This paper highlights the use of clustering algorithms to group power system nodes based on the dynamic responses to large disturbance events. An overall framework of analysis is presented. Starting from the choice of the events to analyze, the features used as inputs to the clustering procedure are defined, and the appropriate clustering algorithm is chosen. The features include parameters taken from the dynamic response and distance matrices calculated from the electrical distance, the Euclidean distance, and the Hausdorff and Wasserstein global distances. A statistically significant analysis is presented to select the number of clusters and compare the results obtained from clustering algorithms that depend on random choices in their solution process. The calculations are carried out on the dynamic model of the Great Britain 36-bus electricity transmission network. The most significant results of this study have been obtained by executing the spectral clustering algorithm with inputs from the Wasserstein distance matrix.

The sensitivity of distribution network losses to the change in net power at the network nodes (and phases of each node for unbalanced distribution systems) conveys key messages about the need to increase or decrease the net power to reduce the network losses. Similar information is provided by the total network losses allocated to nodes and phases, determined by a simple calculation based on the power flow solution. However, the allocated losses are not formally equivalent to the sensitivities of network losses to net load variation. This paper provides original insights into the interpretation and application of the allocated losses in radial distribution systems. New analytical formulations of the sensitivity of the total losses with respect to the node current magnitude are provided, starting from the power flow solution for balanced and unbalanced radial distribution networks. Two fundamental results are then presented for the first time: (i) the sign of the allocated losses is identical to the sign of total loss sensitivities with respect to the node current magnitudes, and (ii) the increase/reduction of the total losses for small net power changes in a node are determined by calculating the product of the sign of the allocated losses and the sign of the net node power, without the need of carrying out further power flow calculations. The results are discussed showing solutions obtained on balanced and unbalanced radial distribution systems with time-varying loads and local generations, even in reverse power flow conditions.