arXiv:2610.20950v1 Announce Type: new Abstract: The generation interconnection queue adds discrete uncertainty to power grid congestion price estimates on the project planning timescale. The conventional approach to this uncertainty is to make an informed guess of the single or few most likely configurations of generators that interconnect. In this paper, we show that Monte Carlo sampling is a more effective alternative. Given an estimate of the joint probability distribution of generator interconnections, a small number of samples yields good estimates of the congestion distribution. Crucially, this problem is not about rare events, but rather about the expected congestion over the worst times of the year, which makes congestion a common outcome over the distribution of interconnection events. We give empirical results on a 2000-bus network, averaging price outcomes from security-constrained DCOPF over eight different loading scenarios. For each line and contingency of the network, we estimate the full distribution as well as mean price and probability of exceeding a price threshold. Single-point estimates are unreliable and can be misleading about whether a line is likely to be congested. Combining the top k probability configurations yields improved estimates; however, sampling the same number from a distribution gives a more robust result of similar accuracy, as well as error estimates. Including correlation in the distribution model introduces small changes, showing that standard Bernoulli distributions suffice in most cases. The sampling approach is also applicable to large-load interconnection and should be of interest for planning both generation and large-load projects.