Search

Summary: The modular multilevel converter (MMC) is a novel prospective multilevel converter topology for high‐voltage or high‐power applications. This paper presents the 3‐ Φ model integrated into a linear model in transient analysis and the design of current controller for MMC. This paper analyzes the control interactions of MMC on nearby turbine generator. The eigenvalue analysis is used to evaluate the impact of different controller modes of MMC. The impact of converter control with nonlinear switches is analyzed through the transient simulation. The eigenvalue analysis and controller design are carried out on a linear model, and the transient simulation analysis is performed on both the D‐Q model and a three‐phase model of MMC using MATLAB‐Simulink. The results show that the transient simulation of three‐phase model on the proposed approach is consistent with the transient simulation of D‐Q model. Also, the transient simulation results show a satisfactory response with the current controller parameters of the MMC at various operating cases. To validate the results of MATLAB‐Simulink model, the proposed system is implemented in hardware‐in‐the‐loop (HIL) simulation with an integrated subsystem built in two real‐time simulators. The subsystem of mathematical model is implemented in dSPACE, and the subsystem of 3‐ Φ MMC with controller is implemented in Typhoon. The HIL simulation results show a satisfactory response and consistent with MATLAB‐Simulink model results. [ABSTRACT FROM AUTHOR]

Summary: As the share of wind power keeps on increasing, the interaction between synchronous and wind generators pose a challenging issue on power system stability. In order to investigate the impact of wind penetration on stability of power system, appropriate modeling of wind energy conversion systems (WECSs) is necessary. Moreover, it is needed to comprehensively study the impact of wind penetration on power system oscillations. This paper presents a didactic approach for integrating a doubly fed induction generator (DFIG)‐based wind farm from SimPower Systems library to a five‐area 68‐bus power system modeled in Simulink. Inter‐area oscillations with and without wind power penetration are investigated for their characteristics. Renewable energy sources are connected to the grid via power electronics converters at the cost of a reduction in inertia. The concept of virtual synchronous generator (VSG) produces virtual inertia by exchanging active power with the power system. The impact of superconducting magnetic energy storage (SMES) and DFIG on enhancing damping performance of inter‐area is investigated. The increase in damping ratios of inter‐area oscillatory modes verifies the enhancement in small signal stability by connecting SMES and DFIG to the power system. The usage of SMES operating in VSG mode to improve the dynamic stability with highly erratic wind profile is also investigated. The developed MATLAB/SIMULINK‐based DFIG model is simple to use and can be expanded to build efficient controllers. The fidelity of the DFIG model and VSG technology is verified in real time by Opal‐RT (OP4510). [ABSTRACT FROM AUTHOR]

This paper focuses on the impact of control system on small‐signal stability of the Hybrid Multi‐Infeed HVDC(H‐MIDC) system, in which the Line‐Commutated‐Converter based HVDC (LCC‐HVDC) and Voltage‐Sourced‐Converter based HVDC (VSC‐HVDC) links feed into an AC system in close mutual proximity. A comprehensive linearized small‐signal model is developed for an H‐MIDC system. Based on the eigenvalue analysis and participation factor analysis, the inherent oscillatory modes of the H‐MIDC system are revealed. Then, the impact of the most sensitive control system parameters on the least‐damped modes are investigated. The studies show that (i) the proportional gains of PLL functions of LCC and VSC stations, and AC voltage outer loop controller of VSC station are highly coupled, and presents the most sensitivity to the least damped modes; (ii) parameters of PLL in LCC station, and outer loop of AC voltage control and PLL in VSC station can highly impact the damping of the oscillatory modes and even cause instability, and (iii) smaller PLL gains in LCC and VSC stations, and smaller proportional gain of AC voltage control of VSC station are preferable and can enhance damping of dominant modes. [ABSTRACT FROM AUTHOR]

To clarify the actual structural performance of an existing traditional timber structure in Japan, vibration measurements were carried out at a 17th century timber guest house (Gekkouden of Gokokuji temple). The results of the micro tremor measurement, earthquake monitoring, and analysis are discussed in this paper. For minute angles of less than 1/5000 rad, it was revealed through earthquake monitoring that each dominant frequency was strongly dependent on the vibration amplitude. It was also confirmed that the dominant frequencies of the lower vibration modes in 1/1000 rad declined to 65%‐75% of the frequencies obtained through micro tremor measurement. We propose a structural model that consists of a joint spring, column, beam, and hanging wall, based on previously reported experiments. In this study, it was clarified that the dominant frequencies determined by the analysis of the proposed structural model were in good agreement with the frequencies obtained through earthquake monitoring. The structural performance of a traditional timber architecture was evaluated through vibration analysis. We selected a 17th century guest house as a subject building, and performed vibration measurements and structural analysis. [ABSTRACT FROM AUTHOR]

This paper deals with the stability analysis of a rotary power flow controller (RPFC). RPFC is a newly presented flexible alternating current transmission system device based on the rotary phase shifting transformer (RPST) configuration. This device comprises a shunt and a series transformer and two RPSTs. In this paper, a linear model is developed for RPFC in the dq-reference frame. The model includes two RPSTs, shunt, and series transformers. Stability of the device is studied using eigenvalues of the state matrix. Effects of system parameters such as resistance, reactance, and phase difference of the shunt and series transformers and RPSTs on stability are investigated using eigenvalue sensitivity analysis. Simulation results using PSCAD/EMTDC software and analytical results based on eigenvalue analysis are presented to evaluate effects of different parameters on stability of RPFC. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Converters are the key for increasing the development of renewable energy generation but their dynamic interaction with the grid has an important impact on stability. Oscillatory instabilities in different grid‐connected converter systems at several frequency ranges are reported. In particular, sub and supersynchronous oscillatory instabilities in AC power systems with type‐3 and type‐4 wind turbine generators (WTGs) were recently registered at several wind farm areas. A number of works based on eigenvalue analysis and frequency domain approaches are carried out to analyse this new stability issue and more research is going on to analyse in detail the electric and control parameters that may affect this phenomenon. This study contributes analysing in detail the influence of system parameters on the subsynchronous oscillations (SSOs) in AC power systems with type‐4 WTGs. This study is based on a new approach for subsynchronous stability assessment which could also be used for analysing other types of SSOs (e.g. subsynchronous control interactions between doubly‐fed induction generators and series‐compensated networks) as well as supersynchronous oscillations. A representative example of weak AC grids with type‐4 WTGs is used to illustrate the contributions of the study. Results are validated with PSCAD/EMTDC time‐domain simulations. [ABSTRACT FROM AUTHOR]

Recent progress in power electronics technology makes it possible to consider applying self-commutated converters using gate turn-off thyristors (GTOs) to HVDC transmission systems. Since the self-commutated converter can be operated stably without depending on ac-side voltage, the magnitude and the phase angle of the converter output voltage can be controlled independently. Therefore, this type of converter will improve voltage stability at its ac side. On the other hand, shaft torsional oscillation of a thermal power plant caused by the interaction between the shaft-generator system and the control system of the self-commutated converter is still an open problem. In this paper, a linearized model for eigenvalue analysis of a power system, including HVDC interconnection with self-commutated converters, is described to analyze the effect of the self-commutated converter on the shaft torsional oscillation of a thermal power plant. Then, numerical results from the eigenvalue analysis of the shaft torsional oscillation are presented. Results obtained by the frequency response method are also reported. The numerical results make it clear that parameter regions of DC-AVR and ACR control systems of self-commutated converters exist where the shaft torsional oscillation may be caused. © 1999 Scripta Technica, Electr Eng Jpn, 128(4): 25–37, 1999 [ABSTRACT FROM AUTHOR]

In western China, large‐scale wind power is generally bundled with thermal power, and transmitted to eastern China by high‐voltage direct current (HVDC) systems. This constitutes the wind–thermal bundled system transmitted by HVDC (WTBH). In this study, a typical studied system of WTBH is presented, and its models for eigenvalue analysis are introduced. To improve the efficiency of eigenvalue analysis, an improved block modelling method is proposed for building the state‐space model of WTBH. By eigenvalue analysis and electromagnetic transient (EMT) simulation, the impact of doubly‐fed induction generator (DFIG)‐based wind farm integration on sub‐synchronous torsional interaction (SSTI) between thermal generators (TGs) and HVDC was investigated. The sensitivity of the operating parameters of DFIG‐based wind farms was analysed, including wind speed, wind farm scale, and distance between the wind farm and HVDC rectifier station. The obtained results show that the integration of DFIG‐based wind farms can mitigate the SSTI between the TG and HVDC. The system becomes more stable as the wind speed and wind farm scale increase or the distance between the wind farm and HVDC rectifier station decreases. The conclusions of this study are validated through EMT simulations in PSCAD/EMTDC, and provide theoretical reference for practical WTBH projects. [ABSTRACT FROM AUTHOR]

This paper presents a general rank-1 matrix formula which allows for proper rearrangement of individual terms in multiproduct forms involving vectors and matrices. A far-reaching application of the new matrix formula to eigenvalue sensitivity evaluation is presented in the paper. Such an application reduces the sensitivity expressions to elegant, very fast and recursive forms with substantial savings in computer resources. The formula is applicable to rank-1 matrices of special structures which may constitute derivatives of the system state matrix, which is widely used in control system applications, with respect to various parameters of interest. In such cases, the use of the rank-1 formula yields exact non-approximate solutions which are identical to those obtained by other conventional formulas. The applicability of the rank-1 formula is believed to cover a wide variety of practical engineering systems pertaining to control and stability. © 1998 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents a method for finding the eigenvalues of some equations, or the zeros of analytic functions. There are two steps in the method. In the first step, integration along the edges of rectangle for an analytic function is performed. From the result of integration, one can know whether the zero exists in the rectangle or not. If the zero of an analytic function exists in the rectangle, we can perform the second step. In the second step, the zero is obtained by iteration. Therefore, the method is called a region searching method. Particular advantage of the suggested method is that the process for finding zero can be visualized. For example, one can clearly indicate the rectangles, which contain the zeros of an analytic function. Three numerical examples are presented. The obtained results are satisfactory even for a complicated case, for example, for finding eigenvalues of a composed wedge of dissimilar materials. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this study, a normal form based excitation controller for oscillatory dynamics in power systems is investigated. Afterwards, instead of using a conventional linear control technique for the secondary controller, a novel non-linear objective for the rotor mode is considered to emulate ideal power system stabiliser (PSS) characteristics. With the aid of eigenvalue analysis, it is shown that the proposed method exhibit ideal PSS characteristics. Moreover, it is demonstrated the proposed technique is robust when compared with the conventional controllers. Time-domain simulation is performed on the third-, fourth-, and sixth-order model (i.e. IEEE model 1.0, 1.1, and 2.2) of the synchronous machines. Simulation results are shown on a single machine infinite bus power system model. [ABSTRACT FROM AUTHOR]

The occurrence of unstable subsynchronous control interaction (SSCI) between wind farms and series‐compensated networks poses a considerable threat to the safety of power system. Different from the conventional eigenvalue analysis and Nyquist method, the black‐box‐model based RLC fitting technique becomes more attractive for the assessment of the SSCI risk. However, the method has merely been verified by radial networks whose SSCI mode can be well explained by an RLC circuit. A practical wind power system, however, can be meshed networks comprising multiple geographically distributed wind farms and series capacitors. Thus, it is questionable whether the application of the RLC fitting technique to such systems can still yield a sufficient accuracy. To clarify this aspect, in this work, the performance of RLC fitting in various test systems was examined. The results indicated that the aggregation technique considerably influences the accuracy of the assessment, and the RLC fitting cannot be applied when multiple series capacitors are involved in the SSCI mode. To address this problem, a more advanced frequency‐domain fitting technique known as vector fitting was adopted, and its robustness and effectiveness were verified considering a modified The Electric Reliability Council of Texas (ERCOT) system. [ABSTRACT FROM AUTHOR]

This study proposes a generic method for modelling and comparison analysis of grid‐connected double‐fed induction generator (DFIG)‐based wind farms in a weak grid. A detailed model of DFIG in a weak grid is established and used as a benchmark. Specifically, the detailed model consists of the mechanical part, generator part, rotor side converter, and phase‐locked loop (PLL). Two simplified models of grid‐connected DFIG‐based wind farms in a weak grid are compared with the detailed model to investigate the mechanism of sub‐synchronous oscillation (SSO) as well as the influential factors through linear system analysis. The first simplified model ignores shafting dynamics, stator flux dynamics, and PLL dynamics. The same assumptions are used in the latter, except that PLL dynamics are considered. Time‐domain simulation and eigenvalue analysis are used to verify the accuracy of the simplified models. The block diagrams of the linearised system are derived based on the proposed model, and the oscillation mechanism is explained by linear system analysis. Through eigenvalue analysis and the root locus method, the influences of the parameters of the DFIG and its controllers on the system stability are identified and analysed. [ABSTRACT FROM AUTHOR]

Summary: In this work, two well‐known approaches for mixed finite elements are combined to render three novel classes of elements. First, the widely used enhanced assumed strain (EAS) method is considered. Its key idea is to enhance a compatible kinematic field with an incompatible part. The second concept is a framework for mixed elements inspired by polyconvex strain‐energy functions, in which the deformation gradient, its cofactor and determinant are three principal kinematic fields. The key idea for the novel elements is to treat enhancement of those three fields separately. This approach leads to a plethora of novel enhancement strategies and promising mixed finite elements. Some key properties of the newly proposed mixed approaches are that they are based on a Hu‐Washizu type variational functional, fulfill the patch test, are frame‐invariant, can be constructed completely locking free and show no spurious hourglassing in elasticity. Furthermore, they give additional insight into the mechanisms of standard EAS elements. Extensive numerical investigations are performed to assess the elements' behavior in elastic and elasto‐plastic simulations. [ABSTRACT FROM AUTHOR]

Copyright of Photogrammetric Record is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In recent years, the low-frequency oscillation (LFO) problem has become increasingly significant with rapid increase in the size of AC/DC interconnected power system containing large-scale wind power. This article aims to conduct the LFO analysis when an offshore wind farm is integrated into the AC power system through module multilevel converter (MMC)-based high-voltage direct current (HVDC). First, the basic mathematical models including the MMC with detailed control strategy and the permanent magnet synchronous generator (PMSG) are described. The eigenvalue analysis is then applied to conduct the LFO study. An interconnected AC/DC test system with a wind farm connected though the MMC-based HVDC transmission line is designed as benchmark. To validate the analysis results, the detailed simulation models built under the PSCAD/EMTDCTM environment together with the Prony analysis are carried out. Different simulation scenarios involving the changes of point of common coupling (PCC), wind speed, length of transmission line, and wind penetration level are elaborately studied. Some meaningful conclusions are drawn to provide basic foundation for the future design of damping controller to mitigate LFO. [ABSTRACT FROM AUTHOR]

This study presents the impact of the doubly fed induction generator (DFIG) with power system stabiliser (PSS) on critical low‐frequency oscillations (LFOs) caused by the synchronous generators (SGs). These LFOs arise due to uncertainties in a system such as generating/loading conditions, intermittent wind power and may cause instability. To improve the stability, the PSS is added. This study studies the effect of varying wind speed, DFIG locations and its capacity with and without PSS on stability. The system is analysed by replacing SGs with DFIG. The sensitivity analysis is carried out with wind power penetration and voltage gain as sensitivity parameters. This identifies electromechanical modes of oscillations that have positive and negative impacts on the system. The transient and small‐signal stability (SSS) investigations are done using non‐linear simulation and eigenvalue analysis, respectively. The system uncertainties are modelled using inverse output additive perturbation structure to elude the mathematical difficulty. The location and selection of best local input signals for PSS are evaluated from residue method and time‐domain simulation analysis. The effectiveness and robustness of the proposed approaches are verified on IEEE 9‐bus test system. The PSS improves the transient stability and SSS of the system. [ABSTRACT FROM AUTHOR]

In recent years, the subsynchronous oscillation (SSO), which occurs in direct‐drive permanent magnetic synchronous generators (D‐PMSGs)‐based wind farm, has great impact on the stability of power system. The different parameters and operation conditions of D‐PMSGs lead to the subsynchronous interaction (SSI) among D‐PMSGs. What is more, the SSI will influence the SSO characteristics of the system of D‐PMSGs‐based wind farm integrated to AC network. Here, considering the difference of parameters or operation conditions among D‐PMSGs in the wind farm, eigenvalue analysis, based on the small‐signal state‐space model of two aggregated D‐PMSGs which are equivalent to wind farm, is carried out. Then the stability and the SSI between D‐PMSGs of the equivalent system can be studied, and the dominant D‐PMSG can be determined based on the participation factors. Lastly, the detailed electromagnetic transient simulation model of D‐PMSGs equivalent system is built in PSCAD/EMTDC. The simulation is conducted to corroborate the eigenvalue analysis. The result shows that an obvious SSI exists between two aggregated D‐PMSGs. Furthermore, the different SSO characteristics among D‐PMSGs in the wind farm indicate the study of SSO problem based on an aggregated D‐PMSGs model may leave out some useful information. [ABSTRACT FROM AUTHOR]

Power system stabilisers (PSSs) are supplementary controllers connected to the excitation system of synchronous generators to damp electromechanical oscillations. Multi‐band PSSs are reported as advanced PSSs with the ability to damp out all oscillation modes present in the power systems. This study presents the design of a robust fractional‐order multi‐band power system stabiliser (Fo‐MBPSS) using a meta‐heuristic hybrid algorithm for dynamic stability improvement of multi‐machine power systems. The large bandwidth, memory effect and flat phase contribution in the frequency response of fractional‐order controllers are exploited to make the Fo‐MBPSS perform well against a wide range of system uncertainties. The parameter tuning problem of Fo‐MBPSS is transformed to an optimisation problem that is solved using a hybrid algorithm by combining a dynamic genetic algorithm (DGA) with a standard particle swarm optimisation (PSO) algorithm. The performance of the proposed DGA‐PSO‐Fo‐MBPSS is evaluated through eigenvalue analysis, non‐linear time‐domain simulations and some performance indices, in two different multi‐machine systems under different loading conditions and disturbances. The results are compared with PSO‐based conventional MBPSS and PSO based Fo‐MBPSS (PSO‐Fo‐MBPSS) to establish the fractional parameter effect on the improvement of the system dynamic response and the relevance of the proposed hybrid optimisation technique in achieving robustness. [ABSTRACT FROM AUTHOR]

A hybrid microgrid has numerous decentralised control loops. Therefore, coordination among hybrid microgrid subsystems with desired performance is essential. This study presents a practical control approach for efficient tuning of proportional–integral (PI) controllers and leads compensators in islanded hybrid microgrids. This method is based on the frequency response characteristic and root‐locus trajectory. It is used to minimise the frequency deviations of an AC hybrid microgrid. The presented well‐tuned controllers are tuned based on droop mechanism, and coordination among hybrid microgrid subsystems with desired damping coefficient and stability margin. Then, the system performance is analysed under several disturbances. The results are compared with PI controllers tuned by Ziegler–Nichols method. As well, the robustness of the proposed approach in a wide range of parameter changes is investigated. Eigenvalue analysis and simulation results show that the minimum frequency deviations and desired relative stability of the hybrid microgrid subsystems are achieved by the proposed controllers. To show generality and efficiency of the proposed approach, the presented method is applied to a different hybrid microgrid model used in the literature. For this purpose, in order to control the frequency deviations in the stand‐alone mode, presented well‐tuned controller is compared with intelligent fuzzy and particle swarm optimisation‐fuzzy controllers. [ABSTRACT FROM AUTHOR]

A novel fuzzy proportional–integral (PI) control with fault ride‐through (FRT) capability is investigated for double fed induction generators (DFIGs), where an approximation error considered Takagi–Sugeno fuzzy observer is employed to approximate the non‐linear model of DFIG. Based on the obtained observer, a H2 controller with PI structure is used to achieve specified engineering purposes, such as maximum power point tracking and automatic voltage regulator. A H∞ controller is proposed to cope with the undetected disturbances in the H2 control, and a robust technique is also proposed to override the effect of approximation error due to the fuzzy approximation. Then, the controller design is formulated as a mixed H2/H∞ suboptimisation problem with the regional pole placement constrain, which can be solved easily by using linear matrix inequality technology. In order to further improve the FRT capability, a power angle compensator is proposed to reduce terminal voltage drop via limiting DFIG power angle jump during faults. The results of dominant eigenvalue analysis and simulation are presented and discussed, which shows the capabilities of DFIG with the proposed control strategy to improve system damping, fault‐tolerant control and FRT, and its contribution on power system transient stability support. [ABSTRACT FROM AUTHOR]

The increasing integration of wind turbines mainly doubly fed induction generators (DFIGs) introduces dynamic interaction with the conventional synchronous generators (SGs) affecting the damping of low‐frequency electromechanical oscillations (LFEOs) in the system. This study presents a complete impact analysis of DFIG integration on system damping. The damping ratio sensitivity to inertia is used to evaluate the impact of DFIG integration on the critical modes. This study identifies that the impact could be positive or negative based on the location of DFIG. The results obtained are verified by detailed eigenvalue analysis and time‐domain simulations for different operating conditions with three‐phase fault. The negative impact on damping is improved by optimally tuned power oscillation dampers (PODs) with input signals obtained from the phasor measurement units. The impact on dynamic performance of the system due to removal of SGs and addition of DFIGs is investigated. The DFIG penetration is increased on the basis of participation of SGs in critical modes and the results of sensitivity analysis. The proposed approach is tested on standard IEEE 39‐bus test system. The investigations carried out in this work can be employed for planning studies of power system integrated with DFIG for identifying their suitable locations and improving LFEO damping with their high penetration. [ABSTRACT FROM AUTHOR]

This study presents a dynamic approach for determining mode shape using time‐domain signal. Signal processing techniques, mode decomposition, and spectral analysis are used here. The quality of signal affects the performance of spectral analysis, especially for estimation of low‐frequency modes. Therefore, before applying spectral analysis, low‐frequency modes are extracted using mode decomposition technique, so that the decomposed modes (DMs) may indicate centre frequency in its spectrum. In the study, two‐stage mode decomposition approach is proposed for accurate and effective mode decomposition. The power spectral density (PSD) and cross‐PSD tools are used to process DMs for estimation of mode frequency and determination of mode shape, respectively. The proposed dynamic approach is tested on simulated signals of IEEE 16‐machine 68‐bus test system and real‐time phasor measurement units (PMUs) signal. The results obtained using proposed dynamic approach on simulated signals are compared with those obtained by steady‐state approach, i.e. eigenvalue analysis. [ABSTRACT FROM AUTHOR]

Mathematical analysis indicates that stator output power of doubly fed induction generator (DFIG) could be directly controlled by the output voltage of rotor‐side converter (RSC). Thus, a direct stator‐power controller (DPC) could be induced. Furthermore, rotor speed can be directly controlled by RSC with direct rotor‐speed controller (DSC). When the rotor speed is selected as a feedback of RSC controller, the equivalent impedance of RSC could be decreased sharply. Under this condition, DFIG will supply little energy for series resonance caused by fixed series compensation. This results in that DFIG with DSC is insusceptible to subsynchronous control interaction (SSCI). Updating DLP into DSC could be selected as a solution of existing SSCI. Eigenvalue analysis and time‐domain simulations prove the effectiveness of DSC in mitigating SSCI. [ABSTRACT FROM AUTHOR]

In this study, small‐signal stability of the power system integrated with ancillary‐controlled large‐scale doubly fed induction generator (DFIG) based wind farm (WF) is studied. A model which considers grid code requirements and ancillary controllers is presented to indicate important DFIG dynamics for the study. The ancillary control of the WF which aims to improve power system voltage/frequency stability is evaluated from the small‐signal stability perspective. It is shown that the ancillary controller deteriorates power system low‐frequency oscillations and/or induces new lightly damped oscillation modes especially in a weak grid. The potential risks may restrict the WF to fulfil gird code requirements and threaten small‐signal stability of the power system. Meanwhile, this study reveals that wind power penetration level and WF connection impedance are two main factors which affect dynamic interactions between the WF and the power system and thus affect system small‐signal stability. The principle of the influence on the small‐signal stability with different grid weakness and ancillary control schemes is evaluated in this study by eigenvalue analysis and verified with time‐domain simulations. [ABSTRACT FROM AUTHOR]

Eigenvalue analysis is a very essential technique for power system small‐signal stability (SSS) determination. Uncertainties in load/generation forecast are very common in power systems due to its geographical spread, size and complexity. These uncertainties can be divided into two types: (a) statistical (b) non‐statistical. It is observed from the literature that the effects of non‐statistical uncertainties in eigenvalue analysis are discussed comparatively less. In this study, a boundary eigenvalue analysis is developed based on boundary power flow to handle the non‐statistical uncertainties in loads and solar photovoltaic generation (SPVG) forecasts. First, mathematical model for evaluation of boundary of the critical eigenvalues for SSS analysis of dynamic power system (DPS) is developed. Then, the upper/lower boundary of a particular eigenvalue for a given range of uncertainties in load/SPVG at various buses is investigated. The boundary eigenvalue analysis predicts the worst‐case scenario for a given range of uncertainty in forecasted data which may help for secure operation of DPS. Second, Hopf bifurcations which may lead in highly stressed DPS is evaluated with increasing load/generation in the system in the presence of non‐statistical uncertainties. Results for two standard test systems are taken to demonstrate the potential of the proposed approach. [ABSTRACT FROM AUTHOR]

This study aims to conduct the sub‐synchronous (SS) resonance analysis of a multi‐machine power system incorporating doubly fed induction generator (DFIG)‐ or permanent magnetic synchronous generator (PMSG)‐based wind farm. The linearised equations involving the dynamics of steam turbine generator, wind farm, shunt capacitor, transmission line, and load are derived, and the detailed state matrix formation process pertinent to each component is presented. Taking the IEEE 16‐machine‐68‐bus test system as example, the eigenvalue analysis along with participation factor is applied to investigate the impacts of the series compensation level of transmission line on the modal frequencies and damping ratios of two groups of oscillatory modes of interest: namely, the SS mode of the series‐compensated transmission line and the shaft modes of the studied steam turbine generator before and after one of the un‐studied steam turbine generators is replaced by the DFIG‐ or PMSG‐based wind farm. Some useful conclusions and comments are drawn. [ABSTRACT FROM AUTHOR]

Contribution to the damping of inter‐area and torsional oscillation modes, in doubly fed induction generators (DFIG) based wind farms, by power oscillation damping controllers (PODCs) based on two conventional structures and a fuzzy control strategy is investigated in this study. In this regard, a PODC with no lead/lag compensation is designed first and then a PODC with one lead/lag block is developed using eigenvalue techniques and the application of an iterative process based on the bat optimisation algorithm (BOA). Moreover, a fuzzy PODC, based on a simple fuzzy controller and tuned with the BOA according to the system transient response under a critical perturbation, is also designed. Comparative performance of the three PODCs is evaluated on a multi‐machine power system. It is observed that all three PODCs can contribute to improving the damping of inter‐area oscillations. However, eigenvalue analysis and non‐linear time domain simulations reveal that each of them may also impact to a lesser or greater extent the shaft torsional oscillation mode damping. Their relative impact in this regard is also investigated. [ABSTRACT FROM AUTHOR]

This study analyses the effect of replacing existing synchronous generators (SGs) equipped with power system stabilisers (PSS) by doubly fed induction generator (DFIG) based wind farms on the damping of power system oscillations in a multi‐machine power system. A power system stabiliser was designed to enhance the capability of DFIG to damp power systems oscillations. The validity and effectiveness of the proposed controller are demonstrated on the widely used New England 10‐machine 39‐bus test system that combines conventional SGs and DFIG based wind farms using eigenvalue analysis and non‐linear simulation. The non‐linear simulation is used to demonstrate how the damping contribution of DFIG based wind farms is affected by different operating conditions within the same wind farm and stochastic wind speed behaviour. The results show that installing conventional fixed parameters PSS within reactive power control loop of DFIG rotor side converter has a positive damping contribution for a wide range of operating conditions. Furthermore, the results clearly show that DFIG based wind farms equipped with the proposed farm level PSS can damp power system oscillations more effectively than SGs PSS. [ABSTRACT FROM AUTHOR]

State‐of‐the‐art time‐domain models of power cables account for the frequency dependency of physical parameters to enable accurate transient simulations of high‐voltage transmission schemes. Owing to their formulation, these models cannot be directly converted into a state‐space form as required for small‐signal eigenvalue analysis. Thus, dc cables are commonly represented in high‐voltage direct current (HVDC) power system stability studies by cascaded pi‐section equivalents that neglect the frequency‐dependent effects. This study demonstrates how the conventional cascaded pi‐section model is unable to accurately represent the damping characteristic of the cable and how this can lead to incorrect stability assessments. Furthermore, an alternative model consisting of cascaded pi‐sections with multiple parallel branches is explored, which allows for a state‐space representation while accounting for the frequency dependency of the cable parameters. The performance of the proposed model is benchmarked against state‐of‐the‐art cable models both in the frequency domain and in the time domain. Finally, the study provides a comparative example of the impact of the cable modelling on the small‐signal dynamics of a point‐to‐point voltage‐source converter (VSC) HVDC transmission scheme. [ABSTRACT FROM AUTHOR]

Torsional damping controllers, such as supplementary excitation damping controllers (SEDCs), are widely used to stabilise subsynchronous resonance (SSR) induced by torsional interactions (TIs) between turbo‐generators and series‐compensated power systems. However, because of the changeable operating situations of a power system, it is a great challenge to design them to guarantee torsional stability under all possible operating conditions. This study proposes a global optimal control‐design procedure for tuning SEDCs to accommodate the variation of system conditions. Considering TI is a small‐signal stability issue, the non‐linear power system is converted into a family of linear parameter varying models and the parameter‐tuning task for multiple SEDCs is formulated into a multi‐model constrained non‐linear optimisation problem. A global optimisation procedure based on genetic algorithm and simulated annealing is designed to efficiently solve this problem and obtain a set of robust or several sets of gain‐scheduling SEDCs. The proposed method is applied to a multi‐machine series‐compensated power system. The results of both eigenvalue analysis and time‐domain simulation have fully demonstrated the effectiveness of the optimised SEDCs in stabilising SSR under all possible operating conditions. [ABSTRACT FROM AUTHOR]

This study proposes an enhanced model of the doubly fed induction generator (DFIG)‐based wind farm (WF) for small‐signal stability (SSS) studies of weak power system. This model consists of a wind turbine, a drive train, a simplified generator/converter module and associated controls. As analysed and verified in this study, the dynamics of the phase‐locked‐loop and the rotor current loop are important for accurate SSS studies of the weak power system involving the DFIG‐based WF and thus should be modelled appropriately. The enhanced model is validated by eigenvalue analysis and time‐domain simulations. Compared with the detailed model, the WT3 model provided by General electric (GE) energy and the conventional model, the enhanced model presents high precision and satisfactory simplification for SSS studies. As the application of the enhanced model, a case study is carried out to explore the impact of WF ancillary voltage/frequency controls on SSS of the weak grid. As indicated in this study, the WF ancillary controls exert distinct impact on SSS. New lightly damped power oscillations can be introduced. Therefore extra measures should be considered if the ancillary controls are required by the WF in order to satisfy the future grid codes. [ABSTRACT FROM AUTHOR]

This work proposes a strategy to mitigate subsynchronous resonance (SSR) in synchronous generators using variable‐speed wind energy conversion systems (WECSs) based on full converter wind turbines. A supplementary active and reactive power to be delivered by WECSs located near synchronous generators is designed to reduce the SSR phenomenon. These supplementary signals are calculated using an observer‐based controller tuned through an optimal quadratic technique which allows to minimise the WECS control effort, whereas a good torsional oscillation damping is accomplished. The power ratio between the WECS and the synchronous generator, impact on the power quality and communication time‐delay requirements are also discussed. The authors compare two control approaches: the first one uses mechanical measurements of the synchronous generator (measures which have high observability of torsional modes), whereas the second one uses voltage measurements at the wind farm connection point. In this way, two control schemes using remote and local measurements are proposed, and advantages and disadvantages of both schemes are presented. The proposed scheme can provide satisfactory torsional damping under a wide range of operating points, avoiding to include dedicated SSR damping equipment, and using the new wind farms installed in the network. Eigenvalue analysis and non‐linear time‐domain simulations confirm the good performance of the WECS‐based SSR damping controller. [ABSTRACT FROM AUTHOR]

SUMMARY In finite element (FE) analysis, traditional penalty methods impose constraints by adding virtual stiffness to the FE system. In dynamics, this can decrease the critical time step of the system when conditionally stable time integration schemes are used by introducing spurious modes with high eigenfrequencies. Recent studies have shown that using mass penalties alongside traditional stiffness penalties can mitigate this effect for systems with a one single-point constraint. In the present work, we extend this finding to include systems with an arbitrary set of multipoint constraints. By analysing the generalised eigenvalue problem, we show that the values of spurious eigenfrequencies may be controlled by the choice of stiffness and mass penalty parameters. The method is demonstrated using numerical examples, including a one-dimensional contact-impact formulation and a two-dimensional crack propagation analysis. The results show that constraint imposition using the bipenalty method can be employed such that the critical time step of an analysis is unaffected, whereas also displaying superiority over the mass penalty method in terms of accuracy and versatility. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Grid synchronisation is crucial for integration of renewable energy sources and distributed generation systems into the grid. Accurate and fast estimation of the fundamental positive sequence component is a necessity for synchronisation of three‐phase distributed generation systems with the grid. In this study, a simple synchronisation technique based on the real‐complex‐coefficient filters is proposed. It has a very simple structure, and can directly estimate the fundamental positive and negative sequences under the distorted, unbalanced and offset conditions with no need of a phase‐locked loop. Furthermore, the dc offset can also be extracted precisely. For optimising the steady‐state and dynamic performance, a parameter tuning guidance is provided from the eigenvalue analysis point of view. In addition, a simple auxiliary unit is presented to remain its frequency‐adaptive feature. Finally, experimental results based on a 32‐bit fixed‐point TMS320F2812 DSP verify the effectiveness of the proposed synchronisation method. [ABSTRACT FROM AUTHOR]

We have developed a new fully anisotropic 3D FDTD Maxwell solver for arbitrary electrically and magnetically anisotropic media for piecewise constant electric and magnetic materials that are co‐located over the primary computational cells. Two numerical methods were developed that are called nonaveraged and averaged methods, respectively. The nonaveraged method is first‐order accurate, while the averaged method is second‐order accurate for smoothly‐varying materials and reduces to first order for discontinuous material distributions. For the standard FDTD field locations with the co‐location of the electric and magnetic materials at the primary computational cells, the averaged method required development of the different inversion algorithms of the constitutive relations for the electric and magnetic fields. We provide a mathematically rigorous stability proof followed by extensive numerical testing that includes long‐time integration, eigenvalue analysis, tests with extreme, randomly placed material parameters, and various boundary conditions. For accuracy evaluation, we have constructed a test case with an explicit analytic solution. Using transformation optics, we have constructed complex, spatially inhomogeneous geometrical object with fully‐anisotropic materials and a large dynamic range of ε_ and μ_, such that a plane wave incident on the object is perfectly reconstructed downstream. [ABSTRACT FROM AUTHOR]