CN112152138B - Method and system for determining capacity of high-voltage shunt reactor - Google Patents

Method and system for determining capacity of high-voltage shunt reactor Download PDF

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CN112152138B
CN112152138B CN202011091208.0A CN202011091208A CN112152138B CN 112152138 B CN112152138 B CN 112152138B CN 202011091208 A CN202011091208 A CN 202011091208A CN 112152138 B CN112152138 B CN 112152138B
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CN112152138A (en
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郭宜果
魏鑫
刘海涛
王鹏
宋卓彦
李越
兰峰
卢福木
张春辉
邱轩宇
李宗蔚
王慧轩
李志�
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State Grid Corp of China SGCC
Economic and Technological Research Institute of State Grid Shandong Electric Power Co Ltd
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State Grid Corp of China SGCC
Economic and Technological Research Institute of State Grid Shandong Electric Power Co Ltd
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02G—INSTALLATION OF ELECTRIC CABLES OR LINES, OR OF COMBINED OPTICAL AND ELECTRIC CABLES OR LINES
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
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Abstract

The method comprises the steps of firstly determining the impedance of systems on two sides of a circuit, calculating the first line maximum overvoltage by adopting a system with higher impedance and a line no-load operation mode, judging whether the first line maximum overvoltage is less than or equal to a set maximum overvoltage multiple, if not, calculating the second line maximum overvoltage, calculating the minimum value and the corresponding capacity distribution coefficient, and finally calculating the capacities of the high-voltage shunt reactors at the head end and the tail end of the line. The system comprises: the device comprises a power system impedance determining module, a first judging module, a first line maximum overvoltage calculating module, a second judging module, a second line maximum overvoltage calculating module, a minimum value calculating module and a high-voltage shunt reactor capacity calculating module. Through the application, the power frequency overvoltage caused by the long-line capacitance effect can be effectively reduced, the overvoltage suppression effect is improved, the efficiency of the equipment is furthest exerted, and the safety and the stability of the power system are further improved.

Description

Method and system for determining capacity of high-voltage shunt reactor
Technical Field
The application relates to the technical field of long-distance power transmission in electrical engineering, in particular to a method and a system for determining capacity of a high-voltage shunt reactor.
Background
In the planning design of a long-distance transmission line power system, the overvoltage of the power system directly influences the insulation level of an electrical element and is directly related to the safe and stable operation of the power system. Along with the increase of the distance of the power transmission line, the capacitance to the ground of the line is increased, when the total capacitive impedance of the line is larger than the inductive impedance, the current flowing through the line is capacitive under the action of the electromotive force of a power supply, the voltage along the line is gradually raised, the voltage is more seriously raised closer to the tail end of the line, and the capacitance effect of the long line is generated. The long-distance line capacitance effect can form power frequency overvoltage, and the overvoltage has great influence on the stability of a power system, so that the power frequency overvoltage in the power system of the long-distance transmission line needs to be reduced.
In a long-distance power transmission line power system, a method for reducing power frequency overvoltage generally adopts a method for installing a high-voltage shunt reactor on a line, and the inductive impedance of the high-voltage shunt reactor is used for supplementing the ground capacitive impedance of the power transmission line. Research shows that the capacity of the high-voltage parallel reactors at the first end and the last end of the long-distance power transmission line is determined, and the distribution of voltage on the line is greatly influenced, so that the key problem is how to determine the capacity of the high-voltage parallel reactors when the method for installing the high-voltage parallel reactors is adopted to reduce power frequency overvoltage.
At present, when a method of installing a high-voltage shunt reactor is adopted in a power system of a long-distance power transmission line to reduce power frequency overvoltage,usually, after the line is determined, the charging power of the line can be obtained by calculating line parameters, and the line compensation degree T is determinedKThen the total capacity Q of the installed high-voltage shunt reactor can be obtainedL. The high-voltage reactors are usually installed at the head end and the tail end of a line, and the capacity of the high-voltage reactor at the head end of the line is set to be QL1The capacity of the high-voltage reactor arranged at the tail end of the line is QL2If the total capacity of the line-mounted high-voltage reactor is the sum Q of the capacities of the first end and the last endL＝QL1+QL2. The capacity of the high-voltage reactor at the head end and the tail end of the line is set to 1/2 of the total capacity of the shunt reactor, namely
Figure BDA0002722174130000011
However, in the existing method for determining the capacity of the high-voltage shunt reactor, the capacity of the high-voltage shunt reactor at the head end and the tail end of the long-distance transmission line is simply selected as the total capacity 1/2 of the high-voltage shunt reactor, the calculation result of the capacity of the high-voltage shunt reactor is not the optimal capacity, and the problem of power frequency overvoltage caused by the capacity effect of a long line cannot be sufficiently reduced. That is, the current determination method of the capacity of the high-voltage shunt reactor cannot reduce the power frequency overvoltage to the maximum extent, so that the stability of the long-distance power transmission line is poor.
Disclosure of Invention
The application provides a method and a system for determining capacity of a high-voltage shunt reactor, which are used for solving the problem that the stability of a power transmission line is poor due to the fact that power frequency overvoltage in the power transmission line cannot be sufficiently reduced by the method in the prior art.
In order to solve the technical problem, the embodiment of the application discloses the following technical scheme:
a method of determining capacity of a high voltage shunt reactor, the method comprising:
determining the impedance of the power systems on two sides of the long-distance power transmission line according to the mode of accessing the long-distance power transmission line into the power systems, wherein the power systems comprise: a first power system and a second power system, the impedance of the first power system is defined as Xs1The impedance of the second power system is Xs2；
Judging whether the impedance of the first power system and the impedance of the second power system meet: xs1＞Xs2；
If yes, disconnecting the long-distance power transmission line from the second power system, and using a formula in a way that the first power system operates in a line-carrying no-load mode
Figure BDA0002722174130000021
Calculating the first line maximum overvoltage K when the high-voltage shunt reactor is not installedN1Wherein, in the step (A),
Figure BDA0002722174130000022
Figure BDA0002722174130000023
Figure BDA0002722174130000024
l is the length of the long-distance transmission line, beta is the transmission constant of the long-distance transmission line, omega is the angular frequency of the power supply, phi is the phase angle of the power supply, and X issIs a power supply reactance, ZcIs the wave impedance of a long-distance transmission line, r0、L0、g0、C0The resistance, the inductance, the conductance and the capacitance of the long-distance transmission line are respectively the unit length;
if the maximum overvoltage K is not met, the long-distance power transmission line is disconnected with the first power system, and the first line maximum overvoltage K when the high-voltage shunt reactor is not installed is calculated in a second power system in a line no-load operation modeN1；
Judging the maximum overvoltage K along the first lineN1Whether the overvoltage is less than or equal to the set maximum overvoltage multiple KA；
If yes, the capacity of the high-voltage shunt reactor at the two ends of the long-distance power transmission line is 0;
if not, using the formula
Figure BDA0002722174130000025
Calculating the second line maximum overvoltage when the high-voltage shunt reactor is installedKN2Wherein, in the step (A),
Figure BDA0002722174130000026
Figure BDA0002722174130000027
Figure BDA0002722174130000028
Figure BDA0002722174130000029
KN2is at the same time
Figure BDA00027221741300000210
The maximum overvoltage along the line of (a),
Figure BDA00027221741300000211
is the reactance value of a reactor at the head end of the line,
Figure BDA00027221741300000212
the reactance value is the reactance value of a reactor at the end of the line;
according to the line compensation degree of the long-distance transmission line, a formula K is utilizedN＝f(M)|Tk＝TkiCalculating the maximum overvoltage K along the second lineN2Minimum value of (K)0And the corresponding value M of M0Wherein Q isL＝QL1+QL2，QL2＝MQL，QL1＝(1-M)QLDefining the degree of line compensation
Figure BDA0002722174130000031
Qc＝ωC0lUe 2M is not less than 0 and not more than 1, M is a capacity distribution coefficient, QLIs the sum of capacities at two ends of a long-distance transmission line, QL1For the capacity, Q, of the high-voltage shunt reactor at the head end of the long-distance transmission lineL2For the capacity, U, of high-voltage parallel reactor at the end of long-distance transmission lineeRated voltage for the power supply, TkiA specific value of the line compensation degree is obtained;
using formula and Q, respectivelyL1＝(1-M0)TkiωC0lUe 2And QL2＝M0TkiωC0lUe 2And calculating to obtain the capacity of the high-voltage shunt reactor at the head end and the tail end of the long-distance power transmission line.
Optionally, the determining the impedance of the power systems on two sides of the long-distance power transmission line according to the manner of accessing the long-distance power transmission line to the power system includes:
determining equivalent network diagrams of power systems on two sides of the long-distance power transmission line according to a mode of accessing the long-distance power transmission line into the power systems;
and determining the impedance of the power systems on two sides of the long-distance power transmission line according to the equivalent network map.
Optionally, the formula K is used according to the line compensation degree of the long-distance power transmission lineN＝f(M)|Tk＝TkiCalculating KN2Minimum value of (K)0And the corresponding value M of M0The method specifically comprises the following steps:
adopting a golden section method in a one-dimensional search method, and utilizing a formula K according to the line compensation degree of the long-distance transmission lineN＝f(M)|Tk＝TkiCalculating KN2Minimum value of (K)0And the corresponding value M of M0。
Optionally, the golden section method in the one-dimensional search method is adopted, and a formula K is used according to the line compensation degree of the long-distance transmission lineN＝f(M)|Tk＝TkiCalculating KN2Minimum value of (K)0And the corresponding value M of M0The method comprises the following steps:
determining an initial interval [ a, b ] of a value of a capacity distribution coefficient M and the accuracy E of numerical calculation;
according to the initial interval and accuracy and golden ratio, taking two initial calculation points m1,n1Wherein m is1＝a1+0.382(b1-a1)，n1＝a1+0.618(b1-a1)；
According to the functional relationship K between the maximum overvoltage and the capacity distribution coefficientN＝f(M)|Tk＝TkiCalculating f (m)1),f(n1) Wherein k is 1;
if f (m)k)≤f(nk) Definition of ak+1＝ak,bk+1＝nk,nk+1＝mk,f(nk+1)＝f(mk),mk+1＝ak+1+0.382(bk+1-ak+1) Calculating f (m)k+1)；
If f (m)k)>f(nk) Definition of ak+1＝mk,bk+1＝bk,mk+1＝nk,f(mk+1)＝f(nk),nk+1＝ak+1+0.618(bk+1-ak+1) Calculating f (n)k+1)；
Judgment bk+1-ak+1Whether the epsilon is not larger than the set value or not is judged;
if so, using a formula
Figure BDA0002722174130000041
And K0＝f(M0) Calculating to obtain M0And K0Wherein, K is0The minimum value of the maximum overvoltage along the second line is obtained;
if not, defining k as k +1, and recalculating new judgment f (m)k+1) And f (n)k+1) Until K is determinedNMinimum value of (K)0And according to K0Determining a corresponding M0。
A system for determining the capacity of a high voltage shunt reactor, the system comprising:
the power system impedance determination module is used for determining the impedance of the power systems on two sides of the long-distance power transmission line according to the mode that the long-distance power transmission line is connected into the power system, wherein the power system comprises: a first power system and a second power system, the impedance of the first power system is defined as Xs1The impedance of the second power system is Xs2；
A first judging module for judging the first powerWhether the impedance of the force system and the impedance of the second power system satisfy: xs1＞Xs2；
A first line maximum overvoltage calculation module for Xs1＞Xs2When the power system is in the idle running mode, the long-distance power transmission line is disconnected with the second power system, and the first power system is in the idle running mode with the line, and the formula is used
Figure BDA0002722174130000042
Calculating the maximum overvoltage K along the line when the high-voltage shunt reactor is not installedN1Wherein, in the step (A),
Figure BDA0002722174130000043
Figure BDA0002722174130000044
Figure BDA0002722174130000045
l is the length of the long-distance transmission line, beta is the transmission constant of the long-distance transmission line, omega is the angular frequency of the power supply, phi is the phase angle of the power supply, and X issIs a power supply reactance, ZcIs the wave impedance of a long-distance transmission line, r0、L0、g0、C0Resistance, inductance, conductance and capacitance, respectively, per unit length of the long-distance transmission line, and, Xs1≤Xs2And disconnecting the long-distance power transmission line from the first power system, and calculating the maximum overvoltage K along the line when the high-voltage shunt reactor is not installed in a no-load operation mode of the second power system with the lineN1；
The second judgment module is used for judging the maximum overvoltage K along the first lineN1Whether the overvoltage is less than or equal to the set maximum overvoltage multiple KAIf yes, judging that the capacity of the high-voltage shunt reactor at the two ends of the long-distance power transmission line is 0;
a second maximum overvoltage calculation module along the first line, which is used for calculating the maximum overvoltage K along the first lineN1> set maximum overvoltage multiple KAUsing a formula
Figure BDA0002722174130000046
Calculating the second line maximum overvoltage K when the high-voltage shunt reactor is installedN2Wherein, in the step (A),
Figure BDA0002722174130000047
Figure BDA0002722174130000048
Figure BDA0002722174130000049
Figure BDA00027221741300000410
KN2is at the same time
Figure BDA00027221741300000411
The maximum overvoltage along the line of (a),
Figure BDA00027221741300000412
is the reactance value of a reactor at the head end of the line,
Figure BDA00027221741300000413
the reactance value is the reactance value of a reactor at the end of the line;
a minimum value calculation module for utilizing formula K according to the line compensation degree of the long-distance transmission lineN＝f(M)|Tk＝TkiCalculating KN2Minimum value of (K)0And the corresponding value M of M0Wherein Q isL＝QL1+QL2，QL2＝MQL，QL1＝(1-M)QLDefining the degree of line compensation
Figure BDA0002722174130000051
Qc＝ωC0lUe 2M is not less than 0 and not more than 1, M is a capacity distribution coefficient, QLIs the sum of capacities at two ends of a long-distance transmission line, QL1For the capacity, Q, of the high-voltage shunt reactor at the head end of the long-distance transmission lineL2For high voltage at the end of long-distance transmission lineCapacity of reactor, UeRated voltage for the power supply, TkiA specific value of the line compensation degree is obtained;
a high-voltage shunt reactor capacity calculation module for respectively using a formula and QL1＝(1-M0)TkiωC0lUe 2And QL2＝M0TkiωC0lUe 2And calculating to obtain the capacity of the high-voltage shunt reactor at the head end and the tail end of the long-distance power transmission line.
Optionally, the power system impedance determination module comprises:
the equivalent network graph establishing unit is used for establishing equivalent network graphs of the power systems on two sides of the long-distance power transmission line according to the mode that the long-distance power transmission line is connected into the power system;
and the impedance determining unit is used for determining the impedance of the power systems on two sides of the long-distance power transmission line according to the equivalent network map.
Optionally, the minimum value calculating module is configured to use a golden section method in the one-dimensional search method, according to the line compensation degree of the long-distance power transmission line, and according to a formula KN＝f(M)|Tk＝TkiCalculating KN2Minimum value of (K)0And the corresponding value M of M0。
Optionally, the minimum value calculating module includes:
the initial interval and accuracy determining unit is used for determining the initial interval [ a, b ] of the value of the capacity distribution coefficient M and the accuracy E of numerical calculation;
golden section calculating point determining unit for taking the first two calculating points m according to golden section ratio based on the initial interval and accuracy1,n1Wherein m is1＝a1+0.382(b1-a1)，n1＝a1+0.618(b1-a1)；
A first calculation unit for calculating a function K of the maximum overvoltage and the capacity distribution coefficientN＝f(M)|Tk＝TkiCalculating f (m)1),f(n1) Wherein k is 1;
a second calculation unit for calculating f (m)k)≤f(nk) When, define
ak+1＝ak,bk+1＝nk,nk+1＝mk,f(nk+1)＝f(mk),mk+1＝ak+1+0.382(bk+1-ak+1) Calculating f (m)k+1)；
A third calculation unit for calculating f (m)k)>f(nk) When, define ak+1＝mk,bk+1＝bk,mk+1＝nk,f(mk+1)＝f(nk),nk+1＝ak+1+0.618(bk+1-ak+1) Calculating f (n)k+1)；
A judging unit for judging bk+1-ak+1Whether the epsilon is not larger than the set value or not is judged;
a fourth calculation unit for calculating bk+1-ak+1When the content is less than or equal to the content, utilizing a formula
Figure BDA0002722174130000061
And K0＝f(M0) Calculating to obtain M0And K0Wherein, K is0The minimum value of the maximum overvoltage along the second line is obtained;
a circulation unit for when bk+1-ak+1When ≦ epsilon is not set, defining k as k +1, and recalculating new judgment f (m)k+1) And f (n)k+1) Until K is determinedNMinimum value of (K)0And according to K0Determining a corresponding M0。
The technical scheme provided by the embodiment of the application can have the following beneficial effects:
the application provides a method for determining the capacity of a high-voltage shunt reactor, which comprises the steps of firstly determining the impedance of systems at two sides of a circuit according to the mode of accessing a long-distance transmission line into a power system, secondly, according to the relation between the two impedances, the power system on the side with smaller impedance is disconnected, the power system with larger impedance is adopted with a line no-load operation mode, the maximum overvoltage along the line when the high-voltage shunt reactor is not installed is calculated by using a formula and is defined as the first maximum overvoltage along the line, then judging whether the maximum overvoltage along the first line is less than or equal to the set maximum overvoltage multiple, if not, calculating the maximum overvoltage along the second line when the high-voltage shunt reactor is installed by using a formula, and according to the line compensation degree, utilizing formula to calculate minimum value of maximum overvoltage along the second line and correspondent capacity distribution coefficient, finally, and (4) respectively calculating the capacities of the high-voltage shunt reactors at the head end and the tail end of the long-distance transmission line by using a formula. In the embodiment, the impedances of the two side systems are determined by combining the specific mode that the long-distance transmission line is connected into the power system, and the no-load operation mode of the power system with the line at the side with the larger impedance is selected according to the impedances at the two sides, so that the practical application scene of the long-distance transmission line can be considered, and the optimal capacity can be selected. And the embodiment respectively calculates the maximum overvoltage along the first line when the high-voltage shunt reactor is not installed and the maximum overvoltage along the second line when the high-voltage shunt reactor is installed, and finally calculates the minimum value of the maximum overvoltage along the second line and the corresponding capacity distribution coefficient by using a formula according to the line compensation degree, thereby providing parameter basis for further accurately calculating the capacity of the high-voltage shunt reactor at the head end and the tail end of the long-distance transmission line, being beneficial to optimizing the capacity of the high-voltage shunt reactor, effectively reducing power frequency overvoltage caused by the capacitance effect of the long line, improving the overvoltage suppression effect, exerting the equipment efficiency to the maximum extent, and further improving the safety and the stability of the power system. In addition, for the same protection effect, the optimized capacity distribution mode of the head-end and tail-end high-voltage shunt reactors is adopted in the embodiment, so that the total capacity of the high-voltage shunt reactors can be effectively reduced, the engineering investment is saved, and better economic benefit is achieved.
The application also provides a system for determining the capacity of the high-voltage shunt reactor, which mainly comprises: the device comprises a power system impedance determining module, a first judging module, a first line maximum overvoltage calculating module, a second judging module, a second line maximum overvoltage calculating module, a minimum value calculating module and a high-voltage shunt reactor capacity calculating module. Through the first line maximum overvoltage calculation module, the second line maximum overvoltage calculation module and the minimum calculation module, the calculation accuracy of the capacity of the high-voltage shunt reactor at the head end and the tail end of the long-distance power transmission line can be effectively improved, and the capacity of the high-voltage shunt reactor can be optimized, so that the power frequency overvoltage caused by the capacitance effect of a long line is effectively reduced, the overvoltage suppression effect is improved, the efficiency of equipment is exerted to the maximum extent, and the safety and the stability of a power system are further improved. In addition, the capacity of the head-end and tail-end high-voltage shunt reactors is optimized, so that the total capacity of the high-voltage shunt reactors can be effectively reduced, the engineering investment is saved, and the economic benefit is improved.
It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the application.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the present application and together with the description, serve to explain the principles of the application.
In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, and it is obvious for those skilled in the art that other drawings can be obtained according to the drawings without creative efforts.
Fig. 1 is a schematic flowchart of a method for determining capacity of a high-voltage shunt reactor according to an embodiment of the present disclosure;
fig. 2 is a schematic diagram of a distributed parameter power transmission line model in an embodiment of the present application;
FIG. 3 is an equivalent network diagram of two sides of the power transmission line in the embodiment of the application;
FIG. 4 is a power frequency voltage calculation model of a long-distance transmission line without a high-voltage shunt reactor;
FIG. 5 is a power frequency voltage calculation model of a long-distance transmission line with high-voltage shunt reactors mounted at two ends;
FIG. 6 is a schematic diagram of an equivalent network of an offshore wind turbine generator set when the wind turbine generator set is connected to an electric power system;
fig. 7 is a schematic structural diagram of a system for determining the capacity of a high-voltage shunt reactor according to an embodiment of the present application.
Detailed Description
In order to make those skilled in the art better understand the technical solutions in the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application, and it is obvious that the described embodiments are only a part of the embodiments of the present application, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present application.
For a better understanding of the present application, embodiments of the present application are explained in detail below with reference to the accompanying drawings.
Example one
Referring to fig. 1, fig. 1 is a schematic flowchart of a method for determining a capacity of a high-voltage shunt reactor according to an embodiment of the present application. As can be seen from fig. 1, the method for determining the capacity of the high-voltage shunt reactor in this embodiment mainly includes the following steps:
s1: and determining the impedance of the power systems on two sides of the long-distance power transmission line according to the mode of accessing the long-distance power transmission line into the power systems.
The power system in this embodiment includes: a first power system and a second power system, the impedance of the first power system is defined as Xs1The impedance of the second power system is Xs2。
Specifically, step S1 in this embodiment includes the following processes:
s11: and determining equivalent network diagrams of the power systems on two sides of the long-distance power transmission line according to the mode of accessing the long-distance power transmission line into the power systems.
In this embodiment, the distribution parameters of each line mainly include: resistance, inductance, conductance and capacitance of each phase of transmission line. Assuming that the resistance, inductance, conductance and capacitance of each phase of power transmission line are uniformly distributed along the lineThe parametric power transmission line model can be seen in fig. 2. In FIG. 2, r0，L0，g0，C0Respectively representing the resistance, inductance, conductance and capacitance of the line per unit length.
With reference to the distribution parameters in fig. 2, according to the manner of accessing the long-distance transmission line to the power system, the equivalent network diagrams of the power systems on both sides of the long-distance transmission line are determined, as shown in fig. 3. The system on both sides of the power transmission line in fig. 3 includes: system 1 and system 2, system 1 being the first power system, the impedance is: xs1 System 2, the second power system, has an impedance of: xs2. A and B represent the two sides of the transmission line respectively: a terminal A and a terminal B.
S12: and determining the impedance of the power systems on two sides of the long-distance power transmission line according to the equivalent network map.
According to the equivalent network diagram shown in fig. 2, a wave equation can be established for the long-distance transmission line:
Figure BDA0002722174130000081
for the high-voltage transmission line, generally, the inductive impedance of the line is far larger than the resistance, so that the resistance can be ignored during analysis, and the analysis is performed according to the wireless transmission line. The voltage and the current of the head end of the long-distance transmission line are defined as follows:
Figure BDA0002722174130000082
the voltage and the current at the tail end of the long-distance transmission line are respectively as follows:
Figure BDA0002722174130000083
solving the wave equation in (1) can obtain:
Figure BDA0002722174130000084
wherein x is the length of the line from the end of the line,
Figure BDA0002722174130000085
Figure BDA0002722174130000086
Figure BDA0002722174130000087
is the voltage at any one point of the voltage,
Figure BDA0002722174130000088
is the current of any point, beta is the transmission constant of the long-distance transmission line, omega is the angular frequency of the power supply, phi is the phase angle of the power supply, and XsIs a power supply reactance, ZcThe wave impedance of the long-distance transmission line.
As can be seen from fig. 1, after determining the impedance of the power system on both sides of the long-distance power transmission line, step S2 is executed: judging whether the impedance of the first power system and the impedance of the second power system meet: xs1＞Xs2。
If X iss1＞Xs2Step S3 is executed: disconnecting the long-distance transmission line from the second power system, and using a formula to realize the no-load operation mode of the first power system with the line
Figure BDA0002722174130000091
Calculating the first line maximum overvoltage K when the high-voltage shunt reactor is not installedN1。
Wherein the content of the first and second substances,
Figure BDA0002722174130000092
Figure BDA0002722174130000093
Figure BDA0002722174130000094
l is the length of the long-distance transmission line, beta is the transmission constant of the long-distance transmission line, omega is the angular frequency of the power supply, phi is the phase angle of the power supply, and X issIs a power supply reactance, ZcIs the wave impedance of a long-distance transmission line, r0、L0、g0、C0Respectively a resistance, an inductance, a conductance and a capacitance of a long-distance transmission line unit length.
If X iss1≤Xs2Step S4 is executed: disconnecting the long-distance power transmission line from the first power system, and calculating the first line maximum overvoltage K when the high-voltage shunt reactor is not installed in a second power system in a line no-load operation modeN1。
Comparing the system impedance values of the two sides of the long-distance power transmission line through the step S2, selecting one side with larger system impedance through the steps S3 and S4, and disconnecting the other side by adopting a no-load operation mode of the strip line. As can be seen from FIG. 3, the value Xs1＞Xs2For example, if the impedance value of the end a is large, the selected line is disconnected from the system 2 at the end B, the calculation is performed only in the no-load operation mode of the system 1 with the line, and a calculation model that the line is not provided with a high-voltage shunt reactor is established.
According to fig. 4, assume the power supply reactance is XsElectromotive force of power supply of
Figure BDA0002722174130000095
The length of the line is l, if the end of the line is open, then
Figure BDA0002722174130000096
According to the formula (2), the following relationship exists:
Figure BDA0002722174130000097
definition of
Figure BDA0002722174130000098
Then:
Figure BDA0002722174130000099
from equation (2), for any point on the line, it can be calculated:
Figure BDA00027221741300000910
according to equation (6), the maximum voltage value on the line occurs at the end of the line (x is 0), and the maximum voltage is:
Figure BDA0002722174130000101
the maximum overvoltage multiple on the line at this time is:
Figure BDA0002722174130000102
in combination with equation (7), it can be calculated:
Figure BDA0002722174130000103
in this embodiment, the maximum overvoltage multiple K is determined according to the voltage class of the long-distance power transmission line system and the set insulation specificationA. Here, K in the formula (8)NNamely the maximum overvoltage K along the first lineN1. Power supply reactance XsThe larger the maximum overvoltage multiple is.
With continued reference to FIG. 1, a formula is utilized
Figure BDA0002722174130000104
Calculating the first line maximum overvoltage K when the high-voltage shunt reactor is not installedN1After that, step S5 is executed: judging the maximum overvoltage K along the first lineN1Whether the overvoltage is less than or equal to the set maximum overvoltage multiple KA。
If the first maximum along-line overvoltage KN1Less than or equal to the set maximum overvoltage multiple KANamely: kN1≤KAStep S6 is executed: long-distance transmission lineAnd (5) ending the calculation when the capacity of the high-voltage parallel reactor at the two ends of the line is 0.
If K isN1>KAStep S7 is executed: using formulas
Figure BDA0002722174130000105
Calculating the second line maximum overvoltage K when the high-voltage shunt reactor is installedN2。
Wherein the content of the first and second substances,
Figure BDA0002722174130000106
Figure BDA0002722174130000107
Figure BDA0002722174130000108
Figure BDA0002722174130000109
KN2is at the same time
Figure BDA00027221741300001010
The maximum overvoltage along the line of (a),
Figure BDA00027221741300001011
is the reactance value of a reactor at the head end of the line,
Figure BDA00027221741300001012
is the reactance value of the line end reactor.
That is, when KN>KAIn the present embodiment, a power frequency voltage calculation model of a long-distance transmission line with high-voltage shunt reactors mounted at two ends is shown in fig. 5.
According to fig. 5, it is assumed that the reactance of the reactor at the head end of the line is of value
Figure BDA00027221741300001013
The reactance value of the end reactor is
Figure BDA00027221741300001014
In the case of the end of the line at this time,
Figure BDA00027221741300001015
according to the formula (2), the following relationship exists:
Figure BDA00027221741300001016
defining:
Figure BDA00027221741300001017
Figure BDA0002722174130000111
then:
Figure BDA0002722174130000112
according to equation (2), for any point on the line:
Figure BDA0002722174130000113
defining:
Figure BDA0002722174130000114
then:
Figure BDA0002722174130000115
in that
Figure BDA0002722174130000116
The voltage value is maximum, and the maximum voltage is:
Figure BDA0002722174130000117
the maximum overvoltage multiple K on the line should not be higher than the permissible overvoltage multiple KA：
Figure BDA0002722174130000118
K≤KA
K in the formula (16) is the maximum overvoltage K along the second lineN2。
With continued reference to fig. 1, it can be seen that the second in-line maximum overvoltage K is determined when installing the high-voltage shunt reactorN2After that, step S8 is executed: according to the line compensation degree of the long-distance transmission line, a formula K is utilizedN＝f(M)|Tk＝TkiCalculating the maximum overvoltage K along the second lineN2Minimum value of (K)0And the corresponding value M of M0。
Wherein Q isLIs the sum of capacities at two ends of a long-distance transmission line, QL1For the capacity, Q, of the high-voltage shunt reactor at the head end of the long-distance transmission lineL2For the capacity, U, of high-voltage parallel reactor at the end of long-distance transmission lineeRated voltage for the power supply, TkiIs a specific value of the line compensation degree. Cable compensation degree T in the embodimentkGenerally, the value is 0.6-0.9. The initial value, T, may be determined first during the calculationkiTake the appropriate calculation step Δ T equal to 0.6kCalculating Tki+1＝Tki+ΔTk。
QL＝QL1+QL2，QL2＝MQL，QL1＝(1-M)QLThat is: high-voltage shunt reactors are usually installed at the head end and the tail end of a power transmission line, and the capacity of the high-voltage reactor at the head end of the power transmission line is set to be QL1The capacity of the high-voltage reactor arranged at the tail end of the line is QL2Then the line is installedThe total capacity of the high-voltage reactor is the sum Q of the capacities of the first end and the last endL＝QL1+QL2. Make circuit end compensate high-voltage reactor capacity QL2＝MQLThen the head end of the line compensates the high-voltage reactor with the capacity of QL1＝(1-M)QL。
Definition of degree of line compensation
Figure BDA0002722174130000119
Qc＝ωC0lUe 2M is more than or equal to 0 and less than or equal to 1, and M is a capacity distribution coefficient. Then there are:
Figure BDA0002722174130000121
formula (17) is substituted for formulae (10) and (13):
Figure BDA0002722174130000122
the maximum overvoltage multiple K on the circuit is obtained by substituting the formula (18) into the formula (16) and is related to M, Tk,ω,C0,l,β,Zc,XsI.e. K ═ f (M, T)k,ω,C0,l,β,Zc,Xs)。
Specifically, step S8 may be implemented as follows:
adopting a golden section method in a one-dimensional search method, and utilizing a formula K according to the line compensation degree of the long-distance transmission lineN＝f(M)|Tk＝TkiCalculating KN2Minimum value of (K)0And the corresponding value M of M0。
In this embodiment, f (M) is a unitary complex function, the value range of the variable M is known, and the value of f (M) can be compared by using a one-dimensional search method, so as to gradually reduce the value space and obtain the value of M meeting the accuracy. The minimum value K is obtained by calculation0And the corresponding value M of M0The optimal M value can be obtained, so that the shunt reactor installed on the long-distance power transmission line can be enabled to play a roleThe optimal effect is beneficial to improving the accuracy of the calculation result and the stability of the system.
Further, the process of step S8 using the golden section method is as follows:
s81: and determining an initial interval [ a, b ] of the value of the capacity distribution coefficient M and the accuracy E of numerical calculation.
S82: according to the initial interval and accuracy and golden ratio, taking two initial calculation points m1,n1Wherein m is1＝a1+0.382(b1-a1)，n1＝a1+0.618(b1-a1)。
S83: according to the functional relationship K between the maximum overvoltage and the capacity distribution coefficientN＝f(M)|Tk＝TkiCalculating f (m)1),f(n1) Wherein k is 1.
S84: if f (m)k)≤f(nk) Definition of
ak+1＝ak,bk+1＝nk,nk+1＝mk,f(nk+1)＝f(mk),mk+1＝ak+1+0.382(bk+1-ak+1) Calculating f (m)k+1)。
S85: if f (m)k)>f(nk) Definition of ak+1＝mk,bk+1＝bk,mk+1＝nk,f(mk+1)＝f(nk),nk+1＝ak+1+0.618(bk+1-ak+1) Calculating f (n)k+1)。
S86: judgment bk+1-ak+1Whether the epsilon is not more than the set value or not is judged.
S87: if so, using a formula
Figure BDA0002722174130000131
And K0＝f(M0) Calculating to obtain M0And K0Wherein, K is0The minimum value of the maximum overvoltage along the second line is obtained.
S88: if not, defining k as k +1, and recalculating new judgmentF (m) is brokenk+1) And f (n)k+1) Until K is determinedNMinimum value of (K)0And according to K0Determining a corresponding M0。
The embodiment adopts the golden section method, the algorithm is simple, the derivative of the function does not need to be solved, the calculation efficiency is favorably improved, and the efficiency and the calculation accuracy of the capacity calculation of the high-voltage shunt reactor are further improved.
With continued reference to FIG. 1, the second in-line maximum overvoltage K is calculatedN2Minimum value of (K)0And the corresponding value M of M0After that, step S9 is executed: using formula and Q, respectivelyL1＝(1-M0)TkiωC0lUe 2And QL2＝M0TkiωC0lUe 2And calculating to obtain the capacity of the high-voltage shunt reactor at the head end and the tail end of the long-distance power transmission line.
Now, taking an offshore wind turbine generator set connected to a power system as an example, the method in the embodiment of the present application is used to perform calculation, and a specific implementation manner of the method in the embodiment in practical application is described.
After the wind power plant is boosted to 220kV voltage level, a wind power plant is divided into 3 multiplied by 500mm2The submarine cable is connected into a power system, the length of the cable is 120km, the equivalent impedance of a wind power plant side system is 65 omega, and the equivalent impedance of the system side is 150 omega. The method provided by the invention is used for calculating the capacity of the high-voltage shunt reactor at two ends of the line and comparing the capacity with the general method for configuring the high-voltage shunt reactor at two ends of the line with equal capacity as follows:
the method comprises the following steps: an iso-network map is created as shown in fig. 6.
Step two: xs1>Xs2Disconnecting the line from the system 2 at the end B, and establishing a calculation model of the line without installing a high-voltage shunt reactor; according to the line structure and the characteristics of the power system, the omega and the C are obtained0,l,β,ZcAnd the like.
The parameter calculations are shown in table 1:
Figure BDA0002722174130000132
Figure BDA0002722174130000141
TABLE 1 Power Transmission line parameter Table
Step three: selecting the maximum overvoltage multiple K allowed to occurA1.3, calculating the maximum overvoltage K along the line when the high-voltage shunt reactor is not installedN＝5.73。
Step four: comparison KNAnd KA，KN>KAIf the overvoltage value does not meet the allowable value, shunt reactors need to be installed at two ends of the circuit.
Step five: and establishing a calculation model of installing high-voltage shunt reactors at two ends of the line. Setting a line compensation Tk. Determining an initial value, Tk1Take the appropriate calculation step Δ T equal to 0.6k(ΔTk＝0.05)，Tki+1＝Tki+ΔTk。
Step six: calculate the correspondence TkiThe functional relationship K ═ f (M) T of the maximum overvoltage value K and the capacity distribution coefficient Mk＝TkiThe golden section method is adopted to obtain the minimum value K ═ K0And the corresponding value M of M0。
And comparing and calculating the maximum overvoltage value K of the line when the high-voltage shunt reactor is configured at two ends of the line in equal capacity.
Step seven: calculated, K at iteration 30＝1.22046，K0≤KA。
Step eight: obtaining the values of the reactance values of the high-voltage shunt reactor reactors at the first and the last ends of the line as follows:
QL2＝163.68Mvar,QL1＝23.16Mvar
the iterative calculation process of the sixth step and the seventh step is shown in table 2:
Figure BDA0002722174130000142
TABLE 2 iterative computation Process Table
As can be seen from Table 2, when the total method of the present embodiment is adopted, the capacity allocation of the final reactor is 0.876Q when the line compensation degree is 0.8L163.68Mvar, head end reactor capacity allocation of 0.124QL23.16Mvar, the maximum value of the overvoltage on the line is 1.22 times, namely the overvoltage exceeds the rated voltage by 0.22 time, and the requirement of an allowable value is met; when the conventional equal-capacity configuration is adopted, the capacities of the reactors at the first end and the last end of the line are both 93.42Mvar, and the maximum value of overvoltage on the line is 1.26 times and exceeds the rated voltage by 0.26 time. Compared with the conventional method, the reactor capacity configuration method provided by the embodiment can reduce the overvoltage by 17.78% under the condition of equal compensation capacity, effectively improve the overvoltage reduction effect of the shunt reactor and improve the reliability of the operation of a power system.
Example two
Referring to fig. 7 on the basis of the embodiments shown in fig. 1 to fig. 6, fig. 7 is a schematic structural diagram of a system for determining the capacity of a high-voltage shunt reactor according to an embodiment of the present application. As can be seen from fig. 7, the system for determining the capacity of the high-voltage shunt reactor in the present embodiment mainly includes: the device comprises a power system impedance determining module, a first judging module, a first line maximum overvoltage calculating module, a second judging module, a second line maximum overvoltage calculating module, a minimum value calculating module and a high-voltage shunt reactor capacity calculating module.
The power system impedance determination module is used for determining the impedance of the power systems on two sides of the long-distance power transmission line according to the mode that the long-distance power transmission line is connected into the power system, wherein the power system comprises: a first power system and a second power system, the impedance of the first power system is defined as Xs1The impedance of the second power system is Xs2. The first judging module is used for judging whether the impedance of the first power system and the impedance of the second power system meet the following conditions: xs1＞Xs2. A first line maximum overvoltage calculation module for Xs1＞Xs2When the first power system is in the idle state, the long-distance power transmission line is disconnected with the second power system, and the first power system is used for carrying out power transmission in the idle stateOperating mode by means of formula
Figure BDA0002722174130000151
Calculating the maximum overvoltage K along the line when the high-voltage shunt reactor is not installedN1Wherein, in the step (A),
Figure BDA0002722174130000152
Figure BDA0002722174130000153
Figure BDA0002722174130000154
l is the length of the long-distance transmission line, beta is the transmission constant of the long-distance transmission line, omega is the angular frequency of the power supply, phi is the phase angle of the power supply, and X issIs a power supply reactance, ZcIs the wave impedance of a long-distance transmission line, r0、L0、g0、C0Resistance, inductance, conductance and capacitance, respectively, per unit length of the long-distance transmission line, and, Xs1≤Xs2And disconnecting the long-distance power transmission line from the first power system, and calculating the maximum overvoltage K along the line when the high-voltage shunt reactor is not installed in a no-load operation mode of the second power system with the lineN1. The second judgment module is used for judging the maximum overvoltage K along the first lineN1Whether the overvoltage is less than or equal to the set maximum overvoltage multiple KAAnd if so, judging that the capacity of the high-voltage shunt reactor at the two ends of the long-distance power transmission line is 0. A second maximum overvoltage calculation module along the first line for calculating the maximum overvoltage K along the first lineN1> set maximum overvoltage multiple KAUsing a formula
Figure BDA0002722174130000155
Calculating the second line maximum overvoltage K when the high-voltage shunt reactor is installedN2Wherein, in the step (A),
Figure BDA0002722174130000156
Figure BDA0002722174130000157
Figure BDA0002722174130000158
Figure BDA0002722174130000159
Figure BDA00027221741300001510
KN2is at the same time
Figure BDA00027221741300001511
The maximum overvoltage along the line of (a),
Figure BDA00027221741300001512
is the reactance value of a reactor at the head end of the line,
Figure BDA00027221741300001513
is the reactance value of the line end reactor. A minimum value calculation module for utilizing formula K according to the line compensation degree of the long-distance transmission lineN＝f(M)|Tk＝TkiCalculating KN2Minimum value of (K)0And the corresponding value M of M0Wherein Q isL＝QL1+QL2，QL2＝MQL，QL1＝(1-M)QLDefining the degree of line compensation
Figure BDA0002722174130000161
Qc＝ωC0lUe 2M is not less than 0 and not more than 1, M is a capacity distribution coefficient, QLIs the sum of capacities at two ends of a long-distance transmission line, QL1For the capacity, Q, of the high-voltage shunt reactor at the head end of the long-distance transmission lineL2For the capacity, U, of high-voltage parallel reactor at the end of long-distance transmission lineeRated voltage for the power supply, TkiA specific value of the line compensation degree is obtained; a high-voltage shunt reactor capacity calculation module for respectively using a formula and QL1＝(1-M0)TkiωC0lUe 2And QL2＝M0TkiωC0lUe 2And calculating to obtain the capacity of the high-voltage shunt reactor at the head end and the tail end of the long-distance power transmission line.
Further, the power system impedance determination module includes: the equivalent network map establishing unit and the impedance determining unit. The system comprises an equivalent network graph establishing unit, a network configuration unit and a network configuration unit, wherein the equivalent network graph establishing unit is used for establishing equivalent network graphs of electric power systems on two sides of a long-distance transmission line according to a mode that the long-distance transmission line is connected into the electric power system; and the impedance determination unit is used for determining the impedance of the power systems on two sides of the long-distance power transmission line according to the equivalent network map.
The minimum value calculation module adopts a golden section method in a one-dimensional search method, and utilizes a formula K according to the line compensation degree of the long-distance power transmission lineN＝f(M)|Tk＝TkiCalculating KN2Minimum value of (K)0And the corresponding value M of M0。
Further, the minimum value calculation module further comprises: the device comprises an initial interval and accuracy determining unit, a golden section calculating point determining unit, a first calculating unit, a second calculating unit, a third calculating unit, a judging unit, a fourth calculating unit and a circulating unit.
Wherein, the initial interval and accuracy determining unit is used for determining the initial interval [ a, b ] of the value of the capacity distribution coefficient M]And the accuracy e of the numerical calculation. A golden section calculation point determining unit for taking the first two calculation points m according to the golden section ratio based on the initial interval and the accuracy1,n1Wherein m is1＝a1+0.382(b1-a1)，n1＝a1+0.618(b1-a1). A first calculation unit for calculating a function K of the maximum overvoltage and the capacity distribution coefficientN＝f(M)|Tk＝TkiCalculating f (m)1),f(n1) Wherein k is 1. A second calculation unit for calculating f (m)k)≤f(nk) When, define ak+1＝ak,bk+1＝nk,nk+1＝mk,f(nk+1)＝f(mk),mk+1＝ak+1+0.382(bk+1-ak+1) Calculating f (m)k+1). A third calculation unit for calculating f (m)k)>f(nk) When, define ak+1＝mk,bk+1＝bk,mk+1＝nk,f(mk+1)＝f(nk),nk+1＝ak+1+0.618(bk+1-ak+1) Calculating f (n)k+1). A judging unit for judging bk+1-ak+1Whether the epsilon is not more than the set value or not is judged. A fourth calculation unit for calculating bk+1-ak+1When the content is less than or equal to the content, utilizing a formula
Figure BDA0002722174130000162
And K0＝f(M0) Calculating to obtain M0And K0Wherein, K is0The minimum value of the maximum overvoltage along the second line is obtained. A circulation unit for when bk+1-ak+1When ≦ epsilon is not set, defining k as k +1, and recalculating new judgment f (m)k+1) And f (n)k+1) Until K is determinedNMinimum value of (K)0And according to K0Determining a corresponding M0。
The working principle and the working method of the system for determining the capacity of the high-voltage shunt reactor in the embodiment are already described in detail in the embodiments shown in fig. 1 to 6, and the two embodiments can be referred to each other and are not described again.
The above description is merely exemplary of the present application and is presented to enable those skilled in the art to understand and practice the present application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the application. Thus, the present application is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims (8)

1. A method of determining the capacity of a high voltage shunt reactor, the method comprising:
determining the impedance of the power systems on two sides of the long-distance power transmission line according to the mode of accessing the long-distance power transmission line into the power systems, wherein the power systems comprise: a first power system and a second power system, the impedance of the first power system is defined as Xs1The impedance of the second power system is Xs2；
Judging whether the impedance of the first power system and the impedance of the second power system meet: xs1＞Xs2；
If yes, disconnecting the long-distance power transmission line from the second power system, and using a formula in a way that the first power system operates in a line-carrying no-load mode
Figure FDA0003198244010000011
Calculating the first line maximum overvoltage multiple K when the high-voltage shunt reactor is not installedN1Wherein, in the step (A),
Figure FDA0003198244010000012
l is the length of the long-distance transmission line, beta is the transmission constant of the long-distance transmission line, omega is the angular frequency of the power supply, phi is the phase angle of the power supply, and X issIs a power supply reactance, ZcIs the wave impedance of a long-distance transmission line, r0、L0、g0、C0The resistance, the inductance, the conductance and the capacitance of the long-distance transmission line are respectively the unit length;
if the maximum overvoltage multiple K is not met, the long-distance power transmission line is disconnected with the first power system, and the first line maximum overvoltage multiple K when the high-voltage shunt reactor is not installed is calculated in a second power system line no-load operation modeN1；
Judging the maximum overvoltage multiple K along the first lineN1Whether the overvoltage is less than or equal to the set maximum overvoltage multiple KA；
If yes, the capacity of the high-voltage shunt reactor at the two ends of the long-distance power transmission line is 0;
if not, using the formula
Figure FDA0003198244010000013
Calculating the second line maximum overvoltage multiple K when the high-voltage shunt reactor is installedN2Wherein, in the step (A),
Figure FDA0003198244010000014
Figure FDA0003198244010000015
KN2is at the same time
Figure FDA0003198244010000016
The maximum overvoltage multiple along the line of the point,
Figure FDA0003198244010000017
is the reactance value of a reactor at the head end of the line,
Figure FDA0003198244010000018
the reactance value is the reactance value of a reactor at the end of the line;
according to the line compensation degree of the long-distance transmission line, a formula K is utilizedN＝f(M)|Tk＝TkiCalculating the maximum overvoltage multiple K along the second lineN2Minimum value of (K)0And the corresponding value M of M0Wherein Q isL＝QL1+QL2，QL2＝MQL，QL1＝(1-M)QLDefining the degree of line compensation
Figure FDA0003198244010000021
Qc＝ωC0lUe 2M is not less than 0 and not more than 1, M is a capacity distribution coefficient, QLIs the sum of capacities at two ends of a long-distance transmission line, QL1For the capacity, Q, of the high-voltage shunt reactor at the head end of the long-distance transmission lineL2For the capacity, U, of high-voltage parallel reactor at the end of long-distance transmission lineeRated voltage for the power supply, TkiA specific value of the line compensation degree is obtained;
using formula and Q, respectivelyL1＝(1-M0)TkiωC0lUe 2And QL2＝M0TkiωC0lUe 2And calculating to obtain the capacity of the high-voltage shunt reactor at the head end and the tail end of the long-distance power transmission line.
2. The method for determining the capacity of the high-voltage shunt reactor according to claim 1, wherein the determining the impedance of the power systems on two sides of the long-distance power transmission line according to the way of accessing the long-distance power transmission line into the power systems comprises:
determining equivalent network diagrams of power systems on two sides of the long-distance power transmission line according to a mode of accessing the long-distance power transmission line into the power systems;
and determining the impedance of the power systems on two sides of the long-distance power transmission line according to the equivalent network map.
3. The method for determining the capacity of the high-voltage shunt reactor according to claim 1, wherein the formula K is used according to the line compensation degree of the long-distance transmission lineN＝f(M)|Tk＝TkiCalculating KN2Minimum value of (K)0And the corresponding value M of M0The method specifically comprises the following steps:
adopting a golden section method in a one-dimensional search method, and utilizing a formula K according to the line compensation degree of the long-distance transmission lineN＝f(M)|Tk＝TkiCalculating KN2Minimum value of (K)0And the corresponding value M of M0。
4. The method for determining the capacity of the high-voltage shunt reactor according to claim 3, wherein the golden section method in the one-dimensional search method is adopted, and a formula K is used according to the line compensation degree of the long-distance transmission lineN＝f(M)|Tk＝TkiCalculating KN2Minimum value of (K)0And the corresponding value M of M0The method comprises the following steps:
determining an initial interval [ a, b ] of a value of a capacity distribution coefficient M and the accuracy E of numerical calculation;
according to the initial interval and accuracy and golden ratio, taking two initial calculation points m1，n1Wherein m is1＝a1+0.382(b1-a1)，n1＝a1+0.618(b1-a1)；
According to the function relation K of the maximum overvoltage multiple and the capacity distribution coefficientN＝f(M)|Tk＝TkiCalculating f (m)1)，f(n1) Wherein k is 1;
if f (m)k)≤f(nk) Definition of ak+1＝ak，bk+1＝nk，nk+1＝mk，f(nk+1)＝f(mk)，mk+1＝ak+1+0.382(bk+1-ak+1) Calculating f (m)k+1)；
If f (m)k)>f(nk) Definition of ak+1＝mk，bk+1＝bk，mk+1＝nk，f(mk+1)＝f(nk)，nk+1＝ak+1+0.618(bk+1-ak+1) Calculating f (n)k+1)；
Judgment bk+1-ak+1Whether the epsilon is not larger than the set value or not is judged;
if so, using a formula
Figure FDA0003198244010000031
And K0＝f(M0) Calculating to obtain M0And K0Wherein, K is0The minimum value of the maximum overvoltage multiple along the second line is obtained;
if not, defining k as k +1, and recalculating new judgment f (m)k+1) And f (n)k+1) Until K is determinedNMinimum value of (K)0And according to K0Determining a corresponding M0。
5. A system for determining the capacity of a high voltage shunt reactor, said system comprising:
the power system impedance determination module is used for determining the impedance of the power systems on two sides of the long-distance power transmission line according to the mode that the long-distance power transmission line is connected into the power system, wherein the power system comprises: a first power system and a second power system, the impedance of the first power system is defined as Xs1The impedance of the second power system is Xs2；
The first judging module is used for judging whether the impedance of the first power system and the impedance of the second power system meet the following conditions: xs1>Xs2；
A first line maximum overvoltage multiple calculation module for Xs1＞Xs2When the power system is in the idle running mode, the long-distance power transmission line is disconnected with the second power system, and the first power system is in the idle running mode with the line, and the formula is used
Figure FDA0003198244010000032
Calculating the first line maximum overvoltage multiple K when the high-voltage shunt reactor is not installedN1Wherein, in the step (A),
Figure FDA0003198244010000033
Figure FDA0003198244010000034
l is the length of the long-distance transmission line, beta is the transmission constant of the long-distance transmission line, omega is the angular frequency of the power supply, phi is the phase angle of the power supply, and X issIs a power supply reactance, ZcIs the wave impedance of a long-distance transmission line, r0、L0、g0、C0Resistance, inductance, conductance and capacitance, respectively, per unit length of the long-distance transmission line, and, Xs1≤Xs2And then disconnecting the long-distance power transmission line from the first power system, and calculating the first line maximum overvoltage multiple K when the high-voltage shunt reactor is not installed in a line no-load operation mode of the second power systemN1；
A second judging module for judging the maximum overvoltage multiple K along the first lineN1Whether or not less thanEqual to a set maximum overvoltage multiple KAIf yes, judging that the capacity of the high-voltage shunt reactor at the two ends of the long-distance power transmission line is 0;
a second line maximum overvoltage multiple calculation module for calculating the first line maximum overvoltage multiple KN1>Set maximum overvoltage multiple KAUsing a formula
Figure FDA0003198244010000041
Calculating the second line maximum overvoltage multiple K when the high-voltage shunt reactor is installedN2Wherein, in the step (A),
Figure FDA0003198244010000042
Figure FDA0003198244010000043
KN2is at the same time
Figure FDA0003198244010000044
The maximum overvoltage multiple along the line of the point,
Figure FDA0003198244010000045
is the reactance value of a reactor at the head end of the line,
Figure FDA0003198244010000046
the reactance value is the reactance value of a reactor at the end of the line;
a minimum value calculation module for utilizing formula K according to the line compensation degree of the long-distance transmission lineN＝f(M)|Tk＝TkiCalculating KN2Minimum value of (K)0And the corresponding value M of M0Wherein Q isL＝QL1+QL2，QL2＝MQL，QL1＝(1-M)QLDefining the degree of line compensation
Figure FDA0003198244010000047
Qc＝ωC0lUe 2M is not less than 0 and not more than 1, M is a capacity distribution coefficient, QLIs the sum of capacities at two ends of a long-distance transmission line, QL1For the capacity, Q, of the high-voltage shunt reactor at the head end of the long-distance transmission lineL2For the capacity, U, of high-voltage parallel reactor at the end of long-distance transmission lineeRated voltage for the power supply, TkiA specific value of the line compensation degree is obtained;
a high-voltage shunt reactor capacity calculation module for respectively using a formula and QL1＝(1-M0)TkiωC0lUe 2And QL2＝M0TkiωC0lUe 2And calculating to obtain the capacity of the high-voltage shunt reactor at the head end and the tail end of the long-distance power transmission line.
6. The system for determining the capacity of the high-voltage shunt reactor according to claim 5, wherein the power system impedance determination module comprises:
the equivalent network graph establishing unit is used for establishing equivalent network graphs of the power systems on two sides of the long-distance power transmission line according to the mode that the long-distance power transmission line is connected into the power system;
and the impedance determining unit is used for determining the impedance of the power systems on two sides of the long-distance power transmission line according to the equivalent network map.
7. The system for determining the capacity of the high-voltage shunt reactor according to claim 5, wherein the minimum value calculating module is configured to use a formula K according to the line compensation degree of the long-distance transmission line by using a golden section method in a one-dimensional search methodN＝f(M)|Tk＝TkiCalculating KN2Minimum value of (K)0And the corresponding value M of M0。
8. The system for determining the capacity of the high-voltage shunt reactor according to claim 7, wherein the minimum value calculation module comprises:
the initial interval and accuracy determining unit is used for determining the initial interval [ a, b ] of the value of the capacity distribution coefficient M and the accuracy E of numerical calculation;
golden section calculating point determining unit for taking the first two calculating points m according to golden section ratio based on the initial interval and accuracy1，n1Wherein m is1＝a1+0.382(b1-a1)，n1＝a1+0.618(b1-a1)；
A first calculation unit for calculating a function K of the maximum overvoltage multiple and the capacity distribution coefficientN＝f(M)|Tk＝TkiCalculating f (m)1)，f(n1) Wherein k is 1;
a second calculation unit for calculating f (m)k)≤f(nk) When, define ak+1＝ak，bk+1＝nk，nk+1＝mk，f(nk+1)＝f(mk)，mk+1＝ak+1+0.382(bk+1-ak+1) Calculating f (m)k+1)；
A third calculation unit for calculating f (m)k)>f(nk) When, define ak+1＝mk，bk+1＝bk，mk+1＝nk，f(mk+1)＝f(nk)，nk+1＝ak+1+0.618(bk+1-ak+1) Calculating f (n)k+1)；
A judging unit for judging bk+1-ak+1Whether the epsilon is not larger than the set value or not is judged;
a fourth calculation unit for calculating bk+1-ak+1When the content is less than or equal to the content, utilizing a formula
Figure FDA0003198244010000051
And K0＝f(M0) Calculating to obtain M0And K0Wherein, K is0The minimum value of the maximum overvoltage multiple along the second line is obtained;
a circulation unit for when bk+1-ak+1When ≦ epsilon is not set, defining k as k +1, and recalculatingNew judgment f (m)k+1) And f (n)k+1) Until K is determinedNMinimum value of (K)0And according to K0Determining a corresponding M0。
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JPH10257971A (en) * 1997-03-18 1998-09-29 Hitachi Home Tec Ltd Breakage-of-wire detecting circuit for dc pump of jar pot
CN101404475A (en) * 2008-11-07 2009-04-08 中国电力科学研究院 Method for restraining hyposynchronous resonance of power system
CN102122821A (en) * 2010-12-17 2011-07-13 中国电力科学研究院 Method for inhibiting power frequency voltage from being raised after switch-on of ultrahigh and extra-high voltage no-load line
CN106099891A (en) * 2016-07-26 2016-11-09 华南理工大学 Marine wind electric field leading-out terminal sea cable is carried out the analysis method that shunt reactor is distributed rationally
CN108666985A (en) * 2018-04-17 2018-10-16 内蒙古电力(集团)有限责任公司内蒙古电力科学研究院分公司 A kind of power transmission line power frequency overvoltage Precise Diagnosis and means of defence

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN86203937U (en) * 1986-06-06 1987-05-20 浙江省电力工业局 Spark gap switching-in mechanism for ultra-high voltage parallel
JPH10257971A (en) * 1997-03-18 1998-09-29 Hitachi Home Tec Ltd Breakage-of-wire detecting circuit for dc pump of jar pot
CN101404475A (en) * 2008-11-07 2009-04-08 中国电力科学研究院 Method for restraining hyposynchronous resonance of power system
CN102122821A (en) * 2010-12-17 2011-07-13 中国电力科学研究院 Method for inhibiting power frequency voltage from being raised after switch-on of ultrahigh and extra-high voltage no-load line
CN106099891A (en) * 2016-07-26 2016-11-09 华南理工大学 Marine wind electric field leading-out terminal sea cable is carried out the analysis method that shunt reactor is distributed rationally
CN108666985A (en) * 2018-04-17 2018-10-16 内蒙古电力(集团)有限责任公司内蒙古电力科学研究院分公司 A kind of power transmission line power frequency overvoltage Precise Diagnosis and means of defence

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