Multi-Objective Energy Management Strategy for PV/FC Hybrid Power Systems

: In this paper, a new control of the DC–DC power converter that interfaces the fuel cell (FC) system with the DC bus of the photovoltaic (PV) power system is proposed to increase the battery lifespan by its operating in charge-sustained mode. Thus, the variability of the PV power and the load demand is compensated by the FC power generated considering the power ﬂows balance on the DC bus. During peak PV power, if the PV power exceeds the load demand, then the excess power on the DC bus will power an electrolyzer. The FC system operation as a backup energy source is optimized using a new fuel economy strategy proposed for fueling regulators. The fuel optimization function considers the fuel efﬁciency and electrical efﬁciency of the FC system to maximize fuel economy. The fuel economy obtained in the scenarios considered in this study is compared with reference strategies reported in the literature. For example, under scenarios considered in this paper, the fuel economy is between 4.82–20.71% and 1.64–3.34% compared to a commercial strategy based on static feed-forward (sFF) control and an advanced strategy recently proposed in the literature, respectively.


Introduction
The issue of the decision to continue using fossil fuels is related to their still very high percentage (about 80%) in world energy production [1]. However, even if new exploits are discovered, it is obvious that the limited amount of fossil fuel, compared to the growing energy demand, will lead, sooner or later, to the need to use alternative energy sources. For example, the predictions of oil companies over the next decade highlighted a peak in the exploitation of fossil fuels, gasoline and natural gas, somewhere in the years 2022-2024 [2]. However, the most serious problem caused by the heavy use of fossil fuels is related to environmental damage and climate change (due to global warming, acid rain, pollution, ozone depletion, etc.) and the annual cost of remedial measures of about USD 5 trillion worldwide [3]. One solution identified and proposed since 1970 is the use of renewable energy sources combined with hydrogen-based energy generation and storage systems [4]. Taking into account the recent research and development activities in laboratories of universities and research institutes, it can be said that hydrogen technology is already mature, and can be used successfully in various mobile [5] and stationary applications [6]. In addition, it is a cleaner and more efficient source of energy compared to, for example, the diesel generator [7], and the price of hydrogen production decreases every year [8,9]. In the electrochemical processes in the fuel cell (FC) system, hydrogen is transformed with an efficiency of 50-60% into electricity [10]. For example, in FC electric vehicles, this energy is converted into mechanical energy much more efficiently than using conventional fuels [11].
However, additionally, the electricity produced by FC systems can be converted to AC energy and used to power buildings or injected into the grid, by integrating renewable/FC hybrid power systems into standalone [12] or grid-connected [13] nano-and micro-grids.
The renewable/FC microgrids based on hybrid energy storage systems (ESS) represent the most viable and performant solutions for reducing Greenhouse Gases (GHG) and other environmentally harmful gases [14]. The microgrids integrate renewable/FC hybrid power systems (called distributed energy resources-DERs), which use locally available energy sources (such as hydro-turbines, photovoltaic (PV) panels, wind turbines, etc.) [15]. The level of energy generated depends directly on the water flow, the level of solar radiation, wind speed, but also indirectly on the ambient temperature, air humidity, weather, season, etc. [16]. In addition, the energy demand is variable during the day and depends on the geographical location, season, etc. [17]. Therefore, an energy storage system [18] or a backup energy source (such as a FC system [19] or diesel generator [20]) is needed to compensate for this variability in power generated and load demand using an appropriate energy management strategy [21][22][23].
If a backup energy source is not used, then the capacity of the batteries is projected based on the forecasts made for renewable energy and load demand, generally resulting in a large capacity for the batteries [24]. In addition, regardless of the type of strategy used [21][22][23][25][26][27], batteries are frequently charged and discharged within state-of-charge (SOC) limits, reducing their lifespan [15,28]. Different algorithms are used to identify the parameters of the FC system [29], PV panel [30] and battery SOC [31].
Therefore, in this study, it is proposed to use a FC system as a green backup power source to operate the battery stack in charging mode in order to reduce the size of the battery and increase its life. The objectives and novelty of this research study are as follows: I Control of the DC-DC power converter that interfaces the FC system with the DC bus to operate the battery stack in charge-sustained mode, increasing their life due to a limited number of charge-discharge cycles (which may occur if it is not used an electrolyzer to be powered by excess power from the DC bus; note that frequent charge-discharge cycles usually appear in a PV/ESS hybrid power system without the support of a backup energy source); a new power-following (PF) control is proposed based on the power flows balance on the DC bus; I Optimization of the FC system operation as a backup energy source; a new fuel economy strategy (called below as strategy S2) is proposed for fueling regulators using a new fuel optimization function based on fuel efficiency and FC electrical efficiency to maximize fuel economy.
The fuel economy obtained is compared with that reported in [31], using the best fuel economy strategy from those analyzed in [32] (called as strategy Air/Fuel-PF in [33] and strategy S1 below), and with the fuel economy obtained using the reference strategy S0 based on the static feed-forward (sFF) control of the fueling regulator [34] and the proposed PF control of the FC power converter.
The architecture of the PV/FC/ESS hybrid power supply system and PF control is presented in Section 2. The results for PV/ESS and PV/FC/ESS are presented in Sections 3 and 4 for comparison in seven scenarios of variable solar irradiation profiles. Total fuel consumption and fuel economy obtained using different PF-based strategies to test the performance of the PV/FC/ESS system are summarized and discussed in Section 4. The main findings are mentioned in Section 5.

PV/FC/ESS Hybrid Power System
The PV/FC/ESS hybrid power system is shown in Figure 1. The inverter and the AC load are equivalent to a DC load at the DC bus level. Thus, the balance of power flows at the DC bus level is given by Equation (1):

PV/FC/ESS Hybrid Power System
The PV/FC/ESS hybrid power system is shown in Figure 1. The inverter and the AC load are equivalent to a DC load at the DC bus level. Thus, the balance of power flows at the DC bus level is given by Equation (1): where: is the PV power available under a solar irradiance set by the insolation sequence; -is the FC net power under fueling flows set by the air flow rate (AirFr) and the fuel flow rate (FuelFr); -is the load demand at the DC bus level set by the selected load profile; -is the power exchanged by the batteries (Batt) stack at the DC bus level; -is the power exchanged by the ultracapacitors (UC) stack via the buck-boost DC-DC power converter to dynamically compensate the balance of power flows at the DC bus level; -and are the efficiency of the boost DC-DC power converters 1 and 2. and is the efficiency of the buck-boost DC-DC power converter; -is the capacitors stack used to filter the voltage = 200 V of the DC bus.
The parameters of the PV/FC/ESS hybrid power system are mentioned in Table 1.  The parameters of the PV/FC/ESS hybrid power system are mentioned in Table 1. (at night) and battery (which has only 10 Ah capacity and will be operated in chargesustained mode).
The design of the battery, UC and C DC has been performed for pulses of load using the design relationships mentioned in [35].
Neglecting the power exchanged by the UC stack and C DC capacitor, Equation (1) can be written as Equation (2): An objective of FC system control is to maintain the state of charge of the battery, avoiding the frequent charge-discharge cycles that occur in the PV/ESS system, as will be shown in Section 3. Therefore, considering p Batt ≈ 0 in Equation (2), the FC net power to be generated is given by Equation (3): Thus, the power requested (p DCreq ) from the FC system to operate the batteries stack in charge-sustained regime will be obtained if the inputs of the fueling regulators or FC current will follow the reference I re f (PF) generated by the power following (PF) controller (see Figures 2 and 3, respectively), which is given by Equation (4): where the p PV(LPF) , p Load(LPF) and V FC(LPF) are the values for PV power, load demand and FC voltage after a low-pass filter (LPF) or a filter block based on average value. It is obvious that I FC ∼ = I re f (PF) . The air flow rate (AirFr) and the fuel flow rate (FuelFr) are measured in liters per minute (Lpm), being given by Equations (5) and (6) [36]: where the default values are used for parameters N C , θ, U f (H2) , U f (O2) , P f (H2) , P f (O2) , x H2 , and y O2 [37] and the fueling flow rates are limited to 100 A/s, which is the maximum slope of the current during the acceleration phase of electric vehicle [38,39]. The optimization of the FC system operation as a backup energy source is based on the new fuel economy strategy of the fueling regulators selected as strategy S2 in Figure 2. Therefore, the references I re f (Air) or I re f (Fuel) are given by Equations (7) and (8): where the FC net power is estimated by (9) Electronics 2021, 10, 1721 5 of 25 and the power losses of the air compressor (P cm ) given by (10) The parameter used in modeling are a 0 = 0.6, a 1 = 0.04, a 2 = −0.00003231, b 0 = 0.9987 and b 1 = 46.02 for the static model Equation (10) and 100 Hz natural frequency and 0.7 damping ratio for the dynamic model based on a second-order transfer function [40,41].
If the switch selects the strategy S1 (as it is presented in Figure 3), then the references I re f (Air) and I re f (Fuel) are given by Equations (11) and (12) [32]: where the reference P re f of 2500 W is set using the sensitivity analysis for this parameter and the FC profile resulting from the case studies analyzed in Section 4.  The air flow rate (AirFr) and the fuel flow rate (FuelFr) are measured in liters per minute (Lpm), being given by Equations (5) and (6) [36]: where the default values are used for parameters , , ( ) , ( ) , ( ) , ( ) , , and [37] and the fueling flow rates are limited to 100 A/s, which is the maximum slope of the current during the acceleration phase of electric vehicle [38,39].
The optimization of the FC system operation as a backup energy source is based on the new fuel economy strategy of the fueling regulators selected as strategy S2 in Figure  2. Therefore, the references ( ) or ( ) are given by Equations (7) and (8): where the FC net power is estimated by (9) The reference strategy S0 based on the sFF control of the fueling regulator and the proposed PF control of the FC power converter is presented in Figure 3. Therefore, the references I re f (Air) or I re f (Fuel) are given by Equations (13) and (14): Thus, all the analyzed strategies (S0, S1 and S2) use PF control of the FC system, and the same control and operation conditions of the PV system for a fair comparison of the fuel economy obtained.
It is worth mentioning that the optimization loop is the same for the S1 and S2 strategies shown in Figure 2, being detailed below. However, the results presented in Section 4 show a substantial fuel economy for strategy S2 compared to strategy S1 due to the use of a variable reference (P re f = 0.5·P FCnet ) instead of a constant one (P re f = 2500 kW).
The optimization function (15) mixes the FC electrical efficiency (η sys =P FCnet/ P FC [%]) and the fuel consumption efficiency (Fuel eff ∼ = P FCnet /FuelFr [W/Lpm]): where vector x represents the FC state variables [34,42], P Load and P PV the perturbations, and k f uel was set to 2 based on sensitivity analysis to maximize the fuel economy. The controler that implement the optimization algorithm is based on the Global Extremum Seeking (GES) [43], but any global maximum search algorithm that meets the performance requirements specific to this application (search time less than 100 ms at an amplitude step jump half of the maximum allowed value, stationary search accuracy higher than 99%, etc.) can be used as well [44]. The GES controller 2 shown in Figure 2 operate using the following modeling relationships [43,45]: The normalized value (y N ) of the optimization function (by using k Ny = 1/100) is processed with a band-pass filter (having the cut-off frequencies ω l = b l ω and ω h = b h ω, where β l = 1.5 and β h = 0.1) to obtain the y BPF signal (an approximation of the first harmonic). By demodulation of the y BPF signal with a sinusoidal dither (s d = sin(ωt), where ω = 2π f d and f d = 100 Hz) is obtained y DM signal. Integration of the y DM signal results in the search gradient (y Gradient ). The search and location signals (p 1 and p 2 ) are tuned using k 1 = 1 and k 2 = 2 to speed up tracking of the best fuel economy. The reference I re f 2 and FC current (I FC ) are the inputs of the hysteresis controller 2 with 0.1 A hysteresis band (which is shown in Figure 2), so the FC current will follow the reference I re f 2 (I FC ∼ = I re f 2 ). The gain k Np = 50 adapts the search range for the reference I re f 2 . The reader interested in designing GES-based control can analyze the design applications presented in [46,47].
The inputs of the fueling regulators or FC current will follow the reference I re f (PF) or the FC current considering the switching rules Equations (7) and (8) for the strategy S2 (or the switching rules Equations (11) and (12) for the strategy S1). As I FC ∼ = I re f (PF) , the switching strategies S1 and S2 produce minor disturbances in the fueling flows after switching. To avoid frequent switching, the power requested (p DCreq ) is low-pass filtered and 500 W hysteresis band is used for the hysteresis controller 3.
In strategy S0 (presented in Figure 3) the reference I re f (PF) and FC current (I FC ) are the inputs of the hysteresis controller 2 with 0.1 A hysteresis band, so the FC current will follow the reference I re f (PF) , resulting I FC ∼ = I re f (PF) . The inputs of the fueling regulators are controlled by the FC current as in the sFF control proposed in [34].
The PV system (shown in top of Figures 1-3) generates 5.4 kW at 1000 W/m 2 solar irradiance. The voltage and current at maximum power are 60 V and 90 A, and the short-cut current is 120 A (see Table 1). Thus, if the GES-based algorithm will be used for maximum power point (MPP) tracking control, then the global MPP will be tracked under variable solar irradiance. The normalized value (y N ) of the PV power will be found using k Ny = 1/3000 and the gain k Np = 20 will adapt the search range for the reference I re f 1 ∼ = I PV (due to use of 0.1 A hysteresis band for the hysteresis controller 1).
The operation of the PV system will be presented in Section 3 without the use of the FC system (see Figure 4) to highlight the operation regime of the batteries stack and the efficiency of harvesting PV power using the GES control. In order to compensate the power flow balance on the DC bus, the battery's power must be at level of the FC power. Thus, a 100 Ah battery is used in simulation of the PV/ESS system.

Results for PV/ESS System
The results for PV/ESS system under variable solar irradiance (SI) profile with slow slopes (SI profile shown in Figure 5), with random pulses of maximum 200 W/m 2 added to the SI profile shown in Figure 5 (see Figure 6) and with very high slopes of the SI profile (see Figure 7).

Results for PV/ESS System
The results for PV/ESS system under variable solar irradiance (SI) profile with slow slopes (SI profile shown in Figure 5), with random pulses of maximum 200 W/m 2 added to the SI profile shown in Figure 5 (see Figure 6) and with very high slopes of the SI profile (see Figure 7).

Results for PV/ESS System
The results for PV/ESS system under variable solar irradiance (SI) profile with slow slopes (SI profile shown in Figure 5), with random pulses of maximum 200 W/m 2 added to the SI profile shown in Figure 5 (see Figure 6) and with very high slopes of the SI profile (see Figure 7).    The plots in Figures 1-3 present (top to down) solar irradiance, dither gain ( signal) and PV power during a cycle of 2.4 s (chosen shorter to obtain a reasonable simulation time duration, but similar to a 24-h cycle for the variation of solar irradiance and which can highlight the performance of the proposed strategies to be analyzed in this paper).  The plots in Figures 1-3 present (top to down) solar irradiance, dither gain ( signal) and PV power during a cycle of 2.4 s (chosen shorter to obtain a reasonable simulation time duration, but similar to a 24-h cycle for the variation of solar irradiance and which can highlight the performance of the proposed strategies to be analyzed in this paper). The plots in Figures 1-3 present (top to down) solar irradiance, dither gain (y BPF signal) and PV power during a cycle of 2.4 s (chosen shorter to obtain a reasonable simulation time duration, but similar to a 24-h cycle for the variation of solar irradiance and which can highlight the performance of the proposed strategies to be analyzed in this paper).
It can be seen that the dither signal has the amplitude almost zero during the constant solar irradiation and variable during changes in solar irradiation. Thus, the search time of next MPP is reduced, and the MPP is found with 99% accuracy and without power ripple, improving the tracking efficiency.
In Figure 8 are added more plots to those presented in Figure 5 to highlight the behavior of the PV system. It can be seen that the dither signal has the amplitude almost zero during the constant solar irradiation and variable during changes in solar irradiation. Thus, the search time of next MPP is reduced, and the MPP is found with 99% accuracy and without power ripple, improving the tracking efficiency.
In Figure 8 are added more plots to those presented in Figure 5 to highlight the behavior of the PV system.  Therefore, beside the three plots from Figure 5, in Figure 8 are presented the following plots (top to down): battery power, load power and DC voltage for different values of battery capacity and C DC capacitance mentioned in the last four plots.
The battery power compensates the power flow balance (1) without FC system (p FCnet = 0), which can be written as below: Therefore, neglecting the power exchanged by the C DC capacitor, (22) can be written as Equation (23): This will cause a lot of battery charging and discharging cycles for variable solar irradiation and load demand, which may reduce battery life. In addition, to maintain DC voltage variation in a range of less than 10%, the battery capacity must be greater than 100 Ah. The high frequency noise of the DC voltage is reduced below 1% if the value of the filter capacitor (C DC ) is higher than 1 F.
The behavior of the PV/FC/ESS system (under variable solar irradiance profile with very high slopes and variable load demand with the profile shown in Figure 8) will be analyzed in next section using a filtering capacitor of 1 F and a UC stack of 5 F, but with a battery capacity of only 10 Ah.

Results for PV/FC/ESS System
Seven scenarios (SC 1-7) have been defined and summarized in Table 2 to highlight the behavior and performance of PV/FC/ESS system.

Scenario 1 (SC1)
The first scenario (SC1) consider the solar irradiance and load demand profiles shown in Figures 5 and 8. The total fuel consumption (Fuel T estimated with Equation (24) during the 2.4 s load cycle LDP1 and measured in liters [L]) is 0.54372 L, 0.52908 L and 0.5114 L for strategies S0, S1 and S2, respectively.
Note that the fuel flow rate (FuelFr) is measured in liters per minute (Lpm). Therefore, for a cycle different to 60 s, it is necessary to use a gain (Gain Fuel ) that is of 1/25 (=2.4 s/60 s) in case studies considered in this paper (see Figures 2 and 3).
For example, it is worth mentioning that the fuel economy for strategy S2 compared to strategy S1 is of 0.01768 L, which means 0.442 Lpm. All data from the scenarios SC 1-7 will be summarized and commented in the discussion section.

Scenario 2 (SC2)
The second scenario (SC2) takes into account the solar irradiance and load demand profiles shown in Figures 7 and 8. The behavior of the PV/FC/ESS system using strategies S0 and S2 is presented in Figures 9 and 10. The plots in Figures 9 and 10 (and those that will be presented in the scenarios below) shown (from top to bottom): load demand profile, harvested PV power, FC net power, ESS power, oxygen excess ratio (OER) estimated using Equation (25), total fuel consumption, fuel consumption efficiency (Fuel eff ∼ = P FCnet /FuelFr) and FC electrical efficiency (η sys =P FCnet/ P FC ).
However, it can be mentioned that the FC system operates safely (OER > 2) and the batteries in charge-sustained mode (except for the time interval when PPV > PLoad, when the batteries are charged). If the system also includes an electrolyzer, then it can take up the excess energy (PPV-PLoad) to produce hydrogen, and the batteries would be operated all the time in charge-sustained mode, as shown in scenario SC7 (where PPV < PLoad).
The PV power profile has higher slopes for SIP2 SIP2 compared to SIP1 (see the 3rd plot in Figure 10 compared with the 3rd plots in Figure 8), which means a little less PV power harvested. It is observed that some differences appear in shapes of the variables plotted for strategies S0 and S2, but these differences are minor for strategies S1 and S2. Therefore, the behavior of the system using the S1 strategy was not represented.
However, it can be mentioned that the FC system operates safely (OER > 2) and the batteries in charge-sustained mode (except for the time interval when P PV > P Load , when the batteries are charged). If the system also includes an electrolyzer, then it can take up the excess energy (P PV -P Load ) to produce hydrogen, and the batteries would be operated all the time in charge-sustained mode, as shown in scenario SC7 (where P PV < P Load ).
The PV power profile has higher slopes for SIP2 SIP2 compared to SIP1 (see the 3rd plot in Figure 10 compared with the 3rd plots in Figure 8), which means a little less PV power harvested.
The total fuel consumption is 0.6648 L, 0.609 L and 0.593 L for strategies S0, S1 and S2. Therefore, the fuel economy for strategy S2 compared to strategy S1 is of 0. 016 L, which means 0.4 Lpm. The fuel economy for strategy S2 is slightly lower in scenario SC2 than that obtained in scenario SC1 due to the photovoltaic power harvested less in scenario SC2 which had to be offset by the FC system, resulting in additional fuel consumption.
This will be much more evident in the SC3 scenario, where the same load demand profile (LDP1) is kept, but solar irradiance is halved (0.5 × SIP2).

Scenario 3 (SC3)
The behavior of the PV/FC/ESS system using S2 strategy is presented in Figure 11. The total fuel consumption is 0.6648 L, 0.609 L and 0.593 L for strategies S0, S1 and S2. Therefore, the fuel economy for strategy S2 compared to strategy S1 is of 0. 016 L, which means 0.4 Lpm. The fuel economy for strategy S2 is slightly lower in scenario SC2 than that obtained in scenario SC1 due to the photovoltaic power harvested less in scenario SC2 which had to be offset by the FC system, resulting in additional fuel consumption.
This will be much more evident in the SC3 scenario, where the same load demand profile (LDP1) is kept, but solar irradiance is halved (0.5 × SIP2).

Scenario 3 (SC3)
The behavior of the PV/FC/ESS system using S2 strategy is presented in Figure 11. Figure 11. The behavior of the PV/FC/ESS system using strategy S2 in the scenario SC3. Figure 11. The behavior of the PV/FC/ESS system using strategy S2 in the scenario SC3.
The FC system will generate additional power in the time interval when P PV < P Load (between 4 and 6 s) and the batteries will operate in charge-sustaining mode, as shown in Figure 11.
The total fuel consumption is 0.74784 L, 0.696 L and 0.682 L for strategies S0, S1 and S2. Therefore, the fuel economy for strategy S2 compared to strategy S1 is of 0.014 L, which means 0.35 Lpm.
This fuel economy will be almost double and triple in next scenarios (SC4 and SC5), where the same solar irradiance is kept (0.5 · SIP2), but the load demand profile is increased (by multiplying with 1.5 and 2).
This fuel economy will almost double and triple in the next two scenarios (SC4 and SC5), where the same solar irradiation is kept (0.5 · SIP2), but the load demand profile is increased by 150% in the Sc5 scenario, and doubled in the SC5 scenario (multiplying by 1.5 and 2 the LDP1 profile).

Scenario 4 (SC4)
The behavior of the PV/FC/ESS system using S2 strategy is presented in Figure 12 under scenario 4.  As the load demand profile is increased compared to scenario SC3, more FC power will be requested to compensate the power flow balance on the DC bus. Thus, the total fuel consumption will be 1.2624 L, 1.027 L and 1.001 L for strategies S0, S1 and S2. Therefore, the fuel economy for strategy S2 compared to strategy S1 is of 0.026 L, which means 0.65 Lpm. Compared to the fuel economy of 0.35 Lpm resulted in scenario SC3, fuel economy of 0.65 Lpm resulted in scenario SC3 increased about twice.
To test whether the fuel economy for the S2 strategy compared to that for the S1 strategy increases with FC power, double the load demand profile is used in the following scenario.

Scenario 5 (SC5)
The behavior of the PV/FC/ESS system using strategies S1 and S2 is shown in Figures 13 and 14 for scenario 5. As mentioned before, minor differences can be observed in the form of the representations in the graphs of Figures 13 and 14. However, the fuel economy obtained using the S2 strategy proposed in this paper is higher than that obtained using the S1 strategy. The total fuel consumption will be 1.46676 L, 1.249 L and 1.213 L for strategies S0, S1 and S2.
Electronics 2021, 10, 1721 18 of 28 Figure 13. The behavior of the PV/FC/ESS system using strategy S1 in the scenario SC5. Figure 13. The behavior of the PV/FC/ESS system using strategy S1 in the scenario SC5.

Scenario 6 (SC6)
The behavior of the PV/FC/ESS system using strategy S2 is shown in Figure 15 for scenario 6. As mentioned before, a load demand of 6 kW is higher than the PV power obtained at a solar irradiance of 0.5 • SIP2 (see plots 1 and 2 in Figure 15). Therefore, except for starting the FC system (see plot 3 in Figure 15) and sharp changes in the PV power or load demand, the battery operates in charge-sustained mode (see plot 4 in Figure 15). Therefore, the fuel economy for strategy S2 compared to strategy S1 is of 0.036 L, which means 0.9 Lpm. Compared to the fuel economy of 0.35 Lpm resulting in scenario SC3, the fuel economy of 0.9 Lpm resulting in scenario SC5 increased about three times.
It turns out that a linear dependency relationship is obtained between fuel economy and FC power. This aspect will be analyzed in future papers, where a linear dependency relationship between fuel economy and FC power will researched for PF control-based strategies.
It can be noticed that the PF control ensures the operation of the batteries in chargesustained mode (see the fourth plot in Figures 12-14). In order to fully highlight that the PF control ensures the operation of the batteries in charge-sustained mode, a load demand of 6 kW is considered in scenario 7, which is higher than the PV power obtained at a solar irradiance of 0.5 · SIP2.

Scenario 6 (SC6)
The behavior of the PV/FC/ESS system using strategy S2 is shown in Figure 15 for scenario 6. As mentioned before, a load demand of 6 kW is higher than the PV power obtained at a solar irradiance of 0.5 · SIP2 (see plots 1 and 2 in Figure 15). Therefore, except for starting the FC system (see plot 3 in Figure 15) and sharp changes in the PV power or load demand, the battery operates in charge-sustained mode (see plot 4 in Figure 15).
Electronics 2021, 10, 1721 20 of 28 Figure 15. The behavior of the PV/FC/ESS system using strategy S2 in the scenario SC6.
The FC system operates safely (with OER higher than 2) and efficiently (see plot 5, and plots 7 and 8 in Figure 15, respectively). The total fuel consumption (see plot 6 in Figure 15) will be 4.23 L, 4.093 L and 4.026 L for strategies S0, S1 and S2. Therefore, the fuel economy for strategy S2 compared to strategy S1 is of 0.067 L, which means 1.6750 Lpm.
The DC voltage variation will be analyzed for the designed values of the battery, UC and mentioned in Table 1 and other values mentioned in Figures 16 and 17 to highlight the voltage regulation performance for scenarios SC3 and SC7. The FC system operates safely (with OER higher than 2) and efficiently (see plot 5, and plots 7 and 8 in Figure 15, respectively). The total fuel consumption (see plot 6 in Figure 15) will be 4.23 L, 4.093 L and 4.026 L for strategies S0, S1 and S2. Therefore, the fuel economy for strategy S2 compared to strategy S1 is of 0.067 L, which means 1.6750 Lpm.
The DC voltage variation will be analyzed for the designed values of the battery, UC and C DC mentioned in Table 1 and other values mentioned in Figures 16 and 17 to highlight the voltage regulation performance for scenarios SC3 and SC7.

Voltage Variation
The DC voltage variation of the PV/FC/ESS system using strategy S2 is shown in Figure 16 for scenario 3. For the designed values of the battery, UC and C DC mentioned in Table 1, the DC voltage is very well regulated (see plot 3 in Figure 16) under sharp profiles of the solar irradiance and load demand (see plots 1 and 2 in Figure 16).
The filtering role of the capacitor C DC (reduction of high frequency noise due to the switching control that is added to the DC voltage) is shown in plot 4 in Figure 15.
The DC voltage variation of the PV/FC/ESS system using strategy S2 is shown in Figure 17 for scenario 7, in which the solar irradiance is for a sunny day (see diagram 1 in Figure 17) and the load demand requires a FC power close to the maximum value of 8.3 kW (see plot 3 in Figure 14).
It can also be seen that for the projected values of the battery, UC and C DC mentioned in Table 1, the DC voltage is still very well regulated, even for a battery capacity of 1 Ah. (see plots 3 and 4 in Figure 17).

Voltage Variation
The DC voltage variation of the PV/FC/ESS system using strategy S2 is shown in Figure 16 for scenario 3. For the designed values of the battery, UC and mentioned in Table 1, the DC voltage is very well regulated (see plot 3 in Figure 16) under sharp profiles of the solar irradiance and load demand (see plots 1 and 2 in Figure 16).
The filtering role of the capacitor (reduction of high frequency noise due to the switching control that is added to the DC voltage) is shown in plot 4 in Figure 15.
The DC voltage variation of the PV/FC/ESS system using strategy S2 is shown in Figure 17 for scenario 7, in which the solar irradiance is for a sunny day (see diagram 1 in Figure 17) and the load demand requires a FC power close to the maximum value of 8.3 kW (see plot 3 in Figure 14).
It can also be seen that for the projected values of the battery, UC and mentioned in Table 1, the DC voltage is still very well regulated, even for a battery capacity of 1 Ah. (see plots 3 and 4 in Figure 17).
The overvoltage observed on the DC voltage (see plot 4 in Figure 17) is due to the fact that PPV > PLoad and the battery will be operated in charging mode. Note that this study did not include an electrolyzer as DC load controlled by excess energy on the DC bus. The control of the electrolyzer based on the excess energy on the DC bus must be maintained to avoid the frequent connection of the electrolyzer to the DC bus and this will be tested in next work for different scenarios.
The results obtained in different scenarios for total fuel consumption are centralized and processed in the next section to analyze the fuel economy obtained using strategy S2 compared to strategies S0 and S1. The overvoltage observed on the DC voltage (see plot 4 in Figure 17) is due to the fact that P PV > P Load and the battery will be operated in charging mode. Note that this study did not include an electrolyzer as DC load controlled by excess energy on the DC bus. The control of the electrolyzer based on the excess energy on the DC bus must be maintained to avoid the frequent connection of the electrolyzer to the DC bus and this will be tested in next work for different scenarios.
The results obtained in different scenarios for total fuel consumption are centralized and processed in the next section to analyze the fuel economy obtained using strategy S2 compared to strategies S0 and S1.

Discussion
The total fuel consumption during a 2.4 s cycle (Fuel T(liter) ) and 60 s cycle (Fuel T(l pm) ) was mentioned in the previous sections in different scenarios considered in this study and summarized in Tables 3 and 4.  Percentage decrease in fuel consumption (%Fuel (S0−S2)/S0 and %Fuel (S1−S2)/S1 ) has been estimated for strategy S2 compared to strategies S0 and S1 using (26) and (27) and the values from Table 3 or Table 4, and registered in Table 5: %Fuel (S1−S2)/S1 = Fuel T(S1) − Fuel T(S2) Fuel T(S1) . It is worth mentioning that the percentage decrease in fuel consumption for the proposed S2 strategy depends on the level of FC power generated (which is set by the profiles of the solar irradiance and load demand, considering the power flow balance on the DC bus and the proposed PF control), being in range 4.82-20.71% and 1.64-3.34% compared to strategies S0 and S1, respectively.
Percentage decrease in fuel consumption %Fuel (S0−S1)/S0 has been estimated for strategy S1 compared to strategy S0 in [32] using (28) for a given profile of the renewable power (a different scenario compared to SC1-SC6): The reported result was 13.43%, so the values obtained for %Fuel (S0−S2)/S0 in the scenarios considered in this study are in the same range (see Table 5), validating the performance of the proposed S2 strategy compared to the S1 strategy.

Conclusions
The new fuel economy strategy (S2 strategy) is proposed in this paper based on PF control and a new technique for switching input references for fuel regulators. The S2 strategy uses the GES control of the DC-DC power converter that interfaces the FC system with the DC bus to maximize fuel economy. A new fuel optimization function based on fuel efficiency and FC electrical efficiency is proposed.
The fuel economy obtained with strategy S2 is compared with other two strategies based on the PF control: strategy S1 [32] and strategy S0 [34].
The main findings of this research study are as follows:

I
The advantage of using a FC system based on PF-control as a backup energy source in a PV/FC/ESS system is highlighted by the operation of the battery in charging mode, which leads to increased life by avoiding frequent charge-discharge cycles;

I
The performance of the S2 strategy compared to the S1 and S0 strategies is demonstrated by the fuel economy obtained in different operating scenarios of the PV/FC/ ESS system;

I
The percentage decrease in fuel consumption for the proposed S2 strategy depends on the level of FC power generated (which is set by the profiles of the solar irradiance and load demand, considering the power flow balance on the DC bus and the proposed PF control), being in range 4.82-20.71% and 1.64-3.34% compared to strategies S0 and S1, respectively, under the scenarios considered in this study; I All strategies based on the proposed PF control operate the battery stack in chargesustained mode with advantages related to its size and lifespan;

I
The new fuel optimization function and the new technique for switching input references for fuel regulators ensure better fuel economy for the S2 strategy compared to other strategies based on PF control.
The advantages of using a FC system as backup energy source for a PV/ESS system are obvious, being related to the battery's capacity (which is ten times lower for the PV/FC/ESS system compared to the PV/ESS system) and its lifespan, but the fuel economy reported in this research study must be validated on a laboratory prototype, using a control technique based on hardware-in-loop (HIL) in the first step, and then implementation and testing in real environmental conditions.
Limiting the application of PF-control-based strategies is mainly related to implementation costs (use of continuously controlled hydrogen flow valve to regulate FC power instead of an operation of FC system at constant power using a fixed flow valve). To overcome this problem, for example, the FC power range can be divided into eight zones. For the eight values of the FC power, the optimal fuel flows are generated using three fixed flow valves and three on-off switches for the hydrogen flow and the appropriate control of the air compressor. This may be the idea for the next paper.