## 4 Simulation Results
### Unit Selection Results Using the APL Method  
Equation (13) indicates that the ramp-up time of UC is influenced by parameter \(\gamma\). The APL method was used to calculate the ramp-up cost \(C_{ramp\_cost}\)(y-axis) and net output (x-axis); a low y-axis value denotes a low cost (Figure 2). To fill in a power gap of 1720 MW of renewable energy, the APL method was used to determine the units included below the area marked with red lines, namely U1-11, U16-U17, and U19; within 10 min the output power can reach 2000 MW. The dispatching principles are as follows: Units that are below the red line (no contact with the red line) are base-load units, and those that are above the red line (no contact with the red line) are peak-load units. Units that are in contact with the red line are the units requiring scheduling. Consequently, the APL method selected six peak-load units and six base-load units that were not involved in the dispatch, and eight intermediate-load units that were involved in the dispatch.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Unit**} & \multicolumn{4}{c}{**Fuel Cost Parameter**} & \multirow{2}{*}{\(\mathbf{P}_{initial}\) **(MW)**} & \multirow{2}{*}{\(\mathbf{P}_{max}\) **(MW)**} \\ \cline{2-2} \cline{5-7}  & \(\alpha\) & & & & & \\ \hline
1–2 & \(-1.26\times 10^{5}\) & \(2.61\times 10^{3}\) & \(-5.99\times 10^{-3}\) & 358 & 720 \\
3–6 & \(9.69\times 10^{5}\) & \(-2.25\times 10^{3}\) & 4.17 & 315 & 708 \\
7–8 & \(7.75\times 10^{4}\) & \(1.20\times 10^{3}\) & 1.19 & 160 & 259 \\
9–10 & \(9.17\times 10^{2}\) & \(1.76\times 10^{3}\) & \(9.16\times 10^{-3}\) & 279 & 380 \\
11 & \(-1.56\times 10^{2}\) & \(1.84\times 10^{3}\) & \(-1.52\times 10^{-3}\) & 230 & 321 \\
12 & \(-3.55\times 10^{5}\) & \(3.41\times 10^{3}\) & \(-1.22\) & 343 & 450 \\
13 & \(-6.04\times 10^{5}\) & \(4.28\times 10^{3}\) & \(-1.61\) & 320 & 450 \\
14 & \(-1.97\times 10^{4}\) & \(1.59\times 10^{3}\) & 1.34 & 340 & 450 \\
15 & \(-3.67\times 10^{5}\) & \(3.01\times 10^{3}\) & \(-7.26\times 10^{-2}\) & 340 & 450 \\
16 & \(-9.94\times 10^{4}\) & \(2.26\times 10^{3}\) & \(-2.02\times 10^{-2}\) & 340 & 450 \\
17 & \(-7.56\times 10^{4}\) & \(1.77\times 10^{3}\) & 1.11 & 206 & 278 \\
18 & \(1.21\times 10^{5}\) & \(-7.94\times 10^{2}\) & 9.88 & 183 & 278 \\
19 & \(-8.68\times 10^{3}\) & \(2.52\times 10^{3}\) & \(3.88\times 10^{-1}\) & 190 & 487 \\
20 & \(-1.81\times 10^{4}\) & \(2.50\times 10^{3}\) & \(4.02\times 10^{-1}\) & 222 & 540 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Natural gas combined cycle unit fuel cost parameters and fuel cost parameters for the natural gas combined-cycle unit and the initial and maximum.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Algorithms**} & \multicolumn{6}{c}{**Initial Parameters of Each Algorithm**} \\ \hline \multirow{2}{*}{\(\mathrm{HA}\)} & \(\omega^{(0)}\) & \(\lambda^{(0)}\) & \(M^{(0)}\) & \(\tau\) & \(\alpha^{(0)}\) & \(\varepsilon\) & \(m\) \\  & 1 & 1 & 0.2 & 1.3 & 2 & \(10^{-5}\) & 50 \\ \hline \multirow{2}{*}{IPSO} & \(N\) & \(w_{max}\) & \(w_{min}\) & \(c_{1}\) & \(c_{2}\) & _iter_ & \(v_{0}\) \\  & 300 & 0.9 & 0.4 & 0.15 & 0.23 & 700 & 0.3 \\ \hline \multirow{2}{*}{SA} & \(t_{max}\) & \(t_{min}\) & _down_ & & & & \\  & 100 & 0.001 & 0.6 & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Initial parameter settings for the algorithm proposed in this study.