CN111159908A - Method for optimizing node rotational inertia of multi-machine power system based on mode inertia - Google Patents

Method for optimizing node rotational inertia of multi-machine power system based on mode inertia Download PDF

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CN111159908A
CN111159908A CN201911418165.XA CN201911418165A CN111159908A CN 111159908 A CN111159908 A CN 111159908A CN 201911418165 A CN201911418165 A CN 201911418165A CN 111159908 A CN111159908 A CN 111159908A
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generator
inertia
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mode
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江叶峰
高辉胜
崔占飞
葛亚明
王大江
徐伟
辛焕海
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Zhejiang University ZJU
State Grid Corp of China SGCC
State Grid Jiangsu Electric Power Co Ltd
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Zhejiang University ZJU
State Grid Corp of China SGCC
State Grid Jiangsu Electric Power Co Ltd
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Abstract

The invention discloses a method for optimizing the node rotational inertia of a multi-machine power system based on mode inertia. Obtaining a closed loop transfer function from power disturbance to frequency of generator nodes and network nodes in a multi-machine power system by a frequency modeling method; respectively injecting power step disturbance to the nodes to obtain frequency response of the nodes, and compressing the network nodes to form a compressed electric sodium array during processing; scaling the compressed electric nano array by using a rotational inertia matrix of the generator to obtain a scaled electric nano array; carrying out characteristic value decomposition on the scaling electric nano array, and carrying out mode decomposition on the disturbed node frequency response according to the decomposition to obtain a mode component of the frequency response; and optimizing the node rotational inertia of the multi-machine power system by using the mode inertia. The method can analyze the frequency intensity of any local (node) in the network by using the mode inertia, thereby optimizing the node rotational inertia of the multi-machine power system and improving the operation stability of the multi-machine power system.

Description

Method for optimizing node rotational inertia of multi-machine power system based on mode inertia
Technical Field
The invention relates to an optimization method of a multi-machine power system, in particular to an optimization method of node rotational inertia of the multi-machine power system based on mode inertia.
Background
Renewable energy penetration rate in modern power systems is continuously increased, and typical control strategies of renewable energy (such as control based on a phase-locked loop) have no equivalent inertia, so that the inertia of the power system is remarkably reduced. This causes the system frequency fluctuation to become large, and poses a challenge to the frequency stability of the system. The frequency intensity of the power system is evaluated to identify whether the system needs additional frequency modulation measures. Therefore, the evaluation of the frequency intensity of the power system has attracted a wide range of attention.
The existing frequency intensity evaluation index has the total inertia of the system and the system frequency H2、Λ2Norm, etc. The indexes mainly aim at the evaluation of the overall frequency intensity of the system, and at present, there are few indexes for evaluating the local (a certain node) frequency intensity of the system. Some local frequency problems may not be found by evaluating only the overall frequency strength of the system. For example, consider a small capacity diesel generator connected to a high inertia ac power grid by a long transmission line. Because the external network has a large inertia, the overall frequency strength of this power system is sufficiently strong. But due to the longer transmission lineThe node frequency of the port of the diesel generator may fluctuate greatly under power disturbance, and the frequency characteristic cannot be represented by overall frequency intensity indexes such as total inertia of the system. Therefore, how to accurately obtain the frequency strength of any node in the multi-machine power system and then accurately optimize the frequency strength is still a challenge faced by the current power system.
Disclosure of Invention
The invention provides a method for optimizing the rotational inertia of nodes of a multi-machine power system based on mode inertia, which aims to evaluate the frequency intensity of any node of the multi-machine power system and further optimize the rotational inertia in the power system.
The technical scheme of the invention comprises the following steps:
1) obtaining a closed-loop transfer function from power disturbance to frequency of generator nodes and network nodes in a multi-machine power system through a frequency modeling method, wherein a network susceptance matrix B is divided into four areas, specifically B, according to the nodes as the generator nodes or the network nodes in the closed-loop transfer functionGG、BGL、BLG、BLLIn which B isGG、BGL、BLG、BLLRespectively representing four areas of the upper left corner, the upper right corner, the lower sitting corner and the lower right corner of the network susceptance matrix B, wherein the subscript G corresponds to a generator node, and the subscript L corresponds to a network node;
2) respectively injecting power step disturbance into the generator node and the network node to obtain the frequency response of the node, and compressing the network node to form a compressed sodium susceptance array B during processingr；
3) Rotational inertia matrix J pair compression susceptance array B using generatorrZooming to obtain a zooming susceptance array Bs＝J-1/2BrJ-1/2；
4) For scaling electric nano-array BsCarrying out eigenvalue decomposition, and carrying out mode decomposition on the disturbed node frequency response according to the decomposition to obtain n mode components of the frequency response, wherein n is the number of generator nodes in the multi-machine power system, so as to obtain the mode inertia of each mode of each node; the reciprocal of the n mode component front coefficients is taken as the mode inertia.
5) And optimizing the node rotational inertia of the multi-machine power system by using the mode inertia.
The multi-machine power system comprises n generator nodes and m + a network nodes, wherein the network nodes are divided into m load nodes and a passive nodes, the generators connected at the same generator node are equivalent to one generator, and the n generator nodes share n generators.
In the step 1), the closed-loop transfer function and the network susceptance matrix of each node power disturbance to frequency in the multi-machine power system are as follows:
Figure BDA0002351711250000021
Figure BDA0002351711250000022
where s represents the Laplace operator, Δ uG(s)、ΔuL(s) power disturbance vectors, Δ ω, representing generator nodes and network nodes, respectivelyG(s)、ΔωL(s) frequency response vectors representing the generator node and the network node, respectively; j is a rotational inertia matrix taking the rotational inertia of n generators as a diagonal element, and J is diag (J)i)，JiRepresenting the moment of inertia of the ith generator; all generators in a multimachine power system are homogeneous, JG(s) represents a transfer function matrix from the frequency of all generators to the active output, JiG(s) represents the transfer function from the frequency of the ith generator to the active output, and G(s) is the reference transfer function from the frequency of the generator to the active output; omega0Represents a frequency reference value; b denotes a network susceptance matrix, BGG、BGL、BLG、BLLAnd four areas of the upper left corner, the upper right corner, the lower left corner and the lower right corner of the network susceptance matrix B are respectively shown, the blocks are generator nodes or network nodes based on the nodes, the subscript G corresponds to the generator nodes, and the subscript L corresponds to the network nodes.
In the step 2), power step disturbance is injected into generator nodes in the multi-machine power system, and the networkNode perturbation is 0, i.e. Δ uG(s)＝PGS, wherein PG＝[P1,P2,…,Pn]T，PiRepresenting the amplitude of the power step disturbance of the ith generator node, wherein i belongs to {1,2, …, n }; solving and obtaining a frequency response vector delta omega of the generator node by adopting a transfer function from the power disturbance of the generator node to the frequency of the generator nodeG(s)：
Figure BDA0002351711250000023
Figure BDA0002351711250000024
Wherein, InIs an n-order unit array, BrG(s) is a reference transfer function from the generator frequency to the active output;
injecting power step disturbance into network nodes in a multi-machine power system, wherein the disturbance of generator nodes is 0, namely delta uG(s)＝0，ΔuL(s)＝PLS, wherein PL＝[Pn+1,Pn+2,…,Pn+m+a]T，Pn+iRepresenting the amplitude of the power step disturbance of the ith network node, i belongs to {1,2, …, m + a }; solving and obtaining a frequency response vector delta omega of the network node by adopting a transfer function from the power disturbance of the network node to the frequency of the network nodeL(s)：
Figure BDA0002351711250000031
Only when the network node injects step power disturbance, the phase angle of the network node has a very fast electromagnetic transient process close to the step in order to balance the power of the network node because the power angle of the generator rotor can not be suddenly changed. The waveform of the network node frequency during the time period (millisecond) of this process is close to a pulse signal. The frequency of the network node will then follow the generator node frequency. The response of the network node frequency after the pulse is considered in the present invention and is represented by the above formula.
In the step 4), the method specifically comprises the following steps:
4.1) scaling the susceptance matrix BsAnd (3) carrying out eigenvalue decomposition to obtain eigenvalues and eigenvectors:
Bs＝-UΛUT
Λ＝diag{λ1,...,λk,...,λn}
U＝[U1,...,Uk,...,Un]
wherein Λ represents an eigenvector matrix of the scaled susceptance matrix, U represents an eigenvector matrix of the scaled susceptance matrix, and λkFor eigenvalues in the eigenvalue matrix Λ, k ∈ {1,2, …, n }, 0 ═ λ1<…<λk<…<λn，UkTaking the eigenvector in the eigenvector matrix U, wherein k belongs to {1,2, …, n };
4.2) carrying out mode decomposition on the frequency response of the generator node or the network node to obtain a mode component Hk(s)：
Figure BDA0002351711250000032
Where k represents the ordinal number of the mode component, Hk(s) n mode components of the generator node or network node frequency response, CGk,CLkCoefficient matrices, H, for generator nodes or network nodes, respectivelyk(s),CGk,CLkRespectively calculated as:
Figure BDA0002351711250000033
Figure BDA0002351711250000034
Figure BDA0002351711250000035
4.3) mixing CGkIs the reciprocal of the ith diagonal element ofMode inertia J of kth mode of i nodes (i generator nodes)Gi,k，CLkAs the mode inertia J of the kth mode of the n + i-th node (i-th network node)Li,ki(ii) a In a multi-machine power system, the node numbers 1-n are generator nodes; n +1 to n + m are load nodes; n + m +1 to n + m + a are passive nodes.
In the step 5), judging according to the mode inertia: in n modes of each node, the first mode is called a common mode, the other modes are called differential modes, and the mode inertia of the common mode of all the nodes is the same; and searching the minimum value of the mode inertia of the generator node differential mode, and if the minimum value is less than 30% of the mode inertia of the common mode, adding a generator at the node corresponding to the minimum value, so as to increase the rotational inertia of the equivalent generator in the node.
The mode inertia of the invention can be used for obtaining the frequency intensity condition of the nodes in the multi-machine power system.
Comparing the magnitude of the mode inertia of each mode of each node, if the mode inertia of the kth mode of a certain node is larger, the coefficient before the kth mode in the frequency response of the node is smaller, which indicates that the influence of the mode on the node is smaller, or the frequency intensity of the kth mode of the node frequency is stronger.
The mode inertia of the first mode of any node is the sum of the inertia of all generators in the network, and the track of the mode in the frequency time domain response of all nodes is the same. I.e. the first mode is a common mode component of frequency and the remaining modes are differential mode components of frequency.
The specific calculation and representation of the steps of the invention are as follows:
A. network susceptance matrix and partitioning
The network susceptance matrix B is represented by the following equation:
Figure BDA0002351711250000041
wherein, BijAre the susceptance matrix elements. The node numbers 1-n are generator nodes; n +1 to n + m are loadsA node; n + m +1 to n + m + a are passive nodes. The load nodes and the passive nodes are collectively referred to as network nodes.
Dividing B into 4 blocks according to the node type as generator node or network node, respectively BGG、BGL、BLG、BLLThe specific expressions are respectively as follows:
Figure BDA0002351711250000042
Figure BDA0002351711250000043
B. generator inertia matrix J
The generator inertia matrix is expressed by the following formula:
J＝diag{J1,J2,...Jn}
wherein, J1,J2,…,JnThe rotational inertia of the 1 st to the nth generators respectively.
C. Scaling susceptance array and eigenvalue decomposition
Compressed electric nano-array BrExpressed by the following formula:
Figure BDA0002351711250000051
scaled susceptance array BsExpressed by the following formula:
Figure BDA0002351711250000052
scaled susceptance array BsThe eigenvalues of (d) are decomposed into:
Bs＝-UΛUT
Λ＝diag{λ1,...,λk,...,λn}
U＝[U1,...,Uk,...,Un]
wherein Λ represents the scaling of the characteristic matrix of the susceptance matrix and U represents the scalingEigenvector matrix, λ, of the susceptance matrixkFor eigenvalues in the eigenvalue matrix Λ, k ∈ {1,2, …, n }, 0 ═ λ1<…<λk<…<λn，UkFor the eigenvectors in the eigenvector matrix U, k ∈ {1,2, …, n }.
D. Mode inertia of generator node or network node
The mode inertia of the kth mode of the ith generator node or the network node is expressed by the following formula:
Figure BDA0002351711250000053
wherein, [ x, y [ ]]Representing the elements in the x-th row and y-th column of the matrix. CGk,CLkThe expressions are respectively:
Figure BDA0002351711250000054
the invention has the beneficial effects that:
the method can analyze the frequency intensity of any local (node) in the network by using the mode inertia, thereby optimizing the node rotational inertia of the multi-machine power system and improving the operation stability of the multi-machine power system.
Drawings
FIG. 1 is a schematic flow diagram of the process of the present invention.
FIG. 2 is a diagram illustrating a multi-machine power system in simulation verification according to an embodiment of the present invention.
Fig. 3 is a schematic diagram of a model of a generator in simulation verification according to an embodiment of the present invention.
Fig. 4 is a frequency-time domain response diagram after each node is disturbed in the simulation verification of the embodiment of the present invention.
Fig. 4(a) is a frequency-time domain response diagram of the 1 st node after injecting power step disturbance into the 1 st node in the simulation verification of the embodiment of the present invention;
fig. 4(b) is a frequency-time domain response diagram of the 2 nd node after injecting power step disturbance into the 2 nd node in the simulation verification of the embodiment of the present invention;
fig. 4(c) is a frequency-time domain response diagram of the 3 rd node after injecting power step disturbance into the 3 rd node in the simulation verification according to the embodiment of the present invention;
FIG. 4(d) is a frequency-time domain response diagram of the 4 th node after injecting a power step disturbance into the 4 th node in the simulation verification according to the embodiment of the present invention;
fig. 4(e) is a frequency-time domain response diagram of the 5 th node after injecting power step disturbance into the 5 th node in the simulation verification of the embodiment of the present invention;
fig. 4(f) is a frequency-time domain response diagram of the 6 th node after injecting power step disturbance into the 6 th node in the simulation verification according to the embodiment of the present invention;
FIG. 4(g) is a frequency-time domain response diagram of the 7 th node after injecting a power step disturbance at the 7 th node in the simulation verification according to the embodiment of the present invention;
fig. 4(h) is a frequency-time domain response diagram of the 8 th node after the 8 th node injects the power step disturbance in the simulation verification of the embodiment of the present invention.
Fig. 5 is a comparison graph of frequency-time domain responses after disturbance of the 4 th node before and after optimization of rotational inertia in simulation verification according to the embodiment of the present invention.
Fig. 5(a) is a frequency-time domain response diagram after injecting power step disturbance at the 4 th node before optimizing the rotational inertia in the simulation verification according to the embodiment of the present invention.
Fig. 5(b) is a frequency-time domain response diagram after power step disturbance is injected at the 4 th node after rotational inertia is optimized in simulation verification according to the embodiment of the present invention.
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 to obtain a closed loop transfer function from power disturbance to frequency response of each node in a multi-machine power system. And calculating a scaling susceptance matrix, decomposing the eigenvalue, decomposing the frequency response of each node into n components according to the eigenvalue decomposition, and further calculating the mode inertia of each node.
The specific implementation example of the invention is as follows:
a multi-machine power system is built in Matlab/Simulink software, as shown in FIG. 2. In the system, nodes 1-4 are generator nodes, and nodes 5-8 are load nodes, and the loads are omitted in the figure and are not shown. There are no passive nodes in the system, so nodes 5-8 are also network nodes. The inertia, damping and primary frequency modulation of the generator are considered in the model of the generator, wherein the primary frequency modulation is approximated by an inertia element, as shown in fig. 3.
Since the generators are isomorphic, D is equal to any i e {1,2, …,4}i/Ji、RiJiAnd TGiAre all equal to Ji、Di、Ri、TGiThe inertia constant, the damping coefficient, the primary frequency modulation difference-adjusting coefficient and the time constant of the ith generator are respectively. Will Di/Ji、RiJiAnd TGiRespectively denoted as d, r and TG. The reference transfer function G(s) of the generator and the transfer function J from the frequency of the ith generator to the active outputiG(s) may be represented by the following formula:
Figure BDA0002351711250000071
Figure BDA0002351711250000072
the parameter values of the system variables are shown in table 1 below.
Table 1 example simulation verification of parameter values of partial system variables
Parameter(s) Value taking
Generator inertia constant J1,J2,J3,J 4 16,12,8,4(p.u.)
Damping coefficient D of generator1,D2,D3,D4 2,1.5,1,0.5(p.u.)
Primary frequency modulation difference regulating coefficient R1,R2,R3,R 4 1/24,1/18,1/12,1/6(p.u.)
Primary frequency modulation time constant TG1,TG2,TG3, T G4 7,7,7,7(s)
Network reactance X1,X2,X3,X4 0.1,0.1,0.1,0.2(p.u.)
Network reactance X5,X6,X7,X8 0.1,0.1,0.4,0.6(p.u.)
In this embodiment there are 4 generators and therefore 4 modes. According to the method of the invention, the mode inertias of the generator nodes 1-4 and the network nodes 5-8 are shown in Table 2.
Table 2 model inertia of each node in simulation verification of embodiment
Figure BDA0002351711250000073
As can be seen from table 2, the mode inertia of the first mode (common mode) of all nodes in the network is 40, which is the sum of all generator inertias in the network. Among all nodes, the network nodes 5, 6, 7 have strong frequency strength: the 3 differential mode inertias of these 3 nodes are all larger. With node 5 having the strongest frequency strength. Whereas the generator nodes 3, 4 are weaker: mode inertia of 1-2 modes existing in the two nodes is small. In particular, generator node 4, which has a small mode inertia for both mode 3 and mode 4, is the weakest node. The weakest mode inertia of the rest nodes is at a medium level, and the node strength is general.
Fig. 4 is a time domain response of the frequency of the disturbance node after the 8 nodes inject power step disturbances of the same size (8 injections, the disturbance of the generator node is a sudden decrease of the output of the prime mover, and the disturbance of the network node is a sudden increase of the load) respectively in the simulation of the embodiment of the invention when t is 5 s. FIGS. 4(a) - (h) correspond to nodes 1-8, respectively. All node frequency traces in fig. 4 are substantially the same because all generators are homogeneous and all nodes have the same common mode inertia. The generator nodes 3, 4 have a large fluctuation in frequency response, with the generator node 4 fluctuating the most. The frequency fluctuations of the network nodes 5, 6, 7 are smaller and smoother, with the network node 5 being the smoothest. The remaining nodes fluctuate, typically, at an intermediate level. This result is consistent with the results of the model inertia analysis for each node in table 2. Therefore, the mode inertia provided by the invention has a remarkable effect on evaluating the node frequency strength.
When the node rotational inertia is optimized according to the method, the minimum value of the generator node differential mode inertia is searched, wherein the minimum value is the 3 rd mode inertia of the generator node 4 in the implementation example of the method and is 7.1. The ratio of the mode inertia to the common mode inertia is 0.178, less than 30%. The generator is added at the generator node 4 to increase the rotational inertia of the node, and the added generator parameters are the same as those of the generator originally located at the generator node 3, and the mode inertia of the generator node 4 is shown in table 3.
Table 3 model inertia of each node in simulation verification of embodiment
Figure BDA0002351711250000081
As can be seen from table 3, after increasing the rotational inertia of generator node 4, the mode inertia of the 3 rd and 4 th modes of the node is significantly increased. The mode inertia of mode 2 is reduced to 16.3, for which the minimum mode inertia of the node is, but still greater than the minimum 7.1 of the mode inertias of the node before optimization. Meanwhile, before and after the moment of inertia is optimized, the frequency time domain response of the generator node 4 after power disturbance is injected is shown in fig. 5. As can be seen from the graph, after the moment of inertia is optimized, the frequency fluctuation intensity of the node is reduced, and the frequency intensity is obviously improved. It can be seen that the use of the method for optimizing the moment of inertia proposed in the present invention has a significant effect.
The present invention is limited only by the appended claims, and any modifications and variations of the present invention are possible within the scope of the invention.

Claims (6)

1. A method for optimizing the node rotational inertia of a multi-machine power system based on mode inertia is characterized by comprising the following steps:
1) obtaining a closed-loop transfer function from power disturbance to frequency of generator nodes and network nodes in a multi-machine power system through a frequency modeling method, wherein a network susceptance matrix B is divided into four areas, specifically B, according to the nodes as the generator nodes or the network nodes in the closed-loop transfer functionGG、BGL、BLG、BLLIn which B isGG、BGL、BLG、BLLRespectively representing four areas of the upper left corner, the upper right corner, the lower sitting corner and the lower right corner of the network susceptance matrix B, wherein the subscript G corresponds to a generator node, and the subscript L corresponds to a network node;
2) respectively injecting power step disturbance into the generator node and the network node to obtain the frequency response of the node, and compressing the network node to form a compressed sodium susceptance array B during processingr；
3) Rotational inertia matrix J pair compression susceptance array B using generatorrZooming to obtain a zooming susceptance array Bs＝J-1/ 2BrJ-1/2；
4) For scaling electric nano-array BsCarrying out characteristic value decomposition, and carrying out mode decomposition on the disturbed node frequency response according to the decomposition to obtain n modes of the frequency responseThe formula component, n is the number of generator nodes in the multi-machine power system, and the mode inertia of each node in each mode is obtained;
5) and optimizing the node rotational inertia of the multi-machine power system by using the mode inertia.
2. The optimization method of the node rotational inertia of the multi-machine power system based on the pattern inertia as claimed in claim 1, wherein: the multi-machine power system comprises n generator nodes and m + a network nodes, wherein the network nodes are divided into m load nodes and a passive nodes, the generators connected at the same generator node are equivalent to one generator, and the n generator nodes share n generators.
3. The optimization method of the node rotational inertia of the multi-machine power system based on the pattern inertia as claimed in claim 1, wherein: in the step 1), the closed-loop transfer function and the network susceptance matrix of each node power disturbance to frequency in the multi-machine power system are as follows:
Figure FDA0002351711240000011
Figure FDA0002351711240000012
where s represents the Laplace operator, Δ uG(s)、ΔuL(s) power disturbance vectors, Δ ω, representing generator nodes and network nodes, respectivelyG(s)、ΔωL(s) frequency response vectors representing the generator node and the network node, respectively; j is a rotational inertia matrix taking the rotational inertia of n generators as a diagonal element, and J is diag (J)i)，JiRepresenting the moment of inertia of the ith generator; all generators in a multimachine power system are homogeneous, JG(s) represents a transfer function matrix from the frequency of all generators to the active output, JiG(s) represents the transfer function from the frequency of the ith generator to the active output, G(s) is the generator frequencyA power to active output reference transfer function; omega0Represents a frequency reference value; b denotes a network susceptance matrix, BGG、BGL、BLG、BLLAnd four areas of the upper left corner, the upper right corner, the lower left corner and the lower right corner of the network susceptance matrix B are respectively shown, the blocks are generator nodes or network nodes based on the nodes, the subscript G corresponds to the generator nodes, and the subscript L corresponds to the network nodes.
4. The optimization method of the node rotational inertia of the multi-machine power system based on the pattern inertia as claimed in claim 1, wherein: in the step 2), power step disturbance is injected to generator nodes in the multi-machine power system, and the network node disturbance is 0, namely delta uG(s)＝PGS, wherein PG＝[P1,P2,…,Pn]T，PiRepresenting the amplitude of the power step disturbance of the ith generator node, wherein i belongs to {1,2, …, n }; solving and obtaining a frequency response vector delta omega of the generator node by adopting a transfer function from the power disturbance of the generator node to the frequency of the generator nodeG(s)：
Figure FDA0002351711240000021
Figure FDA0002351711240000022
Wherein, InIs an n-order unit array, BrG(s) is a reference transfer function from the generator frequency to the active output;
injecting power step disturbance into network nodes in a multi-machine power system, wherein the disturbance of generator nodes is 0, namely delta uG(s)＝0，ΔuL(s)＝PLS, wherein PL＝[Pn+1,Pn+2,…,Pn+m+a]T，Pn+iRepresenting the amplitude of the power step disturbance of the ith network node, i belongs to {1,2, …, m + a }; using a transfer function of the power perturbation of the network node to the frequency of the network node,solving to obtain a frequency response vector delta omega of the network nodeL(s)：
Figure FDA0002351711240000023
5. The optimization method of the node rotational inertia of the multi-machine power system based on the pattern inertia as claimed in claim 1, wherein: in the step 4), the method specifically comprises the following steps:
4.1) scaling the susceptance matrix BsAnd (3) carrying out eigenvalue decomposition to obtain eigenvalues and eigenvectors:
Bs＝-UΛUT
Λ＝diag{λ1,...,λk,...,λn}
U＝[U1,...,Uk,...,Un]
wherein Λ represents an eigenvector matrix of the scaled susceptance matrix, U represents an eigenvector matrix of the scaled susceptance matrix, and λkFor eigenvalues in the eigenvalue matrix Λ, k ∈ {1,2, …, n }, 0 ═ λ1<…<λk<…<λn，UkTaking the eigenvector in the eigenvector matrix U, wherein k belongs to {1,2, …, n };
4.2) carrying out mode decomposition on the frequency response of the generator node or the network node to obtain a mode component Hk(s)：
Figure FDA0002351711240000031
Where k represents the ordinal number of the mode component, Hk(s) n mode components of the generator node or network node frequency response, CGk,CLkCoefficient matrices, H, for generator nodes or network nodes, respectivelyk(s),CGk,CLkRespectively calculated as:
Figure FDA0002351711240000032
Figure FDA0002351711240000033
Figure FDA0002351711240000034
4.3) mixing CGkAs the mode inertia J of the kth mode of the ith nodeGi,k，CLkAs the mode inertia J of the k-th mode of the n + i-th nodeLi,ki。
6. The optimization method of the node rotational inertia of the multi-machine power system based on the pattern inertia as claimed in claim 1, wherein: in the step 5), judging according to the mode inertia: in n modes of each node, the first mode is called a common mode, the other modes are called differential modes, and the mode inertia of the common mode of all the nodes is the same; and searching the minimum value of the mode inertia of the generator node differential mode, and if the minimum value is less than 30% of the mode inertia of the common mode, adding a generator at the node corresponding to the minimum value, so as to increase the rotational inertia of the equivalent generator in the node.
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Application publication date: 20200515