Coordinated Control of a Wind-Methanol-Fuel Cell System with Hydrogen Storage

Abstract

This paper presents a wind-methanol-fuel cell system with hydrogen storage. It can manage various energy flow to provide stable wind power supply, produce constant methanol, and reduce CO₂ emissions. Firstly, this study establishes the theoretical basis and formulation algorithms. And then, computational experiments are developed with MATLAB/Simulink (R2016a, MathWorks, Natick, MA, USA). Real data are used to fit the developed models in the study. From the test results, the developed system can generate maximum electricity whilst maintaining a stable production of methanol with the aid of a hybrid energy storage system (HESS). A sophisticated control scheme is also developed to coordinate these actions to achieve satisfactory system performance.

1. Introduction

In order to curb global warming, international efforts have been devoted to developing renewable energy sources as well as utilizing conventional energy in a cleaner way. Wind energy, as a renewable source of energy, attracts much attention from research community and industry. As the largest CO₂ emitter, China had installed 150 million kW of wind turbines by the end of 2016 [1]. However, wind power is intermittent and its increasing penetration in the power network can create power stability issues. Therefore, much research is focused on the integration of wind energy in the power system for a resilient energy supply [2,3,4,5]. On the other hand, China is also the world’s largest coal producer. Coal is a primary source of energy and accounts for 90% of China’s CO₂ emissions from fossil fuels [6]. How to use coal in a cleaner way is always a challenge facing the successive Chinese governments.

Methanol is a clean-burning liquid that requires only minor modifications to existing engines and fuel-delivery infrastructure. Manufacturing it could even make use of carbon dioxide, which is the main cause for global warming. While methanol’s benefits have long been understood, recent advances in methanol synthesis and methanol fuel cells could make this fuel even more attractive [7]. Conventionally, methanol is a by-product of mining coal through a hydrocarbylation reaction. In this process, 1.526 times of CO₂ could be produced with one unit of methanol. This has led to a significant increase in CO₂ emissions to the environment. In order to tackle this issue, a new representative process has been developed [8] to produce methanol from hydrogen, oxygen and coal which is used in this study.

Energy storage is important to maintain the stable operation of energy systems. Reference [9] presented a new energy storage design to support energy flow in a hybrid wind-hydrogen system. Reference [10] proposed a hybrid energy system consisting of a wind turbine generator, a fuel cell with a water electrolyser and a battery energy storage system. Typically, these energy components are divided into two groups and two PI controllers were used to manage energy flow. By combining wind energy with fuel cells, reference [11] discussed the feasibility of a hybrid system satisfying residential demands when connected to the power grid. Reference [12] proposed an optimal method for sizing a grid-connected wind farm with a hydrogen system. Fuel cell systems with wind energy were also investigated in references [13,14,15,16] in order to find an optimal structure in the hybrid system. New concepts for optimal applications for wind energy were proposed [17,18]. These hybrid energy systems were integrated with integrating wind energy and coal-based methanol production, so as to provide an effective method to utilize local energy resources. Energy management and control methods in multi energy sources are critically important also important. Fuzzy logic control is a popular option for hybrid energy systems. Reference [19] presented a particle swarm-based fuzzy logic control for a hybrid wind-fuel cell-battery system to decrease total harmonic distortion of the power sources. A maximum power point tracking (MPPT) algorithm was used in a wind-fuel cell system [20] to meet variable load. Reference [21] adopted a probability distribution function to manage a wind-fuel cell-turbine with energy storage. The test results for different scenario of load or demand uncertainty. These systems are effective but have their limitations. It is the author’s review that using systematic approaches to integrate the developed techniques will increase multiple functions in the loop of energy generation, utilization, operation, clean environment and so on.

The research project uses Xinjiang, the large territory province in China, as a case background. It is an important energy base in China, it connects advanced provinces in East China eastward, and links to the Central Asia countries westward. Xinjiang is regarded as a strategic hub on the “Silk Road Economic Belt”. It is rich in coal resources and wind energy, which is a perfect match for the project as generated electricity from wind can be used for water electrolysis to produce hydrogen and oxygen. Xinjiang has been one of the five national integrated energy bases [22,23]. Therefore, how to effectively utilise coal sources and wind energy in Xinjiang is one of the crucial issues in China’s national agenda. In national perspective, China has been a major contributor to global warming and thus is committed to play a significant role to cut down its CO₂ emissions. In June 2014, China proposed a radical measure for managing its energy consumption and for developing renewable energy technologies. China has become the largest renewable producer in 2016, according to British Petroleum Statistical Review of World Energy [24].

This study proposes a hybrid system including a wind turbine, hydrogen/oxygen storage tanks through water electrolysis, a coal-base methanol device and a fuel cell. In this multi-source system, energy is managed into different forms: kinetic energy in a turbine; chemical energy in hydrogen/oxygen and fuel cells; electrical energy in the wind turbine/generators and the fuel cells. The hydrogen production through water electrolysis and the charging/discharging of the fuel cells provide flexibility when the intermittent wind power cannot match the energy requested. Meanwhile, methanol production with the new technology reduces the CO₂ emission for the system [17,25] which also in turn increase the revenue from the carbon trading scheme according to the national policy [26,27]. In this system, energy flow is managed by a coordinated control strategy. It determines the electricity generation and methanol production, with a target of maximising utilisation of wind energy. The feasibility and the performance of the strategy are tested through modeling and simulation in the MATLAB/Simulink environment. The novelty and contribution of the study are listed below.

(1)

Integration wind energy into the grid has resulted in degradation of the inertia response, which in turn seriously affects the stability of the power system’s frequency. This problem can be solved by using an active power reserve to stabilize the frequency. Hydrogen/oxygen fuel cell technology is one of solution as a power reserve for this purpose.

(2)

Hydrogen/oxygen production from water electrolysis could provide the resource for fuel cell applications. As typical electricity-to-hydrogen conversion devices, electrolysers are regarded as deferrable loads with the ability to operate under a flexible schedule on the demand side.

(3)

The coal-based methanol production is one of research challenges of clean energy applications of fossil fuels. This study adopts a “greener” process. The oxygen is fed to the gasifier as the gasification agent and then the hydrogen is mixed with the CO-rich gas to adjust H₂/CO so as to produce methanol. However, it requires local supplies of hydrogen/oxygen continuously. Therefore, this kind of applications are limited. However, specific geometry advantages of Xinjiang province is perfect for this kind of applications.

(4)

This innovative application integrates wind power, hydrogen from water electrolysis, hydrogen/oxygen fuel cells and a coal-based methanol production by a “greener” process. The system proposed has advantages of both the renewable sources and sustainable coal industries in China. Methanol receives hydrogen/oxygen to balance the local loads and to increase the overall profits. However, the hybrid construct would increase the system complexity. Therefore, it is necessary to investigate the possible energy management strategy and control mechanism before physical complicated system is build up.

The rest of the main studies are arranged as follows: Section 2 introduces the configuration of the hybrid system; Detailed discussion associated with the control scheme is carried out for energy management of this system; Section 3 provides the simulation outcomes and analysis; Section 4 summarises the main findings and suggests future work.

2. The Hybrid System and Its Control Scheme

The schematic diagram of the system is shown in Figure 1. The system includes a doubly-fed induction generator (DFIG) of a wind turbine, coal-based methanol production sub-system, a water electrolyser for hydrogen production, hydrogen and oxygen storage tanks, fuel cells, a DC link, DC/AC or AC/DC converters. The coal chemical process comprises gasification, mixing, purification, reaction, separation and rectification.

Figure 1. Schematic diagram of the proposed system.

This system is operated on the following basis:

• Wind power is used to generate electricity for supplying the grid and for producing hydrogen through water electrolysis.
• Normally, the generated electricity is fed into the power grid. If the wind power is plenty, the additional power is used for water electrolysis and the energy is stored in hydrogen.
• Hydrogen and oxygen produced are stored in separate tanks and are controlled to be within a range (upper limit 90% and lower limit 20%).
• Fuel cells absorb hydrogen and generate electricity to supply the grid.
• Methanol is produced constantly (from coal, hydrogen and oxygen) at a set value regardless of wind power input.

Figure 2 shows the operation of the proposed system.

Figure 2. The proposed scheme with coordinated control.

2.1. State Index of the Hybrid Energy Storage System (HESS)

In this paper, the HESS consists of a water electrolyser, a hydrogen and an oxygen tank, and fuel cells. The energy flow in the HESS is bi-direction. However, methanol production is single direction and cannot be fed back. Therefore, coal-based methanol production is not involved in the storage system in this study. In the HESS, the equivalent state of charge (ESOC) is evaluated by the state of the hydrogen and oxygen tanks:

$$ESOC=\frac{p_{vre}}{p_{cap}}$$

(1)

where $p_{vre}$ and $p_{cap}$ are the current pressure and full pressure of the tanks, respectively. Based on the average weighting method, the ESOC is calculated as follows:

$$ESO{C}_H=\frac{p_{Hre}}{p_{Hcap}}$$

(2)

$$ESO{C}_O=\frac{p_{Ore}}{p_{Ocap}}$$

(3)

$$ESO{C}_S=\frac{ESO{C}_H\times V_{Hcap}+ESO{C}_O\times V_{Ocap}}{V_{Hcap}+V_{Ocap}}$$

(4)

where $ESO{C}_H$ is the ESOC level of the hydrogen storage tank, $p_{Hre}$ is the pressure of the hydrogen tank, $p_{Hcap}$ is the full pressure of the hydrogen tank, $ESO{C}_O$ is the ESOC level of the oxygen tank, $p_{Ore}$ is the pressure of the oxygen tank, $p_{Ocap}$ is the full pressure of the oxygen tank, $V_{Hcap}$ and $V_{Ocap}$ are the volumes of hydrogen and oxygen tanks, respectively.

In order to operate the HESS effectively, the indicators of $ESO{C}_H$, $ESO{C}_O$, $ESO{C}_S$ should be controlled within reasonable range. Basically, they are divided into two intervals and three situations, as shown in Figure 3. Each interval can be determined by Equation (5):

$$\{\begin{array}{l}Normalinterval:ESO{C}_{X\_\min }\le ESO{C}_X\le ESO{C}_{X\_\max },N_{H_{2}O}=N_{fc}+N_{mhg}\\ Warninginterval:\{\begin{array}{l}ESO{C}_X<ESO{C}_{X\_\min },N_{H_{2}O}>N_{fc}+N_{mhg},X=H,O,S\\ ESO{C}_X>ESO{C}_{X\_\max },N_{H_{2}O}<N_{fc}+N_{mhg}\end{array}\end{array}$$

(5)

where ESOC_{X_min} represents the minimal of ESOC and X represents hydrogen, oxygen and HESS states, respectively. ESOC_{X_max} is the maximal of hydrogen, oxygen and HESS. $N_{H_{2}O}$ is the hydrogen flow rate in water electrolyser. $N_{fc}$ is the hydrogen flow rate in the fuel cell. N_mhg is the hydrogen flow rate used in coal chemical system when producing methanol.

Figure 3. The capacity range of the HESS.

When the tank or ESOC level is in the normal range, the coal chemical system operates normally to produce methanol. The ideal operation state of the system is that hydrogen generated by the water electrolysis is equal to the sum of hydrogen consumption in the methanol production and in the fuel cells discharging while the ESOC of the HESS is still within the normal range.

In the control scheme, ESOC_S is considered as the priority factor in the operation. And the relationship among the wind power output P_wind, the cluster power dispatch demand P_jh, local load demand P_load is defined as follows:

(1)

When ESOC_S > ESOC_{S_max}, let i = 1 and $P_{re}^{\left(i\right)}=P_{wind}-\left(P_{load}+P_{jh}\right)$

(2)

When ESOC_{S_min} ≤ ESOC_S ≤ ESOC_{S_max}, let i = 2 and $P_{re}^{\left(i\right)}=P_{wind}-P_{load}$

(3)

When ESOC_S < ESOC_{S_min}, let i = 3 and $P_{re}^{\left(i\right)}=P_{wind}$

2.2. Operation Scheme of the Hybrid System

The system converts energy between electrical, chemical and mechanical. Hydrogen/oxygen generation is an integral part of the energy flow. The processes involve several reactions as follows [28,29]:

Water electrolysis: $H_{2}O\to \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.O_2+2H^{+}+2e^{-}$, therefore, $n\left(H_2\right):n\left(O_2\right)=2:1$

Coal based methanol production: $\mathrm{CO}+2H_2=C{H}_{3}OH$, therefore:

$$n\left(H_2\right):n\left(O_2\right)=1:1$$

(6)

Electrochemical reactions in a fuel cell: $H_2+\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.O_2\to H_{2}O$, therefore, $n\left(H_2\right):n\left(O_2\right)=1:0.5$

For the constant production of methanol at set power P_mhg, the hydrogen and oxygen are the same. The flow rate of hydrogen N_mhg and power demand $P_{re}^{\left(i\right)}$ are given in Table 1.

Table 1. Interval scheme of power $P_{re}^{\left(i\right)}$ with the flow rate $N_{H_2}$.

	${\mathit{\gamma }}_{\mathbf{1}}$	${\mathit{\gamma }}_{\mathbf{2}}$	${\mathit{\gamma }}_{\mathbf{3}}$	${\mathit{\gamma }}_{\mathbf{4}}$
$P_{re}^{\left(i\right)}$	(0,Pmhg)	[Pmhg,2Pmhg]	(2Pmhg,4Pmhg]	(4Pmhg,+∞)
$N_{H_2}$	(0,Nmhg)	[Nmhg,2Nmhg]	(2Nmhg,4Nmhg]	(4Nmhg,+∞)

When P_H2O and N_H2O are in interval ${\gamma }_1$, hydrogen from water electrolysis is not sufficient to sustain the required methanol production, as a result, the stored hydrogen in the tank is also consumed and ESOC_S slowly reduces. When P_H2O and N_H2O are in interval ${\gamma }_2$, the generated hydrogen is more than the needed for methanol. Extra hydrogen is consumed by fuel cells to generate electricity. In ${\gamma }_3 \mathrm{or}{\gamma }_4$, when the hydrogen is much more than needed, extra hydrogen is used for fuel cells and methanol and increasing tank levels. Table 2 gives detailed explanations.

Table 2. Operational regulation for different scenarios.

Indicator		Scenario	Action
$i=1$ $P_{re}^{\left(i\right)}=P_{wind}-\left(P_{load}+P_{jh}\right)$	$P_{re}^{\left(i\right)}$ < 0	ESOCS is over the upper limit. The wind power is insufficient to satisfy both local demands and cluster power requested by the grid.	The total wind power is fed into the grid. The fuel cells discharge. Water electrolysis suspends, $P_{H_{2}O}$ = 0.
	$P_{re}^{\left(i\right)}$ = 0	ESOCS is over the upper limit. The wind power is sufficient to satisfy both local and cluster power, the rest of the wind power is equal to 0.	The wind power is completely transferred to the grid. Water electrolysis suspends, $P_{H_{2}O}$ = 0.
	$P_{re}^{\left(i\right)}$ ∈ Ƴ1	ESOCS is over the upper limit. The wind power is sufficient to satisfy both local and cluster power. The rest of the wind power is within Ƴ1.	The wind power fed into the grid is set (Pload + Pjh), $P_{H_{2}O}$ = $P_{re}^{\left(i\right)}$.
	$P_{re}^{\left(i\right)}$∈ (Ƴ2 ∪ Ƴ3 ∪ Ƴ4)	ESOCS is over the upper limit. The wind power is sufficient to satisfy both local and cluster power. The rest of the wind power is within Ƴ2 or Ƴ3 or Ƴ4.	The wind power is used for water electrolysis which provide the hydrogen for methanol production. $P_{H_{2}O}$ = $P_{re}^{\left(i\right)}$ and the rest wind power is transferred to the grid.
$i=2$ $P_{re}^{\left(i\right)}=P_{wind}-P_{load}$	$P_{re}^{\left(i\right)}$< 0	ESOCS is within the normal range. The wind power is insufficient to satisfy the local demands.	The total wind power is fed into the grid. The fuel cells discharge with Pfc = |$P_{re}^{\left(i\right)}$|. Water electrolysis process suspends, $P_{H_{2}O}$ = 0.
	$P_{re}^{\left(i\right)}$∈ (Ƴ1 ∪ Ƴ2) or $P_{re}^{\left(i\right)}$∈ (Ƴ3 ∪ Ƴ4)	ESOCS is within the normal range. The wind power is sufficient to satisfy the local demands. The rest of the wind power is within (Ƴ1 ∪ Ƴ2) or (Ƴ3 ∪ Ƴ4).	The fuel cells suspend. Wind power is used for water electrolysis which provide the hydrogen for methanol production with $P_{H_{2}O}$ = |$P_{re}^{\left(i\right)}$| or $P_{H_{2}O}$ = 2Pmhg. The rest wind power is fed to the grid.
$i=3$ $P_{re}^{\left(i\right)}=P_{wind}$	$P_{re}^{\left(i\right)}$= 0	ESOCS is below the lower limit. No wind power provided.	Both The fuel cell and water electrolysis process suspend; No wind power is fed to the grid.
	$P_{re}^{\left(i\right)}$∈ (Ƴ1 ∪ Ƴ2 ∪ Ƴ3)	ESOCS is below the lower limit. The wind power is within (Ƴ1 ∪ Ƴ2 ∪ Ƴ3).	All wind power is used for water electrolysis $P_{H_{2}O}$ = $P_{re}^{\left(i\right)}$.
	$P_{re}^{\left(i\right)}$∈ Ƴ4	ESOCS is below the lower limit. The wind power is within Ƴ4.	The wind power used for water electrolysis $P_{H_{2}O}$ is equal to 4Pmhg. The rest wind power is fed to the grid.

2.3. Electrical Power and ESOC Control

Based on the control priority and the operating state of the system, a power distribution strategy is proposed. Its flow chart is shown in Figure 4. The power consumed by water electrolysis is obtained as follows:

$$P_{H_{2}O}=\{\begin{array}{c}0 P_{re}^{\left(i\right)}\le 0\\ P_{re}^{\left(i\right)} 0< P_{re}^{\left(i\right)}\le 2^{\left(i-1\right)}{P}_{mhg}\\ 2^{\left(i-1\right)}{P}_{mhg} P_{re}^{\left(i\right)}\le 2^{\left(i-1\right)}{P}_{mhg} \end{array}$$

(7)

Figure 4. Control diagram of electric energy allocation.

The fed-in wind power to the grid is given by:

$$P_S=P_{wind}-P_{H_{2}O}$$

(8)

All hydrogen is generated by water electrolysis and is consumed by either fuel cells or methanol production. Thus, the hydrogen distribution can be expressed by:

$$\{\begin{array}{l}{n}_{H_{2}O\_H}+n_{\Delta H}=n_{mhg\_H}+n_{rH}\\ n_{H_{2}O\text{\_}O}+n_{\Delta O}=n_{mhg\_O}+n_{rO}\end{array}$$

(9)

where $n_{H_{2}O\_H}$ and $n_{H_{2}O\_O}$ are the amount of the hydrogen and oxygen produced by electrolysis of water respectively. n_∆H and n_∆O are the amount of the hydrogen and oxygen consumed in the tank respectively. n_rH and n_rO are the amount of hydrogen and oxygen that fed into the fuel cell respectively.

The hydrogen flow rate $N_{H_2}$ from the electrolysis of water power $P_{H_{2}O}$ is obtained:

$$N_{H_2}={\eta }_e{N}_e\frac{I_e}{2F}={\eta }_e{N}_e\frac{P_{H_{2}O}/N_e{U}_e}{2F}=\frac{{\eta }_e{P}_{H_{2}O}}{2U_{e}F}$$

(10)

where ${\eta }_e$ is the electrolysis efficiency of water electrolyser, which is generally between 60% and 80% [30]. N_e is the number of electrolytic cells in series. F is the Faraday constant. Ie is the operating current of the cell which is given by dividing the consumption power $P_{H_{2}O}$ by the electrolyser voltage Ue.

Thus:

$$\{\begin{array}{l}{n}_{H_{2}O\_H}=N_{H_2}\Delta t\\ n_{H_{2}O\_O}=0.5n_{H_{2}O\_H}=0.5N_{H_2}\Delta t\end{array}$$

(11)

Assuming the operation process is ideal, the amount of hydrogen and oxygen consumed in the coal chemical system during ∆t can be written as:

$$n_{mhg\_H}=n_{mhg\_O}=N_{mhg}\times \Delta t$$

(12)

$$N_{mhg}=207\times 0.2\times \frac{M_W}{3.6V_m}$$

(13)

where $M_W$ is the wind turbine output power (MW), and $V_m$ is the hydrogen molar volume 22.4 L/mol.

From Equation (8), $n_{rO}$ can be derived from $n_{\Delta H}$ and $n_{\Delta O}$, and vice versa. Thereby the state of the hydrogen storage system at the end of each cycle can be obtained. Therefore, the hydrogen distribution control is simplified to study the operation state of the fuel cells. The cases for the fuel cells discharging can be summarised as the follows:

(1) If $P_{re}^{\left(1\right)}$ ≥ 0, reduce ESOC_S by consuming more hydrogen and oxygen for electricity generation, Let flag1 = 1. Logical order is to derive $n_{rH}$, $n_{rO}$($P_{fc}$) from $n_{\Delta H}$, $n_{\Delta O}$.

At this moment, the amount of hydrogen and oxygen can reach the upper limits of the tank pressure $n_{\Delta H}$, $n_{\Delta O}$:

$$\{\begin{array}{l}{n}_{\Delta H}^{\prime }=p_{Hcap}{\mathrm{V}}_{Hcap}(ESO{C}_H-ESO{C}_{H\text{\_}\max })/{\mathrm{RT}}_H\\ n_{\Delta O}^{\prime }=p_{Ocap}{\mathrm{V}}_{\text{}Ocap}(ESO{C}_O-ESO{C}_{O\text{\_}\max })/{\mathrm{RT}}_O\end{array}$$

(14)

The calculations of the parameters $n_{\Delta H}$, $n_{\Delta O}$ are shown in Table 3.

Table 3. Parameter selection for the calculation.

	${\mathit{n}}_{\mathbf{\Delta }\mathbf{H}}^{\mathbf{\prime }}$	<0	=0	>0
${\mathit{n}}_{\mathbf{\Delta }\mathbf{O}}^{\mathbf{\prime }}$
<0		-	-	select $n_{\Delta \mathrm{H}}=n_{\Delta \mathrm{H}}^{\prime }$
=0		-	-	select $n_{\Delta \mathrm{H}}=n_{\Delta \mathrm{H}}^{\prime }$
>0		Select $n_{\Delta O}=n_{\Delta O}^{\prime }$	Select $n_{\Delta O}=n_{\Delta O}^{\prime }$	$\{\begin{array}{l}{n}_{\Delta H}=n_{\Delta H}^{\prime }if n_{\Delta H}^{\prime } \ge 2.3n_{\Delta O}^{\prime }\\ n_{\Delta O}=n_{\Delta O}^{\prime }if n_{\Delta H}<n_{\Delta O}^{\prime }\end{array}$

The molar flow rate of the hydrogen and the oxygen in the fuel cell is:

$$1<{\gamma }_{\mathrm{H}-\mathrm{O}}=n_{r\mathrm{H}}\Delta t/n_{r\mathrm{O}}\Delta t<1.25$$

(15)

• The actual stock of the hydrogen is calculated by:

  $$\{\begin{array}{l}{n}_{rH}=n_{H_{2}O\_H}+n_{\Delta H}-n_{mhg\_H}\\ n_{rO}=\frac{n_{rH}}{{\gamma }_{H-O}}\begin{array}{cc}& \end{array}\begin{array}{ccc}& & \end{array}\end{array}$$

  (16)
• The actual stock of the oxygen is calculated by:

  $$\{\begin{array}{l}{n}_{rO}=n_{H_2{O}_O}+n_{\Delta O}-n_{mh{g}_O}\\ n_{rH}={\gamma }_{H-O}{n}_{rO}\begin{array}{cc}& \end{array}\begin{array}{cc}& \end{array}\end{array}$$

  (17)

The partial pressures of hydrogen and oxygen $p_{fc\_H}$, $p_{fc\_o}$ are obtained:

$$\{\begin{array}{l}{p}_{fc\_H}=(\frac{n_{rH}}{N\Delta t}-\frac{d{p}_{fc\_H}}{dt}\cdot \frac{{10}^5{\mathrm{V}}_a}{\mathrm{RT}}-\frac{N{I}_{fc}}{2\mathrm{F}})/{10}^5{K}_{H_2}\\ p_{fc\_O}=(\frac{n_{rO}}{N\Delta t}-\frac{d{p}_{fc\_O}}{dt}\cdot \frac{{10}^5{\mathrm{V}}_{ca}}{\mathrm{RT}}-\frac{N{I}_{fc}}{4\mathrm{F}})/{10}^5{K}_{O_2}\end{array}$$

(18)

where N is the number of the fuel cell units, V_a and V_ca is anode and cathode volumes per unit hydrogen fuel cell respectively, T is the operating temperature of the fuel cell, $I_{fc}$ is the current of the fuel cell, $K_{H_2}$ and $K_{O_2}$ are the molar constant of hydrogen (anode) and oxygen (cathode) respectively.

Based on a fuel cell model, the power of the fuel cell $P_{fc}$ ($P_{fc}$ ≥ 0) can be obtained:

$$P_{fc}=\{\begin{array}{c}{P}_{fc\_\min },\hspace{1em}{\eta }_f(U_{fc}\cdot I_{fc})<P_{fc\_\min }\\ {\eta }_f(U_{fc}\cdot I_{fc}),P_{fc\_\min }\le {\eta }_f(U_{fc}\cdot I_{fc})\le P_{fc\_\max }\\ P_{fc\_\max },\hspace{1em}{\eta }_f(U_{fc}\cdot I_{fc})>P_{fc\_\max }\end{array}$$

(19)

where $U_{fc}$ is the output voltage of the fuel cell, ${\eta }_f$ is the power generation efficiency of the fuel cell, $P_{fc\_\max }$ and $P_{fc\_\min }$ are the upper and the lower limits of the fuel cell stack, respectively. Based on double electric layer phenomenon, the output voltage of the hydrogen fuel cell is calculated as follows [31,32,33]:

$$U_{fc}=N\cdot U_{cell}=N\cdot (E_{nernst}-U_{ohmic}-U_c)$$

(20)

where U_cell is the output voltage of a single fuel cell, E_nernst is the thermodynamic potential, U_ohmic is the ohmic polarization overvoltage, and U_c is the equivalent voltage.

The thermodynamic potential can be calculated by Equation (21):

$$E_{nernst}=1.229-8.5\times {10}^{-4}(\mathrm{T}-298.15)+4.3085\times {10}^{-5}\mathrm{T}\times (\ln p_{fc\_H}+0.5\ln p_{fc\_O})$$

(21)

The ohmic polarization overvoltage is obtained by:

$$U_{ohmic}=I_{fc}(Z_m+Z_c)=I_{fc}(\frac{181.6l[1+0.03\frac{I_{fc}}{A}+0.062{(\frac{\mathrm{T}}{303})}^2{(\frac{I_{fc}}{A})}^{2.5}]}{A(\phi -0.634-3\frac{I_{fc}}{A})\times \exp [4.18(\frac{\mathrm{T}-303}{\mathrm{T}})]}+Z_c)$$

(22)

where Z_m is the equivalent membrane impedance; Z_c is the impedance which represents the proton through the exchange membrane; ρ_M is the resistivity; l is the film thickness; A is the activation area of proton exchange membrane; and φ is the proton exchange membrane moisture content. The cell equivalent voltage can be given by:

$$\begin{array}{l}{U}_c=\{-B\times \ln (1-\frac{J}{J_{\max }})-[{\epsilon }_1+{\epsilon }_2\mathrm{T}+{\epsilon }_3\mathrm{T}\ln (\frac{p_{fc\_O}\times {10}^2}{5.08\times {10}^6\exp (-\frac{498}{\mathrm{T}})})\\ +{\epsilon }_4\mathrm{T}\ln (I_{fc})]\}(1-\frac{C}{I_{fc}}\times \frac{d{U}_c}{dt})\end{array}$$

(23)

where B is the equation coefficient; J is the active current density of the cell; J_max is the maximum current density; C is the equivalent capacitance; and ${\epsilon }_1$, ${\epsilon }_2$, ${\epsilon }_3$, ${\epsilon }_4$, are the empirical parameters of fuel cell.

(2) If ($P_{re}^{\left(2\right)}$ < 0) & (ESOC_S ≥ ESOC_Sa) or ($P_{re}^{\left(1\right)}$ < 0), ESOC_S level is operated within ideal range but the wind power cannot meet the demand. The hydrogen fuel cell discharges to assist wind power with flag1 = 1. n_rH and n_rO can be obtained by the P_fc and then n_∆H and n_∆O can be derived.

$$P_{fc}=\{\begin{array}{l}{P}_{fc\_min},\hspace{1em} \left|P_{re}^i\right|<P_{fc\_\min }\\ \left|P_{re}^i\right|,\hspace{1em} P_{fc\_\min }\le \left|P_{re}^i\right|\le P_{fc\_\max }\\ P_{fc\_\max },\hspace{1em} \left|P_{re}^i\right|>P_{fc\_\max }\end{array}i=1,2$$

(24)

The above equation can be simplified as:

$$n_{rH}=\{\begin{array}{c}{N}_{rH\_\min }\times \Delta t,P_{fc}<P_{fc\_\min }\\ \left|P_{re}^i\right|\times \frac{N_{rH\text{\_}\max }}{P_{fc\_}{}_{\max }}\times \Delta t,P_{fc}=\left|P_{re}^i\right|\\ N_{rH\_\max }\times \Delta t,P_{fc}>P_{fc\_\max }\end{array}i=1,2$$

(25)

where N_{rH_min} is the flow rate of the hydrogen when the fuel cell operates at minimum power output:

$$n_{rO}=n_{rH}/1.2$$

(26)

(3) If ($P_{re}^{\left(2\right)}$ < 0) & (ESOC_S < ESOC_Sa), or $P_{re}^{\left(2\right)}$ ≥ 0 or $P_{re}^{\left(3\right)}$ ≥ 0, the hydrogen fuel cell suspends with flag1 = 0.

Let $P_{fc}=0$, $n_{rH}=n_{rO}=0$, then $n_{\Delta H}=n_{mhg\text{\_}H}-n_{H_{2}O\_H}$, $n_{\Delta O}=n_{mhg\_O}-n_{H_{2}O\_O}$.

According to the above control rules, the HESS pressure p_Hre is obtained:

$$\{\begin{array}{l}{p}_{Hre}=p_{H\text{\_}0}+\Delta p_{H\text{\_}1}+\Delta p_{H\text{\_}2}-\Delta p_{H\text{\_}3}-\Delta p_{H\text{\_}4}\\ \mathrm{s}.\mathrm{t}.\{\begin{array}{l}\Delta p_{H\text{\_}1}=n_{H_2\mathrm{O}\text{\_}H}\Delta t{\mathrm{RT}}_H/{\mathrm{V}}_{Hcap}\\ \Delta p_{H\text{\_}2}={10}^5{k}^{\prime }{K}_{H_2}{p}_{fc\_H}\Delta t{\mathrm{RT}}_H/{\mathrm{V}}_{Hcap}\\ \Delta p_{H\text{\_}3}=n_{mhg}\Delta t{\mathrm{RT}}_H/{\mathrm{V}}_{Hcap}\\ \Delta p_{H\text{\_}4}=n_{rH}\Delta t{\mathrm{RT}}_H/{\mathrm{V}}_{Hcap}\end{array}\end{array}$$

(27)

where p_{H_0} is the initial pressure of the hydrogen tank; ∆p_{H_1} is the pressure increment of the hydrogen caused by water electrolysis; ∆p_{H_2} is the pressure increment of the hydrogen caused by incomplete consumption from the fuel cells. ∆p_{H_3} is the pressure decrement of the hydrogen caused by methanol production. ∆p_{H_4} is the pressure decrement of the hydrogen caused by the fuel cell discharging. k’ is the hydrogen recovery rate.

The pressure of the oxygen tank p_Ore is calculated by:

$$p_{Ore}=p_{O\text{\_}0}+\frac{(n_{H_{2}O\_O}+{10}^5{k}^{\prime }{K}_{O_2}{p}_{fc\_O}\Delta t-n_{mhg}-n_{r\mathrm{O}}){\mathrm{RT}}_O}{{\mathrm{V}}_{Ocap}}$$

(28)

where p_{O_0} is the initial pressure of the oxygen tank.

2.4. Overall Control Scheme

This study is focused on the optimal operation of the hybrid system. When the cluster power is required by the cluster control center, the power from the hybrid system is sent to the grid after the local demand is satisfied. In order to communicate with the cluster control center, a specific indicator “flag2” is used.

By changing flag2, the operation states and the request of the local hybrid system are recorded. The specific actions are as follows:

• If P_s + P_fc < P_load + P_jh, flag2 = −1, the local system does not satisfy with the grid plan and the local system requests the cluster control center to provide power assistance;
• If P_s + P_fc = P_load + P_jh, flag2 = 0, the local system operates in an ideal state and the established target is realised;
• If P_s + P_fc > P_load + P_jh, flag2 = 1, the local system requests assistance from cluster control center and the more power from the local system is sent to the grid.

In order to prevent the amounts of hydrogen and oxygen from reaching their tank limits, an additional control action is developed, as shown in Figure 5.

Figure 5. The extreme cases of hydrogen energy storage system operation.

• As shown in Figure 5a,c, when ESOC_H or ESOC_O is lower than ESOC_{H_min} or ESOC_{O_min}, the hybrid system produces the hydrogen/oxygen in maximum and consumes the hydrogen/oxygen in minimum. ∆t_a should select the smaller one between $\Delta t_{aH}$ and $\Delta t_{aO}$:

  $$\Delta t_a=\{\begin{array}{l}\min (\Delta t_{aH},\Delta t_{aO})\\ s.t.\{\begin{array}{l}\Delta t_{aH}=\frac{(ESO{C}_{H\_\max }-ESO{C}_{H\_\min })p_{Hcap}{\mathrm{V}}_{Hcap}}{(4N_{mhg}-N_{mhg}){\mathrm{RT}}_H}\\ \Delta t_{aO}=\frac{(ESO{C}_{O\_\max }-ESO{C}_{O\_\min })p_{Ocap}{\mathrm{V}}_{Ocap}}{(2N_{mhg}-N_{mhg}){\mathrm{RT}}_O}\end{array}\end{array}$$

  (29)
• As shown in Figure 5b,d, when ESOC_H or ESOC_O is over than ESOC_{H_max} or ESOC_{O_max}, the hybrid system produces the hydrogen/oxygen in minimum and consumes hydrogen/oxygen in maximum. ∆t_b should select the smaller one between $\Delta t_{bH}$ and $\Delta t_{bO}$:

  $$\Delta t_b=\{\begin{array}{l}\min (\Delta t_{bH},\Delta t_{bO})\\ s.t.\{\begin{array}{l}\Delta t_{bH}=\frac{(ESO{C}_{H\_\max }-ESO{C}_{H\_\min })p_{Hcap}{\mathrm{V}}_{Hcap}}{(N_{mhg}+N_{rH\_\max }){\mathrm{RT}}_H}\\ \Delta t_{bO}=\frac{(ESO{C}_{O\_\max }-ESO{C}_{O\_\min })p_{Ocap}{\mathrm{V}}_{Ocap}}{(N_{mhg}+N_{rH\_\max }/g_{H-O}){\mathrm{RT}}_O}\end{array}\end{array}$$

  (30)

Therefore, the time interval ∆t is controlled to be:

$$\Delta t<\min (\Delta t_a, \Delta t_b)$$

(31)

3. Simulation Results

The simulation of a local hybrid system with 10 MW wind power has been carried out by using MATLAB/Simulink. The key parameters of the system are shown in Table 4.

Table 4. Key parameters of the hybrid system.

Parameter	Value	Parameter	Value
Ue	2 V	A	50 cm2
ηe	80%	$\phi$	14
R	8.3145 J/mol·K	C	3 F
VHcap	60 m3	${\epsilon }_1$	−0.9514
VOcap	60 m3	${\epsilon }_2$	3.12 × 10−3
$p_{Hcap}$	5 × 106 Pa	${\epsilon }_3$	7.4 × 10−5
$p_{Ocap}$	5 × 106 Pa	${\epsilon }_4$	−1.87 × 10−4
$p_{H\_0}$	4.499 × 106 Pa	B	0.016
$p_{O\_0}$	4.499 × 106 Pa	Jmax	1.2 A/cm2
TH	298 K	ηf	90%
TO	298 K	Ifc	25 A
$K_{H_2}$	6.781 × 10−2 mol/s·atm	Va	0.005 m3
$K_{O_2}$	6.781 × 10−2 mol/s·atm	Vca	0.01 m3
k′	0.9	Pfc_max	0.2 MW
N	400	Pfc_min	2 × 10−4 MW
T	350 K	NrH_max	27,140 mol/s
l	5.1 × 10−3 cm	$N_{rH\text{\_}\min }$	1.357 mol/s

In the simulation, ESOC_Sa is set 0.31. P_mhg and N_mhg are set 2.48 MW and 5.134 mol/s respectively. According to Equations (28) and (29), ∆t is less than 3.75. Therefore let ∆t = 0.5 s. The input and the output power curves are shown in Figure 6 and Figure 7, respectively. The wind power data are from a real 50 MW wind over a 15-h duration. In order to validate the proposed models, the data are scaled down to fit the 10 MW wind turbine model and the time duration is reduced from 15 min to 1 s. ESOC_S exceed the upper limit (0.9) at 11 s as shown in Figure 7, the fuel cell discharges and the ESOC_S reduces. After a control period, ESOC_S restores normal. From 26 s to 27.5 s and from 31.5 s to 34.5 s, the ESOC_S is in the normal range and the storage state is normal. The fuel cells discharge to assist wind power integration, and ensure the output power of the hybrid system to meet the tied-grid demand.

Figure 6. Output power, load and scheduled power curves.

Figure 7. The wind power and the fuel cell power.

Therefore, actual tied-grid power and tied-grid demand curves of the hybrid system are shown as Figure 8.

Figure 8. Tied-grid power and overall operation status.

It can be seen from Figure 8 that when actual tied-grid power of the hybrid system does not meet the tied-grid demand, that is P_s + P_fc < P_load + P_jh, flag2 is set −1 and the hybrid system requests the cluster center for assistance. Otherwise, flag2 is set 1, the local hybrid system power is excess. If the system power equates the tied-grid demand, the flag2 is set 0. The control objective is achieved. In the above process, the states of the hydrogen/oxygen tanks and HESS are shown in Figure 8, Figure 9, Figure 10 and Figure 11.

Figure 9. The ESOC of the hydrogen tank, oxygen tank and HESS.

Figure 10. The ESOC from 0 s to 26 s.

Figure 11. The ESOC from 26 s to 35 s.

It can be seen from Figure 9 and Figure 10 that the ESOC_S is in the normal range at the beginning. $P_{H_{2}O}$ equates 2P_mhg from 0 s to 4 s and from 6 s to 11 s. The ESOC_H and the ESOC_S rise slowly and the ESOC_O remains unchanged. From 4 s to 6 s, from 11.5 s to 16 s and from 17.5 s to 23 s, $P_{mhg}<P_{H_{2}O}<2P_{mhg}$. The ESOC_H and the ESOC_S rise slowly and the ESOC_O decreases slowly. At 11 s, ESOC_S exceeds the upper limit, and the control priority changes. The fuel cells start, and ESOC_H, ESOC_O and ESOC_S drop rapidly. The ESOC_S restores to the normal range. From 23 s to 26 s, $P_{H_{2}O}$ < P_mhg. The ESOC_H, ESOC_O and ESOC_S decrease slowly.

It can be seen from Figure 7 that $P_{H_{2}O}$ drops rapidly since 26 s. From 26 s to 36 s, $P_{H_{2}O}$ is less than P_mhg and even reduces to zero at 31 s. From 26 s to 27.5 s and from 31 s to 34.5 s, the fuel cells discharge, and the ESOC_H, ESOC_O and ESOC_S decrease rapidly as can be seen in Figure 11. From 27.5 s to 31.5 s, the fuel cells suspend and the hydrogen produced by water electrolysis is less than the hydrogen used for coal chemical process. The ESOC_H, ESOC_O and ESOC_S decrease slowly. At 34.5 s, ESOC_S < ESOC_Sa and the fuel cells suspend. The downward trend of the ESOC_H, ESOC_O and ESOC_S has been curbed.

It can be seen from Figure 7 and Figure 12 that ESOC_{S_min} < ESOC_S < ESOC_Sa between 35 s and 60 s while the fuel cells suspend. From 35 s to 50 s, $P_{H_{2}O}$ = 0 and the hydrogen/oxygen for the coal chemical process are provided by the tanks. ESOC_S decreases slowly. From 50 s onwards, $P_{H_{2}O}$ rises slowly. However, it does not reach 2P_mhg until 60 s. Therefore, ESOC_S is seen decreasing in this period.

Figure 12. The ESOC from 35 s to 60 s.

In Figure 13, when the hydrogen for the methanol production is zero, ESOC_S decreases 0.0004 within 15 s. It is at 1 s that ESOC_S decreases from ESOCs_a to ESOC_{S_min} under unchanged condition. Therefore, let:

$$p_{H\text{\_}0}=1268049.26{\mathrm{P}}_a$$

(32)

and:

$$p_{O\text{\_}0}=732049.26{\mathrm{P}}_a$$

(33)

Figure 13. The power and the flag bit curve beyond lower limit.

The simulations when ESOC_S below the low limit is carried out based on this model. The hydrogen tank and the ESOC of the HESS are shown in Figure 14 and Figure 15. In Figure 14 and Figure 15, the ESOC_S reach the lower limit and the control priority changes. The wind power is used for the water electrolysis at 1 s. The ESOC_S recovers to the normal range at 3 s. After that, the power for the water electrolysis increases and maintains 2P_mhg until 5.5 s. The ESOC_H, ESOC_O and ESOC_S increase slowly.

Figure 14. The curve of the ESOCs below the low limit.

Figure 15. The curve of the ESOC_H and ESOC_O below the low limit.

4. Conclusions

This paper has presented a new hybrid system involving wind turbines, hydrogen energy storage, water electrolyser, and fuel cells. The novelty lies in the coordinated control scheme to maximize the utilisation of wind power with a constant methanol output whilst still reducing CO₂ emissions. All the symbols used in the paper can refer to Table A1 in Appendix A. The main contributions of the study can be concluded as follows:

(1)

This work takes advantage of wind power for electricity generation and for energy storage. In addition, coal-based energy systems for methanol production in a cleaner manner. This is critically important for China as well as many coal-dependent economies.

(2)

It integrates some interdisciplinary techniques into a multi-functional dynamic system to effectively manage various energy sources to enhance stable power supply stability, increase energy efficiency in utilization, and reduce CO₂ emissions.

(3)

It proposes a concept prototype and then implements the structured system in a simulation environment, which significantly reduces the real test cost.

(4)

The simulation results have confirmed the technical feasibility of the proposed system. It paves the way for next stage progression in small scale real tests and future commercialization of the technology.

(5)

Because of the optimal design and control of the hybrid system, energy efficiency and cost efficiency will be improved. This has a significant economic implications. Moreover, the reduction in CO₂ emissions will have an additional benefit from Carbon Trading Scheme in China.

As this is just a theoretical study in pioneering stage in China, there are several pertinent aspects need to be fully investigated before real system implementation and applications. These are:

(1)

Development of a full-scale simulation with hardware-in-loop real-time simulator for feasibility investigation.

(2)

Development of a full scale demonstration experimental setup of the system.

(3)

Conduction economic analysis, costs and gains, energy trading and carbon trading.

(4)

Carrying out a study on other social, environmental, legal impacts to minimize the uptake of the proposed technology.