CN112152197A - Frequency intensity parameter measuring method for multi-machine power system - Google Patents

Frequency intensity parameter measuring method for multi-machine power system Download PDF

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CN112152197A
CN112152197A CN202010804311.9A CN202010804311A CN112152197A CN 112152197 A CN112152197 A CN 112152197A CN 202010804311 A CN202010804311 A CN 202010804311A CN 112152197 A CN112152197 A CN 112152197A
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frequency
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matrix
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inertia
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CN112152197B (en
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辛焕海
高晖胜
张雯欣
李知艺
胡鹏飞
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Zhejiang University ZJU
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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
    • 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
    • H02J3/241—The oscillation concerning frequency
    • 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
    • H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
    • H02J3/46—Controlling of the sharing of output between the generators, converters, or transformers
    • H02J3/48—Controlling the sharing of the in-phase component
    • 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]

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Abstract

The invention discloses a frequency intensity parameter measuring method of a multi-machine power system. Obtaining a compressed Laplace matrix and equivalent disturbance of a generator node and a relation between the equivalent disturbance and frequency in a multi-machine power system comprising a generator; further processing to obtain a plurality of frequency modal components under the generator node and the approximate frequency of the generator node; selecting a frequency track of a node under disturbance as a key track, and determining a frequency modal component dominated by the key track; and aiming at the frequency modal component guided by the key track, converting each generator into an inertia-damping-integral structure to obtain an approximate key track, then performing de-normalization to obtain three parameters of effective modal inertia, effective modal damping and effective modal integral, and then processing to obtain frequency intensity parameters. According to the method, the frequency intensity parameter with higher precision is obtained, the frequency intensity analysis is quantized, and the accurate frequency intensity parameter of the power system of the weak synchronous power grid is obtained.

Description

Frequency intensity parameter measuring method for multi-machine power system
Technical Field
The invention relates to a method for acquiring parameters of an electric power system, in particular to a method for measuring frequency intensity parameters of a multi-machine electric power system.
Background
In recent years, the capacity of new energy connected to a power grid is increasing, and the inertia of a power system is reduced and the frequency characteristic is deteriorated. In order to realize the safety and stability of a power system of a weak synchronization power grid and further improve the permeability of new energy, the frequency stability margin or the frequency intensity of the power grid needs to be quantitatively evaluated.
At present, in the aspect of frequency intensity representation of an electric power system, inertia is a parameter which is commonly used for measuring a frequency change rate, and the total inertia of the electric power system has a clear inverse relation with the frequency change rate. The commonly used parameters also comprise frequency deviation factors which can reflect the primary frequency modulation capability of the power grid and the steady-state frequency after power shortage. In addition, there are parameters that reflect the amount of frequency overshoot (frequency nadir), such as the dynamic frequency response coefficient. The parameters are all based on the assumption that the frequencies of all nodes in the power grid are consistent. In fact, there is a spatial distribution difference in the frequencies of the nodes of the power system, and when the synchronization performance of the power grid is poor, the difference may be large.
At present, many parameters consider the distribution characteristics of frequency, for example, a learner defines the distribution of node inertia quantification inertia in a power grid based on the inherent property that inertia hinders frequency change. H2、H∞The norm may also be used to quantify the frequency characteristics of a multi-machine system. However, at present, there are few literature analyses considering the lowest point problem of the frequency distribution characteristics, and the lowest point parameter form established based on the uniform frequency is also complicated, which is not favorable for the analysis. The lowest point of frequency has important significance in engineering, and is closely related to protective measures such as low-frequency load shedding of a power system. In addition, since the inertia can only reflect the initial frequency change rate after disturbance, when the system damping is large, there may be a certain difference between the initial frequency change rate and the average frequency change rate in a period of time (for example, in hundreds of milliseconds) after disturbance, and the latter is of more concern in practical engineering. Therefore, it is necessary to establish more perfect frequency intensity parameters of the low inertia power system, and to quantitatively consider the frequency distributionThe lowest point and the average rate of change of frequency.
Disclosure of Invention
In order to evaluate the frequency intensity of the weak synchronization power grid, the invention provides a frequency intensity parameter measuring method of a multi-machine power system, which can quantitatively analyze the lowest point of frequency and the average change rate in the weak synchronization power grid through parameters with very simple forms.
The technical scheme of the invention comprises the following steps:
1) in a multi-machine power system including generators such as a synchronous machine and a power electronic power generation device, a compressed Laplace matrix L of generator nodes is obtained by eliminating a part of constant power nodes of load nodes and passive nodes from a Laplace matrix of the multi-machine power systemrAnd equivalent disturbance Deltau uE(s); combining the compressed Laplace matrix LrObtaining the equivalent disturbance delta u of the generator node with the frequency-active transfer function matrix G(s) of the generatorE(s) a relationship with frequency Δ ω(s);
the multi-machine power system comprises a generator node, a load node and a passive node, wherein the generator node is connected with generators such as a synchronous machine and power electronic generating equipment, the load node and the passive node form a constant-power node, the load node is a node connected with electric equipment, and the passive node is a node without the generators and the electric equipment.
2) Processing and obtaining a plurality of frequency modal components delta omega under the generator node according to the relation between the equivalent disturbance and the frequency of the generator nodek(s) to obtain an approximate frequency of the generator node
Figure BDA0002628531580000021
3) Selecting a frequency track of a node of a multi-machine power system under disturbance as a key track delta omegack(s) and determining frequency modal components dominated by the key trajectory;
further, the frequency intensity parameters are obtained from the key trajectory as follows.
4) Converting each generator into an inertia-damping-integral structure aiming at the k-th frequency modal component dominated by the key track through an iterative algorithm to obtain an approximate key track;
5) decomposing and normalizing the approximate key track parameters to obtain three parameters of effective modal inertia, effective modal damping and effective modal integral;
6) and obtaining frequency intensity parameters by utilizing effective modal inertia, effective modal damping and effective modal integration.
In the step 1), the multi-machine power system has n + m nodes in total, wherein the first n generator nodes, m load nodes or constant power nodes of passive nodes;
1.1) establishing a Laplace matrix L of a multi-machine power system, wherein diagonal elements and non-diagonal elements are respectively as follows:
L[i,i]＝Vi∑j∈iBijVjcosθij0
L[i,j]＝-ViVjBijcosθij0
wherein, L [ i, j]Elements representing the ith row and the jth column of the Laplace matrix L; j belongs to i and represents that a node j is directly connected with the node i through a line, i and j represent ordinal numbers of the nodes in the multi-machine power system, and i, j belongs to {1, 2., n + m }; vi、VjThe voltage amplitudes of the nodes i and j are respectively; thetaij0The steady state value of the phase angle difference between the node i and the node j is obtained; b isijElements in the node susceptance matrix B;
dividing the Laplace matrix L into 4 sub-matrixes L according to the relation that elements in the Laplace matrix L belong to generator nodes or constant power nodes11、L12、L21、L22The submatrix L11Is composed of the first n rows and the first n columns of a Laplacian matrix L, a sub-matrix L12Is composed of the first n rows (n +1) to (n + m) th columns of the Laplace matrix L, and the sub-matrix L21Is composed of the first n columns of the (n +1) th to (n + m) th rows of the Laplace matrix L, and the sub-matrix L22Is composed of the (n +1) th column to the (n + m) th column to the (n +1) th column to the (n + m) th column of the Laplace matrix L;
further, a compressed Laplace matrix L is obtained according to the following formularComprises the following steps:
Figure BDA0002628531580000031
1.2) the power disturbance (such as sudden load increase) of each node is delta ui(s)，Δui(s)＝-PuiS, s denotes the Laplace operator, power disturbance Δ ui(s) having a total of n + m components, PuiRepresenting the power disturbance amplitude of the ith node,
by disturbance of power Δ uiThe first n components and the last m components of(s) respectively form disturbance vectors delta u of a generator node and a constant power node1(s) and. DELTA.u2(s) determining the disturbance vector Δ u of the constant power node2(s) disturbance vector Deltau superimposed to a Generator node1(s) obtaining the equivalent disturbance of the generator node as:
Figure BDA0002628531580000033
wherein, Δ uE(s) represents an equivalent disturbance of the generator node;
1.3) per unit of each generator by using the same power base value, wherein the frequency-active transfer function of each generator node is Gi(s), i belongs to {1, 2.., n }, and the frequency and the phase angle of each generator node are delta omegai(s) and Δ θi(s) wherein Δ θi(s)＝ω0Δωi(s)/s，ω0Is a frequency base value; the frequency delta omega of each generator node is measuredi(s) form a column vector Δ ω(s) that defines the phase angle Δ θ of each generator nodei(s) also constitute a column vector Δ θ(s) with the frequency-active transfer function G of each generator nodei(s) establishing a diagonal matrix G(s) for the diagonal elements, G(s) diag { G {(s) }i(s), the off-diagonal elements in the diagonal matrix G(s) are zero, and the relationship between the equivalent disturbance and the frequency of the following generator nodes is established:
Figure BDA0002628531580000032
in the step 2), decomposing the frequency of each node into the sum of a plurality of modal components based on a perturbation theory, wherein the method comprises the following steps:
2.1) selecting one generator as a reference generator, the capacity of the reference generator being a reference capacity, according to the ratio F of the capacity of each generator to the capacity of the reference generatoriObtaining a capacity scaling matrix F, F ═ diag { F }i}; and then processing to obtain a frequency-active transfer function matrix g(s) after each generator node is equivalent to the capacity of the generator node:
g(s)＝F-1G(s)＝diag{gi(s)}
wherein g(s) represents a frequency-active transfer function matrix after each generator node is equivalent to the capacity of the generator node, g(s)i(s) is the frequency-active transfer function of each generator under its own capacity;
the relation between the equivalent disturbance of the generator node and the frequency is transformed into:
F1/2(s)F1/2Δω(s)＝ΔuE(s)
(s)＝Ing(s)+ω0LF/s
wherein, InIs an n-order unit array, LFIs a weighted Laplace matrix, LF＝F-1/2LrF-1/2Weighted Laplace matrix LFThe eigenvalue and eigenvector of (a) are each lambda1,...,λnAnd U1,...,UnAnd satisfy lambda1<...<λn， λ 10; (s) represents a transfer function matrix;
2.2) reconstruction of the auxiliary transfer function matrix
Figure BDA0002628531580000041
Figure BDA0002628531580000042
Wherein the content of the first and second substances,
Figure BDA0002628531580000043
representing a weighted Laplace matrix LFThe first eigenvalue corresponds to the auxiliary frequency-active transfer function, which is formed by the weighted Laplace matrix LFParticipation factor p of first characteristic valuei1For gi(s) weighted summation yields:
Figure BDA0002628531580000044
then the auxiliary transfer function matrix
Figure BDA0002628531580000045
The eigenvalues and eigenvectors of (a) are:
Figure BDA0002628531580000046
to Ψk＝Uk，k∈{1,2,...,n}
Wherein, UkRepresenting a weighted Laplace matrix LFThe kth feature vector of (1); lambda [ alpha ]kRepresenting a weighted Laplacian matrix LFThe kth eigenvalue of (a);
2.3) treating the transfer function matrix(s) as an auxiliary transfer function matrix based on the principle of matrix perturbation
Figure BDA0002628531580000047
Obtaining eigenvalues and eigenvectors of the transfer function matrix(s):
Figure BDA0002628531580000048
Figure BDA0002628531580000049
Figure BDA00026285315800000410
wherein p isikRepresenting a weighted Laplace matrix LFThe participation factor of the kth characteristic value;
Figure BDA00026285315800000411
representing a weighted Laplace matrix LFThe kth eigenvalue corresponds to the auxiliary frequency-active transfer function,
Figure BDA00026285315800000412
is based on a weighted Laplace matrix LFParticipation factor p of k-th characteristic valueikFor gi(s) weighting the resulting transfer function;
Figure BDA00026285315800000413
for high order quantums, O () represents a quanta function; | | represents a matrix norm;
2.4) obtaining a plurality of frequency modal components delta omega under the generator node according to the eigenvalue and the eigenvector of the transfer function matrix(s)k(s) and synthesizing into an approximate frequency of the generator node
Figure BDA00026285315800000414
Figure BDA00026285315800000415
Figure BDA00026285315800000416
Figure BDA00026285315800000417
Wherein the content of the first and second substances,
Figure BDA00026285315800000418
an approximate frequency vector representing the generator node,
Figure BDA00026285315800000419
by approximate frequency of each generator node
Figure BDA00026285315800000420
Composition, i ∈ {1,2,..., n }; Δ ωk(s) represents the generator node down-weighted Laplace matrix LFThe frequency modal component vector, Δ ω, corresponding to the kth eigenvaluek(s) weighting the Laplace matrix L by each generator nodeFFrequency modal component delta omega corresponding to k-th characteristic valueik(s) composition, i ∈ {1, 2.., n }; ckIs a weighted Laplace matrix LFA coefficient matrix of the frequency modal component corresponding to the kth eigenvalue; hk(s) is a weighted Laplace matrix LFAnd the transfer function of the frequency modal component corresponding to the k-th characteristic value.
In the step 3), the method specifically comprises the following steps:
the time domain variation of the frequency is taken as a frequency track, and the frequency track of the key node is taken as a key track delta omegack(s), the key node is obtained by processing according to the following modes:
under the disturbance of the y node, if the approximate frequency of the x generator node is delta omegax(s) curve and weighted Laplace matrix L in the nodeFFrequency modal component delta omega corresponding to k-th characteristic valuexk(s) the general shape and position of the curve coincide, and Δ ωxk(s) weighting the Laplace matrix L at all generator nodesFFrequency modal component Δ ω corresponding to k-th characteristic valueik(s) is the maximum amplitude in the curve, then Δ ω is calculatedxk(s) as the critical trajectory Δ ωck(s) consider the weighted Laplace matrix LFThe frequency modal component corresponding to the kth characteristic value dominates the key track;
if under the disturbance of the y node, the Laplace matrix L is added with the approximate frequency of the node of a generatorFThe general shape and the position of the curve of the frequency modal component corresponding to a certain characteristic value are consistent, or the approximate frequency of a generator node existsΔωx(s) and the node weighted Laplace matrix LFFrequency modal component delta omega corresponding to k-th characteristic valuexkThe general shape and position of the curve(s) are identical, but Δ ωxk(s) weighting the Laplace matrix L at all generator nodesFFrequency modal component delta omega corresponding to k-th characteristic valueikIf the amplitude of the curve(s) is not the maximum, the curve is not processed.
In the step 4), the following inertia-damping-integral structure is established and expressed as:
Figure BDA0002628531580000051
in the formula, Ju、DuAnd KuRespectively an inertia parameter, a damping parameter and an integral parameter of an inertia-damping-integral structure; u represents an inertia-damping-integral structure;
after the generators are converted into inertia-damping-integral structures under different frequency modal components, the modal parameters are different, and the k-th frequency modal component delta omega of the leading key track is aimed atk(s) obtaining the inertia-damping-integral structure parameters of each generator by adopting the following iterative algorithm:
4.1) setting the inertia parameters, the damping parameters and the initial values of the integral parameters of the inertia-damping-integral structure of each generator, and calculating an initial parameter matrix and an initial inertia-damping-integral structure matrix:
Figure BDA0002628531580000052
Figure BDA0002628531580000053
wherein the content of the first and second substances,
Figure BDA0002628531580000054
and
Figure BDA0002628531580000055
respectively representing initial values of an inertia parameter, a damping parameter and an integral parameter of the inertia-damping-integral structure;
Figure BDA0002628531580000056
respectively representing an initial inertia parameter matrix, an initial damping parameter matrix and an initial integral parameter matrix of the generator,
Figure BDA0002628531580000061
representing an initial inertia-damping-integral structure matrix of the generator;
and then calculating an initial auxiliary inertia-damping-integral structure:
Figure BDA0002628531580000062
Figure BDA0002628531580000063
wherein the content of the first and second substances,
Figure BDA0002628531580000064
representing the initial inertia-damping-integral structure matrix of the generator under the capacity of the generator,
Figure BDA0002628531580000065
the initial auxiliary inertia-damping-integral structure represents the k frequency modal component of the generator under the capacity of the generator;
4.2) making the circulation variable r equal to 1, wherein r represents the circulation variable;
4.3) at the r-th iteration, obtaining a frequency track according to the following formula
Figure BDA0002628531580000066
Figure BDA0002628531580000067
Figure BDA0002628531580000068
Figure BDA0002628531580000069
Wherein the content of the first and second substances,
Figure BDA00026285315800000610
the auxiliary inertia-damping-integral structure represents the kth frequency modal component of the generator under the capacity of the generator per se in the (r-1) th iteration;
Figure BDA00026285315800000611
representing a frequency track corresponding to a k frequency modal component of the (r-1) th iteration;
4.4) establishing the following optimization objective function:
Figure BDA00026285315800000612
s.t.
Figure BDA00026285315800000613
Figure BDA00026285315800000614
Figure BDA00026285315800000615
wherein t is0、tfRespectively selecting an initial time and a terminal time of a time period; delta Pk(s) is the power trajectory, Δ P ', calculated from the generator's frequency-active power transfer function matrix G(s) 'k(s) is inertia-damping-integral structure matrix of generator
Figure BDA00026285315800000616
Calculating a power track, wherein the time domain variation of the power is used as the power track; g'k(s) representing an inertia-damping-integral structure matrix of the generator at the r-1 th iteration; power trace Δ Pk(s) obtaining delta P by inverse Ralstonian transformationk(t), Power Trace Δ P'k(s) is subjected to inverse Ralstonia transformation to obtain delta P'k(t)；
Solving the optimized objective function by least square method to obtain parameters
Figure BDA00026285315800000617
And
Figure BDA00026285315800000618
obtaining inertia-damping-integral structure matrix
Figure BDA00026285315800000619
And obtaining an auxiliary inertia-damping-integral structure of the r iteration according to the following formula:
Figure BDA00026285315800000620
Figure BDA0002628531580000071
wherein the content of the first and second substances,
Figure BDA0002628531580000072
the auxiliary inertia-damping-integral structure represents the k frequency modal component of the capacity of the generator under the r iteration;
4.5) making r ═ r +1, and circularly performing the steps 4.2) to 4.4) until the parameters are converged (if the parameter variation after iteration is less than 0.1%), and obtaining the auxiliary inertia-damping-integral structure according to the last iteration
Figure BDA0002628531580000073
The following formula is used to calculate and obtain the approximationKey trajectory
Figure BDA0002628531580000074
Figure BDA0002628531580000075
Figure BDA0002628531580000076
Wherein, Ck[x,y]Is a coefficient matrix CkThe elements of the x-th row and the y-th column,
Figure BDA0002628531580000077
is a matrix
Figure BDA0002628531580000078
The x-th row and y-n-th column, PuyRepresenting the power disturbance amplitude of the y node;
Figure BDA0002628531580000079
Figure BDA00026285315800000710
respectively representing auxiliary inertia-damping-integral structure
Figure BDA00026285315800000711
Inertia parameter, damping parameter, integral parameter.
In the step 5), decomposing and normalizing the approximate key trajectory parameters, specifically:
Figure BDA00026285315800000712
when y is less than or equal to n,
Figure BDA00026285315800000713
Figure BDA00026285315800000714
when n is<When y is less than or equal to n + m,
Figure BDA00026285315800000715
Figure BDA00026285315800000716
wherein n is 2 and Dωk、KωkRespectively representing effective modal inertia, effective modal damping and effective modal integral.
Visible approximate Critical Path available Jωk、Dωk、KωkThe three parameters are respectively effective modal inertia, effective modal damping and effective modal integral.
In the step 6), the method specifically comprises the following steps:
the frequency intensity parameters comprise comprehensive inertia and frequency maximum deviation rate, and are obtained by adopting the following formula:
Figure BDA00026285315800000717
Figure BDA00026285315800000718
wherein ζ ═ Dωk/2/(JωkKωk)1/2Is damping ratio, e is a natural constant parameter, ntExpressed as the number of segments that segment the time from the occurrence of the disturbance to the occurrence of the maximum shift in frequency during the calculation of the integrated inertia.
The comprehensive inertia can reflect the parameter of the average change rate of the frequency, the maximum frequency deviation rate can reflect the parameter of the lowest point of the frequency, and the two parameters can evaluate the frequency intensity of a multi-machine power system.
The invention has the beneficial effects that:
the invention can approximate the frequency response of various generators in the power system by using a very simple structure of an inertia-damping-integral structure, and has higher precision because the frequency track is considered in the process of obtaining parameters; based on the inertia-damping-integral structure establishment, namely the maximum frequency offset rate and the comprehensive inertia, the lowest point characteristic of the frequency distribution characteristic is quantitatively considered, the characteristics of the lowest point of the frequency, the average change rate and the like can be better obtained, and more accurate frequency intensity parameters of the power system of the weak synchronization power grid are obtained.
Drawings
FIG. 1 is a schematic flow diagram of the process of the present invention.
Fig. 2 is a schematic diagram of a three-machine system in simulation verification according to an embodiment of the present invention.
FIG. 3 is a diagram of a steam turbine governor system model in simulation verification according to an embodiment of the present invention.
FIG. 4 is a model diagram of a water turbine speed regulator system in simulation verification according to an embodiment of the invention.
Fig. 5 is a diagram of an inverter model in simulation verification according to an embodiment of the present invention.
FIG. 6 is a diagram illustrating a comparison between a simulated trajectory and a trajectory similar to an inertia-damping-integral structure in simulation verification according to an embodiment of the present invention.
Fig. 6(a) is a comparison graph of a simulation trajectory of the node 3 and an approximate trajectory of the inertia-damping-integral structure under the disturbance of the node 8 in the simulation verification according to the embodiment of the present invention.
Fig. 6(b) is a comparison graph of a simulation trajectory of the node 2 and an approximate trajectory of the inertia-damping-integral structure under the disturbance of the node 2 in the simulation verification of the embodiment of the present invention.
FIG. 7 is an iterative flow diagram for solving an optimization problem.
Detailed Description
The invention is described in further detail below with reference to the drawings and the specific embodiments.
As shown in fig. 1, the method of the present invention is used for processing, and the generator includes a synchronous machine, power electronic equipment and the like in a multi-machine power system. Eliminating constant power nodes such as load nodes and passive nodes to obtain a compressed Laplacian matrix LrAnd equivalent disturbance Deltau uE(s). Binding of LrObtaining equivalent disturbance delta u with the frequency-active transfer function matrix G(s) of the generatorE(s) and generatorsRelation of frequency response Δ ω(s) of the node. Decomposing delta omega(s) into the sum of a plurality of modal components to obtain the approximate frequency of the generator node
Figure BDA0002628531580000081
The time domain variation of the frequency is taken as a frequency track, the position of a key node is judged according to the disturbance of different nodes, and the frequency track of the key node is selected as a key track delta omegack(s). And then, converting each generator into an inertia-damping-integral structure by adopting an iterative algorithm aiming at the kth frequency modal component of the leading key track to obtain an approximate key track. And decomposing and normalizing the approximate key track parameters to obtain three parameters of effective modal inertia, effective modal damping and effective modal integral. And finally, obtaining frequency intensity parameters by utilizing effective modal inertia, effective modal damping and effective modal integration processing.
The specific embodiment of the invention is as follows:
a three-machine power system is built in Matlab/Simulink software, as shown in FIG. 2. In the figure, the capacities of the synchronous machines G1 and G2 at the nodes 1 and 2 are 8000MVA (a single generator with the capacity larger than that is not available in practice, but a plurality of generators connected at the same node can be regarded as one generator) and 100MVA respectively, and the prime movers are a steam turbine and a water turbine respectively. The power electronics equipment at node 3 has an inverter capacity of 2000MVA with virtual inertia control. The nodes 4-6 are network nodes. The nodes 7-9 are load nodes, and the load is a constant power load. The network nodes and the load nodes are collectively referred to as constant power nodes. The line purity is expressed in table 1 when the capacity of G2 is used as a capacity reference value. In a steady state, the voltage of each node is converted into 1, and the phase angle difference of each line is converted into 0.
Table 1 example line reactance values in simulation verification
X14 0.003 X25 0.15 X36 0.012
X47 0.003 X48 0.003 X57 0.03
X59 0.03 X68 0.012 X69 0.012
Using the capacity of G2 as a capacity reference value, F is ═ F1,F2,F3]T＝[80,1,20]T。
G1 frequency-active transfer function G1(s) is:
Figure BDA0002628531580000091
wherein G isTS(s) is the transfer function, modulo, of the G1 governor-turbine system (simply governor system)The pattern is shown in figure 3. The parameters per unit of the rated capacity are as follows: moment of inertia J 18; damping coefficient D 12; the rate of decrease R is 0.05; time constant T of speed regulatorG0.2 s; time constant T of steam inlet chamberCH0.3 s; time constant T of reheaterRH10 s; high pressure cylinder power ratio FHP＝0.3。
G2 frequency-active transfer function G2(s) is:
Figure BDA0002628531580000092
wherein G isTH(s) is the transfer function of the G2 governor system, the model being shown in FIG. 4. The parameters per unit of the self-rated capacity are as follows: moment of inertia J 28; damping coefficient D 22; permanent rate of decrease RP0.04; temporary rate of decrease RT0.25; reset time TR5 s; auxiliary servo time constant TP0.04 s; servo gain Ks is 4; main servo time constant TGH0.2 s; water start time Tw＝1s。
Inverter model as shown in fig. 5, frequency-active transfer function G3(s) is:
Figure BDA0002628531580000101
the values of the parameters are shown in table 1.
Table 1 example simulation verification of parameter values of part of inverter variables
Parameter(s) Value taking
Active power PPED0Reference value 0.3
Reactive power QPEDReference value 0
Differential filter time constant T1 0.05
Frequency modulation control filter time constant T2 0.02
Virtual inertia coefficient J PED 8
Power outer loop PI1 link parameter K P1 2
Power outer loop PI1 link parameter K I1 10
Power outer loop PI2 link parameter K P2 2
Power outer loop PI2 link parameter K I2 10
Current inner loop PI3 link parameter K P3 2
Current inner loop PI3 link parameter K I3 10
Current inner loop PI4 link parameter K P4 2
Current inner loop PI4 link parameter K I4 10
Phase-locked loop PI link parameter KPLLP 60
Phase-locked loop PI link parameter KPLLI 2000
LCL filter inductance L1 0.05
LCL filter inductance L2 0.01
LCL filter inductance C 0.05
Filter inductance branch resistance R of LCL filter C 0
Power measurement filter time constant 0
Time constant of voltage measurement filter 0.02
The method of the invention is adopted to eliminate the constant power nodeAnd 4-9, only reserving the generator nodes 1-3 to obtain a compressed Laplace matrix Lr. Combining the frequency-active transfer function matrix G(s) diag G of each generator1(s),G2(s),G3(s) }, obtaining the relation between disturbance and frequency response:
Figure BDA0002628531580000102
weighted Laplace matrix L in the systemF＝F-1/2LrF-1/2There are three eigenvalues, corresponding to three frequency modal components. The participation factors of the generators in these modes are shown in table 2.
TABLE 2 Generator participation factors
Figure BDA0002628531580000103
Figure BDA0002628531580000111
When 700MW power disturbance occurs at the node 8, the track of the first frequency modal component at the node 3 is selected as a key track. As shown in fig. 7, for the first modal component leading the critical trajectory, the generators are converted into inertia-damping-integral structures within a time range within 4s after disturbance is selected, and an approximate critical trajectory is obtained. And when 100MW power disturbance occurs at the node 2, selecting the track of the third frequency modal component at the node 2 as a key track. And (3) selecting a time range within 4s after disturbance to convert each generator into an inertia-damping-integral structure aiming at the third modal component leading the key track through an iterative algorithm, so as to obtain an approximate key track. The calculation results for these two key trajectories are shown in table 3, respectively.
TABLE 3 inertia-damping-integral structural parameters of each generator
Figure BDA0002628531580000112
By adopting the method of the invention, the inertia parameter, the damping parameter and the integral parameter in the auxiliary inertia-damping-integral structure of the two key tracks are respectively obtained as follows:
Figure BDA0002628531580000113
and
Figure BDA0002628531580000114
Figure BDA0002628531580000115
and normalizing the auxiliary inertia, damping and integral parameters of the two key tracks to obtain the effective modal parameters of the two key tracks which are J respectivelyω1＝97.31、Dω1＝73.84、Kω118.46 and Jω3＝8.06、Dω3＝2.65、Kω3＝1887.79。
According to the method of the invention, the frequency intensity parameter is obtained according to the effective modal parameter. For the first frequency modal component of the key trajectory of the node 3, the calculation shows that the lowest point of the frequency occurs 2-3 s after disturbance, and n is taken when the comprehensive inertia is calculatedtI.e. the average rate of frequency change is calculated with a time of about several hundred milliseconds after the perturbation. For the third frequency modal component of the node 2 critical trajectory, the period is about 500ms of frequency oscillation, and the low point time is about 125ms after the disturbance. To ensure the precision of the parameters, take n t2. The frequency intensity parameter comprehensive inertia and the frequency maximum deviation rate calculated by the method are respectively Jz1＝121.95、 α1105.82 and Jz3＝8.13、α3125.29. Calculating the average frequency change rate of the two key tracks to be-0.41 Hz/s and-6.15 Hz/s respectively according to the parameters; the lowest points of the frequency are-0.47 Hz and-0.40 Hz respectively. And finally, verifying the effectiveness of the analysis in time domain simulation. The frequency trajectory obtained by the simulation is compared with the key trajectory approximated by the inertia-damping-integration structure, as shown in fig. 7. Composed of fig. 6(a)It can be seen that under the disturbance of the node 8, the frequency locus of the node 3 is dominant in the common mode (the first frequency mode component), and almost no differential mode component exists. The key track approximately obtained by the inertia-damping-integral structure is almost consistent with the track of the node 3 in 4s after disturbance. The time of the lowest point is about 2.4s after disturbance, and the lowest point obtained by the parameters is the same as the lowest point of the track of the node 3, namely-0.47 Hz. The average frequency change rate (600 ms after disturbance) -0.41Hz/s obtained by the parameters is about 2 percent different from the average frequency change rate-0.42 Hz/s of the node 3 in the same time period by using J aloneω1The calculated frequency change rate is-0.51 Hz/s, and has a larger difference with the former two. The significance of using the composite inertia can be seen.
As can be seen from fig. 6(b), the node frequency exhibits a large differential mode component under the disturbance at the node 2. The trajectory approximated by the inertia-damping-integration structure is substantially identical to the trajectory of node 2 during the first period, after which the latter trajectory is entirely lower than the former. This is because the locus of the node 2 contains a certain common mode component in addition to the differential mode component, and only the dominant frequency mode, i.e., the differential mode component (the third frequency mode component), is analyzed to facilitate the parameter establishment. The relative error between the lowest point-0.40 Hz of the parameter calculation and the lowest point-0.41 Hz of the track of the node 2 is 2.4 percent. The average rate of change of frequency calculated for the parameters (50 ms after disturbance) -6.15Hz/s differs by about 9% from the average rate of change of frequency of node 2 at the same time period-5.65 Hz/s. Due to the small damping of this mode, J is usedω3The obtained frequency change rate-6.20 Hz/s is not much different from the former two.
The example of the invention proves the effectiveness of the approximation method of the lowest frequency point of the multi-machine power system and the frequency intensity evaluation algorithm, and the established parameters can evaluate the frequency intensity of the average frequency change rate, the lowest point and the like.
The present invention is limited only by the following modifications and variations, which fall within the spirit of the invention and the scope of the appended claims.

Claims (7)

1. A frequency intensity parameter measuring method of a multi-machine power system is characterized by comprising the following steps:
1) in a multi-machine power system comprising generators, a compressed Laplace matrix L of the generator nodes is obtained by eliminating parts of constant power nodes of load nodes and passive nodes from the Laplace matrix of the multi-machine power systemrAnd equivalent disturbance Deltau uE(s); combining the compressed Laplace matrix LrObtaining the equivalent disturbance delta u of the generator node with the frequency-active transfer function matrix G(s) of the generatorE(s) a relationship with frequency Δ ω(s);
2) processing and obtaining a plurality of frequency modal components delta omega under the generator node according to the relation between the equivalent disturbance and the frequency of the generator nodek(s) to obtain an approximate frequency of the generator node
Figure FDA0002628531570000011
3) Selecting a frequency track of a node of a multi-machine power system under disturbance as a key track delta omegack(s) and determining frequency modal components dominated by the key trajectory;
4) converting each generator into an inertia-damping-integral structure aiming at the k-th frequency modal component dominated by the key track through an iterative algorithm to obtain an approximate key track;
5) decomposing and normalizing the approximate key track parameters to obtain three parameters of effective modal inertia, effective modal damping and effective modal integral;
6) and obtaining frequency intensity parameters by utilizing effective modal inertia, effective modal damping and effective modal integration.
2. The method as claimed in claim 1, wherein the method further comprises: in the step 1), the multi-machine power system has n + m nodes in total, wherein the first n generator nodes, m load nodes or constant power nodes of passive nodes;
1.1) establishing a Laplace matrix L of a multi-machine power system, wherein diagonal elements and non-diagonal elements are respectively as follows:
L[i,i]＝Vi∑j∈iBijVjcosθij0
L[i,j]＝-ViVjBijcosθij0
wherein, L [ i, j]Elements representing the ith row and the jth column of the Laplace matrix L; j belongs to i and represents that a node j is directly connected with the node i through a line, i and j represent ordinal numbers of the nodes in the multi-machine power system, and i, j belongs to {1, 2., n + m }; vi、VjThe voltage amplitudes of the nodes i and j are respectively; thetaij0The steady state value of the phase angle difference between the node i and the node j is obtained; b isijElements in the node susceptance matrix B;
dividing the Laplace matrix L into 4 sub-matrixes L according to the relation that the elements in the Laplace matrix L belong to generator nodes or constant power nodes11、L12、L21、L22The submatrix L11Is composed of the first n rows and the first n columns of a Laplace matrix L, and a sub-matrix L12Is composed of the first n rows (n +1) to (n + m) th columns of the Laplace matrix L, and the sub-matrix L21Is composed of the first n columns of the (n +1) th to (n + m) th rows of the Laplace matrix L, and the sub-matrix L22Is composed of the (n +1) th column to the (n + m) th column to the (n +1) th column to the (n + m) th column of the Laplace matrix L;
further, a compressed Laplace matrix L is obtained according to the following formularComprises the following steps:
Figure FDA0002628531570000021
1.2) Power disturbance of each node is Delauui(s)，Δui(s)＝-PuiS, s denotes the Laplace operator, PuiRepresenting the power disturbance amplitude of the ith node,
by disturbance of power Δ uiThe first n components and the last m components of(s) respectively form disturbance vectors delta u of a generator node and a constant power node1(s) and. DELTA.u2(s) determining the disturbance vector Δ u of the constant power node2(s) disturbance vector Deltau superimposed to a Generator node1(s) obtaining the equivalent disturbance of the generator node as:
Figure FDA0002628531570000022
wherein, Δ uE(s) represents an equivalent disturbance of the generator node;
1.3) per unit of each generator by using the same power basic value, wherein the frequency-active transfer function of each generator node is Gi(s), i belongs to {1, 2.., n }, and the frequency and the phase angle of each generator node are delta omegai(s) and Δ θi(s) wherein Δ θi(s)＝ω0Δωi(s)/s，ω0Is a frequency base value; the frequency delta omega of each generator node is measuredi(s) form a column vector Δ ω(s) that defines the phase angle Δ θ of each generator nodei(s) also constitute a column vector Δ θ(s) with the frequency-active transfer function G of each generator nodei(s) establishing a diagonal matrix G(s) for the diagonal elements, G(s) diag { G {(s) }i(s), the off-diagonal elements in the diagonal matrix g(s) are zero, and the relationship between the equivalent disturbance and the frequency of the following generator nodes is established:
Figure FDA0002628531570000023
3. the method as claimed in claim 1, wherein the method further comprises:
in the step 2), the frequency of each node is decomposed into the sum of a plurality of modal components based on a perturbation theory, and the method comprises the following steps:
2.1) selecting one generator as a reference generator, the capacity of the reference generator being a reference capacity, according to the ratio F of the capacity of each generator to the capacity of the reference generatoriObtaining a capacity scaling matrix F, F ═ diag { F }i}; and then processing to obtain a frequency-active transfer function matrix g(s) after each generator node is equivalent to the capacity of the generator node:
g(s)＝F-1G(s)＝diag{gi(s)}
wherein g(s) represents a frequency-active transfer function matrix after each generator node is equivalent to the capacity of the generator node, g(s)i(s) is the frequency-active transfer function of each generator under its own capacity;
the relation between the equivalent disturbance of the generator node and the frequency is transformed into:
F1/2(s)F1/2Δω(s)＝ΔuE(s)
(s)＝Ing(s)+ω0LF/s
wherein, InIs an n-order unit array, LFIs a weighted Laplace matrix, LF＝F-1/2LrF-1/2Weighted Laplace matrix LFThe eigenvalue and eigenvector of (a) are each lambda1,...,λnAnd U1,...,UnAnd satisfy lambda1<...<λn，λ10; (s) represents a transfer function matrix;
2.2) reconstruction of the auxiliary transfer function matrix
Figure FDA0002628531570000036
Figure FDA0002628531570000037
Wherein the content of the first and second substances,
Figure FDA00026285315700000319
representing a weighted Laplace matrix LFThe first eigenvalue corresponds to the auxiliary frequency-active transfer function, which is formed by the weighted Laplace matrix LFParticipation factor p of first characteristic valuei1For gi(s) the weighted sum yields:
Figure FDA0002628531570000038
then the auxiliary transfer function matrix
Figure FDA0002628531570000039
The eigenvalues and eigenvectors of (a) are:
Figure FDA00026285315700000310
to Ψk＝Uk，k∈{1,2,...,n}
Wherein, UkRepresenting a weighted Laplace matrix LFThe kth feature vector of (1); lambda [ alpha ]kRepresenting a weighted Laplace matrix LFThe kth eigenvalue of (a);
2.3) treating the transfer function matrix(s) as an auxiliary transfer function matrix based on the principle of matrix perturbation
Figure FDA00026285315700000311
Obtaining eigenvalues and eigenvectors of the transfer function matrix(s):
Figure FDA0002628531570000031
Figure FDA00026285315700000312
Figure FDA0002628531570000032
wherein p isikRepresenting a weighted Laplace matrix LFThe participation factor of the kth characteristic value;
Figure FDA00026285315700000313
representing a weighted Laplace matrix LFThe kth eigenvalue corresponds to the auxiliary frequency-active transfer function,
Figure FDA00026285315700000314
is based on a weighted Laplace matrix LFParticipation factor p of k-th characteristic valueikFor gi(s) weighting the resulting transfer function; o () represents the same order infinitesimal; | | represents a matrix norm;
2.4) obtaining a plurality of frequency modal components delta omega under the generator node according to the eigenvalue and the eigenvector of the transfer function matrix(s)k(s) and synthesizing into an approximate frequency of the generator node
Figure FDA00026285315700000315
Figure FDA0002628531570000033
Figure FDA0002628531570000034
Figure FDA0002628531570000035
Wherein the content of the first and second substances,
Figure FDA00026285315700000316
an approximate frequency vector representing the generator node,
Figure FDA00026285315700000317
by approximate frequency of individual generator nodes
Figure FDA00026285315700000318
Composition, i ∈ {1,2,..., n }; Δ ωk(s) represents the generator node down-weighted Laplace matrix LFThe frequency modal component vector, Δ ω, corresponding to the kth eigenvaluek(s) weighting the Laplace matrix L by each generator nodeFFrequency modal component delta omega corresponding to k-th characteristic valueik(s) groupA member, i ∈ {1,2,..., n }; ckIs a weighted Laplace matrix LFA coefficient matrix of the frequency modal component corresponding to the kth eigenvalue; hk(s) is a weighted Laplace matrix LFAnd the transfer function of the frequency modal component corresponding to the k-th characteristic value.
4. The method as claimed in claim 1, wherein the method further comprises: in the step 3), the method specifically comprises the following steps:
the time domain variation of the frequency is taken as a frequency track, and the frequency track of the key node is taken as a key track delta omegack(s), the key node is obtained by processing according to the following modes:
under the disturbance of the y node, if the approximate frequency of the x generator node is delta omegax(s) curve and weighted Laplace matrix L in the nodeFFrequency modal component delta omega corresponding to k-th characteristic valuexk(s) has a uniform overall shape and position, and Δ ωxk(s) weighting the Laplace matrix L at all generator nodesFFrequency modal component delta omega corresponding to k-th characteristic valueik(s) is the maximum amplitude in the curve, then Δ ω is calculatedxk(s) as the critical trajectory Δ ωck(s) consider the weighted Laplace matrix LFThe frequency modal component corresponding to the kth characteristic value dominates the key track;
if under the disturbance of the y node, the approximate frequency of a generator node is not consistent with the weighted Laplace matrix L of the nodeFThe general shape and the position of the curve of the frequency modal component corresponding to a certain characteristic value are consistent, or the approximate frequency delta omega of a generator node existsx(s) and the node weighted Laplace matrix LFFrequency modal component delta omega corresponding to k-th characteristic valuexkThe general shape and position of the curve(s) are identical, but Δ ωxk(s) weighting the Laplace matrix L at all generator nodesFFrequency modal component delta omega corresponding to k-th characteristic valueikIf the amplitude of the curve(s) is not the maximum, the curve is not processed.
5. The method as claimed in claim 4, wherein the method further comprises: in the step 4), the following inertia-damping-integral structure is established and expressed as:
Figure FDA0002628531570000041
in the formula, Ju、DuAnd KuInertia parameters, damping parameters and integral parameters of an inertia-damping-integral structure are respectively; u represents an inertia-damping-integral structure;
after the generators are converted into inertia-damping-integral structures under different frequency modal components, the modal parameters are different, and the k-th frequency modal component delta omega of the leading key track is aimed atk(s) obtaining the inertia-damping-integral structure parameters of each generator by adopting the following iterative algorithm:
4.1) setting the inertia parameters, the damping parameters and the initial values of the integral parameters of the inertia-damping-integral structure of each generator, and calculating an initial parameter matrix and an initial inertia-damping-integral structure matrix:
Figure FDA0002628531570000042
Figure FDA0002628531570000043
wherein the content of the first and second substances,
Figure FDA0002628531570000051
and
Figure FDA0002628531570000052
respectively representing initial values of an inertia parameter, a damping parameter and an integral parameter of the inertia-damping-integral structure;
Figure FDA0002628531570000053
respectively representing an initial inertia parameter matrix, an initial damping parameter matrix and an initial integral parameter matrix of the generator,
Figure FDA0002628531570000054
representing an initial inertia-damping-integral structure matrix of the generator;
and then calculating an initial auxiliary inertia-damping-integral structure:
Figure FDA0002628531570000055
Figure FDA0002628531570000056
wherein the content of the first and second substances,
Figure FDA0002628531570000057
representing the initial inertia-damping-integral structure matrix of the generator under the capacity of the generator,
Figure FDA0002628531570000058
the initial auxiliary inertia-damping-integral structure represents the k-th frequency modal component of the generator under the capacity of the generator;
4.2) making a circulation variable r equal to 1;
4.3) at the r-th iteration, obtaining a frequency track according to the following formula
Figure FDA0002628531570000059
Figure FDA00026285315700000510
Figure FDA00026285315700000511
Figure FDA00026285315700000512
Wherein the content of the first and second substances,
Figure FDA00026285315700000513
the auxiliary inertia-damping-integral structure represents the kth frequency modal component of the generator under the capacity of the generator per se in the (r-1) th iteration;
Figure FDA00026285315700000514
representing a frequency track corresponding to a k frequency modal component of the (r-1) th iteration;
4.4) establishing the following optimization objective function:
Figure FDA00026285315700000515
Figure FDA00026285315700000516
Figure FDA00026285315700000517
Figure FDA00026285315700000518
wherein t is0、tfRespectively selecting an initial time and a terminal time of a time period; delta Pk(s) is the power trajectory, Δ P ', calculated from the generator's frequency-active power transfer function matrix G(s) 'k(s) is inertia-damping-integral structure matrix of generator
Figure FDA00026285315700000519
A calculated power trajectory; g'k(s) representing an inertia-damping-integral structure matrix of the generator at the r-1 th iteration; power trace Δ Pk(s) obtaining delta P by inverse Ralstonian transformationk(t), Power Trace Δ P'k(s) is subjected to inverse Ralstonia transformation to obtain delta P'k(t)；
Solving the optimized objective function by least square method to obtain parameters
Figure FDA00026285315700000520
And
Figure FDA00026285315700000521
thereby obtaining an inertia-damping-integral structure matrix
Figure FDA00026285315700000522
And obtaining an auxiliary inertia-damping-integral structure of the r iteration according to the following formula:
Figure FDA0002628531570000063
Figure FDA0002628531570000064
wherein the content of the first and second substances,
Figure FDA0002628531570000065
the auxiliary inertia-damping-integral structure represents the k frequency modal component of the capacity of the generator under the r iteration;
4.5) making r ═ r +1, and circularly performing the steps 4.2) to 4.4) until the parameters are converged, and obtaining an auxiliary inertia-damping-integral structure according to the last iteration
Figure FDA0002628531570000066
By usingCalculating to obtain an approximate key track by the following formula
Figure FDA0002628531570000067
Figure FDA0002628531570000061
Figure FDA0002628531570000068
Wherein, Ck[x,y]Is a coefficient matrix CkThe elements of the x-th row and the y-th column,
Figure FDA0002628531570000069
is a matrix
Figure FDA00026285315700000610
The x-th row and y-n-th column, PuyRepresenting the power disturbance amplitude of the y node;
Figure FDA00026285315700000611
Figure FDA00026285315700000612
respectively representing auxiliary inertia-damping-integral structure
Figure FDA00026285315700000613
Inertia parameter, damping parameter, integral parameter.
6. The method as claimed in claim 5, wherein the method further comprises: in the step 5), decomposing and normalizing the approximate key trajectory parameters, specifically:
Figure FDA0002628531570000062
when y is less than or equal to n,
Figure FDA00026285315700000614
Figure FDA00026285315700000615
when n is<When y is less than or equal to n + m,
Figure FDA00026285315700000616
Figure FDA00026285315700000617
wherein n is 2 and Dωk、KωkRespectively representing effective modal inertia, effective modal damping and effective modal integral.
7. The method as claimed in claim 1, wherein the method further comprises: in the step 6), the method specifically comprises the following steps:
the frequency intensity parameters comprise comprehensive inertia coefficients and frequency maximum deviation rates, and are obtained by adopting the following formula:
Figure FDA00026285315700000618
Figure FDA0002628531570000071
wherein ζ ═ Dωk/2/(JωkKωk)1/2Is damping ratio, e is a natural constant parameter, ntExpressed as the number of segments that segment the time from the occurrence of the disturbance to the occurrence of the maximum shift in frequency during the synthetic inertia calculation.
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