CN107069697B - Power system transient stability judgement and disturbance type screening technique based on track characteristic root - Google Patents
Power system transient stability judgement and disturbance type screening technique based on track characteristic root Download PDFInfo
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Abstract
The present invention provide it is a kind of based on track characteristic root power system transient stability judgement and disturbance type screening technique, the Linearization Method of state equation and generator, governor, excitation system, network equation and load at non-equilibrium point in the case of research unstable state.The higher order linearization model of system is established, realizes the continuous solving of the characteristic root in the case of unstable state, obtains track characteristic root curve, analyzes track characteristic root curvilinear characteristic.The system multidate information contained by track characteristic root under research load disturbance and three phase short circuit fault, it is not limited by whether characteristic value real part is greater than zero, excavate potential rule, the mapping relations set up power system transient stability, disturb type and track characteristic root, to realize fast and accurately power system transient stability judgement and disturbance type screening.By the sample calculation analysis of 9 node of WSCC3 machine, the conclusion that the method for the present invention obtains power-angle curve opposite with generator matches, the feasibility of this verifying the method for the present invention.
Description
Technical field
The present invention relates to power engineering fields, and in particular to it is a kind of based on track characteristic root power system transient stability judgement and
Disturb type screening technique.
Background technique
Transient stability analysis of power system is always the hot spot of power engineering field research.With electric system day increasingly
Exhibition, the dynamic characteristic of system is more complicated, embody it is stronger non-linear and uncertain, with equalization point characteristic root reflect system
Oscillating characteristic is more and more difficult.
In the Perturbation Analysis of electric system, linearization process is carried out usually at equalization point and obtains the state square of system
Battle array, analyzes the characteristic value of the state matrix to judge the small disturbance stability characteristic of system.But the continuous solving of characteristic root is by electric power
Influence in the case of system unstable state is very big, it is single with linearization technique carry out processing cannot reach well support effect.
After system is by major break down, operating point deviates system balancing point.During deviateing equalization point, it is contemplated that be
The strong nonlinearity feature of system does not use linearization technique generally and is handled, and can only seek system mode by numerical integration
The track of amount.Specifically include following two method:
Track cut surface character root method, the starting point of each integration step will be former by virtual condition again by model linearization
The system converting linear system for time-varying calculates the characteristic root of section part according to the state matrix at the moment.This method will balance
Point feature root analyzes the cross sections for expanding to the disturbed track of large disturbances.But system at this time is on non-equilibrium point, it is uneven
Weighing apparatus power is not zero, and the dynamic behaviour of system is no longer individually determined by characteristic root, it is necessary to the influence of meter and imbalance power.Rail
Mark cut surface character root method has ignored the influence of imbalance power, can not definitely reflect non-linear and time-varying factor to frequency of oscillation
It influences.
Step by step integration passes through failure as initial value using the parameters such as the revolving speed of generator, angle, power after failure removal
Admittance matrix iteratively faster after excision calculates generator's power and angle, computationally intensive, is unfavorable for quickly judging system stability.
Summary of the invention
In view of the above-mentioned deficiencies in the prior art, it is an object of the present invention to which it is steady to provide a kind of system transient modelling based on track characteristic root
Fixed judgement and disturbance type screening technique are somebody's turn to do the power system transient stability judgement based on track characteristic root and disturbance type screening technique
The above problem can be well solved.
To reach above-mentioned requirements, the technical solution adopted by the present invention is that: it is temporary to provide a kind of system based on track characteristic root
State stabilization judgment method, should power system transient stability judgment method based on track characteristic root the following steps are included:
S1, linearization process is carried out at non-equilibrium point to generator, governor, excitation system, network equation and load,
Establish the higher order linearization model of system；
S2, according to higher order linearization model, carry out the solution of track characteristic root in the case of unstable state；
S3, it is emulated to obtain track characteristic root curve according to track characteristic root；
S4, according to the fluctuation track of track characteristic root curve, establish the mapping of power system transient stability Yu track characteristic root
Relationship；
S5, power system transient stability is judged according to mapping relations.
A kind of disturbance type screening technique based on track characteristic root is provided, which comprises the following steps:
S1, using inverse Laplace transformation method to generator, governor, excitation system, network equation and load non-
Linearization process is carried out at equalization point, establishes the higher order linearization model of system；
S2, according to higher order linearization model, carry out the solution of track characteristic root in the case of unstable state；
S3, it is emulated to obtain track characteristic root curve according to track characteristic root；
S4, according to the variance of track characteristic root curve, establish the mapping relations of disturbance type and track characteristic root；
S5, the type disturbed according to mapping relations identifying system.
The power system transient stability judgement and disturbance type screening technique based on track characteristic root have the advantage that as follows:
(1) the higher order linearization model of system is established, the continuous solving of the characteristic root in the case of unstable state is realized, obtains rail
Mark characteristic root curve analyzes track characteristic root curvilinear characteristic, passes through track characteristic under research load disturbance and three phase short circuit fault
The system multidate information that root is contained is not limited by whether characteristic value real part is greater than zero, excavates potential rule, it is established that be
System transient stability and track characteristic root, the mapping relations for disturbing type and track characteristic root, so that realization is fast and accurately
Transient stability of uniting judges and disturbance type screening.
(2) existed using the method for inverse Laplace transformation to generator, governor, excitation system, network equation and load
Linearization process is carried out at non-equilibrium point, has many advantages, such as rapidity and accuracy, while being capable of handling various complex models, is had
There is very strong practicability.
Detailed description of the invention
The drawings described herein are used to provide a further understanding of the present application, constitutes part of this application, at this
The same or similar part, the illustrative embodiments and their description of the application are indicated using identical reference label in a little attached drawings
For explaining the application, do not constitute an undue limitation on the present application.In the accompanying drawings:
Fig. 1 is the flow diagram of the application power system transient stability judgment method.
Fig. 2 is the flow diagram of the application system disturbance type screening technique.
Fig. 3 is the application prime mover-governor model TGOV1 transmission function block diagram.
Fig. 4 is the application excitation system model transfer function block diagram.
Fig. 5 is 9 node system schematic diagram of the application WSCC3 machine.
Fig. 6 is the application steady-state operation track characteristic root real part analogous diagram.
Fig. 7 is that the application load increases by 20% track characteristic root real part analogous diagram.
Fig. 8 is that the application load increases by 40% track characteristic root real part analogous diagram.
Fig. 9 is that the application load increases by 80% track characteristic root real part analogous diagram.
Figure 10 is the application sudden load increase generator with respect to power-angle curve analogous diagram.
Figure 11 is the application three phase short circuit fault 0.2s track characteristic root real part analogous diagram.
Figure 12 is the application three phase short circuit fault 0.3s track characteristic root real part analogous diagram.
Figure 13 is the application three phase short circuit fault 0.4s track characteristic root real part analogous diagram.
Figure 14 is the application three phase short circuit fault generator with respect to power-angle curve analogous diagram.
Figure 15 is the application three phase short circuit fault 0.5s track characteristic root real part analogous diagram.
Figure 16 is the application three phase short circuit fault generator with respect to power-angle curve analogous diagram.
Specific embodiment
To keep the purposes, technical schemes and advantages of the application clearer, below in conjunction with drawings and the specific embodiments, to this
Application is described in further detail.
A kind of power system transient stability judgment method based on track characteristic root is provided, as shown in Figure 1, comprising the following steps:
S1, using inverse Laplace transformation to generator, governor, excitation system, network equation and load non-equilibrium
Linearization process is carried out at point, establishes the higher order linearization model of system；
Inverse Laplace transformation method has many advantages, such as rapidity and accuracy, while being capable of handling various complex models,
Show very strong practicability.Concrete model after each submodule Linearization Method is as follows:
A, the linearization process of generator model
Generator model uses 3 rank E 'qVariation model, expression formula equation are as follows:
Equation of rotor motion occurs by power rather than in the form of torque in formula, while retaining electromagnetic power PeWithout using
The form of transient internal voltage and stator current expansion is linearized formula (1) at non-equilibrium using linearization technique, by sitting
Parameter conversion, eliminates stator current and stator voltage, can obtain 3 rank Linearized state equations of synchronous generator:
In formula:C3=
ω0(ωr(0)- 1), E 'qIt is q axis electromotive force, Δ δ is for rotor (position) angle increment, xdIt is d axis synchronous reactance, x 'dIt is that d axis is temporary
State reactance, T ' d0 are d axis open circuit time constant, Δ EfdIt is d axis excitation electric gesture increment, Δ U is voltage increment, and Δ θ is
Node voltage angle increment, Δ ωrIt is rotor velocity increment, H is generator inertia time constant, Δ pmIt is mechanical output increment,
ω0It is synchronous angular velocity, Efd(0)It is d axis excitation voltage initial value, E 'q(0)It is q axis electromotive force initial value, id(0)At the beginning of being d shaft current
Initial value, pm(0)It is mechanical output initial value, pe(0)It is electromagnetic power initial value, KDIt is damped coefficient, ωr(0)It is rotor velocity
Initial value.
B, prime mover-governor model linearization process
A second order prime mover-governor model is chosen to describe governor characteristic, is chosen used in PSS/E
TGOV1 model illustrates the step of linearizing at non-equilibrium point to prime mover-governor, and TGOV1 used by generator passes
Delivery function block diagram such as Fig. 3.It equally can use the method linearized herein for other high-order models to linearize, ignore original
The effect of motivation-governor dead time, TGOV1 transmission function:
Arranging to formula (3) can obtain:
Known primary condition ν (0-) and PT(0-), by inverse Laplace transformation rule:Wherein F
(s) image function for being f (t), f (t) are the original function of F (s), f (0-) it is initial value of the f (t) at 0 moment, it is defaulted as herein most
The latter disturbance excision moment is 0 moment (non-equilibrium point).Inverse Laplace transformation is carried out to formula (4), is arranged:
In formula, δ (t) is unit impulse function, FREFTo preset constant, consider And unit impulse function action time can be ignored, therefore ignore in state equation containing
The influence of δ (t) item arranges formula (5) and obtains:
In formula:
Δ ν (t) is steam turbine valve aperture increment, Δ PTIt (t) is steam turbine mechanical output, Δ PmIt (t) is that steam turbine is transported to generator
Mechanical output, T1、T2、T3It is prime mover-governor time constant, DtIt is prime mover-friction in governor coefficient, R is former dynamic
Machine-governor difference coefficient, ν (0) are steam turbine valve aperture initial value, PTIt (0) is steam turbine mechanical output initial value, Pm(0)
It is the mechanical output that steam turbine is transported to generator.
C, the linearization process of excitation system model
Excitation system is using SEXS model in PSS/E, if disregarding PSS effect and the effect of phase modulation link, transmission function frame
Figure as shown in figure 4, at this time excitation system be with first order inertial loop describe static excitation system, excitation system transmission function,
It is set as (UreF=const.)
In formula,For generator voltage.
It is linearized using linearization technique identical with governor:
In formula,TEIt is electromagnetic torque, k is self-excitation coefficient.
D, the linearization process of load model
Load uses constant-impedance model:
Formula (9) is linearized, then system loading node injecting power Incremental Equation are as follows:
In formula, Δ PLi、ΔQLiActive power, reactive power increment for the injection of load node i；·ΔUiFor node i electricity
The increment of pressure amplitude value.
E, the linearization process of grid equation
Node power equation is linearized at non-equilibrium, essence is to solve conventional Load Flow problem in non-equilibrium point
The Jacobian matrix at place.It shall note here that needs repair respective element according to generator generator terminal power and load power equation
Just.
By taking node i as an example, if node i voltage is Ui∠θiNode admittance matrix Y=[Gij+jBij]nIf node i is power generation
Machine node, then node power equation are as follows:
In formula, Pti、QtiFor generator node i generator terminal active power and reactive power；PLi、QLiFor generator node i generator terminal
Burden with power and load or burden without work；Ui、UjSystem node i, j voltage magnitude；Gij、BijFor the transadmittance between system node i, j, θij
Voltage-phase difference between system node i, j.
If generator terminal load is constant power load model, formula (11) is linearized at non-equilibrium point, and substitute into generator terminal power increment
Equation obtains:
In formula,
If node i is load bus or contact node, P in formula (12)ti=0 and Qti=0, if load is negative for constant-impedance
Formula (11) is linearized at non-equilibrium point, and substitutes into load increment equation by lotus, is obtained:
In formula, Nii、Nij、Hii、Hij、Lii、Lij、Jii、JijIdentical as formula (12) form, the value of i is different.
F, system higher order linearization model
The Incremental Equation of each element of simultaneous and network, can be obtained system state equation.It is more with the n node of m platform generator
For electromechanical Force system, generator uses three rank E 'qVariation model, excitation system use static the encouraging of first order inertial loop description
Magnetic system, governor use TGOV1 second-order model, and load is constant-impedance load.If total system variable arranges in the following manner:
E′q1, E 'q2..., E 'qm, ωr1, ωr2..., ωrm, δ1, δ2..., δm, Efd1, Efd2..., Efdm, PT1, PT2..., PTm, ν1,
ν2..., νm.Then system state equation are as follows:
In formula: E 'q=[E 'q1, E 'q2..., E 'qm]T, ωr=[ωr1, ωr2..., ωrm]T, δ=[δ1, δ2..., δm]T,
Efd=[Efd1, Efd2..., Efdm]T, PT=[PT1, PT2..., PTm]T, ν=[ν1, ν2..., νm]T, U=[U1,
U2..., Un]T, θ=[θ1, θ2..., θn]T, Pm=[pm1, pm2..., pmm]T, a11=diag { ai 11}∈Rm×m, subscript i indicates the
I platform generator.Remaining all kinds of a submatrix is similar；b11=[diag { bi 11}m×m,0m×(n-m)]∈Rm×n, remaining all kinds of b submatrix is similar；
m1=[diag { mi 1}m×m,0(n-m)×m]∈Rn×m, m2、n1、n2、DtIt is similar with -1 submatrix；1=diag 1,1 ..., 1 }n×n,
m4- H=diag { m1 4,…,mm 4,0m+1,…,0n}-[Hij]n×n；N4- J=diag { n1 4,…,nm 4,0m+1,…,0n}-[Jij]n×n。
Enable x ∈ Rm×1For system mode vector, y ∈ R(2n+m)×1The machinery of generator is transported to for node voltage and steam turbine
Vector power, f are systematic observation matrix, and g is the mechanical output algebraic equation that node power and steam turbine are transported to generator, then
Formula (14) can be expressed as:
In formula,For Jacobian matrix of the multi-computer system differential-algebraic equation group at non-equilibrium point.By
Formula (15), has:
In formula,
Formula (16) is the standard type of system state space equation.
S2, according to higher order linearization model, carry out the solution of track characteristic root in the case of unstable state；
S3, it is emulated to obtain track characteristic root curve according to track characteristic root；
S4, according to the fluctuation track of track characteristic root curve, establish the mapping of power system transient stability Yu track characteristic root
Relationship；
The system multidate information contained by track characteristic root under analysis load disturbance and three phase short circuit fault, uses failure
The track characteristic root of system carries out power system transient stability judgement afterwards, establishes the mapping of power system transient stability Yu track characteristic root
Relationship is not limited by whether characteristic value real part is greater than zero.It makes a concrete analysis of as follows:
By analyzing track characteristic root curvilinear characteristic, track characteristic root curve is divided into four regions, each region is corresponding
One index, as shown in Figure 7:
I region is irregular hop region: the track characteristic root variation in the region is irregular to follow；
II region is quasi-continuity surge area: the track characteristic root in the region has certain continuity, while also having
Breakpoint occurs；
III region is continuity surge area: the track characteristic root in the region has continuous fluctuation；
IV region is new steady-sxtate wave motion region: the track characteristic root in the region has reacted the system spy later into new stable state
It levies root and fluctuates situation.
By the feature root locus in the case of the different disturbances of comparison it can be found that later feature root locus occurs for disturbance first
Into I region, II region, III region and IV region are then sequentially entered according to the difference of disturbance situation, with the increase of disturbance,
I region, II region, III region and IV region fluctuation range increase, the duration is longer, when disturbance increase to enable to be
Track characteristic root curve only has I region when uniting unstable, then system can not stable operation after being disturbed.According to this
Rule can accurately identify stability of the system after being disturbed.
The mapping relations are as follows:
Track characteristic root curve has irregular hop region, quasi-continuity surge area, continuity surge area and new
Steady-sxtate wave motion region has I region, II region, III region and IV region, systematic steady state operation；
Track characteristic root curve only has irregular hop region, and only has I region, and system is unstable.
S5, power system transient stability is judged according to mapping relations.
A kind of disturbance type screening technique based on track characteristic root is provided, as shown in Figure 2, comprising the following steps:
S1, using inverse Laplace transformation method to generator, governor, excitation system, network equation and load non-
Linearization process is carried out at equalization point, establishes the higher order linearization model of system；
S2, according to higher order linearization model, carry out the solution of track characteristic root in the case of unstable state；
S3, it is emulated to obtain track characteristic root curve according to track characteristic root；
S4, according to the variance of track characteristic root curve, establish the mapping relations of disturbance type and track characteristic root, the mapping
Relationship are as follows:
When the variance of track characteristic root real part is in [0~6.84e-05] range, system failure-free operation；
When the variance of track characteristic root real part is in [6.84e-05~14] range, system is by load disturbance；
When the variance of track characteristic root real part is in [14~75] range, three phase short circuit fault occurs for system；
When the variance of track characteristic root real part is more than 75, system is by the fault type for keeping system unstable；
S5, the type disturbed according to mapping relations identifying system.
The present invention selects 3 machine of WSCC, 9 node system to make sample calculation analysis, and 9 node system of WSCC3 machine is as shown in figure 5, system
Generator total capacity is 567.5MW, and burden with power 315MW, generator is using three rank E ' q variation models, prime mover-governor
Using TGOV1 model, each governor time constant T1, T2, T3 take 0.5s, 1.5s and 5s respectively, and friction in governor Dt takes 0.01,
Excitation system uses SEXS model, and each time constant TA, TB and TE are taken as 1s, 10s and 0.05s respectively, and load uses constant-impedance
Load.Load disturbance and three-phase shortcircuit analysis are carried out to system.Track characteristic root is calculated, one of oscillation mode pair is chosen
The track characteristic root answered analyzes its real part, other track characteristic root changing rules having the same.
After system is by different disturbances, it is entirely different that track characteristic root fluctuates situation, and shows respective spy
Some changing rules.The present invention, which is respectively set, increases load disturbance and three phase short circuit fault, is become by track spy's root of different disturbances
The changing rule difference of track characteristic root in the case of different disturbances is found out in the comparison of law.
One, non-failure conditions
In the case where no any failure, track characteristic root be not a fixed value but within the scope of some wave
Dynamic, track characteristic root real part is as shown in Figure 6.
Two, load increases separately 20%, 40%, 80% situation
Load disturbs at 1s, the disturbance time be 0.2s, track characteristic root real part analogous diagram respectively as Fig. 7, Fig. 8,
Shown in Fig. 9.
Track characteristic root fluctuation situation is analyzed from following index, as shown in fig. 7, I region is irregular hop region:
The track characteristic root variation in the region is irregular to follow；II region is quasi-continuity surge area: the track characteristic root in the region
With certain continuity, while also there is breakpoint appearance；III region is continuity surge area: the track characteristic root tool in the region
There is continuous fluctuation；IV region be new steady-sxtate wave motion region: the track characteristic root in the region reacted system into new stable state with
Track characteristic root afterwards fluctuates situation.
20% load increases as can be seen from Figure 7, and track characteristic root real part sports -10 by -2 when failure occurs, according to
It is secondary to enter I region, jump range: [- 10~4.8], duration 4.2s；II region, fluctuation range: [- 2.2~4.8] continue
Time 7.5s；III region, fluctuation range: [- 2.2~-1.8], duration 1.4s；IV region, fluctuation range: [- 2.04~-
1.99], entry time: 14.1s.20%, 40% and 80% different load disturbance situation is compared it can be found that as load is disturbed
The increase of momentum, the jump range of track characteristic root real part, noncontinuity fluctuation range, quasi-continuous fluctuation range, continuity wave
Dynamic range and duration all significantly increase.It postpones, is finally restored to needed for the fluctuation pattern of stable operation into steady state time
Time is elongated.
Generator is as shown in Figure 10 with respect to power-angle curve: with the increase of load disturbance amount, generator is with respect to power-angle curve
Oscillation amplitude becomes larger, and duration of oscillation is elongated, and the time needed for eventually entering into stable state is also longer, exists with track characteristic root analysis system
Fluctuation situation in the case of disturbance is consistent, it was demonstrated that this method is correct.
Three, three phase short circuit fault situation
Three phase short circuit fault is arranged to occur in No. 6 buses, failure duration is respectively as follows: 0.2s, 0.3s, 0.4s, and generation is being transported
At row time 1s, track characteristic root real part analogous diagram is as shown in Figure 11, Figure 12 and Figure 13.It was found from Figure 10~Figure 13: with event
Elongated, the jump range of track characteristic root real part of Downtime, noncontinuity fluctuation range, quasi-continuous fluctuation range, continuity
Fluctuation range and duration all significantly increase, and postpone into steady state time, are finally restored to the fluctuation pattern institute of stable operation
It takes time elongated.
Generator is as shown in figure 14 with respect to power-angle curve figure: elongated with fault time, generator is with respect to power-angle curve
Oscillation amplitude becomes larger, and duration of oscillation is elongated, and the time needed for eventually entering into stable state is also longer, exists with track characteristic root analysis system
Fluctuation situation in the case of disturbance is consistent, it was demonstrated that this method is correct.
In the case that three phase short circuit fault continues 0.5s as can be seen from Figure 15, track characteristic root only has region I, is integrally in
Existing irregular jump process, system is unstable, the unstable result phase of system that power-angle curve figure opposite with Figure 16 generator is presented
Symbol, it was demonstrated that this method is correct.
Embodiment described above only indicates several embodiments of the invention, and the description thereof is more specific and detailed, but not
It can be interpreted as limitation of the scope of the invention.It should be pointed out that for those of ordinary skill in the art, not departing from
Under the premise of present inventive concept, various modifications and improvements can be made, these belong to the scope of the present invention.Therefore this hair
Bright protection scope should be subject to the claim.
Claims (5)
1. a kind of power system transient stability judgment method based on track characteristic root, which comprises the following steps:
S1, linearization process is carried out at non-equilibrium point to generator, governor, excitation system, network equation and load, established
The higher order linearization model of system；
S2, according to the higher order linearization model, carry out the solution of track characteristic root in the case of unstable state；
S3, it is emulated to obtain track characteristic root curve according to the track characteristic root；
S4, according to the fluctuation track of the track characteristic root curve, establish the mapping of power system transient stability Yu track characteristic root
Relationship；
S5, power system transient stability is judged according to the mapping relations；
System state space equation in the higher order linearization model of the system are as follows:
Wherein x ∈ Rm×1For system mode vector, Δ x indicates system mode incremental vector,Indicate the single order of system mode increment
Derivative vector,F is systematic observation matrix, and g is that node power and steam turbine are transported to generator
Mechanical output algebraic equation, y ∈ R(2n+m)×1The mechanical output vector of generator is transported to for node voltage and steam turbine, m is hair
Number of motors, n are number of nodes.
2. the power system transient stability judgment method according to claim 1 based on track characteristic root, which is characterized in that described
Step 1 is using inverse Laplace transformation method to generator, governor, excitation system, network equation and load in non-equilibrium point
Place carries out linearization process.
3. the power system transient stability judgment method according to claim 2 based on track characteristic root, which is characterized in that described
Mapping relations are as follows:
The track characteristic root curve has irregular hop region, quasi-continuity surge area, continuity surge area and new
Steady-sxtate wave motion region, systematic steady state operation；
The track characteristic root curve only has irregular hop region, and system is unstable.
4. a kind of disturbance type screening technique based on track characteristic root, which comprises the following steps:
S1, using inverse Laplace transformation method to generator, governor, excitation system, network equation and load non-equilibrium
Linearization process is carried out at point, establishes the higher order linearization model of system；
S2, according to the higher order linearization model, carry out the solution of track characteristic root in the case of unstable state；
S3, it is emulated to obtain track characteristic root curve according to the track characteristic root；
S4, according to the variance of the track characteristic root curve, establish the mapping relations of disturbance type and track characteristic root；
S5, the type disturbed according to the mapping relations identifying system；
System state space equation in the higher order linearization model of the system are as follows:
Wherein x ∈ Rm×1For system mode vector, Δ x indicates system mode incremental vector,Indicate the one of system mode increment
Order derivative vector,F is systematic observation matrix, and g is that node power and steam turbine are transported to power generation
The mechanical output algebraic equation of machine, y ∈ R(2n+m)×1The mechanical output vector of generator, m are transported to for node voltage and steam turbine
For generator quantity, n is number of nodes.
5. the disturbance type screening technique according to claim 4 based on track characteristic root, which is characterized in that the mapping
Relationship are as follows:
When the variance of track characteristic root real part is in [0~6.84e-05] range, system failure-free operation；
When the variance of track characteristic root real part is in [6.84e-05~14] range, system is by load disturbance；
When the variance of track characteristic root real part is in [14~75] range, three phase short circuit fault occurs for system；
When the variance of track characteristic root real part is more than 75, system is by the fault type for keeping its unstable.
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