Comprehensive compensation device and comprehensive compensation method for traction cable through power supply system
Through the comprehensive compensation device and method, the three-phase voltage imbalance problem of traditional single-phase AC 25kV traction power supply system is solved, the power quality and power supply capacity are improved, the stability and reliability of the power system are ensured, and the through-power supply of the traction network is realized.
Patent Information
- Application Number
- CN202510417387.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-04-03
- Publication Date
- 2025-08-01
AI Technical Summary
The three-phase voltage imbalance caused by the traditional single-phase AC 25kV traction power supply system affects the safe and stable operation of the power system, and transient overvoltage and overcurrent are generated when the electrical phase is separated, resulting in train speed loss and regenerative braking energy that cannot be utilized.
The integrated compensation device is adopted, including transformers TT1, TT2, TT3a, TT3b and the current controller PFC. Through the control of the converters β1, β2, β3a and β3b, the comprehensive compensation of the three-phase voltage imbalance, power factor and traction cable bus voltage is achieved. The transformer system composed of three-phase-two-phase wiring transformer and single-phase transformer is used to adjust the voltage and power to achieve optimal compensation.
The power supply capacity and power quality of the traction cable through power supply system is improved, the voltage is avoided, the power supply reliability and effective transmission of power is ensured, and the power supply of the traction network is achieved.
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Figure CN120414550A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of AC electrified railway power supply, and particularly to a comprehensive compensation device and a comprehensive compensation method for a traction cable through-power supply system.
[0002] Background and Significance
[0003] As an efficient, high-speed, and low-carbon long-distance transportation mode, electrified railways are widely used for passenger and freight transportation. As the sole power source for electrified railway trains, the traction power supply system is crucial for ensuring the safe and reliable operation of trains. The traditional single-phase AC 25 kV traction power supply system has been widely adopted in most countries such as China, France, the United Kingdom, and Japan, showing good performance. However, the high power and single-phase load characteristics of trains cause serious three-phase voltage imbalance on the power system side, threatening the operation of generators, relay protection devices, communication lines, and the safe and stable operation of the entire system. The traditional method to reduce the three-phase voltage imbalance is to rotate the phase sequence of the traction substation connected to the power system and set electrical phase separators at the traction substation and the sectionalizing substation between adjacent traction substations. The electrical phase separator is a no-power area. When the train passes through the electrical phase separator, transient overvoltage and overcurrent will be generated, which will affect the operating state of the pantograph and the traction network. At the same time, the train cannot obtain electrical energy, and passing through the electrical phase separator by inertia will cause speed loss, increase the running time of the train, and in severe cases, the train will stop or the braking will fail. In addition, the electrical phase separator also blocks the energy flow between different power supply arms, resulting in a large amount of regenerative braking energy that cannot be utilized by locomotives in the traction mode, and the reverse power sent to the power system exacerbates the unbalanced impact on the power system.
[0004] To eliminate the adverse effects of the electrical phase separator, a traction cable through-power supply system has been proposed by researchers. This system realizes the through-power supply of different traction substations, improves the direct utilization rate of regenerative braking energy, and increases the flexibility of traction substation siting. The current comprehensive compensation method for the traction cable through-power supply system takes the three-phase voltage imbalance degree and power factor as the compensation target values, without considering the constraints of the traction cable busbar. In order to further improve the power supply capacity of the traction cable through-power supply system and give full play to the long-distance power supply advantage of this system, it is necessary to conduct research on a comprehensive compensation device and method for this system with the three-phase voltage imbalance degree, power factor, and traction cable busbar voltage as the compensation target values. Summary of the Invention
[0005] Aiming at the above problems, the present invention aims to provide a comprehensive compensation device and a comprehensive compensation method for a traction cable through-power supply system, specifically involving a comprehensive compensation device and method for the three-phase voltage imbalance degree, power factor, and traction cable busbar voltage of the traction cable through-power supply system, to solve the power quality problem mainly dominated by negative sequence while improving the power supply capacity of this system.
[0006] One of the objectives of the present invention is to provide a comprehensive compensation device for a traction cable through-power supply system, including transformers TT1, TT2, TT 3a , TT 3b and a power flow controller PFC; the power flow controller PFC includes converters β1, β2, β 3a and β 3b ; the transformers TT2, TT 3a and TT 3b all adopt single-phase wiring; the transformer TT1 adopts a three-phase-two-phase transformer, and the three-phase-two-phase transformer includes Vv, Scott and YNvd wiring transformers, and also includes a three-phase-two-phase transformer composed of a single-phase transformer and a YNd wiring transformer.
[0007] Preferably, the primary side of the transformer TT1 is connected to a three-phase power grid; the secondary side port β of the transformer TT1 is connected to one side of the converter β1, and the other side of the converter β1 is respectively connected to the converters β2, β 3a and β 3b through the DC link of the power flow controller PFC. The other side of the converter β2 is connected to the traction cable buses a and b in series after passing through the transformer TT2; two terminals are led out from the secondary side port α of the transformer TT1, and the other side of the converter β 3a is connected to one side of the transformer TT 3a , and the other side of the transformer TT 3a is connected in series between one terminal of the secondary side port α of the transformer TT1 and the traction cable bus a. The other side of the converter β 3b is connected to one side of the transformer TT 3b , and the other side of the transformer TT 3b is connected in series between the other terminal of the secondary side port α of the transformer TT1 and the traction cable bus b; the traction cable buses a and b are respectively connected to the traction cables a and b, and the traction cables a and b supply power to the train loads on the traction network through n traction substations, where n≥1 and n is a positive integer.
[0008] Preferably, according to the amplitude and phase angle of the three-phase voltage unbalance degree at the common connection point of the three-phase power grid of the load on the secondary side of the transformer TT1, the power factor on the secondary side of the transformer TT1, and the compensation target value of the voltage difference increment between the traction cable buses a and b, the active power and reactive power outputs of the converters β1, β2, β 3a and β 3b are controlled to complete the comprehensive compensation of the traction cable through-power supply system.
[0009] Preferably, the compensation target value can be a value that meets the regulations of the railway design standard.
[0010] The second object of the present invention is to provide a comprehensive compensation method for a traction cable through-power supply system, including the following steps:
[0011] S1. Set the complex powers of converters β2, β 3a and β 3b as P β2 +jQ β2 , P β3a +jQ β3a and P β3b +jQ β3b , and define the direction in which the power flows from the DC link of the power flow controller PFC to the traction network as the positive direction;
[0012] Set the complex power of converter β1 as P β1 +jQ β1 , and define the direction in which the power flows from transformer TT1 to the DC link of the power flow controller PFC as the positive direction;
[0013] Set the terminal connection angles ψ α and ψ β as the angles by which the α and β voltages at the secondary side of transformer TT1 lag the reference voltage of phase A of the three-phase power grid respectively;
[0014] According to the electrical quantity relationship between the voltages and currents on the primary and secondary sides of transformer TT1, obtain the calculation formula for the three-phase voltage unbalance degree at the common connection point of the three-phase power grid for the load on the secondary side of transformer TT1 as
[0015]
[0016] where ε U and δ are the amplitude and phase angle of the three-phase voltage unbalance degree at the common connection point; S d is the short-circuit capacity at the common connection point; j is the imaginary unit; P α , Q α are the active power and reactive power of the load at the α port on the secondary side of transformer TT1;
[0017] S2. Set the compensation target value of the power factor on the secondary side of transformer TT1 as According to the law of conservation of energy and power factor constraints, obtain the relationship between the active power and reactive power between different ports of transformer TT1 as
[0018]
[0019] where P L , Q L are the active power and reactive power provided to the train load through traction cable buses a and b;
[0020] S3. Combining equations (1) and (2), we can get the active power and reactive power of converter β1:
[0021]
[0022] Substituting equation (3) into equation (2), we can get the converter β2, β 3a and β 3b The active power and reactive power constraints are
[0023]
[0024] The introduction of the traction cable bus voltage adjustment coefficient ρ affects the converter β 3a The voltage increment of the traction cable busbar a caused by and converter β 3b The voltage increment of the traction cable bus b caused by If constraints are applied, then there is
[0025]
[0026] Among them, ρ x and ρ y are the real and imaginary parts of ρ; is the voltage difference between the traction cable busbars a and b;
[0027] Furthermore, according to formula (5), the converter β is obtained 3a and β 3b The total complex power is
[0028]
[0029] In order to prevent the traction cable bus voltage from exceeding the limit when the power flow controller PFC is running, the converter β 3a and β 3b The active power of the converter is the same, and the converter β 3a and β 3b The reactive power is the same;
[0030] Combining equations (4) and (6), we can obtain the converter β2, β 3a and β 3b The active power and reactive power are
[0031]
[0032] S4. Set ε U ,δ, and ρ, and bring them into equations (4) and (7) to determine the converter β1, β2, β 3a and β 3bThe active power and reactive power are used to achieve the comprehensive compensation of the three-phase voltage unbalance degree of the traction cable through-power supply system, the power factor on the secondary side of the transformer TT1, and the voltage difference increment between the traction cable buses a and b.
[0033] Preferably, according to various wiring modes of the three-phase to two-phase wiring transformer TT1, the port wiring angles ψ in formulas (4) and (7) are respectively determined α and ψ β values, and the converters β1, β2, β 3a and β 3b are controlled to output the active power and reactive power matching the wiring mode of the transformer TT1. The port wiring angles ψ α and ψ β have different values, and the wiring modes of the three-phase to two-phase wiring transformer TT1 are also different. The corresponding output powers of the converters β1, β2, β 3a and β 3b are also different. This scheme can output the power matching different wiring modes of the three-phase to two-phase wiring transformer, achieving the optimal compensation effect.
[0034] Compared with the prior art, the beneficial effects of the present invention are:
[0035] 1) Compared with the existing comprehensive compensation devices and methods with the three-phase voltage unbalance degree and power factor as the compensation targets, the comprehensive compensation device and method proposed in the present invention take the three-phase voltage unbalance degree, power factor, and traction cable bus voltage as the compensation target values, and simultaneously realize the comprehensive compensation of power quality and power supply capacity, which helps to further enhance the long-distance power supply advantage of the traction cable through-power supply system;
[0036] 2) The comprehensive compensation device and method proposed in the present invention can ensure that the traction cable bus voltage of the traction cable through-power supply system works within a reasonable voltage range, avoid the occurrence of traction network voltage over-limit, and improve the power supply reliability;
[0037] 3) The comprehensive compensation device and method proposed in the present invention can realize the power of the converter following the changes of different wiring modes of the three-phase to two-phase wiring transformer, ensure that the three-phase voltage unbalance degree, power factor, and traction cable bus voltage are always in the optimal compensation state, achieve the optimal compensation effect, avoid the occurrence of excessive three-phase voltage unbalance degree, non-compliant power factor, and traction network voltage over-limit, and improve the power supply reliability;
[0038] 4) The comprehensive compensation device and method proposed in the present invention supplies power to the traction cable bus through comprehensive compensation by the transformer and the power flow controller, and then transmits the electric energy with consistent phase to the traction network through the traction cable to realize the through-power supply of the traction network. The structure is simple, the technology is reliable, the performance is excellent, and it is easy to implement. Description of the Drawings
[0039] Figure 1 It is a schematic structural diagram of a traction cable through - connection system for comprehensive compensation using a three - phase to two - phase connection transformer and a power flow controller according to the present invention.
[0040] Figure 2 It is a schematic structural diagram of a traction cable through - connection system for comprehensive compensation using a Scott connection transformer and a power flow controller according to the present invention.
[0041] Figure 3 It is a schematic structural diagram of a traction cable through - connection system for comprehensive compensation using a Vv connection transformer and a power flow controller according to the present invention.
[0042] Figure 4 It is a schematic structural diagram of a traction cable through - connection system for comprehensive compensation using a three - phase to two - phase connection transformer composed of a single - phase connection transformer and a YNd connection transformer and a power flow controller according to the present invention. Specific embodiments
[0043] To enable those skilled in the art to better understand the technical solution of the present invention, the present invention will be further described below in conjunction with the accompanying drawings and specific embodiments. The accompanying drawings do not represent all embodiments.
[0044] As Figure 1 shown, a schematic structural diagram of a traction cable through - connection system for comprehensive compensation using a three - phase to two - phase connection transformer and a power flow controller according to the present invention is provided. An external power source (such as a three - phase power grid) transmits electrical energy to the main traction sub - station MTS through three - phase transmission lines. After step - down and comprehensive compensation in the main traction sub - station MTS, electrical energy at a lower voltage level (such as 110 kV, 220 kV, etc.) is transmitted to n traction sub - stations TS1, TS2, TS3, ···, TSn through traction cable buses a, b and traction cables a, b. Each traction sub - station transmits electrical energy with the same phase to the traction network through the feeder line, realizing through - connection power supply for the traction network.
[0045] This embodiment provides a comprehensive compensation device for a traction cable through - connection power supply system, including transformers TT1, TT2, TT 3a , TT 3b and a power flow controller PFC; the power flow controller PFC includes converters β1, β2, β 3a and β 3b ; transformers TT2, TT 3a and TT 3bAll adopt single-phase connection methods; transformer TT1 adopts a three-phase-two-phase connection transformer, and the three-phase-two-phase connection transformer includes Vv, Scott, and YNvd connection transformers, and also includes a three-phase-two-phase transformer composed of a single-phase transformer and a YNd connection transformer.
[0046] As an optional embodiment, the primary side of transformer TT1 is connected to a three-phase power grid; the secondary side port β of transformer TT1 is connected to one side of converter β1, and the other side of converter β1 is respectively connected to converters β2 and β 3a and β 3b through the DC link of power flow controller PFC; the other side of converter β2 is connected to traction cable buses a and b in series after connecting transformer TT2; two terminals are led out from the secondary side port α of transformer TT1, and the other side of converter β 3a is connected to one side of transformer TT 3a , and the other side of transformer TT 3a is connected in series between one terminal of the secondary side port α of transformer TT1 and traction cable bus a; the other side of converter β 3b is connected to one side of transformer TT 3b , and the other side of transformer TT 3b is connected in series between the other terminal of the secondary side port α of transformer TT1 and traction cable bus b; traction cable buses a and b are respectively connected to traction cables a and b, and traction cables a and b supply power to train loads on the traction network through n traction substations TS1, TS2, TS3, ···, TSn, where n≥1 and n is a positive integer.
[0047] As an optional embodiment, according to the amplitude and phase angle of the three-phase voltage unbalance at the common connection point of the three-phase power grid of the load on the secondary side of transformer TT1, the power factor of the secondary side of transformer TT1, and the compensation target value of the voltage difference increment between traction cable buses a and b, control the active power and reactive power outputs of converters β1, β2, β 3a and β 3b to complete the comprehensive compensation of the traction cable through-power supply system.
[0048] This embodiment also provides a comprehensive compensation method for a traction cable through-power supply system, including the following steps:
[0049] S1. Set the complex powers of converters β2, β 3a and β 3b to be P β2 +jQ β2 , P β3a +jQ β3a and P β3b +jQ β3b, the direction in which power flows from the DC link of the power flow controller PFC to the traction network is defined as the positive direction;
[0050] Set the complex power of the converter β1 to be P β1 +jQ β1 , and the direction in which power flows from the transformer TT1 to the DC link of the power flow controller PFC is defined as the positive direction;
[0051] Set the port connection angle ψ α and ψ β are respectively the angles by which the α and β voltages at the secondary side ports of the transformer TT1 lag behind the reference voltage of phase A of the three-phase power grid;
[0052] According to the electrical quantity relationship between the voltages and currents on the primary and secondary sides of the transformer TT1, the three-phase voltage unbalance degree of the load on the secondary side of the transformer TT1 at the common connection point of the three-phase power grid The calculation formula is
[0053]
[0054] where ε U and δ are the amplitude and phase angle of the three-phase voltage unbalance degree at the common connection point; S d is the short-circuit capacity at the common connection point; j is the imaginary unit; P α , Q α are the active power and reactive power of the load at the α port on the secondary side of the transformer TT1;
[0055] S2. Set the compensation target value of the power factor on the secondary side of the transformer TT1 to be According to energy conservation and power factor constraints, the active and reactive power relationship between different ports of the transformer TT1 is obtained as
[0056]
[0057] where P L , Q L are the active power and reactive power provided to the train load through the traction cable busbars a and b;
[0058] S3. Combine equations (1) and (2) to obtain the active power and reactive power of the converter β1 as
[0059]
[0060] Substitute equation (3) into equation (2) to obtain the active power and reactive power constraints of the converters β2, β 3a and β 3b as
[0061]
[0062] The introduction of the traction cable bus voltage adjustment coefficient ρ affects the converter β 3a The voltage increment of the traction cable busbar a caused by and converter β 3b The voltage increment of the traction cable bus b caused by If constraints are applied, then there is
[0063]
[0064] Among them, ρ x and ρ y are the real and imaginary parts of ρ; is the voltage difference between the traction cable busbars a and b;
[0065] Furthermore, according to formula (5), the converter β is obtained 3a and β 3b The total complex power is
[0066]
[0067] In order to prevent the traction cable bus voltage from exceeding the limit when the power flow controller PFC is running, the converter β 3a and β 3b The active power of the converter is the same, and the converter β 3a and β 3b The reactive power is the same;
[0068] Combining equations (4) and (6), we can obtain the converter β2, β 3a and β 3b The active power and reactive power are
[0069]
[0070] S4. Set ε U ,δ, and ρ, and bring them into equations (4) and (7) to determine the converter β1, β2, β 3a and β 3b The active power and reactive power of the traction cable through-power supply system are used to achieve comprehensive compensation for the three-phase voltage imbalance of the traction cable through-power supply system, the power factor on the secondary side of the transformer TT1, and the voltage difference increment between the traction cable busbars a and b.
[0071] As an optional embodiment, the port connection angles ψ in equations (4) and (7) are determined respectively according to various connection modes of the three-phase to two-phase connection transformer TT1. α and ψ β The value of the control converter β1, β2, β 3a and β 3bOutput the active power and reactive power that match the wiring mode of transformer TT1. The port wiring angle ψ α and ψ β Take different values, and the wiring mode of the three-phase to two-phase wiring transformer TT1 will be different. The corresponding converters β1, β2, β 3a and β 3b The output power is also different. This scheme can output the power that matches different wiring modes of the three-phase to two-phase wiring transformer, achieving the effect of optimal compensation.
[0072] As an alternative embodiment, by determining the port wiring angles ψ α and ψ β in formulas (4) and (7), determine the active power and reactive power of the converters β1, β2, β 3a and β 3b under different compensation schemes. As Figure 2 shown, according to the known train load, adopt the comprehensive compensation scheme composed of Scott wiring transformer and power flow controller, and set ε U , δ, and ρ values, and let the port wiring angles ψ α and ψ β be -30° and -120° respectively, and substitute them into formulas (4) and (7) to determine the active power and reactive power of the converters β1, β2, β 3a and β 3b . As Figure 3 shown, according to the known train load, adopt the comprehensive compensation scheme composed of Vv wiring transformer and power flow controller, and set ε U , δ, and ρ values, and let the port wiring angles ψ α and ψ β be -30° and 90° respectively, and substitute them into formulas (4) and (7) to determine the active power and reactive power of the converters β1, β2, β 3a and β 3b . As Figure 4 shown, according to the known train load, adopt the comprehensive compensation scheme composed of a three-phase to two-phase wiring transformer composed of a single-phase wiring transformer and a YNd wiring transformer and a power flow controller, and set ε U , δ, and ρ values, and let the port wiring angles ψ α and ψ β be -30° and 120° respectively, and substitute them into formulas (4) and (7) to determine the active power and reactive power of the converters β1, β2, β 3a and β 3bThe active power and reactive power. The present invention takes the three-phase voltage unbalance degree, power factor, and the traction cable bus voltage as the compensation target values. By changing the value of the port connection angle, the converter β1, β2, β 3a and β 3b of the active power and reactive power can be obtained, realizing the comprehensive compensation optimization of the traction cable through-power supply system.
[0073] The above is only the preferred embodiment of the present invention. It should be noted that the above preferred embodiment should not be regarded as a limitation of the present invention. The protection scope of the present invention should be subject to the scope defined by the claims. For those of ordinary skill in the art in this technical field, without departing from the spirit and scope of the present invention, several improvements and modifications can also be made, and these improvements and modifications should also be regarded as the protection scope of the present invention.
Claims
1. A comprehensive compensation device for a traction cable through-power supply system, characterized in that: including transformers TT1, TT2, TT 3a , TT 3b and power flow controller PFC; The power flow controller PFC includes converters β1, β2, β 3a and β 3b ; Transformers TT2 and TT 3a and TT 3b both adopt single-phase connection methods; The transformer TT1 adopts a three-phase-two-phase connection transformer, which includes Vv, Scott and YNvd connection transformers, and also includes a three-phase-two-phase transformer composed of a single-phase transformer and a YNd connection transformer; The primary side of transformer TT1 is connected to a three-phase power grid; the secondary side port β of transformer TT1 is connected to one side of converter β1, and the other side of converter β1 is respectively connected to converters β2 and β 3a and β 3b through the DC link of power flow controller PFC; the other side of converter β2 is connected to traction cable buses a and b after being connected in series with transformer TT2; two terminals are led out from the secondary side port α of transformer TT1, and the other side of converter β 3a is connected to one side of transformer TT 3a ; the other side of transformer TT 3a is connected in series between one terminal of the secondary side port α of transformer TT1 and traction cable bus a, and the other side of converter β 3b is connected to one side of transformer TT 3b ; the other side of transformer TT 3b is connected in series between the other terminal of the secondary side port α of transformer TT1 and traction cable bus b; traction cable buses a and b are respectively connected to traction cables a and b, and traction cables a and b supply power to train loads on the traction network through n traction substations, where n≥1 and n is a positive integer; According to the amplitude and phase angle of the three-phase voltage unbalance at the common connection point of the three-phase power grid of the secondary load of transformer TT1, the power factor of the secondary side of transformer TT1, and the compensation target value of the voltage difference increment between traction cable buses a and b, control the active power and reactive power outputs of converters β1, β2, β 3a and β 3b to complete the comprehensive compensation of the traction cable through-power supply system.
2. A comprehensive compensation method for a traction cable through-power supply system using the comprehensive compensation device described in claim 1, characterized in that, The following steps are involved: S1. Set the converter β2 and β 3a and β 3b The complex powers of are P β2 +jQ β2 , P β3a +jQ β3a and P β3b +jQ β3b , and define the direction in which the power flows from the DC link of the power flow controller PFC to the traction network as the positive direction; Set the complex power of the converter β1 as P β1 +jQ β1 , and define the direction in which the power flows from the transformer TT1 to the DC link of the power flow controller PFC as the positive direction; Set the wiring angle ψ of the port α and ψ β are respectively the angles by which the voltages of the secondary side ports α and β of the transformer TT1 lag behind the reference voltage of phase A of the three-phase power grid; The three-phase voltage unbalance degree of the secondary load of transformer TT1 at the common connection point of the three-phase power grid is calculated by the formula where ε U and δ are the magnitudes and phase angles of the three-phase voltage unbalance at the common connection point; S d is the short-circuit capacity at the common connection point; j is the imaginary unit; P α , Q α are the active power and reactive power of the load at the α port on the secondary side of transformer TT1; S2. Set the compensation target value of the power factor on the secondary side of transformer TT1 to be The active and reactive power relationships between different ports of transformer TT1 are Among them, P L , Q L are the active power and reactive power provided to the train load through the traction cable busbars a and b; S3. Combining equations (1) and (2), we can get the active power and reactive power of converter β1: Substitute Equation (3) into Equation (2) to obtain the active power and reactive power constraints of converter β2, β 3a and β 3b as Introduce the traction cable bus voltage adjustment coefficient ρ for the converter β 3a The voltage increment of traction cable bus a caused by and the converter β 3b The voltage increment of traction cable bus b caused by Perform constraints, then there is where ρ x and ρ y are the real and imaginary parts of ρ; is the voltage difference between traction cable busbars a and b; Further, the converter β is obtained according to Equation (5). 3a and β 3b The total complex power is Among them, the active power of converter β 3a and β 3b is the same, and the reactive power of converter β 3a and β 3b is the same; By simultaneously solving equations (4) and (6), the active power and reactive power of the converter β2, β 3a and β 3b are respectively S4. Set ε U , δ, and the values of ρ, substitute them into equations (4) and (7) to determine the active power and reactive power of the converters β1, β2, β 3a and β 3b , and achieve the comprehensive compensation of the three-phase voltage unbalance degree of the traction cable through-power supply system, the power factor on the secondary side of the transformer TT1, and the voltage difference increment between the traction cable buses a and b.
3. The comprehensive compensation method for the traction cable through-power supply system according to claim 2, characterized in that Determine the values of the port connection angles ψ in equations (4) and (7) respectively according to various connection modes of the three-phase to two-phase connection transformer TT1 α and ψ β to control the active power and reactive power output by the converters β1, β2, β 3a and β 3b to match the connection mode of the transformer TT1.