Stability of hybrid stochastic retarded systems

Abstract-In the past few years, hybrid stochastic retarded systems (also known as stochastic retarded systems with Markovian switching), including hybrid stochastic delay systems, have been intensively studied. Among the key results, Mao et al. proposed the Razumikhin-type theorem on exponential stability of stochastic functional differential equations with Markovian switching and its application to hybrid stochastic delay interval systems. However, the importance of general asymptotic stability has not been considered. This paper is to study Razumikhin-type theorems on general theorem moment asymptotic stability of hybrid stochastic retarded systems. The proposed theorems apply to complex systems including some cases when the existing results cannot be used

Stability Performance of Power Electronic Deviceswith Time Delays

This paper deals with the impact of time delays on small-signal stability of power systems with an all converter-interfaced generation. For this purpose, a delay differential algebraic equation model of the voltage source converter and its control scheme is developed. The regulation is based on replicating the dynamical properties of a synchronous machine through appropriate controller configuration. Therefore, a virtual inertia emulation is included in the active power control loop. A transcedental nature of the characteristic equation is resolved by implementing the Chebyshev's discretization method and observing a finite number of critical, low-frequency eigenvalues. Based on the proposed approach, a critical measurement delay is evaluated. Furthermore, a bifurcation analysis of the droop gains and inertia constant is conducted. Stability regions and optimal parametrization of the voltage source converter controls are evaluated and discussed

Inverse Stability Problem and Applications to Renewables Integration

In modern power systems, the operating point, at which the demand and supply are balanced, may take different values due to changes in loads and renewable generation levels. Understanding the dynamics of stressed power systems with a range of operating points would be essential to assuring their reliable operation, and possibly allow higher integration of renewable resources. This letter introduces a non-traditional way to think about the stability assessment problem of power systems. Instead of estimating the set of initial states leading to a given operating condition, we characterize the set of operating conditions that a power grid converges to from a given initial state under changes in power injections and lines. We term this problem as "inverse stability," a problem which is rarely addressed in the control and systems literature, and hence, poorly understood. Exploiting quadratic approximations of the system's energy function, we introduce an estimate of the inverse stability region. Also, we briefly describe three important applications of the inverse stability notion: 1) robust stability assessment of power systems with respect to different renewable generation levels; 2) stability-constrained optimal power flow; and 3) stability-guaranteed corrective action design. ©2017 IEEE.MIT/Skoltech, Ministry of Education and Science of Russian Federation (Grant no.14.615.21.0001.)NSF (1508666)NSF (1550015

Computationally efficient modeling for assessing the energy efficiency of electric drivetrains using convex formulations

High-fidelity models capturing the dynamical behavior can be engaged for the analysis of complex mechatronic systems. Determining the optimal control parameters and design characteristics of such systems necessitates solving multiple interconnected models acting on their respective physical domains and time scales. In this paper, high-fidelity physics-based models are constructed for several electrical subsystems. Loss mechanisms in the various components are inferred because these are key when performing optimal design and control in terms of energy-efficient conversion from power source to actuation. The complexity of the analyzed models is then reduced by introducing convex approximations for the occurring dissipation during power transfers, allowing abstracting the complicated dynamic behavior into a tractable convex formulation, specifically suited for time-efficient numerical simulation. The effectiveness of the strategy is demonstrated on a case study originating from the field of all-electric vehicles, embodying a series interconnection of a battery stack, a buck-boost converter, a voltage source inverter, and an asynchronous electric motor. Results show that the dynamic simulation of the proposed system, composed of multiple time scales, can be reliably computed using the composed convex mappings, hereby reducing the computational time approximately by a factor 461, compromising only 1.8% accuracy regarding energy consumption assessment. The introduced convex formulation can therefore constitute the foundation for optimal control and design of complex mechatronic drives

Modeling and Control of Discrete Event Systems Using Finite State Machines with Variables and Their Applications in Power Grids

Control theories for discrete event systems modeled as finite state machines have been well developed to address various fundamental control issues. However, finite state machine model has long suffered from the problem of state explosion that renders it unsuitable for some practical applications. In an attempt to mitigate the state explosion problem, we propose an efficient representation that appends finite sets of variables to finite state machines in modeling discrete event systems. We also present the control synthesis techniques for such finite state machines with variables (FSMwV). We first present our notion and means of control under this representation. We next present our algorithms for both offline and online synthesis of safety control policies. We then apply these results to the control of electric power grids

Impact of Variability, Uncertainty and Frequency Regulation on Power System Frequency Distribution

This work originates from the observation of the frequency distribution of the Irish system as obtained from a Frequency Disturbance Recorder lent to the last author by the University of Tennessee. The probability density function of such a distribution appears to be bimodal. The paper first investigates how stochastic sources, in particular, load and wind power estimation errors, impact on the distribution of the frequency of a high-voltage transmission system. Then, possible routes to obtain a bimodal distribution of the frequency are explored and the most likely cause that leads to the observed behaviour of the Irish system is identified. Finally, the paper presents a comparison of different frequency regulation strategies and their impact on the distribution of the frequency. A sensitivity analysis of wind speed and load parameters is presented and discussed based on the IEEE-14 bus system

Unified Numerical Stability and Accuracy Analysis of the Partitioned-Solution Approach

This paper focuses on the Partitioned-Solution Approach (PSA) employed for the Time-Domain Simulation (TDS) of dynamic power system models. In PSA, differential equations are solved at each step of the TDS for state variables, whereas algebraic equations are solved separately. The goal of this paper is to propose a novel, matrix-pencil based technique to study numerical stability and accuracy of PSA in a unified way. The proposed technique quantifies the numerical deformation that PSA-based methods introduce to the dynamics of the power system model, and allows estimating useful upper time step bounds that achieve prescribed simulation accuracy criteria. The family of Predictor-Corrector (PC) methods, which is commonly applied in practical implementations of PSA, is utilized to illustrate the proposed technique. Simulations are carried out on the IEEE 39-bus system, as well as on a 1479-bus model of the All-Island Irish Transmission System (AIITS).Swiss National Science Foundatio

Reachability and model prediction based system protection schemes for power systems

Interconnected power systems have been disrupted by unforeseen disturbances from time to time when millions of consumers lose power supply at a very expensive cost. System protection and emergency control to counteract power system instability play an important role in power system operation. Motivated by the industry need to mitigate the effect of disturbances on system operation and improve power system security, this dissertation develops a general framework for system protection scheme based on reachability analysis and Model Predictive Control. A systematic framework to determine switching control strategies is proposed to stabilize the system following a disturbance based on reachability analysis. The computation of the stability region of a stable equilibrium point with the purpose of power system stability analysis is proposed and the validity of discrete controls in transient stability design is studied. Model Predictive Control (MPC) is also adopted to design system protection scheme. A control strategy for maintaining voltage stability following the occurrence of a contingency is presented. Based on economic consideration and control effectiveness, a control switching strategy consisting of a sequence and amounts of shunt capacitors to switch is identified for voltage restoration. The effect of the capacitive control on voltage recovery is measured via trajectory sensitivity. In addition, voltage stability margin is an indication of how far the post-transient operating point is from the voltage collapse point. It is an index of system security. A control scheme to restore voltage following a contingency and to maintain a pre-specified amount of post-transient voltage stability margin is proposed. Moreover, dissimilar controls exist in power system for voltage control. A mixed integer programming based algorithm is presented to study the optimal coordination of the dissimilar controls to improve voltage performance following large disturbances. The developed algorithms are implemented with MATLAB and tested on the WECC system to enhance the performance of voltage and the 39 bus New England system for preventing voltage collapse