Chaos Phenomenon in Power Systems: A Review

This review article puts forward the phenomena of chaotic oscillation in electrical power systems. The aim is to present some short summaries written by distinguished researchers in the field of chaotic oscillation in power systems. The reviewed papers are classified according to the phenomena that cause the chaotic oscillations in electrical power systems. Modern electrical power systems are evolving day by day from small networks toward large-scale grids. Electrical power systems are constituted of multiple inter-linked together elements, such as synchronous generators, transformers, transmission lines, linear and nonlinear loads, and many other devices. Most of these components are inherently nonlinear in nature rendering the whole electrical power system as a complex nonlinear network. Nonlinear systems can evolve very complex dynamics such as static and dynamic bifurcations and may also behave chaotically. Chaos in electrical power systems is very unwanted as it can drive system bus voltage to instability and can lead to voltage collapse and ultimately cause a general blackout.

Chaotic Power System Stabilization Based on Novel Incommensurate Fractional-Order Linear Augmentation Controller

The nonlinear dynamics of an incommensurate fractional-order single-machine infinite-bus (SMIB) power system benchmark model are explored and studied by means of modern nonlinear analysis theories, such as bifurcation, chaos, power spectral density (PSD), and bicoherence methods. The effect of incommensurate order derivatives on power system dynamics is presented. The study reveals that the power system undergoes interesting dynamics such as periodic motion, chaotic oscillations, and multistability whenever the system parameter values fall into particular ranges. A new fractional-order linear augmentation-based control scheme is applied to damp out the power system’s chaotic oscillation, change the stability of the coexisting states, and drive the system from multistability to monostability. The stability of the proposed control system is derived using Lyapunov theory. Simulation results confirmed the effectiveness and robustness of the proposed control scheme in damping power system oscillations and achieving good overall performance. The results in this paper will give a better understanding of the nonlinear dynamic behaviors of the incommensurate fractional-order SMIB power system.

Sliding Mode Control for Chaotic Oscillations in SMIB Power System

Power systems may revelation the harmful and undesirable chaotic phenomenon in certain conditions. This project describes the control of a chaotic oscillation in power system. Chaos may lead the power system to voltage instability and voltage collapse when voltage stability conditions are broken. Chaotic oscillations are very sensitive to parameter and initial conditions of power system. Many controllers are projected in practical to suppress the chaos and avoid voltage collapse. In this thesis, a Conventional Sliding Mode Control is applied for removal of chaotic oscillations. The aim of the controller is to remove the chaotic oscillations and bring the order to the nonlinear system. It is also shown that the proposed controller assurances the system state convergence to their desired ethics. To demonstrate the effectiveness of the projected controller, MATLAB Programming is done. Keywords: Chaotic oscillations, SMIB, Conventional Sliding Mode Control

Fast Synergetic Control for Chaotic Oscillation in the Power System Based on Input-Output Feedback Linearization

This paper presents a fast synergetic control scheme for chaotic oscillation in a three-bus power system model. First, the coupling dynamic model of a controlled power system with the current source converter-based STATCOM device and energy storage device is established. Then, the input-output linearization process for the controlled power system is derived step by step, the control problem for the complex nonlinear power system model is completely transformed into the control of linear systems, and a fast synergetic control scheme is proposed for these linear systems. Since the designed control inputs contain complex system functions which are very difficult to obtain and reduce the engineering practicability of the designed controllers, the assumption that system functions are bounded is introduced into the controller design process, and the controllers are redesigned. The remarkable advantages of the proposed control method are that it improves the rapidity of traditional synergetic control and avoids complex system functions in control inputs. Finally, the effectiveness and the superiority of the control scheme are verified by simulation results.

Chaos Suppressing in a Three-Buses Power System Using an Adaptive Synergetic Control Method

The stability of the power system is a critical issue for the reliable and safe operation of the network. Where maintaining voltage levels constant or within the prescribed permissible limit and robustness against disturbances, while the power system is working near its stability margin due to growth of power consumption, nowadays are great challenges. Chaotic oscillation in power network may lead to system bus voltage collapse, angle divergence and possibly both phenomena simultaneously. These cases directly affect the service quality of the power system. The paper presents the problem of chaos suppressing in a three-bus power system of a six-dimensional model. The dynamics of the power system are investigated through examining the nonlinear system’s behavior analysis tools, such as power spectral density, bicoherence, Poincaré map and the Lyapunov exponents. The chaotic oscillation of the power system is suppressed through a Lyapunov-based adaptive algorithm with synergetic control theory. A nonlinear evolution constraint is used for achieving better transient responses and fast dynamics. The dynamics of the energy storage device and STATCOM compensator are employed within the control loop to restore the synchronous operation and maintain the rated voltage, respectively. Numerical simulations are conducted to verify the effectiveness and robustness of the proposed control algorithm. The stabilization of the chaotic power system dynamics and the fast recovery to the normal state are characterized by a smooth and free-of-chattering controller output.

From Continuous-Time Chaotic Systems to Pseudo Random Number Generators: Analysis and Generalized Methodology

The use of chaotic systems in electronics, such as Pseudo-Random Number Generators (PRNGs), is very appealing. Among them, continuous-time ones are used less because, in addition to having strong temporal correlations, they require further computations to obtain the discrete solutions. Here, the time step and discretization method selection are first studied by conducting a detailed analysis of their effect on the systems’ statistical and chaotic behavior. We employ an approach based on interpreting the time step as a parameter of the new “maps”. From our analysis, it follows that to use them as PRNGs, two actions should be achieved (i) to keep the chaotic oscillation and (ii) to destroy the inner and temporal correlations. We then propose a simple methodology to achieve chaos-based PRNGs with good statistical characteristics and high throughput, which can be applied to any continuous-time chaotic system. We analyze the generated sequences by means of quantifiers based on information theory (permutation entropy, permutation complexity, and causal entropy × complexity plane). We show that the proposed PRNG generates sequences that successfully pass Marsaglia Diehard and NIST (National Institute of Standards and Technology) tests. Finally, we show that its hardware implementation requires very few resources.

A S-Type Bistable Locally-Active Memristor and Its Application in Oscillator Circuit

In this paper, a S-type memristor with tangent nonlinearity is proposed. The introduced memristor can generate two kinds of stable pinched hysteresis loops with initial conditions from two flanks of the initial critical point. The power-off plot verifies that the memristor is nonvolatile, and the DC V-I plot shows that the memristor is locally active with the locally-active region symmetrical about the origin. The equivalent circuit of the memristor, derived by small-signal analysis method, is used to study the dynamics near the operating point in the locally-active region. Owing to the bistable and locally-active properties and S-type DC V-I curve, this memristor is called S-type BLAM for short. Then, a new Wien-bridge oscillator circuit is designed by substituting one of its resistances with S-type BLAM. It find that the circuit system can produce chaotic oscillation and complex dynamic behavior, which is further confirmed by analog circuit experiment.

Fractional-Order Hyperbolic Tangent Sliding Mode Control for Chaotic Oscillation in Power System

Chaotic oscillation will occur in power system when there exist periodic load disturbances. In order to analyze the chaotic oscillation characteristics and suppression method, this paper establishes the simplified mathematical model of the interconnected two-machine power system and analyzes the nonlinear dynamic behaviors, such as phase diagram, dissipation, bifurcation map, power spectrum, and Lyapunov exponents. Based on fractional calculus and sliding mode control theory, the fractional-order hyperbolic tangent sliding mode control is proposed to realize the chaotic oscillation control of the power system. Numerical simulation results show that the proposed method can not only suppresses the chaotic oscillation but also reduce the convergence time and suppress the chattering phenomenon and has strong robustness.

Periodic, Quasi-Periodic and Chaotic Oscillations in Two Heterogeneous AIMD/RED Network Congestion Models with State-Dependent Round-Trip Delays

AIMD and RED are two dominant algorithms for controlling Internet congestion. So this paper explores the periodic solutions and complex dynamical phenomena in the state-dependent round-trip delayed AIMD/RED network congestion model with heterogeneous flows, and its improved model. We first use the semi-analytical and semi-numerical method, known as the harmonic balance method with alternating frequency/time (HB-AFT) domain technique, to derive the analytical approximations of periodic oscillations of the system. The obtained results are compared with the numerical results by WinPP, and they show good consistency. At the same time, this suggests that the method used in this paper is correct and valid. Then for the sake of making the system more realistic, we improve the model by using the hyperbolic tangent function. We obtain the approximate solutions, and find some rich dynamical behaviors of this delayed heterogeneous system, including Period-1 to torus, Period-1 to Period-2 to Period-3 motions and two kinds of mechanisms of chaos, i.e. the windows of Period-2 and Period-3 orbits to chaos, where to the best knowledge of the authors, the former route has never been reported. The periodic oscillations may induce synchronization and further congestion, where chaotic oscillation usually means that the system is unstable and may even collapse. Hence, we need to avoid these abundant dynamics discovered in this paper because they are undesirable and harmful. The derived results can help researchers better understand the performance of the AIMD/RED system, and they can be a guide for choosing parameters in a suitable range in order to maintain the network stability and optimize system performance.