# Hybrid Energy System Model in Matlab/Simulink Based on Solar Energy, Lithium-Ion Battery and Hydrogen

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Input Data

## 3. System Architecture and Control System

## 4. Description of the Partial Models

#### 4.1. PV System Model

#### 4.2. Electrolyser Model

#### 4.3. Hydrogen Storage Model including Compressor

- Compressed hydrogen;
- Liquid hydrogen;
- Liquid Organic Hydrogen Carrier (LOHC);
- Metal hydride hydrogen storage.

#### 4.4. Lithium-Ion Battery Model

#### 4.5. Fuel Cell Model

#### 4.6. Heat Model

## 5. Overall Model and Dimensioning of the Components

## 6. Verification and Data Analysis

^{3}at 1 bar, or 2.985 m³ at 300 bar) produced hydrogen within one year. In return, the fuel cell required 73.52 kg hydrogen for production of 1009.86 kWh energy.

^{3}at 300 bar was assumed, which corresponds to 135 bar, as 300 bar was considered to be 100% SoC.

- Stage 1: Initial stage (only occurs at the beginning of the simulation);
- Stage 2: Li-ion battery charging;
- Stage 3: Li-ion battery discharging;
- Stage 4: Electrolyser switched on;
- Stage 5: Fuel cell switched on.

## 7. Conclusions

## 8. Discussion

## 9. Outlook

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

General | Li-ion battery | |||

DC | direct current | SoC | state of charge | |

DWD | Deutscher Wetterdienst | ${P}_{norm}$ | rated power of the Li-ion battery | |

FC | fuel cell | ${P}_{min,Li-Ion}$ | maximum discharge power of Li-ion battery | |

HE | HOMER Energy | |||

MTTF | mean time to failure | ${P}_{max,Li-Ion}$ | maximum charge power of Li-ion battery | |

PEMFC | proton exchange membrane fuel cell | |||

${P}_{rated}$ | power towards or out of the Li-ion battery | |||

PV | photovoltaic | |||

RES | Renewable Energy Source | |||

VDI | Verein Deutscher Ingenieure | |||

PV system | Electrolyser | |||

STC | standard test conditions | PEM | Proton Exchange Membrane | |

${I}_{y}$ | actual current of the PV system | ${H}_{2}$ | Hydrogen | |

${I}_{SC}$ | short circuit current | $V\left(T,p\right)$ | electrolyser voltage | |

${I}_{MP}$ | maximum power point current | ${e}_{rev}\left(T,p\right)$ | reverse voltage (V) | |

${V}_{y}$ | actual voltage of the PV system | $I$ | electrolyser input current | |

${V}_{MP}$ | maximum power point voltage | ${R}_{i}\left(T,p\right)$ | initial PEM cell resistance | |

${V}_{OC}$ | open circuit voltage | ${n}_{s}$ | cells in series within a stack | |

${I}_{SCS}$ | short circuit current under STC | ${n}_{p}$ | rows of cells in parallel within a stack | |

${I}_{MPS}$ | maximum power point current under ST | |||

${e}_{re{v}_{0}}$ | reference reverse voltage (at 20 °C and 1 bar) | |||

$G$ | actual irradiance | |||

${G}_{s}$ | irradiance under STC | $R$ | universal gas constant | |

${T}_{c}$ | actual cell temperature | $T$ | actual electrolyser temperature | |

${T}_{s}$ | cell temperature under STC | $F$ | Faraday constant | |

${V}_{OCS}$ | open circuit voltage under STC | $p$ | working pressure inside the electrolyser | |

${V}_{MPS}$ | maximum power point voltage under STC | |||

${p}_{0}$ | ambient pressure | |||

$\alpha $ | Temperature coefficient of the current | ${R}_{{i}_{0}}$ | reference cell resistance (at 20 °C and 1 bar) | |

$\beta $ | temperature coefficient of the voltage | ${v}_{{H}_{2}}$ | hydrogen production rate inside the electrolyser | |

$\omega $ | wind speed | ${v}_{m}$ | molar volume | |

${k}_{r}$ | PV module technology dependent coefficient | ${N}_{c}$ | number of cells of the electrolyser stack | |

$k$ | derived curve fitting parameter | |||

Hydrogen storage | Heat exchanger electrolyser | |||

LOHC | Liquid Organic Hydrogen Carrier | ${C}_{th,Stack}$ | thermal capacitance of the electrolyser | |

${P}_{b}$ | actual hydrogen tank pressure | ${\dot{Q}}_{Heat,Stack}$ | total emerging waste heat powerproduced inside the electrolyser | |

${P}_{bi}$ | initial hydrogen tank pressure | |||

${N}_{{H}_{2}}$ | flow rate of the produced hydrogen | ${\dot{Q}}_{Loss}$ | total heat loss due to natural convection and radiation | |

${T}_{b}$ | operating temperature during hydrogen storage procedure | ${\dot{Q}}_{Cooling}$ | heat extracted from the stack by the cooling system | |

${M}_{{H}_{2}}$ | molar mass of hydrogen | ${\dot{Q}}_{Heat,Cell}$ | emerging waste heat inside one electrolyser cell | |

${V}_{B}$ | hydrogen tank volume | |||

$z$ | compressibility factor | ${N}_{cells}^{ELY}$ | number of electrolyser cells | |

${V}_{m}$ | molar volume | ${V}_{Cell}$ | cell voltage of the electrolyser | |

${\rho}_{{H}_{2}}$ | density of hydrogen | ${V}_{tn}$ | reversible voltage of the electrolyser | |

${P}_{el,comp}$ | power for the compression of hydrogen | ${I}_{Cell}$ | cell current of the electrolyser | |

$k$ | heat transfer coefficient between the air and the stack surface area | |||

${\eta}_{el}$ | electrical efficiency | |||

${\eta}_{comp}$ | compressor efficiency | ${A}_{s}$ | lateral surface of the electrolyser | |

$\kappa $ | capacity ratio | ${T}_{a}$ | ambient temperature | |

${\dot{m}}_{inlet}$ | $\mathrm{flow}\text{}\mathrm{rate}\text{}\mathrm{of}\text{}{H}_{2}$ towards the compressor | ${\dot{m}}_{stack}$ | $\mathrm{mass}$ | |

${c}_{p,stack}$ | specific heat of the electrolyser stack | |||

${R}_{j}$ | $\mathrm{specific}\text{}\mathrm{gas}\text{}\mathrm{constant}\text{}\mathrm{of}\text{}{H}_{2}$ | |||

${T}_{1}$ | $\mathrm{temperature}\text{}\mathrm{of}\text{}{H}_{2}$ at entrance | ${T}_{PEME}$ | electrolyser stack temperature | |

${p}_{1}$ | pressures before the compression | |||

${p}_{2}$ | pressures after the compression | |||

Heat exchanger fuel cell | Heat pump | |||

${N}_{cells}^{FC}$ | number of FC cells | ${W}_{HP}$ | energy demand of the heat pump | |

${P}_{Heat}$ | heat power generated in the fuel cell stack | ${Q}_{remaining}$ | remaining energy demand covered by the heat pump | |

${P}_{overall}$ | total power available in the fuel towards the FC | $COP$ | Coefficient of Performance | |

${P}_{el}$ | electrical power output of the FC | |||

${I}_{Stack}$ | FC stack current | |||

${V}_{Stack}$ | FC stack voltage | |||

${V}_{Cells}$ | FC cell voltage | |||

${P}_{HE}^{FC}$ | exchanged heat power by the heat exchanger | |||

${U}_{cool}$ | global heat transfer coefficient | |||

${A}_{cool}$ | coolant contact area | |||

${T}_{PEMFC}$ | FC stack temperature | |||

${T}_{out}$ | coolant cycle output temperature | |||

${T}_{in}$ | coolant cycle input temperature |

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**Figure 1.**Input temperature and wind speed data (daily averaged values) (

**left**) and input global and diffuse irradiance (daily averaged values) (

**right**).

**Figure 3.**System architecture of the household energy system (image sources: [23]).

**Figure 5.**Simulink model of the PV system (own figure based on [25]).

**Figure 8.**Simulink model of hydrogen storage including a compressor (own figure based on [13]).

**Figure 9.**Simulink model of the lithium-ion battery (own figure based on [40]).

**Figure 14.**Energy production (

**left bar**) and energy consumption (

**right bar**) calculated by Simulink simulation for each month.

**Figure 16.**Different curves recorded by simulation of one year using Simulink model (first diagram (top (

**a**)): PV power (blue) and overall load (yellow); second diagram (

**b**): SoC of Li-ion battery (yellow) and SoC of hydrogen storage (blue); third diagram (

**c**): electrolyser turned on (yellow) and fuel cell turned on (blue); fourth diagram (bottom (

**d**)): energy provided by the fuel cell (blue), energy used by the electrolyser (orange) and energy flow towards the Li-ion battery (negative value) and energy supplied by the Li-ion battery (positive value) (yellow), respectively. (x-Axis: data points (1 data point for every minute within 1 year $\widehat{=}525,600$ data points)).

**Figure 17.**Simulation results for the week from 10 March to 16 March. First diagram (top (

**a**)): PV power (blue) and overall load (yellow); second diagram (

**b**): SoC of Li-ion battery (yellow) and SoC of hydrogen storage (blue); third diagram (

**c**): electrolyser turned on (yellow) and fuel cell turned on (blue); fourth diagram (bottom (

**d**)): energy provided by the fuel cell (blue), energy used inside the electrolyser (orange) and energy flow towards the Li-ion battery (negative value) and energy supplied by the Li-ion battery (positive value) (yellow), respectively.

PV System Characteristics | Value |
---|---|

Maximum Power Point at STC (${P}_{\mathrm{mpp}}$) | 310 ${\mathrm{W}}_{\mathrm{p}}$ |

Maximum Power Point Voltage (${V}_{\mathrm{mpp}}$) | 33.3 V |

Maximum Power Point Current (${I}_{\mathrm{mpp}}$) | 9.31 A |

Open Circuit Voltage (${V}_{OC}$) | 40.5 V |

Short Circuit Current (${I}_{SC}$) | 9.81 A |

Temperature Coefficient ${V}_{OC}$ | −0.28%/K |

Temperature Coefficient ${I}_{SC}$ | −0.02%/K |

Number of modules in series | 11 |

Number of parallel strings | 2 |

Electrolyser Characteristics | Value |
---|---|

Nominal hydrogen production rate | 1.10 Nm^{3}/h |

Hydrogen production range | 0.31–1.57 Nm^{3}/h |

Operating pressure | 0–20 bar |

Nominal efficiency | 75% |

Nominal power consumption | 5.00 kW |

Max. power consumption | 9.38 kW |

Nominal operating temperature | 62 °C |

Current | 15–75 A |

Voltage max. | 125 V_{DC} |

Number of cells | 50 |

Li-ion Battery Characteristics | Value |
---|---|

Capacity (usable) | 16 kWh |

Rated power | 12.8 kW |

Rated peak power | 18.4 kW, 5 s |

Efficiency | 95% |

Usage | On/Off Grid |

Ambient temperature | −10 °C to 50 °C |

FC Characteristics | Value |
---|---|

Type of Fuel Cell | PEM |

Rated power | 1240 W |

Maximum power | 2000 W |

Voltage at maximum performance | 24.23 V at 52 A |

${H}_{2}$ pressure | 1.5 bar |

Nominal operating temperature | 55 °C |

Nominal efficiency | 35% |

Number of Cells | 35 |

Household Characteristics | Value |
---|---|

Electricity demand | 2350 kWh/a |

Heat demand | 4000 kWh/a |

Living area | 160 m^{2} |

Dimensions surface area | 9 m × 9 m |

KfW efficiency | $40\text{}\left(\le 25\frac{\mathrm{kWh}}{{\mathrm{m}}^{2}\xb7\mathrm{a}}\right)$ |

Hydrogen Tank Characteristics | Value |
---|---|

Maximum tank pressure | 300 bar |

Tank volume (at 1 bar) | 5 m^{3} |

Initial SoC | 60% |

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**MDPI and ACS Style**

Möller, M.C.; Krauter, S.
Hybrid Energy System Model in Matlab/Simulink Based on Solar Energy, Lithium-Ion Battery and Hydrogen. *Energies* **2022**, *15*, 2201.
https://doi.org/10.3390/en15062201

**AMA Style**

Möller MC, Krauter S.
Hybrid Energy System Model in Matlab/Simulink Based on Solar Energy, Lithium-Ion Battery and Hydrogen. *Energies*. 2022; 15(6):2201.
https://doi.org/10.3390/en15062201

**Chicago/Turabian Style**

Möller, Marius C., and Stefan Krauter.
2022. "Hybrid Energy System Model in Matlab/Simulink Based on Solar Energy, Lithium-Ion Battery and Hydrogen" *Energies* 15, no. 6: 2201.
https://doi.org/10.3390/en15062201