Robust Regression Models for Load Forecasting

One of my doctoral majors is operations research, for which I took many courses in graduate school to build my knowledge in optimization. The topic of my dissertation was on load forecasting. Only two chapters were related to optimization, one on Artificial Neural Networks, and the other on Fuzzy Regression (or Possibilistic Linear Regression).

In fact, the fuzzy regression chapter was the only one that seriously required some optimization skills, which was published as an FODM paper three years after my graduation. To build a fuzzy regression model, I had to formulate the parameter estimation process as a linear program, and solve it in CPLEX. At that time Gurobi was not even able to provide a feasible solution for my fuzzy regression model with 200+ parameters.

After that, I continued my profession in forecasting. I knew my optimization background is helpful to forecasting, but I didn't really expect to apply many optimization skills in forecasting.

About a year ago, we performed a benchmark study to show that four representative load forecasting models would fail miserably with bad input data. That study was published as an IJF paper early this year. At the end of that IJF paper, we mentioned a future research direction of designing more robust load forecasting models.

In this paper, we propose three robust regression models for load forecasting. While all of them are more robust than the ones compared in the IJF paper, the L1 regression model outperform the others. In fact L1 regression is not really new to load forecasting. It has been used for forecast combination, where some people call it Least Absolute Deviation (LAD) regression. Its "general" form, quantile regression, is heavily used in probabilistic load forecasting.

What's new about the L1 regression model in this paper?

We built an L1 regression model with hundreds of parameters. In fact it shares the same variable combination as the Vanilla model used in Global Energy Forecasting Competitions. Building such a model is nontrivial. We didn't find an off-the-shelf package to do what we need, so we formulated it as a linear program and solved it using MATLAB's linprog.

Among hundreds of techniques that are applicable to load forecasting, how did I find L1 regression?

The idea didn't come from nowhere. When I was working on my doctoral dissertation at FANGroup (Fuzzy And Neural Group), a few other students were working on another project sponsored by U.S. Army Research Office. They were investigating some features and applications of l1 norm. Although I was thinking about applying l1 norm to load forecasting, I didn't find a good use case at that time.

Well, it's better late than never. The skills I acquired 10 years ago came handy for this paper.

Citation

Jian Luo, Tao Hong, and Shu-Cherng Fang, "Robust regression models for load forecasting," submitted to IEEE Transactions on Smart Grid, in press.

Robust Regression Models for Load Forecasting

Jian Luo, Tao Hong, and Shu-Cherng Fang

Abstract

Electric load forecasting has been extensively studied during the past century. While many models and their variants have been proposed and tested in the load forecasting literature, most of the existing case studies have been conducted using the data collected under normal operating conditions. A recent case study shows that four representative load forecasting models easily fail under data integrity attacks. To address this challenge, we propose three robust load forecasting models including two variants of the iteratively re-weighted least squares regression models and an L1 regression model. Numerical experiments indicate the dominating performance of the three proposed robust regression models, especially L1 regression, compared to other representative load forecasting models.