A Nonparametric Bayesian Methodology for Synthesizing Residential Solar Generation and Demand Data

Abstract

The uptake of behind-the-meter distributed energy resources in low-voltage distribution networks has reached a level where network issues have started to emerge, which requires new tools for operation and planning. In this paper, we propose a methodology for synthesizing stochastic demand and generation profiles for unobserved customers with rooftop PV, called prosumers. The proposed model bridges the gap between the limited available empirical data, and the large amount of high-quality, stochastic demand and generation data required for probabilistic analysis. The approach employs clustering analysis and a Dirichlet-categorical hierarchical model of the features of unobserved prosumers. Based on the data of clusters of prosumers, Markov chain models of demand and generation profiles are constructed from empirical data, and synthetic demand profiles are subsequently sampled from these. The sampled traces are cross-validated and show a good statistical fit to the observed data. Two case studies are considered to confirm the validity of the proposed methodology. The first studies the impact of behavioral differences on the synthetic demand profiles, while the second looks at the impact of varying solar generation penetration on demand profiles.

Probabilistic impact of electricity tariffs on distribution grids considering adoption of solar and storage technologies

“…Capturing the effect of electricity tariffs and DER technology costs on the long-term security of the distribution network requires an integration of DER adoption models (representing the prosumers' side) with load flow calculations that are able to estimate the steady-state conditions of the distribution grid on the It is important to note that the PLF evaluation employed in this work implies a different time-scale and a different uncertainty characterization when compared with other probabilistic analysis in the context of DER deployment in distribution grids. In fact, most of the PLF algorithms in this domain [29,27,30,28,31] are focused on shorter term aspects of decentralized PV and load uncertainty (related with intra-day consumption variations, radiation intermittence, etc. ), which are relevant for operations and operational planning problems and widely used to support decisions made hours/minutes ahead of the uncertainty realization.…”

“…The estimates of the probability density function (pdf) and cumulative distribution function (cdf) are similarly constructed by the Monte Carlo estimator for the average violations, with the difference that the random variable is not restricted to integers but can take any nonnegative real values. The indicator variable W rviol avg lim " vs indicates whether the average violation has a certain magnitude v, shown in (30), the pdf of the average violation. The estimate for this after n Monte Carlo trials is given by (31).…”

“…On the other hand, the security aspects of the distribution grid associated with the massive adoption of PV have been treated in a more technical perspective, for example through different probabilistic load flow (PLF) methods, applied to utility grid planning [27,28] and operations [29,30] in order to quantify the impact of prosumers' DER adoption and new PV connections into the distribution grid. Some of these PLF methods, e.g.…”

Dirichlet Sampled Capacity and Loss Estimation for LV Distribution Networks With Partial Observability

“…In terms of combining Dirichlet processes with clustering models, as proposed in this paper, Power et al [9,25] developed a model for synthesising solar generation and demand data by sampling feature clusters, established using a k-means model, with a Dirichlet process. In particular, [9] noted that while the proportions of any observable customers having certain characteristics in any data set can be known, this may not be a reliable estimate of the true proportions across all observed and unobserved customers.…”

Probabilistic Assessment of Impact of Flexible Loads Under Network Tariffs in Low-voltage Distribution Networks

“…We then generate a pool of net load traces specific to assigned features based on a Markov chain process. More details on the statistical models of demand and solar PV can be found in [24].…”