## 4 Energy Consumption Model
### Energy Consumption Model Validation  
The objective of creating an energy consumption model was for use as a tool in developing and testing a variable data collection rate system. Before design or performance testing, the degree to which an energy consumption model represented a wildlife behavior monitor needed to be validated.  
Validation of the developed wildlife behavior monitor tracking device model was performed by matching operating parameters for the energy consumption model to empirical data acquired from a CTT-1000a wildlife telemetry device. Real fix rate and battery performance data were collected from a field-deployed behavior monitoring device on a golden eagle free-roaming in eastern North America [7]. The fix interval, battery capacity, PVC voltage, and charge rate (mA) measured at each fix acquisition were analyzed. The initial and continuous battery level in terms of SOC were unknown factors and estimations were made using battery voltage. In order to estimate the battery SOC, a direct relationship of voltage and SOC for a Li-ion battery was developed at known load values using the exact same battery model and capacity as the deployed device. For this particular case, voltage of the battery for a 0.01 C was used as the reference load. In order to develop the relationship, measurements were collected of several 800 \(mA-hr\) batteries of the same type as deployed units. First, A Vencon UBA5 battery tester was used to characterize voltage vs. capacity for the 0.01 C load. Next, the collected curves were averaged together, shown in Figure 4. Finally, linear regression was used resulting in available battery SOC vs. voltage. The particular battery tested was represented by a rational polynomial curve (see Equation (4)) where the polynomial coefficients are represented in Table 3.  
\[B_{SOC}(V)=100-\frac{p_{1}V^{5}+p_{2}V^{4}+p_{3}V^{3}+p_{4}V^{2}+p_{5}V+p_{6} }{q_{1}V^{2}+q_{2}V+q_{3}} \tag{4}\]Measured performance data was compared to the developed energy model by using the following configuration: (1) Solar current generated was linearly interpolated from a rate of 15 min to 1 s to match the model sample period; (2) the fix interval for the model's GPS data collection rate was set to 15 min; (3) the modeled battery capacity was set to 800 \(mA-hr\), and the initial battery SOC was determined by the initial deployed device voltage to Equation (4); and (4) the simulation duration was configured based on the length of time between the first and last data record for each day. Absolute difference between simulated and empirical battery SOC was calculated for each of the 31 days in January 2015 for two behavior monitors. A single day of the device's solar current and SOC were compared with the developed simulation model and shown in Figure 5, where (A) represents the actual PVC data from golden eagles in eastern North America [7], (B) shows the SOC for the device and the models determination of SOC using the PVC data from the device, and (C) shows the difference in the SOC between the model and actual device. Statistical comparisons of the minimum, maximum, and average difference between the model and device data, shown in Table 4, indicate that the model is capable of generating comparable SOC estimations as an actual device given PVC charge rates.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \(P_{x}\) & **Value** & \(Q_{x}\) & **Value** \\ \hline \(p_{1}\) & 28.43 & \(q_{1}\) & 1 \\ \(p_{2}\) & \(-473.1\) & \(q_{2}\) & \(-6.669\) \\ \(p_{3}\) & 3080 & \(q_{3}\) & 11.33 \\ \(p_{4}\) & \(-9749\) & & \\ \(p_{5}\) & 14,850 & & \\ \(p_{6}\) & \(-8526\) & & \\ \hline \hline \end{tabular}
\end{table}
Table 3: Coefficients for voltage conversion equation.  
Figure 4: Relationship between battery voltage and state of charge (SOC).