CN112636380B - Alternating current and direct current power distribution system characteristic value analysis method based on Gehr circle theory - Google Patents

Alternating current and direct current power distribution system characteristic value analysis method based on Gehr circle theory Download PDF

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CN112636380B
CN112636380B CN202011534064.1A CN202011534064A CN112636380B CN 112636380 B CN112636380 B CN 112636380B CN 202011534064 A CN202011534064 A CN 202011534064A CN 112636380 B CN112636380 B CN 112636380B
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CN112636380A (en
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邓卫
裴玮
丁立
庄莹
张学
孔力
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Institute of Electrical Engineering of CAS
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/36—Arrangements for transfer of electric power between ac networks via a high-tension dc link
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
    • H02J3/381—Dispersed generators
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2300/00—Systems for supplying or distributing electric power characterised by decentralized, dispersed, or local generation
    • H02J2300/20—The dispersed energy generation being of renewable origin
    • H02J2300/22—The renewable source being solar energy
    • H02J2300/24—The renewable source being solar energy of photovoltaic origin
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2300/00—Systems for supplying or distributing electric power characterised by decentralized, dispersed, or local generation
    • H02J2300/20—The dispersed energy generation being of renewable origin
    • H02J2300/28—The renewable source being wind energy
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E10/00—Energy generation through renewable energy sources
    • Y02E10/50—Photovoltaic [PV] energy
    • Y02E10/56—Power conversion systems, e.g. maximum power point trackers
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E60/00—Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation
    • Y02E60/60—Arrangements for transfer of electric power between AC networks or generators via a high voltage DC link [HVCD]

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Abstract

The invention relates to a characteristic value analysis method of an alternating current and direct current power distribution system based on a Gehr circle theory, which comprises the following steps: step 1, acquiring a system matrix A of a multi-terminal AC/DC power distribution system; judging system characteristic roots of any Gerr circle; when the system characteristic root of the Geoer circle exists in the left half plane or the right half plane, the whole process is exited; otherwise, the virtual shaft is covered by the Gerr circular disc and the step 2 is carried out; step 2, carrying out similarity transformation on the Geuer circle, and judging the stability of the Geuer circle; if the disc of the Geuer circle still covers the virtual axis, performing the overlapping operation of the Geuer circle; step 3, finding a Gerr circle covering the virtual axis and updating the Gerr circle; and 4, after updating the Gerr circle, obtaining a reduced system characteristic value range for analysis. The invention can rapidly analyze the range of the characteristic value when the complexity of the AC/DC distribution network system is higher, thereby judging the stability of the system and ensuring the safe and stable operation of the system.

Description

Alternating current and direct current power distribution system characteristic value analysis method based on Gehr circle theory
Technical Field
The invention relates to the field of electric power, in particular to a method for quickly analyzing characteristic values of an alternating current and direct current power distribution and utilization system based on a Gerr circle theory.
Background
In recent years, with the rapid development and wide application of new energy, new materials and new power electronic devices, the requirements of users on power supply quality, reliability and the like are increasingly increased. Meanwhile, with the gradual improvement of the permeability of distributed energy sources such as fans, photovoltaics and fuel cells, and the increase of direct current loads such as direct current lighting and electric automobile charging piles, the traditional alternating current power distribution network gradually has difficulty in meeting new requirements of direct current equipment. According to the multi-terminal alternating current and direct current hybrid power distribution technology, a converter station link and a DC/DC converter are added in a traditional alternating current power distribution network, voltage adaptation is achieved, and local consumption of distributed energy can be achieved through control strategies such as master-slave control and droop control. By means of the characteristics of flexible networking mode, various control modes and the like, the multi-terminal alternating current and direct current hybrid power distribution technology can solve the increasing problems of distributed energy access and direct current load power supply, and is a trend of future power distribution network development. By integrating a multi-terminal direct current device (comprising a plurality of converter devices and a direct current network) in an alternating current system, a multi-terminal mutual-aid interconnected power distribution and utilization system is formed. A typical structure corresponding to a multi-terminal ac/dc distribution power system is shown in fig. 1, and integrates three voltage-source converter stations (VSCs), ac sides of the VSCs 1, VSCs 2, and VSCs 3 are respectively connected to an ac system 1, an ac system 2, and an ac system 3, and a dc side is connected to a dc bus through a line of a certain length. The direct current network can be integrated to be connected with distributed energy sources such as wind power and photovoltaic, an energy storage system, a direct current load and the like, and when the voltage level of the equipment is not matched with the voltage level of the direct current bus, the DC/DC converter can be configured to carry out conversion.
In a multi-terminal alternating current and direct current power distribution and utilization system, a characteristic value analysis method is generally adopted to analyze the small disturbance stability of the system, and then a dominant characteristic value of the system is obtained and stability analysis is carried out. Meanwhile, along with the increase of distributed power sources, direct current loads and converter stations in the alternating current and direct current hybrid system, the dimension of a system matrix is increased, the complexity of the system is correspondingly and rapidly increased, and the difficulty is brought to the traditional eigenvalue analysis method for solving the system matrix.
Disclosure of Invention
In order to solve the technical problems, the invention provides a matrix eigenvalue analysis method of an alternating current and direct current distribution system based on the Gehr circle theorem, which can be used for rapidly analyzing the range of the eigenvalue when the complexity of the alternating current and direct current distribution network system is high, so that the stability of the system is judged, and the safe and stable operation of the system is ensured.
The technical scheme of the invention is as follows: a characteristic value analysis method of an alternating current and direct current power distribution system based on a Gehr circle theory comprises the following steps:
step 1, acquiring a system matrix A of a multi-terminal AC/DC power distribution system; judging system characteristic roots of any Gerr circle; when the system characteristic root of the Geoer circle exists in the left half plane or the right half plane, the whole process is exited; otherwise, the virtual shaft is covered by the Gerr circular disc and the step 2 is carried out;
step 2, performing similarity transformation on the Geoer circle, and judging the stability of the Geoer circle; if the disc of the Geer circle still covers the virtual axis, performing the overlapping operation of the Geer circle;
step 3, finding a Geuer circle covering the virtual axis and updating the Geuer circle;
and 4, after updating the Geuer circle, obtaining a reduced system characteristic value range for analysis.
Further, the step 1 specifically includes:
at all G 1 ,G 2 ,…,G n ,…,G N In the Geer circle, wherein G n Denotes the nth Gehr circle, A nn Is the center of the n-th Gehr circle, and is shown as the position of the real axis, r nn Is the radius of the nth guerre circle,
Figure BDA0002849897940000021
j is an intermediate variable, and N represents the rank of the matrix a, i.e. the total number of all geuer circles.
Further, in the step 1, system characteristic root judgment is carried out on any Gerr circle; when the system characteristic root of the Geoer circle exists in the left half plane or the right half plane, the whole process is exited; otherwise, the virtual shaft is covered by the Gerr circular disc and the step 2 is carried out; the method specifically comprises the following steps:
if any of the Gerr circles satisfies:
A nn is less than or equal to 0, and A nn +r nn <0, the system characteristic roots are all in the left half plane, and the system is stable; the whole process is exited, and the calculation is finished;
if at least one Gehr circle occurs:
A nn >0, and A nn -r nn >0, the system characteristic root is in the right half plane, and the system is unstable; the whole process is exited, and the calculation is finished;
if at least one of the Gehr circles satisfies:
A nn is less than or equal to 0, and A nn +r nn >And 0, indicating that the virtual axis is covered by the Geiger circle disc, and switching to the step 2 if the judgment is not intuitive.
Further, the step 2 performs similarity transformation on the Gerr circle and judges the stability of the Gerr circle; the method specifically comprises the following steps:
step 2.1, selecting an initial Gerr circle which is covered by the circular disc and meets the preset conditions:
searching all Geuer circles, selecting N =1,2, \8230, satisfying A in N nn Is less than or equal to 0 and A nn +r nn The Gaur circle corresponding to the largest numerical value is assumed to be the ith Gaur circle, and G i Denotes the ith Gehr circle, A ii Is the center of the ith Gaur circle and is expressed by the position of the real axis, r ii Is the radius of the ith Gaur circle
Figure BDA0002849897940000031
j is an intermediate variable).
Step 2.2 apply B = diag (B) 11 ,B 22 ,...,B nn ,...,B NN ) The ith column is updated accordingly and other data is normalized, i.e. expressed as
Figure BDA0002849897940000032
And performing a diagonal transformation, i.e.:
Figure BDA0002849897940000033
at this time, the ith Gerr circle is reduced to be within the virtual axis, other discs are correspondingly increased, at this time, the judgment is continued, if the disk with the Geuer circle still covers the virtual axis, the Geuer circle overlapping operation is needed at the moment, and the process goes to the step 3.
Further, the step 2.2 continues to judge, including:
if for N =1,2, \8230, any Geuer circle in N satisfies:
A nn is less than or equal to 0, and A nn +r nn <And 0, the characteristic root of the system is in the left half plane, and the system is stable. And exiting the whole flow and finishing the calculation.
If at least one Gehr circle occurs:
A nn >0, and A nn -r nn >And 0, the system characteristic root is in the right half plane, and the system is unstable. And exiting the whole flow and finishing the calculation.
If at least one of the Gehr circles satisfies:
A nn is less than or equal to 0, and A nn +r nn >0, indicating that the disc with the Geer circle still covers the virtual axis, and performing Geer circle overlapping operation to reduce the cross area among different discs to the maximum and reduce further characteristic root range search; and (5) turning to the step 3.
Further, the step 3 finds a bell circle covering the virtual axis and updates the bell circle, which specifically includes:
step 3.1, searching all Geuer circles, selecting N =1,2, \8230, wherein N satisfies A nn Is less than or equal to 0 and A nn +r nn The Gehr circle corresponding to the largest numerical value is assumed to be the k-th Gehr circle, and is represented by G k Denotes the k-th Gehr circle, A kk Is the center of the kth Gaier circle, and is expressed by the position of the real axis, r kk Is the radius of the k-th bell circle,
Figure BDA0002849897940000034
j is an intermediate variable;
step 3.2 apply B = diag (B) 11 ,B 22 ,...,B kk ,...,B NN ) The kth column in the middle is updated accordingly and the other data is normalized, i.e. denoted as B = diag (B) 11 ＝1,B 22 ＝1,...,B kk ＝x,...,B NN = 1), and performs a diagonal transformation, i.e.:
Figure BDA0002849897940000041
Figure BDA0002849897940000042
wherein, the first and the second end of the pipe are connected with each other,
C＝A ii 2 A ik 2 -4A ii 2 A ik r ii +4A ii 2 r ii 2 +2A ii A ik 2 r ii +2A ii A ik A kk r ii -6A ii A ik r ii 2 +4r kk A ii A ik r ii -4A ii A kk r ii 2 +4A ii r ii 3 +A ik 2 r ii 2 +2A ik A kk r ii 2 -2A ik r ii 3 +4r kk A ik r ii 2 +A kk 2 r ii 2 -2A kk r ii 3 +r ii 4
A ii representing the ith row and ith column element in the system matrix, A kk Represents the kth row and kth column elements in the system matrix, A ik Row ith and column kth elements, r ii Represents the radius of the ith Gehr circle, r kk Representing the k-th radius of the bell circle.
And 4, after updating the Gerr circle, obtaining a reduced system characteristic value range for analysis.
And ending and exiting the process.
Has the advantages that:
the alternating current and direct current hybrid power distribution technology provides an effective technical means for the large-scale access and the optimized operation control of distributed energy sources, and becomes one of the important forms of the future power distribution network. When the system safety and stability is analyzed, a characteristic value analysis method is generally adopted to analyze the small disturbance stability of the system, so as to obtain a leading characteristic value and a transmission power boundary of the system, and further determine the system safety margin. Therefore, the invention provides the quick analysis method for the characteristic value of the alternating current and direct current power distribution system based on the Gehr circle theorem, solves the problem that the accurate value of the characteristic value is difficult to obtain when the complexity of the alternating current and direct current power distribution system is high, fills up the blank of the related technology, and has wide application prospect.
Drawings
FIG. 1 is a typical structure diagram of a multi-terminal AC/DC distribution system;
fig. 2 is a flow chart of a method for analyzing a characteristic value of an ac/dc distribution system based on the gehr circle theory.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, rather than all embodiments, and based on the embodiments of the present invention, all other embodiments obtained by a person skilled in the art without creative efforts belong to the protection scope of the present invention.
According to the embodiment of the invention, the alternating current and direct current power distribution system characteristic value analysis method based on the Gehr circle theory specifically comprises the following steps:
step 1, acquiring a system matrix A of a multi-terminal AC/DC power distribution system; judging system characteristic root of any Gerr circle; when the system characteristic root of the Geuer circle exists in the left half plane or the right half plane, the whole process is exited; otherwise, the virtual shaft is covered by the Gerr circular disc and the step 2 is carried out;
step 2, performing similarity transformation on the Geoer circle, and judging the stability of the Geoer circle; if the disc of the Geer circle still covers the virtual axis, performing the overlapping operation of the Geer circle;
step 3, finding a Geuer circle covering the virtual axis and updating the Geuer circle;
and 4, after updating the Gerr circle, obtaining a reduced system characteristic value range for analysis.
The principle of the invention is as follows: after acquiring the system matrix a of the multi-terminal dc system, assume that:
Figure BDA0002849897940000051
A ij an element representing the ith row and the jth column in the system matrix A;
considering that the order of the system matrix is higher and higher, the calculation amount is larger and larger when each detailed characteristic root is solved, so that the approximate position of the characteristic root is quickly judged by means of the Gerr circle theory to accelerate the analysis speed.
With G n Represents the nth Gehr circle of the matrix A, A nn Is the center of the n-th Gehr circle, r nn Is the radius of the nth Gehr circle (
Figure BDA0002849897940000052
j is an intermediate variable), N represents the rank of the matrix A, and according to the Gehr circle theory, the characteristic roots of the matrix A are all in the union of N Gehr circles.
Then each Gerr circle on the complex plane is represented as:
G 1 ：{|z-A 11 |≤r 11 }
G 2 ：{|z-A 22 |≤r 22 }
...
G nn ：{|z-A nn |≤r nn }
...
G NN ：{|z-A NN |≤r NN }
and further finishing to obtain:
Figure BDA0002849897940000061
constructing a diagonal matrix B, and setting:
Figure BDA0002849897940000062
at this time, diagonal transformation is performed:
Figure BDA0002849897940000063
after the similarity transformation of the diagonal matrix is carried out, the characteristic root of the matrix can be unchanged, the radius of each circle can be reduced or enlarged according to the principle, and the originally coincident circles are effectively separated, or the circle near the virtual axis is further reduced, so that the characteristic value is quickly judged on the leftmost semi-plane or the right semi-plane, and the stability analysis is facilitated.
According to the specific embodiment of the invention, as shown in fig. 2, a method for rapidly analyzing a characteristic value of an ac/dc power distribution system based on a bell circle theory includes the following specific implementation steps:
step 1, acquiring a system matrix A of a multi-terminal AC/DC power distribution system; judging system characteristic roots of any Gerr circle; when the system characteristic root of the Geoer circle exists in the left half plane or the right half plane, the whole process is exited; otherwise, the virtual shaft is covered by the Gerr circular disc and the step 2 is carried out;
all G 1 ,G 2 ,…,G n ,…,G N In the cover circle, wherein G n Denotes the nth Geer circle, A nn Is the center of the n-th Gehr circle, and is shown as the position of the real axis, r nn Is the radius of the nth Gehr circle (
Figure BDA0002849897940000064
j is an intermediate variable), N represents the rank of the matrix a, i.e. the total number of all geuer circles. If any of the Gerr circles satisfies:
A nn less than or equal to 0, and A nn +r nn <And 0, the characteristic root of the system is in the left half plane, and the system is stable. And exiting the whole flow and finishing the calculation.
If at least one Gehr circle occurs:
A nn >0, and A nn -r nn >0, the system characteristic root is in the right half-plane, and the system is unstable. And exiting the whole flow and finishing the calculation.
If at least one of the Gehr circles satisfies:
A nn is less than or equal to 0, and A nn +r nn >And 0, indicating that the virtual axis is covered by the Geiger circle disc, and turning to the step 2 if the virtual axis is not visually judged.
Step 2: performing similarity transformation on the Geuer circle, and judging the stability of the Geuer circle;
step 2.1, selecting an initial Gerr circle which is covered by the circular disc and meets the preset conditions:
search all Gehr circles, select N =1,2, \ 8230, satisfy A in N nn Is less than or equal to 0 and A nn +r nn The Gehr circle corresponding to the largest numerical value is assumed to be the ith Gehr circle and is represented by G i Denotes the ith Gehr circle, A ii Is the center of the ith Gaur circle and is expressed by the position of the real axis, r ii Is the radius of the ith Gaur circle
Figure BDA0002849897940000071
j is an intermediate variable).
Step 2.2 assign B = diag (B) 11 ,B 22 ,...,B nn ,...,B NN ) The ith column is updated accordingly and other data is normalized, i.e. expressed as
Figure BDA0002849897940000072
And performing a diagonal transformation, i.e.:
Figure BDA0002849897940000073
at this moment, the ith Gerr circle is reduced to be within the virtual axis, other discs are correspondingly increased, and the judgment is continued:
if for N =1,2, \8230, any of the Gehr circles in N satisfy:
A nn less than or equal to 0, and A nn +r nn <And 0, the characteristic root of the system is in the left half plane, and the system is stable. And exiting the whole flow and finishing the calculation.
If at least one Geuer circle occurs:
A nn >0, and A nn -r nn >And 0, the system characteristic root is in the right half plane, and the system is unstable. And exiting the whole flow and finishing the calculation.
If at least one of the Gehr circles satisfies:
A nn is less than or equal to 0, and A nn +r nn >0, it indicates that the disc still covers the virtual axis, and this time needs to be doneOverlapping the Geer circles to reduce the cross area between different discs to the maximum and reduce further characteristic root range search; turning to the step 3;
step 3, finding the Gerr circle covering the virtual axis and updating the Gerr circle;
step 3.1, searching all Geuer circles, selecting N =1,2, \8230, wherein N satisfies A nn Less than or equal to 0 and A nn +r nn The Gehr circle corresponding to the largest numerical value is assumed to be the k-th Gehr circle, and is represented by G k Denotes the k-th Gehr circle, A kk Is the center of the kth Gaier circle, and is expressed by the position of the real axis, r kk Is the radius of the kth Gehr circle (
Figure BDA0002849897940000081
j is an intermediate variable).
Step 3.2 assign B = diag (B) 11 ,B 22 ,...,B kk ,...,B NN ) Column k is updated accordingly and the other data is normalized, i.e. denoted B = diag (B) 11 ＝1,B 22 ＝1,...,B kk ＝x,...,B NN = 1), and performs a diagonal transformation, i.e.:
Figure BDA0002849897940000082
Figure BDA0002849897940000083
wherein, the first and the second end of the pipe are connected with each other,
C＝A ii 2 A ik 2 -4A ii 2 A ik r ii +4A ii 2 r ii 2 +2A ii A ik 2 r ii +2A ii A ik A kk r ii -6A ii A ik r ii 2 +4r kk A ii A ik r ii -4A ii A kk r ii 2 +4A ii r ii 3 +A ik 2 r ii 2 +2A ik A kk r ii 2 -2A ik r ii 3 +4r kk A ik r ii 2 +A kk 2 r ii 2 -2A kk r ii 3 +r ii 4
A ii representing the ith row and ith column element in the system matrix, A kk Representing the kth row and kth column elements, A, in the system matrix ik Row ith and column kth elements, r ii Represents the radius of the ith Gehr circle, r kk Representing the k-th radius of the bell circle.
And 4, after updating the Gerr circle, obtaining a reduced system characteristic value range for analysis.
And ending and exiting the process.
Although illustrative embodiments of the present invention have been described above to facilitate the understanding of the present invention by those skilled in the art, it should be understood that the present invention is not limited to the scope of the embodiments, but various changes may be apparent to those skilled in the art, and it is intended that all inventive concepts utilizing the inventive concepts set forth herein be protected without departing from the spirit and scope of the present invention as defined and limited by the appended claims.

Claims (3)

1. A method for analyzing a characteristic value of an alternating current and direct current power distribution system based on a Gehr circle theory is characterized by comprising the following steps:
step 1, acquiring a system matrix A of a multi-terminal AC/DC power distribution system; judging system characteristic roots of any Gerr circle; when the system characteristic root with the Geoer circle is on the left half plane, or the system characteristic root with the Geoer circle is on the right half plane, the whole process is exited; otherwise, the virtual shaft is covered by the Gerr circular disc, and the step 2 is carried out;
step 2, carrying out similarity transformation on the Geuer circle, and judging the stability of the Geuer circle; if the disc of the Geer circle still covers the virtual axis, performing the overlapping operation of the Geer circle; performing similarity transformation on the Gerr circle and judging the stability of the Gerr circle; the method specifically comprises the following steps:
step 2.1, selecting an initial Geuer circle of which the disc covers the virtual axis and meets a preset condition:
searching all Geuer circles, selecting N =1,2, \8230, satisfying A in N nn Is less than or equal to 0 and A nn +r nn The Gaur circle corresponding to the largest numerical value is assumed to be the ith Gaur circle, and G i Denotes the ith Gehr circle, A ii Is the center of the ith Gehr circle, and is shown as the position of the real axis, r ii Is the radius of the ith guerre circle,
Figure FDA0003840493730000011
j is an intermediate variable, and N represents the rank of the matrix A;
step 2.2 apply B = diag (B) 11 ,B 22 ,...,B nn ,...,B NN ) The ith column is updated correspondingly, and other data are normalized, namely expressed as
Figure FDA0003840493730000012
And performing a diagonal transformation, i.e.:
Figure FDA0003840493730000013
at this time, the ith Gaier circle is reduced to be within the virtual axis, other discs are correspondingly increased, at this time, the judgment is continued, if some discs of the Gaier circle still cover the virtual axis, the operation of Gaier circle superposition needs to be carried out at this time, and the step 3 is carried out;
step 3, finding a Geuer circle covering the virtual axis and updating the Geuer circle;
step 4, after updating the Gerr circle, obtaining a reduced system characteristic value range for analysis;
the step 2.2 of continuing judging comprises the following steps:
if for N =1,2, \8230, N, the geur circles satisfy:
A nn is less than or equal to 0, and A nn +r nn <0, then system is specialThe roots are all on the left half plane, and the system is stable; the whole process is exited, and the calculation is finished;
if at least one Geuer circle occurs:
A nn >0, and A nn -r nn >0, if the system characteristic root is in the right half plane, the system is unstable, the whole process is exited, and the calculation is finished;
if at least one of the Gehr circles satisfies:
A nn is less than or equal to 0, and A nn +r nn >0, indicating that the disc with the Geer circle still covers the virtual axis, and performing Geer circle overlapping operation to reduce the cross area among different discs to the maximum and reduce further characteristic root range search; turning to the step 3;
step 3, finding the circle covering the virtual axis and updating the circle, specifically including:
step 3.1 search all Geuer circles, select N =1,2, \ 8230, where N satisfies A nn Is less than or equal to 0 and A nn +r nn The Gaur circle with the largest value, assumed to be the k-th Gaur circle, is designated by G k Denotes the kth Gehr circle, A kk Is the center of the kth Gaier circle, and is expressed by the position of the real axis, r kk Is the radius of the k-th bell circle,
Figure FDA0003840493730000021
j is an intermediate variable;
step 3.2 apply B = diag (B) 11 ,B 22 ,...,B kk ,...,B NN ) Column k is updated accordingly and the other data is normalized, i.e. denoted B = diag (B) 11 ＝1,B 22 ＝1,...,B kk ＝x,...,B NN = 1), and performs a diagonal transformation, i.e.:
Figure FDA0003840493730000022
Figure FDA0003840493730000023
wherein the content of the first and second substances,
C＝A ii 2 A ik 2 -4A ii 2 A ik r ii +4A ii 2 r ii 2 +2A ii A ik 2 r ii +2A ii A ik A kk r ii -6A ii A ik r ii 2 +4r kk A ii A ik r ii -4A ii A kk r ii 2 +4A ii r ii 3 +A ik 2 r ii 2 +2A ik A kk r ii 2 -2A ik r ii 3 +4r kk A ik r ii 2 +A kk 2 r ii 2 -2A kk r ii 3 +r ii 4
A ii representing the ith row and ith column element in the system matrix, A kk Represents the kth row and kth column elements in the system matrix, A ik Row ith and column kth elements, r ii Represents the radius of the ith Gehr circle, r kk Representing the k-th radius of the bell circle.
2. The method for analyzing the characteristic value of the alternating current and direct current distribution power system based on the Gehr circle theory as claimed in claim 1, wherein the step 1 specifically comprises:
in all G 1 ,G 2 ,…,G n ,…,G N In the cover circle, wherein G n Denotes the nth Geer circle, A nn Is the center of the n-th Gaur circle and is expressed by the position of the real axis, r nn Is the radius of the nth guerre circle,
Figure FDA0003840493730000031
j is an intermediate variable, and N represents the rank of the matrix a, i.e. the total number of all geuer circles.
3. The method for analyzing the characteristic value of the alternating current-direct current power distribution system based on the Gehr circle theory as claimed in claim 2, wherein in the step 1, system characteristic root judgment is performed on any Gehr circle; when the system characteristic root with the Geoer circle is on the left half plane, or the system characteristic root with the Geoer circle is on the right half plane, the whole process is exited; otherwise, the virtual shaft is covered by the Gerr circular disc, and the step 2 is carried out; the method specifically comprises the following steps:
if any of the Gerr circles satisfies:
A nn less than or equal to 0, and A nn +r nn <0, the system characteristic roots are all in the left half plane, and the system is stable; the whole process is exited, and the calculation is finished;
if at least one Gehr circle occurs:
A nn >0, and A nn -r nn >0, the system characteristic root is in the right half plane, and the system is unstable; the whole process is exited, and the calculation is finished;
if at least one of the Gehr circles satisfies:
A nn is less than or equal to 0, and A nn +r nn >And 0, indicating that the virtual axis is covered by the Geiger circle disc, and turning to the step 2 if the virtual axis is not visually judged.
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