## 6 Conclusions  
The large-scale cascade hydropower plants in southwestern China challenge a new multi- market environment. Considering the price uncertainty and the correlations between multiple markets, this paper has proposed a novel optimization model of long-term generation scheduling for cascade hydropower plants to seek for the overall benefits. The main contributions and conclusions were as follows:  
(1) The correlation of MCP between multiple markets was described. The prediction price was treated as a random variable that consists of its prediction value and a random prediction error. Then, the MCP scenarios for the hybrid market environment were generated by using the Copula theory and further reduced by the hierarchical clustering method combined with inconsistent values. (2) A novel long-term generation scheduling model was constructed based on the stochastic programming theory and the reduced MCP scenarios, in which the market-to-market supply energy ratio constraint and the minimum constraint of supply energy in the provincial market were creatively taken into consideration, so as to meet the actual engineering needs. (3) The scenarios analysis showed that the Gaussian-Copula function has better fitting performance in describing the correlation between the MCPs of the provincial and external markets than other functions. The proposed reduction strategy for the MCP scenarios was effective, after the reduction of scenarios. The minimum number of scenarios from January to December was 47, and the maximum number was 64. (4) The effectiveness analysis showed that the proposed model could better respond to the changing of MCP signals, and so the arrangement of power generation in different months and markets \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Scenario**} & **MAPE** & **MAE** & **R** & **Prediction** \\  & **(\%)** & **(yuan/MWh)** & **R** & **Performance** \\ \hline
1 & 1.92 & 5.65 & 0.9560 & good \\
2 & 2.00 & 5.81 & 0.9609 & good \\
3 & 0 & 0 & 0 & perfect \\
4 & 13.02 & 37.33 & 0.5590 & poor \\
5 & 12.27 & 34.90 & 0.5113 & poor \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The detailed information of different scenarios. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Scenario**} & \multicolumn{3}{c}{**Benefit of Proposed Model**} & \multicolumn{3}{c}{**Benefit of Conventional Model**} \\ \cline{2-7}  & **Market 1** & **Market 2** & **Total** & **Market 1** & **Market 2** & **Total** \\ \hline
1 & 5.369 & 1.813 & 7.182 & 6.250 & 0.788 & 7.039 \\
2 & 5.268 & 1.744 & 7.013 & 6.119 & 0.759 & 6.878 \\
3 & 5.353 & 1.791 & 7.144 & 6.229 & 0.779 & 7.008 \\
4 & 5.467 & 1.668 & 7.135 & 6.163 & 0.796 & 6.959 \\
5 & 5.293 & 1.668 & 6.961 & 6.032 & 0.795 & 6.827 \\ Probability combination & 5.318 & 1.793 & 7.110 & 6.224 & 0.780 & 7.003 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Operation results comparison of multi scenarios (Unit: Billion yuan). was more reasonable. This resulted in an increase of 106.93 million yuan for the total income, although the power generation was less, compared with the conventional model. (5) The robustness analysis showed that the proposed model could better adapt to different price scenarios in the future, even in the adverse scenario, with a serious deviation in the price prediction. This enhanced profitability and robustness for the generation scheduling. It should be mentioned that the market reform in China is still at an early stage and the available samples are in a relatively small quantity. This paper only analyzed qualitatively the price correlation between the provincial and external markets but did not give the specific influence factors and their different roles. With continuous accumulation of data in the future, the interaction characteristics between the markets, consumers, and producers can be analyzed in detail, so as to better describe the price correlation between multiple markets. Conceptualization, B.L. and S.M.M. ; Methodology, B.L., S.M.M. and C.T.C. ; Software, B.L. and L.G.