Segmentation of distribution feeders reduces the number of customers affected by faults. During extreme weather events, multiple faults can occur in a very short period of time, and it can take significantly more time for repair crew to address all of them. This makes segmentation critical particularly during storms. Keeping more customers connected, and especially distributed generation that can be critical in restoring neighboring sections of the network, contributes significantly to the resiliency of the system to severe (major) weather events. This paper introduces a novel method of coordination that reduces engineering effort, allows for greater segmentation, and improves the speed of fault clearing operations.

Traditional TCC-based distribution protection without communications can be slow to operate, especially for faults closer to the source. Furthermore, the number of protective devices that can be placed on a feeder is limited because of the tolerance of their TCC curves. This limits the segmentation capabilities when a fault happens. Many modern relays and feeder protection devices are equipped with communication capabilities.

Time-current coordination of electrical distribution network protection equipment is necessary to minimize the extent of customer outages. Reclosing devices help clear temporary faults but complicate the coordination process for faults that last across several reclose attempts. Misoperations can occur if the reset characteristics of neighboring devices are not considered. This paper improves upon a method to ensure coordination between a fuse and recloser by making it easier to apply and extends it to coordination between two reclosing relays.

Directional elements need to be able to differentiate between load current and fault current when two sources are present in the distribution network (closed-loop). When the fault current is about two-or three-times the load current, this is easy to accomplish. But when the directional element is used in a relay that is protecting a distributed generator (DG) the fault and load current may be within the same range, and the direction to the fault still need to be identified. A new directional element for the phase overcurrent relay is proposed to achieve this using individual phase torques and the negative sequence torque. Yet a bigger contribution of this paper is deriving the minimum pickup thresholds for correct operation of the proposed directional element.

We propose an adaptive controller for a dynamical system, where we need a quadratic function of the state to track a given reference signal. This problem appears in the control of generators in weak-grid conditions for example. While the controller can measure the tracking error, the main difficulty arises from the fact that the parameters of the quadratic function itself are not known to the controller. Our approach consists of simultaneously estimating the quadratic function while tracking the reference signal, similar to the approach employed in adaptive control. The quadratic structure of the tracking function necessitates, however, a new adaptive law for estimating the parameters. Even though estimation and control are in general two contradicting requirements, using this new adaptive law and a multilevel controller we prove that the tracking error converges to zero in the absence of measurement noise. In the presence of bounded noise we show that the tracking error can be driven to a neighborhood around the origin.

The notion of observability, is a measure of how well internal states of a system can be reconstructed using a given set of measurements. In this paper, we derive necessary and sufficient conditions for observability in a power system. Deriving sufficient conditions for observability is quite difficult and algebraic observability is often used as a surrogate tool for observability. We show that algebraic observability is necessary but not sufficient for observability. It is also shown that standard measurement sets of at least one voltage measurement, and paired active and reactive power measurements may lead to unobservability for certain measurement configurations. Using a nonlinear transformation and properties of graph theory, a set of sufficient conditions are derived for observability. These conditions are shown to be dependent on the topological properties as well as the type of available measurements. The efficiency and robustness of the proposed approach is also discussed. All results are validated using an IEEE-14 bus system. The proposed method can be utilized off-line as a planning tool during the initial stages of measurement system design as well as on-line prior to state estimation.

We consider a problem where several agents need to achieve a common control objective. The motivation for this problem is control of power generation in a wind farm under weak-grid conditions, with the individual turbine-generators acting as agents. The control objective is a nonlinear function of the state of the agents. Furthermore, this nonlinear function depends on the parameters of the network connecting the agents, and these parameters are unknown. Based on a newly developed nonlinear adaptive control methodology, a process is designed that simultaneously learns the network parameters and, using individual controllers, drives the agents to their respective steady-state solutions. We also compare the performance of this design to an empirical control design that requires less communication.

We consider here the problem of detecting changes in the status of switching devices, circuit breakers in particular, in distribution networks. The lack of measurements in distribution networks compared to transmission networks is the main challenge of this problem. Using expected values of power consumption, and their variance, we are able to quickly calculate the confidence level of identifying the correct topology, or the current status of switching devices, using any given configuration of real time measurements. This allows to compare between different configurations in order to select the optimal one. The main approach we propose relies on approximating the measurements as normal distributed random variables, and applying the maximum likelihood principle. We also discuss an alternative based on support vectors. Results are demonstrated using the IEEE 123 buses distribution test case.

We consider the problem of achieving input-to-state stability (ISS) with respect to external disturbances for control systems with quantized measurements. Quantizers considered in this paper take finitely many values and have an adjustable “center” and “zoom” parameters. Both the full state feedback and the output feedback cases are considered. Similarly to previous techniques from the literature, our proposed controller switches repeatedly between “zooming out” and “zooming in.” However, here we use two modes to implement the “zooming in” phases, which allows us to attenuate an unknown disturbance while using the minimal number of quantization regions. Our analysis is trajectory-based and utilizes a cascade structure of the closed-loop hybrid system. We further show that our method is robust to modeling errors using a specially adapted small-gain theorem. The main results are developed for linear systems, but we also discuss their extension to nonlinear systems under appropriate assumptions.

We consider the problem of stabilizing a control system using a coarse state quantizer in the presence of time delays. We assume the quantizer has an adjustable “center” and “zoom” parameters, and employ an alternating “zoom out”/“zoom in” mechanism in order to achieve a large region of attraction while having the system converge to a small region around the origin. This mechanism is adopted from our previous work where delays were not considered. Here we show that the control system, using the same mechanism and without making any changes in order to accommodate delays explicitly, remains stable under small delays. The main tool we use to prove the result is the nonlinear small-gain theorem.

We consider a class of control systems where the plant model is unknown and the feedback contains only partial quantized measurements of the state. We use a nonlinear optimization that is taking place over both the model parameters and the state of the plant in order to estimate these quantities. We propose a computationally efficient algorithm for solving the optimization problem, and prove its convergence using tools from convex and non-smooth analysis. We demonstrate the importance of this class of control systems, and our method of solution, using the following application: having a fixed wing airplane follow a desired glide slope on approach to landing. The only feedback is from a camera mounted at the front of the airplane and looking at a runway of unknown dimensions. The quantization is due to the finite resolution of the camera. Using this application we also compare our method to the basic method prevalent in the literature, where the optimization is only taking place over the plant model parameters.

We consider the problem of estimating a state x from noisy and corrupted linear measurements y = Ax + z + e, where z is a dense vector of small-magnitude noise and e is a relatively sparse vector whose entries can be arbitrarily large. We study the behavior of the ℓ1 estimator x̂ = arg minx ||y - Ax||1, and analyze its breakdown point with respect to the number of corrupted measurements ||e||0. We show that the breakdown point is independent of the noise. We introduce a novel algorithm for computing the breakdown point for any given A, and provide a simple bound on the estimation error when the number of corrupted measurements is less than the breakdown point. As a motivational example we apply our algorithm to design a robust state estimator for an autonomous vehicle, and show how it can significantly improve performance over the Kalman filter.

We study control systems where the output subspace is covered by a finite set of quantization regions, and the only information available to a controller is which of the quantization regions currently contains the system's output. We assume the dimension of the output subspace is strictly less than the dimension of the state space. The number of quantization regions can be as small as 3 per dimension of the output subspace. We show how to design a controller that stabilizes such a system, and makes the system robust to an external unknown disturbance in the sense that the closed-loop system has the Input-to-State Stability property. No information about the disturbance is required to design the controller. Achieving the ISS property for continuous-time systems with quantized measurements requires a hybrid approach, and indeed our controller consists of a dynamic, discrete-time observer, a continuous-time state-feedback stabilizer, and a switching logic that switches between several modes of operation. Except for some properties that the observer and the stabilizer must possess, our approach is general and not restricted to a specific observer or stabilizer. Examples of specific observers that possess these properties are included.

In this paper, we investigate the exact conditions under which the ` and ` minimizations arising in the context of sparse error correction or sparse signal reconstruction are equivalent. We present a much simplified condition for verifying equivalence, which leads to a provably correct algorithm that computes the exact sparsity of the error or the signal needed to ensure equivalence. Our algorithm is combinatorial in nature, but for moderate-sized matrices it produces the exact result in a reasonably short time. For `-` equivalence problems involving tall encoding matrices (highly robust error correction) and or wide overcomplete dictionaries (sparse signal reconstruction from few measurements), our algorithm is exponentially faster than the only other algorithm known for this problem. We present an example application that requires such matrices, for which our algorithm can greatly assist with real system design. We also show how, if the encoding matrix is imbalanced, an optimal diagonal rescaling matrix can be computed by linear programming, so that the rescaled system enjoys the widest possible equivalence.

We consider an affine control system whose vector fields span a third-order nilpotent Lie algebra. We show that the reachable set at time T using measurable controls is equivalent to the reachable set at time T using piecewise-constant controls with no more than four switches. The bound on the number of switches is uniform over any final time T. As a corollary, we derive a new sufficient condition for stability of nonlinear switched systems under arbitrary switching. This provides a partial solution to an open problem posed in [D. Liberzon, Lie algebras and stability of switched nonlinear systems, in: V. Blondel, A. Megretski (Eds.), Unsolved Problems in Mathematical Systems and Control Theory, Princeton Univ. Press, 2004, pp. 203–207].