With the emerging deregulated electricity markets, a part of the electricity trading takes place in dayahead markets where producers and retailers place bids in order to maximize their profit. We present a price-maker model for strategic bidding from the perspective of a producer in Price Coupled Regions (PCR) considering a capacitated transmission network between local day-ahead markets. The aim for the bidder is to establish a production plan and set its bids taking into consideration the reaction of the market. We consider the problem as deterministic, that is, the bids of the competitors are known in advance. We are facing a bilevel optimization problem where the first level is a Unit Commitment problem, modeled as a Mixed Integer Linear Program (MILP), and the second level models a market equilibrium problem through a Linear Program. The problem is first reformulated as a single level problem. Properties of the optimal spot prices are studied to obtain an extended formulation that is linearized and tightened using new valid inequalities. Several properties of the spot prices allow to reduce significantly the number of binary variables. Two novel heuristics are proposed, the first applicable in PCR, the second for general formulations with Special Ordered Sets (SOS) of type 1. Our computational experiments highlights the risk of a loss for the bidder if some aspects usually not considered in the literature, such as Price Coupled Regions, or an accurate UC problem, are not taken into account. They also show that the reformulation techniques, combined with new valid inequalities, allow to solve much larger instances than the current state-of-the-art. Finally, our experiments also show that the proposed heuristics deliver very high quality solutions in a short computation time.