## 5 Conclusions  
In this paper, the average tracking error of SPA is proposed to represent its error influence on the solar trough system. We compute the efficiency of the solar trough system with tracking error generated by error of SPAs for each moment over a year and efficiency when average error of SPA is applied. The average efficiency difference of two calculation methods over a year is evaluated for solar trough system. We compute the calculation error of serval of SPAs by comparing to the SPA proposed by NREL and its contribution to tracking error of parabolic trough solar system under three tracking strategy. For the efficiency calculation, we improved the calculation program of the optical efficiency of the trough system developed before [11], taking the change of the focus position caused by the tracking error into account. Due to the lack of relevant experimental data, SolTrace was used to verify the model. 'the annual efficiency of a solar system with main SPAs is given and the influence of their errors on the system efficiency is calculated with the program of optical efficiency for solar trough. We also make an  
Figure 5: Efficiency comparison of two system calculated with tracking error at every moment and average tracking error, respectively, with the Bourges and Lamm method under north–south axis tracking system. \begin{table}
\begin{tabular}{l c c c c} \hline \hline \multirow{2}{*}{**SPAs**} & **Efficiency Calculated with** & **Efficiency** & \multirow{2}{*}{**Average Tracking Error (mrad)**} & **The Relative Difference** \\  & **Average Tracking** & **Tracking Error at** & & **Error (mrad)** & **Difference** \\  & **Error** & & & & \\ \hline Cooper and Woolf & 0.4330 & 0.4214 & 5.5 & 2.75\% \\ [PERSON] and [PERSON] & 0.4291 & 0.4140 & 6 & 3.65\% \\ [PERSON] & 0.4416 & 0.4292 & 4.2 & 2.89\% \\ [PERSON] & 0.4494 & 0.4469 & 2.4 & 0.56\% \\ [PERSON] & 0.4498 & 0.4465 & 2.4 & 0.74\% \\ [PERSON] and Lamm & 0.4526 & 0.4518 & 1.3 & 0.18\% \\ Green method 1 & 0.4515 & 0.4499 & 1.8 & 0.35\% \\ Green method 2 & 0.4537 & 0.4536 & 0.22 & 0.02\% \\ Green method 3 & 0.4538 & 0.4538 & 0.049 & 0\% \\ Green method 4 & 0.4538 & 0.4538 & 0.045 & 0\% \\ Green method 5 & 0.4538 & 0.4538 & 0.003 & 0\% \\ Huang (without & 0.4538 & 0.4538 & 0.056 & 0\% \\ Huang (with & & & & \\ nutation correction) & 0.4538 & 0.4538 & 0.046 & 0\% \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Average annual tracking error and efficiency of system with Cooper and Woolf method under three different tracking methods, efficiency calculated with average tracking error and the relative difference between two results. efficiency comparison calculated with fixed annual average tracking error and normal constantly changing tracking error within a year for each solar trough system, and the main conclusions are as follows:  
* When the average error of SPAs is used to characterize the impact of its error on system efficiency, it is a good approximation for most algorithms. Compared with the result of parabolic trough system that calculate the error of every moment, the efficiency obtained is quite similar, and most of the relative errors are of less than 0.5%;
* For the low-precision SPAs with an annual average error higher than 1.5 mrad, the relative error is within the range of 0.5% to 3% when the average error is used to evaluate its impact on the efficiency of the trough system. Most of them are less than 1%, which can represent the influence of SPA algorithm error on the performance of the system;
* The average error of SPAs is used to represent its precision characteristics. The disadvantage is that for a few algorithms with low complexity, it cannot reflect its annual periodic tracking error changes. In some moments, the error is very small, while in others, the error is large, which introduces larger error of the instantaneous efficiency. Overall, the average error of the SPA is used to evaluate its impact on the efficiency of the solar trough system.