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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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. The mixture of normal distributions provides a useful extension of the normal distribution for modeling of daily changes in market variables with fatter-than-normal tails and skewness. An efficient analytical Monte Carlo method is proposed for generating daily changes using a multivariate mixture of normal distributions with arbitrary covariance matrix. The main purpose of this method is to transform (linearly) a multivariate normal with an input covariance matrix into the desired multivariate mixture of normal distributions. This input covariance matrix can be derived analytically. Any linear combination of mixtures of normal distributions can be shown to be a mixture of normal distributions. This study proposes a new method for direct generation of synthetic wind power time series for a wind farm. The method combines the random nature of wind with the operational information of the wind turbines (i.e., failure and repair rates). It uses chronological or sequential Monte Carlo Simulation instead of non-sequential one due to its usefulness and flexibility in preserving statistical characteristics of the chronological processes. The validity of the synthetic values generated by the proposed method and the conventional Markov Chain Monte Carlo methods is compared with the measured data in terms of average and variance values, Probability Distribution Function, and Auto-Correlation Function. Due to increasing interest in the use of the storage system in paralleling with wind power generation, a practical application of the proposed method is also included. Optimal sizing of various energy storage technologies is obtained through a cost-benefit analysis in a typical Micro-Grid.