Accurate forecasts of electrical substations are mandatory for the efficiency of the Advanced Distribution Automation functions in distribution systems. The paper describes the design of a class of machine-learning models, namely neural networks, for the load forecasts of medium-voltage/low-voltage substations. We focus on the methodology of neural network model design in order to obtain a model that has the best achievable predictive ability given the available data. Variable selection and model selection are applied to electrical load forecasts to ensure an optimal generalization capacity of the neural network model. Real measurements collected in French distribution systems are used to validate our study. The results show that the neural network-based models outperform the time series models and that the design methodology guarantees the best generalization ability of the neural network model for the load forecasting purpose based on the same data.Index Terms-Model design, machine learning, neural network, short-term load forecast, variable selection, virtual leave-one-out.

This paper considers the communication for omniscience (CO) problem: A set of users observe a discrete memoryless multiple source and want to recover the entire multiple source via noise-free broadcast communications. We study the problem of how to determine an optimal rate vector that attains omniscience with the minimum sum-rate, the total number of communications. The results cover both asymptotic and non-asymptotic models where the transmission rates are real and integral, respectively. We propose a modified decomposition algorithm (MDA) and a sum-rate increment algorithm (SIA) for the asymptotic and non-asymptotic models, respectively, both of which determine the value of the minimum sum-rate and a corresponding optimal rate vector in polynomial time. For the coordinate saturation capacity (CoordSatCap) algorithm, a nesting algorithm in MDA and SIA, we propose to implement it by a fusion method and show by experimental results that this fusion method contributes to a reduction in computation complexity. Finally, we show that the separable convex minimization problem over the optimal rate vector set in the asymptotic model can be decomposed by the fundamental partition, the optimal partition of the user set that determines the minimum sum-rate, so that the problem can be solved more efficiently.

This paper considers how to accurately estimate the minimum sum-rate so as to reduce the complexity of solving cooperative data exchange (CDE) problems. The CDE system contains a number of geographically close clients who send packets to help the others recover an entire packet set. The minimum sum-rate is the minimum value of total number of transmissions that achieves universal recovery (the situation when all the clients recover the whole packet set). Based on a necessary and sufficient condition for a supermodular base polyhedron to be nonempty, we show that the minimum sum-rate for a CDE system can be determined by a maximization over all possible partitions of the client set. Due to the high complexity of solving this maximization problem, we propose a deterministic algorithm to approximate a lower bound on the minimum sum-rate. We show by experiments that this lower bound is much tighter than those lower bounds derived in the existing literature. We also show that the deterministic algorithm prevents from repetitively running the existing algorithms for solving CDE problems so that the overall complexity can be reduced accordingly.

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We propose a modified decomposition algorithm (MDA) to solve the asymptotic communication for omniscience (CO) problem where the communication rates could be real or fractional. By starting with a lower estimation of the minimum sum-rate, the MDA algorithm iteratively updates the estimation by the optimizer of a Dilworth truncation problem until the minimum is reached with a corresponding optimal rate vector. We also propose a fusion method implementation of the coordinatewise saturation capacity algorithm (CoordSatCapFus) for solving the Dilworth truncation problem, where the minimization is done over a fused user set with a cardinality smaller than the original one. We show that the MDA algorithm is less complex than the existing ones. In addition, we show that the non-asymptotic CO problem, where the communication rates are integral, can be solved by one more call of the CoordSatCapfus algorithm. By choosing a proper linear ordering of the user indices in the MDA algorithm, the optimal rate vector is also the one with the minimum weighted sum-rate.

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We propose a coalition game model for the problem of communication for omniscience (CO). In this game model, the core contains all achievable rate vectors for CO with sumrate being equal to a given value. Any rate vector in the core distributes the sum-rate among users in a way that makes all users willing to cooperate in CO. We give the necessary and sufficient condition for the core to be nonempty. Based on this condition, we derive the expression of the minimum sum-rate for CO and show that this expression is consistent with the results in multivariate mutual information (MMI) and coded cooperative data exchange (CCDE). We prove that the coalition game model is convex if the sum-rate is no less than the minimal value. In this case, the core is non-empty and a rate vector in the core that allocates the sum-rate among the users in a fair manner can be found by calculating the Shapley value.