CN111210145A - Electric power system transient stability analysis method based on coupling evaluation index - Google Patents

Electric power system transient stability analysis method based on coupling evaluation index Download PDF

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CN111210145A
CN111210145A CN202010008148.5A CN202010008148A CN111210145A CN 111210145 A CN111210145 A CN 111210145A CN 202010008148 A CN202010008148 A CN 202010008148A CN 111210145 A CN111210145 A CN 111210145A
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夏杨红
李悦
彭勇刚
韦巍
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Abstract

The invention relates to a stability analysis technology in the field of power systems, and aims to provide a power system transient stability analysis method based on coupling evaluation indexes. The method comprises the following steps: establishing a space model aiming at the state of the power system, decoupling the space model by using a coupling evaluation index and a nonlinear decoupling method, and approximately converting an original high-order nonlinear system into a series of decoupled first-order secondary and second-order secondary systems; and then judging the attraction domain of each state variable by using a low-order secondary system analysis tool, and reflecting the transient stability of the power system through the numerical value of the state variable and the relation of the obtained attraction domain. According to the coupling evaluation index and the characteristic value of the linear part, different coupling pairs and isolated state variables are screened for guiding system decoupling. The method can overcome the high-dimensional and nonlinear challenges of a power electronic power system, and compared with the traditional Lyapunov method, the method can obviously reduce the conservative property of the result and further effectively guide the parameter design.

Description

Electric power system transient stability analysis method based on coupling evaluation index
Technical Field
The invention relates to a coupling evaluation index-based power system transient stability analysis method, namely a coupling evaluation index-based nonlinear decoupling method, and belongs to a stability analysis technology in the field of power systems.
Background
Most renewable energy sources are connected to a power system by taking a power electronic device as an interface, and as the permeability of the renewable energy sources in the power system is continuously improved, the trend of power electronization of the power system becomes more and more obvious. Compared with the traditional power system taking a synchronous machine as a main factor, the power electronic power system has new characteristics, which mainly show that the inertia of the power electronic power system is low, and the state variables of the system are easy to change in a large range when the system is disturbed, so that the stability of the system, especially the transient stability, is seriously influenced.
At present, the stability research on the power electronic power system mainly focuses on the small signal stability analysis, and has achieved abundant research results. However, the small-signal stability analysis cannot provide information such as an attraction domain, and cannot determine a disturbance variation range which makes a system unstable/stable or makes a small-signal stability analysis conclusion established, so that the application of a new small-signal stability analysis method is limited.
In contrast, transient stability analysis (or large signal stability analysis) does not need small signal approximation, and directly processes the original nonlinear differential equation and judges whether the disturbed track is converged, so that a system attraction domain can be evaluated, and a disturbance range for stabilizing/destabilizing the system is obtained. However, since the transient stability analysis needs to process a nonlinear differential equation system, it is much more difficult to process a linear differential equation system. For a power electronic power system, the characteristics of nonlinearity and high dimensionality are obvious, and at present, no effective transient stability analysis method and framework for the power electronic power system exist.
The nonlinear decoupling method based on the coupling evaluation index is used for solving the problem of transient stability analysis of a power electronic power system, and overcomes the challenges brought by high dimension and nonlinearity in transient stability analysis by forming an effective analysis framework. The nonlinear decoupling method based on the coupling evaluation index has wide universality, has no special requirements on the structure of the researched power electronic power system, and is a new transient stability analysis framework.
Disclosure of Invention
The invention aims to solve the technical problem of overcoming the defects in the prior art and provides a power system transient stability analysis method based on coupling evaluation indexes.
In order to solve the technical problem, the solution of the invention is as follows:
the method comprises the steps of establishing a space model aiming at the state of the power system, decoupling the space model by using a coupling evaluation index and a nonlinear decoupling method, and approximately converting an original high-order nonlinear system into a series of decoupled first-order secondary and second-order secondary systems; then judging the attraction domain of each state variable by using a low-order secondary system analysis tool, and reflecting the transient stability of the power system through the relation between the numerical value of the state variable and the obtained attraction domain;
the method specifically comprises the following steps:
(1) selecting an incorruptable variable and a first order differential quantity in the power system as a state variable, and establishing a state space model for the power system to be analyzed as follows:
Figure BDA0002355909000000021
wherein X ═ X1，x2，...，xn]TSelected state variable vector for X space (i.e. original space), X1，x2，...，xnRepresenting n state variables selected respectively, f (X) being a set of state equations relating to X; since the stability analysis of the nonlinear system is specific to a specific operating point, the system balance point is X without loss of generality *0, the state variables of the system are transformed into values of variation with respect to the respective steady-state values;
f (X) in the state model of the power system is smooth, the formula (1) is expanded according to the Taylor formula, and the calculation is cut off to a quadratic term, namely
Figure BDA0002355909000000022
Wherein A is the Jacobian matrix of f (X), HjJ is 1, 2,.. n is the corresponding quadratic matrix;
(2) the conversion from an X space to a Y space is carried out on the power system model, namely, linear decoupling is carried out, and the following conversion is realized through similarity conversion X-PY:
Figure BDA0002355909000000023
where P is a matrix of eigenvectors of A, and Y ═ Y1，y2，...，yn]TIs a state variable in Y space (i.e., linear decoupling space), Λ ═ P-1AP＝diag{λ1，λ2，...，λnIs a characteristic value λ from A1，λ2，...，λi，...，λj，...，λnFormed diagonal matrix, VjN is a corresponding quadratic matrix and
Figure BDA0002355909000000024
(P-1)jmis P-1Element of (a), vj，klIs a VjAn element of (1);
(3) selecting a coupling pair and an isolated state variable according to the characteristic value and the coupling evaluation index, and establishing a final decoupling form, wherein ziAnd zjThe method specifically includes the following steps:
(3.1) if λiAnd λjIs a pair of complex numbers conjugated to each other, the corresponding state variable ziAnd zjSelected as a coupled pair and then culled out the state variable ziAnd zj；
(3.2) if λiAnd λjIn the case of a real number,then the state variable ziAnd zjIndex I of coupling betweenijIs defined as:
Figure BDA0002355909000000031
and for the state variables corresponding to the remaining m real number characteristic values, calculating the coupling evaluation indexes of the state variables according to the formula (4), and searching the maximum value:
Figure BDA0002355909000000032
the upper-corner mark m represents the maximum coupling evaluation index when m state variables remain in the system; state variable z corresponding to maximum valueiAnd zjSelected as a coupled pair while rejecting the state variable ziAnd zj，m＝m-2；
(3.3) repeating step (3.2) until m is 0 or 1; or if the coupling evaluation index of the residual state variable is too small, selecting the residual state variable as an isolated state variable;
(4) carrying out transformation from Y space to Z space, namely nonlinear decoupling;
by non-linear transformation of Y ═ Z + [ Z ]TT1Z，ZTT2Z，…，ZTTnZ]TThe following transformations are implemented:
Figure BDA0002355909000000033
wherein if z isiAnd zjSelected as a coupled pair, then:
Figure BDA0002355909000000034
wherein wi，klRepresenting the decoupled coefficient of the state variable, tj，klRepresents a transformation process from Y space to Z space;
(since these two state variables have strong interaction effect, they are considered as a whole when stability analysis is performed.) the two state variables finally form a second order quadratic system, as shown in the following formula:
Figure BDA0002355909000000035
if z isiSelected as an isolated state variable, then:
Figure BDA0002355909000000036
at this point in the stability analysis, the isolated state variables are completely decoupled, forming a first order, second order system, as shown in the following equation:
Figure BDA0002355909000000037
(5) ignore o (Z)3) The original system in the X space is approximately converted into a series of decoupled first-order quadratic systems in the Z space as formula (10) and second-order quadratic systems as formula (8); then, the transient stability of the low-order system in the Z space is judged and analyzed through an attraction domain, wherein the attraction domain of the first-order secondary system is judged by combining a state variable derivative and the positive and negative conditions of a state variable, the attraction domain of the second-order secondary system is judged through an inverse trajectory method, and the transient stability of the original system is indirectly reflected by using the result:
when all state variables in the power system model are in the attraction domains corresponding to the state variables, the system meets the transient stability requirement; and if the state variable exceeds the attraction domain, the system is unstable.
In the invention, the quantity of an incorruptable variable and a first order differential in the power system is collected as a state variable to establish a state space model, and the state space model is subjected to decoupling and order reduction to obtain an attraction domain so as to judge the transient stability of the system; for different power systems, monitoring operation values according to the selected state variables, establishing a state space model, and judging the transient stability of the system by combining the attraction domain obtained according to the method and the specific operation value; wherein the content of the first and second substances,
for the photovoltaic system, the state variables at least comprise an inductance current value, a capacitance voltage value and a PI controller integral quantity;
for the fan system, the state variables at least comprise an inductance current value, a capacitance voltage value, a PI controller integral quantity, the angular speed of a wind turbine, the mechanical angular speeds of a low-speed shaft and a high-speed shaft of a gear box, the mechanical angular speed of a generator, a position angle of the wind turbine, position angles of a low-speed side and a high-speed side of the gear box, a position angle of the generator, a stator of the generator and a magnetic linkage of a rotor;
for a fire synchronous machine system, the state variables at least comprise an inductance current value, a capacitance voltage value and winding flux linkage.
In the present invention, in the step (2), if the characteristic value λ isiAnd λjFor real numbers, a state variable z is definediAnd zjIndex I of coupling betweenijComprises the following steps:
Figure BDA0002355909000000041
in the invention, in the step (4), the method for carrying out nonlinear decoupling from Y space to Z space is to select nonlinear transformation T (Z);
wherein when z isiAnd zjSelected as a coupled pair, the nonlinear transformation is:
Figure BDA0002355909000000042
the transformed second-order quadratic system is:
Figure BDA0002355909000000043
when z isiWhen selected as an isolated state variable, the nonlinear transformation is:
Figure BDA0002355909000000044
the transformed first order quadratic system is:
Figure BDA0002355909000000045
description of the inventive principles:
the invention firstly provides a concept of a coupling evaluation index for evaluating the nonlinear coupling degree between system state variables, and then selects different coupling pairs and isolated state variables according to the coupling evaluation index and the characteristic value of a linear part to guide the decoupling of the system. On the basis, the original nonlinear system is approximately converted into a series of decoupled first-order quadratic and second-order quadratic systems through proper nonlinear transformation, and then the detailed transient stability analysis is carried out by utilizing the existing analysis tool.
Compared with the prior art, the invention has the advantages that:
(1) the invention firstly provides a concept of coupling evaluation indexes and uses the nonlinear coupling degree between the state variables of the evaluation system.
(2) According to the coupling evaluation index and the characteristic value of the linear part, different coupling pairs and isolated state variables are screened for guiding system decoupling.
(3) The invention provides a transient stability analysis method of an electric power system, which is characterized in that an X space is converted into a Y space through linear change, the Y space is converted into a Z space through nonlinear change, an original nonlinear system is approximately converted into a series of decoupled first-order secondary systems and second-order secondary systems, and then the detailed transient stability analysis is carried out on the systems by using the existing analysis tools. Therefore, the technical advantages that the high-dimensional and nonlinear challenges of a power electronic power system can be overcome, and the conservative property of the result can be obviously reduced and the parameter design can be guided more effectively compared with the traditional Lyapunov method can be obtained.
Drawings
FIG. 1 is a three-machine DC micro-grid system topology diagram;
FIG. 2 is a photovoltaic topology and control diagram thereof;
FIG. 3 is a diagram of an energy storage topology and control diagram thereof;
FIG. 4 attraction domain of the first order secondary system;
FIG. 5 attraction domain of a second order quadratic system;
FIG. 6 shows z8And z9An attraction domain map;
FIG. 7 is a phase diagram of different bus voltages;
FIG. 8 is a waveform diagram of voltage and current simulation under different initial conditions of bus voltage.
Detailed Description
The invention aims to provide a novel electric power system transient stability analysis framework to solve the problems that a power electronic electric power system is difficult to analyze transient stability due to nonlinearity and high dimension, and a traditional small signal stability analysis method is not suitable for transient stability analysis. The invention is researched by using a three-machine direct-current microgrid topological structure, and the topological structure is shown in figure 1. The figure shows a typical power electronic power system, and the whole system comprises two photovoltaic devices and an energy storage device.
The rated direct current bus voltage of the direct current micro-grid is set to be 300V, the rated load is 1 omega, the model of the used photovoltaic module is KC200GT, the photovoltaic panel of the PV1 is composed of 20 modules in series and 6 modules in parallel, and the photovoltaic panel of the PV2 is composed of 20 modules in series and 5 modules in parallel. Rated irradiance and ambient temperature are 1000W/m respectively2And 25 ℃.
Transient stability analysis is carried out on the stability of the micro-grid system when the stability jumps from two different direct current bus voltages to a rated state, the output of photovoltaic is kept unchanged, and the transient process of the system is carried out when the direct current bus voltage rises from 295V and 285V to 300V respectively.
In an embodiment of the invention:
firstly, carrying out mathematical modeling on a three-machine direct-current micro-grid.
The photovoltaic was modeled first. Fig. 2 is a photovoltaic topology and control diagram thereof. Typically, intermittent energy sources such as photovoltaics operate in a power control mode to provide power support for the power system. According to fig. 2, the photovoltaic outermost ring is controlled to be an MPPT power control ring, and since the response speed of the outer ring is much lower than that of the inner ring, the dynamic characteristic of the outer ring can be ignored during analysis, the variables after the inductor current, the capacitor voltage and the PI controller integration link are selected as state variables, and the photovoltaic mathematical model is derived as follows:
Figure BDA0002355909000000061
where m ═ 1, 2 denotes different photovoltaics, Sc，mIs the output of the integral controller, kPc，mAnd kIc，mProportional and integral coefficients, v, of the PI controller, respectivelyo，iIs the voltage at the ith node (including the energy storage node),
Figure BDA0002355909000000062
riis the line resistance, R, between the ith node and the DC busLIs a lumped load resistor, Cpv，m、Lc，mAnd Cc，mAre the corresponding filter parameters. The photovoltaic system related parameters are shown in table 1.
TABLE 1 photovoltaic System-related parameters
Figure BDA0002355909000000063
Figure BDA0002355909000000071
And modeling the energy storage part. Fig. 3 is an energy storage topology and a control diagram thereof, in which a general energy storage is operated in a voltage control mode to support a bus voltage, and an inductive current, a capacitive voltage, and a variable after an integration link in a PI controller are still selected as state variables, and a mathematical model of the energy storage is derived as follows:
Figure BDA0002355909000000072
wherein SvIs the output of the integral controller, kPvAnd kIvIs the proportional and integral coefficients, R, of a PI controllervIs the active damping coefficient, VsIs electricityTerminal voltage of cell, LvAnd CvAre the corresponding filters. The energy storage related parameters are shown in table 2.
TABLE 2 energy storage related parameters
Figure BDA0002355909000000073
From the photovoltaic and energy storage models derived above, it can be seen that the dc microgrid is a typical high-order quadratic nonlinear system. Therefore, although the transient stability analysis is performed by taking a direct-current micro-grid system consisting of two photovoltaics, one energy storage and one load as an example, the proposed analysis method can be popularized to a multi-machine power system.
According to the method of step (1) in claim 1, since the stability analysis of the nonlinear system is specific to a specific operation point, the state variables can be converted into values of change relative to the respective steady-state values, and the change is represented by Δ. And expanding the photovoltaic and energy storage models to a quadratic term.
The photovoltaic model that retains the quadratic term is:
Figure BDA0002355909000000081
the energy storage model when the quadratic term is retained is as follows:
Figure BDA0002355909000000082
and integrating the two photovoltaic models and one energy storage model to form a complete direct current microgrid model.
And secondly, realizing the transformation from the X space to the Y space through similarity transformation.
Obtaining a system Jacobian matrix A from the obtained photovoltaic model and energy storage model which reserve quadratic terms, obtaining an eigenvector matrix P according to the A matrix, and obtaining the eigenvector matrix P from X-PY, namely Y-P-1X may implement an X-space to Y-space transformation.
And thirdly, selecting a coupling pair and an isolated variable according to the characteristic value and the coupling evaluation index. By calculation ofZ of the direct-current micro-grid system under the rated state of 300V1、z3、z7、z10、z11Is selected as an isolated state variable, z2And z6、z4And z5、z8And z9Are selected as coupled pairs.
And realizing the transformation from the Y space to the Z space through nonlinear transformation according to the selected coupling pairs and the isolated variables. The decoupling state equation of the Z space is obtained as shown in the following formula:
Figure BDA0002355909000000083
meanwhile, initial conditions of different states relative to a rated state can be calculated, and the initial condition calculation steps are as follows:
1) calculating X0：X0＝Xinitial-X*，XinitialIs a system state variable at an initial time, X*Is the point of equilibrium.
2) Calculating Y0：Y0＝P-1X0P is defined in formula (3).
3) Calculating Z0：Z0Can be obtained by solving a nonlinear algebraic equation system Z + [ Z ]TT1Z，ZTT2Z，...，ZTTnZ]T-Y0Obtained when T is 0jJ is 1, 2, n is defined in formula (7) (9). The system of equations may be expressed as an initial value of Z ═ Y0And solving by a Newton-Raphson iteration method.
Through the steps, the initial points of the system at the bus voltage of 295V can be calculated to be-0.0258, -1.0606, 4.073, -0.0247-j0.2716, -0.0247+ j0.2716, 14.6879, 4.1585, -19.691-j6.9423, -19.691+ i6.9423, -0.2529, -0.4951. And the initial point of the system is 0.0868, -0.0168, -2.5205, 0.0581-j0.4326, 0.0581+ j0.4326, 3.8761,. 3.886, -56.7155-j24.0558, -56.7155+ j24.0558, -0.3564, -1.387 when the bus voltage is 285V.
Briefly described are the existing methods of stability for first-order quadratic and second-order quadratic systems: for the first order and second order nonlinear system shown in the formula (10), the stability analysis is relatively easy, the attraction domain can be accurately calculated as shown in the formula, and the corresponding interval is shown in fig. 4.
Figure BDA0002355909000000091
For the second-order quadratic system shown in equation (8), the estimation of the attraction domain is relatively more complicated than that of the first-order quadratic system, but an inverse trajectory method is given in the reference for estimating the attraction domain of this type of system. For the dual system as follows:
Figure BDA0002355909000000092
Figure BDA0002355909000000093
the stable and unstable domains of both are complementary as shown in FIG. 5. according to this property, the system
Figure BDA0002355909000000094
May be integrated by several inverse integrations (i.e. the system)
Figure BDA0002355909000000095
) And several forward integrations (i.e. the system)
Figure BDA0002355909000000096
Own phase trajectory).
The transient stability analysis method for the low-order secondary system is the prior art and is not described herein again.
According to the stability analysis method of the first-order secondary and second-order secondary systems, the isolated state variable z can be obtained7And a coupling pair z8And z9The attraction domain of (1). Wherein z is7Has an attraction domain of (- ∞, 223.34), z8And z9As shown in fig. 6. So as to the variation of the bus voltage，z7Always lies within its attraction domain, i.e. z7Can be kept stable. For a relatively small range of bus voltage variation, i.e. when the bus voltage is raised from 295V to 300V, z8And z9Is within its attraction domain, the system can remain stable. However, for a relatively large range of bus voltage variation, i.e. when the bus voltage is ramped from 285V to 300V, z8And z9Is outside its attraction domain, the system will be unstable. Further, from z8And z9The aforementioned conclusions can also be demonstrated by the phase trace of (c). FIG. 7(a) shows the initial condition, z, for the initial state 295V at the initial point (-19.691, -6.9423)8And z9Can find that the phase trajectory finally converges to the origin, namely can switch to the rated state of 300V. FIG. 7(b) shows the initial condition, z, for an initial point (-56.7155, -24.0558), i.e., initial state 285V8And z9The phase locus change diagram can find that the phase locus finally diverges and is farther away from the origin, namely the system has transient instability and cannot be directly switched to the rated state of 300V.
Fig. 8 shows the dynamic time domain simulation result of the system when the direct current microgrid system suddenly changes from different initial values of the direct current bus voltage to a rated value of 300V. Fig. 8(a) and 8(b) show the variation of the system voltage and the power supply output current when the system jumps from the initial state 295V to the nominal state 300V. Under the condition of switching the state, the direct-current micro-grid system can keep transient stability, and the system voltage and current can track the system change in time. Because the photovoltaic operation is in the MPPT mode, the output power is unchanged, so after the bus voltage is increased from 295V to 300V, the output current of the two photovoltaics is reduced to some extent; the energy storage can timely supplement the power shortage caused by the voltage rise of the bus, so that the output current of the energy storage is obviously increased. Fig. 8(c) and 8(d) show the change in system voltage and power supply output current when the system jumps from the initial state 285V to the nominal state 300V. It can be seen that under this state switching, the dc microgrid system loses stability. In the process that the bus voltage is increased to 300V from 285V, the energy storage cannot track the system change in time, so that the controller of the system is unstable to lock the energy storage, and the output current of the system is directly changed into 0. Due to the loss of the energy storage support, the voltage of the direct current bus continuously drops to about 210V. During this time, the photovoltaic is still operating in MPPT mode, so its output current increases.
Therefore, the provided electric power system transient stability analysis method based on the coupling evaluation index can be effectively used for electric power electronic electric power system transient stability research, the coupling evaluation index provided by the method is utilized, a nonlinear decoupling method provided by the method is used for decoupling a space model aiming at a specific electric power system state space model, an original high-order nonlinear system is approximately converted into a series of decoupled first-order secondary and second-order secondary systems, an existing analysis tool for the low-order secondary system is used for judging the attraction domain of each state variable, and the transient stability of the system is judged by combining the numerical value of the state variable and the obtained attraction domain. When all state variables are within the corresponding attraction domain, the system is transient stable, otherwise not. According to the three-machine system example in the concrete implementation method, the transient stability judgment result using the proposed method is consistent with the simulation result.

Claims (4)

1. A method for analyzing stability of an electric power system based on a coupling evaluation index is characterized in that a space model is established aiming at the state of the electric power system, the space model is decoupled by using the coupling evaluation index and a nonlinear decoupling method, and an original high-order nonlinear system is approximately converted into a series of decoupled first-order secondary systems and second-order secondary systems; then judging the attraction domain of each state variable by using a low-order secondary system analysis tool, and reflecting the transient stability of the power system through the relation between the numerical value of the state variable and the obtained attraction domain;
the method specifically comprises the following steps:
(1) selecting an incorruptable variable and a first order differential quantity in the power system as a state variable, and establishing a state space model for the power system to be analyzed as follows:
Figure FDA0002355908990000011
wherein X ═ X1，x2，...，xn]TSelected state variable vector for X space (i.e. original space), X1，x2，...，xnRepresenting n state variables selected respectively, f (X) being a set of state equations relating to X; since the stability analysis of the nonlinear system is specific to a specific operating point, the system balance point is X without loss of generality*0, the state variables of the system are transformed into values of variation with respect to the respective steady-state values;
f (X) in the state model of the power system is smooth, the formula (1) is expanded according to the Taylor formula, and the calculation is cut off to a quadratic term, namely
Figure FDA0002355908990000012
Wherein A is the Jacobian matrix of f (X), HjJ is 1, 2,.. n is the corresponding quadratic matrix;
(2) the conversion from an X space to a Y space is carried out on the power system model, namely, linear decoupling is carried out, and the following conversion is realized through similarity conversion X-PY:
Figure FDA0002355908990000013
where P is a matrix of eigenvectors of A, and Y ═ Y1，y2，...，yn]TIs a state variable in Y space (i.e., linear decoupling space), Λ ═ P-1AP＝diag{λ1，λ2，...，λnIs a characteristic value λ from A1，λ2，...，λi，...，λj，...，λnFormed diagonal matrix, VjN is a corresponding quadratic matrix and
Figure FDA0002355908990000014
(P-1)jmis P-1Element of (a), vj，klIs a VjAn element of (1);
(3) selecting a coupling pair and an isolated state variable according to the characteristic value and the coupling evaluation index, and establishing a final decoupling form, wherein ziAnd zjThe method specifically includes the following steps:
(3.1) if λiAnd λjIs a pair of complex numbers conjugated to each other, the corresponding state variable ziAnd zjSelected as a coupled pair and then culled out the state variable ziAnd zj；
(3.2) if λiAnd λjIs a real number, then the state variable ziAnd zjIndex I of coupling betweenijIs defined as:
Figure FDA0002355908990000021
and for the state variables corresponding to the remaining m real number characteristic values, calculating the coupling evaluation indexes of the state variables according to the formula (4), and searching the maximum value:
Figure FDA0002355908990000022
the upper-corner mark m represents the maximum coupling evaluation index when m state variables remain in the system; state variable z corresponding to maximum valueiAnd ziSelected as a coupled pair while rejecting the state variable ziAnd zi，m＝m-2；
(3.3) repeating step (3.2) until m is 0 or 1; or if the coupling evaluation index of the residual state variable is too small, selecting the residual state variable as an isolated state variable;
(4) carrying out transformation from Y space to Z space, namely nonlinear decoupling;
by non-linear transformation of Y ═ Z + [ Z ]TT1Z，ZTT2Z，...，ZTTnZ]TThe following transformations are implemented:
Figure FDA0002355908990000023
wherein if z isiAnd zjSelected as a coupled pair, then:
Figure FDA0002355908990000024
wherein wi，klRepresenting the decoupled coefficient of the state variable, tj，klRepresents a transformation process from Y space to Z space;
(since these two state variables have strong interaction effect, they are considered as a whole when stability analysis is performed.) the two state variables finally form a second order quadratic system, as shown in the following formula:
Figure FDA0002355908990000025
if z isiSelected as an isolated state variable, then:
Figure FDA0002355908990000026
at this point in the stability analysis, the isolated state variables are completely decoupled, forming a first order, second order system, as shown in the following equation:
Figure FDA0002355908990000027
(5) ignore o (Z)3) The original system in the X space is approximately converted into a series of decoupled first-order quadratic systems in the Z space as formula (10) and second-order quadratic systems as formula (8); then, the transient stability of the low-order system in the Z space is judged and analyzed through an attraction domain, wherein the attraction domain of the first-order secondary system is judged in combination with the state variable derivative and the positive and negative conditions of the state variable, the attraction domain of the second-order secondary system is judged through an inverse trajectory method, and the result indirectly reflects the temporary stability of the original systemState stability:
when all state variables in the power system model are in the attraction domains corresponding to the state variables, the system meets the transient stability requirement; and if the state variable exceeds the attraction domain, the system is unstable.
2. The method according to claim 1, characterized by collecting the quantity of the non-abrupt variable and the first order differential in the power system as the state variable to establish a state space model, and determining the transient stability of the system by obtaining an attraction domain through decoupling and reducing the order of the state space model; for different power systems, monitoring operation values according to the selected state variables, establishing a state space model, and judging the transient stability of the system by combining the attraction domain obtained according to the method and the specific operation value; wherein the content of the first and second substances,
for the photovoltaic system, the state variables at least comprise an inductance current value, a capacitance voltage value and a PI controller integral quantity;
for the fan system, the state variables at least comprise an inductance current value, a capacitance voltage value, a PI controller integral quantity, the angular speed of a wind turbine, the mechanical angular speeds of a low-speed shaft and a high-speed shaft of a gear box, the mechanical angular speed of a generator, a position angle of the wind turbine, position angles of a low-speed side and a high-speed side of the gear box, a position angle of the generator, a stator of the generator and a magnetic linkage of a rotor;
for a fire synchronous machine system, the state variables at least comprise an inductance current value, a capacitance voltage value and winding flux linkage.
3. The method according to claim 1, wherein in step (2), if the eigenvalue λ isiAnd λjFor real numbers, a state variable z is definediAnd zjIndex I of coupling betweenijComprises the following steps:
Figure FDA0002355908990000031
4. the method according to claim 1, wherein in the step (4), the nonlinear decoupling from the Y space to the Z space is performed by selecting a nonlinear transformation T (Z);
wherein when z isiAnd zjSelected as a coupled pair, the nonlinear transformation is:
Figure FDA0002355908990000032
the transformed second-order quadratic system is:
Figure FDA0002355908990000033
when z isiWhen selected as an isolated state variable, the nonlinear transformation is:
Figure FDA0002355908990000034
the transformed first order quadratic system is:
Figure FDA0002355908990000035
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