This two-part tutorial dives into the field of data-driven power flow
linearization (DPFL), a domain gaining increased attention. DPFL stands out for
its higher approximation accuracy, wide adaptability, and better ability to
implicitly incorporate the latest system attributes. This renders DPFL a
potentially superior option for managing the significant fluctuations from
renewable energy sources, a step towards realizing a more sustainable energy
future, by translating the higher model accuracy into increased economic
efficiency and less energy losses. To conduct a deep and rigorous
reexamination, this tutorial first classifies existing DPFL methods into DPFL
training algorithms and supportive techniques. Their mathematical models,
analytical solutions, capabilities, limitations, and generalizability are
systematically examined, discussed, and summarized. In addition, this tutorial
reviews existing DPFL experiments, examining the settings of test systems, the
fidelity of datasets, and the comparison made among a limited number of DPFL
methods. Further, this tutorial implements extensive numerical comparisons of
all existing DPFL methods (40 methods in total) and four classic physics-driven
approaches, focusing on their generalizability, applicability, accuracy, and
computational efficiency. Through these simulationmethodss, this tutorial aims
to reveal the actual performance of all the methods (including the performances
exposed to data noise or outliers), guiding the selection of appropriate
linearization methods. Furthermore, this tutorial discusses future directions
based on the theoretical and numerical insights gained. As the first part, this
paper reexamines DPFL theories, covering all the training algorithms and
supportive techniques. Capabilities, limitations, and aspects of
generalizability, which were previously unmentioned in the literature, have
been identified.

数据驱动的功率流线性化（DPFL）方法在管理可再生能源的波动、提高经济效率和降低能量损失方面具有潜在优势，本教程全面研究了 DPFL 方法、数值比较和未来发展方向。

数据驱动的功率流线性化理论

Data-driven Power Flow Linearization: Theory

Neural networks have been widely applied in the power system area. They can
be used for better predicting input information and modeling system performance
with increased accuracy. In some applications such as battery degradation
neural network-based microgrid day-ahead energy scheduling, the input features
of the trained learning model are variables to be solved in optimization models
that enforce limits on the output of the same learning model. This will create
a neural network-embedded optimization problem; the use of nonlinear activation
functions in the neural network will make such problems extremely hard to solve
if not unsolvable. To address this emerging challenge, this paper investigated
different methods for linearizing the nonlinear activation functions with a
particular focus on the widely used rectified linear unit (ReLU) function. Four
linearization methods tailored for the ReLU activation function are developed,
analyzed and compared in this paper. Each method employs a set of linear
constraints to replace the ReLU function, effectively linearizing the
optimization problem, which can overcome the computational challenges
associated with the nonlinearity of the neural network model. These proposed
linearization methods provide valuable tools for effectively solving
optimization problems that integrate neural network models with ReLU activation
functions.

本文研究了针对常用的修正线性单元（ReLU）激活函数的线性化方法，为将神经网络模型与 ReLU 激活函数结合的优化问题提供了有效解决工具。