Generating Synthetic Net Load Data with Physics-informed Diffusion Model

TL;DR

The paper tackles the challenge of generating realistic synthetic net-load data under privacy constraints. It introduces a physics-informed diffusion model (PDM) that embeds a solar PV performance model (PVSPM) into a conditional denoising diffusion network and jointly learns both the diffusion parameters and physics parameters. Compared with GAN, VAE, NF, and a baseline diffusion model, PDM achieves at least 20% improvement across multiple accuracy and diversity metrics on the Pecan Street net-load dataset. The approach enables conditional, physically consistent time-series generation with broad generalization potential for distribution planning, scenario analysis, and research.

Abstract

This paper presents a novel physics-informed diffusion model for generating synthetic net load data, addressing the challenges of data scarcity and privacy concerns. The proposed framework embeds physical models within denoising networks, offering a versatile approach that can be readily generalized to unforeseen scenarios. A conditional denoising neural network is designed to jointly train the parameters of the transition kernel of the diffusion model and the parameters of the physics-informed function. Utilizing the real-world smart meter data from Pecan Street, we validate the proposed method and conduct a thorough numerical study comparing its performance with state-of-the-art generative models, including generative adversarial networks, variational autoencoders, normalizing flows, and a well calibrated baseline diffusion model. A comprehensive set of evaluation metrics is used to assess the accuracy and diversity of the generated synthetic net load data. The numerical study results demonstrate that the proposed physics-informed diffusion model outperforms state-of-the-art models across all quantitative metrics, yielding at least 20% improvement.

Figures (8)

• Figure 1: Net load profiles for two distinct customers in the first two months of 2018, with curves of different colors representing various days.
• Figure 2: The overall framework of diffusion process for net load profile generation. The reverse denoising process progressively removes noise by denoising network $p_{\theta} (\mathbf{x}_{n-1} \vert \mathbf{x}_n)$, starting from $\mathbf{x}_N \sim \mathcal{N}(0, \mathbf{I})$, and concluding with $\mathbf{x}_0$.
• Figure 3: The overall architectures of the baseline denoising networks (left) and physics-informed denoising networks (right).
• Figure 4: PV embedding architecture. The input of this module is $\mathbf{y}$. $\boldsymbol{\theta}_{az}$ is the base azimuth angle. PV-basis Embedding and Cond-PV Embedding submodules are parameterized by neural networks.
• Figure 5: Synthetic net load profiles given 5 sets of conditional information. Each row corresponds to a unique condition, while different columns refer to different generative models. We select conditional information with $5$ different net load patterns to showcase the capability of the generative models. The blue curve represent the actual net load profile, while the gray curves are the 20 synthetic net load profiles.