Geometry of injection regions of power networks
Open accessAbstract
We investigate the constraints on power flow in networks and its implications to the optimal power flow problem. The constraints are described by the injection region of a network; this is the set of all vectors of power injections, one at each bus, that can be achieved while satisfying the network and operation constraints. If there are no operation constraints, we show the injection region of a network is the set of all injections satisfying the conservation of energy. If the network has a tree topology, e.g., a distribution network, we show that under voltage magnitude, line loss constraints, line flow constraints and certain bus real and reactive power constraints, the injection region and its convex hull have the same Pareto-front. The Pareto-front is of interest since these are the optimal solutions to the minimization of increasing functions over the injection region. For non-tree networks, we obtain a weaker result by characterizing the convex hull of the voltage constraint injection region for lossless cycles and certain combinations of cycles and trees.
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Prior sufficient conditions for exactness of the SOCP relaxation require load over-satisfaction on some or all buses and do not hold in practice.
“these conditions require some bus to be able to draw infinite power, which is referred to as load over-satisfaction in the literature. For example, the conditions given in [9], [13], [14] require load over-satisfaction on some/all of the buses.”
From Optimal power flow in distribution networks (2018) · cites this paper as [13]
Theorem 2 (section IV.A; page not supplied) relates the paper’s lower-bound conditions to load over-satisfaction, supporting that part of the attribution. But the Introduction explicitly says simulations with practical distribution networks show these requirements are “not stringent in actual operations,” contrary to the claim that they do not hold in practice. (LLM, conf=0.87)
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Experimental — accuracy not yet measuredAll sufficient conditions in the literature that guarantee exactness of the SOCP relaxation require removing some of the constraints in OPF, and do not hold in practice.
“To summarize, all sufficient conditions in the literature that guarantee the exactness of the SOCP relaxation require removing some of the constraints in OPF, and do not hold in practice.”
From Optimal power flow in distribution networks (2018) · cites this paper as [13]
The Introduction (page unavailable) says the paper's conditions retain voltage, line-loss, and line-flow constraints, restrict certain bus-power bounds, and are 'not stringent in actual operations'—contrary to the claim that such conditions do not hold in practice. The paper discusses a convex relaxation; these passages do not identify it specifically as an SOCP relaxation or establish a claim about every sufficient condition in the literature. (LLM, conf=0.82)
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Cites
Boyd, S., & Vandenberghe, L. (2004) · doi:10.1017/cbo9780511804441 · Cited by 56,601 · see citing works
Horn, R. A., & Johnson, C. R. (1985) · Cambridge University Press eBooks · doi:10.1017/cbo9780511810817 · Cited by 10,298 · see citing works
Dommel, H. W., & Tinney, W. F. (1968) · IEEE Transactions on Power Apparatus and Systems · doi:10.1109/tpas.1968.292150 · Cited by 1,668 · see citing works
Zero Duality Gap in Optimal Power Flow Problem
Lavaei, J., & Low, S. H. (2011) · IEEE Transactions on Power Systems · doi:10.1109/tpwrs.2011.2160974 · Cited by 1,197 · see citing works
Stott, B., Jardim, J. L., & Alsaç, O. (2009) · IEEE Transactions on Power Systems · doi:10.1109/tpwrs.2009.2021235 · Cited by 1,058 · see citing works
Demand Response in Electricity Markets: An Overview
Albadi, M., & El-Saadany, E. F. (2007) · IEEE Power Engineering Society General Meeting · doi:10.1109/pes.2007.385728 · Cited by 919 · see citing works
Security analysis and optimization
Stott, B., Alsaç, O., & Monticelli, A. (1987) · Proceedings of the IEEE · doi:10.1109/proc.1987.13931 · Cited by 554 · see citing works
A comparison of the AC and DC power flow models for LMP calculations
Overbye, T. J., Cheng, X., & Sun, Y. (2004) · Hawaii International Conference on System Sciences (HICSS) · doi:10.1109/hicss.2004.1265164 · Cited by 341 · see citing works
Distribution System Modeling and Analysis
Kersting, W. H. (2006) · CRC Press eBooks · doi:10.1201/9781420006162 · Cited by 232 · see citing works
Examining the limits of the application of semidefinite programming to power flow problems
Lesieutre, B. C., Molzahn, D. K., Borden, A. R., & DeMarco, C. L. (2011) · Allerton Conference on Communication, Control, and Computing · doi:10.1109/allerton.2011.6120344 · Cited by 225 · see citing works
Convexity of the Set of Feasible Injections and Revenue Adequacy in FTR Markets
Lesieutre, B. C., & Hiskens, I. A. (2005) · IEEE Transactions on Power Systems · doi:10.1109/tpwrs.2005.857268 · Cited by 120 · see citing works
Quantitative Analysis of Steady State Stability in Power Networks
Jarjis, J., & Galiana, F. D. (1981) · IEEE Transactions on Power Apparatus and Systems · doi:10.1109/tpas.1981.316845 · Cited by 106 · see citing works
Baldick, R. (2006) · Cambridge University Press eBooks · doi:10.1017/cbo9780511610868 · Cited by 96 · see citing works
Optimal power flow over tree networks
Bose, S., Gayme, D. F., Low, S. H., & Chandy, K. M. (2011) · Allerton Conference on Communication, Control, and Computing · doi:10.1109/allerton.2011.6120323 · Cited by 94 · see citing works
Geometry of feasible injection region of power networks
Zhang, B., & Tse, D. N. C. (2011) · Allerton Conference on Communication, Control, and Computing · doi:10.1109/allerton.2011.6120346 · Cited by 89 · see citing works
Self-citationOn Convexity of Power Flow Feasibility Boundary
Makarov, Y. V., Dong, Z. Y., & Hill, D. J. (2008) · IEEE Transactions on Power Systems · doi:10.1109/tpwrs.2008.919307 · Cited by 60 · see citing works
Applied Optimization: List of illustrations
Baldick, R. (2006) · Cited by 58 · see citing works
Applied Optimization: Non-linear simultaneous equations
Baldick, R. (2006) · Cited by 58 · see citing works
Graphs whose positive semi-definite matrices have nullity at most two
van der Holst, H. (2003) · Linear Algebra and its Applications · doi:10.1016/s0024-3795(03)00642-6 · Cited by 52 · see citing works
Voltage control problems on modern distribution systems
O'Gorman, R., & Redfern, M. A. (2004) · IEEE Power Engineering Society General Meeting · doi:10.1109/pes.2004.1372894 · Cited by 37 · see citing works
Competitive equilibria in electricity markets with nonlinearities
Lavaei, J., & Sojoudi, S. (2012) · Proceedings of the ... American Control Conference/Proceedings of the American Control Conference · doi:10.1109/acc.2012.6314606 · Cited by 30 · see citing works
Analytic Functions Optimizing Competing Constraints
Helton, J. W., & Vityaev, A. E. (1997) · SIAM Journal on Mathematical Analysis · doi:10.1137/s0036141095293086 · Cited by 7 · see citing works
Flagged first, then by citations
Research works printed but not linked: 5
- B. Stott, O. Alsac, and A. J. Monticelli, "Security analysis and opti- mization," Proceedings of the IEEE, 1987.
- R. V. Amarnath and N. V. Ramana, "State of the art in optimal power flow solution methodologies," Journal of Theoretical and Applied Information Technology, vol. 30, no. 2, pp. 128-154, 2011.
- S. Sojoudi and J. Lavaei, "Network topologies guaranteeing zero duality gap for optimal power flow problem," Submitted to IEEE Transactions on Power Systems, 2011.
- Distribution Test Feeder Working Group, "Distribution test feeders," http://ewh.ieee.org/soc/pes/dsacom/testfeeders/index.html, 2010.
- H. L. Bodlaender, "A linear time algorithm for finding tree- decompositions of small treewidth," SIAM Journal on Computing, 1996.
Cited by
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A Survey of Distributed Optimization and Control Algorithms for Electric Power Systems
Molzahn, D. K., Dörfler, F., Sandberg, H., Low, S. H., Chakrabarti, S., Baldick, R., & Lavaei, J. (2017) · IEEE Transactions on Smart Grid · doi:10.1109/tsg.2017.2720471 · Cited by 1,278 · see citing works
Convex Relaxation of Optimal Power Flow—Part I: Formulations and Equivalence
Low, S. H. (2014) · IEEE Transactions on Control of Network Systems · doi:10.1109/tcns.2014.2309732 · Cited by 934 · see citing works
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Gan, L., Li, N., Topcu, U., & Low, S. H. (2014) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2014.2332712 · Cited by 516 · see citing works
Strong SOCP Relaxations for the Optimal Power Flow Problem
Kocuk, B., Dey, S. S., & Sun, X. A. (2016) · Operations Research · doi:10.1287/opre.2016.1489 · Cited by 335 · see citing works
An Optimal and Distributed Method for Voltage Regulation in Power Distribution Systems
Zhang, B., Lam, A. Y. S., Domínguez-García, A. D., & Tse, D. N. C. (2014) · IEEE Transactions on Power Systems · doi:10.1109/tpwrs.2014.2347281 · Cited by 325 · see citing works
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Low, S. H. (2014) · Cited by 319 · see citing works
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Molzahn, D. K., & Hiskens, I. A. (2019) · Foundations and Trends® in Electric Energy Systems · doi:10.1561/3100000012 · Cited by 309 · see citing works
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Gan, L., Li, N., Topcu, U., & Low, S. H. (2016) · Cited by 301 · see citing works
Defining and Enabling Resiliency of Electric Distribution Systems With Multiple Microgrids
Chanda, S., & Srivastava, A. K. (2016) · IEEE Transactions on Smart Grid · doi:10.1109/tsg.2016.2561303 · Cited by 287 · see citing works
Ghosh, S., Rahman, S., & Pipattanasomporn, M. (2016) · IEEE Transactions on Sustainable Energy · doi:10.1109/tste.2016.2577559 · Cited by 274 · see citing works
Distributed Reactive Power Feedback Control for Voltage Regulation and Loss Minimization
Bolognani, S., Ruggero Carli, A., Cavraro, G., & Zampieri, S. (2014) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2014.2363931 · Cited by 252 · see citing works
Vrakopoulou, M., Margellos, K., Lygeros, J., & Andersson, G. (2013) · IEEE Transactions on Power Systems · doi:10.1109/tpwrs.2013.2272546 · Cited by 229 · see citing works
Local Solutions of the Optimal Power Flow Problem
Bukhsh, W., Grothey, A., McKinnon, K. I. M., & Trodden, P. A. (2013) · IEEE Transactions on Power Systems · doi:10.1109/tpwrs.2013.2274577 · Cited by 226 · see citing works
Convex Optimization of Power Systems
Taylor, J. A. (2015) · Cambridge University Press eBooks · doi:10.1017/cbo9781139924672 · Cited by 225 · see citing works
AC-feasibility on tree networks is NP-hard
Lehmann, K., Grastien, A., & Van Hentenryck, P. (2016) · IEEE Transactions on Power Systems · doi:10.1109/tpwrs.2015.2407363 · Cited by 221 · see citing works
Geometry of Power Flows and Optimization in Distribution Networks
Lavaei, J., Tse, D. N. C., & Zhang, B. (2013) · IEEE Transactions on Power Systems · doi:10.1109/tpwrs.2013.2282086 · Cited by 180 · see citing works
Self-citationMagnússon, S., Weeraddana, P. C., & Fischione, C. (2015) · IEEE Transactions on Control of Network Systems · doi:10.1109/tcns.2015.2399192 · Cited by 157 · see citing works
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Bose, S., Low, S. H., Teeraratkul, T., & Hassibi, B. (2014) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2014.2357112 · Cited by 152 · see citing works
Optimal Power Flow in Direct Current Networks
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Wei, W., Wang, J., Li, N., & Mei, S. (2017) · IEEE Transactions on Smart Grid · doi:10.1109/tsg.2017.2684183 · Cited by 126 · see citing works
Promises of Conic Relaxation for Contingency-Constrained Optimal Power Flow Problem
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Wang, C., Wei, W., Wang, J., Wu, L., & Liang, Y. (2018) · IEEE Transactions on Power Systems · doi:10.1109/tpwrs.2018.2796179 · Cited by 104 · see citing works
A survey on conic relaxations of optimal power flow problem
Zohrizadeh, F., Josz, C., Jin, M., Madani, R., Lavaei, J., & Sojoudi, S. (2020) · European Journal of Operational Research · doi:10.1016/j.ejor.2020.01.034 · Cited by 97 · see citing works
Linear approximations to AC power flow in rectangular coordinates
Dhople, S. V., Guggilam, S. S., & Chen, Y. C. (2015) · Allerton Conference on Communication, Control, and Computing · doi:10.1109/allerton.2015.7447006 · Cited by 94 · see citing works
Sojoudi, S., & Lavaei, J. (2014) · SIAM Journal on Optimization · doi:10.1137/130915261 · Cited by 91 · see citing works
Feasible Region of Optimal Power Flow: Characterization and Applications
Chiang, H., & Jiang, C. (2017) · IEEE Transactions on Power Systems · doi:10.1109/tpwrs.2017.2692268 · Cited by 83 · see citing works
Reduced-Complexity Semidefinite Relaxations of Optimal Power Flow Problems
Andersen, M. S., Hansson, A., & Vandenberghe, L. (2014) · IEEE Transactions on Power Systems · doi:10.1109/tpwrs.2013.2294479 · Cited by 82 · see citing works
Modern Techniques for the Optimal Power Flow Problem: State of the Art
Risi, B.-G., Fulginei, F. R., & Laudani, A. (2022) · Energies · doi:10.3390/en15176387 · Cited by 75 · see citing works
Li, Q., & Vittal, V. (2017) · IEEE Transactions on Power Systems · doi:10.1109/tpwrs.2017.2712697 · Cited by 75 · see citing works
Li, Q., & Vittal, V. (2016) · IEEE Transactions on Power Systems · doi:10.1109/tpwrs.2016.2594298 · Cited by 65 · see citing works
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Zhang, B., Domínguez-García, A. D., & Tse, D. N. C. (2013) · North American Power Symposium (NAPS) · doi:10.1109/naps.2013.6666945 · Cited by 61 · see citing works
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Liu, Y., Li, J., Wu, L., & Ortmeyer, T. (2017) · IEEE Transactions on Power Systems · doi:10.1109/tpwrs.2017.2707564 · Cited by 53 · see citing works
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Promises of conic relaxation for contingency-constrained optimal power flow problem
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Modeling and online control of generalized energy storage networks
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Zhou, F., Chen, Y., & Low, S. H. (2019) · IEEE Conference on Decision and Control (CDC) · doi:10.1109/cdc40024.2019.9029827 · Cited by 11 · see citing works
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Elizondo, M. A., Samaan, N., Makarov, Y. V., Holzer, J., Vallem, M. R., Huang, R., Vyakaranam, B. G., Ke, X., & Pan, F. (2017) · IEEE Power Engineering Society General Meeting · doi:10.1109/pesgm.2017.8274068 · Cited by 8 · see citing works
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Gan, L., & Low, S. H. (2014) · Power Systems Computation Conference · doi:10.1109/pscc.2014.7038373 · Cited by 7 · see citing works
Stochastic loss minimization for power distribution networks
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Zhang, B. (2013) · eScholarship (California Digital Library) · Cited by 6 · see citing works
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Karapetyan, A., Elbassioni, K., Khonji, M., & Chau, C.-K. (2022) · Annals of Operations Research · doi:10.1007/s10479-022-05054-y · Cited by 3 · see citing works
Masoum, A. S., Abu‐Siada, A., & Islam, S. M. (2016) · Technology and Economics of Smart Grids and Sustainable Energy · doi:10.1007/s40866-016-0012-3 · Cited by 3 · see citing works
Estimating feasible nodal power injections in distribution networks
Al-Digs, A., Dhople, S. V., & Chen, Y. C. (2016) · IEEE Power & Energy Society Innovative Smart Grid Technologies Conference (ISGT) · doi:10.1109/isgt.2016.7781244 · Cited by 3 · see citing works
Distributed Load Control in Multiphase Radial Networks
Gan, L. (2015) · CaltechTHESIS (California Institute of Technology) · doi:10.7907/z9fq9tj0 · Cited by 3 · see citing works
Risk-averse design and operation of renewable energy power grids
Sun, B. N., Lendasse, A., Mudumbai, R., Krokhmal, P., Chen, Y., & Kusiak, A. (2015) · doi:10.17077/etd.n9d4ouj6 · Cited by 3 · see citing works
Huang, S., Wu, Q., Zhao, H., & Liu, Z. (2016) · Energy Procedia · doi:10.1016/j.egypro.2016.10.134 · Cited by 2 · see citing works
Electric Power System with Renewable Generation
Wei, W., & Wang, J. (2019) · Springer eBooks · doi:10.1007/978-3-030-25958-7_2 · Cited by 2 · see citing works
A Sufficient Condition for Local Optima to be Globally Optimal
Zhou, F., & Low, S. H. (2020) · IEEE Conference on Decision and Control (CDC) · doi:10.1109/cdc42340.2020.9303868 · Cited by 2 · see citing works
Power circle diagrams and aggregate flexibility curves for active distribution networks
Sharma, P. A., Mohapatra, A., & Sharma, A. K. (2022) · Electric Power Systems Research · doi:10.1016/j.epsr.2022.107820 · Cited by 2 · see citing works
Distributed Dual Subgradient Methods with Averaging and Applications to Grid Optimization
Liu, H., Bose, S., Nguyễn, Đ. H., Guo, Y., Doan, T. T., & Beck, C. L. (2024) · Journal of Optimization Theory and Applications · doi:10.1007/s10957-024-02385-7 · Cited by 2 · see citing works
2013 Index IEEE Transactions on Power Systems Vol. 28
(2013) · IEEE Transactions on Power Systems · doi:10.1109/tpwrs.2013.2295282 · Cited by 2 · see citing works
Fast Market Clearing Algorithms
Raghunathan, A. U., Curtis, F. E., Takaguchi, Y., & Hashimoto, H. (2018) · The IMA volumes in mathematics and its applications · doi:10.1007/978-1-4939-7822-9_7 · Cited by 1 · see citing works
Dong, L., Tian, A. Z., Pu, T. J., Fan, Z., & Yu, T. (2014) · Advanced materials research · doi:10.4028/www.scientific.net/amr.1070-1072.809 · Cited by 1 · see citing works
DSO and Aggregator Sharing Concept for Distributed Battery Storage System
Gržanić, M., Capuder, T., & Krajcar, S. (2018) · IEEE International Conference on Environment and Electrical Engineering and IEEE Industrial and Commercial Power Systems Europe (EEEIC / I&CPS Europe) · doi:10.1109/eeeic.2018.8493680 · Cited by 1 · see citing works
Zhang, J., Cui, M., & He, Y. (2021) · Energies · doi:10.3390/en14164911 · Cited by 1 · see citing works
Low Complexity Distributed SDP Approach for General OPF Problems with Reactive Power CostPreprint
Chang, C.-Y., & Zhang, W. (2016) · arXiv (Cornell University) · doi:10.48550/arxiv.1612.04508 · Cited by 1 · see citing works
Mathematical study of complex networks: brain, internet, and power grid
Doyle, J. C., & Sojoudi, S. (2013) · doi:10.7907/e750-2m74
- Authors
- Zhang, B., & Tse, D.
- Affiliations
- University of California, Berkeley (US)
- Venue
- IEEE Transactions on Power Systems
- Published
- 2013-05
- Volume
- 28
- Issue
- 2
- Pages
- 788-797
- ISSN
- 0885-8950 (ISSN-L)
- 1558-0679
- OpenAlex
- W2145367961
- Cited by
- 118
- References
- 22
- Citations by year
- 2026: 1 · 2025: 4 · 2024: 3 · 2023: 2 · 2022: 4 · 2021: 8 · 2020: 7 · 2019: 8 · 2018: 10 · 2017: 10 · 2016: 17 · 2015: 10 · 2014: 19 · 2013: 14 · 2012: 1
- FWCI
- 9.00
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- IEEE Transactions on Power Systems (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Optimal Power Flow Distribution
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Electric Power System Optimization
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Power System Optimization and Stability
- Keywords
- power flow constraints, optimal power flow, Pareto front, convex hull, power network topology, tree networks, distribution networks, voltage magnitude constraints, line flow constraints
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