Graphical models are a succinct way to represent the structure in probability distributions. This article analyzes the graphical model of nodal voltages in non-radial power distribution grids. Using algebraic and structural properties of graphical models, algorithms exactly determining topology and detecting line changes for distribution grids are presented along with their theoretical limitations. We show that if distribution grids have cycles/loops of size greater than three, then nodal voltages are sufficient for efficient topology estimation without additional assumptions on system parameters. In contrast, line failure or change detection using nodal voltages does not require any structural assumption. Under noisy measurements, we provide the first non-trivial bounds on the maximum noise that the system can tolerate for asymptotically correct topology recovery. The performance of the designed algorithms is validated with non-linear AC power flow samples generated by Matpower on test grids, including scenarios with injection correlations and system noise.

This paper presents a distributed, robust, and optimal control architecture for a network of multiple dc-dc converters. The network of converters considered form a dc microgrid in order to regulate a desired dc bus voltage and meet prescribed time-varying power sharing criteria among different energy sources. Such coordinated microgrids provide an important framework for leveraging the benefits of distributed power generation and consumption. The proposed control design seamlessly accommodates communication architectures that range from the centralized to decentralized scenarios with graceful degradation of the performance with lessened communication ability. Moreover, the methods developed are applicable to the case where the desired proportion in which the sources provide the power varies with time. A distinguishing feature of the control design approach is that it regards the net load current as a disturbance signal, lending itself to tractable analysis with tools from the robust and optimal control theory. A quantifiable analysis of the closed-loop stability and the performance of the network of converters is performed; the analysis simplifies to studying the closed-loop performance of an equivalent single-converter system. The control approach is demonstrated through simulations and experiments.

Network systems have become a ubiquitous modeling tool in many areas of science where nodes in a graph represent distributed processes and edges between nodes represent a form of dynamic coupling. When a network topology is already known (or partially known), two associated goals are, to derive estimators for nodes of the network, which cannot be directly observed or are impractical to measure; and to quantitatively identify the dynamic relations between nodes. We address both problems in the challenging scenario where only some outputs of the network are being measured and the inputs are not accessible. The approach makes use of the notion of $d$ -separation for the graph associated with the network. In the considered class of networks, it is shown that the proposed technique can determine or guide the choice of optimal sparse estimators. This article also derives identification methods that are applicable to cases where loops are present providing a different perspective on the problem of closed-loop identification. The notion of $d$ -separation is a central concept in the area of probabilistic graphical models, thus an additional contribution is to create connections between control theory and machine learning techniques.

Grid-following and grid-forming inverters are integral components of microgrids and for integration of renewable energy sources with the grid. For grid following (GFL) inverters, which need to emulate controllable current sources, a significant challenge is to address the large uncertainty of the grid impedance. For grid forming (GFM) inverters, which need to emulate a controllable voltage source, large uncertainty due to varying loads has to be addressed. This article presents a generalized control framework by leveraging the voltage-current duality in the plant dynamic model of GFL and GFM inverters. The modeling of uncertainties is also generalized under the control framework by quantifying the uncertainties in grid impedance parameters and the uncertainties in equivalent loading parameters for GFL and GFM inverters, respectively. Based on the generalized control framework, a $\boldsymbol{\mu}$ -synthesis-based robust control design methodology is proposed for both GFL and GFM inverters. The control objectives, while designing the proposed optimal controllers, are reference tracking, disturbance rejection, and harmonic compensation capability with ${i})$ sufficient ${LCL}$ resonance damping under large variations of grid impedance uncertainty for GFL inverters and ${ii})$ with enhanced dynamic response under large variations of equivalent loading uncertainty for GFM inverters. A combined system-in-the-loop, controller hardware-in-the-loop, and power hardware-in-the-loop based experimental validation on $\mathbf {10}$ -kVA microgrid system with two physical inverter systems is conducted in order to evaluate the efficacy and viability of the proposed controllers.

This article reports an algorithm for multiagent distributed optimization problems with a common decision variable, local linear equality, and inequality, constraints and set constraints with convergence rate guarantees. The algorithm accrues all the benefits of the alternating direction method of multipliers (ADMM) approach. It also overcomes the limitations of existing methods on convex optimization problems with linear inequality, equality, and set constraints by allowing directed communication topologies. Moreover, the algorithm can be synthesized distributively. The developed algorithm has: first, a $O(1/k) $ rate of convergence, where $k$ is the iteration counter, when individual functions are convex but not-necessarily differentiable, and second, a geometric rate of convergence to any arbitrary small neighborhood of the optimal solution, when the objective functions are smooth and restricted strongly convex at the optimal solution. The efficacy of the algorithm is evaluated by a comparison with state-of-the-art constrained optimization algorithms in solving a constrained distributed $\ell _{1}$ -regularized logistic regression problem, and unconstrained optimization algorithms in solving a $\ell _{1}$ -regularized Huber loss minimization problem. Additionally, a comparison of the algorithm's performance with other algorithms in the literature that utilize multiple communication steps is provided.