Monograph records
https://feeds.library.caltech.edu/people/Low-S-H/monograph.rss
A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenTue, 16 Apr 2024 13:53:25 +0000Cost of AQM in stabilizing TCP
https://resolver.caltech.edu/CaltechCSTR:2002.008
Authors: {'items': [{'id': 'Kim-Ki-Baek', 'name': {'family': 'Kim', 'given': 'Ki Baek'}}, {'id': 'Low-S-H', 'name': {'family': 'Low', 'given': 'Steven H.'}, 'orcid': '0000-0001-6476-3048'}]}
Year: 2002
DOI: 10.7907/84yds-ahh93
In this paper, we propose a unified mathematical framework based on receding horizon control for analyzing and designing AQM (Active Queue Management) algorithms in stabilizing TCP (Transfer Control Protocol). The proposed framework is based on a dynamical system of the given TCP and a linear quadratic cost on transients in queue length and flow rates. We derive the optimal receding horizon AQMs (RHAs) that stabilizes the linearized dynamical system with the minimum cost. Conversely, we show that any AQM with an appropriate structure solves the same optimal control problem with appropriate weighting matrix. We interpret existing AQM's such as RED, REM, PI and AVQ as different approximations of the optimal AQM, and discuss the impact of these approximations on performance.https://authors.library.caltech.edu/records/84yds-ahh93Analysis and Design of AQM for stabilizing TCP
https://resolver.caltech.edu/CaltechCSTR:2002.009
Authors: {'items': [{'id': 'Kim-Ki-Baek', 'name': {'family': 'Kim', 'given': 'Ki Baek'}}, {'id': 'Low-S-H', 'name': {'family': 'Low', 'given': 'Steven H.'}, 'orcid': '0000-0001-6476-3048'}]}
Year: 2002
DOI: 10.7907/Z9T43R25
In this paper, we propose a unified AQM (Active Queue Management) framework and stabilizing optimal AQMs in stabilizing a given TCP (Transmission Control Protocol) and a real-queue dynamics. Since we formulate the AQM design problem for the given TCP as state-space models, we get three important features. First, we propose a PD-type (Proportional-Derivative) control structure and by applying integral control action technique, a PID-type (Proportional-Integral-Derivative) control structure. Second, we propose memory control structures to compensate explicitly delays
in congestion measure by using memory control structures. Third, we propose stabilizing optimal AQMs by minimizing linear quadratic costs on the transients in queue length, aggregate rate, jitter in the aggregate rate, and congestion measure, which are called RHA (Receding Horizon AQM) in this paper. Conversely, we show that any AQM with an appropriate structure solves the same stabilizing optimal control problem with appropriate weighting matrices.
Finally, we interpret existing AQMs such as RED (Random Early Detection), REM (Random Exponential Marking), PI
(Proportional-Integral) and AVQ as different approximations of the unified AQM structures, and discuss the impact of each structures on performance from the results of the stabilizing optimal AQMs. We illustrate our results through simulation examples for the linearized system of a given nonlinear TCP and queue dynamical system.https://authors.library.caltech.edu/records/ymq8a-1g369Design of AQM in Supporting TCP Based on the Well-Known AIMD Model
https://resolver.caltech.edu/CaltechCSTR:2003.001
Authors: {'items': [{'id': 'Kim-Ki-Baek', 'name': {'family': 'Kim', 'given': 'Ki Baek'}}, {'id': 'Tang-Ao', 'name': {'family': 'Tang', 'given': 'Ao'}, 'orcid': '0000-0001-6296-644X'}, {'id': 'Low-S-H', 'name': {'family': 'Low', 'given': 'Steven H.'}, 'orcid': '0000-0001-6476-3048'}]}
Year: 2003
DOI: 10.7907/Z9DB7ZTC
In this paper, we investigate how to design AQM with a low-pass
filter (average queuing) in supporting TCP based on the well-known
AIMD dynamic model. Since we formulate the AQM design problem for
the given TCP as state-space models, we get three important
features. First, we derive PD-type (Proportional-Derivative) AQM
structure with a low-pass filter which includes P-type
(Proportional) RED in terms of queue length. Second, we compensate
for delays in congestion measure explicitly by adding a memory
control structure that uses the previous dynamic information.
Third, we obtain a stabilizing optimal gains of the proposed AQM
structure by minimizing a linear quadratic cost of the transients
on queue length, aggregate rate, and congestion measure. Finally,
we illustrate the above theoretical results through \emph{ns}
simulations for TCP Reno.https://authors.library.caltech.edu/records/d9dvj-f2e58FAST TCP: From Theory to Experiments
https://resolver.caltech.edu/CaltechCACR:2004.207
Authors: {'items': [{'id': 'Jin-Cheng', 'name': {'family': 'Jin', 'given': 'C.'}}, {'id': 'Wei-Xiaoliang-David', 'name': {'family': 'Wei', 'given': 'D.'}}, {'id': 'Low-S-H', 'name': {'family': 'Low', 'given': 'S. H.'}, 'orcid': '0000-0001-6476-3048'}, {'id': 'Buhrmaster-Gary', 'name': {'family': 'Buhrmaster', 'given': 'G.'}}, {'id': 'Bunn-J', 'name': {'family': 'Bunn', 'given': 'J.'}, 'orcid': '0000-0002-3798-298X'}, {'id': 'Choe-Hyojeong-D', 'name': {'family': 'Choe', 'given': 'H. D.'}}, {'id': 'Cottrell-R-L-A', 'name': {'family': 'Cottrell', 'given': 'R. L. A.'}}, {'id': 'Doyle-J-C', 'name': {'family': 'Doyle', 'given': 'J. C.'}, 'orcid': '0000-0002-1828-2486'}, {'id': 'Feng-Wu-chun', 'name': {'family': 'Feng', 'given': 'W.'}}, {'id': 'Martin-Oliver', 'name': {'family': 'Martin', 'given': 'O.'}}, {'id': 'Newman-H-B', 'name': {'family': 'Newman', 'given': 'H.'}, 'orcid': '0000-0003-0964-1480'}, {'id': 'Paganini-Fernando', 'name': {'family': 'Paganini', 'given': 'F.'}}, {'id': 'Ravot-Sylvain', 'name': {'family': 'Ravot', 'given': 'S.'}}, {'id': 'Singh-Suresh', 'name': {'family': 'Singh', 'given': 'S.'}}]}
Year: 2004
We describe a variant of TCP, called FAST, that can sustain high throughput and utilization at multi-Gbps over large distance. We present the motivation, review the background theory, summarize key features of FAST TCP, and report our first experimental results.https://authors.library.caltech.edu/records/ygj33-23272Equilibrium of Heterogeneous Congestion Control Protocols
https://resolver.caltech.edu/CaltechCSTR:2005.005
Authors: {'items': [{'id': 'Tang-Ao', 'name': {'family': 'Tang', 'given': 'Ao'}, 'orcid': '0000-0001-6296-644X'}, {'id': 'Wang-Jintao', 'name': {'family': 'Wang', 'given': 'Jiantao'}}, {'id': 'Low-S-H', 'name': {'family': 'Low', 'given': 'Steven H.'}, 'orcid': '0000-0001-6476-3048'}, {'id': 'Chiang-Mung', 'name': {'family': 'Chiang', 'given': 'Mung'}}]}
Year: 2005
DOI: 10.7907/Z9FB50XP
When heterogeneous congestion control protocols that react to different pricing signals share the same network, the resulting equilibrium may no longer be interpreted as a solution to the standard utility maximization problem. We prove the existence of equilibrium in general multi-protocol networks under mild assumptions. For almost all networks, the equilibria are locally unique, and finite and odd in number. They cannot all be locally stable unless it is globally unique. Finally, we show that if the price mapping functions that map link prices to effective prices observed by the sources are similar, then global uniqueness is guaranteed. Numerical examples are used throughout the paper to illustrate these results.https://authors.library.caltech.edu/records/qpy2w-n0y44Rate Control for Multicast with Network Coding
https://resolver.caltech.edu/CaltechCDSTR:2006.004
Authors: {'items': [{'id': 'Chen-Lijun', 'name': {'family': 'Chen', 'given': 'Lijun'}}, {'id': 'Ho-Tracey', 'name': {'family': 'Ho', 'given': 'Tracey'}}, {'id': 'Low-S-H', 'name': {'family': 'Low', 'given': 'Steven'}, 'orcid': '0000-0001-6476-3048'}, {'id': 'Chiang-Mung', 'name': {'family': 'Chiang', 'given': 'Mung'}}, {'id': 'Doyle-J-C', 'name': {'family': 'Doyle', 'given': 'John'}, 'orcid': '0000-0002-1828-2486'}]}
Year: 2006
Recent advances in network coding have shown great potential for efficient information multicasting in communication networks, in terms of both network throughput and network management. In this paper, we address the problem of rate control at end-systems for network coding based multicast flows. We develop two adaptive rate control algorithms for the networks with given coding subgraphs and without given coding subgraphs, respectively. With random network coding, both algorithms can be implemented in a distributed manner, and work at transport layer to adjust source rates and at network layer to carry out network coding. We prove that the proposed algorithms converge to the globally optimal solutions. Some related issues are discussed, and numerical examples are provided to complement our theoretical analysis.https://authors.library.caltech.edu/records/9rz0z-ect67Opportunistic Source Coding for Data Gathering in Wireless Sensor Networks
https://resolver.caltech.edu/CaltechCSTR:2007.003
Authors: {'items': [{'id': 'Cui-Tao', 'name': {'family': 'Cui', 'given': 'Tao'}}, {'id': 'Chen-Lijun', 'name': {'family': 'Chen', 'given': 'Lijun'}}, {'id': 'Ho-Tracey', 'name': {'family': 'Ho', 'given': 'Tracey'}}, {'id': 'Low-S-H', 'name': {'family': 'Low', 'given': 'Steven H.'}, 'orcid': '0000-0001-6476-3048'}]}
Year: 2007
DOI: 10.7907/Z9G73BP6
We propose a jointly opportunistic source
coding and opportunistic routing (OSCOR) protocol for
correlated data gathering in wireless sensor networks.
OSCOR improves data gathering efficiency by exploiting
opportunistic data compression and cooperative diversity
associated with wireless broadcast advantage. The design
of OSCOR involves several challenging issues across different
network protocol layers. At MAC layer, sensor nodes
need to coordinate wireless transmission and packet forwarding
to exploit multiuser diversity in packet reception.
At network layer, in order to achieve high diversity and
compression gains, routing must be based on a metric that
is dependent on not only link-quality but also compression
opportunities. At application layer, sensor nodes need a distributed
source coding algorithm that has low coordination
overhead and does not require the source distributions to
be known. OSCOR provides practical solutions to these
challenges incorporating a slightly modified 802.11 MAC,
a distributed source coding scheme based on Lempel-Ziv
code and network coding, and a node compression ratio
dependent metric combined with a modified Dijkstra"s
algorithm for path selection. We evaluate the performance
of OSCOR through simulations, and show that OSCOR
reduces the number of transmissions by nearly 25%
compared with existing greedy scheme in small networks.https://authors.library.caltech.edu/records/dd849-24158Zero Duality Gap in Optimal Power Flow Problem
https://resolver.caltech.edu/CaltechCDSTR:2010.004
Authors: {'items': [{'id': 'Lavaei-J', 'name': {'family': 'Lavaei', 'given': 'Javad'}}, {'id': 'Low-S-H', 'name': {'family': 'Low', 'given': 'Steven'}, 'orcid': '0000-0001-6476-3048'}]}
Year: 2010
The optimal power flow (OPF) problem is nonconvex
and generally hard to solve. We provide a sufficient
condition under which the OPF problem is equivalent to
a convex problem and therefore is efficiently solvable.
Specifically, we prove that the dual of OPF is a semidefinite program and our sufficient condition guarantees that the duality gap is zero and a globally optimal solution of OPF is recoverable from a dual optimal solution. This sufficient condition is satisfied by standard
IEEE benchmark systems with 14, 30, 57, 118 and 300 buses
after small resistance (10^(-5) per unit) is added to every transformer that originally assumes zero resistance.
We justify why the condition might hold widely in practice from algebraic and geometric perspectives. The main underlying reason is that physical quantities such as resistance, capacitance and inductance, are all positive.https://authors.library.caltech.edu/records/934zs-f4t59Frequency-based load control in power systems
https://resolver.caltech.edu/CaltechCDSTR:2011.007
Authors: {'items': [{'id': 'Zhao-Changhong', 'name': {'family': 'Zhao', 'given': 'Changhong'}, 'orcid': '0000-0003-0539-8591'}, {'id': 'Topcu-U', 'name': {'family': 'Topcu', 'given': 'Ufuk'}}, {'id': 'Low-S-H', 'name': {'family': 'Low', 'given': 'Steven H.'}, 'orcid': '0000-0001-6476-3048'}]}
Year: 2011
Maintaining demand-supply balance and regulating frequency are key issues in power system control. Conventional approaches focus on adjusting the generation so that it follows the load. However, relying on solely regulating generation is inefficient, especially for power systems where contingencies like sudden loss in generation or sudden change in load frequently occur and the proportion of intermittent renewable power is increasing. We present a frequency-based load control scheme for demand-supply balancing and frequency regulation. We formulate a load control optimization problem which aims to balance the change in load with the change in supply while minimizing the overall end-use disutility. By studying the power system model that characterizes the frequency response to
real power imbalance between demand and supply, we design
decentralized synchronous and asynchronous algorithms which
take advantage of local frequency measurements to solve the load control problem. Case studies show that the proposed load control scheme is capable of relatively quickly balancing the power and restoring the frequency under generation-loss like contingencies or renewable power penetration. Case studies also show that the proposed scheme still works well when users have the knowledge
of a simplified system model instead of an accurate one.https://authors.library.caltech.edu/records/888vf-8bb79Optimal Decentralized Protocols for Electric Vehicle Charging
https://resolver.caltech.edu/CaltechCDSTR:2011.009
Authors: {'items': [{'id': 'Gan-Lingwen', 'name': {'family': 'Gan', 'given': 'Lingwen'}}, {'id': 'Topcu-U', 'name': {'family': 'Topcu', 'given': 'Ufuk'}}, {'id': 'Low-S-H', 'name': {'family': 'Low', 'given': 'Steven'}, 'orcid': '0000-0001-6476-3048'}]}
Year: 2011
We propose decentralized algorithms for optimally scheduling electric vehicle charging. The algorithms exploit the elasticity and controllability of electric vehicle related loads in order to fill the valleys in electric demand profile. We formulate a global optimization problem whose objective is to impose a generalized notion of valley-filling, study properties of the optimal charging profiles, and give decentralized offline and online algorithms to solve the problem. In each iteration of the proposed algorithms, electric vehicles choose their own charging profiles for the rest horizon according to the price profile broadcast by the utility, and the utility updates the price profile to guide their behavior. The offline algorithms are guaranteed to converge to optimal charging profiles irrespective of the specifications (e.g., maximum charging rate and deadline) of electric vehicles at the expense of a restrictive assumption that all electric vehicles are available for negotiation at the beginning of the planning horizon. The online algorithms relax this assumption by using a scalar prediction of future total charging demand at each time instance and yield near optimal charging profiles. The proposed algorithms need no coordination among the electric vehicles, hence their implementation requires low communication and computation capability. Simulation results are provided to support these results.https://authors.library.caltech.edu/records/fgea1-qdv23Fast Load Control with Stochastic Frequency Measurement
https://resolver.caltech.edu/CaltechCDSTR:2011.010
Authors: {'items': [{'id': 'Zhao-Changhong', 'name': {'family': 'Zhao', 'given': 'Changhong'}, 'orcid': '0000-0003-0539-8591'}, {'id': 'Topcu-U', 'name': {'family': 'Topcu', 'given': 'Ufuk'}}, {'id': 'Low-S-H', 'name': {'family': 'Low', 'given': 'Steven H.'}, 'orcid': '0000-0001-6476-3048'}]}
Year: 2011
Matching demand with supply and regulating frequency
are key issues in power system operations. Flexibility
and local frequency measurement capability of loads offer new regulation mechanisms through load control. We present a
frequency-based fast load control scheme which aims to match
total demand with supply while minimizing the global end-use
disutility. Local frequency measurement enables loads to make decentralized decisions on their power from the estimates of total demand-supply mismatch. To resolve the errors in such estimates caused by stochastic frequency measurement errors, loads communicate via a neighborhood area network. Case studies show that the proposed load control can balance demand with supply and restore the frequency at the timescale faster than AGC, even when the loads use a highly simplified system model in their algorithms. Moreover, we discuss the tradeoff between communication and performance, and show with experiments that a moderate amount of communication significantly improves the performance.https://authors.library.caltech.edu/records/95tzm-njn41Stochastic Distributed Protocol for Electric Vehicle Charging with Discrete Charging Rate
https://resolver.caltech.edu/CaltechCDSTR:2011.011
Authors: {'items': [{'id': 'Gan-Lingwen', 'name': {'family': 'Gan', 'given': 'Lingwen'}}, {'id': 'Topcu-U', 'name': {'family': 'Topcu', 'given': 'Ufuk'}}, {'id': 'Low-S-H', 'name': {'family': 'Low', 'given': 'Steven H.'}, 'orcid': '0000-0001-6476-3048'}]}
Year: 2011
To address the grid-side challenges associated with the anticipated high electric vehicle (EV) penetration level, various charging protocols have been proposed in the literature. Most if not all of these protocols assume continuous charging rates and allow intermittent charging. However, due to charging technology limitations, EVs can only be charged at a fixed rate, and the intermittency in charging shortens the battery lifespan. We consider these charging requirements, and formulate EV charging scheduling as a discrete optimization problem.
We propose a stochastic distributed algorithm to approximately
solve the optimal EV charging scheduling problem in an
iterative procedure. In each iteration, the transformer receives
charging profiles computed by the EVs in the previous iteration,
and broadcasts the corresponding normalized total demand to
the EVs; each EV generates a probability distribution over
its potential charging profiles accordingly, and samples from
the distribution to obtain a new charging profile. We prove
that this stochastic algorithm almost surely converges to one of
its equilibrium charging profiles, and each of its equilibrium
charging profiles has a negligible sub-optimality ratio. Case
studies corroborate our theoretical results.https://authors.library.caltech.edu/records/d5316-qwp84Swing Dynamics as Primal-Dual Algorithm for Optimal Load Control
https://resolver.caltech.edu/CaltechCDSTR:2012.001
Authors: {'items': [{'id': 'Zhao-Changhong', 'name': {'family': 'Zhao', 'given': 'Changhong'}, 'orcid': '0000-0003-0539-8591'}, {'id': 'Topcu-U', 'name': {'family': 'Topcu', 'given': 'Ufuk'}}, {'id': 'Low-S-H', 'name': {'family': 'Low', 'given': 'Steven H.'}, 'orcid': '0000-0001-6476-3048'}]}
Year: 2012
Frequency regulation and generation-load balancing are key issues in power transmission networks. Complementary to generation control, loads provide flexible and fast responsive sources for frequency regulation, and local frequency measurement capability of loads offers the opportunity of decentralized control. In this paper, we propose an optimal load control problem, which balances the load reduction (or increase) with the generation shortfall (or surplus), resynchronizes the bus frequencies, and minimizes a measure of aggregate disutility of participation in such a load control. We find that, a frequency-based load control coupled with the dynamics of swing equations and branch power flows serve as a distributed primal-dual algorithm to solve the optimal load control problem and its dual. Simulation shows that the proposed mechanism can restore frequency, balance load with generation and achieve the optimum of the load control problem within several seconds after a disturbance in generation. Through simulation, we also compare the performance of optimal load control with automatic generation control (AGC), and discuss the effect of their incorporation.https://authors.library.caltech.edu/records/n4c7f-cfb62Corrective control: stability analysis of Unified Controller combining frequency control and congestion management
https://resolver.caltech.edu/CaltechAUTHORS:20190627-103322354
Authors: {'items': [{'id': 'Khamisov-O-O', 'name': {'family': 'Khamisov', 'given': 'O. O.'}}, {'id': 'Chernova-T-S', 'name': {'family': 'Chernova', 'given': 'T. S.'}}, {'id': 'Bialek-J-W', 'name': {'family': 'Bialek', 'given': 'J. W.'}}, {'id': 'Low-S-H', 'name': {'family': 'Low', 'given': 'S. H.'}, 'orcid': '0000-0001-6476-3048'}]}
Year: 2019
DOI: 10.48550/arXiv.1806.10303
This paper analyses stability of the Unified Controller (UC) that combines frequency control and congestion management and therefore makes it possible to move from preventive to corrective power system control. Earlier work by the authors of UC proved asymptotic stability of the methodology but the proof was based on a simplified first-order model of the turbine and turbine governor. We show that a higher order model of the turbine governor leads to eigenvalues with small but positive real parts. Consequently, we develop a modification of the methodology that decouples the physical and control systems and therefore results in all the eigenvalues having negative real parts. We illustrate the effectiveness of the modification on a realistic model of 39-bus model of New England power system implemented in Power System Toolbox (PST).https://authors.library.caltech.edu/records/grqda-tv814Buy or Sell? Energy Sharing of Prosumers on Constrained Networks
https://resolver.caltech.edu/CaltechAUTHORS:20190626-144159570
Authors: {'items': [{'id': 'Chen-Yue', 'name': {'family': 'Chen', 'given': 'Yue'}}, {'id': 'Mei-Shengwei', 'name': {'family': 'Mei', 'given': 'Shengwei'}, 'orcid': '0000-0002-2757-5977'}, {'id': 'Wei-Wei', 'name': {'family': 'Wei', 'given': 'Wei'}, 'orcid': '0000-0002-1018-7708'}, {'id': 'Low-S-H', 'name': {'family': 'Low', 'given': 'Steven H.'}, 'orcid': '0000-0001-6476-3048'}, {'id': 'Wierman-A', 'name': {'family': 'Wierman', 'given': 'Adam'}}, {'id': 'Liu-Feng', 'name': {'family': 'Liu', 'given': 'Feng'}, 'orcid': '0000-0003-2279-2558'}]}
Year: 2019
DOI: 10.48550/arXiv.1906.09891
The advent of intelligent agents who produce and consume energy by themselves has led the smart grid into the era of "prosumer", offering the energy system and customers a unique opportunity to revaluate/trade their spot energy via a sharing initiative. To this end, designing an appropriate sharing mechanism is an issue with crucial importance and has captured great attention. This paper addresses the prosumers' demand response problem via energy sharing. Under a general supply-demand function bidding scheme, a sharing market clearing procedure considering network constraints is proposed, which gives rise to a generalized Nash game. The existence and uniqueness of market equilibrium are proved in non-congested cases. When congestion occurs, infinitely much equilibrium may exist because the strategy spaces of prosumers are correlated. A price-regulation procedure is introduced in the sharing mechanism, which outcomes a unique equilibrium that is fair to all participants. Properties of the improved sharing mechanism, including the individual rational behaviors of prosumers and the components of sharing price, are revealed. When the number of prosumers increases, the proposed sharing mechanism approaches social optimum. Even with fixed number of resources, introducing competition can result in a decreasing social cost. Illustrative examples validate the theoretical results and provide more insights for the energy sharing research.https://authors.library.caltech.edu/records/9swdj-98q23Exact Convex Relaxation of Optimal Power Flow in Tree Networks
https://resolver.caltech.edu/CaltechAUTHORS:20190628-105122130
Authors: {'items': [{'id': 'Gan-Lingwen', 'name': {'family': 'Gan', 'given': 'Lingwen'}}, {'id': 'Li-Na', 'name': {'family': 'Li', 'given': 'Na'}}, {'id': 'Topcu-U', 'name': {'family': 'Topcu', 'given': 'Ufuk'}}, {'id': 'Low-S-H', 'name': {'family': 'Low', 'given': 'Steven H.'}, 'orcid': '0000-0001-6476-3048'}]}
Year: 2019
DOI: 10.48550/arXiv.1208.4076
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 in the network. It is becoming increasingly important for distribution networks, which are tree networks, due to the emergence of distributed generation and controllable loads. In this paper, we study the OPF problem in tree networks. The OPF problem is nonconvex. We prove that after a "small" modification to the OPF problem, its global optimum can be recovered via a second-order cone programming (SOCP) relaxation, under a "mild" condition that can be checked apriori. Empirical studies justify that the modification to OPF is "small" and that the "mild" condition holds for the IEEE 13-bus distribution network and two real-world networks with high penetration of distributed generation.https://authors.library.caltech.edu/records/ncdc2-0yt10Distributed Load Balancing with Nonconvex Constraints: A Randomized Algorithm with Application to Electric Vehicle Charging Scheduling
https://resolver.caltech.edu/CaltechAUTHORS:20190628-094804246
Authors: {'items': [{'id': 'Gan-Lingwen', 'name': {'family': 'Gan', 'given': 'Lingwen'}}, {'id': 'Topcu-U', 'name': {'family': 'Topcu', 'given': 'Ufuk'}}, {'id': 'Low-S-H', 'name': {'family': 'Low', 'given': 'Steven H.'}, 'orcid': '0000-0001-6476-3048'}]}
Year: 2019
DOI: 10.48550/arXiv.1401.7604
With substantial potential to reduce green house gas emission and reliance on fossil fuel, electric vehicles (EVs) have lead to a booming industry, whose growth is expected to continue for the next few decades. However, EVs present themselves as large loads to the power grid. If not coordinated wisely, the charging of EVs will overload power distribution circuits and dramatically increase power supply cost. To address this challenge, significant amount of effort has been devoted in the literature to schedule the charging of EVs in a power grid friendly way. Nonetheless, the majority of the literature assumes that EVs can be charged intermittently at any power level below certain rating, while in practice, it is preferable to charge an EV consecutively at a pre-determined power to prolong the battery lifespan. This practical EV charging constraint is nonconvex and complicates scheduling. 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 profileāa 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.https://authors.library.caltech.edu/records/1caq0-gv292Branch Flow Model: Relaxations and Convexification (Parts I, II)
https://resolver.caltech.edu/CaltechAUTHORS:20190628-073720381
Authors: {'items': [{'id': 'Farivar-M', 'name': {'family': 'Farivar', 'given': 'Masoud'}}, {'id': 'Low-S-H', 'name': {'family': 'Low', 'given': 'Steven H.'}, 'orcid': '0000-0001-6476-3048'}]}
Year: 2019
DOI: 10.48550/arXiv.1204.4865
We propose a branch flow model for the analysis and optimization of mesh as well as radial networks. The model leads to a new approach to solving optimal power flow (OPF) problems that consists of two relaxation steps. The first step eliminates the voltage and current angles and the second step approximates the resulting problem by a conic program that can be solved efficiently. For radial networks, we prove that both relaxation steps are always exact, provided there are no upper bounds on loads. For mesh networks, the conic relaxation is always exact and we characterize when the angle relaxation may fail. We propose a simple method to convexify a mesh network using phase shifters so that both relaxation steps are always exact and OPF for the convexified network can always be solved efficiently for a globally optimal solution. We prove that convexification requires phase shifters only outside a spanning tree of the network graph and their placement depends only on network topology, not on power flows, generation, loads, or operating constraints. Since power networks are sparse, the number of required phase shifters may be relatively small.https://authors.library.caltech.edu/records/5g3ad-4bt56Real-time Flexibility Feedback for Closed-loop Aggregator and System Operator Coordination
https://resolver.caltech.edu/CaltechAUTHORS:20200707-095020631
Authors: {'items': [{'id': 'Li-Tongxin', 'name': {'family': 'Li', 'given': 'Tongxin'}, 'orcid': '0000-0002-9806-8964'}, {'id': 'Low-S-H', 'name': {'family': 'Low', 'given': 'Steven H.'}, 'orcid': '0000-0001-6476-3048'}, {'id': 'Wierman-A', 'name': {'family': 'Wierman', 'given': 'Adam'}}]}
Year: 2020
DOI: 10.48550/arXiv.2006.13814
Aggregators have emerged as crucial tools for the coordination of distributed, controllable loads. However, to be used effectively, aggregators must be able to communicate the available flexibility of the loads they control to the system operator in a manner that is both (i) concise enough to be scalable to aggregators governing hundreds or even thousands of loads and (ii) informative enough to allow the system operator to send control signals to the aggregator that lead to optimization of system-level objectives, such as cost minimization, and do not violate private constraints of the loads, such as satisfying specific load demands. In this paper, we present the design of a real-time flexibility feedback signal based on maximization of entropy. The design provides a concise and informative signal that can be used by the system operator to perform online cost minimization and real-time capacity estimation, while provably satisfying the private constraints of the loads. In addition to deriving analytic properties of the design, we illustrate the effectiveness of the design using a dataset from an adaptive electric vehicle charging network.https://authors.library.caltech.edu/records/rsjeg-8d180Localization & Mitigation of Cascading Failures in Power Systems, Part III: Real-time Mitigation
https://resolver.caltech.edu/CaltechAUTHORS:20200707-100438853
Authors: {'items': [{'id': 'Guo-Linqi', 'name': {'family': 'Guo', 'given': 'Linqi'}}, {'id': 'Liang-Chen', 'name': {'family': 'Liang', 'given': 'Chen'}}, {'id': 'Zocca-A', 'name': {'family': 'Zocca', 'given': 'Alessandro'}, 'orcid': '0000-0001-6585-4785'}, {'id': 'Low-S-H', 'name': {'family': 'Low', 'given': 'Steven H.'}, 'orcid': '0000-0001-6476-3048'}, {'id': 'Wierman-A', 'name': {'family': 'Wierman', 'given': 'Adam'}}]}
Year: 2020
DOI: 10.48550/arXiv.2005.11319
Cascading failures in power systems propagate non-locally, making the control of outages extremely difficult. In Part III of this work, we leverage the properties of tree partitioning developed in Parts I and II to propose a distributed control strategy that offers strong guarantees in both the mitigation and localization of cascading failures. Specifically we adopt a recently developed distributed frequency regulation approach, called the Unified Control, that integrates primary and secondary control as well as congestion management at frequency control timescale. When the balancing areas over which the Unified Control operates form a tree partition, our proposed strategy will regulate the system to a steady state where the impact of initial line outages is localized within the areas where they occur whenever possible and stop the cascading process. When initial line outages cannot be localized, the proposed strategy provides a configurable design that involves and coordinates progressively more balancing areas for failure mitigation in a way that can be optimized for different priorities. We compare the proposed control strategy with the classical automatic generation control (AGC) on the IEEE 118-bus and 2736-bus test networks. Simulation results show that our strategy greatly improves overall reliability in terms of the N-k security standard, and localizes the impact of initial failures in majority of the load profiles that are examined. Moreover, the proposed framework incurs significantly less load loss, if any, compared to AGC, in all of our case studies.https://authors.library.caltech.edu/records/58pdy-njb94DeepOPF: A Feasibility-Optimized Deep Neural Network Approach for AC Optimal Power Flow Problems
https://resolver.caltech.edu/CaltechAUTHORS:20200707-112147912
Authors: {'items': [{'id': 'Pan-Xiang', 'name': {'family': 'Pan', 'given': 'Xiang'}}, {'id': 'Chen-Minghua', 'name': {'family': 'Chen', 'given': 'Minghua'}}, {'id': 'Zhao-Tianyu', 'name': {'family': 'Zhao', 'given': 'Tianyu'}}, {'id': 'Low-S-H', 'name': {'family': 'Low', 'given': 'Steven H.'}, 'orcid': '0000-0001-6476-3048'}]}
Year: 2020
DOI: 10.48550/arXiv.2007.01002
The AC-OPF problem is the key and challenging problem in the power system operation. When solving the AC-OPF problem, the feasibility issue is critical. In this paper, we develop an efficient Deep Neural Network (DNN) approach, DeepOPF, to ensure the feasibility of the generated solution. The idea is to train a DNN model to predict a set of independent operating variables, and then to directly compute the remaining dependable variables by solving the AC power flow equations. While this guarantees the power-flow balances, the principal difficulty lies in ensuring that the obtained solutions satisfy the operation limits of generations, voltages, and branch flow. We tackle this hurdle by employing a penalty approach in training the DNN. As the penalty gradients make the common first-order gradient-based algorithms prohibited due to the hardness of obtaining an explicit-form expression of the penalty gradients, we further apply a zero-order optimization technique to design the training algorithm to address the critical issue. The simulation results of the IEEE test case demonstrate the effectiveness of the penalty approach. Also, they show that DeepOPF can speed up the computing time by one order of magnitude compared to a state-of-the-art solver, at the expense of minor optimality loss.https://authors.library.caltech.edu/records/20wfz-z0p43Combining Model-Based and Model-Free Methods for Nonlinear Control: A Provably Convergent Policy Gradient Approach
https://resolver.caltech.edu/CaltechAUTHORS:20200707-095652399
Authors: {'items': [{'id': 'Qu-Guannan', 'name': {'family': 'Qu', 'given': 'Guannan'}}, {'id': 'Yu-Chenkai', 'name': {'family': 'Yu', 'given': 'Chenkai'}}, {'id': 'Low-S-H', 'name': {'family': 'Low', 'given': 'Steven'}, 'orcid': '0000-0001-6476-3048'}, {'id': 'Wierman-A', 'name': {'family': 'Wierman', 'given': 'Adam'}}]}
Year: 2020
DOI: 10.48550/arXiv.2006.07476
Model-free learning-based control methods have seen great success recently. However, such methods typically suffer from poor sample complexity and limited convergence guarantees. This is in sharp contrast to classical model-based control, which has a rich theory but typically requires strong modeling assumptions. In this paper, we combine the two approaches to achieve the best of both worlds. We consider a dynamical system with both linear and non-linear components and develop a novel approach to use the linear model to define a warm start for a model-free, policy gradient method. We show this hybrid approach outperforms the model-based controller while avoiding the convergence issues associated with model-free approaches via both numerical experiments and theoretical analyses, in which we derive sufficient conditions on the non-linear component such that our approach is guaranteed to converge to the (nearly) global optimal controller.https://authors.library.caltech.edu/records/eh5cv-5em69Reinforcement Learning for Decision-Making and Control in Power Systems: Tutorial, Review, and Vision
https://resolver.caltech.edu/CaltechAUTHORS:20210831-203850710
Authors: {'items': [{'id': 'Chen-Xin', 'name': {'family': 'Chen', 'given': 'Xin'}, 'orcid': '0000-0002-0952-0008'}, {'id': 'Qu-Guannan', 'name': {'family': 'Qu', 'given': 'Guannan'}, 'orcid': '0000-0002-5466-3550'}, {'id': 'Tang-Yujie', 'name': {'family': 'Tang', 'given': 'Yujie'}, 'orcid': '0000-0002-4921-8372'}, {'id': 'Low-S-H', 'name': {'family': 'Low', 'given': 'Steven'}, 'orcid': '0000-0001-6476-3048'}, {'id': 'Li-Na', 'name': {'family': 'Li', 'given': 'Na'}}]}
Year: 2021
DOI: 10.48550/arXiv.2102.01168
With large-scale integration of renewable generation and distributed energy resources (DERs), modern power systems are confronted with new operational challenges, such as growing complexity, increasing uncertainty, and aggravating volatility. Meanwhile, more and more data are becoming available owing to the widespread deployment of smart meters, smart sensors, and upgraded communication networks. As a result, data-driven control techniques, especially reinforcement learning (RL), have attracted surging attention in recent years. In this paper, we provide a tutorial on various RL techniques and how they can be applied to decision-making in power systems. We illustrate RL-based models and solutions in three key applications, frequency regulation, voltage control, and energy management. We conclude with three critical issues in the application of RL, i.e., safety, scalability, and data. Several potential future directions are discussed as well.https://authors.library.caltech.edu/records/sjc89-s6m10Smoothed Least-Laxity-First Algorithm for EV Charging
https://resolver.caltech.edu/CaltechAUTHORS:20210510-080403337
Authors: {'items': [{'id': 'Chen-Niangjun', 'name': {'family': 'Chen', 'given': 'Niangjun'}, 'orcid': '0000-0002-2289-9737'}, {'id': 'Kurniawan-Christian', 'name': {'family': 'Kurniawan', 'given': 'Christian'}}, {'id': 'Nakahira-Yorie', 'name': {'family': 'Nakahira', 'given': 'Yorie'}, 'orcid': '0000-0003-3324-4602'}, {'id': 'Chen-Lijun', 'name': {'family': 'Chen', 'given': 'Lijun'}, 'orcid': '0000-0001-6694-4299'}, {'id': 'Low-S-H', 'name': {'family': 'Low', 'given': 'Steven H.'}, 'orcid': '0000-0001-6476-3048'}]}
Year: 2021
DOI: 10.48550/arXiv.2102.08610
Adaptive charging can charge electric vehicles (EVs) at scale cost effectively, despite the uncertainty in EV arrivals. We formulate adaptive EV charging as a feasibility problem that meets all EVs' energy demands before their deadlines while satisfying constraints in charging rate and total charging power. We propose an online algorithm, smoothed least-laxity-first (sLLF), that decides the current charging rates without the knowledge of future arrivals and demands. We characterize the performance of the sLLF algorithm analytically and numerically. Numerical experiments with real-world data show that it has a significantly higher rate of feasible EV charging than several other existing EV charging algorithms. Resource augmentation framework is employed to assess the feasibility condition of the algorithm. The assessment shows that the sLLF algorithm achieves perfect feasibility with only a 0.07 increase in resources.https://authors.library.caltech.edu/records/7tm6y-8ht67A Spectral Representation of Power Systems with Applications to Adaptive Grid Partitioning and Cascading Failure Localization
https://resolver.caltech.edu/CaltechAUTHORS:20210716-225840003
Authors: {'items': [{'id': 'Zocca-Alessandro', 'name': {'family': 'Zocca', 'given': 'Alessandro'}, 'orcid': '0000-0001-6585-4785'}, {'id': 'Liang-Chen', 'name': {'family': 'Liang', 'given': 'Chen'}}, {'id': 'Guo-Linqi', 'name': {'family': 'Guo', 'given': 'Linqi'}}, {'id': 'Low-S-H', 'name': {'family': 'Low', 'given': 'Steven H.'}, 'orcid': '0000-0001-6476-3048'}, {'id': 'Wierman-A', 'name': {'family': 'Wierman', 'given': 'Adam'}}]}
Year: 2021
DOI: 10.48550/arXiv.2105.05234
Transmission line failures in power systems propagate and cascade non-locally. This well-known yet counter-intuitive feature makes it even more challenging to optimally and reliably operate these complex networks. In this work we present a comprehensive framework based on spectral graph theory that fully and rigorously captures how multiple simultaneous line failures propagate, distinguishing between non-cut and cut set outages. Using this spectral representation of power systems, we identify the crucial graph sub-structure that ensures line failure localization -- the network bridge-block decomposition. Leveraging this theory, we propose an adaptive network topology reconfiguration paradigm that uses a two-stage algorithm where the first stage aims to identify optimal clusters using the notion of network modularity and the second stage refines the clusters by means of optimal line switching actions. Our proposed methodology is illustrated using extensive numerical examples on standard IEEE networks and we discussed several extensions and variants of the proposed algorithm.https://authors.library.caltech.edu/records/1d53p-zja18Stability Constrained Reinforcement Learning for Real-Time Voltage Control
https://resolver.caltech.edu/CaltechAUTHORS:20220304-172338061
Authors: {'items': [{'id': 'Shi-Yuanyuan', 'name': {'family': 'Shi', 'given': 'Yuanyuan'}, 'orcid': '0000-0002-6182-7664'}, {'id': 'Qu-Guannan', 'name': {'family': 'Qu', 'given': 'Guannan'}, 'orcid': '0000-0002-5466-3550'}, {'id': 'Low-S-H', 'name': {'family': 'Low', 'given': 'Steven'}, 'orcid': '0000-0001-6476-3048'}, {'id': 'Anandkumar-A', 'name': {'family': 'Anandkumar', 'given': 'Anima'}, 'orcid': '0000-0002-6974-6797'}, {'id': 'Wierman-A', 'name': {'family': 'Wierman', 'given': 'Adam'}, 'orcid': '0000-0002-5923-0199'}]}
Year: 2022
DOI: 10.48550/arXiv.2109.14854
Deep reinforcement learning (RL) has been recognized as a promising tool to address the challenges in real-time control of power systems. However, its deployment in real-world power systems has been hindered by a lack of formal stability and safety guarantees. In this paper, we propose a stability constrained reinforcement learning method for real-time voltage control in distribution grids and we prove that the proposed approach provides a formal voltage stability guarantee. The key idea underlying our approach is an explicitly constructed Lyapunov function that certifies stability. We demonstrate the effectiveness of the approach in case studies, where the proposed method can reduce the transient control cost by more than 30\% and shorten the response time by a third compared to a widely used linear policy, while always achieving voltage stability. In contrast, standard RL methods often fail to achieve voltage stability.https://authors.library.caltech.edu/records/39nvc-h9r75