CN116054190A - Analysis method for influence of doubly-fed wind power plant control parameters on subsynchronous oscillation - Google Patents
Analysis method for influence of doubly-fed wind power plant control parameters on subsynchronous oscillation Download PDFInfo
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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
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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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- 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
Abstract
The invention discloses an analysis method of the influence of control parameters of a doubly-fed wind power plant on subsynchronous oscillation. The invention can analyze and obtain the control parameter of the converter which is most sensitive to the subsynchronous oscillation mode, can determine the control parameter which plays a key role in the stable operation of the system, can effectively improve the operation stability of the system by reasonably setting the key control parameter, and has important significance for ensuring the safety of the power grid.
Description
Technical Field
The invention belongs to the field of large power grid operation stability analysis, and particularly relates to an analysis method for the influence of control parameters of a doubly-fed wind power plant on subsynchronous oscillation.
Background
With the acceleration of the energy transformation process, the renewable energy permeability in the power grid gradually increases. Wind power, as a representative of renewable energy sources, has the advantage of not consuming fossil fuels and not polluting the environment. However, since the wind power energy is often sent out by a long-distance power transmission line, in order to improve the power transmission capacity of the line, a series compensation device is added in the power transmission line, and unstable subsynchronous interaction between a fan and a series compensation alternating current power grid causes great threat to safe and stable operation of the power grid. The compensation degree of the series compensation capacitor and the control parameter of the doubly-fed fan converter are key parameters affecting the stability level of the system, and the method has important significance on how to analyze and evaluate the compensation degree and the influence of the control parameter on the stability level of the system. Eigenvalue analysis is commonly used for system stability analysis, and therefore, based on the eigenvalue analysis method, the motion track of eigenvalues along with the change of control parameters is studied to analyze which control parameters are more sensitive in the double-fed wind farm instability analysis.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides an analysis method for the influence of control parameters of a doubly-fed wind power plant on subsynchronous oscillation. The invention establishes mathematical models of all the constituent elements of the doubly-fed wind power plant and the communication system, and obtains the characteristic values of the system and the participation factors of all the state variables by carrying out linearization treatment on the mathematical models. And finally, determining the parameter with the greatest influence on the system stability by controlling the characteristic value movement track under the parameter change.
The aim of the invention is realized by the following technical scheme: the analysis method of the influence of the control parameters of the doubly-fed wind power plant on the subsynchronous oscillation specifically comprises the following steps:
(1) Establishing a mathematical model of a doubly-fed wind power plant, wherein the mathematical model comprises a fan transmission system model, an induction generator model, a rotor side converter model, a grid side converter model, a direct current link, a converter transformer model and an external power grid model;
(2) Linearizing the established mathematical model, and calculating characteristic values and participation factors;
(3) And drawing a movement track of the characteristic value by changing the numerical value of the researched control parameter (comprising the converter control parameter and the series compensation degree), so as to analyze and obtain the influence of the control parameter on the interaction of the subsynchronous oscillation.
Further, the step (1) specifically includes:
(1.1) establishing a fan transmission system model:
wherein:
represents ω r Differentiation over time, the dots above the variables below also represent differentiation over time of the variables, H being the equivalent inertia of the turbine, shaft and generator, ω r For angular velocity of rotor, T m Is the mechanical torque of the steam turbine, T e Is the electromagnetic torque of the generator.
(1.2) modeling an induction generator:
wherein: subscripts "s" and "r" denote variables on the stator side and rotor side, respectively; "d" and "q" represent variables of d-axis and q-axis, respectively; omega 0 For reference angular velocity omega s For synchronizing the angular velocity, the values are given in per unit. R, I, V and ψ represent winding resistance, current, voltage and magnetic flux. The stator and rotor currents may be expressed as a magnetic flux as shown in equation (6).
Wherein: delta=l m 2 -L ss -L rr ，L m 、L ss And L rr The coil is respectively an excitation inductance, a stator winding inductance and a rotor winding inductance. The transformer inductance between the stator and the transmission line is already contained in the stator inductance. Based on the formulas (2) to (6), the electromagnetic torque can be expressed as shown in the formula (7).
T e ＝ψ ds I qs -ψ qs I ds (7)
(1.3) establishing a rotor-side converter model:
the d-axis direction of the coordinate system is selected as the stator magnetic flux
Direction, thus there is->
Psi-shaped material qfs =0. The subscripts "df" and "qf" denote the d-axis component and q-axis component in the stator flux reference frame.
The stator reactive power is shown in formula (8). Since the stator voltage is perpendicular to the stator flux, the stator voltage in the stator flux reference direction takes a value of 0, and equation (8) can be written as equation (9).
Equation (10) is obtained from equation (6), and equation (11) is obtained by substituting equation (9). As can be seen from equation (11), the reactive power can be determined by I dfr And controlling. The design of the control of the rotor-side converter is therefore d-axis control of the reactive power Qs and q-axis control of the rotor rotational speed ω r 。
Q s ＝(V qfs I dfs -V dfs I qfs ) (8)
Q s ＝V qfs I dfs (9)
(1.4) establishing a network-side inverter model
The network side converter model is established by taking the voltage of the doubly-fed fan terminal as a reference system. The d-axis direction is consistent with the voltage direction of the wind power outlet end, and d-axis and q-axis components under the reference system are respectively indicated by subscripts 'dt' and 'qt'. The d-axis component is used for controlling direct-current link voltage, and the q-axis component is used for controlling reactive power sent by the converter.
By converting the voltages in the above coordinate system to RI coordinate system by the conversion shown in formulas (12) and (13), U can be obtained gcRe And U gcIm θ in the transformation f Replaced by theta t I.e. the angle between the dt axis and the R axis.
(1.5) establishing a dynamic characteristic model of a direct current link and a converter transformer:
not to take account ofThe loss of the current transformer is considered, and the power P flowing into the rotor-side current transformer r Equal to the power flowing out of the grid-side converter. Based on this, the dynamic characteristics of the dc link between the two converters can be represented by a differential equation as shown in equation (16), where C is the dc link capacitance.
The dynamic characteristics of the converter transformer can be represented by formulas (17) - (18), wherein R g X is the resistance of the winding of the transformer g For winding leakage reactance, I gcRe And I gcIm Is the real and imaginary parts of the network side converter current phasors.
(1.6) building an external power grid model:
using kirchhoff's law, the voltage at the doubly fed fan port can be expressed by equation (19). Wherein: u is the voltage of the outlet end of the doubly-fed fan, B sh For the outlet end to receive, I dtot And I qtot Is the total output current of the doubly-fed fan
(i.e. stator current->
And grid-side inverter current->
And) d-axis and q-axis components, subscripts "Re" and "Im" denote real and imaginary components of the variable under the R-I coordinate system.
The doubly-fed fan is connected with a power grid through a power transmission line, and the resistance of the power transmission line is R L Reactance is X L The capacitance reactance of the series compensation capacitor is X C 。。
Further, the step (2) specifically includes:
(2.1) calculating a characteristic value:
the dynamic characteristics of the doubly-fed wind turbine can be represented by a formula (24), linearization operation is performed near a balance point, the dynamic characteristics can be converted into a formula (25), and the characteristic value of the system can be obtained by a formula (26).
det|A-λI|＝0 (26)
The system eigenvalues typically contain both real and imaginary parts, each eigenvalue corresponding to one oscillation mode. The ith oscillation mode is available lambda i ＝σ i ±jω i Representation, sigma i Represents damping omega i Representing the frequency. Damping of the i-th oscillation mode is represented by formula (27).
(2.2) calculating a participation factor:
for each modality, the degree of participation of each state variable may be measured by a participation factor. The participation factor is dimensionless and is used for measuring the contribution degree of a certain state variable in a certain specific oscillation mode. The contribution of the kth state variable in the ith mode can be determined by equation (28).
Wherein:
is the ith row and the kth column of the left eigenvector of the eigenvector matrix A, and corresponds to the ith eigenvalue; />
Is the kth row and ith column of the right eigenvector of the eigenvector a, corresponding to the ith eigenvalue.
Further, the step (3) specifically includes:
(3.1) analyzing the influence of the control parameters of the converter on the stability and the subsynchronous mode of the system: and (3) the compensation degree of the series compensation device of the fixed system is a certain value, PI parameters of the rotor-side converter and the network-side converter controller are changed, and the movement track of the characteristic root is drawn.
And (3.3) analyzing the influence of the serial compensation level of the transmission line on the system stability and the subsynchronous oscillation mode. And fixing fan control parameters, adjusting the serial compensation degree, and drawing the moving track of the characteristic root.
The invention also provides a system for analyzing the influence of the control parameters of the doubly-fed wind power plant on the subsynchronous oscillation, which comprises a doubly-fed wind power plant system modeling unit, a characteristic value and participation factor calculation unit and a control parameter influence analysis unit, wherein:
double-fed wind farm system modeling unit: inputting relevant parameters, and establishing a mathematical model of the doubly-fed wind power plant, wherein the mathematical model comprises a fan transmission system model, an induction generator model, a rotor side converter model, a grid side converter model, a direct current link, a converter transformer model and an external power grid model;
the eigenvalue and participation factor calculation unit: according to the established double-fed wind farm mathematical model, calculating a system characteristic value and each state variable participation factor under different modes;
control parameter influence analysis unit: and drawing a movement track of the characteristic value by changing the numerical value of the researched control parameter (comprising the converter control parameter and the series compensation degree), so as to analyze and obtain the influence of the control parameter on the interaction of the subsynchronous oscillation.
According to the invention, a mathematical model of the doubly-fed wind power plant system is firstly established, then, based on a characteristic value analysis method, the characteristic value of the system and participation factors of various state variables under different modes are calculated, and finally, the movement track of the characteristic value along with the change of the control parameters is researched to analyze which control parameters are more sensitive in the unstable analysis of the doubly-fed wind power plant.
Compared with the prior art, the invention has the beneficial effects that: under the background that the permeability of new energy is continuously improved, the control parameters playing a key role in the stable operation of the system can be effectively determined, and the operation stability of the system can be effectively improved by reasonably setting the key control parameters, so that the method has important significance in guaranteeing the safety of a power grid.
Drawings
For a more complete and better understanding of the present invention, reference is now made to the following detailed description of the invention taken in conjunction with the accompanying drawings and examples, in which:
FIG. 1 is a flow chart of a method of analyzing the effect of doubly-fed wind farm control parameters on subsynchronous oscillations in accordance with the present invention;
FIG. 2 is a block diagram of an analysis system of the influence of control parameters of a doubly-fed wind farm on subsynchronous oscillations in accordance with the present invention.
Detailed Description
The following describes the invention in more detail.
Example 1
The embodiment provides a method for analyzing the influence of a control parameter of a doubly-fed wind farm on subsynchronous oscillation, referring to a flowchart of the method for analyzing the influence of the control parameter of the doubly-fed wind farm on subsynchronous oscillation shown in fig. 1, comprising the following steps:
step (1): and establishing a mathematical model of the doubly-fed wind power plant, wherein the mathematical model comprises a fan transmission system model, an induction generator model, a rotor side converter model, a grid side converter model, a direct current link, a converter transformer model and an external power grid model. Through the step, the physical model of the doubly-fed wind power plant can be converted into a mathematical model, so that the stability of the wind power plant can be researched by means of mathematical means such as eigenvalue analysis. The method comprises the following steps:
(1.1) establishing a fan transmission system model:
wherein:
represents ω r Differentiation over time, the dots above the variable each represent the differentiation over time of the variable, H is the equivalent inertia of the turbine, shaft and generator, ω r For angular velocity of rotor, T m Is the mechanical torque of the steam turbine, T e Is the electromagnetic torque of the generator.
(1.2) modeling an induction generator:
wherein: subscripts "s" and "r" denote variables on the stator side and rotor side, respectively; "d" and "q" represent variables of d-axis and q-axis, respectively; omega 0 For reference angular velocity omega s For synchronizing the angular velocity, the values are given in per unit. R, I, V and ψ represent winding resistance, current, voltage and magnetic flux. Stator and rotor currentThe usable magnetic flux expression is shown in the formula (6).
Wherein: delta=l m 2 -L ss -L rr ，L m 、L ss And L rr The coil is respectively an excitation inductance, a stator winding inductance and a rotor winding inductance. The transformer inductance between the stator and the transmission line is already contained in the stator inductance. Based on the formulas (2) to (6), the electromagnetic torque can be expressed as shown in the formula (7).
T e ＝ψ ds I qs -ψ qs I ds (7)
(1.3) establishing a rotor-side converter model:
the switching frequency of the power electronics is not considered in the modeling of the rotor-side converter, since it is sufficiently high compared to the target frequency under investigation to be filtered out. The d-axis direction of the coordinate system is selected as the stator magnetic flux
Direction, thus there is->
And +.>
The subscripts "df" and "qf" denote the d-axis component and q-axis component in the stator flux reference frame.
The stator reactive power is shown in formula (8). Since the stator voltage is perpendicular to the stator flux, the stator voltage in the stator flux reference direction takes a value of 0, and equation (8) can be written as equation (9).
Equation (10) is obtained from equation (6), and equation (11) is obtained by substituting equation (9). As can be seen from equation (11), the reactive power can be determined by I dfr And controlling. The design of the control of the rotor-side converter is therefore d-axis control of the reactive power Qs and q-axis control of the rotor rotational speed ω r 。
Q s ＝(V qfs I dfs -V dfs I qfs ) (8)
Q s ＝V qfs I dfs (9)
To obtain a rotor reference voltage at the stator flux reference frame, the dq-axis component of the rotor current is transformed into the stator flux reference frame. The related transformation equation is shown as formulas (12) - (13), wherein theta f The included angle between the d-axis of the dq coordinate system and the df-axis of the stator magnetic flux coordinate system is shown in the formula (14).
(1.4) establishing a network-side inverter model
The network side converter model is established by taking the voltage of the doubly-fed fan terminal as a reference system. The d-axis direction is consistent with the voltage direction of the wind power outlet end, and d-axis and q-axis components under the reference system are respectively indicated by subscripts 'dt' and 'qt'. The d-axis component is used for controlling direct-current link voltage, and the q-axis component is used for controlling reactive power sent by the converter.
By converting the voltages in the above coordinate system to RI coordinate system by the conversion shown in formulas (12) and (13), U can be obtained gcRe And U gcIm θ in the transformation f Replacement ofFor theta t I.e. the angle between the dt axis and the R axis.
(1.5) establishing a dynamic characteristic model of a direct current link and a converter transformer:
the power P flowing into the rotor-side converter irrespective of the loss of the converter r Equal to the power flowing out of the grid-side converter. Based on this, the dynamic characteristics of the dc link between the two converters can be represented by a differential equation as shown in equation (16), where C is the dc link capacitance.
The dynamic characteristics of the converter transformer can be represented by formulas (17) - (18), wherein R g X is the resistance of the winding of the transformer g For winding leakage reactance, I gcRe And I gcIm Is the real and imaginary parts of the network side converter current phasors.
(1.6) building an external power grid model:
using kirchhoff's law, the voltage at the doubly fed fan port can be expressed by equation (19). Wherein: u is the voltage of the outlet end of the doubly-fed fan, B sh For the outlet end to receive, I dtot And I qtot Is the total output current of the doubly-fed fan
(i.e. stator current->
And grid-side inverter current->
And) d-axis and q-axis components, subscripts "Re" and "Im" denote real and imaginary components of the variable under the R-I coordinate system.
The doubly-fed fan is connected with a power grid through a power transmission line, and the resistance of the power transmission line is R L Reactance is X L The capacitance reactance of the series compensation capacitor is X C . The dynamic characteristics of the transmission line and the external grid can be expressed by differential equations (20) - (23).
Wherein: i is the current flowing through the transmission line, U C To series complement the voltage of two ends of the capacitor, U B Is infinite system terminal voltage; the subscripts "Re" and "Im" denote the real and imaginary components of the variable in the R-I coordinate system.
Step (2): and linearizing the established mathematical model, and calculating the characteristic value and the participation factor. By the step, the mode playing the leading role in the doubly-fed wind power plant system can be identified, and the mode can further correspond to the relevant control link of the doubly-fed control system, so that the relevant control parameters can be purposefully set. The method comprises the following steps:
(2.1) calculating a characteristic value:
the dynamic characteristics of the doubly-fed wind turbine can be represented by a formula (24), linearization operation is performed near a balance point, the dynamic characteristics can be converted into a formula (25), and the characteristic value of the system can be obtained by a formula (26).
det|A-λI|＝0 (26)
The system eigenvalues typically contain both real and imaginary parts, each eigenvalue corresponding to one oscillation mode. The ith oscillation mode is available lambda i ＝σ i ±jω i Representation, sigma i Represents damping omega i Representing the frequency. Damping of the i-th oscillation mode is represented by formula (27).
(2.2) calculating a participation factor:
for each modality, the degree of participation of each state variable may be measured by a participation factor. The participation factor is dimensionless and is used for measuring the contribution degree of a certain state variable in a certain specific oscillation mode. The contribution of the kth state variable in the ith mode can be determined by equation (28).
Wherein:
zuo Te of the feature matrix AThe ith row and the kth column of the sign vector correspond to the ith eigenvalue; />
Is the kth row and ith column of the right eigenvector of the eigenvector a, corresponding to the ith eigenvalue.
Step (3): and drawing a movement track of the characteristic value by changing the numerical value of the researched control parameter (comprising the converter control parameter and the series compensation degree), so as to analyze and obtain the influence of the control parameter on the interaction of the subsynchronous oscillation. If a certain control parameter causes the system characteristic value to move from the left half plane to the right half plane, the control parameter is described as a key control parameter, and the value of the control parameter needs to be strictly set. The method comprises the following steps:
(3.1) analyzing the influence of the control parameters of the converter on the stability and the subsynchronous mode of the system: the compensation degree of the series compensation device of the fixed system is a certain value, and PI parameters of the rotor-side converter and the network-side converter controller are changed. The track of the characteristic value along with the change of the parameter is drawn, and the size of the characteristic value mark sign is increased along with the increase of the parameter in order to more intuitively observe the moving direction of the characteristic value.
And (3.2) analyzing the influence of the serial compensation level of the transmission line on the system stability and the subsynchronous oscillation mode. And fixing fan control parameters, increasing the serial compensation level from 10% to 95%, and drawing the movement track of the characteristic root.
Example 2
The embodiment provides a system for analyzing the influence of control parameters of a doubly-fed wind power plant on subsynchronous oscillation, which is shown in a structural diagram of the system for analyzing the influence of the control parameters of the doubly-fed wind power plant on the subsynchronous oscillation, wherein the system comprises a doubly-fed wind power plant system modeling unit, a characteristic value and participation factor calculation unit and a control parameter influence analysis unit; the working process of the system is as follows:
double-fed wind farm system modeling unit: inputting related parameters, establishing a mathematical model of the doubly-fed wind power plant, wherein the mathematical model comprises a fan transmission system model, an induction generator model, a rotor side converter model, a network side converter model, a direct current link, a converter transformer model and an external power grid model, and outputting the mathematical model to a characteristic value and participation factor calculation unit;
the eigenvalue and participation factor calculation unit: receiving input of a doubly-fed wind power plant system modeling unit, and solving a system characteristic value and each state variable participation factor under different modes;
control parameter influence analysis unit: the method comprises the steps of changing the numerical value of the researched control parameter (comprising the converter control parameter and the series compensation degree), repeatedly calling the characteristic value and the participation factor calculation unit, and drawing the movement track of the characteristic value, so that the influence of the control parameter on the interaction of the subsynchronous oscillation is analyzed and obtained.
The modeling unit of the doubly-fed wind power plant system comprises the following specific contents:
(1.1) establishing a fan transmission system model:
wherein:
represents ω r Differentiation over time, the dots above the variables below also represent differentiation over time of the variables, H being the equivalent inertia of the turbine, shaft and generator, ω r For angular velocity of rotor, T m Is the mechanical torque of the steam turbine, T e Is the electromagnetic torque of the generator.
(1.2) modeling an induction generator:
wherein: subscripts "s" and "r" denote variables on the stator side and rotor side, respectively; "d" and "q" represent variables of d-axis and q-axis, respectively; omega 0 For reference angular velocity omega s For synchronizing the angular velocity, the values are given in per unit. R, I, V and ψ represent winding resistance, current, voltage and magnetic flux. The stator and rotor currents may be expressed as a magnetic flux as shown in equation (6).
Wherein: delta=l m 2 -L ss -L rr ，L m 、L ss And L rr The coil is respectively an excitation inductance, a stator winding inductance and a rotor winding inductance. The transformer inductance between the stator and the transmission line is already contained in the stator inductance. Based on the formulas (2) to (6), the electromagnetic torque can be expressed as shown in the formula (7).
T e ＝ψ ds I qs -ψ qs I ds (7)
(1.3) establishing a rotor-side converter model:
the switching frequency of the power electronics is not considered in the modeling of the rotor-side converter, since it is sufficiently high compared to the target frequency under investigation to be filtered out. The d-axis direction of the coordinate system is selected as the stator magnetic flux
Direction, thus there is->
Psi-shaped material qfs =0. The subscripts "df" and "qf" denote the d-axis component and q-axis component in the stator flux reference frame.
The stator reactive power is shown in formula (8). Since the stator voltage is perpendicular to the stator flux, the stator voltage in the stator flux reference direction takes a value of 0, and equation (8) can be written as equation (9).
Equation (10) is obtained from equation (6), and equation (11) is obtained by substituting equation (9). As can be seen from equation (11), the reactive power can be determined by I dfr And controlling. The design of the control of the rotor-side converter is therefore d-axis control of the reactive power Qs and q-axis control of the rotor rotational speed ω r 。
Q s ＝(V qfs I dfs -V dfs I qfs ) (8)
Q s ＝V qfs I dfs (9)
To obtain a rotor reference voltage at the stator flux reference frame, the dq-axis component of the rotor current is transformed into the stator flux reference frame. The related transformation equation is shown as formulas (12) - (13), wherein theta f The included angle between the d-axis of the dq coordinate system and the df-axis of the stator magnetic flux coordinate system is shown in the formula (14).
(1.4) establishing a network-side inverter model
The network side converter model is established by taking the voltage of the doubly-fed fan terminal as a reference system. The d-axis direction is consistent with the voltage direction of the wind power outlet end, and d-axis and q-axis components under the reference system are respectively indicated by subscripts 'dt' and 'qt'. The d-axis component is used for controlling direct-current link voltage, and the q-axis component is used for controlling reactive power sent by the converter.
By converting the voltages in the above coordinate system to RI coordinate system by the conversion shown in formulas (12) and (13), U can be obtained gcRe And U gcIm θ in the transformation f Replaced by theta t I.e. the angle between the dt axis and the R axis.
(1.5) establishing a dynamic characteristic model of a direct current link and a converter transformer:
the power P flowing into the rotor-side converter irrespective of the loss of the converter r Equal to the power flowing out of the grid-side converter. Based on this, the dynamic characteristics of the dc link between the two converters can be represented by a differential equation as shown in equation (16), where C is the dc link capacitance.
The dynamic characteristics of the converter transformer can be represented by formulas (17) - (18), wherein R g X is the resistance of the winding of the transformer g For winding leakage reactance, I gcRe And I gcIm Is the real and imaginary parts of the network side converter current phasors.
(1.6) building an external power grid model:
using kirchhoff's law, the voltage at the doubly fed fan port can be expressed by equation (19). Wherein: u is the voltage of the outlet end of the doubly-fed fan, B sh For the outlet end to receive, I dtot And I qtot Is the total output current of the doubly-fed fan
(i.e. stator current->
And grid-side inverter current->
And) d-axis and q-axis components, subscripts "Re" and "Im" denote real and imaginary components of the variable under the R-I coordinate system.
The doubly-fed fan is connected with a power grid through a power transmission line, and the resistance of the power transmission line is R L Reactance is X L The capacitance reactance of the series compensation capacitor is X C . The dynamic characteristics of the transmission line and the external grid can be expressed by differential equations (20) - (23).
Wherein: i is the current flowing through the transmission line, U C To series complement the voltage of two ends of the capacitor, U B Is infinite system terminal voltage; the subscripts "Re" and "Im" denote the real and imaginary components of the variable in the R-I coordinate system.
The specific contents of the characteristic value and the participation factor calculation unit are as follows:
(2.1) calculating a characteristic value:
the dynamic characteristics of the doubly-fed wind turbine can be represented by a formula (24), linearization operation is performed near a balance point, the dynamic characteristics can be converted into a formula (25), and the characteristic value of the system can be obtained by a formula (26).
det|A-λI|＝0 (26)
The system eigenvalues typically contain both real and imaginary parts, each eigenvalue corresponding to one oscillation mode. The ith oscillation mode is available lambda i ＝σ i ±jω i Representation, sigma i Represents damping omega i Representing the frequency. Damping of the i-th oscillation mode is represented by formula (27).
(2.2) calculating a participation factor:
for each modality, the degree of participation of each state variable may be measured by a participation factor. The participation factor is dimensionless and is used for measuring the contribution degree of a certain state variable in a certain specific oscillation mode. The contribution of the kth state variable in the ith mode can be determined by equation (28).
Wherein:
is the ith row and the kth column of the left eigenvector of the eigenvector matrix A, and corresponds to the ith eigenvalue; />
Is the kth row and ith column of the right eigenvector of the eigenvector a, corresponding to the ith eigenvalue.
The control parameter influence analysis unit comprises the following specific contents:
and (3.1) calculating participation factors of different state variables, and classifying control parameters according to the sizes of the participation factors, wherein the control parameters comprise parameters which have no obvious influence on the subsynchronous oscillation mode, parameters which have an inhibiting effect on the subsynchronous oscillation mode damping ratio, parameters which have an accelerating effect on the subsynchronous oscillation mode damping ratio but have an inhibiting effect on the supersynchronous oscillation mode and parameters which have obvious influence on the subsynchronous oscillation mode.
(3.2) analyzing the influence of the control parameters of the converter on the stability and the subsynchronous mode of the system: the compensation degree of the series compensation device of the fixed system is a certain value, PI parameters of the rotor-side converter and the network-side converter controller are changed, the characteristic value and the participation factor calculating unit are called, the corresponding characteristic value is obtained, the parameters are repeatedly modified, the characteristic value and the participation factor calculating unit are called, a track of the characteristic value changing along with the parameters is drawn, and in order to observe the moving direction of the characteristic value more intuitively, the size of the characteristic value marking symbol is increased along with the increase of the parameters.
And (3.3) analyzing the influence of the serial compensation level of the transmission line on the system stability and the subsynchronous oscillation mode. Fixing fan control parameters, gradually increasing the serial compensation level from 10% to 95%, repeatedly modifying the parameters, calling the characteristic values and the participation factor calculation unit, and drawing the movement track of the characteristic root.
The foregoing description is only of the preferred embodiments of the present invention and is not intended to limit the scope of the invention, and all equivalent structures or equivalent processes using the descriptions and drawings of the present invention or directly or indirectly applied to other related technical fields are included in the scope of the invention.
Claims (5)
1. A method for analyzing the effect of control parameters of a doubly-fed wind farm on subsynchronous oscillations, the method comprising the steps of:
(1) Establishing a mathematical model of a doubly-fed wind power plant, wherein the mathematical model comprises a fan transmission system model, an induction generator model, a rotor side converter model, a grid side converter model, a direct current link and converter transformer model and an external power grid model;
(2) Linearizing the established mathematical model, and calculating characteristic values and participation factors;
(3) And drawing a movement track of the characteristic value by changing the numerical value of the researched control parameter, so that the influence of the control parameter on the interaction of the subsynchronous oscillation is analyzed and obtained, wherein the control parameter comprises a converter control parameter and a series compensation degree.
2. The method for analyzing the influence of the control parameters of the doubly-fed wind farm on the subsynchronous oscillation according to claim 1, wherein the step (1) specifically comprises:
(1.1) establishing a fan transmission system model:
wherein:
represents ω r Differentiation over time, the dots above the variable represent the differentiation over time of the variable, H is the equivalent inertia of the turbine, shaft and generator, ω r For angular velocity of rotor, T m Is the mechanical torque of the steam turbine, T e Is the electromagnetic torque of the generator;
(1.2) modeling an induction generator:
wherein: subscripts "s" and "r" denote variables on the stator side and rotor side, respectively; "d" and "q" represent variables of d-axis and q-axis, respectively; omega 0 For reference angular velocity omega s For synchronizing angular velocity, the values are given in per unit value; r, I, V and ψ represent winding resistance, current, voltage and magnetic flux, respectively; the stator and rotor currents can be expressed with the magnetic flux as follows:
wherein: delta=l m 2 -L ss -L rr Wherein L is m 、L ss And L rr The excitation inductance, the stator winding inductance and the rotor winding inductance are respectively; the transformer inductance between the stator and the transmission line is already contained in the stator inductance; based on the formulas (2) - (6), the electromagnetic torque expression (7) is as follows:
T e ＝ψ ds I qs -ψ qs I ds (7)
(1.3) establishing a rotor-side converter model:
since the switching frequency of the power electronics is sufficiently high compared to the target frequency under investigation, it can be filtered out, becauseThe switch of the power electronic device is not considered in the modeling process of the rotor-side converter; the d-axis direction of the coordinate system is selected as the stator magnetic flux
Direction, thus there is->
Psi-shaped material qfs =0; the subscripts "df" and "qf" denote the d-axis component and q-axis component of the stator flux reference frame;
since the stator voltage is perpendicular to the stator flux, the stator voltage value in the stator flux reference direction is 0, and the stator reactive power expression (8) can be written as expression (9);
formula (10) is obtained from formula (6), and formula (11) is obtained by substituting formula (9); as can be seen from equation (11), the reactive power can be determined by I dfr Performing control; the design of the control of the rotor-side converter is therefore d-axis control of the reactive power Qs and q-axis control of the rotor rotational speed ω r ；
Q s ＝(V qfs I dfs -V dfs I qfs ) (8)
Q s ＝V qfs I dfs (9)
To obtain a rotor reference voltage at a stator flux reference frame, transforming a dq-axis component of the rotor current into the stator flux reference frame; the related transformation equation is shown as formulas (12) - (13), wherein theta f The included angle between the d axis of the dq coordinate system and the df axis of the stator magnetic flux coordinate system is shown as formula (14);
(1.4) establishing a network-side inverter model
The network side converter model is established by taking doubly-fed fan terminal voltage as a reference system; the d-axis direction is consistent with the voltage direction of the wind power outlet end, and d-axis components and q-axis components under the reference system are respectively denoted by subscripts 'dt' and 'qt'; the d-axis component is used for controlling the voltage of the direct current link, and the q-axis component is used for controlling reactive power sent by the converter;
by converting the voltages in the above coordinate system to RI coordinate system by the conversion shown in formulas (12) and (13), U can be obtained gcRe And U gcIm θ in the transformation f Replaced by theta t I.e. the angle between the dt axis and the R axis;
(1.5) establishing a dynamic characteristic model of a direct current link and a converter transformer:
the power P flowing into the rotor-side converter irrespective of the loss of the converter r The power of the grid-side converter is equal to the power of the grid-side converter; based on the dynamic characteristics of the direct current link between the two converters are shown as a formula (16), wherein C is the direct current link capacitance;
dynamic characteristics of the converter transformer are shown as formulas (17) - (18), wherein R g X is the resistance of the winding of the transformer g For winding leakage reactance, I gcRe And I gcIm Is the real part and the imaginary part of the current phasor of the grid-side converter;
(1.6) building an external power grid model:
using kirchhoff's law, the voltage at the doubly fed fan port can be represented by formula (19); wherein: u is the voltage of the outlet end of the doubly-fed fan, B sh For the outlet end to receive, I dtot And I qtot Is the total output current of the doubly-fed fan
The subscripts "Re" and "Im" denote the real and imaginary components of the variable in the R-I coordinate system;
the doubly-fed fan is connected with a power grid through a power transmission line, and the resistance of the power transmission line is R L Reactance is X L The capacitance reactance of the series compensation capacitor is X C The method comprises the steps of carrying out a first treatment on the surface of the The dynamic characteristics of the transmission line and the external power grid can be represented by differential equations (20) - (23);
wherein: i is the current flowing through the transmission line, U C To series complement the voltage of two ends of the capacitor, U B Is infinite system terminal voltage; the subscripts "Re" and "Im" denote the real and imaginary components of the variable in the R-I coordinate system.
3. The method for analyzing the influence of the control parameters of the doubly-fed wind farm on the subsynchronous oscillation according to claim 1, wherein the step (2) specifically comprises:
(2.1) calculating a characteristic value:
the dynamic characteristics of the doubly-fed wind turbine can be represented by a formula (24), linearization operation is carried out near a balance point, the doubly-fed wind turbine can be converted into a formula (25), and the characteristic value of the system can be obtained by a formula (26);
det|A-λI|＝0 (26)
the system characteristic value generally comprises a real part and an imaginary part at the same time, and each characteristic value corresponds to one oscillation mode; the ith oscillation mode is available lambda i ＝σ i ±jω i Representation, sigma i Represents damping omega i Representing the frequency; damping of the ith oscillation mode such as formula (27);
(2.2) calculating a participation factor:
for each modality, the degree of participation of each state variable may be measured by a participation factor; the participation factor is dimensionless and is used for measuring the contribution degree of a certain state variable in a certain specific oscillation mode; the contribution of the kth state variable in the ith mode can be determined by equation (28);
wherein:
is the ith row and the kth column of the left eigenvector of the eigenvector matrix A, and corresponds to the ith eigenvalue; />
Is the kth row and ith column of the right eigenvector of the eigenvector a, corresponding to the ith eigenvalue.
4. The method for analyzing the influence of the control parameters of the doubly-fed wind farm on the subsynchronous oscillation according to claim 1, wherein the step (3) specifically comprises:
(3.1) calculating participation factors of different state variables, and classifying control parameters according to the sizes of the participation factors, wherein the control parameters comprise parameters which have no obvious influence on the subsynchronous oscillation mode, parameters which have an inhibiting effect on the subsynchronous oscillation mode damping ratio, parameters which have an accelerating effect on the subsynchronous oscillation mode damping ratio but have an inhibiting effect on the supersynchronous oscillation mode and parameters which have obvious influence on the subsynchronous oscillation mode;
(3.2) analyzing the influence of the control parameters of the converter on the stability and the subsynchronous mode of the system: the compensation degree of the series compensation device of the fixed system is a certain value, and PI parameters of the rotor-side converter and the network-side converter controller are changed; drawing a track of the characteristic value along with the change of the parameter, and increasing the size of a characteristic value mark symbol along with the increase of the parameter in order to more intuitively observe the moving direction of the characteristic value;
(3.3) analyzing the influence of the serial compensation level of the transmission line on the system stability and the subsynchronous oscillation mode; and fixing fan control parameters, increasing the serial compensation level from 10% to 95%, and drawing the movement track of the characteristic root.
5. A system for analyzing the influence of a doubly-fed wind farm control parameter on subsynchronous oscillations, comprising the method for analyzing the influence of a doubly-fed wind farm control parameter on subsynchronous oscillations according to any one of claims 1-4.
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| CN116799789A (en) * | 2023-06-13 | 2023-09-22 | 广东工业大学 | Distributed new energy interconnection micro-grid cluster oscillation control method |
| CN117200350A (en) * | 2023-09-11 | 2023-12-08 | 国网江苏省电力有限公司电力科学研究院 | Damping contribution stability evaluation method and device for multi-fan grid-connected power generation system |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN116799789A (en) * | 2023-06-13 | 2023-09-22 | 广东工业大学 | Distributed new energy interconnection micro-grid cluster oscillation control method |
| CN116799789B (en) * | 2023-06-13 | 2024-01-09 | 广东工业大学 | Distributed new energy interconnection micro-grid cluster oscillation control method |
| CN117200350A (en) * | 2023-09-11 | 2023-12-08 | 国网江苏省电力有限公司电力科学研究院 | Damping contribution stability evaluation method and device for multi-fan grid-connected power generation system |
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