Method for calculating the turn-off angle of a multi-feed DC system considering harmonic coupling

Abstract

This invention relates to a method, computer-readable medium, and apparatus for calculating the turn-off angle of a multi-infeed DC system. The method includes: establishing an equivalent circuit model of the harmonic coupling of the multi-infeed DC system; obtaining the h-th harmonic voltage generated by the inrush current on the first converter bus of the multi-infeed DC system under AC fault conditions, the amplitude E1 of the first commutation voltage of the first converter bus, and the phase of the first commutation voltage of the first converter bus, and combining these to obtain the commutation angle μ′ of the multi-infeed DC system under AC fault conditions; then, the turn-off angle γ′ of the multi-infeed DC system under AC fault conditions is calculated as γ′ = π - α - μ′ - φ′. This method is used to calculate the converter station turn-off angle under harmonic voltage transmission factors.

Description

Technical Field

[0001] This invention relates to the field of DC power transmission technology, specifically to a method for calculating the shut-off angle of a multi-infeed DC system, a computer-readable medium storing relevant shut-off angle calculation programs, and a shut-off angle calculation device. Background Technology

[0002] When a DC transmission system uses thyristors without self-turn-off capability as converter elements, a fault in the receiving-end AC system can easily lead to commutation failure. Commutation failure causes a surge in DC current and a sharp drop in DC voltage, and in severe cases, it can cause DC blocking and interruption of transmission power. As the number of DC transmission lines fed into the receiving-end AC grid gradually increases, the AC-DC coupling becomes increasingly tight. A commutation failure at a single converter station induced by an AC fault may evolve into successive commutation failures at adjacent converter stations, seriously threatening the safe operation of the AC-DC hybrid power grid.

[0003] In multi-infeed DC systems, the DC landing points are densely packed, and the AC-DC coupling characteristics are more complex. The electrical interconnections between these DC landing points, formed by AC networks and electrical equipment, often expand the fault range, triggering cascading faults in multiple DC lines and causing more severe power surges to the AC grid. Current stability analyses of multi-infeed DC systems mainly focus on converter bus voltage coupling and power exchange, which are affected by the parameters and control characteristics of the receiving-end network. Summary of the Invention

[0004] The purpose of this invention is to provide a method for calculating the turn-off angle of a multi-infeed DC system, a computer-readable medium storing the relevant turn-off angle calculation program, and a turn-off angle calculation device to calculate the turn-off angle of a converter station under harmonic voltage transmission factors.

[0005] The technical solution of this invention is:

[0006] A method for calculating the turn-off angle of a multi-infeed DC system includes the following steps:

[0007] Obtain the h-th harmonic voltage, the amplitude E1 of the first commutation voltage of the first converter bus, and the phase of the first commutation voltage of the first converter bus generated by the inrush current under AC fault conditions in the multi-infeed DC system. Combining equation (1), the commutation angle μ′ of the multi-feed DC system under AC fault is obtained;

[0008]

[0009] In the formula, E n Let n be the amplitude of the commutation voltage. Let be the phase of the nth commutation voltage, α be the firing angle, μ′ be the commutation angle of the multi-infeed DC system under AC fault, E1 be the amplitude of the first commutation voltage, and μ be the commutation angle of the multi-infeed DC system under steady state. The phase of the commutation voltage is n = 2, 3, ..., h;

[0010] For the nth (n=2,3,…,h) harmonic voltage generated by the inrush current on the first converter bus of the multi-infeed DC system under AC fault conditions.

[0011]

[0012] In the formula, E n Let n be the amplitude of the commutation voltage. The phase of the commutation voltage at the nth commutation;

[0013] Then the turn-off angle γ′ of the multi-infeed DC system under AC fault is:

[0014] γ′=π-α-μ′-φ′ (3)

[0015] In the formula, α is the firing angle, μ′ is the commutation angle of the multi-infeed DC system under AC fault, and φ′ is the zero-crossing displacement of the commutation voltage of the multi-infeed DC system under AC fault.

[0016] Among them, the h-th harmonic voltage generated by the fault inrush current on the first converter bus of the multi-infeed DC system under AC fault can be measured.

[0017] Preferably, the method for obtaining the h-th harmonic voltage generated by the inrush current on the first converter bus of a multi-infeed DC system under AC fault conditions is as follows:

[0018] An equivalent circuit model of harmonic coupling in a multi-infeed DC system is established. This model includes converter station 1 and converter bus 2, with converter bus 1 connected to converter bus 2. Converter bus 1 and converter bus 2 are coupled via a transformer. The first converter bus is defined as converter bus 1 within converter station 1. The h-th harmonic current generated by the harmonic current source within converter station 1 is measured. The h-th harmonic current generated by the variable harmonic current source at converter station No. 2 The equivalent impedance Z of the AC system to the nth harmonic at converter bus No. 1 1n The equivalent impedance Z of the AC system at converter bus No. 2 to the nth harmonic. 2n The equivalent impedance Z of the AC-side coupling channel to the nth harmonic current 12n The transformer turns ratio k between converter bus No. 1 and converter bus No. 2;

[0019] The nth (n=2,3,…,h) harmonic voltage generated by the inrush current under an AC fault on the No.1 converter bus of the multi-infeed DC system.

[0020]

[0021] In the formula, Harmonic current The nth harmonic voltage generated on converter bus No. 1; Z is the nth harmonic current generated by the harmonic current source within converter station No. 1; 1n The equivalent impedance of the AC system at converter bus No. 1 to the nth harmonic; Z is the nth harmonic current generated by the variable harmonic current source of converter station No. 2; 2n Z represents the equivalent impedance of the AC system at converter bus No. 2 to the nth harmonic; 12n is the equivalent impedance of the AC-side coupling channel to the nth harmonic current, and k is the transformer turns ratio between converter bus 1 and converter bus 2.

[0022] For the nth (n=2,3,…,h) harmonic voltage generated by the fault inrush current on the No.1 converter bus of the multi-infeed DC system under AC fault conditions.

[0023]

[0024] In the formula, E n Let n be the amplitude of the commutation voltage. The phase of the commutation voltage at the nth commutation;

[0025] Measure the amplitude E1 of the primary commutation voltage of converter bus No. 1 and the phase of the primary commutation voltage of converter bus No. 1. Combined with the amplitude E of the nth commutation voltage generated by the inrush current on the No. 1 converter bus of the multi-infeed DC system under AC fault conditions n nth commutation voltage phase Equation (1) yields the commutation angle μ′ of a multi-feed DC system under AC fault conditions.

[0026] Preferably, the method for obtaining the nth harmonic voltage generated by the inrush current on the first converter bus of a multi-infeed DC system under AC fault conditions is as follows:

[0027] An equivalent circuit model of harmonic coupling in a multi-infeed DC system is established. This model includes converter station 1 and converter bus 2, with converter bus 1 connected to converter bus 2. Converter bus 1 and converter bus 2 are coupled via a transformer. The first converter bus is defined as converter bus 1 within converter station 1. The h-th harmonic current generated by the harmonic current source within converter station 1 is measured. The h-th harmonic current generated by the variable harmonic current source at converter station No. 2 The equivalent impedance Z of the AC system to the nth harmonic at converter bus No. 1 1n The equivalent impedance Z of the AC system at converter bus No. 2 to the nth harmonic. 2nThe equivalent impedance Z of the AC-side coupling channel to the nth harmonic current 12n The transformer turns ratio k between converter bus No. 1 and converter bus No. 2;

[0028] The nth (n=2,3,…,h) harmonic voltage generated by the inrush current under an AC fault on the No. 2 converter bus of the multi-infeed DC system.

[0029]

[0030] In the formula, Harmonic current The nth harmonic voltage generated on converter bus No. 2; Z is the nth harmonic current generated by the harmonic current source within converter station No. 1; 1n The equivalent impedance of the AC system at converter bus No. 1 to the nth harmonic; Z is the nth harmonic current generated by the variable harmonic current source of converter station No. 2; 2n Z represents the equivalent impedance of the AC system at converter bus No. 2 to the nth harmonic; 12n is the equivalent impedance of the AC-side coupling channel to the nth harmonic current, and k is the transformer turns ratio between converter bus 1 and converter bus 2.

[0031] For the nth (n=2,3,…,h) harmonic voltage generated by the fault inrush current on the No.2 converter bus of the multi-infeed DC system under AC fault conditions.

[0032]

[0033] In the formula, E n Let n be the amplitude of the commutation voltage. The phase of the commutation voltage at the nth commutation;

[0034] Measure the amplitude E1 of the primary commutation voltage of converter bus No. 2 and the phase of the primary commutation voltage of converter bus No. 2. Combined with the inrush current under AC fault conditions, the magnitude E of the nth commutation voltage generated on the No. 2 converter bus of the multi-infeed DC system is... n nth commutation voltage phase Equation (1) yields the commutation angle μ′ of a multi-feed DC system under AC fault conditions.

[0035] More preferably, the multi-infeed DC system is a multi-DC single-end feed structure or a multi-end single-layer feed structure, and the transformer ratio k between converter bus 1 and converter bus 2 is 1.

[0036] Preferably, in equation (1), the commutation angle μ of the multi-feed DC system under steady state is calculated by the following formula.

[0037] γ=π-α-μ-φ (9) where γ is the turn-off angle of the multi-infeed DC system set under steady state, α is the trigger angle of the multi-infeed DC system set under steady state, and φ=0.

[0038] A computer-readable medium storing a cutoff angle calculation program, which, when executed by a processor, implements the aforementioned method for calculating the cutoff angle of a multi-feed DC system.

[0039] A breaking angle measurement device includes a processor and the aforementioned computer-readable medium storing a breaking angle measurement program.

[0040] The beneficial effects of this invention are:

[0041] 1. The inventors' research revealed that due to the complex AC-DC and DC-DC coupling characteristics of multi-infeed DC systems, the impact of harmonics on commutation failure is more significant than that of a single DC line. Harmonic components generated during AC fault transients are transmitted through coupling channels in multi-infeed systems, causing voltage distortion at the faulty converter bus and potentially leading to commutation failure on multiple DC lines. Therefore, research on the commutation failure mechanism considering harmonic coupling characteristics and its prevention and control is crucial for the safety and stability analysis and control of multi-infeed DC systems. Based on this approach, the inventors proposed a method for calculating the turn-off angle of a multi-infeed DC system, a computer-readable medium storing the relevant turn-off angle calculation program, and a turn-off angle calculation device to calculate the converter station turn-off angle under harmonic voltage transmission factors.

[0042] The harmonic coupling process of a multi-DC single-ended access system is simplified to obtain the following: Figure 2 The diagram illustrates the harmonic propagation process in a multi-DC single-ended access system. The series of processes triggered by the DC current generated at the faulty near-end converter station entering the converter transformer, as shown in the blue dashed box, can be summarized as follows: a harmonic source is generated at the faulty near-end converter station, injecting harmonic current into the converter bus, causing commutation voltage distortion. Similarly, when harmonic components enter the faulty far-end converter station via AC coupling, the series of processes triggered by the harmonic components, as shown in the blue dashed box, can also be summarized as follows: a harmonic source is generated at the faulty far-end converter station, injecting harmonic current into the converter bus, causing commutation voltage distortion.

[0043] The harmonic coupling process in a DC hierarchical access system is simplified to obtain the following: Figure 3 The diagram illustrates the harmonic coupling relationship in a DC hierarchical access system. The ultimate result of DC coupling is the generation of harmonic sources in both the near-side and far-side converter transformers of the fault, simultaneously inputting harmonic currents to the connected converter buses, causing commutation voltage distortion. Furthermore, due to the presence of AC coupling, harmonic voltage exchange also occurs between the two buses at the receiving end.

[0044] It can be observed that although the coupling processes of multi-DC single-ended feed systems and DC hierarchical access systems differ, the final results caused by harmonic coupling are similar, which can be summarized as follows: 1) Both the near-fault and far-fault converter transformers will form their own harmonic sources. The characteristics of the harmonic current generated by the harmonic sources depend on the inrush current conditions of each converter transformer. The harmonic sources inject harmonics into the AC bus, causing distortion of the converter voltage waveform. 2) Harmonic exchange occurs between converter buses through an AC network. In hierarchical access systems, the impact of transformers between buses of different voltage levels on harmonic transformation must also be considered. Based on the above analysis, a system can be established as follows: Figure 4 The equivalent circuit model of harmonic coupling in a multi-feed DC system is shown.

[0045] Based on the principle of commutation failure. For example... Figure 6 The shaded area is the integral area provided when γ is at the critical minimum, where S d For those unaffected by harmonics, S′ d This is affected by harmonics. The area size is related to the commutation inductance L. c When constant, the DC current I d Since the two areas are equal, the following relationship exists before and after the generation of harmonic components:

[0046]

[0047] In the formula, E n Let n be the amplitude of the commutation voltage. Let α be the phase of the nth commutation voltage, α be the trigger angle, μ′ be the commutation angle of the multi-infeed DC system under AC fault, E1 be the amplitude of the first commutation voltage, μ be the commutation angle of the multi-infeed DC system under steady state, and ω be the angular frequency of the power system. Let be the phase of the first commutation voltage. After simplification, this equation becomes equation (1).

[0048] Combined with the amplitude E of the nth (n=2,3,…,h) harmonic voltage generated by the inrush current on the first converter bus of the multi-infeed DC system under AC fault conditions. n and n (n=2,3,…,h) commutation voltage phase The commutation angle μ′ of the multi-infeed DC system under AC fault can be obtained, and then the turn-off angle γ′ of the multi-infeed DC system under AC fault can be obtained through equation (3). It has been verified that the turn-off angle γ′ of the multi-infeed DC system under AC fault is close to the measured value.

[0049] The method employs the acquisition of the h-th harmonic voltage generated by the inrush current under AC fault conditions on the first converter bus of a multi-infeed DC system, the amplitude E1 of the first commutation voltage of the first converter bus, and the phase of the first commutation voltage of the first converter bus. The calculation of the shut-off angle helps to understand the principle of the change of the shut-off angle of a multi-infeed DC system under AC faults. This method can be applied to computer simulation systems to optimize the design of multi-infeed DC systems.

[0050] 2. In existing technologies, the h-th harmonic voltage generated by the inrush current on the first converter bus of a multi-infeed DC system under AC fault conditions can be measured. However, this invention establishes an equivalent circuit model of harmonic coupling in a multi-infeed DC system, assuming the first converter bus is the No. 1 bus in converter station No. 1, and measures the h-th harmonic current generated by the harmonic current source in converter station No. 1. The h-th harmonic current generated by the variable harmonic current source at converter station No. 2 The equivalent impedance Z of the AC system to the nth harmonic at converter bus No. 1 1n The equivalent impedance Z of the AC system at converter bus No. 2 to the nth harmonic. 2n The equivalent impedance Z of the AC-side coupling channel to the nth harmonic current 12n The transformer turns ratio k between converter bus 1 and converter bus 2; the amplitude E of the nth (n=2,3,…,h) harmonic voltage generated by the inrush current under AC fault on converter bus 1 of the multi-feed DC system is calculated using formula (4). n and nth commutation voltage phase Then measure the amplitude E1 of the primary commutation voltage of converter bus No. 1 and the phase of the primary commutation voltage of converter bus No. 1. Combined with the amplitude E of the nth commutation voltage generated by the inrush current on the No. 1 converter bus of the multi-infeed DC system under AC fault conditions n nth commutation voltage phase Equation (1) yields the commutation angle μ′ of the multi-infeed DC system under AC faults. Calculating the h-th harmonic voltage generated by the inrush current on the first converter bus of the multi-infeed DC system under AC faults helps to understand the principle of harmonic voltage variation in the multi-infeed DC system under AC faults. This method can be applied to computer simulation systems to optimize the design of multi-infeed DC systems.

[0051] 3. In existing technologies, the h-th harmonic voltage generated by the inrush current on the first converter bus of a multi-infeed DC system under AC fault conditions can be measured. However, this invention establishes an equivalent circuit model of harmonic coupling in a multi-infeed DC system, assuming the first converter bus is the No. 2 converter bus in the No. 2 converter station, and measures the h-th harmonic current generated by the harmonic current source in the No. 1 converter station. The h-th harmonic current generated by the variable harmonic current source at converter station No. 2 The equivalent impedance Z of the AC system to the nth harmonic at converter bus No. 1 1n The equivalent impedance Z of the AC system at converter bus No. 2 to the nth harmonic. 2nThe equivalent impedance Z of the AC-side coupling channel to the nth harmonic current 12n The transformer turns ratio k between converter bus 1 and converter bus 2; the amplitude E of the nth (n=2,3,…,h) harmonic voltage generated by the inrush current under AC fault on converter bus 2 of the multi-feed DC system is calculated using formula (6). n and nth commutation voltage phase Then measure the amplitude E1 of the primary commutation voltage of converter bus No. 2 and the phase of the primary commutation voltage of converter bus No. 2. Combined with the inrush current under AC fault conditions, the magnitude E of the nth commutation voltage generated on the No. 2 converter bus of the multi-infeed DC system is... n nth commutation voltage phase Equation (1) yields the commutation angle μ′ of the multi-infeed DC system under AC faults. Calculating the h-th harmonic voltage generated by the inrush current on the first converter bus of the multi-infeed DC system under AC faults helps to understand the principle of harmonic voltage variation in the multi-infeed DC system under AC faults. This method can be applied to computer simulation systems to optimize the design of multi-infeed DC systems.

[0052] 4. Since the computer program can implement the method for calculating the shut-off angle of a multi-infeed DC system according to the present invention when executed by a processor, the present invention also provides a computer-readable medium storing the shut-off angle calculation program and a shut-off angle calculation device. Attached Figure Description

[0053] Figure 1 This is a flowchart of a method for calculating the turn-off angle of a multi-infeed DC system.

[0054] Figure 2 This is a block diagram of harmonic transmission in a multi-DC single-ended access system.

[0055] Figure 3 This is a block diagram of harmonic transmission in a DC hierarchical access system.

[0056] Figure 4 The equivalent model of harmonic coupling of a multi-infeed DC system is established in step S1 of a method for calculating the turn-off angle of a multi-infeed DC system.

[0057] Figure 5 This is a structural diagram of a DC hierarchical access system.

[0058] Figure 6 This is a schematic diagram illustrating the effect of harmonics on the shut-off angle. Detailed Implementation

[0059] The present invention will now be described with reference to the accompanying drawings and embodiments to assist those skilled in the art in understanding and implementing the invention. Unless otherwise stated, the following embodiments and the technical terms therein should not be understood without a background of technical knowledge in this field.

[0060] Example 1: A method for calculating the turn-off angle of a multi-infeed DC system, see [link to example]. Figure 1 This includes the following steps:

[0061] S1. Establish the equivalent circuit model of harmonic coupling in a multi-feed DC system;

[0062] The harmonic coupling process of a multi-DC single-ended access system is simplified to obtain the following: Figure 2 The diagram illustrates the harmonic propagation process in a multi-DC single-ended access system. The series of processes triggered by the DC current generated at the faulty near-end converter station entering the converter transformer, as shown in the blue dashed box, can be summarized as follows: a harmonic source is generated at the faulty near-end converter station, injecting harmonic current into the converter bus, causing commutation voltage distortion. Similarly, when harmonic components enter the faulty far-end converter station via AC coupling, the series of processes triggered by the harmonic components, as shown in the blue dashed box, can also be summarized as follows: a harmonic source is generated at the faulty far-end converter station, injecting harmonic current into the converter bus, causing commutation voltage distortion.

[0063] The harmonic coupling process in a DC hierarchical access system is simplified to obtain the following: Figure 3 The diagram illustrates the harmonic coupling relationship in a DC hierarchical access system. The ultimate result of DC coupling is the generation of harmonic sources in both the near-side and far-side converter transformers of the fault, simultaneously inputting harmonic currents to the connected converter buses, causing commutation voltage distortion. Furthermore, due to the presence of AC coupling, harmonic voltage exchange also occurs between the two buses at the receiving end.

[0064] It can be observed that although the coupling processes of multi-DC single-ended feed systems and DC hierarchical access systems differ, the final results caused by harmonic coupling are similar, which can be summarized as follows: 1) Both the near-fault and far-fault converter transformers will form their own harmonic sources. The characteristics of the harmonic current generated by the harmonic sources depend on the inrush current conditions of each converter transformer. The harmonic sources inject harmonics into the AC bus, causing distortion of the converter voltage waveform. 2) Harmonic exchange occurs between converter buses through an AC network. In hierarchical access systems, the impact of transformers between buses of different voltage levels on harmonic transformation must also be considered. Based on the above analysis, a system can be established as follows: Figure 4 The equivalent circuit model of harmonic coupling in a multi-feed DC system is shown.

[0065] Figure 4An equivalent circuit model of harmonic coupling in a multi-infeed DC system is shown. This model includes converter station 1 and converter bus 2, with converter station 1 connected to converter bus 2. Converter bus 1 and converter bus 2 are coupled via transformers. Z is the nth harmonic current generated by the harmonic current source within converter station No. 1; 1n The equivalent impedance of the AC system at converter bus No. 1 to the nth harmonic; Harmonic current The nth harmonic voltage generated on converter bus No. 1; Z is the nth harmonic current generated by the variable harmonic current source of converter station No. 2; 2n The equivalent impedance of the AC system at converter bus No. 2 to the nth harmonic; Harmonic current The nth harmonic voltage generated on converter bus No. 2; Z represents the nth harmonic current flowing from bus 1 through the AC-side coupling channel; 12n The equivalent impedance of the AC-side coupling channel to the nth harmonic current includes the transformer impedance and the line impedance; k is the transformer ratio between converter bus 1 and converter bus 2. If it is a multi-DC single-ended feed structure or a multi-ended single-layer feed structure, the ratio k is 1; n = 2, 3, ..., h;

[0066] S2. Quantitatively calculate the harmonic voltage transmission of fault inrush current in a multi-feed DC system under AC fault conditions;

[0067] In step S2, the harmonic current generated by the inrush current is... The harmonic voltages generated on converter buses 1 and 2 are:

[0068]

[0069]

[0070] In the formula, Z is the nth harmonic current generated by the harmonic current source within converter station No. 1; 1n The equivalent impedance of the AC system at converter bus No. 1 to the nth harmonic; Harmonic current The nth harmonic voltage generated on converter bus No. 1; Z is the nth harmonic current generated by the variable harmonic current source of converter station No. 2; 2n The equivalent impedance of the AC system at converter bus No. 2 to the nth harmonic; Harmonic current The nth harmonic voltage generated on converter bus No. 2; The nth harmonic current flows from bus 1 through the AC-side coupling channel; k is the transformer turns ratio between converter bus 1 and converter bus 2.

[0071] Since the transformer's transformation law for harmonic components is consistent with its transformation law for the fundamental frequency component, then and Harmonic interchange generated through AC coupling follows the following relationship:

[0072]

[0073] In the formula, Z 12n The equivalent impedance of the AC-side coupling channel to the nth harmonic current includes the transformer impedance and the line impedance.

[0074] By rearranging equations (10), (11), and (12), we can obtain:

[0075]

[0076]

[0077]

[0078] Equation (13) shows that the harmonic interaction between converter buses and the harmonic current generated within their respective stations are related to the harmonic currents generated within each station. Communication network parameters Z 1n Z 2n Z 12n It is related to the ratio of the converter bus voltage level k.

[0079] The nth harmonic voltage coupling coefficient T between converter bus 1 and converter bus 2 12_n for

[0080]

[0081] In the formula, T 12_n This parameter represents the amplitude transformation and phase shift relationship of the nth harmonic voltage between bus 1 and bus 2 near the fault in a multi-feed DC system under harmonic coupling. This parameter is related to the harmonic inrush current conditions within converter stations 1 and 2. Communication network parameters Z 1n Z 2n Z 12n It is related to the voltage level ratio k of the converter bus;

[0082] Previous studies used a real number for the harmonic transfer coefficient, which only expressed the amplitude change of the harmonic during transmission, neglecting the phase shift. Furthermore, it did not consider the effect of the transformer on the harmonic amplitude transformation, resulting in significant calculation errors. This invention addresses these issues by considering the influence of the transformer on harmonic transformation. The resulting harmonic transfer coefficient is a complex number, describing the amplitude transformation and phase shift during harmonic transmission, thus improving the accuracy of quantitative analysis.

[0083] Using the equivalent circuit model of harmonic transmission in a multi-infeed DC system established in step S1, the harmonic voltage transmission of fault inrush current generated in the multi-infeed DC system under AC fault is quantitatively calculated.

[0084] Taking phase A as an example, the harmonic voltage transfer coefficient T 12_n The accuracy of this was verified. See [link / reference]. Figure 5 , Figure 5 The hierarchical access system shown has two receiving-end converter buses injected with second-order harmonic current sources. and Equivalent impedance Z to the second harmonic at converter buses 1 and 2 12 and Z 22 The AC network and AC filter are included, and the impedance is measured by impedance scanning. The equivalent impedance of the AC interconnection channel between converter buses 1 and 2 includes transformer leakage reactance and line impedance, and is measured by impedance scanning. The known parameters of the equivalent circuit model for the second harmonic transmission of the multi-feed DC system are shown in Table 1. Substituting them into equation (16), the second harmonic voltage transmission of converter buses 1 and 2 is calculated. The calculated values ​​and measured values ​​are shown in Table 2.

[0085] Table 1. Known parameters of the equivalent circuit model for second harmonic transfer in a multi-feed DC system.

[0086]

[0087] Table 2 Comparison of calculated and measured values ​​of second harmonic components

[0088]

[0089] As shown in Table 2, the converter bus harmonic voltage calculated based on the multi-infeed DC harmonic transmission equivalent circuit model... and Connection channel coupling current Harmonic voltage transfer coefficient T 12_2 The amplitude and phase of the measured values ​​are in good agreement with the actual values.

[0090] right Figure 5 In the hierarchical access system shown, the two receiving-end converter buses are injected with 2nd, 3rd, and 4th harmonic current sources, respectively. The calculated and measured values ​​of the harmonic voltage coefficients are shown in Table 3.

[0091] Table 3 Comparison of calculated and measured values ​​of the transmission coefficients of each lower harmonic component.

[0092]

[0093] Taking converter bus No. 1 as an example, the harmonic current is calculated. After generating the nth harmonic voltage on converter bus 1, we can obtain:

[0094]

[0095] In the formula, E n Let n be the amplitude of the commutation voltage. Let h be the phase of the commutation voltage at the nth commutation, where n = 2, 3, ..., h;

[0096] Specifically:

[0097]

[0098]

[0099]

[0100] ...

[0101] Taking the No. 2 converter bus as an example, the harmonic current is calculated. After the nth harmonic voltage generated on converter bus No. 2, we can obtain:

[0102]

[0103] In the formula, E n Let n be the amplitude of the commutation voltage. Let h be the phase of the commutation voltage at the nth commutation, where n = 2, 3, ..., h;

[0104] Specifically:

[0105]

[0106]

[0107]

[0108] ...

[0109] S3. Quantitatively calculate the influence of harmonic voltage on the turn-off angle of each converter transformer.

[0110] The following relationship exists before and after the generation of harmonic components:

[0111]

[0112] In the formula, En Let n be the amplitude of the commutation voltage. Let α be the phase of the nth commutation voltage, α be the trigger angle, μ′ be the commutation angle of the multi-infeed DC system under AC fault, E1 be the amplitude of the first commutation voltage, μ be the commutation angle of the multi-infeed DC system under steady state, and ω be the angular frequency of the power system. This refers to the phase of the commutation voltage during the first commutation.

[0113] Based on the principle of commutation failure. For example... Figure 6 The firing angle of the multi-infeed DC system remains constant under steady-state conditions compared to that under AC fault conditions. However, the commutation angle of the multi-infeed DC system changes under steady-state conditions compared to that under AC fault conditions. Furthermore, the zero-crossing displacement of the commutation voltage in the multi-infeed DC system changes under steady-state conditions compared to that under AC fault conditions. The shaded area represents the integral area provided when γ is at its critical minimum, where S... d (The shaded area indicated by the left slash) represents the area unaffected by harmonics, S′. d (The shaded area indicated by the right slash) represents the area affected by harmonics. This area size is within the commutation inductance L. c When constant, the DC current I d Therefore, the two areas are equal, and the left and right sides of equation (19) are equal.

[0114] Equation (19) is simplified to:

[0115]

[0116] In equation (20), the commutation angle μ of the multi-feed DC system under steady state can be calculated by the following formula.

[0117] γ=π-α-μ-φ (21) where γ is the turn-off angle of the multi-infeed DC system set under steady state, α is the trigger angle of the multi-infeed DC system set under steady state, φ is the zero-crossing displacement of the commutation voltage of the multi-infeed DC system under steady state, and φ=0;

[0118] Measure the amplitude E1 and phase of the primary commutation voltage of converter bus No. 1. The magnitude of the nth commutation voltage E obtained by combining equation (17) n nth commutation voltage phase Substituting into equation (20), the commutation angle μ′ of converter No. 1 (belonging to converter station No. 1) in the multi-feed DC system under AC fault can be obtained by solving the equation.

[0119] The zero-crossing displacement φ′ of the commutation voltage of converter bus No. 1 caused by harmonics is obtained by numerical calculation of the waveform zero point by computer.

[0120] Then, under AC fault conditions, the shut-off angle γ′ of converter bus 1 in a multi-infeed DC system is:

[0121] γ′=π-α-μ′-φ′ (22)

[0122] In the formula, α is the firing angle, μ′ is the commutation angle of the multi-infeed DC system under AC fault, and φ′ is the zero-crossing displacement of the commutation voltage of the multi-infeed DC system under AC fault.

[0123] Measure the amplitude E1 and phase of the primary commutation voltage of converter bus No. 2. The magnitude of the nth commutation voltage E obtained by combining equation (18) n nth commutation voltage phase Substituting into equation (20), the commutation angle μ′ of converter No. 2 (belonging to converter station No. 2) in the multi-feed DC system under AC fault can be obtained by solving the equation.

[0124] The zero-crossing displacement φ′ of the commutation voltage of converter bus No. 2 caused by harmonics is obtained by numerical calculation of the waveform zero point by computer.

[0125] Then, under AC fault conditions, the shut-off angle γ′ of converter bus No. 2 in a multi-infeed DC system is:

[0126] γ′=π-α-μ′φ′ (23)

[0127] In the formula, α is the firing angle, μ′ is the commutation angle of the multi-infeed DC system under AC fault, and φ′ is the zero-crossing displacement of the commutation voltage of the multi-infeed DC system under AC fault.

[0128] The accuracy of the quantitative calculation of the turn-off angle considering the harmonic effect is verified below using the harmonic components obtained from the above-mentioned equivalent circuit of multi-infeed DC harmonic transmission. Taking the second harmonic experiment shown in Table 1 as an example, the commutation angle of the second commutation process of the Y / Y connected converter after harmonic injection is calculated. The second harmonic coupling situation calculated according to the known parameters in Table 1 is shown in Table 2. Substituting it into equation (20), the commutation angle μ′ of the multi-infeed DC system under AC fault and the measured value are shown in Table 4.

[0129] Table 4 Comparison of calculated and measured values ​​of commutation angle under the influence of second harmonic component.

[0130]

[0131] As can be seen from Table 4, under the influence of second harmonic coupling, the commutation time of converter 1 increases with the increase of μ′, while the commutation time of converter 2 decreases with the decrease of μ′.

[0132] The zero-crossing displacement φ′ of the commutation voltage obtained by computer numerical solution and the measured value are shown in Table 5. Positive values ​​indicate leftward shift, that is, the zero-crossing time is advanced, and negative values ​​indicate rightward shift, that is, the zero-crossing time is delayed.

[0133] Table 5 Comparison of calculated and measured values ​​of commutation voltage zero-crossing displacement under the influence of second harmonic components.

[0134]

[0135] As can be seen from Table 5, under the influence of the second harmonic, the commutation voltage of converter buses 1 and 2 crosses zero earlier, and φ′ is a positive value.

[0136] The cutoff angle γ′ was calculated, and the cutoff angle γ′ considering the influence of the second harmonic and the measured value are shown in Table 6.

[0137] Table 6 Comparison of calculated and measured values ​​of the shut-off angle under the influence of the second harmonic component.

[0138]

[0139] As can be seen from Table 6, under the influence of the second harmonic, the turn-off angles of both converter buses 1 and 2 decreased, and the turn-off angle of converter bus 1, which has a larger injected harmonic current amplitude, decreased more significantly.

[0140] The cutoff angles γ′ in the 2nd, 3rd, and 4th harmonic experiments shown in Table 3 were calculated respectively, and the comparison between the calculated values ​​and the measured values ​​is shown in Table 7.

[0141] Table 7 Comparison of calculated and measured values ​​of the shut-off angle under the influence of each lower harmonic component.

[0142]

[0143]

[0144] The main reasons for errors in the turn-off angle calculation are as follows: 1) The calculation assumes that the trigger angle α is constant, but in fact, the trigger angle is always in a dynamic feedback adjustment state. Even in steady state, the α of each trigger is different, with a fluctuation range of about 0.25°; 2) The calculation assumes that the fundamental frequency voltage component is constant, but after the harmonic component is injected, the amplitude of the fundamental frequency voltage will change; 3) During the harmonic injection process, the angle value obtained has a fluctuation process rather than a constant value, which will produce errors when reading the measured value; 4) The power system itself contains background harmonics of other frequencies, which are not taken into account in the calculation.

[0145] Based on Example 1, a method for calculating the turn-off angle of a multi-infeed DC system according to the present invention can be obtained, including the following steps:

[0146] Obtain the h-th harmonic voltage generated by the inrush current on the first converter bus of the multi-infeed DC system under AC fault conditions. The amplitude E1 of the primary commutation voltage of the first converter bus and the phase of the primary commutation voltage of the first converter bus Combining equation (24), the commutation angle μ′ of the multi-feed DC system under AC fault is obtained;

[0147]

[0148] In the formula, E n Let n be the amplitude of the commutation voltage. Let be the phase of the nth commutation voltage, α be the firing angle, μ′ be the commutation angle, E1 be the amplitude of the first commutation voltage, and μ be the steady-state value of the commutation angle. The phase of the commutation voltage is n = 2, 3, ..., h;

[0149] For the nth (n=2,3,…,h) harmonic voltage generated by the inrush current on the first converter bus of the multi-infeed DC system under AC fault conditions.

[0150]

[0151] In the formula, E n Let n be the amplitude of the commutation voltage. The phase of the commutation voltage at the nth commutation;

[0152] The h-th harmonic voltage generated by the inrush current on the first converter bus of the multi-infeed DC system under AC fault conditions. By performing Fourier transform processing, the nth (n=2,3,…,h) harmonic voltage generated by the inrush current under AC faults on the first converter bus of the multi-infeed DC system can be obtained.

[0153] Then the turn-off angle γ′ of the multi-infeed DC system under AC fault is:

[0154] γ′π-α-μ′-φ′ (26)

[0155] In the formula, α is the firing angle, μ′ is the commutation angle of the multi-infeed DC system under AC fault, and φ′ is the zero-crossing displacement of the commutation voltage of the multi-infeed DC system under AC fault.

[0156] Among them, the h-th harmonic voltage generated by the fault inrush current on the first converter bus of the multi-infeed DC system under AC fault can be measured.

[0157] Preferably, the method for obtaining the h-th harmonic voltage generated by the inrush current on the first converter bus of a multi-infeed DC system under AC fault conditions is as follows:

[0158] An equivalent circuit model of harmonic coupling in a multi-infeed DC system is established. This model includes converter station 1 and converter bus 2, with converter bus 1 connected to converter bus 2. Converter bus 1 and converter bus 2 are coupled via a transformer. The first converter bus is defined as converter bus 1 within converter station 1. The h-th harmonic current generated by the harmonic current source within converter station 1 is measured. The h-th harmonic current generated by the variable harmonic current source at converter station No. 2 The equivalent impedance Z of the AC system to the nth harmonic at converter bus No. 1 1n The equivalent impedance Z of the AC system at converter bus No. 2 to the nth harmonic. 2n The equivalent impedance Z of the AC-side coupling channel to the nth harmonic current 12n The transformer turns ratio k between converter bus No. 1 and converter bus No. 2;

[0159] The h-th harmonic current generated by the inrush current under AC fault conditions in the harmonic current source of the No. 1 converter station of the multi-infeed DC system. By performing Fourier transform processing, the nth (n=2,3,…,h)th harmonic current generated by the inrush current in the No.1 converter station of the multi-infeed DC system under AC fault conditions can be obtained. The h-th harmonic current generated by the inrush current under AC fault conditions in the harmonic current source of the No. 2 converter station of the multi-infeed DC system. By performing Fourier transform processing, the nth (n=2,3,…,h) harmonic current generated by the inrush current under AC fault conditions in the No. 2 converter station of the multi-infeed DC system can be obtained. The equivalent impedance Z of the AC system to the nth harmonic at converter bus No. 1 1n The equivalent impedance Z of the AC system at converter bus No. 2 to the nth harmonic. 2n The equivalent impedance Z of the AC-side coupling channel to the nth harmonic current 12n These can be measured using the impedance scanning method.

[0160] The nth (n=2,3,…,h) harmonic voltage generated by the inrush current under an AC fault on the No.1 converter bus of the multi-infeed DC system.

[0161]

[0162] In the formula, Harmonic current The nth harmonic voltage generated on converter bus No. 1; Z is the nth harmonic current generated by the harmonic current source within converter station No. 1; 1n The equivalent impedance of the AC system at converter bus No. 1 to the nth harmonic; Z is the nth harmonic current generated by the variable harmonic current source of converter station No. 2; 2n Z represents the equivalent impedance of the AC system at converter bus No. 2 to the nth harmonic; 12n is the equivalent impedance of the AC-side coupling channel to the nth harmonic current, and k is the transformer turns ratio between converter bus 1 and converter bus 2.

[0163] For the nth (n=2,3,…,h) harmonic voltage generated by the fault inrush current on the No.1 converter bus of the multi-infeed DC system under AC fault conditions.

[0164]

[0165] In the formula, E n Let n be the amplitude of the commutation voltage. The phase of the commutation voltage at the nth commutation;

[0166] Measure the amplitude E1 of the primary commutation voltage of converter bus No. 1 and the phase of the primary commutation voltage of converter bus No. 1. Combined with the amplitude E of the nth commutation voltage generated by the inrush current on the No. 1 converter bus of the multi-infeed DC system under AC fault conditions n nth commutation voltage phase Equation (23) yields the commutation angle μ′ of a multi-feed DC system under AC fault conditions.

[0167] Preferably, the method for obtaining the nth harmonic voltage generated by the inrush current on the first converter bus of a multi-infeed DC system under AC fault conditions is as follows:

[0168] An equivalent circuit model of harmonic coupling in a multi-infeed DC system is established. This model includes converter station 1 and converter bus 2, with converter bus 1 connected to converter bus 2. Converter bus 1 and converter bus 2 are coupled via a transformer. The first converter bus is defined as converter bus 1 within converter station 1. The h-th harmonic current generated by the harmonic current source within converter station 1 is measured. The h-th harmonic current generated by the variable harmonic current source at converter station No. 2 The equivalent impedance Z of the AC system to the nth harmonic at converter bus No. 1 1n The equivalent impedance Z of the AC system at converter bus No. 2 to the nth harmonic. 2n The equivalent impedance Z of the AC-side coupling channel to the nth harmonic current 12n The transformer turns ratio k between converter bus No. 1 and converter bus No. 2;

[0169] The nth (n=2,3,…,h) harmonic voltage generated by the inrush current under an AC fault on the No. 2 converter bus of the multi-infeed DC system.

[0170]

[0171] In the formula, Harmonic current The nth harmonic voltage generated on converter bus No. 2; Z is the nth harmonic current generated by the harmonic current source within converter station No. 1; 1n The equivalent impedance of the AC system at converter bus No. 1 to the nth harmonic; Z is the nth harmonic current generated by the variable harmonic current source of converter station No. 2; 2n Z represents the equivalent impedance of the AC system at converter bus No. 2 to the nth harmonic; 12n is the equivalent impedance of the AC-side coupling channel to the nth harmonic current, and k is the transformer turns ratio between converter bus 1 and converter bus 2.

[0172] For the nth (n=2,3,…,h) harmonic voltage generated by the fault inrush current on the No.2 converter bus of the multi-infeed DC system under AC fault conditions.

[0173]

[0174] In the formula, E n Let n be the amplitude of the commutation voltage. The phase of the commutation voltage at the nth commutation;

[0175] Measure the amplitude E1 of the primary commutation voltage of converter bus No. 2 and the phase of the primary commutation voltage of converter bus No. 2. Combined with the inrush current under AC fault conditions, the magnitude E of the nth commutation voltage generated on the No. 2 converter bus of the multi-infeed DC system is... n nth commutation voltage phase Equation (23) yields the commutation angle μ′ of a multi-feed DC system under AC fault conditions.

[0176] More preferably, the multi-infeed DC system is a multi-DC single-end feed structure or a multi-end single-layer feed structure, and the transformer ratio k between converter bus 1 and converter bus 2 is 1.

[0177] Preferably, in equation (24), the commutation angle μ of the multi-feed DC system under steady state is calculated by the following formula.

[0178] γ=π-α-μ-φ (31) where γ is the turn-off angle of the multi-infeed DC system set under steady state, α is the trigger angle of the multi-infeed DC system set under steady state, and φ=0.

[0179] Since the computer program can implement the multi-infeed DC system shutdown angle calculation method of the present invention when executed by a processor, the present invention also provides a computer-readable medium storing a shutdown angle calculation program, which implements the aforementioned multi-infeed DC system shutdown angle calculation method when executed by a processor.

[0180] The present invention also provides a cutoff angle calculation device, including a processor and the aforementioned computer-readable medium storing a cutoff angle calculation program.

[0181] In summary, this invention establishes an equivalent circuit model for harmonic propagation in a multi-infeed DC system, used to describe the coupling process of harmonic currents generated by inrush currents during faults within the system, and quantitatively calculates the amplitude transformation and phase shift during harmonic voltage propagation. Furthermore, it proposes a method based on the equivalent circuit model to quantitatively calculate the impact of harmonic voltage on the converter turn-off angle in a multi-infeed DC system.

[0182] The present invention has been described in detail above with reference to the accompanying drawings and embodiments. It should be understood that it is impossible to exhaustively describe all possible implementations in practice; the inventive concept of the present invention is illustrated to the extent possible through examples. Without departing from the inventive concept of the present invention and without any creative effort, any specific embodiments formed by selecting and combining technical features in the above embodiments, experimentally changing specific parameters, or conventionally replacing the disclosed technical means of the present invention using existing technology should be considered as implicit disclosures of the present invention.

Claims

1. A method for calculating the turn-off angle of a multi-infeed DC system, characterized in that, Includes the following steps: Obtain the h-th harmonic voltage, the amplitude E1 of the first commutation voltage of the first converter bus, and the phase of the first commutation voltage of the first converter bus generated by the inrush current under AC fault conditions in the multi-infeed DC system. Combining equation (1), we obtain the commutation angle μ′ of the multi-feed DC system under AC fault. In the formula, E n Let n be the amplitude of the commutation voltage. Let be the phase of the nth commutation voltage, α be the firing angle, μ′ be the commutation angle of the multi-infeed DC system under AC fault, E1 be the amplitude of the first commutation voltage, and μ be the commutation angle of the multi-infeed DC system under steady state. The phase of the commutation voltage is n = 2, 3, ..., h; For the nth (n=2,3,…,h) harmonic voltage generated by the inrush current on the first converter bus of the multi-infeed DC system under AC fault conditions. In the formula, E n Let n be the amplitude of the commutation voltage. The phase of the commutation voltage at the nth commutation; Then the turn-off angle γ′ of the multi-infeed DC system under AC fault is: γ′=π-α-μ′-φ′ (3) In the formula, α is the firing angle, μ′ is the commutation angle of the multi-infeed DC system under AC fault, and φ′ is the zero-crossing displacement of the commutation voltage of the multi-infeed DC system under AC fault.

2. The method for calculating the turn-off angle of a multi-infeed DC system as described in claim 1, characterized in that, The method for obtaining the h-th harmonic voltage generated by the inrush current on the first converter bus of a multi-infeed DC system under AC fault conditions is as follows: An equivalent circuit model of harmonic coupling in a multi-infeed DC system is established. This model includes converter station 1 and converter bus 2, with converter bus 1 connected to converter bus 2. Converter bus 1 and converter bus 2 are coupled via a transformer. The first converter bus is defined as converter bus 1 within converter station 1. The h-th harmonic current generated by the harmonic current source within converter station 1 is measured. The h-th harmonic current generated by the variable harmonic current source at converter station No. 2 The equivalent impedance Z of the AC system to the nth harmonic at converter bus No. 1 1n The equivalent impedance Z of the AC system at converter bus No. 2 to the nth harmonic. 2n The equivalent impedance Z of the AC-side coupling channel to the nth harmonic current 12n The transformer turns ratio k between converter bus No. 1 and converter bus No. 2; The nth (n=2,3,…,h) harmonic voltage generated by the inrush current under an AC fault on the No.1 converter bus of the multi-infeed DC system. In the formula, Harmonic current The nth harmonic voltage generated on converter bus No. 1; Z is the nth harmonic current generated by the harmonic current source within converter station No. 1; 1n The equivalent impedance of the AC system at converter bus No. 1 to the nth harmonic; Z is the nth harmonic current generated by the variable harmonic current source of converter station No. 2; 2n Z represents the equivalent impedance of the AC system at converter bus No. 2 to the nth harmonic; 12n is the equivalent impedance of the AC-side coupling channel to the nth harmonic current, and k is the transformer turns ratio between converter bus 1 and converter bus 2. For the nth (n=2,3,…,h) harmonic voltage generated by the fault inrush current on the No.1 converter bus of the multi-infeed DC system under AC fault conditions. In the formula, E n Let n be the amplitude of the commutation voltage. The phase of the commutation voltage at the nth commutation; Measure the amplitude E1 of the primary commutation voltage of converter bus No. 1 and the phase of the primary commutation voltage of converter bus No.

1. Combined with the amplitude E of the nth commutation voltage generated by the inrush current on the No. 1 converter bus of the multi-infeed DC system under AC fault conditions n nth commutation voltage phase Equation (1) yields the commutation angle μ′ of a multi-feed DC system under AC fault conditions.

3. The method for calculating the turn-off angle of a multi-infeed DC system as described in claim 2, characterized in that, The multi-infeed DC system is a multi-DC single-end feed structure or a multi-end single-layer feed structure, and the transformer ratio k between converter bus No. 1 and converter bus No. 2 is 1.

4. The method for calculating the turn-off angle of a multi-infeed DC system as described in claim 1, characterized in that, The method for obtaining the nth harmonic voltage generated by the inrush current on the first converter bus of a multi-infeed DC system under AC fault conditions is as follows: An equivalent circuit model of harmonic coupling in a multi-infeed DC system is established. This model includes converter station 1 and converter bus 2, with converter bus 1 connected to converter bus 2. Converter bus 1 and converter bus 2 are coupled via a transformer. The first converter bus is defined as converter bus 1 within converter station 1. The h-th harmonic current generated by the harmonic current source within converter station 1 is measured. The h-th harmonic current generated by the variable harmonic current source at converter station No. 2 The equivalent impedance Z of the AC system to the nth harmonic at converter bus No. 1 1n The equivalent impedance Z of the AC system at converter bus No. 2 to the nth harmonic. 2n The equivalent impedance Z of the AC-side coupling channel to the nth harmonic current 12n The transformer turns ratio k between converter bus No. 1 and converter bus No. 2; The nth (n=2,3,…,h) harmonic voltage generated by the inrush current under an AC fault on the No. 2 converter bus of the multi-infeed DC system. In the formula, Harmonic current The nth harmonic voltage generated on converter bus No. 2; Z is the nth harmonic current generated by the harmonic current source within converter station No. 1; 1n The equivalent impedance of the AC system at converter bus No. 1 to the nth harmonic; Z is the nth harmonic current generated by the variable harmonic current source of converter station No. 2; 2n Z represents the equivalent impedance of the AC system at converter bus No. 2 to the nth harmonic; 12n is the equivalent impedance of the AC-side coupling channel to the nth harmonic current, and k is the transformer turns ratio between converter bus 1 and converter bus 2. For the nth (n=2,3,…,h) harmonic voltage generated by the fault inrush current on the No.2 converter bus of the multi-infeed DC system under AC fault conditions. In the formula, E n Let n be the amplitude of the commutation voltage. The phase of the commutation voltage at the nth commutation; Measure the amplitude E1 of the primary commutation voltage of converter bus No. 2 and the phase of the primary commutation voltage of converter bus No.

2. Combined with the inrush current under AC fault conditions, the magnitude E of the nth commutation voltage generated on the No. 2 converter bus of the multi-infeed DC system is... n nth commutation voltage phase Equation (1) yields the commutation angle μ′ of a multi-feed DC system under AC fault conditions.

5. The method for calculating the turn-off angle of a multi-infeed DC system as described in claim 4, characterized in that, The multi-infeed DC system is a multi-DC single-end feed structure or a multi-end single-layer feed structure, and the transformer ratio k between converter bus No. 1 and converter bus No. 2 is 1.

6. The method for calculating the turn-off angle of a multi-infeed DC system as described in claim 1, characterized in that, In equation (1), the commutation angle μ of the multi-feed DC system under steady state is calculated by the following formula. γ=π-α-μ-φ (9) In the formula, γ is the turn-off angle of the multi-infeed DC system set under steady state, α is the trigger angle of the multi-infeed DC system set under steady state, and φ = 0.

7. A computer-readable medium storing a program for calculating a broken angle, characterized in that, When the shutdown angle calculation program is executed by the processor, it implements the shutdown angle calculation method for a multi-infeed DC system as described in any one of claims 1-6.

8. A device for calculating the shut-off angle, characterized in that, It includes a processor and a computer-readable medium storing, as claimed in claim 7, a program for calculating the angle of failure.

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