CN110474349A - A kind of power system frequency dynamic analysing method based on Continuum Model - Google Patents
A kind of power system frequency dynamic analysing method based on Continuum Model Download PDFInfo
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- CN110474349A CN110474349A CN201910771894.7A CN201910771894A CN110474349A CN 110474349 A CN110474349 A CN 110474349A CN 201910771894 A CN201910771894 A CN 201910771894A CN 110474349 A CN110474349 A CN 110474349A
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/24—Arrangements for preventing or reducing oscillations of power in networks
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Abstract
The invention discloses a kind of power system frequency dynamic analysing method based on Continuum Model, the method step are as follows: one, have N platform generator in hypothesis system, the inertia constant of generator to be allocated is M, and M is evenly distributed to each shortest path, expression formula are as follows:Wherein, MiFor the angular momentum of i-th generator；Two, the inertia constant obtained to distribution, every shortest path reuse height and are continuously allocated with smooth Gauss function to resulting parameter is distributed, the expression formula of distribution are as follows:Wherein: xiIndicate a spatial point of i-th line road, M0Locate the maximum value of (bus position) at the center point for Gauss function；Three, the inertia phase etc. of the inertia and integrated distribution on former bus according to non-individual body before and after the processing, can obtain:Four, after obtaining all paths and corresponding impedance value, by two minor sorts can be obtained by disturbing source to each generator bus shortest path.This method, by only considering the most short propagation path from disturbing source to each generator bus, greatly reduces the computation complexity of parametric distribution, achieves good effect in carrying out parametric distribution.
Description
Technical field
The present invention relates to a kind of power system frequency dynamic analysing method more particularly to a kind of electricity based on Continuum Model
Force system frequency dynamic analysis method, belongs to Power System Analysis technical field.
Background technique
With the increase of the progress and electrical energy demands amount of science, the scale and complexity of electric system increase, so that
The system stable problem that electric system faces becomes increasingly conspicuous.IEEE/CIGER stablizes definition joint working group and is lost according to electric system
Equipment, process and the time frame etc. that steady physical characteristic, the size disturbed and research stable problem must be taken into consideration,
Stability of power system is divided into angle stability, voltage stabilization and frequency stabilization.
Important parameter of the frequency as electric system is one of the main indicator for measuring power quality.When electric system meets with
It is inevitable since system active power balance is destroyed after by various disturbances (such as short circuit, excision generator, excision load)
It will lead to system frequency and disturbance occur to occurrence frequency dynamic process.Frequency disturbance can be propagated with bus, and electromechanics is disturbed
Dynamic propagation in systems may influence whether the safe and stable operation of electric system.The propagation of Electromechanical Disturbance is studied to recognizing deeply
The Dynamic Mechanism for knowing electric system, the control system for carrying out Dynamic Stability Analysis and establishing safety and stability have important meaning
Justice.
As a discrete system when conventional method analyzes electric system, to the various pieces of discrete system
It is individually modeled, finally according to model built to progress global analysis.Since Electromechanical Disturbance is in the non-individual body mould of electric system
Electromechanical Disturbance is propagated and is propagated in discrete system with similar characteristic in type, and related physical quantity is with the corresponding pass having one by one
System.Therefore, for complicated large-scale power system, the communication process of Electromechanical Disturbance in the entire power system is paid close attention to, is used
Non-individual body system can be described from the Dynamic Mechanism that bigger space scale propagates Electromechanical Disturbance, to keep description more quasi-
Really.
Discrete system is pocessed in modeling process using generator parameter as lumped parameter, is built using Continuum Model
The discrete lumped parameter of generator is carried out serialization when mould, to obtain the equation of system under Continuum Model.Using continuous
The model that body surface shows has more superiority than traditional discrete system when describing big system such as global power system.
In non-individual body modeling process, parametric distribution is a critically important problem.The direct shadow of the reasonability of parametric distribution
Ring the accuracy of modeling.Since the path that frequency disturbance is propagated is not unique, usually up to hundreds of, at this time if still used
Gaussian function method (Gaussian Smooth Method, GSM) carries out system parameter distribution, it will due to propagation path number is excessive
The difficulty for increasing parametric distribution, to increase system modelling difficulty.
Summary of the invention
The technical problem to be solved by the present invention is providing a kind of power system frequency dynamic analysis based on Continuum Model
Method, this method pass through the most short propagation path only considered from disturbing source to each generator bus in carrying out parametric distribution, and
All paths of GSM method are not based on, the computation complexity of parametric distribution, the distribution side based on shortest path are greatly reduced
On the one hand method can make parametric distribution and network analysis simpler, on the other hand, also the inhibition for electromechanical wave disturbance provides think of
Road solves the problems, such as above-mentioned.
The technical solution of the present invention is as follows: a kind of power system frequency dynamic analysing method based on Continuum Model, described
Method and step are as follows: one, have N platform generator in hypothesis system, the inertia constant of generator to be allocated is M, by M mean allocation
To each shortest path, expression formula are as follows:Wherein, MiFor the angular momentum of i-th generator；Two, distribution is obtained
Inertia constant, every shortest path reuse height and are continuously allocated with smooth Gauss function to resulting parameter is distributed,
The expression formula of distribution are as follows:Wherein: xiIndicate a spatial point of i-th line road, M0For Gauss function
Locate the maximum value of (bus position) at the center point；Three, according to integrated distribution on non-individual body inertia before and after the processing and former bus
Inertia phase etc., can obtain:Four, after obtaining all paths and corresponding impedance value, pass through
Two minor sorts can be obtained by disturbing source to the shortest path of each generator bus.
The beneficial effects of the present invention are: compared with prior art, using technical solution of the present invention, for continuous volume modeling
Parametric distribution problem in the process proposes one kind and is based on according to electromechanical wave along the difference of different propagated speed and time
The parametric distribution method of shortest path, gives the exact expression of parametric distribution.This method is by finding from generator bus
The most short propagation path to remaining generator bus of hair, and generator inertia constant is evenly distributed on shortest path.It is logical
It crosses and 10 machine of New England, 39 node standard data set is tested, the results showed that, from the path of generator bus
Sum up to thousands of, the number of lines are much larger than shortest path.Therefore, the parameter proposed by the invention based on shortest path point
Method of completing the square is far below traditional GSM on computation complexity.In addition, the parameter distribution based on shortest path be also the later period into
The network analysis of one step and Disturbance Rejection provide research, illustrate the validity of proposed method, achieve well using effect
Fruit.
Detailed description of the invention
Fig. 1 is programming schematic diagram of the invention；
Fig. 2 is the change curve of the frequency increment on generator bus of the invention.
Specific embodiment
To make the object, technical solutions and advantages of the present invention clearer, below with reference to this specification attached drawing to this hair
It is bright to be described in further detail.
Embodiment 1: as shown in attached drawing 1-2, a kind of power system frequency dynamic analysing method based on Continuum Model, institute
State method and step are as follows: one, have N platform generator in hypothesis system, the inertia constant of generator to be allocated is M, by M mean allocation
To each shortest path, expression formula are as follows:Wherein, MiFor the angular momentum of i-th generator；Two, distribution is obtained
Inertia constant, every shortest path reuse height and are continuously allocated with smooth Gauss function to resulting parameter is distributed,
The expression formula of distribution are as follows:Wherein: xiIndicate a spatial point of i-th line road, M0For Gauss function
Locate the maximum value of (bus position) at the center point；Three, according to integrated distribution on non-individual body inertia before and after the processing and former bus
Inertia phase etc., can obtain:Four, after obtaining all paths and corresponding impedance value, pass through
Two minor sorts can be obtained by disturbing source to the shortest path of each generator bus.
The mentality of designing that the present invention will be described in detail again below is as follows:
Following basic assumption need to first be made when analyzing chain type electric system:
1) generator speed ω approaches synchronous rotational speed ωs；
2) ignore the electromagnetic transient of generator nail winding；
3) generator internal impedance is minimum, it is believed that the phase angle of generator built-in potential is close with the phase angle of its generator terminal busbar voltage
Patibhaga-nimitta etc.；
4) voltage effective value of all buses is equal, and sets its per unit value as 1.0；
5) it is all connected to generator and load on each bus in system, inputs in the mechanical output and bus of generator and bears
The power of lotus keeps constant constant.
6) resistance of transmission line of electricity is much smaller than reactance.That is R < < X.
7) disturbance causes the absolute value of the phase angle deviation delta θ of bus smaller, that is, exists | Δ θ | < < 1, therefore sin Δ θ ≈ Δ
θ and cos Δ θ ≈ 1.
Traditional analysis thinks that there are a certain distance between each generator, that is, defining generator is the discrete point in space.
If the angular momentum of i-th generator is Mi, damped coefficient di, accelerating power P∑i, then available to consider generator resistance
In the case of Buddhist nun, i-th generator amature waves equation expression formula in chained form system are as follows:
In practical power systems, generator is dispersedly distributed different positions in system.Tradition research electric system
Generally transmission line of electricity is indicated using lumped parameter in the method for electromechanical dynamic, is failed comprising spatial information, is i.e. only known line
Electric parameter and line length is unknown.However, Continuum Model slave radio wave propagation angle generator inertia space into
The integrated distributions parameters such as generator, the load of distribution discrete in space are passed through continuous treatment by continuous treatment.Due to
The topological relation of grid structure in conventional model is embodied as much as possible during continuous treatment, so that Continuum Model
The electric system of more approaching to reality.
When generator quantity increases considerably in chained form system unit length, the distance between adjacent generator will be approached
With zero, originally at the generator existing for discrete parameter will use density by the way that mathematically continuous density function is indicated
What functional form indicated waves equation are as follows:
If ignoring the power of injection network at attenuation factor and the coordinate x in electromechanical wave communication process, even d=0, g
=0, pm=0, then formula (2) can be changed to classical wave equation:
The relationship of opposite angular velocity omega, power p and voltage phase angle θ are as follows:
Substitute the above to the fundamental equation that approximate description machine radio wave propagation is obtained in classical wave equation are as follows:
It can be seen from the above, serialization is realized in spatial position discrete in original traditional discrete system by non-individual body system,
To which spatial position to be also used as to a variable of system.Which achieves turning from conventional discrete system to non-individual body system
Change.
Continuum Model is the approximate description method of discrete model, and the dynamic characteristic for broad scale research electric system provides
A kind of new means.Continuum Model is different from traditional electromechanical dynamic analysis method, is mainly directed towards complicated large size electricity
Force system, the communication process of concern Electromechanical Disturbance in the entire power system, can be from bigger space scale research aircraft electric disturbance
The dynamic Dynamic Mechanism propagated.
After disturbing generation, electromechanical wave is propagated at limited speeds, and the time of each point is not identical in arrival system
's.In view of the disturbance of practical power systems, the present invention passes through load elder generation increment with the change modeling system initial disturbance of load
Reduce the dynamic process expression for being finally restored to original load level again.It is with 10 machine of New England, 39 system
Example, is arranged the mathematic(al) representation of initial disturbance are as follows:
Wherein, ε (t) is unit jump function.
Setting disturbance generation o'clock passes through the frequency emulated on available each generator bus (30-39) in No. 30 bus
The change curve of rate increment is as shown in Fig. 2.
By attached drawing 2 it is found that the time of the propagation of disturbance to each bus is different after disturbing generation, when disturbance occurs to exist
When No. 30 bus, the time for reaching each bus is as shown in table 1.
1 frequency disturbance of table is to each bus propagation time
Tab.1 The spreading time of frequency destabilization
As shown in Table 1, when disturb occur after, reach the time of each generator bus be it is different, illustrate disturbance exist
The time difference propagated on each path is anisotropic.
In non-individual body modeling process, parametric distribution is a critically important problem, directly affects the accuracy of modeling.Text
It offers [8] and carries out parametric distribution using GSM method, but all paths of frequency propagation must be taken into consideration in this method, and by parametric distribution
Onto all paths.When generating set quantity is more in system, the computation complexity that parametric distribution is calculated in system can be big
It is big to increase, therefore the invention proposes a kind of methods for carrying out parametric distribution by shortest path.
During finding shortest path, common searching algorithm has breadth First and depth-first two ways.By
It needs to safeguard that tree state is searched in the preservation of lining up an of first in first out in breadth-first search, causes algorithm with higher
Space complexity.Depth Priority Algorithm has descendent node that can no longer save more to node had been searched for, and makes to need
The search tree state of preservation greatly reduces, therefore the present invention uses Depth Priority Algorithm.
The present invention has used the searching algorithm of graph theory thought, recurrence thought and depth-first search in algorithm design.
Wherein graph theory thought is used primarily in by the parameter table building adjacency matrix of system and corresponding with adjacency matrix containing impedance
Another matrix of information, their input for functioning as program provide the foundation of judgement for search.Recurrence thought is
For the search in path, when obtaining a value every time, first judge whether to meet the condition terminated, acquired results if being unsatisfactory for
Continue to search for as input, i.e. calling function itself.Depth-first search is scanned for first along certain path, when searching
After rope obtains a paths on earth, backtracking is carried out, other paths are continued searching, and so on, until finding all paths.
To after all paths and corresponding impedance value, disturbing source can be obtained by the most short of each generator bus by two minor sorts
Path.
Because the difference of line parameter circuit value results in the difference of the propagation of disturbance time on different routes, then can only consider to pass
Shorter route between sowing time, by the parametric distribution of generator on the generic line of generator bus connected to it.Assuming that being
There is N platform generator in system, the inertia constant of generator to be allocated is M, and M is evenly distributed to each shortest path, expression formula
Are as follows:
To the obtained inertia constant of distribution, every shortest path reuse height continuously and smooth Gauss function to point
It is allocated with resulting parameter, the expression formula of distribution are as follows:
Wherein xiIndicate a spatial point of i-th line road, M0Locate (bus position) at the center point for Gauss function
Maximum value.According to the inertia phase etc. of integrated distribution on the inertia of non-individual body before and after the processing and former bus, can obtain:
The distribution of generator inertia constant is the important research content in continuous volume modeling, by above-mentioned various it is found that carrying out
By only considering the most short propagation path from disturbing source to each generator bus in parametric distribution, rather than based on GSM method
All paths greatly reduce the computation complexity of parametric distribution.
For the correctness for verifying the method for the present invention, the present invention uses 10 machine of New England, a 39 node normal data
Collection is studied, and is extracted it and is originated bus and termination bus and corresponding impedance information, uses depth by following three conditions
Precedence method scans for:
1) from generator bus, terminated with generator bus；
2) path cannot repeat；
3) every search obtains a paths, records corresponding impedance value.
The schematic diagram for obtaining present procedure design is as shown in Fig. 1.
By attached drawing 1 it is found that program combines recurrence and depth-first search, wherein head is the input of function, initially
Value is defaulted as the number of plies that 40, k is search, i.e., counts to the bus number searched out, initial value k=1.It is every once to be searched
K value using acquired results as input next time, and is added 1 by rope, the search until completing a paths.One road of every completion
The search of diameter, while corresponding impedance value is recorded, backtracking is then carried out, other paths are continued searching.When k value is again equal to 1
When, just complete the search from all paths of certain starting point.This obtains (not wrapping from 40-49 with 40-49 ending
Containing itself) all paths and its corresponding impedance value, wherein respective shortest path is obtained by sequence, and passes through statistics
With sequence obtained each by bus number seniority among brothers and sisters.The meaning of this work is to find after different disturbing sources
Number by which bus is most, then disturbs at the bus, if can be subject on corresponding important bus in time
Inhibit, then can play good effect, reduces influence of the disturbance to system.
Using algorithm for design of the present invention carry out route searching, obtain respectively from the total number of paths of 30-39 bus such as
Shown in table 2.
Table 2 respectively originates the corresponding number of path of bus
Tab.2 The route number of per original wire
It as shown in Table 2, is hundreds of from the number of path of each disturbing source, No. 38 most buses of number of path are corresponding
Number of paths is 650, and the corresponding total number of paths of all buses is 3728.If conventionally carrying out tradition point
Match, then need for generator inertia constant to be assigned in thousands of paths, the computation complexity of parametric distribution is caused to greatly increase,
It is unfavorable for the network analysis in later period.
Since system for use in carrying shares 10 generator bus, i.e. N=10, it is known that female from disturbing source to remaining generator
Line shares 9 shortest paths, if generator inertia constant is M at disturbing source, the result of inertia distribution can be obtained according to formula (3) are as follows:
By formula (10) it is found that the method that generator inertia constant is assigned to thousands of paths compared to tradition, will send out
On the one hand the parameter distribution that motor inertia constant M is equally distributed to 9 shortest paths greatly reduces parametric distribution
Complexity, while also laying a good foundation for the further analysis of later period electric system.
For the parametric distribution problem in non-individual body modeling process, according to electromechanical wave along different propagated speed and time
Difference, propose a kind of parametric distribution method based on shortest path, give the exact expression of parametric distribution.This method is logical
The most short propagation path to remaining generator bus found from generator bus is crossed, and generator inertia constant is averaged
It is assigned on shortest path.By being tested to 10 machine of New England, 39 node standard data set, the results showed that, from hair
The total number of paths that motor bus sets out up to thousands of, the number of lines is much larger than shortest path.Therefore, base proposed by the invention
Traditional GSM is far below on computation complexity in the parameter distribution of shortest path.In addition, the parameter based on shortest path
Distribution method also provides research for later period further network analysis and Disturbance Rejection, illustrates the validity of proposed method.
Place is not described in detail by the present invention, is the well-known technique of those skilled in the art of the present technique.Finally, it is stated that the above reality
It applies example to be only used to illustrate the technical scheme of the present invention and not to limit it, although having carried out specifically the present invention referring to preferred embodiment
It is bright, those skilled in the art should understand that, can with modification or equivalent replacement of the technical solution of the present invention are made, and
The objective and range for not departing from technical solution of the present invention, are intended to be within the scope of the claims of the invention.
Claims (1)
1. a kind of power system frequency dynamic analysing method based on Continuum Model, it is characterised in that: the method step are as follows:
One, there is N platform generator in hypothesis system, the inertia constant of generator to be allocated is M, M is evenly distributed to each shortest path,
Its expression formula are as follows:Wherein, MiFor the angular momentum of i-th generator；Two, the inertia constant that distribution is obtained, every
Shortest path reuses height and is continuously allocated with smooth Gauss function to resulting parameter is distributed, the expression formula of distribution
Are as follows:Wherein: xiIndicate a spatial point of i-th line road, M0Locate at the center point for Gauss function
The maximum value of (bus position)；Three, the inertia phase etc. of the inertia and integrated distribution on former bus according to non-individual body before and after the processing, can
:It four, can by two minor sorts after obtaining all paths and corresponding impedance value
With obtain disturbing source to each generator bus shortest path.
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Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20070150114A1 (en) * | 2005-12-12 | 2007-06-28 | Robert Matthew Gardner | Location determination of power system disturbances based on frequency responses of the system |
| CN103701121A (en) * | 2013-12-31 | 2014-04-02 | 电子科技大学 | Analyzing system of high grid frequency time-space evolution process |
| CN108599143A (en) * | 2018-03-21 | 2018-09-28 | 西南交通大学 | A kind of analysis method that the mains frequency dynamic space-time based on analytical form develops |
-
2019
- 2019-08-21 CN CN201910771894.7A patent/CN110474349A/en active Pending
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20070150114A1 (en) * | 2005-12-12 | 2007-06-28 | Robert Matthew Gardner | Location determination of power system disturbances based on frequency responses of the system |
| CN103701121A (en) * | 2013-12-31 | 2014-04-02 | 电子科技大学 | Analyzing system of high grid frequency time-space evolution process |
| CN108599143A (en) * | 2018-03-21 | 2018-09-28 | 西南交通大学 | A kind of analysis method that the mains frequency dynamic space-time based on analytical form develops |
Non-Patent Citations (1)
| Title |
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| 吕乾勇等: "基于连续体模型的电力系统频率动态研究", 《电力大数据》 * |
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