# Aging Cost Optimization for Planning and Management of Energy Storage Systems

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Inputs and Constraints of the Model

#### 2.2. Optimization Procedure and Outputs

#### 2.3. Battery Cost Model

## 3. Case Study

#### 3.1. The Test Grid

#### 3.2. Cost Functions

## 4. Results

## 5. Discussion

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

ESS | Energy Storage System |

BESS | Battery Energy Storage System |

RES | Renewable Energy Sources |

MPOPF | Multi-Period Optimal Power Flow |

GA | Genetic Algorithm |

GA-MPOPF | Genetic Algorithm-based Multi Period Optimal Power Flow |

SOC | State Of Charge |

VPP | Virtual Power Plant |

BDM | Battery Degradation Model |

BDCM | Battery Degradation Costs Model |

CG | Controllable Generator |

MV | Medium Voltage |

PCC | Point of Common Coupling |

## References

- Facchini, A. Distributed energy resources: Planning for the future. Nat. Energy
**2017**, 2, 17129. [Google Scholar] [CrossRef] - Marongiu, A.; Damiano, A.; Heuer, M. Experimental analysis of lithium iron phosphate battery performances. In Proceedings of the 2010 IEEE International Symposium on Industrial Electronics, Bari, Italy, 4–7 July 2010; pp. 3420–3424. [Google Scholar]
- Beltran, H.; Bilbao, E.; Belenguer, E.; Etxeberria-Otadui, I.; Rodriguez, P. Evaluation of Storage Energy Requirements for Constant Production in PV Power Plants. IEEE Trans. Ind. Electron.
**2013**, 60, 1225–1234. [Google Scholar] [CrossRef] - Haddadian, G.; Khalili, N.; Khodayar, M.; Shahidehpour, M. Optimal scheduling of distributed battery storage for enhancing the security and the economics of electric power systems with emission constraints. Electr. Power Syst. Res.
**2015**, 124, 152–159. [Google Scholar] [CrossRef] - Ghofrani, M.; Arabali, A.; Etezadi-Amoli, M.; Fadali, M.S. A Framework for Optimal Placement of Energy Storage Units within a Power System with High Wind Penetration. IEEE Trans. Sustain. Energy
**2013**, 4, 434–442. [Google Scholar] [CrossRef] - D’Agostino, R.; Baumann, L.; Damiano, A.; Boggasch, E. A Vanadium-Redox-Flow-Battery Model for Evaluation of Distributed Storage Implementation in Residential Energy Systems. IEEE Trans. Energy Convers.
**2015**, 30, 421–430. [Google Scholar] - Mureddu, M.; Damiano, A. A statistical approach for resilience analysis of ESS deployment in RES-based power systems. In Proceedings of the 2017 IEEE 26th International Symposium on Industrial Electronics (ISIE), Edinburgh, UK, 19–21 June 2017; pp. 2069–2074. [Google Scholar]
- Gayme, D.; Topcu, U. Optimal power flow with distributed energy storage dynamics. In Proceedings of the 2011 American Control Conference, San Francisco, CA, USA, 29 June–1 July 2011; pp. 1536–1542. [Google Scholar]
- Warrington, J.; Goulart, P.; Mariethoz, S.; Morari, M. Policy-Based Reserves for Power Systems. IEEE Trans. Power Syst.
**2013**, 28, 4427–4437. [Google Scholar] [CrossRef] - Gopalakrishnan, A.; Raghunathan, A.U.; Nikovski, D.; Biegler, L.T. Global optimization of multi-period optimal power flow. In Proceedings of the 2013 American Control Conference, Washington, DC, USA, 17–19 June 2013; pp. 1157–1164. [Google Scholar]
- Jabr, R.A.; Karaki, S.; Korbane, J.A. Robust Multi-Period OPF With Storage and Renewables. IEEE Trans. Power Syst.
**2015**, 30, 2790–2799. [Google Scholar] [CrossRef] - Rabiee, A.; Parniani, M. Voltage security constrained multi-period optimal reactive power flow using benders and optimality condition decompositions. IEEE Trans. Power Syst.
**2013**, 28, 696–708. [Google Scholar] [CrossRef] - Scott, P.; Thiébaux, S. Distributed Multi-Period Optimal Power Flow for Demand Response in Microgrids. In Proceedings of the 2015 ACM Sixth International Conference on Future Energy Systems (e-Energy’15), Bangalore, India, 14–17 July 2015; pp. 17–26. [Google Scholar]
- Xu, B.; Oudalov, A.; Ulbig, A.; Andersson, G.; Kirschen, D. Modeling of Lithium-Ion Battery Degradation for Cell Life Assessment. IEEE Trans. Smart Grid
**2016**, 28, 1–1. [Google Scholar] [CrossRef] - Holland, J.H. Adaptation in Natural and Artificial Systems; MIT Press: Cambridge, MA, USA, 1992. [Google Scholar]
- Chambers, L. The Practical Handbook of Genetic Algorithms: Applications, 2nd ed.; Chapman&Hall/CRC: London, UK, 2000. [Google Scholar]
- Zimmerman, R.D.; Murillo Sanchez, C.; Thomas, R. MATPOWER: Steady-State Operations, Planning, and Analysis Tools for Power Systems Research and Education. IEEE Trans Power Syst.
**2011**, 26, 12–19. [Google Scholar] [CrossRef] - Chang, G.W.; Chu, S.Y.; Wang, H.L. An Improved Backward/Forward Sweep Load Flow Algorithm for Radial Distribution Systems. IEEE Trans. Power Syst.
**2007**, 22, 882–884. [Google Scholar] [CrossRef] - Langton, C.G. Atificial Life: An Overview; MIT Press: Cambridge, MA, USA, 1997. [Google Scholar]
- Georgilakis, P.; Hatziargyriou, N. Optimal distributed generation placement in power distribution networks: Models, methods, and future research. IEEE Trans. Power Syst.
**2013**, 28, 3420–3428. [Google Scholar] [CrossRef] - Cebrian, J.C.; Kagan, N. Reconfiguration of distribution networks to minimize loss and disruption costs using genetic algorithms. Electr. Power Syst. Res.
**2010**, 80, 53–62. [Google Scholar] [CrossRef] - Lu, T.; Wang, Z.; Ai, Q.; Lee, W.J. Interactive Model for Energy Management of Clustered Microgrids. IEEE Trans. Ind. Appl.
**2017**, 9994, 1739–1750. [Google Scholar] [CrossRef] - Baran, M.E.; Wu, F.F. Optimal capacitor placement on radial distribution systems. IEEE Trans. Power Deliv.
**1989**, 4, 725–734. [Google Scholar] [CrossRef] - Arefifar, S.A.; Mohamed, Y.A.R.I.; El-Fouly, T.H.M. Supply-adequacy-based optimal construction of microgrids in smart distribution systems. IEEE Trans. Smart Grid
**2012**, 3, 1491–1502. [Google Scholar] [CrossRef] - Arefifar, S.A.; Mohamed, Y.A.R.I.; El-Fouly, T.H.M. Optimum microgrid design for enhancing reliability and supply-security. IEEE Trans. Smart Grid
**2013**, 4, 1567–1575. [Google Scholar] [CrossRef] - Malekpour, A.R.; Pahwa, A. Radial Test Feeder including primary and secondary distribution network. In Proceedings of the 2015 North American Power Symposium (NAPS), Charlotte, NC, USA, 4–6 October 2015; pp. 1–9. [Google Scholar]
- IESO. 2017. Available online: http://ieso.ca/ (accessed on 15 May 2017).

**Figure 3.**The used cost functions, and the histogram of the power fluctuations at the network point of common coupling (PCC).

**Figure 4.**Monthly energy losses for different positioning of the battery energy storage system (BESS).

**Figure 5.**Monthly energy losses associated to each different location of the BESS. The losses are given by means of a color code, described in the legend.

**Figure 6.**The power profile at the PCC of the considered virtual power plant (VPP), in both presence and absence of a BESS.

**Figure 8.**The daily cost of the system. The fine cost and the BESS calendar and cycling aging amortization costs are given as a sum. Also, the daily fine cost of the system without the BESS is given as a reference.

**Figure 9.**Histograms of the convergence of the total cost considering the four different tested cost functions. (

**a**) Cubic cost function; (

**b**) Quadratic cost function; (

**c**) Exponential cost function; (

**d**) Linear cost function.

**Figure 10.**Histograms of the running time for different cost functions. (

**a**) Cubic cost function; (

**b**) Quadratic cost function; (

**c**) Exponential cost function; (

**d**) Linear cost function.

Monthly Considered Costs | Costs (Euro) | Cumulative Costs (Euro) |
---|---|---|

Fines with a BESS | 5200 | 5200 |

Calendar aging | 1800 | 7000 |

Cycling aging | 1700 | 8700 |

Fines w/o a BESS | 10,500 | 10,500 |

**Table 2.**Comparison of monthly energy fluctuations $\int |P\left(t\right)-{P}^{*}\left(t\right)|dt$ at the PCC level with and without a BESS.

Type | Energy (MWh) |
---|---|

With a BESS | 49.7 |

Without a BESS | 70.2 |

© 2017 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**

Korjani, S.; Mureddu, M.; Facchini, A.; Damiano, A.
Aging Cost Optimization for Planning and Management of Energy Storage Systems. *Energies* **2017**, *10*, 1916.
https://doi.org/10.3390/en10111916

**AMA Style**

Korjani S, Mureddu M, Facchini A, Damiano A.
Aging Cost Optimization for Planning and Management of Energy Storage Systems. *Energies*. 2017; 10(11):1916.
https://doi.org/10.3390/en10111916

**Chicago/Turabian Style**

Korjani, Saman, Mario Mureddu, Angelo Facchini, and Alfonso Damiano.
2017. "Aging Cost Optimization for Planning and Management of Energy Storage Systems" *Energies* 10, no. 11: 1916.
https://doi.org/10.3390/en10111916