Project One: Train Speed Profile Based on Train Longitudinal Dynamics
Project One: Train Speed Profile Based on Train Longitudinal Dynamics
1.Background
During the operation of a train, various kinds of friction will occur between the train
and the outside world, thereby consuming the energy of train traction. During the
same journey, different driving strategies used by trains often result in different
energy and time consumption. The operation process of a single train between two
platforms is shown in Figure 1.
Figure 1. Single Train Operation
The train is on a horizontal track, starting from the departure platform with an initial
speed of zero and at the time instant 0. After the period of time T, it reaches the arrival
platform, and the speed reduces to zero again.
Based on the optimal train control theory, the optimal control strategies of a train
consists of motoring with maximum traction effort, cruising, coasting and braking
with maximum braking effort, as shown in Figure 2.
Figure 2. Running speed trajectory of energy-saving trains
During the initial stage, the train operates at maximum acceleration to reach
maximum speed (maximum traction process).The train then travels at a constant
speed for a distance (cruise process). Subsequently, the traction of the train is reduced
to zero and the train coasts (coast process). As the train approaches the destination, it
brakes and decelerates continuously. When the train speed decreases to zero, the train
just reaches the destination (braking process).
2. Train operation model
Regarding a train as a single particle, the longitudinal dynamic model as follows:
represents the rotational mass factor of the inertia of the train's rotating components.
When ,The train enters the maximum
traction mode, and the train motor drives the train with the maximum traction
3. Specific tasks
A train starts from platform A and runs to platform B.
Distance between platforms A and B:
The unit of velocity is m/s, and the unit of D (v) is KN.
Task 1
Use any programming language to obtain the train operation trajectory that allows the
train to reach the destination as quickly as possible, and the operation process is the
maximum traction-cruise-braking-combination.
(Hint: Make the train achieve the maximum speed possible and solve the
cruise-braking switching point from the end point in the reverse direction.)
Figure 3. Train operation trajectory during the fastest operation time
Task 2
If the train has a certain operating time, use any computer programming
language to calculate the maximum traction-cruise-braking combination of the train,
so that the train can arrive at the destination on time.
(Hint: You can determine the running time by selecting the cruise speed)
Figure 4. Train Operation Track for task2
Task 3
Based on Task 1, use the maximum acceleration traction, cruise, coasting, braking
combination to obtain the train operation trajectory, so that the train can arrive at
platform B on time (around 660s) and achieve the most energy savings. Given the
running time of your program, how will you quickly and accurately solve the
optimized train operation trajectory?
(Note: After selecting the cruise speed, there is a determined cruise-coasting switching
point to ensure that the punctuality of the train is met.)
Figure 5. Optimal speed and non-optimal speed curve
4. Extended tasks
Consideration of regenerative braking:
If the dynamic characteristics and mechanical/regenerative braking characteristics of
the motor in train operation are considered to be closer to reality. As shown in Figure
6.
Figure 6. Dynamic traction and braking characteristics of an electric railway vehicle
The meaning of mechanical/regenerative braking characteristics is that when the train
is in a low-speed state, it uses mechanical braking, and when the train is in a high
speed state, it uses regenerative braking.
Regenerative braking and train traction are both accomplished through electric motors.
The motor traction process is a dynamic process that includes constant torque zone
(maximum traction force), constant power zone (constant power, reduced traction
force), and power reduction zone (total power decreases). The parameters in this
design are shown in Figure 7:
The mathematic relation for the traction efforts over train speeds can be represented
as:
In addition, the operation of the motor will have a loss of power.
The effective utilization rate of motor traction is 0.9.
The effective recovery rate of regenerative braking is 0.6.
You can modify your model code to re solve and see the changes in the results.
During train operation, there will be certain gradient changes depending on the
location G (x) resistance in Eq.(12)
360
# 12
Slope information available in the attached excel table.
Figure 8. Optimal speed and non-optimal speed curve for Extended task
Consideration of speed limits
The speed limits at different locations during train operation varies, and the speed
changes are shown in the attached excel table. If the train is required to arrive at the
platform on time within 240s at this time, how will you obtain the optimized train
operation curve and how long will it take for the programming to obtain the results?
What is the energy-saving performance after the optimization procedure?
5. Grading criteria and other key information
1. Using any programming software to complete tasks 1, 2, and 3; Correctly
programmed and clearly annotated to understand the program. [50 points]
2. Design report: clearly report the design specifications; Clarify reporting options;
Include all relevant information. [50 points]
3. Appropriate points will be added based on the completion of extended tasks.
4. You should work independently.
The grading of a design report is based not only on the correct answers to the
calculations, but also on the quality of the report:
Organize your report to convey information about your design clearly. In this project,
your design and its expected performance are key deliverables, which are the focus of
the report. Use proper headings to organize information. Start the report with a brief
executive summary; Provide sufficient background knowledge to enable readers
unfamiliar with the project to understand what you are doing; Demonstrate your
findings and include sufficient details about your calculations to convince readers of
your conclusions.
Please avoid sketching by hand – use professional computer-aided tool. The goal is
to at least match the quality of the graphics we provide in our homework questions
and project descriptions. Use the Equation Editor for the equation, and pay attention
to details such as marking on graphics, units, and definition of variables in the
equation.
