# Techno-Economic Efficiency Analysis of Various Operating Strategies for Micro-Hydro Storage Using a Pump as a Turbine

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## Abstract

**:**

## 1. Introduction

## 2. Micro-Hydro Storage System and Operating Strategies

#### 2.1. Operating Strategies

#### 2.1.1. Fixed Operating Point

#### 2.1.2. Throttle Control

#### 2.1.3. Speed Control with a Frequency Converter

#### 2.2. The Simulation Model

#### 2.2.1. Inputs and Basic Data

#### 2.2.2. Program Sequence

#### 2.2.3. Finding the Optimal Site

## 3. Results and Discussion

#### 3.1. Technical Results and Discussion

^{3}. Speed control obtains both the highest efficiency and the best degree of self-sufficiency, which is defined based on the energy obtained from the grid ${W}_{grid}$ and the total energy requirement ${W}_{Load}$:

^{3}and a head ${H}_{opt}$ of 42 m. The third operating mode, fixed OP, has a combined efficiency of the pump and turbine mode ${\eta}_{tot}$ of 35%, placing it between the other two alternatives. In this mode, it is essential to select a centrifugal pump that achieves the best possible combination of pump and turbine efficiencies at the given motor speed. The resulting self-sufficiency is the lowest value of all the alternatives considered. Compared to a self-sufficiency of 34% for the PV-system alone, the application of the micro pump storage results in an increase of 10 to 16 percentage points, depending on the chosen operating mode.

#### 3.2. Economic Results and Discussion

^{3}. The annual discount rate and price increase were set to 2.0% each.

#### 3.2.1. Annuity Calculation Results for Speed Control

^{3}. It is interesting to note that a slight change in the head of around 37–40 m only has a small impact (<100 €) on the annual annuity. Similarly, a change in the size of the storage volume in the range of around 400 to 500 m

^{3}has the same small effect on the annuity.

#### 3.2.2. Annuity Calculation Results for the Fixed OP

^{3}, which is considerably smaller than for speed control, while the optimum head increases to approximately 44 m with an annual annuity of −2200 €.

#### 3.2.3. Annuity Calculation Results for Throttle Control

^{3}, resulting in an annual annuity of −2500 €/kWh. The optimization results for an electricity price of 31.9 cents /kWh show that pumped storage as presented is not profitable for any operation mode at that price. Particularly for speed control, the additional investment costs are currently not cost-effective, but this would change with increasing energy procurement costs, as will now be shown.

#### 3.2.4. Sensitivity Analysis and Comparison of the Different Operating Modes with Increasing Energy Procurement Costs

#### 3.2.5. LCOE Calculation and Comparison with Other Scientific Research Findings

## 4. Conclusions and Outlook

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

Symbol/Abbreviation | Interpretation |

$a$ | annuity factor |

${A}_{N}$ | total annual payments or income |

${A}_{IN}$ | annuity of the maintenance costs |

${A}_{N,B}$ | annuity of the operation-related costs |

${A}_{N,E}$ | annuity of the proceeds |

${A}_{N,K}$ | annuity of the capital-related costs |

${A}_{N,S}$ | annuity of the other costs |

${A}_{N,K}$ | annuity of the demand-related costs |

${A}_{t}$ | sum of costs |

$b$ | cash value factor |

${d}_{N}$ | nominal pipeline diameter |

$E{S}_{t}$ | possible energy sales proceeds |

${f}_{D}$ | Darcy friction factor |

${f}_{Inst}$ | repair expenditure |

${f}_{W+Insp}$ | service factor |

$g$ | gravitational acceleration |

$H$ | head |

${h}_{f}$ | head loss |

${H}_{geo}$ | geodetic head |

${H}_{opt}$ | optimized head |

$i$ | discount rate |

${I}_{0\_stor}$ | investment costs storage |

${I}_{0\_pipe}$ | investment costs pipeline |

${I}_{0\_el}$ | investment costs electrical components |

${I}_{0\_pump}$ | investment costs pump |

${I}_{0\_thrott}$ | investment costs throttle element |

${I}_{0\_\mathrm{oth}}$ | remaining investment costs |

$LCOE$ | levelized cost of energy |

${L}_{pipe}$ | pipeline length |

$M$ | torque |

$n$ | rpm |

${n}_{r}$ | number of replacements |

$O\&{M}_{t}$ | operating and maintenance costs |

$\Delta p$ | pressure loss |

${P}_{L1}$ | load profile |

${P}_{max}$ | maximum power in pump mode |

${P}_{pump}$ | pump power |

${P}_{turb}$ | turbine power |

${P}_{v}$ | power loss |

${P}_{Pv}$ | PV power |

$Pum{p}_{on}$ | number of pump start-ups |

$q$ | interest factor |

$Q$ | flow rate |

${Q}_{max}$ | maximum flow rate |

${Q}_{min}$ | minimum flow rate |

$r$ | price change factor |

$R{I}_{t}$ | reinvestment costs |

$R{W}_{t}$ | residual values |

$t$ | year |

$T$ | observation period |

${T}_{N}$ | service life |

$Tur{b}_{on}$ | number of turbine start-ups |

$v$ | water velocity |

$\dot{V}$ | volume flow |

$V$ | storage capacity |

${V}_{opt}$ | optimized storage capacity |

${W}_{grid}$ | energy obtained from the grid |

${W}_{in}$ | total energy input |

${W}_{load}$ | total energy requirement |

${W}_{out}$ | total energy output |

${W}_{t,el}$ | energy drawn from the pumped storage |

Greek letters | Interpretation |

${\zeta}_{fit}$ | individual dynamic loss coefficient of fittings |

${\zeta}_{tot}$ | total dynamic loss coefficient of fittings |

$\eta $ | efficiency |

${\eta}_{el}$ | efficiency of the electrical components in the drive unit |

${\eta}_{{p}_{m}}$ | average pump efficiency |

${\eta}_{pump\_el}$ | electrical pump efficiency |

${\eta}_{t\_m}$ | average turbine efficiency |

${\eta}_{tot}$ | total efficiency |

${\eta}_{turb\_el}$ | electrical turbine efficiency |

$\lambda $ | coefficient of friction |

$\pi $ | pi |

$\rho $ | density |

## Appendix A

#### Appendix A.1. Annuity and Price Change Factor

#### Appendix A.2. Cost Calculation

#### Appendix A.2.1. Capital-Related Costs

#### Appendix A.2.2. Demand-Related Costs

#### Appendix A.2.3. Operation-Related Costs

#### Appendix A.2.4. Other Costs

#### Appendix A.3. Proceeds

#### Appendix A.4. Annuity of Total Annual Payments

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**Figure 2.**Exemplary simulated power balance of the speed controlled micro pump storage plant including load profile (${P}_{L1}$), pump power (${P}_{Pump}$), PV power (${P}_{PV}$), turbine power (${P}_{Turb}$) and the storage volume ($V$).

**Figure 11.**Sensitivity analysis for storage, the pump-as-turbine (PAT), drive unit and pipeline costs.

**Table 1.**Technical results for pump storage, including optimized storage volume (${V}_{opt}$), optimized head (${H}_{opt}$), total efficiency (${\eta}_{tot}$), average pump efficiency (${\eta}_{p\_m}$), average turbine efficiency (${\eta}_{t\_m}$), number of pump activations ($Pum{p}_{on}$), number of turbine activations ($Tur{b}_{on}$), maximum power in pump mode (${P}_{max}$), storage capacity, and degree of self-sufficiency.

OP Mode | ${\mathit{V}}_{\mathit{o}\mathit{p}\mathit{t}}$ | ${\mathit{H}}_{\mathit{o}\mathit{p}\mathit{t}}$ | ${\mathit{\eta}}_{\mathit{t}\mathit{o}\mathit{t}}$ | ${\mathit{\eta}}_{\mathit{p}\_\mathit{m}}$ | ${\mathit{\eta}}_{\mathit{t}\_\mathit{m}}$ | $\mathit{P}\mathit{u}\mathit{m}{\mathit{p}}_{\mathit{o}\mathit{n}}$ | $\mathit{T}\mathit{u}\mathit{r}{\mathit{b}}_{\mathit{o}\mathit{n}}$ | ${\mathit{P}}_{\mathit{m}\mathit{a}\mathit{x}}$ | Storage Capacity | Degree of Self-Sufficiency |
---|---|---|---|---|---|---|---|---|---|---|

Speed control | 460 m^{3} | 39 m | 42% | 68% | 62% | 860 | 1000 | 13 kW | 48 kWh | 50% |

Throttle control | 280 m^{3} | 42 m | 30% | 63% | 47% | 850 | 990 | 12 kW | 32 kWh | 43% |

Fixed OP | 300 m^{3} | 44 m | 35% | 62% | 57% | 920 | 760 | 10 kW | 36 kWh | 44% |

**Table 2.**Investment costs per unit for storage (${I}_{0\_stor}$), penstock (${I}_{0\_pen}$), pump (${I}_{0\_pump}$), drive unit (${I}_{0\_el}$), control valve (${I}_{0\_thrott}$), other costs (${I}_{0\_oth}$) and total investment for the system (${I}_{0\_tot}$).

OP Mode | ${\mathit{I}}_{0\_\mathit{s}\mathit{t}\mathit{o}\mathit{r}}$ | ${\mathit{I}}_{0\_\mathit{p}\mathit{e}\mathit{n}}$ | ${\mathit{I}}_{0\_\mathit{e}\mathit{l}}$ | ${\mathit{I}}_{0\_\mathit{P}\mathit{u}\mathit{m}\mathit{p}}$ | ${\mathit{I}}_{0\_\mathit{t}\mathit{h}\mathit{r}\mathit{o}\mathit{t}\mathit{t}}$ | ${\mathit{I}}_{0\_\mathit{o}\mathit{t}\mathit{h}}$ | ${\mathit{I}}_{0\_\mathit{t}\mathit{o}\mathit{t}}$ |
---|---|---|---|---|---|---|---|

Speed control | 40 €/m^{3} | 50 €/m | 16,000 € | 3800 € | 1000 € | 5000 € | 56,000 € |

Throttle control | 40 €/m^{3} | 50 €/m | 7200 € | 3800 € | 2500 € | 5000 € | 44,000 € |

Fixed OP | 40 €/m^{3} | 50 €/m | 7200 € | 3800 € | 1000 € | 5000 € | 44,000 € |

Interest Rate | $2\mathit{\%}$ | $4\mathit{\%}$ | $6\mathit{\%}$ | $8\mathit{\%}$ |
---|---|---|---|---|

Speed control | 0.63 €/kWh | 0.74 €/kWh | 0.86 €/kWh | 0.98 €/kWh |

Throttle control | 0.85 €/kWh | 0.99 €/kWh | 1.16 €/kWh | 1.33 €/kWh |

Fixed OP | 0.74 €/kWh | 0.87 €/kWh | 1.01 €/kWh | 1.17 €/kWh |

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**MDPI and ACS Style**

Lugauer, F.J.; Kainz, J.; Gaderer, M. Techno-Economic Efficiency Analysis of Various Operating Strategies for Micro-Hydro Storage Using a Pump as a Turbine. *Energies* **2021**, *14*, 425.
https://doi.org/10.3390/en14020425

**AMA Style**

Lugauer FJ, Kainz J, Gaderer M. Techno-Economic Efficiency Analysis of Various Operating Strategies for Micro-Hydro Storage Using a Pump as a Turbine. *Energies*. 2021; 14(2):425.
https://doi.org/10.3390/en14020425

**Chicago/Turabian Style**

Lugauer, Florian Julian, Josef Kainz, and Matthias Gaderer. 2021. "Techno-Economic Efficiency Analysis of Various Operating Strategies for Micro-Hydro Storage Using a Pump as a Turbine" *Energies* 14, no. 2: 425.
https://doi.org/10.3390/en14020425