This paper studies the resource allocation algorithm design for secure information and renewable green energy transfer to mobile receivers in distributed antenna communication systems. In particular, distributed remote radio heads (RRHs/antennas) are connected to a central processor (CP) via capacity-limited backhaul links to facilitate joint transmission. The RRHs and the CP are equipped with renewable energy harvesters and share their energies via a lossy micropower grid for improving the efficiency in conveying information and green energy to mobile receivers via radio frequency (RF) signals. The considered resource allocation algorithm design is formulated as a mixed non-convex and combinatorial optimization problem taking into account the limited backhaul capacity and the quality of service requirements for simultaneous wireless information and power transfer (SWIPT). We aim at minimizing the total network transmit power when only imperfect channel state information of the wireless energy harvesting receivers, which have to be powered by the wireless network, is available at the CP. In light of the intractability of the problem, we reformulate it as an optimization problem with binary selection, which facilitates the design of an iterative resource allocation algorithm to solve the problem optimally using the generalized Bender's decomposition (GBD). Furthermore, a suboptimal algorithm is proposed to strike a balance between computational complexity and system performance. Simulation results illustrate that the proposed GBD based algorithm obtains the global optimal solution and the suboptimal algorithm achieves a close-to-optimal performance. Besides, the distributed antenna network for SWIPT with renewable energy sharing is shown to require a lower transmit power compared to a traditional system with multiple co-located antennas.