CN110365026A - Design method based on frequency domain margin index adjusting PSS4B parameter power oscillation damping - Google Patents
Design method based on frequency domain margin index adjusting PSS4B parameter power oscillation damping 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
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- H—ELECTRICITY
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Abstract
The present invention relates to a kind of design methods based on frequency domain margin index adjusting PSS4B parameter power oscillation damping, for designing the PSS4B parameter under a variety of methods of operation of multimachine, preferably to inhibit system low frequency and ultra-low frequency oscillation phenomenon, guarantee that system meets stable operation requirement, belongs to power grid security technical field.The design method includes: that one characteristic of order using controlled power grid transfer function matrix near frequency of oscillation calculates singular value and left and right singular vector, and carries out Truncated Singular Value Decomposition；The objective function based on frequency domain margin index adjusting multimachine PSS4B parameter is provided according to the Truncated Singular Value Decomposition of controlled power grid；PSS4B is provided in the phase restriction condition of ultralow frequency range；The critical gain of PSS4B is determined in the diagonal dominance characteristic of excitation mode frequency range according to controlled grid metrics；Solving optimization model obtains designed PSS4B parameter value.
Description
Technical field
The invention belongs to power grid security technical fields, are related to a kind of PSS4B Parameters design, and in particular to one kind is based on
The design method of the adjusting PSS4B parameter power oscillation damping of frequency domain margin index.
Background technique
Water power be dominant AC system ultra-low frequency oscillation phenomenon at home, outer actual electric network operation in be found, have hold
The characteristics of continuous time is long, frequency of oscillation is extremely low (being less than 0.1Hz), threatens system safe and stable operation.Since Yunnan Power System and south
After square power grid major network Asynchronous Interconnection, also there is ultra-low frequency oscillation phenomenon in Yunnan Power System.Inhibit the effective means of ultra-low frequency oscillation
First is that installation power system stabilizer, however traditional power system stabilizer 2B can only inhibit very well frequency higher
Local mode, the commonality schemata inhibitory effect of the region mode relatively low for frequency and ultralow frequency is bad, therefore is considered as
PSS4B is to inhibit ultra-low frequency oscillation.PSS4B has basic, normal, high three branches, and parameter is more, frequency characteristic is more flexible, compares
Traditional PS S has higher freedom degree.However the three of PSS4B branches couple in frequency range, have a large amount of parameter, are it
Adjusting brings difficulty.
PSS4B parameter designing need to comprehensively consider system stability and regulation performance, and should be able to cope with electric under multi-operating condition
The steady demand of Force system.Method proposed by the present invention only relies on the singular value for calculating the underdamping mode under several methods of operation
With singular vector, the optimization object function based on frequency domain nargin can be provided, a complicated parameter tuning problem can be converted
It is the powerful of PSS4B parameter designing for simple and easy Optimization Solution problem, and is never applied to solve ultra-low frequency oscillation
Problem.
The information disclosed in the background technology section is intended only to increase the understanding to general background of the invention, without answering
When being considered as recognizing or imply that the information constitutes the prior art already known to those of ordinary skill in the art in any form.
Summary of the invention
It is an object of the present invention to solve the deficiency of the existing technology and provide one kind to be adjusted based on frequency domain margin index
The design method of PSS4B parameter power oscillation damping, this method have taken into account the stability requirement and regulation performance requirement of system, only
By the singular value and singular vector for calculating each underdamping mode, corresponding Optimized model is solved.
To achieve the above object, The technical solution adopted by the invention is as follows:
Design method based on frequency domain margin index adjusting PSS4B parameter power oscillation damping, comprising the following steps:
1) model analysis is carried out to the underdamping mode of system, determines the unit of installation PSS4B；
2) Truncated Singular Value Decomposition is carried out to controlled grid metrics under each underdamping mode frequency；
3) PSS4B parameter optimization target is determined according to weighted frequency domain nargin；
4) phase restriction condition is determined according to the ideal phase-frequency characteristic curve of PSS4B；
5) parameter bound constraint condition is determined according to the parameter bound of PSS4B；
6) Optimized model determined by optimization aim and phase restriction item, parameter bound constraint condition is solved；
7) PSS4B is solved in the critical gain of excitation mode frequency range；
8) PSS4B parameter is finally determined based on above-mentioned steps.
It is further preferred that the underdamping mode to system in the step 1) carries out model analysis, determine
The unit for installing PSS4B is that participation is higher than 0.8 Power Plant in underdamping mode under each method of operation of real system；
Participation P of the kth platform unit about ith feature valueikIs defined as:
Pik=vkiuki
Wherein, vkiAnd ukiIt is worth k-th of element of corresponding left and right feature vector for ith feature；Assuming that ith feature
Value is the characteristic value of underdamping mode, by PkiIt can determine unit of the participation higher than 0.8 by arrangement from big to small to determine installation
The unit of PSS4B.
It is further preferred that in the step 2) under each underdamping mode frequency to controlled grid metrics
Carry out Truncated Singular Value Decomposition step specifically:
(1) matrix of controlled power grid is G (s), and s is Laplace operator, and s=σ+j ω, σ are the real part of s, and ω is the void of s
Portion, j are imaginary unit；Ignore the real part of underdamping mode characteristic values, i.e. σ ≈ 0, G (s) then can be write G (j by s=j ω
ω)；Singular value decomposition is carried out to controlled grid metrics G (j ω) at each underdamping mode frequency ω:
G (j ω)=U Σ VH, formula (1)；
In formula (1), U and V are right, left singular vector matrix, ()HThe conjugate transposition for taking corresponding matrix is represented, Σ is
Singular value matrix, diagonal element are known as the singular value of matrix G (j ω), meetAnd Σ1=diag (σ1,
σ2,...,σr), it arranges in the following order:
σ1≥σ2≥...≥σr> 0, r=rank (G)；
Wherein, rank (G) indicates to take the order of matrix G；
(2) controlled grid metrics G (j ω) is written as by dyad decomposed form according to above-mentioned relation:
Wherein, i indicates the subscript number of the respectively singular value greater than 0；
(3) according to the characteristic of controlled grid metrics G (j ω), there is r=rank (G) at each underdamping mode frequency ω
≈ 1, therefore obtain the Truncated Singular Value Decomposition of controlled power grid:
G(jω)≈σ1u1v1 H, formula (3)；
In formula (3), σ1It is the maximum singular value of G (j ω), u1And v1For corresponding right, the left singular vector of maximum singular value.
It is further preferred that determining PSS4B parameter optimization target according to weighted frequency domain nargin in the step 3)
Step specifically:
(1) G (s) is the transfer function matrix of controlled power grid, and diagonal matrix H (s) is the transfer function matrix of PSS4B, by G
(s) and the stability margin of the constituted system of H (s) is defined as its return difference matrix D (s)=I-G (s) H (s) determinant to complex plane
The distance S of originm(j ω):
sm(j ω)=| det (D (j ω)) |=| det (I-G (j ω) H (j ω)) |, formula (4)；
(2) stability margin is deformed according to the controlled grid metrics Truncated Singular Value Decomposition of gained in step 2), is obtained
Formula (5)；
sm(j ω)=| det (H-1(jω)-G(jω))×det(H(jω))|≈|det(H-1(jω)-σ1u1v1 H)×
Det (H (j ω)) |, formula (5)；
(3) pay attention to correcting A+uv to Arbitrary Matrix A and its order 1T, following relationship establishment:
det(Α+uvT)=(1+vTA-1U) det (A), formula (6)；
Later, further abbreviation stability margin:
sm(jω)≈|1-σ1v1 HH(jω)u1|×|det(H-1(j ω)) det (H (j ω)) |=| 1- σ1v1 HH(jω)
u1|, formula (7)；
(4) weight Weight of i-th of mode in PSS4B parameter tuning is determinedi, optimization aim finally can be obtained:
In formula (8): N is consideration mode quantity, ωiFor the frequency of oscillation of mode i,For controlled power grid G (j
ωi) maximum singular value and corresponding right, left singular vector, d=[FL(I,H),KL(I,H),TL(I,H)3,TL(I,H)4,TL(I,H)5,
TL(I,H)6]TFor PSS4B parameter vector, WeightiFor the weight of mode i, and meet the following conditions:
It is further preferred that determining phase about according to the ideal phase-frequency characteristic curve of PSS4B in the step 4)
Beam condition step specifically:
(1) ultra-low frequency oscillation mode characteristic values real part σ is determinedulApproximate expression:
In formula (9), ωulFor ultra-low frequency oscillation mode characteristic values imaginary part, KDSIt is asked for each unit rotor kinetic damping coefficient
With M∑For the summation of each set generator rotor motion inertia time constant, e is the column vector that all elements are 1, diagonal matrix
HPSSIt (s) is PSS transfer function matrix；FPSSIt (s) is PSS forward path transfer function matrix, GMiIt (s) is the tune of i-th unit
Fast device-prime mover transmission function, expression formula are as follows:
GMi(s)=- Ggi(s)·Ti(s)
Wherein, GgiIt (s) is i-th machine unit speed regulating device transmission function, TiIt (s) is i-th unit prime mover transmission function；
In active-idle circuit feedback model of electric system system,
In formula: GQ1It (s) is transfer function matrix introduced after consideration automatic voltage adjustor of power generator control；To angular moment
Battle array HPSSIt (s) is PSS transfer function matrix；FPSSIt (s) is PSS forward path transfer function matrix；GEX(s) it is transmitted for excitation system
Jacobian matrix；Diagonal matrix GMIt (s) is governor-prime mover transfer function matrix, i-th of diagonal element GMiIt (s) is i-th machine
Governor-prime mover transmission function of group, expression formula are as follows:
GMi(s)=- Ggi(s)·Ti(s)
Wherein, GgiIt (s) is i-th machine unit speed regulating device transmission function, TiIt (s) is i-th unit prime mover transmission function；
(2) PSS transfer function matrix H is determinedPSS(s) offset angle:
The portion that PSS influences ultra-low frequency oscillation mode characteristic values in ultra-low frequency oscillation mode characteristic values real part approximate expression
Minute mark makees σul-PSS, have:
In formula (10): FPSSji(jωul) it is FPSS(jωul) matrix jth row, i-th arrange element；HPSSi(jωul) be
HPSS(jωul) i-th of diagonal element, i.e., the frequency characteristic of i-th unit PSS；
To the PSS of i-th unit, selection makes HPSSi(jωul) compensation FPSS(jωul) in a certain element FPSSji(jωul)
Delayed phase enhances ultra-low frequency oscillation stability；Due to | FPSSii(jωul)|>|FPSSji(jωul) |, j ≠ i, therefore pass through
HPSSi(jωul) compensation FPSSii(jωul) meet:
arg[HPSSi(jωul)]+arg[FPSSii(jωul)]=0
Wherein, arg () representative takes corresponding argument of complex number；
When it is implemented, need to only meet FPSSji(jωul) and HPSSi(jωul) difference less than 30 °；
|arg[HPSSi(jωul)]-arg[FPSSii(jωul)] |≤30 °, formula (11)
Formula (11) is phase restriction, sets HPSSi(jωul) it is made to meet formula (11), it can best enhance ultralow frequency
Oscillation mode damping.
It is further preferred that the step 5) determines in parameter bound constraint according to the parameter bound of PSS4B,
Determine the bound of the high, medium and low frequency range centre frequency of PSS4B, gain and time constant.
It is further preferred that step 6) solution is determined by optimization aim and phase restriction item, parameter bound constraint condition
Optimized model in, following Optimized model is solved by Matlab optimization toolbox, obtains the parameter of PSS4B；
|arg[HPSSi(jωul)]-arg[FPSSii(jωul)]|≤30°
Wherein FL(I,H)For the centre frequency of the basic, normal, high frequency range of PSS4B, KL(I,H)For the increasing of the basic, normal, high frequency range of PSS4B
Benefit, TL(I,H)3,TL(I,H)4,TL(I,H)5,TL(I,H)6For the time constant of the basic, normal, high frequency range of PSS4B；Its bound is according to practical need
Want sets itself.
It is further preferred that step 7) the solution PSS4B is specific in the critical gain step of excitation mode frequency range
Are as follows:
(1) diagonal matrix K is definedPSSFor critical gain matrix, then it meets following condition:
det(I-G(jω)·KPSSH (j ω))=0；
(2) all number functions are asked to system return difference matrix determinant det (D (s)) under critical gain:
Defining enc () is all number functions, calculates polynomial matrix determinant and surrounds origin clockwise on a complex plane
Number；
Since PSS4B matrix H (s) is free of right half complex plane zero, pole, enc (H (s))=0, and open cycle system G (s) is steady
It is fixed, then according to multi-input multi-output system Nyquist's stability criterion, the necessary and sufficient condition of system closed-loop stabilization are as follows:
(3) since PSS4B matrix H (s) is free of right half complex plane zero, pole, enc (H (s))=0, and open cycle system G (s)
Stablize, then according to multi-input multi-output system Nyquist's stability criterion, the necessary and sufficient condition of system closed-loop stabilization are as follows:
(4) in the higher frequency band where excitation mode, G (s) is diagonally dominant matrix, KPSSIt is diagonal matrix with H (s), therefore
(K-1 PSSH-1(s)-G (s)) it is still diagonally dominant matrix, therefore above formula is equivalent to:
Wherein, M is adjusting PSS4B parameter unit number, KPSSjFor the critical gain of jth platform unit PSS4B, HjIt (s) is the
The transmission function of j platform unit PSS4B, GjjIt (s) is the transmission function of jth platform unit the machine excitation reference voltage to the machine revolving speed；
(5) to jth platform unit, critical gain KPSSjMeet following condition
(6) initial value of each band gain that adjusting obtains in step 6) is multiplied by with the 1/3 of critical gain (as step 6) is asked
Each band gain value that solution obtains), obtain final yield value.
It is further preferred that the PSS4B parameter, time constant in the step 8) are determined according to step 6), each frequency
Duan Zengyi is determined according to the final gain value of step 7).
Underdamping mode of the present invention refers to oscillation mode of the characteristic value damping ratio less than 0.03.
Compared with prior art, the present invention has the advantages that:
Method proposed by the present invention can cope with power system stabilizer 4B parameter tuning problem under multi-operating condition,
Parameter designing process only relies on the system frequency domain response data that measurement obtains and calculates singular value and singular vector, can provide all
Meet the stabilization of system and the PSS4B parameter of regulation performance constraint, can convert a complicated parameter tuning problem to simply
Easy Optimization Solution problem designs PSS4B parameter.This method is guaranteeing designed PSS4B offer appropriate phase compensation rate
Meanwhile its amplitude-frequency characteristic is optimized, the stability margin of system is maximised, and can guarantee that PSS overall gain is no more than and face
Boundary's gain.
Detailed description of the invention
Fig. 1 is setting based on frequency domain margin index adjusting PSS4B parameter power oscillation damping provided in an embodiment of the present invention
The flow chart of meter method；
Fig. 2 is the PSS4B common model that application example of the present invention provides；
Fig. 3 is the frequency departure signal delta ω of application example offer of the present invention as low frequency PSS4B low frequency branch and intermediate frequency
The low-pass filter model structure that the input signal of branch is passed through；
Fig. 4 is the power deviation signal delta P that application example of the present invention provideseWhat the input signal as high-frequency branch was passed through
The model structure of bandpass filter and integrator；
Fig. 5 is the system installation PSS control block diagram that application example of the present invention provides；
Fig. 6 is the line map for four machines, two regional power system that application example of the present invention provides；
Fig. 7 is the waveform of tie-line power transmission after the three-phase shortcircuit excision that application example of the present invention provides.
Fig. 8 is active-idle circuit feedback model of electric system system of the present invention.
Specific embodiment
To make the objectives, technical solutions, and advantages of the present invention clearer, right below with reference to embodiment and attached drawing
The present invention is described in further details.Here, exemplary embodiment and its explanation of the invention is used to explain the present invention, but simultaneously
It is not as a limitation of the invention.
A kind of design method of the adjusting PSS4B parameter power oscillation damping based on frequency domain margin index, including following step
It is rapid:
1) unit that model analysis determines installation PSS4B is carried out to the underdamping mode of system；
2) Truncated Singular Value Decomposition is carried out to controlled grid metrics under each underdamping mode frequency；
3) PSS4B parameter optimization target is determined according to weighted frequency domain nargin；
4) phase restriction is determined according to the ideal phase-frequency characteristic curve of PSS4B；
5) determine that parameter bound constrains according to the parameter bound of PSS4B；
6) Optimized model determined by optimization aim and constraint condition is solved；
7) PSS4B is solved in the critical gain of excitation mode frequency range；
8) PSS4B parameter is finally determined based on above-mentioned steps.
The unit that installation PSS4B is determined in the step 1) is to join in underdamping mode under each method of operation of real system
It is higher than 0.8 Power Plant with degree.
Participation P of the kth platform unit about ith feature valueikIt is defined as
Pik=vkiuki
Wherein, vkiAnd ukiIt is worth k-th of element of corresponding left and right feature vector for ith feature.Assuming that ith feature
Value is the characteristic value of underdamping mode, by PkiIt can determine unit of the participation higher than 0.8 by arrangement from big to small to determine installation
The unit of PSS4B.
Truncated Singular Value Decomposition step is carried out to controlled grid metrics under each underdamping mode frequency in the step 2)
It is rapid:
(1) matrix of controlled power grid be G (s), s=σ+j ω (σ be s real part, ω be s imaginary part, j is imaginary unit),
The real part (i.e. G (s) then can be write G (j ω) by σ ≈ 0, s=j ω) for ignoring underdamping mode characteristic values, in each underdamping
Singular value decomposition is carried out to controlled grid metrics G (j ω) under mode frequency ω:
G (j ω)=U Σ VH
U and V is right, left singular vector matrix in formula, and Σ is singular value matrix, and diagonal element is known as matrix G's (j ω)
Singular value meetsAnd Σ1=diag (σ1,σ2,...,σr), it arranges in the following order:
σ1≥σ2≥...≥σr> 0, r=rank (G)
Wherein rank (G) indicates to take the order of matrix G；
(2) controlled grid metrics G (j ω) is written as by dyad decomposed form according to above-mentioned relation:
Wherein, i indicates the subscript number of the respectively singular value greater than 0.
(3) since controlled grid metrics G (j ω) is when frequency is lower, meetTherefore every
There is r=rank (G) ≈ 1 under a underdamping mode frequency ω, therefore obtain the Truncated Singular Value Decomposition of controlled power grid:
G(jω)≈σ1u1v1 H
σ in formula1It is the maximum singular value of G (j ω), u1And v1For corresponding right, the left singular vector of maximum singular value.
Optimization aim step is determined according to weighted frequency domain nargin in the step 3):
(1) G (s) is the transfer function matrix of controlled power grid, and diagonal matrix H (s) is the transfer function matrix of PSS4B, by G
(s) and the stability margin of the constituted system of H (s) is defined as its return difference matrix D (s)=I-G (s) H (s) determinant to complex plane
The distance S of originm(j ω):
sm(j ω)=| det (D (j ω)) |=| det (I-G (j ω) H (j ω)) |
(2) stability margin is deformed according to the controlled grid metrics Truncated Singular Value Decomposition of gained in step 2),
sm(j ω)=| det (H-1(jω)-G(jω))×det(H(jω))|≈|det(H-1(jω)-σ1u1v1 H)·
det(H(jω))|
(3) pay attention to correcting A+uv to Arbitrary Matrix A and its order 1T, following relationship establishment:
det(Α+uvT)=(1+vTA-1u)×det(A)
Further abbreviation stability margin:
sm(jω)≈|1-σ1v1 HH(jω)u1|×|det(H-1(j ω)) × det (H (j ω)) |=| 1- σ1v1 HH(jω)
u1|
(4) weight Weight of i-th of mode in PSS4B parameter tuning is determinedi, optimization aim finally can be obtained:
In formula: N is consideration mode quantity, ωiFor the frequency of oscillation of mode i,For controlled power grid G (j
ωi) maximum singular value and corresponding right, left singular vector, d=[FL(I,H),KL(I,H),TL(I,H)3,TL(I,H)4,TL(I,H)5,
TL(I,H)6]TFor PSS4B parameter vector, WeightiFor the weight of mode i, and meet the following conditions
Phase restriction step is determined according to the ideal phase-frequency characteristic curve of PSS4B in the step 4):
(1) ultra-low frequency oscillation mode characteristic values real part approximate expression is determined:
ω in above formulaulFor ultra-low frequency oscillation mode characteristic values imaginary part, KDSFor the summation of each unit rotor kinetic damping coefficient, MS
For the summation of each set generator rotor motion inertia time constant, e is the column vector that all elements are 1, diagonal matrix HPSS
It (s) is PSS transfer function matrix；FPSSIt (s) is PSS forward path transfer function matrix, GMiIt (s) is the speed regulation of i-th unit
Device-prime mover transmission function, expression formula are as follows:
GMi(s)=- Ggi(s)×Ti(s)
Wherein GgiIt (s) is i-th machine unit speed regulating device transmission function, TiIt (s) is i-th unit prime mover transmission function.
Active-idle circuit feedback model of electric system system is as shown in Figure 8；
In Fig. 8:
In formula: GQ1It (s) is transfer function matrix introduced after consideration automatic voltage adjustor of power generator control；To angular moment
Battle array HPSSIt (s) is PSS transfer function matrix；FPSSIt (s) is PSS forward path transfer function matrix；GEX(s) it is transmitted for excitation system
Jacobian matrix；Diagonal matrix GMIt (s) is governor-prime mover transfer function matrix, i-th of diagonal element GMiIt (s) is i-th machine
Governor-prime mover transmission function of group, expression formula are
GMi(s)=- Ggi(s)·Ti(s)
Wherein GgiIt (s) is i-th machine unit speed regulating device transmission function, TiIt (s) is i-th unit prime mover transmission function.
(2) PSS transfer function matrix H is determinedPSS(s) offset angle.
The portion that PSS influences ultra-low frequency oscillation mode characteristic values in ultra-low frequency oscillation mode characteristic values real part approximate expression
Minute mark makees σul-PSS, have:
In formula: FPSSji(jωul) it is FPSS(jωul) matrix jth row, i-th arrange element；HPSSi(jωul) it is HPSS(j
ωul) i-th of diagonal element, i.e., the frequency characteristic of i-th unit PSS.
To the PSS of i-th unit, selection makes HPSSi(jωul) compensation FPSS(jωul) in a certain element FPSSji(jωul)
Delayed phase enhances ultra-low frequency oscillation stability.In general | FPSSii(jωul)|>|FPSSji(jωul) |, j ≠ i, thus it is logical
Cross HPSSi(jωul) compensation FPSSii(jωul) meet:
arg[HPSSi(jωul)]+arg[FPSSii(jωul)]=0
Wherein, arg () representative takes corresponding argument of complex number；
When it is implemented, need to only meet FPSSji(jωul) and HPSSi(jωul) difference less than 30 °.
|arg[HPSSi(jωul)]-arg[FPSSii(jωul)] |≤30 °,
Above formula is phase restriction, sets HPSSi(jωul) it meet above formula best to enhance ultra-low frequency oscillation mould
Formula damping.
Parameter bound in the step 5) according to PSS4B determines in parameter bound constraint, determines that PSS4B is high, medium and low
The bound of frequency range centre frequency, gain and time constant；
Solving optimization model in the step 6) passes through Matlab optimization toolbox solving optimization mould
Type；
PSS4B is solved in the critical gain step of excitation mode frequency range in the step 7):
(1) increase to equal proportion the gain link parameter of basic, normal, high three frequency range branches obtained in step 6) simultaneously
KL、KI、KH, low frequency oscillations mode damping is further enhanced.But the gain of PSS is limited by excitation mode, if
Its is excessive to easily lead to DCgenerator motor field mode unstability.Introduce critical gain matrix KPSSConcept.Define diagonal matrix KPSSIt is critical
Gain matrix, then it meets following condition
det(I-G(jω)·KPSSH (j ω))=0
(2) all number functions are asked to system return difference matrix determinant det (D (s)) under critical gain
Defining enc () is all number functions, calculates polynomial matrix determinant and surrounds origin clockwise on a complex plane
Number；
Since PSS4B matrix H (s) is free of right half complex plane zero, pole, enc (H (s))=0, and open cycle system G (s) is steady
Fixed, then according to multi-input multi-output system Nyquist's stability criterion, the necessary and sufficient condition of system closed-loop stabilization is
(3) since PSS4B matrix H (s) is free of right half complex plane zero, pole, enc (H (s))=0, and open cycle system G (s)
Stablize, then according to multi-input multi-output system Nyquist's stability criterion, the necessary and sufficient condition of system closed-loop stabilization is
(4) pay attention in the higher frequency band where excitation mode, G (s) is diagonally dominant matrix, KPSSIt is diagonal matrix with H (s),
Therefore (K-1 PSSH-1(s)-G (s)) it is still diagonally dominant matrix, therefore above formula is equivalent to
In formula: M is adjusting PSS4B parameter unit number, KPSSjFor the critical gain of jth platform unit PSS4B, HjIt (s) is the
The transmission function of j platform unit PSS4B, GjjIt (s) is the transmission function of jth platform unit the machine excitation reference voltage to the machine revolving speed.
(5) to jth platform unit, critical gain KPSSjMeet following condition
(6) it is multiplied by the initial value for adjusting obtained each band gain before with the 1/3 of critical gain, obtains final gain
Value.
PSS4B parameter in the step 8) is determined according to above-mentioned steps.
Application example
In application example of the present invention, multimachine power train under a kind of multi-operating condition based on system frequency response is provided
System hydraulic turbine PID type governor parameter design method, as shown in Figure 1, this method comprises:
Step 101: model analysis being carried out to the underdamping mode of system, determines the unit of installation PSS4B；
Step 102: Truncated Singular Value Decomposition being carried out to controlled grid metrics under each underdamping mode frequency；
Step 103: optimization aim is determined according to weighted frequency domain nargin；
Step 104: phase restriction is determined according to the ideal phase-frequency characteristic curve of PSS4B；
Step 105: determining that parameter bound constrains according to the parameter bound of PSS4B；
Step 106: solving the Optimized model determined by optimization aim and constraint condition；
Step 107: solving PSS4B in the critical gain of excitation mode frequency range；
Step 108: finally determining PSS4B parameter based on above-mentioned steps.
When it is implemented, each undetermined parameter in the PSS4B model that design such as Fig. 2 is provided, wherein K, T are respectively indicated wait adjust
Gain and time constant, usually enable TH9=TH3,TH10=TH4,TH11=TH5,TH12=TH6,TI3=TI4=TI5=TI6=0, Δ
ωL-IIn expression, the input quantity of low-frequency range, Δ ωHIndicate the input quantity of high band, VSTIndicate the output quantity of PSS4B.Corresponding ginseng
Relationship between number is as follows:
There is higher order and control freedom degree compared to traditional one-segment PSS, PSS4B, and super with can independently adjust
Low (0.01-0.1Hz) of preceding delay component and gain link parameter, in (0.1-1Hz), high (1-10Hz) three frequency range branches.
Since power signal has idle anti-tune in low-frequency range, and frequency signal is in high band that there are noises, therefore
PSS4B low frequency and Mid Frequency input signal use frequency departure signal delta ω, and high band input signal uses power deviation signal
ΔPe.Fig. 3 gives frequency departure signal delta ω as warp before low frequency PSS4B low frequency branch and the input signal of intermediate frequency branch
The low-pass filter model structure crossed；Fig. 4 gives power deviation signal delta PeInput signal as high-frequency branch is passed through
Bandpass filter and integrator model structure.
When it is implemented, controlled power grid and the PSS4B installed can be regarded as a control block diagram as shown in Figure 5, scheme
Middle G (s) is the transfer function matrix of controlled power grid, and diagonal matrix H (s) is the transfer function matrix of PSS.Mould is carried out to the system
State analysis, finds out and wherein damps weaker several mode, analyze the participation of each unit, find out the underdamping under each method of operation
Unit of the high unit of participation as installation PSS4B in mode.
Participation P of the kth platform unit about ith feature valuekiIt is defined as
Pik=vkiuki
Wherein, vkiAnd ukiIt is worth k-th of element of corresponding left and right feature vector for ith feature.Assuming that ith feature
Value is the characteristic value of underdamping mode, by PkiIt can determine the high unit of participation by arrangement from big to small.
When it is implemented, carrying out Truncated Singular Value Decomposition to controlled grid metrics under each underdamping mode frequency:
(1) real part for ignoring underdamping mode characteristic values, to controlled grid metrics G at each underdamping mode frequency ω
(j ω) carries out singular value decomposition:
G (j ω)=U Σ VH
U and V is right, left singular vector matrix in formula, and Σ is singular value matrix, and diagonal element is known as matrix G's (j ω)
Singular value meetsAnd Σ1=diag (σ1,σ2,...,σr), it arranges in the following order:
σ1≥σ2≥...≥σr> 0, r=rank (G)
(2) controlled grid metrics G (j ω) is written as by dyad decomposed form according to above-mentioned relation:
(3) according to the characteristic of controlled grid metrics G (j ω), there is r=rank (G) at each underdamping mode frequency ω
≈ 1, therefore obtain the Truncated Singular Value Decomposition of controlled power grid:
G(jω)≈σ1u1v1 H
σ in formula1It is the maximum singular value of G (j ω), u1And v1For corresponding right, the left singular vector of maximum singular value.
When it is implemented, determining optimization aim according to weighted frequency domain nargin:
It (1) is system by the distance definition of system return difference matrix D (s)=I-G (s) H (s) determinant to complex plane origin
Stability margin:
sm(j ω)=| det (D (j ω)) |=| det (I-G (j ω) H (j ω)) |
(2) stability margin is deformed according to the controlled grid metrics Truncated Singular Value Decomposition of gained in step 2),
sm(j ω)=| det (H-1(jω)-G(jω))·det(H(jω))|≈|det(H-1(jω)-σ1u1v1 H)·
det(H(jω))|
(3) further abbreviation stability margin:
sm(jω)≈|1-σ1v1 HH(jω)u1|·|det(H-1(j ω)) det (H (j ω)) |=| 1- σ1v1 HH(jω)
u1|
(4) weight Weight of i-th of mode in PSS4B parameter tuning is determinedi, optimization aim finally can be obtained:
In formula: N is consideration mode quantity, ωiFor the frequency of oscillation of mode i,For controlled power grid G (j ωi)
Maximum singular value and corresponding right, left singular vector, d=[FL(I,H),KL(I,H),TL(I,H)3,TL(I,H)4,TL(I,H)5,TL(I,H)6]TFor
PSS4B parameter vector, WeightiFor the weight of mode i, and meet the following conditions
When it is implemented, determining the constraint condition of Optimized model, including phase restriction and restriction on the parameters.Phase restriction passes through
Ideal phase frequency curve determines, restriction on the parameters by the high, medium and low frequency range centre frequency of PSS4B, gain and time constant bound
It determines.
When it is implemented, if equal proportion increase the gain link parameter K of basic, normal, high three frequency range branches simultaneouslyL、KI、
KH, low frequency oscillations mode damping is further enhanced.But the gain of PSS is limited by excitation mode, if its mistake
DCgenerator motor field mode unstability is easily led to greatly.Therefore consider to seek critical gain of the system under excitation mode frequency.Critical gain
It is acquired by following formula:
After acquiring critical gain, the initial value for adjusting obtained each band gain before is multiplied by with the 1/3 of critical gain, as
The final yield value of each frequency range.So far, the parameter value of PSS4B can be determined completely.
For example, our four machine based on ieee standard, two district systems adjust PSS4B to inhibit low frequency and ultra-low frequency oscillation
Mode.Four machines, two district system is emulated in MATLAB, four machines, two district system model is as shown in fig. 6, wherein G is indicated
Generator, L indicate that load, C indicate capacitor.
Model analysis is carried out to initial data first, it is found that there are 2 underdamping modes under the method for operation, such as table 1.
Table 1
| Characteristic value | Frequency (Hz) | Damping ratio | |
| Mode 1 | -0.00222+0.15080i | 0.0240 | 0.0147 |
| Mode 2 | -0.05976+3.53769i | 0.5630 | 0.0169 |
In order to protrude the effect of PSS4B, tetra- units of G1~G4 all installation PSS4B are selected.
SVD decomposition is carried out under two underdamping mode respective frequencies respectively to controlled grid metrics, it is available controlled
The Truncated Singular Value Decomposition of grid metrics, and determine final optimization object function:
Wherein, weight coefficient
Phase restriction is determined then according to the ideal phase-frequency characteristic curve of PSS4B, is determined according to the parameter bound of PSS4B
Parameter bound constraint, is keyed in into MATLAB corresponding program.
The Optimized model determined by optimization aim and constraint condition is solved, T is enabledH9=TH3,TH10=TH4,TH11=TH5,TH12
=TH6,TI3=TI4=TI5=TI6=0, final setting parameter such as table 2 can be obtained.
Table 2
Gain initial value based on each frequency range of PSS4B that above-mentioned steps acquire, acquires critical gain such as table 3.
Table 3
| G1 | G2 | G3 | G4 |
| 2.4793 | 2.3986 | 4.1687 | 1.9297 |
It is multiplied by the initial value for adjusting obtained each band gain before with the 1/3 of critical gain, obtains final yield value
Such as table 4.
Table 4
| G1 | G2 | G3 | G4 | |
| KL (adjusting) | 8.2643 | 7.9953 | 13.8957 | 6.4323 |
| KI (adjusting) | 3.9088 | 2.8903 | 5.4146 | 3.4916 |
| KH (adjusting) | 4.6285 | 4.7268 | 11.3494 | 3.1687 |
The PSS4B that parameter tuning is finished is installed in actual electric network, and analysis can obtain the system oscillation of PSS4B installation front and back
The variation of mode such as table 5.
Table 5
| Number | Characteristic value | Frequency (Hz) | Former damping ratio | Damping ratio after installation PSS4B |
| 1 | -0.00222+0.15080i | 0.0240 | 0.0147 | 0.1332 |
| 2 | -0.05976+3.53769i | 0.5630 | 0.0169 | 0.2901 |
Obviously, the PSS4B parameter that the present invention adjusts can inhibit the low-frequency oscillation in power grid well.It is shown in Fig. 7
The waveform of tie-line power transmission demonstrates above-mentioned analysis result after three-phase shortcircuit excision.
According to examples detailed above, it is not difficult to find out that, the PSS4B parameter that the present invention adjusts can inhibit low in power grid well
Frequency and ultra-low frequency oscillation.
Obviously, those skilled in the art should be understood that each module of the above-mentioned embodiment of the present invention or each step can be with
It is realized with general computing device, they can be concentrated on a single computing device, or be distributed in multiple computing devices
On composed network, optionally, they can be realized with the program code that computing device can perform, it is thus possible to by it
Store and be performed by computing device in the storage device, and in some cases, can be held with the sequence for being different from herein
The shown or described step of row, perhaps they are fabricated to each integrated circuit modules or will be multiple in them
Module or step are fabricated to single integrated circuit module to realize.In this way, the embodiment of the present invention be not limited to it is any specific hard
Part and software combine.
The foregoing is only a preferred embodiment of the present invention, is not intended to restrict the invention, for the skill of this field
For art personnel, the embodiment of the present invention can have various modifications and variations.All within the spirits and principles of the present invention, made
Any modification, equivalent substitution, improvement and etc. should all be included in the protection scope of the present invention.
Claims (9)
1. the design method based on frequency domain margin index adjusting PSS4B parameter power oscillation damping, which is characterized in that including following
Step:
1) model analysis is carried out to the underdamping mode of system, determines the unit of installation PSS4B；
2) Truncated Singular Value Decomposition is carried out to controlled grid metrics under each underdamping mode frequency；
3) PSS4B parameter optimization target is determined according to weighted frequency domain nargin；
4) phase restriction condition is determined according to the ideal phase-frequency characteristic curve of PSS4B；
5) parameter bound constraint condition is determined according to the parameter bound of PSS4B；
6) Optimized model determined by optimization aim and phase restriction item, parameter bound constraint condition is solved；
7) PSS4B is solved in the critical gain of excitation mode frequency range；
8) PSS4B parameter is finally determined based on above-mentioned steps.
2. the design method according to claim 1 based on frequency domain margin index adjusting PSS4B parameter power oscillation damping,
It is characterized in that, the underdamping mode to system in the step 1) carries out model analysis, the machine of installation PSS4B is determined
Group is that participation is higher than 0.8 Power Plant in underdamping mode under each method of operation of real system；
Participation P of the kth platform unit about ith feature valueikIs defined as:
Pik=vkiuki
Wherein, vkiAnd ukiIt is worth k-th of element of corresponding left and right feature vector for ith feature；Assuming that ith feature value is
The characteristic value of underdamping mode, by PkiIt can determine unit of the participation higher than 0.8 by arrangement from big to small to determine installation PSS4B
Unit.
3. the design method according to claim 1 based on frequency domain margin index adjusting PSS4B parameter power oscillation damping,
It is characterized in that, carrying out truncation singular value to controlled grid metrics under each underdamping mode frequency in the step 2)
Decomposition step specifically:
(1) matrix of controlled power grid is G (s), and s is Laplace operator, and s=σ+j ω, σ are the real part of s, and ω is the imaginary part of s, j
For imaginary unit；Ignore the real part of underdamping mode characteristic values, i.e. σ ≈ 0, G (s) then can be write G (j ω) by s=j ω；?
Singular value decomposition is carried out to controlled grid metrics G (jw) under each underdamping mode frequency ω:
G (jw)=U Σ VH, formula (1)；
In formula (1), U and V are right, left singular vector matrix, ()HThe conjugate transposition for taking corresponding matrix is represented, Σ is singular value
Matrix, diagonal element are known as the singular value of matrix G (jw), meetAnd Σ1=diag (σ1,σ2,...,
σr), it arranges in the following order:
σ1≥σ2≥...≥σr> 0, r=rank (G)；
Wherein, rank (G) indicates to take the order of matrix G；
(2) controlled grid metrics G (jw) is written as by dyad decomposed form according to above-mentioned relation:
Wherein, i indicates the subscript number of the respectively singular value greater than 0；
(3) according to the characteristic of controlled grid metrics G (jw), there is r=rank (G) ≈ 1 at each underdamping mode frequency w, therefore
Obtain the Truncated Singular Value Decomposition of controlled power grid:
G(jw)≈σ1u1v1 H, formula (3)；
In formula (3), σ1It is the maximum singular value of G (jw), u1And v1For corresponding right, the left singular vector of maximum singular value.
4. the design method according to claim 1 based on frequency domain margin index adjusting PSS4B parameter power oscillation damping,
It is characterized in that, determining PSS4B parameter optimization target step according to weighted frequency domain nargin in the step 3) specifically:
(1) G (s) is the transfer function matrix of controlled power grid, and diagonal matrix H (s) is the transfer function matrix of PSS4B, by G (s)
Its return difference matrix D (s)=I-G (s) H (s) determinant is defined as to complex plane original with the stability margin of the constituted system of H (s)
The distance S of pointm(j ω):
sm(jw)=| det (D (jw)) |=| det (I-G (jw) H (jw)) |, formula (4)；
(2) stability margin is deformed according to the controlled grid metrics Truncated Singular Value Decomposition of gained in step 2), obtains formula
(5)；
sm(jw)=| det (H-1(jw)-G(jω))·det(H(jω))|≈|det(H-1(jω)-σ1u1v1 H)·det(H(j
ω)) |, formula (5)；
(3) pay attention to correcting A+uv to Arbitrary Matrix A and its order 1T, following relationship establishment:
det(Α+uvT)=(1+vTA-1U) det (A), formula (6)；
Later, further abbreviation stability margin:
sm(jω)≈|1-σ1v1 HH(jω)u1|·|det(H-1(j ω)) det (H (j ω)) |=| 1- σ1v1 HH(jω)u1|,
Formula (7)；
(4) weight Weight of i-th of mode in PSS4B parameter tuning is determinedi, optimization aim finally can be obtained:
In formula (8): N is consideration mode quantity, ωiFor the frequency of oscillation of mode i,For controlled power grid G (j ωi)
Maximum singular value and corresponding right, left singular vector, d=[FL(I,H),KL(I,H),TL(I,H)3,TL(I,H)4,TL(I,H)5,TL(I,H)6]TFor
PSS4B parameter vector, WeightiFor the weight of mode i, and meet the following conditions:
5. the design method according to claim 1 based on frequency domain margin index adjusting PSS4B parameter power oscillation damping,
It is characterized in that, the ideal phase-frequency characteristic curve according to PSS4B in the step 4) determines that phase restriction condition step has
Body are as follows:
(1) ultra-low frequency oscillation mode characteristic values real part σ is determinedulApproximate expression:
In formula (9), ωulFor ultra-low frequency oscillation mode characteristic values imaginary part, KD∑For the summation of each unit rotor kinetic damping coefficient, MSFor
Each set generator rotor motion inertia time constant summation, e are the column vector that all elements are 1, diagonal matrix HPSS(s)
For PSS transfer function matrix；FPSSIt (s) is PSS forward path transfer function matrix, GMiIt (s) is governor-original of i-th unit
Motivation transmission function, expression formula are as follows:
GMi(s)=- Ggi(s)·Ti(s)
Wherein, GgiIt (s) is i-th machine unit speed regulating device transmission function, TiIt (s) is i-th unit prime mover transmission function；
In active-idle circuit feedback model of electric system system,
In formula: GQ1It (s) is transfer function matrix introduced after consideration automatic voltage adjustor of power generator control；Diagonal matrix
HPSSIt (s) is PSS transfer function matrix；FPSSIt (s) is PSS forward path transfer function matrix；GEX(s) letter is transmitted for excitation system
Matrix number；Diagonal matrix GMIt (s) is governor-prime mover transfer function matrix, i-th of diagonal element GMiIt (s) is i-th unit
Governor-prime mover transmission function, expression formula are as follows:
GMi(s)=- Ggi(s)·Ti(s)
Wherein, GgiIt (s) is i-th machine unit speed regulating device transmission function, TiIt (s) is i-th unit prime mover transmission function；
(2) PSS transfer function matrix H is determinedPSS(s) offset angle:
PSS remembers the part that ultra-low frequency oscillation mode characteristic values influence in ultra-low frequency oscillation mode characteristic values real part approximate expression
Make σul-PSS, have:
In formula (10): FPSSji(jωul) it is FPSS(jωul) matrix jth row, i-th arrange element；HPSSi(jωul) it is HPSS(j
ωul) i-th of diagonal element, i.e., the frequency characteristic of i-th unit PSS；
To the PSS of i-th unit, selection makes HPSSi(jωul) compensation FPSS(jωul) in a certain element FPSSji(jωul) phase
Lag is to enhance ultra-low frequency oscillation stability；Due to | FPSSii(jωul)|>|FPSSji(jωul) |, j ≠ i, therefore pass through HPSSi(j
ωul) compensation FPSSii(jωul) meet:
arg[HPSSi(jωul)]+arg[FPSSii(jωul)]=0
Wherein, arg () representative takes corresponding argument of complex number；
When it is implemented, need to only meet FPSSji(jωul) and HPSSi(jωul) difference less than 30 °；
|arg[HPSSi(jωul)]-arg[FPSSii(jωul)] |≤30 °, formula (11)
Formula (11) is phase restriction, sets HPSSi(jωul) it is made to meet formula (11), it can best enhance ultra-low frequency oscillation
Mode damping.
6. the design method according to claim 1 based on frequency domain margin index adjusting PSS4B parameter power oscillation damping,
It is characterized in that, the step 5) according to the parameter bound of PSS4B determine parameter bound constraint in, determine PSS4B high,
In, the bound of low-frequency range centre frequency, gain and time constant.
7. the design method according to claim 1 based on frequency domain margin index adjusting PSS4B parameter power oscillation damping,
It is characterized in that, step 6) solves in the Optimized model determined by optimization aim and phase restriction item, parameter bound constraint condition,
Following Optimized model is solved by Matlab optimization toolbox, obtains the parameter of PSS4B；
|arg[HPSSi(jωul)]-arg[FPSSii(jωul)]|≤30°
Wherein FL(I,H)For the centre frequency of the basic, normal, high frequency range of PSS4B, KL(I,H)For the gain of the basic, normal, high frequency range of PSS4B,
TL(I,H)3,TL(I,H)4,TL(I,H)5,TL(I,H)6For the time constant of the basic, normal, high frequency range of PSS4B；Its bound is according to actual needs
Sets itself.
8. the design method according to claim 1 based on frequency domain margin index adjusting PSS4B parameter power oscillation damping,
It is characterized in that, the step 7) solves PSS4B in the critical gain step of excitation mode frequency range specifically:
(1) diagonal matrix K is definedPSSFor critical gain matrix, then it meets following condition:
det(I-G(jω)·KPSSH (j ω))=0；
(2) all number functions are asked to system return difference matrix determinant det (D (s)) under critical gain:
Defining enc () is all number functions, calculates time that polynomial matrix determinant surrounds origin clockwise on a complex plane
Number；
Since PSS4B matrix H (s) is free of right half complex plane zero, pole, enc (H (s))=0, and open cycle system G (s) stablizes, then
According to multi-input multi-output system Nyquist's stability criterion, the necessary and sufficient condition of system closed-loop stabilization are as follows:
(3) since PSS4B matrix H (s) is free of right half complex plane zero, pole, enc (H (s))=0, and open cycle system G (s) is steady
It is fixed, then according to multi-input multi-output system Nyquist's stability criterion, the necessary and sufficient condition of system closed-loop stabilization are as follows:
(4) in the higher frequency band where excitation mode, G (s) is diagonally dominant matrix, KPSSIt is diagonal matrix with H (s), therefore (K- 1 PSSH-1(s)-G (s)) it is still diagonally dominant matrix, therefore above formula is equivalent to:
Wherein, M is adjusting PSS4B parameter unit number, KPSSjFor the critical gain of jth platform unit PSS4B, HjIt (s) is jth platform
The transmission function of unit PSS4B, GjjIt (s) is the transmission function of jth platform unit the machine excitation reference voltage to the machine revolving speed；
(5) to jth platform unit, critical gain KPSSjMeet following condition
(6) initial value for being multiplied by each band gain that adjusting obtains in step 6) with the 1/3 of critical gain, obtains final gain
Value.
9. the design method according to claim 1 based on frequency domain margin index adjusting PSS4B parameter power oscillation damping,
It is characterized in that, the PSS4B parameter, time constant in the step 8) determine that each band gain is according to step according to step 6)
Rapid final gain value 7) determines.
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| CN113675841B (en) * | 2021-07-23 | 2023-08-29 | 云南电网有限责任公司 | Excitation mode analysis method and system based on minimum feature trajectory method |
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