The operation and planning of distribution grids require the joint processing of measurements from different grid locations. Since measurement devices in low- and medium-voltage grids lack precise clock synchronization, it is important for data management platforms of distribution system operators to be able to account for the impact of nonideal clocks on measurement data. This paper formally introduces a metric termed Additive Alignment Error to capture the impact of misaligned averaging intervals of electrical measurements. A trace-driven approach for retrieval of this metric would be computationally costly for measurement devices, and therefore, it requires an online estimation procedure in the data collection platform. To overcome the need of transmission of high-resolution measurement data, this paper proposes and assesses an extension of a Markov-modulated process to model electrical traces, from which a closed-form matrix analytic formula for the Additive Alignment Error is derived. A trace-driven assessment confirms the accuracy of the model-based approach. In addition, the paper describes practical settings where the model can be utilized in data management platforms with significant reductions in computational demands on measurement devices.