[b]1 System Introduction[/b] The Yimin-Daqing 500kV transmission line transmits power from the Yimin Pithead Power Plant to load centers such as Daqing over a long distance. Currently, it is planned to install a series compensation device on the Fengtun side to meet the requirement of maximizing power output. At the same time, it is necessary to check the possibility of subsynchronous resonance (SSR) to prevent serious damage to the generator shaft system of the Yimin Power Plant. In the 2000 power grid planning of Northeast Central and Western China [1], the main network voltage is 500kV, and the 220kV and below networks are relatively small, with small exchange power with the main network, and have little impact on the electromagnetic transient process of the system. Only the main network can be retained, and it can be assumed that the Yimin, Fengtun and Daqing busbars have equal constant loads, keeping the generator output, busbar voltage, short-circuit current and other parameters basically consistent with the original system. To analyze SSR, the system diagram can be simplified, as shown in Figure 1. For the study of the electromagnetic transient process of the Yimin-Fengtun line section, the short-circuit capacity at the Harbin South busbar is considered to be 100p. u. This is equivalent to an ideal AC power supply with internal resistance. [img=281,96]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/dwjs/2000-5/10-1.jpg[/img] [b]2 Modal Analysis of the Mechanical Part of the Generator[/b] The Yimin Power Plant will install two 500MW Russian-made steam turbine generator sets and a 600MW imported domestic steam turbine generator set. The shaft system parameters are shown in Table 1 (since the manufacturer did not provide the shaft system model of the 500MW unit, all merging work was completed domestically. In order to meet the requirement that the simplified mass block and the continuous mass block have similar low characteristic frequencies, the natural segmentation point was not used in the processing. Therefore, some of the moments of inertia are inconsistent with the results obtained by conventional segmentation. Here, we will still temporarily name them according to conventional segmentation). The natural torsional vibration frequency fm of the unit shaft system was obtained under uncontrolled and damping-neglected conditions. The results are shown in Table 2. Using the eigenvalue analysis method, a linearized model was established, and the modal diagram was calculated as shown in Figure 2. Mode 1 of the 500MW generator has a natural torsional frequency of 14.949 Hz and a mode polarity reversal, that is, the polarity of the eigenvector elements corresponding to the high-pressure cylinder (HP), intermediate-pressure cylinder (IP), and low-pressure cylinder A (LPA) oscillates out of phase with that of low-pressure cylinder B (LPB), generator (GEN), and exciter (EXC), respectively. The main shaft is twisted between low-pressure cylinder A and low-pressure cylinder B. [img=312,393]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/dwjs/2000-5/11-1.jpg[/img][img=316,391]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/dwjs/2000-5/11-2.jpg[/img] Figure 2 Generator Modal Diagram [img=301,121]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/dwjs/2000-5/11-3.jpg[/img] Figure 3 The electrical system frequency scan shows that mode 2 of the 500MW generator corresponds to a natural torsional vibration frequency of 27.807Hz, with two mode polarity reversals; mode 3 corresponds to a natural torsional vibration frequency of 31.60Hz, with three mode polarity reversals; mode 4 corresponds to a natural torsional vibration frequency of 37.724Hz, with four mode polarity reversals; and mode 5 corresponds to a natural torsional vibration frequency of 50.215Hz, with five mode polarity reversals. The same modal diagrams for a 600MW generator can be analyzed. Typically, a turbine generator shaft system model with N masses, arranged in order of frequency i from low to high, corresponds to the model of the i-th mode, with i polarity reversals. [b]3 System Frequency Scan[/b] In engineering, the frequency sweep method is the most commonly used method for determining whether a power system with series compensation has experienced SSR (Series Surge). It is simple and easy to process. A unit current source is injected into the electrical system shown in the figure. Its frequency is variable. The active component R and reactive component X of the voltage at the system inlet are equivalent to the equivalent impedance, referred to as the system's frequency response. Here, the Frequency Scan function in EMTP is used. The frequency response of the system impedance obtained when the 500 MW generator is running alone (series complement KC = 60%) is shown in Figure 3(a). As can be seen from the figure, R is a small positive value between 18 and 19 Hz, and X changes from negative zero-crossing to positive. The system exhibits electrical resonance at this frequency, which is complementary to the 31.60 Hz mechanical torsional vibration frequency fm of mode 3 of the 500 MW generator shaft system (fe + fm = fN = 50 Hz). Therefore, through frequency sweep analysis, it is found that the system may experience subsynchronous resonance of mode 3 under this operating mode. Using the same method, the frequency response of the system impedance obtained when the 600 MW generator is running alone (series complement KC = 98%) is shown in Figure 3(b). The system's equivalent reactance is out of phase, which corresponds exactly to the subsynchronous resonance of mode 3 near 22.6 Hz of the generator shaft system. Note that the KC value is very high at this time. This is because in the simplified system, the series compensation is only calculated based on the Irving-Vonton line impedance, while the receiving end bus is far from Vonton. If the actual series compensation is calculated based on the Irving generator bus to the receiving end, the maximum is less than 50%. Of course, in the actual system, the series compensation will not be so large. The above analysis shows that the feasible series compensation of the system is mainly constrained by the 500 MW steam turbine generator set and should be below 60% with a margin. In addition, the subsynchronous resonance mode of mode 4 will not occur as can be seen in the following analysis, so frequency sweep analysis of the electrical system will not be performed here. 4 Eigenvalue Analysis The eigenvalue analysis method is widely used in academia. It is based on the small perturbation theory and is introduced in reference [2]. Based on the system in Figure 1, the small perturbation state equation of the machine-grid system is established, and eigenvalue analysis is performed on the state space matrix. For a single 500MW generator (low output Pe = 0.009 p.u.), the variation curve of the attenuation factor σ in the system eigenvalue (－σ±jω) when the series compensation KC in the line changes is shown in Figure 4(a). Similarly, the eigenvalue analysis results of the 600MW generator single-unit system (low output Pe = 0.009 p.u.) can be obtained, as shown in Figure 4(b). [img=315,139]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/dwjs/2000-5/12-1.jpg[/img] Figure 4 Eigenvalue analysis of the generator-grid system As can be seen from Figure 4, for the 500MW and 600MW generators, when the series compensation KC = 58%～67% and KC＞94%, respectively, their respective mode 3 torsional vibrations will occur, corresponding to shaft torsional vibration frequencies of 31.60Hz and 22.6Hz. This result is consistent with the frequency sweep result. Similar to the analysis results in reference [2], for the torsional vibration mode of mode 4, due to the sufficiently large damping effect in the system, the subsynchronous resonance frequency closest to the power frequency will not occur, which is the same for the 500MW and 600MW generator sets and the 892MVA unit in the IEEE first standard model. In Figure 4, the real part of the eigenvalue corresponding to mode 4 is stable at a certain negative value. This also indicates that for this system, the oscillation mode of mode 3 corresponding to the 500MW generator single unit system is the most dangerous and should be taken seriously. [b]5 EMTP Simulation[/b] Time-domain simulation is often used in engineering. For subsynchronous resonance, electromagnetic transient simulation program (EMTP) is usually used. For the system in Figure 1, the generators are 500MW and 600MW respectively. A simulation model is established, and the system has a small output in steady state (Pe = 0.009 pu). When the series compensation degree that induces SSR is used respectively, and the system is subjected to small disturbances, the simulation results are shown in Figure 5. By performing Prony analysis on the spectrum of the simulation results [3], the basic oscillation frequency of the electromagnetic torque Te in Figure 5(a) is 31.6 Hz, and the basic oscillation frequency in Figure 5(b) is 22.6 Hz. The electromagnetic simulation further intuitively describes the process of the occurrence and development of subsynchronous resonance in the system. [img=224,370]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/dwjs/2000-5/12-2.jpg[/img] Figure 5 Simulation results of electromagnetic torque Te of the unit when SSR occurs 6 Discussion on the resonant frequency of the unit shaft system The 500MW steam turbine generator set was supplied by Russia. The manufacturer did not provide the shaft vibration parameters, which could only be calculated by the design department according to the drawings. The natural torsional vibration frequency of mode 5 listed in Table 2 is 50.215 Hz. It is very close to the synchronous rotation frequency of 50 Hz. It is understood that this type of unit has been in operation for 2 years at the Panshan Power Plant in Jixian County without any obvious vibration problems. A request was made to the design department to calculate the natural vibration frequency, but the same result was obtained. The natural torsional vibration frequency of mode 5 in the 600MW steam turbine generator unit is 55.36Hz, which is very close to the 55Hz recorded during the overspeed test before the power plant was put into operation (previously 56Hz). This unit must have undergone an overspeed test before commissioning, so why was no obvious vibration problem found? The damping coefficients of the shaft torsional vibration of both types of steam turbine generator units were not obtained. It is difficult to determine whether this is because the damping of the two vibration modes is particularly large, thus preventing oscillations. Experts from the Shanghai Power Equipment Complete Set Research Institute believe that the natural vibration frequency of the shaft system should differ from the operating frequency by more than 5Hz to ensure safe operation or testing. In the SSR first standard model proposed by the American IEEE, the natural vibration frequencies of the shaft system are 15.7Hz, 20.21Hz, 25.55Hz, 32.28Hz, and 47.45Hz, with the highest frequency differing from the operating frequency of 60Hz by 12.55Hz, indicating that safety considerations were taken into account. The safety margin of the natural torsional vibration frequency of the 500MW and 600MW steam turbine generator sets is insufficient. It is also worth noting that in the simplified mass model of 500MW, the moment of inertia of the high-pressure cylinder is much smaller than that of the exciter mass, which is inconsistent with the usual concept. This is the result of the simplified parameters being provided by the unit that did not segment the generator shaft system according to the natural segmentation in order to obtain a characteristic frequency similar to that of the continuous mass model. [b]7 Summary[/b] (1) Due to the considerable length of the line, there is a possibility of SSR occurring in the system after series compensation. However, the equivalent impedance value of the receiving end is comparable to the impedance value of the compensated line, that is, the equivalent series compensation degree is reduced, so the frequency at which SSR may occur is reduced to one for each. (2) SSR is prone to occur when the Yimin Power Plant operates with a single generator, double circuit, and low generator output. (3) Compared with the 600MW generator, the 500MW generator is more prone to SSR. Therefore, when determining the series compensation degree, the 500MW generator should be the focus of the investigation under light load operation. (4) In actual engineering, the series compensation is 45%, which leaves a margin of 1/3, so SSR will not occur. (5) During the research process, questions were raised about the natural vibration frequencies of the shaft systems of the 500MW and 600MW generator sets. Further investigation has not resolved the issues, and experts are urged to conduct in-depth research. However, the questionable mode 5 is not the critical frequency at which SSR may occur in the system, so it does not affect the rest of the research conclusions.