## 2 Design and Implementation of On-Line PD Monitoring System
### Partial Discharge Detectors
#### 2.2.3 High-Frequency Current Transformer
\[S=\frac{R}{N} \tag{2}\]  
The lower \(-3\) dB cutoff frequency of HFCT sensor is given by  
\[f_{L}\ =\ \frac{R_{c}\|(R+R_{s})}{2\pi L_{m}}\approx\ \frac{R}{2\pi L_{m}} \tag{3}\]  
where \(L_{m}\) is the magnetizing inductance. The HFCT sensors are mostly loaded with non-inductive resistor \(R=50\)\(\Omega\), in order to assure a good impedance matching with the transmission line (usually it is a standard 50-ohm coaxial cable) and with the analog input of signal acquisition unit. Therefore, to achieve a low value of the cutoff frequency \(f_{L}\), the magnetizing inductance should be possibly the highest. The magnetizing inductance \(L_{m}\) on the secondary side is given by  
\[L_{m}\ =\ \frac{\mu_{r}\mu_{0}N^{2}A_{c}}{l_{c}} \tag{4}\]  
Figure 12: High-frequency current transformer model with parasitic components. where \(\mu_{0}\) is the vacuum permeability (magnetic constant), \(A_{c}\) is the core cross-sectional area, and \(l_{c}\) is the toroidal mean length. Equation (4) shows that the high value of the magnetizing inductance \(L_{m}\) may be obtained the easiest using a large number of turns \(N\). Unfortunately, with increasing the number of turns, the sensor sensitivity is reduced. The other way is a choice of a core made of a material with high relative permeability \(\mu_{r}\) (e.g., MnZn soft ferrites) and possibly the smallest toroidal mean length \(l_{c}\)[95; 96]. In turn, the higher -3 dB cutoff frequency of the HFCT sensor mainly depends on stray capacitance \(C\) and the leakage inductance \(L_{l}\) (Equation (5)). To obtain a high value of \(f_{H}\), both parameters should be reduced. \[f_{H}\ =\ \frac{1}{2\pi\sqrt{\left(RC\right)^{2}+\left(\frac{L_{l}}{R_{c}} \right)^{2}}} \tag{5}\]  
The stray capacitance \(C\) consists of several capacitive couplings, which are present in high-frequency current transformer, i.e., turn-to-turn capacitance, winding-to-core capacitance, winding-to-shielded enclosure capacitance, and primary-to-secondary winding capacitance. The stray capacitance can be minimized by reducing the number of turns \(N\), increasing the insulation layer of core and secondary winding (using a material with low dielectric constant \(\varepsilon_{r}\)), increasing the distance between turns, and using a Faraday electrostatic shield [95]. The reduction of the number of turns \(N\) is also favorable from the viewpoint of leakage inductance \(L_{l}\) minimizing. Additionally, the secondary winding should be made wide and have a small thickness. As one may notice, the factors which have the greatest influence on the sensitivity and width of the HFCT sensor band, are the number of windings \(N\) and the type of material, which the toroidal core is made from. The cores made from MnZn and NiZn soft ferrites were selected for the tests. The physical parameters of the materials are listed in Table 4.  
The dimensions of the applied ferrite cores were selected so that, after equipping them in shielding enclosure, they could be easily installed on the wire grounding the transformer tank or the neutral point of the star windings. Since the width of the grounding wire/rail of power transformer usually does not exceed 40 mm, it was decided to choose toroidal cores with an internal diameter equal to 65 mm. The external diameter MnZn ferrite core was 107 mm, and its height was 18 mm. For NiZn ferrite core they were, respectively, 103 and 16 mm. To reduce the skin effect, for manufacturing of the secondary winding, the high-frequency Litz-wire with a diameter of 0.48 mm and external insulation with a thickness of 0.02 mm made from natural silk of dielectric constant \(\varepsilon_{r}\) = 2.6 was used.