This article presents the theoretical and practical foundation of a spherical lower dimensional representation for daily medium voltage load profiles, based on principal component analysis. The objective is to unify and simplify the tasks for (i) clustering visualisation, (ii) outlier detection and (iii) generative profile modelling under one concept. The lower dimensional projection of standardised MV load profiles unveils a latent distribution in a three-dimensional sphere. This spherical structure allows us to detect outliers by fitting probability distribution models in the spherical coordinate system, identifying measurements that deviate from the spherical shape. The same latent distribution exhibits an arc shape, suggesting an underlying order among load profiles. We develop a principal curve technique to uncover this order based on similarity, offering new advantages over conventional clustering techniques. This finding reveals that energy consumption in a wide region can be seen as a continuously changing process. Furthermore, we combined the principal curve with a von Mises-Fisher distribution to create a model capable of generating profiles with continuous mixtures between clusters. The presence of the spherical distribution is validated with data from four municipalities in the Netherlands. The uncovered spherical structure implies the possibility of employing new mathematical tools from directional statistics and differential geometry for load profile modelling.

Due to the increasing penetration of distributed energy resources, congestion problems are already emerging in Dutch distribution grids. The available flexibility of assets in the built environment could have the potential to reduce congestion if prosumers are properly incentivized by distribution grid operators (DSOs). However, it is not yet clear what (combinations of) flexibility a ctivation mechanisms will be effective for congestion management in Dutch Distribution grids. To shed light on this issue, the GO-e consortium aims at performing large-scale agent-based simulations of up to 120 low-voltage networks and a large variety of possible instruments and scenarios. For this reason, we developed a novel scalable time-discrete simulation framework for distributed agent-based simulations of energy systems. We demonstrate the framework on a case-study in which we assess the effectiveness of a dynamic bandwidth tariff instrument on overloading problems in a low-voltage network containing solar panels, batteries, and heat pumps. It was shown that a dynamic bandwidth tariff can successfully resolve forecasted congestion if the associated costs are high enough compared to the day-ahead prices. However, the resulting load shifting can cause new congestion intra-day aswell.