Competitive renewable energy procurement auctions are becoming increasingly prevalent. In a pay-as-bid auction, investors bid the price support required and receive that price if successful. Bidding strategy may be influenced by factors external to the auction, such as transmission expansion planning decisions. This may increase costs. In this paper, we show that integrating a pay-as-bid auction with transmission expansion planning may allow for closer total system cost minimisation over many time periods. This paper develops an auction mechanism and associated modelling framework to carry this out. The contributions of this framework are verified using a numerical example. Our results show that ignoring generation costs in transmission expansion planning can have economic consequences, while traditional pay-as-bid auctions can benefit from incorporating features associated with transmission expansion planning, such as multi-period optimisation. Full integration of both modelling frameworks can lead to efficiency improvements, both in terms of reduced investor rent-seeking and a more efficient deployment path.