CN113890054B - Wind-fire coupling system stability judging and compensating method based on equivalent open loop process - Google Patents
Wind-fire coupling system stability judging and compensating method based on equivalent open loop process Download PDFInfo
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Classifications
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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
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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
- H02J3/38—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
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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
- 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]
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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
- 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
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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
- 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
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- 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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- 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 stability analysis and control of new energy grid-connected systems 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 sagging control into account and a residual subsystem after the fan is removed; respectively establishing a multivariable open-loop frequency domain model for the fan and the residual subsystem which account for virtual inertia and sagging control, and converting the multivariable open-loop frequency domain model into a univariable closed-loop transfer function; and taking the inverse 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 unstable, performing phase compensation on a phase-locked loop of the wind-fire coupling system. The stability judgment result is accurate, and satisfactory frequency modulation effect can be achieved on the premise of ensuring the stability of the coupling system by performing subsynchronous oscillation suppression through phase compensation.
Description
Technical Field
The invention belongs to the technical field of stability analysis and control of new energy grid-connected systems, and particularly relates to a wind-fire coupling system stability judging and compensating 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 into a power grid, and the problem of power system oscillation is increased due to nonlinearity of the power electronic equipment, and the problem of subsynchronous oscillation is particularly remarkable; on the other hand, the mutual coupling between renewable energy sources and the local thermal power generating unit is more and more obvious. The scene is commonly existed in the northern power grid of China, so that a method for accurately analyzing the oscillation stability of the wind-fire coupling system is needed.
The renewable energy sources such as wind and light work in a maximum power point tracking mode during normal operation, enough inertial response and primary frequency modulation capability cannot be provided for a power grid, and the stable operation of the system can be obviously influenced after a large number of renewable energy sources are connected into the power grid. In order to meet the large-scale grid-connected requirement of renewable energy sources, a 'power grid friendly' renewable energy source station is constructed, and a plurality of national standards have provided requirements for active frequency support control of renewable energy sources. For a typical operation scene of a wind-fire coupling system, it is necessary to study multi-characteristic parameter stability criteria of the wind-fire coupling system considering virtual inertia and sagging control and determine stability and safety boundary conditions of the coupling system. However, there are few related studies.
Therefore, the existing wind-fire coupling system has the technical problem that the stability judging result is inaccurate.
Disclosure of Invention
Aiming at the defects or improvement demands of the prior art, the invention provides a wind-fire coupling system stability judging and compensating method based on an equivalent open loop process, thereby solving the technical problem that the existing wind-fire coupling system has inaccurate stability judging result.
In order to achieve the above object, according to one aspect of the present invention, there is provided a wind-fire coupling system stability determining method based on an equivalent open loop process, including the steps of:
(1) Decoupling the wind-fire coupling system through an equivalent open loop process to obtain a fan taking virtual inertia and sagging control into account and a residual subsystem after the fan is removed;
(2) Respectively establishing a multivariable open-loop frequency domain model for the fan and the residual subsystem which account for virtual inertia and sagging control, and converting the multivariable open-loop frequency domain model into a univariable closed-loop transfer function;
(3) And taking the inverse 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 mode of the stability judgment 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 smaller than zero, the wind-fire coupling system is stable, and if the real part is larger 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 larger than zero, the wind-fire coupling system is stable, and if the real part is smaller than zero, the wind-fire coupling system is unstable.
Further, the specific mode of the stability judgment is as follows:
drawing a bird diagram of the characteristic transfer function;
the phase angle in the subsynchronous oscillation frequency range in the bird diagram rotates anticlockwise through the real axis, the angle is increased, and the wind-fire coupling system in the corresponding frequency band is stable;
in the bird's 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 conjugate zero point near the virtual axis in a pair of subsynchronous frequency ranges, and the oscillation frequency of the wind-fire coupling system is larger than the attenuation coefficient.
Further, the step (2) includes:
fan composition open loop subsystem taking virtual inertia and sagging control into account, which is given by the equation of state in the formula ,ΔUg and ΔIg And respectively representing a fan port voltage vector and a fan port current vector under the synchronous rotation coordinate system. A is that g 、B g 、D g and Dg Respectively a fan side state matrix, an input matrix, an output matrix and a direct transmission matrix, delta X g As a state variable of the fan, a subscript g represents a fan side parameter;
the annular frequency domain model of the fan is derived from the state equation of the fan:
in the formula ,Iw Is the identity matrix of the fan, s is the Laplacian, g g11 (s)、g g12 (s)、g g21(s) and gg22 (s) open loop frequency domain model transfer function C of fan respectively g (s) converting to elements in the matrix after the matrix;
the state equation of the remaining subsystems is in the formula ,ΔXs State variables for the remaining subsystems; a is that s 、B s 、C s and Ds The system comprises a residual subsystem state matrix, an input matrix, an output matrix and a direct transmission matrix; subscript s denotes the remaining subsystem parametersA number;
the open loop frequency domain model of the remaining subsystems is as follows:
in the formula ,Is G is identity matrix in the rest subsystem s11 (s)、g s12 (s)、g s21(s) and gs22 (s) open loop frequency domain model transfer functions G for the remaining subsystems, respectively s (s) converting to elements in the matrix after the matrix;
finally, the closed loop transfer function is:
wherein ,
D(s)＝g g11 (s)g s11 (s)+g g12 (s)g s21 (s)+G i (s)[g g11 (s)g s12 (s)+g g12 (s)g s22 (s)]
wherein ,
according to another aspect of the present invention, there is provided a method for compensating 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, the compensation phase angle in the phase compensation process wherein , at a frequency f p The maximum compensation phase angle obtained here, ω represents the oscillation frequency.
In general, the above technical solutions conceived by the present invention, compared with the prior art, enable the following beneficial effects to be obtained:
(1) The wind-fire coupling system considering virtual inertia and sagging 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 characteristics in a subsynchronous frequency range, and a stability safety boundary condition of the coupling system is determined.
(2) The improved stability criterion suitable for the subsynchronous oscillation of the analysis system is simple to deduce and easy to verify, the stability of the wind-fire coupling system can be judged only through the phase frequency characteristic of the characteristic transfer function, 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, wherein the stability of the coupling system can be judged by drawing the bird chart of the characteristic transfer function and observing the direction of the phase passing through the real axis in the subsynchronous oscillation frequency range, the judging mode is simple and effective, and the accuracy is high.
(3) Aiming at the wind-fire coupling system taking virtual inertia and sagging control into account, the invention also provides a subsynchronous oscillation inhibition measure based on phase remodelling control, and the damping characteristic of the subsynchronous oscillation mode is improved by leading the phase of the subsynchronous oscillation mode through a phase compensation phase-locked loop, so that the stability margin of the coupling system taking active frequency support control in the subsynchronous frequency range is improved, and the 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 diagram of a wind-fire coupling system topology provided by an embodiment of the present 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 according to an embodiment of the present invention;
FIG. 4 (a) is a schematic diagram of a circuit of a fire coupling system according to an embodiment of the present invention;
fig. 4 (b) is an equivalent structural diagram of a certain loop of the fire coupling system according to the embodiment of the present invention;
FIG. 5 (a) is a schematic diagram of a first stability criterion of the proposed bill of lading variable system according to an embodiment of the present invention;
FIG. 5 (b) is a schematic diagram of a second stability criterion for the proposed bill of lading variable system according to an embodiment of the present invention;
FIG. 6 (a) is a schematic diagram of an equivalent stability criterion provided by an embodiment of the present invention;
FIG. 6 (b) is a Bode diagram of an equivalent characteristic transfer function provided by an embodiment of the present invention;
FIG. 7 is a characteristic transfer function Bode diagram of an equivalent univariate system provided by an embodiment of the invention;
fig. 8 (a) is a schematic diagram of thermal power generating unit output according to an embodiment of the present invention;
fig. 8 (b) is an enlarged schematic diagram of the thermal power generating unit according to an embodiment of the present invention;
fig. 8 (c) is a schematic diagram of output of a wind turbine according to an embodiment of the present invention;
fig. 8 (d) is an enlarged schematic diagram of the output of the wind turbine according to the embodiment of the present invention;
FIG. 9 is a characteristic transfer function Bode diagram of an equivalent univariate system provided by an embodiment of the invention;
FIG. 10 (a) is a schematic diagram of the system frequency and the output of a wind power and thermal power generating unit when the frequency modulation link is not added according to the embodiment of the invention;
fig. 10 (b) is a schematic diagram of the system frequency and the output of the wind power and thermal power units when the frequency modulation link is added according to the embodiment of the invention;
fig. 10 (c) is a schematic diagram of the system frequency and the output of the wind power and thermal power generating unit when adding the phase compensation link based on adding the frequency modulation link according to the embodiment of the invention.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention. In addition, the technical features of the embodiments of the present invention described below may be combined with each other as long as they do not collide 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) And establishing a wind-fire coupling system frequency domain equivalent model based on an equivalent open-loop process (EOP) and taking active frequency support control into account. And decoupling each loop of the wind-fire coupling system taking virtual inertia and sagging control by using EOP, and converting a multivariable system loop equation into a univariate system loop equation, so as to establish a frequency domain equivalent model of the wind-fire coupling system with single input and single output. The model mainly comprises:
(11) And determining the topology structure of the wind-fire coupling system. The topology structure of the wind-fire coupling system is shown in figure 1. In the figure, synchronous generator G1 represents thermal power, P e and PD The output electromagnetic power of the synchronous generator and the DFIG (doubly fed induction generator), respectively. E & lt delta & gt and U & lt theta & gt represent the internal potential of the synchronous generator and the voltage of the DFIG access point respectively. U (U) s And 0 DEG represents infinite grid voltage. X is X 1 X for line reactance between synchronous generator and PCC point 2 X is the line reactance between the DFIG and the PCC point 3 Is the line reactance between the PCC point and the infinite grid.
(12) A wind power topology is determined that accounts for virtual inertia and droop control. The structure is shown in fig. 2.ω is the system frequency value measured by the phase locked loop; PWM is pulse width modulation; p (P) sref and Qsref The active power reference value and the reactive power reference value are respectively output by the DFIG; p (P) s and Qs The actual active output and the reactive output of the DFIG are respectively; u (U) pcc Is PCC point voltage; u (U) d and Uq The voltage components of the PCC point voltage d axis and the voltage component of the q axis are respectively; θ pll Measuring the obtained PCC point voltage phase angle for the phase-locked loop; k (K) p and Ki Proportional parameters and integral parameters of the phase-locked loop PI controller respectively; k (K) df and Kpf Virtual inertia coefficients and droop coefficients, respectively; t (T) df and Tpf The virtual inertia control response time and the droop control response time are respectively.
(13) And splitting the wind-fire coupling system. And the wind-fire coupling system is split into a fan taking virtual inertia and sagging control into account and a residual subsystem after the fan is removed. The fan in the wind-fire coupling system which takes virtual inertia and sagging control into account can form an open loop subsystem, and the state equation of the open loop subsystem under the synchronous rotation coordinate system is that in the formula ,ΔUg and ΔIg The voltage vector and the current vector of the DFIG port under the synchronous rotation coordinate system are respectively represented as an input vector and an output vector. A is that g 、B g 、C g and Dg The system comprises a DFIG side state matrix, an input matrix, an output matrix and a direct transmission matrix. ΔX g Is a state variable of the DFIG. The subscript g indicates a fan side parameter.
The DFIG side open loop frequency domain model can be derived from the above equation:
in the formula ,Iw And s is a Laplacian operator and is a unit array. g g11 (s)、g g12 (s)、g g21(s) and gg22 (s) the transfer functions G of the DFIG side open-loop frequency domain model g The element in(s).
The air-fire coupling system is also formed into an open loop subsystem by removing the rest subsystem part of the grid-connected fan, and the state equation is that in the formula ,ΔXs to remove all state variables of the remaining subsystems after the blower; a is that s 、B s 、C s and Ds The system comprises a residual subsystem state matrix, an input matrix, an output matrix and a direct transmission matrix; and the subscript s represents the parameters of the subsystem remained after the fan is removed in the wind-fire coupling system.
According to the above equation, the open loop frequency domain model of the remaining subsystems is as follows:
in the formula ,Is Is a unit array. g s11 (s)、g s12 (s)、g s21(s) and gs22 (s) the transfer function G of the open loop frequency domain model of the residual subsystem after the fan is removed s The element in(s).
The blower, taking into account the virtual inertia and droop control, and the remaining subsystems after the blower is removed, may form an interconnected closed loop system, as shown in fig. 3.
(14) The single input single output system is equivalently simplified. The interconnected closed loop system shown in fig. 3 is equivalent to a single input single output system, as shown in fig. 4 (a) and (b). Based on (b) in fig. 4, a closed loop transfer function of the single input single output system can be obtained:
wherein ,
D(s)＝g g11 (s)g s11 (s)+g g12 (s)g s21 (s)+G i (s)[g g11 (s)g s12 (s)+g g12 (s)g s22 (s)]
in the formula ,
(2) The method is suitable for analyzing the stability criterion of the subsynchronous oscillation of the wind-fire coupling system. The criterion is based on a simplified single-input single-output wind-fire coupling system equivalent model, can effectively judge the oscillation characteristics in the subsynchronous frequency range, and determines the stability and safety boundary condition of the coupling system. The criteria mainly include:
as shown in fig. 4 (b), the characteristic transfer function is T(s) =1/D(s) -1, if the characteristic transfer function has a pair of conjugate zero points lambda near the imaginary axis in the subsynchronous frequency range 1，2 ＝σ o ±jω o And satisfy |sigma o |＜＜|ω o The characteristic transfer function of the system can be converted into the following form:
T(s)＝(s-λ 1 )(s-λ 2 )G(s)
wherein G(s) is the remainder of T(s) after removal of the two conjugate zero polynomials, s=jω, when ω is at λ 1，2 The above formula can be expressed as follows:
T(jω)＝(jω-λ 1 )(jω-λ 2 )G(jω)
it is obvious that G (jω) is a rational polynomial, so that the real part and the imaginary part can be separated, i.e., G (jω) =a (ω) +jb (ω), and it is obvious that a (ω) and b (ω) are real functions related to ω, and the above formula can be expressed as follows:
T(jω)＝[-σ o +j(ω-ω o )][-σ o +j(ω+ω o )][a(ω)+jb(ω)]
separating the real and imaginary parts of T (jω) yields the following expression:
let the imaginary part Im [ T (jω) ]=0 of the feature transfer function, the following expression can be obtained:
it is apparent that when |sigma o |＜＜|ω o When I, sigma o /ω o Approximately 0, can find ω r ≈ω o . The dominant oscillation frequency omega of the system can be approximated from the imaginary part of the characteristic transfer function being equal to zero o . The frequency omega of the zero crossing point is calculated r The real part Re [ T (jω) of the transfer function with the in-characteristic]The following expression can be obtained:
the slope of the imaginary part at the zero crossing point can be known as follows:
the positive and negative of b can be determined by the slope of the zero crossing point of the imaginary part. Further according to Re [ T (jω) r )]To judge the attenuation coefficient sigma 0 Positive and negative of (a).
When b > 0, the slope of the imaginary part of the characteristic transfer function at the zero crossing is negative, i.e. the curve crosses from positive to negative at the zero crossing; when b < 0, the slope of the imaginary part of the characteristic transfer function at the zero crossing point is positive, i.e. the curve is positively traversed from negative direction at the zero crossing point; in combination with the preceding equation, the stability criteria of the system can be obtained as follows:
(1) the imaginary part of the characteristic transfer function, i.e. Im [ T (jω) r )]If Re [ T (jω) r )]< 0, sigma 0 < 0, the system is stable; conversely, if Re [ T (jω) r )]> 0, then sigma 0 > 0, the system is unstable.
(2) The imaginary part of the characteristic transfer function, i.e. Im [ T (jω) r )]The slope of the curve at zero crossing is positive if Re [ T (jω) r )]> 0, then sigma 0 < 0, the system is stable; conversely, if Re [ T (jω) r )]< 0, sigma 0 > 0, the system is unstable.
The above expression can be represented by (a) and (b) in fig. 5. Further, the expression is shown in FIG. 6 (a). The direction of the arrow is the direction of the frequency increase. As shown in fig. 6 (b), the phase angle in the characteristic transfer function bode diagram 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 shaft, the angle is reduced, and the corresponding frequency band is unstable. Based on the conclusion, the stability of the coupling system can be judged by drawing a bird diagram of the characteristic transfer function and observing the direction of the phase passing through the real axis (0 DEG or 180 DEG) in the subsynchronous oscillation frequency range.
(3) Subsynchronous oscillation suppression measures based on phase reshaping control. The phase of the primary subsynchronous oscillation mode of the phase-locked loop is compensated by the phase reshaping controller so as to improve the damping characteristic of the phase-locked loop, and the stability margin of the coupling system taking the active frequency support control into account in the subsynchronous frequency range is improved. The control strategy mainly comprises the following steps:
in order to realize compensation of the system phase margin, a phase compensation link is added in a system control loop to compensate the problem of insufficient system phase margin caused by an active frequency support control link. For this purpose, the invention selects a series phase compensation link H(s) after the active frequency support control link, as shown in FIG. 2, with the corresponding expressionFrom the above, the compensation phase angle of phase compensation element H(s) can be determined>The expression of (2) is +.>Assume that the phase compensation link is at frequency f p The maximum compensation phase angle is obtained, and the +.>If the maximum compensation phase angle is set to +>Then according to the above two formulasCan obtain τ 1 The expression of (2) is +.>
The compromise of the invention selects f p ＝10Hz，Thereby obtaining τ 1 ＝0.0190；τ 2 ＝07041。
According to the wind-fire coupling system stability judging and compensating method based on the equivalent open loop process, based on the wind-fire coupling system taking virtual inertia and sagging control into account, the following two groups of embodiments are set, firstly, the stability of the wind-fire coupling system under different frequency modulation parameters is compared, and the validity of the provided criterion is verified. Then, the phase of the dominant mode of the phase-locked loop in the subsynchronous oscillation frequency range is compensated by an additional controller to improve the damping characteristic of the phase-locked loop, and the phase remodeling control provided by the method can achieve a satisfactory frequency modulation effect on the premise of ensuring the stability of a wind-fire coupling system.
Example 1: the validity of the proposed stability criterion is verified.
Fig. 7 shows a bode diagram of the characteristic transfer function of the equivalent single-input single-output system under different modulation parameters. The time domain simulation results of the wind-fire coupling system under the same working conditions as those of fig. 7 are shown in (a) - (d) of fig. 8. As can be seen from fig. 7, the phase frequency characteristic curves in the Case 1 and Case 3 corresponding feature transfer function bode diagrams pass through the imaginary axis clockwise (angle decreases) in the secondary synchronization frequency range, the phase frequency characteristic curves in the Case 2 corresponding feature transfer function bode diagrams pass through the imaginary axis anticlockwise (angle increases) in the secondary synchronization frequency range, and according to the result of the proposed criterion, the Case 1 and Case 3 under-wind-fire coupling systems will oscillate unstably, while the Case 2 under-wind-fire coupling systems will remain stable. In fig. 8, (a) - (d) time domain simulation results show that under load disturbance, the Case 1 and Case 3 corresponding wind-fire coupling systems do generate oscillation instability, while the Case 2 corresponding wind-fire coupling systems do remain stable, and the time domain simulation results verify the validity of the provided criteria.
Example 2: and verifying the validity of the phase remodeling control strategy based on the provided criterion.
Fig. 9 shows a bode diagram of the characteristic transfer function of the equivalent single-input single-output system under different modulation parameters. Fig. 10 (a) - (c) show the time domain simulation results of the wind-fire coupling system under the same working conditions as fig. 9. Case 1 is a simulation working condition of the wind-fire coupling system corresponding to the condition that the frequency modulation link is not added; case 2 is a simulation working condition of the wind-fire coupling system corresponding to the Case of adding the frequency modulation link but not adding the phase compensation link; and Case 3 is the simulation working condition of the wind-fire coupling system corresponding to the time of adding the frequency modulation link and the phase compensation link. As can be seen from fig. 9, the phase frequency characteristic curves in the Case 1 and Case 3 corresponding feature transfer function bode diagrams pass through the imaginary axis counterclockwise (angle increases) in the secondary synchronization frequency range, the phase frequency characteristic curves in the Case 2 corresponding feature transfer function bode diagrams pass through the imaginary axis clockwise (angle decreases) in the secondary synchronization frequency range, and according to the result of the proposed criterion, the Case 1 and Case 3 under-wind-fire coupling systems will remain stable, while the Case 2 under-wind-fire coupling systems will oscillate unstably. The time domain simulation results in fig. 10 (a) - (c) show that the Case 1 corresponding wind-fire coupling system is stable under load disturbance without adding a frequency modulation link. After the frequency modulation link is added, the Case 2 corresponding to the wind-fire coupling system under load disturbance truly responds to the frequency change and plays a certain frequency modulation effect, but meanwhile, the dominant 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, so that the system is in oscillation instability. And a phase compensation link (Case 3) is further added on the basis of adding a frequency modulation link, the phase near the dominant oscillation frequency of the phase-locked loop of the wind-fire coupling system is remodeled, the stability of the wind-fire coupling system is ensured under the same frequency modulation parameter as Case 2, and a satisfactory frequency modulation effect is achieved. The time domain simulation results verify the validity of the phase remodeling control strategy based on the proposed criteria.
It will be readily appreciated by those skilled in the art that the foregoing description is merely a preferred embodiment of the invention and is not intended to limit the invention, but any modifications, equivalents, improvements or alternatives falling within the spirit and principles of the invention are intended to be included within the scope of the invention.
Claims (6)
1. A wind-fire coupling system stability judging method 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 sagging control into account and a residual subsystem after the fan is removed;
(2) Respectively establishing a multivariable open-loop frequency domain model for the fan and the residual subsystem which account for virtual inertia and sagging control, and converting the multivariable open-loop frequency domain model into a univariable closed-loop transfer function;
(3) 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;
the step (2) comprises:
the fan with virtual inertia and sagging control is taken into account to form an open-loop subsystem, and the state equation is that in the formula ,ΔUg and ΔIg Respectively representing a fan port voltage vector and a fan port current vector under a synchronous rotation coordinate system; a is that g 、B g 、C g and Dg Respectively a fan side state matrix, an input matrix, an output matrix and a direct transmission matrix, delta X g As a state variable of the fan, a subscript g represents a fan side parameter;
the annular frequency domain model of the fan is derived from the state equation of the fan:
in the formula ,Iw Is the identity matrix of the fan, s is the Laplacian, g g11 (s)、g g12 (s)、g g21(s) and gg22 (s) open loop frequency domain model transfer function G of fan respectively g (s) converting to elements in the matrix after the matrix;
the state equation of the remaining subsystems is in the formula ,ΔXs State variables for the remaining subsystems; a is that s 、B s 、C s and Ds The system comprises a residual subsystem state matrix, an input matrix, an output matrix and a direct transmission matrix; subscript s represents the remaining subsystem parameters;
the open loop frequency domain model of the remaining subsystems is as follows:
in the formula ,Is G is identity matrix in the rest subsystem s11 (s)、g s12 (s)、g s21(s) and gs22 (s) open loop frequency domain model transfer functions G for the remaining subsystems, respectively s (s) converting to elements in the matrix after the matrix;
finally, the closed loop transfer function is:
wherein ,
D(s)＝g g11 (s)g s11 (s)+g g12 (s)g s21 (s)+G i (s)[g g11 (s)g s12 (s)+g g12 (s)g s22 (s)]
wherein ,
2. the method for judging the stability of the wind-fire coupling system based on the equivalent open loop process according to claim 1, wherein the specific mode of judging the stability 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 smaller than zero, the wind-fire coupling system is stable, and if the real part is larger 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 larger than zero, the wind-fire coupling system is stable, and if the real part is smaller than zero, the wind-fire coupling system is unstable.
3. The method for judging the stability of the wind-fire coupling system based on the equivalent open loop process according to claim 1, wherein the specific mode of judging the stability is as follows:
drawing a bird diagram of the characteristic transfer function;
the phase angle in the subsynchronous oscillation frequency range in the bird diagram rotates anticlockwise through the real axis, the angle is increased, and the wind-fire coupling system in the corresponding frequency band is stable;
in the bird's 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. A method for determining stability of a wind-fire coupled system based on an equivalent open loop process as claimed in claim 2 or 3, wherein the characteristic transfer function has a conjugate zero point near the virtual axis in a pair of subsynchronous frequency ranges, and the oscillation frequency of the wind-fire coupled system is greater than the attenuation coefficient.
5. 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 judging method based on the equivalent open loop process of any one of claims 1-4 judges that the wind-fire coupling system is unstable, the phase compensation is performed on the phase-locked loop of the wind-fire coupling system.
6. The method for compensating a wind-fire coupled system based on an equivalent open loop process according to claim 5, wherein the phase compensation phase angle in the phase compensation process wherein ,at a frequency f p The maximum compensation phase angle obtained here, ω represents the oscillation frequency.
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