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since 2.7.2002
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Graduate applicants: We have just started in Fall 2014 a new, unique, interdisciplinary PhD program in "Computing and Mathematical Sciences". You can apply to either this program in the CMS Department or the EE Department if you are interested in power systems with a strong background in maths. See Adam Wierman's blog for more information.

See the Caltech smart grid website.

Sample: Power Networks

  1. Convex relaxation of optimal power flow (2-part tutorial)
    Extended version with proofs:   Part I   Part II

    S. H. Low
    Part I: formulations and equivalence. IEEE Trans. Control of Network Systems, 1(1):15-27, March 2014
    Part II: exactness. IEEE Trans. Control of Network Systems, 1(2):177-189, June 2014
    [slides: CNLS Grid Science Winter School, Santa Fe, NM, Jan 2015]
  2. Branch flow model: relaxations and convexification (Parts I, II)
    Masoud Farivar and S. H. Low
    IEEE Trans. Power Systems, 28(3):2554-2572, August 2013
    [old slides,   old video (Berkeley i4Energy Seminar, April 2012)]

  3. Exact convex relaxation of optimal power flow in radial networks
    L. Gan, N. Li, U. Topcu and S. H. Low
    IEEE Trans. on Automatic Control, 2014

  4. Design and stability of load-side primary frequency control in power systems
    C. Zhao, U. Topcu, N. Li and S. H. Low
    IEEE Trans. on Automatic Control, 59(5):1177-1189, May 2014

  5. Zero duality gap in optimal power flow problem
    Javad Lavaei and S. H. Low
    IEEE Trans. on Power Systems, 27(1):92-107, February 2012

  6. Optimal demand response: problem formulation and deterministic case
    L. Chen, N. Li, L. Jiang and S. H. Low
    In Control and Optimization Theory for Electric Smart Grids
    Aranya Chakrabortty and Marija Ilic, Editors, Springer 2012

  7. Quadratically constrained quadratic programs on acyclic graphs with application to power flow
    Subhonmesh Bose, Dennice F. Gayme, K. Mani Chandy and S. H. Low
    Submitted for publication, June 2013

  8. Talks:
    • Smart Grid Research
      Cornell University, March 2015
    • OPF Tutorial slides
      CNLS Grid Science Winter School, Santa Fe, NM, Jan 2015
    • Optimal power flow video+slides
      DTC Science & Technology Innovators Lecture, College of Sci & Engr, University of Minnesota, Sept 2013
    • Control architecture for networked DER slides
      Optimization panel at the 12th Int'l Workshop on Electric Power Control Centers (EPCC), Bedford Springs, PA, June 2013
    • Optimal power flow and demand response slides,   video
      i4Energy Seminar, CITRIS, UC Berkeley, April 2012

Sample: Communication Networks

    New paper:

  1. Pricing link by time
    C. D. Lai, S. H. Low, K. C. Leung and V. O. K. Li
    Proc. ACM Sigmetrics Conference, Austin, TX, June 2014

  2. Optimization flow control, I: basic algorithm and convergence
    S. H. Low and D. E. Lapsley
    IEEE/ACM Transactions on Networking, 7(6):861-75, Dec 1999

  3. A duality model of TCP and queue management algorithms
    S. H. Low
    IEEE/ACM Transactions on Networking, 11(4):525-536, Aug 2003

  4. FAST TCP: motivation, architecture, algorithms, performance
    David X. Wei, Cheng Jin, S. H. Low and Sanjay Hegde
    IEEE/ACM Transactions on Networking, 14(6):1246-1259, Dec 2006

  5. Equilibrium of heterogeneous congestion control: existence and uniqueness
    Ao Tang, Jintao Wang, S. H. Low and M. Chiang
    IEEE/ACM Transactions on Networking, 15(4):824-837, Oct 2007

  6. REM: active queue management
    S. Athuraliya, V. H. Li, S. H. Low and Q. Yin
    IEEE Network, 15(3):48-53, May/Jun 2001

  7. Layering as optimization decomposition: a mathematical theory of network architectures
    M. Chiang, S. H. Low, A. R. Calderbank and J. C. Doyle
    Proceedings of the IEEE, 95:255-312, Jan 2007

  8. Tutorial: TCP Congestion control
    slides; video part 1, video part 2
    PURSUIT Summer School, Cambridge University, UK, Aug 2011