This thesis addresses several challenges corresponding to the operation and planning of electricity grids due to severe weather conditions. It considers electricity grid challenges due to natural vulnerabilities including wind speed, wind gusts, and wildfires. A reformulation for the principles of automatic generation control (AGC) in a decomposed convex relaxation algorithm is presented. It finds an optimal solution to the AC optimal power flow (ACOPF) problem that is secure against a large set of contingencies. A surrogate model to quantify the wildfire ignition by each power line under extreme weather conditions is presented. The system operator can use this model to de-energize power lines during Public Safety Power Shutoffs (PSPS). A two-stage robust optimization problem is formulated to ensure the risk-averse resilient operation of the electricity grid under the risk of wildfire for 24 hours. The uncertainty in demand and solar generation are incorporated into the formulation. A 10-year expansion planning of power system under fire hazard weather conditions to find improved balance for proactive de-energization of transmission lines, distributed solar integration, modification of transmission lines, and addition of new lines is presented. The validity of the presented surrogate model and the optimization problems are demonstrated in various test cases.