The short-term forecasting of real-time locational marginal price (LMP) and network congestion is considered from a system operator perspective. A new probabilistic forecasting technique is proposed based on a multiparametric programming formulation that partitions the uncertainty parameter space into critical regions from which the conditional probability distribution of the real-time LMP congestion is obtained. The proposed method incorporates load generation forecast, time varying operation constraints, and contingency models. By shifting the computation cost associated with multiparametric programs offline, the online computation cost is significantly reduced. An online simulation technique by generating critical regions dynamically is also proposed, which results in several orders of magnitude improvement in the computational cost over standard Monte Carlo methods.
The authors of @cite_4 introduce and exploit the decomposition of a multi-dimensional load space into critical regions (called system pattern regions) that are estimated using historical data The estimated critical regions are therefore random quantities. . The work in @cite_4 aims to address the following issue: Given a possible future point @math in a multi-dimensional load space, what is the probability distribution of the estimated critical regions that contain @math ? Since each critical region corresponds to a specific LMP congestion, the technique in @cite_4 gives a heuristic estimate of the probability distribution of LMP congestion by conditioning on load @math at some future point in time.
@cite_4
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We consider the problem of resource allocation in downlink OFDMA systems for multi service and unknown environment. Due to users' mobility and intercell interference, the base station cannot predict neither the Signal to Noise Ratio (SNR) of each user in future time slots nor their probability distribution functions. In addition, the traffic is bursty in general with unknown arrival. The probability distribution functions of the SNR, channel state and traffic arrival density are then unknown. Achieving a multi service Quality of Service (QoS) while optimizing the performance of the system (e.g. total throughput) is a hard and interesting task since it depends on the unknown future traffic and SNR values. In this paper we solve this problem by modeling the multiuser queuing system as a discrete time linear dynamic system. We develop a robust H∞ controller to regulate the queues of different users. The queues and Packet Drop Rates (PDR) are controlled by proposing a minimum data rate according to the demanded service type of each user. The data rate vector proposed by the controller is then fed as a constraint to an instantaneous resource allocation framework. This instantaneous problem is formulated as a convex optimization problem for instantaneous subcarrier and power allocation decisions. Simulation results show small delays and better fairness among users. In power market studies, the forecast of locational marginal price (LMP) relies on the load forecasting results from the viewpoint of planning. It is well known that short-term load forecasting results always carry certain degree of errors mainly due to the random nature of the load. At the same time, LMP step changes occur at critical load levels (CLLs). Therefore, it is interesting to investigate the impact of load forecasting uncertainty on LMP. With the assumption of a certain probability distribution of the actual load, this paper proposes the concept of probabilistic LMP and formulates the probability mass function of this random variable. The expected value of probabilistic LMP is then derived, as well as the lower and upper bound of its sensitivity. In addition, two useful curves, alignment probability of deterministic LMP versus forecasted load and expected value of probabilistic LMP versus forecasted load, are presented. The first curve is designed to identify the probability that the forecasted price in a deterministic LMP matches the actual price at the forecasted load level. The second curve is demonstrated to be smooth and therefore eliminates the step changes in deterministic LMP forecasting. This helps planners avoid the possible sharp changes during decision-making process. The proposed concept and method are illustrated with a modified PJM five-bus system and the IEEE 118-bus system. Given a visual history, multiple future outcomes for a video scene are equally probable, in other words, the distribution of future outcomes has multiple modes. Multimodality is notoriously hard to handle by standard regressors or classifiers: the former regress to the mean and the latter discretize a continuous high dimensional output space. In this work, we present stochastic neural network architectures that handle such multimodality through stochasticity: future trajectories of objects, body joints or frames are represented as deep, non-linear transformations of random (as opposed to deterministic) variables. Such random variables are sampled from simple Gaussian distributions whose means and variances are parametrized by the output of convolutional encoders over the visual history. We introduce novel convolutional architectures for predicting future body joint trajectories that outperform fully connected alternatives DBLP:journals corr WalkerDGH16 . We introduce stochastic spatial transformers through optical flow warping for predicting future frames, which outperform their deterministic equivalents DBLP:journals corr PatrauceanHC15 . Training stochastic networks involves an intractable marginalization over stochastic variables. We compare various training schemes that handle such marginalization through a) straightforward sampling from the prior, b) conditional variational autoencoders NIPS2015_5775,DBLP:journals corr WalkerDGH16 , and, c) a proposed K-best-sample loss that penalizes the best prediction under a fixed "prediction budget". We show experimental results on object trajectory prediction, human body joint trajectory prediction and video prediction under varying future uncertainty, validating quantitatively and qualitatively our architectural choices and training schemes. In this work we consider the problem of an optimal geographic placement of content in wireless cellular networks modelled by Poisson point processes. Specifically, for the typical user requesting some particular content and whose popularity follows a given law (e.g. Zipf), we calculate the probability of finding the content cached in one of the base stations. Wireless coverage follows the usual signal-to-interference-and noise ratio (SINR) model, or some variants of it. We formulate and solve the problem of an optimal randomized content placement policy, to maximize the user's hit probability. The result dictates that it is not always optimal to follow the standard policy “cache the most popular content, everywhere”. In fact, our numerical results regarding three different coverage scenarios, show that the optimal policy significantly increases the chances of hit under high-coverage regime, i.e., when the probabilities of coverage by more than just one station are high enough.