Feedforward Control Strategy of a DC-DC Converter for an Off-Grid Hydrogen Production System Based on a Linear Extended State Observer and Super-Twisting Sliding Mode Control

Abstract

With the large-scale integration of renewable energy into off-grid DC systems, the stability issues caused by their fluctuations have become increasingly prominent. The dual active bridge (DAB) converter, as a DC-DC converter suitable for high power and high voltage level off-grid DC systems, plays a crucial role in maintaining and regulating grid stability through its control methods. However, the existing control methods for DAB are inadequate: linear control fails to meet dynamic response requirements, while nonlinear control relies on detailed model structures and parameters, making the control design complex and less accurate. To address this issue, this paper proposes a feedforward control strategy for a DC-DC converter in an off-grid hydrogen production system based on a linear extended state observer (LESO) and super-twisting sliding mode control (STSMC). Firstly, a reduced-order simplified model of the DAB was constructed through the structure of DAB. Then, based on the reduced-order simplified model, a feedforward control based on LESO and STSMC was designed, and its stability was analyzed. Finally, a simulation comparison of PI, LESO + terminal sliding mode control (TSMC), and LESO + STSMC control methods was conducted in a DC off-grid hydrogen production system. The results verified the proposed control method’s enhancement of the DAB’s rapid dynamic response capability and the system’s transient stability.

1. Introduction

Under the current global goal of reducing carbon emissions, the proportion of traditional fossil energy usage is gradually decreasing, while the share of renewable energy sources such as wind and solar power in electricity generation is steadily increasing [1]. Facilitating the integration and consumption of high proportions of renewable energy into the grid has become an urgent task for countries worldwide in constructing new power systems. Compared to AC grid-connected power systems, off-grid DC systems only require voltage magnitude tracking control without the need to consider phase issues, offering higher controllability and being more suitable for the integration of distributed power sources and loads [2,3]. However, the significant disturbances caused by the integration of power sources and loads pose severe challenges to system stability [4,5,6]. As devices that facilitate energy flow in off-grid DC systems, DC-DC converters play a crucial role in regulating and maintaining transient stability through control adjustments. The isolated dual active bridge (DAB) converter, as a power electronic device suitable for high voltage levels and high power transmission requirements, has become increasingly prevalent in off-grid DC system applications due to its advantages of bidirectional energy transfer and electrical isolation [7]. This widespread application has been attributed to its capability to effectively support system stability and control, particularly in scenarios involving fluctuating power demands and variable generation conditions. As the scale of renewable energy development and utilization expands, the role of DAB converters in ensuring stable voltage levels at DC bus points has become increasingly critical.

In DC microgrids, the rapid dynamic response and disturbance rejection capability of the DAB converter are critical indicators of the energy transmission system’s performance. The design of the DAB converter controller is pivotal to the stability of the entire control system’s output voltage. Single-phase shift control enhances the control efficiency of the DAB converter by adjusting the phase shift of the system. Due to its simplicity and reliability, it is widely applied in the practical engineering control of DAB converters [8,9]. Typically, it is combined with PI control for output voltage regulation. However, conventional PI control generally suffers from large output voltage fluctuations, slow dynamic response, and significant overshoot, making precise control challenging. These shortcomings render it inadequate for meeting the rapid dynamic response requirements of the system in practical applications. Therefore, designing an appropriate controller is essential for improving the rapid dynamic response capability of the DAB converter and enhancing the transient stability of the system.

A load-feedforward control design for DAB converters with current-mode modulation is presented in the literature [10,11], which can enhance the dynamic response to fast load transients and current-reference step changes. In the literature [11], two feedforward formulas were constructed based on the DAB model structure and specific parameters, which can be selected according to the required feedforward accuracy. By using these formulas, the dependency of control modeling on the structure and parameters has been reduced to a certain extent. A simple virtual direct power control (VDPC) scheme, focusing on direct power control, is presented in the literature [12], which is easily implemented as constant frequency control for DAB DC-DC converters to improve the dynamic response. A dual-terminal voltage feedforward-based direct power control scheme (DVF-DPC) with single-phase-shift control is proposed for the DAB DC-DC converter in the literature [13]. Predictive current-mode control for a single-phase high-frequency transformer-isolated dual active bridge DC-DC converter is presented in the literature [14]. However, even though this technique provides flexible multi-objective control, its large signal stability remains in question. In the literature [15], a model predictive current control based on a novel geometric sequence control algorithm is proposed. This control method, through detailed control modeling of the DAB internal structure and principles, eliminates the potential temporary saturation issue of the transformer windings. A predictive control technique named moving discretized control set model predictive control has been introduced in literature [16,17,18,19,20]. However, even if this technique provides flexible multi-objective control, its large signal stability remains in question.

Although the aforementioned control strategies have demonstrated favorable response characteristics in the study of DAB, they fall short of meeting the bus voltage stability requirements when the DAB is used as the DC-DC converter in DC off-grid systems, especially under large disturbances in distributed power sources and loads. Furthermore, these strategies are highly dependent on precise mathematical models, making them inadequate for addressing “black box” issues in practical engineering. This limitation results in restricted applicability and poor portability of such control methods.

Sliding mode control (SMC) is a typical nonlinear control method that does not rely on precise mathematical models of the controlled system. It exhibits strong robustness against load fluctuations and parameter perturbations, making it particularly suitable for controlling nonlinear systems like DAB converters. In the literature [21], a novel control scheme for bidirectional isolated dual active bridge (DAB) DC-DC converters is proposed to regulate output voltage and current using sliding mode (SM) control. However, due to the discontinuous control signal, voltage oscillation issues arise with this control method. The literature [22,23,24] introduces supertwisting sliding mode control (ST-SMC) for the isolated bidirectional dual active bridge (DAB) DC-DC power converter, aimed at enhancing output voltage regulation.

Conventional sliding mode control fails to observe disturbances within and outside the DAB converter, leading to inadequate dynamic response characteristics in control. Therefore, this paper introduces an extended state observer (ESO) to observe system disturbances and further enhance dynamic response capabilities. Independent of the original system’s mathematical model, the ESO treats internal uncertainties and external disturbances collectively as “total disturbance” for observation, demonstrating robustness. It can be used independently to observe total system disturbances or combined with sliding mode control to enhance disturbance rejection and dynamic response characteristics. Literature [25] proposes an active disturbance rejection control (ADRC) scheme based on ESO and current stress optimization to improve the dynamic response of DAB converters. A sliding mode controller (SMC)-based decoupling control scheme, which integrates input matrix diagonalization and an extended state observer, is presented in literature [26]. Literature [27] proposes an MPC control method based on Luenberger observer. It is proved that the Luenberger observer has good adaptability to external disturbances and internal parameters when applied to cascaded, non-isolated DC-DC converters. However, it does not consider the further improvement of control strategy on this basis to increase the dynamic response capability of the DC-DC converter. Literature [28] proposes a simplified method based on digital logic, which can effectively compensate for the blind area in the H-bridge (HB) converter. The structure of a single-phase, three-level HB converter is described in this paper. Compared with the DAB converter, this structure has more switching devices and bridge structure, which can achieve faster target response speed and more stable response characteristics in control and optimization. But at the same time, because of its complex structure, the control design for it is more complicated and has greater difficulty in implementation. When the ESO and SMC control methods mentioned in this paper are applied to the converter, the controller design is complicated, and the parameters are increased because of the need to adapt to its higher order.

MATLAB is a high-level programming language that can perform numerical calculations, visualization, and programming. Data processing utilizes MATLAB software (R2021b) to analyze, solve, model, and apply data. It is applied in many aspects, such as signal processing and communication, image and image processing, control systems, testing and experimentation, computational finance, and computational biology [29]. Therefore, this paper adopts MATLAB Simulink as simulation verification software.

In summary, addressing the complexity of detailed control modeling for bidirectional active bridge (DAB) converters, this paper proposes a feedforward control strategy based on linear extended state observer (LESO) and super-twisting sliding mode control (STSMC). A direct current (DC) microgrid hydrogen production system using DAB as a DC/DC converter is constructed. Comparative analysis of the effects of PI control, LESO+TSMC control, and LESO + STSMC control verifies that the proposed control strategies not only enhance the rapid dynamic response capability of DAB converters to disturbances but also improve the system’s disturbance rejection and transient stability. The main contributions of this paper are as follows:

(1)

The feedforward control strategy based on linear extended state observer (LESO) and super-twisting sliding mode control (STSMC) for DAB converters is proposed in this paper.

(2)

The dynamic response characteristics and disturbance rejection of the direct current (DC) microgrid system utilizing DAB converters have been enhanced in this study.

(3)

The LESO + STSMC feedforward control strategy has been compared with traditional PI control and LESO+TSMC control, demonstrating the effectiveness of this control method in enhancing system transient stability.

The paper is structured as follows: In Section 2, the structure of the DC off-grid hydrogen production system and dual active bridge DAB converter are introduced. A reduced-order simplified model of DAB is developed accordingly. In Section 3, the design of the feedforward control strategy based on LESO + STSMC is completed by integrating the established reduced-order simplified model. In Section 4, a model for a DC microgrid hydrogen production system is constructed, where simulation-based comparisons are conducted among PI control, LESO + TSMC, and LESO + STSMC controls. In Section 5, conclusions are drawn based on the findings of this study.

2. Principles of the Dual Active Bridge (DAB) Converter and Construction of Simplified Models

In this section, the structure of the DC off-grid hydrogen production system and dual active bridge DAB converter are first analyzed, followed by simplified modeling of DAB.

2.1. DC Off-Grid Hydrogen System Structure

DC off-grid systems are often composed of loads, renewable energy sources, converters, and energy storage systems. They are not connected to the external grid, and the generated electricity is entirely self-consumed. In order to effectively isolate system faults, enhance the anti-interference capability of each unit in the DC off-grid hydrogen production system, and improve the overall power supply reliability, achieving stable transmission at high power levels, this paper employs active bridge DAB converters as the DC/DC converters for each unit in the system. The wind turbine unit converts AC output to DC via an AC/DC rectifier, integrating it into the DC bus through the DAB converter. Each unit integrates into the DC bus via DAB converters to mitigate the impact of disturbances on the system. Photovoltaic and wind turbine units employ maximum power point tracking (MPPT) control to achieve constant power output characteristics in short durations. In MPPT control, the photovoltaic system adopts the disturbance observation method and the fan adopts the optimal tip velocity ratio method. The electrolyzer unit maintains constant power operation by controlling the current at the outlet side of the electrolyzer. The bus voltage is controlled by the battery energy storage system (BESS) and its DAB converters.

2.2. Principles of the DAB Converter

The DAB converter is responsible for bidirectional energy flow, and its circuit structure is shown in Figure 1. The DAB converter consists of the front bridge H₁, the back bridge H₂, a transformer, leakage inductance, and input and output side capacitors. Here, U₁ represents the input voltage of the DAB converter; L denotes the leakage inductance of the transformer; C₁ and C₂ are the input and output capacitors, respectively; v_p is the primary side voltage of the front bridge H₁; v_s is the secondary side voltage of the back bridge H₂; i₂ represents the output current; U₂ denotes the output voltage; n:1 represents the turns ratio of the transformer coils, and i_L represents the leakage inductance current.

In the DAB converter, the drive PWM waveforms of the diagonal switches on the front bridge H₁ and the rear bridge H₂ are completely identical (such as switches S₁ and S₄). The drive PWM waveforms of the switches at the same positions on different arms of the front bridge H₁ and the rear bridge H₂ (such as switches S₁ and S₃) are complementary, with a phase-shifting time dT_s between the front bridge H₁ and the rear bridge H₂ PWM waves, where d is the phase-shifting ratio and T_s is half of the period of the PWM drive waveform. Under this PWM waveform drive, square wave voltages v_s and v_p with a duty cycle of 50% are generated on the primary side of the front bridge H₁ and the secondary side of the rear bridge H₂. There is also a phase-shift ratio d (or phase-shifting time dT_s) between the primary voltage v_s and the secondary voltage v_p. For different power transmission directions, the phase-shifting sequence between v_s and v_p. will be different.

2.3. Reduced-Order Model of the DAB Converter

Regarding the basic topology of the DAB converter, a reduced-order model is employed in this paper to establish a simplified model of the DAB converter. In comparison to traditional DC/DC converter modeling, DAB modeling poses greater challenges, as one of its state variables, the inductor current i_L, is purely alternating with an average value of zero. The inductor i_L current is neglected in the reduced-order model, and the characteristics of the current are described by the average values of input and output currents within one switching cycle (or half-cycle).

As depicted in Figure 2, the DAB is simplified into a first-order system, where $〈i_{b1}〉$ and $〈i_{b2}〉$ represent the average values of the input current and output current over a switching cycle. The output power P₀ of the DAB can be expressed as Equation (1).

$$P_o={\displaystyle \frac{n{u}_1{u}_{2}d(1-d)}{2f_{s}L}}$$

(1)

where n, v₁, v₂, and L are as shown in Figure 1, d is the duty cycle input into the DAB, and f_s is the switching frequency of the DAB. Meanwhile, the output power P₀ is represented by Equation (2) as follows:

$$P_o=u_2〈i_{b2}〉$$

(2)

Therefore, we can obtain the following equation $〈i_{b2}〉$ for Equation (3):

$$〈i_{b2}〉={\displaystyle \frac{n{u}_{1}d(1-d)}{2f_{s}L}}$$

(3)

$〈i_{b1}〉$ can similarly be formulated as Equation (4).

$$〈i_{b1}〉={\displaystyle \frac{n{u}_{2}d(1-d)}{2f_{s}L}}$$

(4)

Single phase shift (SPS) modulation is adopted in this paper as the control method for DAB converters. The expression for the duty cycle d under PI control is given by Equation (5).

$$d=k_{vp}({u_2}^{\ast }-u_2)+k_{vi}{\displaystyle \int ({u_2}^{\ast }-u_2)dt}$$

(5)

In the equation, k_vp represents the proportional parameter of PI control, k_vi represents the integral parameter of PI control, and u₂^* denotes the reference voltage u₂. In many single-phase control strategies for DAB converters, traditional PI control is commonly utilized. However, conventional PI control lacks the ability to achieve rapid dynamic response. External disturbances result in prolonged settling times for voltage stability, significant voltage fluctuations, and overshoot issues. To address these challenges, it is necessary to design control methods based on DAB principles that enhance dynamic response and transient stability within the system. The following sections will focus on feedforward control design using linear extended state observers and super-twisting sliding mode control.

3. Feedforward Control Based on Linear Extended State Observer and Super-Twisting Sliding Mode Control

3.1. Current Feedforward Control Based on PI Control

Compared with simple PI control, feedforward combined with PI control for the output current of DAB converters enhances rapid dynamic response by measuring and compensating for disturbances before they affect the output.

In output current feedforward control, the relationship between phase shift ratio d and output power P_o serves as a feedforward term to minimize the error between output voltage and desired voltage. According to Equation (1), the expected output power P_o^* can be expressed as Equation (6).

$${P_o}^{\ast }={\displaystyle \frac{n{u}_1{u}_2{d}^{\ast }(1-d^{\ast })}{2f_{s}L}}$$

(6)

By solving for the desired phase shift ratio d^*, Equation (7) can be obtained.

$$d^{\ast }=\left\{\begin{array}{c}{\displaystyle \frac{1}{2}}-\sqrt{{\displaystyle \frac{1}{4}}-{\displaystyle \frac{2f_{s}L{i}_2}{n{u}_1}}} i_2\ge 0\\ -{\displaystyle \frac{1}{2}}+\sqrt{{\displaystyle \frac{1}{4}}+{\displaystyle \frac{2f_{s}L{i}_2}{n{u}_1}}} i_2<0\end{array}\right.$$

(7)

The schematic diagram of the output current feedforward control is shown in Figure 3.

The control block diagram shown in Figure 3 is derived from the basic PI control and Equation (7) derived above.

In practical applications, the current feedforward control represented by Equation (7) exhibits excessive dependency on the detailed structure and parameters of the DAB converter, leading to a slow response to external disturbances. In the presence of parameter uncertainties, this control method is susceptible to control overshoot due to improper parameter settings, thereby reducing the dynamic response capability of the DAB converter to external disturbances. Therefore, this paper introduces an extended state observer and sliding mode control to replace Equation (7) as part of the PI feedforward control, enhancing both the speed and effectiveness of the control response.

3.2. Feedforward Control Strategy Based on LESO + STSMC

According to Equation (3), the dual active bridge (DAB) converter is simplified to a first-order system. The time-domain expression of the DAB converter can be written as Equation (8).

$$C_2{\displaystyle \frac{d{u}_2}{dt}}={\displaystyle \frac{n{u}_1(1-d)}{2fL}}d-{\displaystyle \frac{u_2}{R_2}}$$

(8)

When the LESO + STSMC control replaces Equation (7) as feedforward control, the expression for duty cycle d is shown in Equation (9).

$$d=k_{vp}({u_2}^{\ast }-u_2)+k_{vi}{\displaystyle \int ({u_2}^{\ast }-u_2)dt}+d^{\ast }$$

(9)

The first-order derivative of Equation (8) can be written as Equation (10).

$${\ddot{u}}_2={\displaystyle \frac{n{u}_1\dot{d}}{2fLC}}-{\displaystyle \frac{n{u}_1\dot{d}d}{fLC}}-{\displaystyle \frac{{\dot{u}}_2}{CR}}$$

(10)

The first-order derivative of Equation (9) can be written as Equation (11).

$$\dot{d}=-{\dot{u}}_2{k}_{vp}+k_{vi}\left({u_2}^{\ast }-u_2\right)+{\dot{d}}^{\ast }$$

(11)

The expanded form of Equation (10) can be obtained by bringing Equations (11) and (9) into Equation (10). It can be written in the following general form.

$$\dot{y}=-a_{1}y+w+bu$$

(12)

The control objective is to stabilize the output voltage u₂, where the control variable is the phase shift ratio d. Therefore, the controller’s output u represents the phase shift ratio d, y denotes the output voltage of the converter, w represents system disturbances, a₁ denotes internal parameters of the DAB converter, and b is the input control gain. Thus, Equation (12) can be represented as Equation (13).

$$\dot{y}=-a_{1}y+w+(b-b_{0}u)+b_{0}u=f+b_{0}u$$

(13)

Equation (13) incorporates both internal and external disturbances of the system. Moreover, due to the compensatory effect of total disturbances, the influence generated by the inductance is negligible.

By selecting state variables x₁ and x₂, where the set x = [x₁ x₂]^T encompasses the system’s state variables and total disturbances, the system’s state equation can be derived as shown in Equation (14).

$$\left\{\begin{array}{l}{\dot{x}}_2=f+b_{0}u\\ x_2={\dot{x}}_1\\ y=x_1\end{array}\right.$$

(14)

Finally, based on this, the LESO state equation of the system is established as shown in Equation (15).

$$\left\{\begin{array}{l}{\dot{z}}_1=z_2-l_1(z_1-y)\\ {\dot{z}}_2=z_3-l_2(z_1-y)+b_{0}u\\ {\dot{z}}_3=-l_3(z_1-y)\\ e=z_1-y\end{array}\right.$$

(15)

where z = [z₁ z₂ z₃]^T represents the state variables of the LESO; L = [l₁ l₂ l₃]^T denotes the gain matrix of the observer. By analyzing simulation results under different gains, appropriate parameters l₁, l₂, and l₃ are selected for the observer to effectively estimate all state variables present in the system, where z₁→x₁, z₂→x₂ and z₃→f.

According to Equation (3), the system’s relative order is determined to be 1, and control design is implemented using the super-twisting sliding mode algorithm.

The sliding surface is designed as shown in Equation (16).

$$s=C_1{e}_s+{\dot{e}}_s$$

(16)

In Equation (16), e_s = u₂ − u₂* = z₁ − y* is the deviation of the desired value of the output voltage from the reference value, y* = 1 kV. C₁ is the gain coefficient of the slip film surface. The ultimate control objective is to stabilize the output voltage of the DAB converter, ensuring the elimination of disturbances. When the sliding surface is reached, the output voltage stabilizes, achieving the control goal.

Taking the time derivative of the sliding surface yields Equation (17).

$$\dot{s}=C_1{z}_2+b_{0}u+z_3$$

(17)

Combining the super-twisting sliding mode controller with LESO, Equation (18) is obtained.

$$-H_1{\left|s\right|}^{1/2}sign(s)+v=C_1{z}_2+b_{0}u+z_3$$

(18)

The final derivation results in the expression of the control output of the super-twisting sliding mode controller as Equation (19).

$$u={\displaystyle \frac{1}{b_0}}\left(-z_3-C_1{z}_2-H_1{\left|s\right|}^{1/2}sign(s)-{\displaystyle {\int }_0^t{H}_{2}sign(s)}d\tau \right)$$

(19)

The control structure of LESO+STSMC is shown in Figure 4.

The control block diagram shown in Figure 4 is obtained from the above Equations (8)–(19).

The combination of linear extended state observer (LESO) and super-twisting sliding mode control (STSMC) forms the control structure shown in the above figure, enhancing the rapid dynamic response capability of the dual active bridge (DAB) converter. The feedforward control diagram based on LESO + STSMC is illustrated in Figure 5.

The control block diagram shown in Figure 5 is obtained by combining the two kinds of control in Figure 3 and Figure 4. This is carried out by replacing Equation (7) in Figure 3 with what is shown in Figure 4. This control structure with LESO + STSMC as feedforward control can improve the fast response ability of the DAB converter to external disturbances and improve the transient stability of the DC off-grid hydrogen production system of the system.

3.3. Stability Verification

In order to demonstrate the stability of the system, a Lyapunov function is constructed for stability analysis, with its mathematical form as follows:

$$V={\displaystyle \frac{1}{2}}{s}^2$$

(20)

Taking the derivative of the above equation yields equation (21).

$$\dot{V}=s\cdot \dot{s}$$

(21)

According to the principle of super-twisting sliding mold design, Equation (21) can be obtained as Equation (22).

$$\dot{V}=s\cdot \left[-H_1{\left|s\right|}^{1/2}sign\left(s\right)-{\displaystyle {\int }_0^t{H}_{2}sign\left(s\right)\mathrm{d}\tau }\right]$$

(22)

The variable p is defined to obtain Equation (23).

$$\dot{p}=-H_{2}sign(s)$$

(23)

Thus, Equation (22) can be transformed into Equation (24).

$$\dot{V}=s\cdot \left(-H_1{\left|s\right|}^{1/2}sign\left(s\right)+p\right)$$

(24)

According to the structure of the super-twisting sliding mode controller [30], it can be determined that Equation (24) complies with this design principle. By selecting appropriate parameters H₁ and H₂, the super-twisting sliding mode surface and its first derivative can be ensured to be zero within a finite time. Therefore, the designed control approach is stable.

The control effectiveness of the feedforward control based on LESO + STSMC will be verified in a DC off-grid system.

4. Simulation Verification

To validate the enhancement of transient stability in the DC off-grid hydrogen production system under disturbance conditions through LESO + STSMC feedforward control, a DC off-grid hydrogen production system was constructed as shown in Figure 6. When the system operates in an off-grid state, due to the absence of support from a large power grid, voltage fluctuations on the DC bus can easily occur if energy instability or variations in distributed power sources result in a mismatch with load demand. In a DC microgrid, the DC bus voltage is the sole indicator for measuring power balance and power quality of the DC grid. Therefore, different control strategies were implemented to regulate the bus voltage, and the effectiveness of the control was evaluated based on the voltage fluctuation of the bus.

In the MATLAB/Simulink environment, a transient electromagnetic simulation model of the DC off-grid hydrogen production system, as shown in Figure 6, is constructed. System parameters are set as shown in

Table 1. Parameter Settings for DC Off-Grid Hydrogen Production System.

Parameters	Data
DC-side capacitance C1/F	0.1
Frequency f/Hz	1000
Transformer turns ratio n	1340:1000
Transformer leakage inductance L/H	0.00143
BESS operating voltage ux/V	750
Control parameters kvp	0.12
Control parameters kip	2
Photovoltaic power Pg/kW	80
Wind turbine power Pf/kW	290
Electrolyzer power Pd/kW	400
Load power PCL/kW	30
Bus voltage udc/V	1000

. Because the bus voltage is directly controlled by the DAB converter connected to the BESS, the parameters in the table mainly include specific parameters of the DAB converter on the BESS and external characteristic parameters of other units. The parameters k_vp and k_ip in the table are control parameters for conventional PI control.

To demonstrate the adaptability of STSMC and its significant enhancement in disturbance rejection, LESO+TSMC and conventional PI control are set as control groups for comparative validation of control strategies. Parameters for LESO, TSMC, and STSMC are detailed in

Table 2. Control Parameters Configuration.

LESO		TSMC		STSMC
Parameters Variables	Control Parameters	Parameters Variables	Control Parameters	Parameters Variables	Control Parameters
b0	351.4	p	11	H1	2
l1	15,000	q	9	H2	5
l2	1000	α	0.2	C1	3
l3	1500	β	0.1
		C1	3

.

Considering that major disturbances in the system are mainly caused by photovoltaic (PV) arrays, wind turbines, and loads, this study conducts simulations for these three scenarios. The initial operating conditions are uniformly set as follows: the PV unit outputs 80 kW, the wind turbine unit outputs 290 kW, the electrolyzer unit inputs 400 kW, and the battery energy storage system (BESS) handles 30 kW. The bus voltage is maintained at 1000 V. At this point, the load power is 30 kW.

For the major disturbances, simulations are configured as follows: at 30 s into the simulation, the load P_cL undergoes step changes from 30 kW to 40 kW due to reduced sunlight intensity, decreased wind speed, and sudden addition of loads. Figure 7, Figure 8 and Figure 9 depict the bus voltage waveforms under these three control strategies after the occurrence of disturbances.

Table 3. Parameters of Bus Voltage Fluctuation Time and Amplitude.

Condition	Control	Voltage Fluctuation Parameter after Perturbation
		Time to Reach Stabilization (s)	Maximum Fluctuation Amplitude (%)
No Disturbance	PI	10.93	9.58
	LESO+TSMC	8.24	8.30
	LESO+STSMC	3.40	5.15
Light intensity reduction	PI	26.98	2.77
	LESO+TSMC	2.66	2.34
	LESO+STSMC	1.70	1.58
Wind speed decrease	PI	18.68	2.40
	LESO+TSMC	3.76	2.15
	LESO+STSMC	2.17	1.30
Sudden load merge	PI	29.06	4.32
	LESO+TSMC	5.30	3.59
	LESO+STSMC	1.35	2.37

provides a quantitative analysis of the bus voltage fluctuations during the startup phase and after disturbances in a DC off-grid hydrogen production system under various control methods and disturbance scenarios.

From Table 3 and Figure 7, Figure 8 and Figure 9, the following conclusions can be drawn: Prior to the occurrence of disturbances, the time required to reach stability is the longest under PI control; it is reduced by 0.32 times under LESO+TSMC compared to PI control; and it is the shortest under LESO+STSMC, being reduced by 2.2 times compared to PI control. In terms of voltage fluctuation amplitude during the stabilization process, PI control exhibits the largest fluctuations; LESO+TSMC reduces these fluctuations by 0.15 times compared to PI control; and LESO+STSMC results in the smallest fluctuations, reducing them by 0.85 times compared to PI control.

After the occurrence of disturbances, the time required to reach stability is the longest under PI control. Compared to PI control, LESO+TSMC reduces the stabilization time by 9.14 times under irradiance disturbances, by 3.97 times under wind speed disturbances, and by 4.48 times under load disturbances. LESO+STSMC, in comparison to PI control, reduces the stabilization time by 14.87 times under irradiance disturbances, by 7.61 times under wind speed disturbances, and by 20.53 times under load disturbances, with the shortest times observed under all three disturbance types. Regarding voltage fluctuation amplitude during the stabilization process, PI control exhibits the largest fluctuations. Compared to PI control, LESO+TSMC reduces the fluctuation amplitude by 0.18 times under irradiance disturbances, by 0.12 times under wind speed disturbances, and by 0.20 times under load disturbances. LESO+STSMC, compared to PI control, reduces the fluctuation amplitude by 0.75 times under irradiance disturbances, by 0.84 times under wind speed disturbances, and by 0.82 times under load disturbances, with the smallest fluctuations observed under all three disturbance types.

Figure 10, Figure 11 and Figure 12 illustrate the duty cycle d waveforms of the controller output to the DAB converter on the BESS side under different disturbances and control strategies.

From the figures, it can be observed that under both undisturbed conditions and after the occurrence of the three types of disturbances, the time required for the duty cycle d to reach stability is the shortest under LESO+STSMC feedforward control. The shorter the time required for the duty cycle d to reach stability, the smaller and shorter the voltage fluctuations, indicating better control performance. Therefore, it can be concluded that the control effect of LESO+TSMC feedforward control is inferior to that of LESO+STSMC control, while PI control exhibits the poorest control performance.

In summary, the proposed feedforward control based on LESO+STSMC effectively enhances the rapid dynamic response of the dual active bridge (DAB) converter and improves transient stability in DC off-grid systems. Simulation results also demonstrate that STSMC is more suitable than TSMC for the simplified model of DAB. Combined with LESO, it reduces both the fluctuation time and magnitude of bus voltage after disturbances, thereby enhancing disturbance rejection and dynamic response capabilities.

5. Conclusions

This study integrates the reduced-order simplified model of the dual active bridge (DAB) converter and proposes a feedforward control strategy based on LESO and STSMC for DC-DC converters in DC off-grid hydrogen systems. A DC off-grid hydrogen system with DAB as the DC/DC converter is established. Under various disturbances and control parameters, the effectiveness of the proposed control strategy in enhancing the rapid dynamic response and transient stability of the DAB converter is validated through comparisons with traditional PI control and LESO+TSMC control results.

The main findings and contributions of this study can be summarized as follows:

(1)

Simulation results demonstrate that the proposed feedforward control based on LESO+STSMC effectively regulates the DC voltage of the DC off-grid hydrogen system with DAB converters. Compared with the ordinary PI control, the perturbation time is reduced by 3–20 times, and the amplitude of the fluctuation is reduced by 1–2 times. This is evident in reduced fluctuations in DC bus voltage, improved dynamic response time, and quicker recovery after faults.

(2)

This control strategy achieves rapid dynamic response of the DAB converter to external disturbances and enhances transient stability of the DC off-grid hydrogen system. It enables the system’s DC voltage to stabilize quickly during faults, maintaining normal system performance metrics.

(3)

Implementing LESO+STSMC as the feedforward control reduces the dependency on detailed models and parameters of the DAB, making it more suitable for engineering applications where structural and parameter uncertainties exist. Simulation results also affirm that STSMC is more suitable than TSMC for the dual active bridge DAB converter. Compared with TSMC control, STSMC reduces the disturbance time by 2–4 times and the fluctuation amplitude by 1–2 times.

This research contributes to advancing control strategies for DC-DC converters in DC microgrids with renewable energy integration, emphasizing improved stability and dynamic performance. Future studies could explore further optimizations and practical implementations of these control strategies in real-world applications.