Electrolyzer

Electric load for electrolyzer

Since R2022a

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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:

$$2H_{2}O\to O_2+4H^{+}+4e^{-}$$

$$4H^{+}+4e^{-}\to 2H_2$$

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

$$\frac{1}{R_T}=\frac{1}{R_{el}}+\frac{1}{R},$$

where:

• R is the external resistance.

• $$R_{el}=\frac{\rho \left(pH\right)x}{A}.$$ 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:

$$G_E=\frac{P_E}{1mol/s}.$$

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

$$G_{\min }=\Delta H-\frac{T}{T_0}{T}_{\Delta S},$$

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

$$mo{l}_e=\{\begin{array}{cc}\frac{\mu \left(G_E-G_{\min }\right)}{e_V{N}_A}& G_E>G_{\min }\\ 0& G_E\le G_{\min }\end{array}$$

$$mo{l}_{H2}=\{\begin{array}{cc}\frac{N_{c}mo{l}_e}{2},& G_E>G_{\min }\\ 0,& G_E\le G_{\min }\end{array}$$

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

$$i=mo{l}_{e}F,$$

where F is the Faraday constant.

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

$$\begin{array}{l}{\dot{m}}_{H2O}=mo{l}_{H2}{M}_{H2O}\\ {\dot{m}}_{H2}=mo{l}_{H2}{M}_{H2}\end{array}$$

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

$$pH=-\ln \left(\frac{x_{hp}}{mo{l}_{H2\_acc}}\right),$$

where:

• $$x_{hp}=\{\begin{array}{cc}{\displaystyle \int mo{l}_e,}& pHassumedconstant\\ {\displaystyle \int \left(1-purge\right)mo{l}_e,}& pHassumeddynamic\end{array}$$ captures the floating hydrons (H+) in the solution.

• $$mo{l}_{H2\_acc}=\frac{V{\rho }_{H2O}\left(T\right)}{M_{H2O}}$$ 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

+ — 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

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

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

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 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

R2024a: The Number of electrode pairs parameter has been removed

The Number of electrode pairs parameter has been removed.