Determination of chaotic behaviour in time series generated by charged particle motion around magnetized Schwarzschild black holes

We study behaviour of ionized region of a Keplerian disk orbiting a Schwarzschild black hole immersed in an asymptotically uniform magnetic field. In dependence on the magnetic parameter ${\cal B}$, and inclination angle $\theta$ of the disk plane with respect to the magnetic field direction, the charged particles of the ionized disk can enter three regimes: a) regular oscillatory motion, b) destruction due to capture by the magnetized black hole, c) chaotic regime of the motion. In order to study transition between the regular and chaotic type of the charged particle motion, we generate time series of the solution of equations of motion under various conditions, and study them by non-linear (box counting, correlation dimension, Lyapunov exponent, recurrence analysis, machine learning) methods of chaos determination. We demonstrate that the machine learning method appears to be the most efficient in determining the chaotic region of the $\theta-r$ space. We show that the chaotic character of the ionized particle motion increases with the inclination angle. For the inclination angles $\theta \sim 0$ whole the ionized internal part of the Keplerian disk is captured by the black hole.Comment: 21 pages, 9 figure

Optimal placement of phasor measurement units using the Advanced Matrix Manipulation algorithm

Includes abstract.Includes bibliographical references.This thesis investigates the problem of the Optimal Placement scheme of Phasor Measurement Units in electrical power systems for State Estimation to facilitate improved monitoring and control of the system parameters. The research work done for this thesis begins with review of Supervisory Control and Data Acquisition systems (SCADA). SCADA-based systems are currently employed for condition monitoring and control of industrial and utility electrical power systems. For utility power networks, the main problem with voltage and current phasor data captured by SCADA systems is that they are not synchronised with respect to each other in a present-time or Real-time framework. This implies that both magnitude and phase angle of the measured phasors tend to get affected by slow data flow provided by SCADA to the points of utilization and also by differences in time instants of data capture. These factors inhibit theefficiency and quality of the power system monitoring and control. “Phasor Measurement Unit” (PMU) is a relatively new technology that, when employed in power networks, offers real-time synchronised measurements of the voltages at buses and currents along the lines that connect them. This is accomplished by using a GPS based monitoring system which facilitates time synchronisation of measurements and unlike SCADA, makes the measured data available in Real-Time format. SCADA is not able to provide Real-time data due to the low speeds at which RTUs (Remote Terminal Units) provide data. Availability of time-stamped phasor measurements makes PMUs preferable for power system monitoring and control applications such as State Estimation, Instability Prediction Analysis, Real-time Monitoring of the system conditions, Islanding Detection, System Restoration and Bad Data Detection

Metric indices for performance evaluation of a mixed measurement based state estimator

With the development of synchronized phasor measurement technology in recent years, it gains great interest the use of PMU measurements to improve state estimation performances due to their synchronized characteristics and high data transmission speed. The ability of the Phasor Measurement Units (PMU) to directly measure the system state is a key over SCADA measurement system. PMU measurements are superior to the conventional SCADA measurements in terms of resolution and accuracy. Since the majority of measurements in existing estimators are from conventional SCADA measurement system, it is hard to be fully replaced by PMUs in the near future so state estimators including both phasor and conventional SCADA measurements are being considered. In this paper, a mixed measurement (SCADA and PMU measurements) state estimator is proposed. Several useful measures for evaluating various aspects of the performance of the mixed measurement state estimator are proposed and explained. State Estimator validity, performance and characteristics of the results on IEEE 14 bus test system and IEEE 30 bus test system are presented