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The Laser Interferometer Space Antenna Pathfinder (LPF) main observable, labeled Δg, is the differential force per unit mass acting on the two test masses under free fall conditions after the contribution of all non-gravitational forces has been compensated. At low frequencies, the differential force is compensated by an applied electrostatic actuation force, which then must be subtracted from the measured acceleration to obtain Δg. Any inaccuracy in the actuation force contaminates the residual acceleration. This study investigates the accuracy of the electrostatic actuation system and its impact on the LPF main observable. It is shown that the inaccuracy is mainly caused by the rounding errors in the waveform processing and also by the random error caused by the analog to digital converter random noise in the control loop. Both errors are one order of magnitude smaller than the resolution of the commanded voltages. We developed a simulator based on the LPF design to compute the close-to-reality actuation voltages and, consequently, the resulting actuation forces. The simulator is applied during post-processing the LPF data. [ABSTRACT FROM AUTHOR]