This chapter addresses optimization problems associated with the secure and economic operation of large-scale power systems. We apply the decomposition techniques discussed earlier in the book to two realistic examples for power systems operations. The chapter explores the use of multiple variants of Benders decomposition to solve the security-constrained unit commitment problem, incorporating enhancements such as (i) multi-cut strategies, (ii) valid inequalities, and (iii) adding representative scenarios to the master problem to improve computational efficiency and scalability. We also explore Augmented Lagrangian Decomposition to solve the multi-area DC optimal power flow problem, focusing on a decentralized optimization framework that render the same solution as the centralized one. Numerical experiments on realistic test systems illustrate the effectiveness of the proposed methods in achieving reliable and cost-effective operation. We present key remarks regarding computational trade-offs and practical implementation challenges.