Continuous-Domain Real-Time Distributed ADMM Algorithm for Aggregator Scheduling and Voltage Stability in Distribution Network
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Automation & Control Systems↗
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Learning-Accelerated ADMM for Distributed DC Optimal Power Flow
We suggest a novel data-driven method to accelerate the convergence of Alternating Direction Method of Multipliers (ADMM) for solving distributed DC optimal power flow (DC-OPF) where lines are shared between independent network partitions. Using previous observations of ADMM trajectories for a given system under varying load, the method trains a recurrent neural network (RNN) to predict the converged values of dual and consensus variables. Given a new realization of system load, a small number of initial ADMM iterations is taken as input to infer the converged values and directly inject them into the iteration. We empirically demonstrate that the online injection of these values into the ADMM iteration accelerates convergence by a significant factor for partitioned 14-, 118-and 2848-bus test systems under differing load scenarios. The proposed method has several advantages: it maintains the security of private decision variables inherent in consensus ADMM; inference is fast and so may be used in online settings; RNN-generated predictions can dramatically improve time to convergence but, by construction, can never result in infeasible ADMM subproblems; it can be easily integrated into existing software implementations. While we focus on the ADMM formulation of distributed DC-OPF in this paper, the ideas presented are naturally extended to other distributed optimization problems.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Learning-Accelerated ADMM for Distributed DC Optimal Power Flow
We propose a novel data-driven method to accelerate the convergence of Alternating Direction Method of Multipliers (ADMM) for solving distributed DC optimal power flow (DC-OPF) where lines are shared between independent network partitions. Using previous observations of ADMM trajectories for a given system under varying load, the method trains a recurrent neural network (RNN) to predict the converged values of dual and consensus variables. Given a new realization of system load, a small number of initial ADMM iterations is taken as input to infer the converged values and directly inject them into the iteration. We empirically demonstrate that the online injection of these values into the ADMM iteration accelerates convergence by a significant factor for partitioned 14-, 118- and 2848-bus test systems under differing load scenarios. The proposed method has several advantages: it maintains the security of private decision variables inherent in consensus ADMM; inference is fast and so may be used in online settings; RNN-generated predictions can dramatically improve time to convergence but, by construction, can never result in infeasible ADMM subproblems; it can be easily integrated into existing software implementations. While we focus on the ADMM formulation of distributed DC-OPF in this paper, the ideas presented are naturally extended to other distributed optimization problems.
alternating direction method of multipliers↗
An Adaptive Multiparameter Penalty Selection Method for Multiconstraint and Multiblock ADMM
This work presents a new method for online selection of multiple penalty parameters for the alternating direction method of multipliers (ADMM) algorithm applied to optimization problems with multiple constraints or functions with block matrix components. ADMM is widely used for solving constrained optimization problems in a variety of fields, including signal and image processing. Implementations of ADMM often utilize a single hyperparameter, referred to as the penalty parameter, which needs to be tuned to control the rate of convergence. However, in problems with multiple constraints, ADMM may demonstrate slow convergence regardless of penalty parameter selection due to scale differences between constraints. Accounting for scale differences between constraints to improve convergence in these cases requires introducing a penalty parameter for each constraint. The proposed method is able to adaptively account for differences in scale between constraints, providing robustness with respect to problem transformations and initial selection of penalty parameters. It is also simple to understand and implement. Our numerical experiments demonstrate that the proposed method performs favorably compared to a variety of existing penalty parameter selection methods.
97 MATHEMATICS AND COMPUTING↗
Robust and Simple ADMM Penalty Parameter Selection
We present a new method for online selection of the penalty parameter for the alternating direction method of multipliers (ADMM) algorithm. ADMM is a widely used method for solving a range of optimization problems, including those that arise in signal and image processing. In its standard form, ADMM includes a scalar hyperparameter, known as the penalty parameter, which usually has to be tuned to achieve satisfactory empirical convergence. In this work, we develop a framework for analyzing the ADMM algorithm applied to a quadratic problem as an affine fixed point iteration. Using this framework, we develop a new method for automatically tuning the penalty parameter by detecting when it has become too large or small. We analyze this and several other methods with respect to their theoretical properties, i.e., robustness to problem transformations, and empirical performance on several optimization problems. Our proposed algorithm is based on a theoretical framework with clear, explicit assumptions and approximations, is theoretically covariant/invariant to problem transformations, is simple to implement, and exhibits competitive empirical performance.
42 ENGINEERING↗
Robust Decentralized Learning Using ADMM With Unreliable Agents
Many signal processing and machine learning problems can be formulated as consensus optimization problems which can be solved efficiently via a cooperative multi-agent system. However, the agents in the system can be unreliable due to a variety of reasons: noise, faults and attacks. Providing erroneous updates leads the optimization process in a wrong direction, and degrades the performance of distributed machine learning algorithms. This paper considers the problem of decentralized learning using ADMM in the presence of unreliable agents. First, we rigorously analyze the effect of erroneous updates (in ADMM learning iterations) on the convergence behavior of the multi-agent system. We show that the algorithm linearly converges to a neighborhood of the optimal solution under certain conditions and characterize the neighborhood size analytically. Next, we provide guidelines for network design to achieve a faster convergence to the neighborhood. Here, we also provide conditions on the erroneous updates for exact convergence to the optimal solution. Finally, to mitigate the influence of unreliable agents, we propose ROAD , a robust variant of ADMM, and show its resilience to unreliable agents with an exact convergence to the optimum.
97 MATHEMATICS AND COMPUTING↗
Using Filter Methods to Guide Convergence for ADMM, with Applications to Nonnegative Matrix Factorization Problems
Nonconvex, nonlinear optimization problems arise naturally in parameter fitting and machine learning. While augmented Lagrangian methods have demonstrated robust convergence for classes of these problems, their convergence for block updates has been relatively unexplored outside of the context of the alternating direction method of multipliers (ADMM). ADMM has seen extensive use in these applications, but may exhibit uncertain convergence behavior in many practical nonconvex settings, and struggles with general nonlinear constraints. In contrast, filter methods have proved effective in enforcing convergence for sequential quadratic programming methods and interior point methods with feasibility criteria. We develop an ADMM-filter method for highly nonlinear and nonconvex problems. Here, we show convergence under mild assumptions for several types of coordinate descent schemes, and demonstrate our algorithm on nonnegative matrix factorization and completion problems in imaging and chemical spectrum analysis.
Nonconvex optimization↗
A Comprehensive Scheduling Framework using SP-ADMM for Residential Demand Response with Weather and Consumer Uncertainties
This paper presents a comprehensive scheduling framework for residential demand response (DR) programs considering both the day-ahead and real-time electricity markets. In the first stage, residential customers determine the operating status of their responsive devices such as heating, ventilation, and air conditioning (HVAC) systems and electric water heaters (EWHs), while the distribution system operator (DSO) computes the amount of electricity to be purchased in the day-ahead electricity market. In the second stage, the DSO purchases insufficient (or sells surplus) electricity in the real-time electricity market to maintain the supply-demand balance. Due to its computational complexity and data privacy issues, the proposed model cannot be directly solved in a centralized manner, especially with a large number of uncertain scenarios. Therefore, this paper proposes a combination of stochastic programming (SP) and the alternating direction method of multipliers (ADMM) algorithm, called SP-ADMM, to decompose the original model and then solve each sub-problem in a distributed manner while considering multiple uncertain scenarios. The simulation study is performed on the IEEE 33-bus system including 121 residential houses. Here, the results demonstrate the effectiveness of the proposed approach for large-scale residential DR applications under weather and consumer uncertainties.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Distributed ADMM Using Private Blockchain for Power Flow Optimization in Distribution Network With Coupled and Mixed-Integer Constraints
The optimization problem for scheduling distributed energy resources (DERs) and battery energy storage systems (BESS) integrated with the power grid is important to minimize energy consumption from conventional sources in response to demand. Conventionally this optimization problem is solved in a centralized manner, limiting the size of the problem that can be solved and creating a high communication overhead because all the data is transferred to the central controller. These limitations are addressed by the proposed distributed consensus-based alternating direction method of multiplier (DC-ADMM) optimization algorithm, which decomposes the optimization problem into subproblems with private cost function and constraints. The distribution feeder is partitioned into low coupling subnetworks/regions, which solves the private subproblem locally and exchanges information with the neighboring regions to reach consensus. The relaxation strategy is employed for mixed-integer and coupled constraints introduced in the optimal power flow (OPF) problem by stationary and transportable BESS because DC-ADMM convergence is only guaranteed for strict convex problems. The information exchange and synchronization between subnetworks/regions are vital for distributed optimization. In this work, both of these aspects are addressed by the blockchain. The smart contract deployed on the blockchain network acts as a mediator for secure data exchange and synchronization in distributed computation. The blockchain-based distributed optimization problem’s effectiveness is tested for a 0.5-MW laboratory microgrid for one hour ahead and day-ahead for the IEEE 123-bus and EPRI J1 test feeders, and results are compared with a centralized solution.
25 ENERGY STORAGE↗
A Scalable and Distributed Algorithm for Managing Residential Demand Response Programs using Alternating Direction Method of Multipliers (ADMM)
For effective engagement of residential demand-side resources and to ensure efficient operation of distribution networks, we must overcome the challenges of controlling and coordinating residential components and devices at scale. To overcome this challenge, we present a distributed and scalable algorithm with a three-level hierarchical information exchange architecture for managing the residential demand response programs. First, a centralized optimization model is formulated to maximize community social welfare. Then, this centralized model is solved in a distributed manner with alternating direction method of multipliers (ADMM) by decomposing the original problem to utility-level and house-level problems. The information exchange between the different layers is limited to the primary residual (i.e., supply-demand mismatch), Lagrangian multipliers, and the total load of each house to protect each customer’s privacy. Simulation studies are performed on the IEEE 33 bus test system with 605 residential customers. The results demonstrate that the proposed approach can save customers’ electricity bills and reduce the peak load at the utility level without much affecting customers’ comfort and privacy. Finally, a quantitative comparison of the distributed and centralized algorithms shows the scalability advantage of the proposed ADMM-based approach, and it gives benchmarking results with achievable value for future research works.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Distributed Optimal Power Management for Battery Energy Storage Systems: A Novel Accelerated Tracking ADMM Approach
Optimal power management (OPM) is critical for large-scale battery energy storage systems. Today’s methods often require formidable computational effort due to the design based on centralized numerical optimization. Thus, this paper investigates computationally distributed OPM where the agents based on the cells communicate over a network to cooperatively solve the OPM problem. We propose an accelerated tracking alternating direction method of multipliers (ADMM) algorithm to solve the distributed OPM. The proposed algorithm embeds dynamic average consensus and Nesterov’s acceleration technique in the ADMM algorithm. Not only is the proposed algorithm fully distributed without a need for fusion or aggregating nodes, but it also accelerates convergence. The paper formulates the OPM in a model predictive control framework where it seeks to regulate the charging/discharging power of each battery cell to minimize the total power losses and promote balanced use of the constituent cells while complying with the safety constraints. The paper provides ample simulation results to demonstrate the effectiveness and advantages of the proposed distributed OPM in terms of computation and convergence.
Farakhor, Amir↗
Autonomous Intelligent Charging/Discharging of Electric Vehicles using Distributed Multi-Agent ADMM Framework for Grid Ancillary Services
The increasing popularity of Electric Vehicles (EVs) in the distribution grid along with technological advancement in EV electronics such as vehicle to grid (V2G) technique has enabled them to participate in grid ancillary services. To achieve this, the EVs need to establish a contract with third-party aggregators and connect to a charging unit, either residential or commercial. At any time they are connected, the EVs can decide to take part in the ancillary services program offered to them by the aggregators. If agreed, the aggregators will use the EVs as a power source capable of charging/discharging power according to the input signal, and in return, they will be compensated. This inter-temporal nature of charging/discharging is also transforming the traditional optimal power flow (OPF) problem into a dynamic OPF problem. This chapter aims at developing a multi-layer time-dependent optimization algorithm to utilize EV potential and provide ancillary services while maximizing its utilization function. Specifically, in the upper layer, an autonomous distributed ADMM algorithm is developed to optimize the cost for charging/discharging EVs while using them to regulate the voltage at each bus in the distribution grid. The distributed ADMM algorithm is also expanded to the lower layer where the individual EVs active and reactive power is controlled for voltage regulation while maintaining the desired state of the charge of the vehicle at the end of the charging period. Here, the effectiveness and performance improvement of the proposed multi-layer algorithm is illustrated through analytical analysis and simulation results.
Rahman, Towfiq↗
Autonomous Intelligent Charging/Discharging of Electric Vehicles using Distributed Multi-Agent ADMM Framework for Grid Ancillary Services
The increasing popularity of Electric Vehicles (EVs) in the distribution grid along with technological advancement in EV electronics such as vehicle to grid (V2G) technique has enabled them to participate in grid ancillary services. To achieve this, the EVs need to establish a contract with third-party aggregators and connect to a charging unit, either residential or commercial. At any time they are connected, the EVs can decide to take part in the ancillary services program offered to them by the aggregators. If agreed, the aggregators will use the EVs as a power source capable of charging/discharging power according to the input signal, and in return, they will be compensated. This inter-temporal nature of charging/discharging is also transforming the traditional optimal power flow (OPF) problem into a dynamic OPF problem. This chapter aims at developing a multi-layer time-dependent optimization algorithm to utilize EV potential and provide ancillary services while maximizing its utilization function. Specifically, in the upper layer, an autonomous distributed ADMM algorithm is developed to optimize the cost for charging/discharging EVs while using them to regulate the voltage at each bus in the distribution grid. The distributed ADMM algorithm is also expanded to the lower layer where the individual EVs active and reactive power is controlled for voltage regulation while maintaining the desired state of the charge of the vehicle at the end of the charging period. The effectiveness and performance improvement of the proposed multi-layer algorithm is illustrated through analytical analysis and simulation results.
Rahman, Towfiq↗
Cooperative Load Scheduling for Multiple Aggregators Using Hierarchical ADMM
Demand response (DR) serves an important role in improving the efficiency and stability of power systems. In recent years, with advances in communication and smart device technologies, many aggregators have emerged to facilitate end customer participation in DR programs. These aggregators, equipped with customized optimal control algorithms, are capable of providing various grid services. Among them is load scheduling during DR events, namely following a load signal provided by the utility company while minimizing overall customer discomfort. However, as the number of aggregators keeps increasing, it becomes challenging for utility companies to conduct load scheduling for multiple aggregators and generate reference signals for each of them. This paper proposes an optimization framework using hierarchical alternating direction method of multipliers (H-ADMM) to optimally generate load following signals for multiple aggregators. Under this framework, utility and multiple aggregators work in a cooperative manner, aiming at minimizing an overall system cost from different levels of the power system hierarchy, while protecting user privacy. A case study has been conducted in a system with multiple aggregators, based on control of HVAC loads. Experimental results validate the effectiveness of the proposed algorithm.
ADMM↗
A novel large-scale EV charging scheduling algorithm considering V2G and reactive power management based on ADMM
Electric vehicle aggregators (EVAs) that utilize vehicle-to-grid (V2G) technologies can function as both controllable loads and virtual power plants, providing key energy management services to the distribution system operator (DSO). EVAs can also balance the grid’s reactive power as a virtual static VAR compensator (SVC) and provide voltage stability by utilizing advanced electric vehicle (EV) chargers that are capable of four-quadrant operations to provide reactive power management. Finally, managed charging can benefit EVAs themselves by minimizing power factor penalties in their electricity bills. In this paper, we propose a novel EV charging scheduling algorithm based on a hierarchical distributed optimization framework that minimizes peak load and provides reactive power compensation for the DSO by collaboration with EVAs that manage both the active and the reactive charging and discharging power of participating EVs. Utilizing the alternative direction method of multipliers (ADMM), the proposed distributed optimization approach scales well with increased EV charging infrastructure by balancing active and reactive power while decreasing computational burden. In our proposed hierarchical approach, each EVA schedules the active and reactive EV charging and discharging power for 1) reactive power compensation in order to minimize power factor penalty and electricity cost accrued by the EVA, 2) satisfaction of each EV’s energy demand at minimal charging cost, and 3) peak shaving and load management for the DSO. When compared with an uncoordinated charging model, the efficacy of this proposed model is successfully demonstrated through a 300% decreased peak EV load for the DSO, 28% lower electricity costs for EV users, and 98.55% smaller power factor penalty, along with 17.58% lower overall electricity costs, for EVAs. The performance of our approach is validated in a case study with 50 EVs at multiple EVAs in an IEEE 13-bus test case and compared the results with uncoordinated EV charging.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Cooperative Load Scheduling for Multiple Aggregators Using Hierarchical ADMM: Preprint
Demand response (DR) serves an important role in improving the efficiency and stability of power systems. In recent years, with advances in communication and smart device technologies, many aggregators have emerged to facilitate end customer participation in DR programs. These aggregators, equipped with customized optimal control algorithms, are capable of providing various grid services. Among them is load scheduling during DR events, namely following a load signal provided by the utility company while minimizing overall customer discomfort. However, as the number of aggregators keeps increasing, it becomes challenging for utility companies to conduct load scheduling for multiple aggregators and generate reference signals for each of them. This paper proposes an optimization framework using hierarchical alternating direction method of multipliers (H-ADMM) to optimally generate load following signals for multiple aggregators. Under this framework, utility and multiple aggregators work in a cooperative manner, aiming at minimizing an overall system cost from different levels of the power system hierarchy, while protecting user privacy. A case study has been conducted in a system with multiple aggregators, based on control of HVAC loads. Experimental results validate the effectiveness of the proposed algorithm.
97 MATHEMATICS AND COMPUTING↗
Scalable Plug-and-Play ADMM with Convergence Guarantees
Plug-and-play priors (PnP) is a broadly applicable methodology for solving inverse problems by exploiting statistical priors specified as denoisers. Recent work has reported the state-of-the-art performance of PnP algorithms using pre-trained deep neural nets as denoisers in a number of imaging applications. However, current PnP algorithms are impractical in large-scale settings due to their heavy computational and memory requirements. This work addresses this issue by proposing an incremental variant of the widely used PnP-ADMM algorithm, making it scalable to problems involving a large number measurements. Here, we theoretically analyze the convergence of the algorithm under a set of explicit assumptions, extending recent theoretical results in the area. Additionally, we show the effectiveness of our algorithm with nonsmooth data-fidelity terms and deep neural net priors, its fast convergence compared to existing PnP algorithms, and its scalability in terms of speed and memory.
97 MATHEMATICS AND COMPUTING↗
Cooperative Load Scheduling for Multiple Aggregators Using Hierarchical ADMM
Demand response (DR) serves an important role in improving the efficiency and stability of power systems. In recent years, with advances in communication and smart device technologies, many aggregators have emerged to facilitate end customer participation in DR programs. These aggregators, equipped with customized optimal control algorithms, are capable of providing various grid services. Among them is load scheduling during DR events, namely following a load signal provided by the utility company while minimizing overall customer discomfort. However, as the number of aggregators keeps increasing, it becomes challenging for utility companies to conduct load scheduling for multiple aggregators and generate reference signals for each of them. This paper proposes an optimization framework using hierarchical alternating direction method of multipliers (H-ADMM) to optimally generate load following signals for multiple aggregators. Under this framework, utility and multiple aggregators work in a cooperative manner, aiming at minimizing an overall system cost from different levels of the power system hierarchy, while protecting user privacy. A case study has been conducted in a system with multiple aggregators, based on control of HVAC loads. Experimental results validate the effectiveness of the proposed algorithm.
97 MATHEMATICS AND COMPUTING↗