CN109378807A - A kind of suppressing method of the set time sliding formwork of ferro-resonance over-voltage chaos - Google Patents
A kind of suppressing method of the set time sliding formwork of ferro-resonance over-voltage chaos Download PDFInfo
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- CN109378807A CN109378807A CN201811299024.6A CN201811299024A CN109378807A CN 109378807 A CN109378807 A CN 109378807A CN 201811299024 A CN201811299024 A CN 201811299024A CN 109378807 A CN109378807 A CN 109378807A
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02H—EMERGENCY PROTECTIVE CIRCUIT ARRANGEMENTS
- H02H9/00—Emergency protective circuit arrangements for limiting excess current or voltage without disconnection
- H02H9/005—Emergency protective circuit arrangements for limiting excess current or voltage without disconnection avoiding undesired transient conditions
- H02H9/007—Emergency protective circuit arrangements for limiting excess current or voltage without disconnection avoiding undesired transient conditions avoiding or damping oscillations, e.g. fenoresonance or travelling waves
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02H—EMERGENCY PROTECTIVE CIRCUIT ARRANGEMENTS
- H02H9/00—Emergency protective circuit arrangements for limiting excess current or voltage without disconnection
- H02H9/04—Emergency protective circuit arrangements for limiting excess current or voltage without disconnection responsive to excess voltage
- H02H9/045—Emergency protective circuit arrangements for limiting excess current or voltage without disconnection responsive to excess voltage adapted to a particular application and not provided for elsewhere
Abstract
The invention discloses a kind of suppressing methods of the set time sliding formwork of ferro-resonance over-voltage chaos, comprising: (1) establishes the mathematical model of ferroresonance system；(2) Integral Sliding Mode face is designed according to set time Theory of Stability；(3) adaptive law of Nonlinear control law and uncertain parameter is obtained by theory deduction；(4) it is determined according to set time Theory of Stability affiliated lemmas and liapunov function stability analysis and stablizes the time range upper bound；(5) its control effect is verified by numerical simulation.The suppressing method of ferro-resonance over-voltage disclosed by the invention can not only be such that system stablizes under conditions of not depending on initial value in finite time, and the upper bound for stablizing the time can be by being calculated, with stronger robustness and anti-interference ability, it can realize system global consistent asymptotic stability in the given time under arbitrary initial conditions, the overvoltage for more effectively inhibiting Analysis on Ferroresonance of Power System Based, improves the stability of electric system.
Description
Technical field
The invention belongs to electrical engineering field, in particular to a kind of set time sliding formwork of ferro-resonance over-voltage chaos
Suppressing method.
Background technique
Both there are many iron inductance elements in electric system, as transformer, voltage transformer, generator, arc suppression coil,
Reactor etc.；There is also many capacity cells, as conducting wire over the ground and capacitive coupling, compensation capacitor, high-tension apparatus it is miscellaneous
Spurious capacitance etc., the oscillation circuit of their complicated composition, if having big disturbance or operation in electric system, it is possible to shake
Swing the longer ferro-resonance over-voltage of duration of exciting in circuit.
Currently, causing electric network composition more complicated along with a large amount of progress of various regions electric network reconstruction and extension project.It is complicated
Electric system also increase ferromagnetic resonance odds.In 110kV isolated neutral system below and 110kV or more
Solidly earthed neutral system in ferromagnetic resonance continually occurs.Overvoltage is not only generated when resonance, will also cause electricity
Stream, and the duration is longer, it might even be possible to it is stabilized, insulation flashover will be caused, keep away blasting cap detonation, equipment damage, seriously
When can cause power outage, the safe operation of power grid generation is seriously threatened.In earth neutral system, passed through by system power supply
The circuit that breaker equalizing capacitance and electromagnetic potential transformer are constituted may also cause ferromagnetic resonance.The heavily fortified point that national grid proposes
" self-healing " functional requirement included in strong smart grid strategy isolates element problematic in power grid simultaneously from system
Seldom or without human intervention in the case where can make system be promptly restored to normal operating condition, to hardly interrupt pair
The electric service of user.Therefore, reinforce having a very important significance the research that ferro-resonance over-voltage early stage inhibits.
In recent years, it is existing in generation ferromagnetic resonance theoretically to have analysed in depth earth neutral system by many experts and scholar
As when chaos state and its characterization, and theoretical point has been carried out to the chaos state that ferro-resonance over-voltage in electric system causes
Analysis and inhibition.In terms of ferro-resonance over-voltage inhibition, constant value pulse is also had proposed, based on chaos such as maximum entropy neural networks
Control method, but all there is certain disadvantage (if control energy consumption is big, method complexity etc.) in these methods, do not have in engineering very strong
Practical significance.
Summary of the invention
In order to overcome the above-mentioned deficiencies of the prior art, the present invention provides a kind of chaos suppression sides of ferro-resonance over-voltage
Method devises a kind of adaptive set time sliding formwork for ferromagnetic resonance chaos system according to set time Theory of Stability
Controller enables ferro-resonance over-voltage to be inhibited in the finite time for not depending on initial value.
The technical scheme adopted by the invention is that: a kind of inhibition side of the set time sliding formwork of ferro-resonance over-voltage chaos
Method, specific steps include:
(1) mathematical model of ferroresonance system is established；
(2) Integral Sliding Mode face is designed according to set time Theory of Stability；
(3) adaptive law of Nonlinear control law and uncertain parameter is obtained by theory deduction；
(4) when determining stable according to set time Theory of Stability affiliated lemmas and liapunov function stability analysis
Between upper range limit；
(5) its control effect is verified by numerical simulation.
Further, for neutral-point solid ground electric system, ferroresonance system mathematical model in step (1),
Its equation are as follows:
In formula: R is the core loss of TV；EmFor power supply amplitude；C=C1+C2For the equivalent capacity in equivalent circuit；It is non-
Magnetic flux in linear inductance；U is the voltage effective value at iron core both ends；ω is system frequency；Magnetize for nonlinear inductance special
PropertyRelationship；U is control input.
Further, sliding-mode surface designed by step (2) are as follows:
Switching function is designed first, and system output tracking target isUd, define the error of controlled quatity are as follows:
In order to which the robustness of system is expanded to whole system and eliminates steady-state error, integral is added in linear sliding-mode surface
, construct following Integral Sliding Mode face:
Further, to the Nonlinear control law of ferro-resonance over-voltage system design in step (3) are as follows:
-ls-ksign(s)|s|a-ksign(s)|s|β
And:
Wherein, 0 < α < 1, β > 1, g are any normal number.
Further, according to set time Theory of Stability Design for Nonlinear System in step (4) are as follows:
WhereinIt is system state variables and mission nonlinear function respectively, if existed for system (7)
Continuous positive definite differentiable function V (x), first derivativeNegative definite, then system (7) Lyapunov stablizes, if existing simultaneously part
Bounded stability function of time T (x), to any t, as t >=T (x), x (t)=0 is permanent to be set up, then at this time system (7) origin can
Referred to as global finite time stability；If the convergence time of system (7) has the upper bound, and dividing value is unrelated with state variable x thereon, that is, exists
Under arbitrary initial conditions,So thatAnd as t >=T (x), x (t) ≡ 0, system (7) at this time
The referred to as global set time stablizes；For nonlinear system (7), it is assumed that there are function V (x): RnThe continuous positive definite of → R can be micro-,
Include balance neighborhood of a point D ∈ R for onen, V (x) satisfaction:
D*V(x)≤-[αVp(x)+βVq(x)]k
Or
Wherein α, β, p, q, k > 0 and pk < 1.If V (x) is from D ∈ R at this timenAny position starts, must in set time T
Surely it can make V (x) ≡ 0, i.e., the system set time stablizes, and its convergence time are as follows:
Further, it is determined according to liapunov function stability analysis and stablizes the time range upper bound:
Construct Lyapunov function:
Using the controller u and corresponding tuner parameters of design, system has been obtained with set time Theory of Stability
The derivative of Lyapunov function:
Wherein:
It is hereby achieved that system stablizes the time upper bound are as follows:
I.e. as t >=t1When, ferro-resonance over-voltage is inhibited.
The adaptive law and nonlinear Control of the uncertain parameter designed in step (2) and step (3) are utilized in step (5)
Device carries out numerical simulation experiment, the control effect of access control device on MATLAB emulation platform.
Compared with the prior art, technical effect of the invention and advantage are embodied in: electric system disclosed by the invention is ferromagnetic
The quick suppressing method of resonance overvoltage can not only be such that system stablizes under conditions of not depending on initial value in finite time, and
And the upper bound for stablizing the time can have stronger robustness and anti-interference ability, it is most important that any by being calculated
System global consistent asymptotic stability can be realized under primary condition in the given time, more effectively inhibits electric system ferromagnetic humorous
The overvoltage of vibration improves the stability of electric system.
Detailed description of the invention
Fig. 1 is a kind of suppressing method process of the set time sliding formwork of ferro-resonance over-voltage chaos provided by the invention
Figure；
Fig. 2 is the typical ferromagnetic resonance circuit theory figure of solidly earthed neutral system substation of the present invention；
Fig. 3 is the single-phase ferro-resonance circuit figure of substation of the present invention and its simplified electrical circuit diagram；
Fig. 4 is the time response of ferro-resonance over-voltage chaos state variable when not adding controller in the embodiment of the present invention
Figure；
Fig. 5 is the phasor of ferro-resonance over-voltage chaos state when not adding controller in the embodiment of the present invention；
Fig. 6 be after the controller of design is added in the embodiment of the present invention ferro-resonance over-voltage chaos state variable when
Between response diagram；
Fig. 7 is ferroresonance system phasor when the controller of design being added in the embodiment of the present invention.
Specific embodiment
In order to deepen the understanding of the present invention, present invention will be further explained below with reference to the attached drawings and examples, the implementation
Example for explaining only the invention, does not constitute protection scope of the present invention and limits.
As shown in Figures 1 to 7, the quick suppressing method of chaos of Analysis on Ferroresonance of Power System Based overvoltage provided by the invention,
First to ferroresonance system founding mathematical models, Integral Sliding Mode face is then designed according to set time Theory of Stability, secondly
The adaptive law of Nonlinear control law and uncertain parameter is obtained by theory deduction and designs controller, when again according to fixing
Between Theory of Stability affiliated lemmas and liapunov function stability analysis determine and stablize the time range upper bound, finally by number
It is worth its control effect of simulating, verifying.
Detailed process is:
(1) according to Fig.2, the typical ferromagnetic resonance circuit theory figure of solidly earthed neutral system substation and its
The simple equivalent circuit founding mathematical models of Fig. 3, as follows:
In formula: R is the core loss of TV；EmFor power supply amplitude；C=C1+C2For the equivalent capacity in equivalent circuit；It is non-
Magnetic flux in linear inductance；U is the voltage effective value at iron core both ends；ω is system frequency；Magnetize for nonlinear inductance special
PropertyRelationship；U is control input.
As selected parameter Cpu=21.9633, Rpu=8.6508,ωpu=1, EmpuWhen=1,
The chaos motion of voltage waveform is clearly demonstrated as shown in Fig. 4 (a), (b), in figure, Fig. 5 is the dynamical phase in the case of this kind
Figure.Phase path in figure is not equilibrium state, does not also have periodic solution, but seemingly mixed and disorderly, but has certain random character
Behavior shows that the ferromagnetic resonance behavior is in chaos state.It such as takes no action to, electric system will be generated immeasurable broken
It is bad.
(2) to realize control target, Integral Sliding Mode face is designed according to set time Theory of Stability.
Switching function is designed first, and system output tracking target isUd=0, the error for defining controlled quatity is as follows:
In order to which the robustness of system is expanded to whole system and eliminates steady-state error, integral is added in linear sliding-mode surface
, construct following Integral Sliding Mode face:
Derivation obtains:
(3) according to formula (1), (3), (4), it can be designed that the nonlinear Control of the chaos suppression of ferro-resonance over-voltage
Rate:
Wherein k is uncertain parameter, adaptive law are as follows:
K=| s |a+1+|s|β+1-(k-g)a-(k-g)β (6)
Wherein, 0 < α < 1, β > 1, g are any normal number.This embodiment takes α=0.5, β=1.5, g=1.
(4) Lyapunov function is constructed:
Using the controller u and corresponding tuner parameters of design, system has been obtained with set time Theory of Stability
The derivative of Lyapunov function:
Wherein:
It is hereby achieved that system stablizes the time upper bound are as follows:
I.e. as t >=t1When, ferro-resonance over-voltage is inhibited.
Each parameter taken in the present embodiment is brought into wherein, obtains t1≤4.38.That is system was stablized on the time
Boundary is in the 4.38s after applying controller, and in other words, after applying controller 4.38s, system centainly reaches stable, ferromagnetic humorous
Vibration overvoltage is inhibited.A kind of process of the chaos suppression method of provided ferro-resonance over-voltage is as shown in Figure 1.
(5) using controller designed by set time Theory of Stability, data are carried out on MATLAB emulation platform
Emulation, the control effect of access control device.The present embodiment initial value is taken asFerro-resonance over-voltage system exists
Be added the time response of state variable and chaos electric system phasor after the controller that designs of the present invention be shown in Fig. 6 (a),
(b) and Fig. 7.There it can be seen that control target has been stabilized to required equalization point, ferro-resonance over-voltage is suppressed,
To demonstrate the validity of controller.
What the embodiment of the present invention was announced is preferred embodiment, and however, it is not limited to this, the ordinary skill people of this field
Member, easily according to above-described embodiment, understands spirit of the invention, and make different amplification and variation, but as long as not departing from this
The spirit of invention, all within the scope of the present invention.
Claims (5)
1. a kind of suppressing method of the set time sliding formwork of ferro-resonance over-voltage chaos characterized by comprising
(1) mathematical model of ferroresonance system is established；
(2) Integral Sliding Mode face is designed according to set time Theory of Stability；
(3) adaptive law of Nonlinear control law and uncertain parameter is obtained by theory deduction；
(4) it is determined according to set time Theory of Stability affiliated lemmas and liapunov function stability analysis and stablizes time model
Place boundary；
(5) its control effect is verified by numerical simulation.
2. the suppressing method of the set time sliding formwork of ferro-resonance over-voltage chaos according to claim 1, feature exist
In, the mathematical model of the Analysis on Ferroresonance of Power System Based in step (1), equation are as follows:
In formula: R is the core loss of TV；EmFor power supply amplitude；C=C1+C2For the equivalent capacity in equivalent circuit；It is non-linear
Magnetic flux in inductance；U is the voltage effective value at iron core both ends；ω is system frequency；For nonlinear inductance magnetization characteristicRelationship；U is control input.
3. the suppressing method of the set time sliding formwork of ferro-resonance over-voltage chaos according to claim 1, feature exist
In the design method in the Integral Sliding Mode face in step (2) are as follows:
Switching function is designed first, and system output tracking target isUd, the error for defining controlled quatity is as follows:
In order to the robustness of system is expanded to whole system and eliminates steady-state error, integral term is added in linear sliding-mode surface,
Construct following Integral Sliding Mode face:
Derivation obtains:
4. the suppressing method of the set time sliding formwork of ferro-resonance over-voltage chaos according to claim 1, feature exist
In nonlinear Control rate and uncertain parameter in step (3) adapt to the design method of rule are as follows:
According to formula (1), (3), (4), the Nonlinear control law of the chaos suppression of ferro-resonance over-voltage can be designed that:
Wherein k is uncertain parameter, adaptive law are as follows:
Wherein, 0 < α < 1, β > 1, g are any normal number.
5. the suppressing method of the set time sliding formwork of ferro-resonance over-voltage chaos according to claim 1, feature exist
In the calculation method in the stable time range upper bound in step (4) are as follows:
According to set time Theory of Stability Design for Nonlinear System are as follows:
WhereinIt is system state variables and mission nonlinear function respectively, if there is company for system (7)
Continuous positive definite differentiable function V (x), first derivativeNegative definite, then system (7) Lyapunov stablizes, if existing simultaneously part has
Boundary stablizes function of time T (x), and to any t, as t >=T (x), x (t)=0 is permanent to be set up, then system (7) can claim in origin at this time
For global finite time stability；If the convergence time of system (7) has the upper bound, and dividing value is unrelated with state variable x thereon, i.e., in office
Under primary condition of anticipating,So thatAnd as t >=T (x), x (t) 30, system at this time
(7) it is stable to be referred to as the global set time；For nonlinear system (7), it is assumed that there are function V (x): RnThe continuous positive definite of → R can
It is micro-, include balance neighborhood of a point D ∈ R for onen, V (x) satisfaction:
D*V(x)≤-[αVp(x)+βVq(x)]k
Or
Wherein α, β, p, q, k > 0 and pk < 1.If V (x) is from D ∈ R at this timenAny position starts, must can in set time T
Make V (x) ≡ 0, i.e., the system set time stablizes, and its convergence time are as follows:
Determine that designed controller control Analysis on Ferroresonance of Power System Based overvoltage is steady according to liapunov function stability analysis
It fixes time upper range limit:
Construct Lyapunov function:
Using the controller u and corresponding tuner parameters of design, system has been obtained with set time Theory of Stability
The derivative of Lyapunov function:
Wherein:
It is hereby achieved that system stablizes the time upper bound are as follows:
I.e. as t >=t1When, ferro-resonance over-voltage is inhibited.
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Cited By (3)
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| CN111130104A (en) * | 2020-01-07 | 2020-05-08 | 西安理工大学 | Passivity sliding mode control method for chaotic oscillation of power system |
| CN113114156A (en) * | 2021-04-15 | 2021-07-13 | 贵州大学 | MEMS resonator self-adaptive chaotic control circuit and method |
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| CN111130104A (en) * | 2020-01-07 | 2020-05-08 | 西安理工大学 | Passivity sliding mode control method for chaotic oscillation of power system |
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| CN113114156B (en) * | 2021-04-15 | 2022-08-02 | 贵州大学 | MEMS resonator self-adaptive chaotic control circuit and method |
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