## 2 Methodology  
Figure 1 describes a basic (eventless) NIALM process consisting of (1) data acquisition: composite electric energy consumption data are measured by a single minimal set of plug-panel current and voltage sensors and digitized for further analysis of load disaggregation; (2) feature extraction: electrical features are extracted as feature data from digitized composite electric energy consumption data for concerned electrical appliances; and (3) load recognition: artificial intelligence (AI) is utilized to recognize extracted electrical features for concerned electrical appliances--their electric demand based on past trends can be predicted. The NIALM investigated in this paper is an eventless NIALM approach. AI conducted in the NIALM is parallel computing accelerated evolutionary computing. The basic NIALM problem can be formulated as follows:  
If (1) \(P(t)\) stands for used composite power consumption acquired at time \(t\) and (2) \(P_{i}(t)\) accounts for real power absorbed by concerned electrical appliance \(i\) (profiling concerned electrical appliances and base load is done in advance), the total power consumption, \(P(t)\) (=y(t)), in an electric power distribution system can be expressed as Equation (1). In Equation (1), the summation of superimposed absorptions \(\Sigma x_{i}(t)P_{i}(t)\) with an unmonitored base load \(P_{\text{base}}(t)\) is made. In Equation (1), \(N\) is the total number of concerned electrical appliances and \(x_{i}(t)\), a unit value from \(\{0,1\}\), is the on/off operational status of electrical appliance \(i\) at time \(t\). NIALM is used to recognize the unknown (possible) operational status of concerned electrical appliances \(x_{i}(t)|i\) = 1, 2,..., \(N\) at time \(t\) when \(P(t)\) (=y(t)) acquired and given with \(P_{\text{base}}(t)\) is known: [\(x_{1}(t)\), \(x_{2}(t)\),..., \(x_{i}(t)\),..., \(x_{N}(t)\)] = \(F(y(t))\) where \(F\) is a function that returns the best \(N\) estimates of \(x_{i}(t)\) at time \(t\) for concerned individual \(N\) electrical appliances. \(F\) above can be any AI algorithm. In this paper, we conduct evolutionary computing, GA, to metaheuristically search for the optimal load combinations \(x_{i}(t)\) of concerned electrical appliances when acquired total power consumption \(P(t)\) with base load \(P_{\text{base}}(t)\) is given at time \(t\) (in Equation (1), profiling concerned electrical appliances to get \(P_{i}(t)\) and statistically computing base load for \(P_{\text{base}}(t)\) from unmonitored electrical appliances is done prior. \[P(t)=\sum_{i=1}^{N}x_{i}(t)P_{i}(t)+P_{\text{base}}(t) \tag{1}\]  
In this paper, NIALM is declared as a combinatorial optimization problem, which is formulated as the objective metric in Equation (2) and solved by a parallel computing accelerated GA.  
\[err(t)=\text{argmin}\left|[P(t)-P_{\text{base}}(t)]-\sum_{i=1}^{N}x_{i}(t)[P_ {i}(t)+\tau_{i}]\right| \tag{2}\]  
where \(\tau_{i}=c_{i}\cdot std(P_{i}(t))\). Figure 1: A basic NIALM process (profiling concerned electrical appliances and statistically computing base load should be done beforehand). In Equation (2), \(P_{i}\) (=mean(\(P_{i}(t)\))) obtained in advance involves profiling each of concerned electrical appliances based on historical data. That is, \(P_{i}(t)\), in Equation (1), or \(P_{i}\), in Equation (2), accounts for the real power that was absorbed by electrical appliance \(i\) and statistically computed for load disaggregation. \(P_{\text{hase}}\), in Equation (2), from \(P_{\text{hase}}(t)\), in Equation (1), is defined in a similar sense, and its standard deviation can be considered. In Equation (2), \(\tau_{i}\), a tolerance term for \(P_{i}\), is considered, where std(\(P_{i}(t)\)) is a function that returns the standard deviation of its input elements \(P_{i}(t)\) from historical data and \(c_{i}\) is a constant that can be designed as a time-dependent parameter.