Satellite communication is an indispensable part of future wireless communications given its global coverage and long-distance propagation. In satellite communication systems, channel acquisition and energy consumption are two critical issues. To this end, we investigate the tradeoff between the total energy efficiency (TEE) and minimum EE (MEE) for robust multigroup multicast satellite communication systems in this paper. Specifically, under the total power constraint, we investigate the robust beamforming aimed at balancing the TEE-MEE, so as to achieve the balance between the fairness and total performance on the system EE. For this optimization problem, we first model the balancing problem as a nonconvex problem while deriving its approximate closed-form average user rate. Then, the nonconvex problem is handled by solving convex programs sequentially with the help of the semidefinite relaxation and the concave-convex procedure. In addition, depending on the solution rank value, Gaussian randomization and eigenvalue decomposition method are applied to generate the feasible solutions. Finally, simulation results illustrate that the proposed approach can effectively achieve the balance between the TEE and MEE, thus realizing a tradeoff between fairness and system EE performance. It is also indicated that the proposed robust approach outperforms the conventional baselines in terms of EE performance.