CN115085224B - New energy power system frequency stability rapid analysis method - Google Patents

New energy power system frequency stability rapid analysis method Download PDF

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CN115085224B
CN115085224B CN202210995878.8A CN202210995878A CN115085224B CN 115085224 B CN115085224 B CN 115085224B CN 202210995878 A CN202210995878 A CN 202210995878A CN 115085224 B CN115085224 B CN 115085224B
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new energy
matrix
power system
energy power
frequency response
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CN115085224A (en
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戴剑丰
阎诚
万磊
汤奕
钱俊良
周吉
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Liyang Research Institute of Southeast University
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/24—Arrangements for preventing or reducing oscillations of power in networks
    • 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
    • H02J3/381—Dispersed generators
    • 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]
    • 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
    • H02J2300/00—Systems for supplying or distributing electric power characterised by decentralized, dispersed, or local generation
    • H02J2300/20—The dispersed energy generation being of renewable origin
    • H02J2300/22—The renewable source being solar energy
    • H02J2300/24—The renewable source being solar energy of photovoltaic origin
    • 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
    • H02J2300/00—Systems for supplying or distributing electric power characterised by decentralized, dispersed, or local generation
    • H02J2300/20—The dispersed energy generation being of renewable origin
    • H02J2300/28—The renewable source being wind energy
    • 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
    • H02J2300/00—Systems for supplying or distributing electric power characterised by decentralized, dispersed, or local generation
    • H02J2300/40—Systems for supplying or distributing electric power characterised by decentralized, dispersed, or local generation wherein a plurality of decentralised, dispersed or local energy generation technologies are operated simultaneously

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Abstract

The invention discloses a method for rapidly analyzing the frequency stability of a new energy power system, which comprises the steps of firstly, establishing a new energy power system frequency response model comprising a traditional generator set frequency response link, a wind power plant frequency response link and a photovoltaic power station frequency response link; secondly, performing model dimensionality reduction on the new energy power system frequency response model to obtain a low-order new energy power system frequency response model; and finally, analyzing the frequency stability by using a low-order frequency response model of the new energy power system, and realizing the rapid evaluation of the frequency stability of the new energy power system. The method fully considers the flexible control potential of new energy multi-frequency modulation resources, can realize the rapid analysis of the stability and dynamic characteristics of a frequency response high-dimensional model, and has profound significance for improving the operation stability of a new energy power system.

Description

New energy power system frequency stability rapid analysis method
Technical Field
The invention relates to the field of frequency stability analysis of power systems, in particular to a method for rapidly analyzing frequency stability of a new energy power system.
Background
The construction and development of a new energy power system is an important guarantee for realizing the double-carbon target, is an important measure for coping with global climate change and fulfilling international commitments, and has important significance for promoting the adjustment of energy structures in China, increasing energy supply and guaranteeing energy safety. The new energy power system comprises various types of typical elements such as wind power, photovoltaic, thermal power generating units, hydroelectric generating units and the like. A prime system formed by the speed regulator of the hydroelectric generating set and the prime motor generates negative damping, and frequency oscillation is caused in a region with high water-electricity ratio, so that the system frequency stability is influenced. The new energy transient process with the converter as an interface has multi-time scale interweaving and discrete events, and the continuous process has characteristics of mixing, leading control strategy and the like, so that the high-order analysis of the model is difficult, and leading poles are difficult to distinguish.
In the existing system frequency response model considering that new energy participates in frequency modulation, the frequency modulation link of the new energy is generally simplified and equivalent, so that the dimension of the model is reduced, and the calculation efficiency is improved. The new energy centralized and distributed construction trend leads to the existence of various frequency modulation resources with different frequency response dynamic characteristics in a new energy power system, and model errors brought by the traditional equivalent mode are not negligible.
Active frequency control of new energy is an important way for improving system frequency stability under high-power shortage, the existing research does not relate to a new energy power system frequency stability analysis method containing multiple frequency modulation resources, and the problem to be solved is that how to realize rapid analysis of new energy power system frequency stability is to be solved by considering the difference of dynamic characteristics of different frequency modulation resources.
Disclosure of Invention
In order to solve the above problems, the present invention provides a method for rapidly analyzing the frequency stability of a new energy power system, which can effectively determine the frequency stability of the new energy power system and analyze the dynamic change of the frequency.
In order to achieve the purpose, the invention is realized by the following technical scheme:
a method for rapidly analyzing frequency stability of a new energy power system comprises the following steps:
step 1: establishing a new energy power system frequency response model of multi-type frequency modulation resources comprising a traditional generator set frequency response link, a wind power plant frequency response link and a photovoltaic power station frequency response link;
step 2: performing model dimensionality reduction on the frequency response model of the new energy power system established in the step 1 to obtain a low-order frequency response model of the new energy power system;
and 3, step 3: and analyzing the frequency stability according to the low-order new energy power system frequency response model.
The invention is further improved in that: the step 1 of establishing a frequency response link of the traditional generator set comprises the step of obtaining a traditional generator set type and corresponding frequency response parameters in a new energy power system, wherein the traditional generator set type at least comprises one of a thermal power generating unit and a hydroelectric generating unit.
The invention is further improved in that: in the step 1, the wind power plant frequency response link adopts comprehensive inertia control, and a transfer function meets the following formula:
Figure 100002_DEST_PATH_IMAGE001
in the formula:
Figure 100002_DEST_PATH_IMAGE002
the active variable quantity of the wind power plant;
Figure 100002_DEST_PATH_IMAGE003
the angular frequency variation of the wind power plant;
Figure 100002_DEST_PATH_IMAGE004
the virtual inertia coefficient of the wind power plant is obtained;
Figure 100002_DEST_PATH_IMAGE005
the droop coefficient of the wind power plant is obtained;
Figure 100002_DEST_PATH_IMAGE006
the required time for transmitting the frequency modulation control command of the wind power plant power control system to the inverter is obtained;
Figure 100002_DEST_PATH_IMAGE007
the execution time of the wind power plant inverter; s is a complex frequency domain;
the frequency response link of the photovoltaic power station adopts droop control, and a transfer function meets the following formula:
Figure 100002_DEST_PATH_IMAGE008
in the formula:
Figure 100002_DEST_PATH_IMAGE009
the active variable quantity of the photovoltaic power station is obtained;
Figure 100002_DEST_PATH_IMAGE010
the angular frequency variation of the photovoltaic power station;
Figure 100002_DEST_PATH_IMAGE011
adjusting a difference coefficient for the photovoltaic power station;
Figure 100002_DEST_PATH_IMAGE012
the required time for transmitting the frequency modulation control command of the photovoltaic power station power control system to the inverter is obtained;
Figure 100002_DEST_PATH_IMAGE013
the required time for the photovoltaic power plant inverter to execute.
The invention is further improved in that: the specific steps of establishing the frequency response model of the new energy power system containing the multi-type frequency modulation resources in the step 1 are as follows: the frequency response links of all frequency modulation resources are connected in parallel to serve as negative feedback of a new energy power system model to form a new energy power system frequency response model, and the new energy power system frequency response model meets the following formula:
Figure 100002_DEST_PATH_IMAGE014
in the formula:
Figure 100002_DEST_PATH_IMAGE015
the angular frequency variation of the new energy power system is obtained;
Figure 100002_DEST_PATH_IMAGE016
the active variable quantity of the new energy power system is obtained;His the inertia time constant of the generator;Dis the system damping coefficient.
The invention is further improved in that: the specific steps of the step 2 are as follows:
step 2.1, converting the frequency response model of the new energy power system established in the step 1 into a state space equation, and satisfying the following formula:
Figure 100002_DEST_PATH_IMAGE017
Figure 100002_DEST_PATH_IMAGE018
in the formula:
Figure 100002_DEST_PATH_IMAGE019
is a roomnThe state vector of the dimension(s) is,
Figure 100002_DEST_PATH_IMAGE020
is composed ofnThe differentiation of the dimensional state vector is performed,
Figure 100002_DEST_PATH_IMAGE021
is composed ofqThe dimensions of the input vector are controlled in such a way that,
Figure 100002_DEST_PATH_IMAGE022
is composed ofpThe vector is output in dimension and the vector is output,Ais a matrix of the system and is,Bin order to input the matrix, the input matrix is,Cto be the output matrix, the output matrix is,D 1is a direct transmission matrix;
step 2.2, calculating a controllable gram matrix of the new energy power systemPAnd considerable gram matrixQThe expression is:
Figure 100002_DEST_PATH_IMAGE023
Figure 100002_DEST_PATH_IMAGE024
in the formula:
Figure 100002_DEST_PATH_IMAGE025
is a transpose of the matrix of the system,
Figure 100002_DEST_PATH_IMAGE026
in order to be a transpose of the input matrix,
Figure 100002_DEST_PATH_IMAGE027
is the transpose of the output matrix;
step 2.3, to the controllable gram matrixPAnd a Zealand matrixQPerforming Cholesky decomposition, wherein the expression is as follows:
Figure 100002_DEST_PATH_IMAGE028
Figure 100002_DEST_PATH_IMAGE029
in the formula:
Figure 100002_DEST_PATH_IMAGE030
representing a controllable gram matrixPCholesky decomposition of (1);
Figure 100002_DEST_PATH_IMAGE031
representing a controllable gram matrixPTranspose of Cholesky decomposition of (1);
Figure 100002_DEST_PATH_IMAGE032
a Cholesky decomposition representing a observable gram matrix Q;
Figure 100002_DEST_PATH_IMAGE033
represents the transpose of the Cholesky decomposition of the observable gram matrix Q;
step 2.4, for
Figure 100002_DEST_PATH_IMAGE034
Performing singular value decomposition:
Figure 100002_DEST_PATH_IMAGE035
in the formula:Uis a unitary matrix;Σis a semi-positive definite diagonal matrix;
Figure 100002_DEST_PATH_IMAGE036
are unitary matrices of different orders;
step 2.5, calculating a balance change matrix:
Figure 100002_DEST_PATH_IMAGE037
Figure 100002_DEST_PATH_IMAGE038
in the formula:
Figure 100002_DEST_PATH_IMAGE039
is a balance change matrix after Cholesky decomposition of the controllable gram matrix P;
Figure 100002_DEST_PATH_IMAGE040
is a considerable gram matrixQThe Cholesky decomposed equilibrium change matrix of (1);
step 2.6, carrying out balance transformation on the state space matrix:
Figure 100002_DEST_PATH_IMAGE041
in the formula:
Figure 100002_DEST_PATH_IMAGE042
a matrix of the system after the balance transformation is represented,
Figure 100002_DEST_PATH_IMAGE043
representing the input matrix after the balance transformation,
Figure 100002_DEST_PATH_IMAGE044
representing the output matrix after the balance transformation,
Figure 100002_DEST_PATH_IMAGE045
the direct transfer matrix after the balance transformation is represented,
Figure 100002_DEST_PATH_IMAGE046
is that
Figure 100002_DEST_PATH_IMAGE047
Transposing;
and 2.7, truncating the state space matrix after the balance transformation according to the expected model order, calculating a state space equation of the new energy power system after the model dimensionality reduction, and converting the state space equation of the new energy power system after the model dimensionality reduction into a transfer function:
Figure 100002_DEST_PATH_IMAGE048
in the formula:
Figure 100002_DEST_PATH_IMAGE049
representing a transfer function of a state space equation of the new energy power system;
Figure 100002_DEST_PATH_IMAGE050
、
Figure 100002_DEST_PATH_IMAGE051
、
Figure 100002_DEST_PATH_IMAGE052
respectively, the transfer function numerator 0 order,m-1order andmthe coefficient of the order;
Figure 100002_DEST_PATH_IMAGE053
、
Figure 100002_DEST_PATH_IMAGE054
are respectively transfer functionsThe order of 0 of the denominator,n-1the coefficients of the order of the first order,
Figure 100002_DEST_PATH_IMAGE055
、
Figure 100002_DEST_PATH_IMAGE056
respectively m-th order of the numerator and n-th order of the denominator.
The invention is further improved in that: the step 3 comprises the following specific steps: calculating a system pole of the frequency response model of the low-order new energy power system in the step 2, wherein the expression is as follows:
Figure 100002_DEST_PATH_IMAGE057
judging the stability of the frequency of the new energy power system according to the positions of the system poles, and if and only if all the system poles are on the left half plane of the complex plane, stabilizing the new energy power system; and selecting the conjugate complex root closest to the imaginary axis as a dominant pole, and analyzing the frequency dynamic characteristic through the position of the dominant pole on the complex plane and the damping ratio of the dominant pole, wherein the larger the imaginary part is, the smaller the damping ratio is, and the weaker the frequency stability of the new energy power system is.
The beneficial effects of the invention are: according to the method, a frequency response model of the new energy power system comprising elements such as a traditional generator set, a wind power plant, a photovoltaic power station and the like is established, the pole of a computing system is solved after dimension reduction processing is carried out on the model, frequency stability analysis is carried out, and rapid assessment of the frequency stability of the new energy power system is achieved. The method fully considers the flexible control potential of new energy multi-frequency modulation resources, can realize the rapid analysis of the stability and dynamic characteristics of a frequency response high-dimensional model, and has profound significance for improving the operation stability of a new energy power system.
Drawings
FIG. 1 is a flow chart of the implementation of the method of the present invention;
FIG. 2 is a frequency response model of a new energy power system according to an embodiment of the present invention;
fig. 3 is a time domain simulation curve of the frequency response model of the new energy power system.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
As shown in fig. 1, the method of the present invention comprises the following steps:
step 1: establishing a new energy power system frequency response model, which comprises establishing a traditional generator set frequency response link, a wind power plant frequency response link and a photovoltaic power plant frequency response link, and establishing a new energy power system frequency response model containing multiple types of frequency modulation resources;
and 2, step: performing model dimensionality reduction on the new energy power system frequency response model established in the step 1 to obtain a low-order new energy power system frequency response model;
and 3, step 3: and analyzing the frequency stability according to the low-order new energy power system frequency response model.
In the step 1, establishing a frequency response link of a traditional generator set, specifically comprising the following steps: the method comprises the steps of obtaining the type of a traditional power generation unit and corresponding frequency response parameters in a new energy power system, wherein the type of the traditional power generation unit comprises at least one of a thermal power generating unit and a hydroelectric generating unit.
When the traditional generating set is a thermal power generating set, the dynamic characteristics of a speed regulator and a prime motor are considered in the frequency response link of the thermal power generating set, and a transfer function meets the following formula:
Figure DEST_PATH_IMAGE058
in the formula:
Figure DEST_PATH_IMAGE059
the active variable quantity of the thermal power generating unit is obtained;
Figure DEST_PATH_IMAGE060
the angular frequency variation of the thermal power generating unit is obtained;
Figure DEST_PATH_IMAGE061
the percentage of the steady-state output power of the high-pressure cylinder to the total output power of the steam turbine is shown;
Figure DEST_PATH_IMAGE062
is the intermediate reheat steam volume effect time constant;
Figure DEST_PATH_IMAGE063
is the high pressure steam volume time constant;Rthe difference adjustment coefficient of the thermal power generating unit is obtained;
Figure DEST_PATH_IMAGE064
the time constant of the thermal power generating unit speed regulator is shown; and S is a complex frequency domain.
When the traditional generator set is a hydroelectric generating set, the frequency response link of the hydroelectric generating set considers the dynamic characteristics of a speed regulator and a prime motor, and the transfer function meets the following formula:
Figure DEST_PATH_IMAGE065
in the formula:
Figure DEST_PATH_IMAGE066
the active variable quantity of the hydroelectric generating set;
Figure DEST_PATH_IMAGE067
the angular frequency variation of the hydroelectric generating set;
Figure DEST_PATH_IMAGE068
is the water flow inertia time constant;
Figure DEST_PATH_IMAGE069
the difference adjustment coefficient of the hydroelectric generating set;
Figure DEST_PATH_IMAGE070
，
Figure DEST_PATH_IMAGE071
and
Figure DEST_PATH_IMAGE072
the proportional coefficient, the integral coefficient and the differential coefficient of the speed regulator are respectively;
Figure DEST_PATH_IMAGE073
is the time constant of the speed regulator of the hydroelectric generating set.
In the step 1, a wind power plant frequency response link and a photovoltaic power station frequency response link respectively adopt comprehensive inertia control and droop control, and a transfer function of the wind power plant frequency response link meets the following formula:
Figure DEST_PATH_IMAGE074
in the formula:
Figure DEST_PATH_IMAGE075
the active power variation of the wind turbine generator is obtained;
Figure DEST_PATH_IMAGE076
the angular frequency variation of the wind turbine generator is obtained;
Figure DEST_PATH_IMAGE077
calculating a virtual inertia coefficient of the wind power plant;
Figure DEST_PATH_IMAGE078
the droop coefficient of the wind power plant is obtained;
Figure DEST_PATH_IMAGE079
the required time for transmitting the frequency modulation control command of the wind power plant power control system to the inverter is obtained;
Figure DEST_PATH_IMAGE080
the required time for the wind farm inverter to execute.
The frequency response link transfer function of the photovoltaic power station meets the following formula:
Figure DEST_PATH_IMAGE081
in the formula:
Figure DEST_PATH_IMAGE082
the active variable quantity of the photovoltaic power station is obtained;
Figure DEST_PATH_IMAGE083
the angular frequency variation of the photovoltaic power station;
Figure DEST_PATH_IMAGE084
adjusting difference coefficients of the photovoltaic power station;
Figure DEST_PATH_IMAGE085
the required time for issuing the frequency modulation control command of the photovoltaic power station power control system to the inverter is obtained;
Figure DEST_PATH_IMAGE086
the required time for the photovoltaic power plant inverter to execute.
And multiplying a traditional generator set frequency response link, a wind power plant frequency response link and a photovoltaic power station frequency response link by a proportional coefficient of each power generation unit accounting for all power output, and connecting the frequency response links of all frequency modulation resources in parallel to form a new energy power system frequency response model as negative feedback of the new energy power system model. The power system model satisfies the following formula:
Figure DEST_PATH_IMAGE087
in the formula:
Figure DEST_PATH_IMAGE088
the angular frequency variation of the new energy power system is obtained;
Figure DEST_PATH_IMAGE089
the active variable quantity of the new energy power system is obtained;His the inertia time constant of the generator;Dis the system damping coefficient.
In the embodiment, a new energy power system comprising a photovoltaic power station, a wind power plant, a thermal power generating unit and a hydroelectric generating unit is selected as an object. And constructing a frequency response model of the new energy power system, as shown in fig. 2. The new energy power system is provided with 2 photovoltaic power stations, 2 wind power stations, 1 thermal power unit and 1 hydroelectric power unit. The parameters are set as follows:
photovoltaic power plant: 1 st photovoltaic power station difference adjustment coefficient
Figure DEST_PATH_IMAGE090
=25, execution time of the 1 st photovoltaic plant inverter
Figure DEST_PATH_IMAGE091
=2, time for sending frequency modulation control command of power control system of 1 st photovoltaic power station to inverter
Figure DEST_PATH_IMAGE092
=0.05, 2 nd photovoltaic power plant adjustment coefficient
Figure DEST_PATH_IMAGE093
Execution time of 2 nd photovoltaic power station inverter =10
Figure DEST_PATH_IMAGE094
Time required for sending frequency modulation control instruction of power control system of No. 2 photovoltaic power station to inverter
Figure DEST_PATH_IMAGE095
=0.02；
Wind power plant: 1 st wind farm virtual inertia
Figure DEST_PATH_IMAGE096
=30, droop coefficient of the 1 st wind farm
Figure DEST_PATH_IMAGE097
=30, frequency modulation of the 1 st wind farm power control systemTime of control command issued to inverter
Figure DEST_PATH_IMAGE098
=2, execution time of the 1 st wind farm inverter
Figure DEST_PATH_IMAGE099
=0.03, virtual inertia of the 2 nd wind farm
Figure DEST_PATH_IMAGE100
=15, droop coefficient of 2 nd wind farm
Figure DEST_PATH_IMAGE101
=15, time for sending frequency modulation control command of 2 nd wind power plant power control system to inverter
Figure DEST_PATH_IMAGE102
=5, execution time of 2 nd wind farm inverter
Figure DEST_PATH_IMAGE103
=0.08；
Thermal power generating unit: percentage of steady state output power of high pressure cylinder to total output power of steam turbine
Figure DEST_PATH_IMAGE104
=0.35, intermediate reheat steam volume effect time constant
Figure DEST_PATH_IMAGE105
=12, high pressure steam volume time constant
Figure DEST_PATH_IMAGE106
=0.3, difference adjustment coefficient of thermal power generating unitR=0.03, time constant of speed regulator of thermal power generating unit
Figure DEST_PATH_IMAGE107
=0.2；
A hydroelectric generating set: water flow inertia time constant
Figure DEST_PATH_IMAGE108
=2.5, difference adjustment coefficient of hydroelectric generating set
Figure DEST_PATH_IMAGE109
=0.04, governor ratio
Figure DEST_PATH_IMAGE110
=1, integral coefficient
Figure DEST_PATH_IMAGE111
=2, differential coefficient
Figure DEST_PATH_IMAGE112
=0.7, time constant of speed regulator of hydroelectric generating set
Figure DEST_PATH_IMAGE113
=0.2；
Parameters of the power system: the equivalent inertia after the new energy is not considered is as follows: inertia time constant of generatorH=4.5, system damping coefficientD=0.1；
Power generation ratio coefficient:
Figure DEST_PATH_IMAGE114
=0.025，
Figure DEST_PATH_IMAGE115
=0.025，
Figure DEST_PATH_IMAGE116
=0.025，
Figure DEST_PATH_IMAGE117
=0.025，
Figure 456243DEST_PATH_IMAGE117
=0.025，
Figure 739588DEST_PATH_IMAGE117
=0.025，
Figure DEST_PATH_IMAGE118
=0.180，
Figure DEST_PATH_IMAGE119
=0.720。
as shown in fig. 2, the original new energy power system is a linear steady control system, the order of the model is 15, and the dimension of the model is reduced, and the specific steps are as follows:
1) Converting the frequency response model of the new energy power system established in the step 1 into a state space equation, and satisfying the following formula:
Figure DEST_PATH_IMAGE120
Figure 345013DEST_PATH_IMAGE018
in the formula:
Figure DEST_PATH_IMAGE121
is composed ofnThe vector of the states of the dimensions is,
Figure DEST_PATH_IMAGE122
representnDifferentiation of the dimensional state vector;
Figure DEST_PATH_IMAGE123
is composed ofqControlling an input vector in dimension;
Figure DEST_PATH_IMAGE124
is composed ofpAnd (5) outputting a vector in a dimension mode.AIn order to be a matrix of the system,Bin order to input the matrix, the input matrix is,Cto be the output matrix, the output matrix is,D 1is a direct transfer matrix.
2) Controllable gram matrix for calculating new energy power systemPAnd considerable gram matrixQ：
Figure DEST_PATH_IMAGE125
Figure DEST_PATH_IMAGE126
In the formula:
Figure DEST_PATH_IMAGE127
is a transpose of the system matrix,
Figure DEST_PATH_IMAGE128
in order to be a transpose of the input matrix,
Figure DEST_PATH_IMAGE129
is the transpose of the output matrix;
3) For controllable gram matrixPAnd a Zealand matrixQCholesky decomposition was performed:
Figure DEST_PATH_IMAGE130
Figure DEST_PATH_IMAGE131
in the formula:
Figure DEST_PATH_IMAGE132
representing a controllable gram matrixPCholesky decomposition of (1);
Figure DEST_PATH_IMAGE133
representing a controllable gram matrixPTranspose of Cholesky decomposition of (1);
Figure DEST_PATH_IMAGE134
a Cholesky decomposition representing a observable gram matrix Q;
Figure DEST_PATH_IMAGE135
a transpose representing the Cholesky decomposition of the observable gram matrix Q;
4) For is to
Figure DEST_PATH_IMAGE136
Performing singular value decomposition:
Figure DEST_PATH_IMAGE137
in the formula:Uis a unitary matrix;Σis a semi-positive definite diagonal matrix; v is a unitary matrix of a different order,
Figure DEST_PATH_IMAGE138
representing transposes of unitary matrices of different orders;
5) Calculating an equilibrium change matrix:
Figure DEST_PATH_IMAGE139
Figure DEST_PATH_IMAGE140
in the formula:
Figure DEST_PATH_IMAGE141
is the equilibrium change matrix after Cholesky decomposition of the observable gram matrix Q;
Figure DEST_PATH_IMAGE142
is a balance change matrix after Cholesky decomposition of the controllable gram matrix P;
6) And (3) carrying out balance transformation on the state space matrix:
Figure 938193DEST_PATH_IMAGE041
in the formula:
Figure DEST_PATH_IMAGE143
a matrix of the system after the balance transformation is represented,
Figure DEST_PATH_IMAGE144
representing the input matrix after the balance transformation,
Figure DEST_PATH_IMAGE145
representing the output matrix after the balance transformation,
Figure 553063DEST_PATH_IMAGE045
the direct transfer matrix after the balance transformation is represented,
Figure DEST_PATH_IMAGE146
is that
Figure DEST_PATH_IMAGE147
Transposing;
7) According to the expected model order, truncating the state space matrix after the balance transformation, calculating a state space equation of the system after the dimensionality reduction, and converting the state space equation of the system after the dimensionality reduction into a transfer function:
Figure DEST_PATH_IMAGE148
in the formula:
Figure DEST_PATH_IMAGE149
representing a transfer function of a state space equation of the new energy power system;
Figure DEST_PATH_IMAGE150
、
Figure DEST_PATH_IMAGE151
、
Figure DEST_PATH_IMAGE152
respectively, the transfer function numerator 0 order,m-1order summCoefficients of order;
Figure DEST_PATH_IMAGE153
、
Figure DEST_PATH_IMAGE154
respectively of the order 0 of the denominator of the transfer function,n-1the coefficients of the order of the first order,
Figure DEST_PATH_IMAGE155
、
Figure DEST_PATH_IMAGE156
respectively m-th order of the numerator and n-th order of the denominator.
Step signals with the model order of 5 and 10 percent after dimensionality reduction are input into the system to obtain a system frequency dynamic response curve, as shown in fig. 3, the process that the system frequency changes and tends to be stable is completely consistent with the original new energy power system, and the model after dimensionality reduction can be well approximated to the dynamic process of the original new energy power system.
Step 3, carrying out frequency stability analysis, solving the model after dimensionality reduction, and calculating a pole, wherein the expression is as follows:
Figure DEST_PATH_IMAGE157
and judging the stability of the frequency of the new energy power system according to the positions of the poles of the system, wherein the new energy power system is stable if and only if all the poles of the system are on the left half plane of the complex plane. And selecting the conjugate complex root closest to the imaginary axis as a dominant pole, analyzing the frequency dynamic characteristic according to the position of the dominant pole on the complex plane and the damping ratio of the dominant pole, wherein the larger the imaginary part is, the smaller the damping ratio is, and the weaker the frequency stability of the system is.
Dominant characteristic roots of the frequency response model of the new energy power system and the frequency response model of the original new energy power system after dimensionality reduction are respectively-0.1959 +/-0.5610iAnd-0.1961. + -. 0.5614iThe damping ratio of the dimensionality reduction model and the full-order model is 0.3296 and 0.3298 respectively, leading feature roots before and after dimensionality reduction are basically consistent, but an original new energy power system contains 15 feature roots, leading poles are difficult to distinguish, and a frequency response model of the new energy power system after dimensionality reduction only has 5 poles, so that the leading poles are easy to distinguish. The order of the reduced-dimension model is further adjusted, and the absolute error of the obtained reduced-order system is shown in table 1:
Figure DEST_PATH_IMAGE158
along with the increase of the order of the model, the absolute error of the reduced-order model and the frequency response model of the original new energy power system is obviously reduced.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (5)

1. A method for rapidly analyzing frequency stability of a new energy power system is characterized by comprising the following steps: the method comprises the following steps:
step 1: establishing a new energy power system frequency response model comprising a traditional generator set frequency response link, a wind power plant frequency response link and a photovoltaic power station frequency response link;
step 2: performing model dimensionality reduction on the new energy power system frequency response model established in the step 1 to obtain a low-order new energy power system frequency response model;
and step 3: analyzing the frequency stability according to a low-order new energy power system frequency response model;
in the step 1, the wind power plant frequency response link adopts comprehensive inertia control, and a transfer function meets the following formula:
Figure DEST_PATH_IMAGE001
in the formula:
Figure DEST_PATH_IMAGE002
the active variable quantity of the wind power plant;
Figure DEST_PATH_IMAGE003
the angular frequency variation of the wind power plant;
Figure DEST_PATH_IMAGE004
calculating a virtual inertia coefficient of the wind power plant;
Figure DEST_PATH_IMAGE005
the droop coefficient of the wind power plant;
Figure DEST_PATH_IMAGE006
the required time for transmitting the frequency modulation control command of the wind power plant power control system to the inverter is obtained;
Figure DEST_PATH_IMAGE007
the required time for the wind farm inverter to execute; s is a complex frequency domain;
the frequency response link of the photovoltaic power station adopts droop control, and a transfer function meets the following formula:
Figure DEST_PATH_IMAGE008
in the formula:
Figure DEST_PATH_IMAGE009
the active variable quantity of the photovoltaic power station is obtained;
Figure DEST_PATH_IMAGE010
the angular frequency variation of the photovoltaic power station;
Figure DEST_PATH_IMAGE011
adjusting difference coefficients of the photovoltaic power station;
Figure DEST_PATH_IMAGE012
the required time for transmitting the frequency modulation control command of the photovoltaic power station power control system to the inverter is obtained;
Figure DEST_PATH_IMAGE013
the required time for the photovoltaic power plant inverter to execute.
2. The method for rapidly analyzing the frequency stability of the new energy power system according to claim 1, wherein the method comprises the following steps: in the step 1, establishing a frequency response link of a traditional generator set comprises acquiring a traditional generator set type and corresponding frequency response parameters in a new energy power system, wherein the traditional generator set type at least comprises one of a thermal power generating unit and a hydroelectric generating unit.
3. The method for rapidly analyzing the frequency stability of the new energy power system according to claim 1, wherein the method comprises the following steps: the specific steps of establishing a new energy power system frequency response model comprising a traditional generator set frequency response link, a wind power plant frequency response link and a photovoltaic power plant frequency response link in the step 1 are as follows: the frequency response links of all frequency modulation resources are connected in parallel to serve as negative feedback of a new energy power system model to form a new energy power system frequency response model, and the new energy power system frequency response model meets the following formula:
Figure DEST_PATH_IMAGE014
in the formula:
Figure DEST_PATH_IMAGE015
the angular frequency variation of the new energy power system is obtained;
Figure DEST_PATH_IMAGE016
the active variable quantity of the new energy power system is obtained;His the inertia time constant of the generator;Dthe damping coefficient of the system is; and S is a complex frequency domain.
4. The method for rapidly analyzing the frequency stability of the new energy power system according to claim 1, wherein the method comprises the following steps: the specific steps of the step 2 are as follows:
step 2.1, converting the frequency response model of the new energy power system established in the step 1 into a state space equation, and satisfying the following formula:
Figure DEST_PATH_IMAGE017
Figure DEST_PATH_IMAGE018
in the formula:
Figure DEST_PATH_IMAGE019
is composed ofnThe state vector of the dimension(s) is,
Figure DEST_PATH_IMAGE020
is composed ofnThe differential of the dimensional state vector is taken,
Figure DEST_PATH_IMAGE021
is composed ofqThe dimensions of the input vector are controlled in such a way that,
Figure DEST_PATH_IMAGE022
is composed ofpThe vector is output in a dimension (D) mode,Ais a matrix of the system and is,Bin order to input the matrix, the input matrix is,Cto be the output matrix, the output matrix is,D 1is a direct transmission matrix;
step 2.2, calculating a controllable gram matrix of the new energy power systemPAnd considerable gram matrixQThe expression is:
Figure DEST_PATH_IMAGE023
Figure DEST_PATH_IMAGE024
in the formula:
Figure DEST_PATH_IMAGE025
is a transpose of the system matrix,
Figure DEST_PATH_IMAGE026
in order to be a transpose of the input matrix,
Figure DEST_PATH_IMAGE027
is the transpose of the output matrix;
step 2.3, to the controllable gram matrixPAnd a Zealand matrixQCholesky decomposition is performed, and the expression is as follows:
Figure DEST_PATH_IMAGE028
Figure DEST_PATH_IMAGE029
in the formula:
Figure DEST_PATH_IMAGE030
representing a controllable gram matrixPCholesky decomposition of (1);
Figure DEST_PATH_IMAGE031
representing a controllable gram matrixPTranspose of Cholesky decomposition of (1);
Figure DEST_PATH_IMAGE032
a Cholesky decomposition representing a observable gram matrix Q;
Figure DEST_PATH_IMAGE033
represents the transpose of the Cholesky decomposition of the observable gram matrix Q;
step 2.4, for
Figure DEST_PATH_IMAGE034
Performing singular value decomposition:
Figure DEST_PATH_IMAGE035
in the formula:Uis a unitary matrix;Σis a semi-positive definite diagonal matrix;
Figure DEST_PATH_IMAGE036
are unitary matrices of different orders;
step 2.5, calculating a balance change matrix:
Figure DEST_PATH_IMAGE037
Figure DEST_PATH_IMAGE038
in the formula:
Figure DEST_PATH_IMAGE039
is the equilibrium change matrix after Cholesky decomposition of the observable grand matrix Q;
Figure DEST_PATH_IMAGE040
is a balance change matrix after Cholesky decomposition of the controllable gram matrix P;
step 2.6, carrying out balance transformation on the state space matrix:
Figure DEST_PATH_IMAGE041
in the formula:
Figure DEST_PATH_IMAGE042
a matrix of the system after the balance transformation is represented,
Figure DEST_PATH_IMAGE043
representing the input matrix after the balance transformation,
Figure DEST_PATH_IMAGE044
represents the balanceThe output matrix after the transformation is then output,
Figure DEST_PATH_IMAGE045
the direct transfer matrix after the balance transformation is represented,
Figure DEST_PATH_IMAGE046
is that
Figure DEST_PATH_IMAGE047
Transposing;
and 2.7, truncating the state space matrix after the balance transformation according to the expected model order, calculating a state space equation of the new energy power system after the model dimensionality reduction, and converting the state space equation of the new energy power system after the model dimensionality reduction into a transfer function:
Figure DEST_PATH_IMAGE048
in the formula:
Figure DEST_PATH_IMAGE049
representing a transfer function of a state space equation of the new energy power system;
Figure DEST_PATH_IMAGE050
、
Figure DEST_PATH_IMAGE051
、
Figure DEST_PATH_IMAGE052
respectively, the order of the transfer function numerator 0,m-1order summCoefficients of order;
Figure DEST_PATH_IMAGE053
、
Figure DEST_PATH_IMAGE054
respectively the 0 th order of the transfer function denominator,n-1of orderThe coefficients of which are such that,
Figure DEST_PATH_IMAGE055
、
Figure DEST_PATH_IMAGE056
respectively m-th order of the numerator and n-th order of the denominator.
5. The method for rapidly analyzing the frequency stability of the new energy power system according to claim 4, wherein the method comprises the following steps: the specific steps of the step 3 are as follows: calculating a system pole of the low-order new energy power system frequency response model in the step 2, wherein the expression is as follows:
Figure DEST_PATH_IMAGE057
judging the stability of the frequency of the new energy power system according to the positions of the system poles, wherein the new energy power system is stable if and only if all the system poles are on the left half plane of the complex plane; and selecting a conjugate complex root closest to the imaginary axis as a dominant pole, analyzing the frequency dynamic characteristic through the position of the dominant pole on a complex plane and the damping ratio of the dominant pole, wherein the larger the imaginary part is, the smaller the damping ratio is, and the weaker the frequency stability of the new energy power system is.
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