Energy-Saving Metro Train Timetable Optimization Method Based on a Dynamic Passenger Flow Distribution
Table 1
Notations of the proposed mathematical model.
Symbols and parameters
Descriptions
Time when train arrives at station
Time when train departs from station
,,
Time points when train transits from traction mode to cruising mode, from cruising mode to coasting mode, and from coasting mode to braking mode in the station segment , respectively
Passenger load of train during its operation in the interval
Number of passengers boarding on train at station
Number of passengers alighting from train at station
Magnitudes of the traction force on train when the train is running in the station segment at time
Magnitudes of the braking force on train when the train is running in the station segment at time
Magnitudes of the resistance on train when the train is running in the station segment at time
Unit basic resistance
Unit additional resistance
,,
Additional resistances at the bend, on the ramp, and in the tunnel, respectively
,,
Empirical coefficients
Total mass of train during its operation in the interval
No-load mass of the train
Average passenger mass
Acceleration of train in the station segment at time
Speed of train in the station segment at time
Position of train in station segment at time
Maximum traction forces
Maximum braking forces
Maximum acceleration
Maximum deceleration
Maximum running speed of the train
Length of station segment
Time granularity
Total traction energy consumption of the timetable
Net energy consumption of the timetable
Total amount of traction energy consumed by all trains in the power supply zone during
Total amount of regenerative braking energy produced by all trains in the power supply zone during
0–1
Binary variable, if the station segment is located in the power supply zone , then, ; otherwise,
,
Efficiency of conversion from mechanical energy to electrical energy and the efficiency of conversion from electrical energy to mechanical energy, respectively
,
Upper and lower limits of the running time in the station segment
,
Upper and lower limits of the dwell time at station
,
Upper and lower limits of the full-line upstream running time, respectively
,
Upper and lower limits of the full-line downstream running time, respectively
,
Maximum and minimum departure intervals, respectively
Decision variables
Descriptions
Interstation running time of each train in the station segment
