Multi-controller deployment in a software-defined network improves the system's stability and scalability. However, since network traffic fluctuates, it presents a new problem for balancing loads on remote controllers. Controller Adaption and Migration Decision (CAMD) and Dynamic and Adaptive Load Balancing (DALB) frameworks are developed for efficient balancing of load on the controller to solve the problem of controller overload due to dynamic network traffic. CAMD was considered to be more efficient than DALB, but when the network is more dynamic, and the incoming traffic flow is elephant flow this leads to the overall reduction in system performance. This study proposed a Convergence Time aware Switch Migration Algorithm (CTSMA) that solved the network challenge when the network is more dynamic and incoming traffic flow is more. This research developed an enhanced switch migration algorithm to address the network difficulty of dynamically changing incoming load. Because of the imbalanced distribution of load on the controllers, processing flows will have longer response times and the controllers' throughput will be reduced. Switch migration is the best method of resolving the issue. Present techniques, on the other hand, focus solely on load balancing performance while ignoring migration efficiency, thereby leading to large migration costs and excessive control overheads. To increase the load and migration efficiency of controllers, this research work developed a convergence time aware switch migration method. To find the group of underloaded controllers in the network, the improved framework looked at controller volatility and average load status. Performance comparison indicators included controller throughput, reaction time, and convergence time. According to simulation studies, CTSMA outperforms CAMD by cutting controller reaction time by roughly 6.1%, increasing controller throughput by 8.0% on average, keeping a decent load balancing rate, lowering migration costs, and maintaining the best load balancing rate.