Sambarta Dasgupta

Real-Time Monitoring of Short-Term Voltage Stability Using PMU Data

We develop a model-free approach for the short-term voltage stability monitoring of a power system. Finite time Lyapunov exponents are used as the certificate of stability. The time-series voltage data from phasor measurement units (PMU) are used to compute the Lyapunov exponent to predict voltage stability in real time. Issues related to practical implementation of the proposed method, such as phasor measurement noise, communication delay, and the finite window size for prediction, are also discussed. Furthermore, the stability certificate in the form of Lyapunov exponents is also used to determine the stability/instability contributions of the individual buses to the overall system stability and for computation of critical clearing time. Simulation results are provided for the IEEE 162-bus system to demonstrate the application of the developed method.

PMU-Based Model-Free Approach for Real-Time Rotor Angle Monitoring

In this letter, we present an algorithm for rotor angle stability monitoring of power system in real-time. The proposed algorithm is model-free and can make use of high resolution phasor measurement units (PMUs) data to provide reliable, timely information about the systems stability. The theoretical basis behind the proposed algorithm is adopted from dynamical systems theory. In particular, the algorithm approximately computes the systems Lyapunov exponent (LE), thereby measuring the exponential convergence or divergence rate of the rotor angle trajectories. The LE serves as a certificate of stability where the positive (negative) value of the LE implies exponential divergence (convergence) of nearby system trajectories, hence, unstable (stable) rotor angle dynamics. We also show the proposed model-free algorithm can be used for the identification of the coherent sets of generators. The simulation results are presented to verify the developed results in the paper on the modified IEEE 162-bus system.

PMU-based model-free approach for short term voltage stability monitoring

In this paper, we propose a model-free approach for short term voltage stability monitoring of power system. Our data-driven approach makes use of Phasor Measurement Units (PMU) data to generate the stability certificate for verifying the voltage stability. We employ Lyapunov exponent, a stability tool adapted from ergodic theory of dynamical system, to generate the stability certificate. The time-series voltage data from PMU is used for the online computation of Lyapunov exponent. The proposed method can not only be used to determine the voltage stability of the entire system but can also be used to determine stability/instability contribution of individual buses to the overall system stability. Simulation results are presented on WSCC nine bus system using different load models.

Contingency Analysis and Identification of Dynamic Voltage Control Areas

Contingency analysis has been an integral part of power system planning and operations. Dynamic contingency analysis is often performed with offline simulation studies, due to its intense computational effort. Due to a large number of possible system variations, covering all combinations in planning studies is very challenging. Contingencies must be chosen carefully to cover a wider group of possibilities, while ensuring system security. This paper proposes a method to classify dynamic contingencies into different clusters, according to their behavioral patterns, in particular, with respect to voltage recovery patterns. The most severe contingency from each cluster becomes the representative of other contingencies in the corresponding cluster. Using the information of contingency clusters, a new concept called dynamic voltage control area (DVCA) is derived. The concept of DVCA will address the importance of the location of dynamic reactive reserves. Simulations have been completed on the modified IEEE 162-bus system to test and validate the proposed method.

Stabilization of system in Lure form over uncertain channels

In this paper, we study the problem of stabilization of nonlinear system in Lure form with uncertainty at the input and output channels. The channel uncertainty is modeled using Bernoulli random variable. Generalization of Positive Real Lemma for stochastic systems are derived to prove the main result of this paper providing sufficient condition for the mean square exponential stability of the closed loop system with erasure channels at the input and output. We generalize this result to provide sufficient condition for stabilization over general uncertain channel at the input and perfect measurement channel at the output. The results in this paper provide synthesis method for the design of controller and observer that are robust to channel uncertainty. Due to nonlinear plant dynamics, the controller and observer design problem are coupled, however we provide explicit relation between the erasure probability of the input and output channels to maintain stability of the feedback control system.

Actuator and sensor placement in linear advection PDE

We study the problem of actuator and sensor placement in a linear advection partial differential equation (PDE). The problem is motivated by its application to actuator and sensor placement in building systems for the control and detection of a scalar quantity such as temperature and contaminants. We propose a gramian based approach to the problem of actuator and sensor placement. The special structure of the advection PDE is exploited to provide an explicit formula for the controllability and observability gramian in the form of a multiplication operator. The explicit formula for the gramian, as a function of actuator and sensor location, is used to provide test criteria for the suitability of a given sensor and actuator location. Furthermore, the solution obtained using gramian based criteria is interpreted in terms of the flow of the advective vector field. In particular, the almost everywhere uniform stability property and ergodic properties of the advective vector field are shown to play a crucial role in deciding the location of actuators and sensors. Simulation results are performed to support the main results of this paper.

Real-time monitoring of short-term voltage stability using PMU data

We develop a model-free approach for the short-term voltage stability monitoring of a power system. Finite time Lya-punov exponents are used as the certificate of stability. The time-series voltage data from phasor measurement units (PMU) are used to compute the Lyapunov exponent to predict voltage stability in real time. Issues related to practical implementation of the proposed method, such as phasor measurement noise, communication delay, and the finite window size for prediction, are also discussed. Furthermore, the stability certificate in the form of Lyapunov exponents is also used to determine the stability/instability contributions of the individual buses to the overall system stability and for computation of critical clearing time. Simulation results are provided for the IEEE 162-bus system to demonstrate the application of the developed method.

Entropy-Based Metric for Characterization of Delayed Voltage Recovery

In this paper, we introduce a novel entropy-based metric to characterize the fault-induced delayed voltage recovery (FIDVR) phenomenon. In particular, we make use of Kullback-Leibler (KL) divergence to determine both the rate and the level of voltage recovery following a fault or disturbance. The computation of the entropy-based measure relies on voltage time-series data and is independent of the underlying system model used to generate the voltage time-series. The proposed measure provides quantitative information about the degree of WECC voltage performance violation for FIDVR phenomenon. The quantitative measure for violation allows one to compare the voltage responses of different buses to various contingencies and to rank order them, based on the degree of violation.

Entropy-based metric for characterization of delayed voltage recovery

In this paper, we introduce a novel entropy-based metric to characterize the fault-induced delayed voltage recovery (FIDVR) phenomenon. In particular, we make use of Kullback-Leibler (KL) divergence to determine both the rate and the level of voltage recovery following a fault or disturbance. The computation of the entropy-based measure relies on voltage time-series data and is independent of the underlying system model used to generate the voltage time-series. The proposed measure provides quantitative information about the degree of WECC voltage performance violation for FIDVR phenomenon. The quantitative measure for violation allows one to compare the voltage responses of different buses to various contingencies and to rank order them, based on the degree of violation.

Identification of critical interactions in uncertain network systems with complex dynamics

In this paper, we propose a novel approach based on tools from system theory and ergodic theory of dynamical systems for the identification of critical interactions responsible for the emergence of complex dynamics in network systems. We consider a network system with multiple uncertain random parameters and operating in non-equilibrium. The objective is to determine which of these multiple parameters are critical for maintaining the stability of non-equilibrium dynamics. We provide necessary condition, expressed in terms of variance of uncertainty and nominal system dynamics, to maintain the stability of network system. The condition is used for rank ordering uncertain parameters and to provide margin of stability for network system. The proposed method is applied for the identification of parameters responsible for limit cycle oscillations in biochemical network involved in yeast cell glycolysis and for robust synchronization in network of Kuramoto oscillators with uncertainty in coupling parameters.