Direct Stability Method Research Articles

Analysis of Transient Stability for Multimachine Power System

The stability is an important guarantee for the safe and reliable operation of the power system, it is a decisive factor to limit the transmission distance and conveying capacity of the power system. Therefore, various measures must be taken to improve the system stability. The stability of the power system includes power angle stability, voltage stability and frequency stability. Among them, the power angle stability includes static stability and transient stability. Considering the importance of stability to the power system, the power system stability analysis methods and the measures to improve the power system stability is studied, so as to provide some useful reference for the safe and reliable operation of the power system. Generally, for multi-machine system transient stability becomes a major concern of wide power system due to load demand increasing day by day. In order to withstand disturbances with power quality issues requires evaluation of power system’s ability. There are many different kinds of methods for analysis of transient stability usually for multi-machine system. These methods include extended equal area criteria, time domain analysis and direct stability methods such as the transient energy function.

Asymptotically stable controller for SSTs based on Lyapunov direct stability method

An asymptotically stable controller for solid-state transformers (SSTs) based on Lyapunov direct stability (LDS) method is presented in this study. The proposed controller has four control objectives for the SST application, which includes unity power factor at medium-voltage AC (VAC) side of the SST, constant DC-link voltage and constant output voltage magnitude and frequency at low-VAC side of the SST. To fulfil the above-mentioned objectives four control laws are derived from the Lyapunov function, directly. The proposed LDS-based controller is simulated using MATLAB/Simulink software. The obtained results indicate the fast and superior dynamic characteristics of the proposed controller. The LDS-based controller is comprehensive and can be adopted for the SST applications.

Controlling an unmanned quad-rotor aerial vehicle with model parameter uncertainty and actuator failure

It is challenging to stabilise an unmanned quad-rotor aerial vehicle when a dynamic change in its model parameters or failure of its actuator occurs. In this paper, a quad-rotor unmanned aerial vehicle UAV is controlled based on model reference adaptive control MRAC and a linear quadratic regulator LQR. The kinematics and dynamics of the quad-rotor are calculated, and Lyapunov's direct stability method is used to design the MRAC. In order to evaluate the performance of the adaptive control algorithms in the presence of thrust loss that may occur due to component failure or physical damage, a real quad-rotor is built from scratch using commercial components. Both controllers are designed, implemented and tested using AVR microcontrollers. Comparison is made between the controllers under normal and faulty situations and the effectiveness of the proposed control strategy is verified. Simulation and experimental results show that both controllers have satisfactory performance under normal conditions and even in the presence of the partial loss of thrust that may occur due to the loss of control effectiveness in one of the rotors or the damage of one propeller, superior system performance is observed using the proposed MRAC controller.

Controlling an unmanned quad-rotor aerial vehicle with model parameter uncertainty and actuator failure

It is challenging to stabilise an unmanned quad-rotor aerial vehicle when a dynamic change in its model parameters or failure of its actuator occurs. In this paper, a quad-rotor unmanned aerial vehicle (UAV) is controlled based on model reference adaptive control (MRAC) and a linear quadratic regulator (LQR). The kinematics and dynamics of the quad-rotor are calculated, and Lyapunov's direct stability method is used to design the MRAC. In order to evaluate the performance of the adaptive control algorithms in the presence of thrust loss that may occur due to component failure or physical damage, a real quad-rotor is built from scratch using commercial components. Both controllers are designed, implemented and tested using AVR microcontrollers. Comparison is made between the controllers under normal and faulty situations and the effectiveness of the proposed control strategy is verified. Simulation and experimental results show that both controllers have satisfactory performance under normal conditions and even in the presence of the partial loss of thrust that may occur due to the loss of control effectiveness in one of the rotors or the damage of one propeller, superior system performance is observed using the proposed MRAC controller.

A heuristic design method for attitude stabilization of magnetic actuated satellites

In this paper a heuristic design strategy for stabilizing the satellite attitude has been proposed. It is assumed that the satellite is actuated by a set of mutually perpendicular magnetic coils. Using well-known Lyapunov direct stability method it is shown that the proposed controller causes to a global asymptotic stable system for all near polar orbits. The design procedure is based on analyzing of the conceptual effects of magnetic coils on the satellite attitude motion. Considering these effects lead to some intuitive results which determine the global stabilizing control law. The performance and robustness of the designed controller against actuators saturation and quantization error have been verified using a real-time-hardware–software in-loop (RTHSIL) simulation results. These results show that the global stability can be achieved although some disturbances and restrictions exist. This stabilizing controller can be simply combined with a linear explicit model predictive controller (EMPC) to achieve a full three-axis control law.

A sharp threshold for disease persistence in host metapopulations

A sharp threshold is established that separates disease persistence from the extinction of small disease outbreaks in an S→E→I→R→S type metapopulation model. The travel rates between patches depend on disease prevalence. The threshold is formulated in terms of a basic replacement ratio (disease reproduction number), ℛ0, and, equivalently, in terms of the spectral bound of a transmission and travel matrix. Since frequency-dependent (standard) incidence is assumed, the threshold results do not require knowledge of a disease-free equilibrium. As a trade-off, for ℛ0>1, only uniform weak disease persistence is shown in general, while uniform strong persistence is proved for the special case of constant recruitment of susceptibles into the patch populations. For ℛ0<1, Lyapunov's direct stability method shows that small disease outbreaks do not spread much and eventually die out.

Transient stability test systems for direct stability methods

The aim of this paper is to present a standard set of power system data with benchmark results against which direct stability techniques to assess transient stability could be compared and tested. The test systems have been selected to display a wide range of dynamic characteristics to provide a robust test of the efficacy and accuracy of the various analytical techniques to analyze transient stability. Transient stability test system data and benchmark results obtained from two commercially available time domain stability analysis packages are presented in this paper.

A simplified model of coupled relaxation oscillators

In this paper we analyze a simplified model of a pair of coupled relaxation oscillators. The simplified model employs a two-dimensional phase space with jump conditions to approximate the behavior in the full four-dimensional phase space. The stability of the phase-locked modes of oscillation for the simplified system is obtained using phase plane techniques and compared to that previously obtained for the full system using asymptotic and numerical methods. It is shown that these results differ qualitatively over a region of the parameter space, and Lyapunov's direct stability method is used to explain this shortcoming of the model.

Stability Limited Load Supply and Interchange Capability

Traditional load supply and interchange capabilities represent maximums based on steady state generation, line flow and voltage constraints. If the system cannot survive a list of transients when operated at these capabilities, the current computational algorithms do not provide a means for systematically determining alternative secure capabilities. In this paper, the recent results in direct stability methods are applied to give reasonably rapid solutions to this problem. The concept of a Potential Energy Boundary Surface (PEBS) is utilized to obtain transient energy stability margins and their sensitivity to load levels. The energy margins and their sensitivities are used to direct a systematic search for approximate stability limited capabilities.

Stability Limited Load Supply and Interchange Capability

Traditional load supply and interchange capabilities represent maximums based on steady state generation, line flow, and voltage constraints. If the system cannot survive a list of transients when operated at these capabilities, the current computational algorithms do no provide a means for systematically determining alternative secure capabilities. In this paper, the recent results in direct stability methods are applied to give reasonably rapid solutions to this problem. The concept of a potential energy boundary surface (PEBS) is utilized to obtain transient energy stability margins and their sensitivity to load levels. The energy margins and their sensitivities are used to direct a systematic search for approximate stability limited capabilities.