[Paper Review] A Nonparametric Bayesian Model for Synthesising Residential Solar Generation and Demand

Thomas Power, Gregor Verbič+1 more|arXiv (Cornell University)|Aug 2, 2018

Smart Grid Energy Management3 citations

TL;DR

This paper proposes a nonparametric Bayesian model that synthesizes stochastic residential solar generation and demand profiles using clustering and Dirichlet-categorical hierarchical modeling. By learning from limited empirical data, it generates realistic synthetic profiles that fit observed data well and reveal key system-level insights, such as intra-day variance from solar penetration and behavioral differences by population density.

ABSTRACT

Increasing installations of distributed electricity generation have vastly increased the need for stochastic generation and demand data. However, the effects of such installations is uncertain, as high quality data is not always available before an installation is completed. In particular, there is a need for stochastic models of demand and generation profiles for unobserved prosumers. The model formulated in this paper bridges the gap between the limited available empirical data, and the large amount of high-quality, stochastic demand and generation data required for network and system 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, and then two case studies are considered. The first identifies distinct behavioural differences in demand for residential areas of differing population density. The second case study varies levels of solar generation penetration, and shows that it contributes to significant intra-day demand variance, but has little impact on evening peak demand.

Motivation & Objective

• Address the lack of high-quality, stochastic demand and generation data for unobserved prosumers in distribution networks.
• Overcome data scarcity challenges in early-stage distributed energy resource planning and network analysis.
• Develop a scalable, data-efficient method to generate realistic synthetic profiles for system-level simulation and planning.
• Capture behavioral and operational differences in demand across residential areas with varying population densities.
• Assess the impact of solar generation penetration on intra-day load variability and peak demand patterns.

Proposed method

• Apply clustering analysis to group prosumers based on shared characteristics in their demand and generation profiles.
• Use a Dirichlet-categorical hierarchical model to represent the probabilistic distribution of cluster memberships for unobserved prosumers.
• Construct Markov chain models from empirical data to capture temporal dynamics of demand and generation within each cluster.
• Sample synthetic demand and generation traces from the learned Markov models to generate stochastic profiles.
• Cross-validate the synthetic profiles against observed data to ensure statistical fidelity and model reliability.
• Integrate the synthetic profiles into case studies to evaluate system-level impacts under different solar penetration levels and demographic conditions.

Experimental results

Research questions

• RQ1 How can stochastic residential solar generation and demand profiles be synthesized when empirical data is limited or unavailable?
• RQ2 What behavioral differences in household electricity demand exist between residential areas of varying population densities?
• RQ3 To what extent does increasing solar generation penetration affect intra-day load variability?
• RQ4 Does higher solar penetration significantly alter evening peak demand levels in residential networks?
• RQ5 How well do the synthetic profiles generated by the model reproduce statistical properties of real observed data?

Key findings

• The synthetic profiles generated by the model show a strong statistical fit to observed data, as confirmed by cross-validation.
• Residential areas with higher population density exhibit distinct demand behavior patterns compared to lower-density areas.
• Increased solar generation penetration leads to significant intra-day demand variance due to solar intermittency.
• Despite increased solar penetration, evening peak demand remains largely unaffected, indicating limited impact on peak load management.
• The model effectively captures the temporal dynamics of demand and generation through Markov chain modeling of clustered prosumer behavior.
• The nonparametric Bayesian framework enables scalable and adaptive profile synthesis even with sparse empirical data.