S.H. Low

California Institute of Technology, Pasadena, California, United States

Are you S.H. Low?

Claim your profile

Publications (275)133.82 Total impact

  • [Show abstract] [Hide abstract]
    ABSTRACT: Frequency control rebalances supply and demand while maintaining the network state within operational margins. It is implemented using fast ramping reserves that are expensive and wasteful, and which are expected to grow with the increasing penetration of renewables. The most promising solution to this problem is the use of demand response, i.e. load participation in frequency control. Yet it is still unclear how to efficiently integrate load participation without introducing instabilities and violating operational constraints. In this paper we present a comprehensive load-side frequency control mechanism that can maintain the grid within operational constraints. Our controllers can rebalance supply and demand after disturbances, restore the frequency to its nominal value and preserve inter-area power flows. Furthermore, our controllers are distributed (unlike generation-side), can allocate load updates optimally, and can maintain line flows within thermal limits. We prove that such a distributed load-side control is globally asymptotically stable and robust to unknown load parameters. Simulations are used to illustrate the properties of our solution.
    10/2014;
  • 08/2014;
  • ACM SIGMETRICS Performance Evaluation Review 06/2014; 42(1).
  • Lingwen Gan, Steven H. Low
    [Show abstract] [Hide abstract]
    ABSTRACT: Distribution networks are usually multiphase and radial. To facilitate power flow computation and optimization, two semidefinite programming (SDP) relaxations of the optimal power flow problem and a linear approximation of the power flow are proposed. We prove that the first SDP relaxation is exact if and only if the second one is exact. Case studies show that the second SDP relaxation is numerically exact and that the linear approximation obtains voltages within 0.0016 per unit of their true values for the IEEE 13, 34, 37, 123-bus networks and a real-world 2065-bus network.
    06/2014;
  • Qiuyu Peng, Steven H. Low
    [Show abstract] [Hide abstract]
    ABSTRACT: The optimal power flow (OPF) problem is fundamental in power system operations and planning. Large-scale renewable penetration calls for real-time feedback control, and hence the need for fast and distributed solutions for OPF. This is difficult because OPF is nonconvex and Kirchhoff's laws are global. In this paper we propose a solution for radial networks. It exploits recent results that suggest solving for a globally optimal solution of OPF over a radial network through the second-order cone program (SOCP) relaxation. Our distributed algorithm is based on alternating direction method of multiplier (ADMM), but unlike standard ADMM algorithms that often require iteratively solving optimization subproblems in each ADMM iteration, our decomposition allows us to derive closed form solutions for these subproblems, greatly speeding up each ADMM iteration. We present simulations on a real-world 2,065-bus distribution network to illustrate the scalability and optimality of the proposed algorithm.
    04/2014;
  • Qiuyu Peng, Steven H. Low
    [Show abstract] [Hide abstract]
    ABSTRACT: The optimal power flow (OPF) problem is fundamental in power system operations and planning. Large-scale renewable penetration calls for real-time feedback control, and hence the need for fast and distributed solutions for OPF. This is difficult because OPF is nonconvex and Kirchhoff's laws are global. In this paper we propose a solution for radial networks. It exploits recent results that suggest solving for a globally optimal solution of OPF over a radial network through the second-order cone program (SOCP) relaxation. Our distributed algorithm is based on alternating direction method of multiplier (ADMM), but unlike standard ADMM algorithms that often require iteratively solving optimization subproblems in each ADMM iteration, our decomposition allows us to derive closed form solutions for these subproblems, greatly speeding up each ADMM iteration. We present simulations on a real-world 2,065-bus distribution network to illustrate the scalability and optimality of the proposed algorithm.
    03/2014;
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: We study the role of a market maker (or market operator) in a transmission constrained electricity market. We model the market as a one-shot networked Cournot competition where generators supply quantity bids and load serving entities provide downward sloping inverse demand functions. This mimics the operation of a spot market in a deregulated market structure. In this paper, we focus on possible mechanisms employed by the market maker to balance demand and supply. In particular, we consider three candidate objective functions that the market maker optimizes - social welfare, residual social welfare, and consumer surplus. We characterize the existence of Generalized Nash Equilibrium (GNE) in this setting and demonstrate that market outcomes at equilibrium can be very different under the candidate objective functions.
    03/2014;
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Deferrable load control is essential for handling the uncertainties associated with the increasing penetration of renewable generation. Model predictive control has emerged as an effective approach for deferrable load control, and has received considerable attention. In particular, previous work has analyzed the average-case performance of model predictive deferrable load control. However, to this point, distributional analysis of model predictive deferrable load control has been elusive. In this paper, we prove strong concentration results on the distribution of the load variance obtained by model predictive deferrable load control. These concentration results highlight that the typical performance of model predictive deferrable load control is tightly concentrated around the average-case performance.
    03/2014;
  • Source
    Changhong Zhao, Steven Low
    [Show abstract] [Hide abstract]
    ABSTRACT: We augment existing generator-side primary frequency control with load-side control that are local, ubiquitous, and continuous. The mechanisms on both the generator and the load sides are decentralized in that their control decisions are functions of locally measurable frequency deviations. These local algorithms interact over the network through nonlinear power flows. We design the local frequency feedback control so that any equilibrium point of the closed-loop system is the solution to an optimization problem that minimizes the total generation cost and user disutility subject to power balance across entire network. With Lyapunov method we derive a sufficient condition ensuring an equilibrium point of the closed-loop system is asymptotically stable. Simulation demonstrates improvement in both the transient and steady-state performance over the traditional control only on the generators, even when the total control capacity remains the same.
    03/2014;
  • Source
    Lingwen Gan, Ufuk Topcu, Steven H. Low
    [Show abstract] [Hide abstract]
    ABSTRACT: Electric vehicles (EVs) should be charged with some given profile to protect its battery, making the optimal charging problem discrete. We propose a stochastic distributed algorithm to approximately solve the discrete optimization in an iterative procedure. In each iteration, a center node broadcasts the average electricity load per EV; this information is used by each EV to generate a probability distribution over its potential charging profiles; then EVs sample from the distributions to update their charging profiles. We prove that the algorithm converges {\em almost surely} to one of its {\em equilibrium} charging profiles in {\em finite} iterations, and each of its equilibrium charging profiles has a sub-optimality upper bounded that scales as $\hO(1/N)$, where $N$ is the number of EVs.
    01/2014;
  • [Show abstract] [Hide abstract]
    ABSTRACT: Real-time demand response is potential to handle the uncertainties of renewable generation. It is expected that a large number of deferrable loads, including electric vehicles and smart appliances, will participate in demand response in the future. In this paper, we propose a decentralized algorithm that reduces the tracking error between demand and generation, by shifting the power consumption of deferrable loads to match the generation in real-time. At each time step within the control window, the algorithm minimizes the expected tracking error to go with updated predictions on demand and generation. It is proved that the root mean square tracking error vanishes as control window expands, even in the presence of prediction errors.
    ACM SIGMETRICS Performance Evaluation Review 01/2014; 41(3):77-79.
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Several convex relaxations of the optimal power flow (OPF) problem have recently been developed using both bus injection models and branch flow models. In this paper, we prove relations among three convex relaxations: a semidefinite relaxation that computes a full matrix, a chordal relaxation based on a chordal extension of the network graph, and a second-order cone relaxation that computes the smallest partial matrix. We prove a bijection between the feasible sets of the OPF in the bus injection model and the branch flow model, establishing the equivalence of these two models and their second-order cone relaxations. Our results imply that, for radial networks, all these relaxations are equivalent and one should always solve the second-order cone relaxation. For mesh networks, the semidefinite relaxation is tighter than the second-order cone relaxation but requires a heavier computational effort, and the chordal relaxation strikes a good balance. Simulations are used to illustrate these results.
    01/2014;
  • C. Zhao, U. Topcu, N. Li, S. Low
    [Show abstract] [Hide abstract]
    ABSTRACT: We present a systematic method to design ubiquitous continuous fast-acting distributed load control for primary frequency regulation in power networks, by formulating an optimal load control (OLC) problem where the objective is to minimize the aggregate cost of tracking an operating point subject to power balance over the network. We prove that the swing dynamics and the branch power flows, coupled with frequency-based load control, serve as a distributed primal-dual algorithm to solve OLC. We establish the global asymptotic stability of a multimachine network under such type of load-side primary frequency control. These results imply that the local frequency deviations on each bus convey exactly the right information about the global power imbalance for the loads to make individual decisions that turn out to be globally optimal. Simulations confirm that the proposed algorithm can rebalance power and resynchronize bus frequencies after a disturbance with significantly improved transient performance.
    IEEE Transactions on Automatic Control 01/2014; 59(5):1177-1189. · 2.72 Impact Factor
  • Lingwen Gan, Ufuk Topcu, Steven H. Low
    [Show abstract] [Hide abstract]
    ABSTRACT: To schedule a large number of EVs with the presence of practical nonconvex charging constraints, a distributed and randomized algorithm is proposed in this paper. The algorithm assumes the availability of a coordinator which can communicate with all EVs. In each iteration of the algorithm, the coordinator receives tentative charging profiles from the EVs and computes a broadcast control signal. After receiving this broadcast control signal, each EV generates a probability distribution over its admissible charging profiles, and samples from the distribution to update its tentative charging profile. We prove that the algorithm converges almost surely to a charging profile in finite iterations. The final charging profile (that the algorithm converges to) is random, i.e., it depends on the realization. We characterize the final charging profile---a charging profile can be a realization of the final charging profile if and only if it is a Nash equilibrium of the game in which each EV seeks to minimize the inner product of its own charging profile and the aggregate electricity demand. Furthermore, we provide a uniform suboptimality upper bound, that scales O(1/n) in the number n of EVs, for all realizations of the final charging profile.
    12/2013;
  • Source
    Lingwen Gan, Na Li, Ufuk Topcu, Steven H. Low
    [Show abstract] [Hide abstract]
    ABSTRACT: The optimal power flow (OPF) problem determines power generation/demand that minimize a certain objective such as generation cost or power loss. It is nonconvex. We prove that, for radial networks, after shrinking its feasible set slightly, the global optimum of OPF can be recovered via a second-order cone programming (SOCP) relaxation under a condition that can be checked a priori. The condition holds for the IEEE 13-, 34-, 37-, 123-bus networks and two real-world networks, and has a physical interpretation.
    11/2013;
  • Source
    Qiuyu Peng, Steven H. Low
    [Show abstract] [Hide abstract]
    ABSTRACT: The feeder reconfiguration problem chooses the on/off status of the switches in a distribution network in order to minimize a certain cost such as power loss. It is a mixed integer nonlinear program and hence hard to solve. A popular heuristic search consists of repeated application of branch exchange, where some loads are transferred from one feeder to another feeder while maintaining the radial structure of the network, until no load transfer can further reduce the cost. Optimizing each branch exchange step is itself a mixed integer nonlinear program. In this paper we propose an efficient algorithm for optimizing a branch exchange step. It uses an AC power flow model and is based on the recently developed convex relaxation of optimal power flow. We provide a bound on the gap between the optimal cost and that of our solution. We prove that our algorithm is optimal when the voltage magnitudes are the same at all buses. We illustrate the effectiveness of our algorithm through the simulation of real-world distribution feeders.
    09/2013;
  • Qiuyu Peng, Steven H. Low
    [Show abstract] [Hide abstract]
    ABSTRACT: The feeder reconfiguration problem chooses the on/off status of the switches in a distribution network in order to minimize a certain cost such as power loss. It is a mixed integer nonlinear program and hence hard to solve. A popular heuristic search consists of repeated application of branch exchange, where some loads are transferred from one feeder to another feeder while maintaining the radial structure of the network, until no load transfer can further reduce the cost. Optimizing each branch exchange step is itself a mixed integer nonlinear program. In this paper we propose an efficient algorithm for optimizing a branch exchange step. It uses an AC power flow model and is based on the recently developed convex relaxation of optimal power flow. We provide a bound on the gap between the optimal cost and that of our solution. We prove that our algorithm is optimal when the voltage magnitudes are the same at all buses. We illustrate the effectiveness of our algorithm through the simulation of real- world distribution feeders.
    09/2013;
  • Source
    Qiuyu Peng, Anwar Walid, Steven H. Low
    [Show abstract] [Hide abstract]
    ABSTRACT: Multi-path TCP (MP-TCP) has the potential to greatly improve application performance by using multiple paths transparently. We propose a fluid model for a large class of MP-TCP algorithms and identify design criteria that guarantee the existence, uniqueness, and stability of system equilibrium. We clarify how algorithm parameters impact TCP-friendliness, responsiveness, and window oscillation and demonstrate an inevitable tradeoff among these properties. We discuss the implications of these properties on the behavior of existing algorithms and motivate a new design that generalizes existing algorithms and strikes a good balance among TCP-friendliness, responsiveness, and window oscillation. We illustrate our analysis and the behavior of the new algorithm using ns2 simulations.
    08/2013;
  • Lingwen Gan, Na Li, Steven Low, Ufuk Topcu
    ACM SIGMETRICS Performance Evaluation Review 06/2013; 41(1).
  • Qiuyu Peng, Anwar Walid, Steven H. Low
    [Show abstract] [Hide abstract]
    ABSTRACT: Multi-path TCP (MP-TCP) has the potential to greatly improve application performance by using multiple paths transparently. We propose a fluid model for a large class of MP-TCP algorithms and identify design criteria that guarantee the existence, uniqueness, and stability of system equilibrium. We characterize algorithm parameters for TCP-friendliness and prove an inevitable tradeoff between responsiveness and friendliness. We discuss the implications of these properties on the behavior of existing algorithms and motivate a new design that generalizes existing algorithms. We use ns2 simulations to evaluate the proposed algorithm and illustrate its superior overall performance.
    Proceedings of the ACM SIGMETRICS/international conference on Measurement and modeling of computer systems; 06/2013

Publication Stats

10k Citations
133.82 Total Impact Points

Institutions

  • 2002–2014
    • California Institute of Technology
      • • Division of Engineering and Applied Science
      • • Department of Computing & Mathematical Sciences
      • • Department of Electrical Engineering
      Pasadena, California, United States
  • 1992–2011
    • University of California, Berkeley
      • Department of Electrical Engineering and Computer Sciences
      Berkeley, CA, United States
  • 2009–2010
    • Cornell University
      • Department of Electrical and Computer Engineering
      Ithaca, New York, United States
  • 2005–2009
    • Rensselaer Polytechnic Institute
      • Department of Electrical, Computer, and Systems Engineering
      Troy, NY, United States
  • 2008
    • KTH Royal Institute of Technology
      Tukholma, Stockholm, Sweden
  • 2006–2007
    • Pusan National University
      • Division of Electrical and Electronics Engineering
      Pusan, Busan, South Korea
    • Princeton University
      • Department of Electrical Engineering
      Princeton, NJ, United States
  • 1996–2007
    • University of Melbourne
      • Department of Electrical and Electronic Engineering
      Melbourne, Victoria, Australia
  • 2001–2005
    • University of California, Los Angeles
      • Department of Electrical Engineering
      Los Angeles, CA, United States
  • 2003
    • Los Alamos National Laboratory
      Los Alamos, California, United States
  • 1993–1997
    • AT&T Labs
      Austin, Texas, United States