Wind energy is crucial to the transition to a carbon-free world. However, new wind farms are increasingly sited on complex terrain, whose influence on turbine performance is still not well understood. Here large-eddy simulations are performed on the flow around a wind turbine sited on three different terrain types: a flat ground, a 2-D hill, and a 3-D hill. We find that hilly terrain can increase the power generated via the speed-up effect, but that it can also increase the wake deficit and deflect the wake center, potentially affecting any turbines downstream. We interpret this deflection as being caused by the topography-induced vertical velocity component, which we model with a passive tracer method. By combining this passive tracer method with engineering-focused wake models, we obtain improved predictions of the velocity deficit and wake deflection. Such a hybrid strategy is fast and accurate, facilitating the design of wind farms sited on steep hilly terrain, which often experience flow separation at the backslope.