Aleksandar M. Stankovic

A survey on modeling of microgrids-From fundamental physics to phasors and voltage sources

Microgrids are an increasingly popular class of electrical systems that facilitate the integration of renewable distributed generation units. Their analysis and controller design requires the development of advanced (typically model-based) techniques naturally posing an interesting challenge to the control community. Although there are widely accepted reduced order models to describe the dynamic behavior of microgrids, they are typically presented without details about the reduction procedure|hampering the understanding of the physical phenomena behind them. The present paper aims to provide a complete modular model derivation of a three-phase inverter-based microgrid. Starting from fundamental physics, we present detailed dynamical models of the main microgrid components and clearly state the underlying assumptions which lead to the standard reduced model representation with inverters represented as controllable voltage sources, as well as static network interconnections and loads.

A robust globally convergent position observer for the permanent magnet synchronous motor

Position observers are essential components in the design of sensorless controllers for electric motors. Their design is complicated by the fact that the motor dynamics is highly nonlinear and contains some uncertain parameters. In this paper a new robust, nonlinear, globally convergent position observer for surface-mount permanent magnet synchronous motors is proposed. A key feature of the proposed observer is that it requires only knowledge of the stator resistance and inductance with the mechanical parameters and the magnetic flux constant being unknown. Thanks to a new reparameterization of the motor dynamics only two parameters are estimated with a regressor consisting of filtered voltage and current, which is persistently exciting in normal motor operation. Realistic simulations and experiments show that the proposed observer outperforms other existing designs from the point of view of robustness and convergence rate.

Secure distributed estimation in cyber-physical systems

Distributed estimation is where the state of a dynamical system is to be estimated via a collection of geographically dispersed measurements over a sensor network. In order to implement the estimator, the sensors, in addition to sensing, implement a simple data fusion protocol that relies on inter-sensor communication. In this paper, we study distributed estimation of cyber-physical systems when there is an adversarial attack on the sensed and communicated information. We propose a novel methodology to address the detection of such attacks, and further incorporate appropriate remedial actions in the estimator. Our methodology is based on the notions of local consistency and nodal consistency and is further reinforced by the exploiting the underlying physical-layer in the cyber-physical description.

Dynamic Voltage Stability Assessment in Large Power Systems With Topology Control Actions

This paper proposes a tractable and scalable algorithm to identify and analyze bifurcation points of a large-scale power system model, which are directly related to dynamic voltage instability problems. Different types of bifurcations are analyzed, including: saddle-node (fold), Hopf, singularity-induced and limit-induced. An algorithm that combines optimization and predictor-corrector procedure is proposed for equilibrium tracing. The algorithm is based on calculation of only critical (rightmost and closest-to-zero) eigenvalues. The proposed algorithm is extended to the case of dynamic voltage stability assessment for power systems with optimized topology (simultaneously subjected to the topology control changes and generation re-dispatch). The proposed approach is illustrated on two (medium- and large-scale real-world) test power systems.

Rapid Small-Signal Stability Assessment and Enhancement Following Changes in Topology

The paper proposes a scalable and tractable algorithm for dynamic topology optimization of power systems involving changes in branch on/off status, while respecting small-signal stability (SSS) constraints. A procedure for fast updates of the system matrices (in descriptor form) and without additional full matrix inversions is proposed. To additionally reduce the computation time, only critical eigenvalues (right-most or those in a specified damping ratio and frequency range) are calculated. A quadratic optimization approach is proposed for optimized generation re-dispatch to satisfy SSS constraints. The approach is applied to two (medium- and large-scale) real-world test power systems.

Approximate bisimulation-based reduction of power system dynamic model with application to transient stability analysis

This paper proposes a new approach to reduction of power system dynamic models based on approximate bisimulation relations. Advantages of these relations for time domain analysis over the model reduction techniques commonly used in system theory are pointed out. The approach is applied to the transient stability analysis in power systems. We propose an algorithm that identifies whether the power system is able to maintain the synchronism after a disturbance, based on linearization and approximate bisimulation relations. During the time simulation, the linearized model is transformed into the appropriate form and reduced using the approximate bisimulation relations. This reduced (and linear) model is used in the numerical integration instead of the original nonlinear one, while the accuracy criterion is satisfied. The New England benchmark power system is used to verify the described algorithm.

Measurement-Directed Reduction of Dynamic Models in Power Systems

The paper describes a new model reduction procedure tailored to power systems. It uses measurement data to devise a family of reduced order nonlinear models while retaining physical interpretability of parameters and equations. The manifold boundary approximation method (MBAM) uses the Fisher information matrix calculated from measurements to identify the least relevant parameter combination in the original model. Next, it numerically constructs a geodesic on the corresponding statistical manifold originating from the initial parameters in the least relevant parameter direction until a manifold boundary is found. MBAM then identifies a limiting approximation in the mathematical form of the model and removes one parameter combination. The simplified model is recalibrated by fitting its behavior to that of the original model, and the process is repeated as appropriate. MBAM is demonstrated on the example of a synchronous generator (SG), which has been treated extensively in the literature. Implications of the proposed model reduction procedure on large power system models are illustrated on a 441-bus, 72-SG dynamical model.

Approximate Bisimulation-Based Reduction of Power System Dynamic Models

In this paper we propose approximate bisimulation relations and functions for reduction of power system dynamic models in differential-algebraic (descriptor) form. The full-size dynamic model is obtained by linearization of the nonlinear transient stability model. We generalize theoretical results on approximate bisimulation relations and bisimulation functions, originally derived for a class of constrained linear systems, to linear systems in descriptor form. An algorithm for transient stability assessment is proposed and used to determine whether the power system is able to maintain the synchronism after a large disturbance. Two benchmark power systems are used to illustrate the proposed algorithm and to evaluate the applicability of approximate bisimulation relations and bisimulation functions for reduction of the power system dynamic models.

Multi-sensor networked state estimation with delayed and irregularly-spaced observations

The performance of a continuous-discrete Kalman filter using multi-sensor observations with irregular sampling patterns and/or delay in the measurement path is analyzed in terms of the associated error-covariance matrix. Such irregularities occur in geographically-distributed systems (such as the electric power grid) when observations are transmitted to an estimation/control center via an unreliable communication link. We extend here our earlier results on lower and upper bounds for the average error covariance to include the effects of communication delay and a more general class of sensor sampling irregularities.

Multi-sensor networked estimation in electric power grids

The performance of a continuous-discrete Kalman filter using multi-sensor observations with irregular sampling patterns is analyzed in terms of the dynamics of the associated (predicted) error-covariance matrix. Irregular sampling may occur as a result of differences in sampling rates and/or lack of synchrony in a geographically-distributed power system. Alternatively, it may also be caused by intermittency (i.e., packet-loss) in the communication link between a sensor and an estimation/control center. We show that the ensemble-and time-averaged error covariance depends only on system parameters and on the characteristic function of the irregular sampling interval of the multi-sensor sampling pattern. We obtain lower and upper bounds on the average error covariance, as well as a necessary condition for its stability, expressed in terms of the region of convergence of the sampling interval characteristic function.