2021 Electrician Cup Mathematical Modeling
Question A High-speed Railway Traction Power Supply System Operation Data Analysis and Equivalent Modeling
Original title reproduced:
my country is the country with the longest electrified railway operating mileage, the most types of electric locomotives in service, and the busiest operations in the world. As of the end of 2020, my country's railways consume approximately 80 billion kilowatt hours of electricity annually, accounting for approximately 80% of the total annual power generation of the Three Gorges.
Figure 1 is a schematic diagram of the high-speed railway traction power supply system, which mainly includes traction substation, traction network and EMU. The traction substation converts 220kV three-phase voltage into 27.5kV single-phase voltage that meets the requirements of electric locomotive operation. Its core component is the traction transformer. The traction network is composed of feeders, contact lines, rails, return lines, etc., and completes the task of transmitting power to electric locomotives.
High-speed EMUs will consume a large amount of electric energy during operation, and their power will vary with the operating conditions of the EMUs. The operation of EMUs will also bring about imbalance and harmonic problems in the voltage and current of the regional power grid, worsening the power quality and giving rise to Grid operation regulation brings adverse effects. Therefore, it is particularly important to evaluate the power quality of regional power grids containing high-speed rail traction loads, formulate energy saving and consumption reduction strategies, and accurately predict traction loads. In this regard, please combine the above background knowledge and the relevant measured data provided in the appendix to solve the following problems.
Question 1: Power quality assessment
As the main load of the traction power supply system, the load of high-speed EMUs has the characteristics of nonlinearity, single-phase, and impact, which leads to power quality problems such as harmonics and negative sequence in the regional power grid. Please combine the measured three-phase voltage and three-phase current data (sampling interval 50 microseconds) of the high-voltage side (220kV) of the traction power supply system provided in Appendix 1 to analyze and calculate the following issues (provide executable source programs): 1) High-speed
EMU The main operating conditions can be divided into no-load, traction, and braking. Under the three operating conditions, the data of 0.2 seconds are taken for each: [1, 4000] (no-load), [1600000, 1604000] (traction), 【4000000, 4004000】(braking)
a. Calculate the positive sequence, negative sequence, and zero sequence components of voltage and current under each operating condition, and draw a sequence component diagram to analyze the difference in voltage and current imbalance in this section.
b. Draw the current spectrum under each operating condition and calculate the amplitude and frequency of the five largest harmonic components.
c. Please combine the national power quality assessment standards in Appendix 1 to calculate the voltage and current imbalance and current total harmonic distortion rate under each operating condition. Based on this, evaluate the impact of the EMU operating conditions on the voltage, current imbalance and current Harmonic effects.
2) Take all data as analysis objects:
a. The operating conditions of high-speed EMUs are changeable, which may cause changes in the degree of current imbalance and harmonic content. Try to draw the curves of the current positive sequence, negative sequence, zero sequence component amplitudes and the third harmonic content changing with time. , analyze the current imbalance degree and third harmonic content rate during the most serious period of imbalance.
b. Calculate the instantaneous power of the train and draw its change curve with time. Try to find the moment when the train's traction power and braking power are maximum, and analyze the relationship between the traction power, braking power, three-phase imbalance and harmonics.
Question 2: Energy Saving and Consumption Reduction Scheme
High-speed EMUs widely apply regenerative braking technology, which converts kinetic energy into electrical energy during braking conditions and feeds it back to the power system free of charge. Combined with the on-site measured data provided in Appendix 1, analyze and calculate the following problems (a executable source program is provided):
a. Based on the instantaneous power calculation results in question 1, count the power consumed and fed back by the high-speed EMU.
b. In order to use regenerative braking energy for high-speed EMU traction, please design a regenerative braking energy utilization plan for on-board energy storage (including the power configuration of the energy storage system and the power electronics access and control plan), and combine Appendix 2 gives the electricity price and energy storage device parameters, and calculates its benefits in reducing the energy consumption of the EMU.
c. Please design a regenerative braking energy utilization energy storage solution placed in the traction substation (including the power configuration of the energy storage system and the power electronics access and control solution), and combine it with the electricity price and energy storage device parameters given in Appendix 2 , to calculate its benefits in reducing the energy consumption of EMUs. Compare the advantages and disadvantages of options b and c from the aspects of economy, technology, safety and reliability, and energy storage capacity utilization.
Issue 3: Accurate prediction of dynamic traction load
Research shows that the dynamic traction load (active power) demand of high-speed railway traction substations is related to the EMU's operation process in the interval (whether it stops at a station), grouping (8 groups and 16 groups), running direction (upward, downward), and vehicle type (different models) Rated power varies) and other factors are closely related. The specific characteristics are: 1) EMUs with the same operating process, grouping, operating direction, and vehicle models have the same dynamic power demand trend and similar electricity consumption/return during interval operation; 2) For the same vehicle model, 16 EMUs are grouped The rated power of the EMU is twice that of the 8-unit EMU; 3) The EMU needs to decelerate and brake for a short time before stopping at the station, which will generate a large amount of regenerative braking energy. Appendix 3 gives the actual measured active power data of a high-speed railway traction substation throughout the day. The sampling interval is 1 second, with a total of 86,400 data. It is assumed that there is no scenario in which power is supplied to two or more EMUs at the same time within the power supply interval of the traction substation. Please combine the measured data to answer the following questions (provide runnable source programs):
a. Extract the dynamic active power demand sequence (dynamic traction load) of each EMU train during interval operation, and form a corresponding dynamic traction load database.
b. Apply correlation and other analysis methods, combined with the EMU operating direction, vehicle type and other information provided in Appendix 3, to achieve classification and identification of the extracted dynamic traction loads.
c. For the classified dynamic traction loads, use linear regression and other methods to establish various dynamic traction load models, and then build a corresponding dynamic traction load model library.
d. Combined with the train timetable provided in Appendix 4, the simulation of the dynamic traction load of the high-speed railway traction substation and the accurate prediction of the power amount are realized.
Question 4: High-speed rail traction substation-traction load equivalent modeling
In order to deeply study the impact of high-speed EMU operation on the power grid, it is necessary to establish a mathematical model that reflects the operation of high-speed EMUs.
The simulation results of an accurate mathematical model should be consistent with the data given in Appendix 1.
Figure 2 gives a schematic diagram of the high-speed rail traction substation - traction load. Please construct a mathematical model that reflects the operating electrical characteristics of the high-speed EMU, and analyze the error between the voltage and current of the model and the measured voltage and current in Appendix 1 (provide available Running source program); illustrate the effectiveness of the model and prospects for improvement.
