Efficient Sampling for Data-Driven Frequency Stability Constraint via Forward-Mode Automatic Differentiation
This work addresses a domain-specific problem in power systems optimization by improving data generation for frequency stability models, representing an incremental advancement in sampling techniques.
The paper tackles the inefficiency of random sampling for generating balanced stable and unstable data points in data-driven frequency stability constraints, proposing a gradient-based method using forward-mode automatic differentiation and gradient surgery, which demonstrates superior performance over existing methods like unrolling differentiation and finite difference.
Encoding frequency stability constraints in the operation problem is challenging due to its complex dynamics. Recently, data-driven approaches have been proposed to learn the stability criteria offline with the trained model embedded as a constraint of online optimization. However, random sampling of stationary operation points is less efficient in generating balanced stable and unstable samples. Meanwhile, the performance of such a model is strongly dependent on the quality of the training dataset. Observing this research gap, we propose a gradient-based data generation method via forward-mode automatic differentiation. In this method, the original dynamic system is augmented with new states that represent the dynamic of sensitivities of the original states, which can be solved by invoking any ODE solver for a single time. To compensate for the contradiction between the gradient of various frequency stability criteria, gradient surgery is proposed by projecting the gradient on the normal plane of the other. In the end, we demonstrate the superior performance of the proposed sampling algorithm, compared with the unrolling differentiation and finite difference. All codes are available at https://github.com/xuwkk/frequency_sample_ad.