A method for correcting harmonic limits in an electrified railway traction power supply system

Abstract

This invention discloses a method for correcting harmonic limits in an electrified railway traction power supply system. First, a two-port network model of harmonic propagation along the line is constructed. Then, based on the load harmonic equivalent model and differences in locomotive load capacity, voltage level, and power factor, a locomotive harmonic model is built, and all parameters are converted to the high-voltage side of the traction transformer. The harmonic voltage generated at the traction substation and the harmonic voltage generated at the grid side after the injection of harmonic current at the traction substation, as well as their ratio, are calculated. Then, based on the two-port network model of harmonic propagation along the line, the grid-side harmonic current is calculated. Finally, based on the grid-side harmonic current, the amplification factor of the grid-side output harmonic current relative to the traction substation input harmonic current is calculated, and the national standard corrected harmonic limit is calculated based on the amplification factor. This invention provides a method for correcting harmonic limits at the traction substation side, correcting the harmonic limit standard at the traction substation side of the line, and ensuring that the grid-side output harmonic current meets the national harmonic standard limits.

Description

Technical Field

[0001] This invention relates to the field of harmonic control technology, specifically a method for correcting harmonic limits in an electrified railway traction power supply system. Background Technology

[0002] Harmonics refer to the components of a periodic non-sinusoidal alternating current that are integer multiples of the fundamental frequency, obtained by Fourier series decomposition. These are commonly referred to as higher harmonics, while the fundamental frequency refers to the component whose frequency is the same as the power frequency (50Hz). Higher harmonic interference is a major "public nuisance" affecting power quality in current power systems, and countermeasures are urgently needed.

[0003] Harmonic amplification is caused by the combined effect of inductance and capacitance in a circuit. Harmonic amplification can be divided into harmonic current amplification and harmonic voltage amplification. If, after a capacitor is connected, the harmonic current in the transformer or capacitor is greater than the harmonic current of the harmonic source, then the harmonic current is amplified. If, after a capacitor is connected, the voltage distortion rate increases compared to before it was connected, then the harmonic voltage is amplified. Harmonic current amplification and harmonic voltage amplification can occur simultaneously or independently. It's possible that the harmonic current is amplified while the voltage harmonic distortion rate decreases, or vice versa.

[0004] The traction power supply system of an electrified railway refers to the power supply system that supplies electricity for the traction of electric locomotives. It mainly consists of traction substations and overhead contact lines. The traction substations convert the 110kV or 220kV three-phase AC power transmitted from the power plant via high-voltage transmission lines into current and voltage suitable for electric locomotives, and then send it to the overhead contact lines, which in turn supply power to the locomotives. Based on the current supply system used to the locomotives, it is classified as either DC or AC.

[0005] Existing research has yielded some results on the propagation law of harmonics through long transmission lines, but it has not addressed the harmonic amplification phenomenon that occurs after harmonics propagate through long transmission lines. Furthermore, it has not further analyzed the specific situation of harmonics output from the grid side, and cannot provide quantitative indicators for the harmonic amplification phenomenon on the grid side. Summary of the Invention

[0006] To address the aforementioned problems, the present invention aims to provide a method for correcting harmonic limits in electrified railway traction power supply systems. It analyzes the mechanism of harmonic amplification phenomena occurring when harmonics injected into the power grid through long-distance transmission lines in electrified railway traction power supply systems, provides a detailed derivation process, quantifies the harmonic amplification phenomenon, and proposes a harmonic limit correction method based on the harmonic amplification mechanism propagating through long transmission lines. This method updates the harmonic limits at the traction substation side, ensuring that harmonics on the power grid side meet national harmonic standards. The technical solution is as follows:

[0007] A method for correcting harmonic limits in an electrified railway traction power supply system includes the following steps:

[0008] Step 1: Construct a two-port network model for harmonic propagation through the transmission line, and determine the equivalent parameters on the traction substation side, the equivalent parameters on the power grid side, and the transmission line parameters;

[0009] Step 2: Based on the load harmonic equivalent model and the differences in locomotive load capacity, voltage level, and power factor, build a locomotive harmonic model and convert all parameters to the high-voltage side of the traction transformer;

[0010] Step 3: Calculate the harmonic voltage generated on the traction substation side and the harmonic voltage generated on the grid side after the harmonic current is injected on the traction substation side, as well as the ratio between the two. Then, simplify the harmonic voltages on the traction substation side and the grid side using the ratio. Finally, calculate the harmonic current on the grid side based on the two-port network model of harmonic propagation through the line.

[0011] Step 4: Based on the harmonic current on the grid side, calculate the amplification factor of the harmonic current output on the grid side relative to the harmonic current input on the traction station side when the harmonic current injected on the traction station side is , and calculate the national standard corrected harmonic limit based on the amplification factor.

[0012] Furthermore, the parameters mentioned in step 1 include the grid-side harmonic impedance Z. sys Its size is determined by the system's short-circuit capacity S. 短 The decision was made to calculate using an approximate formula:

[0013] Z sys ≈jhU 2 / S 短

[0014] Where: h is the harmonic order, and U is the fundamental voltage on the grid side;

[0015] The propagation constant γ of a transmission line is calculated by the following formula:

[0016]

[0017] In the formula: the subscript h represents the harmonic order, r h With x h The resistance and reactance per unit length of the transmission line; g h With b h α represents the conductance and susceptance per unit length of the transmission line; α and β represent the attenuation constant and phase shift constant of the transmission line.

[0018] Furthermore, the parameters described in step 2 are calculated as follows:

[0019]

[0020] In the formula: U n This represents the rated voltage of the busbar under the fundamental frequency; h is the harmonic order; Pn Q represents the active power of the load. n The reactive power of the load; R, X s and X p This is the equivalent impedance in the locomotive harmonic model.

[0021] Furthermore, steps 3 and 4 specifically include:

[0022] When harmonic current is injected at the traction station side Subsequently, the harmonic voltage generated on the traction station side is as follows:

[0023]

[0024] In the formula: For the traction station side harmonic voltage; Z S With Y P Z represents the equivalent impedance and admittance of the line expressed in hyperbolic functions, respectively; L The impedance of other linear loads at the traction station;

[0025] The harmonic voltage generated on the grid side is as follows:

[0026]

[0027] In the formula: Harmonic voltage on the grid side;

[0028] The ratio of harmonic voltages on the traction substation side to those on the power grid side is given by the following formula:

[0029]

[0030] In the formula: l is the line length, Z C Characteristic impedance;

[0031] The harmonic voltages on the traction substation side and the power grid side are simplified using the ratio, as shown in the following formula:

[0032]

[0033] Therefore, based on the two-port network model of harmonic propagation, the harmonic current on the grid side is as follows:

[0034]

[0035] In the formula: This refers to harmonic currents on the power grid side.

[0036] When the harmonic current injected into the traction station side is At that time, the amplification factor of the harmonic current output from the grid side relative to the harmonic current input from the traction substation side is shown in the following formula:

[0037]

[0038] Where: G I This is the harmonic current amplification factor;

[0039] The harmonic current limit on the traction substation side has been recalculated to ensure that the harmonic current on the power grid side meets the national standard. The relevant revisions are as follows:

[0040] I h,修正 =I h,国标 ·G I

[0041] In the formula: I h,修正 To revise the harmonic limits in the national standard, I h,国标 The national standard specifies harmonic limits.

[0042] The beneficial effects of this invention are as follows: This invention studies the traction power supply system of electrified railways under long-distance power transmission lines. By analyzing the mechanism of harmonic amplification phenomenon that occurs when harmonics injected into the power grid by the electrified railway traction power supply system pass through long-distance transmission lines, it shows that there is a possibility that the harmonic current injected at the traction substation side does not exceed the standard, but the harmonic current output at the power grid side exceeds the standard. Based on this, a quantitative index is proposed, a method for correcting the harmonic limit at the traction substation side is given, the harmonic limit standard at the traction substation side is corrected, and the harmonic current output at the power grid side meets the national harmonic standard limit. Attached Figure Description

[0043] Figure 1 Two-port network model for harmonic propagation via a line

[0044] Figure 2 This is the equivalent model for CIGRE load harmonics.

[0045] Figure 3 The flowchart below shows the harmonic limit correction method for the electrified railway traction power supply system of the present invention. Detailed Implementation

[0046] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. The present invention analyzes the mechanism of harmonic amplification phenomenon in the traction power supply system of electrified railways when harmonics are injected into the power grid via long-distance transmission lines, provides a detailed derivation process, quantifies the harmonic amplification phenomenon, and proposes a harmonic limit correction method based on the harmonic amplification mechanism propagating through long transmission lines. This method updates the harmonic limits at the traction substation side, ensuring that the harmonics on the power grid side meet the national harmonic standards. Specifically:

[0047] 1) Harmonic Model of Electric Locomotive

[0048] Frequency converters are widely used in electric locomotives. They can limit the starting current and thus have little impact on the power grid. However, they generate a large number of harmonics during operation, which affects the power quality of the power grid.

[0049] The waveform of a 6-pulse rectifier undergoes six transformations within one cycle. Three-phase full-wave rectification belongs to this type. Therefore, for a three-phase 6-pulse rectifier circuit, the generated harmonics are h = 6n ± 1 (n = 1, 2, ...).

[0050] The harmonic current is calculated based on the empirical formula for calculating the characteristic harmonic current of a three-phase rectified load proposed by the International Council on Large Electric Systems (CIGRE).

[0051]

[0052] In the formula: I1 is the fundamental current, and h is the harmonic order. During 6-pulse rectification, the main harmonic orders are the 5th, 7th, 11th, and 13th. A 12-pulse three-phase bridge rectifier circuit is composed of two 6-pulse three-phase bridge rectifier circuits connected in parallel, and a 24-pulse three-phase bridge rectifier circuit is composed of two 12-pulse three-phase bridge rectifier circuits connected in parallel.

[0053] 2) Equivalent model of harmonic transmission

[0054] The harmonics injected into the power grid by the electrified railway traction power supply system pose a risk of harmonic amplification when transmitted over long distances. The traction substation side and the power grid side can be equivalently represented as a two-port network model to study the harmonic transmission characteristics.

[0055] Two-port network model for harmonic propagation via a line, such as Figure 1 As shown, the two-port network model includes equivalent parameters on the traction station side, equivalent parameters on the power grid side, and transmission line parameters. Z represents the harmonic current injected by the electric locomotive harmonic source into the traction substation side under the h-th harmonic; I2 represents the grid-side current; U1 and U2 represent the substation-side voltage and grid-side voltage, respectively; Z sys Z represents the harmonic impedance on the power grid side; L Z represents the impedance of other linear loads at the traction substation; to consider the distributed parameter characteristics of the line, Z... S With Y P These are the equivalent impedance and admittance of the line expressed in hyperbolic functions, respectively.

[0056] Z sys The size is determined by the system's short-circuit capacity S 短 The decision can be made and can be calculated using an approximate formula.

[0057] Z sys ≈jhU2 / S 短 (2)

[0058] In the formula: h is the harmonic order.

[0059] The propagation constant of a transmission line is γ, which can be calculated using the following formula.

[0060]

[0061] In the formula: the subscript h represents the harmonic order, r h With x h The resistance and reactance per unit length of the transmission line; g h With b h α represents the conductance and susceptance per unit length of the transmission line; α and β represent the attenuation constant and phase shift constant of the transmission line.

[0062] 3) Method for correcting the propagation limit of harmonics through long lines

[0063] Based on the CIGRE load harmonic equivalent model and the differences in locomotive load capacity, voltage level, and power factor, a locomotive harmonic model is constructed, with all parameters converted to the high-voltage side of the traction transformer. The CIGRE load harmonic equivalent model diagram is shown below. Figure 2 As shown.

[0064] The relevant parameters are calculated as follows.

[0065]

[0066] In the formula: U n This represents the rated voltage of the busbar under the fundamental frequency; h is the harmonic order; P n Q represents the active power of the load. n This represents the reactive power of the load.

[0067] Under long-line operating conditions, the line-to-ground capacitance is larger than that under short-line operating conditions. Therefore, when harmonics are injected from the traction substation side and propagate through the long line into the power grid, harmonic distortion will occur. This results in a situation where harmonics at the traction substation side are within limits, while harmonics at the power grid side exceed limits.

[0068] When harmonic current is injected at the traction station side Afterwards, the harmonic voltage generated on the traction station side is as follows.

[0069]

[0070] In the formula: Harmonic voltage on the traction station side

[0071] The harmonic voltage generated on the grid side is as follows.

[0072]

[0073] In the formula: Harmonic voltage on the grid side

[0074] The ratio of harmonic voltages between the traction station side and the power grid side is given by the following formula.

[0075]

[0076] The harmonic voltages on the traction station side and the power grid side are simplified by using a ratio, as shown in the following formula.

[0077]

[0078] Therefore, according to the two-port network model of harmonic propagation, the harmonic current on the grid side is as follows.

[0079]

[0080] In the formula: Harmonic current on the grid side

[0081] When the harmonic current injected into the traction station side is At that time, the amplification factor of the harmonic current output from the grid side compared to the harmonic current input from the traction station side is shown in the following formula.

[0082]

[0083] Where: G I Harmonic current amplification factor

[0084] In the case of long transmission lines, the amplification factor may exceed 1, resulting in harmonic amplification. This causes the harmonic current on the grid side to be greater than that on the traction substation side. Therefore, it is necessary to recalculate the harmonic current limit on the traction substation side in accordance with relevant national standards to ensure that the harmonic current on the grid side meets the national standards. The relevant revisions are as follows.

[0085] I h,修正 =I h,国标 ·G I (11)

[0086] In the formula: I h,修正 To revise the harmonic limits in the national standard, I h,国标 The national standard specifies harmonic limits.

[0087] After obtaining the harmonic limit correction value on the traction substation side, the harmonic current on the traction substation side needs to be processed, such as reducing the number of locomotives running at the same time or installing a filter device, to ensure that it meets the harmonic limit correction value requirements, so that the harmonic output on the grid side meets the national standard requirements after the harmonics propagate through the long transmission line.

[0088] The flowchart of the technical solution of the present invention is as follows: Figure 3As shown, this invention proposes quantitative indicators, provides a method for correcting harmonic limits on the traction substation side, corrects the harmonic limit standard on the traction substation side of the line, and ensures that the harmonic current output on the power grid side meets the national harmonic standard limit.

Claims

1. A method for correcting harmonic limits in an electrified railway traction power supply system, characterized in that, Includes the following steps: Step 1: Construct a two-port network model for harmonic propagation through the transmission line, and determine the equivalent parameters on the traction substation side, the equivalent parameters on the power grid side, and the transmission line parameters; Step 2: Based on the load harmonic equivalent model and the differences in locomotive load capacity, voltage level, and power factor, build a locomotive harmonic model and convert all parameters to the high-voltage side of the traction transformer; Step 3: Calculate the harmonic voltage generated on the traction substation side and the harmonic voltage generated on the grid side after the harmonic current is injected on the traction substation side, as well as the ratio between the two. Then, simplify the harmonic voltages on the traction substation side and the grid side using the ratio. Finally, calculate the harmonic current on the grid side based on the two-port network model of harmonic propagation through the line. Step 4: Based on the harmonic current on the grid side, calculate the amplification factor of the harmonic current output on the grid side relative to the harmonic current input on the traction station side when the harmonic current injected on the traction station side is , and calculate the national standard corrected harmonic limit based on the amplification factor. When harmonic current is injected at the traction station side At that time, the amplification factor of the harmonic current output from the grid side relative to the harmonic current input from the traction substation side is shown in the following formula: Where: G I This is the harmonic current amplification factor; U1 is the grid-side harmonic current; U2 is the grid-side voltage; Z sys G represents the harmonic impedance on the power grid side; U Y is the ratio of the harmonic voltage on the traction substation side to that on the power grid side. P The equivalent admittance of the line is expressed using a hyperbolic function; the harmonic current limit on the traction substation side is recalculated to ensure that the harmonic current on the grid side meets the national standard. The relevant revisions are as follows: I h,修正 =I h,国标 ·G I In the formula: I h,修正 To revise the harmonic limits in the national standard, I h,国标 The national standard specifies harmonic limits; The parameters mentioned in step 2 are calculated as follows: In the formula: U n This represents the rated voltage of the busbar under the fundamental frequency; h is the harmonic order; P n Q represents the active power of the load. n The reactive power of the load; R, X s and X p This is the equivalent impedance in the locomotive harmonic model.

2. The harmonic limit correction method for electrified railway traction power supply system according to claim 1, characterized in that, The parameters mentioned in step 1 include the grid-side harmonic impedance Z. sys Its size is determined by the system's short-circuit capacity S. 短 The decision was made to calculate using an approximate formula: Z sys ≈jhU 2 / S 短 Where: h is the harmonic order, and U is the fundamental voltage on the grid side; The propagation coefficient γ of a transmission line is calculated by the following formula: In the formula: the subscript h represents the harmonic order, r h With x h The resistance and reactance per unit length of the transmission line; g h With b h α represents the conductance and susceptance per unit length of the transmission line; α and β represent the attenuation constant and phase shift constant of the transmission line.

3. The harmonic limit correction method for electrified railway traction power supply system according to claim 2, characterized in that, Steps 3 and 4 specifically include: When harmonic current is injected at the traction station side Subsequently, the harmonic voltage generated on the traction station side is as follows: In the formula: For the traction station side harmonic voltage; Z S With Y P Z represents the equivalent impedance and admittance of the line expressed in hyperbolic functions, respectively; L The impedance of other linear loads at the traction station; The harmonic voltage generated on the grid side is as follows: In the formula: Harmonic voltage on the grid side; The ratio of harmonic voltages on the traction substation side to those on the power grid side is given by the following formula: In the formula: l is the line length, Z C Characteristic impedance; The harmonic voltages on the traction substation side and the power grid side are simplified using the ratio, as shown in the following formula: Therefore, based on the two-port network model of harmonic propagation, the harmonic current on the grid side is as follows: In the formula: This refers to the harmonic current on the power grid side.

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