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This paper presents a gradient-based nonlinear optimization wrapper for an electromagnetic transient simulation program to assist in the design of hardware and control parameters of flexible AC transmission system (FACTS) apparatus. A new second-order sensitivity analysis method is introduced that quantifies the sensitivity of the optimal solution to parameter uncertainties. Using this approach, the sensitivity of the harmonic elimination capability of a pulsewidth-modulated voltage-source converter to variations in switching angles is investigated. This paper also adapts the method of Pareto optimization to the simulation-based design of FACTS apparatus when multiple design objectives are to be satisfied. The developed Pareto optimization tool generates a Pareto frontier plot to visualize the design tradeoffs between the multiple objectives. The effectiveness of the tool is demonstrated through a design example that selects optimal values for the DC-bus capacitor and the control settings of a STATCOM.