**1. Introduction**

In view of reducing greenhouse gas emissions and carbon dependence, modern power systems are experiencing an ever-increasing integration of renewable energy sources and distributed generation [1,2]. Such resources are typically connected via dedicated inverters whose power electronics-based control can not guarantee any rotational inertia or regularization of the energy generation profile [3,4]. As a consequence, power systems are expected to face much faster dynamics, as proven by recent adverse events in South Australia and California [5,6].

In order to address such challenges, also the measurement infrastructure needs to undergo a significant renovation, both in terms of instrumentation and control strategies [7]. In particular, the transition from traditional to digital electrical substations paves the way to more sophisticated and optimized approaches for the collection and aggregation of the quantities of interest, e.g., voltage and current levels at the transformer secondary windings [8]. In this context, the recent IEC Std 61869-9:2016 [9] defines the operational and communication requirements for instrument transformer with digital output. Due to their capability of converting the output signal directly in a digital form (and thus compatible with many processing and storage applications), such transformers are typically referred to as non-conventional instrument transformers, briefly NCIT [10].

In terms of communication protocol, the IEC Std 61850-9-2:2011 [11] introduces the Sampled Values (SV): a publisher/subscriber protocol for information exchange between Stand Alone Merging Units (SAMUs) and Intelligent Electronic Devices (IEDs) over the Ethernet. Originally conceived just as an efficient way to concentrate the outputs of NCITs

**Citation:** Frigo, G.; Agustoni, M. Calibration of a Digital Current Transformer Measuring Bridge: Metrological Challenges and Uncertainty Contributions. *Metrology* **2021**, *1*, 93–106. https://doi.org/ 10.3390/metrology1020007

Academic Editor: Simona Salicone

Received: 31 August 2021 Accepted: 15 September 2021 Published: 3 October 2021

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and SAMUs [12–14], the SV is now directly applied to more sophisticated processing applications, e.g., phasor measurements [15] and protection schemes [16].

The recent EMPIR project FutureGrid II has been investigating the measurement needs and potential of SVs in modern electrical substations. In particular, dedicated calibration infrastructures for transmitting and receiving SVs have been developed and thoroughly characterized [17,18]. However, a rigorous and well-established procedure for the metrological characterization of NCITs is not yet available. The measurement setup typically includes a transformer measuring bridge capable of processing both analog and digital inputs [19]. The calibration of such device, though, is not straightforward and requires a precise assessment of the several uncertainty sources involved in the measurement process. Indeed, the comparison between purely analog quantities and time-stamped digital values represents a non-negligible challenge, especially in terms of synchronization and phase angle uncertainty.

In this paper, we consider the problem of calibrating a measuring bridge for NCITs from a metrological point of view [20,21]. In particular, we describe a novel measurement setup and discuss the implementation challenges and requirements as well as the possible uncertainty contributions. A preliminary calibration campaign confirms the feasibility and reliability of the proposed approach, and sets a realistic performance target for the uncertainty budget of the calibration infrastructure.

The paper is organized as follows: in Section 2, we present the measurement principle inherent in measuring bridges for traditional and non-conventional transformers. Section 3 outlines the measurement setup for the bridge calibration and describes the actual implementation in METAS laboratories. In Section 4, we discuss the main uncertainty contributions and derive a preliminary uncertainty budget based on technical specifications and statistical analysis. In Section 5, we provide an experimental validation by presenting the results of a measurement campaign on a commercial device. Finally, Section 6 provides some closing remarks and outlines the next steps of the research.

#### **2. Measuring Bridge: Configurations and Measurement Principles**

In this section, we briefly describe the measurement principle of measuring bridges for instrument transformers, focusing on the transition from the traditional analog approach to the non-conventional approach based on SV communication protocol. In the following, we refer to the specific case of current transformers but similar considerations apply as well to voltage transformers.

Traditional measuring bridges for instrument transformers rely on the well-known difference method [22]. As shown in Figure 1a, the same current source *Is* is supplied to two current transformers: a standard reference transformer, typically referred to as normal (channel *N*), and the transformer under test (channel *X*). For the sake of comparability, the two transformers adopt the same transformation ratio. As a consequence, they should produce the same current output at the secondary winding.

**Figure 1.** Typical configuration of a measuring bridge based on: difference method (**a**), digital signal processing (**b**), and IEC 61850-9-2 protocol (**c**).

It is worth noticing that, in a calibration context, the current source and the normal transformers are subject to periodic and thorough metrological characterization campaigns: systematic errors are suitably compensated, whereas random contribution determine the source stability and the transformer uncertainty, whose levels are guaranteed to be much lower than the expected performance of the device under test.

By means of current sensors (typically, a calibrated shunt and a voltmeter or a digitizer), the measuring bridge determines the current flowing at the secondary winding of the two transformers, *IN* and *IX*, respectively, as well as their difference *Id* = *IX* − *IN*. In a vector space rotating at the nominal system frequency (e.g., 50 Hz), it is possible to represent these quantities as rotating vectors, whose magnitude and phase depend on the characteristics of the transformer under test.

Based on these measurements, the measuring bridge calculates the complex transformer or excitation error Δ*E* = *Id*/*IN* (The excitation error is not necessarily included in a calibration report as it depends on the accuracy and stability of the selected current source and reference standard transformer. In this paper, we report also Δ*E* as it is one of the measurement values commonly output by a measurement bridge, and thus it might be interesting to associate it with a measurement uncertainty), the transformer ratio error Δ*ε*, and the phase displacement Δ*ϕ* (In this paper, the test waveforms consist of sine waveforms. Therefore, a negative phase displacement corresponds to a current *IX* that is *delayed* with respect to the reference current *IN*).

In Figure 1b, we present an example of new generation of measuring bridges. With the emergence of integrated circuits and fixed-point microprocessors, also measuring bridges have been equipped with Analog-to-Digital Converters (ADCs) and Digital Signal Processing (DSP) units for a more sophisticated treatment of the digitizer outputs. Instead of considering their difference in an analog circuit, each channel is processed independently: by means of a Discrete Fourier Transform (DFT), it is possible to define the complex coefficient associated with the nominal system rate. The comparison between these complex quantities allow for quantifying the excitation and ratio errors and the phase displacements. Moreover, by differentiating the phase information, it is also possible to determine the signal frequency and detect possible distortion introduced in the transformation.

Finally, Figure 1c represents the configuration of a measuring bridge for NCITs. As the transformer under test outputs the current at the secondary winding directly in a digital format, the *X* channel has to be supplied with an Ethernet board responsible of capturing the SV data packets and aligning them with the samples provided by the ADC on the *N* channel.

First, the captured SV data packets are queued in a First-In-First-Out (FIFO) buffer. Then, the time-stamp information is extracted and compared with the internal time of the measuring bridge: in the presence of high discrepancies (e.g., delayed transmission), the comparison with the reference channel values is unfeasible and the measuring bridge outputs an error message due to synchronization loss. Otherwise, the analog quantities are extracted from the SV data packets and transmitted to the DSP for the DFT processing and the error computation.

In this regard, it is reasonable to assume that the excitation error Δ*E* is mostly dependent on the accuracy and stability of the current measurement at the *N*-channel. In the absence of synchronization or packet loss, the SV data stream is characterized by a constant amplitude whose accuracy depends only on the quantization error and on possible numerical errors in the bridge DSP. On the contrary, *IN* is an analog quantity that might vary as function of time, depending on the stability of the current source and on the characteristic of the standard transformer *CTN*.

#### **3. Measurement Setup**

In this section, we present the measurement setup for the metrological characterization of a measuring bridge for non-conventional instrument transformers. Indeed, a detailed analysis of the employed instruments and measurement techniques is crucial in view of the uncertainty analysis in the following section.

As shown in Figure 2, the setup consists of six main components: a time reference, a calibrator, a transconductance amplifier, a calibrated shunt, a set of synchronized voltmeters, and the Device Under Test (DUT), i.e., the measuring bridge.

**Figure 2.** Measurement setup employed for the calibration of measuring bridges for non-conventional instrument transformers.

The time reference is responsible for providing the calibrator with a refined and stable time-base. To this end, a 10-MHz signal overrides the internal clock of the calibrator. It is worth noticing that, in such application, the traceability to Universal Time Coordinate (UTC) time is not mandatory. The only constraint is the exact synchronization between the calibrator analog and digital outputs, as well as between the calibrator and the measuring bridge.

The calibrator consists of three main units:


waveform to be generated as a sample series at the given sampling rate, stores the acquired samples, and processes them in order to estimate (in quasi real-time) the DAC phase offset. On the other side, the controller is responsible for publishing the SV data packets, from the encapsulation of the SV to the actual transmission through a dedicated Ethernet board.

The DAC outputs a low-voltage sinusoidal signal, in the range of ±2 V. The amplitude, frequency and initial phase of the signal can be customized to specific test conditions. The conversion to the current levels expected by the *N* channel of the measuring bridge is carried out by a transconductance amplifier. In this sense, the amplifier ratio represents a further degree of freedom in view of a finer control of the current level, and thus of the excitation. The transconductance amplifier is not an ideal current source and introduces non-negligible uncertainty contributions on both the amplitude and phase of the signal supplied to the measuring bridge.

The ADC re-acquires the amplifier output by means of a calibrated high-precision shunt whose input range is suitably adapted to the specific test configuration. Typically, the shunt output is scaled such that a full input range corresponds to an output range of 0.8 V. Given the calibration context and the high-accuracy of the employed shunts, their contribution in terms of amplitude and phase uncertainty can be reasonably considered as negligible, as further discussed in the next section.

The time-series acquired at the two ADC input channels are processed via a DFTbased routine (further details in [18]) and the phase associated with the fundamental frequency is retrieved. In particular, channel ai1 is representative of the contribution of ADC only, whereas channel ai0 is representative of the entire measurement chain. By properly differentiating these terms, it is possible to define the actual phase of the signal supplied to the measuring bridge.

In the top-centre part of the scheme, a pair of Digital Voltmeters (DVMs) monitors the input and output signal of the series of transconductance amplifier and shunt. The DVMs are employed as high-precision sampling systems that operate in simultaneous mode: the acquired time series are processed via a sine fitting method that allows for accurately estimating the amplitude, frequency and initial phase of the signals under analysis. The DVMs' trigger is not synchronous with the PPS of the synchronization unit, neither is it disciplined to the time reference. As a consequence, the phase information cannot be related to the phase measured on the calibrator. Nevertheless, the difference between the phase measured on each DVM allows for quantifying the phase offset introduced by the amplifier only. It is therefore an independent method to validate the results of DFT-based routine carried out on the re-acquired waveforms.
