A Two-Level ADMM Algorithm for AC OPF With Global Convergence Guarantees

Sun, Kaizhao; Sun, Xu Andy

doi:10.1109/tpwrs.2021.3073116

Cited by 49 publications

(18 citation statements)

References 25 publications

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“…The authors in [31] studied the same problem by applying the alternating direction method of multipliers (ADMM), which is a distributed numerical algorithm. ADMM was also applied in [53] to solve the OPF problem. Optimization theory was applied for DRM in [33].…”

Section: Application Of Optimization Theory In the Smart Gridmentioning

confidence: 99%

Intelligent Charging Management of Electric Vehicles Considering Dynamic User Behavior and Renewable Energy: A Stochastic Game Approach

Chung

Maharjan

Zhang

et al. 2021

IEEE Trans. Intell. Transport. Syst.

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The current energy system is changing, mainly due to the rise of global energy consumption and the depletion of fossil energy sources. Regarding the electric power system, such changes constitute a significant challenge to the electricity grids and call for the development of smart grids. The smart grid is capable of monitoring individual energy consumption, integrating renewable energy, and supporting twoway communication between the grid operators and the customers. Moreover, to meet the requirement of the Paris Agreement, which predicts that the world needs to reduce 1170 giga tons of the cumulative CO 2 emissions between 2015 and 2100, promoting electric vehicles (EVs) and installing renewable energy resources are two main trends in policy making to reduce our dependency on fossil fuel resources. With more and more installation of renewable energy resources, uncertainties associated with renewable energy generation should be addressed when operating the smart grid. That is, weather conditions may influence renewable energy production, and therefore the controllability of that production is not the same as the conventional power generators for the grid operator. Other than the uncertainties associated with renewable energy generation, the maintenance of the generators raises a new challenge to the operator as the renewable energy generators are usually placed at locations with hazardous environments.Apart from the operator side, customers on the traditional power grid can install renewable energy resources in their households (e.g., solar panels on the rooftop). Therefore, customers can be separated into two categories in the smart grid, namely consumers and prosumers. The consumers only consume energy, and the prosumers can both consume and produce energy. The renewable energy production of the prosumers may be larger than their own consumption, and therefore they may want to sell their energy surplus. However, the price of selling energy to the external market is lower than the spot price in the external market. Therefore, peer-to-peer (P2P) energy trading is a much more attractive alternative than selling surplus generation in the external market. The electricity prices in the external market are generated in real time so that both the consumers and the prosumers also need to consider the uncertainty related to electricity prices to form the best strategies. By doing so, the consumers can obtain the minimum electricity costs, and the iii iv Chapter 0 prosumers can increase their revenue.Another method for reducing CO 2 emissions is to promote EVs. However, charging a huge number of EVs simultaneously may cause a sudden increase in energy consumption, and therefore the charging tasks of EVs must be controlled to avoid consuming a considerable amount of energy from the power grid in a short time. Although energy production from renewable energy resources can relieve this situation, the deployment of renewable energy sources cannot satisfy the surge for more energy from an increasing number of EVs. To this end...

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Section: Application Of Optimization Theory In the Smart Gridmentioning

confidence: 99%

Intelligent Charging Management of Electric Vehicles Considering Dynamic User Behavior and Renewable Energy: A Stochastic Game Approach

Chung

Maharjan

Zhang

et al. 2021

IEEE Trans. Intell. Transport. Syst.

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show abstract

“…K. Sun and XA. Sun [63,65] proposed a two-level framework that embeds a specially structured threeblock ADMM inside an ALM. For weakly convex minimization with affine constraints, works [75,77] demonstrate two multi-block variants of the proximal ALM that do not require assumptions (a) or (b).…”

Section: Nonconvex Constraints Workmentioning

confidence: 99%

Dual Descent ALM and ADMM

Sun¹,

Sun²

2021

Preprint

Self Cite

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In this paper we propose and investigate a new class of dual updates within the augmented Lagrangian framework, where the key feature is to reverse the update direction in the traditional dual ascent. When the dual variable is further scaled by a fractional number, we name the resulting scheme scaled dual descent (SDD), and otherwise, unscaled dual descent (UDD). The novel concept of dual descent sheds new light on the classic augmented Lagrangian framework and brings in more possibilities for algorithmic development. For nonlinear equality-constrained multi-block problems, we propose a new algorithm named SDD-ADMM, which combines SDD with the alternating direction method of multipliers (ADMM). We show that SDD-ADMM finds an ǫ-stationary solution in O(ǫ −4 ) iterations, which can be further improved to O(ǫ −3 ) under an additional technical while verifiable assumption. We also propose UDD-ALM, which applies UDD within the augmented Lagrangian method (ALM), for weakly convex minimization over affine constraints. We show that when a certain regularity condition holds at the primal limit point, UDD-ALM asymptotically converges to a stationary point and finds an ǫ-stationary solution in O(ǫ −2 ) iterations. Both SDD-ADMM and UDD-ALM are single-looped, and our iteration complexities are measured by first-order oracles. SDD-ADMM achieves better iteration complexities for a more challenging setting compared to the ADMM literature, while UDD-ALM complements the best-known result of existing ALM-base algorithms. Furthermore, we demonstrate the potential of UDD-ALM to handle nonlinear constraints by assuming a novel descent solution oracle for the proximal augmented Lagrangian relaxation.

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“…Although ADMM has drawn significant attention for power flow analysis (Erseghe, 2014;Kim and Baldick, 2000;Guo et al, 2016), it normally takes quite a few iterates to approach a solution with moderate accuracy. Lately, Sun and Sun (2021) proposed a two-level ADMM for solving distributed AC OPF problem with convergence guarantee. Nonetheless, the power flow model is formulated as a Quadratically Constrained Quadratic Program (QCQP) problem at the expense of accuracy, and the algorithm converges to a modest accuracy slowly.…”

Section: Introductionmentioning

confidence: 99%

Rapid Scalable Distributed Power Flow with Open-Source Implementation

Dai¹,

Cai²,

Jiang³

et al. 2022

Preprint

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This paper introduces a new method for solving the distributed AC power flow (PF) problem by further exploiting the problem formulation. We propose a new variant of the ALADIN algorithm devised specifically for this type of problem. This new variant is characterized by using a reduced modelling method of the distributed AC PF problem, which is reformulated as a zero-residual least-squares problem with consensus constraints. This PF is then solved by a Gauss-Newton based inexact ALADIN algorithm presented in the paper. An open-source implementation of this algorithm, called rapidPF+, is provided. Simulation results, for which the power system's dimension varies from 53 to 10224 buses, show great potential of this combination in the aspects of both the computing time and scalability.

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A Two-Level ADMM Algorithm for AC OPF With Global Convergence Guarantees

Cited by 49 publications

References 25 publications

Intelligent Charging Management of Electric Vehicles Considering Dynamic User Behavior and Renewable Energy: A Stochastic Game Approach

Intelligent Charging Management of Electric Vehicles Considering Dynamic User Behavior and Renewable Energy: A Stochastic Game Approach

Dual Descent ALM and ADMM

Rapid Scalable Distributed Power Flow with Open-Source Implementation

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