## 3 Results and Discussions  
### Start-Stop Reduction Strategies  
Figure 8 shows the numerical solutions given by the DP algorithm to tighten the pollutant emission limits step by step. The SOC is 0.2 at the test trip's start. The emission limits are initially 0.5 g/km for CO, \(6\times 10^{11}\)\(\mathrm{\SIUnitSymbolMicro\second}\)/km for PN, and 0.035 g/km for NO\({}_{\text{x}}\). Due to the more extensive initial setup, these emission limits do not constrain the optimization strategy that targets fuel consumption. In this strategy (Strategy A), the engine runs at the lowest fuel consumption rate condition (2750 \(\mathrm{\SIUnitSymbolMicro\second}\)/min \(\times\) 99.72 N\(\cdot\)m) or stops. As shown by the engine speed curve in Figure 8a, the engine essentially operates only at two-speed condition points, 0 and 2750 \(\mathrm{\SIUnitSymbolMicro\second}\)/min. Moreover, the engine output power should be as close as possible to the driving demand power to reduce the charging and discharging  
Figure 7: Data flow of the action optimization-seeking at the \(j\)-\(k\) grid point.  
of the battery and avoid the losses of energy conversion between electrical energy and chemical energy. To do this power following, the engine frequently switches between these two operating conditions. Since the change in SOC indicates the difference between the engine output power and the driving demand power, the SOC varies only in a tiny range close to 0.2, as noted in the SOC curve in Figure 8a. In addition, a few singular operating points occur during the engine start-stop transients, which are neither at the lowest fuel consumption rate nor in the engine shutdown condition. However, these singular operating points are only about 3 in a thousand and decrease with the reduction of start-stop events or finer SOC grids. Accordingly, these singular operating points are due to interpolation errors in the DP algorithm.  
As the pollutant emission limits become stricter, Strategy B, Strategy C, and Strategy D, given by the DP algorithm with emission constraints, are still to maintain the operating points at the lowest fuel consumption rate condition and the engine stop condition. However, the engine start-stop events are reduced, and the SOC variations are increased, as shown in Figure 8b-d. When pollutant emissions are further restricted, start-stop events are no longer observed. In Figure 8d, Strategy D is a no-start-stop strategy given by the DP solution. Strategy D allows the engine to run at the lowest fuel consumption rate and charge the battery in the initial part of the trip (within the 0 to 2467 s period). Then, the engine is shut down, and purely electrical driving is used during the trip's latter part (within the 2468 to 5579 s time period). The SOC curves in Figure 8d also reflect the charging and discharging characteristics of the no-start-stop strategy. At the end of the first half of the trip, SOC reaches a peak value close to 0.8. Therefore, applying a non-start-stop strategy may be compromised in the case of small battery capacities. Overall, since fuel consumption is not sensitive to engine start-stop events, the cumulative fuel consumption of the no-start-stop strategy in Figure 8d does not differ much from that in Figure 8a-c, except for a small amount of energy loss due to the increased battery charging and discharging, as shown in Figure 9a. However, pollutant emissions are significantly affected by engine start-stop events. Compared to Strategy A, which is without the emission constraints, the CO and NO\({}_{\text{x}}\) emissions under the no-start-stop strategy are only about 30% of the former; the PN emissions are even orders of magnitude lower, as shown in Figure 9b-d. Therefore,  
Figure 8: Start-stop reduction strategies to tighten the pollutant emission limits.  
the start-stop reduction strategies given by the DP algorithm can significantly reduce real driving emissions while maintaining the fuel economy advantage.