Although Power Line Communication (PLC) is not a new technology, its use to support communication with low rate on low voltage (LV) distribution networks is still the focus of ongoing research. In this paper, we propose a PLC channel modeling method based on the bottom-up approach for LV PLC in a narrow, low frequency band between 9 kHz and 490 kHz. We employ the model to derive the transfer function of a typical LV PLC network, which is comprised of two common cable types (copper cables and aluminum conductor steel reinforced). We then investigate the multipath effect of the LV PLC in the studied low frequency bandwidth using numerical computations. Our simulation results based on the proposed channel model show an acceptable performance between neighboring nodes, in terms of bit error rate versus signal to noise ratio, which enables communication required for smart grid applications. Furthermore, we show that data transmission beyond one-hop communication in LV PLC networks will have to rely on upper layer protocols.