A Coordinated Control Strategy for Efficiency Improvement of Multistack Fuel Cell Systems in Electric–Hydrogen Hybrid Energy Storage System

Abstract

A two-layer coordinated control strategy is proposed to solve the power allocation problem faced by electric–hydrogen hybrid energy storage systems (HESSs) when compensating for the fluctuating power of the DC microgrid. The upper-layer control strategy is the system-level control. Considering the energy storage margin of each energy storage system, fuzzy logic control (FLC) is used to make the initial power allocation between the battery energy storage system (BESS) and the multistack fuel cell system (MFCS). The lower-layer control strategy is the device-level control. Considering the individual differences and energy-storage margin differences of the single-stack fuel cell (FC) in an MFCS, FLC is used to make the initial power allocation of the FC. To improve the hydrogen-to-electricity conversion efficiency of the MFCS, a strategy for optimization by perturbation (OP) is used to adjust the power allocation of the FC. The output difference of the MFCS before and after the adjustment is compensated for by the BESS. The simulation and experiment results show that the mentioned coordinated control strategy can enable the HESS to achieve adaptive power allocation based on the energy storage margin and obtain an improvement in the hydrogen-to-electricity conversion efficiency of the MFCS.

1. Introduction

A microgrid is a form of distributed energy supply that effectively integrates renewable energy, energy storage systems, and multiple loads and has greatly promoted the construction of new power systems [1,2]. Renewable energy, such as wind power and photovoltaic power generation, is easily affected by the environment, and its power generation is uncertain and uncontrollable. Therefore, the rational application of energy storage systems and their coordinated control strategy are of great significance for the efficiency and stability of microgrids. A hybrid energy storage system (HESS) composed of hydrogen fuel cells and batteries is a typical energy storage combination used to support the smooth operation of microgrids, which combines the advantages of hydrogen energy storage systems that have a large capacity and long discharge time and the advantages of a battery energy storage system (BESS) with flexible and fast power regulation [3,4]. In actual operation, the power throughput capacity of an HESS is closely related to the level of hydrogen (LoH) in the hydrogen storage tank and the state of charge (SoC) of the battery. In order to give full play to the power response capability of the HESS, it is also necessary to manage the energy of the electric–hydrogen coupled microgrid, coordinate the operation mode of the HESS equipment, and reasonably allocate its operating power. In addition, to solve the problems of low power level, insufficient durability, and limited large-scale application of the current single-stack fuel cell system (FC), an FC is often put into microgrids in the form of multistack array in engineering projects to enhance the overall operation stability and scalability of the hydrogen energy storage system. However, optimizing the power allocation of the FC so that the multistack fuel cell system (MFCS) can operate at the maximum efficiency point as much as possible is still a key problem that needs to be solved in electric–hydrogen coupled systems.

Multi-energy storage systems can achieve energy interconnection and complementarity and improve energy utilization efficiency and power supply stability. However, the increase in the types of energy storage devices also makes energy management and coordinated control more complicated. In terms of an HESS’s energy management, mainstream methods mainly focus on rule-based and optimization control strategies. Refs. [5,6] proposed a minimum hydrogen consumption energy management strategy based on fuzzy logic control (FLC) for HESS. This strategy dynamically adjusts the penalty factor according to the lithium battery SoC, changes the power distribution of the HESS, and, thus, reduces power fluctuations and hydrogen consumption of the fuel cell system. After comparing a large number of optimization algorithms, such as external energy maximization strategy (EEMS), cuckoo search (CS), and grey wolf optimizer (GWO), Ref. [7] selected the Harris Hawks optimizer (HHO) to manage the fuel cell/PV/battery/supercapacitor hybrid energy storage system. The HHO improves the system’s operational efficiency while reducing hydrogen consumption by reasonably allocating power among multiple devices.

Overall, rule-based control strategies can simplify the coordinated control of multisystems and have a high degree of adaptability to different operating conditions of microgrids, but their actual application effect depends on engineering experience. The ability of the optimal control strategy to conduct global multi-objective optimization of a system depends on the degree to which the meta-heuristic algorithm explores and utilizes the search space. The selection of an optimization control strategy that is compatible with the system, makes the search range as comprehensive as possible, avoids falling into local optimality, makes full use of the optimal solution that has been searched, distinguishes the effective search range, and accelerates convergence to improve the speed at which a solution is found is difficult to implement [8,9,10].

In the above research on HESSs, it is not difficult to find that most studies regard fuel cell systems as a whole research object. However, in actual application scenarios with fuel cell systems, such as transportation, aviation, and energy systems [11,12], the power level of the FC often makes it difficult to meet a scenario’s requirements, which further promotes scholars’ research on MFCSs. Ref. [13] analyzed the advantages and disadvantages of the four electrical architectures of MFCSs, namely, series, parallel, cascade, and series-parallel, in terms of voltage level, fault isolation, control form, and operating efficiency, providing a reference for other scholars in the selection of an appropriate MFCS architecture according to the research scenario. Refs. [14,15] studied the dynamic characteristics of an FC and found that the smaller the change in an FC’s output current and the lower the dynamic loading rate, the better the stack’s performance, life, and stability. For the device control of an FC, Ref. [16] proposed an adaptive current distribution method to mitigate the performance degradation of the FC and maintain the overall performance consistency of the MFCS.

It can be seen that reasonable energy management strategies should be formulated to avoid the degradation of the overall performance of the MFCS due to excessive use or loss of the FC. Ref. [17] pointed out that after long-term use the output capacity, efficiency, hydrogen consumption, and other performance indicators of fuel cells will decline. Therefore, an energy management strategy with an adaptive adjustment capability for fuel cell attenuation was proposed in this reference, so that the fuel cell has the lowest energy consumption and the best durability performance over its life cycle. Considering the impact of the environment on an MFCS, Ref. [18] proposed a coordinated optimization allocation strategy for an MFCS based on the concept of maximum efficiency range, which not only makes optimal power allocation for FC but also improves the hydrogen-to-electricity conversion efficiency of the MFCS. Ref. [19] proposed an optimal allocation strategy for the power demand of the MFCS, which reduced hydrogen consumption by optimizing the total output current of the MFCS. After comparing two classic power allocation methods for an MFCS, equidistribution (ED) and daisy chain, Ref. [20] proposed an optimization algorithm that makes the efficiency of the MFCS close to the best efficiency of the FC in a large power range.

It should be noted that although existing power allocation strategies for an MFCS have achieved improvements in efficiency or hydrogen consumption through simple start–stop control or optimized control, most of them assume that the FCs in MFCSs are similar during implementation and have almost no individual differences in performance, power level, etc. Therefore, it is still necessary to explore a control strategy based on the individual differences in FCs to optimize the overall performance of the MFCS. In fact, there is a certain correlation between the output power of the FC and the hydrogen-to-electricity conversion efficiency. Reasonable adjustment of the output power of the FC can allow it to operate at peak efficiency [21,22]. Refs. [23,24] considered the FC differences between stacks and used an optimization algorithm to optimize the power allocation of the FC, thereby achieving the goal of improving the operating efficiency of the MFCS. However, the operational process of an MFCS control strategy based on the optimization algorithm is relatively complicated, and the optimization effect is closely related to the selection of the algorithm; in addition, when microgrid operational objectives or operation modes change, such methods lack rapid adaptability and portability. The perturbation and observation method (P&O) is often used to track the maximum power point in photovoltaic power generation systems [25,26]. This method is simple and easy to implement, and the adjustment of operating constraints and the setting of initial disturbance values are relatively flexible. It can be adapted to various power allocation strategies and has certain portability and superposition of optimization effects. Therefore, it is also widely used in tracking extreme points in the nonlinear characteristic curves of other systems [27,28].

Combined with the above research, this paper took the electric–hydrogen coupled DC microgrid as the research background and proposed a two-layer coordinated control strategy for the HESS. Compared with existing studies, this paper makes improvements in the following aspects:

(1)

The upper-layer control strategy takes the overall LoH of the MFCS and the SoC of the battery as indicators and formulates a system-level fuzzy logic control (FLC) rule to complete the initial power allocation between the MFCS and BESS so that different energy storage systems can maintain an appropriate energy storage margin, as much as possible, when smoothing the power shortage of the microgrid.

(2)

The lower-layer control strategy considers the LoH of the FC to formulate a device-level FLC rule so as to achieve the initial division of the MFCS overall power into the inter-stack FC power and maintain the consistency of the FC energy storage margin during the discharge process.

(3)

A strategy for optimization by perturbation (OP) is proposed based on the power-efficiency characteristics of the FC. The initial power allocation of the FC is adjusted by OP to improve the hydrogen-to-electricity conversion efficiency of the MFCS. In addition, the adaptability of OP to different power allocation strategies is further studied.

This paper aims to realize adaptive power allocation from the system to the device in an HESS and from the array to single stack in an MFCS through a top-down energy management strategy so as to improve the energy autonomy, regulation flexibility, and operation stability of the DC microgrid. Finally, this paper will verify the feasibility and effectiveness of the proposed HESS-coordinated control strategy through simulation and experiments.

2. Electric–Hydrogen Coupled DC Microgrid Model

2.1. Electric–Hydrogen Coupled DC Microgrid Structure

The structure of the electric–hydrogen coupled DC microgrid studied in this paper is shown in Figure 1, which includes a photovoltaic system, electrolytic hydrogen production system, load, MFCS, and BESS. Each system is connected to the DC bus through a power electronic converter and is uniformly controlled by the energy management system (EMS). The HESS is composed of the MFCS and BESS. When the power supply of the DC microgrid is tight, energy storage systems cooperate to compensate for the power shortage and maintain the smooth operation of the microgrid. The MFCS is composed of multiple FCs. In order to play its role better in power regulation, the topology of the structure needs to be fully considered. Common MFCS topologies with converters include series, parallel, cascade, and series-parallel structures. The series structure is relatively simple and can reduce the number of converters used in the entire MFCS, but since it has no bypass circuit, a failure of one FC will paralyze the entire MFCS [29]. In the parallel structure [30] and cascade structure [31], the FC and converter are connected to the DC bus in a one-to-one manner, which can realize independent control of the FC. However, considering that the parallel structure has the advantages of a simple structure and low control difficulty compared with the cascade structure, this paper finally selected an MFCS with a three-stack parallel structure as the research object.

2.2. Modeling of the HESS

2.2.1. Mathematical Model of BESS

The main body of the BESS system is batteries; its model construction method is detailed in the literature [32]. The current conventional measurement methods for the SoC include the coulomb counting method and the voltage method. These methods are based on the measurements of battery voltage and current. There are also methods, such as electrochemical impedance spectroscopy and ultrasonic reflection wave joint estimation, that rely on instrument measurements. These methods can achieve nondestructive measurements of the battery system [33] but are highly sensitive to temperature. Considering that the Coulomb counting method is more convenient, and this article mainly controls the devices by adjusting the current or voltage, the Coulomb counting method shown in Equation (1) is finally selected to calculate the SoC.

$$SoC=So{C}_0-{\displaystyle \frac{1}{C{U}_{\mathrm{bat},t}}}{\displaystyle \int P_{\mathrm{bat},t}\mathrm{d}t}$$

(1)

where SoC₀ is the initial value of SoC; C is the rated capacity of battery; U_bat,t is the voltage of the battery at time t; and P_bat,t is the power of the battery at time t.

2.2.2. Mathematical Model of Fuel Cell System

A proton exchange membrane fuel cell (PEMFC) has the advantages of a high energy conversion efficiency, fast start–stop speed, and clean and low emissions. Therefore, the FC type selected in this paper was a PEMFC, and its mathematical model is shown in Equation (2) [34,35], as follows:

$$\left\{\begin{array}{l}{U}_{\mathrm{fc}}=n_{\mathrm{sfc}}\left(E_{\mathrm{rev}\_\mathrm{fc}}-U_{\mathrm{act}\_\mathrm{fc}}-U_{\mathrm{ohm}\_\mathrm{fc}}-U_{\mathrm{conc}\_\mathrm{fc}}\right)\\ E_{\mathrm{rev}\_\mathrm{fc}}=1.229-0.85\times {10}^{-3}\left(T_{\mathrm{fc}}-298.15\right)+4.3085\times {10}^{-5}{T}_{\mathrm{fc}}\left[\ln \left(p_{{\mathrm{H}}_2}\right)+{\displaystyle \frac{1}{2}}\ln \left(p_{{\mathrm{O}}_2}\right)\right]\\ U_{\mathrm{act}\_\mathrm{fc}}={\zeta }_1+{\zeta }_2{T}_{\mathrm{fc}}+{\zeta }_3{T}_{\mathrm{fc}}\ln \left(I_{\mathrm{fc}}\right)+{\zeta }_4{T}_{\mathrm{fc}}\ln \left(C_{{\mathrm{O}}_2}\right)\\ C_{{\mathrm{O}}_2}={\displaystyle \frac{p_{{\mathrm{O}}_2}}{5.08\times {10}^6\exp \left(\frac{-498}{T_{\mathrm{fc}}}\right)}}\\ U_{\mathrm{ohm}\_\mathrm{fc}}=I_{\mathrm{fc}}\left({\displaystyle \frac{{\rho }_{\mathrm{M}}l}{A}}+R_{\mathrm{c}}\right)\\ U_{\mathrm{conc}\_\mathrm{fc}}=-B\ln \left(1-{\displaystyle \frac{J}{J_{\max }}}\right)\end{array}\right.$$

(2)

where U_fc is the voltage of the FC; n_sfc is the number of fuel cell chips connected in series; E_{rev_fc} is the reversible voltage; U_{act_fc} is the activation overvoltage; U_{ohm_fc} is the ohmic overvoltage; U_{conc_fc} is the concentration difference overvoltage; T_fc is the Kelvin temperature of the FC; $p_{{\mathrm{H}}_2}$ is the anode hydrogen partial pressure; $p_{{\mathrm{O}}_2}$ is the cathode oxygen partial pressure; ζ₁, ζ₂, ζ₃, and ζ₄ are the empirical parameters; I_fc is the current of the FC; $C_{{\mathrm{O}}_2}$ is the oxygen solubility at the gas–liquid interface; ${\rho }_{\mathrm{M}}$ is the resistivity of the proton exchange membrane; l is the thickness of the proton exchange membrane; A is the effective activation area of the proton exchange membrane; R_c is the resistance that prevents protons from passing through the proton exchange membrane; B is a constant; J is the current density of the FC; and J_max is the maximum current density of the FC.

The calculation formula of the LoH of the i-th FC (FC_i) is shown in Equation (3) (i = 1, 2, 3).

$$Lo{H}_{\mathrm{fc}i}={\displaystyle \frac{p_{\mathrm{tank}i}}{p_{\mathrm{tank}\_\max i}}}\times 100\%$$

(3)

where LoH_fci is the LoH of the FC_i; $p_{\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{k}i}$ is the internal pressure of the hydrogen storage tank connected to the FC_i; $p_{\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{k}\_\mathrm{m}\mathrm{a}\mathrm{x}i}$ is the maximum internal pressure that the hydrogen storage tank connected to the FC_i can withstand.

The LoH of the MFCS is determined by the LoH of all FCs. Since the capacity, working pressure, and other parameters of the hydrogen storage tanks used in this paper are consistent, the LoH calculation formula of the MFCS can be inferred, as shown in Equation (4).

$$Lo{H}_{\mathrm{mfcs}}={\displaystyle \frac{Lo{H}_{\mathrm{fc}1}+Lo{H}_{\mathrm{fc}2}+Lo{H}_{\mathrm{fc}3}}{3}}$$

(4)

where LoH_mfcs is the LoH of the MFCS.

2.2.3. Model of Hydrogen-to-Electricity Conversion Efficiency for Fuel Cell Systems

The hydrogen-to-electricity conversion of the FC is completed by the fuel cell stack, auxiliary equipment, and other equipment, involving intermediate processes such as thermoelectric conversion, power conversion, and fuel utilization [36]. The calculation formula for the hydrogen-to-electricity conversion efficiency of the FC_i is shown in Equation (5).

$$\left\{\begin{array}{l}{\eta }_{\mathrm{fc}i}={\eta }_{\mathrm{stack}i}{\eta }_{\mathrm{e}i}{\eta }_{\mathrm{fuel}i}\\ {\eta }_{\mathrm{stack}i}={\displaystyle \frac{U_{\mathrm{sfc}i}}{\Delta H/(2F)}}\times 100\%\\ {\eta }_{\mathrm{e}i}={\displaystyle \frac{P_{\mathrm{out}i}-P_{\mathrm{aux}i}}{P_{\mathrm{out}i}}}\times 100\%\end{array}\right.$$

(5)

where η_fci is the hydrogen-to-electricity conversion efficiency of the FC_i; η_stacki is the thermoelectric conversion efficiency of the FC_i stack; η_ei is the power conversion efficiency of the FC_i; η_fueli is the hydrogen fuel utilization rate of the FC_i; U_sfci is the output voltage of the FC_i stack; ΔH is the calorific value of hydrogen; F is the Faraday constant; P_outi is the output power of the FC_i stack; and P_auxi is the electric power consumed by the FC_i auxiliary machine.

Combined with Equation (5), Figure 2 depicts the hydrogen-to-electricity conversion efficiency curves of the FCs of three power levels.

It can be seen from Figure 2 that the hydrogen-to-electricity conversion efficiency of the FC increased rapidly at first and then decreased slowly with the increase in the stack output power, with an efficiency peak. It can also be observed that because of individual differences in FCs, their hydrogen-to-electricity conversion efficiency curves are also different. In practical applications, factors such as power level, battery performance, and working conditions will affect the hydrogen-to-electricity conversion efficiency of the FC. It is difficult to optimize the efficiency of all FCs and MFCS simultaneously through a unified FC power allocation value. Therefore, in order to further study the output power distribution of the FC_i when MFCS operates at maximum efficiency, it is also necessary to define the hydrogen-to-electricity conversion efficiency of the MFCS as shown in Equation (6).

$${\eta }_{\mathrm{mfcs}}={\displaystyle \frac{P_{\mathrm{fc}1}+P_{\mathrm{fc}2}+P_{\mathrm{fc}3}}{\frac{P_{\mathrm{fc}1}}{{\eta }_{\mathrm{fc}1}}+\frac{P_{\mathrm{fc}2}}{{\eta }_{\mathrm{fc}2}}+\frac{P_{\mathrm{fc}3}}{{\eta }_{\mathrm{fc}3}}}}$$

(6)

where η_mfcs is the hydrogen-to-electricity conversion efficiency of the MFCS; P_fci is the output power of the FC_i; and η_fci is the hydrogen-to-electricity conversion efficiency of the FC_i.

3. Coordinated Control Strategy for Electric–Hydrogen Hybrid Energy Storage System

The voltage and power balance equations of the electric–hydrogen coupled DC microgrid are shown in Equation (7).

$$\left\{\begin{array}{l}{C}_{\mathrm{dc}}{\displaystyle \frac{\mathrm{d}{U}_{\mathrm{dc}}}{\mathrm{d}t}}=I_{\mathrm{pv}}+I_{\mathrm{mfcs}}\pm I_{\mathrm{bat}}-I_{\mathrm{load}}\\ {\displaystyle \frac{1}{2}}{C}_{\mathrm{dc}}{\displaystyle \frac{\mathrm{d}{U}_{\mathrm{dc}}^2}{\mathrm{d}t}}=P_{\mathrm{pv}}+P_{\mathrm{mfcs}}\pm P_{\mathrm{bat}}-P_{\mathrm{load}}\end{array}\right.$$

(7)

where C_dc is the bus capacitor; U_dc is the bus voltage; I_pv is the PV system current; I_mfcs is the MFCS current; I_bat is the BESS current; I_load is the load current; P_pv is the PV system power; P_mfcs is the MFCS power; P_bat is the BESS power; and P_load is the load power.

Equation (7) shows that the premise of microgrid bus voltage stability is the balance between the load and the total power of each micro-source, as shown in Equation (8). The key to microgrid energy management is to smooth the unbalanced power, P_net, of the microgrid through the HESS, that is, to reasonably allocate the power of the MFCS and BESS, as well as the power of the FC_i.

$$\left\{\begin{array}{l}{P}_{\mathrm{net}}=P_{\mathrm{load}}-P_{\mathrm{pv}}=P_{\mathrm{mfcs}}\pm P_{\mathrm{bat}}\\ P_{\mathrm{mfcs}}=P_{\mathrm{fc}1}+P_{\mathrm{fc}2}+P_{\mathrm{fc}3}\end{array}\right.$$

(8)

In order to maintain the stable operation of the microgrid through the coordinated control of the HESS, this paper proposes a two-layer control strategy for the HESS, as shown in Figure 3. The upper-layer control comprehensively considers the charge and discharge margin of the HESS and uses FLC to realize the initial power allocation of the MFCS and BESS. The lower-layer control combines the FC operational characteristics, takes the MFCS’s hydrogen-to-electricity conversion efficiency as the goal, further divides the power of the FC_i, and appropriately adjusts the final allocated power of the MFCS and BESS so that the overall output value of the HESS remains unchanged before and after the adjustment.

In addition, in order to make the control of the MFCS and BESS devices more accurate and stable, this paper adopted current loop control for the FC and voltage-current dual closed-loop control for the battery in the BESS [37]. In Figure 3, P_{fci_ref} is the output power reference value of the FC_i; U_fci is the output voltage of the FC_i; I_fci is the output current of the FC_i; I_{fci_ref} is the output current reference value of the FC_i; D_fci is the duty cycle signal acting on the DC/DC converter connected to the FC_i; P_{bat_ref} is the output power reference value of the battery; U_{dc_ref} is the bus voltage reference value, I_bat is the output current of the battery, I_{bat_ref} is the output current reference value of the battery; and D_bat is the duty cycle signal acting on the DC/DC converter connected to the battery.

3.1. Adaptive Power Allocation of the HESS Based on FLC

FLC is a control method based on customized rules. It has the advantages of strong robustness, high reliability, and fast response in the face of complex control systems [38]. Considering the time-varying and irregular combinations of parameters, such as P_net, LoH_mfcs, and SoC, during the microgrid’s operation, the use of FLC can quickly adapt to the multiple operating conditions of the microgrid and make precise adjustments to the control parameters.

The power adaptive allocation principle of the HESS is to allocate P_net to MFCS and BESS based on their actual charging and discharging margins during operation. Specifically, an initial power allocation factor, k, is introduced. The value of k is adjusted in real time according to the state of the LoH_mfcs and SoC in the current microgrid’s operation so that the energy storage system with a large energy storage margin is given priority to output. The LoH_mfcs and SoC are maintained in a reasonable output range before and after output so as to avoid excessive output of a single energy storage system affecting its safety or life [39].

According to the above rule-making principles, this paper formulates a fuzzy logic rule table with LoH_mfcs and SoC as dual input variables and the MFCS power allocation factor k as a single output variable, as shown in

Table 1. Fuzzy logic rules for power allocation of the HESS.

K		SoC
		VS	S	M	B	VB
LoHmfcs	VS	M	S	S	VS	VS
	S	B	M	S	S	S
	M	B	B	M	S	VS
	B	VB	B	M	M	M
	VB	VB	VB	B	M	M

, and sets the membership function, as shown in Figure 4.

According to the initial power allocation factor, k, solved by FLC, the initial power allocation of the MFCS and BESS can be further obtained, as shown in Equation (9).

$$\left\{\begin{array}{l}{P^{\prime }}_{\mathrm{mfcs}}=k\cdot P_{\mathrm{net}}\\ {P^{\prime }}_{\mathrm{bat}}=P_{\mathrm{net}}-{P^{\prime }}_{\mathrm{mfcs}}\end{array}\right.$$

(9)

where P′_mfcs is the initial power allocation of the MFCS, and P′_bat is the initial power allocation of BESS.

3.2. Optimization of the MFCS Efficiency Based on FC Power Perturbation

Using LoH_mfcs and SoC as the basis for power allocation can keep MFCS and BESS in a reasonable operating range, as much as possible, during operation and retain a certain energy storage margin. However, in actual operation, the energy storage system needs to be fully utilized to ensure the economy and efficiency of the microgrid. The hydrogen-to-electricity conversion efficiency of the FC is closely related to its operating power. Therefore, the problem of how to improve the efficiency of the MFCS by adjusting the power distribution of the FC_i has its research value. To achieve the above objectives, this paper proposes an MFCS efficiency optimization strategy based on FC power perturbation (OP for short), and the implementation steps are shown in Figure 5. The core steps of this strategy can be divided into the following two parts: calculation of the MFCS’s initial efficiency and optimization of the MFCS efficiency based on FC power perturbation.

3.2.1. Calculation of Initial Value of the MFCS Efficiency

The prerequisite for calculating the MFCS’s efficiency is clarifying the output power and corresponding efficiency of the FC_i. Similar to the power allocation principle of the MFCS and BESS, the power allocation of the FC_i is based on its energy storage margin. FLC will be used to allocate the power from MFCS to FC_i. Specifically, the single-stack power allocation factor k′_I is introduced, and the value of k′_I is adjusted according to the state of the LoH_i so that the FC_i with a large LoH_i is given priority to output more power.

The initial power allocation of the FC_i is shown in Equation (10). The corresponding three-input and three-output fuzzy logic rules table is shown in

Table 2. Fuzzy logic rules for power allocation of the PEMFC_i.

LoHfc1, LoHfc2, LoHfc3	kfc1, kfc2, kfc3	LoHfc1, LoHfc2, LoHfc3	kfc1, kfc2, kfc3	LoHfc1, LoHfc2, LoHfc3	kfc1, kfc2, kfc3
S, S, S	M, M, M	M, S, S	B, S, S	B, S, S	B, S, S
S, S, M	S, S, B	M, S, M	M, S, M	B, S, M	B, S, M
S, S, B	S, S, B	M, S, B	M, S, B	B, S, B	B, S, B
S, M, S	S, B, S	M, M, S	M, M, S	B, M, S	B, M, S
S, M, M	S, B, B	M, M, M	M, M, M	B, M, M	B, M, M
S, M, B	S, M, B	M, M, B	M, M, B	B, M, B	B, M, B
S, B, S	S, B, S	M, B, S	M, B, S	B, B, S	B, B, S
S, B, M	S, B, M	M, B, M	M, B, M	B, B, M	B, B. M
S, B, B	S, B, B	M, B, B	M, B, B	B, B, B	B, B, B

, and the membership functions are shown in Figure 6.

$${P^{\prime }}_{\mathrm{fc}i}={k^{\prime }}_i\cdot {P^{\prime }}_{\mathrm{mfcs}}$$

(10)

In order to avoid the collaborative control delay to the HESS caused by the slow real-time calculation speed of η_fci, this paper adopted the offline calculation method to collect the relevant operating parameters of the FC_i in advance, calculate the hydrogen-to-electricity conversion efficiency corresponding to different output powers of the FC_i, and store the results. Therefore, when the initial value of the MFCS efficiency, η_{mfcs_old}, under the initial power allocation of the FC_i is calculated by Equation (11), η′f_ci can be found by only mapping P′_fci in the offline database.

$${\eta }_{\mathrm{mfcs}\_\mathrm{old}}={\displaystyle \frac{{P^{\prime }}_{\mathrm{fc}1}+{P^{\prime }}_{\mathrm{fc}2}+{P^{\prime }}_{\mathrm{fc}3}}{\frac{{P^{\prime }}_{\mathrm{fc}1}}{{{\eta }^{\prime }}_{\mathrm{fc}1}}+\frac{{P^{\prime }}_{\mathrm{fc}2}}{{{\eta }^{\prime }}_{\mathrm{fc}2}}+\frac{{P^{\prime }}_{\mathrm{fc}3}}{{{\eta }^{\prime }}_{\mathrm{fc}3}}}}$$

(11)

3.2.2. Optimization Process of OP

It can be seen from Equations (6) and (11) that when the efficiency of the FC_i reaches the optimal value, η_{fci_max}, the efficiency of the MFCS is also optimized. Therefore, to improve the efficiency of the MFCS, FC_i takes the power value P_{ηi_max} corresponding to η_{fci_max} as the power reference point (η_{fci_max} and P_{ηi_max} can be obtained from the offline database) and the approximates P_{ηi_max} in a perturbation manner based on the current power allocation value P′_fci. The perturbation rule of the FC_i is shown in Equation (12).

$$\left\{\begin{array}{ll}①& {P^{\prime }}_{\mathrm{fc}i}>P_{\eta i\_\max }\\ & {P^{″}}_{\mathrm{fc}i}={\lambda }_1\cdot {P^{\prime }}_{\mathrm{fc}i}& \left(0.9<{\lambda }_1<1\right)\\ ②& {P^{\prime }}_{\mathrm{fc}i}<P_{\eta i\_\max }\\ & {P^{″}}_{\mathrm{fc}i}={\lambda }_2\cdot {P^{\prime }}_{\mathrm{fc}i}& \left(1<{\lambda }_2<1.1\right)\\ ③& {P^{\prime }}_{\mathrm{fc}i}=P_{\eta i\_\max }\\ & {P^{″}}_{\mathrm{fc}i}={\lambda }_3\cdot {P^{\prime }}_{\mathrm{fc}i}& \left({\lambda }_3=1\right)\end{array}\right.$$

(12)

where λ₁, λ₂, and λ₃ are the perturbation factors in three different situations, and P″_fci is the output update value of the FC_i after perturbation. The efficiency curve of the FC has the characteristic of increasing first and then decreasing. Therefore, when P′_fci is on the right side of P_{ηi_max}, P′_fci needs to be reduced to make η′f_ci approach η_{fci_max}, and λ₁ takes a random value in the interval (0.9, 1). Similarly, when P′_fci is on the left side of P_{ηi_max}, λ₂ takes a random value in the interval (1, 1.1); when P′_fci is exactly equal to P_{ηi_max}, λ₃ takes a value of 1, and no perturbation is required.

Furthermore, the output update value P″_mfcs of the MFCS after the perturbation can be calculated as shown in Equation (13).

$${P^{″}}_{\mathrm{mfcs}}={P^{″}}_{\mathrm{fc}1}+{P^{″}}_{\mathrm{fc}2}+{P^{″}}_{\mathrm{fc}3}$$

(13)

The efficiency update value, η_mfcs, of the MFCS after perturbation is shown in Equation (14).

$${\eta }_{\mathrm{mfcs}}={\displaystyle \frac{{P^{″}}_{\mathrm{fc}1}+{P^{″}}_{\mathrm{fc}2}+{P^{″}}_{\mathrm{fc}3}}{\frac{{P^{″}}_{\mathrm{fc}1}}{{{\eta }^{″}}_{\mathrm{fc}1}}+\frac{{P^{″}}_{\mathrm{fc}2}}{{{\eta }^{″}}_{\mathrm{fc}2}}+\frac{{P^{″}}_{\mathrm{fc}3}}{{{\eta }^{″}}_{\mathrm{fc}3}}}}$$

(14)

To avoid frequent fluctuations in the output power of the MFCS during OP, it is necessary to screen the advantages and disadvantages of the η_mfcs and P″_fci. The screening conditions are divided into two levels. The first level is the screening for the efficiency improvement in the MFCS, which requires an improvement in η_mfcs by more than 5%. The second level is the restriction on the output value of the FC_i and MFCS, as shown in Equation (15). The output value of the FC_i after the perturbation should not exceed its upper and lower limits and should consider the output capacity of the BESS so that after the complementary output of the MFCS and BESS, the requirements of P_net can still be met. Additionally, in order to smoothly adjust the MFCS output and avoid damage to the device caused by large fluctuations in the output value of the energy storage system, it is required that the change rate of the MFCS output value before and after the perturbation should not exceed 15%.

$$\left\{\begin{array}{l}{P}_{\mathrm{fc}i\_\min }\le {P^{″}}_{\mathrm{fc}i}\le P_{\mathrm{fc}i\_\max }\\ \left|{\displaystyle \frac{{P^{″}}_{\mathrm{mfcs}}-{P^{\prime }}_{\mathrm{mfcs}}}{{P^{\prime }}_{\mathrm{mfcs}}}}\right|\le 15\%\\ P_{\mathrm{net}}-P_{\mathrm{bat}\_\max }<{P^{″}}_{\mathrm{mfcs}}\le P_{\mathrm{mfcs}\_\max }\end{array}\right.$$

(15)

where P_{fci_min} and P_{fci_max} are the minimum and maximum outputs of the FC_i, respectively; P_{bat_max} is the maximum output of the battery in the BESS; and P_{mfcs_max} is the maximum output of the MFCS.

The P″_fci that satisfies the above two levels of screening can be used as the reference value of the new round of the FC_i power perturbation and participate in the further optimization of the MFCS’s efficiency until the optimization stop instruction is met (such as the sampling interval of EMS is reached). The currently found P″_fci and P″_mfcs that make the η_mfcs optimal are output as the reference values of the FC_i and MFCS, respectively.

4. Simulation Verification

In order to verify the application effect of the strategy proposed in this paper, a model of the HESS with the parameters shown in

Table 3. Parameter settings for the simulation.

Device	Variables	Value
FC1	nsfc1	300
	Pfc1_e	10 kW
	Ufc1	425 V
FC2	nsfc2	420
	Pfc2_e	12 kW
	Ufc2	515 V
FC3	nsfc3	500
	Pfc3_e	15 kW
	Ufc3	595 V
Tank	ptank_max	25 MPa
	Vtank	30 L
Battery	C	30 Ah
	Ubat_e	300 V
	Pbat_e	30 kW
DC Bus	Cdc	2000 μF
	Udc	480 V

was built with the MATLAB R2022a/Simulink platform.

4.1. Verification of the Power Adaptive Allocation

The initial power allocation of the P_net needs to take into account the LoH_i, LoH_mfcs, and SoC so that the output capacity of each energy storage device is compatible with its energy storage margin. Therefore, in order to verify the effectiveness and feasibility of the FLC-based power adaptive allocation strategy, this section sets up two scenarios for the microgrid’s operating environment, as shown in

Table 4. The runtime environment of the DC microgrid.

Time (s)	Ppv (kW)	Pload (kW)
0–1	3.1	10
1–2	4.6	15
2–3	6.2	25
3–4	3.1	25
4–5	7.8	25

. In Scenario 1, the initial values of the energy storage margin are different; in scenario 2, the initial values of the energy storage margin are basically the same.

4.1.1. Scenario 1

The initial values of the energy storage margin of the devices in Scenario 1 are different, so this paper set the values of the LoH_i, LoH_mfcs, and SoC as shown in

Table 5. Initial parameters of the devices in Scenario 1.

LoHfc1	LoHfc2	LoHfc3	LoHmfcs	SoC
0.75	0.5	0.25	0.5	0.7

. The corresponding simulation results of the power of photovoltaic, load, HESS, and the simulation result of bus voltage are shown in Figure 7a; the LoH_i simulation results of the FC_i are shown in Figure 7b.

As can be seen from Figure 7, the P_net compensation amount undertaken by the BESS is higher than that of the MFCS. For the single-stack power allocation of the MFCS, the FC_i output value was positively correlated with the LoH_i. At the same time, in the same period, the LoH_i drop in the FC_i with a higher LoH_i was greater, and the LoH_i drop in the FC_i with a lower LoH_i was lower, which also reflects that the discharge rate of the FC_i is related to the range of LoH_i.

It can also be found that although the PV and load conditions are constantly changing in the microgrid’s operating environment, the microgrid, as a whole, satisfies the supply–demand balance by coordinating the output of the HESS through the FLC strategy so that the DC bus voltage fluctuation is less than 1.5%.

4.1.2. Scenario 2

The initial values of the energy storage margin of the devices in Scenario 2 are basically the same. This paper set the values of the LoH_i, LoH_mfcs, and SoC as shown in

Table 6. Initial parameters of the devices in Scenario 2.

LoHfc1	LoHfc2	LoHfc3	LoHmfcs	SoC
0.45	0.5	0.55	0.5	0.3

. The corresponding simulation results of the power of the photovoltaic, load, HESS, and the simulation result of the bus voltage are shown in Figure 8a; the LoH_i simulation results of the FC_i are shown in Figure 8b.

It can be seen from Figure 8 that the MFCS bears most of the P_net compensation. For the single-stack power allocation of the MFCS, the LoH_i of the FC_i is in a reasonable range, so its output value varies slightly with the LoH_i, but the discharge rate can be approximately regarded as the same. In addition, the DC bus in Scenario 2 also remained stable, with only a slight fluctuation of less than 0.93% occurring when the microgrid’s operating conditions changed.

In summary, the FLC-based primary power allocation strategy enables the HESS to adaptively allocate power according to the energy storage margin of each device in a fluctuating microgrid environment, thereby maintaining the supply and demand balance of the microgrid.

4.2. Verification of OP

Figure 9 shows the operating efficiency of the MFCS with the different combined outputs of the three FC stacks (for ease of observation, P_fc3 = 8 kW, and only P_fc1 and P_fc2 are changed). As shown in Figure 9, when the P_fci of each fuel cell stack approaches P_{ηi_max}, η_mfcs can also achieve a larger value at the same time. Therefore, on the basis of realizing the initial power allocation, the energy storage system should further consider how to make full use of the MFCS by fine-tuning the power allocation of the FC_i. This section will verify the application effect of the OP in improving the efficiency of the MFCS.

4.2.1. Efficiency Optimization Based on FLC Power Allocation Strategy

Figure 10 compares the operation of the MFCS and FC_i before and after the FLC’s initial power allocation strategy superimposed with OP.

In Figure 10a, η_hist is the MFCS efficiency value corresponding to each perturbation result during the OP process. η_mfcs and η″_fci are the efficiency values of the MFCS and FC_i after using OP, respectively. η_mfcs-old and η′f_ci are the corresponding efficiency values when the MFCS and FC_i did not use OP for the initial power allocation given by FLC, respectively. Figure 10b shows the difference in output power before and after the MFCS used OP.

From the operational results of 0–5 s, it can be seen that η_mfcs was always the optimal value of η_hist under various operating conditions. Compared with η_mfcs-old, it can be seen that OP makes the MFCS achieve an efficiency improvement rate of 3.4–9.5%. Synchronously, the efficiency of the FC_i also improved to varying degrees, and the FC_i efficiency improvement rate can reach up to 8.6%. In addition, since OP limits the power fluctuation rate and amplitude of the MFCS, and the output difference of the MFCS can be compensated by the BESS, the power of the MFCS will not fluctuate significantly after using OP, and the bus voltage fluctuation rate did not exceed 0.57%.

4.2.2. Efficiency Optimization Based on ED Power Allocation Strategy

In order to explore whether the efficiency improvement effect presented by OP when acting on the FLC strategy is accidental, this section applied OP to the following classic power allocation strategy used by the MFCS: ED (as shown in Equation (16)). The corresponding simulation results are shown in Figure 11.

$${P^{\prime }}_{\mathrm{Fc}i}={\displaystyle \frac{{P^{\prime }}_{\mathrm{mfcs}}}{3}}$$

(16)

The interpretation of each parameter in Figure 11 is similar to that in Figure 10, except for the difference in the method used to solve the initial parameters. P′_fci in Figure 10 comes from the FLC power allocation strategy, and P′_Fci in Figure 11 comes from the ED power allocation strategy.

From the operational results of 0–5 s, it can be seen that η_Mfcs was always the optimal value of η_Hist under various operating conditions. Compared with η_Mfcs-old, it can also be seen that OP makes the MFCS achieve an efficiency improvement rate of 3.2–9.5%; synchronously, the efficiency improvement rate of the FC_i can reach up to 9.4%. In addition, the bus voltage fluctuation rate was less than 0.55% during the process of OP.

In summary, OP has a certain universality and can be adapted to various MFCS power allocation strategies. OP maintains the stability of the microgrid while improving the electricity–hydrogen conversion efficiency of the MFCS.

5. Experimental Verification

In order to test and verify whether the coordinated control strategy proposed in this paper is feasible in actual working conditions, this section creates a virtual real-time scenario to simulate the microgrid operating environment of the HESS. Considering that HESS-related equipment is expensive and potentially dangerous while in operation, this paper chose the hardware-in-loop (HIL) experimental form and designed a digital experimental platform, as shown in Figure 12, to facilitate the conduct of the experiment and the observation of the results.

The initial values of LoH_i, LoH_mfcs, and SoC in the HIL simulation are shown in

Table 7. Initial parameters of the devices in the HIL experiment.

LoHfc1	LoHfc2	LoHfc3	LoHmfcs	SoC
0.75	0.25	0.5	0.5	0.5

. In order to verify the application of the proposed strategy under variable working conditions, the photovoltaic power was increased from 0.8 kW to 8.5 kW under the premise that the load in the microgrid was constant at 10 kW.

The application effect of the coordinated control strategy is shown in Figure 13. Except for a slight fluctuation in the bus voltage when the photovoltaic power suddenly increased, it stabilized at the rated value of 480 V at other times. During operation, the output power of the FC_i was positively correlated with the LoH_i, and when P_net decreased from 9.2 kW to 2 kW, the power borne by FC_i also decreased synchronously, and the overall output of the MFCS decreased from 5.2 kW to 0.83 kW. The experiment’s results show that the proposed collaborative control strategy could adaptively compensate for the fluctuating P_net based on the margin of the energy storage device so that the bus voltage fluctuation rate was lower than 2.1% and maintained at a stable value.

6. Conclusions

This paper takes the HESS, composed of the MFCS and BESS in a DC microgrid, as the research object and proposes a coordinated control strategy for the efficiency improvement if the MFCS. After simulation and experimental verification of the proposed strategy, the following conclusions were obtained:

(1)

The proposed upper system-level coordinated control strategy can realize the adaptive power allocation of the HESS using FLC according to the energy storage margin of the MFCS and BESS so that the energy storage system with a high energy storage margin can bear most of the fluctuating net power of the microgrid.

(2)

The proposed lower device-level coordinated control strategy can further divide the overall power of the MFCS into single stacks according to the energy storage margin of the FC_i using FLC so that the power borne by the FC_i is positively correlated with LoH_i. The high, medium, and low ranges of the LoH_i also correspond to the faster, moderate, and slower discharge rates of the FC_i.

(3)

The proposed OP takes the power-efficiency characteristic of the FC as the starting point. After comprehensively considering the efficiency improvement in the MFCS, the output fluctuation rate of the MFCS, and the upper and lower limits of the energy storage system output, the power allocation of the FC_i is adjusted in a perturbation manner based on the initial power allocation so that the efficiency improvement rate of the MFCS can reach up to 9.5%, and the efficiency improvement rate of the FC_i can reach up to 8.6%.

(4)

When sudden changes occur in the power of the photovoltaic or load power, the proposed coordinated control strategy can adaptively allocate and adjust the output power of the MFCS, BESS, and FC_i so that the bus voltage can return to the steady-state value after experiencing a slight instantaneous fluctuation, with a fluctuation rate of less than 2.1%.