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In this paper, the distribution static compensator model based on the bond graph (BG) domain is presented. The methodology is applied to reactive power compensation in distribution systems where a traditional phase lock loop for sensing the AC grid frequency is not needed. The control law is developed using the inverse BG model, which is extracted using the bi-causality concept. In this way, it is possible to perform the distribution system analysis completely in the BG domain. This means that the graphical model is inverted by obtaining the open-loop control law structure, and then the close loop is formulated. The balanced and unbalance conditions are analyzed, generating a control structure that is robust and efficient. The efficacy of the proposed methodology is shown through: partial and complete system simulations in MATLAB/Simulink® (MATLAB r2015b, Natick, Massachusetts, 01760, USA), as well as experimental laboratory tests. Such tests use: the rapid control prototyping concept and the real-time simulator Opal-RT Technologies® (Montreal, QC, Canada). [ABSTRACT FROM AUTHOR]