## 3 Operation Optimization
### Charging Schedule Optimization  
At present, the PEB is fully charged for use in the next day when it has finished its last trip back to the station. This may lead to charging congestion and can produce a load peak. Furthermore, the PEBs usually charge during the peak tariffs, so the electricity cost will be high. Therefore, the strategy is to adopt fast-charging during operating time to support the great charging amount, and normal charging at night to reduce the peak load and electricity cost. The normal charging at night is easy to accomplish through an arrangement, considering the number of PEBs, valley tariffs duration, and peak power suppression goal. The peak charging power will not exceed use during the operating hours because of the total electricity demand of the PEBs and the long spare time duration. Regarding the random charging during operating hours, the fact that the drivers charge randomly and frequently is the main factor leading to a huge peak charging power. According to the operation characteristics of the station and the fleet, the peak charging power can be decreased through the charging sequence and duration optimization of each PEB. The optimization model is as follows:  
\[\text{minimize}(\max\sum_{k=1}^{m}P_{ch}^{k}(t)),\,\text{t}\in\left(V_{i,s}^{k },V_{i,e}^{k}\right),\,\text{i}\,=\,1,\,2,\,3\,\ldots\,\text{N}_{B}^{k} \tag{2}\]  
Figure 4: The new charging topology sketch. in Equation (2), it is as follows:  
\[V_{i,e}^{k}=V_{i,s}^{k}+a_{i}^{k} \tag{3}\]  
\[a_{i}^{k}=a_{i}^{k}\cdot t_{i}^{k} \tag{4}\]  
where \(k\) is the PEB number; \(m\) is the total quantity of PEBs of the fleet; \(t\) is time in minute; \(i\) is the sequence of PEB returning to the station; \(P_{ch}^{k}(t)\) is the charging power of PEB \(k\) on \(t\); and \(a_{i}^{k}\) is the actual charging duration of PEB \(k\) on the \(i\)th backing to the station, which belongs to the charging combination matrix. The constraint conditions are as follows. (1) Balance of electricity cost of each PEB  
Assuming that the charging power of each stick is constant, the daily electricity cost of the PEB can be presented by the charging duration of one day. \[\sum_{i=1}^{N_{B}^{k}}a_{i}^{k}=N_{r}^{k}\cdot\beta_{k}\;,\;\mathrm{i}\;=\;1, \;2,\;3\;\dots\;\mathrm{N}_{B}^{k} \tag{5}\]  
where, \(N_{r}^{k}\) is the daily charging number of PEB \(k\) in line \(r\), which can simplify the charging power and electricity of the model by the charging time. It depends on the line distance, unit energy consumption, and daily running mission of PEB \(k\). \(\beta_{k}\) is the charging duration of PEB \(k\) of one loop. (2) One time charging electricity constraint  
For the different running loops of each backing station, the electricity quantity charged to the PEB cannot exceed the consumption of the former operation. \[E_{i}^{k}=E_{(i-1)}^{k}+a_{i}^{k}\cdot p_{ch} \tag{6}\]  
\[0\leq E_{i}^{k}\leq E_{0}^{k} \tag{7}\]  
(3) Number of the sticks  
The synchronous charging service ability is constrained to the number of the sticks, which is the maximum threshold of the charging PEBs at the same time. \[\sum_{k=1}^{m}P_{ch}^{k}(t)\leq p_{ch}\cdot\mathrm{N}_{stick} \tag{8}\]  
(4) Evaluation metric  
The station electricity cost is set as one economic index in order to evaluate the optimization effect. \[\mathrm{C}_{E\_\mathrm{total}}=\sum_{t=a}^{b}\sum_{k=1}^{m}P_{ch}^{k}(t)\cdot c _{ele}\cdot\Delta t \tag{9}\]  
According to the optimal issue's characteristics, the goal is to find solutions that minimize the peak charging power, and the direct result is the bus charging sequence. This is a combinatorial optimization problem that can be solved using the particle swarm optimization (PSO) algorithm. The peak charging power is the algorithm fitness. Depending on the PEBs' charging demand, set the different charging combinations as the particles of the algorithm. Through the algorithm iteration, find the charging schedule corresponding to the minimum peak charging power and its suitable combinations.