# Roadmap to Profitability for a Speed-Controlled Micro-Hydro Storage System Using Pumps as Turbines

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Concept and Initial Data

#### 2.2. Map Calculation

#### 2.2.1. Calculation of Turbine Characteristics at Nominal Speed

#### 2.2.2. Extension of Turbine Maps

#### 2.3. Simulation Model

#### 2.4. Finding the Optimal Site for Each PAT and Scaling Factor

## 3. Results and Discussion

_{PV}and S

_{L}are varied independently. As will be shown later, the specific component costs play an important role, which is why they are discussed in more detail after describing the different pumps investigated.

#### 3.1. Pumps Investigated

#### 3.2. Specific Costs

#### 3.3. Total Efficiency

#### 3.4. Average Electrical Pump Efficiency

#### 3.5. Average Electrical Turbine Efficiency

#### 3.6. Head

#### 3.7. Levelized Cost of Electricity

## 4. Simulation Results for Various Scaling Factors Using the Example of the KSB 8065200

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

Symbol/Abbreviation | Interpretation |

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

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

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

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

$g$ | gravitational acceleration |

$H$ | head |

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

${H}_{L}$ | head of the idle point |

${H}_{m}$ | arithmetic average value of the head |

${H}_{N}$ | head at nominal speed |

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

${H}_{opt}$ | head at the best efficiency point |

${H}_{r}$ | head corresponding to the respective speed |

${H}_{T}$ | turbine head |

$i$ | discount rate |

${I}_{0}$ | investment costs |

${I}_{el}$ | investment for motor and frequency inverter |

${I}_{P}$ | pump investment |

$kWp$ | nominal power (PV) |

$LCOE$ | levelized cost of energy |

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

$M$ | torque |

$n$ | rpm |

${n}_{N}$ | nominal speed |

${n}_{q}$ | specific speed |

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

${P}_{hydr}$ | hydraulic power |

${P}_{L}$ | power demand (consumer) |

${P}_{n}$ | nominal output |

${P}_{N}$ | power at nominal speed |

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

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

${P}_{P,el}$ | electrical pump power |

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

${P}_{r}$ | power corresponding to the respective speed |

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

${P}_{T,el}$ | electrical turbine power |

${P}_{T,mech}$ | mechanical turbine power |

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

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

$Q$ | flow rate |

${Q}_{L}$ | flow rate of the idle point |

${Q}_{m}$ | arithmetic average value of the flow rate |

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

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

${Q}_{N}$ | flow rate at nominal speed |

${Q}_{opt}$ | flow rate at the best efficiency point |

${Q}_{r}$ | flow rate corresponding to the respective speed |

${Q}_{T}$ | turbine flow rate |

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

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

${S}_{L}$ | scaling factor for the annual energy demand |

${S}_{PV}$ | scaling factor for PV power |

$t$ | period of time |

$\dot{V}$ | volume flow |

$V$ | storage capacity |

${V}_{optim}$ | optimized volume of the storage |

${W}_{Grid}$ | grid energy |

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

${W}_{L}$ | annual energy demand |

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

${W}_{PV}$ | annual energy production of the PV system |

Greek letters | Interpretation |

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

$\eta $ | efficiency |

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

${\overline{\eta}}_{P,el}$ | average electrical pump efficiency |

${\overline{\eta}}_{T,el}$ | average electrical turbine efficiency |

${\eta}_{opt}$ | best efficiency point |

${\eta}_{P,opt}$ | best pump efficiency given by the manufacturer |

${\eta}_{q}$ | specific speed |

${\eta}_{T}$ | turbine efficiency |

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

${\eta}_{T,mech}$ | mechanical turbine efficiency |

$\rho $ | density |

## Appendix A

- For the first variant, the BEP in turbine operation is determined from the BEP data of the pump using the following empirical formulas:

- For the second variant, the BEP in turbine operation is also calculated from the BEP of the pump using another set of empirical formulas:

- Gülich states that both methods (Equations (A1)–(A4)) can also be used and an arithmetic mean can be formed from them. When comparing the calculations with the characteristic diagrams given by the manufacturer, the arithmetic mean of the values has proven to be the best method, which is why this is used in our calculations. The the arithmetic average value ${Q}_{m}$ and ${H}_{m}$ is calculated from both variants as well as the determination of the specific speed of the turbine via the formulas:

- To determine the turbine characteristic curve at the nominal speed ${n}_{N}$, the no-load characteristic curve, which at the same time represents the lower limit of the characteristic diagram. The no-load point ${Q}_{L,N}$, ${H}_{L,N}$ are calculated according to Equation (A8). For this, the specific speed of the pump ${\eta}_{P,q}$ is required.

- Calculation of the idle point ${Q}_{L,N}$, ${H}_{L,N}$ for the nominal speed ${n}_{N}$:

- For the approximation of the turbine characteristic ${H}_{T}=f$(${Q}_{T}$) the characteristic curve runs as a parabola through the BEP of the turbine. The head ${H}_{T}$ depends on the flow ${Q}_{T}$ and is calculated using the following formula:

- Calculation of the idle speed characteristic curve (LLK):

- Calculation of the turbine efficiency ${\eta}_{T,opt}$ for the nominal speed:

- The turbine power can then be calculated using the following formula:

## Appendix B

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**Figure 1.**Schema of the speed-controlled MPS including dairy farmer, grid, and PV system, energy demand ${W}_{L}$, grid energy ${W}_{Grid}$, total energy input ${W}_{in}$, total energy output ${W}_{out},$ PV-energy ${W}_{PV}$ [15].

**Figure 2.**Specific costs on the example of the VEM PS1R/PS2R synchronous motor, the ABB ASC 580 FUM, and the Herborner F080-255A (including motor/generator).

**Figure 3.**Total efficiency for equal scaling factors ${S}_{PV}$ = ${S}_{L}$ for various centrifugal pumps.

**Figure 4.**Electrical pump efficiency for equal scaling factors${S}_{PV}$ and ${S}_{L}$ various centrifugal pumps.

**Figure 5.**Electrical turbine efficiency for equal scaling factors ${S}_{PV}$ = ${S}_{L}$ for various centrifugal pumps.

**Figure 6.**Optimized head for equal scaling factors${S}_{PV}$ = ${S}_{L}$ for various centrifugal pumps.

**Figure 9.**Total efficiency for various scaling factors ${S}_{PV}$ and ${S}_{L}$ for the KSB 8065200.

**Figure 10.**Average electrical pump efficiency for various scaling factors ${S}_{PV}$ and ${S}_{L}$ for the KSB 8065200.

**Figure 11.**Average electrical turbine efficiency for various scaling factors ${S}_{PV}$ and ${S}_{L}$ for the KSB 8065200.

**Table 1.**Energy (per year) produced by the PV system ${W}_{PV}$, energy demand ${W}_{L}$, scaling factor ${S}_{L}$ (corresponding to ${W}_{L}$ ) and ${S}_{PV}$ (corresponding to ${W}_{PV}$).

$\mathbf{Scaling}\mathbf{Factor}{\mathit{S}}_{\mathit{L}\mathit{o}\mathit{r}}$${\mathit{S}}_{\mathit{P}\mathit{V}}$ | 0.5 | 0.8 | 1.0 | 1.2 | 1.5 | 2.0 | 3.0 | 4.0 |
---|---|---|---|---|---|---|---|---|

${W}_{L}$ [MWh] | 22 | 34 | 43 | 52 | 65 | 86 | 129 | 172 |

${W}_{PV}$ [MWh] | 35 | 55 | 69 | 83 | 103 | 138 | 207 | 276 |

**Table 2.**The centrifugal pumps investigated, sorted by their nominal power ${P}_{n}$ at their best efficiency given by the manufacturer ${\eta}_{P,opt}$, average electrical pump efficiency ${\overline{\eta}}_{P,el}$, average electrical turbine efficiency ${\overline{\eta}}_{T,el}$, average electrical turbine efficiency ${\eta}_{tot}$, pump investment ${I}_{P}$ and investment for motor and frequency inverter ${I}_{el}$. All results here are given for a scaling factor ${S}_{PV}$ =${S}_{L}$ = 1.0.

Pump | ${\mathit{P}}_{\mathit{n}}$ | ${\mathit{\eta}}_{\mathit{P},\mathit{o}\mathit{p}\mathit{t}}$ | ${\overline{\mathit{\eta}}}_{\mathit{P},\mathit{e}\mathit{l}},$ | ${\overline{\mathit{\eta}}}_{\mathit{T},\mathit{e}\mathit{l}}$ | ${\mathit{\eta}}_{\mathit{t}\mathit{o}\mathit{t}}$ | ${\mathit{I}}_{\mathit{P}}$ | ${\mathit{I}}_{\mathit{e}\mathit{l}}$ |
---|---|---|---|---|---|---|---|

F065-200A-1102H ^{1} | 11.0 kW | 71.1% | 64.2% | 58.5% | 37.5% | 3347 € | 9323 € |

EST 65-160 ^{2} | 15.0 kW | 80.9% | 67.6% | 58.9% | 38.7% | 4246 € | 7343 € |

F080-255A-1502H ^{1} | 15.0 kW | 75.4% | 63.6% | 56.0% | 35.3% | 3419 € | 10,475 € |

KSB 50160174 ^{2} | 15.0 kW | 76.0% | 67.7% | 62.3% | 42.1% | 3808 € | 11,575 € |

F080-255A-1852H ^{1} | 18.5 kW | 75.9% | 64.7% | 57.5% | 37.1% | 4420 € | 12,372 € |

F080-255A-2202H ^{1} | 22.0 kW | 78.4% | 65.9% | 60.9% | 40.1% | 4699 € | 14,348 € |

F080-240A-2202H ^{1} | 22.0 kW | 82.3% | 69.3% | 53.8% | 37.2% | 4377 € | 13,864 € |

F080-330A-2204H ^{1} | 22.0 kW | 78.1% | 63.2% | 56.1% | 35.4% | 4893 € | 15,585 € |

KSB 8065200 ^{3} | 30.0 kW | 80.9% | 65.2% | 58.6% | 38.2% | 2579 € | 12,022 € |

F080-255A-3002H ^{1} | 30.0 kW | 79.2% | 63.1% | 59.1% | 37.2% | 4999 € | 17,465 € |

F080-255A-3702H ^{1} | 37.0 kW | 79.3% | 62.4% | 61.1% | 38.1% | 4871 € | 18,334 € |

^{1}turbine map calculated,

^{2}turbine map given by the manufacturer,

^{3}turbine map partially given by manufacturer and extended via similarity relationships.

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**MDPI and ACS Style**

Lugauer, F.J.; Kainz, J.; Gehlich, E.; Gaderer, M.
Roadmap to Profitability for a Speed-Controlled Micro-Hydro Storage System Using Pumps as Turbines. *Sustainability* **2022**, *14*, 653.
https://doi.org/10.3390/su14020653

**AMA Style**

Lugauer FJ, Kainz J, Gehlich E, Gaderer M.
Roadmap to Profitability for a Speed-Controlled Micro-Hydro Storage System Using Pumps as Turbines. *Sustainability*. 2022; 14(2):653.
https://doi.org/10.3390/su14020653

**Chicago/Turabian Style**

Lugauer, Florian Julian, Josef Kainz, Elena Gehlich, and Matthias Gaderer.
2022. "Roadmap to Profitability for a Speed-Controlled Micro-Hydro Storage System Using Pumps as Turbines" *Sustainability* 14, no. 2: 653.
https://doi.org/10.3390/su14020653