Accurate State of Power (SoP) estimation is important for reliable, safe, and efficient lithium-ion battery packs operation. SoP describes how quickly the host controller permits the addition or reduction of energy from a battery pack without violating some set of design constraints. We propose BiLSTM-based co-estimation algorithm which is a combination of SoC and SoP estimation algorithms. Co-estimation utilizes the relationship between the SoC and SoP using BiLSTM. Co-estimation aims to estimate the SoP accurately by learning the battery parameters automatically from the optimum SoC quantity without using inference systems that have heavy computational cost, like filtering. Unlike LSTM that can only learn from the historical value due to its forward learning behavior, the BiLSTM is able to catch the conceptual information explicitly due to its forward and backward learning capability. This further improves the accuracy of both estimated SoC and SoP. Urban Dynamometer Driving Schedule is used as the dataset in our experiment. It is divided into train and test. The BiLSTM achieved the lowest root mean square error (RMSE) of 14.66 RMSE using SoC and SoP co-estimation approach with 70% data used as training. In the existing works about SoP, the SoP accuracy rely heavily on the SoC accuracy. In addition to that, BiLSTM-based SoP estimation using a maximum current approach is proposed. The proposed method aims to reduce the computational complexity by directly estimating the SoP. Direct estimation is done by estimating the maximum current based on voltage constraint and SoC constraint. The final estimated SoP is the minimum value of the maximum current based on SoC, voltage, and design limit constraint. While the co-estimation method achieved the lowest RMSE and without co-estimation method achieved the fastest computing time, the co-estimation method needs high computing time and without the co-estimation method achieved the lowest accuracy. The proposed method achieved 15.54 of RMSE with only 0.559 hours of computing time.