## 3 Results and Discussion
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Bus**} & \multicolumn{2}{c}{**Voltage Magnitude**} & \multicolumn{2}{c}{**Voltage Angle (\({}^{\circ}\))**} & \multicolumn{2}{c}{**Current Magnitude**} & \multicolumn{2}{c}{**Current Angle (\({}^{\circ}\))**} \\ \cline{2-9}  & **Actual** & **Pred.** & **Actual** & **Pred.** & **Actual** & **Pred.** & **Actual** & **Pred.** \\ \hline
**SOURCEBUS.1** & 66,395 & 66,395 & 29.99 & 29.99 & 16.01 & 13.77 & 2.91 & 5.36 \\
**SOURCEBUS.2** & 66,396 & 66,396 & \(-90.01\) & \(-90.01\) & 18.23 & 18.07 & \(-105.82\) & \(-106.19\) \\
**SOURCEBUS.3** & 66,393 & 66,393 & 149.99 & 149.99 & 20.03 & 18.26 & 123.36 & 118.33 \\
**650.1** & 2402 & 2402 & \(-0.01\) & \(-0.01\) & 0.00 & 10.42 & 0.00 & \(-7.95\) \\
**650.2** & 2402 & 2402 & \(-120.01\) & \(-120.01\) & 0.00 & 16.40 & \(-123.69\) & 169.79 \\
**650.3** & 2402 & 2402 & 119.99 & 119.99 & 0.00 & 27.15 & \(-122.01\) & \(-161.62\) \\
**RG60.1** & 2551 & 2551 & \(-0.01\) & \(-0.01\) & 0.00 & 64.43 & \(-78.12\) & 179.55 \\
**RG60.2** & 2522 & 2522 & \(-120.01\) & \(-120.01\) & 0.00 & 4.62 & \(-29.39\) & \(-47.97\) \\
**RG60.3** & 2566 & 2567 & 119.98 & 119.98 & 0.00 & 16.11 & 135.27 & 61.51 \\
**633.1** & 2466 & 2466 & \(-2.34\) & \(-2.34\) & 0.00 & 0.83 & \(-87.61\) & 178.95 \\
**633.2** & 2501 & 2501 & \(-121.57\) & \(-121.57\) & 0.00 & 0.47 & 0.00 & 95.57 \\
**633.3** & 2449 & 2449 & 117.80 & 117.80 & 0.00 & 0.28 & 0.00 & \(-90.84\) \\
**634.1** & 278 & 279 & \(-2.85\) & \(-2.84\) & 618.29 & 613.84 & 138.59 & 138.72 \\
**634.2** & 284 & 284 & \(-121.97\) & \(-121.97\) & 511.60 & 512.50 & 18.87 & 18.85 \\
**634.3** & 278 & 278 & 117.28 & 117.28 & 516.61 & 515.37 & \(-95.81\) & \(-95.51\) \\
**675.1** & 2400 & 2400 & \(-5.21\) & \(-5.20\) & 197.29 & 197.28 & 154.11 & 153.39 \\
**675.2** & 2543 & 2543 & \(-122.15\) & \(-122.14\) & 34.56 & 34.40 & 15.33 & 14.10 \\
**675.3** & 2363 & 2364 & 116.15 & 116.16 & 173.16 & 173.51 & \(-101.59\) & \(-101.83\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Results from IEEE13 for a random timestamp. Cells with poor ANN predictions are highlighted for clarity. Figure 2: Training metrics for the first 100 epochs for each network: **(a)** IEEE13, **(b)** IEEE34, **(c)** IEEE37, and **(d)** IEEE123. To evaluate the robustness of the models under noisy input conditions, a new dataset was generated consisting of 1000 simulation points for each test network. Gaussian noise was then added to the input power injections at each node to simulate measurement uncertainty. The results, summarized in Table 4, demonstrate that the PINN consistently outperforms the baseline model across all networks and noise levels, particularly in terms of current estimation accuracy. Even as noise increases, the PINN maintains relatively low error metrics and high improvement percentages, highlighting its ability to learn physically consistent representations that generalize well under data perturbations. For instance, in the IEEE37 network under 5% input noise, the PINN reduces the current RMSE by over 94% (from 59.65 to 3.35) compared to the baseline, while the voltage RMSE shows a minor increase of about 13% (from 6.08 to 6.87). In contrast, the baseline model exhibits a steep degradation in performance, especially for larger networks and higher noise levels. These findings underline the inherent advantage of physics-informed training in ensuring model reliability under realistic, imperfect conditions. A similar benchmarking procedure was conducted to evaluate the performance of the models under conditions of partial observability, simulating scenarios with missing measurements. To achieve this, a random subset of the input data (i.e., power injections) was masked, corresponding to 10% and 20% dropout rates, respectively. This emulates the practical challenge of incomplete or faulty metering in distribution networks. The results, presented in Table 5, confirm that the PINN retains a significant advantage over the baseline model, particularly in current estimation.