The Trials and Triumphs of DPFL Research

Table of Links

Abstract and 1. Introduction

2. Evaluated Methods

3. Review of Existing Experiments

4. Generalizability and Applicability Evaluations and 4.1. Predictor and Response Generalizability

4.2. Applicability to Cases with Multicollinearity and 4.3. Zero Predictor Applicability

4.4. Constant Predictor Applicability and 4.5. Normalization Applicability

5. Numerical Evaluations and 5.1. Experiment Settings

5.2. Evaluation Overview

5.3. Failure Evaluation

5.4. Accuracy Evaluation

5.5. Efficiency Evaluation

6. Open Questions

7. Conclusion

Appendix A and References

7. Conclusion

This paper, as the second part of a tutorial series, presents a comprehensive review of existing DPFL experiments, detailing the capabilities and limitations of these experiments. Additionally, it provides an in-depth numerical examination of DPFL methods, complementing the theoretical insights explored in Part I and addressing the limited experimental work found in the existing literature. This dual focus aims to offer a more holistic understanding of DPFL by bridging the gap between theory and practice.

Specifically, this paper analyzes all the approaches’ generalizability towards the selection of predictor and response, as well as their applicability towards multicollinearity, zero predictor, constant predictor, and normalization. Then, through rigorous numerical simulations involving 44 different methods across numerous test cases scaling from 9-bus to 1354-bus, this paper has illustrated the practical performance that mere theoretical analyses could not reveal. The practical performance is evaluated from two angles: accuracy and computational efficiency. For the accuracy evaluation, this paper (i) clarifies the reasons behind the failures encountered by DPFL methods, (ii) provides insights into how DPFL methods compare with traditional PPFL approaches, (iii) offers comprehensive discussions on the uniform outcomes observed across various test cases for all DPFL methods, and (iv) dives into extensive analyses of individual DPFL methods, highlighting their distinctive performances. Regarding the evaluation of computational efficiency, the paper (i) explores the comparative efficiency of DPFL versus PPFL methods, (ii) offers in-depth discussions on the consistent performance metrics of DPFL methods across multiple test scenarios, and (iii) presents detailed evaluations of specific groups of DPFL methods, focusing on their similar performance. Furthermore, drawing on insights from this study and Part I [6], as well as the identified open questions, this paper outlines ten promising yet challenging directions, which sketch a roadmap for future research in DPFL. Addressing these questions will not only advance our understanding of DPFL methods but also contribute to the broader goal of developing more reliable, efficient, and accessible tools for power systems research, education, and applications.

As for our next step, by leveraging our comprehensive repository of documentation and codebase for DPFL methods, we will start with the tenth suggested direction: creating an exhaustive, elegant, and user-friendly toolbox. This toolbox will fully support all DPFL methods and the related functionalities, aiming to offer significant ease of use for researchers and engineers, to support them in exploring and/or leveraging the area of DPFL, thereby reshaping the frontiers of the DPFL research and application.

Appendix A

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