CN112018802A - Method for constructing equivalent state space model of direct current transmission system link delay - Google Patents

Method for constructing equivalent state space model of direct current transmission system link delay Download PDF

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CN112018802A
CN112018802A CN202010928130.7A CN202010928130A CN112018802A CN 112018802 A CN112018802 A CN 112018802A CN 202010928130 A CN202010928130 A CN 202010928130A CN 112018802 A CN112018802 A CN 112018802A
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link
transmission system
delay
state space
space model
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CN112018802B (en
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郭春义
彭意
徐李清
杨硕
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North China Electric Power 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
    • H02J3/36—Arrangements for transfer of electric power between ac networks via a high-tension dc link
    • 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
    • H02J3/36—Arrangements for transfer of electric power between ac networks via a high-tension dc link
    • H02J2003/365—Reducing harmonics or oscillations in HVDC
    • 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]
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E60/00—Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation
    • Y02E60/60—Arrangements for transfer of electric power between AC networks or generators via a high voltage DC link [HVCD]

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  • Power Engineering (AREA)
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Abstract

The invention discloses a method for constructing an equivalent state space model of direct current transmission system link delay, which comprises the steps of equivalently replacing a link delay link of a direct current transmission system to be processed by a first-order inertia link and a Pade approximation link; then, determining the time constant of a first-order inertia link and the order of a Pade approximation link based on a method combining an impedance model and simulation; and then establishing an equivalent state space model of the link delay link of the direct current power transmission system to be processed according to the first-order inertia link with the determined time constant and the Pade approximation link with the determined order. The method can effectively simulate the relevant characteristics of the link delay of the direct-current power transmission system and provide guidance for measures of oscillation suppression.

Description

Method for constructing equivalent state space model of direct current transmission system link delay
Technical Field
The invention relates to the technical field of power transmission and distribution, in particular to a method for constructing an equivalent state space model of link delay of a direct-current power transmission system.
Background
At present, the direct current transmission technology is widely applied at home and abroad by virtue of the advantages of long distance, large capacity transmission and the like, but in recent years, the high-frequency oscillation phenomenon occurs in direct current transmission engineering. Research shows that the high-frequency oscillation problem in the direct-current power transmission system has strong correlation with link delay of the system, and for the high-frequency oscillation phenomenon in the direct-current power transmission system, many documents model the system and analyze high-frequency oscillation characteristics based on an impedance method, but the impedance method is difficult to locate the relevant factors causing system instability. And the dominant mode of high-frequency oscillation and the electrical and control variables of key participation can be determined to a certain extent based on characteristic roots, participation factors and the like of the state space model, and key parameters which are sensitive to the influence of the system stability are found out, so that guidance is provided for measures of oscillation suppression.
Therefore, it is necessary to provide an equivalent state space model of link delay in a dc power transmission system, and apply the equivalent state space model to a state space model of the whole dc power transmission system, so as to more clearly reveal the high-frequency oscillation related characteristics of the dc power transmission system.
Disclosure of Invention
The invention aims to provide a method for constructing an equivalent state space model of the link delay of a direct-current power transmission system, which can effectively simulate the relevant characteristics of the link delay of the direct-current power transmission system and provide guidance for measures of oscillation suppression.
The purpose of the invention is realized by the following technical scheme:
a method for constructing an equivalent state space model of a direct current transmission system link delay comprises the following steps:
step 1, firstly, equivalently replacing a link delay link of a direct current power transmission system to be processed by a first-order inertia link and a Pade approximation link;
step 2, determining a time constant of a first-order inertia link and an order of a Pade approximation link based on a method combining an impedance model and simulation;
and 3, establishing an equivalent state space model of the link delay link of the direct current power transmission system to be processed according to the first-order inertia link with the determined time constant and the Pade approximation link with the determined order.
According to the technical scheme provided by the invention, the method can effectively simulate the relevant characteristics of the link delay of the direct-current power transmission system and provide guidance for measures of oscillation suppression.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on the drawings without creative efforts.
Fig. 1 is a schematic flow chart of a method for constructing an equivalent state space model of a link delay of a direct-current power transmission system according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a comparison result of system dynamic responses when active power of a link delay equivalent state space model and a PSCAD electromagnetic transient model in a flexible direct current power transmission system has a step.
Detailed Description
The technical solutions in the embodiments of the present invention are clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments of the present invention without making any creative effort, shall fall within the protection scope of the present invention.
The following will describe the embodiment of the present invention in further detail with reference to the accompanying drawings, and as shown in fig. 1, a flow chart of a method for constructing an equivalent state space model of a link delay of a dc power transmission system provided by the embodiment of the present invention is shown, where the method includes:
step 1, firstly, equivalently replacing a link delay link of a direct current power transmission system to be processed by a first-order inertia link and a Pade approximation link;
in this step, the expression of the equivalent substitution link is as follows:
e-sT≈τ(s)·R(s)
wherein，e-sTThe transfer function is a link delay link of the direct current power transmission system to be processed; tau(s) is a transfer function of a first-order inertia link; r(s) is a transfer function of the Pade approximation link, wherein:
the expressions for τ(s) and R(s) are as follows:
Figure BDA0002669180770000031
in the above formula, TmIs the time constant of the first-order inertia element; k. l is the order of the denominator and numerator of the Pade approximation link; in the invention, k is equal to l and n, namely, the denominator and the numerator are both taken as n orders, and the coefficients a of the denominator and the numerator are taken at the momentj、bjThe expression (j ═ 0,1, …, n) is:
Figure BDA0002669180770000032
step 2, determining a time constant of a first-order inertia link and an order of a Pade approximation link based on a method combining an impedance model and simulation;
in the step, first-order inertia links with different time constants and Pade approximation links with different orders are selected to replace a link delay link of the direct-current power transmission system to be processed, and a direct-current power transmission system model comprising the delay replacement link (namely the first-order inertia link and the Pade approximation link) is called a substitution model hereinafter;
and then scanning the system impedance of each substitution model, comparing the scanned impedance curve with the impedance curve of the original link delay model, and when the impedance amplitude error and the phase error of the impedance curve in a scanning frequency band are within 5%, determining that the delay substitution link can well simulate a delay link, thereby determining the time constant of a first-order inertia link and the order of a Pade approximation link, wherein the scanning frequency band is determined according to the problem to be researched.
Furthermore, the oscillation amplitude and the oscillation frequency of the active power of the direct-current power transmission system reproduced by the substitution model can be compared with the original link delay model through simulation, so that the accuracy of the selected substitution model is verified.
For example, taking a flexible direct-current power transmission system as an example, taking an impedance scanning frequency band as 1-2000Hz, and according to an impedance characteristic curve of the flexible direct-current power transmission system containing link delay and an impedance characteristic curve of the flexible direct-current power transmission system obtained by equivalently replacing a link delay link with a first-order inertia link and a Pade approximation link, comparing results and matching degrees of the two curves, the example selects a first-order inertia time constant as 1 microsecond and a Pade approximation order as 4 orders.
And 3, establishing an equivalent state space model of the link delay link of the direct current power transmission system to be processed according to the first-order inertia link with the determined time constant and the Pade approximation link with the determined order.
In this step, the expression of the established equivalent state space model is:
Figure BDA0002669180770000033
wherein x is a state variable; u is input; y is the output; A. b, C is a coefficient matrix.
The following will describe the specific derivation process of the state space model according to the determined first-order inertia element time constant TmAnd the order n of the Pade approximate link, the equivalent transfer function of the delay link can be obtained as shown in the following formula:
Figure BDA0002669180770000041
selecting a state variable of a first-order inertia link as z and a state variable of a Pade approximation link as x1、x2、…、xnThe specific expression of the state space model based on the above-mentioned delay equivalent transfer function can be given by the following formula:
Figure BDA0002669180770000042
Figure BDA0002669180770000043
state variable matrix x ═ x1 x2 … xn z]TThe coefficient matrix A, B, C is expressed as follows:
Figure BDA0002669180770000044
fig. 2 is a schematic diagram showing a comparison result of the system dynamic response when the active power of the link delay equivalent state space model and the PSCAD electromagnetic transient model in the flexible direct current transmission system has a step, and it can be seen from fig. 2 that: when active power has a step, the dynamic characteristics of the established equivalent state space model containing the link delay are basically consistent with those of the electromagnetic transient state model in the PSCAD, so that the effectiveness of the proposed equivalent state space model containing the link delay can be demonstrated, and the equivalent state space model containing the link delay can be established according to the method disclosed by the invention for a traditional direct-current transmission system.
It is noted that those skilled in the art will recognize that embodiments of the present invention are not described in detail herein.
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 constructing an equivalent state space model of a direct current transmission system link delay is characterized by comprising the following steps:
step 1, firstly, equivalently replacing a link delay link of a direct current power transmission system to be processed by a first-order inertia link and a Pade approximation link;
step 2, determining a time constant of a first-order inertia link and an order of a Pade approximation link based on a method combining an impedance model and simulation;
and 3, establishing an equivalent state space model of the link delay link of the direct current power transmission system to be processed according to the first-order inertia link with the determined time constant and the Pade approximation link with the determined order.
2. The method for constructing the equivalent state space model of the link delay of the direct-current transmission system according to claim 1, wherein in the step 1, the equivalent substitution process adopts the following expression:
e-sT≈τ(s)·R(s)
wherein e is-sTThe transfer function is a link delay link of the direct current power transmission system to be processed; tau(s) is a transfer function of a first-order inertia link; r(s) is a transfer function of the pade approximation link;
wherein the expressions of τ(s) and R(s) are as follows:
Figure FDA0002669180760000011
in the above formula, TmIs the time constant of the first-order inertia element; k. l is the order of the denominator and numerator of the Pade approximation link; taking k as l as n, i.e. the denominator and the numerator are both taken as n orders, when the coefficients a of the denominator and the numerator are takenj、bjThe expression (j ═ 0,1, …, n) is:
Figure FDA0002669180760000012
3. the method for constructing the equivalent state space model of the link delay of the direct-current transmission system according to claim 1, wherein the process of the step 2 specifically comprises:
firstly, selecting first-order inertia links with different time constants and Pade approximation links with different orders to replace a link delay link of a direct current power transmission system to be processed, and calling a direct current power transmission system model containing a delay replacing link as a replacing model;
then, scanning the system impedance of each substitution model, and comparing the impedance curve obtained by scanning with the impedance curve of the original link delay model;
when the impedance amplitude error and the phase error of the impedance curve in the scanning frequency band are both within 5%, the time-delay substitute link is considered to be capable of well simulating a time-delay link, and then the time constant of the first-order inertia link and the order of the Pade approximation link are determined.
4. The method for constructing the equivalent state space model of the link delay of the direct-current transmission system according to claim 1, wherein in the step 3, the expression of the established equivalent state space model is as follows:
Figure FDA0002669180760000021
wherein x is a state variable; u is input; y is the output; A. b, C is a coefficient matrix.
5. The method for constructing the equivalent state space model of the link delay of the direct-current transmission system according to claim 1 or 4, wherein in the step 3, the process for establishing the equivalent state space model specifically comprises:
according to the determined first-order inertia element time constant TmAnd the order n of the Pade approximate link to obtain an equivalent transfer function of the delay link as shown in the following formula:
Figure FDA0002669180760000022
selecting a state variable of a first-order inertia link as z and a state variable of a Pade approximation link as x1、x2、…、xnThe specific expression of the state space model based on the equivalent transfer function is as follows:
Figure FDA0002669180760000023
Figure FDA0002669180760000024
wherein the state variable matrix x ═ x1 x2…xn z]TThe coefficient matrix A, B, C is expressed as follows:
Figure FDA0002669180760000031
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Citations (4)

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Publication number Priority date Publication date Assignee Title
CN101930487A (en) * 2010-07-09 2010-12-29 南方电网技术研究中心 Hybrid real-time simulation method for continuous long-time steady operation of power system
US20110150071A1 (en) * 2009-10-15 2011-06-23 Hiroshi Takatori Adaptive pade filter and transceiver
CN108879688A (en) * 2017-05-12 2018-11-23 南京理工大学 A kind of mains frequency response Equivalent Model method for building up considering wind-powered electricity generation fluctuation
CN111027008A (en) * 2019-12-03 2020-04-17 全球能源互联网研究院有限公司 Transfer function determination method for dynamic analysis of electric power equipment

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20110150071A1 (en) * 2009-10-15 2011-06-23 Hiroshi Takatori Adaptive pade filter and transceiver
CN101930487A (en) * 2010-07-09 2010-12-29 南方电网技术研究中心 Hybrid real-time simulation method for continuous long-time steady operation of power system
CN108879688A (en) * 2017-05-12 2018-11-23 南京理工大学 A kind of mains frequency response Equivalent Model method for building up considering wind-powered electricity generation fluctuation
CN111027008A (en) * 2019-12-03 2020-04-17 全球能源互联网研究院有限公司 Transfer function determination method for dynamic analysis of electric power equipment

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
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