CN110212570A - Based on the MMSE wind power plant Equivalent Model excavated and its construction method and application - Google Patents
Based on the MMSE wind power plant Equivalent Model excavated and its construction method and application Download PDFInfo
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- H—ELECTRICITY
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Abstract
The invention discloses a kind of wind power plant Equivalent Model excavated based on MMSE and its construction method and applications, belong to wind power plant Equivalent Model research field, wherein, construction method includes: that the multiple dimensioned entropy of blower dynamic process is calculated using the dynamic process time series of blower using the dynamic process time series of the random key factor building blower of every Fans in wind power plant;Wind power plant Equivalent Model is constructed by clustering target of the multiple dimensioned entropy of blower dynamic process.The present invention is extracted its multiple dimensioned entropy using wind power plant dynamic process time series as data mining object, and constructs wind power plant Equivalent Model as clustering target.Compared to traditional wind power plant Equivalent Model, the dynamic process of model of the present invention equal energy preferably simulation wind power plant in all kinds of fault scenes of electric system greatly reduces wind power plant equivalence number.Thus solving current wind-powered electricity generation Equivalent Model, to be applicable in scene single and be difficult to the technical issues of effectively reflecting wind power plant dynamic process.
Description
Technical field
The invention belongs to wind power plant Equivalent Model research fields, are based on MMSE more particularly, to one kind
The wind power plant Equivalent Model and its structure that (multivariate multiscale entropy, multi-component multi-dimension entropy theory) excavates
Construction method and application.
Background technique
With the increase year by year of installed capacity of wind-driven power, the scale of wind power plant is also increasing, wind power plant often by tens very
It is formed to Fans up to a hundred, if establishing its detailed model, necessarily will cause dimension calamity, it is difficult to meet simulation accuracy and efficiency
Research Requirements.
Therefore, it when carrying out simulation analysis to wind power plant, needs to carry out equivalent calculation to it.The single machine of wind power plant is equivalent
Error is larger, therefore is concentrated mainly on multimachine equivalence in wind power plant equivalence research in recent years, and research contents includes: wind power plant
The optimization etc. of clustering algorithm in the building of equivalent index system, equivalence course.For equivalent index research starting compared with
Morning shows technology relative maturity;Clustering algorithm optimization, which is concentrated, to be solved the problems, such as to improve clustering precision.
Although research blower is equivalent from different angles for the above research, Equivalent Model is generally only applicable to more single
Scene, with the change of wind power plant simulation time or service condition, equivalent mode is intended to change, Equivalent Model it is suitable
It is greatly limited with property.
It can be seen that the applicable scene of wind-powered electricity generation Equivalent Model is single at present and is difficult to effectively reflect wind power plant dynamic process.
Summary of the invention
Aiming at the above defects or improvement requirements of the prior art, the present invention provides a kind of wind-powered electricity generations excavated based on MMSE
Equivalent Model and its construction method and application, thus solving current wind-powered electricity generation Equivalent Model, to be applicable in scene single and be difficult to effectively
The technical issues of reflecting wind power plant dynamic process.
To achieve the above object, according to one aspect of the present invention, a kind of wind power plant etc. excavated based on MMSE is provided
It is worth the construction method of model, includes the following steps:
(1) the dynamic process time series of the random key factor building blower of every Fans in wind power plant, benefit are utilized
The multiple dimensioned entropy of blower dynamic process is calculated with the dynamic process time series of blower;
(2) wind power plant Equivalent Model is constructed by clustering target of the multiple dimensioned entropy of blower dynamic process.
Further, random key factor includes: air-blower control mode, wind speed, wind direction and short circuit malfunction position.
Further, step (1) includes:
(11) for the random key factor of every Fans in wind power plant, according to historical data count it is random it is crucial because
The probability nature of element, is input in blower after being sampled using stochastic variable generator to random key factor, obtains blower
Dynamic process time series;
(12) processing of time series coarse is carried out to the dynamic process time series of blower, after obtaining coarse when
Between sequence, utilize time series after coarse to calculate the multiple dimensioned entropy of blower dynamic process.
Further, step (2) includes:
Using the multiple dimensioned entropy of blower dynamic process as clustering target, setting cluster numbers are K, obtain a K equivalent group of planes,
Thus the relevant parameter calculated in each equivalent group of planes constructs wind power plant Equivalent Model.
Further, relevant parameter includes the relevant parameter of equivalent blower, the equivalent parameters of transformer and line impedance
Equivalent parameters.
Further, the blower model in wind power plant and capacity are all the same, and the relevant parameter of the equivalence blower includes:
Wherein, SeqFor the equivalent parameters of the capacity of blower, m indicates the equivalent blower quantity in an equivalent group of planes, SiIt is i-th
The capacity of Fans, PeqFor the equivalent parameters of the active power of blower, PiFor the active power of the i-th Fans, QeqFor blower
The equivalent parameters of reactive power, QiFor the reactive power of the i-th Fans, xm-eqFor the equivalent parameters of field excitation branch line reactance, xmFor
Field excitation branch line reactance, xs-eqFor the equivalent parameters of stator winding reactance, xsFor stator winding reactance, xr-eqFor rotor windings reactance
Equivalent parameters, xrFor rotor windings reactance, rs-eqFor the equivalent parameters of stator winding resistance, rsFor stator winding resistance,
rr-eqFor the equivalent parameters of rotor windings resistance, rrFor rotor windings resistance, HeqFor the equivalence ginseng of shafting inertia time constant
Number, HiFor the shafting inertia time constant of the i-th Fans, KeqFor the equivalent parameters of axis rigidity coefficient, KiFor the i-th Fans
Axis rigidity coefficient, DeqFor the equivalent parameters of shafting damped coefficient, DiFor the shafting damped coefficient of the i-th Fans, 1≤i≤
m。
Further, the equivalent parameters of transformer include:
Wherein, STIndication transformer capacity, xTIndication transformer reactance, ST-eqThe equivalent parameters of indication transformer capacity,
xT-eqThe equivalent parameters of indication transformer reactance, m indicate the equivalent blower quantity in an equivalent group of planes.
Further, the equivalent parameters of line impedance include:
Wherein, ZeqFor the equivalent parameters of branch impedance, ZkFor the branch impedance of kth bar trunk line type cable, PjFor jth platform
The output power of blower, PiFor the output power of the i-th Fans, YeqFor the equivalent parameters of admittance over the ground, YiFor the i-th Fans
The admittance over the ground of middle trunk line type cable, m indicate the equivalent blower quantity in an equivalent group of planes, and 1≤i≤m, n are trunk line type blower branch
Blower number in road, 1≤k≤i, k≤j≤n.
It is another aspect of this invention to provide that providing a kind of wind power plant Equivalent Model excavated based on MMSE, the wind-powered electricity generation
Field Equivalent Model is constructed to obtain by a kind of construction method of wind power plant Equivalent Model excavated based on MMSE.
It is another aspect of this invention to provide that providing a kind of application of wind power plant Equivalent Model excavated based on MMSE, institute
Wind power plant Equivalent Model is stated applied to the dynamic process simulation under all kinds of scenes of electric system.
In general, through the invention it is contemplated above technical scheme is compared with the prior art, can obtain down and show
Beneficial effect:
(1) present invention is extracted its multi-scale entropy using wind power plant dynamic process time series as data mining object
Value, and wind power plant Equivalent Model is constructed as clustering target.Compared to traditional wind power plant Equivalent Model, mould of the present invention
The dynamic process of type equal energy preferably simulation wind power plant in all kinds of fault scenes of electric system, greatly reduces wind power plant etc.
It is worth number.Thus solve current wind-powered electricity generation Equivalent Model be applicable in scene it is single and be difficult to effectively reflect wind power plant dynamic process skill
Art problem.
(2) in terms of equivalent effect, the active output characteristics of wind power plant Equivalent Model of the invention has again with detailed model
The higher goodness of fit, especially after electric system is broken down, wind power plant Equivalent Model of the invention can be anti-well
The dynamic characteristic of blower is answered, to demonstrate the accuracy of wind power plant Equivalent Model of the present invention.
Detailed description of the invention
Fig. 1 is a kind of construction method of wind power plant Equivalent Model excavated based on MMSE provided in an embodiment of the present invention
Overall flow figure;
Fig. 2 is the extraction process of blower clustering target provided in an embodiment of the present invention;
Fig. 3 is the analogue system figure that the embodiment of the present invention 1 provides;
Fig. 4 is the multiple dimensioned entropy for the blower that the embodiment of the present invention 1 provides;
Fig. 5 is disturbed curve at PCC under the different models that the embodiment of the present invention 1 provides.
Specific embodiment
In order to make the objectives, technical solutions, and advantages of the present invention clearer, with reference to the accompanying drawings and embodiments,
The present invention will be described in further detail.It should be appreciated that specific embodiment described herein is only used to explain this hair
It is bright, it is not intended to limit the present invention.In addition, technology involved in the various embodiments of the present invention described below is special
Sign can be combined with each other as long as they do not conflict with each other.
As shown in Figure 1, a kind of construction method for the wind power plant Equivalent Model excavated based on MMSE, is included the following steps:
(1) the dynamic process time series of the random key factor building blower of every Fans in wind power plant, benefit are utilized
The multiple dimensioned entropy of blower dynamic process is calculated with the dynamic process time series of blower;
(2) wind power plant Equivalent Model is constructed by clustering target of the multiple dimensioned entropy of blower dynamic process.
The control of double-fed blower generally includes rotor-side control and net side control.Wherein the target of net side control is usually
Keep DC capacitor voltage constant and the power factor of control blower access point;And the target of rotor-side control is usually real
Existing rotation speed of fan tracks wind speed, to realize variable speed constant frequency.For the external dynamic characteristic of blower, the control mode of blower
It is broadly divided into constant voltage control and constant power factor control.Constant voltage controls the idle adjusting function that can be realized blower, in electricity
After net breaks down, the active fluctuation of blower grid entry point is bigger, and the process into stable state is slower, and fault ride-through capacity is lower;And
Unit dynamic characteristic under constant power factor control is good, can enter stable state quickly after electric network fault generation, but usually
Active recovery value is excessive.
Wind speed is the main factor for influencing the output of blower active power.In addition, in order to realize maximal wind-power tracking simultaneously
Fan operation safety is taken into account, the rotation speed of fan of double-fed blower at different wind speeds has differences with propeller pitch angle action situation, blower
Output also has more complicated mathematical relationship with wind speed, therefore the difference of wind speed increases and exports dynamic process outside blower
Complexity.
Wind power plant is usually made of more Fans, leeward to blower due to by the effect of being blocked of upwind blower, it is defeated
Upwind blower will be lower than by entering wind speed.The blower wake effect model for considering orographic factor, obtains wind speed correlation between blower
Expression formula.Due to the presence of wake effect, the active power dynamic of the dynamic characteristic of different blowers, especially blower output
Characteristic is no longer independent of one another, and there are certain correlations.
When wind vector, blower makes wind wheel blade windward side always perpendicular to coming wind direction under yaw system control,
With the variation of wind direction, the overlapping area between each blower can change, and then influence the wake effect between blower.Wind
The variation that the variation of wake effect will cause rotation speed of fan and propeller pitch angle to act between machine, while wind power plant entirety can be changed
Active power output, and then influence the dynamic process of wind power plant.
Currently, double-fed blower is commonly equipped with crow bar protection.When the grid collapses, the access of crow bar protection can be latched
Fan rotor side current transformer causes blower asynchronous operation to absorb a large amount of reactive power from power grid, and then changes low voltage crossing
The reactive power dynamic process of period double-fed blower.In order to effectively inhibit rotor fault electric current, the resistance value of crow bar protective resistance is needed
Want sufficiently large;However, resistance value, which crosses conference, causes rotor-side overvoltage, and charge to DC bus capacitor, causes direct current side bus
Overvoltage impacts the dynamic process of blower.
Electric power system fault occur rear fan port voltage mainly with short dot short circuit current and blower port and short dot
Mutual impedance it is related, and short dot short circuit current is related with short dot self-impedance.Therefore it (directly closes the position that failure occurs
Be to blower port Voltage Drop degree) variation will cause the difference of blower port dynamic electric voltage, and then influence blower crow bar
The investment situation and fan rotor side size of current of protection.The dynamic process of blower and short circuit malfunction position have compared with high point
Connection.
From above-mentioned analysis it is found that the factor for influencing wind power plant dynamic process is more.The present invention is directed to pass through data mining
Mode obtains the formulation of blower dynamic characteristic, i.e., blower dynamic can be described by obtaining from a large amount of blower dynamic process
The effective information of characteristic, and wind power plant equivalence is carried out as clustering target.In the key factor for influencing blower dynamic characteristic
In, certain factors be for Mr. Yu's Fans it is constant, such as the resistance value of crow bar protective resistance;And more factors are changeable
, such as wind speed, certain Fans dynamic process difference is caused also to be mostly derived from the variation of these random key factors.Therefore, pass through
The numerical value of random key factor is adjusted, and as the input quantity of blower, a large amount of blower dynamic process can be obtained, to connect
The necessary basis that the data mining work got off provides.In the key factor for influencing blower dynamic process, determine under wind direction
Although wake effect, crow bar protective resistance resistance value may be different in different blowers, be for separate unit blower
Fixed;And air-blower control mode, wind speed, wind direction, short circuit malfunction position be it is random and cannot exhaustion.
In conclusion random key factor includes: air-blower control mode, wind speed, wind direction and short circuit malfunction position.
As shown in Fig. 2, step (1) includes:
(11) for the random key factor of every Fans in wind power plant, according to historical data count it is random it is crucial because
The probability nature of element, is input in blower after being sampled using stochastic variable generator to random key factor, obtains blower
Dynamic process time series;
(12) processing of time series coarse is carried out to the dynamic process time series of blower, after obtaining coarse when
Between sequence, utilize time series after coarse to calculate the multiple dimensioned entropy of blower dynamic process.
Further, step (2) includes:
Using the multiple dimensioned entropy of blower dynamic process as clustering target, setting cluster numbers be K, using k-means algorithm into
The clustering of row blower obtains a K equivalent group of planes, thus the relevant parameter calculated in each equivalent group of planes constructs wind power plant
Equivalent Model.
Further, relevant parameter includes the relevant parameter of equivalent blower, the equivalent parameters of transformer and line impedance
Equivalent parameters.
Further, the blower model in wind power plant and capacity are all the same, therefore equivalent fan parameter has with blower quantity
It closes.It is described equivalence blower relevant parameter include:
Wherein, SeqFor the equivalent parameters of the capacity of blower, m indicates the equivalent blower quantity in an equivalent group of planes, SiIt is i-th
The capacity of Fans, PeqFor the equivalent parameters of the active power of blower, PiFor the active power of the i-th Fans, QeqFor blower
The equivalent parameters of reactive power, QiFor the reactive power of the i-th Fans, xm-eqFor the equivalent parameters of field excitation branch line reactance, xmFor
Field excitation branch line reactance, xs-eqFor the equivalent parameters of stator winding reactance, xsFor stator winding reactance, xr-eqFor rotor windings reactance
Equivalent parameters, xrFor rotor windings reactance, rs-eqFor the equivalent parameters of stator winding resistance, rsFor stator winding resistance,
rr-eqFor the equivalent parameters of rotor windings resistance, rrFor rotor windings resistance, HeqFor the equivalence ginseng of shafting inertia time constant
Number, HiFor the shafting inertia time constant of the i-th Fans, KeqFor the equivalent parameters of axis rigidity coefficient, KiFor the i-th Fans
Axis rigidity coefficient, DeqFor the equivalent parameters of shafting damped coefficient, DiFor the shafting damped coefficient of the i-th Fans, 1≤i≤
m。
Further, blower accesses points of common connection by step-up transformer, can be false since fan capacity is identical
If step-up transformer capacity is also identical, the equivalent parameters of transformer include:
Wherein, STIndication transformer capacity, xTIndication transformer reactance, ST-eqThe equivalent parameters of indication transformer capacity,
xT-eqThe equivalent parameters of indication transformer reactance, m indicate the equivalent blower quantity in an equivalent group of planes.
Further, equivalent to line impedance progress based on equivalent front and back voltage loss principle of invariance, line impedance etc.
Value parameter includes:
Wherein, ZeqFor the equivalent parameters of branch impedance, ZkFor the branch impedance of kth bar trunk line type cable, PjFor jth platform
The output power of blower, PiFor the output power of the i-th Fans, YeqFor the equivalent parameters of admittance over the ground, YiFor the i-th Fans
The admittance over the ground of middle trunk line type cable, m indicate the equivalent blower quantity in an equivalent group of planes, and 1≤i≤m, n are trunk line type blower branch
Blower number in road, 1≤k≤i, k≤j≤n.
Embodiment 1
The embodiment of the present invention 1 uses PSCAD simulation software, builds the IEEE14 node mould shown in Fig. 3 containing wind power plant
Type, wind power plant are made of 16 Fans, and number is followed successively by W1-W16, and separate unit fan capacity is 1.5MW, pass through generator terminal transformer
(660V/35kV) sum aggregate electric line is connected on points of common connection PCC, then is connected to by main transformer (35kV/110kV)
In electric system.Assuming that wind speed obeys the Weibull distribution of scale coefficient 10.7, form factor 3.97, air-blower control mode is taken
From Two-point distribution, the position that failure occurs in every route, which is obeyed, to be uniformly distributed.For wind direction, 0 °~360 ° are divided into
16 wind direction areas, the span in each wind direction area are 22.5 °, and wherein the wake effect calculated result of wind direction is as shown in table 1 in Fig. 3.
Table 1
The wind speed of digital representation input blower in table and the ratio of natural wind speed.The crow bar of blower W1-W8 protects resistance value
Crow bar protection resistance value for 0.14 Ω, blower W9-W16 is 0.12 Ω.System configuration used in emulation is Intel (R)
Core (TM) i7-7700CPU 3.60GHz, 16GB memory.
By air-blower control mode, wind speed, wind direction, short circuit malfunction position random combine, to shown in Fig. 3 emulate
System carries out simulation analysis.Where it is assumed that failure occurs in t=3s, trouble duration 0.15s.With the active of fan outlet
Power curve obtains the fan outlet active power curves in the case of various random combines as analysis object.It is poly- using blower
Class index extraction method calculates the multiple dimensioned entropy of W1-W16, as a result as shown in Figure 4.Entropy of the different blowers under multiple dimensioned
The difference reaction difference of blower dynamic process.Using the multiple dimensioned entropy of blower as clustering target, using k-means algorithm
Clustering is carried out, wherein cluster numbers take 4, and cluster result is as shown in table 2.
Table 2
A group of planes | Blower |
An equivalent group of planes 1 | W1, W5, W6, W10, W11, W12, W15 |
An equivalent group of planes 2 | W4, W9 |
An equivalent group of planes 3 | W3, W7, W8, W13, W16 |
An equivalent group of planes 4 | W2, W14 |
For verify wind power plant Equivalent Model precision, provided with the different service condition of wind power plant, as shown in table 3.Equally
Failure is arranged to occur in t=3s, trouble duration 0.15s, under the service condition of table 3, Equivalent Model and detailed model exist
Active power and reactive capability curve at PCC is as shown in Figure 5.
Table 3
Condition | Wind speed (m/s) | Wind direction | Abort situation |
1 | 95 | North wind | Bus9 |
2 | 10 | South wind | Among Bus4-Bus7 |
3 | 105 | Southeaster | Among Bus10-Bus11 |
4 | 11 | East wind | Among Bus4-Bus5 |
5 | 115 | Northwester | Among Bus2-Bus3 |
6 | 12 | Northeaster | Among Bus13-Bus14 |
From fig. 5, it can be seen that in terms of equivalent effect, the active output characteristics of dynamic equivalent model of the present invention and in detail
Model has the higher goodness of fit again, and especially after electric system is broken down, dynamic equivalent model of the present invention can be fine
Ground reacts the dynamic characteristic of blower, to demonstrate the accuracy of wind power plant Equivalent Model of the present invention.
As it will be easily appreciated by one skilled in the art that the foregoing is merely illustrative of the preferred embodiments of the present invention, not to
The limitation present invention, any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should all wrap
Containing within protection scope of the present invention.
Claims (10)
1. a kind of construction method for the wind power plant Equivalent Model excavated based on MMSE, which comprises the steps of:
(1) using the dynamic process time series of the random key factor building blower of every Fans in wind power plant, wind is utilized
The dynamic process time series of machine calculates the multiple dimensioned entropy of blower dynamic process;
(2) wind power plant Equivalent Model is constructed by clustering target of the multiple dimensioned entropy of blower dynamic process.
2. a kind of construction method of wind power plant Equivalent Model excavated based on MMSE as described in claim 1, which is characterized in that
The random key factor includes: air-blower control mode, wind speed, wind direction and short circuit malfunction position.
3. a kind of construction method of wind power plant Equivalent Model excavated based on MMSE as claimed in claim 1 or 2, feature are existed
In the step (1) includes:
(11) for the random key factor of every Fans in wind power plant, the general of random key factor is counted according to historical data
Rate characteristic is input in blower after being sampled using stochastic variable generator to random key factor, obtains the dynamic of blower
Process time sequence;
(12) processing of time series coarse is carried out to the dynamic process time series of blower, the time sequence after obtaining coarse
Column calculate the multiple dimensioned entropy of blower dynamic process using the time series after coarse.
4. a kind of construction method of wind power plant Equivalent Model excavated based on MMSE as claimed in claim 1 or 2, feature are existed
In the step (2) includes:
Using the multiple dimensioned entropy of blower dynamic process as clustering target, setting cluster numbers are K, obtain a K equivalent group of planes, calculate every
Thus relevant parameter in an a equivalence group of planes constructs wind power plant Equivalent Model.
5. a kind of construction method of wind power plant Equivalent Model excavated based on MMSE as claimed in claim 4, which is characterized in that
The relevant parameter includes the equivalent parameters of the relevant parameter of equivalent blower, the equivalent parameters of transformer and line impedance.
6. a kind of construction method of wind power plant Equivalent Model excavated based on MMSE as claimed in claim 5, which is characterized in that
Blower model and capacity in the wind power plant is all the same, and the relevant parameter of the equivalence blower includes:
Wherein, SeqFor the equivalent parameters of the capacity of blower, m indicates the equivalent blower quantity in an equivalent group of planes, SiFor the i-th Fans
Capacity, PeqFor the equivalent parameters of the active power of blower, PiFor the active power of the i-th Fans, QeqFor the idle function of blower
The equivalent parameters of rate, QiFor the reactive power of the i-th Fans, xm-eqFor the equivalent parameters of field excitation branch line reactance, xmFor field excitation branch line
Reactance, xs-eqFor the equivalent parameters of stator winding reactance, xsFor stator winding reactance, xr-eqFor the equivalence ginseng of rotor windings reactance
Number, xrFor rotor windings reactance, rs-eqFor the equivalent parameters of stator winding resistance, rsFor stator winding resistance, rr-eqFor rotor around
The equivalent parameters of group resistance, rrFor rotor windings resistance, HeqFor the equivalent parameters of shafting inertia time constant, HiFor the i-th typhoon
The shafting inertia time constant of machine, KeqFor the equivalent parameters of axis rigidity coefficient, KiFor the axis rigidity coefficient of the i-th Fans,
DeqFor the equivalent parameters of shafting damped coefficient, DiFor the shafting damped coefficient of the i-th Fans, 1≤i≤m.
7. a kind of construction method of wind power plant Equivalent Model excavated based on MMSE as claimed in claim 5, which is characterized in that
The equivalent parameters of the transformer include:
Wherein, STIndication transformer capacity, xTIndication transformer reactance, ST-eqThe equivalent parameters of indication transformer capacity, xT-eqTable
Show that the equivalent parameters of transformer reactance, m indicate the equivalent blower quantity in an equivalent group of planes.
8. a kind of construction method of wind power plant Equivalent Model excavated based on MMSE as claimed in claim 5, which is characterized in that
The equivalent parameters of the line impedance include:
Wherein, ZeqFor the equivalent parameters of branch impedance, ZkFor the branch impedance of kth bar trunk line type cable, PjFor jth Fans
Output power, PiFor the output power of the i-th Fans, YeqFor the equivalent parameters of admittance over the ground, YiFor trunk line type in the i-th Fans
The admittance over the ground of cable, m indicate the equivalent blower quantity in an equivalent group of planes, and 1≤i≤m, n are blower in trunk line type blower branch
Number, 1≤k≤i, k≤j≤n.
9. a kind of wind power plant Equivalent Model excavated based on MMSE, which is characterized in that the wind power plant Equivalent Model is wanted by right
A kind of construction method of any wind power plant Equivalent Model excavated based on MMSE of 1-8 is asked to construct to obtain.
10. a kind of application of wind power plant Equivalent Model excavated based on MMSE as claimed in claim 9, which is characterized in that institute
Wind power plant Equivalent Model is stated applied to the dynamic process simulation under all kinds of scenes of electric system.
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