# Techno-Economic Comparison of Stationary Storage and Battery-Electric Buses for Mitigating Solar Intermittency

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

- A model for balancing fluctuations of solar PV using SESSs or BEBs considering battery ageing and bus operation information obtained from a sophisticated mobility simulator
- Two different objectives for the PV and bus operator to maximise their own revenue
- Comparison of PV curtailment and cost/revenue for both PV and bus operator for use of SESSs and BEBs with the two different objectives
- Revenue comparison of different ramp rate limits
- Revenue comparison for the PV operator and recommendations for both the PV and bus operator

## 2. Problem Description

## 3. Model Formulation for Balancing Ramped Solar PV Using Storage Systems

#### 3.1. Stationary Battery Storage

#### 3.2. Battery Electric Buses

## 4. Battery Ageing Cost Model

_{2}cell, which has a nominal voltage of 3.6 V and a cell rating of 2.25 Ah. The estimated energy fade of a Panasonic battery cell is presented in Figure 1. The ageing cost of a 2.25-Ah battery cell can be evaluated by approximating Figure 1 with two linear functions represented in Equation (32), where ${C}_{\mathrm{ageing}}$ is the battery ageing cost in SGD, ${C}_{\mathrm{batt}}$ is the cost of the battery in SGD, ${P}_{\mathrm{charge}/\mathrm{discharge}}$ is the charging/discharging power, ${Q}_{\mathrm{initial}}$ is the initial battery capacity in $\mathrm{kWh}\phantom{\rule{0.277778em}{0ex}},$${Q}_{\mathrm{end}}$ is the end of life battery capacity in $\mathrm{kWh}\phantom{\rule{0.277778em}{0ex}},$ and ${r}_{\mathrm{ageing}}$ is the ageing ratio between charging and discharging of the battery.

## 5. Case Study

#### 5.1. Use of Stationary Battery Storage

#### 5.2. Use of BEBs

#### 5.3. Revenue Comparison for the PV Operator

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## Abbreviations

$SO{C}_{\mathrm{batt}}\left(t\right)$ | Continuous variable indicating the battery state of charge at time t |

$SO{C}_{\mathrm{ramp}}$ | Parameter indicating the battery ramp in terms of SOC |

$Ch/Dc{h}_{\mathrm{max}}$ | Maximum charging/discharging power |

${Q}_{\mathrm{batt}}$ | Battery capacity in kWh |

${\eta}_{\mathrm{charging}}$ | Charging efficiency |

${\eta}_{\mathrm{discharging}}$ | Discharging efficiency |

${n}_{\mathrm{chargers}}$ | Number of chargers |

${E}_{\mathrm{bus}}(i,t)$ | Continuous variable indicating the battery energy of bus i at time t |

${E}_{\mathrm{PV}}\left(t\right)$ | Energy generated by solar PV plant at time t |

${E}_{\mathrm{PV}2\mathrm{Batt}}\left(t\right)$ | Continuous variable indicating the energy discharged from the solar PV plant to the stationary battery at time t |

${E}_{\mathrm{Batt}2\mathrm{Grid}}\left(t\right)$ | Continuous variable indicating the energy discharged from the stationary battery to the electric grid at time t |

${E}_{2\mathrm{Grid}}\left(t\right)$ | Continuous variable indicating the total energy fed to the electric grid at time t |

${E}_{\mathrm{PVramp},\mathrm{max}}$ | Parameter indicating the solar PV ramp rate |

${C}_{\mathrm{Bus}2\mathrm{Grid}}$ | Cost of energy per kWh when discharged from the bus to the electric grid |

${C}_{\mathrm{Grid}2\mathrm{Bus}}$ | Cost of energy per kWh when purchased by the bus terminal from the electric grid |

${C}_{\mathrm{PV}2\mathrm{Bus}}$ | Cost of energy per kWh when purchased by the bus terminal from the solar PV plant |

${C}_{\mathrm{PV}2\mathrm{Grid}}$ | Cost of energy per kWh when discharged from the solar PV plant to the electric grid |

${E}_{\mathrm{PV}2\mathrm{Bus}}(i,t)$ | Continuous variable indicating the energy charged from the solar PV plant to the bus i at time t |

${E}_{\mathrm{Grid}2\mathrm{Bus}}(i,t)$ | Continuous variable indicating the energy charged from the grid to the bus i at time t |

${E}_{\mathrm{Bus}2\mathrm{GridPV}}(i,t)$ | Continuous variable indicating the energy of bus i discharged to the solar PV plant at time t to be fed back to the grid |

${E}_{\mathrm{charger}}(i,t)$ | Continuous variable indicating the energy of charger i at time t |

${B}_{\mathrm{charging}}(i,t)$ | Binary variable indicating if charger i is charging a bus at time t |

${B}_{\mathrm{discharging}}(i,t)$ | Binary variable indicating if charger i is discharging a bus at time t |

${E}_{2\mathrm{GridPV}}\left(t\right)$ | Continuous variable indicating total energy that is fed back to the grid at time t |

${E}_{\mathrm{PV}2\mathrm{Grid}}\left(t\right)$ | Continuous variable indicating the portion of generated energy from solar PV that is fed back to the grid at time t |

${E}_{\mathrm{PVramped}}\left(t\right)$ | Continuous variable indicating the total generated PV energy that is ramped due to grid ramp rate requirement at time t |

${E}_{\mathrm{PV}2\mathrm{BusTot}}\left(t\right)$ | Continuous variable indicating the total generated energy of the solar PV that is used to charge the BEBs at time t |

${E}_{\mathrm{Bus}2\mathrm{GridPVTot}}\left(t\right)$ | Continuous variable indicating the total energy that is discharged from the BEBs to the solar PV plant to be fed back to the grid at time t |

$\mathcal{B}$ | Set of buses |

$\mathcal{T}$ | Set of time steps |

${\mathcal{T}}_{i}$ | Set of time steps where bus $i\in \mathcal{B}$ is available for charging/discharging |

## List of Acronyms

BEB | battery electric bus |

BEV | battery electric vehicle |

GHG | greenhouse gas |

PV | photovoltaic |

SESS | stationary energy storage system |

SoC | state of charge |

V2G | vehicle-to-grid |

## References

- International Energy Agency. Key World Energy Statistics 2021. Available online: https://www.iea.org/reports/key-world-energy-statistics-2021 (accessed on 11 May 2022).
- Land Transport Authority. Land Transport Master Plan 2040. 2019. Available online: https://www.lta.gov.sg/content/dam/ltagov/who%5fwe%5fare/our%5fwork/land%5ftransport%5fmaster%5fplan%5f2040/pdf/LTA%20LTMP%202040%20eReport.pdf (accessed on 7 February 2022).
- Wu, Y.; Wang, Z.; Huangfu, Y.; Ravey, A.; Chrenko, D.; Gao, F. Hierarchical operation of electric vehicle Charging Station in smart grid integration applications—An overview. Int. J. Electr. Power Energy Syst.
**2022**, 139, 108005. [Google Scholar] [CrossRef] - Torreglosa, J.P.; García-Triviño, P.; Fernández-Ramirez, L.M.; Jurado, F. Decentralized energy management strategy based on predictive controllers for a medium voltage direct current photovoltaic electric vehicle charging station. Energy Convers. Manag.
**2016**, 108, 1–13. [Google Scholar] [CrossRef] - Tarroja, B.; Zhang, L.; Wifvat, V.; Shaffer, B.; Samuelsen, S. Assessing the Stationary Energy Storage Equivalency of Vehicle-to-grid Charging Battery Electric Vehicles. Energy
**2016**, 106, 673–690. [Google Scholar] [CrossRef] - Borghetti, F.; Colombo, C.G.; Longo, M.; Mazzoncini, R.; Panarese, A.; Somaschini, C. Vehicle-to-Grid: A case study of ATM e-bus depots in the city of Milan in Italy. In Proceedings of the 2021 AEIT International Annual Conference (AEIT), Virtual, 4–8 October 2021; pp. 1–6. [Google Scholar]
- Manzolli, J.A.; Trovão, J.P.F.; Antunes, C.H. Electric bus coordinated charging strategy considering V2G and battery degradation. Energy
**2022**, 254, 124252. [Google Scholar] [CrossRef] - Purnell, K.; Bruce, A.G.; MacGill, I. Impacts of electrifying public transit on the electricity grid, from regional to state level analysis. Appl. Energy
**2022**, 307, 118272. [Google Scholar] [CrossRef] - Kikusato, H.; Fujimoto, Y.; Hanada, S.I.; Isogawa, D.; Yoshizawa, S.; Ohashi, H.; Hayashi, Y. Electric Vehicle Charging Management Using Auction Mechanism for Reducing PV Curtailment in Distribution Systems. IEEE Trans. Sustain. Energy
**2020**, 11, 1394–1403. [Google Scholar] [CrossRef] [Green Version] - Alam, M.J.E.; Muttaqi, K.M.; Sutanto, D. Effective Utilization of Available PEV Battery Capacity for Mitigation of Solar PV Impact and Grid Support with Integrated V2G Functionality. IEEE Trans. Smart Grid
**2016**, 7, 1562–1571. [Google Scholar] [CrossRef] [Green Version] - Boström, T.; Babar, B.; Hansen, J.B.; Good, C. The Pure PV-EV Energy System—A Conceptual Study of a Nationwide Energy System Based Solely on Photovoltaics and Electric Vehicles. Smart Energy
**2021**, 1, 100001. [Google Scholar] [CrossRef] - Reddy, K.R.; Meikandasivam, S. Load Flattening and Voltage Regulation Using Plug-In Electric Vehicle’s Storage Capacity With Vehicle Prioritization Using ANFIS. IEEE Trans. Sustain. Energy
**2020**, 11, 260–270. [Google Scholar] [CrossRef] - Arif, S.M.; Lie, T.T.; Seet, B.C.; Ahsan, S.M.; Khan, H.A. Plug-In Electric Bus Depot Charging with PV and ESS and Their Impact on LV Feeder. Energies
**2020**, 13, 2139. [Google Scholar] [CrossRef] - Liu, Y.; Liang, H. A Three-Layer Stochastic Energy Management Approach for Electric Bus Transit Centers with PV and Energy Storage Systems. IEEE Trans. Smart Grid
**2021**, 12, 1346–1357. [Google Scholar] [CrossRef] - Brinkel, N.B.G.; Gerritsma, M.K.; AlSkaif, T.A.; Lampropoulos, I.; van Voorden, A.M.; Fidder, H.A.; van Sark, W.G.J.H.M. Impact of Rapid PV Fluctuations on Power Quality in the Low-voltage Grid and Mitigation Strategies Using Electric Vehicles. Int. J. Electr. Power Energy Syst.
**2020**, 118, 105741. [Google Scholar] [CrossRef] - Wang, M.; Mu, Y.; Xu, X.; Jia, H.; Wang, T.; Jin, X.; Jiang, Q. Load Power Smoothing Control of Distribution Network Including Photovoltaic Generation with Energy Storage from Electric Vehicles. In Proceedings of the 2017 IEEE Power & Energy Society General Meeting, Chicago, IL, USA, 16–20 July 2017; pp. 1–5. [Google Scholar] [CrossRef]
- Aly, M.M.; Abdelkarim, E.; Abdel-Akher, M. Mitigation of Photovoltaic Power Generation Fluctuations Using Plug-in Hybrid Electric Vehicles Storage Batteries. Int. Trans. Electr. Energy Syst.
**2015**, 25, 3720–3737. [Google Scholar] [CrossRef] - Trippe, A.E.; Arunachala, R.; Massier, T.; Jossen, A.; Hamacher, T. Charging Optimization of Battery Electric Vehicles Including Cycle Battery Aging. In Proceedings of the 5th IEEE PES Innovative Smart Grid Technologies, Europe, Istanbul, Turkey, 12–15 October 2014; pp. 1–6. [Google Scholar] [CrossRef]
- Energy Market Authority. Consultation Paper for Proposed Modification to the Transmission Code. 2018. Available online: https://www.ema.gov.sg/cmsmedia/Consultations/Consultation%20Paper_Proposed%20Modifications%20to%20Tx%20Code.pdf (accessed on 7 February 2022).
- Zehe, D.; Nair, S.; Knoll, A.; Eckhoff, D. Towards CityMoS: A Coupled City-scale Mobility Simulation Framework. In Proceedings of the 5th GI/ITG KuVS Fachgespräch Inter-vehicle Communication (FG-IVC 2017), Nürnberg, Germany, 6–7 April 2017; FAU Erlangen-Nuremberg: Erlangen, Germany, 2017; pp. 26–28. Available online: https://opus4.kobv.de/opus4-fau/files/8528/fg-ivc-2017-report.pdf#page=32 (accessed on 21 December 2022).

**Figure 2.**PV generation, PV ramped energy, and energy fed to the grid at 10% ramp requirement over a period of five days.

**Figure 3.**Revenue PV to grid (SGD) and cost of PV ramped (SGD) at 10% ramp requirement over a period of five days.

**Figure 7.**Revenue from PV to grid over PV ramp rate limit for various battery capacities for one year.

**Figure 10.**PV generation, PV 2 Bus, ramped energy, and energy fed to the grid at 10% ramp rate limit for the bus operator’s objective (Equation (17)) over a period of five days.

**Figure 11.**PV generation, ramped power, and energy fed to the grid at 10% ramp rate limit for the PV operator’s objective (Equation (18)) over a period of five days.

**Table 1.**Amount of PV ramped, PV energy fed to buses, grid energy fed to buses, PV energy fed to grid, energy from BEB batteries fed to grid, and total energy fed to the grid (all in kWh) for both objectives and three different ramp rate limits for one week.

Bus Operator | PV Operator | |||||
---|---|---|---|---|---|---|

Ramp Limit | 10% | 5% | 1% | 10% | 5% | 1% |

PV ramped | 3290 | 3300 | 3570 | 62.0 | 180 | 874 |

PV to bus | 17,400 | 17,400 | 18,700 | 803 | 1920 | 6530 |

Grid to bus | 184,000 | 184,000 | 183,000 | 201,000 | 200,000 | 197,000 |

PV to grid | 16,900 | 16,900 | 15,300 | 36,700 | 35,500 | 30,200 |

Bus to grid | 17,100 | 13,500 | 9380 | 3610 | 1820 | 340 |

Total to grid | 34,000 | 30,400 | 24,700 | 40,300 | 37,300 | 30,500 |

**Table 2.**Cost of PV ramped, PV energy fed into buses, grid energy fed into buses, PV energy fed into the grid, energy from BEB batteries fed into the grid, total energy fed into the grid, and battery ageing (all in SGD) for both objectives and three different ramp rate limits for one week.

Bus Operator | PV Operator | |||||
---|---|---|---|---|---|---|

Ramp Limit | 10% | 5% | 1% | 10% | 5% | 1% |

PV ramped | 657 | 661 | 713 | 12.4 | 36.0 | 175 |

PV to bus | 1740 | 1740 | 1870 | 80.0 | 192 | 653 |

Grid to bus | 29,500 | 29,500 | 29,300 | 32,200 | 32,000 | 31,600 |

PV to grid | 3380 | 3380 | 3060 | 7340 | 7090 | 6030 |

Bus to grid | 3430 | 2700 | 1880 | 723 | 363 | 68.0 |

Total to grid | 6810 | 6080 | 4930 | 8060 | 7450 | 6100 |

Battery ageing | 37.0 | 36.0 | 36.0 | 35.0 | 34.0 | 34.0 |

**Table 3.**Total cost incurred for bus operator and total revenue for the PV operator (as negative cost) for both objectives for one week.

Bus Operator | PV Operator | |||||
---|---|---|---|---|---|---|

Ramp Limit | 10% | 5% | 1% | 10% | 5% | 1% |

Bus op.’s cost | 27,800 | 28,500 | 29,200 | 31,500 | 31,900 | 32,200 |

PV op.’s cost | −4460 | −4450 | −4210 | −7410 | −7250 | −6510 |

**Table 4.**Revenue comparison for the PV operator considering no storage, stationary batteries (1% of the installed PV capacity i.e., 13.5 kWh), and BEBs (in SGD) for a ramp rate limit of 10% for one week.

No Battery | Stat. Battery | BEBs | ||
---|---|---|---|---|

Bus op. | PV op. | |||

Stationary battery | – | −65.0 | – | – |

Battery ageing | – | −60.0 | −37.0 | −35.0 |

PV to bus | – | – | 1740 | 80.0 |

PV to grid | 6170 | 6250 | 3380 | 7340 |

Total revenue | 6170 | 6130 | 5080 | 7380 |

**Table 5.**Revenue comparison for the PV operator considering no storage, stationary batteries (1% of the installed PV capacity i.e., 13.5 kWh), and BEBs (in SGD) for a ramp rate limit of 5% for one week.

No Battery | Stat. Battery | BEBs | ||
---|---|---|---|---|

Bus op. | PV op. | |||

Stationary battery | – | −130 | – | – |

Battery ageing | – | −101 | −36.0 | −34.0 |

PV to bus | – | – | 1740 | 192 |

PV to grid | 5890 | 6050 | 3380 | 7090 |

Total revenue | 5890 | 5820 | 5080 | 7250 |

**Table 6.**Revenue comparison for the PV operator considering no storage, stationary batteries (1% of the installed PV capacity i.e., 13.5 kWh), and BEBs (in SGD) for a ramp rate limit of 1%. The ramping costs are not deducted from the total revenue, as they are implicitly included in the lower revenue for PV to battery, bus, or grid for one week.

No Battery | Stationary Battery | Battery-Electric Buses | ||
---|---|---|---|---|

Bus op. | PV op. | |||

Stationary battery | – | −130 | – | – |

Battery ageing | – | −120 | −36.0 | −34.0 |

PV to bus | – | – | 1870 | 653 |

PV to grid | 4960 | 5320 | 3060 | 6030 |

Total revenue | 4960 | 5070 | 4890 | 6650 |

**Table 7.**Revenue comparison for the PV operator considering no storage, stationary batteries (2% of the installed PV capacity i.e., 27 kWh), and BEBs (in SGD) for a ramp rate limit of 1%. The ramping costs are not deducted from the total revenue, as they are implicitly included in the lower revenue for PV to battery, bus, or grid for one week.

No Battery | Stationary Battery | Battery-Electric Buses | ||
---|---|---|---|---|

Bus op. | PV op. | |||

Stationary battery | – | −130 | – | – |

Battery ageing | – | −93.0 | −36.0 | −34.0 |

PV to bus | – | – | 1870 | 653 |

PV to grid | 4960 | 5540 | 3060 | 6030 |

Total revenue | 4960 | 5320 | 4890 | 6650 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 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 (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Ahmed, A.; Massier, T.
Techno-Economic Comparison of Stationary Storage and Battery-Electric Buses for Mitigating Solar Intermittency. *Sensors* **2023**, *23*, 630.
https://doi.org/10.3390/s23020630

**AMA Style**

Ahmed A, Massier T.
Techno-Economic Comparison of Stationary Storage and Battery-Electric Buses for Mitigating Solar Intermittency. *Sensors*. 2023; 23(2):630.
https://doi.org/10.3390/s23020630

**Chicago/Turabian Style**

Ahmed, Arif, and Tobias Massier.
2023. "Techno-Economic Comparison of Stationary Storage and Battery-Electric Buses for Mitigating Solar Intermittency" *Sensors* 23, no. 2: 630.
https://doi.org/10.3390/s23020630