CN104680017B - Time-varying stability of power system analysis system and method - Google Patents
Time-varying stability of power system analysis system and method Download PDFInfo
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Abstract
A kind of time-varying stability of power system analysis system and method, the system include data acquisition module, and wind speed fitting prediction module, time-varying system are set up solves module and result output module with depression of order module, stability criterion, and data acquisition module is used for gathered data；Wind speed fitting prediction module is fitted prediction to condition wind speed trend in the short time, and by wind speed interval, each interval condition flag wind speed probability density matrix is calculated according to model of fit；Time-varying system sets up the continuous Markov time-varying electric power system model set up with depression of order module and consider wind speed random character, and carries out depression of order to system；Stability criterion solves module and utilizes whether the feasibility problems method for solving solving system in LMI is stablized.By the time-varying stability of power system analysis system and method for the present invention, it can effectively solve the problem that time-varying stability of power system is difficult the problem differentiated caused by wind speed random character under blower fan access.
Description
Technical field
The present invention relates to Power System Analysis and control technology field, the stability of time-varying power system is especially related to
Analytical technology.
Background technology
The development of wind-powered electricity generation is the important component of countries in the world future source of energy strategy, but the fluctuation that blower fan is exerted oneself is often
System conditions are caused to change, this brings great risk for the safety and stability of power system with economical operation.Therefore, urgently
Need to analyse in depth the time-varying stability of power system of the random character containing wind speed.
In the prior art, the stability analysis technology about power system under wind power integration is broadly divided into two classes, and a class is
Based on the stability analysis of blower fan itself, another kind of is based on the stability analysis under the single operating condition of grid side.Based on wind
The stability analysis of machine itself accesses influence of the leeward changed power to blower fan self stability as research object using different blower fans,
The stability difference of different blower fans is analyzed, however, stability of this alanysis not to net side power system after blower fan access is entered
Row analysis.Based on the stability analysis under the single operating condition of grid side with net side power train during wind power integration leeward changed power
Oscillation mode of uniting is analysis object, net side stability of power system is analyzed, however, single fortune of this method only for power system
Row operating mode is analyzed, and the larger situation for causing system conditions to occur wide variation of fluctuation is not gone out to blower fan and is carried out
Analysis.Therefore, in the prior art, the analysis for power system under wind power integration is not comprehensive, and accuracy is low.
The content of the invention
In consideration of it, it is an object of the invention to overcome the difficulty of prior art, it is to avoid only wind-driven generator itself is carried out
Stability analysis, thus ignore the stability of net side power system after wind-driven generator access；It it also avoid with wind power integration
Net side power system oscillation pattern is analysis target during leeward changed power, therefore ignores wind-driven generator to go out fluctuation larger
Cause the problem of wide variation occurs for system conditions.A kind of time-varying for considering wind speed random character is proposed for this present invention
Stability of power system analysis system and method.
The present invention can effectively solve the problem that under blower fan access caused by wind speed random character from power system actual state
Power system time-varying stability is difficult the problem differentiated.First with two-parameter Weibull distribution model to condition wind speed in the short time
Trend is fitted prediction, then by wind speed interval, each interval condition flag wind speed probability density matrix is calculated, according to condition
Feature wind speed determines the operating condition of system.Then, the continuous horse for considering wind speed random character is set up according to system rack information
Er Kefu time-varying electric power system models, and reduced order system.Secondly, the present invention, which is built, contains continuous Markov time-varying power system mould
The Lyapunov functional of type, and Duncan lemma is used in the weak infinitesimal operators of the functional, derive and meet interference attenuation degree
Robust Stochastic Stability LMI, whether stability problem is finally converted into feasibility problems solving system
It is stable.
In order to realize this purpose, the technical scheme that the present invention takes is as follows.
A kind of time-varying stability of power system analysis system, the system includes the data acquisition module being sequentially connected, wind
Speed fitting prediction module, time-varying system are set up solves module and result output module, data acquisition with depression of order module, stability criterion
Module is additionally coupled to time-varying system and set up and depression of order module；
The data acquisition module is used to gathering wind farm wind velocity and blower fan force information, network architecture parameters, in system
Generator frequency, generator rotor angle, and gathered data is sent to wind speed fitting prediction module and time-varying system foundation and depression of order module；
Information and wind power plant history real data that the wind speed fitting prediction module is sent according to data acquisition module are right
Condition wind speed trend is fitted prediction in short time, and by wind speed interval, each interval condition is calculated according to model of fit
Feature wind speed probability density matrix；
The time-varying system is set up each interval sub- operating mode as time-varying system with depression of order module, according to blower fan
The continuous Ma Erke of the gathered data foundation consideration wind speed random character of wind speed and exert oneself corresponding relation and data acquisition module
Husband's time-varying electric power system model, and depression of order is carried out to system；
Described stability criterion, which solves module, to be used to form time-varying power system robust convergency criterion, utilizes linear moment
Whether the feasibility problems method for solving solving system in battle array inequality is stablized；
Described result output module is used for output system stability distinguishing result.
A kind of time-varying method for analyzing stability of power system, methods described includes：
A, collection wind farm wind velocity and blower fan force information, network architecture parameters, generator frequency, generator rotor angle in system；
B, the data according to collection and wind power plant history real data, are fitted pre- to condition wind speed trend in the short time
Survey, and by wind speed interval, each interval condition flag wind speed probability density matrix is calculated according to model of fit；
C, using each interval sub- operating mode as time-varying system, corresponding relation and adopted according to blower fan wind speed with exerting oneself
The data of collection set up the continuous Markov time-varying electric power system model for considering wind speed random character, and carry out depression of order to system；
D, formation time-varying power system robust convergency criterion, are asked using the feasibility problems in LMI
Whether solution method solving system is stablized；
E, output time-varying Power System Stability Analysis result.
In step B, under described condition flag wind speed probability density is a certain condition flag wind speed, after predetermined time interval
Wind speed probability density.
In other step B, prediction is fitted to condition wind speed trend in the short time, and by wind speed interval, according to plan
Matched moulds type, which calculates each interval condition flag wind speed probability density matrix, to be included：
B1, utilize the variation tendency under each condition wind speed of two-parameter Weibull distribution models fitting time-varying system；
B2, according to certain siding-to-siding block length by wind speed incision wind speed and cut-out wind speed between carry out intervalization, utilize step
Model of fit in rapid B1 under each condition wind speed determines each interval condition flag wind speed probability density matrix.
Wherein, the two-parameter Weibull distribution model is：
Wherein, viFor current time wind speed；
vjFor condition wind speed；
K is form factor；
C is scale coefficient；
g(vi|vj) it is that condition wind speed is vjShi Dangqian wind speed is viProbability density.
In step C, according to blower fan wind speed and exert oneself corresponding relation and the data foundation consideration wind speed random character of collection
Continuous Markov time-varying electric power system model, and to system carry out depression of order include：
C1, using each interval sub- operating mode as time-varying system, it is true according to blower fan wind speed and the corresponding relation exerted oneself
Determine the corresponding blower fan power output of each interval feature wind speed, and consideration is set up using the blower fan power output and the data of collection
The continuous Markov time-varying electric power system model of wind speed random character；
C2, on the premise of ensureing that interested frequency band input-output characteristic is constant to continuous Markov time-varying power system
Model reduction.
Wherein, the blower fan wind speed is with corresponding relation of exerting oneself：
Wherein, vciWind speed is cut for blower fan；
vcoFor blower fan cut-out wind speed；
vRFor blower fan rated wind speed；
PRFor blower fan rated output power.
Especially, carrying out depression of order to system described in step C2 includes：
C21, by system state equationIt is divided into：
Wherein, X1=[Δ ωT,ΔδT] to retain variable, Δ ω represents the variable quantity of generator's power and angle rotating speed, and Δ δ is represented
Generator's power and angle variable quantity, X2For its dependent variable to be eliminated；
C22, cancellation X2After beX1, wherein I is unit battle array, and p calculates for differential
Son.
In step D, time-varying power system robust convergency criterion is formed, the feasibility in LMI is utilized
Whether problem solving method solving system is stable to include：
The Lyapunov functional of D1, structure containing continuous Markov time-varying electric power system model, and in the weak of the functional
Duncan lemma is applicable in infinitesimal operators, the linear matrix inequality technique for the Robust Stochastic Stability for meeting interference attenuation degree γ is obtained
Formula, obtains time-varying power system robust convergency criterion；
D2, using the feasibility problems method for solving in LMI determine whether system is stablized.
Wherein, the Robust Stochastic Stability criterion can be specifically expressed as：Given normal number γ>0, if there is one group
Positive definite symmetric matrices Pi>0, i ∈ S so that as next group of MATRIX INEQUALITIES is set up：
Then as u (t) ≡ 0, time-varying system robust convergency, and meet disturbance dough softening γ, i.e.,：
By using the time-varying stability of power system analysis system and method for the present invention, it can effectively solve the problem that blower fan is accessed
Time-varying stability of power system is difficult the problem differentiated caused by lower wind speed random character.In addition, the time-varying power train of the present invention
System stability analysis system and method, which need not obtain system operation track, to carry out stability distinguishing to time-varying power system, with
Time-domain-simulation method of the prior art is compared, and is reduced amount of calculation, is improved identification effect.
Brief description of the drawings
Fig. 1 is the structural representation of time-varying stability of power system analysis system in embodiment of the present invention.
Fig. 2 is power of fan curve synoptic diagram.
Fig. 3 is condition wind speed pattern information table.
Fig. 4 is the Weibull distribution fitting coefficient table of condition wind speed probability density under wind speed pattern.
Fig. 5 is one node system structural representation of IEEE4 machines 11 using example of the present invention.
Under 4 machine system either simplex condition situations of change of the Fig. 6 for one application example of the present invention, generator 2-3 is dynamic with respect to generator rotor angle
State responds schematic diagram.
Under 4 machine system multi-state situations of change of the Fig. 7 for one application example of the present invention, generator 2-3 is dynamic with respect to generator rotor angle
State responds schematic diagram
Fig. 8 for the present invention another apply example the node system structural representation of IEEE16 machines 68.
For the present invention, another is applied under 16 machine system either simplex condition situations of change of example Fig. 9, and generator 1-8 is with respect to generator rotor angle
Dynamic response schematic diagram.
For the present invention, another is applied under 16 machine system multi-state situations of change of example Figure 10, and generator 1-8 is with respect to work(
Angle dynamic response schematic diagram.
For the present invention, another applies the minimum damping ratio of each operational mode of 16 machine systems of example to Figure 11.
Embodiment
Below in conjunction with the accompanying drawings, the present invention is elaborated.
The detailed example embodiment of following discloses.However, concrete structure disclosed herein and function detail merely for the sake of
The purpose of example embodiment is described.
It should be appreciated, however, that the present invention is not limited to disclosed particular exemplary embodiment, but covering falls into disclosure model
Enclose interior all modifications, equivalent and alternative.In the description to whole accompanying drawings, identical reference represents identical member
Part.
It will also be appreciated that term "and/or" includes one or more related listing any of item as used in this
With all combinations.It will further be appreciated that when part or unit are referred to as " connecting " or during " coupled " to another part or unit, it
Miscellaneous part or unit are can be directly connected or coupled to, or can also have intermediate member or unit.In addition, for describing
Between part or unit other words of relation should understand in the same fashion (for example, " between " to " directly between ",
" adjacent " is to " direct neighbor " etc.).
In order to introduce technical scheme, the technical principle of the present invention is illustrated first.
Blower fan is exerted oneself is influenceed that a variety of methods of operation are presented by wind speed random character, if the appropriate random character to wind speed enters
Row analysis, simulation is exerted oneself the operation states of electric power system of influence containing blower fan, then can be to considering the time-varying electric power of wind speed random character
The stability of a system is effectively analyzed.
Definition condition wind speed probability density g (vi|vj) be a certain condition flag wind speed under, after predetermined time interval (for example
Sampling interval is usually chosen to 10min, after the predetermined time interval is such a sampling interval or several sampling intervals)
Wind speed probability density.Wind friction velocity probability density curve is fitted using two-parameter Weibull distribution.
Two-parameter Weibull distribution model expression is：
Wherein, viFor current time wind speed；
vjFor condition wind speed；
K is form factor；
C is scale coefficient；
g(vi|vj) it is that condition wind speed is vjShi Dangqian wind speed is viProbability density.
The probability-distribution function of wind speed is：
Ignore the factor such as electrical loss and wind power plant wake flow, the approximate function that blower fan is exerted oneself between wind speed can be with
It is expressed as：
Wherein, vciWind speed is cut for blower fan,
vcoFor blower fan cut-out wind speed,
vRFor blower fan rated wind speed,
PRFor blower fan rated output power,
P(vi) it is that wind speed is viBlower fan rated output power.
The segmentation probability function for obtaining blower fan power output by formula (1)-(3) is：
In addition, the model of time-varying power system can use the continuous Markov system representation to be：
Wherein, xt∈RnIt is state vector,
ut∈RpIt is control input vector,
T is the time,
ωtFor white noise, meet：
{ s (t), t >=0 } is the continuous markoff process of the value in confined space S={ 1,2 ..., l }, corresponds to each
System conditions under wind speed pattern, description system condition is exerted oneself the evolutionary process of change with blower fan.Its state transition probability
Density can be expressed as：
Wherein,
ηtOperating condition during for moment t, Δ is moment t variable quantity,
O (Δ) is the higher order indefinite small of moment t variation delta,
Matrix π represents Markov Transition Probabilities density matrix, πijIt is that system conditions are in i in t, and in t+
The Δ moment is in j transition probability density, and has：
For each st=i ∈ S, note A (st)、B(st)、G(st)、C(st)、D(st)、L(st) it is expressed as Ai、Bi、
Gi、Ci、Di、Li, and uncertain parameter meets matching condition：
ΔA(st, t)=Δ A (i, t)=HiF(i,t)Mi (8)
Wherein, HiAnd MiFor known matrix, I is unit matrix, and real matrix F (i, t) reflects the knot of system uncertain parameter
Structure information, meets：
FT(i,t)F(i,t)≤I (9)
Next stability analysis process is illustrated according to the state equation of system.
The model of the time-varying power system represented for formula (5), as u (t) ≡ 0 and all primary condition x0∈RnWith
s0When ∈ S are set up, if meeting：
So, the time-varying power system Stochastic stable of shape such as formula (5).
In addition, Robust Stochastic Stability criterion can be specifically expressed as：
Given normal number γ>0, if there is one group of positive definite symmetric matrices Pi>0, i ∈ S so that such as next group matrix is not
Formula is set up：
Then as u (t) ≡ 0, time-varying system robust convergency, and meet disturbance dough softening γ, i.e.,：
Using Schur theorems, from formula (11)：
Due to i ∈ S,Therefore：
Therefore, under conditions of need to only determining that formula (15) is set up, system (5) robust convergency, you can illustrate that robust is random
Stability criterion is set up.
Therefore, construction Lyapunov functional is：
As ω (t)=0, by functional V (xt, weak infinitesimal operators i) understands：
There is one group of positive definite matrix Qi>0 (i ∈ S) so that：
So as to have：
By Duncan lemma, have：
From above formula：
Therefore, have：
As t → ∞, have：
Therefore, the time-varying power system Stochastic stable represented by formula (5) is known in formula (15)-(22).
As ω (t) ≠ 0, functional V (xt, weak infinitesimal operators i) is represented by：
Defining target function is：
Due to：
Therefore,
By Duncan lemma, have：
So as to have
Due to E [V (xT,sT)] >=0 and formula (15), have：
JT≤E[V(x0,s0)],
As T → ∞, have：
Known by formula (23)-(26), the time-varying power system that formula (11) represents (5) has disturbance dough softening γ.
Finally, the stability of time-varying power system shown in system (5) can be represented using following optimization problem：
(27)
s.t.(11)(12)
Utilization feasibility problem solving method is solved to LMI, if there is t ＜ 0 and meet positive definite square shown in criterion
Battle array Pi>0, then the time-varying power system robust convergency for representing (5), and meet disturbance dough softening γ；Otherwise, time-varying electric power
System is unstable.
Therefore, as shown in figure 1, the present invention includes a kind of time-varying stability of power system analysis system, the system includes
The data acquisition module being sequentially connected, wind speed fitting prediction module, time-varying system are set up solves mould with depression of order module, stability criterion
Block and result output module, data acquisition module are additionally coupled to time-varying system and set up and depression of order module；
The data acquisition module is used to gathering wind farm wind velocity and blower fan force information, network architecture parameters, in system
Generator frequency, generator rotor angle, and gathered data is sent to wind speed fitting prediction module and time-varying system foundation and depression of order module；
Information and wind power plant history real data that the wind speed fitting prediction module is sent according to data acquisition module are right
Condition wind speed trend is fitted prediction in short time, and by wind speed interval, each interval condition is calculated according to model of fit
Feature wind speed probability density matrix；
The time-varying system is set up each interval sub- operating mode as time-varying system with depression of order module, according to blower fan
The continuous Ma Erke of the gathered data foundation consideration wind speed random character of wind speed and exert oneself corresponding relation and data acquisition module
Husband's time-varying electric power system model, and depression of order is carried out to system；
Described stability criterion, which solves module, to be used to form time-varying power system robust convergency criterion, utilizes linear moment
Whether the feasibility problems method for solving solving system in battle array inequality is stablized；
Described result output module is used for output system stability distinguishing result.
By the time-varying stability of power system analysis system of the present invention, it can effectively solve the problem that the lower wind speed of blower fan access is random
Power system time-varying stability is difficult the problem differentiated caused by feature.First with two-parameter Weibull distribution model to the short time
Interior condition wind speed trend is fitted prediction, then by wind speed interval, calculates each interval condition flag wind speed probability density square
Battle array, the operating condition of system is determined according to condition flag wind speed.Then, set up according to system rack information and consider that wind speed is special at random
The continuous Markov time-varying electric power system model levied, and reduced order system.
Correspondingly, the invention also discloses a kind of time-varying method for analyzing stability of power system, methods described includes：
A, collection wind farm wind velocity and blower fan force information, network architecture parameters, generator frequency, generator rotor angle in system；
B, the data according to collection and wind power plant history real data, are fitted pre- to condition wind speed trend in the short time
Survey, and by wind speed interval, each interval condition flag wind speed probability density matrix is calculated according to model of fit；
C, using each interval sub- operating mode as time-varying system, corresponding relation and adopted according to blower fan wind speed with exerting oneself
The data of collection set up the continuous Markov time-varying electric power system model for considering wind speed random character, and carry out depression of order to system；
D, formation time-varying power system robust convergency criterion, are asked using the feasibility problems in LMI
Whether solution method solving system is stablized；
E, output time-varying Power System Stability Analysis result.
In a detailed embodiment, the condition flag wind speed probability density described in step B is a certain condition flag
Under wind speed, (such as sampling interval is usually chosen to 10min, and the predetermined time interval is adopted to be such a after predetermined time interval
Sample interval or after several sampling intervals) wind speed probability density.
Especially, it is fitted prediction in step B to condition wind speed trend in the short time, and by wind speed interval, according to
Model of fit, which calculates each interval condition flag wind speed probability density matrix, to be included：
B1, utilize two-parameter Weibull distribution models fitting prediction each condition wind speed of time-varying system under variation tendency；
B2, according to certain siding-to-siding block length by wind speed incision wind speed and cut-out wind speed between carry out intervalization, utilize step
Model of fit in rapid B1 under each condition wind speed determines each interval condition flag wind speed probability density matrix.
More specifically, in an embodiment, the two-parameter Weibull distribution model is：
Wherein, viFor current time wind speed；
vjFor condition wind speed；
K is form factor；
C is scale coefficient；
g(vi|vj) it is that condition wind speed is vjShi Dangqian wind speed is viProbability density.
In addition, in the step C of an embodiment, being built according to the data of blower fan wind speed and exert oneself corresponding relation and collection
The vertical continuous Markov time-varying electric power system model for considering wind speed random character, and system progress depression of order is included：
C1, using each interval sub- operating mode as time-varying system, it is true according to blower fan wind speed and the corresponding relation exerted oneself
Determine the corresponding blower fan power output of each interval feature wind speed, and consideration is set up using the blower fan power output and the data of collection
The continuous Markov time-varying electric power system model of wind speed random character；
Especially, the blower fan wind speed is with corresponding relation of exerting oneself：
Wherein, vciWind speed is cut for blower fan；
vcoFor blower fan cut-out wind speed；
vRFor blower fan rated wind speed；
PRFor blower fan rated output power.
In addition, continuous Markov time-varying electric power system model expression formula is specially：
Wherein, xt∈RnIt is state vector,
ut∈RpIt is control input vector,
T is the time,
ωtFor white noise, meet：
{ s (t), t >=0 } is the continuous markoff process of the value in confined space S={ 1,2 ..., l }, corresponds to each
System conditions under wind speed pattern, description system condition is exerted oneself the evolutionary process of change with blower fan.Its state transition probability
Density can be expressed as：
Wherein,
ηtOperating condition during for moment t, Δ is moment t variable quantity,
O (Δ) is the higher order indefinite small of moment t variation delta,
Matrix π represents Markov Transition Probabilities density matrix, πijIt is that system conditions are in i in t, and in t+
The Δ moment is in j transition probability density, and：
For each st=i ∈ S, note A (st)、B(st)、G(st)、C(st)、D(st)、L(st) it is expressed as Ai、Bi、
Gi、Ci、Di、Li, and uncertain parameter meets matching condition：
ΔA(st, t)=Δ A (i, t)=HiF(i,t)Mi,
Wherein, HiAnd MiFor known matrix, I is unit matrix, and real matrix F (i, t) reflects the knot of system uncertain parameter
Structure information, meets：
FT(i,t)F(i,t)≤I。
C2, on the premise of ensureing that interested frequency band input-output characteristic is constant to continuous Markov time-varying power system
Model reduction.
Especially, carrying out depression of order to system described in step C2 includes：
C21, by system state equationIt is divided into：
Wherein, X1=[Δ ωT,ΔδT] to retain variable, Δ ω represents the variable quantity of generator's power and angle rotating speed, and Δ δ is represented
Generator's power and angle variable quantity, X2For its dependent variable；
C22, cancellation X2After beWherein I is unit battle array, and p is differential
Operator.
Above formula can be rewritten asWherein Ar(p) it is the reduced order system factor arrays of operational form.
Two critical natures can be obtained by upper three formula：
(1) if p=λ1(i=1,2 ..., N) is the first formula corresponding system characteristic root, i.e., | λiI-A |=0, then p=λi
For the second formula or the system features root of the 3rd formal depression of order of formula, i.e., also have | λiI-Ar(λi) |=0, characteristic root does not change,
System model is constant.
(2) for original system, λiCharacteristic vector ui, there is Aui=λiui.If reduced order system characteristic root λiCorresponding feature to
Measure as uri, i.e. Ar(λi)uri=λiuri, then uriAnd uiMiddle reservation variable XrCorresponding element is equal, i.e., characteristic vector is corresponding
Element is constant.Therefore, in XrRetain and go to observe same pattern λ at variableiVibration when, relative magnitude is phase invariant, in other words
Mode is constant.
Therefore, frequency band input-output characteristic of concern is remained by complete, while realizing the effect of depression of order.
In addition in the embodiment of the invention, in step D, form time-varying power system robust convergency and sentence
According to including using whether the feasibility problems method for solving solving system in LMI is stable：
The Lyapunov functional of D1, structure containing continuous Markov time-varying electric power system model, and in the weak of the functional
Duncan lemma is used in infinitesimal operators, the linear matrix inequality technique for the Robust Stochastic Stability for meeting interference attenuation degree γ is derived
Formula, obtains time-varying power system robust convergency criterion；
D2, whether stablized using the feasibility problems method for solving solving system in LMI.
Especially, the Lyapunov functional expression formula containing continuous Markov time-varying electric power system model is：
Wherein PiFor positive definite matrix.
In addition, described weak infinitesimal operators expression is：
And described Duncan lemma is expressed as：If function f (x) domain of definition is I：If for belonging to some interval in I
On any two independent variable value x1、x2, work as x1More than x2When have f (x1) it is more than f (x2) so just says f (x) in this area
Between on be increasing function.If the value x for belonging to any two independent variable in I on some interval1、x2, work as x1Less than x2Shi Dou
There are f (x1) it is less than f (x2), then it is exactly that f (x) is subtraction function on this interval.
In addition, the Robust Stochastic Stability criterion can be specifically expressed as：Given normal number γ>0, if there is one group
Positive definite symmetric matrices Pi>0, i ∈ S so that as next group of MATRIX INEQUALITIES is set up：
Then as u (t) ≡ 0, time-varying system robust convergency, and meet disturbance dough softening γ, i.e.,：
In the specific embodiment of the invention, the method for solving of feasibility problems is specific in described LMI
It can be expressed as：
For given LMI system A (x) ＜ B (x), asked by solving the convex optimization of auxiliary shown in following formula
Topic, searches out global minima scalar value tminIf, tmin, then there is x ∈ R in ＜ 0nOr matrix X ∈ RnMeet following formula：
min t
s.t.A(x)-B(x)≤tI。
Illustrate the skill of time-varying stability of power system analysis system of the present invention and method below by way of two specific examples
Art effect.
Example 1
Analyzed by taking actual measurement air speed data in certain wind power plant 1 month as an example, wherein incision wind speed is 3m/s, rated wind speed
For 12m/s, cut-out wind speed is 22m/s, and blower fan output power curve is as shown in Figure 2.Wind speed is divided by interval width of 1m/s
For 10 patterns, continuous Markov Model state set is constituted, S={ 1,2 ..., 10 } is denoted as, each pattern information is in figure 3
Provide.
Weibull distribution fitting is carried out to condition wind speed probability density curve under each wind speed pattern according to mode division in Fig. 3,
Fitting result is as shown in Figure 4.Tried to achieve according to Fig. 4 and formula (1) shown in each condition wind speed probability density matrix such as formula (28).
The node system of IEEE4 machines 11 as shown in Figure 5, the system inclusion region 1 and 2 two, region region are built, wherein
Generator 1 and generator 2 are located at region 1, and generator 3 and generator 4 are located at region 2, the interconnection 7-8 and 8-9 in two regions
It is double loop.Generator uses 6 rank detailed models, and excitation system uses the load under high-speed excitation, benchmark model to use
50% constant-impedance and 50% constant current model.Generator G4 in region 2 is replaced being used for mould with the power source of grade capacity during analysis
Intend the working conditions change situation of blower fan power output.
First, obtain state matrix that the corresponding blower fan of four machine systems goes out under force mode using modal analysis method and utilize SMA
Systematic observation matrix after depression of order and state transition probability density matrix shown in formula (28) are substituted into formula (27), disturbed by method depression of order
Dynamic dough softening γ takes 0.1, and utilization feasibility problem solving method tries to achieve LMI establishments, and there is positive definite matrix Pi, 4 machine systems
Robust convergency.Wherein, formula (29)-(30) give positive part-definite matrix PiValue.
From above-mentioned solving result, the 4 machine system meets condition shown in robust convergency criterion, i.e., the system is being examined
Consider wind speed random character when for robust convergency system.The fortune of Fig. 6 and Fig. 7 respectively with regard to being likely to occur in running
Row working conditions change situation carries out time-domain analysis, wherein, Fig. 6 is in the case of a working conditions change only occurs for system, generator G2 with
Relative generator rotor angle dynamic response schematic diagram between G3, Fig. 7 is that the phase between generator G2 and G3 during multi-state situation of change occurs for system
To generator rotor angle dynamic response schematic diagram.System actual analysis result and time-varying method for analyzing stability of power system of the present invention in figure
Judged result is consistent.It follows that set forth herein time-varying method for analyzing stability of power system can not obtain operation rail
Accurate judgement system stability on the premise of mark, amount of calculation is few, with preferable validity and accuracy.
Example 2
The node system of IEEE16 machines 68 as shown in Figure 8 is built, further examination considers the when power transformation of wind speed random character
The validity and versatility of Force system method for analyzing stability.The system can be divided into 5 big regions, and wherein region 1,2 and 3 is equivalence
System, region 4 is New York system, and region 5 is New England's system, by generator G16 in region 3 with the power source generation of grade capacity
For the situation of change for simulates blower fan power output.Generator uses 6 rank detailed models, and excitation is encouraged using IEEE-DC1 types
Magnetic, load model uses WECC load models, 80% permanent burden with power, 80% permanent reactive impedance load, 20% dynamic
Load.
First with SMA method respectively to systematic observation matrix depression of order under each operating mode, and by the system mode square after depression of order
Battle array substitutes into formula (27) with probability density transfer matrix shown in formula (28), and disturbance dough softening γ takes 0.1, utilization feasibility problem solving
Method tries to achieve LMI establishments.But, due to gained matrix PiMiddle P6There are negative characteristic root -15.3827, i.e. matrix PiExist non-
Positive definite matrix, therefore, the 16 machine system are unsatisfactory for robust convergency condition when considering that blower fan is exerted oneself and changed.
Fig. 9 and Figure 10 carry out time-domain analysis with regard to the operating condition situation of change being likely to occur in running respectively,
Wherein, Fig. 9 is that relative generator rotor angle dynamic response schematic diagram during a working conditions change situation between generator G1 and G8 only occurs for system,
Relative generator rotor angle dynamic response schematic diagram when Figure 10 is multiple working conditions change situation between generator G1 and G8.System as we know from the figure
There is in single and unstable situation during multiple working conditions change situation, this with this method to sentence steady result consistent.
The state matrix of each operating condition of system is analyzed respectively, each state matrix minimum damping such as Figure 11 institutes
Show.As shown in Figure 11, state matrix characteristic value is respectively provided with negative real part under each operational mode, now, if utilizing eigenvalue Method
Any operating condition stability is individually analyzed, analysis result is stabilization.It follows that considering the time-varying of wind speed random character
In power system, when being switched to another steady working condition from a steady working condition unstability may occur for system, and the phenomenon is tradition
Can not be analyzed for the method for analyzing stability of single operating mode, set forth herein time-varying method for analyzing stability of power system energy
Enough effectively to carry out stability distinguishing analysis for this phenomenon, method is easy, with good accuracy and validity.
It should be noted that above-mentioned embodiment is only the present invention preferably embodiment, it is impossible to be understood as to this
The limitation of invention protection domain, under the premise of without departing from present inventive concept, any minor variations done to the present invention and modification
Belong to protection scope of the present invention.
Claims (10)
1. a kind of time-varying stability of power system analysis system, the system includes the data acquisition module being sequentially connected, wind speed
Prediction module, time-varying system is fitted to set up and depression of order module, stability criterion solution module and result output module, data acquisition module
Block is additionally coupled to time-varying system and set up and depression of order module；
The data acquisition module is used to gather wind farm wind velocity with being generated electricity in blower fan force information, network architecture parameters, system
Unit frequency, generator rotor angle, and gathered data is sent to wind speed fitting prediction module and time-varying system foundation and depression of order module；
Information and wind power plant history real data that the wind speed fitting prediction module is sent according to data acquisition module, in short-term
Interior condition wind speed trend is fitted prediction, and by wind speed interval, each interval condition flag is calculated according to model of fit
Wind speed probability density matrix；
The time-varying system is set up each interval sub- operating mode as time-varying system with depression of order module, according to blower fan wind speed
When setting up the continuous Markov for considering wind speed random character with the gathered data of exert oneself corresponding relation and data acquisition module
Become electric power system model, and depression of order is carried out to system；
Described stability criterion, which solves module, to be used to form time-varying power system robust convergency criterion, using linear matrix not
Whether the feasibility problems method for solving solving system in equation is stablized；
Described result output module is used for output system stability distinguishing result.
2. a kind of time-varying method for analyzing stability of power system, methods described includes：
A, collection wind farm wind velocity and blower fan force information, network architecture parameters, generator frequency, generator rotor angle in system；
B, the data according to collection and wind power plant history real data, prediction is fitted to condition wind speed trend in the short time,
And by wind speed interval, each interval condition flag wind speed probability density matrix is calculated according to model of fit；
C, using each interval sub- operating mode as time-varying system, according to blower fan wind speed and exert oneself corresponding relation and collection
Data set up the continuous Markov time-varying electric power system model for considering wind speed random character, and carry out depression of order to system；
D, formation time-varying power system robust convergency criterion, utilize the feasibility problems solution side in LMI
Whether method solving system is stablized；
E, output time-varying Power System Stability Analysis result.
3. the time-varying method for analyzing stability of power system according to claim 2, it is characterised in that described in step B
Condition flag wind speed probability density be a certain condition flag wind speed under, the wind speed probability density after predetermined time interval.
4. the time-varying method for analyzing stability of power system according to claim 3, it is characterised in that to short in step B
Condition wind speed trend is fitted prediction in time, and by wind speed interval, calculates each interval condition according to model of fit special
Levying wind speed probability density matrix includes：
B1, utilize the variation tendency under each condition wind speed of two-parameter Weibull distribution models fitting time-varying system；
B2, according to certain siding-to-siding block length by wind speed incision wind speed and cut-out wind speed between carry out intervalization, utilize step B1
In model of fit under each condition wind speed determine each interval condition flag wind speed probability density matrix.
5. the time-varying method for analyzing stability of power system according to claim 4, it is characterised in that the two-parameter Wei
Primary distributed model is：
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Wherein, viFor current time wind speed；
vjFor condition wind speed；
K is form factor；
C is scale coefficient；
g(vi|vj) it is that condition wind speed is vjShi Dangqian wind speed is viProbability density.
6. the time-varying method for analyzing stability of power system according to claim 2, it is characterised in that in step C, according to
The power transformation when data of blower fan wind speed and exert oneself corresponding relation and collection set up the continuous Markov for considering wind speed random character
Force system model, and system progress depression of order is included：
C1, using each interval sub- operating mode as time-varying system, determined according to blower fan wind speed and the corresponding relation exerted oneself each
The corresponding blower fan power output of interval feature wind speed, and set up using the blower fan power output and the data of collection and consider wind speed
The continuous Markov time-varying electric power system model of random character；
C2, on the premise of ensureing that interested frequency band input-output characteristic is constant to continuous Markov time-varying electric power system model
Depression of order.
7. the time-varying method for analyzing stability of power system according to claim 2, it is characterised in that the blower fan wind speed
Corresponding relation is with exerting oneself：
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Wherein, vciWind speed is cut for blower fan；
vcoFor blower fan cut-out wind speed；
vRFor blower fan rated wind speed；
PRFor blower fan rated output power.
8. the time-varying method for analyzing stability of power system according to claim 6, it is characterised in that described in step C2
Carrying out depression of order to system includes：
C21, by system state equationIt is divided into：
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Wherein, X1=[Δ ωT,ΔδT] to retain variable, Δ ω represents the variable quantity of generator's power and angle rotating speed, and Δ δ represents to generate electricity
Machine generator rotor angle variable quantity, X2For its dependent variable to be eliminated；
C22, cancellation X2After beWherein I is unit battle array, and p is differential operator.
9. the time-varying method for analyzing stability of power system according to claim 2, it is characterised in that in step D, is formed
Time-varying power system robust convergency criterion, utilizes the feasibility problems method for solving solving system in LMI
Whether stablize includes：
The Lyapunov functional of D1, structure containing continuous Markov time-varying electric power system model, and in the weak infinite of the functional
Duncan lemma is applicable in small operator, the LMI for the Robust Stochastic Stability for meeting disturbance dough softening γ is obtained, obtains
Then become power system robust convergency criterion；
D2, using the feasibility problems method for solving in LMI determine whether system is stablized.
10. the time-varying method for analyzing stability of power system according to claim 9, it is characterised in that the robust with
Machine stability criterion can be specifically expressed as：Given γ>0, if there is one group of positive definite symmetric matrices Pi>0, i ∈ S so that as follows
One group of MATRIX INEQUALITIES is set up：
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Then as u (t) ≡ 0, time-varying system robust convergency, and meet disturbance dough softening γ, i.e.,：
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