To mitigate the microgrid instability despite the presence of dense Constant Power Load (CPL) loads in the system, a number of compensation techniques have already been gone through extensive research, proposed, and implemented around the world. In this paper, a storage based load side compensation technique is used to enhance stability of microgrids. Besides adopting this technique here, Sliding Mode Controller (SMC) and Lyapunov Redesign Controller (LRC), two of the most prominent nonlinear control techniques, are individually implemented to control microgrid system stability with desired robustness. CPL power is then varied to compare robustness of these two control techniques. This investigation revealed the better performance of the LRC system compared to SMC to retain stability in microgrid with dense CPL load. All the necessary results are simulated in Matlab/Simulink platform for authentic verification. Reasons behind inferior SMC performance and ways to mitigate that are also discussed. Finally, the effectiveness of SMC and LRC systems to attain stability in real microgrids is verified by numerical analysis.