of the whole power system. 4) The system becomes vulnerable to SSR, especially for torsional mode 2, if only one series-compensated ShangduChengde line is in service. Therefore, special emphasis should be put on this situation in selecting and designing SSR mitigation devices. 5) With new generators and transmission lines, the number of operating condition increases dramatically, which makes system analysis and control much more complicated. If only one Shangdu-Chengde line is in service, mode 2 is the most unstable one among the three torsional modes under the following cases: Case 1) generator Nos. 1–4 are online; Case 2) generator Nos. 1–4 and No. 6 are online; Case 3) generator No. 1 and Nos. 3–6 are online.

XIE et al.: COMBINED APPLICATION OF SEDC AND GTSDC FOR SSR MITIGATION AND ITS FIELD TESTS

771

where

In the analysis, the output power of every generator is about 0.75 p.u. and the power factor is 0.98. Related eigenvalues are presented in Table II, which indicates that SEDC alone cannot stabilize mode 2 under these conditions.

is the nominal gain, is the filtered modal speed, is the amplitude of the unsaturated control signal, and is the hard upper limit of the SEDC output. Equation (2) indicates that is a nonlinear function of the feedback input, the nominal gain, and the hard limit. Noticeably, when the feedback signal is sufficiently large, usually caused by large disturbances such as short-circuit fault, the SEDC output will be clipped and will decrease from the nominal gain to a certain value with respect to the amplitude of the feedback input. The more intense the subsynchronous oscillation is, the smaller and SAI will be. In [9], we have explored the possibility of stabilizing the system by increasing the ceiling excitation voltage and found that it should be raised extremely high, several times the normal level, to damp the SSR under serious conditions. Obviously, this is impractical for actual excitation systems. To sum up, with the change of system topology, TECD increases under some conditions. Hence, the critical stability gain increases dramatically. But the effective gain decreases due to the limitation of ceiling excitation voltage and the increase of transient oscillation amplitude under certain conditions. would not be increased substantially even if a larger nominal gain is adopted. Therefore, the existing SEDC scheme can no longer solve the current SSR problem effectively.

C. Limitation of SEDC

III. THE COMBINED CONTROL SCHEME OF SEDC AND GTSDC

According to [9], the control ability of SEDC could be described by SAI, which is defined as the percentage margin of the effective gain relative to the critical stability gain as follows:

According to above discussion, some other supplementary control devices should be added to mitigate SSR effectively. A new power-electronic based damping scheme has been proposed in [10]. A prototype, named generator terminal subsynchronous damper (GTSSD), has already been developed using cascaded converter. GTSSD could mitigate SSR via injecting properly adjusted super-synchronous and subsynchronous currents into the generator stator. Some initial filed tests have been conducted to confirm its advantages in response speed, deployment flexibility, and land occupation [11]. This new device is renamed as GTSDC in the Shangdu project to keep in accordance with the name of SEDC. GTSDC and SEDC comprise an effective combined SSR damping scheme for SPP. The advantages of this combined scheme includes: 1) it takes advantages from both controllers and thus can stabilize SSR with joint damping efforts from both the rotor and stator sides and 2) SEDC could achieve certain damping ability with very low cost, and properly sized GTSDC could provide expected damping. Hence, this scheme provides a scalable SSR countermeasure with good balance between control performance and investment cost.

Fig. 2. Eigenvalues of shaft torsional modes of Shangdu system.

TABLE II EIGENVALUES OF THE CRITICAL MODE (MODE 2 OF GENERATOR NOS. 1–4)

(1) where the critical stability gain is the minimum gain of SEDC to guarantee SSR stability, while the effective gain is the effective or actually functioning gain of SEDC. If SAI is greater than zero, SEDC can stabilize SSR. Otherwise, SEDC cannot prevent the divergence of SSR. Obviously, the larger or the smaller , the greater the SAI, which results in stronger control ability of SEDC. is determined by a variety of factors. The dominant ones include TECD, parameters and loading levels of generator, time constant and voltage limit of the excitation system. For the Shangdu system, it is revealed in [9] that the increase of maximum TECD raises considerably. Taking case 1 as an example, increases from 190 to 525 after the system change. Therefore, SAI is decreased dramatically. For a specific oscillation mode, the effective gain can be expressed as the following piecewise function:

(2) and (3)

A. General Configuration Fig. 3 shows the combined scheme of SEDC and GTSDC. Both of them adopt shaft deviation speed as feedback signal. The control signal generated by SEDC is apply to the excitation winding, while GTSDC injects certain current into the stator windings of the generator. SEDC uses the real-time shaft speed deviation to generate modal control signals at the concerned torsional frequencies. Then, these signals are summarized, clipped and added to the

772


TABLE III EIGENVALUES OF THE CRITICAL MODE WHEN THE COMBINED SCHEME IS APPLIED

q-axis currents of the generator without GTSDC, and and are the d- and q-axis components of . Then, with some mathematical manipulations, the additional electromagnetic torque provided by SEDC and GTSDC can be expressed as

Fig. 3. Combined mitigation scheme of SEDC and GTSDC.

output of automatic voltage regulator (AVR) to modulate the field voltage. Consequently, the field voltage as well as the excitation current will have additional components at the concerned torsional frequencies, which, if properly controlled, can generate positive damping torque to suppress SSR. GTSDC is a power electronic based SSR damping controller. It consists of a multimodal complementary current calculator (MCCC) and a complementary current generator (CCG). MCCC uses the speed deviation as the input signal similarly as SEDC. Then, it calculates a current reference. CCG consists of a high power voltage sourced converter and a step-up transformer. It generates real current following the mentioned reference signal and injects the currents into the system. These currents consist of both super-synchronous and subsynchronous components complementary to the concerned torsional frequencies. Part of them flow into the stator of the generator and produce damping electromagnetic torque to mitigate the torsional oscillation. B. Theoretic Principles Suppose and are respectively the output of SEDC and the additional currents injected into the generator by GTSDC. To mitigate SSR, the critical issue is to know how they affect the electromagnetic torque of the generator. According to [12], electromagnetic torque can be expressed by (4) (5) (6) where

, ,

, is the excitation voltage, and the meaning of other symbols can be found in [12]. Substituting (5) and (6) into (4), it could be simplified into (7)

(11) , For the parameters of generators in SPP, there are , , , which are suitable for almost all coal-fueled 600-MW generators in China. Hence, . Then, (11) can be simplified into (12) Equations (11) and (12) show that both SEDC and GTSDC contribute to the additional electromagnetic torque. Therefore, if controlled properly, the damping torque generated by SEDC and GTSDC could be superpositioned and strengthened mutually to improve the capability of damping SSR. This is the underlying principle of the combined control scheme. Table III lists critical eigenvalues of Cases 1–3 when this combined scheme is adopted for the Shangdu system. Obviously, the combined scheme can stabilize the system very well. C. Control Structure of SEDC and GTSDC According to (12), and should be carefully generated to achieve maximum positive damping, under which condition the is in the same phase with . The calculation scheme of and reference is shown in Fig. 4. Bandpass filters are adopted to get oscillation signals of modes 1–3. Then, phase shifters and variable gains can be well designed to obtain optimum damping effect for each mode. As discussed in [10] and [11], both super-synchronous currents and subsynchronous currents with proper phase could provide positive damping for SSR. The scheme, as shown in Fig. 4(b), is a little complex in order to adjust the phase of super-synchronous and subsynchronous references at the same time. Current reference calculator operates as follows:

Suppose (8)

(13)

(9) (10) is the excitation voltage without SEDC, is the lag where time of the power circuit of the exciter, , are the d- and

Hence, the phase of super-synchronous and subsynchronous reference could be exactly tuned using proper phase delay and . More details of SEDC and GTSDC have been presented in [5] and [11].


773

TABLE IV GENERATOR OUTPUTS DURING FIELD TESTS

the capacity of GTSDC would not be too large. Taking these two principles into consideration, all GTSDCs have a rating of about 10 MVA and a short-time over-loading capability, which allows them to output as more as 1.2-kA peak currents at the 10-kV side for several tens of seconds. If more capacity of GTSDC is necessary in the future, additional converters can be installed to enlarge the rating of CCG. IV. FIELD TESTS

Fig. 4. Reference calculation of SEDC and GTSDC. (a) Structure of SEDC. (b) MCCC of GTSDC.

Field tests have been carried out to check the SSR damping ability of the combined scheme at SPP in September 2013. In May 2012, some other tests had been implemented also to check the precision of the system model adopted in eigenvalue analysis and time-domain simulation, when there were only SEDC providing SSR damping control. Eigenvalue analysis and time-domain simulation shows that the aforementioned Case 1–3 are operating conditions of the most serious SSR risk. Hence, the field experiments were carried out under these three operating scenarios. In the experiments, one of the Shangdu-Chengde transmission lines is switched off for a few seconds, then switched on automatically, which is named as “switch off/on experiment”. Output power of the generators during the experiments are listed in Table IV. A. Experiment Details of Case 1

Fig. 5. Switch scheme of GTSDC between two generators.

D. Specific Configuration for the Shangdu System A 10-MVA prototype of GTSDC has been tested in 2012 at SPP [11]. The test results confirmed that GTSDC improves torsional damping considerably and can also mitigate device-dependent torsional oscillations. After that, two more 10-MVA GTSDCs were installed at generators Nos. 1 and 4 in the first half of 2013. Hence, three 10-MVA GTSDCs are installed at generators Nos. 1, 4, and 6 separately, while SEDCs and TSRs are applied to all the generators. Since generators Nos. 1 and 2 are identical, just one of them is chosen to install a GTSDC so as to reduce the cost. This is also the case for generator Nos. 3 and 4 and Nos. 5 and 6. Thus, a special scheme, as shown in Fig. 5, is adopted at SPP so that GTSDCs can be switched between units 1 and 2, 3 and 4, and 5 and 6. Consequently, if any one of the generator pair is out of service, GTSDC is still in service. As discussed above, the damping effect of SEDC and GTSDC can be simply superimposed, or there is little coupling between SEDC and GTSDC. Therefore, the design of SEDC and GTSDC could be independent. The key point of the combined scheme is the capacity of GTSDC. First of all, GTSDC and SEDC must have sufficient ability to keep the system stable under present and foreseeable operating conditions. Hence, there is a floor capacity for GTSDC. Second, considering economic efficiency, only reasonable stability margin should be reserved. Therefore,

Shaft speed deviations in the experiments are presented in Fig. 6 when only SEDCs are in service. One transmission line is switched off at 1 s. Then, it is switched on at 6 s. After one line is switched off, the shaft oscillation starts with a comparatively large initial amplitude caused by the switch operation. Then, it increases continuously. At 5.8 s, the oscillation amplitude of generator No. 3 is large enough to trigger the TSR. Then, generator No. 3 is tripped off. After the line is switched on, the shaft oscillation begins to decrease. However, at 6.9 s, the fatigue life loss of generator No. 2 reaches 1%, another threshold of TSR. Hence, TSR trips off this generator also. Experiment results indicate that the SEDC cannot provide enough damping for SSR under this operating condition. Thus the safety of the generator as well as the whole power system would be endangered. Fig. 7 shows the output of SEDC during the experiment. Obviously, when one line is switched off, the output of SEDC reaches its hard limit with the increase of oscillation amplitude. Hence, the effective gain decrease further. SEDCs is unable to provide sufficient damping for the mitigation of SSR. Field test results of the combined scheme are shown in Fig. 8. Clearly, the whole system is stable though the line switch operation could also stimulate mild shaft oscillation. Bandpass filters are adopted to get the information of different torsional modes. The processed results of shaft oscillation are presented in Fig. 9. It shows that Mode 2 is unstable if only SEDC is adopted, but well stabilized by the combined scheme,

774


Fig. 6. Shaft speed deviation when only SEDC is adopted.

Fig. 7. Outputs of SEDC during the field test.

Fig. 9. Oscillation amplitude of different torsional modes in switch off/on experiments. (a) Mode 1. (b) Mode 2. (c) Mode 3.

Fig. 8. Shaft speed deviation when SEDC and GTSDC are in service.

which coincides with the system eigenvalues. GTSDCs hardly improve the damping of Modes 1 and 3, because most of its capacity is deployed to suppress the unstable Mode 2 in the original design of GTSDC. Fig. 10 shows the outputs of SEDC and GTSDC in the experiments. The outputs of SEDC are below the hard limits due to smaller amplitude of shaft oscillation when GTSDC is in service. Hence, SEDC can provide designed damping during the whole process. As the results showing, GTSDCs generate large

currents only when there is high-amplitude oscillation. Therefore, the standby power of GTSDC could be very low. Furthermore, if the short-time overload capability of the converter is taken into consideration, GTSDC could provide more damping. B. Experiment Results of Cases 2 and 3 Switch off/on experiments have also been carried out under operating scenarios of Cases 2 and 3. Comprehensive analyses show that the switch-off interval of Case 2 should be decrease to 3 s to avoid generator tripping when only SEDC is in service. Figs. 11 and 12 show the oscillation amplitude of Mode 2 in Cases 2 and 3. In these cases, when only SEDC is in service,


775

Fig. 12. Amplitude of mode 2 in switch off/on experiments of Case 3.

Fig. 10. Outputs of SEDC and GTSDC. (a) Outputs of SEDC. (b) Output currents of GTSDC.

Fig. 13. Scatter plot of different SSR modes under all operating conditions when the combined scheme is in service.

operating conditions. Hence, the combined scheme provides a scalable solution to SSR. V. EIGENVALUE ANALYSIS OF THE COMBINED SCHEME

Fig. 11. Amplitude of mode 2 in switch off/on experiments of Case 2.

shaft oscillations of generator Nos. 1–4 are still unstable. However, generator Nos. 5 and 6 are stable, because their shaft frequencies of Mode 2 are different from those of Nos. 1–4. Due to the shortened switch-off interval, the oscillation amplitude and fatigue life loss do not reach the thresholds to trip generators in Case 2. Obviously, SEDC still cannot provide sufficient damping itself under Cases 2 and 3. In other words, only the combined scheme could mitigate the SSR under these conditions. These test results agree with the eigenvalue analysis. Generally, field tests prove that the combined scheme of SEDC and GTSDC can provide designed electrical damping for the system and thus stabilize SSR effectively under serious

As discussed in Section II, in the consideration of all system topologies, unit commitment and three typical loading levels of generator, the system has 8316 operating conditions in total. It is impractical to check the system stability using practical experiments under all of these operating conditions. Hence, eigenvalue analysis is adopted again to check the system stability when the combined scheme is adopted. The eigenvalues of the torsional modes associated with the series compensation are depicted in Fig. 13. Compared with Fig. 2, it could be observed that, with the combined scheme, the points of torsional modes 2 and 3 move to the left-hand plane. Hence, the system is well stabilized under any operating condition when this combined scheme is adopted. VI. CONCLUSION In this paper, a combined control scheme integrating supplementary excitation damping controller and generator terminal subsynchronous damping controller is proposed to solve a practically changed SSR problem. SEDC modulates excitation voltage on the rotor side, while GTSDC injects complementary super-synchronous and subsynchronous currents into the stator side. Both of them can generate damping torque. Therefore, an

776


enforced damping effect is achieved. Eigenvalue analysis and time-domain simulations indicate that the combined scheme could not only provide sufficient damping to the system, but also could decrease the capacity of the power electronics converters of GTSDC and the total investment cost. This combined scheme has been applied to Shangdu Power Plant, a practical power system. Field tests fully demonstrate that the combined scheme could significantly improve the torsional damping, and thus solve the SSR problem effectively. Thanks to the flexibility of deployment, changeable capacity, and small size, the combined scheme can be easily adjusted for further situation of the system. It provides a scalable solution to practical SSR issues.

[9] X. Xie, H. Liu, and Y. Han, “SEDC's ability to stabilize SSR: A case study on a practical series-compensated power system,” IEEE Trans. Power Syst., vol. 29, no. 4, pp. 3092–3101, Nov. 2014. [10] L. Wang, X. Xie, Q. Jiang, and H. R. Pota, “Mitigation of multimodal subsynchronous resonance via controlled injection of supersynchronous and subsynchronous currents,” IEEE Trans. Power Syst., vol. 29, no. 3, pp. 1335–1344, Aug. 2014. [11] X. Xie, L. Wang, X. Guo, Q. Jiang, Q. Liu, and Y. Zhao, “Development and field experiments of a generator terminal subsynchronous damper,” IEEE Trans Power Electron., vol. 29, no. 4, pp. 1693–1701, Apr. 2014. [12] P. M. Anderson, B. L. Agrawal, and J. E. Van Ness, Subsynchronous Resonance in Power Systems. New York, NY, USA: Wiley, 1999, p. 288.

REFERENCES [1] Subsynchronous Resonance Working Group of the System Dynamic Performance Subcommittee, “Reader's guide to subsynchronous resonance,” IEEE Trans. Power Syst., vol. 7, no. 1, pp. 150–157, Feb. 1992. [2] IEEE SSR Working Group, “Countermeasures to subsynchronous resonance problems,” IEEE Trans. Power App. Syst., vol. PAS-99, no. 5, pp. 1810–1818, Sep. 1980. [3] C. E. J. Bowler, D. H. Baker, N. A. Mincer, and P. R. Vandiveer, “Operation and test of the Navajo SSR protective equipment,” IEEE Trans. Power App. Syst., vol. PAS-97, no. 4, pp. 1030–1035, 1978. [4] X. Xie, P. Liu, K. Bai, and Y. Han, “Applying improved blocking filters to the SSR problem of the Tuoketuo power system,” IEEE Trans. Power Syst., vol. 28, no. 1, pp. 227–235, Feb. 2013. [5] X. Xie, X. Guo, and Y. Han, “Mitigation of multimodal SSR using SEDC in the Shangdu series-compensated power system,” IEEE Trans. Power Syst., vol. 26, no. 1, pp. 384–391, Feb. 2011. [6] D. G. Ramey, D. S. Kimmel, J. W. Dorney, and F. H. Kroening, “Dynamic stabilizer verification tests at the San Juan station,” IEEE Trans. Power App. Syst., vol. PAS-100, no. 12, pp. 5011–5019, 1981. [7] N. G. Hingorani, B. Bhargava, G. F. Garrigue, and G. D. Rodriguez, “Prototype NGH subsynchronous resonance damping scheme—Part I: Field installation and operating Experience,” IEEE Trans. Power Syst., vol. 2, no. 4, pp. 1037–1039, Nov. 1987. [8] R. J. Piwko, C. A. Wegner, S. J. Kinney, and J. D. Eden, “Subsynchronous resonance performance tests of the Slatt thyristor-controlled series capacitor,” IEEE Trans. Power Del., vol. 11, no. 2, pp. 1112–1119, 1996.

Xiaorong Xie (M’02–SM’14) received the B.Sc. degree from Shanghai Jiao Tong University, Shanghai, China, in 1996, and the Ph.D. degree from Tsinghua University, Beijing, China, in 2001. Currently, he is an Associate Professor with the Department of Electrical Engineering, Tsinghua University, Beijing, China. His current research interests focus on subsynchronous resonance evaluation and its counter-measures, power system analysis and control based on wide-area measurements, and flexible ac transmission systems.

Liang Wang received the B.S. degree from Shandong University, Jinan, China, in 2007, the M.S. degree from South China University of Technology, Guangzhou, China, in 2010, and the Ph.D. degree from Tsinghua University, Beijing, China, in 2014. He is now a Lecturer with the Beijing Institute of Technology, Beijing, China. His research interests include subsynchronous resonance analysis and solutions and modeling and control of the flexible ac transmission systems.

Yingduo Han (SM’95) received the B.S. and M.S. degrees from Tsinghua University, Beijing, China, in 1962 and 1966, respectively, and and the Ph.D. degree from Elangenberg University, Elangenberg, Germany, in 1986. He is a Professor with Tsinghua University, Beijing, China. His research interests include power system stability analysis and control, flexible ac transmission systems, and wide-area monitoring and control systems. Prof. Han is a member of the Chinese Academy of Engineering.