# The Impact of Power Definitions on the Disaggregation of Home Loads for Smart Meter Measurements
## 3 NILM Approach Based on the Genetic Algorithm  
The type of information obtainable from smart meters depends on the data sampling frequency. For instance, hourly or half-hourly data are sufficient for determining household occupancy. However, to accurately detect individual or multiple appliances, high-frequency smart meter data are necessary [49]. Since the purpose is to provide the ability to identify the turned-on appliances at a specific moment, high sampling frequency is required. This enables precise identification of appliance activation times, a capability inherent in modern smart meters. Smart meter data enables the calculation of power values based on the definitions outlined in the previous section. Unbundled smart meters directly provide voltage and current measurements for each phase, eliminating the need for additional computations (provided by the SMM without additional calculations). The SMM can also obtain the following values: active power value on each phase, reactive power value on each phase, power factor value on each phase, homopolar value of the rms voltage, homopolar value of the rms current, angle between voltages, angle between each phase voltage and current, grid frequency. In this work, and considering that harmonics are available up to the order of 32 [60], we deployed the proper code in the unbundled smart meter SMX component to obtain the values presented in (19) and (20). So, to identify which appliances are on at a specific time t involves analyzing the aggregated power measurements from the smart meter. In this way, from the point of view of [PERSON]'s proposal, the several aggregated powers will be given by:  
\[\left\{ \begin{array}{l}P(t)=\sum\limits_{k=1}^{N_{\text{total}}}P_{k}(t)+e(t )\\ Q(t)=\sum\limits_{k=1}^{N_{\text{total}}}Q_{Bk}(t)+e(t)\\ D(t)=\sum\limits_{k=1}^{N_{\text{total}}}D_{Bk}(t)+e(t)\end{array} \right. \tag{19}\]  
where \(P_{k}(t)\), \(Q_{Bk}(t)\) and \(D_{Bk}(t)\) describe the active power, reactive power and distortion power consumptions, respectively, of the specific appliance \(k\) at instant \(t\), and \(e(t)\) is the noise of the measurement. Regarding the perspective of [PERSON]'s proposal, the several aggregate powers are given by (20):  
Figure 2: [PERSON]’s proposal definition for apparent power. \[\left\{ \begin{array}{l}P_{1}(t)=\sum\limits_{k=1}^{N_{\text{total}}}P_{1k}(t)+e(t ),\;\;P_{H}(t)=\sum\limits_{k=1}^{N_{\text{total}}}P_{Hk}(t)+e(t)\\ Q_{1}(t)=\sum\limits_{k=1}^{N_{\text{total}}}Q_{1k}(t)+e(t)\\ D_{I}(t)=\sum\limits_{k=1}^{N_{\text{total}}}D_{Ik}(t)+e(t),\;\;D_{V}(t)=\sum \limits_{k=1}^{N_{\text{total}}}D_{Vk}(t)+e(t)\\ D_{H}(t)=\sum\limits_{k=1}^{N_{\text{total}}}D_{HK}(t)+e(t)\end{array} \right. \tag{20}\]  
where \(P_{1k}(t)\), \(P_{Hk}(t)\), \(Q_{1k}(t)\), \(D_{R}(t)\), \(D_{Vk}(t)\) and \(D_{Hk}(t)\) describe the fundamental active power, harmonic active power, fundamental reactive power, current distortion power, voltage distortion power and harmonic distortion power consumptions, respectively, of the specific appliance \(k\) at instant \(t\). To identify individual or multiple active appliances, we propose an objective function within a metaheuristic framework. This objective function minimizes the difference between the sum of the powers of active appliances and the total power measured by the smart meter at the grid connection point. The decision variables represent the number of active appliances of each type. Based on the preceding discussion, objective functions (21) and (22) are defined. These functions aim to minimize the difference between the aggregated power measured by the smart meter and the sum of the powers of active appliances, aligning with [PERSON]'s and [PERSON]'s power theories. [PERSON]'s approach considers fundamental active power (\(P_{1}\)), fundamental reactive power (\(Q_{1}\)), current distortion power (\(D_{I}\)), and voltage distortion power (\(Q_{V}\)). By incorporating fundamental power and distortion powers, the algorithm becomes more resilient to grid voltage fluctuations and distortions.