When Probabilities Change the Grid Plan
What a sensitivity analysis of stochastic programming tells us about future distribution networks
Over the last few weeks, I have been working on a project about electricity distribution network planning under uncertainty. The question behind the work is practical: if electric vehicle demand grows in an uncertain way , should a network planner invest in conventional network reinforcement (e.g. upgrading the capacity of lines), Smart Charging of EV (i.e. equipment allowing the smart charging of EVs), or some combination of both?
This question is becoming increasingly important. Global electric car sales exceeded 17 million in 2024, reaching more than 20% of total car sales, and the IEA expects continued growth in 2025. At the same time, the IEA has warned that energy transitions require not only more grid infrastructure, but also changes in how grids are planned and managed. Here is an interesting link.
In this project, I compare two network planning frameworks: Stochastic Programming, or SP, and Least Worst Regret, or LWR.
SP uses probabilities. It assigns a likelihood to each scenario in the scenario tree and minimises expected total system cost. The problem is that probabilities are subjective.
LWR does not rely on probabilities. Instead, it minimises the maximum economic regret. In plain English, it asks: “Which investment plan avoids the worst cost-disappointment if the future turns out differently from what we expected?”
For this study, I solved both frameworks across different Smart Charging investment costs, flexibility levels and probability structures. I run roughly two thousand optimization studies (SP, LWR).
Figure 1, below, shows the expected system cost difference between SP and LWR. When probabilities are equal, the two frameworks are close. When probabilities become very different, SP can deliver much lower expected system cost than LWR. So, probabilities are not a modelling detail. They can change the investment plan.
If you want to go deeper into this type of modelling, I also cover it inside The Energy Data Scientist Skool here.
