This paper presents a novel approach for integrating an analytical model of Rogowski coils (RC) directly within microcontroller-based systems to enable local verification of acquired signals and facilitate digital twin implementation at the embedded level. The proposed method embeds a simplified yet accurate coil model into the microcontroller’s firmware, allowing real-time comparison between measured and expected signals. This verification process helps detect deviations caused by network anomalies, coil accuracy degradation, or acquisition issues. The concept is validated experimentally by injecting reference signals into the system and comparing the microcontroller-acquired data with the model’s predictions. This embedded verification mechanism supports adaptive configurations depending on the available computational power, number of channels, and coil characteristics. By demonstrating how digital twins can be implemented and maintained even on low-resource platforms, this work offers a flexible and scalable framework for improving the reliability and intelligence of current-sensing systems in distributed measurement applications. Moreover, the approach is generalizable and may serve as a foundational technique for digital twin design across a broad range of sensor-based monitoring systems.
Phase-Locked Loops (PLLs) play an essential role in a variety of power grid applications and measurement devices. Unfortunately, PLL performance analysis and design are often hindered by their inherent nonlinear nature that cannot be adequately described by standard linearized models. To address these issues, this paper presents a two-step modeling approach. First, a Linear and Time-Periodic (LTP) model is applied. Then, a variant of the harmonic balance method is applied to turn the LTP model into a Linear Time-Invariant (LTI) one, whose smallsignal dynamics can be potentially used to analyze the system behavior of terms other than the fundamental one. The proposed methodology is applied to an advanced three-phase PLL scheme based on an Orthogonal System Generator (OSG) followed by a pair of Mixed Second- and Third-Order Generalized Integrators (MSTOGIs), which provide not only harmonics attenuation, but also DC offset cancellation and imbalance mitigation. Some simulation results under different testing conditions, confirm that the obtained model is very accurate, thus paving the way to optimal PLL design in different power grid applications using standard linear system tools.
Fiber-optic current sensor (FOCS) technology offers intrinsic galvanic isolation, a wide linearity range, immunity to electromagnetic interference, and non-invasive measurement, making it a strong candidate for applications in on-site calibration. However, its use as a traceable reference in metrological applications remains limited so far. Laboratory calibration and cross-institutional comparisons are essential steps toward establishing the reliability and traceability of FOCS in real-world conditions. This paper provides an overview of the FOCS operating principle and evaluates the key performance of a new FOCS sensor tested in two National Metrology Institutes (NMIs), including accuracy, stability, linearity, and temperature dependence. It furthermore describes the on-site measurement campaign using the FOCS for efficiency measurement in a medium-voltage substation. The test results reveal that FOCS can meet the performance requirements under practical conditions and demonstrate excellent repeatability and traceability for on-site calibration in operational environments: the linearity is better than $0.1 \%$ over the 2.4 kA current range, with temperature effects less than $0.2 \%$ from -10 to 60 degrees Celsius. This work contributes to understanding the metrological characteristics of FOCS and supports their broader adoption in on-site calibration.
Harmonic current summation is used by transmission system operators to quantify the global contribution of distribution networks hosting distortion sources. An increase of renewable power plants (non-linear current sources) and the over subscription of hosting capacity in distribution networks, could be a concern in containing THD within compatibility levels. IEC 61000-3-6 use RMS values to propose summation exponents (alpha factors). By using harmonic current phasors, it is shown that alpha factors require careful consideration to produce useful results. Simulation data is first used to identify those assumptions that lead to erroneous results. RMS summation and phasor summation is then compared making use of field data. Phasor summation is shown to be practical and to improve reliability of results.
During the last decades, Medium Voltage (MV) and Low Voltage distribution systems have become increasingly complex due to the increasing penetration of Renewable Energy Sources and – more in general – distributed resources such as evehicles. Therefore, better monitoring and control tools are required. This paper discusses how Digital Twin (DT) architecture for MV distribution grids can improve management, presenting the benefits in a specific use case: State Estimation (SE). This approach has been applied to the distribution grid of Unareti S.p.A., an Italian Distribution System Operator (DSO) operating in northern Italy and serving over one million customers. The suggested architecture combines real-time field measurements, a very detailed virtual model of the physical grid, and an SE algorithm all embedded into Advanced Distribution Management System (ADMS) which is also fully integrated within a more general Information Technology/Operational Technology (IT/OT) ecosystem in order to become a DT. This DT framework enables continuous synchronization with live grid conditions, enriching network observability and improving estimation accuracy, even in areas with a low percentage of monitoring devices. The presented case study focuses on a HV/MV primary substation managed by Unareti and demonstrates the capability of the architecture to deliver real-time state estimations in a real operating environment. The mean percentage error of the SE algorithm is $-4.9 \%$ and the standard deviation is $13.3 \%$.
