Voltage stability design method applied to large-ramp electrified railway traction power supply system

Abstract

A voltage stability design method applied to a large-ramp electrified railway traction power supply system is characterized in that triangular vectors of traction and regeneration working conditions of the large-ramp electrified railway traction power supply system are modeled, iterative computation is quantified, and the voltage stability problems of the two opposite working conditions are compared and analyzed; and a solid foundation and a reliable basis are provided for providing reasonable and effective engineering measures and solutions.

Description

Technical Field

[0001] The present invention relates to the field of electrified railway traction power supply systems, and in particular to a voltage stability design method for a steep-slope electrified railway traction power supply system. Background Art

[0002] my country's electrified railway mobile equipment has experienced a development process from DC transmission to AC transmission. As electric locomotives or EMUs that traction loads, AC transmission is now widely used. Under braking conditions, the AC motor of AC transmission mobile equipment is converted into an AC generator, which converts the potential energy when going downhill into electrical energy and feeds it back to the traction power supply system, causing the traction network voltage to rise. In severe cases, it exceeds the normal operating voltage range of the mobile equipment, and the braking power cannot be fully utilized, endangering driving safety.

[0003] As a locomotive or EMU that pulls loads on electrified railways, traction power output is mainly used to overcome various resistances. When running at high speeds, air resistance and wheel-rail resistance account for a higher proportion, and when running on long and steep slopes, slope resistance becomes an important operating resistance.

[0004] When traction loads are driven uphill on long and steep slopes, they often need to continuously output high power to overcome the slope resistance and other operational resistance. This results in high traction currents, and as the train continues to track, the traction network voltage drops. According to the voltage-power curve for AC transmission trains or EMUs, 100% power is available between 22.5 and 29 kV. Below 22.5 kV and above 19 kV, power decreases gradually, reaching approximately 84% at 19 kV. Below 19 kV, power drops rapidly, reaching zero at 17.5 kV. Furthermore, to maintain normal operating conditions, traction loads on steep slopes are often controlled at constant power. This means that as voltage decreases, current increases, further increasing voltage losses and causing further voltage drops, creating negative feedback. If this voltage drop trend is not corrected, system voltage instability and eventual collapse will occur.

[0005] When a load is pulled down a long slope, the slope resistance becomes a "boost" and the AC motor is transformed into an AC generator, converting the potential energy when going downhill into electrical energy, causing the voltage at the traction load to rise. According to the voltage and power curve of AC transmission trains or EMUs, when the voltage is higher than 29kV, the braking power will drop rapidly. When it reaches 31kV, the braking power is zero and the brakes fail completely, which may cause the train to be unable to brake or stall, endangering safety.

[0006] The design of traction power supply systems for electrified railways on long and steep slopes faces challenges related to forward current carrying, reduced grid voltage, high transformer capacity requirements, high forward power transmission capacity requirements, and forward power quality issues caused by high uphill traction currents. It also faces challenges related to reverse current carrying, increased grid voltage, reduced transformer capacity utilization, high reverse power transmission capacity requirements, and reverse power quality issues caused by high downhill braking currents. Because high traction currents and high regenerative braking currents generate opposing demands on the traction power supply system, particularly in terms of voltage stability, and the design objectives of the related engineering measures are completely different, the design of the traction power supply system must consider and balance the issues and challenges arising from these two extreme operating conditions. Summary of the Invention

[0007] The technical problem to be solved by the present invention is to provide a voltage stability design method for the traction power supply system of an electrified railway with a steep slope, which provides a solid foundation and reliable basis for proposing reasonable and effective engineering measures and solutions.

[0008] The technical solutions adopted by the present invention to achieve the above technical problems are as follows:

[0009] A voltage stability design method for a traction power supply system of an electrified railway with a steep slope includes the following steps:

[0010] Step 1: During regenerative braking, construct a vector triangle with the traction power supply system voltage rise, no-load voltage, and load voltage as edges, and qualitatively analyze the maximum load voltage and its stability. During traction operation, construct a vector triangle with the traction power supply system voltage drop, no-load voltage, and load voltage as edges, and qualitatively analyze the minimum load voltage and its stability.

[0011] Step 2: Use an iterative calculation scheme to calculate the voltage stability value. With the no-load voltage as the constraint condition, the load is based on constant power, the initial load voltage is set, and the voltage increase or voltage decrease vector is calculated. Under regenerative braking conditions, the difference between the initial voltage vector and the voltage increase vector is calculated. Under traction conditions, the sum of the initial voltage vector and the voltage decrease vector is calculated to obtain the calculated no-load voltage. The calculated no-load voltage is compared with the set no-load voltage. If the calculated value and the set value are not equal, the load voltage is adjusted. Repeat the above process until the calculated no-load voltage is equal to the set no-load voltage.

[0012] Step 3: Based on the above analysis conclusions, comprehensively consider the train operation safety and its system tolerance, and propose reasonable and effective engineering measures and solutions.

[0013] The beneficial effects of the present invention are mainly reflected in the following aspects:

[0014] 1. The present invention constructs a vector triangle to conduct qualitative analysis of voltage stability under traction load regenerative braking and traction conditions;

[0015] Second, guided by the conclusions of qualitative analysis, to avoid system instability and non-convergence of calculations, an iterative calculation method was used with no-load voltage as the constraint to carry out quantitative calculations of voltage stability under traction load regenerative braking conditions and traction conditions;

[0016] 3. Comprehensively calculate the results, balance the traction and braking conditions, and formulate reasonable and effective engineering measures and solutions.

[0017] By modeling the triangular vectors of the traction and regeneration operating conditions of the traction power supply system of the electrified railway on long and steep slopes and quantifying the iterative calculation, the voltage stability problems under the two completely opposite operating conditions are compared and analyzed, providing a solid foundation and reliable basis for proposing reasonable and effective engineering measures and solutions.

[0018] Description of the accompanying drawings and tables

[0019] Figure 1 It is the voltage power curve of AC transmission train.

[0020] Figure 2 It is the triangle vector model diagram of regenerative braking voltage increase.

[0021] Figure 3 It is the triangle vector model diagram of voltage reduction in traction condition.

[0022] Figure 4 This is the voltage stability iterative calculation flow chart DETAILED DESCRIPTION

[0023] The present invention will be further described below with reference to the following examples.

[0024] Reference Figure 4 The present invention provides a voltage stability design method for a traction power supply system of an electrified railway with a steep slope, comprising the following steps:

[0025] Step 1: During regenerative braking, construct a vector triangle with the traction power supply system voltage rise, no-load voltage, and load voltage as edges, and qualitatively analyze the maximum load voltage and its stability. During traction operation, construct a vector triangle with the traction power supply system voltage drop, no-load voltage, and load voltage as edges, and qualitatively analyze the minimum load voltage and its stability.

[0026] During regenerative braking, a vector triangle is constructed with the voltage rise of the traction power supply system, the no-load voltage, and the load voltage as the sides, as shown in the following example: Figure 2As shown. The traction load voltage is U1, the lifting voltage is U2, and the no-load voltage is U3, which constitute the sides of the triangular vector. From the sine theorem, we can know that when the angle γ corresponding to the load voltage U1 is a right angle of 90°, the load voltage U1 is the maximum value. This means that in order to control the load voltage rise, effective measures are to reduce the no-load voltage (reduce the circle radius) or increase the angle β corresponding to the no-load voltage (β is an acute angle). For regenerative braking, the regenerative current leads the load voltage. Therefore, reducing the power factor during regeneration can increase the angle β corresponding to the no-load voltage. During traction operation, the vector triangle is constructed with the voltage reduction of the traction power supply system, the no-load voltage, and the load voltage as the sides, as shown in the figure below: Figure 3 As shown in the figure, the traction load voltage is U1, the voltage drop is U2, and the no-load voltage is U3, which form the sides of the triangular vector. From the sine theorem, we know that to control the load voltage drop, effective measures are to increase the no-load voltage (increase the circle radius) or reduce the angle β corresponding to the no-load voltage (β is an obtuse angle). In traction conditions, the traction current lags the load voltage. Therefore, improving the power factor during traction conditions can reduce the angle β corresponding to the no-load voltage. The angle corresponding to the no-load voltage is closely related to the network parameters of the traction power supply system. The traction network impedance angle is approximately 68-75°. The traction transformer is an inductive component, with an impedance angle of approximately 88°. The grid system resistance is approximately 0.1 of the inductive reactance, with an impedance angle of approximately 84°. Increasing the system's comprehensive impedance angle will increase the angle corresponding to the regenerative braking no-load voltage and improve voltage rise.

[0027] Step 2: Use an iterative calculation scheme to calculate the voltage stability value, with the no-load voltage as the constraint condition, the load according to constant power, set the initial load voltage, calculate the voltage rise or voltage reduction vector, the regenerative braking condition, calculate the difference between the initial voltage vector and the voltage rise vector, the traction condition, calculate the sum of the initial voltage vector and the voltage reduction vector, and obtain the calculated no-load voltage. Compare the calculated no-load voltage with the set no-load voltage. If the calculated value and the set value are not equal, adjust the load voltage and repeat the above process until the calculated no-load voltage is equal to the set no-load voltage.

[0028] An iterative calculation scheme is used to calculate the voltage stability value. During regenerative braking, the traction load is kept at constant power, the initial traction load voltage is set, and the voltage rise vector is calculated. A circle is drawn with the vertex of the voltage rise vector as the center and the no-load voltage as the radius. The intersection of the circle and the load voltage vector is the new load voltage. Thus, the new load voltage is substituted and a new round of calculation is started until the calculated load voltage is equal to the substituted load voltage value, which means that the system is stable and the voltage stability value is obtained. If the calculated load voltage is always different from the substituted load voltage value, the system is an unstable system and is in a state of Unstable state; during traction operation, the traction load is operated at constant power, the initial traction load voltage is set, the voltage reduction vector is calculated, and then the vector sum of the load voltage vector and the voltage reduction vector is obtained. A circle is drawn with the starting point of the load voltage vector as the center and the no-load voltage as the radius. If the circle does not intersect with the vector sum of the load voltage vector and the voltage reduction vector, the load voltage is adjusted and updated, and a new round of calculation is started until an intersection appears. This means that the system is stable, and a voltage stability value is obtained. If the circle does not intersect with the vector sum of the load voltage vector and the voltage reduction vector, the system is an unstable system and is in an unstable state.

[0029] Step 3: Based on the above analysis conclusions, comprehensively consider the train operation safety and its system tolerance, and propose reasonable and effective engineering measures and solutions.

[0030] Based on the results of qualitative analysis and quantitative calculations, and taking into account the safety, effectiveness and feasibility of engineering measures, the following solutions are proposed: 1. Improve the system power supply capacity as much as possible, enhance the system resilience, reduce the demand for no-load voltage in traction conditions, and provide space for regenerative braking conditions; 2. Set up reinforcement lines. On the one hand, it can improve the angle corresponding to the no-load voltage vector in the regenerative braking direction, and at the same time reduce the voltage rise under large loads to avoid system instability. On the other hand, it can improve the voltage reduction in the traction direction and avoid voltage collapse; 3. When the two working conditions cannot be fully taken into account, the priority is to ensure braking safety, partially sacrifice traction efficiency, and control the regenerative braking and load voltages to no more than 29kV by reducing the no-load voltage. At the same time, reduce the minimum traction voltage from the conventional 20kV to 19kV (power output is 84% ​​of the rated power).

[0031] This invention proposes a design method to address the voltage stability issue of traction power supply systems on electrified railways with steep slopes. By constructing triangular vector models for both traction and regeneration operating conditions, this system qualitatively analyzes the factors influencing voltage rise and voltage drop under these two conditions. Using no-load voltage as a constraint, an iterative calculation model is constructed and iterative calculations are performed to further verify the accuracy of the qualitative analysis conclusions. Quantitative results are also obtained. Finally, combining the qualitative analysis and quantitative calculation results, and comprehensively considering train operation safety and system tolerance, reasonable and effective engineering measures and solutions are obtained. This design method establishes a comprehensive system for addressing the voltage stability issue of traction power supply systems on electrified railways with steep slopes, ensuring the safety and effectiveness of engineering measures.

[0032] Example:

[0033] For example, a power supply arm on a double-track railway has a length of 22.8 km and a power supply range of 30‰ on a single slope. It operates with separate upstream and downstream catenary power supply, which minimizes voltage stability. The minimum train tracking interval is 8.9 km, the rated power is 19,200 kW, and the power factor is 0.99. The external power system has a short-circuit capacity of 1000 MVA, and the traction transformer has an installed capacity of 40 MVA and an impedance percentage of 8.4%. Given the 22.8 km power arm and the 8.9 km minimum locomotive tracking interval, it can be determined that a maximum of three trains can simultaneously brake or traction within this traction power supply section.

[0034] The design method is carried out in the following steps:

[0035] Step 1:

[0036] 1. Braking of the train in the power supply arm

[0037] The voltage vector triangle of regenerative braking is as follows Figure 2 As shown in Figure 2, since the traction load power factor is 0.99, the vector angle α between the regenerative braking current and the traction network voltage is 8°. Taking into account the traction network impedance, traction transformer impedance, and external power system impedance, the angle β between the voltage rise vector caused by regenerative braking and the load voltage vector is approximately 80°.

[0038] from Figure 2It can be concluded that the γ angle will change with the change of the voltage rise vector amplitude caused by regenerative braking. When the voltage rise vector is small and can form a stable triangle, 100°>γ>90°, the voltage at the traction load will increase with the increase of the voltage rise vector amplitude. When γ=90°, the voltage at the traction load reaches the maximum value. In this process, due to the constant power control strategy, the voltage at the traction load increases, the regenerative current decreases, the voltage rise is suppressed, and positive feedback is formed, and the system is easy to achieve stability; when the voltage rise vector amplitude increases further, β< When γ is less than 90°, the voltage at the traction load will decrease as the amplitude of the voltage lifting vector increases and gradually approach and equal the no-load voltage of the traction network. When the amplitude of the voltage lifting vector increases further, 10° less than γ less than β, the voltage at the traction load will decrease as the amplitude of the voltage lifting vector increases. When γ is equal to 10°, δ is equal to 90°, and the triangle enters a critical instability state. In this process, due to the constant power control strategy, the voltage at the traction load decreases, and the regenerative current increases, further helping to increase the voltage, forming negative feedback, and the system is not easy to stabilize.

[0039] 2. The train in the power supply arm is traction

[0040] The voltage vector triangle of the train traction is as follows Figure 3 As shown in Figure 2, since the traction load power factor is 0.99, the vector angle α between the traction current and the traction network voltage is 8°. Taking into account the traction network impedance, traction transformer impedance, and external power system impedance, the angle β between the voltage drop vector caused by traction and the load voltage vector is approximately 64°.

[0041] from Figure 3 It can be concluded that the γ angle is basically stable and obtuse. As the amplitude of the voltage reduction vector caused by traction increases, the δ angle gradually increases, and the angle corresponding to the voltage vector at the traction load gradually decreases, so its amplitude also gradually decreases. In this process, due to the constant power control strategy, the voltage at the traction load decreases, and the traction current increases, further increasing the voltage reduction, forming negative feedback, and it is not easy for the system to achieve stability.

[0042] Step 2:

[0043] use Figure 4The iterative algorithm shown is used to calculate the voltage under regenerative braking conditions. It is assumed that the no-load voltage is 27.5kV and the initial voltage of the end traction load is set to 25kV. After iterative calculation, the maximum voltage of the stable traction load is 27.92kV, which is lower than 29kV. The no-load voltage is gradually increased. For each increase, the iterative calculation is used to obtain the maximum voltage value of the stable traction load. Finally, when the maximum no-load voltage is 28.56kV, the maximum traction load voltage is 29kV. Based on this, it is concluded that when the no-load voltage is set lower than 28.56kV, the maximum traction load voltage will not exceed 29kV, and the regenerative braking power can be fully utilized.

[0044] use Figure 4 The iterative algorithm shown is used to calculate the voltage under traction conditions. It is assumed that the no-load voltage is 29kV and the initial voltage of the end traction load is set to 25kV. After iterative calculation, the minimum value of the steady-state traction load voltage cannot be converged, and the system voltage collapses. Therefore, engineering measures such as setting reinforcement lines, improving the voltage reduction, and raising the voltage level are adopted. After taking this measure, the minimum value of the steady-state traction load voltage can converge and the voltage can be stabilized. The minimum voltage of the end traction load is 20.16kV, which meets the requirement that the minimum voltage is higher than 20kV as stipulated in the specification.

[0045] Step 3:

[0046] According to the results of qualitative analysis and quantitative calculation, and taking into account the safety, effectiveness and feasibility of the engineering measures, a reinforcement line was set up to avoid voltage collapse in the traction direction system. However, in order to ensure that the maximum voltage value of the traction load in the regenerative condition does not exceed 29kV, the no-load voltage needs to be set lower than 28.56kV. At this time, the minimum voltage of the traction load in the traction condition will be reduced from 20.16kV to 19.74kV, which is lower than the 20kV requirement specified in the specification. The two working conditions cannot be fully taken into account. Therefore, with the priority given to ensuring braking safety, traction efficiency is partially sacrificed. By reducing the no-load voltage, the regenerative braking and load voltage are controlled to not exceed 29kV. At the same time, the minimum traction voltage is reduced from the conventional 20kV to 19kV (power output is 84% ​​of the rated power).

Claims

1. A voltage stability design method for a traction power supply system on an electrified railway with a steep slope, comprising the following steps: Step 1: During regenerative braking, construct a vector triangle with the traction power supply system voltage rise, no-load voltage, and load voltage as edges, and qualitatively analyze the maximum load voltage and its stability. During traction operation, construct a vector triangle with the traction power supply system voltage drop, no-load voltage, and load voltage as edges, and qualitatively analyze the minimum load voltage and its stability. Step 2: Use an iterative calculation scheme to calculate the voltage stability value. With the no-load voltage as the constraint condition, the load is based on constant power, the initial load voltage is set, and the voltage increase or voltage decrease vector is calculated. Under regenerative braking conditions, the difference between the initial voltage vector and the voltage increase vector is calculated. Under traction conditions, the sum of the initial voltage vector and the voltage decrease vector is calculated to obtain the calculated no-load voltage. The calculated no-load voltage is compared with the set no-load voltage. If the calculated value and the set value are not equal, the load voltage is adjusted. Repeat the above process until the calculated no-load voltage is equal to the set no-load voltage. Step 3: Based on the above analysis conclusions, comprehensively consider the train operation safety and its system tolerance, and propose reasonable and effective engineering measures and solutions.

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