## 4 Results and Discussion
### Comparison of Error Distribution of SPAs and Their Influence on Performance of System
\begin{tabular}{c c c c c c c c c c} \hline \hline  & & \multicolumn{6}{c}{**(a) Solar Position Empirical Algorithm**} \\ \hline \multirow{4}{*}{**SPAs**} & \multirow{4}{*}{**Computational**} & \multirow{4}{*}{**Tracking**} & **Annual** & **Annual** & **Variance of** & **Annual** & **Variance of** & **Annual** \\  & & & **Average** & **Average** & **Absolute Error** & **Average Error** & **Absolute Error** & **Absolute Error** & **Absolute Error** \\  & & **Method** & **Tracking Error** & **of the Solar** & **of the Solar** & **of the Solar** & **of the Solar** & **of the Solar** & **of the Solar** & **of the Solar** \\  & & & **(mrad)** & **Azimuth** & **Azimuth** & **Altitude** & **Altitude** & **Altitude** & **Altitude** \\  & & & **(mrad)** & **Azimuth** & **(mrad)** & **(mrad)** & **(mrad)** & **(mrad)** & **(mrad)** \\ \hline \multirow{4}{*}{Cooper and Wool} & \multirow{4}{*}{319} & NS & 5.75 & \multirow{4}{*}{6.94} & \multirow{4}{*}{25.618} & \multirow{4}{*}{5.06} & \multirow{4}{*}{32.08} & \multirow{4}{*}{2.88} \\  & & EW & 3.11 & & & & & \\  & Polar axis & 2.88 & & & & & & \\  & & NS & 2.44 & & & & & \\ Spencer & 397 & & EW & 1.47 & 4.47 & 10.37 & 2.06 & 1.794 & 3.37 \\  & & Polar axis & 3.37 & & & & & \\ Stine and Whillier & 335 & & EW & 3.28 & 8.48 & 25.75 & 5.19 & 17.716 & 4.93 \\  & & Polar axis & 4.93 & & & & & \\ Bourges and Lamm & 456 & & EW & 1.33 & & & & \\  & & Polar axis & 0.78 & 1.68 & 1.096 & 1.16 & 0.577 & 0.89 \\  & & & NS & 4.22 & & & & \\ Wang & 388 & & EW & 2.76 & 5.05 & 16.015 & 3.79 & 8.833 & 1.9 \\  & & Polar axis & 1.9 & & & & & \\ Yu & 327 & & EW & 1.6 & 4.16 & 6.056 & 2.08 & 1.204 & 2.84 \\  & & Polar axis & 2.84 & & & & & \\  & & NS & 1.82 & & & & & \\ Grena method 1 & 428 & & EW & 1.3 & 3.18 & 2.922 & 1.56 & 0.787 & 2.28 \\  & & Polar axis & 2.28 & & & & & \\ \hline \hline \end{tabular} 
\begin{tabular}{c c c c c c c c} \hline \multirow{4}{*}{**SPAs**} & \multirow{4}{*}{**Computational**} & \multirow{4}{*}{**Tracking**} & **Annual** & **Average** & **Arrange** & **Absolute Error** & **Average Error** & **Absolute Error** & **Average Error** \\  & & **Cost** & **Method** & **Tracking Error** & **of the Solar** & **of the Solar** & **of the Solar** & **of the Solar** & **of the Solar** & **of the Solar** \\  & & & **(mrad)** & **Azimuth** & **Azimuth** & **Altitude** & **Altitude** & **Altitude** & **Altitude** \\  & & & **(mrad)** & **(mrad)** & **(mrad)** & **(mrad)** & **(mrad)** & **(mrad)** \\ \hline \multirow{4}{*}{Grena method 2} & \multirow{4}{*}{455} & NS & 0.22 & \multirow{4}{*}{0.17} & \multirow{4}{*}{0.26} & \multirow{4}{*}{0.0725} & \multirow{4}{*}{0.17} & \multirow{4}{*}{0.0133} & \multirow  
The Error Caused by Using Average Error to Evaluate the Effect of SPA's Error on Trough Solar System  
In practical application, due to the processor performance of the tracking system of a parabolic trough system, the algorithm with low computation will be preferred, thus, it will produce tracking error at every moment. When we consider the impact of this SPA on efficiency, the average error can usually be taken as a reference. However, the tracking error caused by error of SPA always changes at every moment. The calculation method that takes the average error as tracking error will increase the efficiency calculation error. Figure 5 shows the comparison of the annual average efficiency calculated directly using the Bourges and Lamm algorithm and result using the average error under the north-south tracking mode. The annual average efficiency obtained under the two calculation methods are 0.4214 and 0.4330, respectively. The efficiency calculated by using the average error is 0.13% higher than that consider the error of every moment, which is quite small. When the algorithm with higher error is adopted, the tracking error will have greater fluctuation, and the average error calculation method may lead to larger error.