The developed electronics module takes over each task in the signal processing chain, from detection and data acquisition to data storage. The returning optical signal from the FOCS is converted into an electric signal by a photo diode (Thorlabs FGA01FC) and sent through an amplifier stage. A custom-made electronics board including a field-programmable gate array (FPGA) carries out the analog-to-digital conversion. Via an onboard digital-to-analog converter, the FPGA chip produces a sinusoidal drive voltage with adjustable frequency to control the LiNbO₃ phase modulator. The current-related phase shift can then be inferred from a Fourier analysis of the detected optical signal. 2ϕ=arctanJ2(Δϕ0)J1(Δϕ0)U(ωm)U(2ωm

The phase shift ϕ is retrieved from the relation of the voltage amplitudes U in the spectrum at the angular modulation frequency ωm and the next harmonic 2ωm. Jn is the Bessel function of the first kind at the value of the modulation depth Δϕ0, which is given by as 3Δϕ0=ϕ0sin⁡ωmT2, with ϕ0 being the amplitude of the modulation signal and T the propagation time of light for one round trip between the LiNbO₃ phase modulator to the mirror. To obtain maximum sensitivity for the demodulation processing, ϕ0 and ωm may be selected so that J1 is at its first maximum (Δϕ0=1.84). Furthermore, modulating at the so-called proper frequency – when one full period of the sinusoidal modulation signal is equivalent to the time of flight T for the light in the interferometer – eliminates bias offsets in the even harmonics, which could lead to drifts over time, especially under changing ambient conditions (). In the literature, there are also other approaches to signal recovery, such as choosing different values of the modulation depth for demodulation so that J1=J2 or including higher harmonics of the modulation frequency ().

From the calculated phase shift, the corresponding current is inferred from Eq. (). The result is sent from the FPGA board via Ethernet to a commercial data hub (Artemes GmbH, Austria), which saves the data on a local hard disk drive and allows remote access via a modem using OpenVPN. Furthermore, this connection allows the remote setting of modulation parameters via the FPGA and a power reset of the electronics module. A schematic of the signal processing chain taken over by the electronics module is shown in Fig. .

To estimate the fundamental detection limit imposed by the optoelectronic detection circuit, we estimated the noise amplitudes for the presented sensor system, which limit its sensitivity. The current that would generate the same output signal as the sum of all noise sources, resulting in a signal-to-noise ratio of 1, can then be given as a figure of merit and is called the noise-equivalent current INE.

For the polarization-rotated reflection interferometer, the generated photocurrent id can be described by 4id=rP02(1+sin⁡ϕ).

Here, r relates to the conversion coefficient of the photo diode, which is usually 1 A W⁻¹ for InGaAs detectors at 1550 nm, and P0=200 µW is the optical power measured at the output port of the circulator. Thus, the photo detector signal consists of a mean contribution 〈i〉=rP02 and a variable term dependent on the Faraday phase shift rP02sin⁡ϕ.

In FOCS, there are three uncorrelated noise sources. Thermal noise, or Johnson–Nyquist noise, concerns the thermal movement of electrons in the electric circuit. Photon shot noise, or Poisson noise, arises from the statistical fluctuations of the number of photons over time from the light source. Finally, light source intensity noise refers to the beating of spectral components at random phases ().

The rms values of the individual noise sources in the signal can be given as 5ith=4kTRLΔf,ish=2e〈i〉Δf,iin=〈i〉2ΔνeΔf.

Here, k is Boltzmann's constant, and T is the ambient temperature, assumed as 25 °C. RL=22 kΩ denotes the resistance experienced by the photocurrent, while the detection bandwidth Δf is determined by the FPGA's Fourier transform algorithm, with a Fourier window bin size of fb=4883 Hz = 2Δf. Furthermore, e is the electron charge, and Δνe=7.49×1012 Hz is the SLD's spectral width.

Using Eq. () and setting the variable term in Eq. () equal to the noise amplitudes in Eq. (), the separate noise-equivalent currents follow for N=50: 6INE(th)=1VNrP0kTRLΔf=0.003A,7INE(sh)=12VNerP0Δf=0.019A,8INE(in)=14VNkTRLΔf=0.1289A.

Thermal noise and shot noise both decrease with increasing optical power. Since the noise sources are uncorrelated, the total noise-equivalent current is the sum of the squared individual contributions. To compare this figure of merit with other sensor systems, it is usually given independent of the measurement bandwidth Δf: 9INE=(INE(th))2+(INE(sh))2+(INE(in))2=0.1305A=^2.64mAHz-1.

It is evident that the dominant noise source in this case is intensity noise. A reduction in the overall noise level by using longer sampling times is not feasible due to the desired simultaneous measurement of AC and DC. We discuss the optimization of noise levels in Sect. .

Infield measurements with the presented FOCS system were carried out in Vienna, Austria, at an electrical substation of the local grid operator Austrian Power Grid AG. The aim was to compare the FOCS measurements on one phase of the electric grid to reference measurements performed by an existing zero-flux measurement system, which detects the total DC of all three phases in the transformer neutral point of the high-voltage side. At the selected 600 MVA 380/220 kV power transformer, significant DC loads have been recorded during periods of increased solar activity over recent years.

The developed FOCS system has exhibited sub-ampere DC resolution for expected AC loads during laboratory tests (). The derivation of small DC biases superimposed on AC signals from the FOCS output has been shown in previous work (). For the zero-flux CT, a current value is recorded every second, and the data are filtered with a cutoff frequency flim=0.5 Hz to keep the quasi-DC components. For comparison, the same filtering has been applied to the FOCS data.

To fit the transformer bushing, a sensing head with a radius of R=24cm was constructed and produced through additive manufacturing, resulting in N=50 spun fiber windings. The cabinet including the optical elements and the electronics module was mounted on ground level and connected to the sensing head via a PMF line (black tube in Fig. ). The proper modulation frequency was calibrated after sensor installation by ensuring a vanishing first harmonic in the spectrum. To avoid spectral beating during demodulation, the modulation frequency fm was set to an integer multiple of the FPGA board's Fourier window bin size, namely fm = 463 867 Hz, resulting in a modulation depth of Δϕ0=1.86.

The FOCS sensing head was first installed on phase b on the low-voltage side of the transformer, as shown in Fig. . The transformer is a YNyn0 type, which means that both neutral points are accessible. However, only the neutral point on the HV side is permanently grounded. For that configuration, the loop via the HV line and the neutral point to ground should not close, and therefore no geomagnetic direct current is expected to flow in phase b.

When considering GICs in HV networks, the measured DCs at the neutral point of the transformer are generally assumed to be evenly distributed across phases a, b, and c. However, in reality, this may not be the case, as the winding resistances of the transformers also differ slightly due to manufacturing tolerances, resulting in a lower or higher resistive path for the GICs in the individual phases.

Due to the different winding resistances of the transformers, this results in an unbalanced resistance bridge, and the induced DC flows between the two rigidly grounded transformers, with a small part of the DC also flowing through the transformer with the isolated neutral point, as shown in Fig. . For this reason, an induced DC may also be recorded by the FOCS measurement system on phase b, when operated as pictured in Fig. . To the best of our knowledge, the occurrence of GICs on the non-grounded transformer side has not been verified before.

According to the National Oceanic and Atmospheric Administration (NOAA), solar storms are categorized using the G1 to G5 space weather scale, which reflects increasing levels of intensity and potential impact (). On 1 January 2025, a geomagnetic storm of class G3 was recorded. The zero-flux CT in the grounded transformer neutral recorded a maximum DC amplitude of IZF=-12.2 A. The FOCS showed a DC bias with a maximum amplitude of IFOCS=-8.4 A, proving for the first time that GICs also flow on the non-grounded transformer side (Fig. ). However, current amplitudes and dynamics may not be directly compared due to the different locations of the two sensors.

Since the FOCS is able to permanently record the AC signal, it is possible to reconstruct the original current waveform and perform a harmonic analysis. In power transformers, the presence of a DC bias shifts the operating point of the core into the nonlinear region of the B–H curve, leading to half-cycle saturation of the transformer core. This saturation manifests in an increase in the even harmonics of the 50Hz AC signal, while one would recognize a humming sound close to the transformer (). The reconstructed AC waveform was Fourier analyzed, with a window size of 1 s. Even harmonics up to the 10th order were extracted and filtered. Indeed, as shown in Fig. , an increase was recorded in even AC harmonics at the time of the DC maximum. As expected, the amplitudes of the harmonics add up to the determined DC value.

For a direct comparison with the reference zero-flux measurement, the FOCS was attached on phase b of the transformer's 380 kV high-voltage side, as shown schematically in Fig. . The predominant assumption, which has been supported by GIC simulations, is that the induced geomagnetic direct current is evenly distributed across the three phases a, b, and c and that therefore the FOCS measurement system should experience one-third of the total DC via the neutral point on the HV side.

In the evening hours of 1 September 2025, a solar particle flare caused a geomagnetic storm of class G1. The zero-flux CT showed a maximum DC bias of IZF=-2.20 A. With the FOCS measurement system, a maximum DC amplitude of IFOCS=-0.97 A was recorded (Fig. ).

While the current measured by the FOCS is not exactly one-third of the total DC, it lies within the expected order of magnitude. Regarding the precision of the developed sensor, it has to be noted that the current magnitudes caused by the G1 storm are near the detection limit of the sensor reported in , which may also serve as an explanation for the reduced signal dynamic. Furthermore, after months of continuous operation, we noticed a constant DC offset in the retrieved current signal, which had to be accounted for during post-processing.

Again, a harmonic analysis of the AC waveform was performed. The amplitudes up to the sixth harmonic show an increase coinciding with the maximum DC bias (Fig. ). However, the precision regarding the sum of the individual amplitudes equaling the total DC has degraded compared to Fig. .