Combined Feed
https://feeds.library.caltech.edu/people/Gan-Lingwen/combined.rss
A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenTue, 16 Apr 2024 15:17:21 +0000Optimal 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.eduhttps://authors.library.caltech.edu/records/fgea1-qdv23Optimal decentralized protocol for electric vehicle charging
https://resolver.caltech.edu/CaltechAUTHORS:20131003-100205684
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
DOI: 10.1109/CDC.2011.6161220
Motivated by the power-grid-side challenges in the integration of electric vehicles, we propose a decentralized protocol for negotiating day-ahead charging schedules for electric vehicles. The overall goal is to shift the load due to electric vehicles to fill the overnight electricity demand valley. In each iteration of the proposed protocol, electric vehicles choose their own charging profiles for the following day according to the price profile broadcast by the utility, and the utility updates the price profile to guide their behavior. This protocol is guaranteed to converge, irrespective of the specifications (e.g., maximum charging rate and deadline) of electric vehicles. At convergence, the l2 norm of the aggregated demand is minimized, and the aggregated demand profile is as "flat" as it can possibly be. The proposed protocol needs no coordination among the electric vehicles, hence requires low communication and computation capability. Simulation results demonstrate convergence to optimal collections of charging profiles within few iterations.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/cjrzr-pn804Stochastic 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.eduhttps://authors.library.caltech.edu/records/d5316-qwp84Energy-efficient congestion control
https://resolver.caltech.edu/CaltechAUTHORS:20161025-154452155
Authors: {'items': [{'id': 'Gan-Lingwen', 'name': {'family': 'Gan', 'given': 'Lingwen'}}, {'id': 'Walid-A', 'name': {'family': 'Walid', 'given': 'Anwar'}}, {'id': 'Low-S-H', 'name': {'family': 'Low', 'given': 'Steven H.'}, 'orcid': '0000-0001-6476-3048'}]}
Year: 2012
DOI: 10.1145/2254756.2254770
Various link bandwidth adjustment mechanisms are being developed to save network energy. However, their interaction with congestion control can significantly reduce network throughput, and is not well understood. We firstly put forward a framework to study this interaction, and then propose an easily implementable dynamic bandwidth adjustment (DBA) mechanism for the links. In DBA, each link updates its bandwidth according to an integral control law to match its average buffer size with a target buffer size. We prove that DBA reduces link bandwidth without sacrificing throughput---DBA only turns off excess bandwidth---in the presence of congestion control. Preliminary ns2 simulations confirm this result.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/dnr2g-fc688Energy-efficient congestion control
https://resolver.caltech.edu/CaltechAUTHORS:20130109-105014583
Authors: {'items': [{'id': 'Gan-Lingwen', 'name': {'family': 'Gan', 'given': 'Lingwen'}}, {'id': 'Walid-Anwar', 'name': {'family': 'Walid', 'given': 'Anwar'}}, {'id': 'Low-S-H', 'name': {'family': 'Low', 'given': 'Steven H.'}, 'orcid': '0000-0001-6476-3048'}]}
Year: 2012
DOI: 10.1145/2318857.2254770
Various link bandwidth adjustment mechanisms are being
developed to save network energy. However, their interaction
with congestion control can significantly reduce throughput,
and is not well understood. We firstly put forward an easily
implementable link dynamic bandwidth adjustment (DBA)
mechanism, and then study its iteration with congestion control.
In DBA, each link updates its bandwidth according
to an integral control law to match its average buffer size
with a target buffer size. We prove that DBA reduces link
bandwidth without sacrificing throughput-DBA only turns
off excess bandwidth-in the presence of congestion control.
Preliminary ns2 simulations confirm this result.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/dajde-cy387Stochastic distributed protocol for electric vehicle charging with discrete charging rate
https://resolver.caltech.edu/CaltechAUTHORS:20170810-112506562
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: 2012
DOI: 10.1109/PESGM.2012.6344847
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.eduhttps://authors.library.caltech.edu/records/1n3dg-b2s46Some Problems in Demand Side Management
https://resolver.caltech.edu/CaltechAUTHORS:20130815-100621563
Authors: {'items': [{'id': 'Gan-Lingwen', 'name': {'family': 'Gan', 'given': 'Lingwen'}}, {'id': 'Jiang-Libin', 'name': {'family': 'Jiang', 'given': 'Libin'}}, {'id': 'Low-S-H', 'name': {'family': 'Low', 'given': 'Steven'}, 'orcid': '0000-0001-6476-3048'}, {'id': 'Topcu-U', 'name': {'family': 'Topcu', 'given': 'Ufuk'}}, {'id': 'Zhao-Changhong', 'name': {'family': 'Zhao', 'given': 'Changhong'}, 'orcid': '0000-0003-0539-8591'}]}
Year: 2012
We present a sample of problems in demand side
management in future power systems and illustrate how they
can be solved in a distributed manner using local information.
First, we consider a set of users served by a single load-serving
entity (LSE). The LSE procures capacity a day ahead. When
random renewable energy is realized at delivery time, it manages
user load through real-time demand response and purchases
balancing power on the spot market to meet the aggregate
demand. Hence optimal supply procurement by the LSE and the
consumption decisions by the users must be coordinated over two
timescales, a day ahead and in real time, in the presence of supply
uncertainty. Moreover, they must be computed jointly by the
LSE and the users since the necessary information is distributed
among them. We present distributed algorithms to maximize
expected social welfare. Instead of social welfare, the second
problem is to coordinate electric vehicle charging to fill the valleys
in aggregate electric demand profile, or track a given desired
profile. We present synchronous and asynchronous algorithms
and prove their convergence. Finally, we show how loads can
use locally measured frequency deviations to adapt in real time
their demand in response to a shortfall in supply. We design
decentralized demand response mechanism that, together with
the swing equation of the generators, jointly maximize disutility
of demand rationing, in a decentralized manner.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/a5yj9-kj319On the exactness of convex relaxation for optimal power flow in tree networks
https://resolver.caltech.edu/CaltechAUTHORS:20131220-094526108
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'}, 'orcid': '0000-0001-6476-3048'}]}
Year: 2012
DOI: 10.1109/CDC.2012.6426045
The optimal power flow problem is nonconvex, and a convex relaxation has been proposed to solve it. We prove that the relaxation is exact, if there are no upper bounds on the voltage, and any one of some conditions holds. One of these conditions requires that there is no reverse real power flow, and that the resistance to reactance ratio is non-decreasing as transmission lines spread out from the substation to the branch buses. This condition is likely to hold if there are no distributed generators. Besides, avoiding reverse real power flow can be used as rule of thumb for placing distributed generators.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/xqngg-p9h45Branch flow model for radial networks: convex relaxation
https://resolver.caltech.edu/CaltechAUTHORS:20170810-114313789
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'}, 'orcid': '0000-0001-6476-3048'}]}
Year: 2012
Power flow optimization is generally nonlinear and non-convex, and a second-order cone relaxation has been proposed recently for convexification. We prove several sufficient conditions under which the relaxation is exact. One of these conditions seems particularly realistic and suggests guidelines on integrating distributed generations.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/0vwxf-41144An optimization-based demand response in radial distribution networks
https://resolver.caltech.edu/CaltechAUTHORS:20130730-133244823
Authors: {'items': [{'id': 'Li-Na', 'name': {'family': 'Li', 'given': 'Na'}}, {'id': 'Gan-Lingwen', 'name': {'family': 'Gan', 'given': 'Lingwen'}}, {'id': 'Chen-Lijun', 'name': {'family': 'Chen', 'given': 'Lijun'}}, {'id': 'Low-S-H', 'name': {'family': 'Low', 'given': 'Steven H.'}, 'orcid': '0000-0001-6476-3048'}]}
Year: 2012
DOI: 10.1109/GLOCOMW.2012.6477803
Demand response has recently become a topic of active research. Most of work however considers only the balance between aggregate load and supply, and abstracts away the underlying power network and the associated power flow constraints and operating constraints. In this paper, we study demand response in a radial distribution network, by formulating it as an optimal power flow problem that maximizes the aggregate user utilities and minimizes the power line losses, subject to the power flow constraints and operating constraints. As the resulting problem is non-convex and difficult to solve, we propose a convex relaxation that is usually exact for the real-world distribution circuits. We then propose a distributed algorithm for the load-serving entity to set the price signal to coordinate the users' demand response so as to achieve the optimum. Numerical examples show that the proposed algorithm converges fast for real-world distribution systems.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/qtmgt-jpt39Real-time deferrable load control: handling the uncertainties of renewable generation
https://resolver.caltech.edu/CaltechAUTHORS:20161025-161438752
Authors: {'items': [{'id': 'Gan-Lingwen', 'name': {'family': 'Gan', 'given': 'Lingwen'}}, {'id': 'Wierman-A', 'name': {'family': 'Wierman', 'given': 'Adam'}}, {'id': 'Topcu-U', 'name': {'family': 'Topcu', 'given': 'Ufuk'}}, {'id': 'Chen-Niangjun', 'name': {'family': 'Chen', 'given': 'Niangjun'}, 'orcid': '0000-0002-2289-9737'}, {'id': 'Low-S-H', 'name': {'family': 'Low', 'given': 'Steven H.'}, 'orcid': '0000-0001-6476-3048'}]}
Year: 2013
DOI: 10.1145/2487166.2487179
Real-time demand response is essential for handling the uncertainties of renewable generation. Traditionally, demand response has been focused on large industrial and commercial loads, however it is expected that a large number of small residential loads such as air conditioners, dish washers, and electric vehicles will also participate in the coming years. The electricity consumption of these smaller loads, which we call deferrable loads, can be shifted over time, and thus be used (in aggregate) to compensate for the random fluctuations in renewable generation. In this paper, we propose a real-time distributed deferrable load control algorithm to reduce the variance of aggregate load (load minus renewable generation) by shifting the power consumption of deferrable loads to periods with high renewable generation. At every time step, the algorithm minimizes the expected variance to go with updated predictions. We prove that suboptimality of the algorithm vanishes as time horizon expands. Further, we evaluate the algorithm via trace-based simulations.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/m4gqe-7j072Optimal Decentralized Protocol for Electric Vehicle Charging
https://resolver.caltech.edu/CaltechAUTHORS:20131003-094643635
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: 2013
DOI: 10.1109/TPWRS.2012.2210288
We propose a decentralized algorithm to optimally schedule electric vehicle (EV) charging. The algorithm exploits the elasticity of electric vehicle loads to fill the valleys in electric load profiles. We first formulate the EV charging scheduling problem as an optimal control problem, whose objective is to impose a generalized notion of valley-filling, and study properties of optimal charging profiles. We then give a decentralized algorithm to iteratively solve the optimal control problem. In each iteration, EVs update their charging profiles according to the control signal broadcast by the utility company, and the utility company alters the control signal to guide their updates. The algorithm converges to optimal charging profiles (that are as "flat" as they can possibly be) irrespective of the specifications (e.g., maximum charging rate and deadline) of EVs, even if EVs do not necessarily update their charging profiles in every iteration, and use potentially outdated control signal when they update. Moreover, the algorithm only requires each EV solving its local problem, hence its implementation requires low computation capability. We also extend the algorithm to track a given load profile and to real-time implementation.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/6bhnt-fy360Exact convex relaxation for optimal power flow in distribution networks
https://resolver.caltech.edu/CaltechAUTHORS:20161025-153928779
Authors: {'items': [{'id': 'Gan-Lingwen', 'name': {'family': 'Gan', 'given': 'Lingwen'}}, {'id': 'Li-Na', 'name': {'family': 'Li', 'given': 'Na'}}, {'id': 'Low-S-H', 'name': {'family': 'Low', 'given': 'Steven H.'}, 'orcid': '0000-0001-6476-3048'}, {'id': 'Topcu-U', 'name': {'family': 'Topcu', 'given': 'Ufuk'}}]}
Year: 2013
DOI: 10.1145/2494232.2465535
The optimal power flow (OPF) problem seeks to control the power generation/consumption to minimize the generation cost, and is becoming important for distribution networks. OPF is nonconvex and a second-order cone programming (SOCP) relaxation has been proposed to solve it. We prove that after a "small" modification to OPF, the SOCP relaxation is exact under a "mild" condition. Empirical studies demonstrate that the modification to OPF is "small" and that the "mild" condition holds for all test networks, including the IEEE 13-bus test network and practical networks with high penetration of distributed generation.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/agta3-mdn57Exact Convex Relaxation for Optimal Power Flow in Distribution Networks
https://resolver.caltech.edu/CaltechAUTHORS:20131008-160444682
Authors: {'items': [{'id': 'Gan-Lingwen', 'name': {'family': 'Gan', 'given': 'Lingwen'}}, {'id': 'Li-Na', 'name': {'family': 'Li', 'given': 'Na'}}, {'id': 'Low-S-H', 'name': {'family': 'Low', 'given': 'Steven H.'}, 'orcid': '0000-0001-6476-3048'}, {'id': 'Topcu-U', 'name': {'family': 'Topcu', 'given': 'Ufuk'}}]}
Year: 2013
DOI: 10.1145/2494232.2465535
The optimal power flow (OPF) problem seeks to control the
power generation/consumption to minimize the generation
cost, and is becoming important for distribution networks.
OPF is nonconvex and a second-order cone programming
(SOCP) relaxation has been proposed to solve it. We prove
that after a "small" modification to OPF, the SOCP relaxation is exact under a "mild" condition. Empirical studies
demonstrate that the modification to OPF is "small" and
that the "mild" condition holds for all test networks, including the IEEE 13-bus test network and practical networks
with high penetration of distributed generation.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/2d15y-8ry21Optimal power flow in tree networks
https://resolver.caltech.edu/CaltechAUTHORS:20170810-113418095
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: 2013
DOI: 10.1109/CDC.2013.6760226
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.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/16qrb-p1t76Optimal Power Flow in Direct Current Networks
https://resolver.caltech.edu/CaltechAUTHORS:20170810-113122736
Authors: {'items': [{'id': 'Gan-Lingwen', 'name': {'family': 'Gan', 'given': 'Lingwen'}}, {'id': 'Low-S-H', 'name': {'family': 'Low', 'given': 'Steven H.'}, 'orcid': '0000-0001-6476-3048'}]}
Year: 2013
DOI: 10.1109/CDC.2013.6760774
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. Direct current (DC) networks (e.g., DC-microgrids) are promising to incorporate distributed generation. This paper focuses on the OPF problem in DC networks. The OPF problem is nonconvex, and we study solving it via a second-order cone programming (SOCP) relaxation. In particular, we prove that the SOCP relaxation is exact if there are no voltage upper bounds, and that the SOCP relaxation has at most one solution if it is exact.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/1dyvw-6kd28Chordal relaxation of OPF for multiphase radial networks
https://resolver.caltech.edu/CaltechAUTHORS:20150203-145330203
Authors: {'items': [{'id': 'Gan-Lingwen', 'name': {'family': 'Gan', 'given': 'Lingwen'}}, {'id': 'Low-S-H', 'name': {'family': 'Low', 'given': 'Steven H.'}, 'orcid': '0000-0001-6476-3048'}]}
Year: 2014
DOI: 10.1109/ISCAS.2014.6865509
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.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/szyhw-g8827Convexification of AC optimal power flow
https://resolver.caltech.edu/CaltechAUTHORS:20170123-174612725
Authors: {'items': [{'id': 'Gan-Lingwen', 'name': {'family': 'Gan', 'given': 'Lingwen'}}, {'id': 'Low-S-H', 'name': {'family': 'Low', 'given': 'Steven H.'}, 'orcid': '0000-0001-6476-3048'}]}
Year: 2014
DOI: 10.1109/PSCC.2014.7038373
This overview paper summarizes the key elements of semidefinite relaxations of the optimal power flow problem, and discusses several open challenges.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/qy345-88r41Convex relaxations and linear approximation for optimal power flow in multiphase radial networks
https://resolver.caltech.edu/CaltechAUTHORS:20170810-114020714
Authors: {'items': [{'id': 'Gan-Lingwen', 'name': {'family': 'Gan', 'given': 'Lingwen'}}, {'id': 'Low-S-H', 'name': {'family': 'Low', 'given': 'Steven H.'}, 'orcid': '0000-0001-6476-3048'}]}
Year: 2014
DOI: 10.1109/PSCC.2014.7038399
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.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/1fcqw-beg37Dynamical bandwidth adjustment of a link in a data network
https://resolver.caltech.edu/CaltechAUTHORS:20170810-113125473
Authors: {'items': [{'id': 'Walid-Angwar-I', 'name': {'family': 'Walid', 'given': 'Anwar I.'}}, {'id': 'Gan-Lingwen', 'name': {'family': 'Gan', 'given': 'Lingwen'}}, {'id': 'Low-S-H', 'name': {'family': 'Low', 'given': 'Steven'}, 'orcid': '0000-0001-6476-3048'}]}
Year: 2014
An apparatus includes a first node configured to receive the data packets from a plurality of source nodes of the data network and to selectively route some of the received data packets to a link via a port of the first node. The apparatus also includes a link-input buffer that is located in the first node and is configured to store the some of the received data packets for transmission to the link via the port. The first node is configured to power off hardware for transmitting received data packets to the link in response to a fill level of the link-input buffer being below a threshold.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/swyj7-wzp22Optimal Power Flow in Direct Current Networks
https://resolver.caltech.edu/CaltechAUTHORS:20141205-135843283
Authors: {'items': [{'id': 'Gan-Lingwen', 'name': {'family': 'Gan', 'given': 'Lingwen'}}, {'id': 'Low-S-H', 'name': {'family': 'Low', 'given': 'Steven H.'}, 'orcid': '0000-0001-6476-3048'}]}
Year: 2014
DOI: 10.1109/TPWRS.2014.2313514
The optimal power flow (OPF) problem determines power generations/demands that minimize a certain objective such as generation cost or power loss. It is non-convex and NP-hard in general. In this paper, we study the OPF problem in direct current (DC) networks. A second-order cone programming (SOCP) relaxation is considered for solving the OPF problem. We prove that the SOCP relaxation is exact if either 1) voltage upper bounds do not bind; or 2) voltage upper bounds are uniform and power injection lower bounds are negative. Based on 1), a modified OPF problem is proposed, whose corresponding SOCP is guaranteed to be exact. We also prove that SOCP has at most one optimal solution if it is exact. Finally, we discuss how to improve numerical stability and how to include line constraints.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/zf7qf-8jb24Distributional analysis for model predictive deferrable load control
https://resolver.caltech.edu/CaltechAUTHORS:20170810-105540217
Authors: {'items': [{'id': 'Chen-Niangjun', 'name': {'family': 'Chen', 'given': 'Niangjun'}, 'orcid': '0000-0002-2289-9737'}, {'id': 'Gan-Lingwen', 'name': {'family': 'Gan', 'given': 'Lingwen'}}, {'id': 'Low-S-H', 'name': {'family': 'Low', 'given': 'Steven H.'}, 'orcid': '0000-0001-6476-3048'}, {'id': 'Wierman-A', 'name': {'family': 'Wierman', 'given': 'Adam'}}]}
Year: 2014
DOI: 10.1109/CDC.2014.7040398
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. Though the average-case performance of model predictive deferrable load control has been analyzed in prior works, the distribution of the performance has been elusive. In this paper, we prove strong concentration results on the load variation obtained by model predictive deferrable load control. These results highlight that the typical performance of model predictive deferrable load control is tightly concentrated around the average-case performance.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/10c4g-rc417Exact Convex Relaxation of Optimal Power Flow in Radial Networks
https://resolver.caltech.edu/CaltechAUTHORS:20150203-084513340
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: 2015
DOI: 10.1109/TAC.2014.2332712
The optimal power flow (OPF) problem determines a network operating point that minimizes a certain objective such as generation cost or power loss. It is nonconvex. We prove that a global optimum of OPF can be obtained by solving a second-order cone program, under a mild condition after shrinking the OPF feasible set slightly, for radial power networks. The condition can be checked a priori, and holds for the IEEE 13, 34, 37, 123-bus networks and two real-world networks.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/7byye-f8609Systems and Methods for Convex Relaxations and Linear Approximations for Optimal Power Flow in Multiphase Radial Networks
https://resolver.caltech.edu/CaltechAUTHORS:20170810-114535705
Authors: {'items': [{'id': 'Gan-Lingwen', 'name': {'family': 'Gan', 'given': 'Lingwen'}}, {'id': 'Low-S-H', 'name': {'family': 'Low', 'given': 'Steven H.'}, 'orcid': '0000-0001-6476-3048'}]}
Year: 2015
Centralized node controllers in accordance with embodiments of the invention enable linear approximation of optimal power flow. One embodiment includes a centralized node controller including: a network interface, a processor, and a memory containing: a centralized power control application a network topology, where the network is multiphase unbalanced and comprises a plurality of connected nodes; wherein the processor is configured by the centralized controller application to: request node operating parameters from the plurality of connected nodes; calculate network operating parameters using a linear approximation of optimal power flow and the node operating parameters from the plurality of connected nodes; send network operating parameters to the plurality of connected nodes.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/s2r8t-0h109Distributed Gradient Descent for Solving Optimal Power Flow in Radial Networks
https://resolver.caltech.edu/CaltechAUTHORS:20170810-114246561
Authors: {'items': [{'id': 'Gan-Lingwen', 'name': {'family': 'Gan', 'given': 'Lingwen'}}, {'id': 'Low-S-H', 'name': {'family': 'Low', 'given': 'Steven H.'}, 'orcid': '0000-0001-6476-3048'}]}
Year: 2016
Node controllers and power distribution networks in accordance with embodiments of the invention enable distributed power control, One embodiment includes a node controller comprising a memory containing: a plurality of node operating parameters; and a plurality of node operating parameters describing operating parameters for a set of at least one node selected from the group consisting of at least one downstream node and at least one upstream node; wherein the processor is configured by the node controller application to: receive and store in memory a plurality of coordinator parameters describing operating parameters of a node coordinator by the network interface; and calculate updated node operating parameters using an iterative gradient projection process to determine updated node parameters using node operating parameters that describe operating parameters of node and operating parameters of the set of at least one node, where each iteration is determined by the coordinator parameters.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/kapyv-n6202An Online Gradient Algorithm for Optimal Power Flow on Radial Networks
https://resolver.caltech.edu/CaltechAUTHORS:20160426-075434882
Authors: {'items': [{'id': 'Gan-Lingwen', 'name': {'family': 'Gan', 'given': 'Lingwen'}}, {'id': 'Low-S-H', 'name': {'family': 'Low', 'given': 'Steven H.'}, 'orcid': '0000-0001-6476-3048'}]}
Year: 2016
DOI: 10.1109/JSAC.2016.2525598
We propose an online algorithm for solving optimal power flow (OPF) problems on radial networks where the controllable devices continuously interact with the network that implicitly computes a power flow solution given a control action. Collectively the controllable devices and the network implement a gradient projection algorithm for the OPF problem in real time. The key design feature that enables this approach is that the intermediate iterates of our algorithm always satisfy power flow equations and operational constraints. This is achieved by explicitly exploiting the network to implicitly solve power flow equations for us in real time at scale. We prove that the proposed algorithm converges to the set of local optima and provide sufficient conditions under which it converges to a global optimum. We derive an upper bound on the suboptimality gap of any local optimum. This bound suggests that any local minimum is almost as good as any strictly feasible point. We explain how to greatly reduce the gradient computation in each iteration by using approximate gradient derived from linearized power flow equations. Numerical results on test networks, ranging from 42-bus to 1990-bus, show a great speedup over a second-order cone relaxation method with negligible difference in objective values.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/hb1hg-80v18Exact 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.eduhttps://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.eduhttps://authors.library.caltech.edu/records/1caq0-gv292