Stability Analysis Using Fractional-Order PI Controller in a Time-Delayed Single-Area Load Frequency Control System with Demand Response

The current study investigates the stability analysis based on gain and phase margin (GPM) using fractional-order proportional-integral (FOPI) controller in a time-delayed single-area load frequency control (LFC) system with demand response (DR). The DR control loop is introduced into the classical LFC system to improve the frequency deviation. Although the DR enhances the system’s reliability, the excessive use of open communication networks in the control of the LFC results in time delays that make the system unstable. A frequency-domain approach is proposed to compute the time delay that destabilizes the system using GPM values and different parameter values of the FOPI controller. This method converts the equation into an ordinary polynomial with no exponential terms by eliminating the exponential terms from the system’s characteristic equation. The maximum timedelay values at which the system is marginally stable are calculated analytically using the new polynomial. Finally, the verification of the time delays calculated is demonstrated by simulation studies in the Matlab/Simulink environment and the root finder (quasi-polynomial mapping-based root finder, QPmR) algorithm to define the roots of polynomials with exponential terms providing information about their locations

The Convergence of Parametric Resonance and Vibration Energy Harvesting

Energy harvesting is an emerging technology that derives electricity from the ambient environment in a decentralised and self-contained fashion. Applications include self-powered medical implants, wearable electronics and wireless sensors for structural health monitoring. Amongst the vast options of ambient sources, vibration energy harvesting (VEH) has attracted by far the most research attention. Two of the key persisting issues of VEH are the limited power density compared to conventional power supplies and confined operational frequency bandwidth in light of the random, broadband and fast-varying nature of real vibration. The convention has relied on directly excited resonance to maximise the mechanical-to-electrical energy conversion efficiency. This thesis takes a fundamentally different approach by employing parametric resonance, which, unlike the former, its resonant amplitude growth does not saturate due to linear damping. Therefore, parametric resonance, when activated, has the potential to accumulate much more energy than direct resonance. The vibrational nonlinearities that are almost always associated with parametric resonance can offer a modest frequency widening. Despite its promising theoretical potentials, there is an intrinsic damping dependent initiation threshold amplitude, which must be attained prior to its onset. The relatively low amplitude of real vibration and the unavoidable presence of electrical damping to extract the energy render the onset of parametric resonance practically elusive. Design approaches have been devised to passively minimise this initiation threshold. Simulation and experimental results of various design iterations have demonstrated favourable results for parametric resonance as well as the various threshold-reduction mechanisms. For instance, one of the macro-scale electromagnetic prototypes (∼1800 cm3) when parametrically driven, has demonstrated around 50% increase in half power band and an order of magnitude higher peak power (171.5 mW at 0.57 ms−2) in contrast to the same prototype directly driven at fundamental resonance (27.75 mW at 0.65 ms−2). A MEMS (micro-electromechanical system) prototype with the additional threshold-reduction design needed 1 ms−2 excitation to activate parametric resonance while a comparable device without the threshold-reduction mechanism required in excess of 30 ms−2. One of the macro-scale piezoelectric prototypes operated into auto-parametric resonance has demon-strated notable further reduction to the initiation threshold. A vacuum packaged MEMS prototype demonstrated broadening of the frequency bandwidth along with higher power peak (324 nW and 160 Hz) for the parametric regime compared to when operated in room pressure (166 nW and 80 Hz), unlike the higher but narrower direct resonant peak (60.9 nW and 11 Hz in vacuum and 20.8 nW and 40 Hz in room pressure). The simultaneous incorporation of direct resonance and bi-stability have been investigated to realise multi-regime VEH. The potential to integrate parametric resonance in the electrical domains have also been numerically explored. The ultimate aim is not to replace direct resonance but rather for the various resonant phenomena to complement each other and together harness a larger region of the available power spectrum

Anomalous statistical properties and fluctuations on multiple timescales

How can fluctuations in one-dimensional time series data be characterized and how can detected effects be decomposed into their dynamical origins or causes? In the context of these questions, a variety of problems are discussed and solutions are introduced. The first issue concerns the causes of anomalous diffusion. A previously proposed framework decomposes the Hurst exponent into the Joseph, Noah, and Moses effects. They represent violations of the three premises of the central limit theorem. Here the framework is applied to an intermittent deterministic system, which exhibits a rich combination of all three effects. Nevertheless, the results provide an intuitive interpretation of the dynamics. In addition, the framework is theoretically discussed and connected to a calculation that proves its validity for a large class of systems. Once the type of anomalous statistical behavior is classified, one might ask what the dynamical origin of the effects is. Especially the property of long range temporal correlations (the Joseph effect) is discussed in detail. In measurements, they might arise from different dynamical origins or can be explained as an emerging phenomenon. A collection of different routes to the observed behavior is established here. A popular tool for detecting long range correlations is detrended fluctuation analysis. Its advantages over traditional methods are stability and smoothness for timescales up to one fourth of the measurement time and the ability to neglect the slow dynamics and trends. Recently, a theory for an analytical understanding of this method was introduced. In this thesis, the method is further analyzed and developed. An approach is presented that enables scientists to use this method for short range correlated data, even if the dynamics is very complex. Fluctuations can be decomposed into a superposition of linear models that explain its features. Therefore, on the one hand, this thesis is about understanding the effects of anomalous diffusion. On the other hand, it is about widening the applicability of one of its detection methods such that it becomes useful for understanding normal or complex statistical behavior. A good example of a complex system, where the proposed stochastic methods are useful, is the atmosphere. Here it is shown how detrended fluctuation analysis can be used to uncover oscillatory modes and determine their periods. One of them is the El Ni\~no southern oscillation. A less well known and more challenging application is a 7--8 year mode in European temperature fluctuations. A power grid is a very different type of complex system. However, using the new method, it is possible to generate a data model that incorporates the important features of the grid frequency

Power System Stability Analysis using Neural Network

This work focuses on the design of modern power system controllers for automatic voltage regulators (AVR) and the applications of machine learning (ML) algorithms to correctly classify the stability of the IEEE 14 bus system. The LQG controller performs the best time domain characteristics compared to PID and LQG, while the sensor and amplifier gain is changed in a dynamic passion. After that, the IEEE 14 bus system is modeled, and contingency scenarios are simulated in the System Modelica Dymola environment. Application of the Monte Carlo principle with modified Poissons probability distribution principle is reviewed from the literature that reduces the total contingency from 1000k to 20k. The damping ratio of the contingency is then extracted, pre-processed, and fed to ML algorithms, such as logistic regression, support vector machine, decision trees, random forests, Naive Bayes, and k-nearest neighbor. A neural network (NN) of one, two, three, five, seven, and ten hidden layers with 25%, 50%, 75%, and 100% data size is considered to observe and compare the prediction time, accuracy, precision, and recall value. At lower data size, 25%, in the neural network with two-hidden layers and a single hidden layer, the accuracy becomes 95.70% and 97.38%, respectively. Increasing the hidden layer of NN beyond a second does not increase the overall score and takes a much longer prediction time; thus could be discarded for similar analysis. Moreover, when five, seven, and ten hidden layers are used, the F1 score reduces. However, in practical scenarios, where the data set contains more features and a variety of classes, higher data size is required for NN for proper training. This research will provide more insight into the damping ratio-based system stability prediction with traditional ML algorithms and neural networks.Comment: Masters Thesis Dissertatio