Optimized Sizing and Scheduling of Hybrid Energy Storage Systems for High-Speed Railway Traction Substations
Abstract
:1. Introduction
- The interaction of HESS sizing and daily scheduling of HESS within the time scope of project service period considering battery degradation are formulated via a bi-level model.
- The electricity bill for rail operators is largely reduced through peak shaving of traction loads, utilization of braking power and the mitigation of bill penalties for power fed back to the utility grid.
- The impact of different electricity pricing schemes, length of project service period and initial SOC of HESS are also analyzed.
2. System Description
2.1. Block Diagram of the System and Model
2.2. Traction Load and Regenerative Braking Power
- Computer simulation method based on traction and power supply calculation.
- Statistical model or sampling method based on measurement data from the meter installed in the traction substation.
2.3. Uncertainty Representation of PV Generation
2.4. Hybrid Energy Storage Systems
3. Master Level: HESS Sizing Problem Formulation
3.1. Battery Degradation Analysis
3.2. Objective Function of the Master Level Model
3.2.1. Capital Cost
3.2.2. Replacement Cost
3.2.3. Operation and Maintenance (O&M) Cost
3.2.4. Salvage Value
3.3. Constraints of the Master Level
4. Slave Level: Diurnal Dispatch Problem Formulation
4.1. Objective Function of the Slave Level Model
- Energy consumption charge. Electric utilities installed in the traction substation meter the energy consumption supplied by utility grid, and this charge is obtained through the energy consumption and corresponding energy price.
- Capacity charge or demand charge. This part of charge is associated with the construction cost of power plant, transmission lines and other facilities. Typically two options are offered to the C&I consumers: transformer-capacity-based charge or peak-demand-based charge. The former is related to the capacity of transformers, and the latter depends on the maximum value of the averaged active power consumption in successive 15 min time intervals, during a billing month (or a day in this study, as the diurnal operation of the elements in RTSEM system is regarded as repeated within the project service period). The latter option is applied in this paper.
- Penalty charge. HSTs have been widely put into service in HSR lines in China. Part of the RBP is absorbed by HSTs running in the same power supply section, and the rest returns to utility power system. However, the RBP fed back to the grid contains a large number of harmonic components and negative sequence components, bring potential threats to the utility power system. Therefore, a bill penalty is charged for the traction power fed back to the utility grid.
- The energy consumption charge can be expressed as:
- The demand charge is derived as:
- The penalty charge is as follows:
4.2. Constraints of the Slave Level Model
4.2.1. Power Balance
4.2.2. HESS Constraints
4.2.3. PV Generation Constraints
4.2.4. Power Exchange Constraints
5. Proposed Approach
5.1. Overview of Grey Wolf Optimizer
5.1.1. Encircling Prey
5.1.2. Hunting
5.1.3. Attacking or Searching for Prey
5.2. Application of GWO Approach with CPLEX Solver Embedded
6. Case Study
6.1. Cases Description and Input Parameters
- Case 1: conventional railway system with no HESS nor PV generation, as the base case;
- Case 2: conventional railway system with HESS only;
- Case 3: conventional railway system with battery energy storage systems only;
- Case 4: conventional railway system with both HESS and PV generation.
6.2. Cases Results Analysis
6.2.1. Case 1
6.2.2. Case 2
6.2.3. Case 3
6.2.4. Case 4
6.2.5. Convergence Performance of GWO
6.3. Sensitivities Analysis
6.4. Cost Savings Analysis of TSSs in the HSR Line
7. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Nomenclature
Abbreviations | |
RTSEM | Railway traction substation energy management |
HESS | Hybrid Energy storage systems |
PCS | Power conversion systems |
BOP | Balance of plant |
RBP | Regenerative braking power |
UC | Ultracapacitor |
LA | Lead-acid |
PV | Photovoltaic |
MILP | Mixed-integer linear programming |
HSR | High-speed railway |
HSTs | High-speed trains |
DOD | Depth of discharge |
SOC | State of charge |
Parameters | |
Railway traction load at time interval t (MW) | |
Regenerative braking power at time interval t (MW) | |
T | Total number of operation time intervals during a day |
∆t | The discretization time interval (1 min) |
Electricity price for power imported from the utility grid (CNY/MWh) | |
penalty charge for power fed back to the utility grid (CNY/MWh) | |
Total area of PV panels (m2) | |
Probability of PV generation scenario | |
Solar irradiance at time interval t for scenario s (kW/m2) | |
Tproj | Project service period (year) |
r0 | Annual discount rate |
, | Upper and lower bounds of power rating of battery (MW) |
, | Upper and lower bounds of capacity of battery (MWh) |
, | Upper and lower bounds of power rating of UC (MW) |
, | Upper and lower bounds of capacity of UC (MWh) |
, | Discharge and charge efficiency of battery |
, | Discharge and charge efficiency of UC |
, | Self-discharging rate of battery and UC |
, | Minimum and maximum SOC limit of battery |
Initial SOC of battery per day | |
, | Minimum and maximum SOC limit of UC |
Initial SOC of UC per day | |
Maximum limit for active power imported from the utility grid (MW) | |
Maximum limit for regenerative braking power fed back to the utility grid (MW) | |
Variables | |
, | Discharge and charge power of battery at time interval t for scenario s (MW) |
, | Discharge and charge power of UC at time interval t for scenario s (MW) |
Power supplied by the utility grid at time interval t for scenario s (MW) | |
Power fed back to utility grid at time interval t for scenario s (MW) | |
PV output power at time interval t for scenario s (MW) | |
, | The energy stored in battery and UC at time interval t for scenario s (MWh) |
, | Binary variable: 1 if battery or UC are discharging at time interval t for scenario s, 0 otherwise |
, | Binary variable: 1 if battery or UC are charging at time interval t for scenario s, 0 otherwise |
, | Binary variable: 1 if battery or UC are in operation mode (charge/discharge) at time interval t for scenario s, 0 otherwise |
Binary variable: 1 if grid supplies power to trains, and 0 if braking power is fed back to grid. | |
Battery lifetime (year), as an intermediate variable | |
, | Rated power of battery and UC (MW) |
, | Rated capacity of battery and UC (MWh) |
, | Operation time of battery and UC per day (hour), as intermediate variables |
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Parameters | Value | Parameters | Value |
---|---|---|---|
Unloaded weight | 479.36 t | Max. traction power | 8800 kW |
Average load | 56.64 t | Max. braking power | 8000 kW |
Power factor (traction) | 0.98 | Auxiliary power | 408 kW |
Power factor (braking) | 0.9 | Max. acceleration (traction) | 0.65 m/s2 |
Transmission efficiency | 0.9 | Max. acceleration (braking) | 1.2 m/s2 |
Parameters | Unit | LA Battery | UC |
---|---|---|---|
PCS costs | CNY/kW | 2838 | 2050 |
Energy capacity costs | CNY/kWh | 4640 | 198,000 |
Replacement costs | CNY/kWh | 1292 | 0 |
BOP costs | CNY/kW | 674 | 674 |
O&M costs (fixed) | CNY/kW/year | 25.5 | 0 |
O&M costs (variable) | CNY/MW/h | 2.78 | 0 |
Efficiency (charge/discharge) | - | 80%/80% | 95%/95% |
SOC range | - | 20~80% | 0~100% |
Initial SOC | - | 50% | 50% |
Self-discharging rate | /mon | 5% | 0 |
Depreciation coefficient | - | 0.7 | 0.7 |
Cases | Case 1 | Case 2 | Case 3 | Case 4 | ||||
---|---|---|---|---|---|---|---|---|
Pricing Schemes | Fixed Tariff | TOU Tariff | Fixed Tariff | TOU Tariff | Fixed Tariff | TOU Tariff | Fixed Tariff | TOU Tariff |
/MW | - | - | 2.9 | 2.2 | 2.9 | 3.0 | 2.7 | 2.7 |
/MWh | - | - | 5.0 | 5.0 | 5.1 | 5.1 | 5.0 | 5.0 |
/MW | - | - | 13.0 | 11.6 | - | - | 16.7 | 14.5 |
/MWh | - | - | 0.43 | 0.43 | - | - | 0.49 | 0.48 |
/year | - | - | 5.47 | 3.26 | 1.21 | 1.1 | 3.95 | 2.84 |
/k CNY | 88.70 | 99.98 | 40.84 | 45.42 | 70.38 | 75.83 | 31.31 | 33.14 |
/k CNY | - | - | 26.72 | 25.75 | 6.22 | 6.29 | 30.18 | 28.98 |
/k CNY | - | - | 3.57 | 7.14 | 19.42 | 21.84 | 5.95 | 8.33 |
/CNY | - | - | 202.60 | 153.70 | 202.60 | 209.60 | 188.63 | 169.52 |
/k CNY | - | - | 0.57 | 1.43 | 0.83 | 1.48 | 1.55 | 1.60 |
/k CNY | 88.70 | 99.98 | 70.76 | 77.02 | 95.39 | 102.69 | 66.08 | 69.04 |
Battery cycles per day (full/half cycles) | - | - | 16/4 | 21/3 | 75/4 | 73/3 | 25/3 | 32/5 |
Electricity Cost Savings | - | - | 53.96% | 54.57% | 20.65% | 24.16% | 64.70% | 66.85% |
Total Cost Savings | - | - | 20.22% | 22.96% | −7.54% | −2.71% | 25.50% | 30.95% |
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Liu, Y.; Chen, M.; Lu, S.; Chen, Y.; Li, Q. Optimized Sizing and Scheduling of Hybrid Energy Storage Systems for High-Speed Railway Traction Substations. Energies 2018, 11, 2199. https://doi.org/10.3390/en11092199
Liu Y, Chen M, Lu S, Chen Y, Li Q. Optimized Sizing and Scheduling of Hybrid Energy Storage Systems for High-Speed Railway Traction Substations. Energies. 2018; 11(9):2199. https://doi.org/10.3390/en11092199
Chicago/Turabian StyleLiu, Yuanli, Minwu Chen, Shaofeng Lu, Yinyu Chen, and Qunzhan Li. 2018. "Optimized Sizing and Scheduling of Hybrid Energy Storage Systems for High-Speed Railway Traction Substations" Energies 11, no. 9: 2199. https://doi.org/10.3390/en11092199