A method for calculating the virtual energy balances of a continuous bilinear system based on the spectral decomposition of its Gramians of controllability and observability is proposed. There were obtained the indicators for the detection of balance anomalies and their expressions through complex-valued quadratic forms. Comparison of the absolute values of these forms makes it possible to identify the balance anomalies and, equally important, point out the specific devices that cause these anomalies. The main contribution of the work can be defined as two main results. Firstly, this is a generalization of the Gramians method developed earlier for discrete bilinear systems to the continuous bilinear systems. Secondly, this is a new method of assembling the Volterra matrix series to calculate the Gramians and energy functionals of the bilinear systems. The elements of the Volterra series are shown to form a geometric progression, the common ratio of which depends on the parameters of two matrices: of the Fadeev matrix in the spectral decomposition of the controllability Gramian of a linear model and the diagonal nonlinearity matrices of series were obtained to guarantee the BIBO stability of the bilinear system. It is demonstrated that the proposed results can be used in a small signal stability problem analysis for the bilinear representations of power systems.