Photovoltaic (PV) systems are broadly utilized, especially for remote electrification. It is easier for installation and is free of greenhouse gases, so the impacts on the environment are reduced. The temperature and irradiance change during the day, and the circumstances are more dynamic on cloudy days. Hence, attaining maximum power under some environmental conditions is complex and also requires individual techniques for tracking the maximum available power. These approaches are named maximum power point tracking (MPPT) methods. These are designed through power electronic converters, which supply the PV power to the load. In recent years, meta-heuristic-based algorithms have emerged because of their local optima avoidance ability and flexibility. However, the maximum power point (MPP) will not be tracked efficiently due to the constraint factors between some circuit parameters. This limitation has to be solved in this study. Here, MPPT constraint conditions of the PV system with an inverter are found by analyzing its integrated mathematical model. The MPP of a PV system is tracked by diverse techniques. Though these approaches differ in complexity, effectiveness, and convergence speed, cost and sensors are required. With the effect of these challenges, the main intention of this paper is to design and develop a new modified MPPT algorithm for enhancing the efficiency of the power grid connected with a DC-AC single-phase full-bridge inverter and a proportional integral derivative (PID) controller. Here, the parameters of the PID controller are tuned or optimized by the newly improved meta-heuristic algorithm termed modified tunicate swarm algorithm with new condition (MTSA-NC) thus maximizing the energy extraction of the PV system. The search process for newly improved MTSA-NC works well to adapt the MPPT to cope with a "grid-connected" inverter by attaining a faster convergence rate. Here, MTSA-NC is adopted by introducing the fitness-based solutions for updating the swarm behavior of tunicates to maximize the energy efficiency of "grid-connected" inverter systems for PV arrays. In MTSA-NC, the optimal fitness value is known as a food source, which is used for determining the solution updating. Finally, the experimental tests validate the success of the designed scheme in a PV system during uniform irradiance and partial shading conditions.