In the last decade, there has been an emergent attention in the utilization of existing power distribution lines for broadband power line communications (BPLC). PLC technology is becoming more widely adopted because of its excellent fit with smart grid and in-home network applications, with no infrastructure cost. However, PLC not only has a limited spectrum (< 30MHz) and limited coverage (< 1 mile) due to power line cable attenuation but also has some time-varying channel impairments, including multipath fading and RF noise. We investigate a quasi-stationary OFDMA-based BPLC local area network (LAN) for the smart home network or small-scale smart grid (also termed micro-grid) services over indoor power lines, where every nodes are assumed to be equipped an impedance matching circuit (IMC); then, since plug-in or switchoff of nodes do not change the network topology anymore, link budgets of the overall BPLC network are easily estimated even with some channel variations (RF noise, etc) and so its resource management with reliability and flexibility is possible. In this paper, we focus on the cluster-based medium access control (MAC) layer design and resource management of the two types of OFDMA-based BPLC LANs: centralized (AP-based) LAN and distributed (ad-hoc based) LAN.