CN103226795A - Method for quantitatively evaluating damping of generator - Google Patents

Method for quantitatively evaluating damping of generator Download PDF

Info

Publication number
CN103226795A
CN103226795A CN2013101692185A CN201310169218A CN103226795A CN 103226795 A CN103226795 A CN 103226795A CN 2013101692185 A CN2013101692185 A CN 2013101692185A CN 201310169218 A CN201310169218 A CN 201310169218A CN 103226795 A CN103226795 A CN 103226795A
Authority
CN
China
Prior art keywords
generator
damping
proper vector
edc
axle
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
CN2013101692185A
Other languages
Chinese (zh)
Other versions
CN103226795B (en
Inventor
陈亦平
程哲
侯君
李建设
卢明富
张宇童
陈磊
闵勇
徐飞
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Tsinghua University
China Southern Power Grid Co Ltd
Original Assignee
Tsinghua University
China Southern Power Grid Co Ltd
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Tsinghua University, China Southern Power Grid Co Ltd filed Critical Tsinghua University
Priority to CN201310169218.5A priority Critical patent/CN103226795B/en
Publication of CN103226795A publication Critical patent/CN103226795A/en
Application granted granted Critical
Publication of CN103226795B publication Critical patent/CN103226795B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Landscapes

  • Control Of Eletrric Generators (AREA)
  • Supply And Distribution Of Alternating Current (AREA)

Abstract

The invention discloses a method for quantitatively evaluating the damping of a generator and belongs to the technical field of electric power system analysis. The method for quantitatively evaluating the damping of the generator comprises the following steps of: linearizing a dynamic equation of the electric power system at an equilibrium point to obtain a linearized system equation; calculating the characteristic value and characteristic vector of a state matrix to obtain the characteristic value and the corresponding right characteristic vector; carrying out stretching transformation on the right characteristic vector, so that the element (corresponding to the rotating speed of the generator with the maximum kinetic energy) in the right characteristic vector after transformation is 1; and calculating the energy consumption coefficient of the generator according to the right characteristic vector and the parameters of the generator, and quantitatively evaluating the damping of the generator according to the energy consumption coefficient. By using the method for quantitatively evaluating the damping of each generator in a multi-unit electric power system, the power grid analysts can accurately grasp the source of the system damping and the contribution of each generator to the system damping and find the key generators influencing the system damping.

Description

The method of a kind of qualitative assessment generator damping
Technical field
The invention belongs to the Power System Analysis technical field, the method for particularly a kind of qualitative assessment generator damping.
Background technology
Low-frequency oscillation is an outstanding problem that threatens safe operation of power system.Damping is the key factor that influences low-frequency oscillation.When system damping was enough big, vibration just can be calmed down very soon; And very little even when negative when system damping, vibration is with last very long even disperse, and threatens the safety of electrical network.Method for feature analysis is adopted in the calculating of system damping, and the dynamic equation of electric system in the linearization of equilibrium point place, is obtained linearizing system equation and is
x . = Jx - - - ( 1 )
Wherein x is a state variable, and J is a state matrix.
State matrix J is carried out eigenvalue calculation, obtain eigenwert σ ± j ω d, the corresponding mode of oscillation of these two eigenwerts, oscillation frequency Damping ratio
Figure BDA00003146255000013
Dampingratio has determined the speed of oscillation amplitude decay.Time of 37% that oscillation amplitude decays to initial value is
Figure BDA00003146255000014
Second or
Figure BDA00003146255000015
The individual cycle.System damping just is meant damping ratio.σ＜0 or ζ＞0 expression system damping is for just, and vibration decays.
But, mode of oscillation eigenwert that signature analysis obtains and damping ratio thereof are corresponding to a system-wide amount, but not only be concerned about the damping ratio that system is total in the operation of power networks, also be concerned about the source of damping, be in the system each element to the contribution of damping, especially each generator does not relate to this problem to the contribution of damping in the signature analysis.For the assessment of generator damping, traditional method is the damping torque analytic approach, utilize the damping of generator damping torque coefficient qualitative assessment generator, but the derivation of damping torque is based on one machine infinity bus system, and is also inapplicable in multi-computer system.Therefore, also there is not good method to come the damping of each generator in the qualitative assessment multi-machine power system at present.
Summary of the invention
The method that the purpose of this invention is to provide the damping of a kind of qualitative assessment generator, can be in multi-machine power system the qualitative assessment generator damping characteristic and to the contribution of system damping.
The method of a kind of qualitative assessment generator provided by the invention damping is characterized in that, may further comprise the steps:
A: the dynamic equation of electric system in the linearization of equilibrium point place, is obtained linearizing system equation
Figure BDA00003146255000021
B: state matrix J is carried out eigenwert and proper vector calculating, obtain eigenvalue=σ+j ω dRight proper vector with correspondence
Figure BDA00003146255000022
C: to right proper vector Carry out stretching, obtain
Figure BDA00003146255000024
α is
Figure BDA000031462550000212
In an element, this element is corresponding to the rotating speed of generator m, generator m is the generator of kinetic energy maximum, promptly satisfies
Figure BDA00003146255000025
The rotor inertia time constant of expression generator i, Represent right proper vector
Figure BDA00003146255000027
In corresponding to the element of generator i rotating speed,
After the conversion in the right proper vector corresponding to the element of the rotating speed of the generator of kinetic energy maximum
Figure BDA00003146255000028
D: the energy consumption COEFFICIENT K of calculating generator i EDC, i, computing formula is:
Figure BDA00003146255000029
Wherein
Figure BDA000031462550000210
Be respectively right proper vector
Figure BDA000031462550000211
In corresponding generator i excitation electromotive force E Fd, q axle transient potential E q' element; T D0, i', X D, i, X D, i' be respectively d axle open circuit transient state time constant, d axle synchronous reactance, the reactance of d axle transient state of generator i; ω 0Be synchronous rotational speed, ω 0=2 π f 0, f 0Be system frequency; Subscript * represents to ask conjugation; Real part is got in expression.
Utilize the energy consumption COEFFICIENT K EDC, iThe damping of qualitative assessment generator.K EDC, iThe damping of＞0 generator is being for just, to the contribution of system damping for just; K EDC, iThe damping of＜0 generator is for negative, to the contribution of system damping for negative; K EDC, iBig more generator damping characteristic is good more.
Beneficial effect of the present invention
Generator damping quantitative evaluating method in the multi-machine power system of the present invention utilizes the oscillation energy of generator to consume the damping of qualitative assessment generator, and analyzes the contribution of this generator to system damping.Described method has improved the low-frequency oscillation analytical technology level of electrical network, the electrical network analysis personnel can accurately grasp the source and the contribution of each generator to system damping of system damping, find the crucial generator that influences system damping, thereby take measure targetedly to improve system damping, guarantee electric network security.
Embodiment
Below method of the present invention and embodiment are described in further detail.Following examples are used to illustrate the present invention, but are not used for limiting protection scope of the present invention.
The method of a kind of qualitative assessment generator damping that the present invention proposes specifically may further comprise the steps:
A: the dynamic equation of electric system in the linearization of equilibrium point place, is obtained linearizing system equation and is
Figure BDA00003146255000031
Wherein x is a state variable, and primary variables has δ i, ω i, E Q, i', E Fd, iDeng, be respectively rotor angle, rotating speed, q axle transient potential, the excitation electromotive force of generator i, be the main state variable of generator.J is a state matrix.
B: state matrix J is carried out eigenwert and proper vector calculating, obtain eigenvalue=σ+j ω dRight proper vector with correspondence
Figure BDA00003146255000032
State matrix J has a plurality of eigenwerts, only selects interested a pair of conjugate complex number eigenwert to analyze, these two mode of oscillation that the eigenwert correspondence is concerned about.Conjugate complex number eigenwert centering, choosing imaginary part is positive eigenvalue=σ+j ω dCalculate.For other mode of oscillation characteristic of correspondence values, analytical approach is identical.
C: to right proper vector
Figure BDA00003146255000033
Carry out stretching, obtain
Figure BDA00003146255000034
α is
Figure BDA00003146255000035
In corresponding to the element of generator m rotating speed, generator m is the generator of kinetic energy maximum, promptly satisfies
Figure BDA00003146255000036
Figure BDA00003146255000037
Rotor inertia time constant and its rotational speed omega of expression generator i iIn right proper vector
Figure BDA00003146255000038
In corresponding element, after the conversion in the right proper vector corresponding to the element of the rotating speed of the generator of kinetic energy maximum
Figure BDA00003146255000039
D: according to right proper vector and generator parameter, the energy consumption coefficient of calculating generator i:
Figure BDA000031462550000310
Wherein
Figure BDA000031462550000311
Be respectively right proper vector
Figure BDA000031462550000312
In corresponding generator i excitation electromotive force E Fd, qAxle transient potential E q' element; T D0, i', X D, i, X D, i' be respectively d axle open circuit transient state time constant, d axle synchronous reactance, the reactance of d axle transient state of generator i; ω 0Be synchronous rotational speed, ω 0=2 π f 0, f 0Be system frequency; Subscript * represents to ask conjugation;
Figure BDA000031462550000313
Real part is got in expression.
The energy consumption COEFFICIENT K EDC, iBe illustrated in mode of oscillation σ ± j ω dDown, the energy consumption of generator i.The total energy consumption of system is each element energy consumption sum, and system's total power consumption and system damping correspondence, total power consumption is many more, and system damping is big more, therefore, K EDC, iRepresent of the contribution of each generator, K to system damping EDC, iBig more, the expression generator is big more to the contribution of system damping, K EDC, i＞0 expression generator consumes energy, damping be for just, to the contribution of system damping for just; K EDC, i＜0 expression generator produce power, damping be for negative, to the contribution of system damping for negative.Therefore, K EDC, iCan be used as the index of generator damping, be used for the damping of qualitative assessment generator.
Principle of the present invention: generator damping quantitative evaluating method of the present invention, utilize the oscillation energy consumption of generator to assess its damping characteristic.Concept of energy has vital role in analysis of the oscillation.Energy size and oscillation amplitude correspondence, the gross energy of system is big more, and amplitude is big more.The consumption of energy produces damping effect, and along with the continuous consumption of energy, system capacity reduces, and amplitude also constantly reduces.Therefore, if the continuous consumed energy of certain generator, then this generator for just, has positive damping to the contribution of oscillatory extinction, and consumed energy is many more, and is big more to the contribution of system damping.The present invention utilizes the damping of above-mentioned thinking assessment generator.
Generator adopts third-order model:
δ . = ω 0 ω
T J ω . = P m - P e - Dω - - - ( 4 )
T d 0 ′ E · q ′ = E fd - E q ′ - ( X d - X d ′ ) I d
δ wherein, ω, E q', E Fd, P m, P e, I dBe respectively rotor angle, rotating speed, q axle transient potential, excitation electromotive force, the input mechanical output of generator, output electromagnetic power, d shaft current; T J, T D0', D, X d, X d' be respectively rotor inertia time constant, d axle open circuit transient state time constant, ratio of damping, d axle synchronous reactance and the reactance of d axle transient state of generator; ω 0Be synchronous rotational speed, ω 0=2 π f 0, f 0Be system frequency.
Do not consider governing system, generator is imported mechanical power P mConstant, and establish D=0.Generator consumes energy calculation formula is:
W e D = - 1 X d - X d ′ ∫ t s t ( Δ E fd - T d 0 ′ ΔE q ′ . dΔ E q ′ - - - ( 5 )
T wherein s, t is respectively the initial moment of calculating and stops constantly.
Suppose state variable Δ E Fd, Δ E q' element corresponding in right proper vector is
Figure BDA00003146255000045
Then the formula of calculating generator energy consumption mean speed is:
Figure BDA00003146255000046
Wherein c is a constant, is arithmetic number.Utilize
Figure BDA00003146255000047
Energy consumption that can the qualitative assessment generator, but for and eigenwert real part or damping ratio between set up clearer and more definite relation, also need to carry out suitable computing.
If generator m is the generator of kinetic energy maximum, its kinetic energy is:
Figure BDA00003146255000051
Wherein
Figure BDA00003146255000052
Be corresponding generator m rotational speed omega in the right proper vector mElement.Right proper vector is carried out stretching to make
Figure BDA00003146255000053
Then W km = 1 2 T Jm ω 0 c .
Gross energy W of system and W KmProportional, i.e. W=β W Km, β is an arithmetic number.Pass between eigenwert real part σ and gross energy, the total power consumption mean speed is:
Figure BDA00003146255000055
Figure BDA00003146255000056
(8)
Figure BDA00003146255000057
Wherein γ is an arithmetic number,
Figure BDA00003146255000059
Expression is to all generator summations.
Therefore, definition generator energy consumption coefficient
Figure BDA000031462550000510
Be used for what of qualitative assessment hunting of generator energy consumption, and have relation between eigenwert real part and the energy consumption coefficient
Figure BDA000031462550000511
γ is an arithmetic number in the formula.
The present invention is that embodiment illustrates above-mentioned steps with one four machine system.Through obtaining an eigenvalue=0.0090+j3.3018 behind steps A, the B, real part is negative greater than 0 expression system damping.Right proper vector
Figure BDA000031462550000512
The element of middle corresponding 4 generator speeds is respectively [0.5692+j0.4721,0.4083+j0.3796 ,-0.5472-j0.4293 ,-0.4817-j0.4672].The rotor inertia time constant T of 4 generators JiBe respectively [117.00,117.00,111.15,111.15], by comparing
Figure BDA000031462550000513
Can get the generator that generator 1 is the kinetic energy maximum, then to right proper vector Carry out stretching α=0.5692+j0.4721 is
Figure BDA00003146255000062
In the element of corresponding generator 1 rotating speed.Right proper vector after the conversion
Figure BDA00003146255000063
The element of middle corresponding 4 generator speeds is respectively [1.0000,0.7527+j0.0426 ,-0.9402+j0.0255 ,-0.9047-j0.0704], corresponding generator excitation electromotive force E FdElement
Figure BDA00003146255000064
Be respectively [335.19+j233.69i, 397.23-j33.49,561.58-j521.33,716.72-j594.46], corresponding q axle transient potential E q' element
Figure BDA00003146255000065
Be respectively [13.9751-j10.5541,4.0572-j12.8677 ,-21.0268-j19.2091 ,-23.2755-j25.0030].The d axle open circuit transient state time constant T of 4 generators D0, i' be respectively [8,8,8,8] d axle synchronous reactance X D, iBe respectively [0.2,0.2,0.2,0.2], d axle transient state reactance X D, i' be respectively [0.0333,0.0333,0.0333,0.0333].Synchronous rotational speed ω 0=2 π * 60=376.9911.The hunting angle frequency is the imaginary part of eigenvalue, i.e. ω d=3.3018.Calculate the energy consumption COEFFICIENT K that can get 4 generators according to formula (9) EDC, iBe respectively [68.1885 ,-8.7833 ,-17.0366 ,-49.0606].Can judge generator 1 damping for just according to the energy consumption coefficient, other generator dampings are for negative, and generator 4 is the poorest generators of damping, need emphasis that generator 4 is taken measures to improve damping.
Generator damping quantitative evaluating method in the multi-machine power system of the present invention utilizes the oscillation energy consumption assessment generator damping of generator, analyzes the contribution of this generator to system damping.Described method has improved the low-frequency oscillation analytical technology level of electrical network, the electrical network analysis personnel are the source and the contribution of each generator to system damping of recognition system damping accurately, find the crucial generator that influences system damping, thereby take measure targetedly to improve system damping, guarantee electric network security.
Above embodiment only is used to illustrate the present invention; and be not limitation of the present invention; the those of ordinary skill in relevant technologies field; under the situation that does not break away from the spirit and scope of the present invention; can also make various variations and modification; therefore all technical schemes that are equal to also belong to category of the present invention, and scope of patent protection of the present invention should be defined by the claims.

Claims (1)

1. the method for qualitative assessment generator damping is characterized in that, comprises step:
A: the dynamic equation of electric system in the linearization of equilibrium point place, is obtained linearizing system equation
Figure FDA00003146254900011
B: state matrix J is carried out eigenwert and proper vector calculating, obtain eigenvalue=σ+j ω dRight proper vector with correspondence
Figure FDA00003146254900012
C: to right proper vector
Figure FDA00003146254900013
Carry out stretching, obtain α is
Figure FDA00003146254900015
In an element, this element is corresponding to the rotating speed of generator m, generator m is the generator of kinetic energy maximum, promptly satisfies
Figure FDA00003146254900016
The rotor inertia time constant of expression generator i,
Figure FDA00003146254900017
Represent right proper vector
Figure FDA00003146254900018
In corresponding to the element of generator i rotating speed, behind the stretching in the right proper vector corresponding to the element of the rotating speed of the generator of kinetic energy maximum
Figure FDA00003146254900019
D: the energy consumption COEFFICIENT K of calculating generator i EDC, i, computing formula is:
Figure FDA000031462549000110
Wherein
Figure FDA000031462549000111
Be respectively right proper vector In corresponding generator i excitation electromotive force E Fd, q axle transient potential
Figure FDA000031462549000113
Element; T D0, i', X D, i, X D, i' be respectively d axle open circuit transient state time constant, d axle synchronous reactance, the reactance of d axle transient state of generator i; ω 0Be synchronous rotational speed, ω 0=2 π f 0, f 0Be system frequency; Subscript * represents to ask conjugation;
Figure FDA000031462549000114
Real part is got in expression.
Utilize the energy consumption COEFFICIENT K EDC, iThe damping of qualitative assessment generator, K EDC, iThe damping of＞0 generator is being for just, to the contribution of system damping for just, K EDC, iThe damping of＜0 generator is for negative, to the contribution of system damping for negative, K EDC, iBig more generator damping characteristic is good more.
CN201310169218.5A 2013-05-06 2013-05-06 A kind of method of qualitative assessment Generator Damping Active CN103226795B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201310169218.5A CN103226795B (en) 2013-05-06 2013-05-06 A kind of method of qualitative assessment Generator Damping

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201310169218.5A CN103226795B (en) 2013-05-06 2013-05-06 A kind of method of qualitative assessment Generator Damping

Publications (2)

Publication Number Publication Date
CN103226795A true CN103226795A (en) 2013-07-31
CN103226795B CN103226795B (en) 2016-05-25

Family

ID=48837232

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201310169218.5A Active CN103226795B (en) 2013-05-06 2013-05-06 A kind of method of qualitative assessment Generator Damping

Country Status (1)

Country Link
CN (1) CN103226795B (en)

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104680323A (en) * 2015-03-02 2015-06-03 华北电力大学 Energy stability-domain building system and method for power system
CN106410782A (en) * 2015-07-31 2017-02-15 国家电网公司 Interconnected power grid dynamic and stable security control strategy optimization method based on damping contribution
CN115940248A (en) * 2022-09-27 2023-04-07 国网甘肃省电力公司经济技术研究院 Damping evaluation method for wind-storage combined power generation system based on EMD and dissipation energy

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2002312575A (en) * 2001-04-16 2002-10-25 Sekisui Chem Co Ltd Electric power monitoring system and electric power saving promoting system and method using financial product
CN101917003A (en) * 2010-07-29 2010-12-15 东南大学 Small interference oscillatory stability decomposed model analysis method for electric power system
CN102064557A (en) * 2010-12-16 2011-05-18 华北电力大学 Subsynchronous resonance characteristic value analysis model of multi-machine system

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2002312575A (en) * 2001-04-16 2002-10-25 Sekisui Chem Co Ltd Electric power monitoring system and electric power saving promoting system and method using financial product
CN101917003A (en) * 2010-07-29 2010-12-15 东南大学 Small interference oscillatory stability decomposed model analysis method for electric power system
CN102064557A (en) * 2010-12-16 2011-05-18 华北电力大学 Subsynchronous resonance characteristic value analysis model of multi-machine system

Cited By (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104680323A (en) * 2015-03-02 2015-06-03 华北电力大学 Energy stability-domain building system and method for power system
CN104680323B (en) * 2015-03-02 2018-05-25 华北电力大学 Electric system energy stabilization domain builds system and method
CN106410782A (en) * 2015-07-31 2017-02-15 国家电网公司 Interconnected power grid dynamic and stable security control strategy optimization method based on damping contribution
CN106410782B (en) * 2015-07-31 2019-03-08 国家电网公司 A kind of interconnected network dynamic stability peace control policy optimization method based on damping contribution
CN115940248A (en) * 2022-09-27 2023-04-07 国网甘肃省电力公司经济技术研究院 Damping evaluation method for wind-storage combined power generation system based on EMD and dissipation energy
CN115940248B (en) * 2022-09-27 2023-07-07 国网甘肃省电力公司经济技术研究院 Wind-storage combined power generation system damping evaluation method based on EMD and dissipated energy

Also Published As

Publication number Publication date
CN103226795B (en) 2016-05-25

Similar Documents

Publication Publication Date Title
Abd-el-Malek et al. Induction motor broken rotor bar fault location detection through envelope analysis of start-up current using Hilbert transform
CN103368175B (en) Power system dynamic stability online evaluation method
CN102801158B (en) Method for calculating time-lag electric power system eigenvalue and discriminating stability based on Pade approximation
CN102928697B (en) Low-frequency-band damping detection method and system of PSS2A (Power System Stabilizer 2A) model of excitation regulator
CN109193752A (en) Containing virtual inertia double-fed blower grid-connected system low-frequency oscillation Optimization about control parameter method
CN106410848A (en) Electric electronic multi-infeed power system low-interference stability evaluation method
CN109063379A (en) Electric-gas integrated energy system probability energy flux computation method based on principle of maximum entropy
CN103487719A (en) Method for distinguishing winding fault types of permanent-magnet synchronous motor stator
CN102299679A (en) Method for determining rotating speed of restarted asynchronous motor
CN102185324A (en) Measured-information-based power system low-frequency oscillation analysis method
CN103226795B (en) A kind of method of qualitative assessment Generator Damping
CN104615882A (en) Large-scale time-lag electric system characteristic value calculation method based on EIGD
CN103336911A (en) Mechanism-based mathematic model establishing method suitable for frequency modulation analysis of multi-machine power system
CN103023418A (en) Online parameter identification method of synchronous generator based on wide-area measurement information
CN104133129B (en) The monitoring method of the low-frequency oscillation of Speed Control System of Turbogenerator Unit and system
CN102914718A (en) Low frequency oscillation distinguishing method based on response ingredient and oscillation characteristic identification
CN104915892B (en) Electric system stochastic Time-Delay method for analyzing stability
CN103986400B (en) Based on the model reference adaptive system parameters automatic setting method that two dimension fuzzy controls
Han et al. Mode shape estimation and mode checking for IAO using correlation analysis technique
Xue et al. Trajectory section eigenvalue method for nonlinear time-varying power system
CN104376195A (en) Method for verifying transient state model of photovoltaic power station
CN104934969B (en) A kind of computational methods of Electrical Power Line Parameter
CN203069669U (en) Harmonic energy measuring system based on parameter analysis
CN103441837A (en) Four-dimensional chaotic system with constant lyapunov exponent
CN107703181A (en) Evaluate the back balance method of low-pressure coal saver energy-saving effect

Legal Events

Date Code Title Description
C06 Publication
PB01 Publication
C10 Entry into substantive examination
SE01 Entry into force of request for substantive examination
C14 Grant of patent or utility model
GR01 Patent grant