CN110994666A - Order reduction method for reducing impedance model to RLC circuit at resonance frequency - Google Patents

Order reduction method for reducing impedance model to RLC circuit at resonance frequency Download PDF

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CN110994666A
CN110994666A CN201910999975.2A CN201910999975A CN110994666A CN 110994666 A CN110994666 A CN 110994666A CN 201910999975 A CN201910999975 A CN 201910999975A CN 110994666 A CN110994666 A CN 110994666A
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李飞
王艺潮
张永新
刘洋
马铭遥
张兴
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Hefei University of Technology
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Abstract

The invention provides a method for reducing an impedance model into an RLC circuit at a resonance frequency. The method is realized by the following steps: and obtaining an impedance model of the new energy power generation system through frequency sweep or theoretical derivation, judging whether the resonance frequency belongs to parallel resonance or series resonance, and performing RLC circuit fitting. The method is simple to realize, and can reduce the resonance information contained in the model into the RLC circuit by only obtaining the impedance model of the system, thereby having obvious superiority.

Description

Order reduction method for reducing impedance model to RLC circuit at resonance frequency
Technical Field
The invention relates to a method for reducing the order of an impedance model of a new energy power generation system at a resonance frequency, in particular to a method for reducing the order of the impedance model of the new energy power generation system by judging whether the resonance frequency belongs to parallel resonance or series resonance according to the obtained impedance model of the new energy power generation system, then performing RLC circuit fitting, extracting the resonance characteristic of the impedance model of the new energy power generation system and realizing the order reduction through the RLC circuit fitting.
Background
Under the background of high power electronization of a power system, when grid-connected permeability is high, the interior of a new energy power generation system is mutually coupled to form a complex multi-scale high-order nonlinear network, and the system is easily affected by internal or external disturbance to be unstable. The increase of power electronic devices increases the possibility of system harmonic interaction under the weak grid condition, and further causes harmonic amplification and even resonance of a grid-connected point of the new energy power generation system. Therefore, how to simplify the impedance model of the new energy power generation system and analyze the stripped important resonance characteristics has very important research value. In related research, there are documents 1 "Yang F, Zeng X, Su Y, et al. RLC equivalent circuit synthesis method for structure-predicted reduced-order model of interconnection in VLSI [ J ]. Commun. Compout. Phys,2008,3(2):376 and 396.; document 2, "spin, Su backstroke, Wangjian, et al," a single-input single-output RCS interconnect circuit order reduction method [ P ] Chinese 1604092A, 2005-04-06; document 3 < Janus, Samsung, Zencao. non-linear circuit time domain model reduction method and apparatus [ P ] China 102467593B,2015-04-22 ]; document 4 "LiuH, Xie X, Gao X, et al.Stablility analysis of SSR in multiple with stimulated reactions to series-compensated Systems using stimulated data network model [ J ]. IEEEtransformations on Power Systems,2017,33(3):3118-3128
Document 1 proposes a distributed RLC circuit model synthesis method applied to transmission line behavior simulation analysis of interconnection lines in a large-scale integrated circuit, which implements model order reduction based on a Krylov state subspace and can well reduce the order of a linear model. Document 2 proposes, on the basis of a distributed RLC circuit model, replacing the model with a reciprocal susceptance S of an inductance to avoid a decrease in simulation accuracy and speed due to an excessively large inductance L matrix in the RLC circuit model, thereby improving simulation efficiency. In document 3, a trajectory is formed in a state space model of the nonlinear circuit by a "training signal", and an expansion point is selected on the trajectory to approximate the nonlinear circuit by a piecewise linear method, so as to implement order reduction. However, the three reduction methods for the integrated circuit are not suitable for reducing the resonance characteristics in the new energy power generation system because the integrated circuit does not have the resonance problem and the reservation of the resonance characteristics is not considered during the reduction. Document 4 proposes a method for aggregating and extracting resonance characteristics based on an impedance model of a new energy power generation system, and although an object to be analyzed is the new energy power generation system, since the object to be analyzed is sub-synchronous resonance, only series resonance is considered to exist on one side, and impedance characteristics of the system cannot be completely considered.
In summary, the above documents have the following disadvantages:
1) the model order reduction method is suitable for the integrated circuit, and the integrated circuit does not have the resonance problem of the new energy power generation system, so the reservation of the resonance characteristic is not considered during order reduction, and the method is not suitable for the order reduction of the resonance characteristic in the new energy power generation system;
2) the method is suitable for a new energy power generation system, and only the application of the method applied to the subsynchronous resonance is considered, so that only series resonance exists in the system, and the method cannot be completely suitable for the new energy power generation system;
3) the simplified procedure is complex, complicated mathematical transformation needs to be carried out on the established model to realize order reduction, and the method is not suitable for engineering application.
Disclosure of Invention
The invention aims to reduce the impedance model of the new energy power generation system to a second-order RLC circuit at the resonance frequency, so that the resonance characteristic of the new energy power generation system is stripped, and the resonance mechanism can be conveniently identified and other applications can be conveniently realized. The order reduction method provided by the invention not only retains the resonance characteristics of the impedance model of the new energy power generation system, but also reduces the difficulty of analyzing the resonance problem. Specifically, an impedance model of the new energy power generation system is obtained through measurement or theoretical derivation and the like, and after whether the resonance frequency belongs to parallel resonance or series resonance is judged, an RLC circuit is used for fitting to achieve order reduction.
The invention aims to realize the purpose, the invention provides a method for reducing the impedance model into an RLC circuit at the resonant frequency, the resonance characteristic of the impedance model of the new energy power generation system is extracted, and the model reduction is realized through the RLC circuit fitting, and the method comprises the following specific steps:
step 1, obtaining amplitude-frequency characteristics and phase-frequency characteristics of the new energy power generation system by measuring an impedance model of the new energy power generation system, specifically, the amplitude-frequency characteristics are expressed by an amplitude-frequency curve, the abscissa and the ordinate of the amplitude-frequency characteristics are frequency and amplitude respectively, the phase-frequency characteristics are expressed by a phase-frequency curve, and the abscissa and the ordinate of the phase-frequency characteristics are frequency and phase respectively;
step 2, according to the amplitude-frequency curve and the phase-frequency curve obtained in the step 1, defining the resonance mode of the new energy power generation system as follows:
when the phase curve crosses 0 degree, the corresponding amplitude-frequency curve is upward convex and is defined as parallel resonance, the original impedance model is equivalent by using an RLC parallel circuit, and the crossing point is marked as a parallel resonance point, and the step 3 is carried out;
when the phase curve crosses 0 degree, the corresponding amplitude-frequency curve is downwards concave and defined as series resonance, the original impedance model is equivalent by using an RLC series circuit, the crossing point is marked as a series resonance point, and the step 5 is carried out;
if the corresponding amplitude-frequency curve does not have the two conditions when the phase curve crosses 0 degrees, the parallel resonance and the series resonance are not realized, and the step 7 is carried out;
step 3, extracting frequency data f of the parallel resonance point and the adjacent points thereof from the amplitude-frequency curve and the phase curve1、f2Amplitude data a1、a2And phase data p1、p2Calculating the corresponding angular frequency s1、s2Resistance r1、r2And reactance x1、x2Then entering step 4;
s1＝2πf1
s2＝2πf2
Figure BDA0002240996420000032
Figure BDA0002240996420000033
Figure BDA0002240996420000034
step 4, setting a resistance parameter R in an equivalent RLC parallel circuitp＝r1The inductance parameter LpAnd a capacitance parameter CpThen this can be obtained from the following relationship:
Figure BDA0002240996420000041
Figure BDA0002240996420000042
entering step 7;
step 5, extracting frequency data F of the series resonance point and the adjacent points thereof from the amplitude-frequency curve and the phase curve1、F2Amplitude data A1、A2And phase data P1、P2Calculating the corresponding angular frequency S1、S2Resistance R1、R2And reactance X1、X2Then entering step 6;
S1＝2πF1
S2＝2πF2
Figure BDA0002240996420000043
Figure BDA0002240996420000044
X1＝R1tan(P1)
X2＝R2tan(P2)
step 6, setting a resistance parameter R in the equivalent RLC series circuits＝R1Inductance parameter LsAnd a capacitance parameter CsThen this can be obtained from the following relationship:
Figure BDA0002240996420000045
Figure BDA0002240996420000046
entering step 7;
and 7, finishing the reduction.
Compared with the prior art, the invention has the following beneficial effects:
1) the method is suitable for a new energy power generation system, and can keep the resonance characteristic while reducing the order of the model;
2) the series resonance and the parallel resonance can completely reflect the resonance type in the new energy power generation system, and the application range is wide;
3) the method does not need complex mathematical transformation, is simple in calculation and is suitable for engineering application.
Drawings
FIG. 1 is a schematic diagram of a 2MW doubly-fed wind grid-connected power generation system according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of an impedance model of a 2MW doubly-fed wind grid-connected power generation system;
FIG. 3 is a schematic diagram of comparison between a reduced-order RLC model at a first series resonance point A and an impedance model of a 2MW doubly-fed wind grid-connected power generation system;
FIG. 4 is a schematic diagram of comparison between a reduced-order RLC model at a first parallel resonance point B and an impedance model of a 2MW doubly-fed wind grid-connected power generation system;
fig. 5 is a schematic diagram comparing the reduced RLC model at the second series resonance point C with the impedance model of the 2MW doubly-fed wind grid-connected power generation system.
FIG. 6 is a flow chart of the order reduction method of the present invention.
Detailed Description
The example takes a 2MW doubly-fed wind power grid-connected power generation system in simulation software Matlab/Simulink as an example, and illustrates a method for reducing an impedance model to an RLC circuit at a resonant frequency.
Fig. 1 is a topological structure diagram of a 2MW doubly-fed wind grid-connected power generation system related in the present example. As can be seen from the figure, the 2MW doubly-fed wind power grid-connected power generation system is composed of two power electronic converters and a doubly-fed motor, where the two power electronic converters (i.e., the rotor-side power electronic converter and the stator-side power electronic converter shown in fig. 1) respectively include a three-phase full bridge and an LC filter, and share a dc-side capacitor CdcTwo power electronic converters pass through a DC side capacitor CdcAnd the two-way filter is connected with the rotor side and the stator side of the doubly-fed motor respectively through respective LC filters. Stator side power electronic converter switching frequency f of double-fed wind power generation systemsStator side LC Filter L for 2000HzsIs 0.35mH, Cs334.2. mu.F; rotor-side power electronic converter switching frequency frFor 2000Hz, a rotor-side LC filter L is usedrIs 70 muH, Cr0.1 muF; the rated power of the double-fed motor is 2.5MW, the rated voltage is 690V, and the rated frequency f0Is 50Hz, stator resistance Rstator0.0008 omega, stator inductance Lstator43.927 μ H, rotor resistance Rrotor0.0013 omega, rotor inductance Lrotor43.608 muH, mutual inductance LmutualIt was 1.2mH and the number of pole pairs was 3.
In this embodiment, an impedance model of the 2MW doubly-fed wind power grid-connected power generation system related to this embodiment is obtained in a frequency sweep manner, and fig. 2 is a frequency sweep result. And finally, processing the frequency sweeping result, extracting resonance information and reducing the impedance model at the resonance frequency into an RLC circuit.
Embodiments of the present invention are described in detail below with reference to fig. 1-6.
In embodiment 1, a flowchart of the order reduction method of the present invention refers to fig. 6, a schematic diagram of an impedance model refers to fig. 2, and as can be seen from fig. 2 and fig. 6, the order reduction method of the present invention for reducing the impedance model to the RLC circuit at the resonant frequency extracts the resonance characteristics of the impedance model of the new energy power generation system and realizes the model order reduction by the RLC circuit fitting, which includes the following specific steps:
step 1, obtaining amplitude-frequency characteristics and phase-frequency characteristics of the new energy power generation system by measuring an impedance model of the new energy power generation system, specifically, the amplitude-frequency characteristics are expressed by an amplitude-frequency curve, the abscissa and the ordinate of the amplitude-frequency characteristics are frequency and amplitude respectively, the phase-frequency characteristics are expressed by a phase-frequency curve, and the abscissa and the ordinate of the phase-frequency characteristics are frequency and phase respectively. The upper graph in fig. 2 is a magnitude-frequency curve and the lower graph is a phase curve.
Step 2, according to the amplitude-frequency curve and the phase-frequency curve obtained in the step 1, defining the resonance mode of the new energy power generation system as follows:
in the state 1, when the phase curve crosses 0 degree, the corresponding amplitude-frequency curve is upwards raised to define parallel resonance, the original impedance model is equivalent by using an RLC parallel circuit, the crossing point is marked as a parallel resonance point, and the step 3 is carried out;
in the state 2, when the phase curve crosses 0 degrees, the corresponding amplitude-frequency curve is downwards sunken to define series resonance, the original impedance model is equivalent by using an RLC series circuit, a crossing point is marked as a series resonance point, and the step 5 is carried out;
in the state 3, if the corresponding amplitude-frequency curve does not have the above two conditions when the phase curve crosses 0 °, the phase curve is neither parallel resonance nor series resonance, and the process proceeds to the step 7.
Step 3, extracting frequency data f of the parallel resonance point and the adjacent points thereof from the amplitude-frequency curve and the phase curve1、f2Amplitude data a1、a2And phase data p1、p2Calculating the corresponding angular frequency s1、s2Resistance r1、r2And reactance x1、x2And then step 4 is entered.
s1＝2πf1
s2＝2πf2
Figure BDA0002240996420000071
Figure BDA0002240996420000072
Figure BDA0002240996420000073
Figure BDA0002240996420000074
Step 4, setting a resistance parameter R in an equivalent RLC parallel circuitp＝r1The inductance parameter LpAnd a capacitance parameter CpThen this can be obtained from the following relationship:
Figure BDA0002240996420000075
Figure BDA0002240996420000076
proceed to step 7.
Step 5, extracting frequency data F of the series resonance point and the adjacent points thereof from the amplitude-frequency curve and the phase curve1、F2Amplitude data A1、A2And phase data P1、P2Calculating the corresponding angular frequency S1、S2Resistance R1、R2And reactance X1、X2Then, the process proceeds to step 6.
S1＝2πF1
S2＝2πF2
Figure BDA0002240996420000081
Figure BDA0002240996420000082
X1＝R1tan(P1)
X2＝R2tan(P2)
Step 6, setting a resistance parameter R in the equivalent RLC series circuits＝R1Inductance parameter LsAnd a capacitance parameter CsThen this can be obtained from the following relationship:
Figure BDA0002240996420000083
Figure BDA0002240996420000084
proceed to step 7.
And 7, finishing the reduction.
And 3, the adjacent points of the parallel resonance points refer to adjacent points with the phase distance from the parallel resonance point to the nearest in the left adjacent point and the right adjacent point of the parallel resonance points.
The concept of the proximity point of the series resonance point and the proximity point of the parallel resonance point described in step 5 is the same, and refers to the left proximity point and the right proximity point of the series resonance point, which have the closest phase distance from the series resonance point.
Example 2, see figure 3, in detail below.
Step 1, obtaining amplitude-frequency characteristics and phase-frequency characteristics of the new energy power generation system by measuring an impedance model of the new energy power generation system, specifically, the amplitude-frequency characteristics are expressed by an amplitude-frequency curve, the abscissa and the ordinate of the amplitude-frequency characteristics are frequency and amplitude respectively, the phase-frequency characteristics are expressed by a phase-frequency curve, and the abscissa and the ordinate of the phase-frequency characteristics are frequency and phase respectively. The upper graph in fig. 3 is a magnitude-frequency curve and the lower graph is a phase curve.
Step 2, defining the resonance mode of the new energy power generation system according to the amplitude-frequency curve and the phase-frequency curve obtained in the step 1:
as can be seen from fig. 3, when the phase curve passes through 0 ° for the first time, the corresponding amplitude-frequency curve is concave downward, and belongs to state 2, i.e. it is defined as series resonance, the original impedance model is equivalent by using the RLC series circuit, and the passing point is marked as the series resonance point a, and the process proceeds to step 5.
Step 5, extracting frequency data F of the series resonance point A and the adjacent points thereof1＝377Hz、F2335Hz, amplitude data A1＝55.52dB、A256.22dB with phase data P1＝3.17°、P2-22.31 °, the corresponding angular frequency S is calculated there1、S2Resistance R1、R2And reactance X1、X2Then, the process proceeds to step 6.
By calculating S1＝2369rad/s，S2＝2104rad/s，R1＝596Ω，R2＝599Ω，X1＝33Ω，X2＝-246Ω。
Step 6, equivalent resistance parameter R in RLC series circuits＝R1Inductance parameter LsAnd a capacitance parameter CsThen this can be obtained from the following relationship:
Figure BDA0002240996420000091
Figure BDA0002240996420000092
calculating to obtain Rs＝596Ω，Ls＝0.50H，CsGo to step 7 at 0.36 μ F.
And 7, finishing the reduction.
Example 3, see figure 4, in detail as follows.
Step 1, obtaining amplitude-frequency characteristics and phase-frequency characteristics of the new energy power generation system by measuring an impedance model of the new energy power generation system, specifically, the amplitude-frequency characteristics are expressed by an amplitude-frequency curve, the abscissa and the ordinate of the amplitude-frequency characteristics are frequency and amplitude respectively, the phase-frequency characteristics are expressed by a phase-frequency curve, and the abscissa and the ordinate of the phase-frequency characteristics are frequency and phase respectively. The upper graph in fig. 4 is a magnitude-frequency curve and the lower graph is a phase curve.
And 2, defining the resonance mode of the new energy power generation system according to the amplitude-frequency curve and the phase-frequency curve obtained in the step 1.
As can be seen from fig. 4, when the phase curve passes through 0 ° for the second time, the corresponding amplitude-frequency curve is convex upward, and belongs to state 1, i.e. it is defined as parallel resonance, the RLC parallel circuit is used to make equivalence on the original impedance model, and the passing point is marked as parallel resonance point B, and the procedure proceeds to step 3.
Step 3, extracting the frequency data f of the parallel resonance point B and the adjacent points thereof1＝677Hz、f2761Hz, amplitude data a1＝72.43dB、a270.69dB with phase data p1＝22.48°、p2-46.99 °, the corresponding angular frequency s is calculated there1、s2Resistance r1、r2And reactance x1、x2And then step 4 is entered.
Calculating to obtain s1＝4254rad/s，s2＝4782rad/s，r1＝4527Ω，r2＝5091Ω，x1＝-0.000091Ω，x2＝0.00021Ω。
Step 4, equivalent resistance parameter R in RLC parallel circuitp＝r1Inductance parameter LpAnd a capacitance parameter CpThen this can be obtained from the following relationship:
Figure BDA0002240996420000101
Figure BDA0002240996420000102
calculating to obtain Rp＝4527Ω，Lp＝0.17H，CpWhen the value is 0.30 μ F, the process proceeds to step 7.
And 7, finishing the reduction.
Example 4, see figure 5, in detail below.
Step 1, obtaining amplitude-frequency characteristics and phase-frequency characteristics of the new energy power generation system by measuring an impedance model of the new energy power generation system, specifically, the amplitude-frequency characteristics are expressed by an amplitude-frequency curve, the abscissa and the ordinate of the amplitude-frequency characteristics are frequency and amplitude respectively, the phase-frequency characteristics are expressed by a phase-frequency curve, and the abscissa and the ordinate of the phase-frequency characteristics are frequency and phase respectively. The upper graph in fig. 5 is a magnitude-frequency curve and the lower graph is a phase curve.
And 2, defining the resonance mode of the new energy power generation system according to the amplitude-frequency curve and the phase-frequency curve obtained in the step 1.
As can be seen from fig. 5, when the phase curve passes through 0 ° for the third time, the corresponding amplitude-frequency curve is concave downward, and belongs to state 2, i.e., it is defined as series resonance, the RLC series circuit is used to make equivalence on the original impedance model, and the passing point is marked as series resonance point C, and the procedure proceeds to step 5.
Step 5, extracting frequency data F of the series resonance point C and the adjacent points thereof1'＝1215Hz、F2' -1081 Hz, amplitude data A1'＝44.27dB、A2' 51.44dB, phase data P1'＝-0.6843°、P2' -56.88 deg., and calculating the corresponding angular frequency S1'、S2', resistance R1'、R2' sum reactance X1'、X2Then go to step 6.
By calculating S1'＝7634rad/s，S2'＝6792rad/s，R1'＝163Ω，R2'＝204Ω，X1'＝-1.95Ω，X2'＝-312.61Ω。
Step 6, setting a resistance parameter R in the equivalent RLC series circuits'＝R1', inductance parameter Ls' AND capacitance parameter Cs' then can be obtained from the following relationship:
Figure BDA0002240996420000111
Figure BDA0002240996420000112
calculating to obtain Rs'＝163Ω，Ls'＝0.17H，Cs' -0.099. mu.F, and proceed to step 7.
And 7, finishing the reduction.
FIG. 3 is a schematic diagram comparing a reduced RLC model at the first series resonance with an impedance model of a 2MW doubly-fed wind grid-connected power generation system. FIG. 4 is a schematic diagram comparing a reduced RLC model at the first parallel resonance with an impedance model of a 2MW doubly-fed wind grid-connected power generation system. FIG. 5 is a schematic diagram comparing a reduced RLC model at the second series resonance with an impedance model of a 2MW doubly-fed wind grid-connected power generation system. The RLC circuit fitting is carried out at the resonant frequency position in the impedance model of the 2MW double-fed wind power grid-connected power generation system related to the embodiment, the result theoretically expected by the method can be obtained, and the effectiveness of the method is proved.
In conclusion, the method is simple to implement, resonance information contained in the model can be reduced into the RLC circuit by obtaining the impedance model of the system, and certain feasibility is achieved.

Claims (1)

1. The order reduction method for reducing the impedance model into the RLC circuit at the resonant frequency is characterized in that the resonance characteristics of the impedance model of the new energy power generation system are extracted, and the model order reduction is realized through RLC circuit fitting, and the specific steps are as follows:
step 1, obtaining amplitude-frequency characteristics and phase-frequency characteristics of the new energy power generation system by measuring an impedance model of the new energy power generation system, specifically, the amplitude-frequency characteristics are expressed by an amplitude-frequency curve, the abscissa and the ordinate of the amplitude-frequency characteristics are frequency and amplitude respectively, the phase-frequency characteristics are expressed by a phase-frequency curve, and the abscissa and the ordinate of the phase-frequency characteristics are frequency and phase respectively;
step 2, according to the amplitude-frequency curve and the phase-frequency curve obtained in the step 1, defining the resonance mode of the new energy power generation system as follows:
when the phase curve crosses 0 degree, the corresponding amplitude-frequency curve is upward convex and is defined as parallel resonance, the original impedance model is equivalent by using an RLC parallel circuit, and the crossing point is marked as a parallel resonance point, and the step 3 is carried out;
when the phase curve crosses 0 degree, the corresponding amplitude-frequency curve is downwards concave and defined as series resonance, the original impedance model is equivalent by using an RLC series circuit, the crossing point is marked as a series resonance point, and the step 5 is carried out;
if the corresponding amplitude-frequency curve does not have the two conditions when the phase curve crosses 0 degrees, the parallel resonance and the series resonance are not realized, and the step 7 is carried out;
step 3, extracting frequency data f of the parallel resonance point and the adjacent points thereof from the amplitude-frequency curve and the phase curve1、f2Amplitude data a1、a2And phase data p1、p2Calculating the corresponding angular frequency s1、s2Resistance r1、r2And reactance x1、x2Then entering step 4;
s1＝2πf1
s2＝2πf2
Figure FDA0002240996410000011
Figure FDA0002240996410000021
Figure FDA0002240996410000022
Figure FDA0002240996410000023
step 4, setting a resistance parameter R in an equivalent RLC parallel circuitp＝r1The inductance parameter LpAnd a capacitance parameter CpThen this can be obtained from the following relationship:
Figure FDA0002240996410000024
Figure FDA0002240996410000025
then entering step 7;
step 5, extracting frequency data F of the series resonance point and the adjacent points thereof from the amplitude-frequency curve and the phase curve1、F2Amplitude data A1、A2And phase data P1、P2Calculating the corresponding angular frequency S1、S2Resistance R1、R2And reactance X1、X2Then entering step 6;
S1＝2πF1
S2＝2πF2
Figure FDA0002240996410000026
Figure FDA0002240996410000027
X1＝R1tan(P1)
X2＝R2tan(P2)
step 6, setting a resistance parameter R in the equivalent RLC series circuits＝R1Inductance parameter LsAnd a capacitance parameter CsThen this can be obtained from the following relationship:
Figure FDA0002240996410000031
Figure FDA0002240996410000032
then entering step 7;
and 7, finishing the reduction.
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CN114880863A (en) * 2022-05-20 2022-08-09 合肥工业大学 Distributed renewable energy cluster impedance aggregation model self-adaptive frequency division order reduction method
CN114880863B (en) * 2022-05-20 2024-03-01 合肥工业大学 Self-adaptive frequency division order reduction method for distributed renewable energy cluster impedance aggregation model

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