Smart Grid (SG) is an innovative concept that aims to implement a communication infrastructure for data exchange between the various entities connected to these networks. In this case, Wireless Sensor Networks (WSNs) have recently been considered as a promoting communication technology for SG applications. However, problems such as noise, interference and fading in SG environments, make reliable and energy-efficient multi-hop routing a challenging task for traditional WSNs routing protocols. Thus, IETF has proposed an IPv6 based routing protocol working under stringent low power and low-cost constraints. This Routing Protocol for Low power and Lossy Network (RPL), selects the ideal routes from a source to a destination node based on certain metrics injected into what is called an Objective Function (OF). In this work, we investigate basics OFs namely Objective Function zero (OF0) and Hysteresis Objective Function (MRHOF). We also study the most influential parameters on the performance using Contiki COOJA simulator and then evaluate the RPL performance in terms of latency, packet delivery ratio, control overhead and supported throughput. The simulation results revealed that these parameters have a great impact and indicated that the performance of RPL within high-density networks for OF0 can provide a better RPL behavior than MRHOF.