Large-eddy simulation (LES) has been used previously to study the effect of either configuration or atmospheric stability on the power generated by large wind farms. This is the first study to consider both stability and wind farm configuration simultaneously and methodically with LES. Two prevailing wind directions, two layouts (turbines aligned versus staggered with respect to the wind) and three stabilities (neutral and moderately unstable and stable) were evaluated. Compared with neutral conditions, unstable conditions led to reduced wake losses in one configuration, to enhanced wake losses in two and to unchanged wake losses in one configuration. Conversely, stable conditions led to increased wake losses in one, decreased wake losses in two and unchanged wake losses in one configuration. Three competing effects, namely, rates of wake recovery due to vertical mixing, horizontal spread of wakes and localized regions of acceleration caused by multiple upstream wakes, were identified as being responsible for the observed trends in wake losses. The detailed flow features responsible for these non-linear interactions could only be resolved by the LES. Existing analytical models ignore stability and non-linear configuration effects, which therefore need to be incorporated. Copyright © 2017 John Wiley & Sons, Ltd. Copyright © 2017 John Wiley & Sons, Ltd.