Method for simultaneously transmitting alternating current and direct current along feeder line based on zigzag transformer

By using zigzag transformers in the distribution network, a synchronous AC-DC transmission structure along the feeder line is constructed, the technical problem of simultaneous AC-DC transmission is solved, the coupling between AC and DC is realized, the transmission method is improved, and economic analysis reference is provided.

CN119482779APending Publication Date: 2025-02-18ECONOMIC TECH RES INST OF STATE GRID ANHUI ELECTRIC POWER
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Patent Information

Application Number
CN202411739489.4
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-11-29
Publication Date
2025-02-18

AI Technical Summary

Technical Problem

The prior art is difficult to transmit AC and DC power simultaneously on the same long-distance ultra-high voltage AC lines, and the research on the zigzag transformer to achieve AC and DC coupling in the medium-voltage power system is insufficient.

Method used

By constructing a structural scheme for synchronous AC-DC transmission along the feeder based on zigzag transformers in the distribution network, theoretical analysis and digital simulation are carried out to verify the feasibility of the system, and economic analysis are carried out to achieve simultaneous transmission of AC-DC along the same feeder.

Benefits of technology

The use of zigzag transformer in the medium voltage power system is realized to couple AC and DC, solve the transformer saturation problem caused by DC current, improve the method of AC and DC transmission along the same feeder at the same time, and provide economic analysis reference for decision makers.

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Abstract

The invention discloses a zigzag transformer-based method for simultaneously transmitting alternating current and direct current along a feeder line, which relates to the technical field of power distribution system network optimization and comprises the following steps of: constructing a structural scheme for transmitting the alternating current and the direct current along the same feeder line in a power distribution network; based on the constraint condition of converting the AC system into the AC-DC hybrid system, performing theoretical analysis on the AC-DC hybrid system to obtain the maximum transmission power of the system in an ideal state; verifying the feasibility of the system through digital simulation; and performing economic analysis on the verified AC / DC power distribution network scheme and AC power distribution network scheme. The problem that research on simultaneous transmission of alternating current and direct current along the same feeder line is insufficient is solved.
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Description

Technical Field

[0001] The present invention relates to the technical field of power distribution system network optimization, and more specifically, to a method for simultaneous transmission of alternating and direct current along a feeder line based on a zigzag transformer. Background Art

[0002] In order to meet the growing demand for power load, the solution is to rebuild new lines to expand the capacity of the power system. However, due to the lack of transmission corridors, this work is difficult to implement and costly. In recent years, a new concept has been proposed in power systems, that is, to transmit AC and DC simultaneously on the same long-distance ultra-high voltage AC line. However, how to use zigzag connection to solve the transformer saturation problem caused by DC current, use zigzag transformers to achieve AC and DC coupling in medium-voltage power systems, and realize AC and DC transmission along the same feeder, the current research is still insufficient.

[0003] In view of the above problems, the present invention proposes a solution. Summary of the invention

[0004] In order to overcome the above-mentioned defects of the prior art, an embodiment of the present invention provides a method for simultaneous transmission of AC and DC along a feeder based on a zigzag transformer. By providing a structural scheme for synchronous transmission of AC and DC along a feeder based on a zigzag transformer in a distribution network, a theoretical analysis of the AC / DC hybrid system is performed, the feasibility of the system is verified through digital simulation, and an economic analysis of the verified AC / DC distribution network scheme and the AC distribution network scheme is performed, so as to solve the problem of insufficient research on simultaneous transmission of AC and DC along the same feeder.

[0005] To achieve the above object, the present invention provides the following technical solutions: A method for simultaneously transmitting AC and DC along a feeder based on a zigzag transformer comprises the following steps: constructing a structural scheme for transmitting AC and DC along the same feeder in a distribution network; conducting a theoretical analysis of the AC and DC hybrid system based on the constraint conditions for the conversion of an AC system into an AC and DC hybrid system to obtain the maximum transmission power of the system in an ideal state; verifying the feasibility of the system through digital simulation; and conducting an economic analysis of the verified AC and DC distribution network scheme and the AC distribution network scheme.

[0006] In a preferred embodiment, the structural scheme for constructing a distribution network in which AC and DC are transmitted along the same feeder is specifically as follows: compared with the AC distribution network, the AC topology part remains unchanged, and the transformer is changed to a zigzag transformer; the DC power of the distributed power source is injected into the neutral point of the connecting winding of the zigzag main transformer; and the DC load is powered at the neutral point of the zigzag distribution transformer.

[0007] In a preferred embodiment, the constraint conditions for converting the AC system into an AC / DC hybrid system are specifically: the constraint conditions include voltage constraint conditions that satisfy feeder thermal limit constraints and current constraint conditions that satisfy feeder thermal limit constraints.

[0008] In a preferred embodiment, the maximum transmission power of the system in the ideal state is specifically obtained by: based on the voltage constraint condition and the current constraint condition, combined with the AC / DC system line transmission power expression and the preset AC / DC system power factor, data analysis is performed to obtain the system ideal state transmission power formula; the preset AC / DC system power factor is adjusted to calculate the maximum transmission power of the system in the ideal state.

[0009] In a preferred embodiment, the economic analysis of the verified AC / DC power distribution network scheme and the AC power distribution network scheme is specifically as follows: based on data and charts, the construction costs of the AC power distribution network and the AC / DC power distribution network are compared; based on different AC power and DC power ratios, data analysis is performed on the cost functions of the source end and the load end to obtain the cost function of the AC distribution network and the cost function of the AC / DC distribution network.

[0010] The technical effects and advantages of the method for simultaneously transmitting AC and DC along a feeder line based on a zigzag transformer of the present invention are as follows: The present invention provides a structural scheme for synchronous transmission of AC and DC along feeders based on zigzag transformers in a distribution network, conducts theoretical analysis on an AC / DC hybrid system based on system constraints, verifies the feasibility of the system through digital simulation, and uses zigzag transformers to achieve coupling of AC and DC in a medium-voltage power system, thereby enabling AC and DC to be transmitted simultaneously along the same feeder, thus improving the method for simultaneous transmission of AC and DC along the same feeder. At the same time, an economic analysis is conducted on the verified AC / DC distribution network scheme and the AC distribution network scheme, providing a reference for decision makers to choose a suitable method to design a distribution network. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Figure 1 The present invention is a schematic structural diagram of a method for simultaneously transmitting AC and DC along a feeder line based on a zigzag transformer.

[0012] Figure 2 This is a typical structural diagram of an AC / DC synchronous system based on a zigzag transformer.

[0013] Figure 3 Schematic diagram of the zigzag transformer simulation model.

[0014] Figure 4 Schematic diagram of the simulation model of the AC / DC hybrid system.

[0015] Figure 5This is an economic analysis diagram for the AC distribution network.

[0016] Figure 6 This is an economic analysis diagram for AC and DC distribution networks.

[0017] Figure 7 Investment cost diagram for AC and AC / DC distribution networks.

[0018] Figure 8 Surface plots for AC and AC / DC distribution network costs. DETAILED DESCRIPTION

[0019] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0020] Embodiment 1, Figure 1 The present invention provides a method for simultaneous transmission of AC and DC along a feeder based on a zigzag transformer, comprising the following steps: Construct a structural scheme for AC and DC transmission along the same feeder in the distribution network; Based on the constraints of the transformation of AC system into AC / DC hybrid system, the AC / DC hybrid system is theoretically analyzed to obtain the maximum transmission power of the system in the ideal state. Verify the feasibility of the system through digital simulation; Conduct economic analysis on the verified AC / DC distribution network scheme and AC distribution network scheme.

[0021] In this embodiment, the structural scheme for constructing a power distribution network in which AC and DC are transmitted along the same feeder is specifically as follows: Compared with the AC distribution network, the AC topology remains unchanged, but the transformer is changed to a zigzag transformer; Inject the DC power of the distributed generation into the neutral point of the connecting winding of the zigzag main transformer; The DC loads are supplied at the neutral point of the zigzag distribution transformer.

[0022] In this embodiment, the constraints for the AC system to be transformed into an AC / DC hybrid system are specifically: The constraint conditions include voltage constraint conditions that satisfy feeder thermal limit constraints and current constraint conditions that satisfy feeder thermal limit constraints.

[0023] In this embodiment, the maximum transmission power of the system in an ideal state is specifically obtained by: Based on the voltage constraint condition and the current constraint condition, combined with the AC / DC system line transmission power expression and the preset AC / DC system power factor, data analysis is performed to obtain the system ideal state transmission power formula; Adjust the preset AC / DC system power factor and calculate the maximum transmission power of the system in the ideal state.

[0024] In this embodiment, the current constraint condition is as follows:

[0025]

[0026] The voltage constraint condition is as follows:

[0027] The AC / DC system line transmission power expression is specifically expressed as follows:

[0028] The ideal state transmission power formula of the system is as follows:

[0029] In the formula, is the total power in the AC / DC system, is the effective value of the AC component voltage, is the DC component voltage, is the effective value of the AC component current, is the DC component current, is the ratio of the effective value of the AC component voltage to the line thermal limit voltage, is the ratio of the effective value of the AC component current to the line thermal limit current, is the preset AC / DC system power factor, is the line thermal limit voltage value, is the thermal limit current value of the line.

[0030] In this embodiment, the economic analysis of the verified AC / DC power distribution network solution and the AC power distribution network solution is specifically as follows: Compare the construction costs of AC and DC distribution networks based on data and diagrams; Based on different ratios of AC power to DC power, data analysis is performed on the cost functions at the source end and the load end to obtain the cost function of the AC distribution network and the cost function of the AC / DC distribution network.

[0031] In this embodiment, the cost function of the AC power distribution network is specifically formulated as follows:

[0032] The cost function of the AC / DC power distribution network is specifically formulated as follows:

[0033] In the formula, is the cost function of the AC distribution network, is the cost function of the AC / DC distribution network, is the ratio of the AC and DC power at the source end, is the ratio of AC to DC power at the load.

[0034] This embodiment provides a structural scheme for synchronous transmission of AC and DC along feeders based on zigzag transformers in a distribution network, conducts theoretical analysis of the AC and DC hybrid system based on system constraints, verifies the feasibility of the system through digital simulation, and uses zigzag transformers to achieve coupling of AC and DC in a medium-voltage power system, thereby allowing AC and DC to be transmitted simultaneously along the same feeder, thus improving the method for simultaneous transmission of AC and DC along the same feeder. At the same time, an economic analysis is conducted on the verified AC and DC distribution network scheme and the AC distribution network scheme, providing a reference for decision makers to choose an appropriate way to design a distribution network.

[0035] Embodiment 2 provides a method for simultaneous transmission of AC and DC along a feeder line based on a zigzag transformer according to the present invention, comprising the following steps: S1, constructs a structural scheme for AC and DC transmission along the same feeder in the distribution network.

[0036] like Figure 2 As shown in the figure, the AC topology part is the same as the distribution network, but the transformer is different. In the AC / DC system, the zigzag connected winding can avoid transformer saturation caused by DC current. Since there are multiple feeders in the distribution network, the transformer is also used to limit the AC and DC currents to a certain range, thereby achieving the coupling and separation of AC and DC currents in the power grid.

[0037] For the DC part, DC power from the distributed generation (DG) is injected into the neutral point of the zigzag connected winding. Since the system is completely symmetrical, the DC current The total current in each line is thus the total DC current One third of the current, and also contains alternating current .

[0038] The DC load can obtain DC power through the neutral point of the zigzag distribution transformer. The DC load connected to the neutral point of the zigzag distribution transformer by the dotted line represents the new DC power demand in the region in the future. This special design based on the zigzag transformer enables the new DC load to be easily connected to the grid. For this AC / DC system, the DC current returns through the earth. Therefore, the AC distribution network is transformed into an AC / DC hybrid system. The superimposed DC amount is not arbitrary, and the effective values ​​of the AC and DC currents should meet the thermal limit constraints of the feeder.

[0039] S2, based on the constraints of the transformation of the AC system into an AC / DC hybrid system, a theoretical analysis of the AC / DC hybrid system is conducted to obtain the maximum transmission power of the system in the ideal state.

[0040] In AC / DC systems, the transmission power on the line is expressed as follows:

[0041] The present invention discusses the maximum transmission power of the line under the voltage and current constraints. The original line, tower structure, circuit breaker and insulator string remain unchanged. In AC and DC systems, the line can be loaded to its thermal limit. Assuming that the voltage of the line at the starting point and the end point is the same, the current constraint should be as follows:

[0042] In the power system, in order to ensure the reliability of the insulator plate, the sign of the instantaneous electric field polarity should change twice in one cycle. In addition, the circuit breaker in the AC system remains unchanged when the system is converted to an AC / DC system. Therefore, the voltage and current in the AC / DC hybrid system should satisfy the following inequality:

[0043]

[0044] Assumptions and , combined with the above formula, the ideal state transmission power formula of the system can be obtained as follows:

[0045] In the formula, is the total power in the AC / DC system, is the effective value of the AC component voltage, is the DC component voltage, is the effective value of the AC component current, is the DC component current, is the ratio of the effective value of the AC component voltage to the line thermal limit voltage, is the ratio of the effective value of the AC component current to the line thermal limit current, is the preset AC / DC system power factor, is the line thermal limit voltage value, is the thermal limit current value of the line.

[0046] It should be noted that in order to verify the line capacity enhancement theory, a case study of 35kV and 10kV medium voltage distribution networks was conducted, and the results are as follows: Under appropriate power factors, the power in AC and DC systems can be significantly increased. The voltage and current still meet the constraints of the insulation, mechanical properties and other parameters of the original AC line. For the 35kV distribution network, the absolute value of the power increase is more significant; and for the 10kV distribution network, the power increase ratio is more significant.

[0047] S3, verify the feasibility of the system through digital simulation.

[0048] In order to verify the feasibility of the proposed scheme and observe the performance of the system, the transformer and system models were established in the digital simulation software PSCAD / EMTDC.

[0049] In order to verify the performance of avoiding saturation, the zigzag transformer is first simulated. The primary winding of the transformer is connected in star shape, and the AC and DC currents provided by the ideal power supply are injected. The simulation results show that the excitation current trend of the star-connected transformer remains stable. When the DC is fully superimposed, the maximum and minimum values ​​of the excitation current are almost symmetrical on the time axis. There is no DC bias phenomenon within the allowable error range. The zigzag transformer performs well in avoiding core saturation caused by DC current. At the same time, based on Figure 4 An AC / DC simulation system was built. The simulation results show that when the DC component is injected into the AC distribution system, the structure of the feeder does not need to be modified; the signs of the instantaneous voltage and current change twice in one cycle, and the polarity of the electric field changes. The circuit breakers used in the original AC system can work normally in the new system; the composite system operates normally. There is no distortion of the voltage and current waveforms, indicating that the saturation phenomenon of the star transformer has been avoided. The results prove that the power distribution of the superimposed DC component is reasonable.

[0050] S4. Conduct economic analysis on the verified AC / DC distribution network scheme and AC distribution network scheme.

[0051] As the number of distributed generation (DG) and DC loads connected to the distribution network increases, the typical distribution network structure (10kV) can be Figure 5 and Figure 6 The economic analysis will be conducted in Figure 5 and Figure 6 In between. Figure 5In the diagram, the AC power source is a conventional synchronous generator or an infinite bus. Equipment such as transformers, circuit breakers, lines, etc. are marked in the figure. When distributed generation (DG) and DC loads are connected to the distribution network, rectifiers and inverters are required. DC loads are divided into Class I and Class II. Electric vehicle charging stations (690V), subway DC systems (±750V), and industrial loads with high power quality requirements are DC loads (I). Other loads, such as computers, TVs, printers, etc., represent DC loads (II). Unlike AC systems, in Figure 6 In the feeder, the transformer is connected in zigzag and only a DC-DC transformer is required without a rectifier or inverter. AC and DC currents are transmitted simultaneously along the feeder.

[0052] In order to further analyze the economic benefits of AC / DC systems, this paper calculates Figure 5 and Figure 6 The cost of the equipment is enclosed by the dashed box in the figure. Since the source and load are part of the original system, they are not taken into account. The prices of transformers, converters and cables can be found in Figure 7 It should be noted that the prices of different equipment are floating and changing. Therefore, the data used here is only a reference for a typical sample based on current technology. The results are mainly used to verify the economic analysis.

[0053] Further, the equipment price is explained: Converter station: Based on the construction experience of existing high-voltage direct current (HVDC) projects, the construction cost of a converter station is related to its conversion capacity, and the price is ¥1000 per kilowatt.

[0054] Substation: For AC substation and distribution station, the construction cost is ¥300 per kilowatt.

[0055] Distribution transformer: The production process of star transformer is more complicated, and the price is ¥200,000 per set. The price of ordinary Y-type transformer is ¥150,000 per set. For DC-DC transformer, the price is determined by the number of IGBTs, and it is ¥390,000 per set.

[0056] Further, the number of devices is explained: Circuit breakers and cables are commonly used equipment in power systems. Figure 7 To simplify the calculation process, this analysis is based on the following assumptions: First, the power transmitted through the cable in the AC system is ; Secondly, the AC load is , and the DC load is The ratio of the two is Therefore, the quantities for each device are as follows: For AC systems: The number of cables is 6, ; The capacity of the substation is 7.2MW. ; The capacity of the converter station is 7.2MW. , because AC to DC and DC to AC converters are needed; The number of distribution transformers is 4, ; Without DC-DC converter: The number of circuit breakers is obviously 6.

[0057] For AC and DC systems: The number of cables is 4, The remaining power can be transmitted through 4 cables, because .

[0058] The capacity of the substation is 7.2MW. .

[0059] No converter station required: The number of distribution transformers is 4 (same as the number of cables).

[0060] The number of DC-DC transformers is 8, one needs to be installed at each end of the cable.

[0061] The number of circuit breakers is obviously 4.

[0062] like Figure 7 As shown, when the power ratio of the AC and DC systems is When the AC power is 200W, the construction cost is much lower than that of the AC system. However, the ratio of AC to DC power is not always ideal in the distribution network. As the ratio changes, the investment cost will also change. Therefore, the cost function of the source and load ends will be analyzed based on different ratios.

[0063] Assumptions: For the source, the ratio of AC to DC power is .

[0064] At the load side, the ratio of AC to DC power is .

[0065] When the ratio changes, it is necessary to adjust the capacity of the rectifier and inverter, and increase or decrease the investment in other related equipment. Figure 7 The formula for the cost function is as follows: The cost function for an AC distribution network is shown below:

[0066] The cost function of the AC / DC distribution network is shown below:

[0067] In the formula, is the cost function of the AC distribution network, is the cost function of the AC / DC distribution network, is the ratio of the AC and DC power at the source end, is the ratio of AC to DC power at the load.

[0068] To express the relationship between these values ​​more clearly, the cost function is Figure 8 The cost of the AC system decreases significantly when S and L increase (i.e. the AC component increases). The cost of the AC / DC system decreases first and then starts to increase when S and L reach a certain value. This figure provides a reference for decision makers. Depending on the ratio of AC and DC power, it is obvious to choose the appropriate way to design the distribution network.

[0069] The present invention proposes a structure of AC and DC synchronous transmission along feeder based on zigzag transformer; then, based on the constraint conditions after the AC system is converted into an AC / DC hybrid system, a method for obtaining the ideal maximum power is proposed by adopting theoretical analysis, which provides a basis for the power analysis of the system; then, a zigzag transformer and an AC / DC hybrid system using the transformer are designed on PSCAD / EMTDC software and simulation analysis is carried out, which verifies the advantages of the AC and DC synchronous transmission along feeder proposed by the present invention; finally, the economic efficiency of the AC system and the AC / DC hybrid system obtained after the transformation is analyzed, which provides a reference basis for the design of the distribution network.

[0070] The above formulas are all dimensionless and numerical calculations. The formula is a formula for the most recent real situation obtained by collecting a large amount of data and performing software simulation. The preset parameters in the formula are set by technicians in this field according to actual conditions.

[0071] The above embodiments may be implemented in whole or in part by software, hardware, firmware or any other combination. When implemented by software, the above embodiments may be implemented in whole or in part in the form of a computer program product.

[0072] Those of ordinary skill in the art will appreciate that the modules and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of this application.

[0073] In addition, each functional module in each embodiment of the present application may be integrated into one processing module, or each module may exist physically separately, or two or more modules may be integrated into one module.

[0074] The above is only a specific implementation of the present application, but the protection scope of the present application is not limited thereto. Any person skilled in the art who is familiar with the present technical field can easily think of changes or substitutions within the technical scope disclosed in the present application, which should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

[0075] Finally: The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for simultaneously transmitting AC and DC along a feeder line based on a zigzag transformer, characterized in that: The steps include: Construct a structural scheme for AC and DC transmission along the same feeder in the distribution network; Based on the constraints of the transformation of AC system into AC / DC hybrid system, the AC / DC hybrid system is theoretically analyzed to obtain the maximum transmission power of the system in the ideal state. Verify the feasibility of the system through digital simulation; Conduct economic analysis on the verified AC / DC distribution network scheme and AC distribution network scheme.

2. The method for simultaneous transmission of AC and DC along a feeder line based on a zigzag transformer according to claim 1, characterized in that: The structural scheme for constructing AC and DC transmission along the same feeder in the power distribution network is specifically as follows: Compared with the AC distribution network, the AC topology remains unchanged, but the transformer is changed to a zigzag transformer; Inject the DC power of the distributed generation into the neutral point of the connecting winding of the zigzag main transformer; The DC loads are supplied at the neutral point of the zigzag distribution transformer.

3. The method for simultaneous transmission of AC and DC along a feeder line based on a zigzag transformer according to claim 2, characterized in that: The constraints for the AC system to be transformed into an AC / DC hybrid system are specifically: The constraint conditions include voltage constraint conditions that satisfy feeder thermal limit constraints and current constraint conditions that satisfy feeder thermal limit constraints.

4. The method for simultaneous transmission of AC and DC along a feeder line based on a zigzag transformer according to claim 3, characterized in that: The maximum transmission power of the system in the ideal state is specifically obtained as follows: Based on the voltage constraint condition and the current constraint condition, combined with the AC / DC system line transmission power expression and the preset AC / DC system power factor, data analysis is performed to obtain the system ideal state transmission power formula; Adjust the preset AC / DC system power factor and calculate the maximum transmission power of the system in the ideal state.

5. The method for simultaneous transmission of AC and DC along a feeder line based on a zigzag transformer according to claim 4, characterized in that: The economic analysis of the verified AC / DC power distribution network solution and the AC power distribution network solution is specifically as follows: Compare the construction costs of AC and DC distribution networks based on data and diagrams; Based on different ratios of AC power to DC power, data analysis is performed on the cost functions at the source end and the load end to obtain the cost function of the AC distribution network and the cost function of the AC / DC distribution network.

6. The method for simultaneous transmission of AC and DC along a feeder line based on a zigzag transformer according to claim 5, characterized in that: The current constraint condition is as follows: The voltage constraint condition is as follows: The AC / DC system line transmission power expression is specifically expressed as follows: The ideal state transmission power formula of the system is as follows: In the formula, is the total power in the AC / DC system, is the effective value of the AC component voltage, is the DC component voltage, is the effective value of the AC component current, is the DC component current, is the ratio of the effective value of the AC component voltage to the line thermal limit voltage, is the ratio of the effective value of the AC component current to the line thermal limit current, is the preset AC / DC system power factor, is the line thermal limit voltage value, is the thermal limit current value of the line.

7. The method for simultaneous transmission of AC and DC along a feeder line based on a zigzag transformer according to claim 6, characterized in that: The cost function of the AC power distribution network is specifically formulated as follows: The cost function of the AC / DC power distribution network is specifically formulated as follows: In the formula, is the cost function of the AC distribution network, is the cost function of the AC / DC distribution network, is the ratio of AC to DC power at the source end, is the ratio of AC to DC power at the load.