Electricity users are the major players of the electric systems, and electricity consumption is growing at an extraordinary rate. The research on electricity consumption behaviors is becoming increasingly important to design and deployment of the electric systems. Unfortunately, electricity load profiles are difficult to acquire. Data synthesis is one of the best approaches to solving the lack of data, and the key is the model that preserves the real electricity consumption behaviors. In this paper, we propose a hierarchical multi-matrices Markov Chain (HMMC) model to synthesize scalable electricity load profiles that preserve the real consumption behavior on three time scales: per day, per week, and per year. To promote the research on the electricity consumption behavior, we use the HMMC approach to model two distinctive raw electricity load profiles. One is collected from the resident sector, and the other is collected from the non-resident sectors, including different industries such as education, finance, and manufacturing. The experiments show our model performs much better than the classical Markov Chain model. We publish two trained models online, and researchers can directly use these trained models to synthesize scalable electricity load profiles for further researches.
Data synthesis is an approach to solving the lack of data. The generative model attractes a lot of attention and a number of models have been proposed in different areas. In the field of marketing, the mixture of normal distributions provides a useful extension of the normal distribution for modeling daily changes in market variables @cite_13 . In the field of solar radiation, the Markov model is used to model and generate the global solar radiation data @cite_10 . In the field of wind power, the chronological or sequential Monte Carlo simulation is applied to model and synthesize wind power time series @cite_6 . However, the model on the electricity consumption behaviours is rare in the field of energy. Duffy @cite_7 develops a generative model---the first order Markov Chain model---to model the electricity load profiles for five individual dwelling types in Ireland. However, the first-order Markov Chain model can not effectively preserve the real features of the user electricity load profiles as shown in Section 4.
@cite_10 @cite_13 @cite_7 @cite_6
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This paper studies the cooperative training of two generative models for image modeling and synthesis. Both models are parametrized by convolutional neural networks (ConvNets). The first model is a deep energy-based model, whose energy function is defined by a bottom-up ConvNet, which maps the observed image to the energy. We call it the descriptor network. The second model is a generator network, which is a non-linear version of factor analysis. It is defined by a top-down ConvNet, which maps the latent factors to the observed image. The maximum likelihood learning algorithms of both models involve MCMC sampling such as Langevin dynamics. We observe that the two learning algorithms can be seamlessly interwoven into a cooperative learning algorithm that can train both models simultaneously. Specifically, within each iteration of the cooperative learning algorithm, the generator model generates initial synthesized examples to initialize a finite-step MCMC that samples and trains the energy-based descriptor model. After that, the generator model learns from how the MCMC changes its synthesized examples. That is, the descriptor model teaches the generator model by MCMC, so that the generator model accumulates the MCMC transitions and reproduces them by direct ancestral sampling. We call this scheme MCMC teaching. We show that the cooperative algorithm can learn highly realistic generative models. Realistic time-resolved data on occupant behaviour, presence and energy use are important inputs to various types of simulations, including performance of small-scale energy systems and buildings' indoor climate, use of lighting and energy demand. This paper presents a modelling framework for stochastic generation of high-resolution series of such data. The model generates both synthetic activity sequences of individual household members, including occupancy states, and domestic electricity demand based on these patterns. The activity-generating model, based on non-homogeneous Markov chains that are tuned to an extensive empirical time-use data set, creates a realistic spread of activities over time, down to a 1-min resolution. A detailed validation against measurements shows that modelled power demand data for individual households as well as aggregate demand for an arbitrary number of households are highly realistic in terms of end-use composition, annual and diurnal variations, diversity between households, short time-scale fluctuations and load coincidence. An important aim with the model development has been to maintain a sound balance between complexity and output quality. Although the model yields a high-quality output, the proposed model structure is uncomplicated in comparison to other available domestic load models. Abstract In this paper, a model for the synthetic generation of 1-min global solar radiation data starting from the daily clearness index is presented. The model is constructed by treating the process generating a normalized form of the 1-min clearness index sequence as a Markov process. Two sets of three-year global solar radiation data taken at 1-min intervals from two locations in Japan are used to construct the Markov transition matrices. Because different days have different statistical characteristics due to different weather conditions, the days in the data set are first clustered into groups based on the daily clearness index values. Transition matrices are then formed for each group and consequently used to synthetically generate 1-min global solar radiation data. Second-order Markov models are selected based on the partial autocorrelation functions of the measured data. The statistical characteristics of the measured and synthetic data sets are found to be in close agreement thus confirming the validity of the model. We propose in this paper a new approach to train the Generative Adversarial Nets (GANs) with a mixture of generators to overcome the mode collapsing problem. The main intuition is to employ multiple generators, instead of using a single one as in the original GAN. The idea is simple, yet proven to be extremely effective at covering diverse data modes, easily overcoming the mode collapsing problem and delivering state-of-the-art results. A minimax formulation was able to establish among a classifier, a discriminator, and a set of generators in a similar spirit with GAN. Generators create samples that are intended to come from the same distribution as the training data, whilst the discriminator determines whether samples are true data or generated by generators, and the classifier specifies which generator a sample comes from. The distinguishing feature is that internal samples are created from multiple generators, and then one of them will be randomly selected as final output similar to the mechanism of a probabilistic mixture model. We term our method Mixture Generative Adversarial Nets (MGAN). We develop theoretical analysis to prove that, at the equilibrium, the Jensen-Shannon divergence (JSD) between the mixture of generators’ distributions and the empirical data distribution is minimal, whilst the JSD among generators’ distributions is maximal, hence effectively avoiding the mode collapsing problem. By utilizing parameter sharing, our proposed model adds minimal computational cost to the standard GAN, and thus can also efficiently scale to large-scale datasets. We conduct extensive experiments on synthetic 2D data and natural image databases (CIFAR-10, STL-10 and ImageNet) to demonstrate the superior performance of our MGAN in achieving state-of-the-art Inception scores over latest baselines, generating diverse and appealing recognizable objects at different resolutions, and specializing in capturing different types of objects by the generators.