CN108228778B - BPA power flow data separation equivalent conversion method based on MATLAB platform - Google Patents

BPA power flow data separation equivalent conversion method based on MATLAB platform Download PDF

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CN108228778B
CN108228778B CN201711465991.0A CN201711465991A CN108228778B CN 108228778 B CN108228778 B CN 108228778B CN 201711465991 A CN201711465991 A CN 201711465991A CN 108228778 B CN108228778 B CN 108228778B
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data
card
node
line
bpa
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CN108228778A (en
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覃海
姬源
周川梅
贺先强
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Guizhou Power Grid Co Ltd
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    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F16/00Information retrieval; Database structures therefor; File system structures therefor
    • G06F16/10File systems; File servers
    • G06F16/17Details of further file system functions
    • G06F16/178Techniques for file synchronisation in file systems
    • G06F16/1794Details of file format conversion
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02JCIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00Circuit arrangements for ac mains or ac distribution networks
    • H02J3/04Circuit arrangements for ac mains or ac distribution networks for connecting networks of the same frequency but supplied from different sources
    • H02J3/06Controlling transfer of power between connected networks; Controlling sharing of load between connected networks
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02JCIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]

Abstract

The invention discloses a BPA (Business process analysis) power flow data separation equivalent conversion method based on an MATLAB (matrix laboratory) platform, which converts the connection relation among various nodes, lines, generators and transformers which are represented by letter names and are partitioned according to geography into a bus/branch model (power flow calculation model) connected by topological nodes and electric elements with impedance between the topological nodes. In the conversion process, a method of extracting data separation data according to the partition names is adopted, so that the search quantity during subsequent data analysis and matching is reduced, the conversion speed is accelerated, and the data conversion time is saved.

Description

BPA power flow data separation equivalent conversion method based on MATLAB platform
Technical Field
The invention relates to the field of network data conversion of a power system, in particular to a BPA power flow data separation equivalent conversion method based on an MATLAB platform.
Background
The BPA data and the Matpower data are two data formats which are widely applied to load flow calculation and analysis, however, the problem that the two data formats cannot be exchanged exists consistently. Based on the above, the rapid power flow calculation is carried out on the Matlab platform by using the Matpower, aiming at the problem of incompatibility between the BPA data and the Matpower in the calculation process, the conversion principle of the BPA-Matpower data interface is invented based on the BPA-Matpower data interface, the conversion principle comprises the corresponding relation between the BPA and the Matpower data structure and the conversion process of the BPA-Matpower data interface, and the data conversion from the BPA data to the Matpower is realized.
In 1984, BPA programs introduced and popularized by the institute of Electrical Power science in China have been rapidly developed in China, have been applied to the management of electric power in the planning department, the dispatching and operating department and the experimental and research department of electric power systems in China, and become one of the important tools for the analysis and calculation of electric power systems in China. The method comprises a detailed generator model, a line model and various excitation models, and has the characteristics of large calculation scale, high calculation speed and good numerical stability. However, since data in the IEEE trend format is recognizable in research and development in colleges and universities, it is necessary to convert data based on a BPA model into IEEE trend data. At present, some documents research on high-resistance cards in the power grid flow data conversion process of the BPA model, but do not provide a complete and effective solution for explaining the BPA flow data conversion process.
Disclosure of Invention
In view of this, the present invention aims to provide a BPA power flow data separation equivalent transformation method based on the MATLAB platform. Aims to overcome the defects of incomplete conversion and large conversion error in the prior art.
The purpose of the invention is realized by the following technical scheme: .
The invention discloses a method for separating, equating and converting BPA flow data on an MATLAB platform, which comprises the following steps:
step 1: DAT file for reading BPA;
step 2: obtaining a balance node, reference power and a region partition name of a required region;
and step 3: extracting again according to the partition names, separating out the required data and realizing efficient extraction;
and 4, step 4: acquiring alternating current node and direct current node data in the region;
and 5: acquiring generator data in the region;
step 6: acquiring data of a line transformer in a region;
and 7: equivalent processing of high-impedance line data and processing of boundary lines;
and 8: outputting IEEE trend format data;
and step 9: and comparing the BPA trend data result with the IEEE trend format data result.
Further, in the step 1, when the DTA data of BPA is read, the following data is mainly read:
1BPA power flow control program; the area control data card comprises a card A, an AC card, an AO card and an I card; node data card B card, BD card, BM card, + card, X card; the branch data card comprises an L card, an LD card, an LM card, a T card, an R card, an E card and an RZ card; the data modification cards are P cards, Z cards and DZ cards.
Further, in the step 2, the area name to be obtained is read into the program from the Excel file, the data obtained in the step 1 is searched, the corresponding area control data card, the balancing node name and the partition name in the area are matched, and the reference power of the power system is extracted from the BPA power flow control program.
Further, in step 3, the data obtained in step 1 is extracted again according to the partition names, the required data is separated, and node data cards B, BD, BM, + and X, branch data cards L, LD, LM, T, R, E, and RZ cards of the area are obtained, so that the data processing amount is reduced again.
Further, the method comprises the following steps: in the step 4, the data obtained in the third step is analyzed to obtain a node data card B card, a BD card, a BM card, a + card, and an X card of the area, the node data card of BPA is converted into a node matrix of a corresponding IEEE power flow data format according to the meanings of the two data structures, and a node name list busist is reserved for subsequent matching and retrieval.
Further, in the step 5, for the data obtained in the third step, the buslist obtained in the fourth step is used for matching to obtain a generator node data card BE card, a BQ card, a BV card and a BF card, and the node data card of BPA is converted into generator matrix data in a corresponding IEEE power flow data format according to the meanings of the two data structures.
Further, in step 6, the data obtained in the third step is analyzed to obtain an L card, an LD card, and a T card of the symmetric line data card, and it is determined whether the first and last node names belong to buslists, and if both are in the node list of the area, it is determined as an internal line, and if only one of the first and last nodes is in the node list of the area, it is determined as a boundary line, and if none of the first and last nodes is in the node list of the area, it is determined as an external line. Thus, the internal line and the boundary line are extracted, and then the two data structures are correspondingly converted according to the meanings of the two data structures.
Further, the step 7 specifically includes the following steps:
step 7.1: initializing;
step 7.2: and taking out the line data and judging whether the line data is L + card data or not. If yes, expanding the character to 72 characters, and if not, turning to step 7.6;
step 7.3: judging whether the head node and the tail node of the L + card data line are in an area node data list or not, if the head node and the tail node are in the area node data list, matching the head node and the tail node with corresponding node numbers according to the head node name and the tail node name, then converting the compensation capacity of the front node and the rear node of the L + card into the capacity of the corresponding voltage level of the high-impedance line, adding the converted capacity value under the Bs of the corresponding node, if only one node is in the area node data list, converting the capacity of the corresponding compensation node only, adding the converted capacity value under the Bs of the corresponding node, and if neither node is in the area node data list, turning to the step 7.4;
step 7.4: active power and reactive power transmitted by a boundary line L card and an L + card are extracted from a PFO file of the BPA;
step 7.5: and matching internal nodes corresponding to the L card and the L + card of the boundary line, and enabling the power transmitted on the boundary line to be equivalent to active and reactive loads of the nodes.
Step 7.6: and (6) ending.
Further, the step 8 specifically includes the following steps:
step 8.1: outputting the reference power;
step 8.2: outputting the Case version;
step 8.3: outputting node data;
step 8.4: outputting generator node data;
step 8.5: outputting line data;
step 8.6: finishing;
the data of the line comprises the output of the power transmission line and the output of the equivalent branch of the transformer; when the transmission line outputs, according to the IEEE format requirement, the resistance, reactance and ground-to-ground susceptance of the transmission line are required to be processed into per unit values; when the equivalent branch of the transformer outputs, the transformer data in the DAT file of BPA needs to be processed into a transformer model of IEEE with a transformer transformation ratio, wherein the transformer transformation ratio is the ratio of the voltage at the head end and the voltage at the tail end of the branch.
Further, the step 9 specifically includes the following steps:
step 9.1: analyzing a PFO file of a power flow operation result file of BPA;
step 9.2: matching each row of node data in the area node data list, if not, turning to the step 9.7, and if so, continuing the following steps;
step 9.3: carrying out field processing on the data, taking a blank as a partition character, and dividing the blank into a plurality of sections;
step 9.4: extracting a voltage reference value and an actual voltage value of a node of the data line, calculating a voltage per unit value of the node, and matching the voltage per unit value with an IEEE data structure line of a corresponding node;
step 9.5: judging whether the node is a PV node, if not, turning to step 9.6, if so, extracting active output power, reactive output power and node voltage data of the generator node, and then matching the data to an IEEE data structure line of the corresponding generator node;
step 9.6: extracting corresponding line data, if the first node and the last node of the line are in the regional node data list, extracting active transmission power and reactive transmission power of the line, calculating the active power and reactive power transmitted in the opposite direction by using other data, and matching the active power and reactive power with an IEEE data structure line of the corresponding line;
step 9.7: and (6) ending.
The invention has the beneficial effects that: compared with the prior art, the method has the advantages of more accurate conversion of equivalent data, shorter conversion time and higher conversion efficiency, and can be used for real-time data conversion and tracking of the power system.
Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention. The objectives and other advantages of the invention will be realized and attained by the structure particularly pointed out in the written description and claims hereof.
Drawings
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be further described in detail with reference to the accompanying drawings, in which:
FIG. 1 is a flow chart of a method for separating equivalence and conversion of BPA power flow data based on an MATLAB platform;
FIG. 2 is a flowchart of a comparison analysis procedure of the BPA power flow calculation result and the IEEE power flow calculation result;
FIG. 3 is a data structure diagram of a node B data card of BPA;
FIG. 4 is a data structure diagram of a BD node data card of BPA;
FIG. 5 is a node matrix data structure diagram of IEEE power flow data;
FIG. 6 is a generator node data card data structure diagram of the BPA;
FIG. 7 is a generator matrix data structure diagram of IEEE power flow data;
FIG. 8 is a diagram of a line data card data structure for a BPA;
FIG. 9 is a diagram of a data structure of a two-terminal DC line data card for BPA;
FIG. 10 is a transformer data card data structure diagram of the BPA;
FIG. 11 is a diagram of a branch matrix data structure for IEEE power flow data;
FIG. 12 is a data structure diagram of a line impedance parameter data card for BPA.
Detailed Description
Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the accompanying drawings. It should be understood that the preferred embodiments are illustrative of the invention only and are not limiting upon the scope of the invention.
As shown in fig. 1, the MATLAB platform-based BPA power flow data separation equivalent conversion method of the present invention includes the following steps:
step 1: DAT file for reading BPA; in this step, because the DAT file is in a text format, a normal file reading mode is directly adopted when reading, and data is directly preprocessed according to characteristics of the BPA DAT file to obtain useful data information, and annotation line information is ignored, so that the data amount is reduced for subsequent search matching, the conversion speed is increased, and the requirements of data conversion are better met, and when reading the BPA DTA data, the following data is mainly read: 1BPA power flow control program; the area control data card comprises a card A, an AC card, an AO card and an I card; node data card B card, BD card, BM card, + card, X card; the branch data card comprises an L card, an LD card, an LM card, a T card, an R card, an E card and an RZ card; the data modification card comprises a P card, a Z card and a DZ card;
step 2: obtaining a balance node, reference power and a region partition name of a required region; reading the area name to be obtained into a program through an Excel file, searching the data obtained in the step 1, matching the corresponding area control data card, a balance node name and a partition name in the area, and extracting the reference power of the power system from a BPA power flow control program;
and step 3: extracting again according to the partition names, separating out the required data and realizing efficient extraction; extracting the data obtained in the step 1 again according to the partition names, separating the required data to obtain node data cards B, BD, BM, + and X, branch data cards L, LD, LM, T, R, E and RZ of the area, and reducing the data processing amount again;
and 4, step 4: acquiring alternating current node and direct current node data in the region; the data obtained in the step 3 are analyzed to obtain a node data card B card, a BD card, a BM card, a + card and an X card of the region, the node data card of the BPA is converted into a node matrix of a corresponding IEEE trend data format according to the meanings of the two data structures, and a node name list buslist is reserved for subsequent matching and retrieval. Fig. 3, 4, and 5 are node data card data structures of BPA and node matrix data structures of IEEE power flow data, respectively.
And 5: acquiring generator data in the region; and specifically, for the data obtained in the step 3, matching is carried out by using the buslist obtained in the step 4 to obtain a BE card, a BQ card, a BV card and a BF card of the node data card of the generator, and the node data card of the BPA is converted into generator matrix data in a corresponding IEEE power flow data format according to the meanings of the two data structures. Fig. 6 and 7 are a generator node data card data structure of BPA and a generator matrix data structure of IEEE power flow data, respectively.
Step 6: acquiring data of a line transformer in a region; the data obtained in the step 3 is analyzed to obtain a symmetrical line data card L card, an LD card and a T card, whether the names of the first and last nodes belong to buslist is judged, if the names of the first and last nodes are both in a node list of a region, the internal line is judged, if only one of the first and last nodes is in the node list of the region, the boundary line is judged, and if the first and last nodes are not in the node list of the region, the external line is judged. Thus, the internal line and the boundary line are extracted, and then the two data structures are correspondingly converted according to the meanings of the two data structures. Fig. 8, 9, 10, and 11 are a line data card data configuration diagram of the BPA, a two-terminal dc line data card data configuration diagram of the BPA, a transformer data card data configuration diagram of the BPA, and a branch matrix data configuration diagram of the IEEE power flow data, respectively.
And 7: equivalent processing of high-impedance line data and processing of boundary lines; the step 7 specifically comprises the following steps:
step 7.1: initializing;
step 7.2: and taking out the line data and judging whether the line data is L + card data or not. If yes, expanding the character to 72 characters, and if not, turning to step 7.6;
step 7.3: judging whether the head node and the tail node of the L + card data line are in an area node data list or not, if the head node and the tail node are in the area node data list, matching the head node and the tail node with corresponding node numbers according to the head node name and the tail node name, then converting the compensation capacity of the front node and the rear node of the L + card into the capacity of the corresponding voltage level of the high-impedance line, adding the converted capacity value under the Bs of the corresponding node, if only one node is in the area node data list, converting the capacity of the corresponding compensation node only, adding the converted capacity value under the Bs of the corresponding node, and if neither node is in the area node data list, turning to the step 7.4;
step 7.4: active power and reactive power transmitted by a boundary line L card and an L + card are extracted from a PFO file of the BPA;
step 7.5: matching internal nodes corresponding to the L card and the L + card of the boundary line, and enabling power transmitted on the boundary line to be equivalent to active and reactive loads of the nodes;
step 7.6: and (6) ending.
FIG. 12 is a data structure diagram of a line impedance parameter data card for a BPA;
and 8: outputting IEEE trend format data; the step 8 specifically comprises the following steps:
step 8.1: outputting the reference power;
step 8.2: outputting the Case version;
step 8.3: outputting node data;
step 8.4: outputting generator node data;
step 8.5: outputting line data;
step 8.6: finishing;
the data of the line comprises the output of the power transmission line and the output of the equivalent branch of the transformer; when the transmission line outputs, according to the IEEE format requirement, the resistance, reactance and ground-to-ground susceptance of the transmission line are required to be processed into per unit values; when the equivalent branch of the transformer outputs, the transformer data in the DAT file of BPA needs to be processed into a transformer model of IEEE with a transformer transformation ratio, wherein the transformer transformation ratio is the ratio of the voltage at the head end and the voltage at the tail end of the branch.
And step 9: comparing the BPA flow data result with the IEEE flow format data result; as shown in fig. 2, step 9 specifically includes the following steps:
step 9.1: analyzing a PFO file of a power flow operation result file of BPA;
step 9.2: matching each row of node data in the area node data list, if not, turning to the step 9.7, and if so, continuing the following steps;
step 9.3: carrying out field processing on the data, taking a blank as a partition character, and dividing the blank into a plurality of sections;
step 9.4: extracting a voltage reference value and an actual voltage value of a node of the data line, calculating a voltage per unit value of the node, and matching the voltage per unit value with an IEEE data structure line of a corresponding node;
step 9.5: judging whether the node is a PV node, if not, turning to step 9.6, if so, extracting active output power, reactive output power and node voltage data of the generator node, and then matching the data to an IEEE data structure line of the corresponding generator node;
step 9.6: extracting corresponding line data, if the first node and the last node of the line are in the regional node data list, extracting active transmission power and reactive transmission power of the line, calculating the active power and reactive power transmitted in the opposite direction by using other data, and matching the active power and reactive power with an IEEE data structure line of the corresponding line;
step 9.7: and (6) ending.
The invention converts the connection relation between various nodes, lines, generators and transformers which are represented by letter names and are partitioned according to geography into a bus/branch model (load flow calculation model) which is connected by topological nodes and electrical elements with impedance between the topological nodes. In the conversion process, a method of extracting data separation data according to the partition names is adopted, so that the search quantity during subsequent data analysis and matching is reduced, the conversion speed is accelerated, and the data conversion time is saved. Meanwhile, when boundary lines are processed and high-impedance lines are processed, reactive compensation of front and rear nodes is processed according to the high-impedance lines, and therefore the accuracy of conversion results is guaranteed. Moreover, after data conversion, the accuracy of the converted IEEE power flow calculation result and the BPA power flow calculation result is verified through comparative analysis.
Finally, the above embodiments are only intended to illustrate the technical solutions of the present invention and not to limit the present invention, and although the present invention has been described in detail with reference to the preferred embodiments, it will be understood by those skilled in the art that modifications or equivalent substitutions may be made on the technical solutions of the present invention without departing from the spirit and scope of the technical solutions, and all of them should be covered by the claims of the present invention.

Claims (7)

1. A BPA power flow data separation equivalent conversion method based on an MATLAB platform is characterized in that: the method comprises the following steps:
step 1: DAT file for reading BPA;
when reading the DTA data of BPA, the following data are read:
1BPA power flow control program; the area control data card comprises a card A, an AC card, an AO card and an I card; node data card B card, BD card, BM card, + card, X card; the branch data card comprises an L card, an LD card, an LM card, a T card, an R card, an E card and an RZ card; the data modification card comprises a P card, a Z card and a DZ card;
step 2: obtaining a balance node, reference power and a region partition name of a required region;
and step 3: extracting again according to the partition names, separating out the required data and realizing efficient extraction;
extracting the data obtained in the step 1 again according to the partition names, separating the required data to obtain node data cards B, BD, BM, + and X, branch data cards L, LD, LM, T, R, E and RZ of the area, and reducing the data processing amount again;
and 4, step 4: acquiring alternating current node and direct current node data in the region;
and 5: acquiring generator data in the region;
step 6: acquiring data of a line transformer in a region;
and 7: equivalent processing of high-impedance line data and processing of boundary lines;
the step 7 specifically comprises the following steps:
step 7.1: initializing;
step 7.2: taking out high impedance line data, judging whether the high impedance line data is L + card data, if so, expanding the high impedance line data to 72 characters, and if not, turning to the step 7.6;
step 7.3: judging whether the head node and the tail node of the L + card data line are in an area node data list or not, if the head node and the tail node are in the area node data list, matching the head node and the tail node with corresponding node numbers according to the head node name and the tail node name, then converting the compensation capacity of the front node and the rear node of the L + card into the capacity of the corresponding voltage level of the high-impedance line, adding the converted capacity value under the Bs of the corresponding node, if only one node is in the area node data list, converting the capacity of the corresponding compensation node only, adding the converted capacity value under the Bs of the corresponding node, and if neither node is in the area node data list, turning to the step 7.4;
step 7.4: active power and reactive power transmitted by a boundary line L card and an L + card are extracted from a PFO file of the BPA;
step 7.5: matching internal nodes corresponding to the L card and the L + card of the boundary line, and enabling power transmitted on the boundary line to be equivalent to active and reactive loads of the nodes;
step 7.6: finishing;
and 8: outputting IEEE trend format data;
and step 9: and comparing the BPA trend data result with the IEEE trend format data result.
2. The MATLAB platform-based BPA power flow data separation equivalent transformation method according to claim 1, characterized in that: in the step 2, the area name required to be obtained is read into the program through an Excel file, the data obtained in the step 1 is searched, the corresponding area control data card, the balancing node name and the partition name in the area are matched, and the reference power of the power system in the area is extracted from the BPA power flow control program.
3. The MATLAB platform based BPA power flow data separation equivalent transformation method of claim 1 or 2, wherein: in the step 4, the data obtained in the third step is analyzed to obtain a node data card B card, a BD card, a BM card, a + card, and an X card of the area, the node data card of BPA is converted into a node matrix of a corresponding IEEE power flow data format according to the meanings of the two data structures, and a node name list busist is reserved for subsequent matching and retrieval.
4. The MATLAB platform based BPA power flow data separation equivalent transformation method of claim 1 or 2, wherein: and in the step 5, for the data obtained in the third step, matching is carried out by using the buslistlist obtained in the fourth step to obtain a BE card, a BQ card, a BV card and a BF card of the node data card of the generator, and the node data card of the BPA is converted into generator matrix data in a corresponding IEEE power flow data format according to the meanings of the two data structures.
5. The MATLAB platform-based BPA power flow data separation equivalent transformation method according to claim 1, characterized in that: in step 6, the data obtained in the third step is analyzed to obtain an L card, an LD card, and a T card of a symmetric line data card, and it is determined whether the first and last node names belong to buslist, if both are in the node list of the area, it is determined as an internal line, if only one of the first and last nodes is in the node list of the area, it is determined as a boundary line, and if none of the first and last nodes is in the node list of the area, it is determined as an external line, so that the internal line and the boundary line are extracted, and then they are correspondingly converted according to the meanings of the two data structures.
6. The MATLAB platform-based BPA power flow data separation equivalent transformation method according to claim 1, characterized in that: the step 8 specifically comprises the following steps:
step 8.1: outputting the reference power;
step 8.2: outputting the Case version;
step 8.3: outputting node data;
step 8.4: outputting generator node data;
step 8.5: outputting line data;
step 8.6: finishing;
the data of the line comprises the output of the power transmission line and the output of the equivalent branch of the transformer; when the transmission line outputs, according to the IEEE format requirement, the resistance, reactance and ground-to-ground susceptance of the transmission line are required to be processed into per unit values; when the equivalent branch of the transformer outputs, the transformer data in the DAT file of BPA needs to be processed into a transformer model of IEEE with a transformer transformation ratio, wherein the transformer transformation ratio is the ratio of the voltage at the head end and the voltage at the tail end of the branch.
7. The MATLAB platform-based BPA power flow data separation equivalent transformation method according to claim 1, characterized in that: the step 9 specifically includes the following steps:
step 9.1: analyzing a PFO file of a power flow operation result file of BPA;
step 9.2: judging whether each row of node data can be matched in the area node data list, if not, turning to the step 9.7, and if so, continuing the following steps;
step 9.3: carrying out field processing on the data, taking a blank as a partition character, and dividing the blank into a plurality of sections;
step 9.4: extracting a voltage reference value and an actual voltage value of a node of the data line, calculating a voltage per unit value of the node, and matching the voltage per unit value with an IEEE data structure line of a corresponding node;
step 9.5: judging whether the node is a PV node or not, if not, turning to a step 9.6, if so, extracting active output power, reactive output power and node voltage data of the generator node, and then matching the data to an IEEE data structure line of the corresponding generator node;
step 9.6: extracting corresponding line data, if the first node and the last node of the line are in the regional node data list, extracting active transmission power and reactive transmission power of the line, calculating the active power and reactive power transmitted in the opposite direction by using other data, and matching the active power and reactive power with an IEEE data structure line of the corresponding line;
step 9.7: and (6) ending.
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