The effect of converter configurations of HVDC links on sub- and super-synchronous disturbances to turbine units

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1 Electric Power Systems Research 74 (2005) The effect of converter configurations of HVDC s on sub- and super-synchronous disturbances to turbine units Chi-Hshiung Lin Department of Electrical Engineering, Kao Yuan Institute of Technology No. 1821, Chung Shan Rd., Lu Chu Hsiang, Kaohsiung County 821, Taiwan, ROC Received 20 September 2004; received in revised form 16 January 2005; accepted 17 January 2005 Available online 2 April 2005 Abstract In this paper, the rotor torque disturbances to turbine generator units arising from harmonic interactions between converters of a HVDC system are studied. It is shown that a distinct-pulse converter configuration will be a better choice for avoiding sub- or super-synchronous resonance. For an HVDC, the risk of electromechanical resonance could be completely got rid of on either side of the, no matter what directions the powers flow, if an 18-pulse converter were used on the 60 Hz side and a 12-pulse converter on the 50 Hz side. Such a configuration could still perform well even under the large frequency deviations. Furthermore, it shows that power system type plays a significant role on the possible excitation of resonance and on the probably damaging sections of a turbine generator unit. Good match of the converter configuration and power system type is significant for a HVDC to exempt from sub- and super-synchronous resonance Elsevier B.V. All rights reserved. Keywords: HVDC; Converter; Sub-synchronous; Super-synchronous; Turbine generator; Resonance 1. Introduction Torsional vibrations on large-scale steam turbine generators have been extensively discussed in many research works. Earlier, studies were focused on sub-synchronous resonance (SSR) arising from series compensation [1]. Later, a lot of researchers pay attention to the fatigue damages on turbine shafts caused by network fault and switching [2] and the long-term damaging effect due to small power system disturbances [3]. At the same time, much more researches were attracted on the countermeasures, which utilize power electronic equipments to modulate the effective and/or reactive power to augment system damping, to alleviate vibrations, for example, static VAR compensation (SVC) [4], thyristor controlled series compensation (TCSC) [5], static compensation (STATCOM) [6], unified power flow control (UPFC) [7], etc. address: lin chi hshiung@hotmail.com. Recently, sub-synchronous resonance caused by noncharacteristic harmonics was gradually noticed, primarily due to proposing of some high power HVDC s to interconnect the East and West European Grid Systems [8,9]. The HVDC scheme could produce non-characteristic harmonics in inverter side of AC system by way of interactions between rectifier and inverter stations. These harmonics can excite onerous torsional vibrations in large steam generator shafts in circumstance of sub-synchronous resonance occurring and put machines to risk. However, almost all studies confined to the standard 12-pulse and not any countermeasures were proposed except an advice for carefully assessing the risk and employing a relaying system to protect the machines. So, the effect of rectifier/inverter configurations on possible excitations of sub-synchronous resonance in a HVDC system is studied in depth. It is found from the results that there exists a best converter configuration, with which a HVDC system could intrinsically exempt from the sub- and super-synchronous resonance /$ see front matter 2005 Elsevier B.V. All rights reserved. doi: /j.epsr

2 428 C.-H. Lin / Electric Power Systems Research 74 (2005) Effect of HVDC harmonics on stressing turbine generator mechanism 2.1. Harmonics induced by interactions of HVDC converter stations Considering a typical HVDC system comprising a p-pulse rectifier station, a q-pulse inverter station and a DC transmission line to transmit power from a grid with frequency of f R to a grid with frequency of f 1, the DC- current is expected to consist of the pth and qth terms of harmonics corresponding to fundamental frequencies of f R and f 1, respectively. Practically, p and q could be 12, 18 and 24, while f R and f 1 could be 50 and 60. In addition, the harmonics attributing to impedances of AC and DC transmission lines as well as to impedances of AC and DC filters will also be expected to be present. So the DC- current can be expressed as following: i dr (t) = I dc + + A k sin(2π(kp)f R t + φ k ) k=1 B j sin(2π(jq)f I t + δ j ) + others (1) j=1 The DC- current will interact with the switching function of inverter, leading to complicated harmonics in the inverter side of AC system. The harmonics can be derived as following by using the theory of modulation [10]. i a INV (t) = i dr 2 3 π { cos 2πf I t + k=1 unlikely for sub- or super-synchronous disturbances to be excited in a synchronous. However, it is inevitable that the system frequencies of both the sending and receiving ends would shift apart from nominal ones and an is thus formed. For an, it turns to be possible to excite the sub- and/or super-synchronous disturbances on rotor torques of a turbine generator, depending on the converter configuration. For the 50 Hz/50 Hz and 60 Hz/60 Hz s, the frequencies of rotor torque disturbance were derived for various converter configurations under the assumption of small deviations in nominal system frequencies ( f R and f I ) of the power grids interconnected and the results are tabulated in Table 1. It can be found that sub-synchronous disturbances would be induced for the identical-pulse converter configurations, yet which are deemed to be harmless to the turbine generator mechanism because their frequencies are so low that far apart from the natural frequencies of almost all turbine generator units. However, there is still the possibility for resonance to be induced on occasion of large frequency deviations. As for the distinct-pulse converter configurations, they induce the high frequency disturbances alone. That means the 50 Hz/50 Hz and 60 Hz/60 Hz s with distinct-pulse converter configurations will exempt from inducing sub- or super-synchronous resonance. Similarly, the frequencies of rotor torque disturbance for the 50 Hz/60 Hz and 60 Hz/50 Hz s are derived and tabulated in Table 2. It can be seen that the [ 1 kq 1 cos 2π(kq 1)f It + 1 ] } kq + 1 cos 2π(kq + 1)f It (2) Since the magnitude would decrease as the harmonic order increased, just the harmonic currents modulated by k = 1 are noticeable. The modulation frequency then can be expressed as following: f mod = pf R (q ± 1)f I (3) 2.2. Disturbance on rotor torque The harmonic currents induced by modulation would inject into generators in close proximity to the inverter station, leading to disturbances on rotor torques of the turbine generator units. The rotor torque frequency complements with the modulation frequency, so the frequency of rotor torque disturbance can be expressed as following. f rotor = pf R (q ± 1)f I f I (4) Such rotor torque disturbances could be fatal on the occasion of offending the natural modes of turbine generator mechanical system. In general, the turbine shaft modes are located in sub-synchronous range, whereas the turbine blade modes in super-synchronous range. According to (4), it is frequencies induced are much more complex. Both the identical-pulse and distinct-pulse converter configurations may induce sub- and/or super-synchronous disturbances. For- Table 1 Frequencies of rotor torque disturbance for the 50 Hz/50 Hz and the 60 Hz/60 Hz s Converter configuration 50 Hz/50 Hz 60 Hz/60 Hz 12-Pulse/12-Pulse 12( f R f I ) a 12( f R f I ) a 18-Pulse/18-Pulse 18( f R f I ) a 18( f R f I ) a 24-Pulse/24-Pulse 24( f R f I ) a 24( f R f I ) a 12-Pulse/18-Pulse f R +16 f I f R +16 f I f R +18 f I f R +18 f I 18-Pulse/12-Pulse f R 14 f I f R 14 f I f R 12 f I f R 12 f I 18-Pulse/24-Pulse f R +22 f I f R +22 f I f R +12 f I f R +24 f I 24-Pulse/18-Pulse f R 20 f I f R 20 f I f R 18 f I f R 18 f I a In the range of sub- or super-synchronous frequency.

3 C.-H. Lin / Electric Power Systems Research 74 (2005) Table 2 Frequencies of rotor torque disturbance for the 60 Hz/50 Hz and the 50 Hz/60 Hz s Converter configuration 60 Hz/50 Hz 50 Hz/60 Hz 12-Pulse/12-Pulse f R 14 f I a 12 f R +10 f I a f R 12 f I f R +12 f I a 18-Pulse/18-Pulse f R 20 f I a f R +16 f I a f R 18 f I f R +18 f I 24-Pulse/24-Pulse f R 26 f I f R +22 f I a f R 24 f I f R +24 f I 12-Pulse/18-Pulse f R +16 f I a f R +16 f I f R +18 f I f R +18 f I 18-Pulse/12-Pulse f R 14 f I f R 14 f I f R 12 f I f R 12 f I 18-Pulse/24-Pulse f R +22 f I a f R +22 f I f R +24 f I a f R +24 f I 24-Pulse/18-Pulse f R 20 f I 24 f R 20 f I a f R 18 f I f R 18 f I a a In the range of sub- or super-synchronous frequency. tunately, most of their frequencies will be very low or be located in the vicinities of the system- or double-frequency, which were apart from the typical turbine natural frequencies. Thus, they should cause no concern in normal except that the system frequencies largely deviated. However, it can also be found that the 12-pulse/12-pulse, 18-pulse/18-pulse, 12-pulse/18-pulse and 18-pulse/24-pulse converter configurations are fatal to a 60 Hz/50 Hz. The disturbance frequencies induced by such configurations are in the vicinities of 20 or 80 Hz, which are within the typical natural frequency range of turbine generator exciter shafts. Thus, it is possible for electromechanical resonance to be induced. Particularly noteworthy is the 12-pulse/12-pulse configuration, which is standard nowadays yet performs badly. Furthermore, it is most important to observe that no sub- and super-synchronous disturbances would be induced under the 12-pulse/18-pulse and 18-pulse/24-pulse converter configurations for a 50 Hz/60 Hz and under the 18-pulse/12- pulse and 24-pulse/18-pulse converter configurations for a 60 Hz/50 Hz. That means neither the 50 Hz side nor the 60 Hz side of turbine generator units would be attacked by the sub- or super-synchronous torque disturbances if an 18(24)-pulse converter were adopted for a 60 Hz system and Fig. 1. Typical frequency distributions of 50 Hz systems. a 12(18)-pulse converter for a 50 Hz system, no matter power flows from the 50 Hz system to the 60 Hz system or reversed. Even under a special case of hydraulic units in sending end, of which the frequency may experience variation from 10% to +40%, the configuration of a 12-pulse converter in conjunction with a 50 Hz system and a 18-pulse converter in conjunction with a 60 Hz system still induces high frequency disturbances alone. It goes without saying that such a configuration is the best for HVDC s Frequency distribution of rotor torque disturbances The frequency distribution of rotor torque disturbances can be evaluated by considering the possible changes of frequency in power grids interconnected. In general, power systems perform different robustness in frequency deviation behaviors and can be divided into the weak and the strong systems. According to [11], the possible frequency changes of a weak and a strong 50 Hz system are in the ranges of and Hz, respectively, as shown in Fig. 1. As to a 60 Hz system, they are in the ranges of and Hz, respectively, for a weak and a strong one. The most probable frequencies are and Hz, respectively, for the strong and weak 50 Hz systems. The ones for the 60 Hz systems are 60.2 and 59.8 Hz, respectively. By applying the above frequency distributions to Table 2, we obtain the frequency distributions of rotor torque disturbances for various power system types in s. For convenience, the power system type is expressed as S/W if the rectifier side of AC system is a strong system and the inverter side of AC system is a weak system. Same meanings apply to S/S, W/S and W/W. Tables 3 and 4 demonstrate the results for a 50 Hz/60 Hz and a 60 Hz/50 Hz s, respectively. It can be seen that there are significant differences in disturbance frequencies under the different combi- Table 3 Frequency ranges (in Hz) of rotor torque disturbance for different power system types in a 60 Hz/50 Hz Converter configuration S/S S/W W/S W/W 12-Pulse/12-Pulse (20.3) (24.4) (15.6) (19.7) (120.6) (124.2) (115.8) (119.4) 18-Pulse/18-Pulse (80.6) (96.6) (73.4) (79.4) 12-Pulse/18-Pulse (80.0) (75.2) (84.8) (80.0) 18-Pulse/24-Pulse (19.7) (13.1) (26.9) (20.3) (120.0) (112.8) (127.2) (120.0) Note: the values in the brackets are the most probable ones.

4 430 C.-H. Lin / Electric Power Systems Research 74 (2005) Table 4 Frequency ranges (in Hz) of rotor torque disturbance for different power system types in a 50 Hz/60 Hz Converter configuration S/S S/W W/S W/W 12-Pulse/12-Pulse (0.2) (3.8) (3.8) (0.2) (120.6) (115.8) (124.2) (119.4) 18-Pulse/18-Pulse (60.5) (54.1) (65.9) (59.5) 24-Pulse/24-Pulse (120.8) (112.0) (128.0) (119.2) 18-Pulse/12-Pulse (59.9) (65.5) (54.5) (60.1) 24-Pulse/18-Pulse (0.4) (7.6) (7.6) (0.4) (120.0) (127.2) (112.8) (120.0) Note: the values in the brackets are the most probable ones. nations of converter configurations and power system type. For example, the most probable sub-synchronous disturbance frequency is 20.3 Hz for the power system type of S/S in a 60 Hz/50 Hz with the 12-pulse/12-pulse converter configuration, it turns to be 24.4, 15.6 and 19.7 Hz, respectively, if the power system type changes to S/W, W/S and W/W. Since a turbine mechanical system is usually a high Q system, the responses will be rapidly decreased if the disturbance frequency shifted a little apart from the natural frequency. Thus, maybe a turbine is safe in some types of power systems, but it will be put into risk in another types. For the 50 Hz/60 Hz with 18-pulse/18-pulse converter configuration, the disturbance frequency spreads from 50.2 to 84.4 Hz for the power system type of W/S; it turns to spread from 35.4 to 68.8 Hz for S/W type. That means we must pay attention to the super-synchronous disturbance for the power system type of W/S, whereas to the sub-synchronous one for S/W type. 3. Case studies The possible excitation of electromechanical resonance will be examined by considering a 60 Hz/50 Hz HVDC. Assume a 1300 MW turbine generator unit is connected to the 50 Hz side of, in paralleling with the grid. The unit comprises multi-stage steam turbines as HP, IP, LP1, LP2, LP3F and LP3R Frequency domain analysis A discrete-mass model, with parameters listing in Table 5, is employed to evaluate the response of turbine generator exciter shafts and blades due to the steadystate excitation by a rotor torque disturbance. Suppose that the terminal of generator rotor is a shaker, to which 1 pu of torque is applied, with frequency increasing from 0.01 to 150 Hz by an interval of 0.01 Hz. Fig. 2 shows the frequency scan responses at various shaft and blade sections of the 1300 MW unit. For reducing graph memories, an interval of 1 Hz is adopted in the figure. It can be found that the 12.51, 21.82, 33.01, and Hz Table 5 Model parameters of the 1300 MW unit Mass Inertia (MW-s/MVA) Damping (MW-s/MVA-rad) HP IP LP LP LP3F LP3R GEN EXC EXC B B B3F B3R Stiffness (MW/MVA-rad) modes are the principal natural modes, of which the previous three correspond to shaft modes and the latter two to blade modes. Table 6 tabulates the modal torques on each of sections for the five principal modes. It is clear that the 12.51, and Hz modes are sensitive at the LP2/LP3F, LP1/LP2 and GEN/EXC1 shaft sections, respectively. The Table 6 Frequency scan responses (in logarithm) of the 1300 MW unit Section Hz Hz Hz Hz Hz HP/IP IP/LP LP1/LP a LP2/LP3F a LP3R/GEN GEN/EXC a B a B a B3F a B3R a a The maximal response for each mode.

5 C.-H. Lin / Electric Power Systems Research 74 (2005) LP2/LP3F shaft will be in danger of damaging under such situations Time domain analysis Fig. 2. Frequency scan responses (in logarithm) at various sections of the 1300 MW unit and Hz modes are sensitive at B1, B2 and B3F, B3R blade sections, respectively. By approximately fitting the frequency ranges in Table 3 with the normal distribution function and further comparing them with the frequency responses of the 1300 MW unit, the probability for rotor torque disturbance to offend the principal modes can be evaluated. It can be found easily that the 12-pulse/12-pulse and 18-pulse/24-pulse converter configurations are harmful. Table 7 depicts the results. Both the and Hz modes would be excited under these two converter configurations no matter what types of power system interconnected. That will threaten the safety of LP1/LP2 shaft and B1, B2 blades, respectively, according to Table 6. The Hz mode will also be excited under the 12-pulse/12- pulse converter configuration for power system types of W/S and W/W and under the 18-pulse/24-pulse converter configuration for power system types of S/S, S/W and W/W. The A time domain simulation is usually clearer to demonstrate the electromechanical resonance behaviors. A program in Matlab-Simu Power System Blockset is thus implemented for this purpose. The system simulated is a 1000 MW (500 kv, 2 ka) DC transmitting power from a 500 kv, 5000 MVA, 60 Hz network to a 345 kv, 10,000 MVA, 50 Hz network. The 12-pulse/12-pulse converter configuration is used. The 1300 MW turbine generator is connected to the converter bus via a step-up transformer and a short transmission line. The DC transmission line is modeled with a 300 km distributed parameter line, with a smoothing reactor of 0.5 H on each side. The reactive power required by the converters is provided by a set of filters (capacitor bank plus 11th, 13th and high-pass filters, total 600 MVAR on each side). Both the rectifier and the inverter have a voltage and a current regulator operating in parallel. The simulation is made under the assumption that the rectifier side of frequency decreased to Hz. It takes about 7 s for the simulation to be stabilized, thus all the parameters are demonstrated from the time of 10 s. In steady state, the triggering angles are about 17 and 143, respectively, in rectifier and inverter units. It is expectable that the 17 and 117 Hz rotor torque disturbances will be induced on the 1300 MW unit. This will lead to electromechanical resonance because the natural mode of Hz will be offended DC- parameters Fig. 3 demonstrates the DC- current (i dr ) measured in rectifier side and the phase-a current in inverter AC-side (ia-inv) as well as their spectrums analyzing by the points FFT. It can be seen that there are about 2% of fluctuations in i dr. The principal AC components are the 12-th harmonics (717 and 600 Hz). For ia-inv, it will ideally be a 12-pulse waveform, yet we can observe that its stepwise waveform has been distorted. The principal distortion components are the 67 and 167 Hz harmonics, just as the prediction of modulation theory. These two harmonic currents Table 7 Probability to offend the principal modes under different combinations of converter configuration and power system type Converter configuration Power system type Hz Hz Hz Hz Hz 12-Pulse/12-Pulse S/S S/W W/S W/W Pulse/24-Pulse S/S S/W W/S W/W

6 432 C.-H. Lin / Electric Power Systems Research 74 (2005) Fig. 3. DC- parameters. Fig. 4. Turbine generator parameters.

7 C.-H. Lin / Electric Power Systems Research 74 (2005) are the sources to induce electromechanical resonance on the 1300 MW turbine generator unit Turbine generator parameters Fig. 4 demonstrates the turbine generator parameters, including the electric power deviation (DPe), spectrum of DPe and the shaft and blade torque deviations. The electric power deviation reflects the rotor torque disturbance on turbine generator exciter shafts. It is significant to observe from the spectrum of DPe that the 17 and 117 Hz components are clearly present just as the prediction. The 117 Hz component is fatal to the machine, even though with only about pu in its maximal peak-to-peak value, because it offends one of the natural modes of turbine blades. Thus, it can be seen that electromechanical resonance has taken place at blade sections with resonant frequency of 117 Hz. It is believed that the vibrations would increase to a level that is capable of damaging blades if the 117 Hz disturbance persists. On the contrary, the vibrations will decrease and stabilize and the blades will be safe if the resonance disappeared. As to shafts, the vibrations are negligible. 4. Conclusions The significant effect of converter configuration of a HVDC on possible excitation of electromechanical resonance has been studied in this paper. The results are summarized as follows. 1. Although the 12-pulse/12-pulse converter configuration is standard, it behaved badly in inducing electromechanical resonance. 2. For 50 Hz/50 Hz and 60 Hz/60 Hz s, the sub- and super-synchronous resonance could be prevented as long as the distinct-pulse converter configurations are adopted. 3. For 50 Hz/60 Hz and 60 Hz/50 Hz s, the risk of sub- and super-synchronous resonance would be wholly got rid of on either side of the even subjecting to large frequency deviations, if an 18-pulse converter was used on the 60 Hz side and a 12-pulse converter on the 50 Hz side. 4. Good match of the converter configuration and power system type is significant for avoiding resonance. However, it must be pointed out here that even though a turbine vibration mode is possibly offended, it does not mean the damages would occur. It still depends on a lot of factors to determine the degree of risk. References [1] M.C. Hall, D.A. Hodges, Experience with 500 kv subsynchronous resonance and resulting turbine generator shaft damage at Mohave Generation Station, IEEE Trans. Power Apparatus Syst. 70 (1976) [2] C. Chyn, R.C. Wu, T.P. Tsao, Torsional fatigue of turbine generator shafts owing to network faults, IEE Proc. Gener. Transm. Distribut. 143 (5) (1996) [3] T.P. Tsao, C.H. Lin, Long term effect of power system unbalance on the corrosion fatigue life expenditure of low pressure turbine blades, IEE Proc. Sci., Meas. Technol. 147 (5) (2000) [4] A.E. Malik, G.S. Hope, M. El-Sadek, Application of a thyristor controlled VAR compensator for damping subsynchronous oscillation in power systems, IEEE Trans. Power Apparatus Syst. 103 (1) (1985) [5] P.S. Dolan, J.R. Smith, W.A. Mittelstadt, A study of TCSC optimal damping control parameters for different operating conditions, IEEE Trans. Power Syst. 10 (November (4)) (1995) [6] B.K. Keshavan, N. Prabhu, Damping of subsynchronous oscillations using STATCOM a FACTS device, in: Transmission and Distribution Conference and Exposition, IEEE/PES, vol. 1, 2001, pp [7] B. Wan, Y. Zhang, Damping subsynchronous oscillation using UPFC- a FACTS device, Power System Technology, 2000, in: Proceedings of thepowercon 2002 International Conference, vol. 4, 2002, pp [8] T.J. Hammons, C.K. Lim, Y.P. Lim, P. Kacejko, Proposed 4 GW Russia Germany Link impact of 1 GW inverter station on torsional stressing of generators in Poland, IEEE Trans. Power Syst. 13 (1) (February 1998) [9] T.J. Hammons, T.C. Chua, K.H. Chew, Proposed Ireland North Wales power : steam turbine generator shaft torques due to steady harmonic ripple currents superimposed on the HVDC current in an, Int. J. Power Energy Syst. 21 (1) (2001) [10] R. Yacamini, How HVDC schemes can excite torsional oscillations in turbo-alternator shafts, IEE Proc., Pt. C 133 (6) (1986) [11] T.J. Hammons, P.A. Kacejko, J.J. Bremner, Torque in turbine generator exciter shafts due to DC currents in HVDC s, Electr. Machines Power Syst. 25 (1997)