Chance-constrained optimal power flow for improving line flow and voltage security of power transmission networks

Abstract

With the growing penetration of renewable energy, the impact of renewable uncertainties on power system secure operation is of increasing concern. Based on a recently developed linear power flow model, we formulate a chance-constrained optimal power flow (CC-OPF) in transmission networks that provides a concise way to regulate the security regarding both power and voltage behaviors under renewable uncertainties, the latter of which fails to be captured by the conventional DC power flow model. The formulated CC-OPF finds an optimal operating point for the forecasted scenario and the corresponding generation participation scheme for balancing power fluctuations such that the expectation of generation cost is minimized and the probabilities of line overloading and voltage violations are sufficiently low. The problem under the Gaussian distribution of renewable fluctuations is reformulated into a deterministic problem in the form of second-order cone programming, which can be solved efficiently. The proposed approach is also extended to the non-Gaussian uncertainty case by making use of the linear additivity of probability terms in the Gaussian mixture model. The obtained results are verified via numerical experiments on several IEEE test systems.

Keywords

Power systems / Optimal power flow / Chance constraint / Second-order cone programming

References

[1] Gomez-Exposito A., Conejo A.J., Canizares C.. Electric Energy Systems: Analysis and Operation, 2018, Boca Raton. CRC Press

[2] Song Y., Liu T., Hill D.J.. Chance constrained economic dispatch considering the capability of network flexibility against renewable uncertainties. IEEE Trans. Power Syst., 2024, 39(5): 6636-6648.

[3] Zhang H., Li P.. Chance constrained programming for optimal power flow under uncertainty. IEEE Trans. Power Syst., 2011, 26(4): 2417-2424.

[4] Duan C., Fang W., Jiang L., Yao L., Liu J.. Distributionally robust chance-constrained approximate AC-OPF with Wasserstein metric. IEEE Trans. Power Syst., 2018, 33(5): 4924-4936.

[5] Jabr R.A.. Adjustable robust opf with renewable energy sources. IEEE Trans. Power Syst., 2013, 28(4): 4742-4751.

[6] Gan D., Thomas R.J., Zimmerman R.D.. Stability-constrained optimal power flow. IEEE Trans. Power Syst., 2000, 15(2): 535-540.

[7] Xu Y., Dong Z.Y., Zhang R., Hill D.J.. Multi-timescale coordinated voltage/var control of high renewable-penetrated distribution systems. IEEE Trans. Power Syst., 2017, 32(6): 4398-4408.

[8] Bienstock D., Chertkov M., Harnett S.. Chance-constrained optimal power flow: risk-aware network control under uncertainty. SIAM Rev., 2014, 56(3): 461-495.

[9] Chertkov M., Dvorkin Y.. Chance constrained optimal power flow with primary frequency response. Proc. IEEE Conf. Dec. Control, 20174484-4489

[10] Mühlpfordt T., Faulwasser T., Hagenmeyer V.. A generalized framework for chance-constrained optimal power flow. Sustain. Energy Grids Netw., 2018, 16: 231-242.

[11] Roald L., Andersson G.. Chance-constrained AC optimal power flow: reformulations and efficient algorithms. IEEE Trans. Power Syst., 2017, 33(3): 2906-2918.

[12] Venzke A., Halilbasic L., Markovic U., Hug G., Chatzivasileiadis S.. Convex relaxations of chance constrained ac optimal power flow. IEEE Trans. Power Syst., 2018, 33(3): 2829-2841.

[13] T. Muhlpfordt, L. Roald, V. Hagenmeyer, T. Faulwasser, S. Misra, Chance-constrained AC optimal power flow–a polynomial chaos approach. IEEE Trans. Power Syst., 4806–4816 (2019)

[14] Brust J.J., Anitescu M.. Convergence analysis of fixed point chance constrained optimal power flow problems. IEEE Trans. Power Syst., 2022, 37(6): 4191-4201.

[15] Yang J., Zhang N., Kang C., Xia Q.. A state-independent linear power flow model with accurate estimation of voltage magnitude. IEEE Trans. Power Syst., 2017, 32(5): 3607-3617.

[16] Camm E., Behnke M., Bolado O., Bollen M., Bradt M., Brooks C., Dilling W., Edds M., Hejdak W., Houseman D., et al. . Characteristics of wind turbine generators for wind power plants. Proc. IEEE Power Energy Soc. Gen. Meeting, 20091-5

[17] K.B. Petersen, M.S. Pedersen, The Matrix Cookbook. Technical University of Denmark, Copenhagen, Denmark (2008)

[18] M. Grant, S. Boyd, CVX: Matlab Software for Disciplined Convex Programming, version 2.1 (2014). http://cvxr.com/cvx

[19] Goodfellow I., Bengio Y., Courville A.. Deep Learning, 2016, Cambridge. MIT Press

[20] Hu Z., Sun W., Zhu S.. Chance constrained programs with Gaussian mixture models. IISE Trans., 2022, 54(12): 1117-1130.

[21] S. Boone, J. McMahon, Non-Gaussian chance-constrained trajectory control using Gaussian mixtures and risk allocation, in Proc. IEEE Conf. Dec. Control, pp. 3592–3597

[22] Chen G., Zhang H., Song Y.. Chance-constrained DC optimal power flow with non-Gaussian distributed uncertainties. Proc. IEEE Power Energy Soc. Gen. Meeting, 20221-5

[23] Zimmerman R.D., Murillo-Sánchez C.E., Thomas R.J.. Matpower: steady-state operations, planning, and analysis tools for power systems research and education. IEEE Trans. Power Syst., 2011, 26(1): 12-19.

Funding

National Natural Science Foundation of China(62403362, 62088101)

Fundamental Research Funds for Central Universities of the Central South University

Shanghai Municipal Science and Technology Commission Explorers Program(24TS1401600)

Xiaomi Fundation

RIGHTS & PERMISSIONS

The Author(s)