GNN-based surrogate modeling for collection systems costs

Abstract

There are no known polynomial-time algorithms to perform the cable layout optimization (CLO) for the electrical network within a wind power plant (WPP). This means the computational cost for solving the CLO problem grows exponentially with plant size, which often postpones its solution to until after most design decisions are made, thus forgoing some trade-offs that would be beneficial to the plant’s goal. This work presents a method to obtain a fast estimate of the CLO that can be performed at each iteration of the broader optimization framework. The proposed surrogate model comprises of a graph neural network (GNN) regression model, as this architecture resembles the graph nature of the CLO problem. The GNN is trained with a dataset of procedurally generated site instances that are optimized by costly solving an integer linear programming model. While the inference time for GNNs is constant, the features calculation proposed has time complexity O(N log N) (where N is the number of wind turbines). This still means a major speed up for problems of non-trivial size when compared to exact CLO. A simpler feed-forward neural network (FNN) was trained on the same dataset and used as baseline. Both GNN and FNN achieved r 2 scores of 0.997 for the regression on unseen data of actual WPP, with standard deviations of the relative errors of 1.59% for the FNN and 1.66% for the GNN. Although the GNN did not improve on the performance of the FNN, the latter is an original contribution to the state of the art and an useful tool for the integrated optimization of WPP. This work looked only into a sliver of what is possible with GNNs, leaving ample space for improvements in applying that architecture to the CLO problem.