1 Introduction
2 Simulation as a potential tool
2.1 Train movement and performance calculation
2.2 DC traction power supply
3 Strategy for regenerative braking energy management with OBESS
3.1 Regenerative braking energy management with the OBESS
3.2 Proposed peak cutting strategy
3.3 Charging algorithm
3.4 The discharging algorithm
4 Problem formulations for optimal energy saving
4.1 Objective function
4.2 Control parameters
4.3 Constraints
5 Simulation results and discussion
5.1 Test system
Specific data | Information | |
---|---|---|
Train parameters
| ||
Voltage | Nominal voltage | 750 V |
Weight | Tare weight | 153 ton |
Payload AW3 | 75 ton | |
Movement feature | Max. speed | 80 km/h |
Max. acceleration | 0.87 m/s2
| |
Max. deceleration | 1.00 m/s2
| |
Efficiency | Gear, motor, inverter | 98%, 88%, 98% |
EDLC, chopper | 86%, 95% | |
Auxiliary power | Constant load | 270 kW |
Train resistance |
A = 4025, B = 118.67, C = 0.871 | |
Power system parameters
| ||
Traction substation | No-load voltage rated power | 790 V 2550 kVA (CEN, S02, S05, S07) 3300 kVA (S09, S11, S12) |
Third rail and running rail | Third rail resistance | 8.23 mΩ/km |
Running rail resistance | 40.46 mΩ/km | |
Conductivity to earth | 0.1 S/km | |
OBESS parameters
| ||
MITRAC energy saver [26] | Installed energy | 1 kWh/module |
Max output power | 300 kW/module | |
Weight | 428 kg/module |
Case | OBESS | Trip time control |
---|---|---|
Based | Without | Max. deceleration |
1 | With |
k
dec* Max. deceleration |
2 | With |
L
coast + Max. deceleration |
3 | With |
L
coast + k
dec* Max. deceleration |
Parameters | Values |
---|---|
Control variables | |
Number of the OBESS modules (N
ESS) | [8, 14] |
Initial SOC of the OBESS (SOCstart
)
| [20, 95] |
Gain of deceleration control (
k
dec
)
| [0.8, 1] |
Coasting point (
L
coast
)
| [200, 2000] |
Generation | Nvar × 20 |
Population | Nvar × 10 |
Crossover probability | 0.9 |
Mutation probability | 0.1 |
Function tolerance | 1 × 10−6
|
Parameters | Case 1 | Case 2 | Case 3 |
---|---|---|---|
N
ESS
| 11 | 11 | 10 |
SOCstart
| 44.8% | 44.8% | 40.9% |
k
dec
|
k
dec,7 = 0.80452 | – |
k
dec,7 = 0.95216 |
k
dec,8 = 0.84933 |
k
dec,8 = 0.94633 | ||
k
dec,9 = 0.85840 |
k
dec,9 = 0.99529 | ||
k
dec,10 = 0.92247 |
k
dec,10 = 0.97604 | ||
k
dec,11 = 0.83889 |
k
dec,11 = 0.98407 | ||
k
dec,12 = 0.86245 |
k
dec,12 = 0.97851 | ||
L
coast
| – |
L
coast,7 = 200.00 |
L
coast,7 = 304.72 |
L
coast,8 = 202.89 |
L
coast,8 = 218.39 | ||
L
coast,9 = 269.95 |
L
coast,9 = 280.00 | ||
L
coast,10 = 200.68 |
L
coast,10 = 209.32 | ||
L
coast,11 = 200.00 |
L
coast,11 = N/A | ||
L
coast,12 = N/A |
L
coast,12 = 200.00 | ||
Fitness function (ϕ) | 0.13715 | 0.15248 | 0.15564 |
Case |
\(P_{{{\text{TSS}}1}}\) (MW) |
\(P_{{{\text{TSS}}2}}\) (MW) |
\(P_{{{\text{TSS}}3}}\) (MW) |
\(P_{{{\text{TSS}}4}}\) (MW) |
\(P_{{{\text{TSS}}5}}\)(MW) |
\(P_{{{\text{TSS}}6}}\) (MW) |
\(P_{{{\text{TSS}}7}}\) (MW) |
---|---|---|---|---|---|---|---|
Based | 3.04 | 2.00 | 2.23 | 2.19 | 2.18 | 2.16 | 2.48 |
1 | 1.74 [42.68] | 0.73 [63.49] | 1.75 [21.39] | 1.31 [40.05] | 1.45 [33.62] | 1.56 [27.74] | 1.22 [50.89] |
2 | 1.74 [42.68] | 0.73 [63.49] | 1.75 [21.39] | 1.31 [40.05] | 1.47 [32.81] | 1.59 [26.12] | 1.22 [50.89] |
3 | 1.95 [35.85] | 0.73 [63.49] | 1.75 [21.38] | 1.31 [40.06] | 1.48 [31.99] | 1.56 [27.74] | 1.22 [50.95] |
Item (unit) | Based case | Case 1 | Case 2 | Case 3 |
---|---|---|---|---|
Energy consumed by train (kWh) | 298.95 | 260.90
[12.73]
| 256.08
[14.34]
| 255.13
[14.66]
|
Energy consumption at substation (kWh) | 314.20 | 271.11 [13.71] | 266.29 [15.25] | 265.30 [15.56] |
Energy losses (kWh) | 15.25 | 10.20 [33.07] | 10.21 [33.03] | 10.16 [33.34] |
Regenerated energy available (kWh) | 87.55 | 72.15 [17.58] | 66.94 [23.54] | 66.29 [24.28] |
Energy wasted in brake resistor (kWh) | 71.13 | 0.33 [99.54] | 0.63 [99.12] | 0.12 [99.83] |
Recovery coefficient (%) | – | 59.72 | 71.58 | 73.76 |