Due to the increasing requirements of safety and reliability in more electrified applications (transportation for example), fault detection and diagnosis (FDD) of electrical systems has become a hot research topic. In the process of FDD, there are three steps: fault detection, fault isolation and fault estimation. The first two items are the commonly addressed while the last one is less tackled as it requires the development of a fault model which parameters are relevant of the fault. In this paper, we propose an analytical model of multiple fault effects on a three phases electrical system. The model is based on the expressions of the currents in the (d,q) or Park synchronous rotating reference frame. We prove through simulation results the efficiency of the model for fault combination of gain, offset and phase shift. The results show also the accuracy of the model that could be used for fault estimation purpose.