An adaptive power allocation by minimizing grid power consumption for the Orthogonal Frequency Division Multiplexing (OFDM) system with the hybrid energy supply under a fast fading channel is proposed in this paper. To solve the non-convex problem, two adaptation algorithms have been presented. The first is Lagrangian algorithm and the second is a successive convex approximation (SCA) algorithm. The theoretical analysis and simulation results show that the proposed algorithms are effective. Compared with traditional OFDM systems with grid energy supply only, the proposed algorithms can reduce the power consumption of the grid. Also, different proposed algorithms have different performance. Lagrangian algorithms with higher computational complexity have better performance. However, there is a trade-off between computational complexity and performance.
