Collection of numerous power flow solutions of standard ieee test systems

This DATASET serves as a contemporary benchmark data set for solving multiple (or all) real-valued solutions for algebraic power flow problems. When this DATASET was originally created in 2019, it contained a huge collection of real-valued power flow solutions (up to dozens of thousands for some cases) for five standard IEEE test cases, i.e. 14-bus, 30-bus, 39-bus, 57-bus, and 57-bus-modified. In November 2023, we included an incomplete solution set for the IEEE 118-Bus test system under the default loading and generation profile. These solutions were obtained by the holomorphic embedding-based continuation (HEBC) method developed by Prof. Dr. Dan Wu at the Huazhong University of Science and Technology (previously at MIT) and Prof. Dr. Bin Wang at the University of Texas at San Antonio (previously at TAMU). The method used for solving these solutions can be found in [1][2]. Analysis and applications can be found in [3].

For the 118-Bus case, the cardinality of its solution set is 1,000,784 by November 2023, which is slightly beyond 1 million. This solution set is far from complete since finishing searching all the real-valued solutions to this system can be extremely time-consuming, even with our best algorithm. Therefore, we interrupted the search when the number reached 1 million and uploaded the solution set here as a partial benchmark. From our pessimistic estimation, the total number of real-valued solutions to this system can easily reach 5 million and is very likely to be beyond 10 million or more. Being fully aware of this situation, we are still very excited to announce this partial result because we entered an untouched realm in which our frequently used system begins to exhibit its hidden features. Moreover, we hope it could also serve as an interesting prelude for the study of the fundamental complexities and difficulties in power system engineering from real algebraic geometry and computational algebraic geometry point of view. 

Dan Wu and Bin Wang

Nov. 2023

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[1] D. Wu and B. Wang, "Holomorphic Embedding Based Continuation Method for Identifying Multiple Power Flow Solutions," in IEEE Access, vol. 7, pp. 86843-86853, 2019.

[2] B. C. Lesieutre and D. Wu, "An Efficient Method to Locate All the Load Flow Solutions- Revisited," in 53rd Annual Allerton Conference on Communication, Control, and Computing, 2015, pp. 381-388, 29 Sep-2 Oct 2015. 

[3] B. Wang, D. Wu, X. Su, K. Sun and L. Xie, "A long-term voltage stability margin index based on multiple real power flow solutions," in 2023 IEEE Power & Energy Society General Meeting, Jul 2023.