Decentralized Hydrogen Production from Magnesium Hydrolysis for Off-Grid Residential Applications

Abstract

This work explores water hydrolysis using magnesium as a decentralized dihydrogen source for off-grid households. A dedicated reactor design enabled on-demand dihydrogen generation, coupled with a Proton Exchange Membrane Fuel Cell (PEMFC) for electricity and heat production. Different energy management strategies were compared, highlighting the limitations of single-purpose approaches and the benefits of converting surplus electricity to heat. The integration of photovoltaic generation further reduced magnesium demand by 30%, thus reducing storage requirements to close to 1565 kg of magnesium powder per year, i.e., a volume of 0.9 m³ to cover the heat and electricity needs of a four-person household. Results demonstrate that combining water hydrolysis with magnesium and renewables provides a feasible and sustainable solution for autonomous energy supply in isolated sites.

1. Introduction

Many specialists today regard dihydrogen (H₂) as a crucial facilitator for the future of sustainable energy—not just in mobility, but also for supplying power to remote and off-grid areas [1]. This excitement stems from various technical benefits: hydrogen can be used in both internal combustion engines and fuel cells, providing significant versatility in its applications. It boasts a remarkably high gravimetric energy density—about three times that of traditional hydrocarbons—making it an outstanding medium for chemical energy storage. This is particularly pertinent in situations where renewable energy sources, such as solar and wind, are present but not consistently available [1,2]. In addition, hydrogen serves as a clean energy carrier. When used in a fuel cell, the sole by-product is water, with no CO₂ emissions or particles, rendering it a highly appealing choice for minimizing environmental impact [3]. These features are especially beneficial for remote regions such as islands, mountainous areas, or rural off-grid communities, where energy supply frequently depends on diesel generators, which are both polluting and expensive to maintain and refuel [4].

Despite the many benefits, the widespread adoption of hydrogen and hydrogen-based combined heat and power (CHP) systems [5] encounters various obstacles [6], such as challenges in system design and optimization [7] and the integration with onsite hydrogen production [8]. As a result, significant research efforts have been undertaken in recent years to tackle these issues and investigate innovative strategies for improving the performance and feasibility of hydrogen-based CHP systems [9]. In most of these improvements, CHP systems are coupled with renewable energy sources like solar or biomass energy [10,11] or consist of applications in the power generation and transportation sectors [12]. Nevertheless, there is a notable gap in the literature regarding hydrogen-based CHP systems that are integrated with hydrogen production and storage, revealing that the most pressing issue is the absence of sufficient infrastructure for its production, storage, and distribution. In numerous countries, this infrastructure is either lacking or inadequately developed, and establishing it requires considerable investment. This infrastructure deficit hampers both transportation applications and the electrification of off-grid locations. Furthermore, the majority of dihydrogen currently available in the market is generated through hydrocarbon reforming, a process that releases substantial amounts of CO₂. This results in a paradox: a clean energy vector produced through a polluting method, thus constraining its authentic environmental advantages [13].

To fully realize the potential of dihydrogen gas, it is crucial to encourage local production from renewable sources through water electrolysis [14,15]. This method would facilitate the decentralized generation of green hydrogen, particularly in areas with abundant solar or wind resources, offering clean energy independence to remote communities or targeted uses such as mountain shelters, research stations, or microgrids on islands.

In this context, the present paper investigates the feasibility of coupling magnesium hydrolysis with Proton Exchange Membrane Fuel Cells (PEMFC) in order to simultaneously provide electricity and heat to a remote household. This is an example of cogeneration involving a PEMFC that is a little different from what is found in the literature [16]. It requires a dedicated reactor presented in the paper, in order to optimize the reaction kinetics and thermal recovery. With this reactor, several energy management strategies are evaluated. The objective is to identify the most efficient operating conditions to minimize magnesium consumption while ensuring full coverage of residential energy needs.

2. Hydrogen Generation by Hydrolysis with Magnesium

This section revisits certain findings related to the hydrolysis of water through the use of magnesium and introduces new outcomes in hydrogen production.

Magnesium ranks as the seventh most abundant element on the planet. This abundance makes it a favorable choice for hydrogen production. Additionally, it is economically viable, priced at approximately 2 EUR€/kg. The reaction between magnesium (Mg) and water yields pure hydrogen, as represented by the following chemical equation:

Mg + 2 H₂O = Mg(OH)₂ + H₂ Δ_rH° = −354 kJ.mol⁻¹

(1)

The global reaction (1) results in fact in a “local” electrochemical cell that experiences the subsequent redox and acid-base reactions:

Magnesium oxidation: Mg = Mg²⁺ + 2 e⁻

(2)

Water auto-protolysis: 2 H₂O = 2 OH⁻ + 2 H⁺

(3)

Magnesium hydroxide formation: Mg²⁺ + 2 OH⁻ = Mg(OH)₂

(4)

Water reduction (di-hydrogen production): 2H⁺ + 2e⁻ = H₂

(5)

However, the reaction of the electrolyte is promptly halted by a passive layer of magnesium hydroxide that develops on the surface of magnesium or its hydride. Numerous published studies have suggested various solutions to address the issue of passivation, specifically [17,18]:

-

Raising the water temperature to improve the hydrolysis rate of Mg;

-

Incorporating additives during hydrolysis, such as ion exchangers or buffering agents, to postpone the development of the passive layer (Mg(OH)₂);

-

Employing both doping additives and mechanical grinding to exfoliate the hydroxide layer, thereby generating multiple surface defects.

In this study, the third solution was chosen. A mixture composed of ball-milled Mg powder combined with a carbon additive was used. According to refs. [19,20], carbon-doped ball-milled Mg demonstrates the following:

-

an increase in reaction rate (two to three times);

-

reduction of full hydrolysis time from >20 min to 6–7 min;

-

an increase in conversion ratio from ≈60–70% (raw Mg) to >95%;

-

improved resistance to passivation due to exfoliation of Mg(OH)₂.

Moreover, the hydrolysis reaction was carried out using an aqueous solution that included NaCl. It indicates that 10 wt.% Mg with carbon in an aqueous solution, together with 3.5 wt.% NaCl, demonstrates superior hydrolysis reaction performance compared to those previously documented in the literature [19]. The majority of hydrogen is produced within the first few minutes, with a conversion yield of almost 80% after 4 min (and even complete conversion after 6 to 7 min).

Of course, these results depend on the Mg particle size.

-

Large Mg particles (>200 μm) suffer from incomplete conversion because diffusion is limited once a passivating Mg(OH)₂ shell forms [20].

-

Small particles (<50 μm) indeed yield faster kinetics but introduce safety concerns related to dust explosivity when handled in air.

To mitigate this, our system uses controlled-size particles of around 80–120 μm. To make the system even more secure, this constraint on the particle size can be combined with the following:

-

inert N₂ storage;

-

automated feeding;

-

reduced oxygen exposure;

-

a wet reaction environment that eliminates dust-ignition risk.

Compared with aluminum, magnesium offers faster kinetics and simpler by-product handling, since Mg(OH)₂ is non-toxic and easily recyclable, whereas Al₂O₃ layers are harder to remove and require alkaline activation [18]. Compared with NaBH₄, magnesium is cheaper and environmentally benign, while NaBH₄ suffers from high synthesis cost and complex regeneration [17,21]. Although Mg hydrolysis is exothermic (−354 kJ mol⁻¹), it is not too exothermic (as in the case of NaBH4, which makes the recovery and heat control more complex); its energy density and recyclability potential make it better suited for stationary off-grid systems where heat recovery is beneficial [22,23].

Relation (1) outlines a spontaneous and thorough reaction (provided the preparation follows the previous guidelines [20,24]). The reaction ceases only when one of the two reagents (magnesium or water) is entirely consumed. To eliminate the need for a storage tank in electrical applications powered by a PEMFC, the optimal approach is to generate hydrogen as needed, while the PEMFC simultaneously generates electricity [25]. Consequently, a solution was developed to regulate the kinetics of the reaction and to produce hydrogen on demand [26]. The reaction described by relations (1) to (5) is highly exothermic and produces a heat of 14.712 kJ/g of Mg at 298 K. It is intended to be carried out inside a reactor, such as the one shown in Figure 1a.

The construction of this reactor prototype is based on previously validated kinetic datasets. The kinetic and thermal parameters were taken from experimental studies using C-doped ball-milled Mg powders [19]. The reaction time (6–7 min for complete conversion) and conversion yield (≈95%) were verified experimentally in prior works by our team [26].

With such a reactor, the hydrogen is produced using the following cycle:

1-

Insertion of the magnesium powder (approximately 20 g) through the top motorized valve;

2-

Gradual injection of water to maintain the pressure inside the reactor at 2 bar and, thus, produce hydrogen on demand;

3-

At the end of the reaction (evaluated using a hydrogen flow meter), ejection of the reaction products through the bottom motorized valve and rinsing of the reactor;

4-

Return to step 1.

As shown in Figure 2, continuous production can be obtained by multiplying the number of reactors operating in parallel, thus maintaining the hydrolysis reaction permanently despite the insertion and ejection phases. By reacting 10 g of magnesium every minute, a reaction chamber has a power of 2 kW in terms of hydrogen production (the chemical energy provided by the hydrolysis reaction is shown in Section 4). Reacted Mg(OH)₂ does not accumulate in the reactor. It appears as a liquid that flows out by gravity when the motorized valve at the bottom of the reactor (which is conical in shape) opens. This flow is insufficient to remove all traces of Mg(OH)₂; therefore, the water spray system used for the reaction is employed to rinse the inside of the reactor.

To recover the thermal energy from the reaction, the reactor barrel and its bottom are equipped with a coil in which water circulates, as shown in Figure 1b,d. A waterproof wall around the reactor barrel serpentine shown in Figure 1c, allows the serpentine to be immersed in water for better thermal exchange.

As shown in Figure 1e, which is a scheme of the hydrogen/heat generator used in this work, the reactor and its thermal exchanger, previously described, are covered with insulating foam. By controlling the pump shown in Figure 1e, it is possible to control the temperature of the reactor and the water in the exchanger. A temperature of 70 °C for the reactor is perfectly acceptable. A more detailed thermal study of the reactor will be presented in a separate paper.

It is important to mention that the system is still only a prototype and that operational stability, material endurance, and reliability tests have not yet been carried out. However, taking into account all the tests that have been carried out, over about a hundred cycles (insertion–reaction–discharge–rinsing), a stable hydrogen production was obtained without observable degradation of the aluminum chamber or clogging by Mg(OH)₂ residues. The internal surfaces are protected by a passivation layer, and periodic water rinsing prevents accumulation. A long-term durability study and a redesign study still need to be conducted if pre-industrialization is being considered.

3. Study Case

The hydrogen production solution is intended to power a dwelling in an isolated location in the center of France. The energy needs are assumed to be covered by a reactor such as that described in Figure 1 and Figure 2. The reaction efficiency is assumed to be ${\eta }_r=95\%$ (conversion efficiency of magnesium to hydrogen by the hydrolysis reaction). Hydrogen is converted into electricity using a PEMFC with an efficiency of ${\eta }_e=50\%$ and a DC/AC converter with an efficiency of ${\eta }_e=80\%$. It is assumed that the energy lost as heat by the fuel cell is not recovered, which could be an avenue for improvement. As shown in Figure 3, the electricity is intended to cover the needs for lighting and for the operation of electrical appliances (washing machine, refrigerators, TV, etc.). The heat exchanger associated with the reactor is assumed to reconvert heat with an efficiency of ${\eta }_Q=40\%$. This value is deliberately low to place the study in an unfavorable case. This heat is used to cover the needs for domestic hot water (DHW) and air heating.

The electricity and heating needs of a family of four were estimated using data from ADEME (the French Environment and Energy Management Agency) for the electrical needs, and literature data for the heating needs.

Regarding electricity needs, data were collected from the results of the Panel ElecDom project [27,28] concerning average daily consumption (several types of accommodation, several locations in France, different numbers of occupants, …) recorded for different types of consumption (computers, cooking, washing, etc.). The electrical needs data used in this paper, denoted in the sequel $E_{cons} [\mathrm{k}\mathrm{W}.\mathrm{h}]$, were obtained by removing from ref. [29] the data relating to heating needs (DHW and air heating). Daily data from three consecutive months were averaged to reflect consumption over four seasons. They are shown in Figure 4.

The heat-need definition relies on the synthesis carried out in ref. [29], which provides

-

average daily domestic hot water consumption by end-use data from a US study [30] (

Table 1. Domestic hot water consumption.

End-Use	Volume (L/Day) [30]	Temperature T (°C) [31]
Shower	67.4	40.6
Sink	58.3	40.6
Bath	9.8	40.6

);

-

end-use water temperature from ref. [31] (

Table 2. Daily magnesium consumption for four seasons with strategies 3, 4, and 5.

Season	Winter	Spring	Summer	Autumn	Total for 1 Year [kg]
Daily magnesium consumption [kg] with strategy 3	7.09	5.67	5.58	5.56	2150
Daily magnesium consumption [kg] with strategy 4	7.07	4.34	2.46	3.51	1565
Daily magnesium consumption [kg] with strategy 5	6.59	3.97	2.19	4.08	1514

);

-

daily hot water–use profile consumption from ref. [31] (Figure 2).

As indicated in ref. [29], despite the source of the data (United States), the daily quantities proposed in ref. [29] fairly accurately reflect the DHW needs identified by the French group COSTIC [32].

To obtain hourly information on energy linked to hot water consumption, only data relating to the shower, sink, and bath were retained. They are grouped in Table 1.

To obtain the energy consumed each hour by DHW, these data were combined with the daily profile from ref. [21] (which provides DHW $[\%/\mathrm{h}]$) using the following relation:

$$\mathrm{D}\mathrm{H}\mathrm{W}=\mathrm{V}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{m}\mathrm{e}[{\mathrm{m}}^3/\mathrm{d}\mathrm{a}\mathrm{y}]\times {\displaystyle \frac{\mathrm{D}\mathrm{H}\mathrm{W}[\%/\mathrm{h}]}{100}}\times {\rho }_{water}\times {Cp}_{water}\times (T-T_0) [\mathrm{J}]$$

(6)

In relation (6), $T$ is the temperature in the third column of Table 1, ${Cp}_{water}=4180 \mathrm{J}/\mathrm{K}/\mathrm{k}\mathrm{g}$, ${\rho }_{water}=1000 \mathrm{k}\mathrm{g}/{\mathrm{m}}^3$ and $T_0=15 °\mathrm{C}$ denote, respectively, the water heat capacity and the initial water temperature.

However, these data do not consider seasonality and the need for air heating. To overcome these problems, the electrical data of ref. [28] were used again.

The total annual amount of electrical energy used for DHW in ref. [28] was calculated, as well as the total energy for each season, in order to calculate a percentage for each season, denoted $p_{season}$. This percentage was used to introduce seasonality into the data from relation (6) using the following relation:

$$\underset{Season consumption}{\underbrace{9\mathrm{O}\stackrel{\begin{array}{c}1 day \\ consumption\end{array}}{\overbrace{\sum _{day}{\mathrm{D}\mathrm{H}\mathrm{W}}_{season}}}}}=\underset{1 year consumption}{\underbrace{\left(4\times \underset{\begin{array}{c}Average season \\ consumption\end{array}}{\underbrace{9\mathrm{O}\stackrel{\begin{array}{c}1 day \\ consumption\end{array}}{\overbrace{\sum _{day}\mathrm{D}\mathrm{H}\mathrm{W} \mathrm{f}\mathrm{r}\mathrm{o}\mathrm{m} \left(6\right)}}}}\right)}}\times p_{season}$$

(7)

Thus, for each hour

$${\mathrm{D}\mathrm{H}\mathrm{W}}_{season}=4\times \mathrm{D}\mathrm{H}\mathrm{W}\times p_{season}\left[\mathrm{J}\right]$$

Finally, the electrical energy dedicated in ref. [28] to air heating and denoted $Q_{air}$ was added to relation (7) to define what we subsequently call the thermal energy $Q_{cons}$ required by the home for each season and hour by hour:

$$Q_{cons}={\mathrm{D}\mathrm{H}\mathrm{W}}_{season}+Q_{air} \left[\mathrm{J}\right]$$

(8)

This same energy, expressed in kWh, is defined by the relation

$$Q_{cons} [\mathrm{k}\mathrm{W}.\mathrm{h}]={\displaystyle \frac{Q_{cons} \left[\mathrm{J}\right]}{3.6\times {10}^6}}$$

(9)

and is represented for each season and hour in Figure 5.

4. Evaluation of Magnesium Consumption According to Several Strategies

This section is dedicated to calculating the magnesium mass required to cover the heat and/or electricity needs of the household considered, according to various energy-production strategies. Five strategies will be analyzed in the sequel; the logic of introducing a new strategy is to minimize magnesium consumption compared to the previous one. For this purpose, the following parameters and notations were used.

-

Density of hydrogen: ${\rho }_{H_2}=0.08988 \mathrm{g}/\mathrm{L}$;

-

Density of magnesium: ${\rho }_{M_g}=1730 \mathrm{g}/\mathrm{L}$;

-

Mass of hydrogen produced by the hydrolysis of magnesium with 100% conversion efficiency: $m_{100\%}=83 \mathrm{g}/\mathrm{k}\mathrm{g}$;

-

Chemical energy of hydrogen: $E_{H_2}=114.5 \mathrm{k}\mathrm{J}/\mathrm{g}$;

-

Heat produced by the reaction at 298 K: $Q_{Mg}=\mathrm{353,100} \mathrm{J}/\mathrm{m}\mathrm{o}\mathrm{l}=\mathrm{14,712.5} \mathrm{J}/\mathrm{g}$;

-

Hydrolysis reaction efficiency: ${\eta }_r=95\%$;

-

PEMFC and DC/AC converter efficiency [16]: ${\eta }_c=50\%$;

-

DC/AC converter efficiency [33]: ${\eta }_e=80\%;$;

-

Heat exchanger efficiency [34]: ${\eta }_Q=40\%$.

Note that the hydrolysis reaction efficiency is deliberately underestimated to account for these possible parameter variations (Mg purity, ambient temperature, …). The other yields have been set at their low value. In terms of error or uncertainty, the quantities produced and consumed are analyzed in the sequel; therefore, the overall conclusions of the paper will only be more favorable. Also note that the Mg conversion kinetics are not taken into account in this study. Very high conversion kinetics should be obtained by increasing the number of reactors working in parallel. Using these definitions, the following quantities are considered to be obtained in the sequel:

-

Mass of hydrogen produced: $m_{H_2}={\eta }_r{m}_{100\%}=78.85{\displaystyle \frac{\mathrm{g}}{\mathrm{k}\mathrm{g}}} of Mg$;

-

Chemical energy produced: $E_{chem}=m_{H_2}{E}_{H_2}=9028.32 \mathrm{k}\mathrm{J}$/kg;

-

Electrical energy produced: $E_{elec}=E_{chem}{\eta }_c{\eta }_e=4514.16 \mathrm{k}\mathrm{J}/\mathrm{k}\mathrm{g}=1.25 \mathrm{k}\mathrm{W}\mathrm{h}/\mathrm{k}\mathrm{g}$;

-

Heat energy produced: $Q_{therm}=Q_{Mg}{\eta }_r{\eta }_Q=5590.7 \mathrm{k}\mathrm{J}/\mathrm{k}\mathrm{g}=1.55 \mathrm{k}\mathrm{W}\mathrm{h}/\mathrm{k}\mathrm{g}$.

4.1. Strategy 1: Magnesium Consumption to Cover Electrical Needs

To cover the electrical needs at each hour and each season, the mass of magnesium required is defined by

$$m_{m_g}={\displaystyle \frac{E_{cons}}{E_{elec}}} [\mathrm{k}\mathrm{g}]$$

(10)

The resulting heat produced is defined by

$$Q_{prod}=m_{m_g}{Q}_{therm} [\mathrm{k}\mathrm{W}\mathrm{h}]$$

(11)

and the difference between the heat required and the heat produced is defined by

$$Q_{diff}=Q_{prod}-Q_{cons} [\mathrm{k}\mathrm{W}\mathrm{h}]$$

(12)

Figure 6 shows, for each season and at every hour, the electricity and heat required— namely $E_{cons}$ and $Q_{cons}$—as well as the heat actually produced $Q_{prod}$ and the resulting difference $Q_{diff}$. $E_{cons}$ is equal to $E_{prod},$ as it is imposed by the energy-production strategy studied. This figure highlights that the energy production strategy considered cannot work, since in winter, there is a lack of heat produced throughout the day. One can also note a significant excess of heat in summer, which is then lost.

4.2. Strategy 2: Magnesium Consumption to Cover Heat Needs

In this strategy, magnesium is consumed to cover the heat needs for each hour and each season. The mass of magnesium required is defined by

$$m_{m_g}={\displaystyle \frac{{\mathrm{Q}}_{cons}}{Q_{therm}}} [\mathrm{k}\mathrm{g}]$$

(13)

The resulting electricity produced is defined by

$$E_{prod}=m_{m_g}{E}_{elec} [\mathrm{k}\mathrm{W}\mathrm{h}]$$

(14)

and the difference between the heat required and the heat produced is defined by

$$E_{diff}=E_{prod}-E_{cons} \left[\mathrm{k}\mathrm{W}\mathrm{h}\right]$$

(15)

Figure 7 shows, for each season and at every hour, the electricity and heat required, respectively $E_{cons}$ and $Q_{cons}$, the electricity was really produced $E_{prod}$ and the difference $E_{diff}$. $Q_{cons}$ is equal to $Q_{prod}$ since imposed by the energy production strategy studied. Yet again, this figure shows that the energy production strategy considered cannot work since in summer, there is a lack of electricity produced throughout the day. One can also note a significant excess of heat in winter, which is then lost.

4.3. Strategy 3: Magnesium Consumption to Cover Heat Needs with Conversion of Excess Electricity into Heat

In strategy 2, an excess of electricity is highlighted in some seasons. In this new strategy, it is therefore assumed that part of the electricity, denoted $\mathsf{\alpha },$ is converted into heat (with a resistor) with an efficiency ${\eta }_{ce}=0.95$. According to the conversion coefficients computed at the beginning of Section 4 ($E_{elec}=1.25 \mathrm{k}\mathrm{W}\mathrm{h}/\mathrm{k}\mathrm{g}$ and $Q_{therm}=1.55 \mathrm{k}\mathrm{W}\mathrm{h}/\mathrm{k}\mathrm{g}$), energy production is thus described by the equations

$$\begin{array}{l}{Q}_{prod}=1.55m_{m_g}+1.25\alpha {\eta }_{ce}{m}_{m_g} \\ E_{prod}=\left(1-\alpha \right)1.25m_{m_g} \end{array}[\mathrm{k}\mathrm{W}\mathrm{h}] 0\le \alpha \le 1$$

(16)

To cover heat and electricity needs, the following equations must be verified: $Q_{cons}=Q_{prod}$ and $E_{cons}=E_{prod}$, which leads to the solutions of system (16) to

$$m_{m_g}={\displaystyle \frac{Q_{cons}-{\eta }_{ce}{E}_{cons}}{1.55+1.25{\eta }_{ce}}} [\mathrm{k}\mathrm{g}] \mathrm{and} \alpha =1-{\displaystyle \frac{E_{cons}}{1.25m_{m_g}}}$$

(17)

With relations (17), parameter $\alpha$ is negative in certain situations, reflecting a lack of electricity, as is clearly shown in Figure 7 in summer. To solve this problem, when the parameter $\alpha$ is negative, the magnesium mass is recalculated to cover electricity needs, leading to the following relations as $E_{elec}=1.25 \mathrm{k}\mathrm{W}\mathrm{h}/\mathrm{k}\mathrm{g}$ (see the beginning of Section 4):

$$\mathrm{if} \alpha <0, \alpha =0, m_{m_g}={\displaystyle \frac{E_{cons}}{1.25}} \left[\mathrm{k}\mathrm{g}\right]$$

(18)

With this condition and as $Q_{therm}=1.55 \mathrm{k}\mathrm{W}\mathrm{h}/\mathrm{k}\mathrm{g}$ (see above), heat and electricity needs are covered, and there is sometimes an excess of heat, which is evaluated using the relation

$$Q_{exces}=1.55m_{m_g}-Q_{cons}\left[\mathrm{k}\mathrm{W}\mathrm{h}\right]$$

(19)

Figure 8 shows the daily variation of $Q_{cons}$, $E_{cons,}$ and $Q_{exces}$ for each season, and Figure 9 gives the corresponding variation of the parameter $\alpha$.

Magnesium consumption for each season and for an entire day is shown in Table 2. Considering a season length of 90 days, this leads to an annual magnesium consumption of 2150 kg, thus a volume of 1.24 m³. This is a reasonable quantity to consider for annual delivery and storage on an isolated site.

An equivalent reasoning would involve studying a similar strategy in which we seek to cover the electrical needs and to convert the excess heat in certain time slots into electricity by means of a Rankine machine. This would lead to a similar problem and result, with sometimes a lack of heat that would have to be filled by creating an excess of electricity, which could be dissipated into the air by a resistor, as in strategy 3. Instead of equipping the house with a Rankine machine [35] and a means of converting electricity into heat, however, it is preferable to study the following case.

4.4. Strategy 4: Magnesium Consumption to Cover Heat Needs with Conversion of Excess Heat and Electricity

Based on the closing comments in the previous section, it is now assumed that

-

part of the electricity, denoted $\alpha$, is converted into heat with an efficiency ${\eta }_{ce}=0.95$ in case of excess electricity;

-

part of the heat, denoted $\beta$, is converted into electricity with an efficiency ${\eta }_{cc}=0.5$ in case of excess heat.

Energy production can thus be described by the equations

$$\left\{\begin{array}{l}{Q}_{prod}=\left(1-\beta \right)1.55m_{m_g}+1.25\alpha {\eta }_{ce}{m}_{m_g}\\ E_{prod}=\left(1-\alpha \right)1.25m_{m_g}+1.55\beta {\eta }_{cc}{m}_{m_g}\end{array}\right.\left[\mathrm{k}\mathrm{W}\mathrm{h}\right] 0\le \alpha \le 1 0\le \beta \le 1$$

(20)

This system of two equations has three unknowns, or one unknown too many. To solve it, the following algorithm is used:

1-

A vector of 1000 values of $\beta$ is created with $0\le \beta \le 1$.

2-

For each season, each hour, and each value of $\beta ,$ system (20) is solved, and the values of $\alpha$ are computed using the relation:

$$\alpha ={\displaystyle \frac{1.25Q_{cons}+1.55{\beta {\eta }_{cc}Q}_{cons}+{1.55\left(\beta -1\right)E}_{cons}}{1.25{\eta }_{ce}{E}_{cons}-1.25Q_{cons}}}$$

(21)

3-

If $0\le \alpha \le 1$, then the corresponding values of $m_{m_g}$ are computed using

$$m_{m_g}={\displaystyle \frac{Q_{cons}}{1.55\left(1-\beta \right)+1.25\alpha {\eta }_{ce}}} \left[\mathrm{k}\mathrm{g}\right]$$

(22)

4-

If $\alpha <0$ (the case $\alpha >1$ does not occur) then $\beta$ is set to 1 in Equation (20), and the values of $\alpha$ and $m_{m_g}$ are computed using

$$m_{m_g}={\displaystyle \frac{Q_{cons}+{{\eta }_{ce}E}_{cons}}{1.55+1.25{\eta }_{ce}}} \left[\mathrm{k}\mathrm{g}\right] \alpha =1-{\displaystyle \frac{E_{cons}}{1.25m_{m_g}}}$$

(23)

5-

For a season and a time slot, this resolution can produce several possible values of $\alpha$ and $\beta ,$ which cover heat and electricity needs (due to parameter $\beta$ gridding). Those that lead to the minimum value of $m_{m_g}$ are then retained.

For all the seasons and all the time slots, the values of $\alpha$ and $\beta$ obtained are shown in Figure 10.

According to Table 2, strategy 4 leads to an annual magnesium consumption of 1565 kg, thus a volume of 0.9 m³ (considering a season length of 90 days).

4.5. Strategy 5: Magnesium Consumption to Cover Heat Needs with Conversion of Excess Electricity into Heat and an External Electrical Energy Source

In this section, we return to strategy 3, which consisted of converting a portion $\alpha$ of electricity into heat. Situations were highlighted where, in order to cover all needs, the parameter $\alpha$ was negative, which corresponded to a lack of electrical energy. This lack is represented in Figure 11 and will be referred to subsequently as $E_{lack}$. To cover this lack, we propose to include an external energy source in the system, i.e., to produce part of the electricity using photovoltaic panels, which addresses the problem of production in an isolated site.

The photovoltaic solar system was sized to respond to the most critical case, that is to say, in accordance with Figure 7, to overcome the lack of electricity in summer. For this, the online tool PVGIS (Photovoltaic Geographical Information System) was used. It made it possible to retrieve local climatic data and, in particular, an estimate of the photovoltaic energy production for a power of 1 kWp of installed panels. These climatic data were grouped and averaged by season. The power to be installed was sized so that the energy production was 30% higher than the energy shortfall observed in summer with strategy 1 (that covers heat needs), i.e.,

$$P_{PV}=1.3{\displaystyle \frac{{\sum }_{day}{E}_{lack}}{E_{1000}}} \left[\mathrm{W}\mathrm{p}\right]$$

(24)

In relation (24), $E_{1000}$ denotes the energy produced over a day in summer by a 1000 W peak power panel and $P_{PV}$ denotes the peak power required for the installation. Numerically ${\sum }_{day}{E}_{lack}=5.40 \mathrm{k}\mathrm{W}\mathrm{h}$, $E_{1000}=4.56 kWh,$ and thus $P_{PV}=1.18 kWp$. This represents approximately three panels of 400 Wp each. Figure 11 represents the missing energy for each season, the missing energy $E_{lack},$ and the energy produced $E_{PV}$ by the solar panels with a peak power $P_{PV}$.

Table 3. Daily sum defined by relation (25) for the four seasons with strategy 5.

Season	Winter	Spring	Summer	Autumn
Sum (25) $\left[\mathrm{k}\mathrm{W}\mathrm{h}\right]$	1.82	3.81	1.25	1.23

groups together the sum

$${\sum }_{day}\left(E_{PV}+E_{lack}\right)\left[\mathrm{k}\mathrm{W}\mathrm{h}\right]$$

(25)

which is the difference ($E_{lack}$ being negative, which, therefore, corresponds to an excess of energy) between the energy provided by solar panels and that to be compensated.

This figure shows two things:

-

For all seasons, photovoltaic production will cover the electricity shortage caused by the use of magnesium to cover heating needs, and there is even an excess of electricity.

-

Photovoltaic energy production is not synchronized with the lack of electricity.

Regarding the second point, the synchronization problem can be solved by associating a storage system. This storage can be sized by analyzing the $max\left\{E_{PV}+E_{lack},0\right\}$ curves in Figure 11. The $max\left\{E_{PV}+E_{lack},0\right\}$ curve corresponds to the electrical energy not used when the photovoltaic panels are producing and which can, therefore, be used later when the photovoltaic panels are not producing. The storage system can thus be calibrated to store the following amount of energy:

$$P_{PV}=1.5{\sum }_{day}max\left\{E_{PV}+E_{lack},0\right\}\left[\mathrm{k}\mathrm{W}\mathrm{h}\right]$$

(26)

The coefficient 1.5 in (26) was chosen to ensure a sufficient margin in the sizing of the storage system.

The energy storage capacity is greatest in spring, at 6.34 kWh, which corresponds to a 260 Ah battery at 24 V.

However, instead of storing all this electrical energy, it can be used to produce heat, thus reducing the amount of magnesium used and also decreasing the capacity of the electrochemical storage system required. Considering that a quantity of electrical energy, denoted $E_{ext}$, is included in Equation (16), the energy production can then be described by the equations

$$\left\{\begin{array}{l}{Q}_{prod}=1.55m_{m_g}+\alpha {\eta }_{ce}\left(1.25m_{m_g}+E_{ext}\right)\\ E_{prod}=\left(1-\alpha \right)\left(1.25m_{m_g}+E_{ext}\right)\end{array}\right. \left[\mathrm{k}\mathrm{W}\mathrm{h}\right] 0\le \alpha \le 1$$

(27)

The share of electrical energy to be converted into heat, represented by the parameter $\alpha$, can be determined for each season via the following optimization problem:

$$\underset{\alpha \left(t\right)\mathit{t}\in \left[\mathrm{0,23}\right]}{\min }\left(\sum _{day}{m}_{m_g}\right) 0\le \alpha \le 1$$

(28)

under the constraints

$$1\text{-} \mathrm{relations} \left(27\right)$$

(29)

$$2\text{-} {\sum }_{day}{E}_{ext}\le 0.8{\sum }_{day}{E}_{PV}$$

(30)

$$3\text{-} 0\le m_{m_g}$$

(31)

In the set of constraints, constraint 1 allows for compliance with heat and electrical requirements. Constraint 2 accounts for losses in electronic components such as voltage converters. Constraint 3 ensures that the mass of magnesium consumed is positive. A nonlinear Levenberg–Marquardt optimization algorithm is used to minimize criterion (28).

For each season, Figure 12 compares the mass of magnesium consumed over the hours in the case of strategy 3 and strategy 5, following the resolution of the optimization problem described previously. This figure shows that for all seasons, the daily consumption of magnesium is lower with strategy 5.

The variations of the parameter $\alpha$ resulting from the resolution of the optimization problem are represented in Figure 13. This figure demonstrates that the constraint $0\le \alpha \le 1 \mathrm{i}\mathrm{s} \mathrm{r}\mathrm{e}\mathrm{s}\mathrm{p}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{e}\mathrm{d}$. The figure also highlights that, whatever the season, the variations of $\alpha$ are similar and that it is mainly the average level of these curves that changes according to the season. In the context of an implementation of this strategy (see Section 4.6), a simplifying solution could, therefore, consist of fixing $\alpha$ as constant over the whole day.

The daily variations in the energies $E_{ext}$ and $E_{PV}$ for the four seasons are shown in Figure 14. $E_{ext}$ remains greater than 0 for all seasons except winter. Indeed, in winter, to cover the heat needs, it is necessary at certain times to produce excess electricity in order to reuse it later in the day. As expected, the conversion of electrical energy into heat, allowed by strategy 5, leads to using more electrical energy during the day and reduces the need for electrochemical storage.

The storage requirement can be defined from the $E_{PV}-E_{ext}$ graph depicted in Figure 15. This storage requirement can be defined by the positive parts of these graphs, which are shown in Figure 15, and defined by the relation $max\left\{E_{PV}-E_{ext},0\right\}$. The values provided by this relation are grouped in

Table 4. Values of $max\left\{E_{PV}-E_{ext},0\right\}$ for the four seasons with strategy 5.

Season	Winter	Spring	Summer	Autumn
${\sum }_{day}max\left\{E_{PV}+E_{ext},0\right\}$ (kWh)	1.91	3.19	3.37	2.04

. This table reveals that the energy storage capacity required is almost halved compared to strategy 3 and corresponds to a 140 Ah battery at 24 V.

Thanks to the energy input from the solar panels, magnesium consumption is reduced compared to strategy 3. The mass of magnesium consumed each day for the four seasons is reported in Table 2. The data in this table are complemented by

Table 5. Comparison of the five strategies studied.

Strategy	Mg Consump.	H2 Yield	Electricity Efficiency	Heat Efficiency	Additional Source	Battery Need	System Cost
1	Lack of heat in winter: unusable strategy
2	Lack of electricity in summer: an unusable strategy
3	2150 kg/year	95%	40%	32%	No	No	+
4	1565 kg/year	95%	38%	38%	No	No	+++
5	1516 kg/year	95%	40%	38%	PV	Yes	++

+ low, ++ moderate, +++ high.

, which compares all the strategies mentioned with additional criteria such as efficiency, storage requirements, the need for an external source, etc.

All these data allow us to deduce that the annual mass of magnesium consumed would be 1514 kg, i.e., an annual saving of 636 kg compared to strategy 3 and approximately 50 kg compared to strategy 4. Considering a magnesium cost of 2.1 EUR/kg and an annual consumption of 1514 kg, the energy cost amounts to ≈0.20 EUR/kWh, which decreases further when heat recovery is monetized. This positions the system competitively with diesel generators (>0.35 EUR/kWh) in isolated regions.

4.6. A Solution for the Implementation of Strategy 5

Strategy 5 can be implemented as shown in the block diagram in Figure 16. The diagram also shows an element not mentioned until now, the “outside heat exchanger”, which will be used to evacuate the excess heat to the outside if necessary. It shows that at least three quantities must be monitored:

SOC: The state of charge of the electrochemical storage system (batteries);

P_H2: The pressure of H₂ inside the reactor bulk;

T_r: The temperature of the reactor and the heat exchanger.

To monitor these three quantities, several variables are introduced:

-

for SOC: SOC_20% < SOC_90% < SOC_100%;

-

for P_H2: P_min < P_low < P_nom < P_high < P_max, for instance, P_nom = 2 bar;

-

for Tr: T_min < T_nom < T_max, for instance, T_nom = 70 °C.

For a given time slot of 1 h and a given season, the value of $\alpha$ and $E_{ext}$ will be considered constant (equal to the average value over this slot) and equal to the value computed in strategy 5. The operation of the system can then be described by the following algorithm.

If $P_{H2}\ge P_{max}$ and $T_r\ge T_{max}$, stop the magnesium supply to the reactor: Stop phase.

If $P_{H2}<P_{max}$ or $T_r<T_{max}$, supply the reactor with magnesium: Production phase.

In the Production phase, if ${P_{low}\le P}_{H2}\le P_{high}$, produce heat with the heating resistor such that the power produced is $\alpha P_{elec}\left(t\right)$. The heating resistor will be sized such that, for a given slot, $\alpha E_{cons}={\int }_{1 hour}\alpha P_{elec}\left(\tau \right)d\tau$. Impose on the DC/AC converter the amount of energy of $E_{ext}$ be exchanged with the battery during the one-hour slot.

-

if ${P_{high}\le P}_{H2}\le P_{max}$, create a proportional increase in $\alpha$ to reach the value 1 if $P_{H2}=P_{max}$;

-

if $P_{H2}\ge P_{max}$(not enough electricity consumed) $\alpha =1$ and $E_{ext}<0$ if $SOC\le {SOC}_{90\%}$(battery recharge) and $\alpha =1$, produce heat with the heating resistor to maintain $P_{H2}=P_{max}$ if $SOC>{SOC}_{90\%}$;

-

if ${P_{min}\le P}_{H2}\le P_{low}$, create a proportional decrease in $\alpha$ to reach the value 0 if $P_{H2}=P_{min}$;

-

if ${P_{min}>P}_{H2}$ (too much electricity consumed), $\alpha =0$ and $P_{cons}$ will come from the battery over a short period (which will not last since the reactor is sized to be able to cover the electrical power demands);

-

if $T_r>T_{max}$, evacuate the excess heat with the “outside heat exchanger”.

Whatever the operating phase:

if $SOC>{SOC}_{100\%}$, solar panel disconnected and only $E_{ext}>0$;

if ${SOC}_{90\%}>SOC>{SOC}_{100\%}$, solar panel connected and only $E_{ext}>0$;

if $SOC<{SOC}_{20\%}$, solar panel connected and only $E_{ext}<0$.

Regarding safety, the following measures must be adopted:

• Hydrogen pressure control: Operation limited to 2 bar nominal pressure (P_nom = 2 bar, P_max < 3 bar) using automatic valves and redundant pressure sensors.
• Temperature management: The reactor is equipped with dual temperature sensors and an external water-cooling circuit maintaining T < 70 °C.
• Hydrogen leak mitigation: All joints must use PTFE seals; gas lines must be fitted with check valves and external venting in compliance with ISO 16111 [36] (hydrogen storage–metal hydride safety).
• Powder handling: Mg powder is stored in inert N₂ atmosphere cartridges; feeding is automated to minimize human exposure.
• Thermal runaway prevention: An electronic cut-off is activated if reactor T > T_max.
• In case of abnormal pressure or temperature rise, Mg feed is automatically halted, and hydrogen is vented externally. Hydrogen detection sensors ensure safe operation under residential conditions.

These precautions align with recent safety recommendations for solid-state hydrogen carriers [3].

5. Conclusions

The paper is not an experimental work but a case study based on a dihydrogen production solution at the functional prototype stage. In terms of novelty, it uniquely couples:

• A Mg–H₂O reactor capable of on-demand H₂ generation (regulated at 2 bar);
• An integrated heat recovery loop;
• A multi-strategy energy management approach combining photovoltaic generation and cogeneration optimization.

Also, this integrated analysis of five control strategies (Section 4.1, Section 4.2, Section 4.3, Section 4.4 and Section 4.5) has not been previously reported. Earlier studies [18,26] focused either on the kinetics of Mg hydrolysis or stand-alone PEMFC operation, but not on a complete cogeneration of electricity by a waste heat recovery optimization framework.

This study has highlighted the potential of water hydrolysis using magnesium powder as a decentralized dihydrogen production pathway, capable of supplying both electricity and heat to isolated dwellings. Five strategies have been analyzed to cover the heat and electricity needs that were defined using data from the literature. The different strategies analyzed demonstrate that optimizing the conversion between thermal and electrical energy streams is essential to ensure full coverage of domestic needs while minimizing magnesium consumption. Among the proposed approaches, the integration of photovoltaic power (strategy 5) proved to be the most effective, as it significantly reduces annual magnesium powder requirements, involves very low electrochemical storage needs (in comparison with a pure photovoltaic solution), and enhances the overall energy autonomy of the site.

To summarize, the proposed Mg–H₂O + PEMFC + PV system achieves:

• A reduction of ≈30% in Mg consumption (from 2150 kg to 1514 kg year⁻¹);
• A reduction of ≈50% in battery capacity compared to a PV-only system;
• A compact design, requiring <1 m³ Mg storage volume.

These improvements directly enhance the energy autonomy and material sustainability of off-grid dwellings. The environmental advantage stems from the recyclability of Mg(OH)₂ and the absence of carbon emissions during operation. Scalability is achieved through modular reactor design (Figure 2).

Already, the findings confirm that coupling magnesium hydrolysis with PEMFC, combined with a careful management of thermal and electrical flows, offers a credible alternative to conventional solutions for off-grid applications. Technically, the system ensures on-demand hydrogen generation (controlled at 2 bar) with integrated heat recovery (40% exchanger efficiency), allowing simultaneous production of electricity and heat. This hybrid cogeneration capability reduces electrochemical storage requirements and enhances year-round self-sufficiency. Economically, the use of low-cost, recyclable magnesium powder (≈2 EUR/kg) enables a competitive cost per kWh when the recovered thermal energy is accounted for, especially compared with Li-ion battery storage (≈200 EUR/kWh installed). Moreover, the annual Mg demand (≈1.5 t) corresponds to a storage volume of <1 m³, facilitating logistics for isolated households. Compared to a diesel-based system, the proposed solution does not generate fine particles or direct CO₂ emissions. The reaction residues can be recovered or even recycled. The system is thus particularly suitable [2] for off-grid dwellings, mountain shelters, or remote microgrids where regular fuel supply or maintenance is impractical.

Regarding the sustainability aspects, the magnesium used can be sourced from non-recycled industrial Mg waste (about 50% of the total Mg alloys waste) or seawater extraction [8]. Its recyclability through thermal reduction or carbothermic pathways of Mg(OH)₂ with green hydrogen or electrolysis can be achieved, reducing lifecycle impact. Recent theoretical studies and pilot regeneration experiments indicate that significant energy recovery and partial regeneration of Mg(OH)₂ may be achievable through a two-step pathway (dehydration to MgO followed by electrochemical or thermochemical reduction). However, the experimental literature on complete cyclic Mg ↔ Mg(OH)₂ systems and practical energy-return figures is rather limited; further pilot-scale work is required to quantify overall cycle efficiencies [37], and this is a complete study by itself. This has been discussed as a critical direction for future research. The effective cost per useful kWh, considering Mg regeneration, is estimated at 0.18–0.25 EUR/kWh, competitive with rural off-grid PV-battery systems.

Additional work needs to be carried out to improve the concept and to lift some limitations, including the following:

-

taking into account the dynamics of electricity and heat production by the reactor;

-

evaluating the benefits of using waste heat, for example, from the PEMFC stack, while also maintaining it at a temperature equal to that of the heat exchanger (the same heat exchanger could cool both the reactor and the stack);

-

evaluating the benefits of calculating the $\alpha$ and $E_{ext}$ profiles in strategy 5 for each month rather than for each season;

-

evaluating whether the implementation strategy of Section 4.5 unduly deteriorates the expected magnesium consumption levels when the consumption profiles no longer correspond entirely to the profile used with strategy 5;

-

evaluating the possibility of scaling up the concept;

-

analyzing the system lifecycle;

-

developing efficient solutions, Mg(OH)_2, which is a limitation to the diffusion of such a cogeneration system.

Such developments open promising perspectives for both green mobility and sustainable local energy generation.