CN106610590A - Method for building iterative identification wide-area damping controller capable of improving stability of electric power system - Google Patents
Method for building iterative identification wide-area damping controller capable of improving stability of electric power system Download PDFInfo
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- CN106610590A CN106610590A CN201710056581.4A CN201710056581A CN106610590A CN 106610590 A CN106610590 A CN 106610590A CN 201710056581 A CN201710056581 A CN 201710056581A CN 106610590 A CN106610590 A CN 106610590A
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
- G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
- G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
- G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance
Abstract
The invention relates to a method for building an iterative identification wide-area damping controller capable of improving the stability of an electric power system, and belongs to the technical field of electric power system identification and control. The method comprises the steps of selecting a low-order electric power system initial model and a corresponding initial wide-area damping controller model; performing identification on the low-order electric power system initial model by using a recursive least-squares method so as to acquire an electric power system identification model set; solving a v-gap distance between an electric power system model and the electric power system identification model set by using a v-gap formula, and sequentially solving the maximum distance based on the electric power system model; then solving a stability margin based on the electric power system model and the wide-area damping controller; and selecting a condition meeting minority electric power system identification model set and an optimal electric power system identification model according to the v-gap distance and the stability margin, and acquiring a corresponding wide-area damping controller model. According to the method provided by the invention, an optimal electric power system identification model and an optimal wide-area damping controller model can be acquired, and thus the control stability of the electric power system is improved.
Description
Technical field
The invention belongs to power system identification and control technology field, more particularly to a kind of raising stability of power system
Iteration recognizes damping controller construction method.
Background technology
With the continuous expansion of power system scale and developing rapidly for China's electric utility, the daily fortune of interconnected electric power system
Capable stability and the structure of various control and protection devices and operational management are proposed to the accuracy of electric system simulation
Very high request.At present, due to caused by the factors such as electric network composition, load uncertainty, generator excitation control underdamping define
Power system under many interference environments, this may result in interaction passive between power system control oscillation modes, can dislike
Change damping control effect.
The structure of wide area damp of electrical power system controller is carried out based on electric power system identification model under many interference environments,
Then need first to recognize power system true model to obtain electric power system identification model.Therefore, based on power train
In the wide area damping control building process of system identification model, the accuracy of electric power system identification model is most important.But,
Due to being affected by various disturbing factors in actual wide area damping control control process, electric power system identification model with it is electric
Mismatch between Force system true model is certainly existed, i.e., there is Identification Errors factor between the two, Identification Errors have with
Machine and be difficult to define priori Robust Stability Conditions, therefore using conventional method build wide area damping control do not ensure that
It is stable to real power system control；Meanwhile, on the premise of stability of power system is ensured, how to guarantee the wide of structure
The control performance of domain damping controller is continuously available improvement, preferably suppresses the low-frequency oscillation of power system, is also to face at present
Subject matter.
According to the practical operation situation of power system, electric power system identification model under many interference environments shown in Fig. 1 is built,
For studying power system identification problem.The random nature that many places load is present in simulation power system is slightly disturbed, true
Several interference signals in diverse location are added in power system, as a example by it there are 2 interference signals in system, wherein：
U, y represent respectively power system input, output signal, and e represents that average is zero, variance for λ smooth random disturbance signal, r tables
Show the pumping signal separate with signal e, G (q, θ) represent forward path electric power system identification model, H (q, θ) represent before to
The filter model of channel interference signals e, K (q, θ) represents feedback channel wide area damping control model, and θ represents electricity to be identified
Force system model parameter, t=1,2 ....
It is the wide area damping control construction method most close with the present invention to have Runge-Kutta iteration discrimination method at present,
It is, for simulating an important class of ordinary differential equation solution implicitly or explicitly iterative method, can to recognize in power system well
Apply with control field, but the identification precision of Runge-Kutta iteration discrimination method is not high enough, and changed by Runge Kutta
For the electric power system identification model that obtains of discrimination method identification reach in the presence of wide area damping control the stable time compared with
Long, stability of power system can not be still fine.
Least square method of recursion：Least square method of recursion refers to the systematic parameter to being identified, and obtains once new every
After measurement data, just on the basis of a front estimated result, the result of previous estimation is modified using new measurement data,
So as to recursively draw new estimates of parameters.So with the introducing of new measurement data, parameter Estimation is constantly carried out, until
Till estimate reaches satisfied levels of precision.The basic thought of least square method of recursion is：
V-gap distances：V-gap distances can simply be interpreted as the distance between two frequency responses, represent two transmission
A kind of measurement of distance, is abbreviated as v-gap between function, uses symbol δvRepresent.Transfer function matrix G1With transfer function matrix G2
V-gap distances be expressed as：
Wherein, G*(ejω)=G (e-jω), η (G) represents that G's opens RHP limit number,Represent that closing for G is right partly flat
Face limit number, wno (G) represents that the nyquist plot of transmission function G surrounds counterclockwise the number of turns of round dot, when G has in the imaginary axis
During limit, nyquist plot will avoid these limits.κ(G1,G2) represent G1、G2Throwing to obtained by unit Riemann's spheric projection
The chordal distance (Chordal distance) of shadow point.
Stability margin：The stability margin of stable closed-loop system [G, K] is represented with b, if closed-loop system [G, K] is unstable
It is fixed, then b=0.
Stability margin computing formula is：
Wherein, T (Gi,Ki) it is closed-loop system transfer function matrix, Gi is the power system identification mould that i ＆ lt identification is obtained
Type, Ki is the wide area damping control model that i ＆ lt builds.According to Fig. 1, T (Gi,Ki) expression formula such as formula (3) shown in：
The content of the invention
The purpose of the present invention is for the deficiencies in the prior art, there is provided a kind of iteration identification of raising stability of power system
Wide area damping control construction method.The method, apart from iterative Identification, can be obtained based on least square method of recursion and v-gap
To power system optimum identification model and wide area damp optimal controller model, so as to improve electric power system control stability.
The present invention proposes a kind of iteration identification wide area damping control construction method for improving stability of power system, and it is special
Levy and be, the method is comprised the following steps：
1) a low order power system initial model G and its corresponding initial wide area damping control mould are selected from document
Type K；
2) it is initial to low order power system using least square method of recursion using white noise signal as initial excitation signal
Model G is recognized, and the electric power system identification model set comprising low order power system initial model G is obtained after identification
Bi；
3) according to the basic theories of v-gap, using v-gap formula (1) electric power system model G is asked fori(GiIt is now power train
System identification model set BiIn certain element) with electric power system identification model set BiBetween v-gap apart from δv(Gi, Bi),
And according to v-gap apart from δv(Gi, Bi) ask for successively based on electric power system model G according to formula (4)iUltimate range δWC(Gi,
Bi):
That is, as i=1, G is asked for1With electric power system identification model set BiBetween ultimate range；As i=2, G is asked for2
With electric power system identification model set BiBetween ultimate range；The electric power system model G of i=3,4,5 ... 100 is asked for successivelyiWith electric power
System identification model set BiBetween ultimate range；
4) electric power system identification model set BiCorresponding wide area damping control is designated as Ki, according to the base of stability margin
This theory, asks for based on electric power system model G according to formula (3)iWith wide area damping control KiStability margin b (Gi,Ki)；
5) stability is improved to wide area damping control according to power system closed-loop system stability energy condition：
By stability margin b (Gi,Ki) with step 3) ultimate range δ that obtainsWC(Gi, Bi) be compared, filter out satisfaction steady
Determine nargin b (Gi,Ki) it is more than electric power system model GiWith electric power system identification model set BiBetween ultimate range δWC(Gi,Bi)
Set, if being unsatisfactory for, makeObtain wide area damping control
Wherein Si=(1+GiKi)-1,P be a single-input single-output transmission function, KopBe it is maximum away from
From δWC(Gi, Bi) in electric power system identification model set BiIn the design of corresponding optimal electrical power system model optimum wide area damp
Controller；
6) according to step 3) δ that obtainsv(Gi, Bi) and b (Gi,Ki), pick out and meet formula | δv(G,Bi)-δv(Gi,Bi)|
≤ ε and δmin(G,BiThe minority electric power system identification model set ψ of)≤ε, ε are an infinitesimal constant；Meet condition entrance
Step 7), if being unsatisfactory for condition, return to step 2) carry out identification process again；
7) in step 6) corresponding δ is picked out in the minority power system that obtains identification set ψv(Gi, Bi) minimum electric power
System identification model, as optimal electrical power System identification model Go that identification is obtainedp(apart from real power system model distance most
Model that is little and meeting stability of power system), and according to step 5) obtain corresponding wide area damping control model Kop。
Of the invention the characteristics of and beneficial effect：
The inventive method proposes a kind of iteration identification wide area damping control structure side of raising stability of power system
Method, this method combines least square method of recursion and v-gap apart from basic theories, can obtain power system optimal models and wide area
Damping controller optimal models, so as to improve stability of power system, be solve stability of power system propose it is a kind of new
Thinking.The theoretical and embodiment of the present invention all shows that the method can be met the power system mould of stability of power system energy
Type, and finally realize improving the purpose of stability of power system, in being allowed to be more applicable for power system identification and control.
Description of the drawings
Fig. 1 is the structural representation of the electric power system identification model that the inventive method is adopted.
Fig. 2 is the inventive method FB(flow block).
Fig. 3 is the initial model G and electric power system identification model set B of the present inventioniBetween v-gap distance maps.
Fig. 4 is that the power system based on iterative Identification of embodiments of the invention exports response diagram.
Specific embodiment
The present invention proposes a kind of iteration identification wide area damping control construction method of raising stability of power system, under
Face combines the drawings and specific embodiments, and that the present invention is described in more detail is as follows.
A kind of iteration identification wide area damping control construction method for improving stability of power system proposed by the present invention, always
Body flow process is as shown in Fig. 2 the method is comprised the following steps：
1) a low order power system initial model G and its corresponding initial wide area damping control mould are selected from document
Type K；
2) it is initial to low order power system using least square method of recursion using white noise signal as initial excitation signal
Model G is recognized, and the electric power system identification model set comprising low order power system initial model G is obtained after identification
Bi；
3) according to the basic theories of v-gap, using v-gap formula (1) electric power system model G is asked fori(GiIt is now power train
System identification model set BiIn any element (i=1,2,3 ... 100) and electric power system identification model set BiBetween v-
Gap is apart from δv(Gi, Bi) as follows；
And
And according to v-gap apart from δv(Gi, Bi) ask for successively based on electric power system model G according to formula (4)iMaximum away from
From δWC(Gi,Bi).That is, as i=1, G is asked for1With electric power system identification model set BiBetween ultimate range；As i=2, ask
Take G2With electric power system identification model set BiBetween ultimate range；Each electric power system model of i=3,4,5 ... 100 is asked for successively
GiWith electric power system identification model set BiBetween ultimate range；
4) electric power system identification model set BiIn wide area damping control corresponding to each electric power identification system be designated as
Ki, it is theoretical according to stability margin, ask for based on electric power system model GiWith wide area damping control KiStability margin b (Gi,Ki)；
Stability margin computing formula is：
T(Gi,Ki) expression formula such as formula (3) shown in：
5) stability is improved to wide area damping control according to power system closed-loop stabilization performance condition；By step 4)
Stability margin b (the G for arrivingi,Ki) with step 3) the electric power system model G that obtainsiWith electric power system identification model set BiBetween
Ultimate range δWC(Gi, Bi) be compared, filter out and meet stability margin b (Gi,Ki) it is more than ultimate range δWC(Gi,Bi) electricity
Force system identification model simultaneously enters step 6)；If meeting screening conditions without electric power system identification model, make Obtain wide area damping controlWherein Si=(1+GiKi)-1,P be a single-input single-output transmission function, KopIt is ultimate range δWC(Gi, Bi) in electricity
Force system identification model set BiIn the design of corresponding optimal electrical power system model optimum wide area damping control；
6) according to step 3) δ that obtainsv(Gi, Bi), pick out and meet Performance of Closed Loop System improvement condition | δv(G,Bi)-δv
(Gi,Bi) |≤ε and δvmin(G,Bi)≤ε (ε is an infinitesimal constant, and the present embodiment takes ε for 0.05, this value it is more little then
Illustrate recognize precision it is higher, can be according to the accuracy selection for reaching) electric power system identification model composition minority power system distinguish
Know model set ψ；
Performance of Closed Loop System improves condition 1：|δv(G,Bi)-δv(Gi,Bi) |≤ε, judge electric power system identification model and electricity
Whether the absolute value of the difference between Force system initial model v-gap distances is less than or equal to setting error ε, the absolute value of this difference
It is more little, illustrate that the precision for recognizing is higher；
Performance of Closed Loop System improves condition 2：δvmin(G,Bi)≤ε, δvmin(G,Bi) it is electric power system model GiWith power train
System identification model set BiBetween v-gap minimum ranges.Whether this v-gap minimum range is judged less than or equal to setting error ε,
This distance is more little, illustrates finally to recognize optimal electrical power System identification model G for obtainingopMore approach power system initial model
G。
If presence meets above-mentioned two Performance of Closed Loop System improves the electric power system identification model of condition, into step
7)；If there is no the electric power system identification model for meeting condition, step 2 is returned to) recognized.
7) in step 6) in the minority power system that obtains identification set ψ, v-gap is picked out apart from δv(Gi, Bi) value minimum
Electric power system identification model, as recognize optimal electrical power System identification model G for obtainingop(this modal distance real power system
System model G is apart from model that is minimum and meeting stability of power system), and according to step 5) obtain the corresponding optimum of the model
Wide area damping control model Kop, structure terminates.
From above-mentioned conclusion, the iteration based on least square method of recursion and v-gap distances recognizes wide area damping control
Construction method is extraordinary selection.Using the method for the invention, compared with prior art, electric power system control is improve steady
It is qualitative, it is allowed to be more applicable for power system identification and control in application.
With reference to a specific embodiment, the inventive method is further described as follows：
1) a three rank power system initial model G and its corresponding initial wide area damping control model K, transmission are selected
Function model is as follows：
2) it is initial to low order power system using least square method of recursion using white noise signal as initial excitation signal
Model G is recognized, and the electric power system identification model set comprising three rank power system initial model G is obtained after identification
Bi。
3) according to the correlation theory of v-gap, using following v-gap formula
Ask for electric power system model Gi(GiIt is now electric power system identification model set BiIn certain element) and power system
Identification model set BiBetween v-gap apart from δv(Gi, Bi), it is calculated:
And
And according to v-gap apart from δv(Gi, Bi) ask for successively based on electric power system model GiUltimate range δWC(Gi,Bi)；
Three rank power system initial model G and electric power system identification model set B can be obtainediBetween v-gap distances, such as
Shown in Fig. 4, Fig. 4 shows from recognizing the electric power system model that obtains for the first time to recognizing the electric power system model that obtains for the last time
It is less and less with the distance between three rank power system initial model G, finally give optimal electrical power System identification model GopWith three
V-gap distances between rank power system initial model G are 0.01059.
4) electric power system identification model set BiCorresponding wide area damping control is designated as Ki, according to the base of stability margin
This theory, asks for based on electric power system model GiWith wide area damping control KiStability margin b (Gi,Ki)；
Wherein T (Gi,Ki) expression formula be：
Therefore, using iterative Identification in embodiment application process, corresponding stability margin b of each Identification Data
(Gi,Ki) and identification model and true model between v-gap distance values it is as shown in table 1.
The corresponding frequency stable nargin of each identified parameters data and v-gap distances in the iterative Identification application process of table 1
Value
5) stability is improved to wide area damping control according to power system closed-loop stabilization performance condition.
By stability margin b (Gi,Ki) with step 3) ultimate range δ that obtainsWC(Gi, Bi) be compared, filter out satisfaction steady
Determine nargin b (Gi,Ki) it is more than electric power system model GiWith electric power system identification model set BiBetween ultimate range δWC(Gi,Bi)
Collection be combined into step 6), if being unsatisfactory for, makeObtain wide area damping controlWherein Si=(1+GiKi)-1,P is a single input
Single output-transfer function, KopIt is ultimate range δWC(Gi, Bi) in electric power system identification model set BiIn corresponding optimal electrical power
The optimum wide area damping control of system model design.
As can be drawn from Table 1, Identification Data starts stability margin from the 5th group more than v-gap distances.In algorithm steps 5)
In recognizing the model set for obtaining afterwards, about 2/3 identification model it is screened fall, that is, the identification model for having 1/3 meets b
(Gi,Ki)>δWC(Gi,Bi), be left 1/3 identification model enter step 6) screening process in.
6) according to step 3) δ that obtainsv(Gi, Bi), pick out and meet formula | δv(G,Bi)-δv(Gi,Bi) |≤ε and δvmin
(G,Bi(ε is an infinitesimal constant to)≤ε, for example, take ε for minority electric power system identification model set ψ 0.05).
Performance of Closed Loop System improves condition 1：|δv(G,Bi)-δv(Gi,Bi) |≤0.05, judge between two v-gap distances
Difference be within error 0.05, this difference is more little, illustrate recognize precision more and more higher.
Performance of Closed Loop System improves condition 2：δvmin(G,Bi)≤0.05, by distance controlling within 0.05, this value more it is little then
Illustrate to recognize the optimal electrical power system model G for obtainingopMore approach power system initial model G.
Step 7 is entered if above-mentioned condition is met), if being unsatisfactory for condition, need return to step 2) recognized again
Process.
7) in step 6) corresponding δ is picked out in the minority power system that obtains identification set ψv(Gi, Bi) minimum electric power
System identification model, that is, recognize optimal electrical power System identification model G for obtainingopIt is (minimum apart from real power system model distance
And meet the model of stability of power system), and according to step 5) obtain corresponding wide area damping control model Kop。
According to above-mentioned steps, optimum three ranks electric power system identification model and corresponding optimum wide area damp may finally be obtained
The identified parameters of controller model are：
a1:5.0142 b1:1.0835
a2:5.3237 b2:2.9540
a3:5.0670 b3:2.1717
I.e.：
In final result, δvmin(G,Bi)=0.0106<0.05 and b (Gop,Kop)=0.1124, distinguishes in iteration
The output response curve that knowledge method carries out electric power system model identification process is as shown in Figure 4.It is initial closest to three rank power systems
The amplitude of model G is 0.427dB, and the response time is in 11s or so.
Above-described is only the preferred embodiments of the present invention, and the present invention is not limited solely to above-described embodiment, it is all
Local change, equivalent, improvement for being done within the spirit and principles in the present invention etc. should be included in the protection model of the present invention
Within enclosing.
Claims (2)
1. a kind of iteration for improving stability of power system recognizes wide area damping control construction method, it is characterised in that the party
Method is comprised the following steps：
1) a low order power system initial model G and its corresponding initial wide area damping control model K is selected from document；
2) using white noise signal as initial excitation signal, using least square method of recursion to low order power system initial model
G is recognized, and the electric power system identification model set B comprising low order power system initial model G is obtained after identificationi；
3) according to the basic theories of v-gap, using v-gap formula (1) electric power system model G is asked foriWith electric power system identification model
Set BiBetween v-gap apart from δv(Gi, Bi), and according to v-gap apart from δv(Gi, Bi) ask for being based on successively according to formula (4)
Electric power system model GiUltimate range δWC(Gi,Bi)：
In formula, GiIt is now electric power system identification model set BiIn certain element, as i=1, ask for G1Distinguish with power system
Know model set BiBetween ultimate range；As i=2, G is asked for2With electric power system identification model set BiBetween ultimate range；
I=3,4,5 ... 100, electric power system model G are asked for successivelyiWith electric power system identification model set BiBetween ultimate range；
4) electric power system identification model set BiCorresponding wide area damping control is designated as Ki, according to the basic reason of stability margin
By being asked for based on electric power system model G according to formula (3)iWith wide area damping control KiStability margin b (Gi,Ki)；
5) stability is improved to wide area damping control according to power system closed-loop system stability energy condition：
By stability margin b (Gi,Ki) with step 3) ultimate range δ that obtainsWC(Gi, Bi) be compared, filter out satisfaction and stablize abundant
Degree b (Gi,Ki) it is more than electric power system model GiWith electric power system identification model set BiBetween ultimate range δWC(Gi,Bi) collection
Close, if being unsatisfactory for, makeObtain wide area damping control
Wherein Si=(1+GiKi)-1,P be a single-input single-output transmission function, KopIt is maximum
Apart from δWC(Gi, Bi) in electric power system identification model set BiIn the design of corresponding optimal electrical power system model the resistance of optimum wide area
Buddhist nun's controller；
6) according to step 3) δ that obtainsv(Gi, Bi) and b (Gi,Ki), pick out and meet formula | δv(G,Bi)-δv(Gi,Bi) |≤ε and
δmin(G,BiThe minority electric power system identification model set ψ of)≤ε, ε are an infinitesimal constant；Meet condition and enter step
7), if being unsatisfactory for condition, return to step 2) carry out identification process again；
7) in step 6) corresponding δ is picked out in the minority power system that obtains identification set ψv(Gi, Bi) minimum power system
Identification model, as optimal electrical power System identification model G that identification is obtainedop, the model be apart from real power system model away from
From model that is minimum and meeting stability of power system, and according to step 5) obtain corresponding wide area damping control model
Kop。
2. iteration as claimed in claim 1 recognizes wide area damping control construction method, it is characterised in that the step is asked for
Based on electric power system model GiWith wide area damping control KiStability margin b (Gi,Ki) formula be：
T(Gi,Ki) expression formula such as formula (3) shown in：
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