Multiple Timescale Dispatch and Scheduling for Stochastic Reliability in Smart Grids with Wind Generation Integration

Integrating volatile renewable energy resources into the bulk power grid is challenging, due to the reliability requirement that at each instant the load and generation in the system remain balanced. In this study, we tackle this challenge for smart grid with integrated wind generation, by leveraging multi-timescale dispatch and scheduling. Specifically, we consider smart grids with two classes of energy users - traditional energy users and opportunistic energy users (e.g., smart meters or smart appliances), and investigate pricing and dispatch at two timescales, via day-ahead scheduling and realtime scheduling. In day-ahead scheduling, with the statistical information on wind generation and energy demands, we characterize the optimal procurement of the energy supply and the day-ahead retail price for the traditional energy users; in realtime scheduling, with the realization of wind generation and the load of traditional energy users, we optimize real-time prices to manage the opportunistic energy users so as to achieve systemwide reliability. More specifically, when the opportunistic users are non-persistent, i.e., a subset of them leave the power market when the real-time price is not acceptable, we obtain closedform solutions to the two-level scheduling problem. For the persistent case, we treat the scheduling problem as a multitimescale Markov decision process. We show that it can be recast, explicitly, as a classic Markov decision process with continuous state and action spaces, the solution to which can be found via standard techniques. We conclude that the proposed multi-scale dispatch and scheduling with real-time pricing can effectively address the volatility and uncertainty of wind generation and energy demand, and has the potential to improve the penetration of renewable energy into smart grids.Comment: Submitted to IEEE Infocom 2011. Contains 10 pages and 4 figures. Replaces the previous arXiv submission (dated Aug-23-2010) with the same titl

Multiuser Scheduling in a Markov-modeled Downlink using Randomly Delayed ARQ Feedback

We focus on the downlink of a cellular system, which corresponds to the bulk of the data transfer in such wireless systems. We address the problem of opportunistic multiuser scheduling under imperfect channel state information, by exploiting the memory inherent in the channel. In our setting, the channel between the base station and each user is modeled by a two-state Markov chain and the scheduled user sends back an ARQ feedback signal that arrives at the scheduler with a random delay that is i.i.d across users and time. The scheduler indirectly estimates the channel via accumulated delayed-ARQ feedback and uses this information to make scheduling decisions. We formulate a throughput maximization problem as a partially observable Markov decision process (POMDP). For the case of two users in the system, we show that a greedy policy is sum throughput optimal for any distribution on the ARQ feedback delay. For the case of more than two users, we prove that the greedy policy is suboptimal and demonstrate, via numerical studies, that it has near optimal performance. We show that the greedy policy can be implemented by a simple algorithm that does not require the statistics of the underlying Markov channel or the ARQ feedback delay, thus making it robust against errors in system parameter estimation. Establishing an equivalence between the two-user system and a genie-aided system, we obtain a simple closed form expression for the sum capacity of the Markov-modeled downlink. We further derive inner and outer bounds on the capacity region of the Markov-modeled downlink and tighten these bounds for special cases of the system parameters.Comment: Contains 22 pages, 6 figures and 8 tables; revised version including additional analytical and numerical results; work submitted, Feb 2010, to IEEE Transactions on Information Theory, revised April 2011; authors can be reached at [email protected]/[email protected]/[email protected]

Scheduling with Rate Adaptation under Incomplete Knowledge of Channel/Estimator Statistics

In time-varying wireless networks, the states of the communication channels are subject to random variations, and hence need to be estimated for efficient rate adaptation and scheduling. The estimation mechanism possesses inaccuracies that need to be tackled in a probabilistic framework. In this work, we study scheduling with rate adaptation in single-hop queueing networks under two levels of channel uncertainty: when the channel estimates are inaccurate but complete knowledge of the channel/estimator joint statistics is available at the scheduler; and when the knowledge of the joint statistics is incomplete. In the former case, we characterize the network stability region and show that a maximum-weight type scheduling policy is throughput-optimal. In the latter case, we propose a joint channel statistics learning - scheduling policy. With an associated trade-off in average packet delay and convergence time, the proposed policy has a stability region arbitrarily close to the stability region of the network under full knowledge of channel/estimator joint statistics.Comment: 48th Allerton Conference on Communication, Control, and Computing, Monticello, IL, Sept. 201

Exploiting channel memory for joint estimation and scheduling in downlink networks

We address the problem of opportunistic multiuser scheduling in downlink networks with Markov-modeled outage channels. We consider the scenario in which the scheduler does not have full knowledge of the channel state information, but instead estimates the channel state information by exploiting the memory inherent in the Markov channels along with ARQ-styled feedback from the scheduled users. Opportunistic scheduling is optimized in two stages: (1) Channel estimation and rate adaptation to maximize the expected immediate rate of the scheduled user; (2) User scheduling, based on the optimized immediate rate, to maximize the overall long term sum-throughput of the downlink. The scheduling problem is a partially observable Markov decision process with the classic ‘exploitation vs exploration ’ trade-off that is difficult to quantify. We therefore study the problem in the framework of restless multi-armed bandit processes and perform a Whit-tle’s indexability analysis. Whittle’s indexability is traditionally known to be hard to establish and the index policy derived based on Whittle’s indexability is known to have optimality properties in various settings. We show that the problem of downlink scheduling under imperfect channel state information is Whittle indexable and derive the Whittle’s index policy in closed form. Via extensive numerical experiments, we show that the index policy has near-optimal performance. Our work reveals that, under incomplete channel state infor-mation, exploiting channel memory for opportunistic scheduling can result in significant performance gains and that almost all of these gains can be realized using an easy-to-implement index policy