The Impact of Integration of the VSC-HVDC Connected Offshore Wind Farm on Torsional Vibrations of Steam Turbine Generators

: For remote offshore wind farms, transmitting power to the main onshore grid via a Voltage Source Converter High Voltage Direct Current (VSC-HVDC) system is the mainstream of power transmission. It is not only cost-effective in long-distance transmission, but also can fully meet the grid side requirements such as black start, voltage support, fault ride through and frequency support. However, it still has some problems, such as the possible impact on the power grid needing to be paid attention to. In this paper, its impact on the torsional responses of turbine generator units neighboring to the onshore side of AC bus is studied by using the DIgSILENT PowerFactory software. It is found that the effects of the Sub-Synchronous Torsional Interaction (SSTI) with onshore controls and the generator de-rating operations can signiﬁcantly affect the damping ratio of turbine torsional modes, whereas the effects of the machine conﬁgurations and the amount of wind farm power integrated can affect the electrical torque disturbance. The most noteworthy is that their effects can be superimposed on each other if these factors act simultaneously, which would lead to increased vibrations and reduce the turbine shaft’ s life. The ﬁndings will be helpful for avoiding accidents caused by torsional vibrations when it is going to integrate a VSC-HVDC connected wind farm into a power grid.


Introduction
As offshore wind farms tend to be increasingly remote from land, VSC-HVDC transmission systems become the most suitable transmission method for transmitting wind power to onshore main grid. Such a VSC-HVDC connected offshore wind farm has the capabilities for black start and voltage (or reactive power) supporting to meet the grid side requirements. However, there are still challenges in capabilities of Fault Ride Through (FRT) and frequency (or active power) supporting, and thus, it attracts the attention of many researchers.
As for the studies on FRT, a lot of control strategies have been proposed. In [1], they proposed a control strategy for VSC-HVDC connecting a Permanent Magnet Synchronous Generator (PMSG)-based offshore wind power plant. The proposed strategy could wholly utilize the HVDC converters' capability. During the normal operation conditions, the normal loading capabilities of converters were fully used. During the fault periods, the overloading capabilities of converters were used to enhance the FRT performance. In [2], after considering time delay and reliability problems, they abandoned the commonly used communication methods adopted in offshore wind farms and proposed three offshore VSC-HVDC control strategies based only on local measurements. Each of the control strategy could meet all the requirements of frequency response, FRT, and power control. In [3], they proposed a control method for enhancing the FRT capacity of VSC-HVDC connected wind farms. When a fault takes place in power grid, a controlled voltage drop in the wind farm grid would be initiated. A preset DC voltage was then injected to suppress the DC component of the short-circuit current. Once the short-circuit current was decreased, the impact on both the Doubly-Fed Induction Generator (DFIG)-based units and the converters were alleviated. In [4], a FRT coordinated control strategy was proposed for the VSC-HVDC connected wind power system. The strategy improved the operation performance of both the VSC-HVDC system and the wind farms, however, the equipment investment didn't increase. During the grid fault periods, by reducing the power output of the wind farm, the VSC-HVDC system not only provided reactive power support for the power grid, but also effectively maintains power balance and DC voltage stability. In [5], they proposed an enhanced control strategy for the HVDC-link connected offshore wind farm arrays. In order to improve the FRT capabilities of HVDC-link and wind farms, a frequency controller was designed with the third harmonic injection technology. After the simulation analysis, the control strategy was proven to be effective in improving the reliability of offshore wind farm arrays. Recently, a review on this topic have been presented in [6]. The control methods of the VSC-HVDC transmission system were discussed on meeting the grid requirements, and the control strategies for enhancing FRT capability were focused on.
For the research on frequency supporting, even more strategies have been proposed, which were mainly based on adjusting the DC-link voltage of the VSC-HVDC system and coordinating the control of the VSC-HVDC system with that of wind farms. In [7], they proposed a control strategy for a VSC-HVDC system to provide inertial response. By using this control strategy, the VSC-HVDC-connected wind farm could behave like a synchronous generator with inertia, and the stability could thus be enhanced. The control strategy was achieved by two control approaches. The one was the inertial synchronizing control which was applied in the receiving end converter. The other was the frequency mirroring control which was applied in the sending end converter. This control strategy was particularly suitable for applying to the weak grid condition. In [8], a control strategy was proposed to improve system inertia. They adopted a cascaded control scheme to exert the DC capacitor energy and wind turbine inertia. The control strategy could not only provide inertia to enhance frequency stability, but also minimize the control impacts when utilizing wind energy. However, the communication between offshore and onshore converters was still necessary for such a control strategy. In [9], they proposed a coordinated control strategy for a VSC-HVDC system to imitate the inertia of synchronous generators without the necessity of remote communication. For the grid side converter, there is a droop DC voltage control, by which the DC link capacitors released or absorbed energy. For the wind farm side converter, it changed the output frequency according to the DC voltage. Based on such a mechanism, the two side of AC systems were coupled. In [10], they also developed an artificial coupling between the wind farm grid and the main grid. The frequency coupling was achieved by the use of droop controllers for the DC voltage control. In [11], they proposed a coordinated control scheme to support the system frequency regulation. The approach was to control the DC link voltage by releasing or absorbing the energy of the capacitors. The most noteworthy was that such a frequency supporting control could be finely coordinated with the offshore wind farm, according to the delay of offshore wind farm responding to onshore grid frequency excursion, to further enhance the system frequency response. In [12], they proposed a frequency regulation strategy for a VSC-HVDC-integrated offshore wind farm. The approach consisted of two stages. The first was the frequency decrease stage. In this stage, the rotor kinetic energy of wind turbines was used to suppress the frequency decrease. The second was the rotor-speed recovery stage. In this stage, the DC capacitors were used to release power to compensate for the output power deficiency of wind farms. In [13], they proposed a coordinated control scheme for a VSC-HVDC-connected wind farm with a battery energy storage system. Not only the wind farms, but also the battery energy storage system contributed to generating the synthetic inertia. For the VSC-HVDC system, the frequency supporting was achieved by regulating the DC-link voltage just as the usual. However, during the rotor-speed recovery of wind turbines, the deficiency power was supplied by the battery energy storage system. Since the research on this topic was quite comprehensive, some reviews have been proposed recently. In [14], they reviewed and compared various frequency-control strategies for a VSC-HVDC connected wind farm. The advantages and drawbacks of each frequency regulation method were presented. Furthermore, for verifying the effectiveness and robustness of those strategies, simulation studies were made by using the PSCAD/EMTDC software.
It can be seen from the literature survey that the barriers for the integration of VSC-HVDC-connected wind farm to meet the grid side requirements have been almost overcome. However, in fact, there are still the impacts of VSC-HVDC-connected wind farms on grids that need to be paid attention to. One of the most noteworthy is the Super-or Sub-Synchronous Oscillation (SSO) problem. In [15], they found that the high frequency resonance could also occur in the interconnected system where the VSC-HVDC connects to the DFIG-based wind farm. The occurrence mechanism of such a high-frequency resonance was investigated based on the impedance model of both the DFIG and the VSC-HVDC system. Furthermore, a damping control approach was proposed to improve the high frequency resonance problem. In [16], the SSO that occurred in a DFIG-based wind farm integrated with a VSC-HVDC system was investigated. They proposed an impedancebased simplified equivalent circuit to assess the start-oscillating condition for the SSO. The circuit of DFIGs was equivalent to an inductance in series with a negative resistance, while the equivalent circuit of VSC-HVDC had a resistance-capacitance structure. When the DFIG-based wind farm integrated with the VSC-HVDC system, an equivalent RLC resonance circuit with negative resistance was formed. The oscillation would be induced if any of the oscillation modes had negative damping. In [17], the SSO problem of the VSC-HVDC-connected direct-drive wind farms was investigated. They established the dynamic mathematical models for the direct-drive wind farm and for the VSC-HVDC system. Modal analysis was adopted for the investigation. Based on the studying results of participation factor, it was shown that the SSO was mainly affected by the grid-side converter controls of the direct-drive wind farm and the rectifier controls of the VSC-HVDC system. In [18], a path analysis method was proposed for studying the SSO mechanism for a direct-drive wind farm connecting with a VSC-HVDC system. The studies were focused on the oscillation mode dominated by the DC capacitor link. It was shown from the results that the disturbance transfer path between the direct-drive wind farm and the VSC-HVDC presented a four-loop coupling relationship, which would lead to the SSO. As the research on this topic is still under development, no review has yet appeared.
It can be seen from the above surveys that almost all research on the SSO induced by the VSC-HVDC-connected wind farm was focused on a single factor: the SSTI. As a matter of fact, there are other factors could affect the SSO; to make up for the deficiency, in addition to the SSTI, three factors (i.e., the generator de-rating operations, the machine configurations, and the amount of wind farm power integrated) are also studied in this paper. This paper is focused the torsional responses of turbine generator units neighboring to the onshore side of the VSC-HVDC system. Furthermore, the effect when these factors act simultaneously is further studied. The results show that the effect of these factors can be superimposed on each other. Therefore, the influence of the VSC-HVDC-connected wind farm on sub-synchronous torsional vibrations cannot only consider a single factor, but must consider the combined effect of all factors.

System Studied
The system studied is shown in Figure 1, which is modified with reference to the demonstration system in [19,20]. A VSC-HVDC transmission system, of which the capacity is 400 MW, is designed to transmit the power of an offshore wind farm to the onshore grid. The wind farm consists of 80 wind turbines. Each wind turbine is equipped with the DFIG units and has a nominal active power of 5 MW. If all the wind turbine generator units are operational, the wind farm can generate up to 400 MW of power in total. The AC bus voltages of the sending and receiving ends are 155 kV and 110 kV, respectively. At the receiving end of AC bus, there are two traditional steam turbine generator units, G1 and G2. The G1 is a 255 MVA unit, and the G2 is a 192 MVA unit.

System Model
The DIgSILENT PowerFactory software is adopted for the analysis and simulations. Built-in models are employed to implement the system studied. However, the model of steam turbine generator units needs to be modified, and the controllers of DFIG and VSC-HVDC need to be properly set.

Steam Turbine Generator Unit
For studying the behaviors of the turbine generator unit, the built-in six-order model is adopted for modeling the synchronous generator. And the IEEE Type1 AVR (Automatic Voltage Regulator) is adopted for the voltage regulation. However, for the turbine-andgenerator mechanism, the two-mass model is adopted in the built-in synchronous generator model, which is not enough for the studies. Thus, the turbine-and-generator mechanism is modified to the multi-mass model. For the G1 unit, which is equipped with a high-pressure turbine (HP), an intermediate pressure turbine (IP), and two low pressure turbines (LPA and LPB) in additional to the generator rotor (GEN), the five-mass model is used. For the G2 unit, which is equipped with HP, IP, LP, and GEN, the four-mass model is used. The lumped mass-damping-spring model of the multi-mass model is shown in Figure 2, of which the model parameters are listed in Table 1. Based on the model, the dynamic equations can be obtained as the following. It must be noted that T i will be the minus electromagnetic torque (−T e ) for the generator rotor section.

DFIG
The built-in DFIG generator model provided by the DIgSILENT PowerFactory software is adopted, of which the architecture is shown in Figure 3. Mainly, it is divided into four parts: wind turbine, induction generator, power controller, and protection system. For the wind turbine part, it adopts the lumped mass-damping-spring model with two masses. The large mass and the small mass correspond to the wind turbine inertia and the generator rotor inertia, respectively. For the shaft, only the low-speed shaft is considered, and the high-speed shaft is assumed to be rigid. Moreover, there is a pitch control system to regulate turbine speed.
For the induction generator part, it is a model integrating the induction machine and the converter. The behaviors of the induction machine can be described by the following equations.
T e = p w s ψ qr i dr + ψ dr i qr = p w s ψ ds i qs + ψ qs i ds (5) u s ,i s ,ψ s : space vector of stator voltage, current and flux; u r ,i r ,ψ r : space vector of rotor voltage, current and flux; i qs ,i qr ,ψ qs ,ψ qr : q-axis stator current, rotor current, stator flux and rotor flux; i ds ,i dr ,ψ ds ,ψ dr : d-axis stator current, rotor current, stator flux and rotor flux; T e : electromagnetic torque; p: pole pair; w s : synchronous angular velocity; w r : angular velocity of rotor.
For the converter, the grid-side converter is neglected, and the DC-link is assumed to have a constant voltage. The Rotor-Side Converter (RSC) is controlled by the modulation indices (i.e., P mq and P md ) to generate the AC-voltage at the slip rings, which can be expressed as the following: where U rnom is the nominal rotor voltage. For the power controller part, there is an outer loop to regulate the active and reactive power, and an inner loop to regulate the active and reactive current. By regulating the qand d-axis rotor currents, respectively, the active and reactive power can be controlled. The active power reference is obtained from the maximum power tracking algorithm, while the reactive power reference is obtained from the power factor controller. For the protection system, two of the more important are the over-frequency protection and the crowbar protection. The over-frequency protection is to modify the active power reference in case of fault situations. The crowbar protection is to disable the RSC during fault periods to cause DFIG to behave as a squirrel cage induction generator with an increased resistance.

HVDC Controls
The HVDC control is based on a generic structure. It consists of two separate composite models: one controls the onshore converter with chopper resistors, and the other one controls the offshore converter.

Onshore Converter Control
The built-in generic onshore controller is shown in Figure 4. The onshore converter is a voltage source converter. It can control the active current as well as the reactive current. The control objective of the active current is the DC voltage, which is done by a PI controller with proportional gain K d and integral time constant T d . The control objective of the reactive current can be selected by the mode switch. The mode 1 (i.e., the control objective is the voltage via a droop) is selected here in the studies. The PI controller with proportional gain K u , and integral constant K iu is used to regulate the reactive current. The reference currents are given by the following equations. The current limiter has the priority adjudication function. In normal operation, the active current takes priority, and the reactive current is limited. When a fault occurs, the reactive current gets priority, and the active current is limited.
The current controller takes the reference currents from the main controller and calculates the modulation index which is then passed to the converter. The PI controller with proportional gain K pm and integral time constant T pm is used to regulate the modulation index by the following equations.
To protect the converter, the system is equipped with a chopper-controlled resistor on the onshore side. The control architecture is shown in Figure 5. When there is a fault taking place on the onshore grid, the DC circuit will be charged. When the DC voltage exceeds a certain limit, the chopper controller will send gate signals to trigger the chopper DC valves to limit the voltage to an appropriate value.

Offshore Converter Control
The built-in generic offshore controller is shown in Figure 6. It regulates and maintains the voltage and frequency of the offshore grid by the modulation index P m and frequency command f 0 . The modulation index is controlled by two cascaded PI controllers and a forward controller. The first stage PI controller regulates the voltage to generate the reactive current reference which is then output to the second stage PI controller. The second stage PI controller continues to regulate the reactive current to generate reference voltage which is then output to the feedforward controller. The reference reactive current and the reference voltage are given by the following equations. Finally, the feedforward controller adjusts the reference voltage according to the modulation method to generate the modulation index. Figure 6. Offshore controller.

Preliminary Studies
In order to understand the torsional characteristics of the generator units studied, a basic study including modal analysis and transient simulation has been done. It is assumed in the study that the steam turbine generator units (G1 and G2) operate with rated power, and all the wind power generator units are active.
By using the modal analysis function provided by DIgSILENT PowerFactory, the eigen-analysis can be made to obtain the torsional modes of the steam turbine generator units. The results are listed in Table 2. It can be seen that there are four torsional modes for the G1 unit. The frequencies are 16.59, 23.38, 29.66, and 40.16 Hz, respectively, for the modes 1, 2, 3, and 4. For the G2 unit, there are three torsional modes. The frequencies are 24.76, 28.04, and 46.62 Hz, respectively, for the modes 1, 2, and 3. Since none of the damping ratio of modes is negative, the G1 and G2 units will be stable in torsional dynamics. The time-domain torsional vibrations can be simulated by using the electromagnetic transient simulation function provided by the DIgSILENT PowerFactory. Based on the resulting torsional responses, the main vibration modes for various turbine shafts are tabulated in Table 3. It can be seen that the torsional response at the shaft LPB_GEN of G1 unit will be dominated by the mode 3, whereas that at the shaft HP_IP will be dominated by the mode 2.

Studies and Discussions
In order to comprehensively investigate the influence of the VSC-HVDC-connected wind farm on sub-synchronous torsional vibrations of turbine generator units neighboring to the onshore side of VSC-HVDC system, each of the four factors (i.e., the SSTI with onshore controls, the generator de-rating operations, the machine configurations and the amount of wind farm power integrated) is studied individually. After that, the combined effects of the four factors are further studied.

Effect of SSTI with Onshore Controls
In general, both the DFIG controls and the HVDC controls might have the potential to cause SSTI problems. However, since the DFIGs are decoupled from grid by the VSC-HVDC system, there won't be the SSTI between the DFIG controls and torsional modes of steam turbine generator units on the onshore side of network. So, only the SSTI with the HVDC controls needs to be studied. For the HVDC controls, however, the offshore converter controller is also decoupled from the onshore network via the DC link, there is also no possibility of causing SSTI. Therefore, only the onshore converter controls are focused on here for the studies on SSTI.
The regulation function of onshore converter control is achieved mainly by the three controllers: DC voltage controller, droop controller and current controller. The nominal setting of parameters is tabulated in Table 4. Firstly, modal analysis is made. For studying the effect of K d on SSTI, K d is varied from 0.1 to 40 for the modal analysis. The result for the G1 unit is shown in Figure 7. The effect is small for the modes 1, 2 and 3, while the mode 4 is completely unaffected. The most affected one is the mode 3, of which the damping ratio has a 17% change (varying from 0.000377 to 0.000442). The trend of influence is that the larger the K d , the greater the damping ratio.
For studying the effect of K u on SSTI, K u is varied from 1 to 30 for the modal analysis. The result for the G1 unit is shown in Figure 8. It can be seen that the effect is significant for the modes 1, 2 and 3, while the mode 4 is completely unaffected. The damping ratio of mode 1, 2 and 3, respectively, has a 13%, 8%, and 46% change (respectively varying from 0.002757 to 0.002451, from 0.002187 to 0.00203, and from 0.000489 to 0.000386). The trend of influence is that the larger the K u , the smaller the damping ratio.  For studying the effect of K pm on SSTI, K pm is varied from 0.2 to 3 for the modal analysis. The result for the G1 unit is shown in Figure 9. The effect is also significant for the modes 1, 2 and 3, while the mode 4 is completely unaffected. The damping ratio of mode 1, 2 and 3, respectively, has a 20%, 9%, and 65% change (respectively varying from 0.002148 to 0.002595, from 0.001934 to 0.002111, and from 0.000276 to 0.000456). The trend of influence is that the larger the K pm , the greater the damping ratio. Since modal analysis only shows the change in the damping ratio of torsional modes, it is necessary to further make transient simulations to understand how much the shafts vibrations have actually changed. For the transient simulations, it is assumed that a threephase short circuit fault is applied to the 380 kV bus at the onshore side of network at 0.1 s, and is cleared after 0.15 s. The two parameter settings listed in the following are studied.
For the two settings, the damping ratio of modes 1, 2, and 3, respectively, has a 16%, 10% and 55% change (respectively changing from 0.002654 to 0.002284, from 0.002136 to 0.001943 and from 0.000496 to 0.00032). In Figure 10, it shows the torsional angles of various turbine shafts for the G1 unit for the two settings. It can be seen obviously that the setting 1 is better than the setting 2. For the setting 1, each shaft exhibits slighter vibration than that for the setting 2. The shaft LPB_GEN is found to present the most significant change in vibration. This is due to that the vibration at this shaft is dominated by the mode 3.

Studies on the G2 Unit
Similar results can be obtained for the G2 unit. For the two different parameter settings, the damping ratios of G2 modes are shown in Table 5. There can be 28% of difference for the mode 2. The transient torsional responses shown in Figure 11 reflect such a difference in attenuation behaviors.  Figure 11. Torsional responses of G2 unit for different parameter settings.

Effect of Generator De-Rating Operations
Since the incorporation of wind farms into a system can replace some of the power of traditional generator units, traditional units may operate with de-rated power. The de-rating operation might cause their torsional characteristics to change, so such an effect needs to be studied.

Studies on the G1 Unit
Firstly, the modal analysis is made by varying the operation power of G1 from 100% to 70% of rated power. The resulting damping ratios of various modes are shown in Figure 12. The damping ratios are significantly affected by the de-rating operations. The trend of influence is that the less the operation power, the smaller the damping ratio. Among the modes, mode 2 is the most affected one, of which the damping ratio decreases from 0.002079 to 0.000304, which is a staggering 85% drop. For the modes 1, 3 and 4, there are 58%, 21% and 46% of drop, respectively. Then, the transient simulation is made by using the events the same as the previous studies. The torsional responses for operations with 100% and 80% of rated power are compared. In Figure 13, it shows the results. The de-rated power operation condition shows greater vibrations compared to the rated power operation condition. Among the shafts, the shaft HP_IP and the shaft IP_LPA present the greatest difference in vibrations. This is due to that the main vibration composition of these two shafts is the mode 2.

Studies on the G2 Unit
For the G2 unit, similar results can be obtained. The damping ratios of G2 modes as affected by de-rating operations are shown in Figure 14. The most affected one is the mode 3. The transient torsional responses shown in Figure 15 present a significant difference in vibrations between the operation conditions with rated power and with de-rated power.

Effect of Machine Configurations
When the wind farm power introduced is sufficient enough, it is possible to shut down some of the nearby traditional generator units. This leads to the change in machine configuration, to which attention should be especially paid. For studying such an effect, the following two machine configurations are adopted for the comparison studies. Both modal analysis and transient simulations are then conducted to understand the responses of G2 unit. G1 + G2 configuration: both G1 and G2 are active; G2 alone configuration: G1 is shut down.

Studies on the G2 Unit
For the modal analysis, the damping ratios of G2 modes for the different machine configurations are shown in Table 6. It can be seen that the damping ratio of each vibration mode changes only slightly. That means the effect of machine configurations will hardly affect the behavior of torsional responses. For the transient simulation, the responses subjecting to the same events as previous are studied. In Figure 16, it shows the electrical torque of G2 for the different machine configurations. It can be seen that for the G2 alone configuration, the electrical torque of G2 presents larger disturbance during the fault and fault clearance. The larger disturbance, of course, would excite larger vibrations on shafts. In Figure 17, it shows the torsional responses of various shafts. It can be seen that every shaft presents severer vibrations for the G2 alone configuration. For the shaft HP_IP and the shaft IP_LP, the difference in peak-to-peak value of initial vibrations can reach up to 1.5 times. By observing the shape of these vibrations, it can be found that although the vibration amplitude becomes larger, the attenuation rate does not change. This means that the increase in electrical torque disturbance is the main cause of the greater vibrations, instead of the change in damping ratio of torsional modes.

Studies on the G1 Unit
For the G1 unit, similar results can be obtained. In Figure 18, it shows the torsional responses of shafts. It can be seen that every shaft presents severer vibrations for the G1 alone configuration.

Effect of the Amount of Wind Farm Power Integrated
The generation power of wind farm (or the transmission power of VSC-HVDC system) is the other factor that could influence the electrical torque disturbance of turbine generator units. For studying such an effect, it is assumed that half of the wind turbine generator units are shut down for the modal analysis and transient simulations. The results for integration of different wind farm power are then compared.

Studies on the G2 Unit
For the modal analysis, in Table 7 are shown the damping ratios of torsional modes of G2 unit for integration of various wind farm power. The amount of wind farm power integrated can hardly have influence on the damping ratio of torsional modes. By comparing the results of integration of 400 MW and 200 MW of wind farm power, the damping ratio of modes 1 and 2 has only 1% and 3% change, respectively.  Figure 19, the electrical torque of G2 is shown when integrating different wind farm power. It can be observed that there is a slight difference between the two situations. For the integration of 200 MW of wind farm power, the electrical torque disturbance caused by the fault and fault clearing is slightly greater than that for the integration of 400 MW of wind farm power. However, although the difference in electrical torque disturbance is small, the difference in shafts vibrations caused by it is obvious. In Figure 20, it shows the shafts' torsional responses for integration of different wind farm power. It can be seen obviously that the torsional vibrations for the integration of 200 MW of wind farm power are severer. In the case of shaft HP_IP, the difference in peak-to-peak value of initial vibrations is about 1.3 times.

Studies on the G1 Unit
For the G1 unit, similar results can be obtained. In Figure 21, it shows the shafts torsional responses for integration of different amount of wind farm power. It can be seen obviously that the torsional vibrations for the integration of less wind farm power are severer.

Discussions on Combined Effect
According to the results in previous studies, it can be seen that the effect of SSTI with onshore controls and the effect of generator de-rating operations are to influence the damping ratio of torsional modes but would not affect the electrical torque disturbance. The role of machine configurations and the role of the amount of wind farm power integrated are just the opposite, which will affect the electrical torque disturbance but can hardly affect the damping ratio of torsional modes. It is interesting to know what will happen if various factors occur at the same time. For figuring out the problem, the following 5 cases as shown in Table 8 are studied by the modal analysis and transient simulations. The case 1 is the basic case. The cases 2, 3, 4, and 5, respectively, are to successively examine the effects of SSTI with onshore controls, the amount of wind farm power integrated, machine configurations and generator de-rating operations.   For the modal analysis, the damping ratios of G1 modes for the 5 cases are shown in Figure 22. The effects of various factors are superimposed. Firstly, the bad control parameter setting greatly reduces the damping ratios. Then the less wind farm power integrated and the single unit configuration make the damping ratios continue to decrease slightly. Finally, the generator de-rating operation greatly reduces the damping ratios once more. Furthermore, according to this figure, the degree of influence of various effects can be distinguished. The de-rating operation has the largest effect, the SSTI with onshore control comes next, the following is the machine configuration, and the amount of wind farm power integrated has the smallest effect. For the transient simulations, the shafts torsional responses for the five cases have been studied under the same events as previous. In order to compare the effects of the five cases, the torsional responses of shaft LPB_GEN for the five cases are shown in Figure 23.
The effect of various cases layered on top of each other can be seen. Once again, it confirms that various effects have the characteristics of superposition on each other. Due to the characteristics of superposition for various effects, the torsional responses will be significantly different under the good and the bad situations. In Figure 24, it shows the torsional responses of various shafts for the cases 1 and 5. It can be seen from the figures that the initial vibrations of each shaft differ by about 10%. Then, the difference in vibration magnitude gradually increases. Finally, the difference reaches up to six times or so.

Studies on the G2 Unit
For the G2 unit, similar results can be obtained. In Figure 25, the damping ratios of G2 modes for the 5 cases are shown. The effects of the various factors are superimposed. In Figure 26, the torsional responses of shaft LP_GEN for the 5 cases are shown. The effect of various cases layered on top of each other can be seen. It confirms again that various effects have the characteristics of superposition on each other.

Conclusions
It can be seen from the studies of the paper that some factors could influence the subsynchronous torsional vibrations of turbine generator units when a VSC-HVDC connected offshore wind farm is integrated into a power grid. The noteworthy results are summarized in the following points: (1) For the effect of SSTI with onshore controls, the bad parameter setting could result in a reduction in damping ratio of turbine torsional modes for more than 50%. This would cause the vibrations to last much longer. (2) For the effect of generator de-rating operations, the reduction in damping ratio of torsional modes can be up to 85% when the generator unit operates with 70% of rated power. It has an even greater impact on the damping ratio of torsional modes than the effect of SSTI with onshore controls, however, less attention has been paid to it.