# Non-Contact High Voltage Measurement in the Online Partial Discharge Monitoring System
## 2 Concept of High Voltage Measurement with the Use of a Capacitive Probe  
The measurement of high voltage with the use of a capacitive probe is similar to the measurement using a capacitive divider, which is commonly used in high voltage laboratories [31]. Of course, this similarity results primarily from the nature of the coupling of the measuring system with the test object. In both cases, we are dealing with a high-voltage coupling capacitance with a high impedance and a low-voltage measuring capacitance with a lower impedance, on which the voltage drop is measured and properly calculated taking into account the so-called divider ratio, which is a function of both of these capacitances (Figure 3). While the main idea of measurement in both systems is similar, the specificity of their performance and the nature of certain dependencies are radically different. In the case of a capacitive divider, we deal with the constant parameters of individual components (and thus a constant voltage ratio) and a galvanic connection of the measuring system with the test object. The system using a capacitive probe is portable, easy to install, low cost, and the value of the coupling capacity (directly influencing the value of the voltage ratio) is determined dynamically by changing the probe's position. Importantly, the measurement is performed in a completely non-contact manner, i.e., without a galvanic connection to the high-voltage circuit. Thanks to this, it is a safe method for both the personnel and measuring equipment. In addition, measurement with a capacitive probe does not load the voltage source and does not interfere with the distribution of the electric field in the vicinity of the tested object.  
The accuracy of the high voltage measurement using a capacitive probe depends mainly on the precise determination of the voltage ratio, and therefore primarily the value of the capacitive coupling \(C_{1}\) between the HV test object and the probe. The value of the voltage ratio is described by a slightly more complicated relationship than it is for a typical capacitive divider because a number of elements that are part of the measurement chain itself should be taken into account, such as the input impedance of an acquisition card or an oscilloscope, cable capacitance, etc. If, in accordance with the diagram shown in Figure 4, it is assumed that the maximum voltage (peak value) can be calculated using the formula:  
\[U_{1}=v\cdot U_{2} \tag{1}\]  
Figure 3: Schematic diagram of non-contact high voltage measurement with the use of a capacitive probe for an autonomous online partial discharge monitoring system.  
where \(v\) is the voltage ratio, and \(U_{2}\) is the voltage measured with the capacitive probe, then the formula for the voltage ratio can be written as:  
\[v=\frac{Z_{1}+Z_{2}}{Z_{2}}=\frac{\frac{1}{\hbar\omega C_{1}}+\frac{R_{s}}{1+j \omega C_{2}R_{s}}}{\frac{R_{s}}{1+j\omega C_{2}R_{s}}} \tag{2}\]  
where \(\omega\) is the angular frequency, \(R_{s}\) is the voltmeter (or oscilloscope, digital acquisition card, etc.) input resistance, \(C_{1}\) is the coupling capacitance, and \(C_{2}\) is the resultant capacitance which is the sum of the probe capacitance \(C_{p}\), the coaxial cable capacitance \(C_{c}\), and the voltmeter input capacitance \(C_{s}\):  
\[C_{2}=C_{p}+C_{c}+C_{s} \tag{3}\]  
After simplifying Equation (2), the voltage ratio can finally be written as:  
\[v=\frac{C_{1}+C_{2}}{C_{1}}-j\frac{1}{\omega C_{1}R_{s}} \tag{4}\]  
The individual elements of the equivalent circuit shown in Figure 4 are determined in the laboratory, except for the value of the capacitive coupling \(C_{1}\), which is determined at the power substation after installing the PD monitoring system and the probe calibration procedure. This procedure consists of obtaining information about the instantaneous voltage value from the substation SCADA system (to which the voltage transformers are connected) and performing calculations using Equations (1) and (4).