In countries such as India with low grid prices, energy firms are offering competitive PPA tariffs by setting up large solar farms. Given lower margins in operating these farms, there is great sensitivity to panels underperforming. To detect under-performance, existing condition monitoring methods compare generated power with an ideal yield calculated based on local weather conditions. Applying such methods to a 1.2MW farm with 6 different PV technologies over 3 years, we observed prediction errors large enough to mask under-performance. To reduce these errors, this work proposes two approaches. Firstly, a piecewise regression approach is proposed which improves estimation accuracy by applying a set of regression models, each corresponding to a partition of the predictor space. This helps capture the inherent non-linearities in PV power output. Secondly, we explicitly model the Maximum Power Point Tracker (MPPT) in a two-step prediction method. In doing so, we combine a regression method on irradiance data with physical modeling of I-V characteristics of panels, resulting in an average reduction in error by about 16%. While the piecewise regression approach requires only power measurements, the I-V approach requires both voltage and ampere measurements. The proposed predictors may be used to monitor the performance of solar farms, leading to timely identification of operational problems and aging.