CN113131467B - Wind power system transient characteristic modeling and optimizing method based on amplitude-phase motion equation - Google Patents
Wind power system transient characteristic modeling and optimizing method based on amplitude-phase motion equation Download PDFInfo
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Abstract
The invention discloses a modeling and optimizing method for transient characteristics of a wind power system based on an amplitude-phase motion equation, which comprises the steps of firstly establishing a four-machine two-area power system model, then establishing a fan typical fan amplitude-phase motion equation model of a first generator based on the amplitude-phase motion equation, using the traditional thermal generator model for the rest generators, then modeling network side components in the four-machine two-area power system by an impedance method, and finally feeding back output current and terminal voltage of current-limiting control to a phase error, so that the phase is more directly influenced by terminal voltage and current-limiting current, and the typical fan amplitude-phase motion equation model is optimized.
Description
Technical Field
The invention belongs to the technical field of electric power system safety analysis, and particularly relates to a wind power system transient characteristic modeling and optimizing method based on an amplitude-phase motion equation.
Background
The problems of global warming, air pollution, environmental pollution and the like are inevitable in the traditional thermal power generation; even if these direct negative effects on human beings and the earth are eliminated, the reserves of fuel such as coal used in conventional thermal power generation cannot be exhausted. From the perspective of green or sustainable development, research on new energy such as renewable energy needs to be accelerated, and wind power generation is a mature and high-potential one. High wind power permeability is the development trend of energy conservation, emission reduction and green energy, and the installed capacity of wind power in China is promoted year by year. When the wind turbine generator is connected to a power grid, a large number of power electronic devices are used for adjustment, and compared with a traditional generator, the power electronic devices are low in inertia, so that more harmonic waves are generated inevitably, the oscillation problem is obvious, the response time of the power electronic devices is faster than that of the traditional generator, and the problem of multi-time-scale control of the power grid is caused.
The dynamic behavior of the power system is being changed deeply by the wind power with larger and larger occupation ratio, and the dynamic behavior of the power system is bound to threaten the stability of the system, so that the research on the dynamic stability problem of the power system under different occupation ratios of the output of the wind driven generator is urgent, especially the stability research under higher occupation ratios. The study of transient stability of a power system under high wind power permeability requires a low-order, accurate and open wind turbine electromechanical transient model. The current modeling analysis methods are mainly classified into 3 types: model analysis, impedance analysis, and amplitude-phase equation of motion.
The model analysis method is also called as a state space characteristic value analysis method, firstly, a small signal method is used for carrying out linearization processing on the system, then a linear space equation set of the system is written out, the characteristic value of the system is obtained, and the Nyquist stability criterion is utilized to judge the stability of the system. The method belongs to a time domain method, the result is accurate, but the model is complex, and the simulation speed is slow. The impedance analysis method is characterized in that each device in the power grid is equivalent to an impedance (or the impedance and a power supply) according to the relation between voltage and current, and the power supply is equivalent to the impedance and an ideal power supply. The equivalent impedance model needs to be recalculated when the power grid structure changes caused by system short-circuit faults and the like; the small signal characteristics of the system can be changed due to the increase of the generated energy, and the system is nonlinear at the moment, even has electronic equipment which does not meet the voltage-current relationship, and is inconvenient for impedance analysis.
The former two models mainly rely on mathematical and structural ideas to model the wind turbine generator in an electromechanical time scale, so that the obtained electromechanical transient model can be conveniently realized and applied in numerical simulation software, but the physics and the generalization abstraction of the electromechanical scale dynamic characteristics of the double-fed wind turbine generator are lacked. And (3) modeling an amplitude-phase motion equation, namely driving the voltage vector change of the equipment by the unbalanced power of the equipment. It is understood from physics that the study object can be regarded as one or several black boxes, when the input power and the actual output power of the system are unbalanced, the voltage of the equipment in the system will change in amplitude and phase to reach a new balance.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a wind power system transient characteristic modeling and optimizing method based on a magnitude-phase motion equation.
In order to achieve the aim, the invention provides a wind power system transient characteristic modeling and optimizing method based on an amplitude-phase motion equation, which is characterized by comprising the following steps of:
(1) Establishing a model of the two-area power system;
the two-area power system comprises N generators, and the number of the generators is 1-N respectively; the method comprises the following steps of (1) regarding a two-region power system as a linear system by using a small signal method, dividing the whole system into N subsystems, wherein each subsystem only comprises one generator, the rest generators not related in each subsystem are regarded as disconnection processing, and then analyzing the voltage and current of each node under the combined action of the N subsystems by using a linear superposition theory;
(2) Establishing a typical fan amplitude-phase motion equation model of the fan for the generator with the number of 1;
establishing a typical fan amplitude-phase motion equation model of the fan in MATLAB/SIMULINK based on an amplitude-phase motion equation;
wherein P is the active power output by the fan, Q is the reactive power output by the fan, and V t To fan output voltage, θ t Is the phase position of the voltage at the output end of the fan,
respectively, active and reactive current, I, in dq phase-locked coordinate system pll Is the output current of the phase-locked loop, theta pll Is the output phase of the phase locked loop;
let the phase error theta err Comprises the following steps:
θ err ＝θ t -θ pll (2)
substituting formula (2) into formula (1) to obtain:
and (3) expanding the formula by using an Euler formula to obtain:
on the electromechanical time scale, the active power P and the reactive power Q output by the fan are approximately considered to be the active power P to be output * Reactive power Q * And (4) is expressed by a matrix form when the time is equal to each other:
(3) Using a traditional thermal power generator model for generators with the numbers of 2-N, extracting m generators from the N-1 generators and setting the generators as PQ nodes, and setting the rest generators as PV nodes;
(4) Modeling the network side components in the two-area power system by using an impedance method;
for the network side components in the two-area power system: the transmission line, the transformer, the load and the compensation capacitor are modeled by adopting an impedance method, namely, each component is respectively equivalent into an impedance model according to the relationship between the terminal voltage of the component and the current flowing through the component;
(5) Optimizing a typical fan amplitude-phase motion equation model;
(5.1) by applying a phase error θ err Adding in
And V t To obtain a new phase error
Wherein i max Is the maximum transient current, k, of the fan v In order to control the parameters of the device,
representing the output end voltage of the fan in normal operation;
(5.2) utilizing the phase error
Replacing the original phase error theta err And substituting the equation into a formula (4) to obtain an optimized typical fan amplitude-phase motion equation model.
The invention aims to realize the following steps:
the invention relates to a wind power system transient state characteristic modeling and optimizing method based on an amplitude-phase motion equation, which comprises the steps of firstly establishing a four-machine two-area power system model, then establishing a fan typical fan amplitude-phase motion equation model of a first generator based on the amplitude-phase motion equation, using the traditional thermal generator models for the other generators, then modeling network side components in the four-machine two-area power system through an impedance method, and finally feeding back output current and terminal voltage of current-limiting control to phase errors, so that the phase is more directly influenced by the terminal voltage and the current-limiting current, and the typical fan amplitude-phase motion equation model is optimized.
Meanwhile, the wind power system transient characteristic modeling and optimizing method based on the amplitude-phase motion equation also has the following beneficial effects:
(1) The invention establishes a fan electromechanical transient state optimization model by using MATLAB/SIMULIK based on an amplitude-phase motion equation, and simultaneously establishes a four-machine two-zone power system according to the additivity under a small signal model, wherein the power equipment in the power grid is established by equivalently using an impedance equivalence method as an admittance unit, so that the established power system is consistent with the expression form of a typical fan electromechanical transient state model.
(2) The invention feeds back the output current and the terminal voltage of the current-limiting control to the phase error, so that the phase is more directly influenced by the terminal voltage and the current-limiting current, the feedback loop of the fan is more perfect, and the information in the output voltage is closer to the reality.
(3) In practical situations, the wind output is not allowed to change significantly with the change of the wind speed, otherwise, the wind output is an access device with too high randomness for the power grid, and the instability of the whole power grid can be caused. When disturbance such as wind speed change occurs, the model provided by the invention is better in robustness than a typical amplitude-phase equation of motion model, is a simple, practical, robust and accurate simulation research model, and can be used for simulation research of a power system.
Drawings
FIG. 1 is a flow chart of a wind power system transient characteristic modeling and optimizing method based on an amplitude-phase motion equation;
FIG. 2 is a block diagram of a constructed amplitude-phase equation of motion model;
FIG. 3 is a block diagram of a four-machine two-zone power system design;
FIG. 4 shows a fan output P 1 When =1, a load terminal voltage current curve in a four-machine two-zone power system;
FIG. 5 is a graph of load terminal voltage current in a four-machine, two-zone power system as wind speed changes over time;
FIG. 6 is a graph showing the voltage-current variation at the load terminal when the load increases in the four-machine two-zone power system;
FIG. 7 is a curve of load end voltage current changing with wind speed in a four-machine two-zone power system before fan optimization.
Detailed Description
Specific embodiments of the present invention are described below in conjunction with the accompanying drawings so that those skilled in the art can better understand the present invention. It is to be expressly noted that in the following description, a detailed description of known functions and designs will be omitted when it may obscure the subject matter of the present invention.
Examples
FIG. 1 is a flow chart of a wind power system transient characteristic modeling and optimizing method based on an amplitude-phase motion equation.
In this embodiment, as shown in fig. 1, the method for modeling and optimizing the transient characteristics of the wind power system based on the amplitude-phase motion equation of the present invention includes the following steps:
s1, establishing a four-machine two-area power system model;
in this embodiment, a four-machine two-zone power system is taken as an example for modeling, and the four-machine two-zone power system includes four generators, which are numbered 1, 2, 3, and 4; the method comprises the following steps of (1) regarding a four-machine two-area power system as a linear system by using a small signal method, dividing the whole system into four subsystems, wherein each subsystem only comprises one generator, other generators which are not involved in each subsystem are regarded as disconnection processing, and then analyzing the voltage and current of each node under the combined action of each subsystem by using a linear superposition theory; in this embodiment, the voltage and current conditions of each node in the system when a single generator acts on the power system can be analyzed respectively, and finally, according to a linear superposition principle, the voltage and current of each node under the independent action of the four subsystems are superposed to obtain the voltage and current data of each node under the joint action of the four generators. It should be noted that when a small impedance element is involved, since it may be at the position of the denominator during the simulation, it is necessary to equate it to an admittance model, i.e. the inverse of the impedance, in order not to make the denominator too small for the case of an amplification equivalent error.
S2, establishing a typical fan amplitude-phase motion equation model of the fan for the generator with the number of 1;
establishing a typical fan amplitude-phase motion equation model of the fan in MATLAB/SIMULINK based on an amplitude-phase motion equation;
wherein P is the active power output by the fan, Q is the reactive power output by the fan, and V t For the fan output voltage, θ t Is the phase position of the voltage at the output end of the fan,
respectively, active and reactive current, I, in dq phase-locked coordinate system pll Is the output current of the phase-locked loop, theta pll Is the output phase of the phase locked loop;
let the phase error theta err Comprises the following steps:
θ err ＝θ t -θ pll (2)
substituting formula (2) into formula (1) to obtain:
and (3) expanding the formula by using an Euler formula to obtain:
on the electromechanical time scale, the active power P and the reactive power Q output by the fan are approximately considered to be the active power P to be output * And reactive power Q * And (4) is expressed by a matrix form when the time is equal to each other:
in this embodiment, the MATLAB/simple equation of motion equation optimization model established according to the above derivation is shown in fig. 2, where the left side of the block diagram is the actual output active and reactive power of the wind turbine, the right side is the terminal voltage of the wind turbine, and the middle is the control module made according to the derived equation.
And S3, using a traditional thermal generator model for the generators 2, 3 and 4, setting the generators 2 and 4 as PQ nodes, and setting the generator 3 as a PV node.
In the present embodiment, as shown in fig. 3, the four-machine two-zone power system model includes a fan model to be optimized and three conventional thermal power generators, wherein the generator G3 of the third subsystem is a PV node formed by a conventional generator set, and the generators G2 and G4 of the second and fourth subsystems are PQ nodes formed by a conventional generator set.
According to the established model, the simulation operation conditions are set as follows: the No. 1 generator gets: the fan parameter is P 1 ＝1，Q 1 =0.2, two constant impedance loads take R L1 +jX L1 ＝R L2 +jX L2 =1.02+ j1.02, namely: y is L1 ＝Y L2 =0.4902-j0.4902; the No. 2 generator gets: v t2 ＝1，P 2 ＝1，Q 2 =0.2; the No. 3 generator gets: u shape 3 =1; no. 4 generator fetch: v t4 ＝1，P 4 ＝1，Q 4 =0.2; a load terminal voltage current curve diagram in the power system is obtained through simulation operation, as shown in fig. 4, it can be seen from the diagram that a curve after 15s tends to be stable, the system reaches a stable state, and the stabilized voltage current value is in a reasonable range.
S4, modeling a network side component in the two-area power system by using an impedance method;
for the network side components in the two-area power system: the transmission line, the transformer, the load and the compensation capacitor are modeled by adopting an impedance method, namely, each component is respectively equivalent into an impedance model according to the relationship between the terminal voltage of the component and the current flowing through the component;
in this embodiment, a general transmission line is equivalent to a complex impedance model of resistance plus reactance, and a long-distance transmission line needs to be equivalent to a parallel connection form of complex impedance and line-to-ground capacitance admittance; the transformer is equivalent to three complex impedances in mixed connection by using an n-shaped equivalent model; the compensation capacitor uses a form that admittance is equivalent to G + jB; the load model uses a constant impedance model, represented by complex impedance.
S5, optimizing a typical fan amplitude-phase motion equation model;
the generator-end voltage output by a typical amplitude-phase motion equation model is closely related to voltage amplitude dynamics, but the feedback of phase dynamic changes of the generator-end voltage is not perfect enough, so that the response of the output-end voltage to the phase dynamics is different from the actual situation, therefore, the established typical amplitude-phase motion equation fan model needs to be optimized by the method, namely the previous phase error theta is err Output active current of middle-added current-limiting control link
Voltage V at output end of wind turbine t The specific operation process is as follows:
when the system voltage drops, the active component in the current will decrease due to inertia, and the reactive component will increase to raise the voltage as much as possible:
taking into account the voltage drop Δ V t The range of the strain will not exceed [0,0.4 ]]Then, there are: Δ V t ＝0.9-V t ；i max The maximum transient current capacity of the fan is 1.22pu by default; k is a radical of v For control of the parameters, the default value is 3.05.
In dq phase-locked coordinate system, according to the mathematical geometry relation of dq axes:
and the actual output power of the fan is obtained by multiplying the output voltage of the fan end by the conjugate of the current, so that the actual output active power and reactive power are calculated as follows:
order:
therefore, the temperature of the molten steel is increased,
the formula (8) is expanded by using the Euler formula and then substituted into the formula (9), and the following results are obtained:
observing the above formula, the real part on the right side of the equation is active power P, the imaginary part is reactive power Q, and the active and reactive powers are respectively expressed as two formulas:
the above two equations are expressed in the form of a matrix, that is,
at phase error theta err Output active current of middle-added current-limiting control link
Voltage V at output end of wind turbine t The specific process is as follows:
the relation that the dq-axis current expressed by the expression (7) should satisfy can be obtained, and since the reactive current command must satisfy (7), there are:
from equation (6) and the maximum voltage drop range considered, the following can be derived:
substituting equations (13) and (14) into (9) to obtain new phase error
Finally, the phase error is used
Replacing the original phase error theta err And substituting the equation into a formula (10) to obtain an optimized typical fan amplitude-phase motion equation model.
Therefore, the amplitude values of the output current and the terminal voltage of the current-limiting control are coupled into the phase change of the terminal voltage, so that the phase can more directly reflect the influence of the terminal voltage of the fan and the change of the current-limiting current in the fan. The feedback loop of the obtained fan model is more perfect, the terminal voltage output by the fan can reflect the dynamic change condition of the phase, and the information in the output voltage is closer to the reality. The fan end voltage matches the active power input to the fan better than typical fan models. Secondly, in practical situations, the wind output is not allowed to change significantly with the change of the wind speed, otherwise, the wind output is an access device with too much randomness for the power grid, and the instability of the whole power grid can be caused. When disturbance such as wind speed change occurs, the model provided by the invention is better in robustness, and the terminal voltage output by the fan cannot change rapidly along with the change of the wind speed. Therefore, as the wind power permeability increases year by year, a low-order, accurate and open fan electromechanical transient model is needed for researching the transient stability of the power system under high wind power permeability, and the fan model provided by the invention is a simple, practical, robust and accurate simulation research model and can be used for simulation research of the power system.
When the wind speed changes with time, the distribution of the wind speed in a day is not uniform under the condition of the load terminal voltage current in the four-machine two-area power system as shown in fig. 5, and the wind speed is relatively larger when the temperature change and the pressure difference are large at the same position. The invention approximately divides the change of wind speed in one day into five time intervals for simulation, and the wind speeds are 1.1 (6-9 points), 0.9 (9-13 points), 0.85 (13-17 points), 1.25 (17-19 points) and 1 (after 19 points), respectively. Simulation results in the figure show that the variation of wind speed directly causes the variation of fan output, thereby influencing the value of the voltage current at the constant impedance load end in the power grid.
Fig. 7 is a curve of voltage current at load end changing with wind speed when feedback control mentioned in the present invention is not added to a typical amplitude-phase equation of motion wind turbine model. The various operating conditions of fig. 7 are identical to those of fig. 5, with the difference between fig. 7 and 5 being that: FIG. 7 is a typical amplitude-phase equation of motion fan model, and FIG. 5 is an optimized model of the present invention. Wherein, each key parameter of the simulation is as follows: the change of the wind speed is divided into five sections, the simulation conditions of the model are consistent after the feedback idea control is added, and the simulation conditions are sequentially distributed to be 1.1, 0.9, 0.85, 1.25 and 1; the power output of the conventional generator 2 is P 2 ＝1，Q 2 =0.2, the output voltage of the pv node generator 3 is 1, and the output power of the conventional generator 4 is P 4 ＝1，Q 4 =0.2, and the two constant impedances in the power system both take the value Y L1 ＝Y L2 =0.4902-j0.4902. The simulation result shows that the voltage of the output end of the fan model changes along with the change of the wind speed; compared with the optimized model, the wind speed model is sensitive to the change of the wind speed, namely, the robustness of the wind speed model is not as strong as that of the optimized wind turbine model. In practice, the wind output is not allowed to change significantly with the change of wind speed, otherwise it is an access device with too much randomness for the power grid, which may cause instability of the whole power grid.In addition, the voltage and the current at two ends of the load in the system are high in a false mode, and the false height is well restrained in the optimized model, so that the false height is kept at about 1 of the standard.
When the active power output of the fan accounts for 4% of the total power generation of all the generators, the voltage and current of the load end change along with the increase of the load in the four-generator two-area power system. At this time, the number 1 generator takes: the fan parameter is P 1 ＝0.125，Q 1 ＝-0.2，Y L1 ＝Y L2 =0.6250-j0.6250 to 0.3846-j0.3846 taper; the No. 2 generator gets: v t2 ＝1，P 2 ＝1，Q 2 =0.2; the No. 3 generator gets: u shape 3 =1; the No. 4 generator gets: v t4 ＝1，P 4 ＝1，Q 4 =0.2; the results in fig. 6 show the terminal voltage current change conditions as follows: the current variation amplitude is larger than the voltage variation amplitude, wherein the variation amplitude of the load 2 is larger than that of the load 1, but the whole trend that the voltage current at the load terminal is reduced along with the increase of the load impedance is presented.
Although illustrative embodiments of the present invention have been described above to facilitate the understanding of the present invention by those skilled in the art, it should be understood that the present invention is not limited to the scope of the embodiments, and various changes may be made apparent to those skilled in the art as long as they are within the spirit and scope of the present invention as defined and defined by the appended claims, and all matters of the invention which utilize the inventive concepts are protected.
Claims (2)
1. A wind power system transient characteristic modeling and optimizing method based on an amplitude-phase motion equation is characterized by comprising the following steps:
(1) Establishing a model of the two-area power system;
the two-area power system comprises N generators, and the number of the generators is 1-N respectively; the method comprises the following steps of (1) regarding a two-region power system as a linear system by using a small signal method, dividing the whole system into N subsystems, wherein each subsystem only comprises one generator, the rest generators not related in each subsystem are regarded as disconnection processing, and then analyzing the voltage and current of each node under the combined action of the N subsystems by using a linear superposition theory;
(2) Establishing a typical fan amplitude-phase motion equation model of the fan for the generator with the number of 1;
establishing a typical fan amplitude-phase motion equation model of the fan in MATLAB/SIMULINK based on an amplitude-phase motion equation;
wherein P is the active power output by the fan, Q is the reactive power output by the fan, and V t For the fan output voltage, θ t Is the phase position of the voltage at the output end of the fan,
respectively, active and reactive current, I, in dq phase-locked coordinate system pll Is the output current of the phase-locked loop, theta pll Is the output phase of the phase locked loop;
let the phase error theta err Comprises the following steps:
θ err ＝θ t -θ pll (2)
substituting formula (2) into formula (1) to obtain:
and (3) expanding the formula by using an Euler formula to obtain:
on the electromechanical time scale, the active power P and the reactive power Q output by the fan are approximately considered to be the active power P to be output * Reactive power Q * And (4) is expressed by a matrix form when the time is equal to each other:
(3) Using a traditional thermal power generator model for generators with the numbers of 2-N, extracting m generators from the N-1 generators and setting the generators as PQ nodes, and setting the rest generators as PV nodes;
(4) Modeling the network side components in the two-area power system by using an impedance method;
for the network side components in the two-zone power system: the power transmission line, the transformer, the load and the compensation capacitor are modeled by adopting an impedance method, namely, each component is respectively equivalent into an impedance model according to the relationship between the terminal voltage of the component and the current flowing through the component;
(5) Optimizing a typical fan amplitude-phase motion equation model;
(5.1) passing through the phase error theta err Adding in
And V t To obtain a new phase error
Wherein i max Is the maximum transient current, k, of the fan v In order to control the parameters of the device,
representing the output end voltage of the fan in normal operation;
(5.2) utilizing the phase error
Replacing the original phase error theta err Then substituting into formula (4) to obtain the final productAnd (4) transforming the transformed typical fan amplitude-phase equation of motion model.
2. The amplitude-phase motion equation-based wind power system transient characteristic modeling and optimizing method according to claim 1, wherein the power transmission line is modeled by adopting an impedance method as follows: the transmission line is equivalent to a complex impedance model of resistance and reactance, and the remote transmission line is equivalent to a parallel connection form of complex impedance and line ground capacitance admittance; the transformer is modeled by adopting an impedance method as follows: the transformer is equivalent to three complex impedances in mixed connection by using an n-shaped equivalent model; the compensation capacitor is modeled by adopting an impedance method as follows: the compensation capacitor uses a form that admittance is equivalent to G + jB, wherein G is conductance, and B is susceptance; the load is modeled by adopting an impedance method as follows: the load uses a constant impedance model, represented by the complex impedance.
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