# Rio Madeira HVDC System: Commissioning of the Ground Electrode for Bipole 2 at Porto Velho
## 5 Electrode Commissioning
### Electrode Resistance  
At the converter substation, the transient fault recorder registered 3067 V as the average potential of the neutral DC bar to the grounding grid during the commissioning tests. The electrode line has two conductors, AAC 2282.8 MCM, in parallel with a total length of 58 km, resulting in an equivalent resistance of 0.0125 \(\Omega\)/km (coefficient of variation of resistance with a temperature equal to 0.004). Considering 45 \({}^{\circ}\)C as the cable temperature (10 \({}^{\circ}\)C above the ambient temperature on the day of the test), the final resistance of the electrode line (R\({}_{\text{EL}}\)) was so calculated:  
* R\({}_{\text{EL}}\) = 58 \(\times\) [0.0125 \(\times\) (1 + 0.004 \(\times\) 25)] = 0.80 \(\Omega\). The total resistance of the electrode line plus the electrode can be thus calculated:
* R\({}_{\text{total}}\) = V\({}_{\text{dn}}\)/I\({}_{\text{ellec}}\) = 1.17 \(\Omega\). Discounting the electrode line resistance, the first approach electrode resistance (RE) was calculated:
* R\({}_{\text{EL}}\) = 1.17 \(-\) 0.80 = 0.37 \(\Omega\). The above-calculated resistance is considered the first approach because of the premise that the DC potential of the grounding grid of the converter substation is equal to zero. However, this is not true, because it was measured as a total of 47 A\({}_{\text{DC}}\) going up in the neutrals of the Y-connected windings of the 500 kV converter transformers, demonstrating that a resistive coupling does exist between the grounding grid of the converter substation and the electrode, despite the 40 km distance in a straight line. [PERSON] et al. (2010) presents the results of the tests conducted by Eletrobras/IE Madeira (partners of this HVDC project) with the first electrode built, which was only 15 km away from the converter substation. The tests included the measurement of the currents in the neutrals of the converter transformers (329 A) and the net currents in the ground wires of the transmission lines leaving the substation (282 A). The authors calculated the potential induced by the original electrode on the converter substation grounding grid to be 400 V, considering the overload current injection in the electrode. Referring to the nominal electrode current, this ground potential reduces to 300 V.  
The ratio between the total measured DC currents in the converter transformer neutrals for the old and new electrodes was 329/47 = 7. Applying this same ratio for inferring the net current leaving the converter substation grounding grid by the ground wires, it can be expected that for the new electrode at nominal current, the DC ground-wire current  
Figure 4: The measured distribution of the electrode current within the section feeders (blue line) and the desired uniform distribution (red line), with reference to the nominal current (2625 A). will be 282/7 = 40 A. Applying to the ground potentials this same factor of 7, the potential of the converter substation grounding grid was inferred to be about 43 V for the nominal electrode current. This is an approximation; such linearity cannot be expected because the two electrodes have different locations with similar but different geoelectric structures. Considering that the new site has a better subsurface geoelectric structure, it is probable that the induced potential at the converter substation will be a bit lower than the inferred value. Figure 5a presents the ground loop of the DC current circulation between the electrode and the converter substation, where the two coupled grounding resistances (electrode and substation) were substituted by the equivalent Y connection. Considering the second Kirchhoff law (meshes law), the equations of Figure 5b can be formulated. Applying the inferred parameters (listed below the equations in Figure 5b) in the last equation, the electrode resistance can be calculated as \(\mathrm{R_{E}}\) = 0.35 \(\Omega\). The difference between the first approach resistance and the adjusted value is only 5%, which is a small deviation.