Most of the world's power grids are controlled remotely. Their control messages are sent over potentially insecure channels, driving the need for an authentication mechanism. The main communication mechanism for power grids and other utilities is defined by an IEEE standard, referred to as DNP3; this includes the Secure Authentication v5 (SAv5) protocol, which aims to ensure that messages are authenticated. We provide the first security analysis of the complete DNP3: SAv5 protocol. Previous work has considered the message-passing sub-protocol of SAv5 in isolation, and considered some aspects of the intended security properties. In contrast, we formally model and analyse the complex composition of the protocol's sub-protocols. In doing so, we consider the full state machine, the protocol's asymmetric mode, and the possibility of cross-protocol attacks. Furthermore, we model fine-grained security properties that closely match the standard's intended security properties. For our analysis, we leverage the Tamarin prover for the symbolic analysis of security protocols. Our analysis shows that the core DNP3: SAv5 design meets its intended security properties. Notably, we show that a previously reported attack does not apply to the standard. However, our analysis also leads to several concrete recommendations for improving future versions of the standard.