Optimal Design of an Off-Grid Wind–Solar Hydrogen Storage for Green Methanol Synthesis System Considering Multi-Factor Coordination

Abstract

As the energy and power sector transitions toward clean and low-carbon development, the installed capacity of renewable energy sources such as wind and photovoltaic power has been rapidly increasing. Wind–solar hydrogen production via water electrolysis can enhance renewable energy utilization and enable the supply of green hydrogen. Meanwhile, the $H_2/C{O}_2$ molar ratio in the syngas produced by conventional biomass gasification generally cannot directly meet the 2:1 stoichiometric requirement for methanol synthesis. To address this issue, this paper proposes an off-grid coordinated system integrating wind–solar hydrogen production and biomass gasification for methanol synthesis. The system incorporates multi-operating-condition constraints of electrolyzers, coordinated regulation between electrochemical energy storage and hydrogen storage, and coordinated matching between biomass gasification and the water–gas shift reaction. Based on the system energy and material balance, a mixed-integer linear programming (MILP) model is formulated with the objective of minimizing the annualized total cost and is solved using the Gurobi solver in the MATLAB environment. To highlight the roles of HES and the WGS reaction, four comparative scenarios are designed for validation. The results show that the system with an annual methanol production capacity of 100,000 tons achieves an annualized total cost of 318 million CNY, with a wind–solar utilization rate of 98.86%. The system is configured with 12 electrolyzers of 5 MW each. The biomass consumption per ton of methanol is 3.06, and the $C{O}_2$ emissions per ton of methanol are 2.37. Finally, a sensitivity analysis of the levelized methanol cost (LCOM) was conducted, providing guidance for cost reduction in green methanol production.

1. Introduction

1.1. Background

The global energy system is rapidly decarbonizing. The share of renewable energy is increasing. Green hydrogen is becoming an important low-carbon energy, especially for long-timescale energy storage and scheduling. Existing studies have reviewed hydrogen storage, water electrolysis, and renewable-driven hydrogen production, showing their potential in future low-carbon energy systems [1,2,3]. However, the performance of green hydrogen systems is strongly affected by renewable power fluctuations, storage pathways, transportation conditions, and cost [4,5]. Environmental and economic benefits also vary across regions. Resource, power structure, and local natural conditions can significantly influence system evaluation and planning results [6,7]. Green methanol has attracted increasing attention because it can reduce carbon emissions and serve as an energy carrier. Recent studies show that green methanol can provide substantial emission reduction benefits, but its cost remains sensitive to scale effects, hydrogen price, feedstock conditions, and system configuration [8,9,10,11]. Off-grid renewable hydrogen systems coupled with methanol synthesis further indicate that hydrogen production cost is a key factor affecting green methanol economics [12]. In addition, coordinated operation of electrochemical energy storage and hydrogen storage can improve wind–solar utilization and reduce the levelized cost of methanol, demonstrating the feasibility of off-grid wind–solar hydrogen-based methanol synthesis [13].

1.2. Related Work

Existing studies show parallel progress in model optimization and system planning. At the technological level of water electrolysis, existing studies have reviewed AEL and PEM electrolyzer [14,15,16]. These studies show that AEL is mature and cost-effective for large-scale hydrogen production, while PEM offers advantages in renewable energy integration and dynamic response. However, efficiency improvement, material stability, catalyst cost, and degradation control remain key challenges for large-scale application. These factors directly affect system-level capacity planning and operation optimization.

At the levels of system planning and operation, research has expanded from single energy storage configuration to multi-storage coupling. Hybrid configurations of HS and EES can reduce total cost under uncertainty. They can also improve market participation capability. The two types of storage show functional complementarity in different ramping services [17]. An off-grid wind–solar–PEMEL capacity optimization study based on Homer Pro showed that electrolyzer capacity has a decisive impact on LCOH. It also indicated that PEM electrolyzer cost strongly affects system economics [18]. To address wind–solar uncertainty, a multi-timescale coordinated operation strategy for joint AEL–PEMEL hydrogen production has been proposed [19]. Reference [20] proposes a coordinated strategy that combines electrolyzer mode allocation with day-ahead planning of energy storage and applies NSGA-II for capacity optimization. The results show that this strategy can significantly reduce the unit hydrogen production cost and the wind–solar curtailment rate. In the field of methanol synthesis, studies on dynamic modeling and control strategies for offshore green methanol synthesis emphasize the importance of controlling the $H_2/C{O}_2$ feed ratio. This control helps maintain high conversion efficiency. It also supports stable operation under fluctuating feed conditions. These findings provide effective evidence for the stable operation of methanol processes driven by fluctuating energy sources [21]. Reference [22] analyzes a CCU process that integrates water electrolysis, electrochemical reverse water–gas shift (E-RWGS), and methanol synthesis. The study further points out that E-RWGS can avoid $C{O}_2$ emissions associated with conventional methods. Reference [23] investigates the coupling of biomass, hydrogen, and methanol. The results show that this pathway can significantly reduce carbon intensity. It also demonstrates system value in addressing wind–solar intermittency. The study proposes a pathway for stable methanol synthesis.

Recent studies have further expanded the research scope from individual processes to integrated systems. Reference [24] evaluated green hydrogen systems in five locations in Saudi Arabia. The systems included PV panels, wind turbines, batteries, and electrolyzers. The results show that location conditions and local economic factors have a clear impact on the net present cost and hydrogen cost. Reference [25] proposed a multigeneration system that combines biomass gasification, water electrolysis, carbon capture, and methanol synthesis. The system achieved high energy and exergy efficiencies and low $C{O}_2$ emissions, indicating the potential of using green hydrogen together with biomass-based carbon sources. Reference [26] showed that electrolytic hydrogen can improve biomass conversion to fuels because gas produced from biomass usually lacks sufficient hydrogen. However, matching variable renewable electricity with gasifier operation remains a technical challenge. Reference [27] compared PEM electrolysis, SOEC electrolysis, and biomass gasification for hydrogen-assisted methane and methanol synthesis. The results show that the hydrogen production route affects hydrogen purity, energy consumption, water demand, and its suitability for methanol synthesis.

1.3. Research Objectives

Although existing studies have made considerable progress in water electrolysis for hydrogen production, energy storage configuration and biomass gasification for methanol synthesis, several gaps remain. Most studies focus on single-subsystem optimization or local process optimization. Few studies consider the coordinated optimization of multiple subsystems. In addition, many existing studies use short-term optimization horizons. This makes it difficult to fully reflect on the cross-day regulation advantage of hydrogen storage. Therefore, based on previous studies, this paper proposes an off-grid green methanol synthesis optimization method with multi-device and multi-factor coordination.

This paper focuses on the multi-factor coordinated operation of wind–solar hydrogen production, hybrid energy storage (HES), biomass gasification, and the water–gas shift (WGS) reaction. The objective is to meet the same demand with smaller installed capacities and lower total cost. This paper also develops refined models for various devices. These models aim to represent engineering characteristics as accurately as possible.

The main forms of multi-factor coordination considered in this paper can be classified into the following three categories:

(1)

The coupling of wind power generation and photovoltaic power generation;

(2)

The coupling of electrochemical energy storage and hydrogen storage;

(3)

The coupling of biomass gasification, WGS reaction, and hydrogen production via water electrolysis.

2. System Description and Component Modeling

2.1. System Architecture

The Off-Grid Wind–Solar Hydrogen Storage for Green Methanol Synthesis System (hereafter referred to as the PHM system) is based on an energy conversion chain of wind–solar power generation, hydrogen production via water electrolysis, HES, biomass-based hydrogen production, and methanol synthesis. The system achieves flexible hydrogen production and methanol synthesis under fluctuating wind–solar conditions through the dual coupling of electrical energy and hydrogen energy. The PHM system mainly consists of a renewable power generation unit, a water electrolysis hydrogen production unit, a HES unit, a biomass hydrogen production unit, and a methanol synthesis unit. The units are connected through the conversion of electrical energy, hydrogen energy, and carbon energy. They jointly support the stable operation of the overall system. The structure of the PHM system is shown in Figure 1. The red arrows represent electricity flow. The black arrows represent hydrogen flow. The yellow arrows represent carbon flow.

The variables, parameters, and index used throughout this study are summarized in

Table 1. List of variables and indices.

Electrical Decision Variables
$P_{s,i,t}^{AEL}$	Standby power consumption of AEL $i$ at time $t$	$F_{i,t}^{AEL}$	1 if AEL $i$ is in normal mode at time $t$ otherwise, 0
$P_{f,i,t}^{AEL}$	Hydrogen production power of AEL $i$ at time $t$	${\mathrm{S}}_{i,t}^{AEL}$	1 if AEL $i$ is in standby mode at time $t$; otherwise, 0
$P_t^{Elec}$	Power consumption of AELs at time t	${\mathrm{D}}_{i,t}^{AEL}$	1 if AEL $i$ is in shutdown mode at time $t$; otherwise 0
$P_{ch,t}^{Ess}$, $P_{dis,t}^{Ess}$	Charging and discharging power of the battery at time $t$	$W_{i,t}^{AEL}$	Start-up state of AEL $i$ at time $t$
$P_t^{Fc}$	Power output of the fuel cell at time $t$	$I_{i,t}^{AEL}$	1 if AEL $i$ is enabled at time $t$
$P_t^{Comp}$	Power consumption of the compressor at time $t$	${\mathrm{Y}}_{i,t}^{AEL}$	On states of AEL $i$ at time $t$
$P_t^{Gas}$	Power consumption of gasification unit at time $t$	${\mathrm{Z}}_{i,t}^{AEL}$	Off states of AEL $i$ at time $t$
$P_t^{Syn}$	Power consumption of methanol synthesis at time $t$	$U_t^{\mathrm{ch}}$, $U_t^{dis}$	Charging and discharging states at time $t$
$P_r^{AE}$	Rated power of a single AEL	$E_t^{\mathrm{Ess}}$	Energy stored in the battery at time $t$
$A_j$	Rated capacity of device $j$	$A^{Ess}$	Installed energy capacity of the battery
$A^{AEL}$	Installed capacity of AELs	$A^{Pss}$	Installed capacity of the Pss
$A^{Fc}$	Installed capacity of fuel cell	$A^{Gas}$	Installed capacity of gasification unit
$A^{Hst}$	Installed capacity of the storage tank	$A^{Syn}$	Installed capacity of the methanol synthesis unit
Other Decision Variables
$v_{C{O}_2,t}^{Aban}$	$C{O}_2$ emission flow rate from biomass unit at time $t$	$v_{{\mathrm{H}}_2,t}^{\mathrm{Gas}}$	$H_2$ flow rates from biomass gasification at time $t$
$v_{{\mathrm{CO}}_2,t}^{\mathrm{Gas}}$	$C{O}_2$ flow rates from biomass gasification at time $t$	$v_t^{AEL}$	Total hydrogen production at time $t$
$v_{H_2,t}^{\mathrm{Syn}}$	Hydrogen required for methanol synthesis at time $t$	$v_{H_2,t}^{Hst}$	External hydrogen supply rate at time $t$
$v_{\mathrm{CO},\mathrm{t}}^{\mathrm{Syn}}$	$CO$ flow rates to methanol synthesis at time $t$	$v_t^{Fc}$	Hydrogen consumption rate of the fuel cell at time $t$
$v_{\mathrm{CO},\mathrm{t}}^{\mathrm{Gas}}$	$CO$ flow rates from biomass gasification at time $t$	$H_t^{\mathrm{Hst}}$	Hydrogen mass in the storage tank at time $t$
$v_{\mathrm{CO},\mathrm{t}}^{\mathrm{Wgs}}$	$CO$ flow rates to WGS at time $t$	$m_{\mathrm{MeOH},\mathrm{t}}$	Methanol synthesis rate at time $t$
$v_{H_2,t}^{Wgs}$	$H_2$ flow rate generated by WGS at time $t$	$m_t^{Gas}$	Biomass feed rate at time $t$
Parameters
$C$	Annual total cost of the PHM system	$M$	Set of system components
$C_{inv}$	Annual investment cost of the PHM system	$r$	Discount rate
$C_{op}$	Annual operating cost of the PHM system	$N$	Planning horizon
$C_{bio}$	Biomass feedstock cost	$CEA$	Carbon emission quota
$C_{c{o}_2}$	Carbon emission cost from WGS process	$LCoM$	Levelized cost of methanol
$C_{aban}$	Wind–solar curtailment penalty cost	${\eta }^{AEL}$	Hydrogen production efficiency of AEL
$c_{\mathrm{bio}}$	Unit cost of biomass feedstock	${\eta }_{\mathrm{ch}}$, ${\eta }_{\mathrm{dis}}$	Charging and discharging efficiencies of the battery
$c_{c{o}_2}$	Unit carbon emission cost	${\eta }^{Fc}$	Efficiency of the fuel cell
$c_{ab}$	Unit wind–solar curtailment cost	${\eta }^{Syn}$	Methanol synthesis efficiency
$c_j$	Unit investment cost of device $j$	${\alpha }^{Comp}$	Operating coefficient of the compressor
$m_j$	Annual unit O&M cost of device $j$	$H_{HV}$	Higher heating value of hydrogen
$w_{h,t}$	Weight of representative hour $t$
Index
$i$	Index of AEL unit	$j$	Index of device $j$
$t$	Time index	$T$	Simulation horizon

.

The wind–solar power generation unit is the sole electricity source of the PHM system. Its green electricity can directly supply the load of the methanol synthesis unit. It can also drive the operation of the water electrolysis hydrogen production unit. The hydrogen production unit adopts alkaline electrolyzers (AELs) due to their low cost and technological maturity. AELs convert intermittent electricity into stable hydrogen output.

The HES unit consists of electrochemical energy storage (EES) and hydrogen storage (HS). EES includes battery energy storage. HS includes hydrogen storage tanks and fuel cells. A compressor is installed between the water electrolysis unit and the HES unit for pressure regulation. Hydrogen produced by water electrolysis is first compressed to meet the pressure requirements of the hydrogen storage tank. The compressed hydrogen is stored in the tank. It is used to buffer hydrogen supply under wind–solar fluctuations. It also provides a long-term hydrogen source for the methanol synthesis unit. When wind–solar power is insufficient for a prolonged period, the system must ensure the safe operation of the methanol synthesis unit. At this time, hydrogen stored in the tank can be converted back into electricity by the fuel cell. This process compensates for power shortages and satisfies safety constraints.

The biomass hydrogen production unit provides a stable source of carbon monoxide for methanol synthesis. Carbon monoxide produced by biomass gasification can directly participate in methanol synthesis with hydrogen. A WGS reaction unit is also configured to regulate the carbon-to-hydrogen ratio in methanol synthesis. The methanol synthesis unit consumes electricity, carbon, and hydrogen to produce green methanol.

2.2. Water Electrolysis Hydrogen Production Unit

The water electrolysis hydrogen production unit is the core component of the PHM system. It converts intermittent wind–solar electricity into high-energy-density hydrogen. Its operating state directly determines hydrogen production efficiency, hydrogen storage level, and external hydrogen supply capability. This section explains the operating mechanism of the hydrogen production unit from the perspective of operational scheduling. It provides the basis for the subsequent capacity configuration and scheduling model.

This section establishes a multi-operating-condition model for AELs. The start-up and shutdown characteristics of AELs are modeled in detail. The model can realistically reflect AEL behavior under wind–solar fluctuations. This modeling approach improves the accuracy of hydrogen production process simulation. It also provides more precise physical constraints for subsequent optimization models.

As shown in the state transition diagram of the AEL in Figure 2, the operating modes of the AEL include normal operation mode, standby mode, and shutdown mode. The AEL cannot switch directly from the shutdown mode to the normal operation mode. It must pass through the standby mode for 1 h.

The AEL is defined with three operating modes: normal operation, standby operation, and shutdown, denoted as $F_{i,t}^{AEL}$, ${\mathrm{S}}_{i,t}^{AEL}$, and ${\mathrm{D}}_{i,t}^{AEL}$, respectively. The start-up state is defined as the sum of the normal and standby modes:

$$W_{i,t}^{AEL}=F_{i,t}^{AEL}+{\mathrm{S}}_{i,t}^{AEL}$$

(1)

Binary variable $I_{i,t}^{AEL}$ indicates whether the AEL is enabled, and ${\mathrm{Y}}_{i,t}^{AEL}$/${\mathrm{Z}}_{i,t}^{AEL}$ denotes the start-up action of the AELs.

For the AEL, electricity is consumed in both normal and standby modes. However, hydrogen is only produced in the normal operation mode. Therefore, the electricity consumption power and hydrogen production power are distinguished and modeled as follows:

$$\left\{\begin{array}{l}0.45\cdot F_{i,t}^{AEL}\cdot P_r^{AEL}\le P_{f,i,t}^{AEL}\le 1.15\cdot F_{i,t}^{AEL}\cdot P_r^{AEL}\\ P_{s,i,t}^{AEL}=0.15\cdot S_{i,t}^{AEL}\cdot P_r^{AEL}\end{array}\right.$$

(2)

The hydrogen production rate of the AELs at time $t$ is given by:

$$v_t^{AEL}={\displaystyle \sum _i^{N^{AEL}}\frac{{\eta }^{AEL}\cdot P_{f,i,t}^{AEL}}{H_{HV}\cdot \Delta t}}$$

(3)

$$A^{AEL}=N^{AEL}\cdot P_r^{AEL}$$

(4)

Equation (4) represents the total installed capacity of the AELs.

2.3. HES Unit

Due to the fluctuations of wind–solar output, a single energy storage technology cannot simultaneously satisfy short-term power balancing and long-term energy balancing. Therefore, this study proposes a HES structure. By exploiting the complementary characteristics of different technologies, coordinated optimization is achieved across the time and energy domains. This structure provides stable support for subsequent capacity configuration and operational scheduling.

2.3.1. EES

EES is represented by batteries. It features fast response, high regulation accuracy, and high energy conversion efficiency. It is mainly used for power balancing on the minute-to-hour timescale. The battery model used in this study is described as follows.

$$E_t^{\mathrm{Ess}}=E_{t-1}^{\mathrm{Ess}}+{\eta }_{\mathrm{ch}}{P}_{ch,t}^{Ess}\cdot \Delta t-{\displaystyle \frac{P_{dis,t}^{Ess}\cdot \Delta t}{{\eta }_{\mathrm{dis}}}}$$

(5)

$$0.1A^{Ess}\le E_t^{\mathrm{Ess}}\le A^{Ess}$$

(6)

Equation (5) represents the recursive relationship of the internal energy of the battery between two consecutive time steps. Equation (6) enforces the $SOC$ limits of the battery to protect it from deep discharge.

2.3.2. HS

The HS unit consists of a compressor, a hydrogen storage tank, and a fuel cell. The compressor collects the hydrogen produced by the AELs and compresses it before injection into the storage tank. The storage tank manages the hydrogen flow, including hydrogen storage, hydrogen supply to the methanol synthesis unit, and hydrogen discharge for power generation by the fuel cell. The detailed model is described as follows.

$$P_t^{Comp}={\alpha }^{Comp}\cdot {\displaystyle \sum _i^{N^{AEL}}{P}_{f,i,t}^{AEL}}$$

(7)

$$H_t^{\mathrm{Hst}}=H_{t-1}^{\mathrm{Hst}}+v_t^{\mathrm{AEL}}\cdot \Delta t-v_t^{\mathrm{Fc}}\cdot \Delta t-v_{H_2,t}^{Hst}\cdot \Delta t$$

(8)

$$P_t^{Fc}={\eta }^{Fc}\cdot v_t^{Fc}\cdot H_{HV}$$

(9)

Equation (7) provides a linear model for the power consumption of the compressor. Equation (8) describes the recursive relationship of the hydrogen amount in the storage tank between two consecutive time steps. It mainly accounts for hydrogen inflow from water electrolysis and hydrogen outflow for fuel cell power generation and methanol synthesis. Equation (9) represents the hydrogen-to-electricity conversion model of the fuel cell. It converts hydrogen consumption into electrical power based on the heating value of hydrogen.

2.4. Biomass Gasification Unit

The biomass unit is the only source of carbon in the entire system. It provides carbon monoxide required for methanol synthesis and also supplies hydrogen. The WGS reaction is used to regulate the carbon-to-hydrogen ratio in the system.

$$v_{\mathrm{CO},\mathrm{t}}^{\mathrm{Gas}}={\alpha }_{CO}{m}_t^{Gas}$$

(10)

$$v_{{\mathrm{H}}_2,t}^{\mathrm{Gas}}={\alpha }_{H_2}{m}_t^{Gas}$$

(11)

$$v_{{\mathrm{CO}}_2,t}^{\mathrm{Gas}}={\alpha }_{C{O}_2}{m}_t^{Gas}$$

(12)

Equations (10)–(12) calculate the flow rates of $CO$, $H_2$ and $C{O}_2$ produced by biomass gasification based on the carbon and hydrogen contents of the biomass feedstock.

$$v_{\mathrm{CO},\mathrm{t}}^{\mathrm{Gas}}=v_{\mathrm{CO},\mathrm{t}}^{\mathrm{Syn}}+v_{\mathrm{CO},\mathrm{t}}^{\mathrm{Wgs}}$$

(13)

Equation (13) ensures that the total amount of $CO$ allocated to methanol synthesis and the water–gas shift reaction equals the $CO$ produced by biomass gasification.

$$\mathrm{CO}+{\mathrm{H}}_2\mathrm{O}\to {\mathrm{H}}_2+{\mathrm{CO}}_2$$

(14)

$$0.9v_{CO,t}^{Wgs}=v_{C{O}_2,t}^{Wgs}=v_{H_2,t}^{Wgs}$$

(15)

$$v_{C{O}_2,t}^{Aban}=v_{{\mathrm{CO}}_2,t}^{\mathrm{Gas}}+v_{C{O}_2,t}^{Wgs}$$

(16)

Reaction (14) shows the chemical equation of the WGS reaction. Equation (15) is derived from the stoichiometric molar ratios of the chemical reaction. It ensures that the amount of $CO$ participating in the WGS reaction equals the amount of $H_2$ produced and is equal to the amount of $C{O}_2$ emitted. The loss of WGS is 0.1. Equation (16) indicates that the emitted $C{O}_2$ is generated from biomass gasification and the WGS reaction.

2.5. Methanol Synthesis Unit

The main reactants in the methanol synthesis unit are carbon monoxide and hydrogen. Carbon monoxide is entirely supplied by biomass gasification. Hydrogen is supplied by biomass gasification, the WGS reaction, and hydrogen discharged from the storage tank.

$$\mathrm{CO}+2{\mathrm{H}}_2\to {\mathrm{CH}}_3\mathrm{OH}$$

(17)

Reaction (17) presents the reaction equation of the methanol synthesis unit.

$$m_{\mathrm{MeOH},\mathrm{t}}=1.43\times {\eta }^{Syn}\cdot v_{\mathrm{CO},\mathrm{t}}^{\mathrm{Syn}}$$

(18)

$$MeOH={\displaystyle \sum _t^T{m}_{\mathrm{MeOH},\mathrm{t}}}$$

(19)

Equation (18) represents the methanol production rate, where 1.43 is the conversion coefficient used to convert the volumetric rate into the mass rate. Equation (19) represents the annual methanol production.

$$v_{H_2,t}^{\mathrm{Syn}}=2v_{\mathrm{CO},\mathrm{t}}^{\mathrm{Syn}}$$

(20)

$$v_{H_2,t}^{Hst}=v_{H_2,t}^{\mathrm{Syn}}-v_{{\mathrm{H}}_2,t}^{\mathrm{Gas}}-v_{H_2,t}^{\mathrm{Wgs}}$$

(21)

Equation (20) calculates the $H_2$ consumption based on the amount of $CO$ involved in the methanol synthesis reaction. Equation (21) gives the calculation of the $H_2$ to be supplied by the hydrogen storage tank.

$$P_t^{Gas}={\theta }^{Gas}\cdot m_t^{Gas}$$

(22)

$$P_t^{Syn}={\theta }^{Syn}\cdot m_{\mathrm{MeOH},\mathrm{t}}$$

(23)

Equations (22) and (23) represent the power consumption of the biomass gasification unit and the methanol synthesis unit, respectively.

3. Capacity Configuration Optimization of the PHM System

3.1. Objective Function

This study minimizes the annual investment cost, operation and maintenance cost, biomass feedstock cost, carbon emission cost, and wind–solar curtailment cost of the PHM system. Based on this objective, an optimization model for the off-grid wind–solar hydrogen-to-methanol system with multi-factor coordination is established. The objective function is formulated as follows.

$$\min C=C_{inv}+C_{op}+C_{bio}+C_{c{o}_2}+C_{aban}$$

(24)

Equation (24) defines the objective function of the PHM system optimization model, which aims to minimize the annual comprehensive cost.

$$C_{\mathrm{inv}}={\displaystyle \sum _{j\in M}\frac{r{(1+r)}^N}{{(1+r)}^N-1}}{c}_j{A}_j$$

(25)

$$C_{\mathrm{op}}={\displaystyle \sum _{j\in M}{m}_j{A}_j}$$

(26)

$$C_{\mathrm{bio}}=c_{\mathrm{bio}}{\displaystyle \sum _{t=1}^T{m}_t^{Gas}}$$

(27)

$$C_{c{o}_2}=c_{c{o}_2}\cdot \left({\displaystyle \sum _{t=1}^T{v}_{{\mathrm{CO}}_2,t}^{\mathrm{Aban}}-CEA}\right)$$

(28)

$$C_{aban}=c_{ab}{\displaystyle \sum _{t=1}^T{P}_t^{aban}}$$

(29)

Equation (25) presents the calculation of the annual investment cost, where the total life-cycle investment cost is converted into an annual value using the discount rate and the planning horizon. Equation (26) gives the calculation of the annual operation and maintenance cost, which is determined using fixed O&M cost coefficients.

The set $M$ includes wind–solar power generation units, AELs, batteries, fuel cells, hydrogen storage tanks, biomass gasification unit and the methanol synthesis unit.

Equation (27) calculates the biomass feedstock cost, which is obtained by multiplying the unit cost by the consumption. Equation (28) represents the carbon emission cost, which penalizes carbon emissions exceeding the emission quota. Equation (29) defines the wind–solar curtailment penalty cost.

3.2. Constraints

3.2.1. Multi-Operating-Mode Constraints of the AEL

The multi-operating-mode behavior of the AEL described above must satisfy the following constraints. Equation (30) below fully couples the operating-mode transitions and the start-up/shut-down behavior of the AEL.

$$\left\{\begin{array}{l}{F}_{i,t}^{AEL}{+\mathrm{S}}_{i,t}^{AEL}{+\mathrm{D}}_{i,t}^{AEL}=I_{i,t}^{AEL}\\ W_{i,t}^{AEL}=F_{i,t}^{AEL}+{\mathrm{S}}_{i,t}^{AEL}\\ {\mathrm{Y}}_{i,t}^{AEL}\le {\mathrm{S}}_{i,t}^{AEL}\\ W_{i,t}^{AEL}-W_{i,t-1}^{AEL}\le {\mathrm{Y}}_{i,t}^{AEL}\le 1-W_{i,t-1}^{AEL}\\ W_{i,t-1}^{AEL}-W_{i,t}^{AEL}\le {\mathrm{Z}}_{i,t}^{AEL}\le W_{i,t-1}^{AEL}\\ {\mathrm{Z}}_{i,t}^{AEL}\le 1-W_{i,t}^{AEL}\\ {\mathrm{Y}}_{i,t}^{AEL}+{\mathrm{Z}}_{i,t}^{AEL}\le 1\end{array}\right.$$

(30)

3.2.2. HES Constraints

(1)

Battery charging and discharging constraints

Equation (31) shows that the battery can only be in one operating state (charging or discharging) at each time step.

$$\left\{\begin{array}{l}0\le P_{ch,t}^{Ess}\le U_{ch,t}{A}^{Pss}\\ 0\le P_{dis,t}^{Ess}\le U_{dis,t}{A}^{Pss}\\ U_{ch,t}+U_{dis,t}\le 1\end{array}\right.$$

(31)

(2)

Fuel cell discharging constraints

$$\left\{\begin{array}{l}0\le P_t^{Fc}\le A^{Fc}\\ 0\le v_t^{Fc}\end{array}\right.$$

(32)

(3)

Hydrogen storage tank capacity constraints

$$0.1A^{Hst}\le H_t^{\mathrm{Hst}}\le A^{Hst}$$

(33)

3.2.3. Biomass Gasification Unit Constraints

$$P_t^{Gas}\le A^{Gas}$$

(34)

Equation (34) represents the capacity constraint of the biomass gasification unit.

3.2.4. Methanol Synthesis Unit Constraints

$$0.6A^{Syn}\le P_t^{Syn}\le A^{Syn}$$

(35)

$$-0.05A^{Syn}\le P_t^{Syn}-P_{t-1}^{Syn}\le 0.05A^{Syn}$$

(36)

Equation (35) requires the operating power of the methanol synthesis unit to vary only within 0.6 to 1.0 of its rated power. Equation (36) defines the ramping constraint of the methanol synthesis unit, which limits the power change to 5% per hour. Both constraints are safety constraints of the methanol synthesis unit and must be strictly satisfied [28].

3.2.5. Power Balance Constraints

The power balance constraint requires that the total power output on the generation side must equal the total power consumption on the load side. According to the system structure, at each time step, the wind–solar power output plus the discharging power of the battery and the fuel cell must equal the power consumption of the AELs and the compressor, the battery charging power, the curtailed power, and the power consumption of the methanol synthesis unit.

For the AEL, in addition to the power consumed in the normal operating mode, power is also consumed in the standby mode. Therefore, the standby power of the AELs is included in the power balance constraint. Equation (37) gives the calculation of the AELs’ power consumption. Equation (38) gives the power balance constraint.

$$P_t^{Elec}={\displaystyle \sum _i^{N^{AEL}}(P_{f,i,t}^{AEL}+P_{s,i,t}^{AEL}})$$

(37)

$$P_t^{Wind}+P_t^{Solar}+P_{dis,t}^{\mathrm{Ess}}+P_t^{Fc}=P_t^{Elec}+P_t^{Comp}+P_{ch,t}^{\mathrm{Ess}}+P_t^{Aban}+P_t^{Gas}+P_t^{Syn}$$

(38)

3.3. Solution Algorithm

The proposed model is a mixed-integer linear programming (MILP) model that considers both capacity configuration and operational scheduling.

The solution process is divided into two stages. In the first stage, capacity configuration is performed. The wind and solar output series are used as inputs to determine the installed capacities of wind and solar power, the number of AELs, the capacity of the methanol synthesis unit, the capacities of devices in the hybrid energy storage unit, and the biomass consumption. Based on these decisions, the annual investment cost and the biomass feedstock cost are calculated. In the second stage, operational simulation is conducted. Under the determined capacities, device models are established and operational constraints are applied to obtain feasible scheduling strategies. The annual operation and maintenance cost, carbon emission cost, and curtailment cost are then evaluated. The annual comprehensive cost is obtained by aggregating all cost components, and the solution is updated through iterative optimization. The model contains multiple integer variables and continuous variables and remains linear in formulation, thus constituting a MILP problem. The model is solved in MATLAB (version R2023b) using the YALMIP toolbox with the Gurobi solver.

Figure 3 shows the flowchart of the optimization algorithm for the proposed model.

4. Case Study and Analysis

4.1. Data Preparation

The wind and solar data used in this study are measured output data from a region in Northeast China, with a time resolution of 1 h and a total duration of 8760 h. The annual methanol production is required to be 100,000 tons. Figure 4 shows the per-unit wind and solar output over the entire year in the study area.

The study area has abundant wind and solar resources. The terrain is dominated by mountains and hills, and significant wind shortages mainly occur in summer. Solar output is relatively stable throughout the year but exhibits large day–night fluctuations. To fully capture the complementary characteristics of wind and solar power, the installed capacities of wind and solar are treated as decision variables in the model for capacity configuration.

To balance the temporal characteristics of wind and solar power output with the computational efficiency of the optimization model, the original 8760 h wind–solar data are reduced into typical scenarios in this paper. If the full-year hourly data are directly used for coordinated optimization, the model complexity will increase significantly, and the solution efficiency will decrease accordingly. Therefore, it is necessary to reduce the dimensionality of the annual data while preserving the original temporal characteristics and seasonal differences as much as possible.

Traditional K-means clustering may lead to the loss of temporal continuity in the annual data and cannot reflect the cross-seasonal storage advantage of hydrogen storage. In contrast, pure time-series clustering cannot account for the delayed start-up of hot standby operation in AELs. Therefore, this paper adopts a typical-day construction method based on “monthly stratification, intra-month clustering, and sequential concatenation.” First, the annual data are divided into 12 months, and the number of typical days is determined according to the number of days in each month. Second, Ward’s hierarchical clustering method is applied to cluster all daily output curves within each month. Taking the minimum increment of the within-cluster sum of squares as the criterion, the Ward method can improve the consistency of curve patterns within the same cluster. For each cluster, the real day with the shortest distance to the cluster center is selected as the representative typical day, and the number of original days contained in that cluster is taken as its weight to reflect the representativeness of the typical day over the year. Subsequently, the typical days selected from each month are arranged in chronological order and concatenated end to end to reconstruct a typical output sequence with a length of 744 h. Meanwhile, the number of original days represented by each typical day is recorded as its weight to reflect its statistical importance over the year.

In the subsequent optimization model, the 744 h typical sequence is used as the input time series for system operation constraints and energy balance, while the weights corresponding to each typical day are used to scale indicators such as operation and maintenance cost, curtailed energy, and carbon emissions to the annual level, thereby ensuring that the dimension-reduced results still retain annual statistical significance.

After applying the above clustering method, the original 365 days of data are reduced to 31 typical days, and the hourly data are reduced from 8760 h to 744 h.

Equation (39) describes the dimensionality reduction process.

$$\left\{\begin{array}{l}{j}_1,j_2,\dots ,j_{31}\to J_1,J_2,J_3\\ f_1,f_2,\dots ,f_{28}\to F_1,F_2\\ .....\\ d_1,d_2,\dots ,d_{31}\to D_1,D_2,D_3\end{array}\right.$$

(39)

Here, $j_1,j_2,\dots ,j_{31}$ denote the days of January, and $J_1,J_2,J_3$ denote the representative days of January after clustering; the same applies to other months. For months with 31 days, three representative days are selected, while for months with 30 days or fewer, two representative days are selected, resulting in a total of 31 representative days. Figure 5 shows the wind and solar output curves after clustering.

To fully account for the cross-day regulation capability of hydrogen storage in the HES system, constraints were applied to both the EES and HS units. The EES is required to operate in a daily cycle, returning to its initial state every 24 h. The HS calculates the net hydrogen change for each typical day, which is then weighted by the corresponding day’s coefficient. At the end of the 744 h horizon, the HS returns to its initial state.

The equipment data used in the case study are listed in

Table 2. System Configuration Parameters of the PHM System.

Cost Item			Value
Unit investment cost of wind power (CNY/kW)			4200
Unit investment cost of solar power (CNY/kW)			3500
Unit investment cost of PCS (CNY/kW)			500
Unit investment cost of battery capacity (CNY/kWh)			650
Unit investment cost of fuel cell (CNY/kW)			3000
Unit investment cost of AEL (CNY/kW)			2200
Unit investment cost of hydrogen storage tank (CNY/kg)			1500
Unit investment cost of the biomass gasification unit (CNY/kW)			4000
Unit investment cost of methanol synthesis unit (CNY/kW)			3500
Rated power of a single AEL (MW)			5
Parameter	Value	Parameter	Value
${\eta }^{AEL}$	0.62	$r$	0.05
${\eta }_{\mathrm{ch}}$,${\eta }_{\mathrm{dis}}$	0.93/0.93	$N$	15 years
${\eta }_{FC}$	0.6	$H_{HV}$	3.54 kWh/Nm3
${\alpha }_{comp}$	0.06	$c_{\mathrm{bio}}$	450 CNY/t
${\eta }^{Syn}$	0.9	$c_{c{o}_2}$	1.96 CNY/Nm3
${\alpha }_{CO}$	0.0143	${\theta }^{Gas}$	0.08
${\alpha }_{H_2}$	0.0147	${\theta }^{Syn}$	1.98
${\alpha }_{C{O}_2}$	0.0149

.

The 744 h model was solved using the Gurobi solver setting with a MIP Gap of 0.5%. The model contains 36,468 variables and 24,500 constraints. All configured scenarios were solved within 20 min, with deviations from the theoretical optimum not exceeding 0.5%.

4.2. Analysis of Optimization Results

To verify the effectiveness of the proposed multi-factor coordinated hydrogen-to-methanol approach, four comparative scenarios are designed and compared with the proposed scenario.

(1)

Scenario 1: Photovoltaic capacity is not considered, and wind turbines are the only source of electricity. This scenario is used to illustrate the role of wind–solar coordination in the PHM system.

(2)

Scenario 2: Electrochemical energy storage is used as the only storage device, and no fuel cell is configured.

(3)

Scenario 3: No electrochemical energy storage is configured. Scenarios 2 and 3 are jointly used to illustrate the short-term and long-term coordinated effects achieved by hybrid energy storage in the PHM system.

(4)

Scenario 4: The water–gas shift reaction is not considered. This scenario is used to illustrate the role of the coordination between biomass gasification and the water–gas shift reaction in the PHM system.

(5)

Scenario 5: The PHM system proposed in this paper.

As shown in

Table 3. Optimization Results.

Item	Scenario 1	Scenario 2	Scenario 3	Scenario 4	Scenario 5
Installed wind capacity (MW)	159.96	68.02	94.10	111.69	98.31
Installed solar capacity (MW)	0.00	189.61	89.63	182.16	66.98
PCS capacity (MW)	61.49	64.41	0.00	61.08	45.40
Battery capacity (MWh)	114.37	257.63	0.00	223.30	113.87
Fuel cell capacity (MW)	14.88	0.00	18.16	5.01	9.95
Hydrogen storage capacity (kNm3)	4198.71	62.61	654.35	1748.11	534.74
Number of AELs	19	16	16	21	12
Biomass consumption (104 t)	29.38	28.45	30.79	24.21	30.62
Annual wind–solar power generation (GWh)	576.13	572.70	493.87	717.16	469.82
Wind–solar curtailment rate (%)	1.89	2.11	2.27	1.44	1.14
Annual comprehensive cost (100 million CNY)	3.87	3.51	3.29	3.81	3.18

, the wind and solar installed capacities of Scenario 5, namely the PHM system, are 98.31 MW and 66.98 MW, respectively, with an annual power generation of 469.82 GWh. In terms of annual electricity generation, the PHM system requires the lowest annual output from renewable capacity among all scenarios, while Scenarios 2 and 3 are slightly higher. Since the water–gas shift reaction is not considered in Scenario 4, the hydrogen storage tank is required to supply more hydrogen, which in turn requires more AELs. Accordingly, the demand for electricity on the source side is also the highest in this scenario. Scenario 1 lacks the complementary characteristics of wind and photovoltaic generation, which leads to the need for more installed capacity to satisfy the power balance during certain extreme periods. This also indirectly results in the highest equivalent annual comprehensive cost among the five scenarios due to the higher cost of wind turbines.

While maintaining a relatively high scale of renewable energy output, Scenario 5 achieves a coordinated regulation mechanism across short- and long-timescales by configuring 45.40 MW/113.87 MWh of EES and a 9.95 MW fuel cell. By comparison, Scenario 2 lacks the long-timescale regulation capability of hydrogen storage, and the configured capacity of the hydrogen storage tank is only 62.61 kNm³. As a result, most of the hydrogen produced by electrolysis is directly supplied to the methanol synthesis unit. Therefore, in order to maintain overall system balance and hydrogen supply capability, Scenario 2 chooses to expand the capacity of the higher-cost battery storage, which leads to a relatively high cost. In contrast, Scenario 3 lacks the fast power support provided by batteries and thus requires a larger-capacity fuel cell to undertake the regulation task. Meanwhile, this also causes the configured hydrogen storage capacity in Scenario 3 to be much higher than that in Scenario 2 and the PHM system in Scenario 5. Taken together, Scenarios 2 and 3 indicate that a single energy storage mode often results in an excessively large capacity allocation for a certain type of equipment, thereby increasing the overall cost. By contrast, considering a hybrid energy storage system makes it possible to achieve a better balance among different types of equipment.

Compared with the PHM system, the disadvantages of Scenario 4 are quite evident. First, its total wind and photovoltaic installed capacity reach 293.85 MW, with an annual power generation of 717.16 GWh, which is significantly higher than the PHM system, whose total wind–solar installed capacity and annual power generation are 165.29 MW and 469.82 GWh, respectively. This means that the power supply demand in Scenario 4 increases by nearly 53%. Owing to the insufficient hydrogen supply in Scenario 4, the configured AELs capacity is nearly twice that of the PHM system, while the configured hydrogen storage capacity is more than three times larger. Although Scenario 4 requires less biomass feedstock, the cost of biomass feedstock is expected to continue decreasing in the future. Therefore, this scenario would only have an advantage in regions where biomass feedstock prices are extremely high. Overall, the importance of the water–gas shift reaction in the PHM system is self-evident.

In terms of cost performance, the PHM system has an equivalent annual comprehensive cost of CNY 318 million, which is the lowest among the five scenarios. Scenarios 2 and 3 exhibit slightly higher costs because both adopt only a single energy storage mode. Although Scenario 4 avoids the carbon emissions associated with the water–gas shift reaction, it requires a more expensive configuration on the wind–solar–hydrogen storage side. The high cost of Scenario 1 is mainly caused by the over-allocation of wind turbines and hydrogen storage tanks, making it the most expensive among the five scenarios. The comparison indicates that wind–solar coordination is crucial in the PHM system, especially given the current high cost of wind turbines. In addition, a HES configuration is more economically advantageous than any system relying on a single storage mode and is therefore more consistent with practical engineering requirements. Meanwhile, considering the water–gas shift reaction to regulate the carbon-to-hydrogen ratio after biomass gasification can also significantly reduce the overall system cost.

Overall, the PHM system proposed in this paper incorporates wind–solar coordination, hybrid energy storage coordination, and the coordination between biomass gasification and the water–gas shift reaction, making it the most comprehensive among the five scenarios. It achieves the lowest wind and solar curtailment rate as well as the lowest equivalent annual comprehensive cost, thereby balancing renewable energy accommodation and economic performance. Therefore, considering factors such as installed equipment capacity, economic benefits, and wind–solar utilization, the PHM system performs optimally among the five scenarios, which verifies the effectiveness and feasibility of the proposed scheme.

4.3. Analysis of Energy Flows

Under the optimal results obtained in Scenario 5 of the previous section, the annual energy flows of the PHM system are illustrated in Figure 6. The combined annual electricity generation from wind and solar reaches 469.8 GWh, of which approximately 49% is allocated to the AEL units for hydrogen production, yielding a total of 40,560 kNm³ of hydrogen. Around 47% of the generated electricity is supplied to the biomass gasification and methanol synthesis units. The fuel cell contributes 8.6 GWh of electricity generation. The system experiences 5.4 GWh of curtailed electricity, corresponding to a curtailment rate of 1.14%, which demonstrates the PHM system’s effective capability for accommodating renewable energy.

Based on the analysis of material flows in the PHM system, the AEL units produce 40,560 kNm³ of hydrogen annually. Among this, 36,512 kNm³ of hydrogen is supplied as green hydrogen to the methanol synthesis unit, while the remaining approximately 10% is utilized for electricity generation via the fuel cell. To achieve an annual methanol production of 100,000 tons, the PHM system consumes 306,200 tons of biomass and emits 236,600 tons of $C{O}_2$. Compared with an existing biomass-coupled green hydrogen-to-methanol project in China, the proposed scheme achieves a lower $C{O}_2$ emission per ton of methanol—2.366 t/t MeOH versus 2.62 t/t MeOH—demonstrating the effectiveness of the proposed approach in reducing carbon emissions.

4.4. Analysis of Operational Results

This subsection further analyzes the operational performance of the PHM system under the optimal capacity configuration of Scenario 5 based on the 744 h representative time horizon.

Figure 7 presents the power balance results of the operation simulation. It can be seen that wind power and photovoltaic power jointly constitute the main energy sources of the system. During periods of high wind–solar output, AELs preferentially absorb renewable electricity, while the battery is charged to undertake part of the peak-shaving function. During periods of low wind–solar output, in order to maintain the stable operation of the methanol synthesis unit, the PHM system requires the fuel cell and the battery to discharge jointly to maintain the power balance, as specifically reflected in periods such as 85–95 h and 300–400 h.

Wind and solar curtailment mainly occur during periods when wind–solar output remains continuously high while the absorption capacity of the AELs and the HES system is constrained by power limits and boundary conditions. As shown in the figure, wind and solar resources are extremely abundant around 150 h, 220 h, and 280 h, resulting in a small amount of curtailed electricity.

Figure 8 shows the hydrogen balance of the hydrogen storage tank. Hydrogen produced by the AELs is the only source of hydrogen entering the tank, and the hydrogen production rate fluctuates with the power consumption of the AEL. When the hydrogen production rate exceeds the external hydrogen demand and the hydrogen consumption rate of the fuel cell, the surplus hydrogen is stored in the hydrogen tank. Conversely, during periods of insufficient wind–solar output when the power supply side is supported by fuel cell discharge, hydrogen released from the storage tank becomes the main source of hydrogen supply.

Figure 9a–c present the internal operating states of each device in the HES unit. It can be observed that the battery is mainly used for short-term power balancing and intra-day fluctuation mitigation. When wind and solar power are abundant and AELs and loads have not yet fully absorbed the available electricity, the battery is charged and its stored energy increases. When wind–solar output declines or the load rises and leads to a power deficit, the battery rapidly discharges to maintain system balance. The fuel cell appears only when the power supply is severely insufficient and usually operates at a relatively high output power. Specifically, when renewable generation is inadequate and battery discharge is constrained by power or energy capacity limits, the fuel cell is activated to compensate for the power shortfall. During periods of abundant wind–solar output and high hydrogen production by AELs, the hydrogen storage tank inventory increases and approaches its upper limit. In contrast, during periods of insufficient wind–solar output and high hydrogen demand from the methanol synthesis unit and the fuel cell, the tank inventory decreases and approaches its lower limit.

Figure 9b shows the power output of the fuel cell. It exhibits an intermittent and pulse-like operating pattern: during most periods, it remains at low output or does not operate, and it is activated only when renewable generation is insufficient, the battery capacity is low, and the power demand of the methanol synthesis unit cannot be met. This indicates that, in the optimization model, the fuel cell is positioned as a medium- to short-term backup and supporting power source.

Figure 9c reflects the dynamic variation in the hydrogen storage inventory. It exhibits a cyclical fluctuation pattern of “charging–consumption–recharging,” demonstrating that hydrogen storage can provide energy storage over a long timescale: the inventory increases when hydrogen production by electrolysis is surplus, and decreases when hydrogen consumption for fuel cell power generation and methanol synthesis rises.

Figure 10 shows the methanol synthesis rate. It can be observed that, through the regulating effects of the HES and the WGS reaction, the methanol synthesis rate remains relatively smooth. This verifies that the PHM system is capable of converting fluctuating renewable electricity into methanol energy.

Combined with Figure 9 and Figure 10, it can be concluded that the battery mainly undertakes hourly level power balancing and fluctuation smoothing; the AELs and hydrogen storage realize day-level energy shifting by converting surplus wind–solar power into hydrogen and storing it; the fuel cell acts as a backup power source to provide compensation during critical power shortage periods; and the methanol synthesis unit maintains relatively stable operation under ramping and minimum load constraints.

As a result, while meeting the annual production target, the system achieves multi-energy coordinated optimization of “Power–Hydrogen–Methanol”.

4.5. Sensitivity Analysis

In the previous section, the efficiencies of the AELs and the fuel cell were both treated as constant values to simplify the model. Based on this assumption, this section conducts a sensitivity analysis on the efficiencies of the AELs and the fuel cell, respectively, in order to evaluate the impact of efficiency variations on the capacity configuration.

For the AELs and the fuel cell, the efficiency varied from 0.5 to 0.7, with seven and six experiments conducted within this range. The resulting capacities of each device, as well as the biomass consumption and $C{O}_2$ emissions per ton of methanol, were recorded, as shown in

Table 4. Sensitivity Analysis of AEL Efficiency.

AEL Efficiency	Installed Wind Capacity (MW)	Installed Solar Capacity (MW)	Number of AELs	Battery Capacity (MWh)	PCS Capacity (MW)	Fuel Cell Capacity (MW)	Hydrogen Storage Capacity (kNm3)	Biomass Consumption per Unit of Methanol (t/t)	CO2 Emissions per Unit of Methanol (t/t)
0.5	80.60	71.31	10	148.65	37.74	8.35	620.75	3.31	2.67
0.54	88.71	70.40	11	136.36	38.74	8.79	550.23	3.21	2.55
0.58	94.49	68.03	12	128.61	43.84	9.15	533.62	3.13	2.50
0.62	98.31	66.98	12	113.87	45.40	9.95	534.74	3.06	2.37
0.66	93.97	65.13	11	114.36	41.54	10.3	599.77	3.08	2.39
0.7	93.05	67.55	11	100.20	41.98	11.2	620.97	3.04	2.24
0.74	90.87	67.16	11	94.76	40.25	11.6	647.81	3.03	2.33

and

Table 5. Sensitivity Analysis of Fuel Cell Efficiency.

Fuel Cell Efficiency	Installed Wind Capacity (MW)	Installed Solar Capacity (MW)	Number of AELs	Battery Capacity (MWh)	PCS Capacity (MW)	Fuel Cell Capacity (MW)	Hydrogen Storage Capacity (kNm3)	Biomass Consumption per Unit of Methanol (t/t)	CO2 Emissions per Unit of Methanol (t/t)
0.45	94.16	73.82	12	150.31	42.33	7.55	617.1	3.07	2.37
0.5	95.12	70.04	12	144.07	43.00	7.99	598.5	3.08	2.38
0.55	96.22	70.14	12	127.47	43.80	9.12	542.8	3.07	2.37
0.6	98.31	66.98	12	113.87	45.40	9.95	534.7	3.06	2.37
0.65	99.56	63.88	12	102.00	45.19	10.86	529.3	3.06	2.37
0.7	99.51	61.97	12	97.50	44.25	11.43	518.1	3.07	2.38

.

Analysis of Table 4 and Table 5 indicates that the installed capacities of wind and solar power, as well as the configuration of the AELs, are relatively insensitive to changes in efficiency. As efficiency increases, the same amount of electricity produces more hydrogen. It slightly reduces the effective value of hydrogen within the system. This leads the system to rely more on the fuel cell for power regulation, resulting in a reduced battery capacity. Consequently, the capacities of both the fuel cell and the hydrogen storage tank show an increasing trend. Simultaneously, as the effective value of hydrogen decreases, the biomass consumption per ton of methanol and the $C{O}_2$ emissions are also reduced. Overall, the fluctuations in the system’s capacity configuration remain within an acceptable range.

Figure 11a,b illustrate the effects of variations in the efficiencies of the AELs and the fuel cell on the PHM system’s annual comprehensive cost and curtailment electricity rate.

4.6. Analysis of the Levelized Cost of Methanol (LCOM)

To better evaluate the feasibility of integrating biomass with renewable electricity–based hydrogen production, this section analyzes the levelized cost of methanol.

The calculation method of the levelized cost of methanol (LCOM) for the PHM system is as follows [13]:

$$LCoM={\displaystyle \frac{{\displaystyle \sum _{n=0}^N\frac{C_{inv}+C_{op}+C_{bio}}{{(1+r)}^n}}}{{\displaystyle \sum _{n=0}^N\frac{{\displaystyle \sum _{t=1}^T{m}_{\mathrm{MeOH},\mathrm{t}}\cdot w_{h,t}}}{{(1+r)}^n}}}}$$

(40)

Based on the above calculation, the unit cost of methanol produced by the PHM system is 3189 CNY/t. The main cost components are shown in Figure 12.

As indicated in Figure 12, the biomass feedstock cost constitutes the largest share of the methanol cost, followed by the investment cost of wind–solar renewable power generation equipment.

Based on the above cost analysis, a tornado diagram is constructed to further evaluate the effects of price fluctuations and parameter variations on the LCOM. As shown in Figure 13, the unit price of biomass feedstock has the most significant influence on the LCOM, followed by the unit investment costs of wind power and photovoltaic power. In addition, the cost associated with $C{O}_2$ emissions also exerts a non-negligible impact.

With technological progress, the cost of biomass feedstock is expected to decrease to less than 30% of its current level. At the same time, the cost of wind and solar power generation equipment is also showing a clear downward trend, which will further reduce the cost of methanol. In the future, methanol synthesis via the integration of biomass gasification and renewable electricity–based hydrogen production is expected to achieve better economic performance.

5. Conclusions

The main research conclusions of this study are as follows.

(1)

Coordinated wind–solar generation reduces overall system costs and improves renewable utilization. It lowers annual electricity generation by 18.6%. The hybrid energy storage requirements are also reduced. PCS capacity decreases by 26%, and hydrogen storage drops to less than 10% of the comparison case. Including hydrogen storage in HES reduces the equivalent annual comprehensive cost by 10% compared with the case without HS. EES and AEL capacities, annual electricity generation, and curtailment rates all decrease. Configuring EES lowers the cost by 3%. The required hydrogen storage tank capacity is 80% of the case without EES. Considering the WGS reaction further reduces costs by 17%. However, it requires larger HES and AEL capacities. Its advantage diminishes if biomass feedstock costs continue to decline.

(2)

When the AEL efficiency increased from 0.50 to 0.74, the PHM system’s annual comprehensive cost decreased from 325 million CNY to 311 million CNY, a reduction of 4.3%. When the fuel cell efficiency increased from 0.45 to 0.70, the cost decreased from 322 million CNY to 315 million CNY, a reduction of 2.2%. The energy utilization rate of the PHM system remained within an acceptable range. Using constant efficiencies in optimization can significantly reduce model complexity. Therefore, it is necessary to adopt constant efficiency optimization in the PHM system.

(3)

To better analyze the future economic performance of the PHM system, the LCOM is calculated. The results show that the biomass feedstock cost accounts for 43% of the total system cost and is the dominant cost component. The investment costs of wind power and solar power generation equipment account for 13% and 7%, respectively. Carbon emission penalty accounts for 7%. These components together constitute the majority of the methanol cost. The cost sensitivity analysis shows that the biomass feedstock cost has the largest impact on LCOM, far exceeding other factors. The wind and solar installed capacity costs have the next largest effect. $C{O}_2$ emission costs and the investment costs of other equipment have relatively small impacts on LCOM.

Off-grid systems generally have higher system costs than grid-connected systems. However, they offer advantages in energy independence and carbon emissions. Grid-connected systems are suitable for regions with reliable grids and price-sensitive markets. Off-grid systems are more suitable for remote areas with abundant wind and solar resources.

Finally, it should be noted that this study provides a practical MILP-based mathematical model for integrated planning–operation optimization of similar systems. However, there remain directions for further improvement. This study uses 744 h typical day clustering rather than full 8760 h hourly modeling. This may overlook the impacts of extreme weather fluctuations on wind and solar generation. The effects of equipment lifetime degradation are not considered. Planning is based on annual methanol production and does not account for market price fluctuations.

In the future, similar planning can be applied to regions with different wind and solar resources to study their impact on optimal system capacity and identify region-specific designs. The effects of methanol market fluctuations can be considered by introducing dynamic methanol prices. Full 8760 h simulations can be explored using appropriate solution methods for long-term optimization. Additionally, equipment degradation can be incorporated into the analysis.