Control Strategy of a Multi-Source System Based on Batteries, Wind Turbines, and Electrolyzers for Hydrogen Production

Abstract

Multi-source systems are gaining attention as an effective approach to seamlessly incorporate renewable energies within electrical networks. These systems offer greater flexibility and better energy management possibilities. The considered multi-source system is based on a 50 MW wind farm connected to battery energy storage and electrolyzers through modular multi-level DC/DC converters. Wind energy systems interface with the DC-bus via rectifier power electronics that regulate the DC-bus voltage and implement optimal power extraction algorithms for efficient wind turbine operation. However, integrating intermittent renewable energy sources with optimal microgrid management poses significant challenges. It is essential to mention that the studied multi-source system is connected to the DC loads (modular electrolyzers and local load). This work proposes a new regulation method designed specifically to improve the performance of the system. In this strategy, the excess wind farm energy is converted into hydrogen gas and may be stored in the batteries. On the other hand, when the wind speed is low or there is no excess of energy, electrolyzer operations are stopped. The battery energy management depends on the power balance between the DC load (modular electrolyzers and local load) requirements and the energy produced from the wind farm. This control should lead to eliminating the fluctuations in energy production and should have a high dynamic performance. This work presents a nonlinear control method using a backstepping concept to improve the performances of the system operations and to achieve the mentioned goals. To evaluate the developed control strategy, some simulations based on real meteorological wind speed data using Matlab are conducted. The simulation results show that the proposed backstepping control strategy is satisfactory. Indeed, by integrating this control strategy into the multi-source system, we offer a flexible solution for battery and electrolyzer applications, contributing to the transition to a cleaner, more resilient energy system. This methodology offers intelligent and efficient energy management.

1. Introduction

The continuously expanding global population, along with advancements in industry and technology, are the main causes of the increase in atmospheric pollutants, rising global temperatures, sea level rise, and other major environmental issues. It is estimated that electricity production, industrial companies, and transportation are responsible for 40%, 23%, and 23% of global carbon emissions, respectively, while the remaining 14% comes from various sources [1]. Electric energy is one of the most essential resources for modern society. Electric power generation system’s implements various actions to meet the needs of different end users [2]. Fossil fuels currently account for approximately 80% of the global energy supply, and global energy consumption is expected to grow at a rate of about 2.3% per year from 2015 to 2040 [3]. Although a large portion of the global energy demand is currently met by fossil fuels, the harmful impacts of burning these fuels are undeniable: greenhouse gases, acid rain, etc., which are devastating for the environment and humans [4]. With growing concerns about climate change, alternative sources of clean energy are urgently needed to meet the anticipated increase in global energy demand [5]. In recent years, research and development in the energy sector have increasingly focused on the integration of renewable energy sources (RES) due to the depletion of fossil fuel reserves, the rising levels of greenhouse gases, and escalating pollution. The detrimental effects of climate change have raised significant concerns among governments and the scientific community. This makes the incorporation of RES crucial not only in electricity generation but also in other sectors heavily reliant on fossil fuels as their primary energy source [6]. One of the most significant challenges in using renewable energy is the impact of natural events that fluctuate over time. These events, which cannot be predicted, create difficulties in meeting energy demands. The disruptions in energy production caused by these unpredictable occurrences can be addressed by storing energy when demand is high or when energy production is abundant [7].

Storage technologies can effectively address the issue of renewable energy production limitations [8]. There are various energy storage methods, such as mechanical energy storage, including water pumping and compressed air, as well as rotating flywheels; electrical energy storage, such as supercapacitors and superconducting materials; thermal energy storage, like phase change materials; and electrochemical storage, such as lead-acid and lithium-ion batteries. Each of these methods has its own advantages and disadvantages [9,10]. Batteries are highly suitable for short-term energy storage compared to mechanical and thermal energy storage due to their ability to support instantaneous load peaks, as well as fluctuations in wind energy. However, they are less suited for long-term storage applications because of their low energy density and issues related to self-discharge and energy loss [11]. Many studies and technical reports consider hydrogen to be a suitable energy storage system, with high energy density, which could be beneficial for maintaining a reliable supply in a renewable energy grid when combined with batteries [12]. Hydrogen, recognized as a zero-emission energy carrier, has an energy density several times higher than most traditional energy sources [13]. Its immense potential for application has sparked global interest in research. The predominant method of hydrogen production currently relies on coal or natural gas reforming, a process that emits a substantial amount of greenhouse gases (GHGs) and produces low-purity gray hydrogen [14]. In contrast, water electrolysis technology, using emission-free renewable energy sources, stands out for its ability to efficiently produce high-purity green hydrogen [15]. Although only 5% of hydrogen is currently produced through electrolysis, this figure is expected to reach 25% by 2050 [16]. Electrolysis is a process that uses electricity to decompose deionized water into hydrogen and oxygen. This chemical reaction is carried out using an electrolyzer (EL) [17]. Electrolyzers have proven their importance in the production of green hydrogen from environmentally friendly energy sources, which is considered one of the key fuels to meet future energy demands. Despite the various technologies developed and reported in the literature for electrolyzers (i.e., solid oxide electrolyzers, anion exchange membrane electrolyzers, alkaline electrolyzers, and proton exchange membrane (PEM) electrolyzers), only alkaline and PEM electrolyzers have reached commercial stages. Among these two technologies, PEM electrolyzers have demonstrated better responsiveness when coupled with renewable energies due to their operational flexibility [18,19]. As the demand for hydrogen increases, electrolyzers are becoming an increasingly interesting topic as an alternative hydrogen production system. Energy from renewable electricity can be converted into hydrogen through power converters connected to electrolyzers [20]. However, the renewable energy production system (REPS) has the potential for further development if we can produce hydrogen within the power fluctuations and surplus generation from the REPS, which cause power outages due to imbalances between supply and demand [21]. In grid-connected systems, it is crucial to mitigate power fluctuations from renewable energy sources to ensure consistent hydrogen production and maintain a high-capacity factor of the system operations. To achieve these goals simultaneously, several methods have been proposed [21,22]. To ensure the proper functioning of hybrid systems based on renewable energies, guarantee demand, and improve system performance, control is necessary [23].

Several control methods are used to maintain system stability. In [24], the paper proposes a new coordinated control method for the wind farm and the hydrogen production system (HPS). The proposed coordinated control method helps to reduce the power fluctuations from the wind farm and achieve a high-capacity factor in the HPS. The reference [25] proposes three resilient predictive control methods (ER-MPC) to control the PEM electrolyzer (PEMEL) in order to improve frequency regulation under severe denial-of-service attacks. In [26], a lithium battery-based energy storage system and a hydrogen energy storage system are integrated as a multi-energy storage system for a hybrid AC/DC microgrid. In this case, the operational cost of each energy storage system (ESS) and the slow power response caused by the addition of the hydrogen energy storage system (HESS) must be taken into account when designing a control method. In the studied system, a self-regulating hierarchical control is proposed to improve the power response and achieve economic operation. Also, in [27], a new generic strategy for simultaneously compensating for rapid and slow power fluctuations based on ramp rate is proposed to smooth the output of PV solar panels and meet fast load demands using a multi-level hybrid storage system.

In this paper, an energy management strategy based on the backstepping method is proposed to ensure the load’s power supply without interruptions. In the literature, this method is classical based on cascaded control. In this work, the method is based on direct control of electrolyzers and battery currents to maintain the stability of the system. It relies on monitoring the load demand and then activating the appropriate energy source to meet it. Any excess energy generated is directed toward storage in the batteries or used to produce hydrogen. The advantages of backstepping controllers are linked to the use of DC converter dynamics models and Lyapunov functions to guarantee system stability and robustness, thus improving system performance. An example of the electrical configuration of an HES is shown in Figure 1. In this system, the load represents both the grid and modular electrolyzers. A wind farm is connected to the DC-bus via a controlled AC/DC converter to regulate the DC-bus voltage. The battery’s modules are connected to the DC-bus through the modular multi-level DC/DC converters for the transient power management between the sources and the loads.

This work is structured as follows: Section 2 presents the modeling of the multi-source system; Section 3 covers the study of the control strategy; Section 4 proposes the simulations and results with analysis; and conclusions are presented in Section 5.

2. Modeling of the Multi-Source System

2.1. Behavior Model of Electrolyzers

PEM electrolyzer cells offer several advantages; for instance, they can operate at high current densities (more than 2 A/cm²), have relatively low operational costs, and experience reduced ohmic losses compared to alkaline electrolyzers, thanks to the thinner electrolyte layer [28]. Additionally, PEM electrolyzers offer a fast response to proton transport through the membrane, making them well-suited for operation with a wide range of power inputs, especially since they are powered by the renewable energy sources that present sudden fluctuations. Lastly, PEM electrolyzers produce hydrogen at high pressure through electrochemical compression, which simplifies storage [29]. Figure 2 illustrates the basic operating principle of the PEM electrolyzers. The PEM electrolyzer cell consists of two half-cells separated by a thin membrane. The reactions in each half-cell at each electrode (anode and cathode), as well as the overall reaction, are described in [30].

The electrical response of an electrolyzer cell is generally characterized by a relatively fast response time (e.g., 50 ms for a PEM cell) compared to the overall system response time. Therefore, the static approach is commonly used to model the electrochemical response of an electrolyzer cell. In this approach, it is assumed that the electrical equilibrium of the cell is established instantly at each simulation time step. As a result, the cell can be modeled as a voltage source in series with a nonlinear resistive element. This involves the mathematical description of the current–voltage characteristics of the cell (and the stack), commonly referred to as polarization curves. These curves can be described using either analytical or empirical models [31,32].

The mathematical models used to describe the dynamic behavior of electrolyzer cells are based on physical laws and empirical equations and involve parameters with physical significance. Used equations in this model are designed to describe every parameter of the circuit, including the reversible potential V_rev, as well as the overvoltage resulting from the activation overvoltage η_act in the anode η_act,a and in the cathode η_act,c, the ohmic overvoltage η_ohm, and the diffusion overvoltage η_diff [33,34].

$$\left\{\begin{array}{c}{V}_{cell}=V_{rev}+{\eta }_{act}+{\eta }_{ohm}+{\eta }_{diff} \\ V_{rev}=1.229-0.9\ast {10}^{-3}\ast \left(T_{cell}-T_0\right)+{\displaystyle \frac{{R.T}_{cell}}{n.F}}\ast \ln \left({\displaystyle \frac{P_{H_2}{\left(P_{O2}\right)}^{0.5}}{P_{H_{2}0}}} \right) \\ {\eta }_{act}={\eta }_{act,a}+ {\eta }_{act,c} \\ {\eta }_{ohm }={\eta }_{ohm,mem}+{\eta }_{ohm, ele } \\ {\eta }_{diff}=-{\displaystyle \frac{R\ast T}{n\ast F{\ast \alpha }_a}}\ast \ln \left(1-{\displaystyle \frac{j_{cell}}{j_{lim}}}\right) \end{array}\right.$$

(1)

where F is the Faraday constant; R is the gas constant; T_cell is the cell temperature; P_H2O is the water vapor saturation pressure; P_O2 is the oxygen pressure; P_H2 is the hydrogen pressure; n is the number of moving electrons in the chemical reaction (n = 2); α_α is the charge transfer coefficient; and j_cell is the cell’s current density.

Figure 3 shows the electric equivalent circuit for the voltage of a PEM electrolyzer based on electrical behavior modeling. Therefore, this circuit is useful for constructing an actual equivalent circuit to emulate the voltage of a PEM electrolyzer [18].

2.2. Electric Behavior Model of the Batteries

Lithium-ion batteries are considered in this paper due to their efficiency and high energy density compared to NiMH, lead-acid, or NiCd batteries [35]. Various electric models which have been used to describe the electrochemical processes of the batteries are available in the literature [36]. The used lithium battery model is presented in Figure 4, and the mathematical model is presented in Equation (2). In this model, V_bat presents the battery module’s voltage, $E_{bat}$ is the open circuit voltage of the battery’s cell, R_Ω and R_C correspond to the series and polarization resistances, respectively, C_c presents the capacitance of the parallel circuit, and Ns and Np denote the number of cells in series and parallel, respectively [37].

$$\left\{\begin{array}{c}{V}_{bat} \approx N_S \ast E_{bat}- {\displaystyle \frac{N_S}{N_P}} \ast Z \ast I_{bat}\\ \tau = C_C \ast R_C\\ Z= R_{\Omega }+ {\displaystyle \frac{R_C}{1+ \tau \ast s}} \end{array}\right.$$

(2)

2.3. Configuration of Power Electronics Converters

Unfortunately, the electrical energy produced by renewable energy sources (RES) cannot be used directly for hydrogen production or battery energy storage because the voltage delivered by an RES system is not usually adapted to the input voltage requirement of electrolyzers/batteries. For this reason, power electronics converters are necessary to interface the sources and energy storage devices. In this paper, the electrolyzers and batteries are connected to DC-bus using modular multi-level DC/DC converters, as shown in Figure 5.

An important feature expected for the DC/DC converter connected to the PEM electrolyzer is a high step-down conversion ratio to handle the high voltage of the DC-bus. Medium-/high-voltage DC/DC converters are generally required in DC networks to interconnect two different DC voltage levels. Various converter topologies have been studied from existing research, which can be broadly categorized into combined topologies (composed of several converter modules) and multi-level modular topologies [38]. In this study, the modular multi-level converters are considered as shown in Figure 5. This configuration is adopted in order to reduce the voltage constraints on power transistors (IGBTs), so as not to exceed the maximum voltage that each IGBT can withstand. Modular multi-level buck converters are used on the electrolyzer side to optimize the hydrogen production. On the battery side, the modular multi-level buck–boost converters are considered to manage the power fluctuations and imbalance, which is necessary to obtain an optimal operation of the hydrogen production system. Detailed configuration of each modular DC/DC converter is presented in the next section.

3. Batteries–Wind Turbines–Electrolyzers System Control Strategy

Various control methods of the multi-source systems-based linear and nonlinear approaches are proposed in the literature [7]. The nonlinear control methods, such as Model Predictive Control (MPC), trajectory planning-based, or the backstepping method, offer fast, dynamic response and robustness. The nonlinear controls are adapted to multi-source system energy management, which necessitates an optimal operation in the complex dynamics interactions conditions [39]. This study proposes the backstepping control method based on modular multi-level DC/DC converters used for power management of the batteries and electrolyzers for hydrogen production. The backstepping control method is a recursive design procedure that links the choice of a control Lyapunov function with the design of a feedback controller, which guarantees global asymptotic stability of strict feedback systems [40]. A detailed description of the method is proposed in the next subsection.

3.1. Power Control in the Electrolyzer Side

Obtaining hydrogen by electrolysis is a gas energy storage technology (power-to-gas) that facilitates the large-scale integration of intermittent renewable energy sources into future energy systems. To ensure the good performance of the PEM electrolyzer under all operating conditions (power variations) and to guarantee the correct overall energy efficiency of the system, the electrolyzer’s power (current) is controlled. Figure 6 shows the configuration of the modular DC/DC converter, which links the electrolyzer to the DC-bus. It is in buck configuration because the rated voltage of the electrolyzer (4 kV) is lower than the DC-bus voltage (45 kV). The input voltage of each module is equal to V_bus/n, where n is the number of the DC/DC modules, as shown in Figure 5. Therefore, the input voltage of each module is lower than the DC-bus voltage and so the voltage across the power switches in the modular converter can remain in the rated voltage range. Consequently, a multi-level modular buck converter is obtained. In this configuration, S₁ and S₄ switches of all modules are working at the same time. When the power transistors are switched ON, all modules of electrolyzers will be in series, and they are submitted to the same current I_el, as shown in Figure 6. Based on Figure 5 and Figure 6, the modules of the buck converter are in series, and Equation (8) can be written for the multi-level modular buck converter.

$$\left\{\begin{array}{c}{\displaystyle \frac{d}{dt}}\left(I_{el}\right)= {\displaystyle \frac{V_{bus}}{L_{eq}}} \ast \alpha -{\displaystyle \frac{1}{L_{eq}}} \ast V_{eq}\\ V_{eq}= {\displaystyle \sum _{i=1}^n}{V}_{eli}\\ L_{eq}= {\displaystyle \sum _{i=1}^n}{L}_i\end{array}\right.$$

(3)

In this equation, the variables V_eli and I_el present, respectively, the voltage and current of the electrolyzer, L_i is the inductor of a modular converter, and α ∈ [0, 1] is the duty cycle of the modular buck converter. In this work, a backstepping-based approach is suggested to control the modular buck converter. The backstepping method is a recursive design methodology. It involves the systematic construction of both feedback control laws and the associated Lyapunov functions. The aim of this study is to use backstepping control to manage the current of modular electrolyzers. Figure 7 shows the flowchart of the control law. It starts with the determination of the current error, z_el, presented in Equation (4).

$$z_{el}= I_{el}- I_{el\_ref}$$

(4)

The Lyapunov function is defined by Equation (5).

$$U= {\displaystyle \frac{1}{2}} \ast z_{el}^2$$

(5)

To determine the control law, the derivative of Lyapunov function U should be developed, which gives the following:

$$\dot{U}=z_{el} \ast {\dot{z}}_{el}= \left(I_{el}- I_{el\_ref}\right)\left[\left({\displaystyle \frac{V_{bus}}{L_{eq}}} \ast \alpha -{\displaystyle \frac{1}{L_{eq}}} \ast V_{eq} \right)- {\dot{I}}_{el\_ref}\right]$$

(6)

It is necessary to obtain $\dot{U}=-k {\times z}_{el}^2<0$ for the system’s stability. This is why we obtain Equation (7), where k is the control parameter, which must be positive:

$$\left(I_{el}- I_{el\_ref}\right)\left[\left({\displaystyle \frac{V_{bus}}{L_{eq}}} \ast \alpha -{\displaystyle \frac{1}{L_{eq}}} \ast V_{eq} \right)- {\dot{I}}_{el\_ref}\right]=-k \ast z_{el}^2$$

(7)

$$\left({\displaystyle \frac{V_{bus}}{L_{eq}}} \ast \alpha -{\displaystyle \frac{1}{L_{eq}}} \ast V_{eq} \right)- {\dot{I}}_{e{l}_{ref}}=-k \ast z_{el}$$

(8)

From Equation (8), the control law is determined for the buck converter in the electrolyzer side:

$${\displaystyle \frac{V_{bus}}{L_{eq}}} \ast \alpha = {\displaystyle \frac{1}{L_{eq}}}{V}_{eq}+ {\dot{I}}_{e{l}_{ref}}-k \ast z_{el}$$

(9)

$$\alpha = {\displaystyle \frac{1}{V_{bus}}} \left[V_{eq}+L_{eq} \ast \left({\dot{I}}_{el\_ref}-k \ast z_{el}\right)\right]$$

(10)

where α is the control duty cycle that can be used for generating the switching signal for the buck converter power transistors.

The power control of the electrolyzer system is then controlled based on the current control loop, because the DC-bus voltage is kept constant around the desired value. The proposed control loop is illustrated in Figure 8. In this strategy, if the wind speed is lower than 3.5 m/s, the electrolyzer is stopped.

3.2. Battery Side Power Control

To develop the model of the bidirectional converter, the buck and boost operating modes need to be analyzed. Bidirectional DC-DC converters can be efficiently interfaced with energy sources such as batteries and supercapacitors (SC) to supply and store energy [37]. In this work, the batteries are connected to the DC-bus via bidirectional multi-level buck–boost converters. Figure 9 shows the configuration of one cell of the modular multi-level buck–boost converter used for battery power management. The voltages of the battery modules are lower than the DC-bus voltage. The input voltage of each module is equal to V_bus/n, where n is the number of the modular DC/DC converter, as seen in Figure 5. In Figure 9, V_bus/n presents the input voltage of the one cell of the modular converter; C₁ and C₂ are the DC-bus voltage smoothing capacitors; and L_bati presents the inductor in one module of the converter. To control the bidirectional modular multi-level buck–boost converter, the K₁ and K₄ are derived simultaneously to obtain the multi-level modular buck converter operation mode. To obtain the multi-level modular boost converter operation mode, K₂ and K₃ are derived simultaneously. The average model of the multi-level modular buck–boost converter is given by Equation (11), where β is the sign of the battery current and α is the duty cycle of the converter control signals. The considered converter operates as a boost converter from low voltage to high voltage and as a buck converter from high voltage to low voltage. Each operating mode consists of two active components and two passive components, with reduced electrical and thermal stress. The continuous conduction mode is considered in this paper.

$$\left\{\begin{array}{c}{V}_{Lbat}= L_{eqbat}{\displaystyle \frac{d}{dt}}\left(I_{bat}\right)=\beta \ast \left(V_{bat}- \alpha \ast V_{bus}\right) \\ L_{eqbat}= {\displaystyle \sum _{i=1}^n}{L}_{bati}\\ V_{bat}= {\displaystyle \sum _{i=1}^n}{V}_{bati}\end{array}\right.$$

(11)

To develop the model of the modular multi-level bidirectional buck–boost converter, the buck and boost operating modes need to be analyzed. In buck mode, the semiconductors S₁ and S₄ are working, while S₂ and S₃ are switched OFF. In contrast to this mode, S₂ and S₃ are switched ON, while S₁ and S₄ are switched OFF. For this study, I_bat is assumed negative during the batteries’ charge operations (buck mode), and it is positive during the batteries’ discharge (boost mode). In the average model of the converter, which is given in Equation (11), α takes the following values:

• For the boost converter, β = 1 and α = 1 − α₁, where α₁ is the boost converter duty cycle average value.
• For the buck converter, β = −1 and α = α₂, where α₂ is the buck converter duty cycle average value.

This system exhibits non-linear characteristics due to interactions among control variables and state variables (I_bat and V_bus). V_bat and I_bat can potentially interfere with the control, so they need to be monitored and incorporated into the control loop to maintain dynamic regulation [37].

$$L_{eqbat}{\displaystyle \frac{d}{dt}}\left(I_{bat}\right)=\beta \ast \left(V_{bat}-\alpha \ast V_{bus}\right)$$

(12)

The aim is to use the backstepping control to track the battery’s reference current. For this purpose, z_bat is defined as the error of the battery current presented in Equation (13).

$$z_{bat}= I_{bat}- I_{bat\_ref}$$

(13)

The Lyapunov function U can now be defined as presented in Equation (14).

$$U= {\displaystyle \frac{1}{2}} z_{bat}^2$$

(14)

To determine the control law, we calculate the derivation of this expression, which gives the following:

$$\dot{U}=z_{bat} \ast {\dot{z}}_{bat}= \left(I_{bat}- I_{ba{t}_{ref}}\right) \ast \left[{\displaystyle \frac{\beta }{L_{eqbat}}}\left(V_{bat}-\alpha \ast V_{bus}\right)-{\dot{I}}_{bat\_ref}\right]$$

(15)

It is necessary to obtain $\dot{U}=-k \ast z_{bat}^2 <0$. For this reason, the control parameter k should be positive. Substituting $\dot{U}$ in Equation (15) leads to the following:

$$\left(I_{bat}- I_{bat\_ref}\right)\left[{\displaystyle \frac{\beta }{L_{eqbat}}}\left(V_{bat}-\alpha \ast V_{bus}\right)- {\dot{I}}_{bat\_ref}\right]=-k{ \ast z}_{bat}^2$$

(16)

$${\displaystyle \frac{\beta }{L_{eqbat}}}\left(V_{bat}-\alpha { \ast V}_{bus}\right)- {\dot{I}}_{ba{t}_{ref}}=-k \ast { z}_{bat}$$

(17)

From Equation (17), the control law is determined as presented in Equation (18), where α is the appropriate control signal that can be used to control the bidirectional converter power transistors. The control law of the boost converter mode is obtained from Equation (19), considering β = 1 and α₁ = 1 − α, and that of the buck converter mode is obtained for β = −1 and α₂ = α, as presented in Equation (19).

$$\alpha = {\displaystyle \frac{1}{V_{bus}}} \left[V_{bat}- {\displaystyle \frac{L_{eqbat}}{\beta }}\left({\dot{I}}_{bat\_ref}-k \ast z_{bat}\right)\right]$$

(18)

$$\left\{\begin{array}{c}{\alpha }_1=1- {\displaystyle \frac{1}{V_{bus}}}\left[V_{bat}-L_{eqbat}\left({\dot{I}}_{ba{t}_{ref}}-k \ast z_{bat}\right)\right]\\ {\alpha }_2= {\displaystyle \frac{1}{V_{bus}}} \left[V_{bat}+L_{eqbat} \ast \left({\dot{I}}_{bat\_ref}-k \ast z_{bat}\right)\right]\end{array} \right.$$

(19)

Figure 10 shows the flowchart of the backstepping control of the battery power through the current management.

The battery’s power control is then controlled like to electrolyzer unit via the current control, as the DC-bus voltage is maintained constant around an average value through the wind farm. The proposed control loop is illustrated in Figure 11.

4. DC-Bus Voltage Management

DC-bus voltage regulation is based on the two cascaded regulation loops, where the inner loop concerns the PMSG current control and the outer loop is based on the DC-bus voltage regulation, as seen in Figure 12. As shown in Figure 12, I_qref is derived from the DC-bus voltage regulation loop, while I_dref is set to zero to ensure maximum torque extraction from the wind generators. A pair of PI-based current regulation loops is used to obtain dq voltage references with consideration of the decoupling terms. Using dq voltage references V_dref and V_qref, the three-phase voltage references V_abcref are computed through the dq to abc Park transformation. Comparing V_abcref with the triangle carrier waveform, the switching signals (Sa, Sb, Sc) for the three-phase rectifiers can be obtained.

5. Simulation Results and Discussions

5.1. Simulation Conditions

The system considered includes a wind farm which consists of 10 wind turbines with a rated power of 5 MW for each turbine, 5 modules of PEM electrolyzers with a rated power of 1 MW, 5 modules of batteries with a rated voltage of 4 kV, two modular multi-level DC/DC converters, and a load. The wind speed (Ws) profile is obtained from the real wind speed data measured in the city of Le Havre in France. The control of the wind farm is not detailed here, as this part has been developed in previous works [37,41]. On the wind farm side, the power converter, consisting of a three-phase rectifier, not only regulates the output voltage of the wind farm but also keeps the DC-bus voltage constant. In the energy management strategy, electrolyzer modules are considered as the load. The batteries are used to smooth the power fluctuations from the wind turbines.

5.2. Simulation and Analysis of Results

To evaluate the performance of the controls, the simulations are conducted in the Matlab/Simulink environment.

Table 1. System’s parameters.

Characteristics	Symbols	Values
DC-bus voltage	Vbus	40 kV
DC-bus capacitor	C	50 mF
Rated voltage of the battery modules	Vbati	4 kV
Wind farm rated power	PWT	50 MW
Maximum power of electrolyzers	Pel	5 MW

shows the system’s parameters. It is assumed that each wind turbine operates in the optimum operating zone, i.e., that it produces the maximum power according to the wind speed. The load power profile is shown in Figure 13, and that of the wind speed is presented in Figure 14, where the low limit of the wind speed is depicted on it. That helps the electrolyzer’s operation control remain in the optimal range with fewer power fluctuations. This low limit of the wind speed corresponding to the wind turbine start speed is around 3.5 m/s.

Although there is a disparity in the energy output from the wind turbines caused by the variations of the speed applied to each turbine, we focus on the total power contribution from the wind farm to the DC-bus. Figure 15 illustrates the total electrical power produced by the wind farm. The maximum power of the wind farm is about 50 MW.

The result of the voltage control in the coupling point is shown in Figure 16, where the reference voltage V_bus-ref is set to 40 kV at first and then to 45 kV to prove the performance of this method. Figure 16 illustrates how the DC-bus voltage closely follows the setpoint but exhibits some fluctuations due to the power transistors switching in AC/DC converters.

Figure 17 shows that for electrolyzer power management based on the backstepping control, the measured power is close to the reference ones. Two setpoints are given to the reference to evaluate the control strategy. These values are set by the method of regulation for optimizing the operation of the hydrogen generation process. The control strategy sets the electrolyzer power to zero when the wind speed is lower than or equal to 3.5 m/s, as shown in Figure 14.

Figure 18a shows hydrogen production according to the electric power requirement in the input of the electrolyzers. In our scenario, the electrolyzers stop when the wind speed is lower than or equal to 3.5 m/s. On the other hand, Figure 18b shows the amount of hydrogen that the system is capable of producing based on the power of the electrolyzer. This green hydrogen production reduces CO₂ gas emissions. According to the most recent data from the International Energy Agency (IEA), the production of hydrogen from natural gas by steam methane reforming (SMR), without the use of carbon capture and storage (CCS), generates direct emissions approaching 9 kg CO₂ per equivalent kilogram (eq/kg) of produced hydrogen. When a carbon capture and storage system is integrated, emissions linked to the chemical reaction can be considerably reduced, reaching around 0.7 kg CO₂-eq/kg H₂, i.e., a capture rate of around 93% [42].

The results of the battery module power regulation are presented in Figure 19, where the reference is determined by the difference between the power profile of the forecast wind generation and that demanded by the local load and the electrolyzer modules. We can see here that the control is well executed because the measured power follows the reference with a good concordance. In Figure 19, the negative power corresponds to the battery module charge operations, and the positive power corresponds to the battery module discharge operations.

6. Conclusions

In this article, an innovative power management approach using current-regulation loops for electrolyzers and battery modules is proposed using the backstepping method. Indeed, increasing the growing deployment of renewable energy technologies, such as wind turbines, into electric microgrids, including electrolyzer systems, requires robust control techniques to ensure optimized and dependable energy supervision for electrolyzers.

The implemented control strategy is focused on the backstepping technique, which enables the system to adapt dynamically to real-time operation conditions. Based on this method, the system can handle the non-linearities and uncertainties inherent in the renewable energy sources and the load’s demand, ensuring stable and efficient operation. The control strategy aims to maximize the use of renewable energies, minimize dependence on conventional energy sources, and improve the overall energy efficiency of the electrolyzers and battery modules.

The results of the simulations show the reliability of the proposed control strategy, which promotes significant improvements at several levels. Initially, the method-based backstepping control method, which is used to manage energy flows, optimizes electrolyzer efficiency. By integrating battery storage and other energy sources (electrolyzer and fuel cell set), the stability and performance of the microgrid can be considerably improved, even in the event of fluctuations in renewable energy production or variable load conditions. The proposed control strategy can maximize the use of renewable energies and reduce the power fluctuations stress for electrolyzers. This approach is still flexible and adaptable to more complex microgrids, enabling the incorporation of more modules for other energy sources or loads.