Study on the Dynamic Optimal Control Strategy of an Electric-Hydrogen Hybrid Energy Storage System for a Direct Drive Wave Power Generation System

Abstract

A direct drive wave power generation system (DDWPGS) has the advantages of a simple structure and easy deployment, and is the first choice to provide electricity for islands and operation platforms in the deep sea. However, due to the off-grid, the source and load cannot be matched, so accommodation is an important issue. Hydrogen storage is the optimal choice for offshore wave energy accommodation. Therefore, aiming at the source-load mismatch problem of the DDWPGS, an electric-hydrogen hybrid energy storage system (HESS) for the DDWPGS is designed in this paper. Based on the characteristics of the devices in the electric-hydrogen HESS, a new dynamic power allocation strategy and its control strategy are proposed. Firstly, empirical mode decomposition (EMD) is utilized to allocate the power fluctuations that need to be stabilized. Secondly, with the state of charge (SOC) of the battery and the operating characteristics of the alkaline electrolyzer being considered, the power assignments of the battery and the electrolyzer are determined using the rule-based method. In addition, model predictive control (MPC) with good tracking performance is used to adjust the output power of the battery and electrolyzer. Finally, the supercapacitor (SC) is controlled to maintain the DC bus voltage while also balancing the system’s power. A simulation was established to verify the feasibility of the designed system. The results show that the electric-hydrogen HESS can stabilize the power fluctuations dynamically when the DDWPGS captures instantaneous power. Moreover, its control strategy can not only reduce the start-stop times of the alkaline electrolyzer but also help the energy storage devices to maintain a good state and extend the service life.

1. Introduction

Wave energy has been identified as one of the most promising marine energy sources [1]. The direct drive wave power generation system (DDWPGS) has become one of the most feasible methods in the utilization of wave energy owing to its simplified system architecture, higher energy conversion efficiency, and lower maintenance costs [2]. However, the output power of the DDWPGS will fluctuate significantly as a result of changes in wave amplitude and frequency. Moreover, a DDWPGS works in the deep sea, and the controllable load on an island is limited, so the source-load mismatch will be caused. Consequently, a DDWPGS must be equipped with a high-capacity energy storage system (ESS) to accommodate power fluctuations [3].

An ESS can be categorized as electric energy storage (battery, SC, etc.), mechanical energy storage (flywheel, compressed air, etc.), and hydrogen energy storage (hydrogen fuel cell and electrolyzer) [4,5]. Electrical energy storage is inexpensive, and storage devices can be designed and manufactured in any size according to the availability of voltage and current. The main advantage of mechanical energy storage is that it can easily convert and deliver energy whenever it is needed [6]. As for hydrogen energy storage, electrolysis of water is presently the most practicable method for producing hydrogen on a modest scale [7]. Hydrogen energy storage has a high energy density, low energy storage costs, and is easy to store and transport. Furthermore, hydrogen energy does not need to be transmitted via submarine cables, which reduces energy losses and lowers costs. Hydrogen energy storage and wave power generation have natural adaptability. However, the above ESSs all have a few drawbacks. When using only electrical energy storage in the DDWPGS, under certain specific conditions, there will be a long-term build-up of energy in the battery, occupying the capacity of the battery, and affecting the state of the energy storage devices, leading to wave abandonment [8]. Mechanical energy storage has the problems of high costs and large maintenance [9]. As for hydrogen energy storage, its response time is slow, and using fluctuating electrical energy to produce hydrogen could cause security risks [10]. Additionally, the above energy storage devices can be divided into power-type and energy-type according to their functions; the former has large power density and fast response speed, but small energy density. SC and flywheel are common power-type devices. The latter has high energy density, but poor dynamic response ability. Representative devices include batteries, compressed air energy storage, and hydrogen energy storage. As a result, the energy storage device with a single form to store energy or a single function cannot satisfy the requirements of the system, thus, the HESS came into being.

On the basis of the aforementioned characteristics of the ESS used for wave power generation, evaluating the investment cost, maintenance, and adaptability to wave power generation, an electric-hydrogen HESS composed of a battery, SC, and alkaline electrolyzer is proposed in this paper, as shown in Figure 1. In this system, not only hydrogen storage and wave power generation are combined, but also the operation characteristics of the electrolyzer and the optimal management of energy storage are concerned. The battery and the SC complement each other and, respectively, undertake the electric energy of different energy densities and power densities. The hydrogen storage system is complementary to the battery, which provides stable and controllable power for hydrogen production to enhance safety. Hydrogen storage systems are conducive to maintain a good state of charge (SOC) of the battery and reduce wave abandonment by assisting in absorbing excess energy.

For an HESS, the key technology is a power allocation algorithm among different storage systems [11]. The battery and electrolyzer have a high energy density but a low dynamic response capacity, whereas the SC has a high power density, a rapid response speed, and a low energy density [12]. Therefore, the primary challenge of designing an electric-hydrogen HESS is to formulate an appropriate power allocation strategy according to the characteristics of energy storage devices. The existing power allocation methods mainly include rule-based methods, intelligent methods, and frequency filter methods [11]. The explicit rule-based methods can transition between working modes based on a threshold. Ying Han regulated the operation of an HESS according to the power required by the generator and the SOC of SC, thus achieving power allocation. This method is straightforward to control and implement [13]. The singular working mode and inability to adapt to intricate working conditions is a limitation of this system. The fuzzy rule-based methods accomplish power allocation through the formulation of a rule base. Hongwen He conducted fuzzy control according to vehicle speed, voltage state of SC, SOC of battery, and required power of the generator [14]. This method has good robustness and can be used for complex nonlinear control. Nevertheless, it requires a large amount of historical experience data, and the rule base needs to be modified frequently. In recent years, the intelligent power allocation method based on multi-objective optimization, which can make full use of sensors, has become the focus of research. Intelligent methods achieve clear optimization objectives through model predictive control (MPC), particle swarm optimization algorithm, and other methods. Hredzak B. optimizes the power allocation of SC and battery using MPC [15]. However, this control method has not been compared with other methods, and its superiority cannot be demonstrated. Ziyou Song makes a comparative study of MPC that can achieve instantaneous optimization and a rule-based method. The results show that MPC is not practical, and the rule-based method performs better in practice. It can be seen that MPC needs further development [16]. Sarma U. takes the size of the fuel cell and the cost of the battery as optimization objectives and uses a particle swarm optimization algorithm to distribute the power of the HESS [17]. Although intelligent methods can achieve simultaneous optimization of multiple objectives, these methods all require a large amount of computation, long operation time, and high demands on the processor. Frequency filter methods implement power allocation based on the frequency scale, which is easy to be applied. The low-pass filter (LPF) method, Fourier transform, and wavelet transform are common frequency filter methods. Yaai Chen used LPF to filter the required power. The battery undertook the power output of the LPF, and the SC provided the power difference [18]. However, the LPF method has a fixed cutoff frequency and cannot adapt to varying sea conditions. Therefore, some scholars implement Fourier transform [19] and wavelet transform into the power allocation of the HESS. Despite the fact that the two methods have no fixed cutoff frequency, parameters must be set beforehand. To address the aforementioned problems, some researchers are beginning to employ methods that can dynamically divide frequency without requiring the initialization of parameters. Empirical mode decomposition (EMD) is one of the typical methods. Yuan Tiejiang used EMD to decompose the original wind power signal into direct grid-connected components and HESS power tasks [20]. This method can decompose the signal according to the time scale characteristics of the data itself, which is very suitable for the decomposition of wave energy with large randomness.

The HESS in the above references consists of one or two types of devices and consequently requires at most a single power allocation. However, our designed electric-hydrogen HESS has three devices and requires two power allocations. In addition, the power allocated to the electrolyzer should be considered not only the frequency but also the range of the power. Therefore, it is urgent to propose a new power allocation strategy for the electric-hydrogen HESS. In this paper, firstly, EMD and the Hilbert spectrum transform are employed to decompose the power fluctuations. The battery and electrolyzer accommodate the low frequency and high amplitude power fluctuations in the decomposition result. Secondly, according to the SOC of the battery and the dynamic characteristics of the alkaline electrolyzer, the power of the battery and the electrolyzer are determined using the rule-based method, and the power allocation is completed. Based on the results of allocation, the output power of the electrolyzer and battery is controlled by MPC. The SC is used to stabilize the bus voltage, and at the same time absorbs the power fluctuations of high frequency and low amplitude in the result of EMD, achieving the power balance of the system.

To address the issue of source-load mismatch when applying the DDWPGS, an electric-hydrogen HESS, as well as its dynamic power allocation strategy and control strategy, are suggested. The theoretical basis of the power allocation is presented in Section 2. The application of the proposed power allocation strategy in the electric-hydrogen HESS is explained in Section 3. The power control strategy is described in Section 4. In Section 5, we describe the setup of the simulation and list the parameters used. In Section 6, the simulation results are analyzed to verify the effectiveness of the proposed strategy.

2. The Theoretical Basis of Power Allocation Strategy

2.1. EMD and Hilbert Spectrum Transformation

EMD is an adaptive signal processing method that does not require the specification of prior parameters [21], which is very suitable for analyzing the output power of a DDWPGS. The detailed steps for decomposing P(t) using EMD are shown in Figure 2.

In Figure 2, the intrinsic mode functions (IMF) must satisfy the following requirements: (1) In all time ranges, the number of local extreme points and zero crossing points must be equal or at most one different. (2) The mean value of the upper envelope and the lower envelope must be 0 at any time point, that is, every IMF must be symmetries about the time axis [22].

By convolving the original signal with the fixed signal, the Hilbert transform can produce the instantaneous frequency of the original signal, thereby enabling the frequency domain decomposition of the power fluctuations. Based on the results of the EMD, the Hilbert transformation is carried out for each IMF. The expression of the Hilbert spectrum transformation is shown in Equation (1).

$$H[x(t)]={\displaystyle {\int }_{-\infty }^{\infty }x(\tau )}h(t-\tau )d\tau =\frac{1}{\pi }{\displaystyle {\int }_{-\infty }^{\infty }\frac{x(\tau )d\tau }{t-\tau }},$$

(1)

where x(t) is the original signal, which in this article is each IMF. h(t) is the fixed signal, h(t) = 1/(πt).

The frequency-time curve (c_n(t)) corresponding to IMF_n (n = 1, 2, …, i) can be obtained through Equation (1). c_n(t) is the premise for the subsequent frequency division. In this paper, the principle of minimum frequency aliasing is adopted to determine the frequency division point of power allocation. The frequency aliasing of c_n(t) is:

$$E_n={\displaystyle \sum _{j=1}^m|c_{n-1}(t_j)|\cdot \Delta t}+{\displaystyle \sum _{k=1}^s|c_{n+1}(t_k)|\cdot \Delta t},$$

(2)

where the period when c_n−1(t) is lower than c_n(t) is t_j (j = 1, 2, …, m), and a c_n+1(t) higher than c_n(t) is t_k (k = 1, 2, …, s).

Assuming that when n = g, E_n is minimum, then the frequency division point (c_g(t)) can be obtained to complete the power allocation.

2.2. Rule-Based Power Allocation Strategy Considering the Characteristics of Electrolyzer

The U-I equation of the alkaline electrolyzer is [23]:

$$\left\{\begin{array}{l}{U}_{cell}=U_{rev}+\frac{r_1+r_2{T}_{el}}{A_{el}}{I}_{el}+\left(s_1+s_2{T}_{el}+s_3{T}_{el}^2\right)\lg \left(\frac{t_1+\frac{t_2}{T_{el}}+\frac{t_3}{T_{el}^2}}{A_{el}}{I}_{el}+1\right),\\ U_{el}=N_{el}{U}_{cell},\end{array}\right.$$

(3)

where U_cell denotes the voltage across one electrolyzer cell, U_rev denotes the reversible cell voltage varying slowly with the temperature and pressure, r₁ and r₂ are the parameters for the electrolyte’s ohmic resistance, T_el denotes the temperature of the electrolyte, A_el is the area of the electrode, I_el and U_el represent the electrolyzer’s generated current and voltage, respectively, t_i and s_i (i = 1, 2, 3) are the parameters for overvoltage on the electrodes, and N_el represents the quantity of electrolyzer cells.

According to the ideal gas equation of state, the mathematical model of the hydrogen storage tank is [24]:

$$\left\{\begin{array}{l}{\eta }_{\mathrm{i}}=a_1\exp \left(\frac{a_2+a_3{T}_{\mathrm{el}}}{I_{\mathrm{cl}}/A_{\mathrm{el}}}+\frac{a_4+a_5{T}_{\mathrm{el}}}{{\left(I_{\mathrm{cl}}/A_{\mathrm{el}}\right)}^2}\right),\\ M=M_0+\int \frac{{\eta }_{\mathrm{i}}{N}_{el}{I}_{el}}{zF}\mathrm{d}t,\\ p_{\mathrm{H}2}=\frac{M{R}_{\mathrm{c}}{T}_{\mathrm{c}}}{V_{\mathrm{c}}},\end{array}\right.$$

(4)

where η_i is the hydrogen-production rate and α_i (i = 1, 2, …, 5) are derived from measurements and listed in Table 1. M is the stored hydrogen quantity, M₀ is the initial stored hydrogen quantity, z is the number of moles of transferred electrons per mole of water, F is the Faraday constant, p_H2 is hydrogen pressure in the electrolyzer, V_c is the volume of the cathode, T_c is the temperature in the electrolyzer, and R_c is the universal gas constant.

In actual operation, the alkaline electrolyzer should operate between 25% and 100% of its rated voltage. Otherwise, flammable compounds of hydrogen and oxygen will be formed at relatively low operating currents [25]. In addition, the transient process characterized by sharp current fluctuations is inevitable during the start and stop of the electrolyzer, which can also cause danger if not properly operated.

The power allocated to the electrolyzer should not only consider the frequency, but also concern the range of power. Therefore, the frequency filter method, which only takes into account the frequency, is excluded. Next, the fuzzy control method and intelligent method were eliminated, in view of the requirements of the processor, the practicality of the strategy, and the lack of a large amount of historical data. The rule-based method is simple and reliable. At the same time, this method can sufficiently adjust to the operating characteristics of the electrolyzer. Thus, it was decided to adopt a rule-based method for the secondary allocation.

Most rule-based power allocation methods realize power allocation by switching the working modes according to the required power of the generator and the SOC of the device. Figure 3 shows the rule-based method for a HESS consisting of a battery and SC.

In Figure 3, P_HESS is the power assignment of the HESS, P_ave is the average power, and P is the output power of the HESS. When P_HESS < 0, the HESS needs to absorb power. batSOC is the SOC of the battery. SOC_min and SOC_max are the lower and upper limits of batSOC, respectively. When using this method separately, less concern is given to the characteristics of the devices, severely reducing the service life of the HESS and the effect of smoothing fluctuations. In our design, this method is combined with the EMD. EMD is used for primary power allocation, and then the rules-based method is used to determine the respective output power of the electrolyzer and battery. This greatly extends the service life of the HESS. The detailed implementation method of the improved power allocation strategy designed in this paper is shown in Section 3.

3. Power Allocation Strategy

3.1. Initial Power Allocation Strategy Based on EMD

Ignoring line loss and converter loss, the target power of the electric-hydrogen HESS P_gp can be calculated using Equation (5):

$$P_{gp}=P_{load}-P_{wave},$$

(5)

where P_load and P_wave, respectively, represent the load power and the output power of the DDWPGS.

Using EMD to process P_gp, a series of IMF are obtained. The Hilbert transformation is carried out through Equation (1), and the frequency division point (c_g(t)) is determined based on Equation (2). Then, P_gp can be divided into P_high and P_low:

$$P_{high}=im{f}_1+im{f}_2+\cdots im{f}_g,$$

(6)

$$P_{low}=im{f}_{g+1}+im{f}_{g+2}+\cdots im{f}_m.$$

(7)

SC is responsible for P_high, while both the hydrogen storage system and the battery absorb P_low.

The operating characteristics of the alkaline electrolyzer and battery will directly affect the secondary allocation of P_low. The storage process of the battery is relatively straightforward. However, the power of the electrolyzer will change sharply in the process of starting and stopping, which is easy to produce a flammable gas mixture. Moreover, the electrolyzer must operate within a specific voltage range. If the power of the electrolyzer is not controlled, the stability of the system will be seriously affected. Therefore, EMD mainly based on frequency should not be used in allocating P_low. It is necessary to develop a new allocation strategy according to the characteristics of the electrolyzer.

3.2. Secondary Power Allocation Strategy through Rule-Based Method

Reference [26] examines the transient characteristics of a 250 kW alkaline electrolyzer during startup and shutdown. Based on the experimental results in [26], the power change curve of the electrolyzer at start and stop was obtained by piecewise-linear fitting, and it was applied to the 400 W electrolyzer used in this paper.

As shown in Figure 4, when the electrolyzer is started, the power of P_elec satisfies:

$$P_{elec}=\left\{\begin{array}{l}3.66t\begin{array}{cc}& (0\le t<99.7868),\end{array}\\ 0.192t+347.049\begin{array}{cc}& (99.7868\le t<292.8535),\end{array}\\ 400\begin{array}{cc}& (t\ge 292.8535).\end{array}\end{array}\right.$$

(8)

As shown in Figure 5, when the electrolyzer is shut down, the power of P_elec satisfies:

$$P_{elec}=\left\{\begin{array}{l}3.6t+400\begin{array}{cc}& (0\le t<89.9),\end{array}\\ 1100e^{-t/40}-40\begin{array}{cc}& (89.9\le t<132.5),\end{array}\\ 0\begin{array}{cc}& (t\ge 132.5).\end{array}\end{array}\right.$$

(9)

In this paper, there are only three operating states for the electrolyzer: start, run at rated power (400 W), and shut down. This working mode can ensure the safe operation of the electrolyzer and maximize the hydrogen production rate. The startup and shutdown time of the alkaline electrolyzer is determined according to the SOC of the battery (batSOC). When batSOC = SOC_start, and the battery is charging, the electrolyzer should be started. When batSOC = SOCstop, and the battery is discharging, the electrolyzer should be turned off.

During these operations, the energy absorbed by the battery is:

$$P_{bat}=P_{low}-P_{elec}.$$

(10)

Figure 6 shows the power allocation strategy of P_low. In the traditional strategy, the SC would undertake the P_low when the batSOC > SOC_max or batSOC < SOC_min. As a result, the SOC of both the battery and SC would remain in a limited state for a long time, resulting in low power and capacity utilization. In the improvement strategy proposed in this paper, (1) When the battery is being charged, if batSOC < SOC_start, the battery absorbs P_low. When batSOC = SOC_start, the electrolyzer should be started. When SOC_start < batSOC < SOC_max, P_low is absorbed by both the electrolyzer and battery. During this time period, the electrolyzer can be supported by the battery, which reduces the frequent start-stop of the electrolyzer. Moreover, it enables the electrolyzer to operate at the target power so that the safety and hydrogen production efficiency will not be affected by the fluctuating power of the DDWPGS. When batSOC > SOC_max, the battery stops charging. The electrolyzer absorbs P_low, and the battery supports the normal operation of the electrolyzer. If P_low exceeds the rated power of the electrolyzer, the excess energy is abandoned. (2) When the battery is discharging, if SOC_stop < batSOC < 1, the battery undertakes P_low while continuing to ensure the normal operation of the electrolyzer. When batSOC = SOC_stop, the electrolyzer will enter the shutdown process. If SOC_min < batSOC < SOCstop, after the electrolyzer is completely shut down, the battery will undertake P_low alone. When batSOC < SOC_min, P_low is undertaken by SC.

In the strategy suggested in this paper, two operating modes are added: (1) The battery and the electrolyzer undertake P_low together and (2) the electrolyzer absorbs P_low. These two modes can help the SOC of the battery to be in good condition and extend the service life of the battery without influencing the SC. It also decreases the wave abandonment and increases the income of hydrogen production. In addition, unlike existing studies that directly use fluctuating electrical energy for hydrogen production, the battery can help the electrolyzer maintain stable operation.

4. Power Control Strategy

An electric-hydrogen HESS has characteristics such as nonlinearity, multivariable coupling, and uncertainty. The traditional proportional integral control method is difficult to describe its mathematical model accurately, and the control effect is limited. MPC is a control strategy based on numerical optimization. By predicting the future dynamic information of the system, it can optimize the control target in the prediction time domain [27]. It has good rapidity and robustness. In this section, MPC is used to control the power of the battery and alkaline electrolyzer based on the power allocation results obtained in Section 3.

The main circuit structure of the electric-hydrogen HESS is shown in Figure 7. In the figure, V_bat and I_bat are the voltage and current of the battery, respectively. V_elec and I_elec are the voltage and current of the electrolyzer, respectively. V_sc and I_sc are the voltage and current of the SC, C_BUS is the capacitance on the DC bus and V_DC is the DC bus voltage.

According to Figure 7, a continuous mathematical model of the conversion circuit is established:

$$\left\{\begin{array}{l}\frac{L_{1}d{I}_{bat}}{dt}=V_{bat}-V_{DC}{S}_{w1},\\ \frac{L_{2}d{I}_{elec}}{dt}=V_{elec}-V_{DC}{S}_{w3},\end{array}\right.$$

(11)

where S_w1 is the switching signal of S₁ and S_w3 is the switching signal of S₃. If S_w = 1, S is turned on, and if S_w = 0, S is turned off. When the sampling period is T_s, the corresponding discrete model can be written as:

$$\left\{\begin{array}{l}{I}_{bat}(k+1)=I_{bat}(k)+\frac{T_S}{L_1}\left[V_{bat}(k)-V_{DC}(k)S_{w1}(k)\right],\\ I_{elec}(k+1)=I_{elec}(k)+\frac{T_S}{L_2}\left[V_{elec}(k)-V_{DC}(k)S_{w3}(k)\right].\end{array}\right.$$

(12)

Considering that the voltage of the battery and electrolyzer cannot change suddenly, it can be obtained that:

$$\left\{\begin{array}{l}{P}_{bat}(k+1)=I_{bat}(k+1)V_{bat}(k),\\ P_{elec}(k+1)=I_{elec}(k+1)V_{elec}(k).\end{array}\right.$$

(13)

Based on the control objective of power balance, the following cost function is written as:

$$J=\alpha {\left|P_{bat}-P_{bat}(k+1)\right|}^2+\beta {\left|P_{elect}-P_{elect}(k+1)\right|}^2,$$

(14)

where α and β are the power control coefficients of the battery and electrolyzer, respectively, which are used to improve the control effect. In this paper, α = 1 and β = 1.

Based on the voltage closed-loop control strategy, SC is used to stabilize the bus voltage by controlling S4 and S5. Since there is no harmonic flow of reactive power in the DC microgrid system, the control of energy balance in the system mainly comes down to the problem of stabilizing the DC bus voltage and power quality management. The only indicator reflecting whether the system power is balanced is the DC bus voltage. Therefore, while stabilizing the bus voltage, SC also undertakes P_high in the EMD results, achieving power balance.

5. Parameter Setting and Simulation

The structural diagram of the electric-hydrogen HESS for the DDWPGS proposed in this paper is shown in Figure 8. It consists of a direct drive wave generator module, electric-hydrogen HESS module, energy management module, power control module, and DC loads module. The battery and the SC are connected to the DC bus through the bidirectional DC/DC converter. The alkaline electrolyzer is connected to the bus bar through a BUCK converter. The DC load includes a seawater desalination plant (desalinated sea water, used for producing hydrogen using water electrolysis) and other consumer equipment. They draw power from the grid through the BUCK converter. We construct a simulation in Simulink which corresponds to Figure 8.

5.1. Simulation

A direct drive wave generator module adopts the permanent magnet linear generator (PMLG). Through the zero d-axis current vector control, the DDWPGS works in the state of maximum power capture, as shown in Figure 9.

The float speed of the wave generator under irregular wave action is defined as: [28]:

$$v=A_1\sin ({\omega }_{1}t)+A_2\sin ({\omega }_{2}t+{\phi }_2)+\cdots .$$

(15)

The float speed is set as a superposition of three sinusoidal functions with different frequencies and different amplitudes, as shown in Equation (16). In the equation, the sine signal with a frequency of 0.1 Hz has the maximum amplitude, which is used to simulate wave fluctuations with high energy density and low power density. A sine signal with a frequency of 5 Hz has the smallest amplitude and is used to simulate wave fluctuations with high power density and low energy density. A signal with a frequency of 1 Hz simulates wave fluctuations with medium power density and energy density.

$$v=0.62\cdot \left[\sqrt{2}\sin \left(\frac{\pi }{5}t\right)+\frac{\sqrt{2}}{20}\sin (2\pi t+\frac{3}{4}\pi )+\frac{\sqrt{2}}{100}\sin (10\pi t+\frac{\pi }{2})\right].$$

(16)

The float speed and electromagnetic power of the DDWPGS vary periodically, as shown in Figure 10. The alkaline electrolyzer is simulated according to the empirical model of Equation (3). The energy management module is constructed on the basis of Section 3. The power control module applies the principles in Section 4. The DC loads module consists of resistors. In addition, in order to test the dynamic response characteristics of the electric-hydrogen HESS, the DC load is set to 400 Ω in the period of 0 to 450 s. The resistance is set to 100 Ω for the period from 450 s to 800 s. The simulation time is set to 800 s, the discrete mode. With a comprehensive consideration of the calculation accuracy and the hardware resources of the computer, the sampling time was set to 1 × 10⁻⁵.

5.2. Parameter Setting

Equations (3) and (4) are from the empirical model, where the parameters are obtained using measurements and calculations. We have set the parameters in Equations (3) and (4) based on reference [23]. SOC_start is the SOC of the battery when the electrolyzer is started. SOC_end is the SOC of the battery when the electrolyzer enters the shutdown state. batSOC_min and batSOC_max are the lower and upper SOC limits of the battery, respectively. SCSOC_min and SCSOC_max are the lower and upper SOC limits of the SC, respectively. The parameters in the simulation are listed in Table 1.

Table 1. Simulation parameter setting of the electric-hydrogen HESS for the DDWPGS.

Parameter	Symbol	Value	Source
The parameter 1 for ohmic resistance of electrolyte	r1	7.35 × 10−5 Ωm2	Equation (3)
The parameter 2 for ohmic resistance of electrolyte	r2	−1.11 × 10−7 Ωm2/℃
Electrolyzer temperature	Tel	80 ℃
Area of the electrode	Ael	0.25 m2
The parameters for overvoltage on electrodes	t1	1.6 × 10−2 m2/A
	t2	−1.302 m2℃/A
	t3	4.21 × 102 m2℃/A
	s1	1.59 × 10−1 V
	s2	1.38 × 10−3 V/℃
	s3	−1.61 × 10−5 V/℃
The number of electrolyzer cells	Nel	14
The parameters calculated from measurements	a1	99.5%	Equation (4)
	a2	−9.5788 m2/A
	a3	−0.0555 m2/A/℃
	a4	1502.71 m4/A
	a5	−70.8 m4/A/℃
The universal gas constant	Rc	8.3144 J/Kmol
The number of moles of transferred electrons per mole of water	z	2
Faraday constant	F	96,485 Cmol
Minimum value of battery SOC	batSOCmin	20%	Figure 6
Maximum value of battery SOC	batSOCmax	80%
SOC of the battery at the start of the electrolyzer start-up	SOCstart	60%
SOC of the battery when the electrolyzer starts to close	SOCend	58%
Inductance of battery circuit	L1	0.1 H	Equation (11)
Inductance of electrolyzer circuit	L2	0.1 H
Inductance of SC circuit	L3	10 μH	-
Capacitance for stabilizing bus voltage	C	2000 μF
Nominal voltage of battery	Vbat,r	30 V
Rated capacity of battery	Cbat	50 Ah
Rated voltage of SC	VSC,r	200 V
Rated capacitance of SC	CSC	10 F
Minimum value of SC SOC	SCSOCmin	10%
Maximum value of SCSOC	SCSOCmax	90%

Table 1. Simulation parameter setting of the electric-hydrogen HESS for the DDWPGS.

Parameter	Symbol	Value	Source
The parameter 1 for ohmic resistance of electrolyte	r1	7.35 × 10−5 Ωm2	Equation (3)
The parameter 2 for ohmic resistance of electrolyte	r2	−1.11 × 10−7 Ωm2/℃
Electrolyzer temperature	Tel	80 ℃
Area of the electrode	Ael	0.25 m2
The parameters for overvoltage on electrodes	t1	1.6 × 10−2 m2/A
	t2	−1.302 m2℃/A
	t3	4.21 × 102 m2℃/A
	s1	1.59 × 10−1 V
	s2	1.38 × 10−3 V/℃
	s3	−1.61 × 10−5 V/℃
The number of electrolyzer cells	Nel	14
The parameters calculated from measurements	a1	99.5%	Equation (4)
	a2	−9.5788 m2/A
	a3	−0.0555 m2/A/℃
	a4	1502.71 m4/A
	a5	−70.8 m4/A/℃
The universal gas constant	Rc	8.3144 J/Kmol
The number of moles of transferred electrons per mole of water	z	2
Faraday constant	F	96,485 Cmol
Minimum value of battery SOC	batSOCmin	20%	Figure 6
Maximum value of battery SOC	batSOCmax	80%
SOC of the battery at the start of the electrolyzer start-up	SOCstart	60%
SOC of the battery when the electrolyzer starts to close	SOCend	58%
Inductance of battery circuit	L1	0.1 H	Equation (11)
Inductance of electrolyzer circuit	L2	0.1 H
Inductance of SC circuit	L3	10 μH	-
Capacitance for stabilizing bus voltage	C	2000 μF
Nominal voltage of battery	Vbat,r	30 V
Rated capacity of battery	Cbat	50 Ah
Rated voltage of SC	VSC,r	200 V
Rated capacitance of SC	CSC	10 F
Minimum value of SC SOC	SCSOCmin	10%
Maximum value of SCSOC	SCSOCmax	90%

6. Results and Analysis

Using EMD to decompose P_gp, the results are shown in Figure 11. Subsequently, the Hilbert transformation was performed on IMF and RES to obtain the frequency-time curve as shown in Figure 12. At 450 s, the DC load changes suddenly. Each IMF component and RES in Figure 11 also change in signal amplitude to varying degrees at 450 s.

The power allocation results obtained according to the minimum frequency aliasing principle are shown in Figure 13. P_gp is decomposed into P_low with a lower frequency and larger power amplitude, and P_high with a higher frequency and smaller power amplitude.

Figure 14 shows the actual power and reference power of the electrolyzer. It can be seen that the strategy proposed in this paper fully considers the start-stop characteristics and operation characteristics of the electrolyzer. In addition, the electrolyzer only starts and stops once within 800 s, which effectively prolongs its service life. The response time of the power control strategy based on MPC is 0.33 s, and the control effect is good.

Figure 15 shows the average exchange power and the reference value of the average exchange power of the battery under each wave period. It can be seen from Figure 15 that the actual average exchange power of the battery and the reference average power are basically equal, indicating the high accuracy of the power control strategy. The instantaneous output power and reference power of the battery when the battery is activated are shown in Figure 16. The output power of the battery reaches the reference power at 0.02 s, illustrating that the response speed of the power control is fast. Figure 17 demonstrates the variation of the battery output power from 440 s to 460 s. It shows that the control effect on the battery is not affected by sudden changes in the DC load. In addition, it also becomes clear from Figure 16 and Figure 17 that the battery absorbs the fluctuations with low frequencies and high amplitudes. It conforms to the characteristics of high energy density and low power density of the battery.

As shown in Figure 18, when the electrolyzer starts up, the SOC of the battery is 60%; when the electrolyzer starts to shut down, the SOC of the battery is 58%. The simulation results are in line with expectations.

The voltage of the DC bus under the control of SC is shown in Figure 19. When the system starts up, the SC responds quickly so that the bus bar voltage reaches stability at 0.03 s. At 450 s, the DC load suddenly changes, and the bus voltage is not affected and remains stable at 400 V.

The hydrogen production of the electrolyzer is shown in Figure 20. A total of 0.2 mol, or 4.44 L, of hydrogen is produced during 800 s.

For the DDWPGS, the HESS composed of the battery and SC and the electric-hydrogen HESS proposed in this paper are, respectively, used. The SOC of the battery is shown in Figure 21. As shown in the figure, after the SOC of the battery reaches SOC_start, the SOC of the battery increases more slowly when the electric-hydrogen HESS is used. After the SOC of the battery reaches the SOC_end, the electrolyzer is closed to slow down the descent rate of the SOC. Compared with a traditional HESS, the electric-hydrogen HESS designed in this paper and its control strategy can maintain the battery in a good state of charge, ensure that it has sufficient power and capacity space to smooth out fluctuations, and extend its service life.

7. Conclusions

In this paper, the characteristics of different ESSs used in the DDWPGS are considered comprehensively, and the electric-hydrogen HESS is designed. The power allocation strategy considering the characteristics of energy storage devices is developed. Then, the allocation results are achieved by using a control strategy based on MPC. The simulation was verified in Simulink, and the following conclusions are drawn:

• The electric-hydrogen HESS for the DDWPGS combines hydrogen energy and wave energy. It overcomes the shortcomings of existing research, uses stable and controllable electric energy to produce hydrogen, and also pays attention to the optimization management of energy storage.
• A strategy combining EMD and the rule-based method is adopted for twice the power allocation. The power assignments of the three energy storage devices are obtained. This strategy makes up for the limitation of the traditional rule-based method, has good adaptability, and is very suitable for wave energy with large randomness. Moreover, the start-stop characteristics and operation characteristics of the electrolyzer are considered to ensure the safety of the operation process of the electrolyzer.
• The complementary mechanism is proposed. The battery and the SC complement each other and undertake the electric energy of different energy densities and power densities, respectively. The hydrogen energy storage system is complementary to the battery, which can provide stable and controllable power for hydrogen production. Hydrogen energy storage systems can help the battery maintain a good SOC.
• A power control strategy for a nonlinear electric-hydrogen HESS based on MPC is established. This strategy has good rapidity, accuracy, and robustness.

Based on the conclusion of this paper, the technical reference of equipping an electric-hydrogen HESS for a DDWPGS is provided.