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Electrolyzer

Electric load for electrolyzer

Since R2022a

Libraries:
Simscape / Electrical / Sources

Description

The Electrolyzer block represents the electric load associated with an electrolyzer. An electrolyzer consists of an anode and a cathode separated by an electrolyte. The block calculates the amount of produced hydrogen based on the electrical energy provided and the water temperature in the tank.

In polymer electrolyte membrane (PEM) electrolyzers, these chemical reactions define the anode and cathode conversions:

$2 H_{2} O \to O_{2} + 4 H^{+} + 4 e^{-}$

$4 H^{+} + 4 e^{-} \to 2 H_{2}$

An electrolysis stack comprises several series-connected individual electrolyzer cells. Specify the Assumption pH parameter to model this block either in a pH-dependent state or in an ideal state with constant pH.

Equations

The Electrolyzer block calculates the electrical power by using

$P_{E} = \frac{v^{2}}{R_{T}},$

where v is the voltage and R_T is the total resistance. The total resistance, R_T, is defined by

$\frac{1}{R_{T}} = \frac{1}{R_{e l}} + \frac{1}{R},$

where:

R is the external resistance.
$R_{e l} = \frac{ρ (p H) x}{A} .$ This value is a resistive term obtained from the cross-sectional transport area, A, the distance anode-cathode, x, and the electrical resistivity of the solution, ρ(pH).

The molar energy stored across the electrical load enables the process of water electrolysis and is calculated by this equation:

$G_{E} = \frac{P_{E}}{1 m o l / s} .$

To accomplish electrolysis, the electrolyzer requires a minimum amount of energy

$G_{\min} = Δ H - \frac{T}{T_{0}} T_{Δ S},$

where:

ΔH is the water enthalpy.
T_ΔS is the reaction entropy.
T is the water temperature.
T₀ is the reference temperature.

If the electrical energy is not sufficient to dissociate the water, the electrolyzer does not produce hydrogen. Therefore, the Electrolyzer block calculates the mole rate of electron, mol_e, and the mole rate of hydrogen, mol_H2

$m o l_{e} = {\begin{matrix} \frac{μ (G_{E} - G_{\min})}{e_{V} N_{A}} & G_{E} > G_{\min} \\ 0 & G_{E} \leq G_{\min} \end{matrix}$

$m o l_{H 2} = {\begin{matrix} \frac{N_{c} m o l_{e}}{2}, & G_{E} > G_{\min} \\ 0, & G_{E} \leq G_{\min} \end{matrix}$

where:

N_A is the Avogadro constant.
e_V is the energy per electron.
N_c is the number of cells.
μ is the temperature-dependent efficiency of the electrolysis.

The current that flows through the electrolyzer tank is then obtained as

$i = m o l_{e} F,$

where F is the Faraday constant.

The Electrolyzer block calculates the mass rates of consumed water and generated hydrogen by using these equations:

$\begin{array}{l} {\dot{m}}_{H 2 O} = m o l_{H 2} M_{H 2 O} \\ {\dot{m}}_{H 2} = m o l_{H 2} M_{H 2} \end{array}$

where M_H2O is the molar mass of water and M_H2 is the molar mass of hydrogen.

To compute the pH of the water in the tank, the block uses

$p H = - \ln (\frac{x_{h p}}{m o l_{H 2_a c c}}),$

where:

$x_{h p} = {\begin{matrix} \int m o l_{e}, & p H a s s u m e d c o n s t a n t \\ \int (1 - p u r g e) m o l_{e}, & p H a s s u m e d d y n a m i c \end{matrix}$ captures the floating hydrons (H+) in the solution.
$m o l_{H 2_a c c} = \frac{V ρ_{H 2 O} (T)}{M_{H 2 O}}$ is the number of moles of water.
V is the volume.
ρ_H2O(T) is the density of the water in the tank.

The residual protons in the solution inside the electrolyzer naturally increases the pH and conductivity of the water in the tank over time. The increase in conductivity leads to a run-away phenomenon. To prevent the run-away, you must purge the water in the tank by taking out the volume of the tank and fill it with clean water.

Examples

Green Hydrogen Microgrid

A DC islanded microgrid that provides power to an electrolyzer using a solar array and an energy storage system. You can use this model to evaluate the operational characteristics of producing green hydrogen over a 7-day period by power from a solar array, or from a combination of a solar array and an energy storage system. The model includes electrical, thermal liquid, and thermal gas domains.

Open Model

Ports

Conserving

expand all

+ — Positive terminal
electrical

Electrical conserving port associated with the anode of the electrolyzer tank.

- — Negative terminal
electrical

Electrical conserving port associated with the cathode of the electrolyzer tank.

Input

expand all

purge — Purge logic input, unitless
physical signal

Purge logic input, specified as a physical signal. This signal enables the substitution of the water in the tank.

vol — Water volume, m^3
physical signal

Water volume in the electrolyzer tank, in m³, specified as a physical signal.

T — Water temperature, K
physical signal

Water temperature, in K, specified as a physical signal.

Output

expand all

volPurging — Purged water volume, m^3
physical signal

Volume of water consumed for purging, in m³, specified as a physical signal.

pH — Water pH, unitless
physical signal

Water pH in the electrolyzer tank, specified as a physical signal.

mdotH2 — Mass flow rate of hydrogen, g/s
physical signal

Mass flow rate of the hydrogen, in g/s, specified as a physical signal.

mdotH2O — Mass flow rate of consumed water, g/s
physical signal

Mass flow rate of the consumed water, in g/s, specified as a physical signal.

Parameters

expand all

Assumption pH — Constant or dynamic pH
`Constant` (default) | `Dynamic`

Whether to assume constant or dynamic pH in the electrolyzer tank.

Resistance — External resistance
`10` `Ohm` (default) | nonnegative scalar

Amount of external resistance.

Cross-sectional transport area — Cross-sectional transport area
`0.04` `m^2` (default) | positive scalar

Normal area to the vector that links the anode and the cathode. Positively charged ions travel across this area from anode to cathode, where they get reduced and the hydrogen is produced.

Distance anode-cathode — Distance between anode and cathode
`0.01` `m` (default) | positive scalar

Distance between the anode and the cathode, submerged in the electrolytic solution.

Number of electrode pairs — Electrode pairs
`4` (default) | positive scalar

Number of electrode pairs.

Number of cells — Number of cells
`50` (default) | positive scalar

Number of cells in the electrolyzer.

Initial pH — Initial pH
`0` (default) | scalar

Initial pH value of the water in the tank.

Constant pH — Constant pH
`6` (default) | scalar

Constant pH value of the water in the tank.

Dependencies

To enable this parameter, set Assumption pH to Constant.

pH vector, pH_vec — pH vector
`[5, 5.5, 6, 6.5, 7]` (default) | row vector of positive scalars

Vector of pH values. This parameter must have the same number of elements as the Electrical resistivity vector, rho_vec parameter.

Dependencies

To enable this parameter, set Assumption pH to Dynamic

Electrical resistivity vector, rho_vec — Electrical resistivity vector
`[.2, .75, 2.5, 8, 18.2]` `MOhm*cm` (default) | vector of scalars

Vector of electrical resistivity values. This parameter must have the same number of elements as the pH vector, pH_vec parameter.

Dependencies

To enable this parameter, set Assumption pH to Dynamic

Temperature vector for efficiency, T_vec — Efficiency temperature vector
`[273, 298, 323, 348, 373]` `K` (default) | vector of scalars

Vector of temperatures for efficiency. This parameter must have the same number of elements as the Electrolysis efficiency vector, efficiency(T) parameter.

Electrolysis efficiency vector, efficiency(T) — Electrolysis efficiency vector
`ones(5, 1)` (default) | vector of scalars

Vector of electrolysis efficiency values. This parameter must have the same number of elements as the Temperature vector for efficiency, T_vec parameter.

References

[1] Maximilian Schalenbach et al. “A Perspective on Low-Temperature Water Electrolysis - Challenges in Alkaline and Acidic Technology”. International Journal of Electrochemical Science 13, (2018): 1173-1226.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2022a

Electrolyzer

Description

Equations

Examples

Green Hydrogen Microgrid

Ports

Conserving

+ — Positive terminal electrical

- — Negative terminal electrical

Input

purge — Purge logic input, unitless physical signal

vol — Water volume, m^3 physical signal

T — Water temperature, K physical signal

Output

volPurging — Purged water volume, m^3 physical signal

pH — Water pH, unitless physical signal

mdotH2 — Mass flow rate of hydrogen, g/s physical signal

mdotH2O — Mass flow rate of consumed water, g/s physical signal

Parameters

Assumption pH — Constant or dynamic pH Constant (default) | Dynamic

Resistance — External resistance 10 Ohm (default) | nonnegative scalar

Cross-sectional transport area — Cross-sectional transport area 0.04 m^2 (default) | positive scalar

Distance anode-cathode — Distance between anode and cathode 0.01 m (default) | positive scalar

Number of electrode pairs — Electrode pairs 4 (default) | positive scalar

Number of cells — Number of cells 50 (default) | positive scalar

Initial pH — Initial pH 0 (default) | scalar

Constant pH — Constant pH 6 (default) | scalar

Dependencies

pH vector, pH_vec — pH vector [5, 5.5, 6, 6.5, 7] (default) | row vector of positive scalars

Dependencies

Electrical resistivity vector, rho_vec — Electrical resistivity vector [.2, .75, 2.5, 8, 18.2] MOhm*cm (default) | vector of scalars

Dependencies

Temperature vector for efficiency, T_vec — Efficiency temperature vector [273, 298, 323, 348, 373] K (default) | vector of scalars

Electrolysis efficiency vector, efficiency(T) — Electrolysis efficiency vector ones(5, 1) (default) | vector of scalars

References

Extended Capabilities

C/C++ Code Generation Generate C and C++ code using Simulink® Coder™.

Version History

See Also

+ — Positive terminal
electrical

- — Negative terminal
electrical

purge — Purge logic input, unitless
physical signal

vol — Water volume, m^3
physical signal

T — Water temperature, K
physical signal

volPurging — Purged water volume, m^3
physical signal

pH — Water pH, unitless
physical signal

mdotH2 — Mass flow rate of hydrogen, g/s
physical signal

mdotH2O — Mass flow rate of consumed water, g/s
physical signal

Assumption pH — Constant or dynamic pH
`Constant` (default) | `Dynamic`

Resistance — External resistance
`10` `Ohm` (default) | nonnegative scalar

Cross-sectional transport area — Cross-sectional transport area
`0.04` `m^2` (default) | positive scalar

Distance anode-cathode — Distance between anode and cathode
`0.01` `m` (default) | positive scalar

Number of electrode pairs — Electrode pairs
`4` (default) | positive scalar

Number of cells — Number of cells
`50` (default) | positive scalar

Initial pH — Initial pH
`0` (default) | scalar

Constant pH — Constant pH
`6` (default) | scalar

pH vector, pH_vec — pH vector
`[5, 5.5, 6, 6.5, 7]` (default) | row vector of positive scalars

Electrical resistivity vector, rho_vec — Electrical resistivity vector
`[.2, .75, 2.5, 8, 18.2]` `MOhm*cm` (default) | vector of scalars

Temperature vector for efficiency, T_vec — Efficiency temperature vector
`[273, 298, 323, 348, 373]` `K` (default) | vector of scalars

Electrolysis efficiency vector, efficiency(T) — Electrolysis efficiency vector
`ones(5, 1)` (default) | vector of scalars

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.