As the power system grows more complex and active, equivalent models have become a solution for modelling parts of the network that have limited observability or are confidential or too complex to simulate otherwise. In the past decade, this topic has also made its way to distribution networks because of its transition towards an active network, which was not the case before. The current grey- and black-box techniques for equivalent modelling create models that are fitted to the average dynamic response of the system or have limited applicability. Also, the existing methods lack extensive verification under different system conditions, and these works rarely focus on active distribution networks (ADNs) with multiple points of common coupling (PCCs). This thesis aims to develop an equivalent model that can estimate the dynamic response of an active distribution network with multiple PCCs and under diverse operating conditions and topological changes.

The proposed approach is based on a graph-time convolutional neural network (GTCNN) that relates available PMU measurements inside the distribution network on a graph structure 𝒢_GTCNN. The graph 𝒢_GTCNN is obtained by taking a modified line graph of the graph representation of the power system and is expanded using the Cartesian product graph rule to include the temporal dependencies of nodes on their past values. The inputs of the equivalent model are the voltage magnitude |V| and angle θ at the PCC and the initial power injections P₀ and Q at non-PCC nodes, while the model outputs the active P and reactive Q power at the PCC nodes. The GTCNN explicitly considers the initial power injections P₀ and Q₀ at non-PCC nodes to help the model learn how different operating conditions and topological changes impact the dynamic response. The DSO trains the equivalent model using simulation data or collected PMU measurements. The model is exchanged with the TSO every month, who can use the equivalent in co-simulation with their transmission network model to perform transient stability studies.

The GTCNN-based equivalent model showed promising performance as an equivalent model for transient stability. The GTCNN was benchmarked against two state-of-the-art Long Short-Term Memory (LSTM)-based equivalent models and a hybrid GTCNN-LSTM model. The evaluation was performed on a real Dutch distribution network using three datasets, each focussing on a different system condition: different fault events, different operating conditions and different hidden topological changes. The GTCNN-based equivalent model had a mean-squared error (MSE) below 0.02 for each dataset, which means it can accurately reproduce the dynamics. This accuracy is comparable to the LSTM-based equivalent models, but the GTCNN could train 4x faster. The GTCNN also showed good generalisation performance, as its accuracy did not decrease on the validation and test sets. A study on scaling performance suggested that the MSE of the GTCNN-based equivalent model increases slower than that of the LSTM-based models while its training time increases faster. Therefore, the GTCNN-based equivalent model trains faster for smaller ADNs but will be more accurate with more measurement nodes. However, the proposed GTCNN has difficulty learning the response at different close-by PCC terminals if the dynamics are different.

The developed GTCNN-based equivalent model can predict the dynamic response accurately under changing topologies and operating conditions at a similar performance level to existing LSTM-based approaches. However, its training time is much faster, which can result in a more accurate equivalent model by a more frequent model exchange between the DSO and TSO or a more extensive dataset being used to train the model. In future research, the GTCNN performance will be evaluated on a more comprehensive dataset containing all three system conditions to establish how much data is needed to train the equivalent model accurately. Also, the system frequency will be considered as an additional input. Moreover, its scaling performance will be evaluated more extensively and with a more efficient coding implementation. Furthermore, a heterogenous graph convolutional operator will be implemented to learn the connection per relational type (source node - edge type - target node). Finally, the co-simulation interface between the equivalent model and popular simulation tools will be explored.