Steven H. Low

California Institute of Technology, Pasadena, California, United States

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Publications (192)100.31 Total impact

  • Yunjian Xu, Na Li, Steven H. Low
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    ABSTRACT: We study the problem faced by an operator who aims to allocate a certain amount of load adjustment (either load reduction or increment) to multiple consumers so as to minimize the aggregate consumer disutility. We propose and analyze a simple uniform-price market mechanism where every consumer submits a single bid to choose a supply function from a group of parameterized ones. These parameterized supply functions are designed to ensure that every consumer's load adjustment is within an exogenous capacity limit that is determined by the current power system operating condition. We show that the proposed mechanism yields bounded efficiency loss at a Nash equilibrium. In particular, the proposed mechanism is shown to achieve approximate social optimality at a Nash equilibrium, if the total capacity limit excluding the consumer with the largest one is much larger than the total amount of load to be adjusted. We complement our analysis through numerical case studies.
    IEEE Transactions on Power Systems 01/2015; DOI:10.1109/TPWRS.2015.2421932 · 3.53 Impact Factor
  • Qiuyu Peng, Yujie Tang, Steven H. Low
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    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. In this paper, we propose a heuristic algorithm that is based on the recently developed convex relaxation of the ac optimal power flow problem. The algorithm is computationally efficient and scales linearly with the number of redundant lines. It requires neither parameter tuning nor initialization for different networks. It successfully computes an optimal configuration on all four networks we have tested. Moreover, we have proved that the algorithm solves the feeder reconfiguration problem optimally under certain conditions for the case where only a single redundant line needs to be opened. We also propose a more computationally efficient algorithm and show that it incurs a loss in optimality of less than 3% on the four test networks.
    IEEE Transactions on Power Systems 01/2015; 30(4):1793-1804. DOI:10.1109/TPWRS.2014.2356513 · 3.53 Impact Factor
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    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.
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    ABSTRACT: Most mobile devices today come with multiple access interfaces, \emph{e.g.}, 4G and WiFi. Multipath TCP (MP-TCP) can greatly improve network performance by exploiting the connection diversity of multiple access interfaces, at the expense of higher energy consumption. In this paper, we design MP-TCP algorithms for mobile devices by jointly considering the performance and energy consumption. We consider two main types of mobile applications: realtime applications that have a fixed duration and file transfer applications that have a fixed data size. For each type of applications, we propose a two-timescale algorithm with theoretical guarantee on the performance. We present simulation results that show that our algorithms can reduce energy consumption by up to 22$\%$ without sacrificing throughput compared to a baseline MP-TCP algorithm.
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    ABSTRACT: The combination of loss-based TCP and drop-tail routers often results in full buffers, creating large queueing delays. The challenge with parameter tuning and the drastic consequence of improper tuning have discouraged network administrators from enabling AQM even when routers support it. To address this problem, we propose a novel design principle for AQM, called the pricing-link-by-time (PLT) principle. PLT increases the link price as the backlog stays above a threshold β, and resets the price once the backlog goes below β. We prove that such a system exhibits cyclic behavior that is robust against changes in network environment and protocol parameters. While β approximately controls the level of backlog, the backlog dynamics are invariant for β across a wide range of values. Therefore, β can be chosen to reduce delay without undermining system performance. We validate these analytical results using packet-level simulation.
    ACM SIGMETRICS Performance Evaluation Review 06/2014; 42(1). DOI:10.1145/2637364.2591974
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    ABSTRACT: Demand response is crucial for the incorporation of renewable energy into the grid. In this paper, we focus on a particularly promising industry for demand response: data centers. We use simulations to show that, not only are data centers large loads, but they can provide as much (or possibly more) flexibility as large-scale storage if given the proper incentives. However, due to the market power most data centers maintain, it is difficult to design programs that are efficient for data center demand response. To that end, we propose that prediction-based pricing is an appealing market design, and show that it outperforms more traditional supply function bidding mechanisms in situations where market power is an issue. However, prediction-based pricing may be inefficient when predictions are inaccurate, and so we provide analytic, worst-case bounds on the impact of prediction error on the efficiency of prediction-based pricing. These bounds hold even when network constraints are considered, and highlight that prediction-based pricing is surprisingly robust to prediction error.
    ACM SIGMETRICS Performance Evaluation Review 06/2014; 42(1). DOI:10.1145/2591971.2592004
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    Lingwen Gan, Steven H. Low
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    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.
  • Lingwen Gan, Steven H. Low
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    ABSTRACT: We formulate optimal power flow problem for unbalanced multiphase radial networks. We show that there is an equivalent single-phase mesh network that has a radial structure at the macro-level and a clique structure corresponding to each line in the radial network. Existing sufficient conditions for exact semidefinite relaxation are therefore applicable to unbalanced multiphase networks. In particular, they imply that if a semidefinite relaxation is exact over each of the cliques in the mesh equivalent network, then it is exact for the entire network.
    2014 IEEE International Symposium on Circuits and Systems (ISCAS); 06/2014
  • Na Li, Lijun Chen, Changhong Zhao, Steven H. Low
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    ABSTRACT: Automatic generation control (AGC) regulates mechanical power generation in response to load changes through local measurements. Its main objective is to maintain system frequency and keep energy balanced within each control area so as to maintain the scheduled net interchanges between control areas. The scheduled interchanges as well as some other factors of AGC are determined at a slower time scale by considering a centralized economic dispatch (ED) problem among different generators. However, how to make AGC more economically efficient is less studied. In this paper, we study the connections between AGC and ED by reverse engineering AGC from an optimization view, and then we propose a distributed approach to slightly modify the conventional AGC to improve its economic efficiency by incorporating ED into the AGC automatically and dynamically.
    2014 American Control Conference - ACC 2014; 06/2014
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    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 05/2014; 59(5):1177-1189. DOI:10.1109/TAC.2014.2298140 · 3.17 Impact Factor
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    Qiuyu Peng, Steven H. Low
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    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.
  • 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.
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    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.
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    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.
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    Changhong Zhao, Steven Low
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    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.
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    Lingwen Gan, Ufuk Topcu, Steven H. Low
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    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.
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    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. DOI:10.1145/2567529.2567553
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    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.
    IEEE Transactions on Automatic Control 01/2014; 60(3). DOI:10.1109/TAC.2014.2357112 · 3.17 Impact Factor
  • Lingwen Gan, Ufuk Topcu, Steven H. Low
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    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.
  • Lingwen Gan, Na Li, Ufuk Topcu, Steven H. Low
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    ABSTRACT: The optimal power flow (OPF) problem seeks to control power generation/demand to optimize certain objectives such as minimizing the generation cost or power loss. It is becoming increasingly important for tree distribution networks due to the emerging distributed generation and controllable loads. The OPF problem is nonconvex. We prove that after modifying the OPF problem, its global optimum can be recovered via a second-order cone programming (SOCP) relaxation for tree networks, under a condition that can be checked in advance. Empirical studies justify that the modification is “small”, and that the condition holds, for the IEEE 13-bus network and two real-world networks.
    2013 IEEE 52nd Annual Conference on Decision and Control (CDC); 12/2013

Publication Stats

5k Citations
100.31 Total Impact Points

Institutions

  • 2001–2014
    • California Institute of Technology
      • • Division of Chemistry and Chemical Engineering
      • • Department of Computing & Mathematical Sciences
      • • Division of Engineering and Applied Science
      Pasadena, California, United States
    • University of California, Los Angeles
      • Department of Electrical Engineering
      Los Angeles, CA, United States
  • 2011
    • University of California, Berkeley
      • Department of Electrical Engineering and Computer Sciences
      Berkeley, CA, United States
  • 2008
    • KTH Royal Institute of Technology
      • School of Electrical Engineering (EE)
      Tukholma, Stockholm, Sweden
  • 2006
    • Princeton University
      • Department of Electrical Engineering
      Princeton, New Jersey, United States
  • 2005
    • Rensselaer Polytechnic Institute
      • Department of Electrical, Computer, and Systems Engineering
      Troy, NY, United States
  • 1997–2001
    • University of Melbourne
      • Department of Electrical and Electronic Engineering
      Melbourne, Victoria, Australia
  • 1995–1996
    • AT&T Labs
      Austin, Texas, United States