Our society depends heavily on the electric power infrastructure. To ensure its reliability, key power grid components such as transformers are extensively monitored for signs of failures and errors. This work concentrates on a type of event known as the partial discharge (PD) because it is the symptom of insulation weakness, the most common cause of transformer failures. More specifically, our work is to locate the position of a partial discharge to provide information for preventive maintenance. Our method utilizes the information from a set of ultra-high frequency (UHF) sensors inside the transformer, and proceeds in two steps: first determine the signal arrival time and then locate the position based on time differences. To determine the arrival time, we develop a convolutional filtering method based on the Savitzky-Golay filter. To provide accurate locations, we simulate the electromagnetic wave propagation using finite-difference time-domain (FDTD) to generate a reference table of the travel time from each FDTD mesh point to the sensors. We exercise our method using two sets of UHF measurements with different signal to noise ratios. In both cases, our method provides more accurate locations than other methods. The difference is particularly prominent when the signal is weak. With weak signals, the best existing method, the cumulative energy method, was only able to predict the PD location within 300 mm of the known sources in 13% of the test cases, while our method is correct in 48% of the test cases.