# Non-Contact High Voltage Measurement in the Online Partial Discharge Monitoring System
## 5 Distance Characteristics  
When measuring the voltage with a capacitive probe in the near field, it should be taken into account that the distance between the source of the electromagnetic wave and the probe is of fundamental importance for the amplitude of the registered voltage signal. This is a direct result of the distribution of the electric field around the object on the potential. Using the classic example of a heterogeneous field in the sphere-to-plate electrode system (Figure 11), this relationship can be described by the formula:  
\[V(r)=\int\limits_{\infty}^{P_{1}}E\cdot dr=\int\limits_{P_{1}}^{\infty}\frac{ q}{4\pi\epsilon_{0}r^{2}}dr=\frac{q}{4\pi\epsilon_{0}r} \tag{22}\]  
where \(q\) is the total electric charge of the sphere and \(P_{1}\) is a point in space at a distance \(r\) from the center of the sphere.  
The presented dependence \(V(r)=1/r\) is a great simplification in relation to reality, but it illustrates well its general character. In order to verify the adopted hypothesis about the influence of distance on the voltage recorded by the capacitive probe, an experiment was carried out. Of course, due to the influence of many factors related to, for example, the vicinity of various types of live devices and earthed elements, the presented results of the experiment are primarily quantitative. Nevertheless, in the context of the described measurement method, their presentation in this article seems to be important.  
The distance characteristics, i.e., the dependence of the amplitude of the signal recorded by the probe on the distance from the voltage source, was determined as follows: the capacitive probe was placed at a distance of \(r=\) (30-160) cm from a stable signal source, which was a spherical electrode with a diameter of 10 cm, supplied with an alternative current (AC) voltage with a frequency of 50 Hz (Figure 12). In order to obtain high accuracy,  
Figure 11: Distribution of electric field strength \(E\) and potential \(V\) in a heterogeneous sphere-to-plate system.  
the distance of a given probe from the source was measured with a laser rangefinder. The effective value of the voltage generated by the test transformer was 25 kV. For the duration of the measurements, all unnecessary elements were removed from the HV test hall, which could somehow change the electric field distribution in the space between the capacitive probe and the spherical electrode. In addition, the probe was placed on an insulating tripod at a distance of 1.5 m from the ground.  
Figure 13 shows the dependence of the amplitude of the voltage signal recorded with the capacitive probe on the distance \(r\) from the signal source. Additionally, the approximating function is shown according to the adopted equation:  
\[y=\frac{A}{r} \tag{23}\]  
where \(A\) is the function parameter. The parameter \(A\) of the non-linear function \(A/r\) was determined in the OriginLab program using the Levenberg-Marquardt algorithm.  
When analyzing Figure 13, it can be noticed that the applied approximating function (Equation (2)) correctly reflects the nature of the dependence of the amplitude of the signal recorded with the capacitive probe on the distance \(r\). This is confirmed by the high value of the \(R^{2}\) coefficient, equal to 0.94. As previously mentioned, the obtained characteristic has little practical significance, but it allows us to show that the distance \(r\) of the capacitive probe from the monitored HV device is a parameter having a large impact on the value of the voltage ratio of the measuring system.