TY - JOUR
T1 - Fast Inverter Control by Learning the OPF Mapping Using Sensitivity-Informed Gaussian Processes
AU - Jalali, Mana
AU - Singh, Manish Kumar
AU - Kekatos, Vasileios
AU - Giannakis, Georgios B.
AU - Liu, Chen Ching
N1 - Publisher Copyright:
IEEE
PY - 2023/5/1
Y1 - 2023/5/1
N2 - Fast inverter control is a desideratum towards the smoother integration of renewables. Adjusting inverter injection setpoints for distributed energy resources can be an effective grid control mechanism. However, finding such setpoints optimally requires solving an optimal power flow (OPF), which can be computationally taxing in real time. Previous works have proposed learning the mapping from grid conditions to OPF minimizers using Gaussian processes (GPs). This GP-OPF model predicts inverter setpoints when presented with a new instance of grid conditions. Training enjoys closed-form expressions, and GP-OPF predictions come with confidence intervals. To improve upon data efficiency, we uniquely incorporate the sensitivities (partial derivatives) of the OPF mapping into GP-OPF. This expedites the process of generating a training dataset as fewer OPF instances need to be solved to attain the same accuracy. To further reduce computational efficiency, we approximate the kernel function of GP-OPF leveraging the concept of random features, which is neatly extended to sensitivity data. We perform sensitivity analysis for the second-order cone program (SOCP) relaxation of the OPF, whose sensitivities can be computed by merely solving a system of linear equations. Extensive numerical tests using real-world data on the IEEE 13- and 123-bus feeders corroborate the merits of GP-OPF.
AB - Fast inverter control is a desideratum towards the smoother integration of renewables. Adjusting inverter injection setpoints for distributed energy resources can be an effective grid control mechanism. However, finding such setpoints optimally requires solving an optimal power flow (OPF), which can be computationally taxing in real time. Previous works have proposed learning the mapping from grid conditions to OPF minimizers using Gaussian processes (GPs). This GP-OPF model predicts inverter setpoints when presented with a new instance of grid conditions. Training enjoys closed-form expressions, and GP-OPF predictions come with confidence intervals. To improve upon data efficiency, we uniquely incorporate the sensitivities (partial derivatives) of the OPF mapping into GP-OPF. This expedites the process of generating a training dataset as fewer OPF instances need to be solved to attain the same accuracy. To further reduce computational efficiency, we approximate the kernel function of GP-OPF leveraging the concept of random features, which is neatly extended to sensitivity data. We perform sensitivity analysis for the second-order cone program (SOCP) relaxation of the OPF, whose sensitivities can be computed by merely solving a system of linear equations. Extensive numerical tests using real-world data on the IEEE 13- and 123-bus feeders corroborate the merits of GP-OPF.
KW - Gaussian processes
KW - learning-to-optimize
KW - random features
KW - second-order cone program
KW - sensitivity analysis
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U2 - 10.1109/TSG.2022.3210837
DO - 10.1109/TSG.2022.3210837
M3 - Article
AN - SCOPUS:85139488144
SN - 1949-3053
VL - 14
SP - 2432
EP - 2445
JO - IEEE Transactions on Smart Grid
JF - IEEE Transactions on Smart Grid
IS - 3
ER -