CN108054768B - Power system transient stability evaluation method based on principal component analysis - Google Patents

Power system transient stability evaluation method based on principal component analysis Download PDF

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CN108054768B
CN108054768B CN201711352495.4A CN201711352495A CN108054768B CN 108054768 B CN108054768 B CN 108054768B CN 201711352495 A CN201711352495 A CN 201711352495A CN 108054768 B CN108054768 B CN 108054768B
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principal component
generator
delta
virtual generator
rotor angle
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CN108054768A (en
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吴俊勇
张若愚
席雅雯
邵美阳
李宝琴
郝亮亮
刘自程
卢育梓
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Beijing Jiaotong University
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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
    • 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
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]

Abstract

The invention discloses a transient stability evaluation method of a power system based on principal component analysis, which comprises the steps of obtaining time domain tracks of all generator rotor angles within 25 cycles after fault removal based on a WAMS system, and carrying out principal component analysis after standardization processing; constructing a first principal component virtual generator for the calculation example that the first principal component variance contribution rate is greater than 85%; and with time as a parameter, mapping the rotor angle of the first principal component virtual generator, the corresponding equivalent output power and the equivalent mechanical power into a two-dimensional coordinate one by one to form a P-delta mapping track of the first principal component virtual generator. And calculating the stability margin of the first principal component virtual generator by utilizing an equal area rule, and recording the transient stability margin obtained by calculation as the transient stability margin of the original system. The method does not need modeling and simulation, can judge the stability of the system only by responding information in real time after the fault is removed, and realizes the online transient stability judgment completely based on response.

Description

Power system transient stability evaluation method based on principal component analysis
Technical Field
The invention relates to power system stability evaluation, in particular to a power system transient stability evaluation method based on principal component analysis.
Background
With the development of the cross-regional interconnected power grid and the implementation of the application and policy of various new technologies, the dynamic behavior of the power system is more complicated and changeable, and the transient stability problem of the power system is more easily caused. How to rapidly and accurately judge the transient stability of the power system is one of the important problems of the safety control of the power system.
The existing methods for evaluating the transient stability of the power system mainly comprise the following types: (1) time domain simulation method. The method is visual, rich in information quantity and applicable to various element scales and large-scale power systems, but is slow in calculation speed, depends on system models and parameters, and cannot directly give a stable margin value of the system. (2) A transient energy function method. The method can quickly make stable judgment without calculating the running track of the whole system, but only considers a system of a simple model, can only evaluate the stability of the initial pendulum, and the analysis result is easy to be conservative. (3) An extended equal-area criterion (EEAC) is used as a representative equivalent method. The method can quantitatively evaluate transient stability, but the correctness of its evaluation depends on the correct identification of critical clusters. (4) And (3) a mixing method. The method combines the advantages of the time domain simulation method and the direct method, and has the disadvantages of the time domain simulation method and the direct method. (5) Artificial intelligence method. The method can be used for judging the transient stability of the non-model power system, has the advantages of high online calculation speed and the like, but cannot be used as a substitute of the traditional mechanism-based method and can only be used as a supplement of the traditional mechanism-based method
In recent years, a research trend of transient stability analysis and control of a power system based on response is raised at home and abroad, and the research mainly focuses on two directions of power angle track trend prediction and machine learning. However, no matter research based on power angle trajectory trend prediction or machine learning, they can only determine whether the transient stability of the system is stable, but cannot quantitatively evaluate the transient stability degree of the power system.
The invention overcomes the defects of the existing method on the basis of the existing research, provides the electric power system transient stability evaluation method based on principal component analysis, does not need modeling and simulation, realizes online transient stability dimension reduction evaluation and critical cluster automatic identification completely based on response, and has good application prospect.
Disclosure of Invention
The invention aims to provide a power system transient stability evaluation method based on principal component analysis, so as to overcome the problems in the prior art.
In order to solve the technical problems, the invention adopts the following technical scheme:
and (3) evaluating the transient stability of the power system based on the principal component analysis of the rotor angular trajectory information after the fault. The method comprises the following steps:
the method comprises the following steps that (1) data information acquired by a power system is screened based on a WAMS system, time domain tracks of all generator rotor angles in 25 cycles after fault removal are obtained, and an original data set is formed;
step (2), firstly, carrying out standardization processing on the original data, and then carrying out principal component analysis;
step (3), for the calculation example that the variance contribution rate of the first principal component is greater than 85%, constructing a first principal component virtual generator by using the first principal component;
and (4) calculating the transient stability margin of the first principal component virtual generator by using an equal area rule, wherein the margin is the transient stability margin of the original power system.
In the step (1), an inertia center angle of the power system is defined
Figure GDA0002990623530000031
Wherein
Figure GDA0002990623530000032
i＝1,2,…,n，MiIs the inertia time constant of the ith generator, n is the number of generators, deltaiIs the rotor angle in the original coordinate system. The generator rotor angle in the inertial center coordinate system is marked as
Figure GDA0002990623530000033
Under a certain fault condition, obtaining all generator rotor angle tracks of 25 cycles after fault clearing, and recording the angle tracks as a track matrix in an inertia center reference coordinate system: [ delta ] isij]25×n。
In the step (2), a track matrix [ delta ] is subjected toij]25×nPrincipal component analysis was performed.
First, to matrix [ delta ]ij]25×nAnd (4) carrying out standardization:
Figure GDA0002990623530000034
wherein i is 1,2, …,25, j is 1,2, …, n,
Figure GDA0002990623530000037
sjobserving the indicator delta for each generator separatelyjMean and variance of. Matrix X after normalization:
Figure GDA0002990623530000035
then, the covariance matrix R of X is calculated as(s)ij)n×n：
Figure GDA0002990623530000036
Determining a characteristic value lambda of RiAnd corresponding orthogonalized unit feature vector ui＝[ui1,ui2,…,uin]. Arranging the eigenvalues from large to small with lambda1≥λ2≥…≥λm，λiCorresponding unit feature vector uiIs the main component FiWith respect to the coefficient of the original variable, the ith principal component F of the original variableiComprises the following steps:
Fi＝ui1δ1+ui2δ2+…+uinδn
the variance contribution of the principal component is used to reflect the magnitude of the information quantity, betaiComprises the following steps:
Figure GDA0002990623530000041
the final selection of the principal components is determined by accumulating the variance contribution rates G (m), which are expressed as:
Figure GDA0002990623530000042
when the cumulative variance contribution rate is greater than 85%, the principal component variables are considered to sufficiently reflect the information of the original variables, and the corresponding m are the first m principal components extracted.
In the step (3), for the calculation example that the first principal component variance contribution rate is greater than 85%, the first principal component is extracted, and the first principal component virtual generator is constructed. The equation of motion of the rotor of the first principal component virtual generator is expressed as:
Figure GDA0002990623530000043
in the formula:
Figure GDA0002990623530000044
Figure GDA0002990623530000045
Figure GDA0002990623530000051
Figure GDA0002990623530000052
wherein, F1A rotor angle of the first principal component virtual generator; w is a1A rotor angular velocity of the first principal component virtual generator; omeganIs the synchronous rotor angular velocity; pm、PeThe equivalent mechanical power and the equivalent output power of the first principal component virtual generator are respectively.
In the step (3), the generator corresponding to the first principal component coefficient being a positive value is an advanced cluster, and the generator corresponding to the first principal component coefficient being a negative value is a delayed cluster.
And (4) with time as a parameter, mapping the rotor angle of the first principal component virtual generator, the corresponding equivalent output power and the equivalent mechanical power into a two-dimensional coordinate one by one to form a P-delta mapping track of the first principal component virtual generator. And calculating the stability margin of the first principal component virtual generator by utilizing an equal area rule, and recording the transient stability margin obtained by calculation as the transient stability margin of the original system.
The formula for calculating the equal area rule is as follows:
for the destabilizing calculation example, the stability margin ηunExpressed as:
Figure GDA0002990623530000053
in the formula:
Figure GDA0002990623530000054
Figure GDA0002990623530000061
wherein A isincIncreasing the area of the kinetic energy from the fault occurrence time to the cutting-off time tau; a. thedecReducing the area of the kinetic energy from the fault clearing moment to an unstable equilibrium point UEP; deltaoA rotor angle of a first principal component virtual generator at a system operating point before a fault; deltaτVirtualizing a rotor angle of the generator for the first principal component at the time of fault removal; deltaUEPA first principal component virtual generator rotor angle at an unstable equilibrium point UEP; peThe equivalent output power of the first principal component virtual generator; pmThe equivalent mechanical power of the first principal component virtual generator.
For the stable calculation example, the first point is predicted by firstly swinging the first few points of the FEP of the farthest point by using a quadratic function least square method with higher redundancyThe virtual power angle curve from the swing most distal point FEP to the unstable equilibrium point UEP. Let virtual PeThe (δ) curve is:
Pe(δ)＝a0+a1δ+a2δ2,a0≠0
in the formula a0，a1，a2Is the variable to be solved.
The stability margin η is expressed as:
Figure GDA0002990623530000062
in the formula:
Figure GDA0002990623530000063
Figure GDA0002990623530000071
wherein A isdec.potRepresenting an increased implantation energy required to bring the image to the critical destabilization state, it can be used to construct a path P in the P-delta planee(δ)、Pm(δ), δ -axis and straight line δ ═ δFEPThe enclosed area is measured. A. the* decArea is reduced for kinetic energy of the system from the fault removal time tau to the farthest point FEP; deltaτVirtualizing a rotor angle of the generator for the first principal component at the time of fault removal; deltaFEPA first principal component at the leading edge FEP is taken as a virtual generator rotor angle; deltaUEPVirtualizing a generator rotor angle for a first principal component at the first pendulum UEP; peThe equivalent output power of the first principal component virtual generator; pmThe equivalent mechanical power of the first principal component virtual generator. EtaunIs in the range of [ -1,0 ]]，ηunThe smaller the value is, the larger the system instability degree is; eta value range [0,1 ]]And the larger the value of eta is, the larger the system stability margin is.
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The following detailed description of embodiments of the invention is provided in conjunction with the appended drawings:
FIG. 1 is a schematic diagram of a method for evaluating transient stability of a power system based on principal component analysis according to the present invention;
fig. 2 shows a topology structural diagram of a new england 10 machine 39 node system in the present embodiment;
FIG. 3 shows an exemplary first principal component variance contribution ratio of the New England 10 machine 39 node system in this embodiment;
FIG. 4 shows a P-delta curve of a first principal component virtual generator of the machine 39 node system of example 1 of the present embodiment 10;
fig. 5 shows a P- δ curve of the first principal component virtual generator of the machine 39 node system example 2 of the present embodiment 10.
Detailed Description
The invention discloses a method for evaluating transient stability of a power system based on principal component analysis of rotor angular trajectory information after a fault. The method comprises the following steps:
the method comprises the following steps that (1) data information acquired by a power system is screened based on a WAMS system, time domain tracks of all generator rotor angles in 25 cycles after fault removal are obtained, and an original data set is formed;
step (2), firstly, carrying out standardization processing on the original data, and then carrying out principal component analysis;
step (3), for the calculation example that the variance contribution rate of the first principal component is greater than 85%, constructing a first principal component virtual generator by using the first principal component;
and (4) calculating the transient stability margin of the first principal component virtual generator by using an equal area rule, wherein the margin is the transient stability margin of the original power system.
In the step (1), an inertia center angle of the power system is defined
Figure GDA0002990623530000081
Wherein
Figure GDA0002990623530000082
i＝1,2,…,n，MiFor the ith hairInertia time constant of motor, n is number of generators, deltaiIs the rotor angle in the original coordinate system. The generator rotor angle in the inertial center coordinate system is marked as
Figure GDA0002990623530000083
Under a certain fault condition, obtaining all generator rotor angle tracks of 25 cycles after fault clearing, and recording the angle tracks as a track matrix in an inertia center reference coordinate system: [ delta ] isij]25×n。
In the step (2), a track matrix [ delta ] is subjected toij]25×nPrincipal component analysis was performed.
First, to matrix [ delta ]ij]25×nAnd (4) carrying out standardization:
Figure GDA0002990623530000084
wherein i is 1,2, …,25, j is 1,2, …, n,
Figure GDA0002990623530000095
sjobserving the indicator delta for each generator separatelyjMean and variance of. Matrix X after normalization:
Figure GDA0002990623530000091
then, the covariance matrix R of X is calculated as(s)ij)n×n：
Figure GDA0002990623530000092
Determining a characteristic value lambda of RiAnd corresponding orthogonalized unit feature vector ui＝[ui1,ui2,…,uin]. Arranging the eigenvalues from large to small with lambda1≥λ2≥…≥λm，λiCorresponding unit feature vector uiIs the main componentFiWith respect to the coefficient of the original variable, the ith principal component F of the original variableiComprises the following steps:
Fi＝ui1δ1+ui2δ2+…+uinδn
the variance contribution of the principal component is used to reflect the magnitude of the information quantity, betaiComprises the following steps:
Figure GDA0002990623530000093
the final selection of the principal components is determined by accumulating the variance contribution rates G (m), which are expressed as:
Figure GDA0002990623530000094
when the cumulative variance contribution rate is greater than 85%, the principal component variables are considered to sufficiently reflect the information of the original variables, and the corresponding m are the first m principal components extracted.
In the step (3), for the calculation example that the first principal component variance contribution rate is greater than 85%, the first principal component is extracted, and the first principal component virtual generator is constructed. The equation of motion of the rotor of the first principal component virtual generator is expressed as:
Figure GDA0002990623530000101
in the formula:
Figure GDA0002990623530000102
Figure GDA0002990623530000103
Figure GDA0002990623530000104
Figure GDA0002990623530000105
wherein, F1A rotor angle of the first principal component virtual generator; w is a1A rotor angular velocity of the first principal component virtual generator; omeganIs the synchronous rotor angular velocity; pm、PeThe equivalent mechanical power and the equivalent output power of the first principal component virtual generator are respectively.
In the step (3), the generator corresponding to the first principal component coefficient being a positive value is an advanced cluster, and the generator corresponding to the first principal component coefficient being a negative value is a delayed cluster.
And (4) with time as a parameter, mapping the rotor angle of the first principal component virtual generator, the corresponding equivalent output power and the equivalent mechanical power into a two-dimensional coordinate one by one to form a P-delta mapping track of the first principal component virtual generator. And calculating the stability margin of the first principal component virtual generator by utilizing an equal area rule, and recording the transient stability margin obtained by calculation as the transient stability margin of the original system.
The formula for calculating the equal area rule is as follows:
for the destabilizing calculation example, the stability margin ηunExpressed as:
Figure GDA0002990623530000111
in the formula:
Figure GDA0002990623530000112
Figure GDA0002990623530000113
wherein A isincTo failThe kinetic energy from the occurrence time to the excision time tau increases the area; a. thedecReducing the area of the kinetic energy from the fault clearing moment to an unstable equilibrium point UEP; deltaoA rotor angle of a first principal component virtual generator at a system operating point before a fault; deltaτVirtualizing a rotor angle of the generator for the first principal component at the time of fault removal; deltaUEPA first principal component virtual generator rotor angle at an unstable equilibrium point UEP; peThe equivalent output power of the first principal component virtual generator; pmThe equivalent mechanical power of the first principal component virtual generator.
For the stable calculation example, a quadratic function least square method with high redundancy is firstly applied to the first few points of the FEP to predict a virtual power angle curve from the FEP to the UEP. Let virtual PeThe (δ) curve is:
Pe(δ)＝a0+a1δ+a2δ2,a0≠0
in the formula a0，a1，a2Is the variable to be solved.
The stability margin η is expressed as:
Figure GDA0002990623530000121
in the formula:
Figure GDA0002990623530000122
Figure GDA0002990623530000123
wherein A isdec.potRepresenting an increased implantation energy required to bring the image to the critical destabilization state, it can be used to construct a path P in the P-delta planee(δ)、Pm(δ), δ -axis and straight line δ ═ δFEPThe enclosed area is measured. A. the* decFor removing the time tau to faultThe kinetic energy of the system at the most distant point, FEP, reduces the area; deltaτVirtualizing a rotor angle of the generator for the first principal component at the time of fault removal; deltaFEPA first principal component at the leading edge FEP is taken as a virtual generator rotor angle; deltaUEPVirtualizing a generator rotor angle for a first principal component at the first pendulum UEP; peThe equivalent output power of the first principal component virtual generator; pmThe equivalent mechanical power of the first principal component virtual generator. EtaunIs in the range of [ -1,0 ]]，ηunThe smaller the value is, the larger the system instability degree is; eta value range [0,1 ]]And the larger the value of eta is, the larger the system stability margin is.
The invention has the following beneficial effects:
according to the technical scheme, the method does not need to establish an analysis model and simulation of the power system, and directly evaluates the transient stability of the power system only according to the rotor angle, mechanical power and output power information of the generator after the fault is removed, which are obtained by the WAMS system, so that the online transient stability judgment based on response is realized. The method does not need manual grouping on the power system, and has the capability of automatically identifying the critical unit and the instability mode. With the enlargement of the system scale, the method only needs to judge the stability characteristic of the first principal component virtual generator, the calculated amount is not obviously increased, and the advantages are more obvious compared with the traditional method.
The invention is further illustrated by the following set of examples:
the present embodiment is described by taking a 39-node system of a new england 10 machine as an example. The system adopts constant impedance load, the load level is under 100% standard load level, 5 different generated forces are set, three-phase short-circuit fault is set in the middle of 34 lines, 5 cycles remove near-end fault after fault occurs, 6 cycles remove far-end fault, or 9 cycles remove near-end fault, 10 cycles remove far-end fault, or 19 cycles remove near-end fault, 20 cycles remove far-end fault, 5 × 34 × 3 is generated totally as 510 calculation examples. The actual measured rotor angle track information of the generator after the failure by the PMU is simulated by data obtained by simulation of simulation software Power System Tool (PST)3.0, and the simulation frequency is 60 Hz.
And extracting the rotor angle track information of 25 cycles after the fault is removed, and obtaining the rotor angle track information under an inertia center coordinate system after inertia center transformation. And then, principal component analysis is carried out on the first principal component variance contribution rate of each calculation example, as shown in fig. 3.
From fig. 3, it can be known that the first principal component variance contribution rates of the 510 examples generated by the 10-machine 39-node system simulation are all greater than 85% for 100% of the examples, and therefore, according to the principle of principal component extraction in multivariate statistical principal component analysis, the first principal component contains most of the original generator rotor angle trajectory information. Therefore, the first principal component virtual generator constructed by the method contains most information of the rotor angle locus of each unit of the original system.
And with time as a parameter, mapping the rotor angle of the first principal component virtual generator, the corresponding equivalent output power and the equivalent mechanical power into a two-dimensional coordinate one by one to form a P-delta mapping track of the first principal component virtual generator.
When the first principal component virtual generator rotor angle disturbed trajectory δ (t) is unstable, the corresponding P- δ mapping curve must encounter an Unstable Equilibrium Point (UEP). Stability margin eta of instability mapping before per unitunExpressed as:
ηun＝Adec-Ainc (1)
this value can be per unit:
Figure GDA0002990623530000141
in the formula:
Figure GDA0002990623530000142
Figure GDA0002990623530000143
when it is firstWhen the main component virtual generator P- δ mapping curve meets the most distant point of the first swing (FEP), the swing can be judged to be stable, and at this time, a existsdecAnd AincAre equal. The imaginary path can be predicted by applying quadratic least squares with high redundancy to the first few points of the FEP, assuming that the map trajectory has ideal autonomy after the FEP, and injecting additional kinetic energy into the map at the FEP. Let virtual PeThe (δ) curve is:
Pe＝a0+a1δ+a2δ2,a0≠0
(5)
in the formula a0，a1，a2Is the variable to be solved.
Potential kinetic energy reduction area Adec.potRepresenting an increased implantation energy required to bring the image to the critical destabilization state, it can be used to construct a path P in the P-delta planee(δ)、Pm(δ), δ -axis and straight line δ ═ δFEPThe enclosed area is measured. The total kinetic energy can be used to reduce the area (A)* dec+Adec.pot) Increase of area A with actual kinetic energyincThe difference being Adec.potAs a margin of stability before per unit. The stability margin eta after per unit is as follows:
Figure GDA0002990623530000151
in the formula:
Figure GDA0002990623530000152
Figure GDA0002990623530000153
A* decarea reduction, δ, for kinetic energy of the system at FEP to the farthest point from the time of fault removal τoFor this reasonRotor angle, delta, of a first principal component virtual generator at a pre-obstacle system operating pointτFor the moment of fault removal, the rotor angle, delta, of the first principal component virtual generatorFEPTo first pendulum the first principal component at FEP virtual generator rotor angle, δUEPThe first principal component at the leading edge UEP is the virtual generator rotor angle. Eta is shown by the formulas (2) and (6)unIs in the range of [ -1,0 ]]，ηunThe smaller the value is, the larger the system instability degree is; eta value range [0,1 ]]And the larger the value of eta is, the larger the system stability margin is. To verify the correctness of the stability and stability obtained by the method herein, an index M based on the limiting excision time (CCT) is introduced to quantify the stability of the original system, and the index M is defined as follows:
Figure GDA0002990623530000161
M∈[-1,1]when M is larger than zero, the system is in a stable state, and the system is more stable as the system approaches 1; when M is equal to zero, the system is in a critical state; and when M is less than zero, the system is in a destabilization state, and the system is unstable as the system approaches-1. t is tCCTThe value of (a) can be obtained by repeatedly trying out t by a time domain simulation methodclThe time is actually cut off for the fault.
For example 1, three-phase short-circuit fault occurs at 0s at 50% of No. 24 line, 9 cycles remove near-end fault after fault occurs, and 10 cycles remove far-end fault. Principal component analysis was performed on the generator rotor angle information of 25 cycles after the fault was removed in the inertial center coordinate system of example 1, and the first principal component coefficient was obtained as shown in table 1.
TABLE 110 first principal component coefficient of 39-node system example 1
Figure GDA0002990623530000162
Figure GDA0002990623530000171
Observing the first principal component coefficient, the absolute values of the weight coefficients of the generators are nearly equal, the generator weight coefficients of the bus numbers 30-38 are positive values, and the generator weight coefficient of the bus number 39 is negative values. The generator weight coefficients of the bus numbers 30-38 are opposite to the generator weight coefficient of the bus number 39, and are consistent with the phenomenon that the swinging curve trend of the time domain simulation generator is opposite. In the existing EEAC method, generators with bus numbers of 30-38 are combined into a lead unit, the equal weights of the generators are all 1.0, and generators with bus numbers of 39 serve as lag units, and the equal weights of the generators are all 1.0. And subtracting the rotor angles of the two motors to form a single-motor infinite system, and judging the transient stability of the system by using an equal-area rule. Comparing these two methods, it can be seen that the first principal component coefficient is similar to the weighting coefficient of each generator in the EEAC method and is more objective than the EEAC method. The principal component analysis is a correlation between the generators obtained from the real-time response data characteristics of the system, and is not a method of artificially setting the weight coefficients of the generators. It can be seen that the EEAC method assigns each generator weight only as a limiting special case of the PCA-based virtual generator method. The weight coefficient given by the virtual generator method based on PCA realizes the function of automatically identifying the instability mode and the critical unit.
And constructing a first principal component virtual generator according to the principal component coefficient corresponding to the first principal component. The first principal component virtual generator rotor angle δ is:
Figure GDA0002990623530000181
output power P of first principal component virtual generatoreComprises the following steps:
Figure GDA0002990623530000182
mechanical power P of first principal component virtual generatormComprises the following steps:
Figure GDA0002990623530000183
Figure GDA0002990623530000184
MT＝M30+M31+…+M39
(14)
fig. 4 shows a P- δ curve of the first principal component virtual generator of example 1, in which a first hollow pentagonal center represents FEP in the top swing, a second hollow pentagonal center represents virtual UEP, a horizontal straight line represents mechanical power Pm (δ) of the first principal component virtual generator, a solid curve represents output power Pe (δ) of the first principal component virtual generator, and a dotted line represents a fictional Pe (δ) locus from FEP to UEP. Example 1 stability analysis data are shown in table 2.
Stability analysis data of Table 210 machine 39 node System example 1
Figure GDA0002990623530000185
Figure GDA0002990623530000191
As can be seen from Table 2, when the first principal component virtual generator rotor angle first run hits FEP, there is A* dec＝Ainc. Calculating to obtain a first principal component virtual generator stability margin eta of 0.4546 by using the formula (6) based on the limit excision time tCCTWhen the calculated original system stability index M is 0.4706, it can be seen that η and M are both positive numbers and have equivalent values, that is, the stability of the first principal component virtual generator is consistent with that of the original system, and both are in a stable state.
For the embodiment 2, the three-phase short-circuit fault occurs at 0s at 50% of the No. 6 line, the near-end fault is removed by 19 cycles after the fault occurs, and the far-end fault is removed by 20 cycles. The equivalent power angle curve of the first principal component virtual generator of example 2 is shown in fig. 5. The curve in the graph represents the output power Pe (delta) of the first principal component virtual generator, the horizontal straight line represents the mechanical power Pm (delta) of the first principal component virtual generator, and the hollow pentagon represents UEP. Example 2 stability analysis data are shown in table 3.
Table 310 stability analysis data of node system example 2 of machine 39
Figure GDA0002990623530000192
Figure GDA0002990623530000201
As can be seen from Table 3, the first principal component virtual generator stability margin ηun-0.9087, based on the limit resection time tCCTThe calculated original system stability indicator M-0.8947. From this it can be seen thatunThe M is a negative number and the value is equivalent to the value, namely, the stability of the first principal component virtual generator and the original system are in a destabilization state.
The results of the 10 machine 39 node system part of the example analysis are shown in table 4. Through simulation verification, when the first main component virtual generator rotor angle first pendulum meets FEP in Table 4, all A exists* dec＝AincTherefore, the stability margin η of the stability example can be calculated by using the formula (6); when the first principal component virtual generator rotor angle crosses the UEP, η is calculated using equation (2)unThereby obtaining the stability margin eta of the instability calculation exampleun。
Table 410 machine 39 node system stability analysis result
Figure GDA0002990623530000202
Figure GDA0002990623530000211
Figure GDA0002990623530000221
Figure GDA0002990623530000231
Figure GDA0002990623530000241
As can be seen from table 4: the two stability margin index values calculated based on the PCA method and the time domain simulation method have the same signs and the same absolute values. The transient stability of the first principal component virtual generator is consistent with the stability of an original system, and the first principal component virtual generator constructed based on a principal component analysis method can be used for transient stability evaluation of a multi-machine system.
It should be understood that the above-mentioned embodiments of the present invention are only examples for clearly illustrating the invention, and are not intended to limit the embodiments of the present invention, and it will be obvious to those skilled in the art that various changes and modifications may be made on the basis of the above-mentioned description, and all embodiments may not be exhaustive, and all obvious changes and modifications may be made within the scope of the present invention.

Claims (2)

1. The transient stability evaluation method of the power system based on the principal component analysis is characterized by comprising the following steps of:
the method comprises the following steps that (1) data information acquired by a power system is screened based on a WAMS system, time domain tracks of all generator rotor angles in 25 cycles after fault removal are obtained, and an original data set is formed;
step (2), firstly, carrying out standardization processing on the original data, and then carrying out principal component analysis;
step (3), for the calculation example that the variance contribution rate of the first principal component is greater than 85%, constructing a first principal component virtual generator by using the first principal component;
step (4), calculating the transient stability margin of the first principal component virtual generator by using an equal area rule, wherein the margin is the transient stability margin of the original power system;
in the step (3), for the calculation example that the variance contribution rate of the first principal component is greater than 85%, the first principal component is extracted, and a first principal component virtual generator is constructed, wherein a rotor motion equation of the first principal component virtual generator is expressed as:
Figure FDA0002990623520000011
in the formula:
Figure FDA0002990623520000012
Figure FDA0002990623520000021
Figure FDA0002990623520000022
Figure FDA0002990623520000023
wherein, F1A rotor angle of the first principal component virtual generator; w is a1A rotor angular velocity of the first principal component virtual generator; omeganIs the synchronous rotor angular velocity; pm、PeRespectively obtaining equivalent mechanical power and equivalent output power of the first principal component virtual generator;
in the step (4), the rotor angle of the first principal component virtual generator, the corresponding equivalent output power and the equivalent mechanical power are mapped into a two-dimensional coordinate one by taking time as a parameter to form a P-delta mapping track of the first principal component virtual generator; calculating the stability margin of the first principal component virtual generator by utilizing an equal-area rule, and recording the transient stability margin obtained by calculation as the transient stability margin of the original system;
the formula for calculating the equal area rule is as follows:
for the destabilizing calculation example, the stability margin ηunExpressed as:
Figure FDA0002990623520000024
in the formula:
Figure FDA0002990623520000025
Figure FDA0002990623520000031
wherein A isincIncreasing the area of the kinetic energy from the fault occurrence time to the cutting-off time tau; a. thedecReducing the area of the kinetic energy from the fault clearing moment to an unstable equilibrium point UEP; deltaoA rotor angle of a first principal component virtual generator at a system operating point before a fault; deltaτVirtualizing a rotor angle of the generator for the first principal component at the time of fault removal; deltaUEPA first principal component virtual generator rotor angle at an unstable equilibrium point UEP; peThe equivalent output power of the first principal component virtual generator; pmThe equivalent mechanical power of the first principal component virtual generator;
for the stable calculation example, firstly, a quadratic function least square method with high redundancy is applied to the first few points of the FEP to predict a virtual power angle curve from the FEP to the UEP, and the virtual P is seteThe (δ) curve is:
Pe(δ)＝a0+a1δ+a2δ2,a0≠0
in the formula a0，a1，a2Is a variable to be solved;
the stability margin η is expressed as:
Figure FDA0002990623520000032
in the formula:
Figure FDA0002990623520000033
Figure FDA0002990623520000041
wherein A isdec.potRepresenting an increased implantation energy required to bring the image to the critical destabilization state, it can be used to construct a path P in the P-delta planee(δ)、Pm(δ), δ -axis and straight line δ ═ δFEPThe enclosed area is measured; a. the* decArea is reduced for kinetic energy of the system from the fault removal time tau to the farthest point FEP; deltaτVirtualizing a rotor angle of the generator for the first principal component at the time of fault removal; deltaFEPA first principal component at the leading edge FEP is taken as a virtual generator rotor angle; deltaUEPVirtualizing a generator rotor angle for a first principal component at the first pendulum UEP; peThe equivalent output power of the first principal component virtual generator; pmThe equivalent mechanical power of the first principal component virtual generator; etaunIs in the range of [ -1,0 ]]，ηunThe smaller the value is, the larger the system instability degree is; eta value range [0,1 ]]The larger the value of eta is, the larger the system stability margin is;
in the step (1), an inertia center angle of the power system is defined
Figure FDA0002990623520000042
Wherein
Figure FDA0002990623520000043
MiIs the inertia time constant of the ith generator, n is the number of generators, deltaiThe rotor angle of the generator in the inertial center coordinate system is recorded as the rotor angle in the original coordinate system
Figure FDA0002990623520000044
Under a certain fault condition, obtaining all generator rotor angle tracks of 25 cycles after fault clearing, and recording the angle tracks as a track matrix in an inertia center reference coordinate system: [ delta ] isij]25×n；
In the step (2), a track matrix [ delta ] is subjected toij]25×nThe analysis of the main components is carried out,
first, to matrix [ delta ]ij]25×nAnd (4) carrying out standardization:
Figure FDA0002990623520000045
wherein i is 1,2, …,25, j is 1,2, …, n, δj，sjObserving the indicator delta for each generator separatelyjMean and variance of, matrix X after normalization:
Figure FDA0002990623520000051
then, the covariance matrix R of X is calculated as(s)ij)n×n：
Figure FDA0002990623520000052
Determining a characteristic value lambda of RiAnd corresponding orthogonalized unit feature vector ui＝[ui1,ui2,…,uin]Arranging the eigenvalues from large to small with lambda1≥λ2≥…≥λm，λiCorresponding unit feature vector uiIs the main component FiWith respect to the coefficient of the original variable, the ith principal component F of the original variableiComprises the following steps:
Fi＝ui1δ1+ui2δ2+…+uinδn
the variance contribution of the principal component is used to reflect the magnitude of the information quantity, betaiComprises the following steps:
Figure FDA0002990623520000053
the final selection of the principal components is determined by accumulating the variance contribution rates G (m), which are expressed as:
Figure FDA0002990623520000054
when the cumulative variance contribution rate is greater than 85%, the principal component variables are considered to sufficiently reflect the information of the original variables, and the corresponding m are the first m principal components extracted.
2. The evaluation method according to claim 1, wherein: in the step (3), the generator corresponding to the first principal component coefficient being a positive value is an advanced cluster, and the generator corresponding to the first principal component coefficient being a negative value is a delayed cluster.
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