This paper proposes a new method to identify the real power transfer between generators and load using modified nodal equations. Based on solved load flow results, the method partitions the Y-bus matrix to decompose the current of the load buses as a function of the generators' current and load voltages. Then it uses the modified admittance matrix to decompose the load voltage dependent term into components of generator dependent terms. Finally using these two decompositions of current and voltage terms, the real power transfer between loads and generators are obtained. Next part of this paper focuses on creating an appropriate Artificial Neural Network (ANN) to solve the same problem in a simpler and faster manner. For this purpose, supervised learning paradigm and feedforward architecture have been chosen for the proposed ANN power transfer allocation technique. Almost all system variables obtained from load flow solutions are utilised as inputs to the neural network. Moreover, tan-sigmoid activation functions are incorporated in the hidden layer to realise the non-linear nature of the power transfer allocation. The modified IEEE 30-bus system is utilised as a test system to illustrate the effectiveness of the ANN technique compared to that of the modified nodal equations method.