Sai Pushpak

Stability analysis and controller synthesis for continuous-time linear stochastic systems

In this paper, we derive results for the stochastic stability analysis and controller synthesis for continuous-time stochastic system. The important feature considered here is the multiplicative nature of the stochastic uncertainty in system dynamics. We generalize the existing small-gain type results for stability of discrete-time system with stochastic uncertainty in feedback loop to continuous-time dynamics. Further, LMI-based computable necessary and sufficient conditions are provided for the mean square stability of feedback system. The proposed stability analysis results are used for the synthesis of dynamic robust stabilizing feedback controller with stochastic uncertainty in the feedback loop between the plant and the controller. Fundamental limitation result for the mean square stabilization of system over stochastic channels is presented. Finally, we demonstrate the proposed framework on pendulum on a cart system.

Fragility of decentralized load-side frequency control in stochastic environment

In this paper, we demonstrate the fragility of decentralized load-side frequency algorithm proposed in [1] against stochastic parametric uncertainty in power network model. The stochastic parametric uncertainty is motivated through the presence of renewable energy resources in power system model. We show that relatively small variance value of the parametric uncertainty affecting the system bus voltages cause the decentralized load-side frequency regulation algorithm to become stochastically unstable. The critical variance value of the stochastic bus voltages above which the decentralized control algorithm become mean square unstable is computed using an analytical framework developed in [2], [3]. Furthermore, the critical variance value is shown to decrease with the increase in the cost of the controllable loads and with the increase in penetration of renewable energy resources. Finally, simulation results on IEEE 68 bus system are presented to verify the main findings of the paper.

Control of inter-area oscillation with noise corrupted wide area measurement

There is increased research trend towards the use of Phasor Measurement Units (PMUs) for real-time stability monitoring and active feedback control of power system. In this paper, we address the problem of control of inter-area oscillations when the measurements from Phasor Measurement Units (PMUs) are corrupted with noise. Unlike existing results, we assume that the noise enters multiplicatively in system measurements. We provide systematic procedure based on the solution of Linear Matrix Inequalities (LMI) for the mean square stochastic stability verification of power system with measurement uncertainties. Furthermore, an optimization-based procedure is proposed for the synthesis of measurement-based feedback controller robust to wide area measurement noise. Finally, simulation results are provided to demonstrate the application of the developed framework on WSCC 9 bus system.

Vulnerability analysis of large-scale dynamical networks to coordinated attacks

We study the vulnerability of large-scale linear dynamical networks to coordinated attacks. We consider scenarios in which an attacker can tamper with the links connecting the network components and can also manipulate input injections at the nodes. When these two types of attacks take place simultaneously, the attack is referred to as a coordinated attack. We assume that network links are attacked with a certain probability and that malicious data is injected at the input ports. We employ Markov jump linear systems to model link-based attacks and the system input matrix to model data injection attacks. System theoretic vulnerability metrics developed in earlier work are used to analyze network vulnerability to coordinated attacks. These measures of vulnerability allow us to characterize the impact of coordinated attacks and the difficulty associated with detecting them. Finally, we analyze the vulnerability of coordinated attacks on the New England 39 bus power network.

Power sharing in microgrids with minimum communication control

Proportionate sharing of load changes in a microgrid without communication among the generators is a difficult problem. In this paper an exact power sharing algorithm is developed that uses an optimization-based technique to minimize the exchange of state information among the generators. To demonstrate the application of the developed framework we present simulation results for a system constructed using the data obtained from IEEE 14 bus system. Simulation results reveal that power sharing can be achieved using relatively few communication links among the generators.

Vulnerability analysis of dynamical power networks to stochastic link failure attacks

In this paper, we present results for the vulnerability analysis of a power network to stochastic link failure attacks. We assume a network links are subjected to attacks where the link-based attack is modeled as stochastic perturbation to link weight. The objective is to determine which links in the network can tolerate the least amount of stochastic perturbation to maintain stochastic stability of a power network. We develop a system theoretical-based, analytical, and computation framework that allows us to rank links in the order of their critical importance to maintain stochastic stability of the network. The computational approach relies on solving a Linear Matrix Inequality (LMI). The developed framework is applied to a structure preserving model of the power network. The structure preserving model allows for the representation of original network topology, thereby identifying critical links connecting generators and load buses. Simulations are performed on IEEE 14 bus system to demonstrate the application of the developed framework.