At the heart of power system operations, alternating current optimal power
flow (ACOPF) studies the generation of electric power in the most economical
way under network-wide load requirement, and can be formulated as a highly
structured non-convex quadratically constrained quadratic program (QCQP).
Optimization-based solutions to ACOPF (such as ADMM or interior-point method),
as the classic approach, require large amount of computation and cannot meet
the need to repeatedly solve the problem as load requirement frequently
changes. On the other hand, learning-based methods that directly predict the
ACOPF solution given the load input incur little computational cost but often
generates infeasible solutions (i.e. violate the constraints of ACOPF). In this
work, we combine the best of both worlds -- we propose an innovated framework
for learning ACOPF, where the input load is mapped to the ACOPF solution
through a neural network in a computationally efficient and reliable manner.
Key to our innovation is a specific-purpose "activation function" defined
implicitly by a QCQP and a novel loss, which enforce constraint satisfaction.
We show through numerical simulations that our proposed method achieves
superior feasibility rate and generation cost in situations where the existing
learning-based approaches fail.

ACOPF 学习的创新框架结合了经典的基于优化的方法和基于神经网络的方法，通过特殊的激活函数和损失函数，实现了高效可靠的解决方案，提高了可行性率和发电成本。

QCQP-Net: 可靠地学习交流最优功率流解决方案

QCQP-Net: Reliably Learning Feasible Alternating Current Optimal Power  Flow Solutions Under Constraints

In this work we design and compare different supervised learning algorithms
to compute the cost of Alternating Current Optimal Power Flow (ACOPF). The
motivation for quick calculation of OPF cost outcomes stems from the growing
need of algorithmic-based long-term and medium-term planning methodologies in
power networks. Integrated in a multiple time-horizon coordination framework,
we refer to this approximation module as a proxy for predicting short-term
decision outcomes without the need of actual simulation and optimization of
them. Our method enables fast approximate calculation of OPF cost with less
than 1% error on average, achieved in run-times that are several orders of
magnitude lower than of exact computation. Several test-cases such as
IEEE-RTS96 are used to demonstrate the efficiency of our approach.

通过设计和比较不同的监督学习算法来计算 ACOPF 的成本，我们提出了一种快速计算 OPF 成本的方法，能够在多重时间协调框架中预测短期决策结果，从而避免了实际模拟和优化的需要，并且在保证均值误差小于 1% 的情况下，运行时间比精确计算低几个数量级。

基于监督学习的最优功率流实时代理

Supervised Learning for Optimal Power Flow as a Real-Time Proxy

Formulating the alternating current optimal power flow (ACOPF) as a
polynomial optimization problem makes it possible to solve large instances in
practice and to guarantee asymptotic convergence in theory.

用多项式优化问题表达交流最优电力流（ACOPF）问题可以在实践中解决大规模实例，并在理论上保证渐近收敛。