CN113419418A - Reduced-order modeling method suitable for multi-converter direct-current system - Google Patents

Reduced-order modeling method suitable for multi-converter direct-current system Download PDF

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CN113419418A
CN113419418A CN202110686189.4A CN202110686189A CN113419418A CN 113419418 A CN113419418 A CN 113419418A CN 202110686189 A CN202110686189 A CN 202110686189A CN 113419418 A CN113419418 A CN 113419418A
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converter
transfer function
loop transfer
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朱琳
赵学深
卢浩
李霞林
郭力
赵波
邓占锋
宋洁
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Tianjin University
Global Energy Interconnection Research Institute
Electric Power Research Institute of State Grid Zhejiang Electric Power Co Ltd
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Global Energy Interconnection Research Institute
Electric Power Research Institute of State Grid Zhejiang Electric Power Co Ltd
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    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
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    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
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Abstract

The invention relates to a reduced-order modeling method suitable for a multi-converter direct-current system, which is characterized by comprising the following steps of: step 1: establishing an open-loop transfer function of the equivalent converter; step 2: establishing a closed-loop transfer function of the equivalent converter considering state feedback control; k1And K2Respectively equivalent converter state feedback control fcProportional and derivative control gains of(s); and step 3: establishing a closed-loop transfer function of the equivalent converter considering voltage control; and 4, step 4: establishing a closed loop transfer function of the equivalent converter considering droop control; and 5: and analyzing the dynamic stability of the multi-converter direct-current system through one zero and three poles obtained by the closed-loop transfer function of the equivalent converter.

Description

Reduced-order modeling method suitable for multi-converter direct-current system
Technical Field
The invention belongs to the field of reduced-order modeling of a multi-converter direct-current system, and particularly relates to a reduced-order modeling method suitable for the multi-converter direct-current system.
Background
With the rapid development of renewable energy sources such as photovoltaic power generation and the like in China, the direct current load ratio is gradually improved. Compared with the ac system, the dc system has more and more obvious advantages in terms of receiving renewable energy and dc loads, so the dc system will be the key development direction of the future power distribution system. The renewable energy and the direct current load can be connected to the direct current system through the converter, and the negative resistance characteristic of the direct current load brings great challenges to the dynamic stability of the direct current system, so that the analysis of the dynamic stability of the multi-converter direct current system is particularly important. The full-order model, although being able to describe the dynamic stability of the multi-converter dc system in sufficient detail, has many disadvantages. For example, the modeling process is complex, the model order is high, the calculation amount is large, and the like. Therefore, order-reduced modeling is necessary to reduce the difficulty of dynamic stability analysis of the multi-converter direct-current system. A reduced-order model of the multi-converter direct-current system is obtained based on a conventional reduced-order modeling method, and the process can be generally divided into two steps. Firstly, establishing a reduced-order model of each converter when the converter operates independently. And secondly, connecting the reduced-order models of the converters based on the system topology to obtain the reduced-order model of the multi-converter direct-current system. The conventional reduced-order modeling method has the defect that when a certain converter cannot obtain a reduced-order model of the converter, the reduced-order model of the multi-converter direct-current system cannot be established. Therefore, when a certain converter cannot obtain the reduced-order model, the dynamic stability of the multi-converter direct-current system can be analyzed only by using the full-order model. The dynamic stability analysis model of the single converter is low in order, so that the dynamic stability analysis difficulty of the single converter is far smaller than that of a multi-converter direct-current system.
In summary, in order to reduce the difficulty of analyzing the dynamic stability of the multi-converter dc system and fully exert the advantages of the multi-converter dc system, a reduced-order modeling method suitable for the multi-converter dc system is required.
Disclosure of Invention
The invention aims to provide a reduced-order modeling method suitable for a multi-converter direct-current system. The technical scheme is as follows:
a reduced-order modeling method suitable for a multi-converter direct-current system is characterized by comprising the following steps:
step 1: establishing an open-loop transfer function of an equivalent converter
Open loop transfer function G of the x-th converter in a multi-converter DC systemvdx(s) represented by the following formula:
Figure BDA0003124680510000021
in the above formula, x is 1,2, …, n, n is the number of inverters; esThe input direct current voltage of each converter; l isfxThe output filter inductor is the output filter inductor of the x converter; req、CeqAnd LeqRespectively an equivalent resistor, an equivalent filter capacitor and an equivalent filter inductor of the multi-converter direct-current system; s is the laplace operator.
Dividing the open-loop transfer function G of each convertervdx(s) phase accumulation to obtain the open-loop transfer function G of the equivalent convertervd(s) represented by the following formula:
Figure BDA0003124680510000022
step 2: establishing a closed-loop transfer function of an equivalent converter taking into account state feedback control
Taking into account state feedback control f in a multi-converter DC systemcx(s) closed loop transfer function G of the x stage convertervdfcx(s) represented by the following formula:
Figure BDA0003124680510000023
in the above formula, K1xAnd K2xRespectively, state feedback control fcxProportional and differential control gains of(s) for adjusting the closed-loop transfer function G of each convertervdfcx(s) phase accumulation to obtain a closed-loop transfer function G of the equivalent converter considering state feedback controlvdfc(s) represented by the following formula:
Figure BDA0003124680510000024
in the above formula, K1And K2Respectively equivalent converter state feedback control fcProportional and derivative of(s) controls the gain.
And step 3: establishing a closed loop transfer function for voltage controlled equivalent converters
Closed loop transfer function G of xth converter considering voltage control and state feedback control simultaneously in multi-converter direct current systemvvfcx(s) represented by the following formula:
Figure BDA0003124680510000025
in the above formula, Gvcx(s) a voltage controller for the x-th converter, a closed-loop transfer function G for each convertervvfcx(s) phase accumulation to obtain a closed loop of the equivalent converter taking into account both voltage control and state feedback controlTransfer function Gvvfc(s) represented by the following formula:
Figure BDA0003124680510000026
in the above formula, GvcAnd(s) is a voltage controller of the equivalent converter.
And 4, step 4: establishing a closed loop transfer function for an equivalent converter taking into account droop control
Closed loop transfer function G of xth converter considering droop control in multi-converter DC systemvvkfcx(s) represented by the following formula:
Figure BDA0003124680510000031
in the above formula, k is the equivalent droop coefficient, and is the closed loop transfer function G of each convertervvkfcx(s) phase accumulation to obtain closed-loop transfer function G of equivalent convertervvkfc(s) represented by the following formula:
Figure BDA0003124680510000032
and 5: closed loop transfer function G through equivalent convertervvkfcAnd(s) analyzing the dynamic stability of the multi-converter direct current system by using the obtained zero and three poles.
Drawings
FIG. 1 is a typical topology and control block diagram of a multi-converter DC system;
FIG. 2 is a topology and control block diagram of an iso-converter;
FIG. 3 is a zero pole plot of an equivalent converter;
fig. 4 is an experimental waveform diagram of a multi-converter dc system and its equivalent converter.
Detailed Description
The present invention provides a reduced-order modeling method for a multi-converter dc system, which is described in detail below with reference to the accompanying drawings and specific implementation.
(1) Establishing an open-loop transfer function of an equivalent converter
The research object of the invention is a multi-converter direct current system, and the typical topology of the system is shown in figure 1. In FIG. 1, CfxAnd LfxThe filter capacitors and the filter inductors are output filter capacitors and output filter inductors of the x-th converter respectively, wherein x is 1,2, …, n and n are the number of the converters; i isxAnd Dx(s) the output filter inductance current and the duty ratio of the xth converter respectively; vrefAnd EsThe reference value of the output voltage and the input direct-current voltage of each converter are respectively; k1xAnd K2xRespectively, state feedback control fcxProportional and derivative control gains of(s); vkxAnd Dvcx(s) a droop control link and a voltage controller G for the xth convertervcx(s) an output signal; p is a radical ofxAnd kdsxRespectively is the power distribution coefficient and the droop coefficient of the x converter; cLfAnd ILAn input filter capacitor and a load current which are respectively a direct current load; s is a laplace operator; and V is the direct current bus voltage.
Open loop transfer function G of the x-th converter in a multi-converter DC systemvdx(s) represented by the following formula:
Figure BDA0003124680510000041
in the above formula, ReqIs the equivalent resistance of the multi-converter DC system, which is equal to the load current ILThe ratio to the dc bus voltage V; ceqIs an equivalent filter capacitor of a multi-converter DC system, which is equal to all output filter capacitors CfxAnd an input filter capacitor CLfA parallel value of (d); l iseqIs equivalent filter inductance of multi-converter DC system, which is equal to all output filter inductances LfxThe parallel value of (c).
The topology of the equivalent converter of the multi-converter direct current system is shown in figure 2. In FIG. 2, CfAnd LfOutput filter capacitors of equivalent current converter respectivelyAnd an output filter inductor; i and D(s) are output filter inductance current and duty ratio of the equivalent current converter respectively; k1And K2Respectively equivalent converter state feedback control fcProportional and derivative control gains of(s); vkAnd Dvc(s) is equivalent converter droop control link and voltage controller G respectivelyvc(s) an output signal; and k is the equivalent droop coefficient of the equivalent converter.
Dividing the open-loop transfer function G of each convertervdxThe(s) phases are accumulated to obtain the open-loop transfer function G of the equivalent convertervd(s) represented by the following formula:
Figure BDA0003124680510000042
from the above analysis, the open-loop transfer function G based on the equivalent convertervd(s) to fully analyze the open-loop transfer function G of all converters in the DC systemvdxThe overall characteristics of(s).
(2) Establishing a closed-loop transfer function of an equivalent converter taking into account state feedback control
State feedback control f of the xth converter in a multi-converter DC systemcx(s) the expression, as shown below:
fcx(s)＝(K1x+K2xs)V
taking into account state feedback control fcxAfter(s), the closed loop transfer function G of the xth converter can be obtainedvdfcx(s) represented by the following formula:
Figure BDA0003124680510000043
state feedback control f of equivalent converterc(s) the expression, as shown below:
fc(s)＝(K1+K2s)V
taking into account state feedback control fcAfter(s), obtaining the closed loop transfer function G of the equivalent convertervdfc(s) represented by the following formula:
Figure BDA0003124680510000044
assuming a closed loop transfer function Gvdfc(s) equal to the closed loop transfer function G of the convertersvdfcx(s), it can be deduced that the following expression holds:
Figure BDA0003124680510000051
according to the corresponding relation of the state feedback control gain between each converter and the equivalent converter, the closed loop transfer function G based on the equivalent converter is knownvdfc(s) can fully analyze the closed-loop transfer function G of all converters in the direct current systemvdfcxThe overall characteristics of(s).
(3) Establishing a closed loop transfer function for voltage controlled equivalent converters
Voltage controller G of the x-th converter in a multi-converter DC systemvcx(s) the expression, as shown below:
Figure BDA0003124680510000052
in the above formula, kpvxAnd kivxAre respectively a voltage controller GvcxProportional gain and integral gain of(s). Taking into account state feedback control fcx(s) and a voltage controller GvcxAfter(s), the closed loop transfer function G of the xth converter can be obtainedvvfcx(s) represented by the following formula:
Figure BDA0003124680510000053
voltage controller G of equivalent convertervc(s) the expression, as shown below:
Figure BDA0003124680510000054
in the above formula, kpvAnd kivAre respectively a voltage controller GvcProportional gain and integral gain of(s). Taking into account state feedback control fc(s) and a voltage controller GvcAfter(s), obtaining the closed loop transfer function G of the equivalent convertervvfc(s) represented by the following formula:
Figure BDA0003124680510000055
assuming a closed loop transfer function Gvvfc(s) equal to the closed loop transfer function G of the convertersvvfcx(s), it can be deduced that the following expression holds:
Figure BDA0003124680510000056
the corresponding relation of the voltage control gain between each converter and the equivalent converter can be known, and the closed loop transfer function G based on the equivalent convertervvfc(s) can fully analyze the closed-loop transfer function G of all converters in the direct current systemvvfcxThe overall characteristics of(s).
(4) Establishing a closed loop transfer function for an equivalent converter taking into account droop control
Taking into account state feedback control f in a multi-converter DC systemcx(s) Voltage controller Gvcx(s) closed loop transfer function G of the x stage converter after droop controlvvkfcx(s) represented by the following formula:
Figure BDA0003124680510000061
taking into account state feedback control fc(s) Voltage controller GvcAfter(s) and droop control, a closed-loop transfer function G of the equivalent converter can be obtainedvvkfc(s)As shown in the following formula:
Figure BDA0003124680510000062
based on the corresponding relation of the control gain between each converter and the equivalent converter, the closed-loop transfer function G of the equivalent converter can be obtainedvvkfc(s) equal to the closed loop transfer function G of the convertersvvkfcx(s) accumulated sum. So far, the closed loop transfer function G through the equivalent convertervvkfcAnd(s) obtaining one zero point and three poles, and analyzing the dynamic stability of the multi-converter direct-current system.
In order to verify the effectiveness of the order-reducing modeling method suitable for the multi-converter direct-current system, the order-reducing modeling method is verified based on a multi-converter direct-current system switch model built by an RT-BOX hardware-in-the-loop experiment platform, and partial theoretical analysis and experiment results are respectively shown in fig. 3 and fig. 4. At 0.1 second, the DC load suddenly increased from 6MW to 12 MW.
As can be seen from fig. 3, the dynamic stability of the dc system of the multi-converter can be described by a pair of conjugate poles due to the cancellation effect of the real zero and the real pole. From the pair of conjugate poles, the oscillation frequency f of the multi-converter DC system is knowns22.4Hz, damping ratio ζsIs 0.29.
As can be seen from fig. 4, the dynamic steady-state characteristics of the dc voltages of the multi-converter dc system and the equivalent converter thereof have extremely high consistency, and the effectiveness of the reduced-order modeling method provided by the invention is verified. The oscillation frequency of the experimental result of fig. 4 is about 21.5Hz, which is basically consistent with the theoretical analysis value of 22.4Hz in fig. 3, and the effectiveness of the order-reduction modeling method provided by the invention is verified.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting the same, and although the present invention is described in detail with reference to the above embodiments, those of ordinary skill in the art should understand that: modifications and equivalents may be made to the embodiments of the invention without departing from the spirit and scope of the invention, which is to be covered by the claims.

Claims (1)

1. A reduced-order modeling method suitable for a multi-converter direct-current system is characterized by comprising the following steps:
step 1: establishing an open-loop transfer function of an equivalent converter
Open loop transfer function G of the x-th converter in a multi-converter DC systemvdx(s) represented by the following formula:
Figure FDA0003124680500000011
in the above formula, x is 1,2, …, n, n is the number of inverters; esThe input direct current voltage of each converter; l isfxThe output filter inductor is the output filter inductor of the x converter; req、CeqAnd LeqRespectively an equivalent resistor, an equivalent filter capacitor and an equivalent filter inductor of the multi-converter direct-current system; s is the laplace operator.
Dividing the open-loop transfer function G of each convertervdx(s) phase accumulation to obtain the open-loop transfer function G of the equivalent convertervd(s) represented by the following formula:
Figure FDA0003124680500000012
step 2: establishing a closed-loop transfer function of an equivalent converter taking into account state feedback control
Taking into account state feedback control f in a multi-converter DC systemcx(s) closed loop transfer function G of the x stage convertervdfcx(s) represented by the following formula:
Figure FDA0003124680500000013
in the above formula, K1xAnd K2xRespectively, state feedback control fcxProportional and differential control gains of(s) for adjusting the closed-loop transfer function G of each convertervdfcx(s) phase accumulation to obtain a closed-loop transfer function G of the equivalent converter considering state feedback controlvdfc(s) represented by the following formula:
Figure FDA0003124680500000014
in the above formula, K1And K2Respectively equivalent converter state feedback control fcProportional and derivative control gains of(s);
and step 3: establishing a closed loop transfer function for voltage controlled equivalent converters
Closed loop transfer function G of xth converter considering voltage control and state feedback control simultaneously in multi-converter direct current systemvvfcx(s) represented by the following formula:
Figure FDA0003124680500000015
in the above formula, Gvcx(s) a voltage controller for the x-th converter, a closed-loop transfer function G for each convertervvfcx(s) phase accumulation to obtain a closed-loop transfer function G of the equivalent converter taking into account both voltage control and state feedback controlvvfc(s) represented by the following formula:
Figure FDA0003124680500000021
in the above formula, Gvc(s) a voltage controller for the equivalent converter;
and 4, step 4: establishing a closed loop transfer function for an equivalent converter taking into account droop control
Closed loop transfer function G of xth converter considering droop control in multi-converter DC systemvvkfcx(s) represented by the following formula:
Figure FDA0003124680500000022
in the above formula, k is the equivalent droop coefficient, and is the closed loop transfer function G of each convertervvkfcx(s) phase accumulation to obtain closed-loop transfer function G of equivalent convertervvkfc(s) represented by the following formula:
Figure FDA0003124680500000023
and 5: closed loop transfer function G through equivalent convertervvkfcAnd(s) analyzing the dynamic stability of the multi-converter direct current system by using the obtained zero and three poles.
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Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114048698A (en) * 2021-10-26 2022-02-15 天津大学 Multi-machine parallel direct current system control parameter design method considering dynamic interaction
CN114172143A (en) * 2021-12-08 2022-03-11 天津大学 Direct-current system equivalent modeling method based on voltage and current double-loop control
CN115360757A (en) * 2022-08-31 2022-11-18 国网上海能源互联网研究院有限公司 Single-machine equivalent modeling method for multi-converter grid-connected flexible interconnection system

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Cited By (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114048698A (en) * 2021-10-26 2022-02-15 天津大学 Multi-machine parallel direct current system control parameter design method considering dynamic interaction
CN114048698B (en) * 2021-10-26 2023-04-04 天津大学 Multi-machine parallel direct current system control parameter design method considering dynamic interaction
CN114172143A (en) * 2021-12-08 2022-03-11 天津大学 Direct-current system equivalent modeling method based on voltage and current double-loop control
CN114172143B (en) * 2021-12-08 2022-10-11 天津大学 Direct-current system equivalent modeling method based on voltage and current double-loop control
CN115360757A (en) * 2022-08-31 2022-11-18 国网上海能源互联网研究院有限公司 Single-machine equivalent modeling method for multi-converter grid-connected flexible interconnection system
CN115360757B (en) * 2022-08-31 2023-04-25 国网上海能源互联网研究院有限公司 Single-machine equivalent modeling method for multi-converter grid-connected flexible interconnection system

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