CN104331571A - Critical clearing time method for power system disturbance based on frequency synchronization theory of second-order inhomogeneous Kuramoto model - Google Patents

Abstract

The invention discloses a critical clearing time method for power system disturbance based on a frequency synchronization theory of a second-order inhomogeneous Kuramoto model, relates to a critical clearing time method for a power system after disturbance, and aims at solving the problems that an existing method cannot well correspond to a power system model, and an attraction domain degree of a system balance point is not researched in the existing method and cannot be applied to transient stability analysis. The method comprises the following steps: 1 building a second-order inhomogeneous Kuramoto model corresponding to the power system model; 2 modifying parameters of the second-order inhomogeneous Kuramoto model; 3 solving a state variable of the system at the disturbance clearance moment, and solving parameters C (delta0, omega0 and alpha) in a criterion according to the state variable; 4 judging whether the system can be kept in synchronism stability after certain disturbance according to the parameters in a synchronization criterion, and calculating the critical clearing time that the system can be kept unstable after the system is disturbed. The critical clearing time method is applied to the field of electric power system.

Description

Based on the Power System Disturbances critical clearing time method of second order non-homogeneous Kuramoto model frequency Synchronization Theory

Technical field

The present invention relates to a kind of electric system by the critical clearing time method after disturbance.

Background technology

From the twenties in 20th century, the scholar of field of power has just had realized that power system stability problem, and it can be used as the importance guaranteeing system safety operation to be studied.The unstable accident of system not only causes huge economic loss and social influence, also reflects the importance and necessity of research power system stability problem simultaneously.Constantly interconnected along with electric system, and the rise of intelligent grid, the scale of electrical network becomes more and more huger, and the complicacy of electrical network becomes more and more higher; And with the development of generation of electricity by new energy technology, increasing distributed energy is integrated into electric system, and due to randomness and the undulatory property of distributed energy, electrical network will bear increasing disturbance.Therefore the transient stability problem of electric system will become severe all the more, and this just requires transient stability analysis method: succinct, quick, accurate.

Analytical approach about transient stability problem is broadly divided into the large classification of time-domain-simulation and direct method two, and time-domain-simulation method can the variation track of the disturbed rear state variable of observing system.But for large-scale electrical power system, use the calculated amount that the transient stability sexual needs of time-domain-simulation method judgement system are very large, be therefore difficult to on-line operation; Direct method carrys out the transient energy function of tectonic system according to the stability theory of power system, and judges the stability of Disturbed Power Systems by the character of transient energy function.Direct method computing velocity is fast, may be used for on-line operation.But the structure of transient energy function, solving of the determination of system transition energy and stable equilibrium point basin of attraction are a very difficult job.

In recent years, the scholars in complex network field start sight to turn to this huge and nonlinear network of complexity of electric system, and recognize the similarity between the Frequency Synchronization problem in complex network and the transient stability problem in electric system gradually.Wherein Kuramoto model as research stationary problem time modal model, its dynamics more and more in depth understand by people.It avoids the difficulty of direct method when processing transient stability problem, the basin of attraction of direct embodiment Disturbed Power Systems stable equilibrium point, Kuramoto can portray the dynamics of system, the basin of attraction providing synchronous point is estimated, Kuramoto model is corresponded to transient stability analysis electric power system model used, the basin of attraction scope of the disturbed back balance point of the theoretical estimating system of Kuramoto mold sync can be used, thus quick judgement can be made to the transient stability situation of system.

But current research is only limitted to single order Kuramoto model, mostly the method for employing is to analyze after model linearization, and the model of single order is not containing rotary inertia item, can not be well corresponding with electric power system model; And study the restriction paid close attention to critical coupling intensity more, and study the impact of network structure on stability of power system by the size of the method statistic basin of attraction of probability and emulation.Owing to not studying the basin of attraction degree of system balancing point, so cannot be applied in transient stability analysis.

Summary of the invention

The present invention is that will to solve existing method be analyze after model linearization, and the model of single order is containing rotary inertia item, can not be well corresponding with electric power system model; Existing method is not studied the basin of attraction degree of system balancing point, cannot be applied to the problem in transient stability analysis, and provide the Power System Disturbances critical clearing time method based on second order non-homogeneous Kuramoto model frequency Synchronization Theory.

Based on the Power System Disturbances critical clearing time method of second order non-homogeneous Kuramoto model frequency Synchronization Theory, it realizes according to the following steps:

Step one: set up the non-homogeneous Kuramoto model of the second order corresponding with electric power system model, and Power Systems output and through-put power are calculated, electricity grid network is reduced to only containing the full-mesh electricity grid network of generator interior nodes, forms the corresponding of free-running frequency item in second order non-homogeneous Kuramoto model and the coupling coefficient of network and the power stage in electric system and through-put power;

Step 2: if certain node generation disturbance in electric system, according to the structure of electricity grid network after disturbance excision, to the non-homogeneous Kuramoto model parameter amendment of second order;

Step 3: carry out time domain numerical simulation in the time period of former electricity grid network being excised to the moment from disturbance start time to disturbance, and solve the state variable of disturbance excision moment system, solve parameter C (δ in criterion according to this state variable ₀, ω ₀, α);

Step 4: according to parameter in synchronous criterion, decision-making system is by whether keeping synchronism stability after certain disturbance, and computing system is by keeping unstable critical clearing time after disturbance.

Invention effect:

The present invention breaches this limitation, estimate the basin of attraction the non-homogeneous Kuramoto model of second order, give the synchronous criterion based on second order non-homogeneous Kuramoto model, and set up the corresponding method of electric power system transient stability and second order non-homogeneous Kuramoto mold sync criterion, thus the system that provides disturbed after critical clearing time computing method.The method and time-domain simulation results are compared analysis, it serves to show that this side calculates simple, fast, accurately, convenient for on-line operation.

The object of the invention is a kind ofly calculate simple in order to provide and facilitate the electric system synchronism stability analytical approach of on-line operation, provide computing system by the critical clearing time method after disturbance.Therefore, the present invention estimates second order non-homogeneous Kuramoto mold sync basin of attraction, and set up the corresponding of transient stability analysis of power system and second order non-homogeneous Kuramoto model frequency Synchronization Theory, provide the criterion differentiating that power system frequency is synchronous, and theory gives the computing method of the critical clearing time of system by disturbance (system failure) based on this.Thus, the invention provides a kind of power system transient stability decision method based on second order non-homogeneous Kuramoto model frequency Synchronization Theory newly.This safe and stable operation for electric system has important using value.

The present invention estimates second order non-homogeneous Kuramoto mold sync basin of attraction first, and provides the criterion of system synchronization, breaches the difficult problem that nonlinear system basin of attraction is portrayed, thus can computing system by the original state thresholding that can keep synchronism stability after disturbance.Further, the present invention establishes the corresponding relation of the non-homogeneous Kuramoto model of second order and electric system, and model simplification is become the system of full-mesh by the method using Korn to simplify, and provides the computing method of parameter in the method; In addition, the method based on second order non-homogeneous Kuramoto model frequency Synchronization Theory is applied to the mute time after system disturbance and calculates by the present invention further, gives the computing method of critical clearing time after fault.Finally, the present invention is based on the transient stability analysis of power system method of second order non-homogeneous Kuramoto model frequency Synchronization Theory, the transient stability of system can be reflected from the angle of the strength of joint of network topological diagram, the approximate range of post-fault system stable equilibrium point basin of attraction can be estimated by simple algebraic operation, only need to system carry out in age at failure time-domain-simulation solve failure removal moment system state variable can judgement system disturbed after transient stability situation, computing velocity is fast, and result of calculation accurately and reliably.

Accompanying drawing explanation

Fig. 1 is the schematic flow sheet of method of the present invention;

Fig. 2 is 3 machine 9 node Iarge-scale system figure used in emulation experiment;

Fig. 3 is emulation experiment interior joint 1 fault clearing time Synchronous generator rotor angle rocking curve when being 0.691 second;

Fig. 4 is emulation experiment interior joint 1 fault clearing time Synchronous generator rotor angle rocking curve when being 0.692 second.

Embodiment

Embodiment one: the Power System Disturbances critical clearing time method based on second order non-homogeneous Kuramoto model frequency Synchronization Theory of present embodiment, it realizes according to the following steps:

Step one: set up the non-homogeneous Kuramoto model of the second order corresponding with electric power system model, and Power Systems output and through-put power are calculated, electricity grid network is reduced to only containing the full-mesh electricity grid network of generator interior nodes, forms the corresponding of free-running frequency item in second order non-homogeneous Kuramoto model and the coupling coefficient of network and the power stage in electric system and through-put power;

Step 2: if certain node generation disturbance in electric system, according to the structure of electricity grid network after disturbance excision, to the non-homogeneous Kuramoto model parameter amendment of second order;

Step 3: carry out time domain numerical simulation in the time period of former electricity grid network being excised to the moment from disturbance start time to disturbance, and solve the state variable of disturbance excision moment system, solve parameter C (δ in criterion according to this state variable ₀, ω ₀, α);

Step 4: according to parameter in synchronous criterion, decision-making system is by whether keeping synchronism stability after certain disturbance, and computing system is by keeping unstable critical clearing time after disturbance.

Present embodiment effect:

Present embodiment breaches this limitation, estimate the basin of attraction the non-homogeneous Kuramoto model of second order, give the synchronous criterion based on second order non-homogeneous Kuramoto model, and set up the corresponding method of electric power system transient stability and second order non-homogeneous Kuramoto mold sync criterion, thus the system that provides disturbed after critical clearing time computing method.The method and time-domain simulation results are compared analysis, it serves to show that this side calculates simple, fast, accurately, convenient for on-line operation.

The object of present embodiment a kind ofly calculate simple in order to provide and facilitate the electric system synchronism stability analytical approach of on-line operation, provides computing system by the critical clearing time method after disturbance.Therefore, the present invention estimates second order non-homogeneous Kuramoto mold sync basin of attraction, and set up the corresponding of transient stability analysis of power system and second order non-homogeneous Kuramoto model frequency Synchronization Theory, provide the criterion differentiating that power system frequency is synchronous, and theory gives the computing method of the critical clearing time of system by disturbance (system failure) based on this.Thus, the invention provides a kind of power system transient stability decision method based on second order non-homogeneous Kuramoto model frequency Synchronization Theory newly.This safe and stable operation for electric system has important using value.

Present embodiment estimates second order non-homogeneous Kuramoto mold sync basin of attraction first, and provide the criterion of system synchronization, breach the difficult problem that nonlinear system basin of attraction is portrayed, thus can computing system by the original state thresholding that can keep synchronism stability after disturbance.Further, the present invention establishes the corresponding relation of the non-homogeneous Kuramoto model of second order and electric system, and model simplification is become the system of full-mesh by the method using Korn to simplify, and provides the computing method of parameter in the method; In addition, the method based on second order non-homogeneous Kuramoto model frequency Synchronization Theory is applied to the mute time after system disturbance and calculates by the present invention further, gives the computing method of critical clearing time after fault.Finally, the present invention is based on the transient stability analysis of power system method of second order non-homogeneous Kuramoto model frequency Synchronization Theory, the transient stability of system can be reflected from the angle of the strength of joint of network topological diagram, the approximate range of post-fault system stable equilibrium point basin of attraction can be estimated by simple algebraic operation, only need to system carry out in age at failure time-domain-simulation solve failure removal moment system state variable can judgement system disturbed after transient stability situation, computing velocity is fast, and result of calculation accurately and reliably.

Embodiment two: present embodiment and embodiment one unlike: described step one is specially:

Step is one by one: set up the non-homogeneous Kuramoto model of the second order corresponding with electric power system model, under the raw data of analytic system converts unified reference value:

First, an electric system containing n platform generator, in disturbance cases, the equation of every platform generator can be written as

$M_i\frac{d^2{\mathrm{\δ}}_i}{{\mathrm{dt}}^2}+D_i\frac{d{\mathrm{\δ}}_i}{\mathrm{dt}}=P_{\mathrm{mi}}-P_{\mathrm{ei}},i=\mathrm{1,2},...,n---\left(1\right)$

Wherein:

M _ibe the inertia constant of i-th motor, unit quadratic power second/radian (s2/rad);

D _ibe the ratio of damping of i-th generator, unit second/radian (s/rad);

P _mifor being input to the mechanical output (p.u.) of i-th generator;

P _eiit is the electromagnetic power (p.u.) that i-th generator exports;

δ _ibe the rotor angle of i-th generator, unit radian (rad);

Under the hypothesis of electric system classical model, be only containing the network of n generator interior nodes by system equivalent, ignore the Transfer conductance in network, generator exports electromagnetic power and is written as:

$P_{\mathrm{ei}}={\left|E_i\right|}^2{G}_{\mathrm{ii}}-\left|E_i\right|\underset{j\≠i}{\overset{n}{\underset{j=1}{\mathrm{\Σ}}}}\left|E_j\right|\left|Y_{\mathrm{ij}}\right|\sin ({\mathrm{\δ}}_j-{\mathrm{\δ}}_i),i=\mathrm{1,2},...,n---\left(2\right)$

Wherein:

| E _i|, | E _j| be respectively i-th, the amplitude (p.u.) of j platform synchronous generator transient state reactance after-potential;

G _iirepresent the self-conductance (p.u.) of generator i in the network after equivalence;

for the mould (p.u.) of transadmittance between generator i and j in the network after equivalence;

δ _ijrepresent the difference of rotor angle between i, j two generators, i.e. δ _ij=δ _i-δ _j;

(2) are substituted into (1), and makes $P_i=P_{\mathrm{mi}}-{\left|E_i\right|}^2{G}_{\mathrm{ii}},P_{\max \mathrm{ij}}=\left|E_i\right|\left|E_j\right|\left|Y_{\mathrm{ij}}\right|,$ Electric power system model can be written as:

$M_i{\stackrel{\·\·}{\mathrm{\δ}}}_i+D_i{\stackrel{\·}{\mathrm{\δ}}}_i=P_i+\underset{j\≠i}{\overset{n}{\underset{j=1}{\mathrm{\Σ}}}}{P}_{\max \mathrm{ij}}\sin ({\mathrm{\δ}}_j-{\mathrm{\δ}}_i),i=\mathrm{1,2},...,n---\left(3\right)$

Wherein:

P _ifor the meritorious injecting power perunit value of i-th generator in system, P _maxijfor the maximum active power perunit value can carried between i-th generator and jth platform generator in system;

Second order non-homogeneous Kuramoto model is as follows:

$m_i{\stackrel{\·\·}{\widehat{\mathrm{\θ}}}}_i+d_i{\stackrel{\·}{\widehat{\mathrm{\θ}}}}_i={\widehat{\mathrm{\Ω}}}_i+{\mathrm{\Σ}}_{j=1}^N{a}_{\mathrm{ij}}\sin ({\widehat{\mathrm{\θ}}}_j-{\widehat{\mathrm{\θ}}}_i),t>0,i=\mathrm{1,2},...,N---\left(4\right)$

Comparison expression (3) and formula (4), electric power system model and second order non-homogeneous Kuramoto model completely the same;

Step one two: Load flow calculation is carried out to system according to the parameter after system conversion, the voltage of each node and phase angle in acquisition system;

Step one three: electromotive force and phase angle thereof after calculating the reactance of each generator transient state by Load flow calculation the data obtained, load is carried out equivalence by constant impedance, and form the admittance battle array of network thus; Each generator is regarded as constant potential source and be connected to generator end Nodes corresponding with it in former network by the reactance of d-axis transient state, and form the admittance battle array of augmentation network.

Other step and parameter identical with embodiment one.

Embodiment three: present embodiment and embodiment one or two unlike: be specially in described step 2:

Step 2 one: first adopt Kron yojan method to be contracted to by electricity grid network only containing the full-mesh network of generator interior nodes, if system node generation disturbance, setting initial disturbance mute time t _c=0.001s;

Step 2 two: according to the structure of electricity grid network after disturbance excision, modify to the admittance battle array of augmentation network, form the admittance battle array of the rear augmentation network of disturbance excision, carries out equivalence to the admittance battle array of augmentation network after disturbance excision;

Step 2 three: the electric system one being contained to n platform generator, δ (t)=(δ ₁(t) ..., δ _n(t)), ω (t)=(ω ₁(t) ..., ω _n(t)) set of each generator amature angle and angular velocity in expression system respectively, δ ₀=δ (0), ω ₀=ω (0) represents the set of initial rotor angle and the initial angular velocity set of system, the following parameter of electricity grid network parametric solution according to after contraction:

${\mathrm{\δ}}_m=\underset{1\≤i\≤n}{\min }{\mathrm{\δ}}_i,{\mathrm{\δ}}_M=\underset{1\≤i\≤n}{\max }{\mathrm{\δ}}_i,$ D(δ)＝δ _M-δ _m， $\stackrel{\·}{D}\left({\mathrm{\δ}}_0\right)=\frac{d}{\mathrm{dt}}D\left(\mathrm{\δ}\left(t\right)\right){|}_{t=0^{+}},$

$D\left(\stackrel{\‾}{P}\right)=\underset{1\≤i\≤n}{\max }\left\{\frac{P_i}{M_i}\right\}-\underset{1\≤i\≤n}{\min }\left\{\frac{P_i}{M_i}\right\}$

$L=\underset{1\≤i\≠j\≤n}{\min }\{(\frac{1}{M_i}+\frac{1}{M_j})P_{\max \mathrm{ij}}+\underset{k\≠i,j}{\mathrm{\Σ}}\min \{\frac{P_{\max \mathrm{ik}}}{M_i},\frac{P_{\max \mathrm{jk}}}{M_j}\left\}\right\}$

$C({\mathrm{\δ}}_0,{\mathrm{\ω}}_0,\mathrm{\α})=\max \{D\left({\mathrm{\δ}}_0\right),D\left({\mathrm{\δ}}_0\right)+\frac{1}{\mathrm{\α}}\stackrel{\·}{D}\left({\mathrm{\δ}}_0\right)\}.$

Other step and parameter identical with embodiment one or two.

Embodiment four: one of present embodiment and embodiment one to three unlike: described step 4 is specially:

Step 4 one: according to parameter C (δ in criterion criterion ₀, ω ₀, α) whether drop in the basin of attraction of the rear network stabilization equilibrium point of disturbance excision, if do not meet, decision-making system can not keep synchronism stability, exports fault clearing time t _c=t _c-0.001s; If meet, then decision-making system now can keep synchronism stability;

Described synchronous criterion constraint condition:

Theorem 1: if the parameter of the electric system starting condition after Eliminating disturbance meets:

$\left.\begin{array}{cc}L>\frac{D\left(\stackrel{\‾}{P}\right)}{\sin D_c}& \\ \frac{\sqrt{2D\left(\stackrel{\‾}{P}\right)}}{\mathrm{\α}}\frac{\sqrt{D_c-\tan (D_c/2)}}{\mathrm{\π}-2D_c}=1,& D_c\∈(0,\frac{\mathrm{\π}}{2})\end{array}\right\}$

$\left.\begin{array}{cc}0<C({\mathrm{\&delta;}}_0,{\mathrm{\&omega;}}_0,\mathrm{\&alpha;})<\mathrm{\&pi;}-K& \\ \sin K=D\left(\stackrel{\&OverBar;}{P}\right)/L,& K\&Element;(0,D_c)\end{array}\right\}$

Then system can keep transient stability after Eliminating disturbance;

Step 4 two: when decision-making system can keep synchronism stability, the disturbance mute time is modified, t _c=t _c+ 0.001s, returns step 3 and recalculates network parameter C (δ ₀, ω ₀, α), whether can continue to keep synchronism stability according to criterion decision-making system, until Account Dept can stablize, calculation system is by the critical clearing time after disturbance.

Other step and parameter identical with one of embodiment one to three.

Emulation experiment:

Step one: set up electric power system model corresponding with second order non-homogeneous Kuramoto model, and electric system is calculated, electricity grid network is reduced to only containing the full-mesh electricity grid network of generator interior nodes, forms the corresponding of free-running frequency item in second order non-homogeneous Kuramoto model and the coupling coefficient of network and the power stage in electric system and through-put power;

Step 2: if certain node generation disturbance in electric system, according to the structure of electricity grid network after disturbance excision, revises model parameter;

Step 3: carry out time domain numerical simulation in the time period of former electricity grid network being excised to the moment from disturbance start time to disturbance, and solve the state variable of disturbance excision moment system, solve parameter C (δ in criterion according to this state variable ₀, ω ₀, α);

Step 4: according to parameter in synchronous criterion, decision-making system is by whether keeping synchronism stability after certain disturbance, and computing system is by keeping unstable critical clearing time after disturbance.

Emulation experiment:

Step one: set up the non-homogeneous Kuramoto model of the second order corresponding with electric power system model, and Power Systems output and through-put power are calculated, electricity grid network is reduced to only containing the full-mesh electricity grid network of generator interior nodes, forms the corresponding of free-running frequency item in second order non-homogeneous Kuramoto model and the coupling coefficient of network and the power stage in electric system and through-put power;

Step 2: if certain node generation disturbance in electric system, according to the structure of electricity grid network after disturbance excision, to the non-homogeneous Kuramoto model parameter amendment of second order;

Step 3: carry out time domain numerical simulation in the time period of former electricity grid network being excised to the moment from disturbance start time to disturbance, and solve the state variable of disturbance excision moment system, solve parameter C (δ in criterion according to this state variable ₀, ω ₀, α);

Step 4: according to parameter in synchronous criterion, decision-making system is by whether keeping synchronism stability after certain disturbance, and computing system is by keeping unstable critical clearing time after disturbance.

Table 1 is WSCC 3 machine 9 node system alternator data;

Table 2 is WSCC 3 machine 9 node system track data;

Table 3 is WSCC 3 machine 9 node system parameter;

The WSCC 3 machine 9 node system node failure critical clearing time that table 4 is tried to achieve for this method;

Table 1

Table 2

Table 3

Table 4

Fig. 2 is 3 machine 9 node Iarge-scale system figure used in emulation experiment;

Synchronous generator rotor angle rocking curve when Fig. 3 node 1 fault clearing time is 0.691 second;

Synchronous generator rotor angle rocking curve when Fig. 4 node 1 fault clearing time is 0.692 second.

As Fig. 3,4 can find out, critical clearing time is 0.691 second, and when the mute time is 0.692 second, Account Dept can keep stable.

Claims (4)

1., based on the Power System Disturbances critical clearing time method of second order non-homogeneous Kuramoto model frequency Synchronization Theory, it is characterized in that it realizes according to the following steps:

Step one: set up the non-homogeneous Kuramoto model of the second order corresponding with electric power system model, and Power Systems output and through-put power are calculated, electricity grid network is reduced to only containing the full-mesh electricity grid network of generator interior nodes, forms the corresponding of free-running frequency item in second order non-homogeneous Kuramoto model and the coupling coefficient of network and the power stage in electric system and through-put power;

Step 2: if certain node generation disturbance in electric system, according to the structure of electricity grid network after disturbance excision, to the non-homogeneous Kuramoto model parameter amendment of second order;

Step 3: carry out time domain numerical simulation in the time period of former electricity grid network being excised to the moment from disturbance start time to disturbance, and solve the state variable of disturbance excision moment system, solve parameter C (δ in criterion according to this state variable ₀, ω ₀, α);

Step 4: according to parameter in synchronous criterion, decision-making system is by whether keeping synchronism stability after certain disturbance, and computing system is by keeping unstable critical clearing time after disturbance.

2. the Power System Disturbances critical clearing time method based on second order non-homogeneous Kuramoto model frequency Synchronization Theory according to claim 1, is characterized in that described step one is specially:

Step is one by one: set up the non-homogeneous Kuramoto model of the second order corresponding with electric power system model, under the raw data of analytic system converts unified reference value:

First, an electric system containing n platform generator, in disturbance cases, the equation of every platform generator can be written as

$M_i\frac{d^2{\mathrm{\&delta;}}_i}{{\mathrm{dt}}^2}+D_i\frac{{\mathrm{d\&delta;}}_i}{\mathrm{dt}}=P_{\mathrm{mi}}-P_{\mathrm{ei}},i=\mathrm{1,2},...,n---\left(1\right)$

Wherein:

M _ibe the inertia constant of i-th motor, unit quadratic power second/radian (s2/rad);

D _ibe the ratio of damping of i-th generator, unit second/radian (s/rad);

P _mifor being input to the mechanical output (p.u.) of i-th generator;

P _eiit is the electromagnetic power (p.u.) that i-th generator exports;

δ _ibe the rotor angle of i-th generator, unit radian (rad);

Under the hypothesis of electric system classical model, be only containing the network of n generator interior nodes by system equivalent, ignore the Transfer conductance in network, generator exports electromagnetic power and is written as:

$P_{\mathrm{ei}}={\left|E_i\right|}^2{G}_{\mathrm{ii}}-\left|E_i\right|\underset{j\&NotEqual;i}{\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}}\left|E_j\right|\left|Y_{\mathrm{ij}}\right|\sin ({\mathrm{\&delta;}}_j-{\mathrm{\&delta;}}_i),i=\mathrm{1,2},...,n---\left(2\right)$

Wherein:

| E _i|, | E _j| be respectively i-th, the amplitude (p.u.) of j platform synchronous generator transient state reactance after-potential;

G _iirepresent the self-conductance (p.u.) of generator i in the network after equivalence;

| Y _ij| be the mould (p.u.) of transadmittance between generator i and j in the network after equivalence;

δ _ijrepresent the difference of rotor angle between i, j two generators, i.e. δ _ij=δ _i-δ _j;

(2) are substituted into (1), and makes P _i=P _mi-| E _i| ²g _ii, P _maxij=| E _i|| E _j|| Y _ij|, electric power system model can be written as:

$M_i{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&delta;}}}_i+D_i{\stackrel{\&CenterDot;}{\mathrm{\&delta;}}}_i=P_i+\underset{j\&NotEqual;i}{\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}}{P}_{\max \mathrm{ij}}\sin ({\mathrm{\&delta;}}_j-{\mathrm{\&delta;}}_i),i=\mathrm{1,2},...,n---\left(3\right)$

Wherein:

P _ifor the meritorious injecting power perunit value of i-th generator in system, P _maxijfor the maximum active power perunit value can carried between i-th generator and jth platform generator in system;

Second order non-homogeneous Kuramoto model is as follows:

$m_i{\stackrel{\stackrel{\&CenterDot;\&CenterDot;}{^}}{\mathrm{\&theta;}}}_i+d_i{\stackrel{\stackrel{\&CenterDot;}{^}}{\mathrm{\&theta;}}}_i+{\widehat{\mathrm{\&Omega;}}}_i+{\mathrm{\&Sigma;}}_{j=1}^N{a}_{\mathrm{ij}}\sin ({\widehat{\mathrm{\&theta;}}}_j-{\widehat{\mathrm{\&theta;}}}_i),t>0,i=\mathrm{1,2},...,N---\left(4\right)$

Comparison expression (3) and formula (4), electric power system model and second order non-homogeneous Kuramoto model completely the same;

Step one two: Load flow calculation is carried out to system according to the parameter after system conversion, the voltage of each node and phase angle in acquisition system;

Step one three: electromotive force and phase angle thereof after calculating the reactance of each generator transient state by Load flow calculation the data obtained, load is carried out equivalence by constant impedance, and form the admittance battle array of network thus; Each generator is regarded as constant potential source and be connected to generator end Nodes corresponding with it in former network by the reactance of d-axis transient state, and form the admittance battle array of augmentation network.

3. the Power System Disturbances critical clearing time method based on second order non-homogeneous Kuramoto model frequency Synchronization Theory according to claim 1, is characterized in that described step 2 is specially:

Step 2 one: first adopt Kron yojan method to be contracted to by electricity grid network only containing the full-mesh network of generator interior nodes, if system node generation disturbance, setting initial disturbance mute time t _c=0.001s;

Step 2 two: according to the structure of electricity grid network after disturbance excision, modify to the admittance battle array of augmentation network, form the admittance battle array of the rear augmentation network of disturbance excision, carries out equivalence to the admittance battle array of augmentation network after disturbance excision;

Step 2 three: the electric system one being contained to n platform generator, δ (t)=(δ ₁(t) ..., δ _n(t)), ω (t)=(ω ₁(t) ..., ω _n(t)) set of each generator amature angle and angular velocity in expression system respectively, δ ₀=δ (0), ω ₀=ω (0) represents the set of initial rotor angle and the initial angular velocity set of system, the following parameter of electricity grid network parametric solution according to after contraction:

${\mathrm{\&delta;}}_m=\underset{1\&le;i\&le;n}{\min }{\mathrm{\&delta;}}_i,{\mathrm{\&delta;}}_M=\underset{1\&le;i\&le;n}{\max }{\mathrm{\&delta;}}_i,D\left(\mathrm{\&delta;}\right)={\mathrm{\&delta;}}_M-{\mathrm{\&delta;}}_m,\stackrel{\&CenterDot;}{D}\left({\mathrm{\&delta;}}_0\right)=\frac{d}{\mathrm{dt}}D\left(\mathrm{\&delta;}\left(t\right)\right){|}_{t=0^{+}},$

$D\left(\stackrel{\&OverBar;}{P}\right)=\underset{1\&le;i\&le;n}{\max }\left\{\frac{P_i}{M_i}\right\}-\underset{1\&le;i\&le;n}{\min }\left\{\frac{P_i}{M_i}\right\}$

$L=\underset{1\&le;i\&NotEqual;j\&le;n}{\min }\{(\frac{1}{M_i}+\frac{1}{M_j})P_{\max \mathrm{ij}}+\underset{k\&NotEqual;i,j}{\mathrm{\&Sigma;}}\min \{\frac{P_{\max \mathrm{ik}}}{M_i},\frac{P_{\max \mathrm{jk}}}{M_j}\left\}\right\}$

$C({\mathrm{\&delta;}}_0,{\mathrm{\&omega;}}_0,\mathrm{\&alpha;})=\max \{D\left({\mathrm{\&delta;}}_0\right),D\left({\mathrm{\&delta;}}_0\right)+\frac{1}{\mathrm{\&alpha;}}\stackrel{\&CenterDot;}{D}\left({\mathrm{\&delta;}}_0\right)\}.$

4. the Power System Disturbances critical clearing time method based on second order non-homogeneous Kuramoto model frequency Synchronization Theory according to claim 1, is characterized in that described step 4 is specially:

Step 4 one: according to parameter C (δ in criterion criterion ₀, ω ₀, α) whether drop in the basin of attraction of the rear network stabilization equilibrium point of disturbance excision, if do not meet, decision-making system can not keep synchronism stability, exports fault clearing time t _c=t _c-0.001s; If meet, then decision-making system now can keep synchronism stability;

Described synchronous criterion constraint condition:

Theorem 1: if the parameter of the electric system starting condition after Eliminating disturbance meets:

$\left.\begin{array}{cc}L>\frac{D\left(\stackrel{\&OverBar;}{P}\right)}{\sin D_c}& \\ \frac{\sqrt{2D\left(\stackrel{\&OverBar;}{P}\right)}}{\mathrm{\&alpha;}}\sqrt{\frac{D_c-\tan (D_c/2)}{\mathrm{\&pi;}-{2D}_c}}=1,& D_c\&Element;(0,\frac{\mathrm{\&pi;}}{2})\end{array}\right\}$

$\left.\begin{array}{cc}0<C({\mathrm{\&delta;}}_0,{\mathrm{\&omega;}}_0,\mathrm{\&alpha;})<\mathrm{\&pi;}-K& \\ \sin K=D\left(\stackrel{\&OverBar;}{P}\right)/L,& K\&Element;(0,D_c)\end{array}\right\}$

Then system can keep transient stability after Eliminating disturbance;

Step 4 two: when decision-making system can keep synchronism stability, the disturbance mute time is modified, t _c=t _c+ 0.001s, returns step 3 and recalculates network parameter C (δ ₀, ω ₀, α), whether can continue to keep synchronism stability according to criterion decision-making system, until Account Dept can stablize, calculation system is by the critical clearing time after disturbance.