This paper presents a novel approach to optimize complex variables for stabilizing integrated power grids, focusing on the detection and mitigation of gas leaks in combined natural gas and green hydrogen systems. The research addresses the critical challenges of maintaining grid stability and reliability in the transition to renewable energy sources. By leveraging complex analysis in fluid mechanics, the study proposes an innovative method for gas leak detection using the complex potential and streamline distortion analysis. The methodology includes a genetic algorithm with multi-level optimization to enhance system stability while minimizing costs. The paper demonstrates the application of this approach on a 9-bus 8-node integrated grid, showcasing its potential to improve safety, reduce economic losses, and enhance the overall efficiency of power systems. This work was able to stabilize the integrated grid, as to maintain the same power and gas demand supply, by redirecting the gas route, decreasing the damage and cost caused by the gas leak, which promoted a economy of $14,000 dollars per active day of the grid.