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This paper studies the impact of stochastic load variations on distributed optimal load tracking and allocation (OLTA) problems in cyber-physical DC microgrids (MGs) for transportation electrification. Without load variations, the distributed optimization strategies developed in our earlier work can achieve convergence to global optimal solutions in a multi-objective optimization that balances fair load allocation and power loss reduction. Under persistent stochastic load variations, this paper develops distributed optimal strategies to track time-varying loads under noisy observations and establishes their convergence properties and error bounds. The limiting behavior of the errors characterizes the fundamental impact of the step size on irreducible errors due to conflict between attenuating observation noises and tracking load changes. Optimality conditions and algorithms for selecting the optimal step size are introduced to guide step size selection in practical applications. Simulation studies on real-world systems demonstrate the effectiveness of the proposed algorithms and validate the theoretical results. [ABSTRACT FROM AUTHOR]

This article considers a general model of distributed convex optimization with possibly local constraints, coupled equality constraints, and coupled inequality constraints, where the coupled equality constraints are affine and the coupled inequality constraints can be nonaffine. To solve this problem, we present two algorithms. The first algorithm is similar to a dual subgradient algorithm that requires a center node in the network. The main advantage of the first algorithm is that it achieves the optimal convergence rate O([1√k]). Moreover, it does not require additional treatment for the primal recovery. These merits are achieved by using an iterate-averaging feedback technique on the basis of the dual subgradient method. The second algorithm further removes the requirement of a center node by employing consensus tracking iterates. As a result, the second algorithm is fully distributed at the price of achieving an O([ln k/√k]) convergence rate. [ABSTRACT FROM AUTHOR]

Distributed algorithms have been proposed as options to scale control propositions to the massive number of intelligent energy devices, sub-systems, and distributed energy resources being integrated into the electricity grid. Distributed algorithms rely on the communication network for exchanging information. Failures in the communication network can jeopardize distributed decision-making and in the worst-case scenario can lead to system-level stability problems. This paper proposes a communication-failure-resilient architecture for distributed operation and control in smart grids with hybrid producer/consumer (prosumer) agents. We describe the relations between system-wide performance and communication failures and identify topological conditions on the cyber-physical network, under which prosumers can perform key operating tasks, such as distributed frequency regulation through an imperfect communication network. [ABSTRACT FROM AUTHOR]

This paper is concerned with distributed energy management and control issues of both generators and loads. It aims to maximize the total social welfare that balances generation-side expanses, user-side payments, and transmission line costs. A distributed control strategy with continuous information exchange among neighbors is first proposed. It is shown that this distributed algorithm achieves the global optimal power outputs on generators and the optimal electricity usage on loads asymptotically. To reduce communication resource consumptions, the distributed optimization algorithm is further expanded to incorporate event-triggered communication and control mechanism. In this new algorithm, an event-triggering condition for each generator and each load is employed to determine when its related state information should be sampled and transmitted to its neighbors. Compared with the standard periodic sampling and communication schemes, this new distributed and event-triggered algorithm can significantly reduce communication data flows while achieving the nearly identical control performance to that under continuous data communications. The theoretical results of this paper are validated by using a simulation case study with distributed generators and multiple loads on an IEEE 9-bus system. [ABSTRACT FROM AUTHOR]

This paper establishes exponential convergence rates for a class of primal–dual gradient algorithms in distributed optimization without strong convexity. The convergence analysis is based on a carefully constructed Lyapunov function. By evaluating metric subregularity of the primal–dual gradient map, we present a general criterion under which the algorithm achieves exponential convergence. To facilitate practical applications of this criterion, several simplified sufficient conditions are derived. We also prove that although these results are developed for the continuous-time algorithms, they carry over in a parallel manner to the discrete-time algorithms constructed by using Euler's approximation method. [ABSTRACT FROM AUTHOR]

This paper proposes a learning-based distributed optimization framework to enhance the resilience of distributed power system algorithms against communication failures. The autoregressive-moving-average (ARMA) model is used to estimate the missing states and control actions of neighboring agents during communication contingencies. The proposed framework allows agents to predict the future control actions of neighbors. Thus, even during complete loss of communication, agents can efficiently perform distributed optimization. We use the Distributed Optimal Frequency Control (DOFC) algorithm, which includes optimal power sharing to achieve frequency stability, as a benchmark application platform to show the effectiveness of the proposed framework. The theoretical findings are evaluated on two practical power systems. The results show that the ARMA-based DOFC algorithm can asymptotically reach the same convergence rate as the power system without communication interruptions. • Developing ARMA model to estimate the states and control actions of neighboring agents. • Embedding ARMA model into DOFC algorithm to mitigate communication failures. • Characterizing relationship between estimation errors and convergence rates of ARMA-based DOFC. • Developing a practical criterion for reliability of DOFC under communication uncertainties. • Illustrating the convergence rate of ARMA-based DOFC can asymptotically reach the CR lower bound. [ABSTRACT FROM AUTHOR]

This paper proposes an architectural solution to enhance the resilience of distributed decision-making and control in microgrids and smart grids with respect to communication delays. The paper develops a resource allocation framework to optimally place the multiple-input multiple-output (MIMO) communication technology on critical channels to reduce the communication bottle neck and expedite the convergence speed of distributed online optimization algorithms, which require convergence in the cyber network before the solution can be implemented on the physical grid. The paper shows that optimal placement of the MIMO technology can decrease communication transmission delays, which in turn improves the reliability of power system operational protocols, such as distributed frequency regulation. Illustrative case studies using data from real-world power systems show that only upgrading the critical communication channels is sufficient to achieve system-wide performance improvement. • Proposing an architectural solution to enhance the resilience of distributed optimization in smart grids with respect to communication delays. • Determining an upper bound on the communication delays under different MIMO communication architectures. • Developing a resource allocation algorithm to optimally place the MIMO technology and to increase the resilience of communication networks. [ABSTRACT FROM AUTHOR]

This paper introduces distributed adaptive algorithms for optimal step size selection in a distributed constrained optimization problem that involves stochastic target variations and noisy observations. The limit behavior of the step size sequences reflects fundamental impact that must be balanced between tracking the target changes and attenuating observation noises. Algorithms for simultaneously estimating target variation, tracking the global optimal solution, and finding the optimal step size are derived, which are shown to achieve convergence on all the sequences simultaneously to their respective optimal values. [ABSTRACT FROM AUTHOR]