## 2 Methodology
### Proposed Tracking Strategy
```
1:Calculate solar path \(\blacktriangleright\) Solar Algorithm
2:Segmentation of solar path, \(\bar{\beta}~=~{}[\beta_{1},\ldots,\beta_{k},\ldots,\beta_{n}]^{T}\)\(\bar{\gamma}~{}=~{}[\gamma_{1},\ldots,\gamma_{k},\ldots,\gamma_{n}]^{T}\)
3:Calculate insolation vector, \(I_{tot}~=~{}[I_{tot,1},\ldots,I_{tot,k},....I_{tot,n}]^{T}\)
4:Define time of day vector, \(\bar{t}_{S}~=~{}[t_{S,1},\ldots,t_{S,k},\ldots,t_{S,n}]^{T}\)
5:Define consumption constraint factor \(\kappa_{c}\) for \(\kappa_{c}\leq 0.03\)
6:Set monitoring device configuration
7:Initialize real-time monitoring process
8:Initialize \(k=1\)
9:for\(k~{}=~{}1:n\)do
10:if\(k~{}=~{}n\)then
11: Move to home position, \((\beta_{1},\gamma_{1})\)
12: Save overall day data
13: Stop tracking and monitoring processes
14:else
15: Move \((\beta_{k},\gamma_{k})\) to \((\beta_{k+1},\gamma_{k+1})\)
16:while\((\beta_{k+1,rt},\gamma_{k+1,rt})\
eq(\beta_{k+1},\gamma_{k+1})\)do
17: Minimize \(|\varepsilon_{m,k}|\) until \(|\varepsilon_{m,k}|\leq|\varepsilon_{max}|\)\(\blacktriangleright\) Control strategy
18:endwhile
19: Stop tracking in position \((\beta_{k+1},\gamma_{k+1})\)
20: Save power reference value, \(P_{pv,ref}\)
21:if\(P_{pv,rt}\approx P_{pv,ref}\) or \(P_{pv,rt}>P_{pv,ref}\)then
22: Hold tracking position \((\beta_{k+1},\gamma_{k+1})\)
23:else
24: Measure insolation in real time, \(I_{tot,rt}\)
25:if\(I_{tot,rt}\approx I_{tot,k+1}\) or \(I_{tot,rt}>I_{tot,k+1}\)then
26: Hold tracking position \((\beta_{k+1},\gamma_{k+1})\)
27: Send Alarm \(\blacktriangleright\) Sunny with partly cloudy or damage
28: Save Data \(\blacktriangleright\) Future analysis and prediction
29:else
30: Send Alarm \(\blacktriangleright\) Cloudy, dirty, or damage
31: Save Data \(\blacktriangleright\) Future analysis and prediction
32: Compare \(t_{S,rt}\) with \(\bar{t}_{S}\)
33: Define new value of \(k\)
34:endif
35:endif
36:endif
37: Calculate energy balance, \(E_{tot}(\tau)~=~{}E_{pv}(\tau)+E_{c}(\tau)\)
38:if\(E_{c}(\tau)>\kappa_{c}\cdot E_{pv}(\tau)\)then
39: Send alarm \(\blacktriangleright\) Out of energy balance
40: Save data \(\blacktriangleright\) Future analysis and prediction
41:else
42: Send alarm \(\blacktriangleright\) Within the energy balance
43: Save data \(\blacktriangleright\) Future analysis and prediction
44:endif
45:endforSubsequently, the total insolation vector \(\bar{I}_{tot}~{}=~{}[I_{tot,1},\ldots,I_{tot,k},...I_{tot,n}]^{T}\) is calculated, where the \(k\)-point of the trajectory for two-axis solar tracking with clear sky is expressed by:

\[I_{tot,k}~{}=~{}I_{BC,k}+I_{DC,k}+I_{RC,k} \tag{9}\]

where \(I_{BC,k}\), \(I_{DC,k}\), and \(I_{RC,k}\) are the beam, diffuse, and reflected insolation on the collector, respectively. In the general form, they are determined as follows:

\[I_{BC}~{}=~{}A\cdot e^{-\theta m} \tag{10}\]

\[I_{DC}~{}=~{}C\cdot I_{BC}\bigg{[}\frac{1+\cos(90^{\circ}-\beta)}{2}\bigg{]} \tag{11}\]

\[I_{RC}~{}=~{}\rho\cdot I_{BC}\cdot(\sin\beta+C)\bigg{[}\frac{1-\cos(90^{\circ }-\beta)}{2}\bigg{]} \tag{12}\]

where \(A\) is the apparent extraterrestrial solar insolation, \(\theta\) the atmospheric optical depth, \(m\) the air mass ratio, and \(C\) the sky diffuse factor, which can be calculated for each day by:

\[C~{}=~{}0.095+0.04\cdot\sin\bigg{[}\frac{360}{365}(N-100)\bigg{]} \tag{13}\]

where \(N\) is the day number, with 1 January as day 1 and 31 December as day number 365. For more details on the calculation, consult [38]. Based on the trajectory and the solar algorithm, the time of day is defined for each k-point, expressed as the vector \(\bar{f_{5}}=[t_{5,1},\ldots,t_{5,k},\ldots,t_{5,n}]^{T}\), see Figure 1. Additionally, considering the profitability of the tracker, where the energy consumption must be between 2 and 3% of the energy increase due to solar tracking [31], the consumption constraint factor \(\kappa_{c}\leq 0.03\) is proposed, which helps in the decision-making and future prediction based on energy balance calculations. Then, we set the monitoring device and initialized the real-time monitoring process.