Search Results (10)

Model predictive control (MPC) is a commonly used online strategy for maximizing economic benefits in smart homes that integrate photovoltaic (PV) panels, electric vehicles (EVs), and battery energy storage systems (BESSs). However, prediction errors associated with PV power and load demand can lead to economic losses. Scenario-based MPC can mitigate the impact of prediction errors by computing the expected objective value of multiple stochastic scenarios. However, reducing the number of scenarios is often necessary to lower the computation burden, which in turn causes some economic loss. To achieve online operation and maximize economic benefits, this paper proposes utilizing the consensus alternating direction method of multipliers (C-ADMM) algorithm to quickly calculate the scenario-based MPC problem without reducing stochastic scenarios. First, the system layout and relevant component models of smart homes are established. Then, the stochastic scenarios of net load prediction error are generated through Monte Carlo simulation. A consensus constraint is designed about the first control action in different scenarios to decompose the scenario-based MPC problem into multiple sub-problems. This allows the original large-scale problem to be quickly solved by C-ADMM via parallel computing. The relevant results verify that increasing the number of stochastic scenarios leads to more economic benefits. Furthermore, compared with traditional MPC with or without prediction error, the results demonstrate that scenario-based MPC can effectively address the economic impact of prediction error. Full article

Robust geometric fitting is one of the crucial and fundamental problems in computer vision and pattern recognition. While random sampling and consensus maximization have been popular strategies for robust fitting, finding a balance between optimization quality and computational efficiency remains a persistent obstacle. In this paper, we adopt an optimization perspective and introduce a novel maximum consensus robust fitting algorithm that incorporates the maximum entropy framework into the consensus maximization problem. Specifically, we incorporate the probability distribution of inliers calculated using maximum entropy with consensus constraints. Furthermore, we introduce an improved relaxed and accelerated alternating direction method of multipliers (R-A-ADMMs) strategy tailored to our framework, facilitating an efficient solution to the optimization problem. Our proposed algorithm demonstrates superior performance compared to state-of-the-art methods on both synthetic and contaminated real datasets, particularly when dealing with contaminated datasets containing a high proportion of outliers. Full article

This paper introduces a dynamic consensus-based economic dispatch (ED) algorithm utilizing the Alternating Direction Method of Multipliers (ADMM) to optimize real-time pricing and generation/demand decisions within a decentralized energy management framework. The increasing complexity of modern energy markets, driven by the proliferation of Distributed Energy Resources (DER) and variable demands from hybrid electric vehicles, necessitates a departure from traditional centralized dispatch methods. This research proposes a novel ADMM-based solution tailored for non-responsive and responsive demand units that integrates demand response mechanisms to adaptively manage real-time fluctuations while enhancing security and privacy through distributed data management. The testing of the algorithm on the IEEE 39 bus system under various load conditions over 24 h demonstrated the algorithm’s effectiveness in handling traditional and renewable energy sources, particularly highlighting the economic benefits of shifting controllable loads to periods of low-cost renewable availability. The findings underscore the algorithm’s potential to reduce energy costs, enhance energy efficiency, and offer a scalable solution across diverse grid systems, contributing significantly to advancing global energy policy and sustainable management practices. Full article

In this paper, a fully distributed strategy for the economic dispatch problem (EDP) in the smart grid is proposed. The economic dispatch model considers both traditional thermal generators and wind turbines (WTs), integrating generation costs, carbon trading expenses, and the expected costs associated with the unpredictability of wind power. The EDP is transformed into an equivalent optimization problem with only an equality constraint and thus can be solved by an alternating-direction method of multipliers (ADMM). Then, to tackle this problem in a distributed manner, the outer-layer framework of the proposed strategy adopts a parallel ADMM, where different variables can be calculated simultaneously. And the inner-layer framework adopts a finite-step consensus algorithm. Convergence to the optimal solution is achieved within a finite number of communication iterations, which depends on the scale of the communication network. In addition, leveraging local and neighbor information, a distributed algorithm is designed to compute the eigenvalues of the Laplacian matrix essential for the finite-step algorithm. Finally, several numerical examples are presented to verify the correctness and effectiveness of the proposed strategy. Full article

In this paper, we propose a novel distributed algorithm based on model predictive control and alternating direction multiplier method (DMPC-ADMM) for cooperative trajectory planning of quadrotor swarms. First, a receding horizon trajectory planning optimization problem is constructed, in which the differential flatness property is used to deal with the nonlinear dynamics of quadrotors while we design a relaxed form of the discrete-time control barrier function (DCBF) constraint to balance feasibility and safety. Then, we decompose the original trajectory planning problem by ADMM and solve it in a fully distributed manner with peer-to-peer communication, which induces the quadrotors within the communication range to reach a consensus on their future trajectories to enhance safety. In addition, an event-triggered mechanism is designed to reduce the communication overhead. The simulation results verify that the trajectories generated by our method are real-time, safe, and smooth. A comprehensive comparison with the centralized strategy and several other distributed strategies in terms of real-time, safety, and feasibility verifies that our method is more suitable for the trajectory planning of large-scale quadrotor swarms. Full article

This paper focuses on the dynamic economic emission dispatch (DEED) problem, to coordinate the distributed energy resources (DERs) in a power system and achieve economical and environmental operation. Distributed energy storages (ESs) are introduced into problem formulation in which charging/discharging efficiency is taken into account. By relaxing the nonconvexity induced by the charging/discharging model of ESs and network losses, we convert the non-convex DEED problem into its convex equivalency. Then, through a Lagrangian duality reformulation, an equivalent unconstrained consensus optimization model is established—a novel consensus-based decentralized algorithm, where the incremental cost is chosen as the consensus variable. At each iteration, only one primal variable requires sub-optimization, and it is completely locally updated. This is different from the well-known alternating direction method of multiplier (ADMM)-based algorithms where more than one subproblem needs to be solved at each iteration. The results of the comparative experiments also reflect the algorithm’s advantage in terms of computational efficiency. The simulation results validate the effectiveness of the proposed algorithm, achieving a balance between emissions and economic considerations. Full article

In the electricity market, prosumers are becoming more and more prevalent due to the fast development of distributed energy resources and demand response management, which also promote the appearance of peer-to-peer (P2P) trading mechanisms for energy. Optimization-based methods are efficient tools to design the P2P energy trading negotiation mechanism. However, the main drawback for market mechanisms based on optimization methods is that the incentive compatibility cannot be satisfied, which means participants can obtain more profit by providing untruthful biddings. To overcome this challenge, a novel consensus mechanism based on Proof of Solution (PoSo) is proposed for P2P energy trading. The optimization results will be verified by neighboring agents according to the KKT conditions in a fully decentralized and symmetric manner, which means agents will check each other’s solutions. However, the verification process may leak the private information of agents, and a privacy-preserving consensus mechanism is designed using Shamir’s secret sharing method. After that, we explore a method to realize that trusted agents can recover the right information even under the misbehavior of malicious agents by inheriting the philosophy of Practical Byzantine Fault Tolerance (PBFT). The numerical results demonstrate the effectiveness and efficiency of our proposed consensus mechanisms. In more detail, (1) when the message delivery success rate is not lower than 0.7, the consensus mechanisms almost guarantee success; (2) if the proportion of untrusted agents satisfies $4f+1\le N_{{\omega }_n}$, the proposed method guarantees the correctness of the consensus verification results; (3) the communication times among agents can be highly reduced by more than 60% by only verifying the optimality of the received results for the first three and last few iterations. Full article

Many data analysis problems can be modeled as a constrained optimization problem characterized by nonsmooth functionals, often because of the presence of ${\ell }_1$-regularization terms. One of the most effective ways to solve such problems is through the Alternate Direction Method of Multipliers (ADMM), which has been proved to have good theoretical convergence properties even if the arising subproblems are solved inexactly. Nevertheless, experience shows that the choice of the parameter $\tau$ penalizing the constraint violation in the Augmented Lagrangian underlying ADMM affects the method’s performance. To this end, strategies for the adaptive selection of such parameter have been analyzed in the literature and are still of great interest. In this paper, starting from an adaptive spectral strategy recently proposed in the literature, we investigate the use of different strategies based on Barzilai–Borwein-like stepsize rules. We test the effectiveness of the proposed strategies in the solution of real-life consensus logistic regression and portfolio optimization problems. Full article

At present, the power system has the characteristics of mutual independence but interconnection, and the interconnection between the various subsystems brings certain challenges to the distributed computing of the power grid. In addition, a substantial amount of naturally uncertain renewable resources are incorporated into the power system, which will impose volatile dynamics on the grid. In this paper, an alternating direction multiplier method (ADMM) is proposed for the power system with real-time renewables to tackle the online optimal power flow (OPF) problem. Due to the adoption of the Lagrangian duality, the proposed distributed ADMM scheme utilizes consensus ADMM to solve the dual OPF problem, which only discloses boundary coupling via the Lagrangian multiplier and further reduces the amount of information communication. Given the natural uncertainty of distributed energy resources (DER), the algorithm avoids the double-loop implementation or the uncertainty of traditional distributed methods of using the boundary information as equality constraints caused by dynamic DER. It is thus capable of providing a provable performance guarantee and is inherently developed to cope with the dynamic OPF problem with renewables in an online fashion. Taking the IEEE 30-bus system as a test feeder, the simulation results verify the efficiency and robustness of the proposed algorithms in solving both the static and dynamic OPF problems; in addition, the online method can effectively avoid the violent fluctuations of the conventional generator output copying with renewables rapid variation in comparison with the offline algorithms. Full article

With the upcoming fifth Industrial Revolution, humans and collaborative robots will dance together in production. They themselves act as an agent in a connected world, understood as a multi-agent system, in which the Laplacian spectrum plays an important role since it can define the connection of the complex networks as well as depict the robustness. In addition, the Laplacian spectrum can locally check the controllability and observability of a dynamic controlled network, etc. This paper presents a new method, which is based on the Augmented Lagrange based Alternating Direction Inexact Newton (ALADIN) method, to faster the convergence rate of the Laplacian Spectrum Estimation via factorization of the average consensus matrices, that are expressed as Laplacian-based matrices problems. Herein, the non-zero distinct Laplacian eigenvalues are the inverse of the stepsizes $\{{\alpha }_t,t=1,2,\dots \}$ of those matrices. Therefore, the problem now is to carry out the agreement on the stepsize values for all agents in the given network while ensuring the factorization of average consensus matrices to be accomplished. Furthermore, in order to obtain the entire Laplacian spectrum, it is necessary to estimate the relevant multiplicities of these distinct eigenvalues. Consequently, a non-convex optimization problem is formed and solved using ALADIN method. The effectiveness of the proposed method is evaluated through the simulation results and the comparison with the Lagrange-based method in advance. Full article