CN113890054A - Wind-fire coupling system stability determination and compensation method based on equivalent open loop process - Google Patents

Wind-fire coupling system stability determination and compensation method based on equivalent open loop process Download PDF

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CN113890054A
CN113890054A CN202111077449.4A CN202111077449A CN113890054A CN 113890054 A CN113890054 A CN 113890054A CN 202111077449 A CN202111077449 A CN 202111077449A CN 113890054 A CN113890054 A CN 113890054A
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wind
coupling system
loop
fire coupling
transfer function
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CN113890054B (en
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姚伟
严才
胡博
艾小猛
方家琨
文劲宇
顾洪群
吕旭明
崔岩
刘景峰
黄笑伯
郭任
周桂平
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Huazhong University of Science and Technology
State Grid Liaoning Electric Power Co Ltd
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Huazhong University of Science and Technology
State Grid Liaoning Electric Power Co Ltd
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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
    • H02J3/241—The oscillation concerning frequency
    • 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
    • H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
    • H02J3/381—Dispersed generators
    • 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
    • H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
    • H02J3/46—Controlling of the sharing of output between the generators, converters, or transformers
    • H02J3/466—Scheduling the operation of the generators, e.g. connecting or disconnecting generators to meet a given demand
    • 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]
    • 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
    • H02J2300/00—Systems for supplying or distributing electric power characterised by decentralized, dispersed, or local generation
    • H02J2300/20—The dispersed energy generation being of renewable origin
    • H02J2300/28—The renewable source being wind energy
    • 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
    • H02J2300/00—Systems for supplying or distributing electric power characterised by decentralized, dispersed, or local generation
    • H02J2300/40—Systems for supplying or distributing electric power characterised by decentralized, dispersed, or local generation wherein a plurality of decentralised, dispersed or local energy generation technologies are operated simultaneously
    • 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
    • Y02E10/00—Energy generation through renewable energy sources
    • Y02E10/70—Wind energy
    • Y02E10/76—Power conversion electric or electronic aspects

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  • Engineering & Computer Science (AREA)
  • Power Engineering (AREA)
  • Control Of Position, Course, Altitude, Or Attitude Of Moving Bodies (AREA)
  • Control Of Eletrric Generators (AREA)

Abstract

The invention discloses a wind-fire coupling system stability judging and compensating method based on an equivalent open loop process, which belongs to the technical field of new energy grid-connected system stability analysis and control and comprises the following steps: decoupling the wind-fire coupling system through an equivalent open loop process to obtain a fan taking virtual inertia and droop control into consideration and a residual subsystem after the fan is removed; establishing a multivariable open-loop frequency domain model for the fan and the residual subsystems considering virtual inertia and droop control respectively, and converting the multivariable open-loop frequency domain model into a univariate closed-loop transfer function; and taking the reciprocal of the closed-loop transfer function as a characteristic transfer function, and judging the stability of the wind-fire coupling system through the characteristic transfer function. And when the wind fire coupling system is judged to be unstable, phase compensation is carried out on a phase-locked loop of the wind fire coupling system. The method has accurate stability judgment result, and can achieve satisfactory frequency modulation effect on the premise of ensuring the stability of a coupled system by performing subsynchronous oscillation suppression through phase compensation.

Description

Wind-fire coupling system stability determination and compensation method based on equivalent open loop process
Technical Field
The invention belongs to the technical field of stability analysis and control of a new energy grid-connected system, and particularly relates to a wind-fire coupling system stability judgment and compensation method based on an equivalent open loop process.
Background
With the rapid development of renewable energy sources, on one hand, power electronic equipment is widely connected to a power grid, the nonlinearity of the power electronic equipment causes the oscillation problem of a power system to increase, and the subsynchronous oscillation problem is particularly obvious; on the other hand, the mutual coupling between renewable energy sources and local thermal power units is more and more obvious. The same grid-connected point is coupled and integrated into a unified regulation and control object, and the scene generally exists in a power grid in northern China, so that a method capable of accurately analyzing the oscillation stability of a wind-fire coupling system is urgently needed.
When renewable energy sources such as wind, light and the like normally operate, the system works in a maximum power point tracking mode, cannot provide enough inertial response and primary frequency modulation capability for a power grid, and can have obvious influence on the stable operation of the system after being connected into the power grid in large quantity. In order to meet the large-scale grid-connected requirement of renewable energy sources and construct a 'power grid-friendly' renewable energy source station, a plurality of national standards already provide requirements for the active frequency support control of the renewable energy sources. Aiming at a typical operation scene of the wind-fire coupling system, a multi-characteristic parameter stabilization criterion of the wind-fire coupling system, which takes virtual inertia and droop control into consideration, needs to be researched to determine a stable safety boundary condition of the coupling system. However, there are few related studies.
Therefore, the technical problem that the stability judgment result of the existing wind-fire coupling system is inaccurate exists.
Disclosure of Invention
Aiming at the defects or improvement requirements of the prior art, the invention provides a wind-fire coupling system stability judgment and compensation method based on an equivalent open loop process, so that the technical problem that the stability judgment result of the existing wind-fire coupling system is inaccurate is solved.
In order to achieve the above object, according to an aspect of the present invention, there is provided a method for determining stability of a wind-fire coupling system based on an equivalent open-loop process, including the following steps:
(1) decoupling the wind-fire coupling system through an equivalent open loop process to obtain a fan taking virtual inertia and droop control into consideration and a residual subsystem after the fan is removed;
(2) establishing a multivariable open-loop frequency domain model for the fan and the residual subsystems considering virtual inertia and droop control respectively, and converting the multivariable open-loop frequency domain model into a univariate closed-loop transfer function;
(3) and taking the reciprocal of the closed-loop transfer function as a characteristic transfer function, and judging the stability of the wind-fire coupling system through the characteristic transfer function.
Further, the specific manner of the stability determination is as follows:
dividing the characteristic transfer function into a real part and an imaginary part;
when the slope of the curve of the imaginary part at the zero-crossing point is negative, if the real part is less than zero, the wind-fire coupling system is stable, and if the real part is greater than zero, the wind-fire coupling system is unstable;
when the slope of the curve of the imaginary part at the zero-crossing point is positive, if the real part is greater than zero, the wind-fire coupled system is stable, and if the real part is less than zero, the wind-fire coupled system is unstable.
Further, the specific manner of the stability determination is as follows:
drawing a bode diagram of the characteristic transfer function;
in the Berde diagram, a phase angle in a subsynchronous oscillation frequency range rotates anticlockwise through a real axis, the angle is increased, and a wind-fire coupling system in a corresponding frequency band is stable;
in the Berde diagram, the phase angle in the subsynchronous oscillation frequency range rotates clockwise through the real axis, the angle is reduced, and the wind-fire coupling system in the corresponding frequency band is unstable.
Further, the characteristic transfer function has a pair of conjugate zeros close to the virtual axis in the subsynchronous frequency range, and the oscillation frequency of the wind-fire coupled system is greater than the attenuation coefficient.
Further, the step (2) includes:
the fan taking the virtual inertia and the droop control into account forms an open-loop subsystem, and the state equation of the open-loop subsystem is
Figure BDA0003261721570000021
in the formula ,ΔUg and ΔIgRespectively representing the voltage vector and the current vector of the fan port under the synchronous rotating coordinate system. A. theg、Bg、Dg and DgRespectively, a fan side state matrix, an input matrix, an output matrix and a direct transmission matrix, delta XgSubscript g represents a fan-side parameter, which is a state variable of the fan;
the ring frequency domain model of the fan is derived from the state equation of the fan:
Figure BDA0003261721570000031
in the formula ,IwIs the unit matrix of the fan, s is Laplace operator, gg11(s)、gg12(s)、gg21(s) and gg22(s) open-loop frequency domain model transfer functions C for the wind turbine, respectivelyg(s) converting to elements in the matrix after the matrix;
the state equation of the remaining subsystem is
Figure BDA0003261721570000032
in the formula ,ΔXsIs the state variable of the remaining subsystem; a. thes、Bs、Cs and DsRespectively a state matrix, an input matrix, an output matrix and a direct transmission matrix of the residual subsystem; subscript s denotes the remaining subsystem parameters;
the open-loop frequency domain model of the remaining subsystems is as follows:
Figure BDA0003261721570000033
in the formula ,IsIs the identity matrix in the remaining subsystems, gs11(s)、gs12(s)、gs21(s) and gs22(s) open-loop frequency domain model transfer function G for the residual subsystem, respectivelys(s) converting to elements in the matrix after the matrix;
finally, the closed loop transfer function is:
Figure BDA0003261721570000034
wherein ,
D(s)＝gg11(s)gs11(s)+gg12(s)gs21(s)+Gi(s)[gg11(s)gs12(s)+gg12(s)gs22(s)]
wherein ,
Figure BDA0003261721570000035
according to another aspect of the present invention, there is provided a compensation method for a wind-fire coupling system based on an equivalent open loop process, comprising:
when the wind-fire coupling system stability judging method based on the equivalent open loop process judges that the wind-fire coupling system is unstable, phase compensation is carried out on a phase-locked loop of the wind-fire coupling system.
Further, a compensating phase angle in the phase compensation process
Figure BDA0003261721570000041
wherein ,
Figure BDA0003261721570000042
Figure BDA0003261721570000043
at a frequency fpThe maximum compensation phase angle, ω, taken at (a) represents the oscillation frequency.
In general, compared with the prior art, the above technical solution contemplated by the present invention can achieve the following beneficial effects:
(1) the wind-fire coupled system considering virtual inertia and droop control is equivalent to a single-variable closed-loop transfer function based on an equivalent open-loop process theory, the single-variable closed-loop transfer function can effectively judge the oscillation characteristic in a subsynchronous frequency range, the stable and safe boundary condition of the coupled system is determined, and the method disclosed by the invention is adopted for stability judgment, so that the result is accurate, simple and visual.
(2) The improved stability criterion suitable for analyzing the subsynchronous oscillation of the system is simple to deduce and easy to verify, the stability of the wind-fire coupling system can be judged only through the characteristic transfer function phase-frequency characteristic, and the method has the potential of carrying out stability quantitative analysis on an actual complex new energy grid-connected system. The invention also provides a stability judging mode, which is characterized in that a Berde diagram of the characteristic transfer function is drawn, and the stability of the coupling system can be judged by observing the direction of the phase passing through the real axis in the subsynchronous oscillation frequency range, so that the judging mode is simple and effective, and the accuracy is high.
(3) Aiming at the wind-fire coupling system considering virtual inertia and droop control, the invention also provides a subsynchronous oscillation suppression measure based on phase remodeling control, the damping characteristic of the wind-fire coupling system is improved by leading the phase of a subsynchronous oscillation mode through a phase compensation phase-locked loop, the stability margin of the coupling system considering active frequency support control in a subsynchronous frequency range is improved, and a satisfactory frequency modulation effect can be achieved on the premise of ensuring the stability of the wind-fire coupling system.
Drawings
FIG. 1 is a schematic view of a wind-fire coupling system topology provided by an embodiment of the invention;
FIG. 2 is a schematic diagram of virtual inertia and droop control provided by an embodiment of the present invention;
FIG. 3 is a schematic diagram of a closed loop structure of a wind-fire coupling system provided by an embodiment of the invention;
fig. 4 (a) is a structure diagram of a loop of a fire coupling system according to an embodiment of the present invention;
fig. 4 (b) is an equivalent structural diagram of a loop of the fire coupling system according to an embodiment of the present invention;
FIG. 5 (a) is a schematic diagram illustrating a first stability criterion of the proposed univariate system according to an embodiment of the present invention;
FIG. 5 (b) is a schematic diagram illustrating a second stability criterion of the proposed univariate system according to the embodiment of the present invention;
FIG. 6 (a) is a schematic diagram illustrating an equivalent stability criterion provided by an embodiment of the present invention;
FIG. 6 (b) is a bode plot of equivalent characteristic transfer functions provided by an embodiment of the present invention;
FIG. 7 is a bode plot of the characteristic transfer function of an equivalent univariate system provided by an embodiment of the present invention;
fig. 8 (a) is a schematic diagram of the thermal power generating unit output provided by the embodiment of the present invention;
fig. 8 (b) is an enlarged schematic diagram of the output of the thermal power generating unit according to the embodiment of the present invention;
fig. 8 (c) is a schematic diagram of the output of the wind turbine provided by the embodiment of the invention;
fig. 8 (d) is an enlarged schematic diagram of the output of the wind turbine provided by the embodiment of the invention;
FIG. 9 is a bode plot of the characteristic transfer function of an equivalent univariate system provided by an embodiment of the present invention;
fig. 10 (a) is a schematic diagram of system frequency and output of wind power and thermal power generation units when a frequency modulation link is not added according to an embodiment of the present invention;
fig. 10 (b) is a schematic diagram of system frequency and wind power and thermal power generation unit output when a frequency modulation link is added according to an embodiment of the present invention;
fig. 10 (c) is a schematic diagram of system frequency and output of wind power and thermal power generation units when a phase compensation link is added on the basis of adding a frequency modulation link according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
The invention provides a wind-fire coupling system stability judging and compensating method based on an equivalent open loop process, which comprises the following steps:
(1) establishing an equivalent frequency-domain equivalent model of the wind-fire coupling system based on an equivalent open-loop process (EOP) and taking active frequency support control into account. Decoupling loops of the wind-fire coupled system considering virtual inertia and droop control by using EOP (equivalent-error-degree-of-arrival), and converting a loop equation of a multivariable system into a loop equation of a univariate system, thereby establishing a single-input single-output wind-fire coupled system frequency domain equivalent model. The model mainly comprises:
(11) and determining the topological structure of the wind-fire coupling system. The wind-fire coupling system topology structure is shown in figure 1. In the figure, the synchronous generator G1 represents thermal power, Pe and PDThe output electromagnetic power of a synchronous generator and a DFIG (doubly-fed asynchronous wind generator) respectively. E & lt delta and U & lt theta respectively represent the internal potential of the synchronous generator and the DFIG access point voltage. U shapesAnd the angle 0 degrees represents infinite grid voltage. X1Is the line reactance between the synchronous generator and the PCC point, X2Is the line reactance between the DFIG and the PCC point, X3Is the line reactance between the PCC point and the infinite grid.
(12) And determining a wind power topological structure considering virtual inertia and droop control. The structure is shown in fig. 2. Where ω is the system frequency value measured by the phase locked loop; PWM is pulse width modulation; psref and QsrefRespectively an active power reference value and a reactive power reference value output by the DFIG; ps and QsRespectively the actual active output and the reactive output of the DFIG; u shapepccIs the PCC point voltage; u shaped and UqD-axis and q-axis voltage components of the PCC point voltage respectively; thetapllMeasuring the voltage phase angle of the PCC point for the phase-locked loop; kp and KiRespectively are a proportional parameter and an integral parameter of the phase-locked loop PI controller; kdf and KpfRespectively a virtual inertia coefficient and a droop coefficient; t isdf and TpfThe virtual inertia control response time and the droop control response time are respectively.
(13) And (4) splitting the wind-fire coupling system. The wind-fire coupling system is divided into a fan for considering virtual inertia and droop control and a residual subsystem after the fan is removed. The fan taking the virtual inertia and the droop control into account in the wind-fire coupling system can form an open-loop subsystem, and the state equation of the open-loop subsystem under the synchronous rotating coordinate system is
Figure BDA0003261721570000071
in the formula ,ΔUg and ΔIgThe vector of the DFIG port voltage and the vector of the current under the synchronous rotating coordinate system are respectively represented as an input vector and an output vector. A. theg、Bg、Cg and DgThe DFIG side state matrix, the input matrix, the output matrix and the direct transmission matrix are respectively. Δ XgIs the state variable of DFIG. The subscript g indicates the fan side parameters.
The DFIG side open-loop frequency domain model can be derived by the following formula:
Figure BDA0003261721570000072
in the formula ,IwIs a unit matrix, and s is the laplace operator. gg11(s)、gg12(s)、gg21(s) and gg22(s) are respectively DFIG side open-loop frequency domain model transfer functions Gg(s) elements in(s).
The remaining subsystem part except the grid-connected fan in the wind-fire coupling system also forms an open-loop subsystem, and the state equation is
Figure BDA0003261721570000073
in the formula ,ΔXsRemoving all state variables of the remaining subsystems after the fan is removed; a. thes、Bs、Cs and DsRespectively a state matrix, an input matrix, an output matrix and a direct transmission matrix of the residual subsystem; and subscript s represents the remaining subsystem parameters after the fan is removed in the wind-fire coupled system.
According to the above equation, the open-loop frequency domain model of the remaining subsystems is as follows:
Figure BDA0003261721570000074
in the formula ,IsIs a unit array. gs11(s)、gs12(s)、gs21(s) and gs22(s) respectively removing the fan and then remaining the open-loop frequency domain model transfer function G of the subsystems(s) elements in(s).
The fan, taking into account virtual inertia and droop control, and the remaining subsystems, excluding the fan, may form an interconnected closed loop system, as shown in fig. 3.
(14) The single-input single-output system is equivalent and simplified. The interconnected closed loop system shown in fig. 3 is equivalent to a single-input single-output system, as shown in (a) and (b) of fig. 4. Based on (b) in fig. 4, a closed-loop transfer function of a single-input single-output system can be obtained:
Figure BDA0003261721570000081
wherein ,
D(s)＝gg11(s)gs11(s)+gg12(s)gs21(s)+Gi(s)[gg11(s)gs12(s)+gg12(s)gs22(s)]
in the formula ,
Figure BDA0003261721570000082
(2) the method is suitable for analyzing the stability criterion of the subsynchronous oscillation of the wind-fire coupled system. The criterion is based on a simplified single-input single-output wind-fire coupling system equivalent model, the oscillation characteristic in a subsynchronous frequency range can be effectively judged, and the stable and safe boundary condition of the coupling system is determined. The criterion mainly comprises:
as shown in fig. 4 (b), the characteristic transfer function is t(s) ═ 1/d(s) — 1, if the characteristic transfer function exists a pair of conjugate zeros λ near the imaginary axis in the subsynchronous frequency range1，2＝σo±jωoAnd satisfies | σo|＜＜|ωoThe characteristic transfer function of the system can now be converted into the form:
T(s)＝(s-λ1)(s-λ2)G(s)
wherein G(s) is the residue of T(s) except two zero-point polynomials with conjugate zero, and s is j ω when ω is λ1，2In the fine neighborhood of (a), the above formula can be expressed as follows:
T(jω)＝(jω-λ1)(jω-λ2)G(jω)
it is clear that G (j ω) is a rational polynomial and therefore the real and imaginary parts can be separated, i.e. G (j ω) ═ a (ω) + jb (ω), and it is clear that a (ω) and b (ω) are real functions related to ω, in which case the above formula can be expressed as follows:
T(jω)＝[-σo+j(ω-ωo)][-σo+j(ω+ωo)][a(ω)+jb(ω)]
separating the real part and imaginary part of T (j ω) can obtain the following expression:
Figure BDA0003261721570000083
let imaginary part Im [ T (j ω) ] of the characteristic transfer function be 0, the following expression can be obtained:
Figure BDA0003261721570000091
Figure BDA0003261721570000092
it is clear that when |. sigma.)o|＜＜|ωoWhen l, σo/ωoIs approximately equal to 0, and omega can be foundr≈ωo. The dominant oscillation frequency ω of the system can be approximated by the imaginary part of the characteristic transfer function being equal to zeroo. Frequency omega of zero crossing pointrReal part of transfer function with characteristic Re [ T (j omega) ]]The following expression can be obtained:
Figure BDA0003261721570000093
the slope of the imaginary part at the zero crossing point can be further known as follows:
Figure BDA0003261721570000094
the sign of b can be determined by the slope of the imaginary zero crossing. Further according to Re [ T (j omega) ]r)]To judge the attenuation coefficient sigma0Positive and negative.
When b > 0, the slope of the imaginary part of the characteristic transfer function at the zero-crossing point is negative, i.e. the curve crosses from positive to negative at the zero-crossing point; when b is less than 0, the slope of the imaginary part of the characteristic transfer function at the zero-crossing point is positive, namely the curve passes through from negative to positive at the zero-crossing point; in combination with the foregoing formula, the following criteria for system stability can be obtained:
characteristic transfer function imaginary part, namely Im [ T (j omega)r)]When the slope of the curve at the zero-crossing point is negative, if Re [ T (j ω)r)]If < 0, then σ0< 0, the system is stable; on the contrary, if Re [ T (j ω)r)]If > 0, then σ0(> 0), the system is unstable.
② the imaginary part of the characteristic transfer function, namely Im [ T (j ω)r)]If the slope of the curve at the zero crossing point of Re [ T (j ω) is positiver)]If > 0, then σ0< 0, the system is stable; on the contrary, if Re [ T (j ω)r)]If < 0, then σ0(> 0), the system is unstable.
The above expression can be represented by (a) and (b) in fig. 5. Further, it can be expressed as shown in (a) of fig. 6. The direction of the arrow is the direction of increasing frequency. As shown in fig. 6 (b), the phase angle in the bode plot of the characteristic transfer function rotates counterclockwise through the real axis (0 ° or 180 °), the angle increases, and the corresponding frequency band is stable; the phase angle rotates clockwise through the real axis, the angle is reduced, and the corresponding frequency band is unstable. Based on the conclusion, a Berde diagram of the characteristic transfer function can be drawn, and the stability of the coupling system can be judged by observing the direction of the phase passing through the real axis (0 degrees or 180 degrees) in the subsynchronous oscillation frequency range.
(3) Subsynchronous oscillation suppression measures based on phase reshaping control. The phase remolding controller compensates the phase of the phase-locked loop leading subsynchronous oscillation mode to improve the damping characteristic of the phase-locked loop, and the stability margin of the coupling system considering the active frequency support control in a subsynchronous frequency range is improved. The control strategy mainly comprises:
in order to realize the compensation of the phase margin of the system, a phase compensation link is added in a system control loop to make up for the problem of insufficient phase margin of the system caused by an active frequency support control link. Therefore, the invention selects a series phase compensation link H(s) after the active frequency support control link, as shown in FIG. 2, and the corresponding expression is
Figure BDA0003261721570000101
The compensation phase angle of the phase compensation link H(s) can be obtained from the above formula
Figure BDA0003261721570000102
Is expressed as
Figure BDA0003261721570000103
Assuming that the phase compensation element is at frequency fpThe maximum compensation phase angle is obtained, and the method can be known according to the above formula
Figure BDA0003261721570000104
If the maximum compensation phase angle is set to
Figure BDA0003261721570000105
Then τ is obtained from the above two equations1Is expressed as
Figure BDA0003261721570000106
Compromise selection f in the inventionp＝10Hz，
Figure BDA0003261721570000107
Thus obtaining τ1＝0.0190；τ2＝07041。
The invention provides a method for judging and compensating the stability of a wind-fire coupling system based on an equivalent open loop process. Then, the additional controller compensates the phase of the phase-locked loop dominant mode in the subsynchronous oscillation frequency range to improve the damping characteristic of the phase-locked loop dominant mode, and the phase remodeling control provided by the method is verified to achieve a satisfactory frequency modulation effect on the premise of ensuring the stability of the wind-fire coupled system.
Example 1: and verifying the effectiveness of the stability criterion.
Fig. 7 shows a bode plot of the characteristic transfer function of an equivalent single-input single-output system under different frequency modulation parameters. Fig. 8 (a) - (d) show the time domain simulation results of the wind-fire coupled system under the same working conditions as fig. 7. As can be seen from fig. 7, the phase-frequency characteristic curves in the bode plots of the feature transfer functions corresponding to Case 1 and Case 3 pass through the imaginary axis clockwise (angle decreases) in the subsynchronous frequency range, and the phase-frequency characteristic curves in the bode plots of the feature transfer functions corresponding to Case 2 pass through the imaginary axis counterclockwise (angle increases) in the subsynchronous frequency range, according to the result of the proposed criterion, the fire-wind coupled system under Case 1 and Case 3 will oscillate and destabilize, while the fire-wind coupled system under Case 2 will remain stable. Time domain simulation results (a) - (d) in fig. 8 show that the wind-fire coupling systems corresponding to Case 1 and Case 3 are indeed subjected to oscillation instability under load disturbance, the wind-fire coupling systems corresponding to Case 2 are indeed kept stable, and the time domain simulation results verify the effectiveness of the provided criterion.
Example 2: and verifying the effectiveness of the phase remodeling control strategy based on the provided criterion.
Fig. 9 shows a bode plot of the characteristic transfer function of an equivalent single-input single-output system under different frequency modulation parameters. Fig. 10 (a) - (c) show the time domain simulation results of the wind-fire coupled system under the same working conditions as fig. 9. Case 1 is the corresponding wind-fire coupling system simulation working condition without the frequency modulation link; case 2 is the corresponding wind-fire coupling system simulation working condition when a frequency modulation link is added but a phase compensation link is not added; case 3 is the corresponding wind-fire coupling system simulation working condition when the frequency modulation link and the phase compensation link are added. As can be seen from fig. 9, the phase-frequency characteristic curves in the bode plots of the feature transfer functions corresponding to Case 1 and Case 3 pass through the imaginary axis counterclockwise (the angle increases) in the subsynchronous frequency range, and the phase-frequency characteristic curves in the bode plots of the feature transfer functions corresponding to Case 2 pass through the imaginary axis clockwise (the angle decreases) in the subsynchronous frequency range, according to the result of the proposed criterion, the fire-wind coupling system under Case 1 and Case 3 will remain stable, while the fire-wind coupling system under Case 2 will oscillate unstably. Time domain simulation results (a) - (c) in fig. 10 show that the wind-fire coupled system corresponding to Case 1 is really stable under load disturbance without adding frequency modulation loop. After the frequency modulation link is added, the wind-fire coupled system corresponding to the Case 2 under load disturbance really responds to frequency change and plays a certain frequency modulation effect, but simultaneously, the leading characteristic root of the phase-locked loop moves to the right half plane of the polar coordinate system due to the addition of the frequency modulation link, and the system is subjected to oscillation instability. And further, on the basis of adding a frequency modulation link, a phase compensation link (Case 3) is added to reshape the phase near the leading oscillation frequency of the phase-locked loop of the wind-fire coupling system, so that the stability of the wind-fire coupling system is ensured under the same frequency modulation parameter as that of the Case 2, and a satisfactory frequency modulation effect is achieved. The time domain simulation result verifies the effectiveness of the phase remodeling control strategy based on the provided criterion.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (7)

1. A method for judging the stability of a wind-fire coupling system based on an equivalent open loop process is characterized by comprising the following steps:
(1) decoupling the wind-fire coupling system through an equivalent open loop process to obtain a fan taking virtual inertia and droop control into consideration and a residual subsystem after the fan is removed;
(2) establishing a multivariable open-loop frequency domain model for the fan and the residual subsystems considering virtual inertia and droop control respectively, and converting the multivariable open-loop frequency domain model into a univariate closed-loop transfer function;
(3) and taking the reciprocal of the closed-loop transfer function as a characteristic transfer function, and judging the stability of the wind-fire coupling system through the characteristic transfer function.
2. The method for determining the stability of the wind-fire coupling system based on the equivalent open loop process as claimed in claim 1, wherein the stability determination is specifically performed by:
dividing the characteristic transfer function into a real part and an imaginary part;
when the slope of the curve of the imaginary part at the zero-crossing point is negative, if the real part is less than zero, the wind-fire coupling system is stable, and if the real part is greater than zero, the wind-fire coupling system is unstable;
when the slope of the curve of the imaginary part at the zero-crossing point is positive, if the real part is greater than zero, the wind-fire coupled system is stable, and if the real part is less than zero, the wind-fire coupled system is unstable.
3. The method for determining the stability of the wind-fire coupling system based on the equivalent open loop process as claimed in claim 1, wherein the stability determination is specifically performed by:
drawing a bode diagram of the characteristic transfer function;
in the Berde diagram, a phase angle in a subsynchronous oscillation frequency range rotates anticlockwise through a real axis, the angle is increased, and a wind-fire coupling system in a corresponding frequency band is stable;
in the Berde diagram, the phase angle in the subsynchronous oscillation frequency range rotates clockwise through the real axis, the angle is reduced, and the wind-fire coupling system in the corresponding frequency band is unstable.
4. The method for determining the stability of the wind-fire coupled system based on the equivalent open loop process as claimed in claim 2 or 3, wherein the characteristic transfer function has a pair of conjugate zeros close to the imaginary axis in the subsynchronous frequency range, and the oscillation frequency of the wind-fire coupled system is greater than the damping coefficient.
5. A wind-fire coupling system stability determination method based on an equivalent open loop process according to any one of claims 1 to 3, wherein the step (2) comprises:
the fan taking the virtual inertia and the droop control into account forms an open-loop subsystem, and the state equation of the open-loop subsystem is
Figure FDA0003261721560000021
in the formula ,ΔUg and ΔIgRespectively representing the voltage vector and the current vector of the fan port under the synchronous rotating coordinate system. A. theg、Bg、Cg and DgRespectively, a fan side state matrix, an input matrix, an output matrix and a direct transmission matrix, delta XgFor the state variables of the wind turbine, the subscript g denotes the wind turbine side parametersCounting;
the ring frequency domain model of the fan is derived from the state equation of the fan:
Figure FDA0003261721560000022
in the formula ,IwIs the unit matrix of the fan, s is Laplace operator, gg11(s)、gg12(s)、gg21(s) and gg22(s) open-loop frequency domain model transfer functions G for the wind turbine, respectivelyg(s) converting to elements in the matrix after the matrix;
the state equation of the remaining subsystem is
Figure FDA0003261721560000023
in the formula ,ΔXsIs the state variable of the remaining subsystem; a. thes、Bs、Cs and DsRespectively a state matrix, an input matrix, an output matrix and a direct transmission matrix of the residual subsystem; subscript s denotes the remaining subsystem parameters;
the open-loop frequency domain model of the remaining subsystems is as follows:
Figure FDA0003261721560000024
in the formula ,IsIs the identity matrix in the remaining subsystems, gs11(s)、gs12(s)、gs21(s) and gs22(s) open-loop frequency domain model transfer function G for the residual subsystem, respectivelys(s) converting to elements in the matrix after the matrix;
finally, the closed loop transfer function is:
Figure FDA0003261721560000031
wherein ,
D(s)＝gg11(s)gs11(s)+gg12(s)gs21(s)+Gi(s)[gg11(s)gs12(s)+gg12(s)gs22(s)]
wherein ,
Figure FDA0003261721560000032
6. a compensation method of a wind-fire coupling system based on an equivalent open loop process is characterized by comprising the following steps:
when the wind-fire coupling system stability determination method based on the equivalent open loop process according to any one of claims 1 to 5 determines that the wind-fire coupling system is unstable, phase compensation is performed on a phase-locked loop of the wind-fire coupling system.
7. The method for compensating the wind-fire coupling system based on the equivalent open loop process as claimed in claim 6, wherein the compensating phase angle in the phase compensation process
Figure FDA0003261721560000033
wherein ,
Figure FDA0003261721560000034
Figure FDA0003261721560000035
at a frequency fpThe maximum compensation phase angle, ω, taken at (a) represents the oscillation frequency.
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