Efficient Topology Design Algorithms for Power Grid Stability

Bhela, Siddharth; Nagarajan, Harsha; Deka, Deepjyoti; Kekatos, Vassilis

doi:10.1109/lcsys.2021.3088888

Efficient Topology Design Algorithms for Power Grid Stability

Journal Article · Mon Jun 14 00:00:00 EDT 2021 · IEEE Control Systems Letters

DOI:https://doi.org/10.1109/lcsys.2021.3088888· OSTI ID:1998111

^[1]; ^[2]; ^[2]; ^[3]

Siemens Technology, Princeton, NJ (United States)
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States)

The dynamic response of power grids to small disturbances influences their overall stability. This letter examines the effect of network topology on the linearized time-invariant dynamics of electric power systems. The proposed framework utilizes H₂ -norm based stability metrics to study the optimal placement of lines on existing networks as well as the topology design of new networks. The design task is first posed as an NP-hard mixed-integer nonlinear program (MINLP) that is exactly reformulated as a mixed-integer linear program (MILP) using McCormick linearization. To improve computation time, graph-theoretic properties are exploited to derive valid inequalities (cuts) and tighten bounds on the continuous optimization variables. Moreover, a cutting plane generation procedure is put forth that is able to interject the MILP solver and augment additional constraints to the problem on-the-fly. Finally, the efficacy of our approach in designing optimal grid topologies is demonstrated through numerical tests on the IEEE 39-bus network.

View Accepted Manuscript (DOE)

Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: National Science Foundation (NSF); USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE National Nuclear Security Administration (NNSA); USDOE Office of Electricity (OE)

Grant/Contract Number:: 89233218CNA000001

OSTI ID:: 1998111

Report Number(s):: LA-UR--21-22364

Journal Information:: IEEE Control Systems Letters, Journal Name: IEEE Control Systems Letters Vol. 6; ISSN 2475-1456

Publisher:: IEEECopyright Statement

Country of Publication:: United States

Language:: English

References (23)

Improving damping of power networks: Power scheduling and impedance adaptation Mallada, Enrique; Tang, Ao IEEE Conference on Decision and Control and European Control Conference https://doi.org/10.1109/cdc.2011.6161287	conference	December 2011
Designing Power Grid Topologies for Minimizing Network Disturbances: An Exact MILP Formulation Bhela, Siddharth; Deka, Deepjyoti; Nagarajan, Harsha 2019 American Control Conference (ACC) https://doi.org/10.23919/acc.2019.8814435	conference	July 2019
Optimal Placement of Virtual Inertia in Power Grids Poolla, Bala Kameshwar; Bolognani, Saverio; Dorfler, Florian arXiv https://doi.org/10.48550/arxiv.1510.01497	text	January 2015
Tightening McCormick Relaxations for Nonlinear Programs via Dynamic Multivariate Partitioning Nagarajan, Harsha; Lu, Mowen; Yamangil, Emre arXiv https://doi.org/10.48550/arxiv.1606.05806	preprint	January 2016
Computability of global solutions to factorable nonconvex programs: Part I — Convex underestimating problems McCormick, Garth P. Mathematical Programming, Vol. 10, Issue 1 https://doi.org/10.1007/BF01580665	journal	December 1976
An analysis of approximations for maximizing submodular set functions—I Nemhauser, G. L.; Wolsey, L. A.; Fisher, M. L. Mathematical Programming, Vol. 14, Issue 1 https://doi.org/10.1007/BF01588971	journal	December 1978
Inverse M-matrices Johnson, Charles R. Linear Algebra and its Applications, Vol. 47 https://doi.org/10.1016/0024-3795(82)90238-5	journal	October 1982
Effective graph resistance Ellens, W.; Spieksma, F. M.; Van Mieghem, P. Linear Algebra and its Applications, Vol. 435, Issue 10 https://doi.org/10.1016/j.laa.2011.02.024	journal	November 2011
Convex Optimization Boyd, Stephen; Vandenberghe, Lieven https://doi.org/10.1017/CBO9780511804441	book	January 2004
Improving performance of droop-controlled microgrids through distributed PI-control Tegling, Emma; Andreasson, Martin; Simpson-Porco, John W. 2016 American Control Conference (ACC) https://doi.org/10.1109/ACC.2016.7525264	conference	July 2016
Improving damping of power networks: Power scheduling and impedance adaptation Mallada, Enrique; Tang, Ao IEEE Conference on Decision and Control and European Control Conference https://doi.org/10.1109/CDC.2011.6161287	conference	December 2011
Graph Laplacian Spectrum and Primary Frequency Regulation Guo, Linqi; Zhao, Changhong; Low, Steven H. 2018 IEEE Conference on Decision and Control (CDC) https://doi.org/10.1109/CDC.2018.8619252	conference	December 2018
Transmission Expansion Planning: Literature Review and Classification Mahdavi, Meisam; Sabillon Antunez, Carlos; Ajalli, Majid IEEE Systems Journal, Vol. 13, Issue 3 https://doi.org/10.1109/JSYST.2018.2871793	journal	September 2019
A review of transmission switching and network topology optimization Hedman, Kory W.; Oren, Shmuel S.; O'Neill, Richard P. 2011 IEEE Power & Energy Society General Meeting, 2011 IEEE Power and Energy Society General Meeting https://doi.org/10.1109/PES.2011.6039857	conference	July 2011
Design of Optimal Sparse Interconnection Graphs for Synchronization of Oscillator Networks Fardad, Makan; Lin, Fu; Jovanovic, Mihailo R. IEEE Transactions on Automatic Control, Vol. 59, Issue 9 https://doi.org/10.1109/TAC.2014.2301577	journal	September 2014
Optimal Placement of Virtual Inertia in Power Grids Poolla, Bala Kameshwar; Bolognani, Saverio; Dorfler, Florian IEEE Transactions on Automatic Control, Vol. 62, Issue 12 https://doi.org/10.1109/TAC.2017.2703302	journal	December 2017
The Price of Synchrony: Evaluating the Resistive Losses in Synchronizing Power Networks Tegling, Emma; Bamieh, Bassam; Gayme, Dennice F. IEEE Transactions on Control of Network Systems, Vol. 2, Issue 3 https://doi.org/10.1109/TCNS.2015.2399193	journal	September 2015
Kron Reduction of Graphs With Applications to Electrical Networks Dorfler, Florian; Bullo, Francesco IEEE Transactions on Circuits and Systems I: Regular Papers, Vol. 60, Issue 1 https://doi.org/10.1109/TCSI.2012.2215780	journal	January 2013
JuMP: A Modeling Language for Mathematical Optimization Dunning, Iain; Huchette, Joey; Lubin, Miles SIAM Review, Vol. 59, Issue 2 https://doi.org/10.1137/15M1020575	journal	January 2017
Algorithm 97: Shortest path Floyd, Robert W. Communications of the ACM, Vol. 5, Issue 6 https://doi.org/10.1145/367766.368168	journal	June 1962
Optimal topology design for disturbance minimization in power grids Deka, Deepjyoti; Nagarajan, Harsha; Backhaus, Scott 2017 American Control Conference (ACC) https://doi.org/10.23919/ACC.2017.7963363	conference	May 2017
Designing Power Grid Topologies for Minimizing Network Disturbances: An Exact MILP Formulation Bhela, Siddharth; Deka, Deepjyoti; Nagarajan, Harsha 2019 American Control Conference (ACC) https://doi.org/10.23919/ACC.2019.8814435	conference	July 2019
Impact of Low Rotational Inertia on Power System Stability and Operation Ulbig, Andreas; Borsche, Theodor S.; Andersson, Göran IFAC Proceedings Volumes, Vol. 47, Issue 3 https://doi.org/10.3182/20140824-6-ZA-1003.02615	journal	January 2014

Similar Records

Joint Topology Identification and State Estimation in Unobservable Distribution Grids

Journal Article · Mon Aug 02 20:00:00 EDT 2021 · IEEE Transactions on Smart Grid · OSTI ID:1907350

Substation-Level Grid Topology Optimization Using Bus Splitting

Conference · Wed Jul 28 00:00:00 EDT 2021 · OSTI ID:1814610

Substation-Level Grid Topology Optimization Using Bus Splitting: Preprint

Conference · Mon May 31 20:00:00 EDT 2021 · OSTI ID:1786975

Related Subjects

24 POWER TRANSMISSION AND DISTRIBUTION
measurement
network topology
power grids
power system dynamics
power system stability
stability analysis
topology design

Efficient Topology Design Algorithms for Power Grid Stability

Citation Formats

References (23)

Similar Records

Related Subjects