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Electronic textiles (e-textiles), known as computational fabrics, offer an emerging platform for constructing ambient intelligent applications. Computational nodes in e-textiles are driven by batteries. Unlike wireless sensor networks, not each computational node in e-textiles has its own battery. Instead, many computational nodes in e-textiles share a battery. Existing e-textiles use one fixed battery to drive a fixed set of computation nodes (or power consuming electronic components). The fixed battery-component connection may result in electronic components stopping functioning and/or energy waste in batteries when link connection problems occur. In this paper, we propose a new infrastructure of the power networks for e-textiles: flexible power network (FPN). Under the FPN infrastructure, a power consuming node (PCN) is not just connected to one single fixed battery. Instead, it is connected to multiple batteries and can obtain power energy from one of the available battery nodes (BNs) with the help of a battery selector. The electrical features of battery selectors and overcurrent protectors that protect the batteries from wasting the charge when short-circuit faults occur are illustrated. Moreover, by modeling the number of fault occurrence at conductive wires and nodes stochastically, an evaluation algorithm is proposed to analyze the reliability of FPN and to compare the metrics of different design schemes under the perspective of both the BNs and the PCNs. Experimental results show that our FPN is more dependable than some common e-textile electric networks published before with the occurrence of short- and/or open-circuit faults.