The AC-OPF problem is the key and challenging problem in the power system operation. When solving the AC-OPF problem, the feasibility issue is critical. In this paper, we develop an efficient Deep Neural Network (DNN) approach, DeepOPF, to ensure the feasibility of the generated solution. The idea is to train a DNN model to predict a set of independent operating variables, and then to directly compute the remaining dependable variables by solving the AC power flow equations. While this guarantees the power-flow balances, the principal difficulty lies in ensuring that the obtained solutions satisfy the operation limits of generations, voltages, and branch flow. We tackle this hurdle by employing a penalty approach in training the DNN. As the penalty gradients make the common first-order gradient-based algorithms prohibited due to the hardness of obtaining an explicit-form expression of the penalty gradients, we further apply a zero-order optimization technique to design the training algorithm to address the critical issue. The simulation results of the IEEE test case demonstrate the effectiveness of the penalty approach. Also, they show that DeepOPF can speed up the computing time by one order of magnitude compared to a state-of-the-art solver, at the expense of minor optimality loss.

中文翻译：

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DeepOPF：针对交流最优潮流问题的可行性优化深度神经网络方法

AC-OPF问题是电力系统运行中的关键和具有挑战性的问题。在解决 AC-OPF 问题时，可行性问题至关重要。在本文中，我们开发了一种高效的深度神经网络 (DNN) 方法 DeepOPF，以确保生成的解决方案的可行性。其思想是训练一个 DNN 模型来预测一组独立的运行变量，然后通过求解交流潮流方程直接计算剩余的可靠变量。虽然这保证了潮流平衡，但主要的困难在于确保获得的解决方案满足发电、电压和支流的运行限制。我们通过在训练 DNN 时采用惩罚方法来解决这个障碍。由于惩罚梯度使得常见的基于一阶梯度的算法由于难以获得惩罚梯度的显式表达式而被禁止，我们进一步应用零阶优化技术来设计训练算法以解决关键问题. IEEE 测试用例的仿真结果证明了惩罚方法的有效性。此外，他们表明，与最先进的求解器相比，DeepOPF 可以将计算时间加快一个数量级，但代价是最优性损失很小。