# A New Multi-Objective Unit Commitment Model
## 5 Conclusions  
This paper proposes a novel MOUC model and a decomposition coordination method to solve it considering tie-line constraint. To minimize the production cost and emission, the multi-objective problem is transformed into a single objective, instead of generating a complete Pareto front or assigning weight to each objective, we minimize the Euclidean distance to the Utopian point, as a result, a better solution which is more satisfied with the proposed criterion could be found. Then, we calculate the revised problem by an iteration process. During the iteration process, the margin price in connected subsystems is regarded as the coordinator to update tie-line, and we realize exact step control by considering the margin price, total load, etc. Each subsystem is solved separately and locally by the branch and bound method. Test cases indicate that our method could obtain an improved result than weighted-sum and NBI. Besides, solving local MOUC problem avoids the need for uploading units parameters, which protects the data privacy of generating companies. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Weighted Sum** & **NBI** & **MOUC Method in This Paper** \\ \hline Time (S) & 1775 & 3647 & 1294 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Computation times. Figure 5: \(F_{1}-F_{2}\) plane. For any given two subsystems, if the subsystem with a high margin price generates less while the other generates more, the total cost would be decreased. However, the step size is chosen by a subjective approach, and we have not found the optimal step. In addition, the solution is very sensitive to the initialization strategy, maybe we could solve MOUC based on a parallel way, with different initialized tie-line. Furthermore, we could apply DNN [42] to find the underlying relationship among units, load, tie-line as well as step size in the future. All authors contributed equally to this manuscript. This research received no external funding  
The authors declare no conflict of interest. \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline \multirow{2}{*}{**Index**} & \(\mathbf{a}\) & \(\mathbf{b}\) & \(\mathbf{c}\) & \(\mathbf{S^{H}}\) & \(\mathbf{S^{C}}\) & \(\mathbf{d}\) & \(\mathbf{e}\) & \(\mathbf{f}\) \\  & **(\(\mathbf{S}/(\text{MW})^{2}\))** & **(\(\mathbf{5}/\text{MW}\))** & **(\(\mathbf{5}\))** & **(\(\mathbf{5}\))** & **(\(\mathbf{5}\))** & **(\(\mathbf{t}/(\text{MW})^{2}\))** & **(\(\mathbf{t}/\text{MW}\))** & **(\(\mathbf{0}\))** \\ \hline
1 & 0.00048 & 16.19 & 1000.0 & 4500.0 & 9000.0 & 0.002 & 0.52 & 29.4 \\
2 & 0.00031 & 17.26 & 970.0 & 5000.0 & 10000.0 & 0.0022 & 0.52 & 30.5 \\
3 & 0.002 & 16.6 & 700.0 & 550.0 & 1100.0 & 0.0026 & 0.52 & 29.5 \\
4 & 0.00211 & 16.5 & 680.0 & 560.0 & 1120.0 & 0.003 & 0.45 & 31.5 \\
5 & 0.00398 & 19.7 & 450.0 & 900.0 & 1800.0 & 0.0045 & 0.574 & 28.4 \\
6 & 0.00712 & 22.26 & 370.0 & 170.0 & 340.0 & 0.004 & 0.483 & 28.5 \\
7 & 0.00079 & 27.74 & 480.0 & 260.0 & 520.0 & 0.0034 & 0.53 & 28.8 \\
8 & 0.00414 & 25.92 & 660.0 & 30.0 & 60.0 & 0.007 & 0.3 & 29.5 \\
9 & 0.00222 & 27.27 & 665.0 & 30.0 & 60.0 & 0.0068 & 0.34 & 38.8 \\
10 & 0.00173 & 27.79 & 670.0 & 30.0 & 60.0 & 0.0055 & 0.3 & 33.8 \\ \hline \hline \end{tabular}
\end{table} 
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