CN102136036A  Doublefeed wind power station equivalent modeling method applied to analysis on small signal stability of power system  Google Patents
Doublefeed wind power station equivalent modeling method applied to analysis on small signal stability of power system Download PDFInfo
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Abstract
The invention discloses a doublefeed wind power station equivalent modeling method applied to analysis on the small signal stability of a power system. Point of interconnection frequency serves as a boundary signal, and the wind power station is equivalent to a power source controlled by the frequency of a power grid, so that a highdimensional dynamic model of the doublefeed wind power station is simplified into an algebraic constraint equation. Compared with the prior art, the invention simplifies the highdimensional dynamic model of the wind power station into the simple algebraic constraint equation so as to greatly simplify the mathematical modeling of the wind power station. Simulation researches made under a plurality of conditions prove that the equivalent simplified model is effective for the analysis on characteristic values of the power system with the wind power station in an electromechanical mode.
Description
Technical Field
The invention relates to an electrical engineering technical system, in particular to a modeling method of a gridconnected doublefed wind turbine generator wind power plant in an electric power system.
Background
In recent years, the construction of wind power plants in China keeps a highspeed development situation, the influence of the wind power plants on a power system is increasingly prominent along with the rapid increase of the installed scale of wind power plants, and the modeling of the wind power plants and the influence of the modeling of the wind power plants on the dynamic characteristics of the power system become research hotspots in the field. As the number of the units of the large wind power plant can reach tens to hundreds, when the power system is stably analyzed, if all the units use detailed models, the calculation cost is hard to bear, and therefore, the equivalent model of the wind power plant is very necessary to be established. Document [1] proposes a continuous power flow calculation model containing a wind turbine generator, which can be used for static voltage stability research; document [2] establishing a wind power plant reduced order model by using a singular perturbation theory; document [35] replaces a wind farm with a combination of a wind turbine and a doublyfed machine for studying wind farm dynamic behavior and the influence on grid damping characteristics; document [6] after the wind power plant units are grouped, the equivalence is a multimachine system, and the simulation precision is improved to a certain extent; the equivalent model given in the document [7] considers the wake effect of the wind power plant and the influence of the position of the wind turbine on the injection wind speed.
In the study of the stability of the power system, the conventional equivalent model has the following defects: firstly, the power response of the wind power plant caused by the wind speed change is emphasized on one hand, the time scale concerned by the instability problem of the first swing is not more than 2 seconds in the transient stability analysis, and the significance of discussing the wind speed waveform and the wind speed change is not great in such a short time period. Furthermore, for small disturbance stability problems, neither equilibrium point stability nor structural stability is directly linked to the wind speed waveform. Secondly, the degree of curve coincidence is pursued on one side. When the validity of the equivalent model is checked, the curve fit degree is not necessarily a scientific evaluation index. For transient stability, the power limit or critical ablation time should be taken as an evaluation index; for small perturbation stability, the dominant mode frequency and damping are checked again. Therefore, on the wind power plant equivalent modeling problem, an equivalent strategy is provided according to the problem property and the effectiveness of an equivalent model is scientifically evaluated according to the specific problem requirement.
[1] Wang Chengshan, Sun Wei, Wang Xinggan. Calculation of maximum transmission capacity of Power system including large wind farm [ J ] Power System Automation (Automation of Electric Power Systems), 2007, 31(2) 1721, 31;
[2] M.G. Castro, J.M. Ferreira. A wind park reducedorder model using singular perturbations theory[J]. IEEE transactions on Energy Conversion, 1996, 11(4):735741；
[3] L. M. Fernandez, F. Juradob, J. R. Saenz. Aggregated dynamic model for wind farms with doubly fed induction generator wind turbines [J]. Renewable Energy, 2008, 33(1):129140；
[4] G. G. Miguel, M. P. Comech, J. Sallan, A. Llombart. Modelling wind farms for grid disturbance studies [J]. Renewable Energy, 2008, 33(1):21092121；
[5] royal, Shilibao, Yao Libao, et al, (WANG Chen, SHI Libao, YAO Lianggzhong, et al), Small disturbance stability analysis of LargeScale doublyfed wind farms (Small signal stability analysis of the Largescale with farm DFIGs) [ J ], Chinese Motor engineering reports (Proceedings of the CSEE), 2010, 30(4): 6370;
[6] Akhmatov V, Knudsen H. An aggregated model of a gridconnected, largescale offshore wind farm for power stability investigations—importance of windmill mechanical system. Electric Power Energy Syst. 2002, 24: 709–717；
[7] L. M. Fernandez, C. A. Garcia, F. Jurado, J. R. Saenz. Aggregation of Doubly Fed Induction Generators Wind Turbines Under Different Incoming Wind Speeds[C]// IEEE Power Tech conference, St. Petersburg,Russia:2005。
disclosure of Invention
Based on the prior art, the invention provides a doublefed wind power plant equivalent modeling method suitable for small disturbance stability analysis of a power system, and provides a method for simply realizing equivalent modeling of a wind power plant by taking gridconnected point frequency as a boundary signal and enabling the wind power plant to be equivalent to a power source controlled by grid frequency.
The invention provides a doublyfed wind power plant equivalent modeling method suitable for small disturbance stability analysis of a power system, which is characterized in that gridconnected point frequency is used as a boundary signal, a wind power plant is equivalent to a power source controlled by grid frequency, and a doublyfed wind power plant is simplified into an algebraic constraint equation by a highdimensional dynamic model, and the method comprises the following steps:
The doublefed wind power plant is provided with a doublefed wind turbine generator, wherein the grid frequency of a gridconnected point B isThe amplitude of the voltage is；
Is provided withSmall value sinusoidal oscillations occur, i.e.，Is the amplitude of the wave, and,is the oscillation frequency. Get，A first wave curve of active output of the unit;
the oscillation amplitude of the first waveform curve is 60kW, and the oscillation amplitude of the second waveform curve is 2 kW;
the first step is as follows: according to the analysis conclusion of the power response correlation processing of the doublyfed motor under the sine excitation, input signals are ignoredThe effect of (1), i.e. the transfer function matrix at the wind farm dynamic subsystemIn, ignoreAndwill beSimplified to：
Wherein,representing the input of the gridconnected bus frequency, and taking the active power of a fan as the transfer function of the output;representing a transfer function with input of gridconnected bus frequency and fan reactive power as output;representing a transfer function taking gridconnected bus voltage as input and taking fan active power as output;representing a transfer function with gridconnected bus voltage as input and fan reactive power as output;
transfer function matrix for conventional grid dynamic subsystems，Is its output signal and, accordingly,simplified toThe method comprises the following steps:
the second step is that: consider thatSteady state characteristic under sine excitation, and output quantity of wind turbine generator under sine steady state conditionAndare all sine phasorsAnd。is only a complex gain matrixWherein，；
simplified grid subsystem () Is a twoinput singleoutput system; doublyfed machine set () Is a singleinput twooutput system;
and 3, simplified interface processing of the doublefed wind power plant and the power grid comprises the following steps:
setting a wind power plant to install n doublyfed wind power sets, wherein the upstream of the n doublyfed wind power sets is a common bus B, and when smallvalue oscillation occurs in a conventional power grid, the input variable of any one doublyfed wind power set is phasor(ii) a The total power output of the wind power plant is combined with the parallel relation of n unitsAndthe phasor superposition of the power output of each doublyfed unit. The interaction expression of the whole n wind power plants and the power grid is as follows:
based on the interaction between the wind power plant and the power grid, the simplified analysis of the electromechanical mode of the power system comprising the doublyfed wind power plant is realized, and the steps are as follows:
the first step is as follows: obtaining the wind power plant output at the balance point through load flow calculationAndto power ofAndthe constant power source is connected to a bus B;
secondly, calculating after linearization according to the mathematical model of the single doublefed wind turbine generatorAnd find a complex gain matrix；
Third step according to formula
Equating dynamic behavior of wind farm as being composed ofThe controlled power source is controlled, and the controlled power source and the constant power source are combined into an equivalent model;
and fourthly, embedding the equivalent model into a conventional power grid, obtaining a power angle swing curve of the synchronous motor through small disturbance time domain simulation, and obtaining a dominant electromechanical characteristic value of the system through Prony fitting. According to the mathematical model of the single doublefed wind turbine generator, calculation is carried out after linearizationAnd find a complex gain matrixThe same for the units of the same type in the wind power plantAnd (3) calculating only one doublyfed wind turbine generator.
Compared with the prior art, the wind power plant is simplified into a simple algebraic constraint equation from a highdimensional dynamic model, the mathematical modeling method for the wind power plant is greatly simplified, and simulation research under various conditions proves that the equivalent simplified model provided by the invention is effective for analyzing the characteristic value of the electromechanical mode of the power system containing the wind power plant.
Drawings
FIG. 1 is a schematic diagram of a gridconnected wind farm;
FIG. 2 is a schematic illustration of the interaction of a wind farm with a conventional power grid;
fig. 3 is a structural diagram of a gridconnected doublefed wind turbine generator system, and fig. 4 is an active response schematic diagram under the excitation of a sine signal;
FIG. 5 is a simplified process diagram of a dynamic model of a single unit;
FIG. 6 is a simplified schematic diagram of a wind farm dynamic model;
FIG. 7 is a schematic diagram of an exemplary system for verifying validity of an equivalent model of a doublyfed wind farm;
FIG. 8 is a graph comparing power angle response based on an equivalent model and a detailed model.
Detailed Description
Under the meaning of small disturbance, the interaction of a conventional power grid and a wind power plant is represented as follows: the influence of sineshaped microvariation of the voltage amplitude of the gridconnected point on the wind power plant is small, and the influence of sineshaped microvariation of the voltage frequency on the wind power plant is large. Based on the fact, the invention provides that the gridconnected point frequency is used as a boundary signal, the wind power plant is equivalent to a power source controlled by the grid frequency, the wind power plant is simplified into a simple algebraic constraint equation from a highdimensional dynamic model through the processing, and the mathematical modeling of the wind power plant is greatly simplified. And simulation researches under various conditions prove that the equivalent simplified model provided by the invention is effective for analyzing the characteristic value of the electromechanical mode of the power system containing the wind power plant.
As shown in figure 1, the doublyfed wind farm is on the busIs connected to the grid and has boundary signals of、、And。
FIG. 2 shows the interaction of a wind farm with a conventional grid during which changes in the amplitude and frequency of the gridtie point voltage will cause changes in the active and reactive power of the wind farm for the wind farm, soAndis an input signal for the wind farm,andis its output signal; just the opposite for the grid, a change in the injected power will cause the grid to runThe variation in bus voltage and frequency, it can be seen that for the grid,andit becomes the input signal that is the signal to be input,andis the output signal.
Between the grid and the wind farm are two dynamic subsystems of a feedback connection.
In FIG. 2Expressing the conventional grid dynamics subsystem of FIG. 1;and expressing a wind power plant dynamic subsystem.At the same time output theThe input of (a) is performed,is simultaneously outputtedIs input. Therefore, the interaction between the conventional power grid and the wind farm is represented by feedback coupling between subsystems. According to the dimension of the input and output signals,andare 2 x 2 dimensional transfer function matrices. Namely:
the elements of the transfer function matrix expressing the dynamic characteristics of a singleinput singleoutput system, e.g.The method comprises the steps of representing a transfer function which takes the injection active power of a gridconnected bus as input and the bus frequency as output, and reflecting the action and the result of wind power injection on a power grid;the method represents a transfer function which takes the frequency of the gridconnected bus as input and wind power active power as output, and reflects the response characteristic of the frequency change of the gridconnected bus to the power of the wind power plant. The physical meaning of other transfer functions may be similarly inferred.
According to the characteristics of conventional power grid and wind power plant, transfer function arrayAndare transfer functions of extremely high order. In addition, the interaction relation is also suitable for the interaction between a single wind turbine generator and a power grid, and the interaction method and the interaction device are also suitable for the interaction environment between the single wind turbine generator and the power grid.
The simplified expression of interaction between the doublyfed wind power plant and the power grid comprises the following processing:
1. power response of doublyfed machines under sinusoidal excitation
Low frequency oscillations may be caused when weakly (or negatively) damped electromechanical oscillation modes are present in the synchronous grid. In the lowfrequency oscillation process, the voltage amplitude and the voltage frequency of the related bus are both expressed as sinusoidal oscillation with the same frequency. As can be seen from fig. 1, the lowfrequency oscillation behavior of the conventional grid is equivalent to applying a sinusoidal excitation signal to the wind farm; the reaction effect of the wind farm on the conventional grid depends on the response characteristics of the wind farm to the sinusoidal excitation. Therefore, the power response of the doublyfed motor under the sine excitation is considered, and the 'response equivalence' is taken as the theoretical basis of the equivalence of the wind power plant. In addition, the excitation of the wind farm has both voltage and frequency signals, and the differences in their responses must be analyzed.
It is assumed that only one doublyfed wind turbine is present in the wind farm, as shown in fig. 3. Grid frequency of gridconnected point B isThe amplitude of the voltage is. When the synchronous power grid is in steadystate operation,andare all constant. Now, the following sine excitation small disturbance simulation test is carried out:
is provided withSmall value sinusoidal oscillations occur, i.e.，Is the amplitude of the wave, and,is the oscillation frequency. Get，The waveform of the active output of the unit is shown as curve 1 in fig. 4. Reissue to order，Andstill taking the original value, the waveform of the active output of the unit is shown as curve 2 in fig. 4. The curve data shows that the oscillation amplitude of curve 1 is 60kW and that of curve 2 is only 2 kW.
It can be seen that under the excitation of the sinusoidal signal, the response of the doublyfed machine to frequency is much greater than its response to voltage, i.e. the fact that: in frequency bands of interest, e.g.Is provided withIs far greater thanIt can also be verified that:is far greater than。
This section will be rightTwostep simplification is made. According to the analysis conclusion of the power response correlation processing of the doublyfed motor under the sine excitation, the input signal can be ignoredIn a matrix of transfer functionsIn, ignoreAnd. Then willSimplified toThe method comprises the following steps:
for the，Is its output signalAnd the process of, accordingly,simplified toThe method comprises the following steps:
thus, fig. 2 is simplified to fig. 5 (a), which is a first step simplification.
The second step simplifies the key consideration: how the access of the wind farm affects the low frequency oscillation mode of the synchronous motor. Only need to considerThe steadystate characteristic under the sine excitation can meet the requirement of the analysis of the electromechanical oscillation mode. Under the condition of sine steady state, the output quantity of the wind turbine generatorAndare all sine phasorsAnd. At this time, the process of the present invention,is only a complex gain matrixWherein，. Then, fig. 5 (a) is further simplified to fig. 5 (b). Simplified grid subsystem () Is a twoinput singleoutput system; doublyfed machine set () Is a singleinput twooutput system.
3. Simplified interface calculation of doublefed wind power plant and power grid
If n doublyfed wind turbines are installed in the wind farm in fig. 1, since the upstream of the n turbines is the common bus B, when smallvalue oscillation occurs in the conventional power grid, the input variable of any turbine is phasor(ii) a Simultaneously, the parallel relation of n sets and the total power output of the wind power plant are consideredAndthe phasor superposition of the power output of each doublyfed unit. Thus, the interaction of the entire nmachine wind farm with the grid can be expressed with fig. 6 (a). Thus, there is the following formula:
based on fig. 6 (a), simplified analysis of the electromechanical mode of the power system with the doublyfed wind farm can be achieved, with the following steps: firstly, obtaining the output of the wind power plant at a balance point through load flow calculationAndto power ofAndthe constant power source is connected to a bus B; secondly, calculating after linearization according to the mathematical model of the single doublefed wind turbine generatorAnd find a complex gain matrix(having the same for units of the same type in a wind farm)Array, one calculation is needed). According to the formula (5), the dynamic behavior of the wind power plant is equivalent to the dynamic behavior of the wind power plantControlled power source, controlled power source and constant power source are combined into an equivalent model, as shown in fig. 6 (b). Embedding the equivalent model into a conventional power grid, obtaining a power angle swing curve of the synchronous motor through small disturbance time domain simulation, and obtaining a dominant electromechanical characteristic value of the system through Prony fitting.
The following is an example analysis of the above modeling method of the present invention:
in order to verify the validity of the equivalent model of the doublyfed wind farm proposed herein, the exemplary system shown in fig. 7 was constructed using Matlab/Simulink. SG1 and SG2 are conventional synchronous generators, WG is a wind farm, which contains 6 doublefed units of two models.
Example analysis procedure: firstly, forming an equivalent model shown in fig. 6 (B) by using the method described in section 3, sequentially connecting the equivalent model to buses B5, B6 and B7, and setting voltage drop disturbance at a position B3 to obtain a power angle swing curve of the synchronous generator; secondly, a detailed model of the wind power plant is used (electromagnetic and electromechanical transient states of each unit are simulated in detail, and no aggregation, equivalence or simplification is performed), and a simulation test completely identical to that of the first step is performed. FIGS. 8 (a), (b) and (c) are based on the simulation results of the above two models, and the curves in the graphs are the power angle rocking curves of SG1 (only the small amplitude oscillation curves following the perturbation are intercepted because only the small perturbation analysis is concerned; SG2 is in harmony with SG1, so the power angle curve of SG2 is not given). From the variation trend of the power angle curve, the equivalent model and the original detailed model have high consistency. And then all curves Prony in the graph are subjected to fitting analysis to obtain characteristic values of the dominant electromechanical mode under each condition, and the characteristic values are summarized
In table 1.
TABLE 1 dominant eigenvalues based on the equivalence model and the detailed model
Wind farm location  Equivalent model  Detailed model 
B6  0.9968±j12.777  1.0128±j12.767 
B5  1.0074±j12.689  1.0431±j12.656 
B7  0.9985±j12.660  1.0618±j12.620 
As can be seen from table 1, the results of the electromechanical mode analysis based on the equivalent model closely approximate the results of the analysis based on the detailed model. The errors of the imaginary parts of the characteristic values caused by equivalence of the wind power plant are all less than 0.5 percent; the real part errors caused by wind farms at B6, B5 and B7 were 1.78%, 3.45% and 5.96%, respectively. It can be seen that the equivalent model presented herein is not only highly compact but also has ideal accuracy.
Claims (2)
1. A doublyfed wind power plant equivalent modeling method suitable for small disturbance stability analysis of a power system is characterized in that gridconnected point frequency is used as a boundary signal, and a wind power plant is equivalent to a power source controlled by grid frequency, so that a doublyfed wind power plant is simplified into an algebraic constraint equation from a highdimensional dynamic model, and the method comprises the following steps:
step (1), establishing a small disturbance power response model of the doublyfed motor under sinusoidal excitation
Only one doublefed wind turbine generator in a doublefed wind power plant is arranged, wherein the grid frequency of a gridconnected point B is The amplitude of the voltage is；
Is provided withSmall value sinusoidal oscillations occur, i.e.，Is the amplitude of the wave, and,is the oscillation frequency. Get，A first wave curve of active output of the unit;
the oscillation amplitude of the first waveform curve is 60kW, and the oscillation amplitude of the second waveform curve is 2 kW;
step (2), transfer function matrix of single machine setThe simplified treatment is carried out, and the method also comprises the following steps:
the first step is as follows: according to the analysis conclusion of the power response correlation processing of the doublyfed motor under the sine excitation, input signals are ignoredThe effect of (1), i.e. the transfer function matrix at the wind farm dynamic subsystemIn, ignoreAndwill beSimplified to：
Wherein,representing the input of the gridconnected bus frequency, and taking the active power of a fan as the transfer function of the output;representing a transfer function with input of gridconnected bus frequency and fan reactive power as output;representing a transfer function taking gridconnected bus voltage as input and taking fan active power as output;representing a transfer function with gridconnected bus voltage as input and fan reactive power as output;
transfer function matrix for conventional grid dynamic subsystems，Is its output signal and, accordingly,simplified toThe method comprises the following steps:
the second step is that: consider thatSteady state characteristic under sine excitation, and output quantity of wind turbine generator under sine steady state conditionAndare all sine phasorsAnd。is only a complex gain matrixWherein，；
simplified grid subsystem () Is a twoinput singleoutput system; doublyfed machine set () Is a singleinput twooutput system;
and (3) simplified interface processing of the doublefed wind power plant and the power grid comprises the following steps:
setting a wind power plant to install n doublyfed wind power sets, wherein the upstream of the n doublyfed wind power sets is a common bus B, and when smallvalue oscillation occurs in a conventional power grid, the input variable of any one doublyfed wind power set is phasor(ii) a The total power output of the wind power plant is combined with the parallel relation of n unitsAndthe phasor superposition of the power output of each doublyfed unit. The interaction expression of the whole n wind power plants and the power grid is as follows:
based on the interaction between the wind power plant and the power grid, the simplified analysis of the electromechanical mode of the power system comprising the doublyfed wind power plant is realized, and the steps are as follows:
the first step is as follows: obtaining the wind power plant output at the balance point through load flow calculationAndto power ofAndthe constant power source is connected to a bus B;
secondly, calculating after linearization according to the mathematical model of the single doublefed wind turbine generatorAnd find a complex gain matrix；
Third step according to formula
Dynamic behavior of wind farm, etcEffect is composed ofThe controlled power source is controlled, and the controlled power source and the constant power source are combined into an equivalent model;
and fourthly, embedding the equivalent model into a conventional power grid, obtaining a power angle swing curve of the synchronous motor through small disturbance time domain simulation, and obtaining a dominant electromechanical characteristic value of the system through Prony fitting.
2. The equivalent modeling method of the doublyfed wind farm suitable for the smalldisturbance stability analysis of the power system as claimed in claim 1, characterized in that the calculation is performed after linearization according to a mathematical model of a single doublyfed wind turbine generatorAnd find a complex gain matrixWhen the units of the same type in the wind power plant have the sameAnd (3) calculating only one doublyfed wind turbine generator.
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