Ubiquitous connectivity is already transforming residential dwellings into smart homes. As citizens continue to embrace the smart home paradigm, a new generation of low-rate and low-power communication systems is required to leverage the mass market presented by energy management in homes. Although Power Line Communication (PLC) technology has evolved in the last decade, the adaptation of PLC for constrained networks is not fully charted. By adapting some features of IEEE 802.15.4 and IPv6 over Low-power Wireless Personal Area Network (6LoWPAN) into power lines, this paper demonstrates a low-rate, low-power PLC system over the IPv6 network (referred to as 6LoPLC), for Home Energy Management System (HEMS) applications. The overall idea is to provide a framework for assessing various scenarios that cannot be easily investigated with the limited number of evaluation hardware available. In this respect, a network model is developed in NS-3 (Version 21) to measure several important characteristics of the designed system and then validated with experimental results obtained using the Hanadu evaluation kits. Following the good agreement between the two, the NS-3 model is utilised to investigate more complex scenarios and various use-cases, such as the effects of impulsive noise, the number of nodes and packet size on the latency and Bit Error Rate (BER) performances. We further demonstrate that for different network and application configurations, optimal data sizes exist. For instance, the results reveal that in order to guarantee 99% system reliability, the HEMS application data must not exceed 64 bytes. Finally, it is shown that with impulsive noise in a HEMS network comprising 50 appliances, provided the size of the payload does not exceed 64 bytes, monitoring and control applications incur a maximum latency of 238.117 ms and 248.959 ms, respectively; both of which are within acceptable limits.