CN107240921A - Based on the SVC sliding-mode controls for integrating adaptive backstepping - Google Patents

Based on the SVC sliding-mode controls for integrating adaptive backstepping Download PDF

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CN107240921A
CN107240921A CN201710442915.1A CN201710442915A CN107240921A CN 107240921 A CN107240921 A CN 107240921A CN 201710442915 A CN201710442915 A CN 201710442915A CN 107240921 A CN107240921 A CN 107240921A
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msub
mrow
mover
msubsup
mfrac
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李昊昊
徐子安
强龙龙
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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
    • H02J3/12—Circuit arrangements for ac mains or ac distribution networks for adjusting voltage in ac networks by changing a characteristic of the network load
    • H02J3/16—Circuit arrangements for ac mains or ac distribution networks for adjusting voltage in ac networks by changing a characteristic of the network load by adjustment of reactive power
    • 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
    • H02J3/18—Arrangements for adjusting, eliminating or compensating reactive power in networks
    • 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
    • Y02E40/00—Technologies for an efficient electrical power generation, transmission or distribution
    • Y02E40/10—Flexible AC transmission systems [FACTS]
    • 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
    • Y02E40/00—Technologies for an efficient electrical power generation, transmission or distribution
    • Y02E40/30—Reactive power compensation

Abstract

The invention discloses a kind of based on the SVC sliding-mode controls for integrating adaptive backstepping, including setting up the one machine infinity bus system dynamic mathematical models equipped with SVC, it is then based on integration backstepping method design controller, the tracking error of design point variable first, and add integral term in error term, the uncertainty of systematic parameter is considered simultaneously, construct liapunov function, online adaptive handles uncertain parameter, it is eventually adding Terminal sliding-mode surfaces, obtain SVC and integrate adaptive backstepping stability controller, complete based on the SVC sliding formwork controls for integrating adaptive backstepping.The present invention eliminates remaining poor using Adaptive Integral method, and adds Terminal sliding formwork controls so that system has stronger robustness to interference and Systematic forest, and the present invention can maintain set end voltage with rapid damping power oscillation, improve the transient stability of power system.

Description

Based on the SVC sliding-mode controls for integrating adaptive backstepping
Technical field
The present invention relates to a kind of based on the SVC sliding-mode controls for integrating adaptive backstepping, belong to SVC electric power system controls Technical field.
Background technology
SVC (SVC), which is widely used in modern power systems, carries out reactive balance and raising electric power The stability of a system.With the rapid development of the national economy, the structure of modern power systems is also increasingly complicated, with extra-high voltage, far The characteristics of distance, Large Copacity and transregional interconnection so that the stable operation of system is easier by various natures and human factor Interference and destroyed.SVC is commonly used with solution to this problem at present, is accessed at load or burden without work access point It after SVC device, can effectively suppress the impact of load or burden without work, filter out higher hamonic wave, balance three phase network, stable PCC points electricity Pressure, lifts the stability of power system.Therefore, have for the research equipped with SVC electric power system stability control technologies critically important Meaning.
Backstepping design methods are a kind of Systematic Methods for uncertain system, generally with Lyapunov types adaptive law is used in combination, that is, considers control law and adaptive law, meets whole closed-loop system and expects Dynamic and static state performance.The basic thought of Backstepping methods is to resolve into complicated nonlinear system no more than system rank Several subsystems, then ensure subsystem have it is constringent on the basis of, be each subsystem design part Lyapunov letters Count and intermediate virtual controlled quentity controlled variable, pusher so as to complete the design of whole control law, and combines Lyapunov to whole system always Function method for analyzing stability ensures the convergence of whole system.Adaptive backstepping technologies therein are by non-thread Property dynamical feedback, constructs system-wide Control pH (CLF), its essential idea is parameter Estimation a step by a step.This The controller of sample not only can guarantee that system mode bounded, and can reach that tracking error converges on zero purpose.Because it does not have Have and any linearisation, thus the complete nonlinear characteristic for remaining system are carried out to original system.
The principle of Sliding mode variable structure control, is super flat come the switching of design system according to the desired dynamic characteristic of system Face, makes system mode be collected from the extroversion tangential-hoop method of hyperplane by sliding mode control.Sliding formwork control not only to There is robustness with interference, and once enter sliding formwork state closed-loop system, there is consistency to external disturbance.Tied because sliding formwork becomes Construction system algorithm is simple, fast response time, has stronger robustness to interference and Parameter Perturbation, should in electric power system control With relatively broad.And Terminal sliding formworks are a kind of new sliding-mode controls, by introducing non-thread in the design of sliding-mode surface Property function so that error can Fast Convergent, be a kind of improved sliding-mode control.
The content of the invention
The technical problems to be solved by the invention are that the defect for overcoming prior art is based on integration adaptive inversion there is provided one kind The SVC sliding-mode controls pushed away, solve the problems, such as that SVC electric power system stability controls are housed.
In order to solve the above technical problems, the present invention provides a kind of based on the SVC sliding-mode controls for integrating adaptive backstepping, Comprise the following steps：
1) the one machine infinity bus system dynamic mathematical models equipped with SVC are set up；
2) design adaptive inversion pushes away sliding mode controller, obtains SVC control input amount, specifically includes following steps：
2-1) the tracking error of design point variable, and add in tracking error integral term；
2-2) construct liapunov function, online adaptive processing uncertain parameter；
Quick Terminal sliding-mode surfaces 2-3) are constructed, SVC is obtained and integrates adaptive backstepping stability controller, and then obtain SVC control input amount.
Foregoing step 1) in, the one machine infinity bus system dynamic mathematical models equipped with SVC are set up, are comprised the following steps：
1-1) assume that generator is classical second mathematical model, while generator transient potential and generator mechanical power Constant, obtaining the one machine infinity bus system dynamic mathematical models equipped with SVC is：
In formula：
X1=X'd+XT+XL, X2=XL,
Wherein, δ is generator amature power angle, and ω is generator amature angular speed, ω0At the beginning of generator amature angular speed Initial value, E'qFor generator transient potential, PmFor generator mechanical power, D is damped coefficient, and H is mechanical rotation inertia, TCFor SVC and regulating system inertia time constant；BLFor SVC inductance value, BL0For BLInitial value, u is SVC control input amount, VS For infinite busbar voltage, V is takenS=1, BLMeet：
X1=X'd+XT+XL, X2=XL,
Wherein, X'dFor generator d axle transient state reactance, XTFor transformer reactance, XLFor line reactance；
1-2) introduce new state variable：x1=δ-δ0, x2=ω-ω0, x3=BL-BL0,
δ0For δ initial value, ω0For ω initial value,
Order
OrderFor uncertain parameter, then the mathematical modeling of formula (1) is represented by：
Foregoing step 2-1), the tracking error of design point variable is as follows：
Wherein：e1, e2, e3For tracking error, x2d, x3dFor virtual controlling variable, k1、k2For constant coefficient,
Foregoing step 2-2), construct liapunov function, online adaptive processing uncertain parameter, including following step Suddenly：
2-2-1) construction liapunov function V1For：
Make x2d=-c1e1-k1x1, then have：
Wherein, c1For constant, c1＞ 0；
2-2-2) in order to ensure e2→ 0, construction liapunov function V2For：
In formula, r is arbitrary constant,For uncertain parameter θ evaluated error, meet：
For uncertain parameter θ estimate；
Formula (6) derivation can be obtained：
On this basis, the adaptive control laws for obtaining uncertain parameter θ are：
Order：
Bringing formula (8) into formula (7) can obtain：
Wherein, c2For constant；
2-2-3) in order to simplify calculating process, by e3It is reduced to：e3=x3-x3d,
Formula (10) is substituted into, then is had
Take e3=a1e2sin(x1+δ0), formula (11) is substituted into, then is had：
Foregoing step 2-3) in, Terminal sliding-mode surfaces are：
In formula：S is sliding-mode surface function, and α, β is constant coefficient, α, β ＞ 0；Q, p are whole odd number, and q ＜ p；
Take
It is foregoing according to formula (13) and formula (15), obtain：
Wherein,
It is rightDerivation, is obtained：
The control input amount that can obtain SVC by formula (18) is：
The beneficial effect that the present invention is reached：
(1) kinetic model equipped with SVC system that the present invention is set up considers Systematic forest, parameter and is difficult precisely really Fixed and design controller can produce the influence of the non-linear factors such as remaining difference, eliminate remaining poor using Adaptive Integral method, according to Backstepping design methods construct nonlinear autoregressive device, and add Terminal sliding formwork controls so that system pair Interference and Systematic forest have stronger robustness；(2) overall situation one of all closed signals of Lyapunov theoretical proof systems half is utilized Cause bounded；(3) controller designed by the present invention can maintain set end voltage with rapid damping power oscillation, improve power system Transient stability.
Brief description of the drawings
Fig. 1 is the one machine infinity bus system structure chart equipped with SVC；
Fig. 2 is the analogue system of the present invention by small interference transient state response curve figure；(a) it is generator rotor angle transient state response curve Figure, (b) is rotating speed transient state response curve figure, (c) SVC output admittance transient state response curve figures；
Fig. 3 is the analogue system of the present invention by the big interference transient state response curve figure of three-phase shortcircuit；(a) it is generator rotor angle transient state phase Curve map is answered, (b) is rotating speed transient state response curve figure, (c) SVC output admittance transient state response curve figures；
Fig. 4 be small disturbed condition under, the comparison diagram of the inventive method and conventional method；(a) it is generator rotor angle transient state response curve Figure, (b) is rotating speed transient state response curve figure, (c) SVC output admittance transient state response curve figures.
Embodiment
The invention will be further described below.Following examples are only used for clearly illustrating the technical side of the present invention Case, and can not be limited the scope of the invention with this.
The present invention provides a kind of based on the SVC sliding-mode controls for integrating adaptive backstepping, solves that SVC power systems are housed Stable control, comprises the following steps：To carrying out mathematical description equipped with SVC power systems；Based on integration backstepping method design control The tracking error of device processed, first design point variable, and integral term is added in error term, while considering the uncertain of systematic parameter Property, handled using adaptive law；And Terminal sliding-mode surfaces are added in final step, obtain SVC and integrate adaptive backstepping stabilization Controller, is completed based on the SVC sliding formwork controls for integrating adaptive backstepping.
It is specific as follows：
Step 1：Set up the one machine infinity bus system dynamic mathematical models equipped with SVC shown in Fig. 1；
1-1) assume that generator is classical second mathematical model, while the transient potential E' of generatorqWith generator Mechanical output PmConstant, obtaining the one machine infinity bus system dynamic mathematical models equipped with SVC is：
In formula：
Pe=E'qVsBLSin δ,
X1=X'd+XT+XL, X2=XL。
Wherein, δ is generator amature power angle, and unit is rad；ω is generator amature angular speed, ω0Turn for generator Sub- angular speed initial value；E'qFor generator transient potential；D is damped coefficient；H is mechanical rotation inertia；TCFor SVC and regulation system The inertia time constant of system；BLFor SVC inductance value, initial value is BL0；U is SVC control input amount；VSFor infinite busbar Voltage, takes VS=1；X'dFor generator d axle transient state reactance；XTFor transformer reactance；XLFor line reactance.
G is generator, X in Fig. 1 one machine infinity bus system equipped with SVCTFor transformer equivalent reactance, Vm、VSFor line end Voltage, XL1、XL2For line equivalent reactance.
1-2) introduce new state variable：x1=δ-δ0, x2=ω-ω0, x3=BL-BL0, δ0、ω0、BL0For each variable Initial value,
Order
OrderFor uncertain parameter, then the mathematical modeling of formula (1) is represented by：
Step 2：Design adaptive inversion pushes away sliding mode controller；
The tracking error of controller, first design point variable 2-1) is designed based on integration backstepping method, and added in error term Enter integral term；Tracking error is as follows：
In formula：e1, e2, e3For tracking error, x2d, x3dFor virtual controlling variable, k1、k2For constant coefficient,
x1, x2For the remaining difference introduced in integral term, only in tracking error e1, e2, e3The middle definition using above-mentioned integrated form Formula, for the x individually occurred1, x2, such as the x in formula (4)1, the x in formula (6)2, still by x1=δ-δ0, x2=ω-ω0Calculate.
Liapunov function 2-2) is constructed,
Make x2d=-c1e1-k1x1, c1For constant, c1＞ 0, then have：
2-3) in order to ensure e2→ 0, following liapunov function is chosen,
In formula, r is arbitrary constant,For uncertain parameter θ evaluated error, meet：
θ is uncertain parameter,For uncertain parameter θ estimate；
Formula (6) derivation can be obtained：
To causeThe adaptive control laws for obtaining uncertain parameter θ are：
Order：
c2For constant,
Bringing formula (8) into formula (7) can obtain：
2-4) in order to simplify calculating process, by e in the step3Simplify, take e3=x3-x3d,
Formula (10) is substituted into, then is had
Take e3=a1e2sin(x1+δ0), formula (11) is substituted into, then is had：
2-5) construct quick Terminal sliding-mode surfaces：
In formula：S is sliding-mode surface function, constant coefficient α, β ＞ 0；Q, p are whole odd number, and q ＜ p.
Many documents are all it was demonstrated that sliding-mode surface function s can be in Finite-time convergence to zero, and no matter its initial value is many Lack, and its convergence time is：
Sliding-mode surface when s (0) is t=0,
Take：
Formula (15) is substituted into formula (13), had：
In formula,
It can be obtained by formula (16)：
It is rightDerivation, has：
It can thus be concluded that SVC control input amount is：
Emulation experiment is as follows：
The power system equipped with SVC is chosen as controlled device, the parameter of backstepping controllers is chosen：c1=c2 =1, c3=2.Systematic parameter chooses H=8s；D=5；Vs=1；The original state of system is set to：x0=[0*pi/180000]；
Emulation 1：System works at steady state originally, in t=0.1s, suddenly by an extraneous gadget work( Rate is disturbed, and recovers normal operation in t=0.16s, and the transient response curve of system is as shown in Figure 2.
Analogous diagram 2 is as can be seen that generator rotor angle Fig. 2 (a) and speed diagram 2 (b) of power system are in after by mechanical disturbance Concussion state, system quickly revert to stable state under the controller action of the present invention, this show to be proposed based on integration The SVC sliding-mode controls of adaptive backstepping, it is possible to achieve effective suppression of interference.Fig. 2 (c) curves show, although SVC's is defeated Going out admittance its numerical value after being interfered can become big, but can finally return to new steady s tate.In addition, overcoming system ginseng Number changes the influence to performance, with very strong robustness.
Emulation 2, the robustness in order to further illustrate designed controller, carry out another emulation, in t=0.1s, Three phase short circuit fault occurs for line scan pickup coil side, and parameter is chosen：xl1=0, recover normal operation, the transient response of system in t=0.16s Curve is as shown in Figure 3.
From figure 3, it can be seen that generator rotor angle Fig. 3 (a) of power system and speed diagram 3 (b) are after by three-phase shortcircuit large disturbances, System quickly revert to stable state under the controller action of design, this show to be proposed based on integrating adaptive backstepping SVC sliding-mode controls, also have a very strong robustness for larger disturbance, SVC output admittance amplitude Fig. 3 (c) changes compared with It is small, also smaller is influenceed on system operation.
As a comparison, under small disturbed condition, being contrasted with conventional method, as shown in Figure 4.Solid line is the present invention in figure Waveform obtained by the controller of design, dotted line is the waveform obtained by conventional method design controller.By Fig. 4's (a) and Fig. 4 (b) Waveform is understood, under small disturbed condition, and the controller that the present invention is designed has faster response speed and preferably reduces concussion energy Power, SVC output admittance amplitude Fig. 4 (c) changes are smaller, influence also smaller to system operation, better than conventional method.
One aspect of the present invention design adaptive parameter estimation device handles uncertain parameter online, utilizes simultaneously The problem of flexible design of backstepping methods solves mission nonlinear, with good robustness.
The method that the inventive method is designed according to backstepping progressively constructs liapunov function, it is considered in construction virtual controlling Can have a surplus difference during device, introduce error value product subitem, unknowm coefficient is handled with adaptive law, and add Terminal sliding-mode surfaces, obtain Final control law, suppresses interference so that in finite time, correlated variables converges to zero, and emulation experiment shows the present invention The controller of design can maintain set end voltage with rapid damping power oscillation, improve the transient stability of power system.
Described above is only the preferred embodiment of the present invention, it is noted that for the ordinary skill people of the art For member, without departing from the technical principles of the invention, some improvement and deformation can also be made, these improve and deformed Also it should be regarded as protection scope of the present invention.

Claims (6)

1. based on the SVC sliding-mode controls for integrating adaptive backstepping, it is characterised in that comprise the following steps：
1) the one machine infinity bus system dynamic mathematical models equipped with SVC are set up；
2) design adaptive inversion pushes away sliding mode controller, obtains SVC control input amount, specifically includes following steps：
2-1) the tracking error of design point variable, and add in tracking error integral term；
2-2) construct liapunov function, online adaptive processing uncertain parameter；
Quick Terminal sliding-mode surfaces 2-3) are constructed, SVC is obtained and integrates adaptive backstepping stability controller, and then obtain SVC's Control input amount.
2. it is according to claim 1 based on the SVC sliding-mode controls for integrating adaptive backstepping, it is characterised in that described Step 1) in, the one machine infinity bus system dynamic mathematical models equipped with SVC are set up, are comprised the following steps：
It is classical second mathematical model 1-1) to assume generator, while generator transient potential and generator mechanical power are permanent Fixed, obtaining the one machine infinity bus system dynamic mathematical models equipped with SVC is：
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In formula：
<mrow> <msub> <mi>B</mi> <mi>L</mi> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <msub> <mi>X</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>X</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>X</mi> <mn>1</mn> </msub> <msub> <mi>X</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>B</mi> <mi>L</mi> </msub> <mo>-</mo> <msub> <mi>B</mi> <mrow> <mi>L</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>,</mo> </mrow>
X1=X'd+XT+XL, X2=XL,
Wherein, δ is generator amature power angle, and ω is generator amature angular speed, ω0For generator amature angular speed initial value, E'qFor generator transient potential, PmFor generator mechanical power, D is damped coefficient, and H is mechanical rotation inertia, TCFor SVC and tune The inertia time constant of section system；BLFor SVC inductance value, BL0For BLInitial value, u is SVC control input amount, VSTo be infinite Big busbar voltage, takes VS=1, BLMeet：
<mrow> <msub> <mi>B</mi> <mi>L</mi> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <msub> <mi>X</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>X</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>X</mi> <mn>1</mn> </msub> <msub> <mi>X</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>B</mi> <mi>L</mi> </msub> <mo>-</mo> <msub> <mi>B</mi> <mrow> <mi>L</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>,</mo> </mrow>
X1=X'd+XT+XL, X2=XL,
Wherein, X'dFor generator d axle transient state reactance, XTFor transformer reactance, XLFor line reactance；
1-2) introduce new state variable：x1=δ-δ0, x2=ω-ω0, x3=BL-BL0,
δ0For δ initial value, ω0For ω initial value,
Order
OrderFor uncertain parameter, then the mathematical modeling of formula (1) is represented by：
<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mover> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>&amp;CenterDot;</mo> </mover> <mo>=</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mover> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>&amp;CenterDot;</mo> </mover> <mo>=</mo> <msub> <mi>&amp;theta;x</mi> <mn>2</mn> </msub> <mo>+</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>3</mn> </msub> <mo>+</mo> <msub> <mi>B</mi> <mrow> <mi>L</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mi>sin</mi> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>&amp;delta;</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>a</mi> <mn>0</mn> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mover> <msub> <mi>x</mi> <mn>3</mn> </msub> <mo>&amp;CenterDot;</mo> </mover> <mo>=</mo> <mo>-</mo> <msub> <mi>b</mi> <mn>0</mn> </msub> <msub> <mi>x</mi> <mn>3</mn> </msub> <mo>+</mo> <msub> <mi>b</mi> <mn>0</mn> </msub> <mi>u</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> <mo>.</mo> </mrow>
3. it is according to claim 2 based on the SVC sliding-mode controls for integrating adaptive backstepping, it is characterised in that described Step 2-1), the tracking error of design point variable is as follows：
<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>e</mi> <mn>1</mn> </msub> <mo>=</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>e</mi> <mn>2</mn> </msub> <mo>=</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>x</mi> <mrow> <mn>2</mn> <mi>d</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <msub> <mi>x</mi> <mn>1</mn> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>e</mi> <mn>3</mn> </msub> <mo>=</mo> <msub> <mi>x</mi> <mn>3</mn> </msub> <mo>-</mo> <msub> <mi>x</mi> <mrow> <mn>3</mn> <mi>d</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <msub> <mi>x</mi> <mn>2</mn> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>
Wherein：e1, e2, e3For tracking error, x2d, x3dFor virtual controlling variable, k1、k2For constant coefficient,
<mrow> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>=</mo> <msubsup> <mo>&amp;Integral;</mo> <mn>0</mn> <mi>t</mi> </msubsup> <msub> <mi>e</mi> <mn>1</mn> </msub> <mi>d</mi> <mi>t</mi> <mo>,</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>=</mo> <msubsup> <mo>&amp;Integral;</mo> <mn>0</mn> <mi>t</mi> </msubsup> <msub> <mi>e</mi> <mn>2</mn> </msub> <mi>d</mi> <mi>t</mi> <mo>.</mo> </mrow>
4. it is according to claim 3 based on the SVC sliding-mode controls for integrating adaptive backstepping, it is characterised in that described Step 2-2), liapunov function is constructed, online adaptive processing uncertain parameter comprises the following steps：
2-2-1) construction liapunov function V1For：
<mrow> <msub> <mi>V</mi> <mn>1</mn> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <msubsup> <mi>e</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mo>+</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <msub> <mi>k</mi> <mn>1</mn> </msub> <msubsup> <mi>x</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>
Make x2d=-c1e1-k1x1, then have：
<mrow> <mover> <msub> <mi>V</mi> <mn>1</mn> </msub> <mo>&amp;CenterDot;</mo> </mover> <mo>=</mo> <msub> <mi>e</mi> <mn>1</mn> </msub> <mover> <msub> <mi>e</mi> <mn>1</mn> </msub> <mo>&amp;CenterDot;</mo> </mover> <mo>+</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <msub> <mi>x</mi> <mn>1</mn> </msub> <mover> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>&amp;CenterDot;</mo> </mover> <mo>=</mo> <mo>-</mo> <msub> <mi>c</mi> <mn>1</mn> </msub> <msubsup> <mi>e</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mo>+</mo> <msub> <mi>e</mi> <mn>1</mn> </msub> <msub> <mi>e</mi> <mn>2</mn> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> <mo>;</mo> </mrow>
Wherein, c1For constant, c1＞ 0；
2-2-2) in order to ensure e2→ 0, construction liapunov function V2For：
<mrow> <msub> <mi>V</mi> <mn>2</mn> </msub> <mo>=</mo> <msub> <mi>V</mi> <mn>1</mn> </msub> <mo>+</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <msubsup> <mi>e</mi> <mn>2</mn> <mn>2</mn> </msubsup> <mo>+</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <msub> <mi>k</mi> <mn>2</mn> </msub> <msubsup> <mi>x</mi> <mn>2</mn> <mn>2</mn> </msubsup> <mo>+</mo> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <mi>r</mi> </mrow> </mfrac> <msup> <mover> <mi>&amp;theta;</mi> <mo>~</mo> </mover> <mn>2</mn> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>
In formula, r is arbitrary constant,For uncertain parameter θ evaluated error, meet：
For uncertain parameter θ estimate；
Formula (6) derivation can be obtained：
<mrow> <msub> <mover> <mi>V</mi> <mo>&amp;CenterDot;</mo> </mover> <mn>2</mn> </msub> <mo>=</mo> <mo>-</mo> <msub> <mi>c</mi> <mn>1</mn> </msub> <msubsup> <mi>e</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mo>+</mo> <msub> <mi>e</mi> <mn>2</mn> </msub> <mo>&amp;lsqb;</mo> <msub> <mi>e</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>&amp;theta;x</mi> <mn>2</mn> </msub> <mo>+</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>3</mn> </msub> <mo>+</mo> <msub> <mi>B</mi> <mrow> <mi>L</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>&amp;delta;</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>a</mi> <mn>0</mn> </msub> <mo>+</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <msub> <mi>e</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>c</mi> <mn>1</mn> </msub> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>+</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>&amp;rsqb;</mo> <mo>-</mo> <mfrac> <mn>1</mn> <mi>r</mi> </mfrac> <mover> <mi>&amp;theta;</mi> <mo>~</mo> </mover> <mover> <mover> <mi>&amp;theta;</mi> <mo>^</mo> </mover> <mo>&amp;CenterDot;</mo> </mover> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow>
On this basis, the adaptive control laws for obtaining uncertain parameter θ are：
<mrow> <mover> <mover> <mi>&amp;theta;</mi> <mo>^</mo> </mover> <mo>&amp;CenterDot;</mo> </mover> <mo>=</mo> <msub> <mi>re</mi> <mn>2</mn> </msub> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow>
Order：
<mrow> <msub> <mi>x</mi> <mrow> <mn>3</mn> <mi>d</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mo>-</mo> <msub> <mi>c</mi> <mn>2</mn> </msub> <msub> <mi>e</mi> <mn>2</mn> </msub> <mo>-</mo> <mover> <mi>&amp;theta;</mi> <mo>^</mo> </mover> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <msub> <mi>e</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mi>c</mi> <mn>1</mn> </msub> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>e</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>a</mi> <mn>0</mn> </msub> </mrow> <mrow> <msub> <mi>a</mi> <mn>1</mn> </msub> <mi>sin</mi> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>&amp;delta;</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>-</mo> <msub> <mi>B</mi> <mrow> <mi>L</mi> <mn>0</mn> </mrow> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow>
Bringing formula (8) into formula (7) can obtain：
<mrow> <msub> <mover> <mi>V</mi> <mo>&amp;CenterDot;</mo> </mover> <mn>2</mn> </msub> <mo>=</mo> <mo>-</mo> <msub> <mi>c</mi> <mn>1</mn> </msub> <msubsup> <mi>e</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mo>+</mo> <msub> <mi>e</mi> <mn>2</mn> </msub> <mo>&amp;lsqb;</mo> <mover> <mi>&amp;theta;</mi> <mo>^</mo> </mover> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>+</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>3</mn> </msub> <mo>+</mo> <msub> <mi>B</mi> <mrow> <mi>L</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mi>sin</mi> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>&amp;delta;</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>a</mi> <mn>0</mn> </msub> <mo>+</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <msub> <mi>e</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>c</mi> <mn>1</mn> </msub> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>+</mo> <msub> <mi>e</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>&amp;rsqb;</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> <mo>;</mo> </mrow> 2
Wherein, c2For constant；
2-2-3) in order to simplify calculating process, by e3It is reduced to：e3=x3-x3d,
Formula (10) is substituted into, then is had
Take e3=a1e2sin(x1+δ0), formula (11) is substituted into, then is had：
<mrow> <msub> <mover> <mi>V</mi> <mo>&amp;CenterDot;</mo> </mover> <mn>2</mn> </msub> <mo>=</mo> <mo>-</mo> <msub> <mi>c</mi> <mn>1</mn> </msub> <msubsup> <mi>e</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mo>-</mo> <msub> <mi>c</mi> <mn>2</mn> </msub> <msubsup> <mi>e</mi> <mn>2</mn> <mn>2</mn> </msubsup> <mo>-</mo> <msubsup> <mi>a</mi> <mn>1</mn> <mn>2</mn> </msubsup> <msubsup> <mi>e</mi> <mn>2</mn> <mn>2</mn> </msubsup> <msup> <mi>sin</mi> <mn>2</mn> </msup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>&amp;delta;</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>12</mn> <mo>)</mo> </mrow> <mo>.</mo> </mrow>
5. it is according to claim 4 based on the SVC sliding-mode controls for integrating adaptive backstepping, it is characterised in that described Step 2-3) in, Terminal sliding-mode surfaces are：
<mrow> <mover> <mi>s</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>=</mo> <mo>-</mo> <mi>&amp;alpha;</mi> <mi>s</mi> <mo>-</mo> <msup> <mi>&amp;beta;s</mi> <mrow> <mi>q</mi> <mo>/</mo> <mi>p</mi> </mrow> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>13</mn> <mo>)</mo> </mrow> </mrow>
In formula：S is sliding-mode surface function, and α, β is constant coefficient, α, β ＞ 0；Q, p are whole odd number, and q ＜ p；
Take
<mrow> <mi>s</mi> <mo>=</mo> <msub> <mi>e</mi> <mn>2</mn> </msub> <msubsup> <mi>a</mi> <mn>1</mn> <mn>2</mn> </msubsup> <msup> <mi>sin</mi> <mn>2</mn> </msup> <mrow> <mo>(</mo> <mrow> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>&amp;delta;</mi> <mn>0</mn> </msub> </mrow> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <msub> <mi>x</mi> <mn>3</mn> </msub> <mi>sin</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>&amp;delta;</mi> <mn>0</mn> </msub> </mrow> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>c</mi> <mn>2</mn> </msub> <msub> <mi>e</mi> <mn>2</mn> </msub> <mo>-</mo> <mover> <mi>&amp;theta;</mi> <mo>^</mo> </mover> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <msub> <mi>e</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mi>c</mi> <mn>1</mn> </msub> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>e</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>a</mi> <mn>0</mn> </msub> <mo>-</mo> <msub> <mi>B</mi> <mrow> <mi>L</mi> <mn>0</mn> </mrow> </msub> <msub> <mi>a</mi> <mn>1</mn> </msub> <mi>sin</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>&amp;delta;</mi> <mn>0</mn> </msub> </mrow> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>15</mn> <mo>)</mo> </mrow> <mo>.</mo> </mrow>
6. it is according to claim 5 based on the SVC sliding-mode controls for integrating adaptive backstepping, it is characterised in that according to Formula (13) and formula (15), are obtained：
<mrow> <mover> <msub> <mi>x</mi> <mn>3</mn> </msub> <mo>&amp;CenterDot;</mo> </mover> <mo>=</mo> <mo>&amp;lsqb;</mo> <mi>m</mi> <mo>-</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <msub> <mi>x</mi> <mn>3</mn> </msub> <mi>cos</mi> <mo>(</mo> <mrow> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>&amp;delta;</mi> <mn>0</mn> </msub> </mrow> <mo>)</mo> <mover> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>&amp;CenterDot;</mo> </mover> <mo>-</mo> <msub> <mi>c</mi> <mn>2</mn> </msub> <mover> <msub> <mi>e</mi> <mn>2</mn> </msub> <mo>&amp;CenterDot;</mo> </mover> <mo>-</mo> <mover> <mover> <mi>&amp;theta;</mi> <mo>^</mo> </mover> <mo>&amp;CenterDot;</mo> </mover> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>-</mo> <mover> <mi>&amp;theta;</mi> <mo>^</mo> </mover> <mover> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>&amp;CenterDot;</mo> </mover> <mo>-</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <mover> <msub> <mi>e</mi> <mn>1</mn> </msub> <mo>&amp;CenterDot;</mo> </mover> <mo>-</mo> <msub> <mi>c</mi> <mn>1</mn> </msub> <mover> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>&amp;CenterDot;</mo> </mover> <mo>-</mo> <mover> <msub> <mi>e</mi> <mn>1</mn> </msub> <mo>&amp;CenterDot;</mo> </mover> <mo>-</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <mover> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>&amp;CenterDot;</mo> </mover> <mo>-</mo> <msub> <mi>B</mi> <mrow> <mi>L</mi> <mn>0</mn> </mrow> </msub> <msub> <mi>a</mi> <mn>1</mn> </msub> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>&amp;delta;</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mover> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>&amp;CenterDot;</mo> </mover> <mo>+</mo> <mi>&amp;alpha;</mi> <mi>s</mi> <mo>+</mo> <msup> <mi>&amp;beta;s</mi> <mrow> <mi>q</mi> <mo>/</mo> <mi>p</mi> </mrow> </msup> <mo>&amp;rsqb;</mo> <mo>/</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>&amp;delta;</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>17</mn> <mo>)</mo> </mrow> </mrow>
Wherein,
It is rightDerivation, is obtained：
<mrow> <mover> <msub> <mi>x</mi> <mn>3</mn> </msub> <mo>&amp;CenterDot;</mo> </mover> <mo>=</mo> <mo>-</mo> <mfrac> <mrow> <msub> <mi>b</mi> <mn>0</mn> </msub> <msub> <mi>X</mi> <mn>1</mn> </msub> <msub> <mi>X</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>3</mn> </msub> <mo>-</mo> <mi>u</mi> <mo>)</mo> </mrow> </mrow> <msup> <mrow> <mo>&amp;lsqb;</mo> <msub> <mi>X</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>X</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>X</mi> <mn>1</mn> </msub> <msub> <mi>X</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>B</mi> <mi>L</mi> </msub> <mo>-</mo> <msub> <mi>B</mi> <mrow> <mi>L</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mn>2</mn> </msup> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>18</mn> <mo>)</mo> </mrow> </mrow>
The control input amount that can obtain SVC by formula (18) is：
<mrow> <mi>u</mi> <mo>=</mo> <mfrac> <mrow> <msup> <mrow> <mo>&amp;lsqb;</mo> <msub> <mi>X</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>X</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>X</mi> <mn>1</mn> </msub> <msub> <mi>X</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>B</mi> <mi>L</mi> </msub> <mo>-</mo> <msub> <mi>B</mi> <mrow> <mi>L</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mn>2</mn> </msup> <mover> <msub> <mi>x</mi> <mn>3</mn> </msub> <mo>&amp;CenterDot;</mo> </mover> </mrow> <mrow> <msub> <mi>b</mi> <mn>0</mn> </msub> <msub> <mi>X</mi> <mn>1</mn> </msub> <msub> <mi>X</mi> <mn>2</mn> </msub> </mrow> </mfrac> <mo>+</mo> <msub> <mi>x</mi> <mn>3</mn> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>19</mn> <mo>)</mo> </mrow> <mo>.</mo> </mrow> 3
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CN108418442B (en) * 2018-01-29 2020-08-04 浙江工业大学 Sliding mode control method for integral terminal of high-voltage direct-current transmission system of two-end voltage source type converter
CN109378807A (en) * 2018-11-01 2019-02-22 中国矿业大学 A kind of suppressing method of the set time sliding formwork of ferro-resonance over-voltage chaos
CN109782591A (en) * 2018-12-26 2019-05-21 贵州电网有限责任公司 A kind of SVC individual-phase control method based on fuzzy self-adaption sliding Mode Algorithm
CN110501912B (en) * 2019-04-01 2022-09-27 东北电力大学 Self-adaptive fuzzy dynamic surface sliding mode control method for multi-machine power system meeting preset output tracking performance
CN110501912A (en) * 2019-04-01 2019-11-26 东北电力大学 Meet the multi-machine power system adaptive fuzzy dynamic surface sliding-mode control of default output tracking performance
CN110034562A (en) * 2019-04-26 2019-07-19 西安工程大学 A kind of control method of static synchronous compensator and generator excitation Robust Coordinated
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CN111969597A (en) * 2020-08-03 2020-11-20 东北电力大学 Dynamic surface integral sliding mode controller with SVC (static Var compensator) for multi-machine infinite power system
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CN112467766A (en) * 2020-10-26 2021-03-09 南京工程学院 Control method of optical storage system in micro-grid
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