# Comparison of Tank and Battery Storages for Photovoltaic Water Pumping

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

^{3}and 6 m

^{3}of water for daily domestic use. Meunier et al. optimized a PVWPS for domestic use for 280 inhabitants of a village in Burkina Faso [13].

## 2. Methodology

#### 2.1. Architectures

#### 2.2. Technical Models

#### 2.2.1. Tank Architecture

#### 2.2.2. Battery Architecture

#### 2.3. Economic Model

## 3. Case Study

#### 3.1. PVWPS in Gogma, Burkina Faso

_{p}, the motor-pump reference $MP$ is a SQFlex 5A-7 (Grundfos) and the tank volume ${V}_{t}$ is 11.4 m

^{3}. The PVWPS provides water to around 280 inhabitants of the village. Around 8 m

^{3}are pumped daily during the dry season and around 6 m

^{3}during wet season [26].

#### 3.2. Technical and Economic Models Parameters

## 4. Quantitative Comparison through Techno-Economic Optimization

#### 4.1. Method

#### 4.2. Formulation

_{p}and the tank volume between 5 and 30 m

^{3}[13]. The principal constraint is to meet the current water demand at Gogma’s PVWPS. We formulate this constraint by checking that the volume delivered between the arrival of a group i (at ${t}_{i}$) and the arrival of the next group (at ${t}_{i+1}$) is larger than the water demand volume of the group ${g}_{i}$ (see Figure 3 and Section 3.1). The groups are constructed in such a way that they are separated by at least 20 min or a period without demand. ${N}_{g}$ is the number of groups of users. Another constraint is that the water level in the borehole must remain above the position of the motor-pump. In Gogma, the motor-pump is 30 m below ground. The last constraint is that the total dynamic head $TDH$ must remain lower than the maximum pumping height ${H}_{p,max}\left(MP\right)$ given in the datasheet of the motor-pump reference MP [41].

## 5. Results of the Optimizations and Comparison of Architectures

## 6. Conclusions

^{3}volume. For volumes between 2 and 10 m

^{3}, plastic tanks, which are cheaper, are usually used. A study of their costs in Burkina Faso has already been performed [44] but a study of their suitability for drinkable water is necessary before including them into the optimization.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

$b\left(t\right)$ | triggering signal from the switch |

$Ca{p}_{b}$ | battery capacity (Wh) |

${C}_{b},{C}_{cc},{C}_{MP},$${C}_{pv},{C}_{t}$ | CAPEX (battery, charge controller, motor-pump, PV array, tank) ($) |

$C{F}_{SOC,final,k}$ | final state of charge of cycle k |

${C}_{init,var}$ | initial variable cost ($) |

${C}_{maint,var}$ | maintenance variable cost ($) |

${C}_{repla,var}$ | replacement variable cost ($) |

$\gamma $ | temperature coefficient of the maximum power point (°C^{−1}) |

$DO{D}_{k}$ | depth of discharge of cycle k |

$\overline{DOD}$ | amplitude of reference |

$dr$ | discount rate |

${\delta}_{tap}$ | state of the tap (open/close) |

${\delta}_{b},{\delta}_{t}$ | type of architecture (battery/tank) |

${E}_{a}$ | activation energy (J/mol) |

${E}_{sto}$ | energy stored in battery (Wh) |

${G}_{pv}$ | irradiance on the plane of PV (W/m^{2}) |

${g}_{i}:\left({t}_{i},{V}_{ci}^{*}\right)$ | group of users (time of arrival, volume of water demanded (m^{3})) |

${H}_{t,b}$ | height between bottom of the tank and water level in the tank (m) |

${H}_{t,c}$ | height of tank (m) |

${H}_{t,i}$ | height between top of the tank and its entry level (m) |

${H}_{t,s}$ | height between entry level and stop level in the tank (m) |

${H}_{t,r}$ | height between stop level and restart level in the tank (m) |

${H}_{t}\left(t\right)$ | level of water in the tank (m) |

${H}_{b,s}$ | height between ground level and static water level in the borehole (m) |

${H}_{b,d}\left(t\right)$ | height between static water level and water level during pumping (m) |

${H}_{fo}$ | height between ground level and fountain (m) |

${H}_{p,max}\left(MP\right)$ | maximum TDH for motor-pumps (m) |

${\eta}_{b}$ | efficiency of battery charging |

${\eta}_{cc}$ | efficiency of charge controller |

${i}_{b}\left(t\right)$ | current from battery to motor-pump (A) |

${i}_{max}$ | maximum current from battery (A) |

${i}_{MP,nom}$ | nominal current of motor-pump (A) |

${\kappa}_{0}$ | aquifer losses coefficient (s/m^{2}) |

${L}_{b},{L}_{cc,}{L}_{MP,}$${L}_{pv},{L}_{t}$ | lifetime (battery, charge controller, motor-pump, PV array, tank) (year) |

$LCC$ | life cycle cost ($) |

$LC{C}_{fixe}$ | fixed part of life cycle cost ($) |

$MP$ | reference of motor pump |

${\mu}_{0}$ | borehole losses coefficients (s^{2}/m^{5}) |

$NR\left(i\right)$ | variable replacement costs of year i ($) |

NOCT | Normal Operating Cell Temperature |

${P}_{MP}\left(t\right)$ | power consumed by the motor-pump (W) |

${P}_{MP,max}\left(t\right)$ | maximum power to motor-pump (W) |

${P}_{pv}\left(t\right)$ | power generated by PV array (W) |

${P}_{pv,p}$ | peak power of PV array (Wp) |

${P}_{sto}\left(t\right)$ | power to battery (W) |

${Q}_{p}^{*}$ | reference flow rate (m^{3}/s) |

${Q}_{c,0}$ | nominal flow rate of the fountain tank (m^{3}/s) |

${Q}_{c,t}\left(t\right)$, ${Q}_{c,b}\left(t\right)$ | collected flow rate of tank/battery architecture (m^{3}/s) |

${Q}_{p}\left(t\right)$ | pumped flow rate (m^{3}/s) |

${R}_{b}$ | battery resistance (Ω) |

$R$ | Arrhenius constant (J.mol^{−1}.K^{−1}) |

${S}_{t}$ | surface of the base of the tank (m^{2}) |

$SOC\left(t\right)$ | state of charge of the battery |

${T}_{a}\left(t\right)$ | ambient temperature (°C) |

$TDH\left(t\right)$ | total dynamic head (m) |

${v}_{abs},{v}_{fl}$ | voltage of battery during absorption/float phase (V) |

${v}_{b}$(t) | voltage of battery (V) |

${v}_{b,r}$ | reconnection level of motor-pump for charge controller (V) |

${v}_{b,s}$ | disconnection level of motor-pump for charge controller (V) |

${V}_{t}$ | volume of tank (m^{3}) |

$\psi $ | pipe pressure losses coefficient (s^{2}/m^{5}) |

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**Figure 1.**(

**a**) Tank PVWPS. (

**b**) Battery PVWPS. ${H}_{t,b}$: height between the ground level and the bottom of the tank, ${H}_{t,c}$: tank height, ${H}_{t,i}$ (<0): height between the top of the tank and the water entry in the tank, ${H}_{t,s}$ (<0): height between the water entry and the stop controller level, ${H}_{t,r}$ (<0): height between the stop controller level and the restart level, ${H}_{t}\left(t\right)$: water level in the tank, ${H}_{b,s}$ (<0): height between the ground level and the static water level in the borehole, ${H}_{b,d}\left(t\right)$ (<0): height between the static level and the water level in the borehole (i.e., the drawdown), ${H}_{fo}$: the height between the ground level and the fountain’s tap.

**Figure 3.**(

**a**) Overview of the PVWPS of Gogma. (

**b**) Measured irradiance on the plane of the PV modules ${G}_{pv}$ and ambient temperature ${T}_{a}$ (model inputs). (

**c**) Measured collected flow rate. (

**d**) Group of users ${g}_{i}$ (model inputs).

**Figure 4.**(

**a**) Comparison of pumped flow rates for both optimized architectures. (

**b**) Comparison of collected flow rates for both optimized architectures.

Common to the Tank and Battery PVWPS | Relative to the Tank PVWPS | Relative to the Battery PVWPS |
---|---|---|

System | Tank [45] | Lead-acid batteries [34,35,36] |

L = 20 years | ${H}_{t,b}$ = 4.2 m | ${v}_{b}$ = 48 V |

${H}_{t,t}$ = 3.4 m | ${R}_{b}$ = 6 mΩ | |

PV array [45] | ${H}_{t,r}$ = 0.4 m | $\beta $ = 43.2 V |

$NOCT=32\xb0\mathrm{C}$ | ${H}_{t,s}$ = 0.1 m | $\alpha $ = 7.5 V |

$\gamma =-0.004\xb0{\mathrm{C}}^{-1}$ | ${H}_{t,i}$ = 0.1 m | ${L}_{max}$ = 8 years |

Motor-pump [29,41] | Fountain | Charge controller [46] |

${i}_{MP,nom}$ = 8.4 A | ${Q}_{0}=$ 5.5 × 10^{−4} m^{3}/s | ${v}_{b,s}$ = 44.4 V |

Models: SQFlex 5A-3, SQFlex | ${v}_{b,r}$ = 55.2 V | |

0.6–2, SQFlex 8A-5, SQFlex8A- | ${v}_{abs}$ = 57.6 V | |

3, SQFlex 11A-3, SQFlex 1.2-2 | ${v}_{fl}$ = 55.2 V | |

SQFlex 5A-7 and SQFlex2.5-2 | ${\eta}_{cc}$ = 98% | |

${i}_{max}$ = 20 A | ||

Hydraulic model [41] | ||

${\kappa}_{0}$ = 2.4 × 10^{3} s/m^{2} | Fountain | |

${\mu}_{0}$ = 8.4 × 10^{5} s²/m^{5} | ${H}_{fo}$ = 1 m | |

$\psi $ = 4.9 × 10^{6} s²/m^{5} | ||

${H}_{b,s}$ = 7.5 m |

Common to Tank and Battery PVWPS | Relative to the Tank PVWPS | Relative to the Battery PVWPS |
---|---|---|

PV array [13] | Steel tank [13] | Lead-acid batteries [30] |

${C}_{pv}=$$0.79{P}_{pv,p}$ [$] ${L}_{pv}$ = 20 years | ${C}_{t}$ = $6.2\times {10}^{2}{V}_{t}+5.2\times {10}^{3}[\$]$ ${L}_{t}$ = 20 years | ${C}_{b}=0.19Ca{p}_{b}+126[\$]$ ${L}_{b}$ is obtained from Equation (11) |

Motor-pump [13] | Charge controller [30,46] | |

${C}_{MP}=2.2\times {10}^{3}$ $ ${L}_{MP}$ = 10 years | ${C}_{cc}=$150 $ ${L}_{cc}$ = 5 years | |

Discount rate [44] | ||

$dr$ = 5.6% | ||

Fixed costs [13] | ||

$LC{C}_{fixe}=1.78\times {10}^{4}\$$ |

Tank PVWPS | Battery PVWPS | ||
---|---|---|---|

Sizing | PV peak power ${P}_{pv,p}$ | 410 W_{p} | 462 W_{p} |

Motor-pump reference $MP$ | SQFlex 2.5-2 | SQFlex 2.5-2 | |

Tank volume ${V}_{t}$ | 5 m^{3} | ||

Battery capacity $Ca{p}_{b}$ | 1673 Wh | ||

$\mathrm{Control}\mathrm{Variable}{Q}^{*}$ | 30.4 L/min | ||

Economic | Variable costs | $13.3 k | $6.3 k |

Fixed costs | $17.8 k | $17.8 k | |

$LCC$ | $31.1 k | $24.1 k | |

Maintenance | Storage replacements | 0 | 5 |

Starts and stops per day | max: 8–mean: 4 | max: 107–mean: 84 | |

Availability of spare parts | Not applicable | Low | |

Environment | Toxicity | Low | High (lead) |

Maximum pumped flow rate | 48.3 L/min | 30.4 L/min | |

Lowest water level in the borehole | −10.0 m | −8.9 m |

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**MDPI and ACS Style**

Soenen, C.; Reinbold, V.; Meunier, S.; Cherni, J.A.; Darga, A.; Dessante, P.; Quéval, L. Comparison of Tank and Battery Storages for Photovoltaic Water Pumping. *Energies* **2021**, *14*, 2483.
https://doi.org/10.3390/en14092483

**AMA Style**

Soenen C, Reinbold V, Meunier S, Cherni JA, Darga A, Dessante P, Quéval L. Comparison of Tank and Battery Storages for Photovoltaic Water Pumping. *Energies*. 2021; 14(9):2483.
https://doi.org/10.3390/en14092483

**Chicago/Turabian Style**

Soenen, Camille, Vincent Reinbold, Simon Meunier, Judith A. Cherni, Arouna Darga, Philippe Dessante, and Loïc Quéval. 2021. "Comparison of Tank and Battery Storages for Photovoltaic Water Pumping" *Energies* 14, no. 9: 2483.
https://doi.org/10.3390/en14092483