The power grid is becoming more intertwined with communication technologies, forming what is known as the smart grid. This integration allows for more efficient management of the power grid, which can help reduce emissions. However, the increasing connectivity with communication technology also expands the attack surface for cybercriminals or cybercriminal organisations. In 2015, a Ukrainian power station was attacked via a cyberattack, leading to an outage that affected almost 1.4 million people. The growing interconnection between the power grid and communication technologies can thus have severe impacts. Therefore, this research introduces an interdependent communication network and power grid to investigate how failures in the communication network affect the power grid's robustness. For generating communication networks, we use Python’s NetworkX package, and for the power grid, we use pandapower’s IEEE 118-bus test system. We analyse the robustness of the smart grid by examining two different communication networks: a mesh network and a double-star network. We simulate attacks on the communication network by initiating failures based on random selection, degree, betweenness, and closeness centrality, with an increasing number of node failures. We also distinguish between two failure behaviours: one that includes communication network failure propagation (e.g., the spread of malware or the failure of dependency nodes within the communication network) and one without this failure propagation behaviour. In general, the smart grid shows higher robustness with a mesh communication network. However, under different failure behaviours, attack strategies, and numbers of nodes attacked, this can vary. Prioritisation should focus on reducing communication network failure propagation, as this significantly impacts the robustness of the smart grid. Even though degree centrality and betweenness centrality have the most impact on double-star networks, for mesh networks, closeness centrality should also be considered, especially in scenarios without network failure propagation.