# Bottom-Up Model of Random Daily Electrical Load Curve for Office Building
## 2 Modeling Approach
### Appliance Model
#### 2.3.2. Power Simulation Model  
1. Base Appliances  
The instantaneous power of the base appliance is the rated power at the current moment, and the calculation formula is as Equation (4):  
\[P_{b,t}=P_{e,t} \tag{4}\]  
where \(P_{e,t}\) is the rated power of the electrical appliance at time \(t\).  
Figure 4: The algorithm flow of determining appliance combination in an office building.  
2. Single-Use Appliances  
Single-Use Appliances, mainly referring to the computer, combined with simple practical research can determine the power distribution between 0 and 150 W. The range of potential computer power is divided into several intervals of 10 W, and the power usage probability in different intervals is calculated every 15 min. Monte Carlo extraction is used to determine the instantaneous power of the computer. Using random number to compare with cumulative probability and determine the instantaneous power of a single computer at time \(t\) as Equation (5):  
\[P_{s,s}=\left\{\begin{array}{ccc}L_{1}^{s}&&0<\beta<\sum\limits_{i=1}^{1}p_{t, i}\\ L_{2}^{s}&&\sum\limits_{i=1}^{1}p_{t,i}<\beta<\sum\limits_{i=1}^{2}p_{t,i}\\ &&\vdots\\ &&\vdots\\ L_{k}^{s}&&\sum\limits_{i=1}^{k-1}p_{t,i}<\beta<\sum\limits_{i=1}^{k}p_{t,i} \end{array}\right. \tag{5}\]  
where \(L_{k}^{s}\) is the power value of the computer in the kth interval, \(\beta\) is the random number, and \(p_{t,i}\) is the probability of power in different intervals at time \(t\). Combined with the effective number of electricity users determined by the personnel model, the total power of all computers at time \(t\) is obtained as Equation (6):  
\[P_{s,t}=\sum\limits_{i=1}^{n_{t}}P_{s,s,i} \tag{6}\]  
The specific calculation process is shown in Figure 5:  
Figure 5: Computer instantaneous power value calculation process.  
3. Communual Appliances For Communual Appliances, it is assumed that the average power is linearly correlated with the effective number of people [25], and the calculation formula is as Equation (7): \[P_{m,t}=S_{m}\cdot\left[P_{min}\Big{(}1-\frac{n_{t,m}}{M}\Big{)}+P_{max}\cdot \frac{n_{t,m}}{M}\right]\] (7)  
For different appliance \(m\), \(P_{min}\) is the standby power, \(P_{max}\) is the power used, \(S_{m}\) is the total number of appliances \(m\), and the calculation formula is as in Equation (8). \(n_{t,m}\) is the number of effective power users; the calculation formula is as Equation (9): \[S_{m}=\alpha_{m}\cdot M\] (8) where \(\alpha_{m}\) is the sharing coefficient of appliance \(m\), reflecting how many people use appliance m together. \[n_{t,m}=n_{t}\cdot r_{t,m}\] (9) where \(r_{t,m}\) is the use probability of different appliances. The instantaneous power value of communal appliances can be determined by summarizing various appliances, as Equation (10): \[P_{com,t}=\sum P_{m,t}\] (10) (iv) Other Appliances Apart from base appliances, single-use appliances, and communal appliances in an office building, there are still appliances related to working hours and the number of personnel, including elevators and office lighting. The power of the elevator is determined according to the change of the effective number of people, as Equation (11): \[P_{ele,t}=\left\{\begin{array}{cc}P_{b}&otherwise\\ P_{b}+P_{w}&|n_{t+1}-n_{t}|\geq M\times 10\%\end{array}\right.\] (11) where \(P_{b}\) is the standby power of the elevator, and \(P_{w}\) is the operating power.  
Office lighting power is determined according to the effective number and vertical solar radiation, as Equation (12): \[P_{lig,t}=n_{t}\cdot P_{lig,pp}\cdot\frac{I_{g,max}-I_{g,t}}{I_{g,max}-I_{g, min}}\] (12) where \(P_{lig,pp}\) is the per capita power density of office lighting, \(I_{g,t}\) is the vertical solar radiation at time \(t\), \(I_{g,max}\) and \(I_{g,min}\) are the upper and lower limits of vertical solar radiation.  
Finally, the total power load of office buildings can be determined by superposition of the loads of various types of appliances as Equation (13): \[P=P_{b,t}+P_{s,t}+P_{com,t}+P_{ele,t}+P_{lig,t}\] (13)