Junjian Qi

Shaopan Wei, Ming Yang, Junjian Qi et al.

Recent research has demonstrated that the rotor angle stability can be assessed by identifying the sign of the system maximal Lyapunov exponent (MLE). A positive (negative) MLE implies unstable (stable) rotor angle dynamics. However, because the MLE may fluctuate between positive and negative values for a long time after a severe disturbance, it is difficult to determine the system stability when observing a positive or negative MLE without knowing its further fluctuation trend. In this paper, a new approach for online rotor angle stability assessment is proposed to address this problem. The MLE is estimated by a recursive least square (RLS) based method based on real-time rotor angle measurements, and two critical parameters, the Theiler window and the MLE estimation initial time step, are carefully chosen to make sure the calculated MLE curves present distinct features for different stability conditions. By using the proposed stability assessment criteria, the developed approach can provide timely and reliable assessment of the rotor angle stability. Extensive tests on the New-England 39-bus system and the Northeast Power Coordinating Council 140-bus system verify the effectiveness of the proposed approach.

Junjian Qi, Ahmad F. Taha, Jianhui Wang

Kalman filters and observers are two main classes of dynamic state estimation (DSE) routines. Power system DSE has been implemented by various Kalman filters, such as the extended Kalman filter (EKF) and the unscented Kalman filter (UKF). In this paper, we discuss two challenges for an effective power system DSE: (a) model uncertainty and (b) potential cyber attacks. To address this, the cubature Kalman filter (CKF) and a nonlinear observer are introduced and implemented. Various Kalman filters and the observer are then tested on the 16-machine, 68-bus system given realistic scenarios under model uncertainty and different types of cyber attacks against synchrophasor measurements. It is shown that CKF and the observer are more robust to model uncertainty and cyber attacks than their counterparts. Based on the tests, a thorough qualitative comparison is also performed for Kalman filter routines and observers.

Ahmad F. Taha, Mohammadhafez Bazrafshan, Sebastian Nugroho et al.

Uncertainty from renewable energy and loads is one of the major challenges for stable grid operation. Various approaches have been explored to remedy these uncertainties. In this paper, we design centralized or decentralized state-feedback controllers for generators while considering worst-case uncertainty. Specifically, this paper introduces the notion of $\mathcal{L}_{\infty}$ robust control and stability for uncertain power networks. Uncertain and nonlinear differential algebraic equation model of the network is presented. The model includes unknown disturbances from renewables and loads. Given an operating point, the linearized state-space presentation is given. Then, the notion of $\mathcal{L}_{\infty}$ robust control and stability is discussed, resulting in a nonconvex optimization routine that yields a state feedback gain mitigating the impact of disturbances. The developed routine includes explicit input-bound constraints on generators' inputs and a measure of the worst-case disturbance. The feedback control architecture can be centralized, distributed, or decentralized. Algorithms based on successive convex approximations are then given to address the nonconvexity. Case studies are presented showcasing the performance of the $\mathcal{L}_{\infty}$ controllers in comparison with automatic generation control and $\mathcal{H}_{\infty}$ control methods.

Sebastian A. Nugroho, Ahmad F. Taha, Junjian Qi

Power system dynamics are naturally nonlinear. The nonlinearity stems from power flows, generator dynamics, and electromagnetic transients. Characterizing the nonlinearity of the dynamical power system model is useful for designing superior estimation and control methods, providing better situational awareness and system stability. In this paper, we consider the synchronous generator model with a phasor measurement unit (PMU) that is installed at the terminal bus of the generator. The corresponding nonlinear process-measurement model is shown to be locally Lipschitz, i.e., the dynamics are limited in how fast they can evolve in an arbitrary compact region of the state-space. We then investigate different methods to compute Lipschitz constants for this model, which is vital for performing dynamic state estimation (DSE) or state-feedback control using Lyapunov theory. In particular, we compare a derived analytical bound with numerical methods based on low discrepancy sampling algorithms. Applications of the computed bounds to dynamic state estimation are showcased. The paper is concluded with numerical tests.

Junjian Qi, Shengwei Mei

Cascading failures triggered by trivial initial events are encountered in many complex systems. It is the interaction and coupling between components of the system that causes cascading failures. We propose a simple model to simulate cascading failure by using the matrix that determines how components interact with each other. A careful comparison is made between the original cascades and the simulated cascades by the proposed model. It is seen that the model can capture general features of the original cascades, suggesting that the interaction matrix can well reflect the relationship between components. An index is also defined to identify important links and the distribution follows an obvious power law. By eliminating a small number of most important links the risk of cascading failures can be significantly mitigated, which is dramatically different from getting rid of the same number of links randomly.

Ahmad F. Taha, Junjian Qi, Jianhui Wang et al.

Phasor measurement units (PMUs) can be effectively utilized for the monitoring and control of the power grid. As the cyber-world becomes increasingly embedded into power grids, the risks of this inevitable evolution become serious. In this paper, we present a risk mitigation strategy, based on dynamic state estimation, to eliminate threat levels from the grid's unknown inputs and potential cyber-attacks. The strategy requires (a) the potentially incomplete knowledge of power system models and parameters and (b) real-time PMU measurements. First, we utilize a dynamic state estimator for higher order depictions of power system dynamics for simultaneous state and unknown inputs estimation. Second, estimates of cyber-attacks are obtained through an attack detection algorithm. Third, the estimation and detection components are seamlessly utilized in an optimization framework to determine the most impacted PMU measurements. Finally, a risk mitigation strategy is proposed to guarantee the elimination of threats from attacks, ensuring the observability of the power system through available, safe measurements. Case studies are included to validate the proposed approach. Insightful suggestions, extensions, and open problems are also posed.

Ahmad F. Taha, Junjian Qi, Jianhui Wang et al.

Utilizing highly synchronized measurements from synchrophasors, dynamic state estimation (DSE) can be applied for real-time monitoring of smart grids. Concurrent DSE studies for power systems are intolerant to unknown inputs and potential attack vectors --- a research gap we will fill in this work. Particularly, we (a) present an overview of concurrent estimation techniques, highlighting key deficiencies, (b) develop DSE methods based on cubature Kalman filter and dynamic observers, (c) rigorously examine the strengths and weaknesses of the proposed methods under attack-vectors and unknown inputs, and (d) provide comprehensive recommendations for DSE. Numerical results and in-depth remarks are also presented.