## 4 Performance Assessment of Branch Power Change Estimation
### Experimental Verification  
To verify the suggested method a test bed consisting of a sum meter, consumer meter MUT, branch cable \(R_{\alpha}\), ohmmeter OM, relay control block RB and personal computer for loads control and data collection was constructed (Figures 13 and 14). The sum meter and the consumer MUT type was Elgama Gama150 Type G15 ([[https://www.elgama.eu/G15-en](https://www.elgama.eu/G15-en)]([https://www.elgama.eu/G15-en](https://www.elgama.eu/G15-en)), accessed on 5 June 2025). Both meters are capable of measuring active power, voltage and current in 1-phase 2-wire networks. Accuracy class B (IEC 50470-3) for active power. Electrical quantities measured by smart meters are transmitted with the period of 1 s via P1 port according to Companion Standard DSMR (Dutch Smart Meter Requirements) ver. 5.0.2, 2016 ([[https://www.netbeheernederland.nl/publicatie/dsmr-502-p1-companion-standard](https://www.netbeheernederland.nl/publicatie/dsmr-502-p1-companion-standard)]([https://www.netbeheernederland.nl/publicatie/dsmr-502-p1-companion-standard](https://www.netbeheernederland.nl/publicatie/dsmr-502-p1-companion-standard)), accessed on 5 June 2025). The resolution of readings in P1 port packets were 0.1 V for a single-phase voltage, 0.001 kW for active instantaneous import power and 1 A for a single-phase current. However, assuming the nominal voltage \(V_{n}\) = 230 V and using active power and voltage to calculate current, the achievable current resolution is 0.001 kW/230 V \(\approx\) 0.005 A. The distribution grid branch resistance \(R_{\alpha}\) was 15 m length with cross-sectional area of 1 mm\({}^{2}\) of copper wire. The actual value of \(R_{\alpha}\) resistance was measured using D.C. Milli-Ohm Meter GOM-802 (OM) with 0.05% accuracy using four-wire measurement mode. To measure \(R_{\alpha}\) using ohmmeter, the \(R_{\alpha}\) was multiplexed using two contact relays K\({}_{1}\) and K\({}_{2}\). Relays K\({}_{3}\), K\({}_{4}\), and K\({}_{5}\) were used to multiplex loads according to a pre-programmed sequence during the experiment. Smart meters and ohmmeter readings were recorded with Matlab R2024b software in personal computer interfaced via P1 (RS-232) to USB converter. To record smart meters messages, interrupt routine was written in Matlab, which was executed on every message received via USB (RS232) for every meter separately. Resistance readings were requested from Ohmmeter (OM). Relays were controlled by relay block (RB) containing the preprogrammed  
Figure 12: Relative error of \(\overline{dP_{n}}\) estimation versus \(e_{P}\) (**a**), and versus absolute error of \(e_{P}\) estimation (**b**). Meter accuracy case M3 and the T3 training data/testing data case from Table 7 are used. Every sample of relative error of \(\overline{dP_{n}}\) was obtained by averaging 10 estimates of \(dP_{n}\) acquired at 10 different noise ensembles of random injected error. The load \(P_{C}\) is switched on and off 10 times with the period of 30 s to generate power event. The total duration of power event recording was approximately 3 h. All loads were of resistive type, their nominal powers were \(P_{L1}\) = (0, 2.0) kW, \(P_{L2}\) = (0, 0.4) kW, \(P_{C1}\) = (0, 0.25, 0.5) kW, and consumer power step sizes were \(dP_{C}\) = (0.25, 0.5, 0.7, 1.0, 1.5) kW. In total 195 power events were recorded with the combinations of initial power consumption of test bed loads shown in Figure 15. According to the circuit shown in Figure 13, a 2 kW nominal power heater is used for implementation of load \(P_{L1}\), a 0.4 kW heater for load \(P_{L2}\), two 0.25 kW incandescent lamp blocks (a and b), a 0.2 kW incandescent lamp (c), and a 0.8 kW heater (d) are used for load \(P_{c1}\). In total, 6 different loads are used.