This paper describes mathematical models for estimating measurement uncertainties of a new sampling primary standard for maintaining traceability of alternating current (ac) quantities to the time-invariant (or direct current (dc)) quantities of the International System of Units at the Physikalisch-Technische Bundesanstalt (PTB). A high-resolution analogue-to-digital conversion is used to determine effective values of ac quantities at low frequencies with uncertainty of some microvolts per volt and short measurement times. The system operates according to the synchronous generation and simultaneous analogue-to-digital conversion technique (Ramm G et al 1999 A new scheme for generating and measuring active, reactive and apparent power at power frequencies with uncertainties of 2.5 × 10 −6 IEEE Trans. Instrum. Meas. 48 422-6 [1], Kürten Ihlenfeld W G 2001 Maintenance and traceability of ac voltages by synchronous digital synthesis and sampling PTB Report E-75, Braunschweig [2]), and extensive comparisons with the primary thermal converters of the PTB show that the sampling system and the ac-dc thermal transfer technique agree within about ±0.5 µV V −1 .