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In this paper, a holistic nonlinear state-space model of a system with multiple converters is developed, where the converters correspond to the wind turbines in a wind farm and are equipped with grid-following control. A novel generalized methodology is developed, based on the number of the system's converters, to compute the equilibrium points around which the model is linearized. This is a more solid approach compared with selecting operating points for linearizing the model or utilizing EMT simulation tools to estimate the system's steady state. The dynamics of both the inner and outer control loops of the power converters are included, as well as the dynamics of the electrical elements of the system and the digital time delay, in order to study the dynamic issues in both high- and low-frequency ranges. The system's stability is assessed through an eigenvalue-based stability analysis. A participation factor analysis is also used to give an insight into the interactions caused by the control topology of the converters. Time domain simulations and the corresponding frequency analysis are performed in order to validate the model for all the control interactions under study. [ABSTRACT FROM AUTHOR]

In the static stability analysis of the grid-connected photovoltaic (PV) generation and energy storage (ES) system, the grid-side is often simplified using an infinite busbar equivalent, which streamlines the analysis but neglects the dynamic characteristics of the grid, leading to certain inaccuracies in the results. Furthermore, the control parameter design does not consider the coupling relationships among parameters, resulting in arbitrary values and the inability to achieve overall optimality. To address these issues, this paper presents a comprehensive parameter optimization method for the oscillation characteristics of grid-connected PV generation and ES systems in various frequency ranges. Firstly, a detailed modeling of the grid-connected PV generation and ES system is conducted, resulting in the derivation of the system's small-signal model. This study investigates the impact of parameters related to PV arrays, ES units, and the virtual synchronous generator (VSG) on the system's characteristic roots using participation factors, sensitivity analysis, and eigenvalue root trajectories. Subsequently, based on the analysis of system root trajectories and the Particle Swarm Optimization (PSO) algorithm, a holistic parameter optimization design method for the system's oscillation modes is proposed, and the parameter optimization results are obtained. Finally, the accuracy of the theoretical analysis is validated through perturbation testing using both Matlab/Simulink models and the small-signal model. [ABSTRACT FROM AUTHOR]

New energy sources, storage facilities, power electronics devices, advanced and complex control concepts, economic operating doctrines, and cost-optimized construction and production of machines and equipment in power systems adversely affect small-signal stability associated with local oscillations. The objective of the article is to analyze local oscillations and the causes that affect them in order to reduce their negative impact. There are no recognized analyses of the oscillations of modern operating synchronous generators exposed to new conditions in power systems. The basic idea is to perform a numerical analysis of local oscillations of a large number of synchronous generators in the power system. The paper represents the local mode data obtained from a systematic analysis of synchronous generators in the Slovenian power system. Analyzed were 74 synchronous generators of the Slovenian power system, plus many additional synchronous generators for which data were accessible in references. The mathematical models convenient for the study of local oscillations are described first in the paper. Next, the influences of transmission lines, size of the synchronous generators, operating conditions, and control systems were investigated. The paper's merit is the applicable rules that have been defined to help power plant operators avoid stability-problematic situations. Consequently, boundaries were estimated of the eigenvalues of local modes. Finally, experiments were performed with a laboratory-size synchronous generator to assess the regularity of the numerically obtained conclusions. The obtained results enable the prediction of local oscillations' frequencies and dampings and will be useful in PSS planning. [ABSTRACT FROM AUTHOR]

This paper provides an H∞ robust control strategy for a permanent magnet synchronous generator (PMSG)-based wind farm to realize subsynchronous resonance suppression (SSR) subject to uncertain system distortions and parameter perturbation. Firstly, an eighth-order state space mathematical model of a PMSG-based wind farm is established, including the grid-side converter (GSC), GSC controller, and phase-locked loop (PLL) model. Secondly, the SSR characteristics of a PMSG-based wind farm are analyzed through eigenvalue analysis. Thirdly, a robust subsynchronous damping controller is designed based on eigenvalue analysis of SSR. Finally, the designed robust subsynchronous damping controller is validated with case studies of wind farms. The results show that the controller can increase the stability of PMSG-based wind farm systems and restrain SSR. [ABSTRACT FROM AUTHOR]

This paper proposes a novel robust thyristor-controlled series compensator (TCSC) controller based on proportional integral derivative with filter (PIDF) and uses a new hybrid optimisation evolutionary programming sine cosine algorithm (EPSCA) to improve the power system's angle stability. The problem of the PIDF-TCSC design is transformed into an optimisation problem based on performance indices, such as damping factor, damping ratio, and eigenvalues, where the multi-objective function is employed to obtain the optimal stabiliser parameters. To examine the robustness of PIDF-TCSC, it was tested on a single-machine infinite-bus power system under different operating conditions. The performance of the system with the PIDF-TCSC controller was compared with the simulation results, and the results obtained with the proposed EPSCA were compared with those obtained with SCA, moth flame optimisation, and EP-based PIDF-TCSC methods. Simulation results showed the effectiveness of EPSCA for the PIDF-TCSC design and the superior robust performance for the enhancement of power system stability compared with other techniques in different cases. [ABSTRACT FROM AUTHOR]

This paper presents the advanced control theory's original utilisation to realise a system that controls the fermentation process in batch bioreactors. Proper fermentation control is essential for quality fermentation products and the economical operation of bioreactors. Batch bioreactors are very popular due to their simple construction. However, this simplicity presents limitations in implementing control systems that would ensure a controlled fermentation process. Batch bioreactors do not allow the inflow/outflow of substances during operation. Therefore, we have developed a control system based on a stirrer drive instead of material flow. The newly developed control system ensures tracking of the fermentation product time course to the reference trajectory by changing the stirrer's speed. Firstly, the paper presents the derivation of the enhanced mathematical model suitable for developing a control system. A linearisation and eigenvalue analysis of this model were made. Due to the time-consuming determination of the fermentation model and the variation of the controlled plant during operation, the use of adaptive control is advantageous. Secondly, a comparison of different adaptive approaches was made. The model reference adaptive control was selected on this basis. The control theory is presented, and the control realisation described. Experimental results obtained with the laboratory batch bioreactor confirm the advantages of the proposed adaptive approach compared to the conventional PI-control. [ABSTRACT FROM AUTHOR]

This paper discusses the numerical solution of the generalized non-Hermitian eigenvalue problem. It provides a comprehensive comparison of existing algorithms, as well as of available free and open-source software tools, which are suitable for the solution of the eigenvalue problems that arise in the stability analysis of electric power systems. The paper focuses, in particular, on methods and software libraries that are able to handle the large-scale, non-symmetric matrices that arise in power system eigenvalue problems. These kinds of eigenvalue problems are particularly difficult for most numerical methods to handle. Thus, a review and fair comparison of existing algorithms and software tools is a valuable contribution for researchers and practitioners that are interested in power system dynamic analysis. The scalability and performance of the algorithms and libraries are duly discussed through case studies based on real-world electrical power networks. These are a model of the All-Island Irish Transmission System with 8640 variables; and, a model of the European Network of Transmission System Operators for Electricity, with 146,164 variables. [ABSTRACT FROM AUTHOR]

As the installed capacity of the power system is scaled up and the distance of transmission increases constantly, high-voltage direct current (HVDC) transmission technology has been widely applied across the power system. The HVDC system can lead to sub-synchronous oscillations (SSO) in the turbine and new energy generation systems. When the SSO caused by HVDC are studied through small signal analysis, it is usually necessary to establish the detailed state space model and electromagnetic transient model, which shows various disadvantages such as the high complexity of the model, the high order of the state space matrix, the complex calculation of eigenvalues, and the slow pace of simulation. In the present study, a simplified model intended for the HVDC transmission system is proposed, which can be used to simplify the calculation model and accelerate the simulation by omitting the high-frequency component and simultaneously keeping the sub-synchronous frequency component unchanged. The time domain simulation method is used to compare the dynamic response of the proposed simplified simulation model with that of the original detailed model, and the accuracy of the proposed model is demonstrated. The proposed simplified simulation model is applied to explore the SSO of wind-thermal power bundling in the HVDC transmission system. Additionally, the simulation results of SSO are compared by using the simplified model and the detailed model; the results of which demonstrate the effectiveness and rapidity of the simplified simulation model. The simplified model proposed can greatly improve the efficiency of SSO risk assessment. By selecting reasonable types and parameters of new energy units, SSO of the system can be avoided under risky operation mode, and the power grid operation mode can be monitored and adjusted to ensure the safe operation of the system. Finally, it can promote the sustainable development of the power system. [ABSTRACT FROM AUTHOR]

The accurate prediction of rotating stall inception is critical for determining the stable operating regime of a compressor. Among the two widely accepted pathways to stall, namely, modal and spike, the former is plausibly believed to originate from a global linear instability, and experiments have partially confirmed it. As for the latter, recent computational and experimental findings have shown it to exhibit itself as a rapidly amplified flow perturbation. However, rigorous analysis has yet to be performed to prove that this is due to global linear instability. In this work, an eigenanalysis approach is used to investigate the rotating stall inception of a transonic annular cascade. Steady analyses were performed to compute the performance characteristics at a given rotational speed. A numerical stall boundary was first estimated based on the residual convergence behavior of the steady solver. Eigenanalyses were then performed for flow solutions at a few near-stall points to determine their global linear stability. Once the relevant unstable modes were identified according to the signs of real parts of eigenvalues, they were examined in detail to understand the flow destabilizing mechanism. Furthermore, time-accurate unsteady simulations were performed to verify the obtained eigenvalues and eigenvectors. The eigenanalysis results reveal that at the rotating stall inception condition, multiple unstable modes appear almost simultaneously with a leading mode that grows most rapidly. In addition, it was found that the unstable modes are continuous in their nodal diameters, and are members of a particular family of modes typical of a dynamic system with cyclic symmetries. This is the first time such an interesting structure of the unstable modes is found numerically, which to some extent explains the rich and complex results constantly observed from experiments but have never been consistently explained. The verified eigenanalysis method can be used to predict the onset of a rotating stall with a CPU time cost orders of magnitude lower than time-accurate simulations, thus making compressor stall onset prediction based on the global linear instability approach feasible in engineering practice. [ABSTRACT FROM AUTHOR]

This work deals with doubly fed induction generator (DFIG) modeling and stability when connected to weak AC grids. A detailed state-space model that includes the phase-locked loop (PLL) is developed. This work aims to determine the influence of the network's strength on DFIG stability through the short-circuit ratio (SCR). The critical values of the proportional control parameters of the grid-side and rotor-side converters (RSC and GSC), as well as PLL, which make the system unstable, are calculated for different SCR values. Finally, PSCAD/EMTDC dynamic simulations are used to validate the critical control parameters obtained by studying the eigenvalues of the DFIG state-space model regarding system stability. [ABSTRACT FROM AUTHOR]

This research systematically analyzes the behaviors of correlations among stock prices and the eigenvalues for correlation matrices by utilizing random matrix theory (RMT) for Chinese and US stock markets. Results suggest that most eigenvalues of both markets fall within the predicted distribution intervals by RMT, whereas some larger eigenvalues fall beyond the noises and carry market information. The largest eigenvalue represents the market and is a good indicator for averaged correlations. Further, the average largest eigenvalue shows similar movement with the index for both markets. The analysis demonstrates the fraction of eigenvalues falling beyond the predicted interval, pinpointing major market switching points. It has identified that the average of eigenvector components corresponds to the largest eigenvalue switch with the market itself. The investigation on the second largest eigenvalue and its eigenvector suggests that the Chinese market is dominated by four industries whereas the US market contains three leading industries. The study later investigates how it changes before and after a market crash, revealing that the two markets behave differently, and a major market structure change is observed in the Chinese market but not in the US market. The results shed new light on mining hidden information from stock market data. [ABSTRACT FROM AUTHOR]

This paper proposes a novel hybrid algorithm combining chaotic Jaya (CJaya) and sequential quadratic programming (SQP), namely CJaya-SQP, for solving the coordinated design problem of static var compensator (SVC) and power system stabilizers (PSSs). The CJaya serves as a global optimizer and the SQP as a local optimizer for fine-tuning the solution. In the proposed algorithm, chaotic maps are used to generate the initial solutions and control the search process. In order to prove the performance of the CJaya-SQP, a set of benchmark optimization problems is used where the results are compared with those of the basic Jaya and other recognized algorithms. The proposed optimization method is then applied for the optimal tuning of PSSs and SVC controllers in such a way that damping ratios and damping factors of the electromechanical modes are optimally improved. To illustrate the robustness of the CJaya-SQP-based coordinated PSSs and SVC controllers, the four-machine, two-area system is used. Eigenvalue analysis and nonlinear time-domain simulation vividly show that the CJaya-SQP-based coordinated controllers improve greatly the system's dynamic stability with a robust damping of local and inter-area power oscillations. [ABSTRACT FROM AUTHOR]

The application of high-power DC equipment further increases the power supply scale of DC systems. But, it is difficult for a single converter to support high transmission power, so multiple converters must operate in parallel for efficient power transmission. In a parallel system comprising many IPOS phase-shifting full-bridge converters, current sharing can be realized via droop control. However, the stability of the parallel system using current-sharing control will appear poor in light load conditions, so it is necessary to analyze the stability of parallel systems in light load conditions. Firstly, a single IPOS phase-shifted full-bridge control system is modeled; on this basis, the state space model of the n-module paralleled IPOS phase-shifted full-bridge converters system is derived. Then, the influence of load power and the number of parallel IPOS phase-shifted full-bridge converters on the system stability is analyzed via eigenvalue analysis, and an optimal control strategy based on a particle swarm optimization algorithm is proposed. The control parameters are optimized for the parallel system of eight IPOS phase-shifted full-bridge converters. Finally, the above results are simulated to verify the accuracy of the stability analysis and the feasibility of the optimized control strategy. [ABSTRACT FROM AUTHOR]

The potential instability issues caused by the dynamic interactions between parallel grid-forming inverters are examined. The approach adopted for analysis is s-domain admittance-based eigenvalue and mode shape analysis. This admittance is based on a five-node circuit diagram after the conversion of each electric circuit element and inverter control unit into impedance models. Eigenvalue analysis results show that unstable resonance modes may exist due to the interactions of two parallel inverters. Impacts of transmission line length, the converter control's virtual impedance unit, and the voltage feed-forward unit are examined via the eigenvalue and mode shape analysis. The results show that the virtual impedance control has a negligible influence on the resonance while the voltage feed-forward unit stabilizes the resonance. Finally, the stability analysis is validated using electromagnetic transient (EMT) simulations. [ABSTRACT FROM AUTHOR]

The impact of subsynchronous oscillation (SSO) on grid security is becoming increasingly prominent with the rapid development of a large new energy base. However, the SSO modes and characteristics in complex power systems where series-complementary AC systems, DC systems, wind farms, and thermal power plants co-exist simultaneously are still not well understood, and relevant research has yet to be conducted. To address these issues, this study aims to investigate the SSO oscillation modes and the participation of specific influencing factors using eigenvalue and participation factor analysis. Additionally, the influence of system operation mode and control parameters on the SSO characteristics is studied through eigenvalue analysis. The findings of this study suggest that multiple oscillation sources and the co-existence of various oscillation patterns in hybrid AC–DC transmission systems cause SSO problems. The SSOs arise due to inappropriate system operation or parameter selection. As the series compensation increases, the system tends to become unstable. The system stability improves when the wind power output increases or the thermal power output decreases while keeping the output power of other sources constant. On the other hand, the system stability decreases as the DC transmission power gradually decreases. In terms of the control parameters, a higher value of the inner-loop proportionality coefficient of the converter current on the rotor side of the wind turbine results in a more unstable system. However, the rotor-side converter outer loop parameters and the stator-side control loop PI parameters have a negligible effect on the oscillation frequency and damping of the system. Matlab time domain simulations are conducted to verify the accuracy of the theoretical analysis. [ABSTRACT FROM AUTHOR]

Active power outputs of a wind farm connected to a weak power grid greatly affect the stability of grid-connected voltage source converter (VSC) systems. This paper studies the impact of active power outputs and control parameters on the subsynchronous oscillation characteristics of full-converter wind farms connected weak power grids. Eigenvalue and participation factor analysis was performed to identify the dominant oscillation modes of the system under consideration. The impact of active power output and control parameters on the damping characteristics of subsynchronous oscillation is analysed with the eigenvalue method. The analysis shows that when the phase-locked loop (PLL) proportional gain is high, the subsynchronous oscillation damping characteristics are worsened as the active power output increases. On the contrary, when the PLL proportional gain is small, the subsynchronous oscillation damping characteristics are improved as the active power output increases. By adjusting the control parameters in the PLL and DC link voltage controllers, system stability can be improved. Time-domain results verify the analysis and the findings. [ABSTRACT FROM AUTHOR]

The DC-link voltage control (DVC) timescale (i.e., the frequency dynamics covering converter outer controls) instabilities in wind generation have gained increased attention recently. This paper presents DVC timescale modeling and stability analysis for multi doubly-fed induction generators (DFIGs) connected to weak AC grids. A reduced-order, small-signal model of a grid-tied multi-DFIG system, designed for DVC dynamics analysis, is firstly proposed. The model allows for the dynamic interactions among the DC-link voltage control, active power control (APC), terminal voltage control (TVC) and phase-locked loop (PLL). Eigenvalue and participation factor analyses are conducted to explore the potential instabilities and correlated critical factors for such a multi-machine system. The sensitivity studies find that instability can occur at high levels of power generations or low short-circuit ratio (SCR) conditions. In addition, the dominant mode is identified to be highly related to the PLL, and its modal damping is decreased when the bandwidths of PLLs in different generators are close. Detailed model-based time domain simulations verified the analysis above. [ABSTRACT FROM AUTHOR]

In recent years, ultralow-frequency oscillation has repeatedly occurred in asynchronously connected regional power systems and brought serious threats to the operation of power grids. This phenomenon is mainly caused by hydropower units because of the water hammer effect of turbines and the inappropriate Proportional-Integral-Derivative (PID) parameters of governors. In practice, hydropower and solar power are often combined to form an integrated photovoltaic (PV)-hydro system to realize complementary renewable power generation. This paper studies ultralow-frequency oscillations in integrated PV-hydro systems and analyzes the impacts of PV generation on ultralow-frequency oscillation modes. Firstly, the negative damping problem of hydro turbines and governors in the ultralow-frequency band was analyzed through the damping torque analysis. Subsequently, in order to analyze the impact of PV generation, a small-signal dynamic model of the integrated PV-hydro system was established, considering a detailed dynamic model of PV generation. Based on the small-signal dynamic model, a two-zone and four-machine system and an actual integrated PV-hydro system were selected to analyze the influence of PV generation on ultralow-frequency oscillation modes under different scenarios of PV output powers and locations. The analysis results showed that PV dynamics do not participate in ultralow-frequency oscillation modes and the changes of PV generation to power flows do not cause obvious changes in ultralow-frequency oscillation mode. Ultra-low frequency oscillations are mainly affected by sources participating in the frequency adjustment of systems. [ABSTRACT FROM AUTHOR]

With the continuous proliferation of renewable energy generation, distributed photovoltaic inverters operating at a maximum power point reduce the inertia of power systems, degrading system frequency stability and potentially causing severe oscillations in systems after being disturbed. The virtual synchronous generator (VSG) control method, which causes photovoltaic inverters to possess inertia and damping, now plays an important role in the field of distributed generation. However, while introducing the advantages of synchronous machines, problems with oscillations are also introduced and the stochastic fluctuation characteristic of photovoltaics results in the stochastic drifting of the operating point. This paper presents an adaptive controller parameter design method for a photovoltaic-VSG (PV-VSG) integrated power system. Firstly, a small-signal model of the PV-VSG is built and a state space model is deduced. Then, the small-signal stability and low frequency oscillation characteristics of the photovoltaic power generation system are analyzed. Finally, considering the limitations of system oscillations and the stochastic drifting of the operating point, a global optimization design method for controller parameters used to improve system stability is proposed. The time domain simulation shows that an optimized PV-VSG could provide sufficient damping in the case of photovoltaic power output changes across a wider range. [ABSTRACT FROM AUTHOR]

This paper discusses the imbalance netting process (INP) between control areas (CAs) that was developed due to the high costs of balancing energy. The main objective of INP is to net the demand for balancing energy between the participating CAs with opposite signs of interchange power variation. However, INP incorporates a frequency term; hence, it affects the frequency response of participating CAs inherently, which is not discussed in the literature. Therefore, the impacts of INP on the frequency quality and provision of load-frequency control (LFC) are shown thoroughly with dynamic simulations of a three-CA testing systems, in addition to an eigenvalue analysis of a two CA system. It is shown clearly herein that INP changes the eigenvalues of the system matrix, which results in decreased damping of the entire power system. Furthermore, the simulation results confirmed that INP reduces balancing energy, releases regulating reserve and reduces the unintended exchange of energy; thus, LFC performance indicators were improved. However, the impact of INP on frequency quality is not so explicit, since cases exist of frequency quality improvement and deterioration. [ABSTRACT FROM AUTHOR]

Recent works have shown that phase-locked loop (PLL) synchronized wind turbines (WTs) suffer stability issues when integrated into weak grids. However, most of the current studies are limited to a single machine case, the interactions among the WTs are usually overlooked. This paper studies the stability of multiple doubly-fed induction generators (DFIGs) that are connected in parallel to a weak AC grid. A state space model of a two-DFIG system is firstly presented. Subsequently, eigenvalue sensitivity analysis shows that instability can occur at low short-circuit ratio (SCR) or heavy loading conditions. Meanwhile, participation factor analysis implies that the unstable mode is primarily induced by the interactions between the PLLs of the two WTs. Further, to make out how the PLLs interact to cause instability, a reduced-order model is proposed for analysis simplicity, and an explanation in terms of transfer function residue is given for illustration. Detailed model-based time domain simulations are conducted to validate the analyses' results. [ABSTRACT FROM AUTHOR]

The well-developed unified power flow controller (UPFC) has demonstrated its capability in providing voltage support and improving power system stability. The objective of this paper is to demonstrate the capability of the UPFC in mitigating oscillations in a wind farm integrated power system by employing eigenvalue analysis and dynamic time-domain simulation approaches. For this purpose, a power oscillation damping controller (PODC) of the UPFC is designed for damping oscillations caused by disturbances in a given interconnected power system, including the change in tie-line power, the changes of wind power outputs, and others. Simulations are carried out for two sample power systems, i.e., a four-machine system and an eight-machine system, for demonstration. Numerous eigenvalue analysis and dynamic time-domain simulation results confirm that the UPFC equipped with the designed PODC can effectively suppress oscillations of power systems under various disturbance scenarios. [ABSTRACT FROM AUTHOR]

In this study, a Monte Carlo simulation (MCs)-based isogeometric stochastic Finite Element Method (FEM) is proposed for uncertainty quantification in the vibration analysis of piezoelectric materials. In this method, deterministic solutions (natural frequencies) of the coupled eigenvalue problem are obtained via isogeometric analysis (IGA). Moreover, MCs is employed to solve various uncertainty parameters, including separate elastic and piezoelectric constants and their combined cases. [ABSTRACT FROM AUTHOR]

For real time monitoring of the wing state, in this paper, the inverse Finite Element Method (iFEM) is applied, which describes the displacement field of beam according to the Timoshenko theory, to sense the wing frame deformation. In order to maintain the accuracy and stability of frame deformation sensing with iFEM, an optimal placement model of strain sensors based on eigenvalue analysis is constructed. Through the model solution with the Particle Swarm Optimization (PSO) algorithm, two different optimal placement schemes of sensors are obtained. Finally, a simulation is performed on a simple cantilever beam and a static load experiment is conducted on an aluminum alloy wing frame. The results demonstrate that the iFEM is able to accurately sense the deformation of the wing frame, when the two optimal placement schemes of sensors are used. [ABSTRACT FROM AUTHOR]

Aiming for large-scale renewable energy sources (RES) integrated to power systems with power electronic devices, the technology of virtual synchronous generator (VSG) has been developed and studied in recent years. It is necessary to analyze the damping characteristics of the power system with RES generation based on VSG and develop its corresponding damping controller to suppress the possible low frequency oscillation. Firstly, the mathematical model of VSG in a per unit (p.u) system is presented. Based on the single-machine infinite bus system integrated with an RES power plant, the influence of VSG on the damping characteristics of the power system is studied qualitatively by damping torque analysis. Furthermore, the small-signal model of the considered system is established and the damping ratio of the system is studied quantitatively by eigenvalue analysis, which concluded that adjusting the key control parameters has limited impacts on the damping ratio of the system. Consequently, referring to the configuration of traditional power system stabilizer (PSS), an auxiliary damping controller (ADC) for VSG is designed to suppress the low frequency oscillation of the power system. Finally, simulations were performed to verify the validity of theoretical analysis and the effectiveness of designed ADC. [ABSTRACT FROM AUTHOR]

Power systems may encounter disturbances during operation as a result of switching of various components, etc. Such perturbations include transformer tap-changing action, load variations, and line outages due to various types of faults of which an earth fault is the most common. Stability analysis of a transmission system is necessary for us to determine the stability state of the system so that appropriate control measures can be implemented to guarantee system stability. This article presents the use of eigenvalue obtained from the system-linearized eigenvectors to analyze the stability state of the system. The choice of the eigenvalue principle is based on the strength of accuracy of the method to determine the actual state of the system providing adequate data for easy solution to the problem. The node admittance parameters computed from the line parameters is applied to the eigenvalue–eigenvector model to determine the system stability state. The state of the eigenvalue is used as an input to a control system, which utilized static volt-ampere reactive (VAR) compensators (SVC) to automatically stabilize the non-stable buses in the transmission network. The 6 × 6 nodal admittance matrix is formed and fed to the developed eigenvalue–eigenvector model via MATLAB in order to compute the right and left eigenvectors and the diagonal or eigenvalue of the network under steady-state and contingency condition. After this, the system stability state is determined, and necessary control actions by the SVC are implemented to guarantee system security. The developed model was tested on the 6 bus Eastern Grid Nigerian Transmission Network and validated using a 41 bus network of the same country. The compensated model showed considerable efficiency in improving the transient stability state of the transmission networks in terms of ease of operation, seamless integration into existing control system, and efficient utilization of SVS to compensate for reactive power imbalances. The results from the step response graph of the compensated model shows performance accuracy as the system regained stability in less than 0.5 s, which is a significant improvement over the uncompensated model. [ABSTRACT FROM AUTHOR]

The present research aims at investigating the vibration period of structural units (SUs) of a typical masonry aggregate located in the historical center of Mirandola, a municipality in the province of Modena. The clustered building consists of eighteen SUs mutually interconnected to each other, which are characterized by solid brick walls and deformable floors. First of all, non-linear static analyses are performed by adopting the 3Muri software focusing on two distinct modelling techniques concerning the analyzed SUs in isolated and clustered configurations. Congruently to the procedure adopted, in order to evaluate a reliable seismic structural response of the SUs arranged in aggregate conditions, the contribution in terms of stiffness and mass derived from adjacent buildings is considered. The analysis results are represented in terms of risk factor, stiffness, and ductility. Secondly, the eigenvalue analysis is faithfully developed to identify the main vibration modes of the investigated SUs by proposing an empirical formulation, that allows for predicting the vibration period of structural units placed in aggregate configuration starting from the corresponding isolated ones. Finally, fragility functions are derived for both the heading and intermediate SUs to point out the expected damages under earthquakes with different intensities. [ABSTRACT FROM AUTHOR]