Distributed Dual Gradient Tracking for Economic Dispatch in Power Systems with Noisy Information

Distributed algorithms can be efficiently used for solving economic dispatch problem (EDP) in power systems. To implement a distributed algorithm, a communication network is required, making the algorithm vulnerable to noise which may cause detrimental decisions or even instability. In this paper, we propose an agent-based method which enables a fully distributed solution of the EDP in power systems with noisy information exchange. Through the novel design of the gradient tracking update and introducing suppression parameters, the proposed algorithm can effectively alleviate the impact of noise and it is shown to be more robust than the existing distributed algorithms. The convergence of the algorithm is also established under standard assumptions. Moreover, a strategy are presented to accelerate our proposed algorithm. Finally, the algorithm is tested on several IEEE bus systems to demonstrate its effectiveness and scalability.

[1]  J.E. Mazo,et al.  Digital communications , 1985, Proceedings of the IEEE.

[2]  Lihua Xie,et al.  A Dual Splitting Approach for Distributed Resource Allocation With Regularization , 2019, IEEE Transactions on Control of Network Systems.

[3]  Gregor Verbic,et al.  Accelerated Methods for the SOCP-Relaxed Component-Based Distributed Optimal Power Flow , 2018, 2018 Power Systems Computation Conference (PSCC).

[4]  Tao Yang,et al.  Accelerated Distributed Energy Management for Microgrids , 2018, 2018 IEEE Power & Energy Society General Meeting (PESGM).

[5]  Usman A. Khan,et al.  A General Framework for Decentralized Optimization With First-Order Methods , 2020, Proceedings of the IEEE.

[6]  Jiaqi Zhang,et al.  Decentralized Stochastic Gradient Tracking for Empirical Risk Minimization , 2019, ArXiv.

[7]  Shi Pu.  A Robust Gradient Tracking Method for Distributed Optimization over Directed Networks , 2020, 2020 59th IEEE Conference on Decision and Control (CDC).

[8]  Angelia Nedic,et al.  Distributed stochastic gradient tracking methods , 2018, Mathematical Programming.

[9]  P. Alam.  ‘S’ , 2021, Composites Engineering: An A–Z Guide.

[10]  Shanying Zhu,et al.  An ADMM-based Distributed Algorithm for Economic Dispatch in Multi-energy Systems , 2021, 2021 IEEE Power & Energy Society General Meeting (PESGM).

[11]  David Wenzhong Gao,et al.  Noiseless Consensus Based Algorithm for Economic Dispatch problem in Grid-connected Microgrids to Enhance Stability among Distributed Generators , 2019, 2019 North American Power Symposium (NAPS).

[12]  W. Marsden.  I and J , 2012 .

[13]  Yurii Nesterov,et al.  Introductory Lectures on Convex Optimization - A Basic Course , 2014, Applied Optimization.

[14]  Jian-Xin Xu,et al.  Consensus based approach for economic dispatch problem in a smart grid , 2013, IECON 2013 - 39th Annual Conference of the IEEE Industrial Electronics Society.

[15]  Wei Shi,et al.  Push–Pull Gradient Methods for Distributed Optimization in Networks , 2021, IEEE Transactions on Automatic Control.

[16]  Fanghong Guo,et al.  Push-Based Distributed Economic Dispatch in Smart Grids Over Time-Varying Unbalanced Directed Graphs , 2021, IEEE Transactions on Smart Grid.

[17]  Xiaoqing Lu,et al.  Stochastic Distributed Secondary Control for AC Microgrids via Event-Triggered Communication , 2020, IEEE Transactions on Smart Grid.

[18]  Josep M. Guerrero,et al.  Distributed Noise-Resilient Secondary Voltage and Frequency Control for Islanded Microgrids , 2019, IEEE Transactions on Smart Grid.

[19]  Usman A. Khan,et al.  Distributed Nesterov Gradient Methods Over Arbitrary Graphs , 2019, IEEE Signal Processing Letters.

[20]  Henrik Sandberg,et al.  A Survey of Distributed Optimization and Control Algorithms for Electric Power Systems , 2017, IEEE Transactions on Smart Grid.

[21]  N.D. Hatziargyriou,et al.  Centralized Control for Optimizing Microgrids Operation , 2008, IEEE Transactions on Energy Conversion.

[22]  Xiaofeng Liao,et al.  Achieving Acceleration for Distributed Economic Dispatch in Smart Grids Over Directed Networks , 2020, IEEE Transactions on Network Science and Engineering.

[23]  Thinh T. Doan,et al.  Convergence Rates of Distributed Gradient Methods Under Random Quantization: A Stochastic Approximation Approach , 2021, IEEE Transactions on Automatic Control.

[24]  Stephen P. Boyd,et al.  Optimal Scaling of a Gradient Method for Distributed Resource Allocation , 2006 .

[25]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[26]  Allen J. Wood,et al.  Power Generation, Operation, and Control , 1984 .

[27]  R. Sarpong,et al.  Bio-inspired synthesis of xishacorenes A, B, and C, and a new congener from fuscol† †Electronic supplementary information (ESI) available. See DOI: 10.1039/c9sc02572c , 2019, Chemical science.

[28]  Usman A. Khan,et al.  A Linear Algorithm for Optimization Over Directed Graphs With Geometric Convergence , 2018, IEEE Control Systems Letters.

[29]  Tingwen Huang,et al.  Optimizing the Dynamic Economic Dispatch Problem by the Distributed Consensus-Based ADMM Approach , 2020, IEEE Transactions on Industrial Informatics.

[30]  Frank L. Lewis,et al.  Distributed Noise-Resilient Networked Synchrony of Active Distribution Systems , 2018, IEEE Transactions on Smart Grid.

[31]  K. Schittkowski,et al.  NONLINEAR PROGRAMMING , 2022 .

[32]  Alfred O. Hero,et al.  Robust Distributed Fixed-Time Economic Dispatch Under Time-Varying Topology , 2019, IEEE Control Systems Letters.

[33]  Keyou You,et al.  Distributed Conjugate Gradient Tracking for Resource Allocation in Unbalanced Networks , 2019, ArXiv.