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A methodology is developed to assess the time-domain power quality state estimation (PQSE) in electrical systems based on the Kalman filter implemented using parallel processing techniques through graphics processing units (GPUs) to reduce the execution time. The measurements used by the state estimation algorithm are taken from the simulation and transient propagation response of the power network. The parallel Kalman filter (PKF) state estimation obtains the waveforms for busbar voltages and line currents with several sources of time-varying electromagnetic transients. The PKF is evaluated using the compute unified device architecture (CUDA) platform and the CUDA basic linear algebra subprograms library, the parallel filter is executed on GPU cards. Case studies are applied to solve the time-domain state estimation using the proposed PKF-PQSE method, obtaining an execution time reduction and including time-varying harmonics, short circuit faults, and load transient conditions. The speed-up depends on the number of state variables modeling the electrical system under analysis. The PKF-PQSE results are successfully compared and validated against the power systems computer aided design/electromagnetic transients including direct current simulator.