# Techno-Economic Modeling and Analysis of Redox Flow Battery Systems

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Approach

_{Area_needs}) or housing (C

_{Facilities}) for the whole battery installation in the subsequent analysis.

## 3. Model Development and Description

#### 3.1. Cell Voltage

_{rev}) can be calculated by the Nernst equation as follows:

_{ox}and c

_{red}are the molar concentration of the oxidant and reductant. Since a cell has different kinds of losses, the effective cell voltage is calculated as the reversible cell voltage subtracted by all losses inside the cell:

_{act}is the activation overpotential, U

_{con}is the concentration overpotential, and U

_{ohm}is the ohmic overpotential. The non-linear response of the overpotential U

_{act}with the current density can be taken into account using the Butler–Volmer equation, although this requires a knowledge of the material-dependent exchange current densities i

_{0}and the symmetry factors α (or β) for reactions in a complete cell or cell stack [10]. Chen et al. calculated them with Equations (4) and (5) [11], although it must be remembered that the symmetry factor α and the exchange current density i

_{0}are strongly electrode material dependent and usually not the same for the charge and discharge process.

_{0}, and the limiting current density i

_{L}are difficult to obtain, U

_{act}and U

_{con}were left as constants in an initial approximation so as to be able to supplement the model with measured values later. The overpotentials result in all cases in heat generation, which means a loss in energy and lower battery efficiency. The ohmic losses consist of material resistances and contact resistances between the different cell components. As the choice of component directly influences the ohmic losses, this part is described in more detail with Equations (6) and (7):

_{Active}is the active cell area, and R is the ohmic resistance.

#### 3.2. Costs of Power Conversion

_{Active}) of a single cell can be varied for a modification of the power of one stack. At this step of the model, the current density (i) was supposed to be fixed. The stack voltage is the sum of single cell voltages and the current is the product of current density and active area of a single cell. The overall costs of the power components can be summarized by the following simplified formula:

_{Active}):

_{P,Assembling}or of the stacks C

_{S,Assembling}could be calculated using the necessary man-hours, specific man-hour costs (costs per hour), and the specific energy costs (costs per hour):

_{Active}) or the number of cells.

#### 3.2.1. Calculation of Costs of Power Conversion by Specification of Active Cell Area

_{Active}) and the costs could be calculated as a function of the output power. The advantage of this method was that, with a fixed current density, the current needed for the cell voltage calculation could be calculated.

#### 3.2.2. Calculation of Costs of Power Conversion by Specification of Stack Voltage

#### 3.3. Cost of Components

^{2}or kg, or as costs per unit, and fabrication costs (FC). Most components do not have the same size as the active cell area. One also has to take into account that parts of the material are wasted during fabrication, so a factor for the real material demand per active cell area was needed for that reason. This factor can either be proportional or fixed. In this case, the factor (X

_{component}) was supposed to be fixed to the active cell area.

#### 3.4. Cost of Energy Storage

^{−1}), z is the number of electron equivalents per mol, and c is the molar concentration of vanadium species (mol·L

^{−1}).

## 4. Calculations for a 10 kW/120 kWh Vanadium Redox Flow Battery System

#### Results and Discussion

_{System}), or €1078/kWh (c

_{System}) for 12 h storage time. The power-related costs were €79,228 (C

_{Power}); the energy-related costs were €50,083, or €417/kWh (c

_{Energy}). The general equation for the specific storage costs is:

## 5. Variation in the Values of Influencing Factors

#### 5.1. Influence of Current Density and Active Material Concentration

_{Power}. The total of C

_{Stack}and C

_{Energy}was less than C

_{System}because the peripheral costs such as power electronics, sensors, etc. were absent, but scaled linearly with the current density from a plateau caused by the constant activation and concentration over potential loss. With rising current density the system costs initially fell sharply from €2620/kWh at 10 mA/cm², to attain their minimum of approx. €915/kWh in the 100–150 mA/cm² range. The system costs increased again at current densities of over 150 mA/cm².

#### 5.2. Influence of the Bipolar Plates

#### 5.3. Influence of Cell Voltage and Active Material Costs

#### 5.4. Influence of Current Density and Cell Voltages

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Components and layout of a redox flow battery stack (after [9]).

**Figure 5.**Costs of a 10 kW/120 kWh VRFB system, showing (

**a**) variation in current density and (

**b**) variation in current density and in the concentration of vanadium.

**Figure 6.**Influence of the conductivity and cost of bipolar plates on the system costs of a 10 kW/120 kWh vanadium redox flow battery system.

**Figure 7.**Influence of active material costs and cell voltage on the system costs of a VRFB with a current density of 50 mA/cm².

**Figure 8.**Influence of cell voltage and current density on the system costs of redox flow battery systems.

**Table 1.**Input values for calculating the specific costs and cost distributions of a 10 kW/120 kWh vanadium redox flow battery.

Parameter | Value | Unit | Parameter | Value | Unit |
---|---|---|---|---|---|

Mean power | 10,000 | W | Energy cost | 0.3 | €/kW |

Storage time | 12 | h | Stack assembling energy | 0.3 | kWh/cell |

Current density | 50 | mA/cm² | System assembling | – | – |

Active area | 580 | cm² | Power cond. system cost | 500 | €/kW |

Rev. cell voltage | 1.255 | V | Heat exchanger cost | 1500 | 1/unit |

Act. overpotential | 0.005 | V | Number of heat exchanger | 2 | unit |

Conc. overpotential | 0.02 | V | Pump cost | 1000 | 1/unit |

Number of stacks | 10 | unit | Number of pumps | 2 | unit |

Stack | – | – | Piping length | 50 | m |

Membrane conductivity | 1.44 | S/m | Piping cost | 20 | €/m |

Membrane cost | 250 | €/m² | Number of valves | 14 | unit |

Membrane factor | 1.5 | Valve cost | 30 | €/unit | |

Felt conductivity | 83.3 | S/m | Number of actuators | 2 | unit |

Felt cost | 150 | €/m² | Actuator cost | 330 | €/unit |

Felt factor | 1.5 | Number of sensors | 10 | unit | |

BPP conductivity | 5300 | S/m | Sensor cost | 250 | €/unit |

BPP cost | 418 | €/m² | System assembling man hour | 300 | h |

BPP factor | 1.5 | – | System assembling energy | 1 | kW/h |

Gasket cost | 392 | €/m² | Energy | – | – |

Gasket fabr. cost | 5 | €/unit | Min theoretical SOC | 0.2 | – |

Cell frame cost | 100 | €/m² | Max theoretical SOC | 0.8 | – |

Cell frame fabrication cost | 5 | €/unit | Tank cost | 1.1 | – |

Current collector | 700 | €/m² | Active species cost (Vanadium) | 1.5 | €/L |

Current collector fabrication cost | 5 | €/unit | Active species concentration (Vanadium) | 1.6 | mol/L |

Isolation plate cost | 300 | 300 €/m² | Solvent cost (H_{2}SO_{4}) | 0.0083 | €/mol |

Isolation plate fabr. cost | 20 | €/unit | Solvent concentration (H_{2}SO_{4}) | 2 | mol/L |

End plate cost | 600 | €/m² | Additive 1 cost (H_{3}PO_{4}) | 0.98 | €/mol |

Endplate fabr. cost | 20 | €/unit | Additive 1 conc. (H_{3}PO_{4}) | 0.05 | mol/L |

Stack connection cost | 3 | €/unit | Electrolyte production cost | 2.5 | €/L |

Stack assembling man hour | 0.3 | h/cell | – | – | – |

Man hour cost | 30 | €/h | – | – | – |

Parameter | Value | Unit | Parameter | Value | Unit |
---|---|---|---|---|---|

Total cost | 129,310 | € | Ohmic resistance electrolyte | 0.2 | mΩ |

Total specific cost | 1078 | €/kWh | Ohmic resistance contact | 0.2 | mΩ |

Power cost | 79,228 | € | BPP cost | 11,211 | € |

Power specific cost | 7923 | €/kWh | Felt cost | 11,047 | € |

Energy cost | 50,083 | € | Frame cost | 3,066 | € |

Energy specific cost | 417 | €/kWh | Membrane cost | 6,656 | € |

Stack cost | 52,648 | € | Gasket cost | 16,974 | € |

Stack specific cost | 5265 | €/kWh | Assembling cost | 2,782 | € |

System assembling cost | 9,000 | € | End plate cost | 435 | € |

Power electronics cost | 5,000 | € | Isolation plate cost | 217 | € |

Fluid components cost | 3,420 | € | Current collector cost | 141 | € |

Control engineering cost | 9,160 | € | Energy | – | – |

Stack | – | – | Electrolyte cost | 41,000 | € |

Effective cell voltage | 1.1286 | V | Volume of electrolyte | 8,257 | L |

Number of cells | 306 | – | Tank cost | 9,082 | € |

IR drop cell | 0.1014 | V | Active material cost | 19,816 | € |

Ohmic resistance cell | 3.5 | mΩ | Solvent cost | 542 | € |

Ohmic resistance membrane | 0.60 | mΩ | Additive cost | 405 | € |

Ohmic resistance BPP | 0.0017 | mΩ | Fabrication cost | 20,641 | € |

Ohmic resistance felt | 2.48 | mΩ | – | – | – |

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Noack, J.; Wietschel, L.; Roznyatovskaya, N.; Pinkwart, K.; Tübke, J. Techno-Economic Modeling and Analysis of Redox Flow Battery Systems. *Energies* **2016**, *9*, 627.
https://doi.org/10.3390/en9080627

**AMA Style**

Noack J, Wietschel L, Roznyatovskaya N, Pinkwart K, Tübke J. Techno-Economic Modeling and Analysis of Redox Flow Battery Systems. *Energies*. 2016; 9(8):627.
https://doi.org/10.3390/en9080627

**Chicago/Turabian Style**

Noack, Jens, Lars Wietschel, Nataliya Roznyatovskaya, Karsten Pinkwart, and Jens Tübke. 2016. "Techno-Economic Modeling and Analysis of Redox Flow Battery Systems" *Energies* 9, no. 8: 627.
https://doi.org/10.3390/en9080627