CN109245097A - A kind of method and system calculating the ac and dc systems voltage coupling factor based on extension Jacobian matrix - Google Patents
A kind of method and system calculating the ac and dc systems voltage coupling factor based on extension Jacobian matrix Download PDFInfo
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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
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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
- H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
- H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
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Abstract
The present invention provides a kind of method and system that the ac and dc systems voltage coupling factor is calculated based on extension Jacobian matrix, the power balance equation of every bus of the described method and system based on ac and dc systems, establish the equation X based on the extension Jacobian matrix constant voltage coupling factor really, network parameter values and dynamic element parameter value further according to described more every buses of feed-in ac and dc systems of acquisition solve the value of each element in extension Jacobian matrix, and the value based on each element in extension Jacobian matrix, equation X is solved using Sparse technology, determine every DC transmission system change of current bus to the voltage coupling factor of the receiving end ac bus of the failure, described method and system keeps the rapid evaluation result of multi-feed HVDC receiving end power grid enabling capabilities more accurate, apply the present invention to alternating current-direct current system The fields such as system planning, design and operation, for instructing the planning of bulk power grid and safeguarding that the safe and stable operation of bulk power grid is of great significance.
Description
Technical field
The present invention relates to Power System Planning and operation field, and more particularly, to one kind based on extension Jacobi
The method and system of the matrix calculating ac and dc systems voltage coupling factor.
Background technique
In ac and dc systems theoretical research and engineer application, the concept of short-circuit ratio and effective short-circuit ratio is generallyd use to comment
Estimate opposite strong or weak relation between AC system and direct current system, direct current maximum transmission power, overvoltage level and possible
Resonance frequency.The effect of intercoupling in multi-feed HVDC system, between direct current system, while AC network is had an impact,
Conventional method can not consider the problem that influences each other between multiple-circuit line system.In view of the above deficiencies, electric power research field mentions
Go out the indexs such as more feed-in short-circuit ratioes, more feed-in interaction factors, can be used for multi-feed HVDC receiving end power grid enabling capabilities
Preliminary rapid evaluation.Wherein, have in the prior art and critical more feed-in reciprocations are derived based on critical extinction angle judgment criteria
The calculation formula of the factor, quickly to judge whether multi-infeed HVDC system commutation failure can occur simultaneously and provide new approaches, but
Due to the limitation that more feed-in interaction factors define, this method is only applicable to what change of current bus in DC inversion side broke down
Situation.Therefore, under the inspiration that more feed-in interaction factors define, ac and dc systems voltage coupling is had also been proposed in the prior art
The concept of acting factor is closed, is defined as:
Assuming that three-phase symmetrical inductive grounding failure occurs for receiving-end system ac bus k, so that under the voltage on the bus
When drop, the voltage variety of inverter side change of current bus j is Δ Uj, define combined-voltage coupling factors A DVCFjkCalculating
Formula are as follows:
ADVCFjk=Δ Uj/ΔUk
The method of the above-mentioned calculating combined-voltage coupling factor is in receiving end AC system equivalent impedance matrix
The ratio between element substitutes the ratio between voltage magnitude variable quantity, and in electric power networks be pure perception and load be also in pure perceptual situation is of equal value
's.But this method has been done certain it is assumed that not considering the influence of Electrical Power System Dynamic element characteristic.
Summary of the invention
Electrical Power System Dynamic element is not considered for the method for calculating the combined-voltage coupling factor in the prior art
The technical issues of influence of characteristic, the present invention are provided a kind of coupled based on extension Jacobian matrix calculating ac and dc systems voltage and made
With the method for the factor, which comprises
Determine the power balance equation of every bus in more feed-in ac and dc systems, and in more feed-in ac and dc systems
A receiving end ac bus break down disturbance when, the voltage by the power balance equation two sides to the bus to break down
Every DC transmission system change of current bus pair in the more feed-in ac and dc systems of determination based on extension Jacobian matrix is established in derivation
The equation X of the voltage coupling factor of the receiving end ac bus of the failure；
The network parameter values and dynamic element parameter value of described more every bus of feed-in ac and dc systems are acquired, and according to institute
State the value that parameter value solves each element in extension Jacobian matrix, wherein the network parameter includes that more feed-ins are handed over directly
Conductance, susceptance and phase difference of voltage in streaming system between the effective voltage value and bus and bus of every bus, it is described dynamic
State component parameters are the parameters of the power of the dynamic element in determining more feed-in ac and dc systems, and the dynamic element includes
Generator, load, DC converter and dynamic reactive compensation device；
Based on the value for calculating each element in determining extension Jacobian matrix, equation X is solved using Sparse technology,
Determine every DC transmission system change of current bus to the voltage coupling factor of the receiving end ac bus of the failure.
Further, it is determined that in more feed-in ac and dc systems every bus power balance equation, and in more feed-ins
One receiving end ac bus of ac and dc systems break down disturbance when, by the power balance equation two sides to breaking down
Every DC transmission system in the more feed-in ac and dc systems of determination based on extension Jacobian matrix is established in the voltage derivation of bus
Change of current bus includes: to the equation X of the voltage coupling factor of the receiving end ac bus of the failure
When more feed-in ac and dc systems include that m returns direct current, altogether when n bus, the power-balance side of every bus
Journey indicates are as follows:
In formula, Δ Pi、ΔQiRespectively indicate the active power variable quantity and reactive power variable quantity of node i injection, formula (1)
In equation be respectively node i active power equation and reactive power equation, PGi、QGiRespectively indicate generator injection node i
Active power output and idle power output, PLi、QLiRespectively indicate the burden with power and load or burden without work of node i, PDiIndicate the straight of node i
Flow power, QDiIndicate the reactive power of DC converter injection node i, Ui、UjRespectively indicate the voltage of node i, j, QSiIt indicates
Dynamic reactive compensation device injects the idle power output of node i, Gij、BijRespectively indicate the conductance and susceptance between node i, j, θij
Node i, the phase difference of voltage between j are indicated, for the DC transmission system in more feed-in ac and dc systems, in formula (1)
Direct current active power rectifying negative sign side-draw, in inversion positive sign side-draw；
When the moment that receiving end AC system kth ac bus breaks down, for formula (1), the kth ac bus
There is amount of unbalance Δ Q on the left of corresponding reactive power equationk, and the Δ P of the buskAnd the power equation of other buses is still
So keep left term be zero, if in more feed-in ac and dc systems i-th bus of DC transmission system voltage effective value
For Ui, the variable quantity of the voltage effective value is Δ Ui, the voltage effective value of the kth bus of receiving end AC system is Uk, voltage
The variable quantity of virtual value is Δ Uk, coefficient delta Ui/ΔUkIt is i-th change of current bus of DC transmission system with respect to receiving end AC system
Kth bus voltage coupling factors A DVCFik, as 1≤i≤m, 1≤k≤n, it is based on formula (1) power-balance side
Journey, and consider the influence of dynamic element generating set, direct current system, part throttle characteristics and dynamic reactive compensation device, by formula (1)
Two sides are to UkDerivation, production (2), expression formula are as follows:
Enable the element in formula (2) right-hand-side vectorProduction (3), expression
Formula are as follows:
In formula (3), the extension Jacobian matrix are as follows:
Element H as i ≠ j, in Jacobian matrixij、Nij、Mij、LijCalculation formula it is as follows:
Element H as i=j, in Jacobian matrixii、Nii、Mii、LiiCalculation formula it is as follows:
By formula (3) it is found that Jacobian matrix is that 2n ties up square matrix, the total 2n-1 of variable to be solved is a, the idle function of interior joint k
The corresponding 2k behavior redundant row of rate equation,For unknown quantity, 2k column are corresponded toLeave out
2k column are moved on on the left of formula (3), obtain equation X, expression formula by 2k row are as follows:
Further, the network parameter values and dynamic element ginseng of described described more every buses of feed-in ac and dc systems of acquisition
Numerical value, and include: according to the value that the parameter value solves each element in extension Jacobian matrix
As i ≠ j, determined according to the network parameter values of more every buses of feed-in ac and dc systems of acquisition and formula (4) refined
Gram than the element H in matrixij、Nij、Mij、LijValue；
As i=j, according to the network parameter values, dynamic element parameter of more every buses of feed-in ac and dc systems of acquisition
Value and formula (5) determine the element H in Jacobian matrixii、Nii、Mii、LiiValue, in which:
For non-power generator node, the derivative term of relevant generator in formula (5)For
Zero, in generator node, generator is approximately considered in disturbance moment subtranient reactance X "dElectromotive force E " afterwards is kept constant, hair
Output power of motor expression formula is formula (6), wherein θδFor generator built-in potential E " and end voltage UiAngle difference, generator function
Rate is formula (7) to the derivative term of voltage:
For non-load bus, derivative term of the load power to voltage in formula (5)It is zero, in addition, load
Power is only related with feeding point voltage effective value, and unrelated with its angle, therefore load power is to the derivative of level angleIt is zero；
For load bus, when the load is firm power load, constant current load power expression formula and its right
The derivative of voltage is formula (8):
DC converter voltage, the current equation indicated with famous value is formula (9), the inverter function derived by formula (9)
Rate equation is formula (10), wherein the voltage quantities in equation (10) about change of current bus only have Ui, be free of level angle, formula
(9) and formula (10) is as follows:
In formula, UdIndicate DC voltage, ntIndicate six pulse conversion devices series connection number, kTIndicate converter transformers no-load voltage ratio,
θdIndicate the direct current angle of overlap of rectifier or the blow-out angle of inverter, XcIndicate equivalent commutating reactance, IdIndicate DC current, k γ
Indicate the equivalent no-load voltage ratio of converter power transformer,Indicate Equivalent Power Factor angle, IiIndicate the electric current of direct current injection AC system；
When DC transmission system rectification side uses constant current control, and gamma kick is determined in inverter side use, direct current system
The derivative for the power vs. voltage that inverter side inverter is drawn from AC system is equation (11):
When dynamic reactive compensation device is Static Var Compensator, the Static Var Compensator is using controlled bus
Voltage deviation is as input signal, the equivalent susceptance through ratio enlargement Absent measures compensation device, negligible delay link, output
The relationship of equivalent susceptance and voltage deviation is formula (12), and the derivative to voltage is formula (13):
Bi=-K Δ Ui=-K (Ui-Ui0) (12)
Further, described as i=j, according to the network parameter values of more every buses of feed-in ac and dc systems of acquisition,
Dynamic element parameter value and formula (5) determine the element H in Jacobian matrixii、Nii、Mii、LiiValue further include:
For load bus, when the load is constant impedance load, the expression formula of load power and its to voltage
Derivative is formula (14):
When DC transmission system rectification side uses constant dc power control, and gamma kick is determined in inverter side use, in change of current mother
Apply small voltage fluctuation on line, application control strategy calculates the changed power of two sides converter station, and application difference substitution is partially micro-
Point；
When dynamic reactive compensation device is static synchronous compensator, believe the voltage deviation of controlled bus as input
Number, steady-state equation may be expressed as:
Δ U=UREF- U=KDIS (15)
IS=Δ U/KD=BSΔU (16)
The equivalent susceptance of static synchronous compensator is expressed as BS=1/KD, when KD takes zero, the control of static synchronous compensator
Node processed is indifference control, but is limited by static synchronous compensator output electric current, and the derivative to voltage is formula (17):
According to another aspect of the present invention, the present invention provides a kind of based on extension Jacobian matrix calculating ac and dc systems electricity
The system for pressing the coupling factor, the system comprises:
Equation determination unit, is used to determine the power balance equation of every bus in more feed-in ac and dc systems, and
When the receiving end ac bus failure disturbance of more feed-in ac and dc systems, by the power balance equation two sides pair
The voltage derivation of the bus to break down is established straight based on every in the more feed-in ac and dc systems of determination for extending Jacobian matrix
Transmission system change of current bus is flowed to the equation X of the voltage coupling factor of the receiving end ac bus of the failure；
Element computing unit is used to acquire the network parameter values and dynamic of described more every bus of feed-in ac and dc systems
Device parameter values, and the value for extending each element in Jacobian matrix is solved according to the parameter value, wherein the network parameter
Conductance, susceptance between effective voltage value and bus and bus including every bus in more feed-in ac and dc systems
And phase difference of voltage, the dynamic element parameter are the ginsengs of the power of the dynamic element in determining more feed-in ac and dc systems
Number, the dynamic element includes generator, load, DC converter and dynamic reactive compensation device；
Factor specifying unit is used for based on the value for calculating each element in determining extension Jacobian matrix, and use is dilute
The technology of dredging solves equation X, determines every DC transmission system change of current bus to the electricity of the receiving end ac bus of the failure
Press the coupling factor.
Further, the equation determination unit determines the power-balance side of every bus in more feed-in ac and dc systems
Journey, and when a receiving end ac bus of more feed-in ac and dc systems breaks down and disturbs, by the power-balance side
The more feed-in ac and dc systems of determination based on extension Jacobian matrix are established in voltage derivation of the journey two sides to the bus to break down
In every DC transmission system change of current bus to the equation X of the voltage coupling factor of the receiving end ac bus of the failure
Include:
When more feed-in ac and dc systems include that m returns direct current, altogether when n bus, the power-balance side of every bus
Journey indicates are as follows:
In formula, Δ Pi、ΔQiRespectively indicate the active power variable quantity and reactive power variable quantity of node i injection, formula (1)
In equation be respectively node i active power equation and reactive power equation, PGi、QGiRespectively indicate generator injection node i
Active power output and idle power output, PLi、QLiRespectively indicate the burden with power and load or burden without work of node i, PDiIndicate the straight of node i
Flow power, QDiIndicate the reactive power of DC converter injection node i, Ui、UjRespectively indicate the voltage of node i, j, QSiIt indicates
Dynamic reactive compensation device injects the idle power output of node i, Gij、BijRespectively indicate the conductance and susceptance between node i, j, θij
Node i, the phase difference of voltage between j are indicated, for the DC transmission system in more feed-in ac and dc systems, in formula (1)
Direct current active power rectifying negative sign side-draw, in inversion positive sign side-draw；
When the moment that receiving end AC system kth ac bus breaks down, for formula (1), the kth ac bus
There is amount of unbalance Δ Q on the left of corresponding reactive power equationk, and the Δ P of the buskAnd the power equation of other buses is still
So keep left term be zero, if in more feed-in ac and dc systems i-th bus of DC transmission system voltage effective value
For Ui, the variable quantity of the voltage effective value is Δ Ui, the voltage effective value of the kth bus of receiving end AC system is Uk, voltage
The variable quantity of virtual value is Δ Uk, coefficient delta Ui/ΔUkIt is i-th change of current bus of DC transmission system with respect to receiving end AC system
Kth bus voltage coupling factors A DVCFik, as 1≤i≤m, 1≤k≤n, it is based on formula (1) power-balance side
Journey, and consider the influence of dynamic element generating set, direct current system, part throttle characteristics and dynamic reactive compensation device, by formula (1)
Two sides are to UkDerivation, production (2), expression formula are as follows:
Enable the element in formula (2) right-hand-side vectorProduction (3),
Expression formula are as follows:
In formula (3), the extension Jacobian matrix are as follows:
Element H as i ≠ j, in Jacobian matrixij、Nij、Mij、LijCalculation formula it is as follows:
Element H as i=j, in Jacobian matrixii、Nii、Mii、LiiCalculation formula it is as follows:
By formula (3) it is found that Jacobian matrix is that 2n ties up square matrix, the total 2n-1 of variable to be solved is a, the idle function of interior joint k
The corresponding 2k behavior redundant row of rate equation,For unknown quantity, 2k column are corresponded toLeave out
2k column are moved on on the left of formula (3), obtain equation X, expression formula by 2k row are as follows:
Further, the element computing unit acquires the network parameter values of described more every bus of feed-in ac and dc systems
With dynamic element parameter value, and the value of each element in extension Jacobian matrix is solved according to the parameter value and includes:
As i ≠ j, determined according to the network parameter values of more every buses of feed-in ac and dc systems of acquisition and formula (4) refined
Gram than the element H in matrixij、Nij、Mij、LijValue；
As i=j, according to the network parameter values, dynamic element parameter of more every buses of feed-in ac and dc systems of acquisition
Value and formula (5) determine the element H in Jacobian matrixii、Nii、Mii、LiiValue, in which:
For non-power generator node, the derivative term of relevant generator in formula (5)For
Zero, in generator node, generator is approximately considered in disturbance moment subtranient reactance X "dElectromotive force E " afterwards is kept constant, hair
Output power of motor expression formula is formula (6), wherein θδFor generator built-in potential E " and end voltage UiAngle difference, generator function
Rate is formula (7) to the derivative term of voltage:
For non-load bus, derivative term of the load power to voltage in formula (5)It is zero, in addition, load
Power is only related with feeding point voltage effective value, and unrelated with its angle, therefore load power is to the derivative of level angleIt is zero；
For load bus, when the load is firm power load, constant current load power expression formula and its right
The derivative of voltage is formula (8):
DC converter voltage, the current equation indicated with famous value is formula (9), the inverter function derived by formula (9)
Rate equation is formula (10), wherein the voltage quantities in equation (10) about change of current bus only have Ui, be free of level angle, formula
(9) and formula (10) is as follows:
In formula, UdIndicate DC voltage, ntIndicate six pulse conversion devices series connection number, kTIndicate converter transformers no-load voltage ratio,
θdIndicate the direct current angle of overlap of rectifier or the blow-out angle of inverter, XcIndicate equivalent commutating reactance, IdIndicate DC current, kγ
Indicate the equivalent no-load voltage ratio of converter power transformer,Indicate Equivalent Power Factor angle, IiIndicate the electric current of direct current injection AC system；
When DC transmission system rectification side uses constant current control, and gamma kick is determined in inverter side use, direct current system
The derivative for the power vs. voltage that inverter side inverter is drawn from AC system is equation (11):
When dynamic reactive compensation device is Static Var Compensator, the Static Var Compensator is using controlled bus
Voltage deviation is as input signal, the equivalent susceptance through ratio enlargement Absent measures compensation device, negligible delay link, output
The relationship of equivalent susceptance and voltage deviation is formula (12), and the derivative to voltage is formula (13):
Bi=-K Δ Ui=-K (Ui-Ui0) (12)
Further, the element computing unit is in i=j, according to more every buses of feed-in ac and dc systems of acquisition
Network parameter values, dynamic element parameter value and formula (5) determine the element H in Jacobian matrixii、Nii、Mii、LiiValue also wrap
It includes:
For load bus, when the load is constant impedance load, the expression formula of load power and its to voltage
Derivative is formula (14):
When DC transmission system rectification side uses constant dc power control, and gamma kick is determined in inverter side use, in change of current mother
Apply small voltage fluctuation on line, application control strategy calculates the changed power of two sides converter station, and application difference substitution is partially micro-
Point；
When dynamic reactive compensation device is static synchronous compensator, believe the voltage deviation of controlled bus as input
Number, steady-state equation may be expressed as:
Δ U=UREF- U=KDIS (15)
IS=Δ U/KD=BSΔU (16)
The equivalent susceptance of static synchronous compensator is expressed as BS=1/KD, when KD takes zero, the control of static synchronous compensator
Node processed is indifference control, but is limited by static synchronous compensator output electric current, and the derivative to voltage is formula (17):
What technical solution of the present invention provided calculates the ac and dc systems voltage coupling factor based on extension Jacobian matrix
Method and system comprehensively consider dynamic element model characteristics in electric system, by generator, load, direct current, dynamic reactive mend
It repays the dynamic elements model such as device to bring into the calculating of the ac and dc systems voltage coupling factor, by calculating refined gram of extension
Value than each element in matrix determines every DC transmission system change of current bus to the voltage of the receiving end ac bus of the failure
The coupling factor, thus keep the rapid evaluation result of multi-feed HVDC receiving end power grid enabling capabilities more accurate, it will be of the invention
Applied to fields such as ac and dc systems planning, design and operations, for instructing the planning of bulk power grid and safeguarding the safety of bulk power grid
Stable operation is of great significance.
Detailed description of the invention
By reference to the following drawings, exemplary embodiments of the present invention can be more fully understood by:
Fig. 1 is to calculate the coupling of ac and dc systems voltage based on extension Jacobian matrix according to the preferred embodiment for the present invention
The flow chart of the method for acting factor；
Fig. 2 is to calculate the coupling of ac and dc systems voltage based on extension Jacobian matrix according to the preferred embodiment for the present invention
The structural schematic diagram of the system of acting factor.
Specific embodiment
Exemplary embodiments of the present invention are introduced referring now to the drawings, however, the present invention can use many different shapes
Formula is implemented, and is not limited to the embodiment described herein, and to provide these embodiments be at large and fully disclose
The present invention, and the scope of the present invention is sufficiently conveyed to person of ordinary skill in the field.Show for what is be illustrated in the accompanying drawings
Term in example property embodiment is not limitation of the invention.In the accompanying drawings, identical cells/elements use identical attached
Icon note.
Unless otherwise indicated, term (including scientific and technical terminology) used herein has person of ordinary skill in the field
It is common to understand meaning.Further it will be understood that with the term that usually used dictionary limits, should be understood as and its
The context of related fields has consistent meaning, and is not construed as Utopian or too formal meaning.
Fig. 1 is to calculate the coupling of ac and dc systems voltage based on extension Jacobian matrix according to the preferred embodiment for the present invention
The flow chart of the method for acting factor.It is handed over as shown in Figure 1, being calculated described in this preferred embodiment based on extension Jacobian matrix
The method 100 of the direct current system voltage coupling factor is since step 101.
In step 101, the power balance equation of every bus in more feed-in ac and dc systems is determined, and in more feed-ins
One receiving end ac bus of ac and dc systems break down disturbance when, by the power balance equation two sides to breaking down
Every DC transmission system in the more feed-in ac and dc systems of determination based on extension Jacobian matrix is established in the voltage derivation of bus
Equation X of the change of current bus to the voltage coupling factor of the receiving end ac bus of the failure；
In step 102, the network parameter values and dynamic element parameter of described more every buses of feed-in ac and dc systems are acquired
Value, and the value for extending each element in Jacobian matrix is solved according to the parameter value, wherein the network parameter includes described
Conductance, susceptance and voltage phase in more feed-in ac and dc systems between the effective voltage value and bus and bus of every bus
Angular difference, the dynamic element parameter is the parameter of the power of the dynamic element in determining more feed-in ac and dc systems, described
Dynamic element includes generator, load, DC converter and dynamic reactive compensation device；
In step 103, based on the value for calculating each element in determining extension Jacobian matrix, using Sparse technology other side
Formula X is solved, and determines voltage coupling of the every DC transmission system change of current bus to the receiving end ac bus of the failure
The factor.
Preferably, it determines the power balance equation of every bus in more feed-in ac and dc systems, and is handed in more feed-ins
When the receiving end ac bus failure disturbance of direct current system, by the power balance equation two sides to the mother to break down
The voltage derivation of line is established every DC transmission system in the more feed-in ac and dc systems of determination based on extension Jacobian matrix and is changed
Flow bus includes: to the equation X of the voltage coupling factor of the receiving end ac bus of the failure
When more feed-in ac and dc systems include that m returns direct current, altogether when n bus, the power-balance side of every bus
Journey indicates are as follows:
In formula, Δ Pi、ΔQiRespectively indicate the active power variable quantity and reactive power variable quantity of node i injection, formula (1)
In equation be respectively node i active power equation and reactive power equation, PGi、QGiRespectively indicate generator injection node i
Active power output and idle power output, PLi、QLiRespectively indicate the burden with power and load or burden without work of node i, PDiIndicate the straight of node i
Flow power, QDiIndicate the reactive power of DC converter injection node i, Ui、UjRespectively indicate the voltage of node i, j, QSiIt indicates
Dynamic reactive compensation device injects the idle power output of node i, Gij、BijRespectively indicate the conductance and susceptance between node i, j, θij
Node i, the phase difference of voltage between j are indicated, for the DC transmission system in more feed-in ac and dc systems, in formula (1)
Direct current active power rectifying negative sign side-draw, in inversion positive sign side-draw；
When the moment that receiving end AC system kth ac bus breaks down, for formula (1), the kth ac bus
There is amount of unbalance Δ Q on the left of corresponding reactive power equationk, and the Δ P of the buskAnd the power equation of other buses is still
So keep left term be zero, if in more feed-in ac and dc systems i-th bus of DC transmission system voltage effective value
For Ui, the variable quantity of the voltage effective value is Δ Ui, the voltage effective value of the kth bus of receiving end AC system is Uk, voltage
The variable quantity of virtual value is Δ Uk, coefficient delta Ui/ΔUkIt is i-th change of current bus of DC transmission system with respect to receiving end AC system
Kth bus voltage coupling factors A DVCFik, as 1≤i≤m, 1≤k≤n, it is based on formula (1) power-balance side
Journey, and consider the influence of dynamic element generating set, direct current system, part throttle characteristics and dynamic reactive compensation device, by formula (1)
Two sides are to UkDerivation, production (2), expression formula are as follows:
Enable the element in formula (2) right-hand-side vectorProduction (3),
Expression formula are as follows:
In formula (3), the extension Jacobian matrix are as follows:
Element H as i ≠ j, in Jacobian matrixij、Nij、Mij、LijCalculation formula it is as follows:
Element H as i=j, in Jacobian matrixii、Nii、Mii、LiiCalculation formula it is as follows:
By formula (3) it is found that Jacobian matrix is that 2n ties up square matrix, the total 2n-1 of variable to be solved is a, the idle function of interior joint k
The corresponding 2k behavior redundant row of rate equation,For unknown quantity, 2k column are corresponded toLeave out
2k column are moved on on the left of formula (3), obtain equation X, expression formula by 2k row are as follows:
Preferably, the network parameter values and dynamic element parameter of described described more every buses of feed-in ac and dc systems of acquisition
Value, and include: according to the value that the parameter value solves each element in extension Jacobian matrix
As i ≠ j, determined according to the network parameter values of more every buses of feed-in ac and dc systems of acquisition and formula (4) refined
Gram than the element H in matrixij、Nij、Mij、LijValue；
As i=j, according to the network parameter values, dynamic element parameter of more every buses of feed-in ac and dc systems of acquisition
Value and formula (5) determine the element H in Jacobian matrixii、Nii、Mii、LiiValue, in which:
For non-power generator node, the derivative term of relevant generator in formula (5)For
Zero, in generator node, generator is approximately considered in disturbance moment subtranient reactance X "dElectromotive force E " afterwards is kept constant, hair
Output power of motor expression formula is formula (6), wherein θδFor generator built-in potential E " and end voltage UiAngle difference, generator function
Rate is formula (7) to the derivative term of voltage:
For non-load bus, derivative term of the load power to voltage in formula (5)It is zero, in addition, load
Power is only related with feeding point voltage effective value, and unrelated with its angle, therefore load power is to the derivative of level angleIt is zero；
For load bus, when the load is firm power load, constant current load power expression formula and its right
The derivative of voltage is formula (8):
DC converter voltage, the current equation indicated with famous value is formula (9), the inverter function derived by formula (9)
Rate equation is formula (10), wherein the voltage quantities in equation (10) about change of current bus only have Ui, be free of level angle, formula
(9) and formula (10) is as follows:
In formula, UdIndicate DC voltage, ntIndicate six pulse conversion devices series connection number, kTIndicate converter transformers no-load voltage ratio,
θdIndicate the direct current angle of overlap of rectifier or the blow-out angle of inverter, XcIndicate equivalent commutating reactance, IdIndicate DC current, kγ
Indicate the equivalent no-load voltage ratio of converter power transformer,Indicate Equivalent Power Factor angle, IiIndicate the electric current of direct current injection AC system；
When DC transmission system rectification side uses constant current control, and gamma kick is determined in inverter side use, direct current system
The derivative for the power vs. voltage that inverter side inverter is drawn from AC system is equation (11):
When dynamic reactive compensation device is Static Var Compensator, the Static Var Compensator is using controlled bus
Voltage deviation is as input signal, the equivalent susceptance through ratio enlargement Absent measures compensation device, negligible delay link, output
The relationship of equivalent susceptance and voltage deviation is formula (12), and the derivative to voltage is formula (13):
Bi=-K Δ Ui=-K (Ui-Ui0) (12)
Preferably, described as i=j, according to the network parameter values of more every buses of feed-in ac and dc systems of acquisition, move
State device parameter values and formula (5) determine the element H in Jacobian matrixii、Nii、Mii、LiiValue further include:
For load bus, when the load is constant impedance load, the expression formula of load power and its to voltage
Derivative is formula (14):
When DC transmission system rectification side uses constant dc power control, and gamma kick is determined in inverter side use, in change of current mother
Apply small voltage fluctuation on line, application control strategy calculates the changed power of two sides converter station, and application difference substitution is partially micro-
Point；
When dynamic reactive compensation device is static synchronous compensator, believe the voltage deviation of controlled bus as input
Number, steady-state equation may be expressed as:
Δ U=UREF- U=KDIS (15)
IS=Δ U/KD=BSΔU (16)
The equivalent susceptance of static synchronous compensator is expressed as BS=1/KD, work as KDWhen taking zero, the control of static synchronous compensator
Node processed is indifference control, but is limited by static synchronous compensator output electric current, and the derivative to voltage is formula (17):
Fig. 2 is to calculate the coupling of ac and dc systems voltage based on extension Jacobian matrix according to the preferred embodiment for the present invention
The structural schematic diagram of the system of acting factor.As shown in Fig. 2, described in this preferred embodiment based on extension Jacobian matrix
Calculate the ac and dc systems voltage coupling factor system 200 include:
Equation determination unit 201 is used to determine the power balance equation of every bus in more feed-in ac and dc systems, and
When a receiving end ac bus of more feed-in ac and dc systems breaks down disturbance, by the power balance equation two sides
Voltage derivation to the bus to break down establishes in the more feed-in ac and dc systems of determination based on extension Jacobian matrix every
Equation X of the DC transmission system change of current bus to the voltage coupling factor of the receiving end ac bus of the failure；
Element computing unit 202, be used to acquire described more every bus of feed-in ac and dc systems network parameter values and
Dynamic element parameter value, and the value for extending each element in Jacobian matrix is solved according to the parameter value, wherein the network
Parameter include conductance in more feed-in ac and dc systems between the effective voltage value and bus and bus of every bus,
Susceptance and phase difference of voltage, the dynamic element parameter are the power of the dynamic element in determining more feed-in ac and dc systems
Parameter, the dynamic element includes generator, load, DC converter and dynamic reactive compensation device；
Factor specifying unit 203 is used to use based on the value for calculating each element in determining extension Jacobian matrix
Sparse technology solves equation X, determines every DC transmission system change of current bus to the receiving end ac bus of the failure
The voltage coupling factor.
Preferably, the equation determination unit 201 determines the power-balance side of every bus in more feed-in ac and dc systems
Journey, and when a receiving end ac bus of more feed-in ac and dc systems breaks down and disturbs, by the power-balance side
The more feed-in ac and dc systems of determination based on extension Jacobian matrix are established in voltage derivation of the journey two sides to the bus to break down
In every DC transmission system change of current bus to the equation X of the voltage coupling factor of the receiving end ac bus of the failure
Include:
When more feed-in ac and dc systems include that m returns direct current, altogether when n bus, the power-balance side of every bus
Journey indicates are as follows:
In formula, Δ Pi、ΔQiRespectively indicate the active power variable quantity and reactive power variable quantity of node i injection, formula (1)
In equation be respectively node i active power equation and reactive power equation, PGi、QGiRespectively indicate generator injection node i
Active power output and idle power output, PLi、QLiRespectively indicate the burden with power and load or burden without work of node i, PDiIndicate the straight of node i
Flow power, QDiIndicate the reactive power of DC converter injection node i, Ui、UjRespectively indicate the voltage of node i, j, QSiIt indicates
Dynamic reactive compensation device injects the idle power output of node i, Gij、BijRespectively indicate the conductance and susceptance between node i, j, θij
Node i, the phase difference of voltage between j are indicated, for the DC transmission system in more feed-in ac and dc systems, in formula (1)
Direct current active power rectifying negative sign side-draw, in inversion positive sign side-draw；
When the moment that receiving end AC system kth ac bus breaks down, for formula (1), the kth ac bus
There is amount of unbalance Δ Q on the left of corresponding reactive power equationk, and the Δ P of the buskAnd the power equation of other buses is still
So keep left term be zero, if in more feed-in ac and dc systems i-th bus of DC transmission system voltage effective value
For Ui, the variable quantity of the voltage effective value is Δ Ui, the voltage effective value of the kth bus of receiving end AC system is Uk, voltage
The variable quantity of virtual value is Δ Uk, coefficient delta Ui/ΔUkIt is i-th change of current bus of DC transmission system with respect to receiving end AC system
Kth bus voltage coupling factors A DVCFik, as 1≤i≤m, 1≤k≤n, it is based on formula (1) power-balance side
Journey, and consider the influence of dynamic element generating set, direct current system, part throttle characteristics and dynamic reactive compensation device, by formula (1)
Two sides are to UkDerivation, production (2), expression formula are as follows:
Enable the element in formula (2) right-hand-side vectorProduction (3),
Expression formula are as follows:
In formula (3), the extension Jacobian matrix are as follows:
Element H as i ≠ j, in Jacobian matrixij、Nij、Mij、LijCalculation formula it is as follows:
Element H as i=j, in Jacobian matrixii、Nii、Mii、LiiCalculation formula it is as follows:
By formula (3) it is found that Jacobian matrix is that 2n ties up square matrix, the total 2n-1 of variable to be solved is a, the idle function of interior joint k
The corresponding 2k behavior redundant row of rate equation,For unknown quantity, 2k column are corresponded toLeave out
2k column are moved on on the left of formula (3), obtain equation X, expression formula by 2k row are as follows:
Preferably, the element computing unit 202 acquires the network parameter of described more every bus of feed-in ac and dc systems
Value and dynamic element parameter value, and include: according to the value that the parameter value solves each element in extension Jacobian matrix
As i ≠ j, determined according to the network parameter values of more every buses of feed-in ac and dc systems of acquisition and formula (4) refined
Gram than the element H in matrixij、Nij、Mij、LijValue；
As i=j, according to the network parameter values, dynamic element parameter of more every buses of feed-in ac and dc systems of acquisition
Value and formula (5) determine the element H in Jacobian matrixii、Nii、Mii、LiiValue, in which:
For non-power generator node, the derivative term of relevant generator in formula (5)For
Zero, in generator node, generator is approximately considered in disturbance moment subtranient reactance X "dElectromotive force E " afterwards is kept constant, hair
Output power of motor expression formula is formula (6), wherein θδFor generator built-in potential E " and end voltage UiAngle difference, generator function
Rate is formula (7) to the derivative term of voltage:
For non-load bus, derivative term of the load power to voltage in formula (5)It is zero, in addition, load
Power is only related with feeding point voltage effective value, and unrelated with its angle, therefore load power is to the derivative of level angleIt is zero；
For load bus, when the load is firm power load, constant current load power expression formula and its right
The derivative of voltage is formula (8):
DC converter voltage, the current equation indicated with famous value is formula (9), the inverter function derived by formula (9)
Rate equation is formula (10), wherein the voltage quantities in equation (10) about change of current bus only have Ui, be free of level angle, formula
(9) and formula (10) is as follows:
In formula, UdIndicate DC voltage, ntIndicate six pulse conversion devices series connection number, kTIndicate converter transformers no-load voltage ratio,
θdIndicate the direct current angle of overlap of rectifier or the blow-out angle of inverter, XcIndicate equivalent commutating reactance, IdIndicate DC current, k γ
Indicate the equivalent no-load voltage ratio of converter power transformer,Indicate Equivalent Power Factor angle, IiIndicate the electric current of direct current injection AC system；
When DC transmission system rectification side uses constant current control, and gamma kick is determined in inverter side use, direct current system
The derivative for the power vs. voltage that inverter side inverter is drawn from AC system is equation (11):
When dynamic reactive compensation device is Static Var Compensator, the Static Var Compensator is using controlled bus
Voltage deviation is as input signal, the equivalent susceptance through ratio enlargement Absent measures compensation device, negligible delay link, output
The relationship of equivalent susceptance and voltage deviation is formula (12), and the derivative to voltage is formula (13):
Bi=-K Δ Ui=-K (Ui-Ui0) (12)
Preferably, the element computing unit 202 is in i=j, according to more every buses of feed-in ac and dc systems of acquisition
Network parameter values, dynamic element parameter value and formula (5) determine the element H in Jacobian matrixii、Nii、Mii、LiiValue also wrap
It includes:
For load bus, when the load is constant impedance load, the expression formula of load power and its to voltage
Derivative is formula (14):
When DC transmission system rectification side uses constant dc power control, and gamma kick is determined in inverter side use, in change of current mother
Apply small voltage fluctuation on line, application control strategy calculates the changed power of two sides converter station, and application difference substitution is partially micro-
Point；
When dynamic reactive compensation device is static synchronous compensator, believe the voltage deviation of controlled bus as input
Number, steady-state equation may be expressed as:
Δ U=UREF- U=KDIS (15)
IS=Δ U/KD=BSΔU (16)
The equivalent susceptance of static synchronous compensator is expressed as BS=1/KD, work as KDWhen taking zero, the control of static synchronous compensator
Node processed is indifference control, but is limited by static synchronous compensator output electric current, and the derivative to voltage is formula (17):
The present invention is described by reference to a small amount of embodiment.However, it is known in those skilled in the art, as
Defined by subsidiary Patent right requirement, in addition to the present invention other embodiments disclosed above equally fall in it is of the invention
In range.
Normally, all terms used in the claims are all solved according to them in the common meaning of technical field
It releases, unless in addition clearly being defined wherein.All references " one/described/be somebody's turn to do [device, component etc.] " are all opened ground
At least one example being construed in described device, component etc., unless otherwise expressly specified.Any method disclosed herein
Step need not all be run with disclosed accurate sequence, unless explicitly stated otherwise.
Claims (8)
1. a kind of method for calculating the ac and dc systems voltage coupling factor based on extension Jacobian matrix, which is characterized in that
The described method includes:
Determine the power balance equation of every bus in more feed-in ac and dc systems, and the one of more feed-in ac and dc systems
Receiving end ac bus break down disturbance when, the voltage of the bus to break down is sought in the power balance equation two sides
It leads, establishes based on every DC transmission system change of current bus in the more feed-in ac and dc systems of determination for extending Jacobian matrix to institute
State the equation X of the voltage coupling factor of the receiving end ac bus of failure；
The network parameter values and dynamic element parameter value of described more every bus of feed-in ac and dc systems are acquired, and according to the ginseng
Numerical solution extends the value of each element in Jacobian matrix, wherein the network parameter includes more feed-in alternating current-direct currents system
Conductance, susceptance and phase difference of voltage in system between the effective voltage value and bus and bus of every bus, the dynamic member
Part parameter is the parameter of the power of the dynamic element in determining more feed-in ac and dc systems, and the dynamic element includes power generation
Machine, load, DC converter and dynamic reactive compensation device；
Based on the value for calculating each element in determining extension Jacobian matrix, equation X is solved using Sparse technology, is determined
The voltage coupling factor of the every DC transmission system change of current bus to the receiving end ac bus of the failure.
2. the method according to claim 1, wherein determining the power of every bus in more feed-in ac and dc systems
Equilibrium equation, and when a receiving end ac bus of more feed-in ac and dc systems breaks down and disturbs, by the power
Voltage derivation of the equilibrium equation two sides to the bus to break down, the more feed-ins of determination established based on extension Jacobian matrix are handed over directly
Every DC transmission system change of current bus is to the voltage coupling factor of the receiving end ac bus of the failure in streaming system
Equation X includes:
When more feed-in ac and dc systems include that m returns direct current, altogether when n bus, the power balance equation table of every bus
It is shown as:
In formula, Δ Pi、ΔQiThe active power variable quantity and reactive power variable quantity for respectively indicating node i injection, in formula (1)
Equation is respectively the active power equation and reactive power equation of node i, PGi、QGiRespectively indicate having for generator injection node i
Function power output and idle power output, PLi、QLiRespectively indicate the burden with power and load or burden without work of node i, PDiIndicate the direct current function of node i
Rate, QDiIndicate the reactive power of DC converter injection node i, Ui、UjRespectively indicate the voltage of node i, j, QSiIndicate dynamic
Reactive power compensator injects the idle power output of node i, Gij、BijRespectively indicate the conductance and susceptance between node i, j, θijIt indicates
Phase difference of voltage between node i, j is straight in formula (1) for the DC transmission system in more feed-in ac and dc systems
It flows active power and is rectifying negative sign side-draw, in inversion positive sign side-draw；
When the moment that receiving end AC system kth ac bus breaks down, for formula (1), the kth ac bus is corresponding
Reactive power equation on the left of there is amount of unbalance Δ Qk, and the Δ P of the buskAnd the power equation of other buses is still protected
Holding left term is zero, if the voltage effective value of i-th bus of DC transmission system is U in more feed-in ac and dc systemsi,
The variable quantity of the voltage effective value is Δ Ui, the voltage effective value of the kth bus of receiving end AC system is Uk, voltage is effective
The variable quantity of value is Δ Uk, coefficient delta Ui/ΔUkKth for i-th change of current bus of DC transmission system with respect to receiving end AC system
The voltage coupling factors A DVCF of busik, as 1≤i≤m, 1≤k≤n, it is based on formula (1) power balance equation, and examine
The influence for considering dynamic element generating set, direct current system, part throttle characteristics and dynamic reactive compensation device, by formula (1) two sides pair
UkDerivation, production (2), expression formula are as follows:
Enable the element in formula (2) right-hand-side vectorProduction (3), expression
Formula are as follows:
In formula (3), the extension Jacobian matrix are as follows:
Element H as i ≠ j, in Jacobian matrixij、Nij、Mij、LijCalculation formula it is as follows:
Element H as i=j, in Jacobian matrixii、Nii、Mii、LiiCalculation formula it is as follows:
By formula (3) it is found that Jacobian matrix is that 2n ties up square matrix, the total 2n-1 of variable to be solved is a, the reactive power side of interior joint k
The corresponding 2k behavior redundant row of journey,For unknown quantity, 2k column are corresponded toLeave out 2k
2k column are moved on on the left of formula (3), obtain equation X, expression formula by row are as follows:
3. according to the method described in claim 2, it is characterized in that, described described more every buses of feed-in ac and dc systems of acquisition
Network parameter values and dynamic element parameter value, and according to the parameter value solve extension Jacobian matrix in each element value
Include:
As i ≠ j, Jacobi is determined according to the network parameter values of more every buses of feed-in ac and dc systems of acquisition and formula (4)
Element H in matrixij、Nij、Mij、LijValue；
As i=j, according to the network parameter values of more every buses of feed-in ac and dc systems of acquisition, dynamic element parameter value and
Formula (5) determines the element H in Jacobian matrixii、Nii、Mii、LiiValue, in which:
For non-power generator node, the derivative term of relevant generator in formula (5)It is zero,
Generator node is approximately considered generator in disturbance moment subtranient reactance X "dElectromotive force E " afterwards is kept constant, and generator is defeated
Power expression is formula (6) out, wherein θδFor generator built-in potential E " and end voltage UiAngle difference, generator power is to electricity
The derivative term of pressure is formula (7):
For non-load bus, derivative term of the load power to voltage in formula (5)It is zero, in addition, load power
It is only related with feeding point voltage effective value, and it is unrelated with its angle, therefore load power is to the derivative of level angleIt is zero；
For load bus, when the load is firm power load, constant current load power expression formula and its to voltage
Derivative be formula (8):
DC converter voltage, the current equation indicated with famous value is formula (9), the converter power side derived by formula (9)
Formula is formula (10), wherein the voltage quantities in equation (10) about change of current bus only have Ui, be free of level angle, formula (9) and
Formula (10) is as follows:
In formula, UdIndicate DC voltage, ntIndicate six pulse conversion devices series connection number, kTIndicate converter transformers no-load voltage ratio, θdTable
Show the direct current angle of overlap of rectifier or the blow-out angle of inverter, XcIndicate equivalent commutating reactance, IdIndicate DC current, kγIt indicates
The equivalent no-load voltage ratio of converter power transformer,Indicate Equivalent Power Factor angle, IiIndicate the electric current of direct current injection AC system；
When DC transmission system rectification side uses constant current control, and gamma kick is determined in inverter side use, direct current system inversion
The derivative for the power vs. voltage that side inverter is drawn from AC system is equation (11):
When dynamic reactive compensation device is Static Var Compensator, the Static Var Compensator is using the voltage for being controlled bus
Deviation is as input signal, the equivalent susceptance through ratio enlargement Absent measures compensation device, negligible delay link, output equivalent
The relationship of susceptance and voltage deviation is formula (12), and the derivative to voltage is formula (13):
Bi=-K Δ Ui=-K (Ui-Ui0) (12)
4. according to the method described in claim 3, it is characterized in that, described as i=j, according to more feed-in alternating current-direct currents of acquisition
The network parameter values, dynamic element parameter value and formula (5) of every bus of system determine the element H in Jacobian matrixii、Nii、
Mii、LiiValue further include:
For load bus, when the load is constant impedance load, the expression formula of load power and its derivative to voltage
For formula (14):
When DC transmission system rectification side uses constant dc power control, and gamma kick is determined in inverter side use, on change of current bus
Apply small voltage fluctuation, application control strategy calculates the changed power of two sides converter station, and application difference substitutes partial differential；
When dynamic reactive compensation device is static synchronous compensator, using the voltage deviation of controlled bus as input signal,
Steady-state equation may be expressed as:
Δ U=UREF- U=KDIS (15)
IS=Δ U/KD=BSΔU (16)
The equivalent susceptance of static synchronous compensator is expressed as BS=1/KD, work as KDWhen taking zero, the control section of static synchronous compensator
Point is that indifference controls, but is limited by static synchronous compensator output electric current, and the derivative to voltage is formula (17):
5. a kind of system for calculating the ac and dc systems voltage coupling factor based on extension Jacobian matrix, which is characterized in that
The system comprises:
Equation determination unit is used to determine the power balance equation of every bus in more feed-in ac and dc systems, and described
When the receiving end ac bus failure disturbance of more feed-in ac and dc systems, by the power balance equation two sides to generation
It is defeated to establish every direct current in the more feed-in ac and dc systems of determination based on extension Jacobian matrix for the voltage derivation of the bus of failure
Equation X of the electric system change of current bus to the voltage coupling factor of the receiving end ac bus of the failure；
Element computing unit is used to acquire the network parameter values and dynamic element of described more every bus of feed-in ac and dc systems
Parameter value, and solve according to the parameter value value of each element in extension Jacobian matrix, wherein the network parameter includes
Conductance, susceptance and electricity in more feed-in ac and dc systems between the effective voltage value and bus and bus of every bus
Phase angle difference is pressed, the dynamic element parameter is the parameter of the power of the dynamic element in determining more feed-in ac and dc systems,
The dynamic element includes generator, load, DC converter and dynamic reactive compensation device；
Factor specifying unit is used for based on the value for calculating each element in determining extension Jacobian matrix, using sparse skill
Art solves equation X, determines every DC transmission system change of current bus to the voltage coupling of the receiving end ac bus of the failure
Close acting factor.
6. system according to claim 5, which is characterized in that the equation determination unit determines more feed-in ac and dc systems
In every bus power balance equation, and a receiving end ac bus of more feed-in ac and dc systems failure disturb
When dynamic, the voltage derivation by the power balance equation two sides to the bus to break down is established based on extension Jacobian matrix
The more feed-in ac and dc systems of determination in every DC transmission system change of current bus to the electricity of the receiving end ac bus of the failure
Pressure the coupling factor equation X include:
When more feed-in ac and dc systems include that m returns direct current, altogether when n bus, the power balance equation table of every bus
It is shown as:
In formula, Δ Pi、ΔQiThe active power variable quantity and reactive power variable quantity for respectively indicating node i injection, in formula (1)
Equation is respectively the active power equation and reactive power equation of node i, PGi、QGiRespectively indicate having for generator injection node i
Function power output and idle power output, PLi、QLiRespectively indicate the burden with power and load or burden without work of node i, PDiIndicate the direct current function of node i
Rate, QDiIndicate the reactive power of DC converter injection node i, Ui、UjRespectively indicate the voltage of node i, j, QSiIndicate dynamic
Reactive power compensator injects the idle power output of node i, Gij、BijRespectively indicate the conductance and susceptance between node i, j, θijIt indicates
Phase difference of voltage between node i, j is straight in formula (1) for the DC transmission system in more feed-in ac and dc systems
It flows active power and is rectifying negative sign side-draw, in inversion positive sign side-draw；
When the moment that receiving end AC system kth ac bus breaks down, for formula (1), the kth ac bus is corresponding
Reactive power equation on the left of there is amount of unbalance Δ Qk, and the Δ P of the buskAnd the power equation of other buses is still protected
Holding left term is zero, if the voltage effective value of i-th bus of DC transmission system is U in more feed-in ac and dc systemsi,
The variable quantity of the voltage effective value is Δ Ui, the voltage effective value of the kth bus of receiving end AC system is Uk, voltage is effective
The variable quantity of value is Δ Uk, coefficient delta Ui/ΔUkKth for i-th change of current bus of DC transmission system with respect to receiving end AC system
The voltage coupling factors A DVCF of busik, as 1≤i≤m, 1≤k≤n, it is based on formula (1) power balance equation, and examine
The influence for considering dynamic element generating set, direct current system, part throttle characteristics and dynamic reactive compensation device, by formula (1) two sides pair
UkDerivation, production (2), expression formula are as follows:
Enable the element in formula (2) right-hand-side vectorProduction (3), expression formula are as follows:
In formula (3), the extension Jacobian matrix are as follows:
Element H as i ≠ j, in Jacobian matrixij、Nij、Mij、LijCalculation formula it is as follows:
Element H as i=j, in Jacobian matrixii、Nii、Mii、LiiCalculation formula it is as follows:
By formula (3) it is found that Jacobian matrix is that 2n ties up square matrix, the total 2n-1 of variable to be solved is a, the reactive power side of interior joint k
The corresponding 2k behavior redundant row of journey,For unknown quantity, 2k column are corresponded toLeave out 2k
2k column are moved on on the left of formula (3), obtain equation X, expression formula by row are as follows:
7. system according to claim 5, which is characterized in that the element computing unit acquires more feed-in alternating current-direct currents
The network parameter values and dynamic element parameter value of every bus of system, and solved in extension Jacobian matrix according to the parameter value
The value of each element includes:
As i ≠ j, Jacobi is determined according to the network parameter values of more every buses of feed-in ac and dc systems of acquisition and formula (4)
Element H in matrixij、Nij、Mij、LijValue；
As i=j, according to the network parameter values of more every buses of feed-in ac and dc systems of acquisition, dynamic element parameter value and
Formula (5) determines the element H in Jacobian matrixii、Nii、Mii、LiiValue, in which:
For non-power generator node, the derivative term of relevant generator in formula (5)It is zero,
Generator node is approximately considered generator in disturbance moment subtranient reactance X "dElectromotive force E " afterwards is kept constant, and generator is defeated
Power expression is formula (6) out, wherein θδFor generator built-in potential E " and end voltage UiAngle difference, generator power is to electricity
The derivative term of pressure is formula (7):
For non-load bus, derivative term of the load power to voltage in formula (5)It is zero, in addition, load power
It is only related with feeding point voltage effective value, and it is unrelated with its angle, therefore load power is to the derivative of level angleIt is zero；
For load bus, when the load is firm power load, constant current load power expression formula and its to voltage
Derivative be formula (8):
DC converter voltage, the current equation indicated with famous value is formula (9), the converter power side derived by formula (9)
Formula is formula (10), wherein the voltage quantities in equation (10) about change of current bus only have Ui, be free of level angle, formula (9) and
Formula (10) is as follows:
In formula, UdIndicate DC voltage, ntIndicate six pulse conversion devices series connection number, kTIndicate converter transformers no-load voltage ratio, θdTable
Show the direct current angle of overlap of rectifier or the blow-out angle of inverter, XcIndicate equivalent commutating reactance, IdIndicate DC current, kγIt indicates
The equivalent no-load voltage ratio of converter power transformer,Indicate Equivalent Power Factor angle, IiIndicate the electric current of direct current injection AC system；
When DC transmission system rectification side uses constant current control, and gamma kick is determined in inverter side use, direct current system inversion
The derivative for the power vs. voltage that side inverter is drawn from AC system is equation (11):
When dynamic reactive compensation device is Static Var Compensator, the Static Var Compensator is using the voltage for being controlled bus
Deviation is as input signal, the equivalent susceptance through ratio enlargement Absent measures compensation device, negligible delay link, output equivalent
The relationship of susceptance and voltage deviation is formula (12), and the derivative to voltage is formula (13):
Bi=-K Δ Ui=-K (Ui-Ui0) (12)
8. system according to claim 7, which is characterized in that the element computing unit is in i=j, according to acquisition
The network parameter values, dynamic element parameter value and formula (5) of more every buses of feed-in ac and dc systems determine in Jacobian matrix
Element Hii、Nii、Mii、LiiValue further include:
For load bus, when the load is constant impedance load, the expression formula of load power and its derivative to voltage
For formula (14):
When DC transmission system rectification side uses constant dc power control, and gamma kick is determined in inverter side use, on change of current bus
Apply small voltage fluctuation, application control strategy calculates the changed power of two sides converter station, and application difference substitutes partial differential；
When dynamic reactive compensation device is static synchronous compensator, using the voltage deviation of controlled bus as input signal,
Steady-state equation may be expressed as:
Δ U=UREF- U=KDIS (15)
IS=Δ U/KD=BSΔU (16)
The equivalent susceptance of static synchronous compensator is expressed as BS=1/KD, when KD takes zero, the control section of static synchronous compensator
Point is that indifference controls, but is limited by static synchronous compensator output electric current, and the derivative to voltage is formula (17):
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| CN112350595A (en) * | 2020-11-19 | 2021-02-09 | 中南大学 | Analog impedance control method for inhibiting input unbalance influence of AC/DC matrix converter |
| CN112350595B (en) * | 2020-11-19 | 2021-09-03 | 中南大学 | Analog impedance control method for inhibiting input unbalance influence of AC/DC matrix converter |
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