New Study Reveals the Best AI Models for Power Grid Optimization

Authors: (1) Mengshuo Jia, Department of Information Technology and Electrical Engineering, ETH Zürich, Physikstrasse 3, 8092, Zürich, Switzerland; (2) Gabriela Hug, Department of Information Technology and Electrical Engineering, ETH Zürich, Physikstrasse 3, 8092, Zürich, Switzerland; (3) Ning Zhang, Department of Electrical Engineering, Tsinghua University, Shuangqing Rd 30, 100084, Beijing, China; (4) Zhaojian Wang, Department of Automation, Shanghai Jiao Tong University, Dongchuan Rd 800, 200240, Shanghai, China; (5) Yi Wang, Department of Electrical and Electronic Engineering, The University of Hong Kong, Pok Fu Lam, Hong Kong, China; (6) Chongqing Kang, Department of Electrical Engineering, Tsinghua University, Shuangqing Rd 30, 100084, Beijing, China. 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 ABSTRACT Building on the theoretical insights of Part I, this paper, as the second part of the tutorial, dives deeper into data-driven power flow linearization (DPFL), focusing on comprehensive numerical testing. The necessity of these simulations stems from the theoretical analysis’s inherent limitations, particularly the challenge of identifying the differences in real-world performance among DPFL methods with overlapping theoretical capabilities and/or limitations. The absence of a comprehensive numerical comparison of DPFL approaches in the literature also motivates this paper, especially given the fact that over 95% of existing DPFL studies have not provided any open-source codes. To bridge the gap, this paper first reviews existing DPFL experiments, examining the adopted test scenarios, load fluctuation settings, data sources, considerations for data noise/outliers, and the comparison made so far. Subsequently, this paper evaluates a total of 44 methods, containing over 30 existing DPFL approaches, some innovative DPFL techniques, and several classic physics-driven power flow linearization methods for benchmarking. The evaluation spans various dimensions, including generalizability, applicability, accuracy, and computational efficiency, using numerous different test cases scaling from 9-bus to 1354-bus systems. The numerical analysis in this paper identifies and examines significant trends and consistent findings across all methods under various test cases. Meanwhile, it offers theoretical insights into phenomena like under-performance, failure, excessive computation times, etc. Overall, this paper identifies the differences in the performances of the wide range of DPFL methods, reveals gaps not evident from theoretical discussions, assists in method selection for real-world applications, and provides thorough discussions on open questions within DPFL research, indicating ten potential future directions. (Word Count: 9668). 1. Introduction Linear power flow models are of critical importance in power systems computations, subject to extensive research and widespread application across academia and industry, unlocking markets worth trillions and impacting every global consumer [1, 2, 3, 4]. The precision and computational efficiency of these linearization methods are pivotal for operating and planning power systems, particularly the systems with high penetrations of renewable energy due to the fast varying nature of the resulting power flows. Enhancing the accuracy and efficiency of linear power flow models is therefore not just a nice-to-have technical improvement but a significant advance towards a sustainable energy future. Data-driven power flow linearization (DPFL) has emerged as a promising method for acquiring high-precision linear models under must relaxed conditions, e.g., no need to know the physical model of the power system. It is thus garnering wide attention [5]. Despite being in the developing stage, DPFL has already cultivated a substantial knowledge base. This two-part tutorial aims to provide a comprehensive examination of DPFL approaches. The first part of this tutorial [6] offered a thorough classification and theoretical analysis of all existing DPFL methods, including their mathematical foundations, analytical solutions, and critical assessments of each method’s capabilities, limitations, and applicability. This work serves as a foundational guide, catering to both beginners and experts ORCID(s): 0000-0002-2027-5314 (M. Jia) within this area, as well as professionals from other disciplines simply seeking reliable linearization techniques. Despite the thoroughness of the theoretical analysis in [6], it has limitations: when many linearization methods have similar strengths and/or weaknesses, it is almost impossible to predict their differences in terms of practical performance. Hence, with only [6], identifying the most suitable method for specific needs still remains difficult. More importantly, existing numerical comparisons in the literature do not fully show the whole picture regarding the actual performance of DPFL approaches. The lack of a clear understanding of the actual performance differences among existing DPFL methods could mask the problems that are not apparent from the theoretical analysis of the capabilities and limitations, obscure the judgment of researchers within the DPFL community, and complicate the selection of appropriate linearization methods for potential users from other research fields. Indeed, implementing a comprehensive comparison requires substantial efforts, owing to the lack of open-source codes for over 95% of the related literature. Nevertheless, in order to clarify ambiguities, outline future research paths, and benefit the community, this paper, as the second part of the tutorial, intends to fill this gap. Specifically, this paper conducts exhaustive simulations for all DPFL methods, some newly introduced DPFL methods to showcase DPFL’s modular nature, and several classical physics-driven power flow linearization (PPFL) approaches as benchmarks, totaling 44 methods. The major focus of this paper is a thorough assessment of these methods in terms of generalizability, applicability, accuracy, and computational efficiency. The evaluation outcomes also support the identification of potential future directions. The contributions of this paper are therefore threefold: (i) A comprehensive review of existing DPFL experiments is presented, examining the adopted test scenarios, load fluctuation settings, data sources, and the considerations for data noise/outliers. The review also gives an overview over the existing comparisons made among DPFL approaches, outlines the capabilities and limitations of previous experiments, and demonstrates the critical need for a comprehensive numerical comparison of all DPFL approaches. (ii) An exhaustive numerical simulation of 44 linearization methods is conducted, including 36 existing DPFL approaches, four newly developed DPFL methods, and four classic PPFL algorithms. A detailed comparative analysis of these 44 methods is presented, discussing their generalizability, applicability, accuracy, and computational efficiency, thereby clarifying the actual performance of all the evaluated approaches. (iii) An in-depth discussion regarding the open research questions is provided, outlining ten promising but challenging future directions for DPFL research, informed by the numerical findings gained here and the theoretical conclusions drawn from the first part of the tutorial [6]. The remainder of this paper is organized as follows: Section II introduces the 44 methods. Section III reviews existing experiments in DPFL. Section IV assesses the methods regarding their generalizability and applicability. Section V details the numerical evaluations in terms of accuracy and computational efficiency. Section VI discusses open questions in the fields of DPFL, summarizing possible future directions. Section VII concludes the paper. Remark: We have made every effort to accurately replicate the methods described in the original research papers. However, due to factors such as the absence of open-source code (with very few exceptions) and often incomplete details in the literature, we cannot assure that our implementations perfectly reflect the original authors’ intentions, although when the details were particularly vague, we even have developed multiple versions of the methods, as shown in Table 1 in the next section. Nevertheless, we acknowledge that it is impossible to create exact replicas of the methods as envisioned by their creators. Additionally, it is important to note that no method is without flaws. The analysis of limitations in this paper is not meant as criticism but as part of a thorough evaluation under certain cases with given hyperparameters. This paper is available on arxiv under CC BY-NC-ND 4.0 Deed (Attribution-Noncommercial-Noderivs 4.0 International) license. Authors: (1) Mengshuo Jia, Department of Information Technology and Electrical Engineering, ETH Zürich, Physikstrasse 3, 8092, Zürich, Switzerland; (2) Gabriela Hug, Department of Information Technology and Electrical Engineering, ETH Zürich, Physikstrasse 3, 8092, Zürich, Switzerland; (3) Ning Zhang, Department of Electrical Engineering, Tsinghua University, Shuangqing Rd 30, 100084, Beijing, China; (4) Zhaojian Wang, Department of Automation, Shanghai Jiao Tong University, Dongchuan Rd 800, 200240, Shanghai, China; (5) Yi Wang, Department of Electrical and Electronic Engineering, The University of Hong Kong, Pok Fu Lam, Hong Kong, China; (6) Chongqing Kang, Department of Electrical Engineering, Tsinghua University, Shuangqing Rd 30, 100084, Beijing, China. Authors: Authors: (1) Mengshuo Jia, Department of Information Technology and Electrical Engineering, ETH Zürich, Physikstrasse 3, 8092, Zürich, Switzerland; (2) Gabriela Hug, Department of Information Technology and Electrical Engineering, ETH Zürich, Physikstrasse 3, 8092, Zürich, Switzerland; (3) Ning Zhang, Department of Electrical Engineering, Tsinghua University, Shuangqing Rd 30, 100084, Beijing, China; (4) Zhaojian Wang, Department of Automation, Shanghai Jiao Tong University, Dongchuan Rd 800, 200240, Shanghai, China; (5) Yi Wang, Department of Electrical and Electronic Engineering, The University of Hong Kong, Pok Fu Lam, Hong Kong, China; (6) Chongqing Kang, Department of Electrical Engineering, Tsinghua University, Shuangqing Rd 30, 100084, Beijing, China. Table of Links Abstract and 1. Introduction Abstract and 1. Introduction 2. Evaluated Methods 3. Review of Existing Experiments 3. Review of Existing Experiments 4. Generalizability and Applicability Evaluations and 4.1. Predictor and Response Generalizability 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 4.2. Applicability to Cases with Multicollinearity and 4.3. Zero Predictor Applicability 4.4. Constant Predictor Applicability and 4.5. Normalization Applicability 4.4. Constant Predictor Applicability and 4.5. Normalization Applicability 5. Numerical Evaluations and 5.1. Experiment Settings 5. Numerical Evaluations and 5.1. Experiment Settings 5.2. Evaluation Overview 5.2. Evaluation Overview 5.3. Failure Evaluation 5.3. Failure Evaluation 5.4. Accuracy Evaluation 5.4. Accuracy Evaluation 5.5. Efficiency Evaluation 5.5. Efficiency Evaluation 6. Open Questions 6. Open Questions 7. Conclusion 7. Conclusion Appendix A and References Appendix A and References ABSTRACT Building on the theoretical insights of Part I, this paper, as the second part of the tutorial, dives deeper into data-driven power flow linearization (DPFL), focusing on comprehensive numerical testing. The necessity of these simulations stems from the theoretical analysis’s inherent limitations, particularly the challenge of identifying the differences in real-world performance among DPFL methods with overlapping theoretical capabilities and/or limitations. The absence of a comprehensive numerical comparison of DPFL approaches in the literature also motivates this paper, especially given the fact that over 95% of existing DPFL studies have not provided any open-source codes. To bridge the gap, this paper first reviews existing DPFL experiments, examining the adopted test scenarios, load fluctuation settings, data sources, considerations for data noise/outliers, and the comparison made so far. Subsequently, this paper evaluates a total of 44 methods, containing over 30 existing DPFL approaches, some innovative DPFL techniques, and several classic physics-driven power flow linearization methods for benchmarking. The evaluation spans various dimensions, including generalizability, applicability, accuracy, and computational efficiency, using numerous different test cases scaling from 9-bus to 1354-bus systems. The numerical analysis in this paper identifies and examines significant trends and consistent findings across all methods under various test cases. Meanwhile, it offers theoretical insights into phenomena like under-performance, failure, excessive computation times, etc. Overall, this paper identifies the differences in the performances of the wide range of DPFL methods, reveals gaps not evident from theoretical discussions, assists in method selection for real-world applications, and provides thorough discussions on open questions within DPFL research, indicating ten potential future directions. (Word Count: 9668). 1. Introduction Linear power flow models are of critical importance in power systems computations, subject to extensive research and widespread application across academia and industry, unlocking markets worth trillions and impacting every global consumer [1, 2, 3, 4]. The precision and computational efficiency of these linearization methods are pivotal for operating and planning power systems, particularly the systems with high penetrations of renewable energy due to the fast varying nature of the resulting power flows. Enhancing the accuracy and efficiency of linear power flow models is therefore not just a nice-to-have technical improvement but a significant advance towards a sustainable energy future. Data-driven power flow linearization (DPFL) has emerged as a promising method for acquiring high-precision linear models under must relaxed conditions, e.g., no need to know the physical model of the power system. It is thus garnering wide attention [5]. Despite being in the developing stage, DPFL has already cultivated a substantial knowledge base. This two-part tutorial aims to provide a comprehensive examination of DPFL approaches. The first part of this tutorial [6] offered a thorough classification and theoretical analysis of all existing DPFL methods, including their mathematical foundations, analytical solutions, and critical assessments of each method’s capabilities, limitations, and applicability. This work serves as a foundational guide, catering to both beginners and experts ORCID(s): 0000-0002-2027-5314 (M. Jia) within this area, as well as professionals from other disciplines simply seeking reliable linearization techniques. Despite the thoroughness of the theoretical analysis in [6], it has limitations: when many linearization methods have similar strengths and/or weaknesses, it is almost impossible to predict their differences in terms of practical performance. Hence, with only [6], identifying the most suitable method for specific needs still remains difficult. More importantly, existing numerical comparisons in the literature do not fully show the whole picture regarding the actual performance of DPFL approaches. The lack of a clear understanding of the actual performance differences among existing DPFL methods could mask the problems that are not apparent from the theoretical analysis of the capabilities and limitations, obscure the judgment of researchers within the DPFL community, and complicate the selection of appropriate linearization methods for potential users from other research fields. Indeed, implementing a comprehensive comparison requires substantial efforts, owing to the lack of open-source codes for over 95% of the related literature. Nevertheless, in order to clarify ambiguities, outline future research paths, and benefit the community, this paper, as the second part of the tutorial, intends to fill this gap. Specifically, this paper conducts exhaustive simulations for all DPFL methods, some newly introduced DPFL methods to showcase DPFL’s modular nature, and several classical physics-driven power flow linearization (PPFL) approaches as benchmarks, totaling 44 methods. The major focus of this paper is a thorough assessment of these methods in terms of generalizability, applicability, accuracy, and computational efficiency. The evaluation outcomes also support the identification of potential future directions. The contributions of this paper are therefore threefold: (i) A comprehensive review of existing DPFL experiments is presented, examining the adopted test scenarios, load fluctuation settings, data sources, and the considerations for data noise/outliers. The review also gives an overview over the existing comparisons made among DPFL approaches, outlines the capabilities and limitations of previous experiments, and demonstrates the critical need for a comprehensive numerical comparison of all DPFL approaches. (ii) An exhaustive numerical simulation of 44 linearization methods is conducted, including 36 existing DPFL approaches, four newly developed DPFL methods, and four classic PPFL algorithms. A detailed comparative analysis of these 44 methods is presented, discussing their generalizability, applicability, accuracy, and computational efficiency, thereby clarifying the actual performance of all the evaluated approaches. (iii) An in-depth discussion regarding the open research questions is provided, outlining ten promising but challenging future directions for DPFL research, informed by the numerical findings gained here and the theoretical conclusions drawn from the first part of the tutorial [6]. The remainder of this paper is organized as follows: Section II introduces the 44 methods. Section III reviews existing experiments in DPFL. Section IV assesses the methods regarding their generalizability and applicability. Section V details the numerical evaluations in terms of accuracy and computational efficiency. Section VI discusses open questions in the fields of DPFL, summarizing possible future directions. Section VII concludes the paper. Remark : We have made every effort to accurately replicate the methods described in the original research papers. However, due to factors such as the absence of open-source code (with very few exceptions) and often incomplete details in the literature, we cannot assure that our implementations perfectly reflect the original authors’ intentions, although when the details were particularly vague, we even have developed multiple versions of the methods, as shown in Table 1 in the next section. Nevertheless, we acknowledge that it is impossible to create exact replicas of the methods as envisioned by their creators. Additionally, it is important to note that no method is without flaws. The analysis of limitations in this paper is not meant as criticism but as part of a thorough evaluation under certain cases with given hyperparameters. Remark We have made every effort to accurately replicate the methods described in the original research papers. However, due to factors such as the absence of open-source code (with very few exceptions) and often incomplete details in the literature, we cannot assure that our implementations perfectly reflect the original authors’ intentions, although when the details were particularly vague, we even have developed multiple versions of the methods, as shown in Table 1 in the next section. Nevertheless, we acknowledge that it is impossible to create exact replicas of the methods as envisioned by their creators. Additionally, it is important to note that no method is without flaws. The analysis of limitations in this paper is not meant as criticism but as part of a thorough evaluation under certain cases with given hyperparameters. This paper is available on arxiv under CC BY-NC-ND 4.0 Deed (Attribution-Noncommercial-Noderivs 4.0 International) license. This paper is available on arxiv under CC BY-NC-ND 4.0 Deed (Attribution-Noncommercial-Noderivs 4.0 International) license. available on arxiv