Mitigation of Multimodal SSR Using SEDC in the ... - IEEE Xplore

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IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 26, NO. 1, FEBRUARY 2011

Mitigation of Multimodal SSR Using SEDC in the Shangdu Series-Compensated Power System Xiaorong Xie, Member, IEEE, Xijiu Guo, and Yingduo Han, Senior Member, IEEE

Abstract—The Shangdu power plant has four 600-MW turbinegenerators connected to the North-China Grid through two 500-kV transmissions, which are compensated with 45% fixed series capacitors. Extensive studies conducted on the system model indicate that the system suffers from multimodal subsynchronous resonance (SSR). To solve the problem, a countermeasure is developed by combining the supplementary excitation damping control (SEDC) and the torsional stress relay (TSR). In this paper, the characteristics of the SSR problem are investigated. Then the developed SEDC is presented. To validate the effectiveness of the proposed SEDC as well as the results of model studies, field tests were conducted under various operating conditions. The tests fully exposed the realistic threat of SSR in the system. Meanwhile, it is demonstrated that the developed SEDC can improve torsional damping significantly, and thus solve the multimodal SSR problem effectively. This is the first time in China that practical SEDCs have been developed and their ability to mitigate multimodal SSR has been verified in a real series-compensated system. Index Terms—Field test, fixed series capacitor, subsynchronous resonance, supplementary excitation damping control (SEDC).

I. INTRODUCTION ECENTLY, fixed series capacitors (FSCs) have been widely used in Chinese power systems to increase the transfer capability of long-distance transmission lines. However, they may bring about the subsynchronous resonance (SSR) problem that would result in damages to the turbine-generator shaft if not handled properly [1]. Therefore, mitigation methods must be applied if the preliminary analysis shows that the system is at risk of unstable SSR [2]. In this paper, the SSR issue and the corresponding countermeasure of the Shangdu series-compensated system is discussed. The Shangdu power plant in Inner Mongolia has four 600-MW steam turbine generators connected to the North-China Power Grid via two 500-kV transmission lines, which are compensated with 45% FSCs. Extensive studies based on the system model indicated that the turbine-generators would be exposed to SSR resulting from the application of series capacitors. To solve the problem, various measures, including the blocking filter [3], [4], supplementary excitation

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Manuscript received December 31, 2009; revised January 02, 2010. First published April 26, 2010; current version published January 21, 2011. This work was supported in part by the National Basic Research Program (Grant No. 2004CB217906), State Key Lab. of Power System (Grant No. SKLD08M02), and State Grid Corporation of China. Paper no. TPWRS-01020-2009. 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]). X. Guo is with the Northern United Power Corporation, Huhehaote 010020, Inner Mongolia, China. Digital Object Identifier 10.1109/TPWRS.2010.2047280

damping control (SEDC) [3]–[6], static var compensator (SVC) [7]–[9], and torsional stress relay (TSR) [3], [4], had been evaluated. Finally, the “SEDC TSR” strategy was considered as the most appropriate for its effectiveness and low cost. In this combinative method, SEDC is used to improve the torsional damping for SSR mitigation, meanwhile TSR functions as a protective device to trip any generator that is exposed to harmful torsional oscillations. As a countermeasure to SSR, SEDC was implemented some 30 years ago [3], [4]. Since then, however, most of the research conducted in this area focuses on theoretical work [10]–[14]. There is very little practical exploration. Even for the few engineering applications that were reported [3], [4], no detailed results of field tests could be found to validate its effectiveness in a real system. In China, for the first time, we investigated SSR phenomena and SEDC’s damping effect in a real series-compensated system. The research and development started from scratch. It took about three years to complete the work from theory to practice, which includes the following steps: 1) evaluation of SSR risk based on an electromagnetic model of the target system; 2) preliminary selection of SSR countermeasures through economic and technical comparison; 3) the effectiveness and feasibility analysis of the SEDC TSR scheme; 4) development of the prototypes of SEDC and TSR; 5) interface test between SEDC and the excitation control system in both hardware and software aspects; 6) real-time simulation study of the prototype SEDC and TSR on the real-time digital simulators (RTDS); 7) field tests of the improved prototype SEDC and TSR in the Shangdu system without FSC; 8) manufacturing and installation of industrial SEDCs and TSRs; 9) final field tests of all SEDCs and TSRs under various operating conditions and with FSC put into service. With the extensive work that has been done, this paper will focus on three of the most important aspects of the project, i.e., the characteristics of the SSR problem (Section II), the functionality of SEDC (Section III), and the results of the final field tests (Section IV). II. SERIES-COMPENSATED SYSTEM AND ITS SSR EVALUATION A. Description of the Shangdu System The Shangdu power plant (SPP), located in the Inner Mongolia Autonomous Region, is about 300 kilometers north of Beijing city. It has four 600-MW steam turbine-generators connected to the North China Power Grid through 500-kV transmission lines. Fig. 1 illustrates the one-line diagram of the equivalent transmission system. To improve the transferring capability

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XIE et al.: MITIGATION OF MULTIMODAL SSR USING SEDC

Fig. 1. One-line diagram of the equivalent transmission system.

TABLE I MEASURED MECHANICAL DAMPING OF UNIT 4 AT THREE LOADING LEVELS

as well as system stability, FSCs are applied to the parallel transmission lines between Shangdu power plant and Chengde substation with 45% compensation degree. The four turbine-generators are subcritical air-cooled machines with almost the same parameters. Each turbine-generator consists of four rotors, i.e., a high-and-intermediate-pressure (HIP) turbine rotor, two low-pressure (LPA and LPB) turbine rotors, and the generator rotor, thus resulting in three subsynchronous torsional modes. The characteristic frequencies (in Hz) are 15.19–15.33 (mode 1), 26.01–26.12 (mode 2), and 30.25–30.54 (mode 3). B. Evaluation of SSR Risk A thorough evaluation of the severity of the SSR problem was conducted under all possible system conditions, which comprised the following stages. First, frequency scanning was used to check if the electrical resonant frequency of the compensated network was close to the complement of the torsional frequencies of the generator shaft. The results did indicate there were such possibilities under certain operating conditions. Second, the torsional frequencies and modal damping were measured for Unit 4 through the load-rejection tests at several loading levels. Table I gives the measured mechanical damping of Unit 4 at three representative loading conditions, in which 0% and 100% means the smallest and the largest mechanical damping, while 40% is the minimum load to keep the boiler burning stably without oil-firing aid. Based on the measurements and shaft data provided by the manufacturer, a springmass shaft model was developed, which includes four masses standing for the HIP, LPA, LPB, and generator rotors, respectively. Then, eigenvalue analyses and electromagnetic transient (EMT) simulation were fulfilled to further investigate the SSR characteristics of the target system. During this stage, the model of networks and generators (including their excitation/governor control systems) were considered in detail. With eigenvalue analysis, the modal damping (i.e., the negative real part of the torsional eigenvalue, which is a combined outcome of mechanical and electrical damping) can be obtained with respect to different operating conditions. To illustrate, 24

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representative conditions are selected as the “evaluation conditions” (listed in Table II), which cover the full range of generator output levels as well as the status of the Shangdu-Chengde lines. Table II also lists the calculated modal damping (see the “No SEDC” column). Thus, the severity of SSR is quantified and the most risky situations are identified. The EMT study, conducted with the PSCAD/EMTDS program, further investigated the SSR dynamics of the system when there are large disturbances, such as short-circuit faults. The objective is to evaluate the transient torque and shaft loss-of-life of the generators associated with transmission system faults under different plant and system operating conditions. Through the evaluation study, characteristics of the SSR problem are summarized as follows. 1) Mode 1 is well-damped in all operating conditions; however, modes 2 and 3 may be under-damped or even unstable under some conditions. Thus, the SSR problem is a multimodal one. 2) Mode 2 is the worst damped and tends to be unstable for numbers of operating conditions, especially when only one Shangdu-Chengde line is in service or the generator output is relatively low (corresponding to a lower mechanical damping). 3) Modal damping is affected by several factors. It decreases when one of the Shangdu-Chengde lines is out of service, or when more units stay online at low load levels. It increases as the generator output gets higher (so does the mechanical damping). What is more, each torsional mode has a most undesirable (or least damped) condition unique to its own, making it a challenge to design a controller adaptable to all operating conditions. 4) Some serious faults, for instance a three-phase short-circuit on the Shangdu-Chengde lines near bus bar, may cause SSR instability. Subsequently, the shaft torque grows steadily to a huge value, resulting in unacceptable fatigue damage to the generator shafts. Therefore, countermeasures must be applied to solve the SSR problem in order to maintain the stability of the system and the security of the generators. III. SUPPLEMENTARY EXCITATION DAMPING CONTROLLER A. SEDC

TSR Scheme

Various countermeasures, including the blocking filter [3], [4], SVC [7]–[9], and SEDC, were considered to handle the SSR problem of the Shangdu system. SEDC was finally chosen as the SSR-depressing device through delicate study and technical versus economic comparison. As a complementary measure, TSR is applied to trip generators that are exposed to growing or intolerable torsional oscillations resulting from extremely serious faults. Since TSR is widely used and will not be elaborated here, the rest of the paper mainly focuses on the basic principle, the functional structure, and the field tests of the developed SEDC. B. Configuration of the Proposed SEDC SEDC is a real-time control system that works through the excitation system by modulating the field voltage at the tor-

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TABLE II TORSIONAL DAMPING WITH/WITHOUT SEDC UNDER THE EVALUATION CONDITIONS (COMPENSATION LEVEL

Fig. 2. Signal relationship of the SEDC and the excitation regulators.

sional frequencies. Fig. 2 illustrates the signal relationship of the SEDC, the excitation regulator, the generator, and the grid. As a supplementary control loop, SEDC uses the mechanical speed as the only feedback signal to generate of the HIP turbine is then the subsynchronous control output to form a modulated control added to the output of AVR signal , which drives the excitation circuit to yield the field . There is a time delay between and , voltage mainly due to signal sampling, data processing, and thyristor transport lag. This time delay, generally several to a dozen milliseconds, is important to the practicality of SEDC’s design, since it is comparable with the period of torsional modes, which, if not taken into consideration, would deteriorate or even destabilize the SEDC-controlled system. Fig. 3 shows the block diagram of the proposed SEDC. The mechanical speed of the HIP turbine provides the input, which after proper filtering and conditioning becomes the deviation . It then passes through three separate control signal paths. Each control path, tuned to a specific mode, comprises a , and a unity-gain phase-shifter band-pass filter, an amplifier to generate the control signal for the corresponding mode. The control signals of all torsional modes

= 45%)

Fig. 3. Configuration of SEDC.

are summarized, clipped, and finally added to the AVR output to modulate the field voltage. Consequently, three subsynchronous components are generated in the excitation current, which in turn produce subsynchronous torque upon the generator shafts. If the gains and phase-shifts are appropriately set, this torque provided by SEDCs will play a role in damping SSR. To a large extent, each torsional mode can be separately controlled with a well-designed band-pass filter of the corresponding control path, and such a SEDC has little effect on the regular AVR/PSS functions. So proper determination of the , in Fig. 3, is gains and time constants, i.e., crucial to mitigate the multimodal SSR. C. Evaluation Study of the SEDC-Controlled System Before developing the hardware SEDC, an extensive evaluation study was fulfilled to confirm its effectiveness in solving the SSR problem of the target system. First of all, the parameters of SEDC were delicately tuned using an adapted genetic and simulating annealing algorithm [15], which, as a nonlinear optimization based on the linearized system model, can simultaneously work out all SEDC parameters considering multiple


torsional modes and different system conditions. Then, to verify the tuned SEDC, both eigenvalue analysis and EMT simulation were fulfilled on the close-loop system under all possible working situations. The SEDC-controlled system is assessed in the aspect of damping improvement, transient response, as well as the robustness to system uncertainties. Through the all-around assessment, the following conclusions were obtained. 1) SEDC can supply sufficient torsional damping to maintain small-signal SSR stability under all normal and N-1 operating conditions. The modal damping of the three modes concerned is displayed in Table II. Obviously, with SEDC, it has been increased considerably so that all unstable cases of the evaluation conditions are well stabilized. 2) The EMT study shows that SEDC can effectively damp out SSR following ordinary system operations (including switching on/off lines, tripping or synchronizing generators, and adjusting generator output) and most short-circuit faults under all operating conditions, insuring stability of the system and security of the generator shafts. 3) In some very rare situations, for instance a three-phase short-circuit fault occurring on one of the ShangduChengde lines and less than 10 km away from the 500-kV bus bar of Shangdu, it is required that TSR trip one generator to avoid too much damage to the generator shafts. Considering that this happens with an extremely low probability, it is reasonable for such a protective action. Even in such extreme cases, the fatigue loss-of-life can be limited to a tolerable value (5%). Therefore, in theory, the SEDC TSR scheme is feasible for solving the SSR problem of the Shangdu system. D. SEDC Development and Laboratory Tests Since this is the first time in China that SEDC is applied to solve a practical SSR problem, a prototype SEDC was developed. Extensive laboratory tests were conducted to verify its basic principles and characteristics. First, the transfer function of SEDC (as described by Fig. 3) was examined in detail on the implemented hardware SEDC by analyzing its input-output relationship. Second, as one of the key issues, the interface between SEDC and the excitation controller is closely examined by analyzing the responses of the AVR and the thyristor-based power circuit to simulative control signals produced by the prototype SEDC. Then, SEDC was further verified with the real-time digital simulator (RTDS), wherein the detailed EMT model of the Shangdu system was developed. During the above-mentioned laboratory tests, the prototype SEDC underwent much improvement. Finally, by the end of 2007, the first industrial SEDC controller was made and installed in Unit 4 of the Shangdu power plant. IV. FIELD TESTS By the end of October 2008, all SEDCs and TSRs were put into their places. The two FSCs of the Shangdu-Chengde lines were also ready for operation. Therefore, a series of field tests were arranged to optimize and verify the effectiveness of the developed SEDCs. The field tests were carried out in two phases,

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i.e., the parameter-tuning test before FSCs were put in operation, and the verification test with FSCs in service. A. Parameter-Tuning Tests of SEDC Before FSCs were put into service, the parameter-tuning tests were conducted on each SEDC, which included the following sub-steps. 1) Examination of SEDC’s Interface With the Excitation System: To check its interface with the excitation system, the SEDC generated a series of virtual control signals that contain components of one or three torsional modes. They were combined with the AVR output to drive the thyristor-based excitation circuit. By investigating the amplitude and phase relationship between the SEDC-generated control signals and the resulted field voltage and current, the interface of SEDC with the excitation system was evaluated. The test results showed that the developed SEDC matches the excitation system very well. The subsynchronous control signals produced by the former went through the latter smoothly. The time delay is in the range of 8–12 ms. This lays the foundation of using SEDC for SSR-mitigation purpose. 2) Detection of Modal Frequencies and Identification of Open-Loop System Characteristics: For each generator, its modal frequencies were first determined in a rough way by the FFT-based spectrum analysis of the steady-state speed of the HIP turbine rotor. Frequency-scanning tests were subsequently initiated, by which modal signals with specific frequencies, amplitudes, and time-durations generated by SEDC were injected into the excitation system. As a result, torsional oscillation was excited. By adjusting the frequency of the injected signal, the amplitude of the resulted oscillation changed accordingly. If the stimulant frequency matches the inherent torsional frequency, the most intense subsynchronous oscillation could be observed. By this way, the modal frequencies can be accurately determined with a resolution of 0.01 Hz. For each of the measured torsional modes, the signal-injection tests were repeated several times with different signal amplitudes. The excited subsynchronous oscillations as well as the input signals were recorded. Then, based on the collected input-output data, the open-loop gain and phase-shift of each torsional mode could be identified, which were next used to adjust the parameters of SEDC. After extensive tests and a careful comparison between the test results and those obtained via model analysis, the parameters of SEDCs were set as in Table III. It can be observed that the phase shifts for Units 3 and 4 are different than the phase shifts for Units 1 and 2, because of the discrepancy in shaft parameters and torsional frequencies of the four generators. At this stage, the gains of SEDC were given a range of variation. They were finally determined in the following tests, because they are closely related to the actual response of the system with FSCs in operation. 3) Validation of Modal Damping Improvement by SEDC: To validate the effectiveness of SEDC in improving modal damping, the signal-injection test was employed again, first without SEDC and then with SEDC switched on immediately after the termination of the injected signal. Fig. 4 depicts the result of a typical test on Unit 2, wherein the injected signal’s

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TABLE III MODAL FREQUENCIES AND SEDC GAINS AND PHASE-SHIFTS

Fig. 5. Dynamics of mode 2 during FSCs’ switching-on/off operations under the three-machine condition (unit 4).

Fig. 4. Dynamics of mode 2 during the signal-injection test (unit 2).

parameters are as follows: the frequency is 26.12 Hz (the same as torsional mode 2), the amplitude is 45% of the rated excitation voltage, and the time duration is 10 s. Obviously, the mode-2 torsional oscillation was excited soon with the injected signal. Without SEDC, the torsional oscillation died out with the attenuation rate determined by the inherent damping of the system. However, if SEDC is applied following the end of the triggering signal, the torsional oscillation was damped out more quickly, which demonstrated the SEDC’s ability to provide additional torsional damping. For this specific test, the damping ratio is increased from 0.14 (1/s) to 0.69 (1/s) by SEDC. B. Verification Tests of SEDC With FSC in Service Model analysis indicates that Shangdu power plant has greater SSR risk when more than two machines are online and only one Shangdu-Chengde line is in operation. So the verification tests were carried out under the three- and four-machine conditions, respectively. 1) Tests Under the Three-Machine Condition: The initial operating condition of the tested system was as follows: units 1, 2, and 4 were online and half-loaded; unit 3 was out of service; both Shangdu-Chengde lines were in operation; FSCs were out of service but ready for operation. Switching On/Off FSCs With/Without SEDC: First, with all SEDCs in service, the two FSCs were switched on and then they

were switched off one by one. During these operations, the torsional oscillation was observed in real time and each operation was initiated only after the dynamics that was triggered by the previous operation completely died away. The next stage involved quitting all SEDCs and repeating the above switch-on/off operations of FSCs. The major results of this test are summarized as follows. 1) The torsional oscillation of the online machines are convergent under both the SEDC-off and the SEDC-on conditions, while the SEDC can considerably improve the modal damping and make the oscillation converge much more quickly, as shown in Fig. 5. 2) It is also observed that during these tests, torsional mode 2 had the largest oscillatory amplitude, with the peak value reaching 0.3 rad/s, while mode 1 and mode 3 had relatively smaller amplitudes, with less than 0.10 rad/s and 0.15 rad/s, respectively. Tripping and Reclosing of One Shangdu-Chengde Line: This test was also performed with and without SEDC, respectively. At the initial state, both Shangdu-Chengde lines were in service but only one FSCs was switched on (i.e., k1, k3, and k4 were closed and k2 was open; see Fig. 1). Breaker k3 was first opened to trip one Shangdu-Chengde line and then reclosed after 5 s. This test was meant to check the system response under the three-machine and one-line condition. Figs. 6 and 7 illustrate the dynamics of torsional mode 2 during the operation. It can be seen that during the short period of the three-machine one-line condition, without SEDC, unit 1 and 2 suffered diverging SSR, while for unit 4, the torsional oscillation converges, but with a very weak damping ratio. The reason is that units 1/2 have a higher mode-2 frequency than units 3/4 (see Table III) and thus are exposed to a greater SSR risk in this operating condition. If SEDCs were applied, however, the torsional oscillation can be damped out soon and the SSR risk is avoided effectively for all units online. 2) Synchronizing Unit 3 to the Grid: Generally, a generator will experience relatively greater risk when it is lightly loaded because of the less mechanical torsional damping at low loading level. This test is designed to check the performance of SEDCs


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Fig. 6. Dynamics of mode 2 during switching operations of Shang-Cheng line #1 under the three-machine condition (unit 1).

Fig. 8. Dynamics of mode 2 during the synchronizing operation of unit 3.

Fig. 7. Dynamics of mode 2 during switching operations of Shang-Cheng line #1 under the three-machine condition (unit 4).

Fig. 9. Dynamics of mode 2 during FSCs’ switching-on/off operations under the four-machine condition (unit 4).

during the operation of synchronizing a no-load machine (unit 3) to the grid, when it is most vulnerable to SSR. During the operation, both Shangdu-Chengde lines and FSCs were in service. The outputs of unit 1, 2, and 4 were 350 MW, 350 MW, and 300 MW, respectively. All SEDCs were put into use. Unit 3 was started gradually and then connected to the grid via the automatic synchronizing device. Fig. 8 depicts the modal speed of the HIP turbine. It is observed that the torsional oscillation excited by the connecting operation is quite small and can be depressed quickly with SEDCs. The maximum modal-2 oscillation is only about 0.04 rad/s. In addition, this test had a much smaller impact on other units. 3) Tests Under the Four-Machine Condition: Like the threemachine conditions, the tests under the four-machine condition were also carried out in two sub-steps. Switching On/Off FSCs With/Without SEDC: This test was carried out by the same procedures as under the three-machine situation, except that unit 3 was online and the mode-2 gain of the SEDC was increased from 150 to 260 based on the analysis of close-loop system response. The main results of the test are as follows.

1) The torsional oscillations of all generators are convergent with or without SEDCs, while SEDC can considerably improve the modal damping and depress the torsional vibration much more quickly, as shown in Fig. 9. 2) During the test, mode 2 has the largest oscillatory amplitude, with a peak value of about 0.21 rad/s, while the maximum value of modes 1 and 3 were much smaller, less than 0.08 rad/s and 0.07 rad/s, respectively. Tripping and Reclosing of One Shangdu-Chengde Line: The pretest condition and the test procedures were similar to the three-machine test except that the outputs of units 1 to 4 were 350 MW, 350 MW, 70 MW, and 300 MW, respectively. According to the preliminary study, the SSR problem is the most serious under the four-machine one-line situation. Without SEDC, the growing SSR may cause damage to generator shafts even within 5 s. Therefore, in this test, the SEDCs were always in operation to insure the safety of the machines and the grid. One objective of the test was to investigate the influence of the control gains of the SEDC on the SSR-damping performance. Therefore, the smaller and larger gains of mode 2, i.e., 150 and 260, respectively, were tested.

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Fig. 10. Dynamics of mode 2 during switching operations of Shang-Cheng line #1 under the four-machine condition (unit 1).

Figs. 10–12 illustrate the dynamics of torsional mode 2 during the test. It can be seen that within the short period of the four-machine one-line condition, with higher gains SEDC can effectively depress SSR, while with smaller gains the heavily-loaded generators (unit 1, 2, and 4), which have relatively high mechanical damping, were SSR stable though the converging speed is not so fast. However, the lightly-loaded generator (unit 3), whose mechanical damping was smaller, experienced diverging SSR. Thus, higher gains are required in order to stabilize SSR under different operating conditions, even in the case of low generator outputs (with low mechanical damping). During this test, the torsional mode 2 had the largest oscillatory amplitude. When the mode-2 gain was 150, the maximum torsional oscillation of units 1–4 were 0.35 rad/s, 0.30 rad/s, 0.53 rad/s, and 0.35 rad/s while with the gain increased to 260, they were 0.23 rad/s, 0.25 rad/s, 0.26 rad/s, and 0.22 rad/s, respectively. In both cases, mode 1 and mode 3 converged quickly and had much smaller oscillatory amplitudes, about 0.04 rad/s and 0.09 rad/s.

C. Summary of the Field Test From the results of the field tests, the following can be concluded. 1) There is real danger of SSR for the Shangdu series-compensated system, especially for mode 2, which exhibits instability when three or four machines are online while only one Shangdu-Chengde line is in service. 2) With SEDC applied, the damping of all torsional modes is significantly improved so that the unstable modes become stabilized, which guarantees the safety of the generator shaft and the stability of the system. 3) The field test includes various operations and covers different working conditions. Especially, the most dangerous conditions previously recognized (i.e., the condition of three/four machine and one Shangdu-Chengdu line) were tested sufficiently. Therefore, the effectiveness as well as the robustness of SEDC is very well validated.




4) By the field testing, the engineering parameters of SEDC were determined. The SEDC TSR scheme is confirmed for resolving the SSR problem. Soon after the test, SEDCs, TSRs, and FSCs were put into practical operation. Consequently, transient stability and transferring capability of the system was greatly improved. In May 2009, about half a year later, an inter-phase short circuit occurred on the 500-kV bus bar of the Shangdu power plant and was cleared by the protective device. SEDCs functioned as expected to depress the torsional oscillation successfully. The maximum fatigue loss-of-life was less than 0.2%, which was calculated based on S-N curves provided by the machine manufacturer. The speeds of the high-pressure turbines were recorded during the fault. The mode-2 speed of unit 2 was extracted and compared with that obtained with the electromagnetic simulation. As shown in Fig. 13, it indicated a good consistence between the real measurement and that resulted from model simulation. This also confirmed SEDCs’ functionality during large disturbances.


Fig. 13. Comparison of recorded and simulated mode-2 speed during the interphase fault (unit 2).

V. CONCLUSIONS In this paper, a practical application of SEDC is presented to mitigate SSR in the Shangdu series-compensated transmission system. An all-around evaluation study was conducted first on the electromagnetic model, which indicated that the system is threatened by multimodal SSR. To handle this problem, the proposed SEDC incorporates three separate control paths, with each corresponding to a torsional mode. Thus, the damping of the three modes concerned can be improved simultaneously. To validate the effectiveness of the developed SEDC as well as the results of model studies, field tests were carried out under various operating conditions. The tests showed the realistic threat of SSR in the system. Further, they fully demonstrated that SEDCs could improve torsional damping significantly, and thus solve the multimodal SSR problem effectively. The validity of the SEDC scheme was further confirmed by a short-circuit fault that occurred later in the system. The Shangdu project presented in this paper is the first in China for which practical SEDCs were developed, and their ability to mitigate multimodal SSR verified in a real series-compensated system.

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[5] Q. Li, D. Zhao, and Y. Yu, “A new pole-placement method for excitation control design to damp SSR of a nonidentical two-machine system,” IEEE Trans. Power Syst., vol. 4, no. 3, pp. 1176–1181, Aug. 1989. [6] L. Wang and Y. Y. Hsu, “Damping of subsynchronous resonance using excitation controllers and static VAR: A comparison study,” IEEE Trans. Energy Convers., vol. 3, no. 1, pp. 6–13, Mar. 1988. [7] 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, pp. 5011–5019, Dec. 1981. [8] D. S. Kimmel, M. P. Carter, J. H. Bednarek, and W. H. Jones, “Dynamic stabilizer on-line experience,” IEEE Trans. Power App. Syst., vol. PAS-103, pp. 72–75, Jan. 1984. [9] N. Rostamkolai, R. J. Piwko, E. V. Larsen, D. A. Fisher, M. A. Mobarak, and A. E. Poitras, “Subsynchronous interactions with static VAR compensators-concepts and practical implications,” IEEE Trans. Power Syst., vol. 5, no. 4, pp. 1324–1332, Nov. 1990. [10] L. Wang, “Damping of torsional oscillations using excitation control of synchronous generator: The IEEE second benchmark model investigation,” IEEE Trans. Energy Convers., vol. 6, no. 1, pp. 47–54, Mar. 1991. [11] Y. Y. Hsu and L. H. Jeng, “Damping of subsynchronous oscillations using adaptive controllers tuned by artificial neutral networks,” Proc. Inst. Elect. Eng. Gen., Transm., Distrib., vol. 142, no. 4, pp. 415–422, Jul. 1995. [12] A. M. Harb and M. S. Widyan, “Modern nonlinear theory as applied to SSR of the IEEE second benchmark model,” in Proc. 2003 IEEE Bologna Power Tech. Conf., Jun. 2003, vol. 3, pp. 1–3. [13] K. K. Anaparthi, B. C. Pal, and H. El-Zobaidi, “Coprime factorisation approach in designing multi-input stabiliser for damping electromechanical oscillations in power systems,” Proc. Inst. Elect. Eng. Gen., Transm., Distrib., vol. 152, no. 3, pp. 301–308, May 2005. [14] L. Wang and Y. Y. Hsu, “Damping of subsynchronous resonance using excitation controllers and static VAR compensations: A comparative study,” IEEE Trans. Energy Convers., vol. 3, no. 1, pp. 6–13, Mar. 1988. [15] D. Zhang, X. Xie, S. Liu, and S. Zhang, “An intelligently optimized SEDC for multimodal SSR mitigation,” Elect. Power Syst. Res., vol. 7, pp. 1018–1024, Jul. 2009. Xiaorong Xie (M’02) received the B.Sc. degree from Shanghai Jiao Tong University, Shanghai, China, in 1996 and the Ph.D./M.Eng. degrees from Tsinghua University, Beijing, China, in 2001. From 2001 to 2005, he was a Lecturer with the Department of Electrical Engineering, Tsinghua University. Since 2005, he works as an Associate Professor in the same department. 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.

Xijiu Guo received the B.Sc. degree in electrical engineering from Tsinghua University, Beijing, China, in 1978. From 1978–2004, he was with the Inner Mongolia Power Administration. From 2004 to the present, he has been with Northern United Power Corporation, Huhehaote, China. Currently, he works as the Vice Chief Engineer. His research interests include high-voltage equipments and test, power system analysis, and control.

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