CN107070332B - Generator L based on quadratic sum decomposition technique2Robust integrated control method - Google Patents
Generator L based on quadratic sum decomposition technique2Robust integrated control method Download PDFInfo
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P9/00—Arrangements for controlling electric generators for the purpose of obtaining a desired output
- H02P9/10—Control effected upon generator excitation circuit to reduce harmful effects of overloads or transients, e.g. sudden application of load, sudden removal of load, sudden change of load
- H02P9/105—Control effected upon generator excitation circuit to reduce harmful effects of overloads or transients, e.g. sudden application of load, sudden removal of load, sudden change of load for increasing the stability
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/24—Arrangements for preventing or reducing oscillations of power in networks
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P9/00—Arrangements for controlling electric generators for the purpose of obtaining a desired output
- H02P9/14—Arrangements for controlling electric generators for the purpose of obtaining a desired output by variation of field
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- Power Engineering (AREA)
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- Control Of Eletrric Generators (AREA)
Abstract
The invention discloses a kind of generators based on quadratic sum decomposition techniqueL 2Robust Comprehensive Control, the transient stability for improving electric system and robustness.First, ensure that the performance of system is satisfied with one group of state correlation inequality：When the inequality is positive semidefinite, system is asymptotically stable, and is had to interferenceL 2Gain rejection.Then, it will determine that the problem of whether state correlation inequality is Positive is converted to and judge whether it can resolve into quadratic sum（SOS）The problem of form.Finally, SOS resolution problems are solved with the tool boxes SOSTOOLS, obtains the quadratic sum of generatorL 2Robust integrated controller.
Description
Technical field
The present invention relates to generator control field, specifically a kind of generator L based on quadratic sum decomposition technique2Robust is comprehensive
Combination control method.
Background technology
Excitation con-trol influences synchronizing torque, and then can effectively improve electric system by the magnetic field of change generator
Stability.Prime mover speed regulating control is improving Power Systems balance and is carrying due to the development of quick electric-liquid type governing system
In terms of high stability, increasingly important role is played.Therefore, the Excitation and governor control of generator is organically combined
Come, realize Comprehensive Control, becomes the rich potential probing direction of generator control field.Various nonlinear control method priority quilts
In being studied applied to Integrated control for generator unit, such as：Differential geometry method[1], direct feedback linearization (DFL)[2], Hamilton systems
Method[3]、backstepping[4]Deng.
There is various uncertainties for the generator of actual motion, ignore the non-thread of probabilistic model when based on modeling
Property control method can not give full play to its effect.Therefore, consider during system modelling and controller design uncertain
Property influence to system electric system robust control come into being, become a big hot topic of current electric power system control circle research
Project, H∞Control[5], dissipativeness[6]And self adaptive control[7]Equal nonlinear robust controls method is successively applied in electric system
Realize robust control.Wang Baohua etc.[8]For probabilistic Infinite bus power system excitation and porthole system is considered, it is based on
Backstepping methods carry out the design of robust controller.This method has fully considered the nonlinear characteristic of system, can not only
Construct system Lyapubov functions, moreover it is possible to obtain the non linear robust excitation controller of generator.Lan Hai[9]Deng for power generation
The Harmonic Control of machine proposes a kind of L2Disturbance restraining method under gain sense, with backstepping method recursion
The Hamilton-Jacobi inequality of construction system, the tuning controller of accomplished AF panel.It is integrated in generator robust
In control, L can be handled well with backstepping methods2The problem of gain disturbance, but as recurrence derives
The design process of the increase of step number, controller will be very complicated.
In recent years, research boom is presented in quadratic sum (SOS) decomposition technique in control field[10].Document [11] is by SOS
Decomposition technique is used for the stability analysis of flight control system；Papachristodoulou et al.[12]Skill is decomposed using SOS
Art carries out stability analysis to F/A-18 model aircrafts, and designs its robust controller.Ataei et al.[13]It is decomposed using SOS
Technology releases the robust controller of the non-linear supersonic plane model containing uncertain parameter.Document [14] decomposes skill with SOS
Art successfully designs the L that can guarantee nonlinear system2The controller of gain rejection.SOS decomposition techniques are in non-linear Shandong
Application advantage in stick control is：The robust controller of system can be gone out with SOSTOOLS Toolbox structures, design process is kept away
Cumbersome recurrence method has been opened, derivation is simplified, has been easy to Project Realization.Therefore, for including probabilistic nonlinear system
System, the introducing of SOS decomposition techniques reduce the complexity of its robust Controller Design.
There are numerous in electric system comprising probabilistic nonlinear model, and SOS decomposition techniques are but not yet applied to
In relative control research.
Bibliography
[1] Wang Ni, Liu Hui, Chen Wuhui waits synchronous generator energy stabilization excitation con-trol [J] China electrical engineering
Report, 2013,33 (28):81-87.
[2]Wang Yinsong,Yu Xinghuo.New Coordinated Control Design for Thermal
Power Generation Units[J].IEEE Transactions on Industrial Electronics,2010,57
(11): 3848-3856.
[3] Li Xiaocong, Cheng Shijie, Wei Hua wait to have steam turbine generator nonlinear integrated control [J] of multi-performance index
Proceedings of the CSEE, 2003,23 (4):96-101.
[4]Mehraeen Shahab,Jagannathan S,Crow Mariesal.Novel dynamic
representation and control of power systems with FACTS devices[J].IEEE
Transactions on Power Systems,2010,25(3):1542-1554.
[5] Zheng Shaoming, Wang Peng, plum give birth to big Large Hydroelectric Sets water valve aperture and control zero dynamics method [J]
Automation of Electric Systems, 2008,32 (22):21-25.
[6] Yan Wei, Wu Wensheng, Hua Zhiming wait direct feedback linearization method [J] China of .SSSC nonlinear Controls
Electrical engineering journal, 2003,23 (3):65-68.
[7] horse is into Xi Rong, Mei Shengwei wait generator porthole and excitation of the based on Hamilton energy theories non-linear
Design [J] Proceedings of the CSEEs of stability controller, 2002,22 (5):88-93.
[8] Multi-infeed HVDC transmission system modulation controller designs of Wang Maohai, Sun Yuanzhang, Song Yong the China based on Backstepping
[J] Proceedings of the CSEEs, 2005,25 (23):7-11.
[9] Huang Wenchao, Sun Hongfei, Zeng Jianping one kind State Responses of Nonlinear Polynomial Systems robusts H∞Control [J] control theories with
Using 2012,29 (12):1587-1593.
[10] blue sea, Li Dianpu, Gong Wei wait to be based on dissipative system and realize power system excitation robust nonlinear control
[J] Electric Machines and Controls, 2003,7 (3):255-259,263.
[11]Yan Rui,Dong Zhaoyang,Saha Tk,et al.A power system nonlinear
adaptive decentralized controller design[J].Automatica,2010,46(2):330-336.
[12] Wang Baohua, Yang Chengwu, the nonlinear Adaptive Inverses of strong generators push away Comprehensive Control [J] control theories with
Using 2006,23 (1):60-64.
[13] blue sea, Xu Dianguo, Liu Sheng wait TCSCs of the based on Dissipative Theory to coordinate control research [J] systems with excitation
Emulate journal, 2006,18 (8):2230-2234.
[14]Okou FA,Dessaint LA,Akhrif O.A robust adaptive voltage and speed
regulator for multimachine power systems[J].Canadian Journal of Electrical
and Computer Engineering,2005,30(1):29-38。
Invention content
To solve the above problems, overcoming the shortcomings of prior art, SOS decomposition techniques are applied to by applicant for the first time
In the nonlinear Control of electric system, a kind of generator L based on quadratic sum decomposition technique is provided2Robust integrated control method.
The present invention realizes that the technical solution of foregoing invention purpose is as follows.
Generator L based on quadratic sum decomposition technique2Robust integrated control method, including：1) first, Lyapunov is steady
Under theorem opinion, ensure that the performance of system is satisfied with one group of state correlation inequality：When the inequality is positive semidefinite, it is
System is asymptotically stable, and has L to interference2Gain rejection.2) it then, will determine that whether state correlation inequality is half
The problem of orthotropicity, which is converted to, judges the problem of whether it can resolve into quadratic sum form, 3) use the tool boxes SOSTOOLS journey
Quadratic sum resolution problem is solved to sequence, the non linear robust integrated control law of generator is obtained.
Specifically, it is described 1) in, include the system of uncertain noises
Wherein：
xi=[δi ωi E′qi Pmi]T
wi=[w1i；w2i；w3i]T
hiIt is smooth function, ziFor output vector；For input nonlinearities vector,Indicate the L of extension2It is empty
Between, it is defined as follows：
Wherein,
δiIndicate the generator rotor angle of generator；ω0Indicate the synchronous rotational speed of generator amature；ωiIndicate generator amature angle speed
Degree；E′qiIndicate generator transient potential；PmiIndicate the mechanical output of generator；EfiAnd UTiIt is controlled quentity controlled variable, indicates power generation respectively
Machine excitation voltage and steam valve opening amount signal；PeiIndicate generator active power；IdiIndicate generator unit stator direct-axis current；xdiWith
x′diD-axis reactance and the d-axis transient state reactance of generator are indicated respectively；TJiIndicate the rotor inertia time constant of generator；
T′d0iIndicate Exciting Windings for Transverse Differential Protection time constant when generator unit stator open circuit；TV∑iIndicate the equivalent time constant of steam turbine；DiIt indicates
The damped coefficient of generator；w1iIt indicates to act on the torque disturbance in generator speed control loop；w2iExpression acts on generator and encourages
Electromagnetic distu in magnetic loop；w3iExpression acts on the external disturbance of generator regulating valve；δiUnit be radian (rad), ω0
And ωiUnit be radian per second (rad/s)；Time constant TJi、T′d0iAnd TV∑iThe unit second (s), surplus is perunit value
(pu)；
By the Lyapunov functions V of system (1)iIt is chosen for classical field formalism shown in formula (2)：
Wherein z1i=δi-δi0, δi0For the stable equilibrium point of generator rotor angle；c1iIt is undetermined normal
Number；c2iFor normal number undetermined；z4i=Pmi-Pm0i,
Pm0iTo input the stable equilibrium point of mechanical output.ViTime diffusion along system (1) track is
WhereinIt chooses
And formula (4) and (5) are substituted into formula (3), can be obtained
In formula (6)：uESOSi、uUSOSi、c3iAnd c4iIt is quantitative to wait for.
It is for generator robust complex control system, control targe as shown in formula (1)：First, it is ensured that system is gradually
Closely stablize；Second, system is finite gain L2Stable, and input nonlinearities wiFor system output ziL2Gain is less than one
A given positive number γi.Following theorem provides guarantee system (1) Asymptotic Stability and finite gain L2The condition of stability：
Theorem 1xi0=0 is the equalization point of system (1)；To include xi0Domain；It enablesAnd assume to remove x in Si0Outer other solutions not comprising system.There are one it is continuously differentiable partly just
Determine function Vi:B → R, and have Vi(xi0)=0 meets inequality (7)：
So, work as wiWhen=0, the equalization point x of systemi0=0 is asymptotically stability；Work as wiWhen ≠ 0, system (1) is limited
Gain L2Stable, and its L2Gain is less than or equal to given positive number γi。
According to theorem 1, the L of system (1) is provided2Robust Integrated Control Design method (L2Robust Coordinated
Control Approach, referred to as:LRCCA)：
LRCCA：For system (1), if there are multinomial uESOSi、uUSOSi、c1i、c2i、c3iAnd c4iSo that the following conditions at
It is vertical：
c1i≥0,c2i≥0,c3i≥0,c4i≥0 (9)
So, work as wiWhen=0, the equalization point x of system (1)i0=0 is asymptotically stability；Work as wiWhen ≠ 0, system (1) is that have
Limit gain L2Stable, and its L2Gain is less than or equal to given positive number γi.Whereinzi=
[z1i；z2i；z3i；z4i]；γiFor given positive number.
Further, it is described 2) in, will judgement inequality (7) and (8) whether be Positive is converted into whether judging it
Condition (9) and (10) that quadratic sum form can be resolved into, then a kind of quadratic sum L can be obtained2Robust integrated control method
(sum of squares L2Robust coordinated control scheme, referred to as：SOSCCS)：
SOSCCS：For system (1), if there are multinomial uESOSi、uUSOSi、c1i、c2i、c3iAnd c4iSo that the following conditions at
It is vertical：
It is SOS multinomials (9)
c1i,c2i,c3iAnd c4iIt is SOS monomials (10)
So, work as wiWhen=0, the equalization point x of system (1)i0=0 is asymptotically stability；Work as wiWhen ≠ 0, system (1) is that have
Limit gain L2Stable, and its L2Gain is less than or equal to given positive number γi.Whereinzi=
[z1i；z2i；z3i；z4i]；γiFor given positive number.Obviously meet the u of formula (9) and (10)ESOSi、uUSOSi、c1i、c2i、c3iAnd c4i
It is convex, can solves to come with the tool boxes SOSTOOLS.The u that solution is obtainedESOSi、uUSOSi、c1i、c2i、c3iAnd c4i's
As a result formula (4) and (5) is substituted into respectively, obtains the integrated control law of system：
SOS decomposition techniques are applied in the nonlinear Control of electric system by applicant for the first time.For with not
It determines damped coefficient and the generator excitation and speed-adjusting and control system of interference, proposes that a kind of quadratic sum L2 robust Comprehensive Controls are set
Meter method, the transient stability for improving electric system and robustness.The control method and traditional robust control method phase
Than, it is advantageous that：The robust integrated controller of system can be constructed with SOSTOOLS toolkit programs；Design process
Cumbersome recurrence method is avoided, derivation is simplified；And without solving Hamilton-Jacobi inequality；SOS decomposition techniques
Introducing reduce generator robust integrated control law design complexity, have good engineering application value.
Description of the drawings
The present invention will be further described in detail with reference to the accompanying drawings and detailed description；
Fig. 1 is three electro-mechanical force system models, and gives the initial flow data of the electric system；
Generator G when Fig. 2 is external disturbance2System response curve.Wherein, (a)：Set end voltage response curve, (b)：
Generator rotor angle response curve, (c)：Active power response curve, (d)：Mechanical output response curve；Figure includes system in SOSCCS,
Under the action of tri- kinds of difference controllers of PID+PSS and LOCC, the response in relation to quantity of state；
Generator G when Fig. 3 is external disturbance3System response curve.Wherein, (a)：Set end voltage response curve, (b)：
Generator rotor angle response curve, (c)：Active power response curve, (d)：Mechanical output response curve；Figure includes system in SOSCCS,
PID+PSS (speed governing uses PID control, excitation to use the classic control scheme of PSS controls) and LOCC (linear optimal Comprehensive Controls
Scheme) under the action of three kinds of different controllers, the response in relation to quantity of state；
Generator G when Fig. 4 is three-phase shortcircuit disturbance2System response curve.Wherein, (a)：Set end voltage response curve,
(b)：Generator rotor angle response curve, (c)：Active power response curve, (d)：Mechanical output response curve；Figure includes that system exists
Under the action of the different controllers of tri- kinds of SOSCCS, PID+PSS and LOCC, the response in relation to quantity of state；
Generator G when Fig. 5 is three-phase shortcircuit disturbance3System response curve.Wherein, (a)：Set end voltage response curve,
(b)：Generator rotor angle response curve, (c)：Active power response curve, (d)：Mechanical output response curve；Figure includes that system exists
Under the action of the different controllers of tri- kinds of SOSCCS, PID+PSS and LOCC, the response in relation to quantity of state.
Specific implementation mode
Above-mentioned quadratic sum L2The validity of robust integrated control method will carry out in as shown in Figure 13 electromechanical Force systems
Verification.The initial flow data of the electric system is given in Fig. 1.
Generator G in Fig. 11It is Infinite bus system.G2And G3It is equipped with quadratic sum L2Robust integrated controller, model ginseng
Number such as table 1：
1 generator G of table2And G3Model parameter
By γiThe value taken as：
γ2=0.1, γ3=0.1 (13)
SOS multinomials uESOSi、uUSOSi、c1i、c2i、c3iAnd c4iIt can be solved by the tool boxes SOSTOOLS：
Condition (9) and (10) can be made to set up for verification multinomial (13)-(15), by formula (13)-(15) substitution formula (9) and
(10), quadratic sum decomposition is carried out to formula (9) and (10) with the tool boxes SOSTOOLS：
Wherein：
Pi=[z4i；z3i；z2i；z1i；w3i；w2i；w1i] (17)
Q2And Q3For 7 × 7 matrix, characteristic value is as follows：
eig(Q2)=[34.7；12.97；6.08；0.0047；0.036；0.05；6.07] (18)
eig(Q3)=[34.69；12.77；6.27；0.0047；0.036；0.05；6.25] (19)
Obviously, matrix Q2And Q3It is positive definite.
Using theorem 1, can release to draw a conclusion：
A) work as wiWhen=0, equalization point zi=0 is the Asymptotic Stability equalization point of system (1).
B) the disturbance input w of system (1)iTo output ziL2Gain is no more than given positive number γi=0.1.
By the u in formula (13)-(15)Esosi、uUsosi、c1i、c2i、c3iAnd c4iResult of calculation substitute into respectively formula (11) and
(12), the control law of system can be obtained：
UT2=(- 24.11z42-1.72z32)TV∑2+Pm2 (20)
UT3=(- 35.03z43-2.29z33)TV∑3+Pm3 (21)
The excitation controller shown in formula (22) and formula (23), IdiAnd IqiIt is difficult to measure, but they can be used easily to be
Meter calculates.It can arrange to obtain by formula (2)-(4)：
It can be seen that by formula (24) and (25), IdiAnd IqiExpression formula only include easily measure Pei、QeiAnd IiDeng.Therefore, it controls
Device problem of implementation is resolved.
In order to verify quadratic sum L2The validity of robust integrated controller (SOSCCS) disturbs schemes for following 2 kinds,
By its control program progress simulation comparison with two kinds：One is excitations to be controlled using PSS, and speed governing uses the classics of PID control
Control program, another kind are linear optimal Comprehensive Control schemes (LOCC).
A) external disturbance
Before disturbance occurs, system is in stable state.In 0.5s~1.5s, generator G is acted on2And G3Interference
Respectively w12=0.5sin (t), w22=0.5sin (t), w32=0.5sin (t) and w13=-sin (t), w23=-sin (t),
w33=-sin (t).System is under the action of tri- kinds of different controllers of SOSCCS, PID+PSS and LOCC, the response in relation to quantity of state
Curve is as shown in Figures 2 and 3
Fig. 2 and 3 shows when generator is by external disturbance, the set end voltage of generator, generator rotor angle, active power and machine
Tool power SOSCCS effect under dynamic property than under the action of LOCC and PSS+PID will be good, this is embodied
SOSCCS is inhibited to interfering.Compared to LOCC and PSS+PID, SOSCCS can not only quickly calm down unit in transient state
The overshoot of the better suppression system of mechanical oscillation and energy in the process, so that generator has good dynamic property and Shandong
Stick.
B) three-phase shortcircuit disturbs
Before disturbance occurs, system is in stable state.In 0.5s, the circuit between 5 and No. 8 busbares is (close to No. 5 mothers
At line end) three-phase metallic short circuit occurs, failure is removed after continuing 0.15s, the system reclosing success in 0.9s.Work as system
It is respectively adopted SOSCCS, response curve of the system in relation to quantity of state when PSS+PID with LOCC controllers is as shown in Figure 4 and Figure 5.
Fig. 4 (a), (c) and Fig. 5 (a), (c) show when system occur large disturbances when, although the set end voltage of generator and
Active power is all restored under the action of 3 kinds of control laws, but SOSCCS ratio LOCC and PID can more quickly restore generator terminal electricity
It is pressed onto initial level, calms down the swing of active power earlier.SOSCCS ratios are shown by Fig. 4 (b), (d) and Fig. 5 (b), (d)
LOCC and PID can preferably calm down system frequency oscillation, so that system is returned to initial launch point, more effectively inhibit and be
The overshoot of system so that generator has good dynamic and static performance.
This 3 kinds of control programs of SOSCCS, LOCC and PSS+PID occur three-phase shortcircuit disturb failure when critical removing when
Between (CCT) it is as follows：
CCTSOSCCS=0.23s；CCTLOCC=0.18s；CCTPSS=0.17s (26)
Formula (26) shows in 3 kinds of control methods, and SOSCCS enables to the system operation at most, to be under fault condition
Most effectively improve the control method of the transient stability of electric system.
Claims (1)
1. a kind of generator L based on quadratic sum decomposition technique2Robust integrated control method, it is characterised in that：The control method
Include the following steps：
1) ensure that the performance of system is satisfied with one group of state correlation inequality：When the inequality is positive semidefinite, system
It is asymptotically stable, and there is L to interference2Gain rejection；
The system is：
Wherein：System includes uncertain noises, and
fclose(i)(xi, Efi, UTi, wi)=fi(xi)+g1i(xi)Efi+g2i(xi)UTi+Gi(xi)wi
xi=[δi ωi E′qi Pmi]T
wi=[w1i；w2i；w3i]T
hiIt is smooth function, ziFor output vector；For input nonlinearities vector,Indicate the L of extension2Space is determined
Justice is as follows：
Wherein,
δiIndicate the generator rotor angle of generator；ω0Indicate the synchronous rotational speed of generator amature；ωiIndicate generator amature angular speed；E′qi
Indicate generator transient potential；PmiIndicate the mechanical output of generator；EfiAnd UTiIt is controlled quentity controlled variable, indicates generator excitation respectively
Voltage and steam valve opening amount signal；PeiIndicate generator active power；IdiIndicate the stator direct-axis current of generator；xdiWith x 'diPoint
Not Biao Shi generator d-axis reactance and d-axis transient state reactance；TJiIndicate the rotor inertia time constant of generator；T′d0iIt indicates
Exciting Windings for Transverse Differential Protection time constant when generator unit stator is opened a way；TV∑iIndicate the equivalent time constant of steam turbine；DiIndicate generator
Damped coefficient；w1iIt indicates to act on the torque disturbance in generator speed control loop；w2iExpression acts in generator excitation circuit
Electromagnetic distu；w3iExpression acts on the external disturbance of generator regulating valve；δiUnit be radian (rad), ω0And ωiList
Position is radian per second (rad/s)；Time constant TJi、T′d0iAnd TV∑iThe unit second (s), surplus is perunit value (pu)；
The inequality such as formula (7)：
xi0=0 is the equalization point of system (1)；To include xi0Domain；It enablesAnd it is false
If removing x in Si0Outer other solutions not comprising system, continuously differentiable positive semidefinite function Vi:B → R, and have Vi(xi0)=0；
2) it then, will determine that the problem of whether state correlation inequality (7) is Positive is converted to and judge whether it can divide
The problem of solution is at SOS forms：
For system (1), if there are multinomial uESOSi、uUSOSi、c1i、c2i、c3iAnd c4iSo that the following conditions are set up：
It is SOS multinomials (9)
c1i,c2i,c3iAnd c4iBe SOS monomials (10) so, work as wiWhen=0, the equalization point x of system (1)i0=0 is gradually
Into stable；Work as wiWhen ≠ 0, system (1) is finite gain L2Stable, and its L2Gain is less than or equal to given positive number
γi, wherein wi=[w1i；w2i；w3i]T；zi=[z1i；z2i；z3i；z4i]；
3) SOS resolution problems finally, are solved with the tool boxes SOSTOOLS, obtain the quadratic sum L of generator2Robust Comprehensive Control
Device：
The u that will be solved with SOSTOOLS toolkit programsESOSi、uUSOSi、c1i、c2i、c3iAnd c4iResult generation respectively
Enter formula (4) and (5), obtains the integrated control law of system：
Wherein formula (4) and (5) are as follows：
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