Optimizing Parameters of the DC Power Flow (2310.00447v2)
Abstract: Many power system operation and planning problems use the DC power flow approximation to address computational challenges from the nonlinearity of the AC power flow equations. The DC power flow simplifies the AC power flow equations to a linear form that relates active power flows to phase angle differences across branches, parameterized by coefficients based on the branches' susceptances. Inspired by techniques for training machine learning models, this paper proposes an algorithm that seeks optimal coefficient and bias parameters to improve the DC power flow approximation's accuracy. Specifically, the proposed algorithm selects the coefficient and bias parameter values that minimize the discrepancy, across a specified set of operational scenarios, between the power flows given by the DC approximation and the power flows from the AC equations. Gradient-based optimization methods like Broyden-Fletcher-Goldfarb-Shanno (BFGS), Limited-Memory BFGS (L-BFGS), and Truncated Newton Conjugate-Gradient (TNC) enable solution of the proposed algorithm for large systems. After an off-line training phase, the optimized parameters are used to improve the accuracy of the DC power flow during on-line computations. Numerical results show several orders of magnitude improvements in accuracy relative to a hot-start DC power flow approximation across a range of test cases.
- B. Stott, “Review of load-flow calculation methods,” Proceedings of the IEEE, vol. 62, no. 7, pp. 916–929, 1974.
- D. Mehta, D. K. Molzahn, and K. Turitsyn, “Recent advances in computational methods for the power flow equations,” in American Control Conference (ACC), Boston, MA, USA, July 2016, pp. 1753–1765.
- D. Bienstock and A. Verma, “Strong NP-hardness of AC power flows feasibility,” Operations Research Letters, vol. 47, no. 6, pp. 494–501, 2019.
- I. A. Hiskens and R. J. Davy, “Exploring the power flow solution space boundary,” IEEE Transactions on Power Systems, vol. 16, no. 3, pp. 389–395, August 2001.
- T. J. Overbye, X. Cheng, and Y. Sun, “A comparison of the AC and DC power flow models for LMP calculations,” in 37th Annual Hawaii International Conference on System Sciences (HICSS), 2004.
- D. K. Molzahn and I. A. Hiskens, “A survey of relaxations and approximations of the power flow equations,” Foundations and Trends in Electric Energy Systems, vol. 4, no. 1-2, pp. 1–221, 2019.
- H. R. Wilson, “An approximate method of calculating short-circuit current in an alternating-current system,” General Electric Review, vol. 19, pp. 475–479, 1916.
- B. Stott, J. Jardim, and O. Alsac, “DC power flow revisited,” IEEE Transactions on Power Systems, vol. 24, no. 3, pp. 1290–1300, Aug. 2009.
- T. Mühlpfordt, V. Hagenmeyer, D. K. Molzahn, and S. Misra, “Optimal adaptive power flow linearizations: Expected error minimization using polynomial chaos expansion,” in IEEE Milan PowerTech, 2019.
- Z. Shao, Q. Zhai, J. Wu, and X. Guan, “Data based linear power flow model: Investigation of a least-squares based approximation,” IEEE Transactions on Power Systems, vol. 36, no. 5, pp. 4246–4258, 2021.
- P. Buason, S. Misra, and D. K. Molzahn, “A sample-based approach for computing conservative linear power flow approximations,” Electric Power Systems Research, vol. 212, p. 108579, 2022, presented at the 22nd Power Systems Computation Conference (PSCC 2022).
- J. Chen and L. A. Roald, “A data-driven linearization approach to analyze the three-phase unbalance in active distribution systems,” Electric Power Systems Research, vol. 211, p. 108573, 2022, presented at the 22nd Power Systems Computation Conference (PSCC 2022).
- Y. Liu, Z. Li, and S. Sun, “A data-driven method for online constructing linear power flow model,” to appear in IEEE Transactions on Industry Applications, 2023.
- M. Jia and G. Hug, “Overview of data-driven power flow linearization,” in IEEE Belgrade PowerTech, 2023.
- M. Jia, G. Hug, N. Zhang, Z. Wang, and Y. Wang, “Tutorial on data-driven power flow linearization–Part I: Challenges and training algorithms,” preprint available at https://doi.org/10.3929/ethz-b-000606654, 2023.
- ——, “Tutorial on data-driven power flow linearization–Part II: Supportive techniques and experiments,” preprint available at https://doi.org/10.3929/ethz-b-000606656, 2023.
- P. A. Ruiz, E. Goldis, A. M. Rudkevich, M. C. Caramanis, C. R. Philbrick, and J. M. Foster, “Security-constrained transmission topology control MILP formulation using sensitivity factors,” IEEE Transactions on Power Systems, vol. 32, no. 2, pp. 1597–1605, 2017.
- E. B. Fisher, R. P. O’Neill, and M. C. Ferris, “Optimal transmission switching,” IEEE Transactions on Power Systems, vol. 23, no. 3, pp. 1346–1355, 2008.
- S. G. Nash, “Newton-type minimization via the Lanczos method,” SIAM Journal on Numerical Analysis, vol. 21, no. 4, pp. 770–788, 1984.
- A. B. Birchfield, T. Xu, K. M. Gegner, K. S. Shetye, and T. J. Overbye, “Grid structural characteristics as validation criteria for synthetic networks,” IEEE Transactions on Power Systems, vol. 32, no. 4, pp. 3258–3265, 2016.
- IEEE PES Task Force on Benchmarks for Validation of Emerging Power System Algorithms, “The Power Grid Library for benchmarking AC optimal power flow algorithms,” August 2019, arXiv:1908.02788.
- C. Coffrin, R. Bent, K. Sundar, Y. Ng, and M. Lubin, “PowerModels.jl: An open-source framework for exploring power flow formulations,” in 20th Power Systems Computation Conference (PSCC), 2018.