# A Dual-Stage Modeling and Optimization Framework for Wayside Energy Storage in Electric Rail Transit Systems

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## Abstract

**:**

## 1. Introduction

## 2. Theory: Operating Principle of Transit System and ESSs

#### 2.1. Electric Rail Transit System

#### 2.2. ESS: Type and Parameters

#### 2.2.1. Battery Energy Storage System (BESS)

#### 2.2.2. Supercapacitor Energy Storage System (SCESS)

#### 2.2.3. Flywheel Energy Storage System (FESS)

## 3. Stage 1 of Proposed Method: Mathematical Modeling and Optimization

#### 3.1. Mathematical Modeling

#### 3.2. Optimization Algorithm

## 4. Stage 2 of Proposed Method: Simulation Modeling

#### 4.1. Substation Modeling

#### 4.2. Rail Network Modeling

#### 4.3. Train Modeling

#### 4.4. Parameters for ESS Sizing

## 5. Results and Discussion

#### 5.1. Results from Optimization

#### 5.2. Results from Simulation

#### 5.2.1. 15% Energy Energy Saving

#### 5.2.2. 45% Energy Saving

#### 5.2.3. 24 h Power Profile

#### 5.3. Payback Time Estimation

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

Symbol | Description | Symbol | Description |

${E}_{+/-}$ | Total energy charged (+)/discharged (-) by the combination of ESSs, (Wh) | ${E}_{B+/-}$ | Energy charged/discharged by BESS, (Wh) |

${E}_{SC+/-}$ | Energy charged/discharged by SCESS, (Wh) | ${E}_{F+/-}$ | Energy charged/discharged by FESS, (Wh) |

${V}_{b}$ | Open-circuit voltage of a battery, (V) | ${V}_{nom},{V}_{exp}$ | Nominal, exponential voltages of the battery respectively, (V) |

${t}_{nom},{t}_{exp}$ | Time at which battery voltage reaches its exponential and nominal voltages respectively, (h) | ${t}_{B+/-}$ | Battery charging/discharging time, (h) |

${I}_{B+/-}$ | Battery charging/discharging current, (A) | ${C}_{Ah}$ | Capacity of a battery, (Ah) |

${N}_{S}$ | Number of batteries in series | ${\eta}_{B+/-}$ | Battery charging/discharging efficiency |

${\eta}_{conv,B/SC/F}$ | Converter efficiency for battery/ supercapacitor/ flywheel | k | Peukert’s constant |

H | Rated discharge time, (h) | ${V}_{SC}$ | Open-circuit voltage of supercapacitor, (V) |

${U}_{T}$ | Utilization time of a battery | ${\epsilon}_{SC}$ | Utilization factor of a supercapacitor |

${P}_{SC+/-}$ | Maximum charging/discharging power of SCESS, (W) | $\Delta {t}_{acc}$ | Acceleration time of a train, (h) |

${\eta}_{SC+/-}$ | Supercapacitor charging/discharging efficiency | $\Delta {t}_{reg}$ | Deceleration time of a train, (h) |

${\eta}_{F+/-}$ | Flywheel charging/discharging efficiency | ${\omega}_{min/max}$ | Minimum/maximum speed of flywheel, (rpm) |

${P}_{F+/-}$ | Maximum charging/discharging power of flywheel, (W) | $So{C}_{B/F}$ | State of charge of battery/flywheel |

${C}_{capital}$ | Capital cost, ($) | ${C}_{operating}$ | Operating cost, ($) |

${C}_{kWh\_B/SC/F}$ | Cost of energy for battery/supercapacitor/flywheel, ($/kWh) | ${C}_{kW\_B/SC/F}$ | Cost of power for battery/supercapacitor/flywheel, ($/kW) |

${\eta}_{DoD}$ | Depth of discharge of battery | ${N}_{cycle\_B/SC/F}$ | Number of cycles of battery/supercapacitor/Flywheel |

${C}_{saving}$ | Cost of total saving, ($) | ${C}_{utility\_kWh}$ | Cost of energy by utility, ($/kWh) |

${N}_{peak}$ | The average highest number of train cycles in a 15 mins period of a day | ${C}_{utility\_peak}$ | Demand charges by the utility, ($/kW) |

## Abbreviations

BESS | Battery Energy Storage System |

DoD | Depth of Discharge |

EMS | Energy Management System |

ESS | Energy Storage System |

FESS | Flywheel Energy Storage System |

GA | Genetic Algorithm |

HESS | Hybrid Energy Storage System |

SCESS | Supercapacitor Energy Storage System |

SoC | State of Charge |

SoH | State of Health |

WESS | Wayside Energy Storage System |

## Appendix A

Type | Parameter | Unit | Value |
---|---|---|---|

SS | kV | 13.2 | |

TS1 | Y/D | ||

kV | 13.2/0.465 | ||

Substation | TS2 | D/D | |

kV | 13.2/0.465 | ||

CS1, CS2 | F | 10^{−3} | |

RS1 | m$\mathsf{\Omega}$ | 1.08 | |

Third | Third Rail resistance | m$\mathsf{\Omega}$/km | 170 |

Rail and | Running Rail resistance | m$\mathsf{\Omega}$/km | 17.2 |

Running | Distance between passenger stations | m | 596.6 |

Rail | Nominal Third Rail Voltage (${V}_{nom}$) | V | 650 |

Max speed of train | m/s | 18 | |

Max/Min train acceleration | m/s^{2} | +/−2.5 | |

Effective mass of Train | t | 380 | |

Rolling resistance factor | - | 0.002 | |

Gravity (g) | N/kg | 9.81 | |

Rail slope ($\alpha $) | - | 0 | |

Drag coefficient | - | 0.5 | |

Train | Air density ($\rho $) | kg/m^{3} | 1.225 |

Front area of the train (A) | m^{2} | 9 | |

Wheel radius | m | 0.432 | |

Number of cars | - | 11 | |

Gearbox efficiency | - | 94% | |

Motor efficiency | - | 93% | |

Inverter efficiency | - | 93% | |

${C}_{B}$ | $\mathsf{\mu}$F | 7500 | |

${R}_{B}$ | $\mathsf{\Omega}$ | 0.125 | |

${L}_{T}$ | $\mathsf{\mu}$H | 20 | |

${R}_{BD}$ | $\mathsf{\Omega}$ | 0.01 | |

${L}_{BD}$ | mH | 10.2 | |

Bidirectional Converter | ${C}_{BD}$ | $\mathsf{\mu}$F | 54 |

PI1 | - | 0.002, 0.2 | |

PI2 | - | 0.02, 2 |

Symbol | Values | Symbol | Values |
---|---|---|---|

${V}_{th,min/max}$ | 580 V/720 V | ${V}_{b}$ | 1.3 V |

${V}_{nom}$ | 1.15 V | ${V}_{exp}$ | 1.4 V |

${t}_{B+/-}$ | 23.1/25 s | ${\eta}_{B+/-}$ | 0.75 |

${\eta}_{conv}$ | 0.99 | ${N}_{S}$ | 357 |

k | 1.3 | H | 20 h |

${\eta}_{DoD}$ | 0.3 | ${V}_{SC}$ | 500 V |

${U}_{T}$ | 20% | $\epsilon $ | 0.5 |

${\Delta}_{acc}$ | 30.9 s | ${\Delta}_{reg}$ | 20 s to 25 s |

${\eta}_{SC+/-}$ | 0.95 | ${\eta}_{F+/-}$ | 0.9 |

${\eta}_{cycle\_B/SC/F}$ | $5000/1\times {10}^{6}/1\times {10}^{5}$ | ${t}_{F+/-}$ | 30.9/25 s |

${C}_{kWh\_B/SC/F}$ | $600/500/2000 | ${C}_{kW\_B/SC/F}$ | $1200/100/150 |

${C}_{utility\_kWh}$ | $0.035 | ${C}_{utility\_peak}$ | $8.03 |

${N}_{peak}$ | 27.25 |

Parameter | Values | Parameter | Values |
---|---|---|---|

Constraint Tolerance | Positive Scalar ($1\times {10}^{-3}$) | Crossover Fraction | Positive Scalar 0.8 |

Fitness limit | -inf | Function Tolerance | $1\times {10}^{-6}$ |

Initial Population Range | −10 to 10 | Maximum stall generations | 50 |

Initial Population Range | −10 to 10 | Maximum stall generations | 50 |

Migration Fraction | 0.2 | Migration Interval | 20 |

Mutation Function | Gaussian | Population Size | 50 |

Pareto Fraction | 0.38 |

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**Figure 8.**Comparison of different combinations of ESS for 15% regenerative energy saving, where BE: Battery Energy, BP: Battery Power, SCE: SC Energy, SCP: SC Power, FE: Flywheel Energy, FP: Flywheel Power. The axes for energy are scaled from 0–67 kWh, those for power are scaled from 0–1037 kW, and the axis for cost is scaled from $$0.57\times {10}^{5}$–$7\times {10}^{5}$.

**Figure 9.**Comparison of different combinations of ESS for 25% regenerative energy saving, where BE: Battery Energy, BP: Battery Power, SCE: SC Energy, SCP: SC Power, FE: Flywheel Energy, FP: Flywheel Power. The axes for energy are scaled from 0–109 kWh, those for power are scaled from 0–1690 kW, and the axis for cost is scaled from $$0.93\times {10}^{5}$–$11.2\times {10}^{5}$.

**Figure 10.**Comparison of different combinations of ESS for 35% regenerative energy saving, where BE: Battery Energy, BP: Battery Power, SCE: SC Energy, SCP: SC Power, FE: Flywheel Energy, FP: Flywheel Power. The axes for energy are scaled from 0–157 kWh, those for power are scaled from 0–2420 kW, and the axis for cost is scaled from $$1.3\times {10}^{5}$–$16\times {10}^{5}$.

**Figure 11.**Comparison of different combinations of ESS for 45% regenerative energy saving, where BE: Battery Energy, BP: Battery Power, SCE: SC Energy, SCP: SC Power, FE: Flywheel Energy, FP: Flywheel Power. The axes for energy are scaled from 0–198 kWh that for power are scaled from 0–3026 kW, and the axis for cost is scaled from $$1.68\times {10}^{5}$–$20\times {10}^{5}$.

**Figure 14.**Substation1 and Battery Current, Battery SoC, Substation1, and Battery Voltage for 15% energy saving with standalone BESS.

**Figure 15.**Substation1 and SC Current, SC SoC, Substation1 and SC Voltage for 15% energy saving with standalone SCESS.

**Figure 16.**Substation1 and Battery Current, Battery SoC, Substation1 and Battery Voltage for 45% energy saving with standalone BESS.

**Figure 17.**Substation1 and SC Current, SC SoC, Substation1 and SC Voltage for 45% energy saving with standalone SCESS.

**Figure 18.**Substation1, Battery, and SC parameters for 45% energy saving with an HESS consisting of battery and SC.

Energy Saving | Type of ESS | Time |
---|---|---|

BESS | 2372.5 days | |

15% | SCESS | 134 days |

FESS | 178 days | |

BESS | 1825 days | |

45% | SCESS | 293 days |

FESS | 302 days | |

HESS | 547.5 days |

Application | Energy Saving (%) | Type of WESS | Reason |
---|---|---|---|

Congestion | <25 | SCESS | Lowest cost |

Control | >30 | FESS | Better peak demand |

reduction and a comparable cost | |||

<25 | None | No significant technical-economic | |

Resiliency | trade-off | ||

>30 | HESS | Best system performance and | |

(BESS + SCESS) | economic trade-off | ||

<25 | SCESS | Lowest cost and | |

Energy | simplicity of converter | ||

Saving only | >45 | BESS | Better utilization |

factor of a battery | |||

25–45 | HESS | Best system performance | |

(BESS + SCESS) | and cost-benefit analysis |

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## Share and Cite

**MDPI and ACS Style**

Dutta, O.; Saleh, M.; Khodaparastan, M.; Mohamed, A. A Dual-Stage Modeling and Optimization Framework for Wayside Energy Storage in Electric Rail Transit Systems. *Energies* **2020**, *13*, 1614.
https://doi.org/10.3390/en13071614

**AMA Style**

Dutta O, Saleh M, Khodaparastan M, Mohamed A. A Dual-Stage Modeling and Optimization Framework for Wayside Energy Storage in Electric Rail Transit Systems. *Energies*. 2020; 13(7):1614.
https://doi.org/10.3390/en13071614

**Chicago/Turabian Style**

Dutta, Oindrilla, Mahmoud Saleh, Mahdiyeh Khodaparastan, and Ahmed Mohamed. 2020. "A Dual-Stage Modeling and Optimization Framework for Wayside Energy Storage in Electric Rail Transit Systems" *Energies* 13, no. 7: 1614.
https://doi.org/10.3390/en13071614