When the mass of ESS increases, we can increase their capacity in power and energy and provide a significant reduction in fuel cell use. This will allow the fuel cell not to give the maximum power peaks of each profile, but to be able to give the average power of each one. The analysis of this variation, expressed in percentages of energy supplied by the storage elements and in the reduction of fuel cell use, will be presented below. Furthermore, the power profile of battery, supercapacitor, and fuel cell will also be plotted for a particular ESS mass value. Finally, in each profile, the monetary cost involved in increasing the power of the ESS will be reported in a graph.

#### BADC Driving Profile

During the sizing process, the total mass of the storage elements should be constant

where

${m}_{ess}$ is the total mass and is constant and

${m}_{bat}$ and

${m}_{sup}$ are the ones that are going to vary. As indicated, supercapacitors allow recovery of a greater amount of power from braking, but they are more expensive than the battery. If the storage system is composed only of supercapacitors, the power of the fuel cell used in the system decreases, but the momentary cost of the storage system increases. Then, the objective is to find the mass of batteries and supercapacitors to reduce the cost of the storage system, but without forgetting the objectives of fuel economy control and SOC variation. For this reason, the case where the storage system has the lowest cost will not be optimal. This optimal case will depend on the compendium of the cost of the storage system and the other control objectives. A system with only supercapacitors (

${m}_{bat}=0$) is initially dimensionalized and mass is added to the batteries in each iteration. This is done to decrease the cost associated with the storage system in each iteration and to know how the fuel saving varies. Then, the initial configuration will be

${m}_{bat}=0$ and

${m}_{sup}={m}_{ess}$. In order to fulfill with the power profile using the fuel cell described in

Table 4, the minimum mass of supercapacitors should be 30 kg. Otherwise, if it is lower, the power profile is not fulfilled.

In the total mass, the mass of each element varies with respect to the other as follows. For example, in case 1: (a) When the mass of the supercapacitor is 30 kg, the battery mass should be 0 kg; (b) when the mass of the supercapacitor is 29 kg, the battery mass should be 1 kg. For each mass variation in batteries or supercapacitors, there is a new cost involved, and a new power and energy capacity. For example, for the same examples, in case 1, the cost of the battery is 0 €, while that of the supercapacitor is 2650 €. For case 2, the cost of the battery is 33.87 €, while the cost of the supercapacitor is 2561.67 €. As we can see, the total mass remains constant, but the economic value varies for each case. The final case will be when we have 28 kg of battery and 2 kg of supercapacitors, with a cost of 948.39 €, and 176.67 €, respectively. The configuration of 29 kg of batteries and 1 kg of supercapacitors is not considered, because with this configuration the power profile derived from the speed profile is not fulfilled. The weight, power and cost of the fuel cell remains constant for each configuration of batteries and supercapacitors in this scenario. The weight of the battery, supercapacitor and fuel cell, is added to the total mass for calculating the power profile, shown in Equation (

1), to achieve a more realistic scenario. The cost of fuel cell FCveloCity-HD is 100 k€.

Contrarily to the case without hybridization, if the mass of the storage elements is different from 0, with a certain minimum value, we can reduce the size of the fuel cell. For the first case, where the mass of the supercapacitor is 30 kg (${m}_{sup}=30$) and the mass of the battery is 0 kg (${m}_{bat}=0$) the reduction in fuel cell usage is the highest with 46.98%. The cost of the storage system for this same case is also the highest with a value of 2650 €. For the last possible case, in which the mass of the supercapacitors is 2 kg (${m}_{sup}=2$) and the mass of the battery is 28 kg (${m}_{bat}=28$) the reduction in the consumption of the fuel cell is 30.4% and the storage system has the lowest cost, with 1125.05 €. Although 1125.05 €, is the cheapest cost of the storage system, the reduction in fuel cell usage is only 30.4%, while the battery delivers 55.98% of energy, being the same the highest of all configurations. This causes the variation of the SOC to be increased.

Figure 11 shows graphically the reduction in fuel cell consumption as a percentage of energy, compared to the percentage of energy recovered by the battery for each configuration. Even though the percentage of energy recovered by the battery increases, the reduction in fuel cell consumption decreases because the mass of the supercapacitors decreases. This shows that although the mass of the battery increases, the system does not absorb large peaks of power, so the fuel cell must provide more power.

Figure 12 shows the same behavior of the fuel cell with the supercapacitor. Since supercapacitors have a high power density, they allow the system to recover the highest power peaks of the profile and the reduction in fuel cell consumption increases.

Figure 13 shows the variation of hydrogen consumption Equation (

19) in relation to the cost of the storage system. The BADC profile has 1864 seconds of operation (31.06 min). A bus normally rolls 15 h per day. In one day, it would roll 29 times the profile, in one month it would roll 870 times and in a year 10.585 times.

In the Y axis of the

Figure 13, the variation of the cost of hydrogen is indicated for a year of operation of the bus, and in the X axis the cost of the storage system is indicated. From the figure, it can be observed that with the lowest cost of the storage system (1125.05 €), a greater amount of hydrogen is consumed. This corresponds to the point of 28 kg of batteries and 2 kg of supercapacitors. Increasing the cost of the storage system reduces the consumption of hydrogen. In the maximum point the cost is 2650 € with 30 Kg of supercapacitors and 0 Kg of batteries.

However, it can be observed that from 2200 €, with the increase in the mass of the storage system, the decrease in hydrogen consumption is almost linear. This point corresponds to 9 Kg of batteries and 21 Kg of supercapacitors. According to this analysis, this will be the optimum point. In this configuration, the fuel cell consumption reduction is 45.82% (average reduction in fuel cell consumption for BADC mass variation), and 87.54% of the energy from the regenerative brake is recovered.

Therefore, for case 1 with a storage element cost of 2650 €, the energy delivered by the fuel cell is 53.02%. For the case 2 with a storage element cost of 2595.54 €, the energy delivered by the fuel cell is 53.37%. While for the last case, with a storage system cost of 1125.05 €, the fuel cell delivers 69.55% of energy to the movement. It can be observed how the fuel cell delivers a greater amount of energy, given the price decrease of the total storage system. In this sense, when we decrease the size of the supercapacitor system, the power can be recovered from regenerative braking decreases, and therefore, the fuel cell must provide more power to achieve the profile.

Figure 14 shows the supplied power by each element, while

Figure 15, shows the battery SOC and supercapacitor SOE variation. The SOC has a slower variation than the SOE, due to the penalty of the cost function.

The sum of the battery, supercapacitor, and fuel cell powers in

Figure 15 are equal to the power required to reach the BADC speed profile.