Complex Torque Coefficient Method Research Articles

Corrected complex torque coefficient method for synchronization stability analysis of grid‐connected VSC

AbstractSub‐synchronous oscillation of grid‐connected voltage source converter (VSC) dominated by phase locked loop (PLL) is an important stability issue in nowadays power systems. The complex torque coefficient method has been used to investigate the issue because of its advantage of giving insights into source of damping and contributions of different components on damping. However, it is found that the classic complex torque coefficient method is not entirely applicable for stability analysis of VSC because of the proportional term in PLL. This paper proposes a corrected complex torque coefficient method and defines synchronous and damping coefficients. Based on the proposed method, a small‐signal stability criterion is obtained, in which the system stability depends on the sign of corrected damping coefficient. The impacts of different elements on system damping can be quantitatively evaluated through the method. It is drawn that current control loop and line dynamics contribute negative damping, whereas power control loop contributes positive damping. Moreover, the impacts of operating conditions and controller parameters on damping of different elements are analysed. The eigenvalue analyses and electromagnetic transient simulations have verified the theoretical analysis.

Method to Evaluate the Impact of Integration of PMSG on Stability of Synchronous Generator Shaft Under Weak Grid Connection

With the continuous growth in the amount of wind power accessed by the AC grid, the impact of the grid connection of wind-power generators with the power system has gradually increased. In this study, the subsynchronous oscillation of a synchronous generator (SG) shaft caused by the integration of direct-drive permanent-magnet synchronous generators (PMSGs) was investigated. The mechanism governing the effect of the connection strength between the PMSG and AC power system on the stability of the generator shaft system was analyzed based on the complex torque coefficient method. When the connection strength between the PMSG and AC power system weakens, the same voltage variation that occurs at the point of common coupling of the PMSG stimulates more intense power fluctuations in the PMSG, and the electrical damping injected by the PMSG into the SG increases considerably. This may cause the oscillation mode dominated by the generator shaft system to move to the right half of the complex plane, thereby reducing the stability of the generator shaft system. In addition, the evaluation process of the influence of the PMSG on the SG shaft system was summarized, and the proposed method can determine the stability of the AC power system after the integration of the PMSG. Finally, the effectiveness of the proposed method was validated via study cases, and conclusions were drawn. This method is expected to serve as a useful tool for the risk assessment of subsynchronous oscillations in wind farms.

Research on Aggregation Model of Wind Farm Based on SSO Complex Torque Coefficient Analysis

In order to study the influence of the clustering aggregation of doubly-fed wind turbines (DFIG) in the wind-fire bundling system on the system subsynchronous oscillation (SSO), the expression of the DFIG output active power on the electrical damping De of thermal power units is first derived. Then the wind-thermal bundling system is built based on the IEEE first bench mark, and the wind farm is aggregated to several groups according to the rated power. The complex torque coefficient method is used to analyze the two cases of the same running state of the wind turbine and the difference of wind speed between the turbine and verified by time-domain simulation. The results show that the difference in wind speed within the DFIG groups has little effect on the system oscillation frequency before and after the aggregation of the wind farm, but there may be a slight error in the electrical damping coefficient before and after the aggregation,but the error does not affect the trend and analysis of damping characteristics of system. When studying the influencing factors of wind-fire bundling system SSOthe aggregated model can be uesd to improve simulation efficiency.

The occurrence mechanism and damping method of ultra‐low‐frequency oscillations

The ultra-low-frequency oscillation (ULFO) problem has reappeared in China recently. Although the hydraulic generator is supposed to have a strong connection to this problem, the conditions for ULFO appearance and detailed reasons are not clear yet. In order to clarify the occurrence mechanism of ULFO, this paper studies each important part of hydraulic generator system, including the governor, exciter and power system stabiliser (PSS). The weak connection is confirmed to have an important impact on the occurrence of the ULFO. Nevertheless, by studying each device's contribution to ULFO through the complex torque coefficient method, it is shown that the negative damping effect of the hydraulic governor will cause the instability in the ultra-low-frequency band, while the exciter and the PSS have little influence on ULFO. Additionally, the proportional–integral parameters of the hydraulic governor system are also studied to clarify their influence on ULFO based on the complex torque coefficient method. Based on the above analysis, two damping methods for ULFO suppression are finally proposed. To verify theory and damping methods, the simulations are implemented in PSCAD and PSASP software.

Impact of Power Grid Strength and PLL Parameters on Stability of Grid-Connected DFIG Wind Farm

This paper investigates the impact of powergrid strength and phase-locked loop (PLL) parameters on small signal stability of grid-connected doubly fed induction generator (DFIG)based wind farm. Modal analysis of the grid-connected DFIG wind turbine under different operating conditions and various power grid strengths are investigated at first. Modal analysis results reveal that the DFIG connected to a weak grid may easily lose stability under the heavy-duty operating conditions due to PLL oscillation. The object of this paper is to identify the PLL oscillation mechanism as well as influence factors and propose a damping solution for this oscillation mode. A simplified linear system model of the grid-connected DFIG wind turbine is proposed for analyzing the PLL oscillation. Through the complex torque coefficients method and using this model, the oscillation mechanism and influence factors including the power grid strength and the PLL parameters are identified. To suppress this PLL oscillation, a mixed H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> /H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> robust damping controller is proposed and designed for the DFIG. Electromagnetic transient simulation results of both singleDFIG system and multiply-DFIG system verify the correctness of the analysis results and effectiveness of the proposed damping controller.

Investigation on sub‐synchronous oscillations in DFIG‐based transmission system based on improved complex torque coefficients method

The complex torque coefficients (CTC) method has been widely adopted to investigate the conventional sub-synchronous oscillation (SSO) issues. However, the application of the CTC method is limited when large-scale wind power generations are integrated into power systems. Therefore, in order to overcome the disadvantages of the CTC method on the aspects of frequency scan and stability determination, this paper proposes an improved CTC method based on the shaft system modal decoupling and small-signal self-excitation theory. The improved method is demonstrated and validated through the IEEE first benchmark power system (FBMPS). By establishing the small-signal model of the series-compensated DFIG-based transmission system, the proposed method is applied to examine the SSO in a grid-connected DFIG system. Moreover, the impacts of different parameters on the electrical damping characteristics of the system are deeply analysed. In addition, an effective VSC control strategy for suppression of the SSO in series-compensated DFIG-based transmission system is proposed.

Large-Scale Power Base’s Impact on Low Frequency Oscillation Characteristic in UHVAC Power Transmission System

The dynamic stability of ultra-high voltage alternating current (UHVAC) transmission system with large-scale power bases has not been clearly discussed before. This paper studies the low frequency oscillation (LFO) characteristic of UHVAC system through complex torque coefficient method (CTCM) and finds out the reasons why UHVAC system is more vulnerable to LFO problem. It is pointed out that the bulk capacity and long distance make UHVAC system’s damping torque coefficient much smaller than conventional system’s, which lets UHVAC system’s operation point closer to the safety edge and decreases system’s dynamic stability. The comparisons between UHVAC system and conventional system in practical multi-machine systems further validate the theoretical analysis. Finally, the suggestions for UHVAC systems are given based on the analysis in the view of dynamic stability.

Application of UPFC to mitigate SSR in series‐compensated wind farms

Flexible AC transmission systems have shown effective functionalities in promoting the system operation security and service reliability. Facing with series-compensated lines, subsynchronous resonance (SSR) may jeopardise the stability and mechanical facilities. The control strategy and simulation model of a unified power flow controller (UPFC) based on the dq decoupling control are deduced and constructed. Considering the impacts of grid-connected wind farms, SSR characteristics of the series-compensated system with UPFC are studied by the complex torque coefficient method and time-domain simulation. The results verify the capability of UPFC in attenuating SSR in wind farm integrations by utilising subsynchronous damping controllers coordinated with UPFC's main controllers. It also suggests that the shunt transformer−converter has a slight effect on SSR, whereas the series transformer−converter affects the system resonance characteristics significantly. Simulations are carried out on a typical power system model integrated with wind turbines.

Positive-Net-Damping Stability Criterion in Grid-Connected VSC Systems

Resonance instabilities in power systems can be assessed with the positive-net-damping stability criterion. This criterion is a review of the complex torque coefficients method, but it does not provide the frequency of the closed-loop oscillatory modes. This paper presents an alternative approach of the positive-net-damping stability criterion to analyze electrical resonance instability. In this approach, resonance instabilities are identified in feedback systems derived from impedance-based equivalent circuits. The proposed approach is used to characterize the frequency of closed-loop oscillatory modes and identify the physical and control parameters of the system that increase or reduce the damping of these modes. The extension of the proposed approach to study the stability of single-input single-output and multiple-input multiple-output feedback systems is analyzed, and the approach is also compared with other stability methods in the literature. An example of an offshore wind power plant illustrates the theoretical study and compares the proposed approach with different methods to evaluate stability. Time-domain simulations in Power System Computer Aided Design/Electro Magnetic Transient Design and Control (PSCAD/EMTDC) are shown to validate the stability study.

Small Signal Dynamics of DFIG-Based Wind Turbines During Riding Through Symmetrical Faults in Weak AC Grid

Instability issues of the grid-connected doubly fed induction generator (DFIG) based wind turbines (WTs) during low-voltage ride-through (LVRT) have got little attention yet. In this paper, the small-signal behavior of DFIG WTs attached to weak ac grid with high impedances during the period of LVRT is investigated, with special attention paid to the rotor-side converter. First, based on the studied LVRT strategy, the influence of the high-impedance grid is summarized as the interaction between phase-looked loop (PLL) and rotor current controller (RCC). As modal analysis result indicates that the underdamped poles are dominated by PLL, complex torque coefficient method, which is conventionally applied in power system to study the interaction between mechanical and electrical subsystems of synchronous generator, is generalized to analyze how the PLL-RCC interaction influence the phase motion of PLL. Then, the concerned small-signal stability of the PLL-synchronized DFIG system can be discerned by the developed complex phase coefficients. Impacts of PLL's and RCC's parameters are highlighted, as well as the system's operating conditions during LVRT. Finally, the analytical result is validated by experiments.

Analysis of frequently over‐threshold subsynchronous oscillation and its suppression by subsynchronous oscillation dynamic suppressor

To mitigate the frequently over-threshold subsynchronous oscillation (FOSSO) phenomenon which occurred in Hulunbuir power plant in the northeast of China, a novel equipment based on voltage source converter (VSC), named subsynchronous oscillation dynamic suppressor (SSODS) is developed and installed. In this study, the root cause of FOSSO is revealed by analysing the response characteristics of the system. Then the control strategy of the developed SSODS is presented. Damping characteristics of SSODS are analysed by the complex torque coefficient method. To verify the effectiveness of the control strategy and the physical controller of VSC, as well as provide initially optimised controller parameters for the field tests, real-time closed-loop tests are carried out. A novel method of torsional modal frequency measure for onsite commissioning test is proposed. The operation and field verification test of SSODS is introduced, and test results demonstrate that SSODS can mitigate the new SSO phenomenon dramatically, proving the validity of SSODS.

Analysis on Sub-Synchronous Damping Characteristic of VSC-HVDC

The study on the HVDC based on voltage-source converter focuses mainly on the control strategy while less on the impact of electrical damping on the adjacent units by VSC-HVDC. The mechanism of VSC-HVDC on inhibiting sub-synchronous oscillation is analyzed theoretically in the respect of its operation principle. Then the complex torque coefficient method realized by time domain simulation-the test signal method, is adopted to investigate the impact of the unit interaction factor, control mode, active power level and reactive power level on the electrical damping on the adjacent units.

A Case Study on the Application of the Nyquist Stability Criterion as Applied to Interconnected Loads and Sources on Grids

As the penetration of complex grid-connected devices, such as power electronic inverters, increases, so too does the complexity of analyzing system stability. A graphical application of the Nyquist stability criterion is presented that indicates how an individual load and source each contribute to the closed-loop system grid eigenvalues. The case study is not limited to particular impedance forms or scenarios like the more common complex torque coefficient method or passivity theory method. From the individual frequency responses of the load and source impedances, the graphical technique indicates how each impedance contributes to the system stability. Examples are provided that successfully indicate the cause of instability for a digitally controlled voltage source inverter (VSI) operating as a microgrid, with a current source inverter as a load. A second example is provided that identifies the potential instability of a VSI running an induction machine. A 42-kW inverter system is used to confirm the findings, showing a close correlation with the theoretical analysis.

Damping multimodal subsynchronous resonance using a generator terminal subsynchronous damping controller

This paper presents a generator terminal subsynchronous damping controller (GTSDC) for mitigating multimodal subsynchronous resonance (SSR) that may occur in series-compensated power systems. The proposed GTSDC system is composed of a digital controller and a power electronic inverter with current tracking control. It uses the shaft speed deviation of the generator turbine as feedback to modulate the dynamic current reference of the inverter through multimodal control paths. By exactly tracking the reference value, the power electronic inverter generates current at frequencies complementary to the torsional modes. Part of the current flows into the generator and creates damping torque on the shaft system to damp SSR. The relationship between the output current of GTSDC and the resulting electromagnetic torque is derived based on the complex torque coefficient method. Furthermore, a nonlinear optimization method is implemented to obtain the optimal parameters for all modal-control paths, thereby effectively enhancing the damping of all torsional modes under different operating conditions. The case study on a real series-compensated power system through eigenvalue analysis and electromagnetic simulations validates the effectiveness of the controller.

Damping analysis of primary and auxiliary control of HVDC systems

AbstractIt is well documented that an inappropriate HVDC controller will cause dynamic instability in an AC/DC system. In order to have a better analysis on the mechanism of this phenomenon, this paper proposes a generic theoretical equation of electric damping coefficient of a HVDC link using the complex torque coefficient (CTC) method for quantitatively analysis of the damping characteristics of different types of HVDC control systems. Furthermore, a theoretical design methodology will also be established to improve the performances of the HVDC primary and auxiliary control systems with an application example. Copyright © 2009 John Wiley &amp; Sons, Ltd.

Improvement on Sampled-data Model of High-voltage Direct Current Converter and Its Validation in Subsynchronous Oscillation Studies

This article presents an improved sampled-data model of a 12-pulse high-voltage direct current converter that is suited for linearized analyses of power systems using frequency domain methods. The applications of this model of converter with pure equidistant firing control and phase-locked loop control are discussed, respectively. Under small perturbations, the process of igniting is considered in detail. Therefore, the accuracy of the model is improved. The model is validated by time domain simulations in PSCAD/EMTDC. The results from the presented model, the quasi-steady model, and the former sampled-data model are compared by eigenvalue analysis and the complex torque coefficient method. The investigations show that the presented model is accurate and valuable in studying subsynchronous oscillations.

On the Application of the Complex Torque Coefficients Method to the Analysis of Torsional Dynamics

The complex torque coefficients method has been widely accepted for the analysis of the phenomenon of torsional interaction of turbine-generator units in power systems. This paper shows that, depending on the system parameters and the operating point, the complex torque coefficients method may exhibit limitations and not accurately and fully predict the system behavior in the frequency range of interest. These shortcomings consist of inability to i) predict monotonic instability due to real poles, ii) identify all electromechanical oscillatory modes, and iii)accurately predict damping (and consequently stability) of the oscillatory modes. This paper develops mathematical expressions to highlight the limitations of the complex torque coefficients method. Quantitative results based on three case studies, including a study on the first IEEE Benchmark System, are reported and results from eigenvalue analysis method, complex torque coefficients method, and time-domain simulation are presented and compared. This paper concludes that the complex torque coefficients method can be used only as a preliminary method for the investigation of torsional interactions and the results must be verified by other methods.