# Dynamic Line Rating--An Effective Method to Increase the Safety of Power Lines
## 2 Problem Identification--Materials and Methods
### Results of the Field Measurement and Numerical Simulation  
Five measurements were performed in the observed span (M1-M5). The first three were carried out in the first three measurement planes, one in each. The results of measurement 4 and 5 (M4-M5) can be seen in Figure 2. Both were performed in measuring plane 4 because this plane includes the critical part of the OHL with the lowest clearance reserve. Figure 2 shows that the low-frequency electric field exceeds the 5 kV/m limit value required for the general public, while the temperature is well below the maximum operating limit. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Measuring Plane**} & **Load of the OHL** & **Ambient** & **Max. Value of the** \\  & **(Overhead Line)** & **Temperature** & **E-Field** \\ \hline Plane 1 & 276.5 A & 34.5 \({}^{\circ}\)C & 1.277 kV/m \\ Plane 2 & 292.0 A & 35.0 \({}^{\circ}\)C & 3.060 kV/m \\ Plane 3 & 348.0 A & 36.0 \({}^{\circ}\)C & 4.679 kV/m \\
**Plane 4** & **278.5 A** & **33.8 \({}^{\circ}\)C** & **7.150 kV/m** \\
**Plane 4** & **348.0 A** & **35.5 \({}^{\circ}\)C** & **7.420 kV/m** \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Results of the electric field measurement. Figure 2: Measured electric field distribution at 1.8 m height above the ground (M4–M5). To validate the field measurements' result, numerical, finite-element simulations were carried out for the observed OHL geometry. The physics of the simulation is based on Equations (1)-(3):  
\[\
abla J=0 \tag{1}\]  
where (\(J\)) is the current density in A/m\({}^{2}\),  
\[J=\
abla\times H=\sigma E+j\omega D \tag{2}\]  
where (\(H\)) is the magnetic field strength in [A/m], (\(E\)) is the electric field strength in [V/m] and (\(D\)) is the electric displacement field in [As/m\({}^{2}\)]. \[E=-\
abla V-j\omega A \tag{3}\]  
where (\(E\)) is the electric field strength in [V/m] and (\(A\)) is the magnetic vector potential in [T/m]. In the analytical calculation, we used several approximations that do not affect the magnitude of the results, but greatly simplify the calculation. The conductors' voltages were phase-shifted phase-to-ground voltages of a 400 kV system, and a grounded conductive plate modeled the surface of the ground at the bottom of the model. We assumed the conductors to be infinite in length parallel to the ground surface and one strand of aluminum. We considered the number of free charge carriers in the air to be 0. To increase the accuracy of the simulation, a finer meshing was set to the model. The physical parameters applied in the COMSOL model is in Table 3.  
The results of the performed simulations are in Figure 3a,b. Figure 3: Simulated electric field distribution at 1.8 m height above the ground. (**a**) Results at phase conductor clearance from 9 m to 13 m; (**b**) results at phase conductor clearance of 8 m. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Description** & **Value** & **Unit** \\ \hline Aluminum diameter & 31.06 & [mm] \\ Aluminum conductivity & 37.74 & [MS/m] \\ Relative permittivity of & 1 & [-] \\ Aluminum & 1 & [-] \\ Relative permittivity of air & 1 & [-] \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Conductor and insulator model parameters. Figure 3 presents the E-field distribution at different clearance values in the OHL's cross-section at 1.8 m above the ground level. The curves represent cases with different clearance values from 13 m to 8 m, the legally defined safety distance for a 400 kV power line. Clearance values were simulated every 20 cm, but Figure 3a only includes whole meter results. Figure 3b shows visualization of the results for 8 m clearance around the power line. The line monitoring sensor measured the phase conductor temperature every 5 min, from which the clearance was determined mathematically [30; 31]. The typical error rate of the clearance calculation algorithm is 0.1-0.15 m which was validated by the catenary curve and sensor measurements based on different methods in the FLEXITRANSTORE and FARCROSS projects.