# Quantifying the Demand Response Potential of Inherent Energy Storages in Production Systems

^{*}

## Abstract

**:**

## 1. Introduction

#### Related Work

## 2. Modelling of IES

- ${P}_{\mathrm{el}}:$electrical power required by the energy converter,
- $\eta $: efficiency of the converter in the conversion of electricity into useful energy,
- ${P}_{\mathrm{use}}:$ generated useful energy per time,
- $C$: the theoretical storage capacity,
- ${C}_{\mathrm{high}}:$upper level of usable storage capacity (upper level of storage content),
- ${C}_{\mathrm{low}}:$lower level of usable storage capacity (lower level of storage content),
- ${P}_{\mathrm{losses}}:$losses per time,
- ${P}_{\mathrm{demand}}:$energy demand per time of the production process.

#### 2.1. Examples for IES in Production

^{3}) and specific heat capacity ${c}_{p}$ (4.12 kJ/kgK) of water and a target temperature $T$ of 60–65 °C the calculation of useful energy content results in 5.72 kWh. Since the conversion efficiency of the heating element can be assumed to be 100%, the equivalent electrical energy storage capacity is 5.72 kWh for this example, too. Assuming a nominal electrical power of 10 kW for the heating element and losses and demand to be zero, the minimum time the converter needs to fill the energy storages is 5.72 kWh/10 kW = 34.3 min. Regarding a compressed air system with a volume ${V}_{2}$ of 1 m

^{3}and a target pressure ${p}_{2}$ of 7 bar, the calculation of the useful energy content results in 0.38 kWh, if the ambient pressure ${p}_{1}$ of 1 bar is taken as reference point. As the conversion efficiency of compressed air generation systems is at around 60%, the equivalent electrical energy storage for this example is 0.38 kWh/0.6 = 0.63 kWh. Thus, the minimum time for filling the storage amounts to 0.63 kWh/10 kW = 3.8 min in case of a compressor with a nominal electrical power of 10 kW. This simple assessment indicates that the thermal inherent energy storage has a far greater electrical flexibility potential, than the compressed air system although the volume of the storage and the nominal electrical power of the energy converter are equal. In this calculation, however, the losses and the demand for useful energy from the production process have been neglected. In the following, we discuss how these values influence the actual flexibility potential of the devices. For this purpose, it is necessary to explain the most important mathematical interrelationships for describing the operation of inherent energy storages: Many IES are two-point, respectively hysteresis controlled. This means that the energy converter switches on ($s=1$), when the content in the storage reaches its lower limit which is defined by the operator. Afterwards, as long as the content is below the upper level, the converter remains in the switched-on state. Such devices can be modelled as a hybrid system consisting of discrete and continuous states [34]:

#### 2.2. General Remarks on the Calculation of the Flexibility Potential Calculation for IES

- ${t}_{0}$ to ${t}_{1}$: Activation time (from first load change to reach of final load level) $\Delta {t}_{\mathrm{activation}}$
- ${t}_{1}$ to ${t}_{2}$: Holding time (constant load level) $\Delta {t}_{\mathrm{hold}}$
- ${t}_{2}$ to ${t}_{3}$: Deactivation time (from load level to zero) $\Delta {t}_{\mathrm{deactivation}}$
- ${t}_{3}$ to ${t}_{4}$: Break time (time until load recovery starts) $\Delta {t}_{\mathrm{break}}$
- ${t}_{3}$ to ${t}_{5}$: Regeneration time (time until load recovery is completed) $\Delta {t}_{\mathrm{regeneration}}$

#### 2.3. Reference Load Profile

#### 2.4. Calling a Flexibility Measure

#### 2.5. Method for Quantifying the State-Dependent Flexibility Potential of IES

## 3. Case Study

- ▪
- Compressor: Increase of the upper pressure level up to 8 bar possible
- ▪
- Cleaning machine: Extension of the upper hysteresis limit up to 68 °C is possible

## 4. Discussion and Conclusions

_{2}equivalent. Converted to a capacity of 3.1 kWh, this would result in 162.5 kg CO2 equivalent if a new electrical battery would be produced instead of using the flexibility potential of the cleaning machine, which already exist. This idea will be further developed in subsequent research work. In addition, it will be analyzed how a flexible operation affects the efficiency of the devices—for example, heat losses increase when the bath temperature of cleaning machines is increased, which was not considered in the present study. The developed tool for load analysis will be improved in further work, especially regarding the partial load behavior of the devices and the use of advanced data analysis techniques. For example, clustering methods can be used to identify time spans with regular cycle times and thus reliably available flexibility potentials. The developed procedure for the extraction of the characteristic values of IES from measurement data is to be tested in the ETA research factory in real operation, in which the algorithm continuously updates the flexibility potential of the devices. This will provide further insights into how the approaches can be applied under real network conditions. In particular, an analysis of the reliability of the forecasts of the useful energy demand and thus of the possible call times for the maximum flexibility potential will be examined more closely.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Connolly, D.; Lund, H.; Mathiesen, B.V. Smart Energy Europe: The technical and economic impact of one potential 100% renewable energy scenario for the European Union. Renew. Sustain. Energy Rev.
**2016**, 60, 1634–1653. [Google Scholar] [CrossRef] - Samad, T.; Koch, E.; Stluka, P. Automated Demand Response for Smart Buildings and Microgrids: The State of the Practice and Research Challenges. Proc. IEEE
**2016**, 104, 726–744. [Google Scholar] [CrossRef] - Ulbig, A.; Andersson, G. Analyzing operational flexibility of electric power systems. Int. J. Electr. Power Energy Syst.
**2015**, 72, 155–164. [Google Scholar] [CrossRef] - Alizadeh, M.I.; Parsa Moghaddam, M.; Amjady, N.; Siano, P.; Sheikh-El-Eslami, M.K. Flexibility in future power systems with high renewable penetration: A review. Renew. Sustain. Energy Rev.
**2016**, 57, 1186–1193. [Google Scholar] [CrossRef] - BDEW. Stromverbrauch in Deutschland Nach Verbrauchergruppen 2019. Available online: https://www.bdew.de/media/documents/Nettostromverbrauch_nach_Verbrauchergruppen_2019_online_o_jaehrlich_Ki_12032020.pdf (accessed on 22 April 2020).
- Torriti, J.; Hassan, M.G.; Leach, M. Demand response experience in Europe: Policies, programmes and implementation. Energy
**2010**, 35, 1575–1583. [Google Scholar] [CrossRef] [Green Version] - Li, B.; Shen, J.; Wang, X.; Jiang, C. From controllable loads to generalized demand-side resources: A review on developments of demand-side resources. Renew. Sustain. Energy Rev.
**2016**, 53, 936–944. [Google Scholar] [CrossRef] - Council of the EU Directive (EU). 2019/944 on Common Rules for the Internal Market for Electricity and Amending Directive 2012/27/EU: 2019. Available online: https://eur-lex.europa.eu/eli/dir/2019/944/oj (accessed on 10 August 2020).
- Wattjes, F.D.; Janssen, S.L.L.; Slootweg, J.G. Framework for estimating flexibility of commercial and industrial customers in Smart Grids. In Proceedings of the IEEE PES ISGT Europe 2013, Lyngby, Denmark, 6–9 October 2013; IEEE: Piscataway, NJ, USA, 2013; pp. 1–5. [Google Scholar]
- Petersen, M.K.; Edlund, K.; Hansen, L.H.; Bendtsen, J.; Stoustrup, J. A taxonomy for modeling flexibility and a computationally efficient algorithm for dispatch in Smart Grids. In Proceedings of the 2013 American Control Conference, Washington, DC, USA, 17–19 June 2013; IEEE: Piscataway, NJ, USA, 2013; pp. 1150–1156. [Google Scholar]
- Deng, R.; Yang, Z.; Chow, M.-Y.; Chen, J. A Survey on Demand Response in Smart Grids: Mathematical Models and Approaches. IEEE Trans. Ind. Inf.
**2015**, 11, 570–582. [Google Scholar] [CrossRef] - VDI. Energieflexible Fabrik: Grundlagen (VDI 5207 Blatt 1); Beuth Verlag: Berlin, Germany, 2019. [Google Scholar]
- Schoepf, M.; Weibelzahl, M.; Nowka, L. The Impact of Substituting Production Technologies on the Economic Demand Response Potential in Industrial Processes. Energies
**2018**, 11, 2217. [Google Scholar] [CrossRef] [Green Version] - Zhang, X.; Hug, G.; Kolter, Z.; Harjunkoski, I. Industrial demand response by steel plants with spinning reserve provision. In Proceedings of the 2015 North American Power Symposium (NAPS), Charlotte, NC, USA, 4–6 October 2015; IEEE: Piscataway, NJ, USA, 2015; pp. 1–6. [Google Scholar]
- Zhang, X.; Hug, G.; Harjunkoski, I. Cost-Effective Scheduling of Steel Plants with Flexible EAFs. IEEE Trans. Smart Grid
**2017**, 8, 239–249. [Google Scholar] [CrossRef] - Otashu, J.I.; Baldea, M. Scheduling chemical processes for frequency regulation. Appl. Energy
**2020**, 260, 114125. [Google Scholar] [CrossRef] - Bohlayer, M.; Fleschutz, M.; Braun, M.; Zöttl, G. Energy-intense production-inventory planning with participation in sequential energy markets. Appl. Energy
**2020**, 258, 113954. [Google Scholar] [CrossRef] - Summerbell, D.L.; Khripko, D.; Barlow, C.; Hesselbach, J. Cost and carbon reductions from industrial demand-side management: Study of potential savings at a cement plant. Appl. Energy
**2017**, 197, 100–113. [Google Scholar] [CrossRef] - Rohde, C. Erstellung von Anwendungsbilanzen für die Jahre 2018 bis 2020 für die Sektoren Industrie und GHD; Fraunhofer Society: Karlsruhe, Germany, 2019. [Google Scholar]
- Shoreh, M.H.; Siano, P.; Shafie-khah, M.; Loia, V.; Catalão, J.P.S. A survey of industrial applications of Demand Response. Electr. Power Syst. Res.
**2016**, 141, 31–49. [Google Scholar] [CrossRef] - Eisenhauer, S.; Reichart, M.; Sauer, A.; Weckmann, S.; Zimmernann, F. Energieflexibilität in der Industrie: Eine Metastudie; Institut für Energieeffizienz in der Produktion, Universität Stuttgart: Stuttgart, Germany, 2018. [Google Scholar]
- Conte, F.; Massucco, S.; Silvestro, F.; Ciapessoni, E.; Cirio, D. Stochastic modelling of aggregated thermal loads for impact analysis of demand side frequency regulation in the case of Sardinia in 2020. Int. J. Electr. Power Energy Syst.
**2017**, 93, 291–307. [Google Scholar] [CrossRef] - Wai, C.H.; Beaudin, M.; Zareipour, H.; Schellenberg, A.; Lu, N. Cooling Devices in Demand Response: A Comparison of Control Methods. IEEE Trans. Smart Grid
**2015**, 6, 249–260. [Google Scholar] [CrossRef] - Koch, S.; Zima, M.; Andersson, G. Active Coordination of Thermal Household Appliances for Load Management Purposes. IFAC Proc. Vol.
**2009**, 42, 149–154. [Google Scholar] [CrossRef] [Green Version] - Rui, X.; Liu, X.; Meng, J. Dynamic Frequency Regulation Method Based on Thermostatically Controlled Appliances in the Power System. Energy Procedia
**2016**, 88, 382–388. [Google Scholar] [CrossRef] [Green Version] - van der Heijde, B.; Sourbron, M.; Arance, F.V.; Salenbien, R.; Helsen, L. Unlocking flexibility by exploiting the thermal capacity of concrete core activation. Energy Procedia
**2017**, 135, 92–104. [Google Scholar] [CrossRef] [Green Version] - Stadler, I. Demand Response: Nichtelektrische Speicher für Elektrizitätsversorgungssysteme mit Hohem Anteil Erneuerbarer Energien; Habilitation, der Universität Kassel: Berlin, Germany, October 2006. [Google Scholar]
- Koch, S.; Mathieu, J.; Callaway, D.S. Modeling and control of aggregated heterogeneous thermostatically controlled loads for ancillary services. Proc. PSCC
**2011**, 1–7. Available online: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.460.6240 (accessed on 10 August 2020). - Sterner, M.; Stadler, I. Energiespeicher-Bedarf, Technologien, Integration; Springer: Berlin/Heidelberg, Germany, 2017. [Google Scholar]
- Bundesamt für Energie BFE. Kälte Effizient Erzeugen: Das Wichtigste Zur kälteerzeugung Nach SIE 382/1; Bern, Switzerland, 2016; Available online: https://pubdb.bfe.admin.ch/de/publication/download/8559 (accessed on 10 August 2020).
- Gloor, R. Druckluftsysteme: Kennzahlen und Informationen über Energiesparmöglichkeiten bei Druckluftanlagen. Available online: https://energie.ch/druckluft/ (accessed on 24 April 2020).
- DIN Deutsches Institut für Normung e.V. Energetische Bewertung von Gebäuden—Lüftung von Gebäuden: Teil 3: Lüftung von Nichtwohngebäuden (DIN EN 16798-3:2017); Beuth Verlag GmbH: Berlin, Germany, 2017. [Google Scholar]
- Kuhrke, B. Methode Zur Energie-und Medienbedarfsbewertung Spanender Werkzeugmaschinen. Zugl.: Darmstadt. Ph.D. Dissertation, Technival University of Darmstadt, Berlin, Germany, 2011. [Google Scholar]
- Heemels, W.; Lehmann, D.; Lunze, J.; Schutter, B. Introduction to hybrid systems. In Handbook of Hybrid Systems Control: Theory, Tools, Applications; Cambridge University Press: Cambridge, UK, 2009; pp. 3–30. [Google Scholar]
- European Network of Transmission System Operators for Electricity (ENTSO-E). Electricity Balancing in Europe: An Overview of the European Balancing Market and Electricity Balancing Guideline; ENTSO-E: Brussels, Belgium, 2018. [Google Scholar]
- Oldewurtel, F.; Borsche, T.; Bucher, M.; Fortenbacher, P.; Gonzalez Vaya, M.; Haring, T.; Mathieu, J.L.; Mégel, O.; Vrettos, E.; Andersson, G. A framework for and assessment of demand response and energy storage in power systems. In Proceedings of the 2013 IREP Symposium Bulk Power System Dynamics and Control-IX Optimization, Security and Control of the Emerging Power Grid, Rethymnon, Crete, Greece, 25–30 August 2013; IEEE: Piscataway, NJ, USA, 2013; pp. 1–24. [Google Scholar]
- Moura, S.; Bendtsen, J.; Ruiz, V. Parameter identification of aggregated thermostatically controlled loads for smart grids using PDE techniques. Int. J. Control
**2014**, 87, 1373–1386. [Google Scholar] [CrossRef] - Qu, Z.; Xu, C.; Ma, K.; Jiao, Z. Fuzzy Neural Network Control of Thermostatically Controlled Loads for Demand-Side Frequency Regulation. Energies
**2019**, 12, 2463. [Google Scholar] [CrossRef] [Green Version] - Angeli, D.; Kountouriotis, P.-A. A Stochastic Approach to “Dynamic-Demand” Refrigerator Control. IEEE Trans. Contr. Syst. Technol.
**2012**, 20, 581–592. [Google Scholar] [CrossRef] - Postnikov, A.; Albayati, I.M.; Pearson, S.; Bingham, C.; Bickerton, R.; Zolotas, A. Facilitating static firm frequency response with aggregated networks of commercial food refrigeration systems. Appl. Energy
**2019**, 251, 113357. [Google Scholar] [CrossRef] - Popp, R.S.-H.; Liebl, C.; Zaeh, M.F. Energy Flexible Machine tool Components—An Investigation of Capabilities. Procedia CIRP
**2016**, 57, 692–697. [Google Scholar] [CrossRef] - Xie, K.; Hui, H.; Ding, Y. Review of modeling and control strategy of thermostatically controlled loads for virtual energy storage system. Prot. Control Mod. Power Syst.
**2019**, 4, 23. [Google Scholar] [CrossRef] - Abele, E.; Beck, M.; Flum, D.; Schraml, P.; Panten, N.; Junge, F.; Bauerdick, C.; Helfert, M.; Sielaff, T. Gemeinsamer Schlussbericht zum Projekt ETA-Fabrik Energieeffiziente Fabrik für Interdisziplinäre Technologie-und Anwendungsforschung; Technische Universität Darmstadt: Darmstadt, Germany, 2019. [Google Scholar]
- Sonnen. Technische Daten sonnenBatterie 10. Available online: https://media.sonnen.de/de/media/62/download/inline (accessed on 14 May 2020).
- Tesla. Powerwall: Die Powerwall-Ihr Stromspeicher. Available online: https://www.tesla.com/de_DE/powerwall (accessed on 14 May 2020).
- GSMArena. Apple iPhone 11. Available online: https://www.gsmarena.com/apple_iphone_11-9848.php (accessed on 15 May 2020).
- Osthoff, A. Test Lenovo ThinkPad T490s (i5, Low-Power-FHD) Laptop. Available online: https://www.notebookcheck.com/Test-Lenovo-ThinkPad-T490s-i5-Low-Power-FHD-Laptop.416248.0.html (accessed on 15 May 2019).
- VDI Zentrum Ressourceneffizienz. Ökologische und Ökonomische Bewertung des Ressourcenaufwands: Stationäre Energiespeichersysteme in der Industriellen Produktion, 2nd ed.; VDI Zentrum Ressourceneffizienz: Berlin, Germany, 2018. [Google Scholar]
- Arcos-Vargas, Á.; Canca, D.; Núñez, F. Impact of battery technological progress on electricity arbitrage: An application to the Iberian market. Appl. Energy
**2020**, 260, 114273. [Google Scholar] [CrossRef] - Nier, H. Preisverfall bei Lithium-Ionen-Batterien. Available online: https://de.statista.com/infografik/20280/preisentwicklung-von-lithium-ionen-batterien/ (accessed on 4 August 2020).

**Figure 1.**Simplified substitute model of an inherent energy storage consisting of the energy converter, which converts electricity into the energy form required by the production process and the inherent storage capacity.

**Figure 2.**The effectiveness of a flexibility measure from the electricity grids’ point of view is calculated according to [12] from the difference between the load profile in normal operation (reference load) and the one in energy flexible operation (flexible load).

**Figure 3.**Resulting reference load profile for a heated water tank (volume = 1 m

^{3}, temperature hysteresis = 5 K, nominal electrical power of heating element = 10 kW, discharging power = 40% of nominal electrical power constantly).

**Figure 4.**Program flow chart of the load analysis function for extraction of the characteristic values from measured data of the electrical power of the energy converter or the SOC indicator.

**Figure 5.**Program flow chart of calling a flexibility measure to calculate the flexible load profile.

**Figure 6.**Resulting flexible load profile for a flexibility call of type DLC (Direct Load Control) at time step ${t}_{x}$ = 150 and a desired load reduction (${d}_{load}=-1$ ) in comparison to the reference load profile without flexibility call.

**Figure 7.**Resulting flexible load profile for a flexibility call of type HYST (adapting hysteresis limits) at time step ${t}_{x}$ = 150 and a desired load reduction (${d}_{load}=-1$) in comparison to the reference load profile without flexibility call.

**Figure 8.**By defining the re-entry-point ${t}_{\mathrm{re}-\mathrm{entry}}$ in the reference load profile (intersection of the reference load and the flexible load profile), a defined load shift can be achieved. This can be quantified by the standard key indicators for flexibility products.

**Figure 9.**Two parameters can limit the holding time of the flexibility measure: The time interval $\Delta {t}_{\mathrm{SOC}}$ in which the limit of energy content of the storage is reached in flexible operation mode (

**a**) or the time until the next switching time in reference mode is reached $\Delta {t}_{\mathrm{switch}}$ (

**b**).

**Figure 10.**Holding time of the flexibility measure in dependence of the call time of the flexibility measure within one charging cycle. In normal operation the energy converter is switched on from time step 0 to 57.6, thus the measure of load reduction is available in this period. Load increase can only be called in the second part of the charging cycle time.

**Figure 11.**Load difference when shifting both hysteresis limits at the same time. The figure shows the results for the heated water tank example when shifting the temperature limits from 60–65 °C to 85–90 °C.

**Figure 13.**Electrical load profile of the compressed air generator and pressure in the network on 13.02.2019.

**Figure 14.**Electrical load profile of the cleaning machine and temperature in the heated water tank on 13.02.2019.

**Figure 15.**Result of load analysis for compressor in standby operation (4 a.m. to 7.30 a.m.). Each dot in the left pictures represents a full charging cycle. On the right side, the frequency with which the respective values occurred is shown. The resulting average cycle time is 41.75 min, the mean load factor 8.4%.

**Figure 16.**Result of load analysis for compressor during production (8 a.m to 4 p.m). The resulting average cycle time is 4.83 min, the mean load factor of all full cycles is 69.7%.

**Figure 17.**Result of load analysis for cleaning machine during production (8 a.m to 4 p.m). The resulting average cycle time is 21.63 min, the mean load factor of all full cycles is 25.8%.

SOC Indicator | Example | Typical Converter with Typical Efficiency | Formula for Inherent Storage Capacity ^{1} | |
---|---|---|---|---|

Temperature ($T$) | Heated water tank | Heating element 100% | $V\xb7\rho \xb7{c}_{p}\xb7\left({T}_{high}-{T}_{low}\right)$ | [29] |

Temperature ($T$) | Machine cooling | Compression chiller 350% ^{2} | $V\xb7\rho \xb7{c}_{p}\xb7\left({T}_{high}-{T}_{low}\right)$ | [27] |

Pressure ($p$) | Compressed air generation with buffer tank | Compressor 60% ^{3} | $V\xb7{p}_{high}\xb7ln\frac{{p}_{high}}{{p}_{low}}$ | [27] ^{4} |

Concentration ($c$) | Ventilated hall with CO2-Sensor | Ventilation System 0.35–0.56 Wh/m^{3} ^{5} | $V\xb7\left({c}_{high}-{c}_{low}\right)$ | [27] |

Filling level ($c$) | Lifting pump in machine tool | Pump 55 Wh/m^{3 6} | $V\xb7\left({c}_{high}-{c}_{low}\right)$ | [27] |

^{1}with volume ($V$), density ($\rho $), specific heat capcity (${c}_{p}$).

^{2}typical value for coefficient of performance [30].

^{3}including motor and compressor losses, no leakage or pressure losses in pipes considered [31].

^{4}formula for isothermal compression and ideal gas.

^{5}minimum efficiency requirements for ventilation systems in non-residential buildings [32]

^{6}specific electrical power consumption of a machine tool’s lifting pump [33].

1 | Calculation of the amount of electrical energy consumed by the system (integral of the electrical load profile) |

2 | Measurement of the electrical load peak and average electrical power |

3 | Counting the full charging cycles in the considered time interval |

4 | Determination of the duration and load factor of the respective cycle (according to Formulas (11) and (12)) |

5 | Calculation of the maximum shiftable amount of energy per cycle as well as the call times in case of fixed hysteresis limits (according to Formulas (16) and (17)) |

6 | Extracting the hysteresis limits in standard operation mode from the measured data |

7 | Calculation of the possible flexibility potential by shifting the hysteresis limits (according to Formulas (19) and (23)) |

Key Indicators | Compressor 04:00–07:30 | Compressor 08:00–16:00 | Cleaning Machine 08:00–16:00 |
---|---|---|---|

Electrical energy demand | 2.47 kWh | 29.40 kWh | 26.31 kWh |

Peak load | 4.13 kW | 7.34 kW | 13.32 kW |

Mean load | 0.70 kW | 3.80 kW | 3.37 kW |

Number of full charging cycles | 4 | 99 | 19 |

Mean cycle time ($\Delta {t}_{\mathrm{cycle}}$) | 41.75 min | 4.8 min | 21.63 min |

Mean load factor ($a$) | 8.4% | 69.7% | 25.8% |

Maximum holding time of flexibility measure ($\Delta {t}_{\mathrm{hold},\mathrm{max}}$) | 3.22 min | 1.02 min | 4.12 min |

Call time for load increase ( ${t}_{x,E\_\mathrm{shift},\mathrm{max}}$) | 35.01 min | 0.44 min | 11.91 min |

Call time for load reduction ( ${t}_{x,E\_\mathrm{shift},\mathrm{max}}$) | 0.30 min | 2.35 min | 1.44 min |

Shiftable energy amount per cycle (${E}_{\mathrm{shift},\mathrm{max}}$) | 0.22 kWh | 0.12 kWh | 0.92 kWh |

Total shiftable energy amount | 0.88 kWh | 11.88 kWh | 17.48 kWh |

Share of flexible energy in energy demand | 35.6% | 40.1% | 66.3% |

Key Indicators | Compressor 04:00–07:30 | Compressor 08:00–16:00 | Cleaning Machine 08:00–16:00 |
---|---|---|---|

Upper limit of SOC Indicator | 7.46 bar | 7.45 bar | 60.47 °C |

Lower limit of SOC Indicator | 6.95 bar | 6.88 bar | 57.29 °C |

Hysteresis range in normal operation | 0.51 bar | 0.57 bar | 3.18 °C |

Limit value for the increase factor of energy content ^{1} $\left(x\right)$ | $\frac{1}{0.084}=11.90$ | $\frac{1}{0.697}=1.43$ | $\frac{1}{0.258}=3.88$ |

New possible hysteresis range ^{1} | 6.07 bar | 0.82 bar | 12.34 °C |

New possible upper limit of SOC Indicator ^{1} | 13.53 bar | 8.27 bar | 72.81 °C |

New upper limit of SOC Indicator ^{2} | 8.00 bar | 8.00 bar | 68 °C |

Actual increase factor of the energy content $\left(x\right)$ ^{3} | $\frac{8.00\mathrm{bar}-7.46\mathrm{bar}}{0.51\mathrm{bar}}=1.06$ | $\frac{8.00\mathrm{bar}-7.45\mathrm{bar}}{0.57\mathrm{bar}}=0.96$ | $\frac{68\xb0\mathrm{C}-60.47\xb0\mathrm{C}}{3.18\xb0\mathrm{C}}=2.37$ |

Additional amount of energy $\left({E}^{*}\right)$ | $1.06\cdot 0.22\mathrm{kWh}=0.23\mathrm{kWh}$ | $0.96\cdot 0.12\mathrm{kWh}=0.12\mathrm{kWh}$ | $2.37\cdot 0.92\mathrm{kWh}=2.18\mathrm{kWh}$ |

^{1}Limit value up to which it is possible to describe the flexibility potential of load increase using standard key figures, see Equation (22).

^{2}The maximum values given by experts are below the theoretically possible values, which is why they were used for the further calculation.

^{3}Assuming a constant efficiency of the converter over time and linear dependence between SOC indicator and storage content.

© 2020 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/).

## Share and Cite

**MDPI and ACS Style**

Strobel, N.; Fuhrländer-Völker, D.; Weigold, M.; Abele, E.
Quantifying the Demand Response Potential of Inherent Energy Storages in Production Systems. *Energies* **2020**, *13*, 4161.
https://doi.org/10.3390/en13164161

**AMA Style**

Strobel N, Fuhrländer-Völker D, Weigold M, Abele E.
Quantifying the Demand Response Potential of Inherent Energy Storages in Production Systems. *Energies*. 2020; 13(16):4161.
https://doi.org/10.3390/en13164161

**Chicago/Turabian Style**

Strobel, Nina, Daniel Fuhrländer-Völker, Matthias Weigold, and Eberhard Abele.
2020. "Quantifying the Demand Response Potential of Inherent Energy Storages in Production Systems" *Energies* 13, no. 16: 4161.
https://doi.org/10.3390/en13164161