arXiv subjects

Lang Tong

Publications and source records attributed to Lang Tong.

At least 91 records · Page 5Linked to original sources

arXiv2016

Coordinated Multi-area Economic Dispatch via Critical Region Projection

A coordinated economic dispatch method for multi-area power systems is proposed. Choosing boundary phase angles as coupling variables, the proposed method exploits the structure of critical regions in local problems defined by active and inactive constraints. For a fixed boundary state given by the coordinator, local operators compute the coefficients of critical regions containing the boundary state and of the optimal cost functions then communicate them to the coordinator who in turn optimizes the boundary state to minimize the overall cost. By iterating between local operators and the coordinator, the proposed algorithm converges to the global optimal solution in finite steps, and it requires limited information sharing.

math.OC↗

arXiv2016

Large-scale Charging of Electric Vehicles: A Multi-Armed Bandit Approach

The successful launch of electric vehicles (EVs) depends critically on the availability of convenient and economic charging facilities. The problem of scheduling of large-scale charging of EVs by a service provider is considered. A Markov decision process model is introduced in which EVs arrive randomly at a charging facility with random demand and completion deadlines. The service provider faces random charging costs, convex non-completion penalties, and a peak power constraint that limits the maximum number of simultaneous activation of EV chargers. Formulated as a restless multi-armed bandit problem, the EV charging problem is shown to be indexable. A closed-form expression of the Whittle's index is obtained for the case when the charging costs are constant. The Whittle's index policy, however, is not optimal in general. An enhancement of the Whittle's index policy based on spatial interchange according to the less laxity and longer processing time principle is presented. The proposed policy outperforms existing charging algorithms, especially when the charging costs are time varying.

math.OC↗

arXiv2016

Online Learning and Optimization of Markov Jump Affine Models

The problem of online learning and optimization of unknown Markov jump affine models is considered. An online learning policy, referred to as Markovian simultaneous perturbations stochastic approximation (MSPSA), is proposed for two different optimization objectives: (i) the quadratic cost minimization of the regulation problem and (ii) the revenue (profit) maximization problem. It is shown that the regret of MSPSA grows at the order of the square root of the learning horizon. Furthermore, by the use of van Trees inequality, it is shown that the regret of any policy grows no slower than that of MSPSA, making MSPSA an order optimal learning policy. In addition, it is also shown that the MSPSA policy converges to the optimal control input almost surely as well as in the mean square sense. Simulation results are presented to illustrate the regret growth rate of MSPSA and to show that MSPSA can offer significant gain over the greedy certainty equivalent approach.

cs.IT↗

arXiv2016

Dynamic Pricing and Distributed Energy Management for Demand Response

The problem of dynamic pricing of electricity in a retail market is considered. A Stackelberg game is used to model interactions between a retailer and its customers; the retailer sets the day-ahead hourly price of electricity and consumers adjust real-time consumptions to maximize individual consumer surplus. For thermostatic demands, the optimal aggregated demand is shown to be an affine function of the day-ahead hourly price. A complete characterization of the trade-offs between consumer surplus and retail profit is obtained. The Pareto front of achievable trade-offs is shown to be concave, and each point on the Pareto front is achieved by an optimal day-ahead hourly price. Effects of integrating renewables and local storage are analyzed. It is shown that benefits of renewable integration all go to the retailer when the capacity of renewable is relatively small. As the capacity increases beyond a certain threshold, the benefit from renewable that goes to consumers increases.

math.OC↗

arXiv2016

Dynamic Scheduling for Charging Electric Vehicles: A Priority Rule

We consider the scheduling of multiple tasks with pre-determined deadlines under random processing cost. This problem is motivated by the potential of large scale adoption of plug-in (hybrid) electric vehicles (PHEVs) in the near future. The charging requests of PHEVs usually have deadline constraints, and the electricity cost associated with PHEV charging is usually random due to the uncertainty in both system load and renewable generation. We seek to properly schedule the battery charging of multiple PHEVs so as to minimize the overall cost, which is derived from the total charging cost and the penalty for not completing charging before requested deadlines. Through a dynamic programming formulation, we establish the Less Laxity and Longer remaining Processing time (LLLP) principle that improves any charging policy on a sample-path basis, when the non-completion penalty is a convex function of the additional time needed to fulfill the uncompleted request. Specifically, the LLLP principle states that priority should be given to vehicles that have less laxity and longer remaining processing times. Numerical results demonstrate that heuristic policies that violate the LLLP principle, for example, the earliest deadline first (EDF) policy, can result in significant performance loss.

math.OC↗

arXiv2016

Renewables and Storage in Distribution Systems: Centralized vs. Decentralized Integration

The problem of integrating renewables and storage into a distribution network is considered under two integration models: (i) a centralized model involving a retail utility that owns the integration as part of its portfolio of energy resources, and (ii) a decentralized model in which each consumer individually owns and operates the integration and is capable of selling surplus electricity back to the retailer in a net-metering setting. The two integration models are analyzed using a Stackelberg game in which the utility is the leader in setting the retail price of electricity, and each consumer schedules its demand by maximizing individual consumer surplus. The solution of the Stackelberg game defines the Pareto front that characterizes fundamental trade-offs between retail profit of the utility and consumer surplus. It is shown that, for both integration models, the centralized integration uniformly improves retail profit. As the level of integration increases, the proportion of benefits goes to the consumers increases. In contrast, the consumer-based decentralized integration improves consumer surplus at the expense of retail profit of the utility. For a profit regulated utility, the consumer based integration may lead to smaller consumer surplus than that when no renewable or storage is integrated at either the consumer or the retailer end.

math.OC↗

arXiv2016

Stochastic Interchange Scheduling in the Real-Time Electricity Market

The problem of multi-area interchange scheduling in the presence of stochastic generation and load is considered. A new interchange scheduling technique based on a two-stage stochastic minimization of overall expected operating cost is proposed. Because directly solving the stochastic optimization is intractable, an equivalent problem that maximizes the expected social welfare is formulated. The proposed technique leverages the operator's capability of forecasting locational marginal prices (LMPs) and obtains the optimal interchange schedule without iterations among operators.

eess.SY↗

arXiv2015

Market Dynamics and Indirect Network Effects in Electric Vehicle Diffusion

The diffusion of electric vehicles (EVs) is studied in a two-sided market framework consisting of EVs on the one side and EV charging stations (EVCSs) on the other. A sequential game is introduced as a model for the interactions between an EVCS investor and EV consumers. A consumer chooses to purchase an EV or a conventional gasoline alternative based on the upfront costs of purchase, the future operating costs and the availability of charging stations. The investor, on the other hand, maximizes his profit by deciding whether to build charging facilities at a set of potential EVCS sites or to defer his investments. The solution of the sequential game characterizes the EV-EVCS market equilibrium. The market solution is compared with that of a social planner who invests in EVCSs with the goal of maximizing the social welfare. It is shown that the market solution underinvests EVCSs, leading to slower EV diffusion. The effects of subsidies for EV purchase and EVCSs are also considered.

econ.GN↗

arXiv2015

Estimation after Parameter Selection: Performance Analysis and Estimation Methods

In many practical parameter estimation problems, prescreening and parameter selection are performed prior to estimation. In this paper, we consider the problem of estimating a preselected unknown deterministic parameter chosen from a parameter set based on observations according to a predetermined selection rule, $Ψ$. The data-based parameter selection process may impact the subsequent estimation by introducing a selection bias and creating coupling between decoupled parameters. This paper introduces a post-selection mean squared error (PSMSE) criterion as a performance measure. A corresponding Cramér-Rao-type bound on the PSMSE of any $Ψ$-unbiased estimator is derived, where the $Ψ$-unbiasedness is in the Lehmann-unbiasedness sense. The post-selection maximum-likelihood (PSML) estimator is presented .It is proved that if there exists an $Ψ$-unbiased estimator that achieves the $Ψ$-Cramér-Rao bound (CRB), i.e. an $Ψ$-efficient estimator, then it is produced by the PSML estimator. In addition, iterative methods are developed for the practical implementation of the PSML estimator. Finally, the proposed $Ψ$-CRB and PSML estimator are examined in estimation after parameter selection with different distributions.

cs.IT↗

arXiv2014

PMU based Detection of Imbalance in Three-Phase Power Systems

The problem of imbalance detection in a three-phase power system using a phasor measurement unit (PMU) is considered. A general model for the zero, positive, and negative sequences from a PMU measurement at off-nominal frequencies is presented and a hypothesis testing framework is formulated. The new formulation takes into account the fact that minor degree of imbalance in the system is acceptable and does not indicate subsequent interruptions, failures, or degradation of physical components. A generalized likelihood ratio test (GLRT) is developed and shown to be a function of the negative-sequence phasor estimator and the acceptable level of imbalances for nominal system operations. As a by-product to the proposed detection method, a constrained estimation of the positive and negative phasors and the frequency deviation is obtained for both balanced and unbalanced situations. The theoretical and numerical performance analyses show improved performance over benchmark techniques and robustness to the presence of additional harmonics.

stat.AP↗

arXiv2014

Subspace Methods for Data Attack on State Estimation: A Data Driven Approach

Data attacks on state estimation modify part of system measurements such that the tempered measurements cause incorrect system state estimates. Attack techniques proposed in the literature often require detailed knowledge of system parameters. Such information is difficult to acquire in practice. The subspace methods presented in this paper, on the other hand, learn the system operating subspace from measurements and launch attacks accordingly. Conditions for the existence of an unobservable subspace attack are obtained under the full and partial measurement models. Using the estimated system subspace, two attack strategies are presented. The first strategy aims to affect the system state directly by hiding the attack vector in the system subspace. The second strategy misleads the bad data detection mechanism so that data not under attack are removed. Performance of these attacks are evaluated using the IEEE 14-bus network and the IEEE 118-bus network.

cs.CR↗

arXiv2014

Data Framing Attack on State Estimation

A new mechanism aimed at misleading a power system control center about the source of a data attack is proposed. As a man-in-the-middle state attack, a data framing attack is proposed to exploit the bad data detection and identification mechanisms currently in use at most control centers. In particular, the proposed attack frames meters that are providing correct data as sources of bad data such that the control center will remove useful measurements that would otherwise be used by the state estimator. The optimal design of a data framing attack is formulated as a quadratically constrained quadratic program (QCQP). It is shown that the proposed attack is capable of perturbing the power system state estimate by an arbitrary degree controlling only half of a critical set of measurements that are needed to make a system unobservable. Implications of this attack on power system operations are discussed, and the attack performance is evaluated using benchmark systems.

cs.CR↗

arXiv2014

An online learning approach to dynamic pricing for demand response

In this paper, the problem of optimal dynamic pricing for retail electricity with an unknown demand model is considered. Under the day-ahead dynamic pricing (a.k.a. real time pricing) mechanism, a retailer obtains electricity in a twosettlement wholesale market and serves its customers in real time. Without knowledge on the aggregated demand function of its customers, the retailer aims to maximize its retail surplus by sequentially adjusting its price based on the behavior of its customers in the past. An online learning algorithm, referred to as piecewise linear stochastic approximation (PWLSA), is proposed. It is shown that PWLSA achieves the optimal rate of learning defined by the growth rate of cumulative regret. In particular, the regret of PWLSA is shown to grow logarithmically with respect to the learning horizon, and no other on-line learning algorithm can have the growth rate slower than that of PWLSA. Simulation studies are presented using traces of actual day-ahead prices, and PWLSA compares favorably under both static and dynamically changing parameters.

math.OC↗

arXiv2013

A Subspace Technique for The Identification of Switched Affine Models

The problem of estimating parameters of switched affine systems with noisy input-output observations is considered. The switched affine models is transformed into a switched linear one by removing its intersection subspace, which is estimated from observations. A subspace technique is proposed to exploit the observations' permutation structure, which transforms the problem of associating observations with subsystems into one of de-permutating a block diagonal matrix, referred as adjacency matrix. Then a normalized spectral clustering algorithm is presented to recover the block structure of adjacency matrix, from which each observation is related to a particular subsystem. With the labelled observations, parameters of the submodel are estimated via the total least squares (TLS) estimator. The proposed technique is applicable to switched affine systems with arbitrarily shaped domain partitions, and it offers significantly improved performance and lowered computation complexity than existing techniques.

stat.ME↗

arXiv2013

Impact of Data Quality on Real-Time Locational Marginal Price

The problem of characterizing impacts of data quality on real-time locational marginal price (LMP) is considered. Because the real-time LMP is computed from the estimated network topology and system state, bad data that cause errors in topology processing and state estimation affect real-time LMP. It is shown that the power system state space is partitioned into price regions of convex polytopes. Under different bad data models, the worst case impacts of bad data on real-time LMP are analyzed. Numerical simulations are used to illustrate worst case performance for IEEE-14 and IEEE-118 networks.

math.NA↗

arXiv2013

Spectral Clustering on Subspace for Parameter Estimation of Jump Linear Models

The problem of estimating parameters of a deterministic jump or piecewise linear model is considered. A subspace technique referred to as spectral clustering on subspace (SCS) algorithm is proposed to estimate a set of linear model parameters, the model input, and the set of switching epochs. The SCS algorithm exploits a block diagonal structure of the system input subspace, which partitions the observation space into separate subspaces, each corresponding to one and only one linear submodel. A spectral clustering technique is used to label the noisy observations for each submodel, which generates estimates of switching time epoches. A total least squares technique is used to estimate model parameters and the model input. It is shown that, in the absence of observation noise, the SCS algorithm provides exact parameter identification. At high signal to noise ratios, SCS attains a clairvoyant Cramér-Rao bound computed by assuming the labeling of observation samples is perfect.

stat.ME↗

arXiv2013

Maximum Likelihood Fusion of Stochastic Maps

The fusion of independently obtained stochastic maps by collaborating mobile agents is considered. The proposed approach includes two parts: matching of stochastic maps and maximum likelihood alignment. In particular, an affine invariant hypergraph is constructed for each stochastic map, and a bipartite matching via a linear program is used to establish landmark correspondence between stochastic maps. A maximum likelihood alignment procedure is proposed to determine rotation and translation between common landmarks in order to construct a global map within a common frame of reference. A main feature of the proposed approach is its scalability with respect to the number of landmarks: the matching step has polynomial complexity and the maximum likelihood alignment is obtained in closed form. Experimental validation of the proposed fusion approach is performed using the Victoria Park benchmark dataset.

stat.AP↗

arXiv2013

Distributed Learning and Multiaccess of On-Off Channels

The problem of distributed access of a set of N on-off channels by K<N users is considered. The channels are slotted and modeled as independent but not necessarily identical alternating renewal processes. Each user decides to either observe or transmit at the beginning of every slot. A transmission is successful only if the channel is at the on state and there is only one user transmitting. When a user observes, it identifies whether a transmission would have been successful had it decided to transmit. A distributed learning and access policy referred to as alternating sensing and access (ASA) is proposed. It is shown that ASA has finite expected regret when compared with the optimal centralized scheme with fixed channel allocation.

math.OC↗