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A real-time transient simulation of nonlinear elements in transmission networks requires significant computational power. This paper proposes an iterative nonlinear transient solver on a field-programmable gate array. The parallel solver, based on the compensation method and the Newton-Raphson algorithm (continuous and piecewise), is entirely implemented in Very high speed integrated circuit Hardware Description Language. It also involves sparsity techniques, deeply pipelined arithmetic floating-point processing, and parallel Gauss-Jordan elimination. To validate the new solver, two case studies are simulated in real time: surge arrester transients in a series-compensated line and ferroresonance transients in a transformer, with time steps of 5 and 3 μs, respectively. The captured real-time oscilloscope results demonstrate high accuracy of the simulator in comparison to the offline simulation of the original system in the ATP version of electromagnetic transient program.