Many electric vehicles (EVs) are using today’s distribution grids, and their flexibility can be highly beneficial for the grid operators. This flexibility can be best exploited by DC power networks, as they allow charging and discharging without extra power electronics and transformation losses. From the grid control perspective, algorithms for planning EV charging are necessary. This paper studies the problem of EV charging planning under limited grid capacity and extends it to the partially observable case. We demonstrate how limited information about the EV locations in a grid may disrupt the operation planning in DC grids with tight constraints. We introduce two methods to change the grid topology such that partial observability of the EV locations is resolved. The suggested models are evaluated on the IEEE 16 bus system and multiple randomly generated grids with varying capacities. The experiments show that these methods efficiently solve the partially observable EV charging planning problem and offer a trade-off between computational time and performance.

Predict and optimize is an increasingly popular decision-making paradigm that employs machine learning to predict unknown parameters of optimization problems. Instead of minimizing the prediction error of the parameters, it trains predictive models using task performance as a loss function. The key challenge to train such models is the computation of the Jacobian of the solution of the optimization problem with respect to its parameters. For linear problems, this Jacobian is known to be zero or undefined; hence, approximations are usually employed. For non-linear convex problems, however, it is common to use the exact Jacobian. This paper demonstrates that the zero-gradient problem appears in the non-linear case as well -- the Jacobian can have a sizeable null space, thereby causing the training process to get stuck in suboptimal points. Through formal proofs, this paper shows that smoothing the feasible set resolves this problem. Combining this insight with known techniques from the literature, such as quadratic programming approximation and projection distance regularization, a novel method to approximate the Jacobian is derived. In simulation experiments, the proposed method increases the performance in the non-linear case and at least matches the existing state-of-the-art methods for linear problems.