In the present article we propose a mixed-integer approximation of adjustable-robust optimization problems, that have both, continuous and discrete variables on the lowest level. As these trilevel problems are notoriously hard to solve, we restrict ourselves to weakly-connected instances. Our approach allows us to approximate, and in some cases exactly represent, the trilevel problem as a single-level mixed-integer problem. This allows us to leverage the computational efficiency of state-of-the-art mixed-integer programming solvers. We demonstrate the value of this approach by applying it to the optimization of power systems, particularly to the control of smart converters.

在本文中，我们提出了可调鲁棒优化问题的混合整数近似，该问题在最低级别上同时具有连续变量和离散变量。由于这些三级问题非常难以解决，因此我们将自己限制在弱连接实例上。我们的方法使我们能够将三级问题近似地表示为单级混合整数问题，并且在某些情况下精确地表示为单级混合整数问题。这使我们能够利用最先进的混合整数编程求解器的计算效率。我们通过将这种方法应用于电力系统的优化，特别是智能转换器的控制来证明其价值。