For more than a century, conventional marine vessels spatter the atmosphere with CO_{2} emissions and detrimental particles when operated by diesel motors/generators. Fuel cells have recently emerged as one of the most promising emission-free technologies for the electrification of ship propulsion systems. In fuel cell-based ship electrification, the entire marine power system is viewed as a direct current (DC) microgrid (MG) with constant power loads (CPLs). A challenge of such settings is how to stabilize the voltages and currents of the ship’s grid. In this paper, we propose a new modified backstepping controller to stabilize the MG voltage and currents. Finally, to study the performance and efficiency of our proposal, we run an experiment simulation using dSPACE real-time emulator.
Energy Technology Development and Demonstration Program (EUDP)64018-07211. Introduction
Nowadays, air emissions (e.g., carbon dioxide (CO_{2}) and sulfur dioxide gases) are changing habitats all over the world. Big parts of these air emissions originate from burning distinct forms of fuel in cars, vessels, and aircraft. According to the International Maritime Organization (IMO), the massive marine transport system streaming through oceans and seas accounts for 2% of the global world CO_{2} emission. Nevertheless, vessels play a significant role in the international trading system, providing occupations and transportation as well as supporting offshore businesses like fishing [1–4].
Even though marine vessel emissions have not been considered in the Kyoto accord, stringent rules have been established by first world countries. For instance, the European Union (EU) has applied stringent rules to control and monitor the sulfur dioxide emission in exclusively sensitive sea zones, containing the Baltic Sea Zones and the Western European seas. In the mentioned zones, the fuel utilized in marine vessel systems should not contain sulfur over 0.1%. But, in most ship fuels, this value is more than 1%. Thus, the importance of developing substitutive renewable energy supplies has become a significant problem for the marine vessel propulsion [5, 6].
One of the most promising renewable energy source technologies, which can be utilized in marine power systems, is fuel cell (FC) systems [7]. FCs, dissimilar to energy storage devices, utilize an outside supply of the hydrogen and oxygen to generate power and work as long as the hydrogen gas and oxygen source are sustained [8, 9]. The main advantages of FCs, which cause them as the best possible alternative marine power source, are their great power production density, efficiency, reliability, and durability [1]. In general, a hydrogen fuel cell converts oxygen and hydrogen (or air) into the direct current power. In practice, fuel cells in most immobile and mobile vehicle applications are paired with other power electronic devices (such as DC/DC boost converters) to improve the performance and reliability of the whole system and also accurately regulate the output voltage of the FC [10]. There have been very few successful implementations of FCs for vehicles [7] and marine applications [9, 11, 12] in the past few years. Most of the existing results for the FCs use linearized representation and controllers [13]. To improve the performance, nonlinear control methods such as model predictive [14], intelligent-based PID [15], and sliding mode control [10, 16] are presented. However, in a marine power system with FC, power electronic devices and loads can be considered as a kind of mobile DC microgrid with constant power loads (CPLs). In other words, FC in the special DC maritime MG is considered as a distributed generation, and ship motors and loads can be considered as CPLs, whenever a load is regulated to keep constant output power. Now, by considering this particular case study, a robust and high-performance controller is required to stabilize the voltage and current of the marine power grid, which is not investigated in the abovementioned approaches.
Up to now, many different approaches are suggested to reduce the detrimental effects of CPLs in DC maritime MGs [17–25]. Passive damping and active damping are two elementary methods to solve this issue [17]. In passive damping resistors, by increasing damping resistors to the filters, the destructive effect of CPLs can be mitigated. In spite of the fact that this technique has some advantages (e.g., it is simple and effective), it generates a huge dissipation [10]. On the other hand, active damping applies a modified control loop, which operates a virtual resistor [18]. In general, in active damping methods, the power is actively injected into the grid to diminish the effects of CPLs [19]. Furthermore, the methods based on small-signal models for the active damping can only guarantee system stability close to the operating point. In [17, 26], the model predictive controller is proposed for controlling the switching function of a converter that it sources a constant power load. Nevertheless, according to its computational burden, the proposed control method is not useful for real-time high-order industrial applications [27]. In [28], by controlling the duty ratio, a new modified nonlinear controller based on the sliding mode technique is suggested to stabilize a buck converter that it sources a constant power load. The proposed method in [14] can easily stabilize the whole system under any operating range changes. Nonetheless, this approach needs to measure the current of the capacitor, which is very expensive and causes ripple filtering degradation and the output impedance increase [29]. However, in those approaches, it is assumed that the DC source is ideal and the source current is independent of its voltage. This assumption is not applicable to the marine systems fed by FCs.
To sum up, this work studies an adaptive tracking control for hydrogen fuel cell systems in maritime applications. The marine power system with fuel cell and power electronic devices can be regarded as a special mobile stand-alone DC microgrid with constant power loads. Therefore, we first investigate a dynamic model of a special DC MG with CPLs for the marine power system by considering fuel cell and ship motors. Next, we extract the mathematical model of the whole system to apply the proposed control technique. Then, we develop a backstepping nonlinear control approach to stabilize the voltage and current of the ship’s grid. From the control engineering viewpoint, the main difficulty in utilizing a backstepping controller for the fuel cell-based marine power systems is that the overall structure of the fuel cell does not belong to the strict-feedback form and the virtual control inputs are not affine. Therefore, in this paper, we propose a novel control method to achieve the tracking issue of the DC MG voltage and currents. The proposed control is inspired by conventional backstepping controller methods. Finally, we apply the dSPACE real-time emulator system to investigate the performance and effectiveness of our approach for marine applications.
2. Stand-Alone DC Marine Microgrid Dynamics
In general, a marine power system with a fuel cell (as a main source of the ship power), power electronic devices (as interfaces for renewable energy systems), and loads (like ship motors and navigation systems) can be considered as a special mobile islanded DC microgrid with constant power loads. Figure 1 presents the general concept of maritime DC MG with CPLs.
The overall scheme of the stand-alone DC zero-emission ferry ships.
In the maritime systems, for the case of a ship constant speed, the ship engine should generate a constant torque. Therefore, it should receive constant power. However, in practice, any voltage fluctuations may change the power of the ship engine. Here, in this paper, the concept of the CPL is utilized in which the ship engine consuming power is tightly regulated by a DC/DC converter, and the DC bus voltage variation will not affect the ship speed. Besides the ship engine, which is assumed to act as a CPL behavior, resistive loads of the ship are also connected by the DC bus. Consequently, the fuel cell generator must feed a CPL and resistive loads. It is proved that the nonlinear CPLs degrade the stability of the DC MG, and if the voltage and/or the current of the DC bus vary from the equilibrium operating point of the system, then the overall DC MG will be unstable, which leads to a sudden drop in the DC bus voltage and spoils the CPL behavior. On the other hand, the fuel cell is a slow-response generator and any small perturbation on the DC MG makes it unstable. This fact shows the necessity of the active control of the DC bus voltage and the fuel cell power, as well, to assure the closed-loop stability and performance. To theoretically assure the stability, it is necessary to derive the state-space representation of the maritime DC MG.
Now, we work on extracting the mathematical model of the islanded marine DC MG with CPLs extracted. Totally, in the special case study of this paper, the fuel cell is used as a main power source of the ship to reduce the cost of fossil fuels and air emissions. Moreover, the power electronic devices (e.g., DC/DC boost converter) are utilized to connect the fuel cell, ship engine, and load to the DC bus link. Figure 2 shows the circuit diagram of the stand-alone DC marine MG with the fuel cell and a CPL. In this work, the ship engine is considered as a constant power load to tightly regulate the speed of the marine vessel system via a DC/DC converter. The mathematical model of the case study based on Figure 2 can be written as follows [10, 30]:(1)dVCPLdt=1Cbihfc1−u1−PCPLVCPL−VCPLR,(2)dihfcdt=−nRohmLihfc−nLVat−VCPLL1−u1+nRgTst2LFarlnPH2+12lnPO2+n2LFarΔG1+Δs1Tst−Thfc,(3)dVatdt=ihfcCd−VatRatCd,(4)dPH2dt=−PH2τH2+qH2in−2kγihfcτH2kH2,(5)dPO2dt=−PO2τO2+qO2in−2kγihfcτO2kO2,(6)dqH2indt=u2−qH2inτqH2,(7)dqO2indt=u3−qO2inτqO2.
Circuit diagram of the marine DC MG with a fuel cell and a CPL.
As shown in Figure 2, a proton exchange membrane fuel cell has been applied in this study to transform the chemical energy liberated during the electrochemical reaction of hydrogen and oxygen to electrical energy [31].
The detailed definition and value of the system parameters can be found in [10]. Also, the nominal values of the parameters of the system are provided in Table 1. The control inputs u1, u2, and u3 are related to the DC/DC converter connected to the fuel cell and the injecting hydrogen and oxygen flows of the fuel cell. These control inputs will be designed by applying the backstepping control as explained in Section 3.
The parameters of the DC marine microgrid.
Parameter and definition
Nominal value
Far (Faraday constant)
96485.309C/mol
Tst (fuel cell operating temperature)
353 K
Thfc (fuel cell reference temperature)
298.15 K
Rg (universal gas constant)
8.3143J/mol.K
ΔG (Gibbs free energy)
237160.89J/mol
ΔS (standard molar entropy)
164.025J/mol.K
τH2 (hydrogen actuator flow rate valve time constant)
3.37 sec
τO2 (oxygen actuator flow rate valve time constant)
6.47 sec
Kγ (consumed hydrogen flow rate)
9.07×10−8mol/C
KH2 (hydrogen molar constant)
4.22×10−5Kmol.atm/sec
KO2 (oxygen molar constant)
2.11×10−5Kmol.atm/sec
n (number of fuel cells)
5
Cd (double-layered capacitor)
35×10−6 F
Rohm (variable internal resistor of the fuel cell)
1.5Ω
LDC (DC/DC converter inductor)
4×10−3 H
CDC (DC/DC converter inductor)
5×10−4 F
PCPL (CPL power)
400 W
R (ship resistive load)
80Ω
3. Modified Backstepping Controller
In this section, we present the procedure of designing the backstepping controller. Since the two desired references are introduced, the backstepping design procedure is split into two parts. The primary control objective is to manipulate the DC/DC boost converter that stabilizes the voltage of the DC bus VCPL toward its desired valueVref. The control signal is then used to generate pulse-width modulation (PWM) gate signals for the converter [32]. Moreover, the secondary goal is to manipulate the fuel cell generator to provide the power to the loads. Assuming that the DC/DC converter is ideal and does not consume power, therefore, the generated power should be equal to the demand power. Here, since only CPLs are considered, the total power demand will be the net sum of the instantaneous CPL power. Without loss of generality, consider one CPL with the power level PCPL and the one resistive load R. Thus, the current should track the reference [32] Iref=Ptotall/Vthfc, where Ptotall=Pcpl+VCPL2/R and Vthfc is the voltage of the fuel cell and input of the DC/DC converter, computed as follows [10]:(8)Vthfc=nVhfc,Vhfc=Ehfc−ihfcRohm−Vat,Ehfc=12FarΔG1+Δs1Tst−Thfc+RgTstlnPH2+12lnPO2.
For the dynamic (1), the goal of VCPL is tracking Vref. Defining the error e1=VCPL−Vref and variable change v1=1−u1 results in(9)e˙1=V˙CPL−V˙ref=−PCPLCbVCPL−VCPLCbR−V˙ref+ihfcCbv1.
Let us choose the control input v1 as(10)v1=Cbihfc−γ1e1+PCPLVCPLCb+VCPLCbR+V˙ref,the dynamic (9) will be then(11)e˙1=−γ1e.
In the next part, the goal is to design the control inputs u2 and u3 such that ihfc tracks the ireft. Let v3=lnPH2+1/2lnPO2 to be the virtual control input in (2), e2=ihfc−iref and e3=v3−v3d. Therefore,(12)e˙2=dihfcdt−i˙ref=nRgTst2LFare3+Γ1+nRgTst2LFarv3d−i˙ref.
Taking time derivative of the Lyapunov candidate V2=1/2e22 along with the (13) results in(14)V˙2=e2e˙2=−γ2e22+nRgTst2LFare2e3.
In the next stage, the dynamic of the error e3 is computed as(15)e˙3=v˙3−v˙3d=1PH2dPH2dt+12PO2dPO2dt−v˙3d=−1τH2+qH2in−2kγihfcτH2kH2PH2−12τO2+qO2in−2kγihfc2τO2kO2PO2−v˙3d=Γ2+qH2inτH2kH2PH2+qO2in2τO2kO2PO2,where Γ2=−1/τH2−1/2τO2−2kγihfc/τH2kH2PH2−kγihfc/τO2kO2−v˙3d. Now, we define e4=qH2in−x4d and e5=qO2in−x5d. Therefore,(16)e˙3=e4τH2kH2PH2+e52τO2kO2PO2+Γ2+x4dτH2kH2PH2+x5d2τO2kO2PO2.
Let us write(17)x4d=τH2kH2PH2−γ32e3−Γ22−nRgTst4LFare2,x5d=2τO2kO2PO2−γ32e3−Γ22−nRgTst4LFare2,
Therefore, (16) will be rewritten as follows:(18)e˙3=e4τH2kH2PH2+e52τO2kO2PO2−γ3e3−nRgTst2LFare2.
Taking time derivative of V3=V2+1/2e32 results in(19)V˙3=V˙2+e3e˙3=−γ2e22+nRgTst2LFare2e3+e3e4τH2kH2PH2+e52τO2kO2PO2−γ3e3−nRgTst2LFare2=−γ2e22−γ3e32+e3e4τH2kH2PH2+e3e52τO2kO2PO2.
In the final stage, we compute the dynamics e4and e5 as follows:(20)e˙4=qH2in˙−x˙4d=u2−qH2inτqH2−x˙4d,(21)e˙5=qO2in˙−x˙5d=u3−qO2inτqO2−x˙5d.
Let the control inputs be(22)u2=τqH2−γ4e4−e3τH2kH2PH2+qH2inτqH2+x˙4d,(23)u3=τqO2−γ5e5−e32τO2kO2PO2+qO2inτqO2+x˙5d.
Therefore, the dynamics (20) and (21) are simplified as follows:(24)e˙4=−e3τH2kH2PH2−γ4e4,e˙5=−e32τO2kO2PO2−γ5e5.
Taking time derivative of V4=V3+1/2e42+1/2e52 results in(25)V˙4=V˙3+e4e˙4+e5e˙5−γ2e22−γ3e32+e3e4τH2kH2PH2+e3e52τO2kO2PO2+e4−e3τH2kH2PH2−γ4e4+e5−e32τO2kO2PO2−γ5e5=−γ2e22−γ3e32−γ4e42−γ5e52.
Finally, by considering the Lyapunov candidate V=V4+V1, we obtain(26)V˙=−γ1e12−γ2e22−γ3e32−γ4e42−γ5e52.
Since the time derivative of the Lyapunov function is negative definite, the error is asymptotically stable and the states VCPL and ihfc track the desired references. The proof is complete.
Remark 1 (difficulties of the design of the proposed controller).
This work proposes a novel backstepping control law which is proposed for the marine power systems (1)–(7). These dynamics are not in the form of the conventional strict-feedback forms as the virtual inputs PH2 and PO2 are not affine in (2) and the overall dynamics comprise three control inputs. So, the conventional backstepping design procedure [32] is not applicable. However, in this paper, such difficulties are handled by (i) defining the tracking error e3 as a nonlinear function of the virtual inputs, (ii) splitting the overall design procedure into two parts, and (iii) introducing an additional time-varying reference for the current of the fuel cell based on the properties of the nonlinear DC MG. These are the main distinctive features of the proposed approach over the existing backstepping techniques. The overall schematic of the proposed backstepping controllers to the regulate DC MG is given in Figure 3. Also, the detailed algorithm of deriving the control inputs u1, u2, and u3 is given in Algorithm 1.
The overall schematic of the proposed control approach.
<bold>Algorithm 1: </bold>The algorithm of computing control inputs.
First control input (u1)
Get Vref.
Compute V˙ref and e1=VCPL−Vref.
Compute v1 by (10).
Apply the control input u1=1−v1.
Second and third control inputs (u2 and u3)
Get iref.
Compute I˙ref and e2=ihfc−iref.
Compute v3d=2LFar/nRgTst−γ2e2−Γ1+i˙ref.
Compute v˙3d and e3=v3−v3d.
Compute x4d and x5d by (17).
Compute x˙4d, x˙5d, e4=x4−x3d and e5=x5−x5d.
Apply the control inputs (22) and (23).
4. Model-in-the-Loop Results
In this section, to show the applicability and low computational time of the proposed nonlinear controller, we carry out a model-in-the-loop (MiL) real-time simulation [33]. For the MiL simulation as depicted in Figure 4, dSPACE 1202 board has been selected as the rapid prototyping solution. The solver is the Euler method, and the sampling frequency is 10 kHz. The MiL application of the suggested technique was done on a real-time simulator (RTS) wherein both the controller and grid system are embedded in a single RTS. The load-side converter tightly regulates the voltage of the ship engine. Therefore, the consuming power of the ship engine is constant and the overall converter and load act as a CPL. This control action is dependent on the proposed control actions u1, u2, and u3. However, the load-side converter regulation action and the proposed control laws are designed by the dSPACE simulator.
MiL real-time setup and configuration of the marine DC MG benchmark.
The MiL simulation is carried out for the system parameters given in Table 1 and the CPL voltage reference Vref=400 V. Note that, in practice, the parameters Rat, Cd, and Rohm are uncertain parameters, but in the controller law, their nominal values given in Table 1 are considered.
Moreover, the control design parameters of the proposed backstepping controller are set as γi=1 for i=1,2,…,5.
Furthermore, to show the performance improvement of the proposed approach, the sliding mode controller designed for the same case study in [10] is considered. In [10], in addition to the fuel cell, a supercapacitor is also connected to the DC bus through a buck/boost converter. Furthermore, only resistive loads are considered. However, to apply the sliding mode approach of [10] to the considered case study, the PWM input signal of the buck/boost converter is assumed to be zero and the dynamic of the DC bus voltage is updated to involve the CPL behavior. The parameters of the sliding mode controller and the way of its implementation are presented in [10].
Figures 5(a)–5(c) show the current, voltage, and generated power of the fuel cell, respectively, for both proposed approach and sliding mode controller [10].
The (a) current, (b) voltage, and (c) generated power of the fuel cell (the proposed approach by the red line and the sliding mode approach by the blue line).
As one can see in Figures 5(a)–5(c), the proposed approach leads to a more smooth current and voltage for the fuel cell and less power fluctuation than in [10]. The main source of these fluctuations is uncertainties in the fuel cell parameters. Since both the proposed sliding mode approaches use the nominal values and the considered fuel cell dynamics are severely nonlinear, power and voltage fluctuations are inevitable.
Figure 6 illustrates the voltage of the DC bus for both approaches. Figure 6 reveals reliable marine DC MG. The reason is that the voltage of the DC bus (i.e., the CPL voltage) is regulated to its desired reference better and more accurate than that of [10]. For instance, the DC bus voltage based on the proposed controller converges to its reference almost at t=2sec and the fluctuation amplitude is less than 2V. However, the sliding mode approach [10] leads to about 6V fluctuations in the DC bus voltage.
The voltage of the DC bus (the proposed approach by the red line and the sliding mode approach by the blue line).
However, from Figure 7, one concludes that there are still some oscillations in the DC but voltage, especially, when the power level of the CPL changes promptly at t=10sec. The reason is that the fuel cell generator is a slow-response unit and it takes time to precisely regulate its power. Since there are no other fast-response units such as a battery or a supercapacitor, the injecting power to the CPL and resistive load is not constant and equal to the demand power. So, the resistive load receives nonconstant power and its voltage is changed by time.
The power received to the resistive load is illustrated in Figure 7. As can be seen in Figures 5(c) and 7, the proposed approach provides a smoother power than the sliding mode approach [10]. Furthermore, the approach of [10] injects more extra power to the resistive load. The ideal value for the resistive load power is 2kW, for which the DC but voltage will kept at 400V. The higher injected power not only reduces the performance of the system but also results in more hydrogen and oxygen consumption. Therefore, the compressed tanks for the hydrogen and oxygen will be emptied faster than the proposed approach. However, note that the power surplus (undersupply) and the voltage oscillation can be compensated by connecting a battery or a supercapacitor to the DC bus. However, in this paper, such compensation is not considered and only the attempt was made to propose a novel nonlinear control approach to enhance the transient and steady-state regulation of the hydrogen fuel cell.
The injected power to the resistive load (the proposed approach by the red line and the sliding mode approach by the blue line).
Moreover, to show the steady-state performance of the proposed approach and the sliding mode control [10], Table 2 is provided. As can be seen in Table 2, the steady-state error of the proposed approach is more than 60% which is improved over the sliding mode approach [10].
Steady-state error of different approaches.
Proposed approach
Sliding mode approach [10]
Performance improvement (%)
VCPL
1.572
4.103
61.68
ihfc
3.637
47.323
92.31
Vhfc
0
3.191
100
Power
498.344
1578.723
68.43%
5. Conclusion
The goal of this research was to stabilize a special DC marine MG that has uncertain time-varying loads and drive the DC voltage of the bus to track the desired voltage. To this aim, an additional reference for the current of the hydrogen fuel cell is defined and the controller design procedure is carried out by considering two backstepping controllers operating in parallel. To implement the controllers, first, some nonlinear error dynamics are defined to facilitate stabilizing the non-strict-feedback model of the system. Then, the virtual control signals are obtained step by step, by constructing suitable control Lyapunov functions (CLF) and providing the stability conditions, until the desired control signal is obtained. To illustrate the effectiveness of the proposed controller, it is compared with the state-of-the-art method sliding mode controller. The real-time simulation results demonstrated the ability of the proposed controller in tracking the desired voltage of the bus for sudden and continuous changes of the load power.
Data Availability
The data used to support the findings of this study are available from the corresponding author upon request.
Conflicts of Interest
The authors declare that there are no conflicts of interest regarding the publication of this paper.
Acknowledgments
This work was supported by the Energy Technology Development and Demonstration Program (EUDP) under Grant (64018-0721), “HFC: Hydrogen Fuel Cell and Battery Hybrid Technology for Marine Applications”.
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