CN102545216B - Projection method for generator node voltage during electric power system transient stability simulation process - Google Patents

Projection method for generator node voltage during electric power system transient stability simulation process Download PDF

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CN102545216B
CN102545216B CN 201210017819 CN201210017819A CN102545216B CN 102545216 B CN102545216 B CN 102545216B CN 201210017819 CN201210017819 CN 201210017819 CN 201210017819 A CN201210017819 A CN 201210017819A CN 102545216 B CN102545216 B CN 102545216B
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generator
node voltage
generator node
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electric power
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CN102545216A (en
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王建全
赵志奇
杨飞燕
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Zhejiang University ZJU
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Zhejiang University ZJU
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Abstract

The invention discloses a projection method for a generator node voltage during an electric power system transient stability simulation process. Compared with the prior art, the generator node voltage at a next integral step time can be more accurately projected through the time generator node voltage and the correlative state variable. The basic concept adopted by the invention is that when the generator node voltage is required to be projected, the whole electric power system is separately regarded as an electric generating set and an external system represented by equivalent admittance which are connected; the system equivalent admittance outside each generator is approximately regarded as to maintain invariability in an integral step; and a time state variable estimation value is projected through an explicit integral, and the predominant value of each generator node voltage can be obtained according to an approximate system equivalent impedance corresponding to each generator andthe state variable projection value. The generator node voltage projected by the method provided by the invention serves as the initial estimation value of each integral step simulation, and the iteration frequency during the solution process can be remarkably reduced.

Description

The generator node voltage Forecasting Methodology that is used for electric power system transient stability emulation
Technical field
The invention belongs to Automation of Electric Systems, particularly be used for the method for prediction generator node voltage in a kind of electric power system transient stability simulation process.
Background technology
Transient stability analysis of power system is one of content basic, the most most crucial during power system analysis is calculated.Online dynamic security analysis, the advanced technologies such as safety and stability emergency control, prevention and control, intelligent scheduling progressively require to apply in electric power system.The precondition that realizes these advanced technologies is can be fast, accurately, the transient stability emulation reliably large-scale electrical power system carried out.
Numerical integration is accurate, the most reliable method of electric power system transient stability simulation calculation.The disadvantage of numerical integrating is that amount of calculation is large, although computer speed has had raising at full speed, for large-scale electrical power system, still is difficult to satisfy the requirement that online dynamic security analysis, prevention and control, emergency control etc. are calculated computing time.
In existing electric power system transient stability numerical integration method, in order to guarantee the numerical stability of algorithm, usually adopt implicit integration algorithm.Implicit integration algorithm is in basis
Figure 201210017819X100002DEST_PATH_IMAGE001
State variable constantly With the operation variable Value is asked for
Figure 201210017819X100002DEST_PATH_IMAGE004
State variable constantly
Figure 201210017819X100002DEST_PATH_IMAGE005
With the operation variable
Figure 201210017819X100002DEST_PATH_IMAGE006
During value, need first given
Figure 324185DEST_PATH_IMAGE004
The constantly discreet value of state variable and operation variable
Figure 201210017819X100002DEST_PATH_IMAGE007
,
Figure 201210017819X100002DEST_PATH_IMAGE008
, pass through again iterative.When considering the generator saliency, usually also need iterative when finding the solution network equation, namely need to provide the initial discreet value of generator and load bus voltage.If can provide good initial estimate, can reduce iterations, thereby significantly reduce the amount of calculation of transient stability emulation.
At present, usually use explicit numerical integration algorithm for state variable and just can provide preferably discreet value, and for the active node voltage in the system, particularly the generator node voltage then is difficult to dope more accurately discreet value.Initial estimate for each integration step generator node voltage in the transient stability emulation is provided by two kinds of methods usually: a kind of is with the preceding integration calculated value in step, as this integration initial estimate in step, namely gets
Figure 201210017819X100002DEST_PATH_IMAGE009
Another kind is the calculated value of getting former integration steps, obtains by the curve extrapolation, namely gets
Figure 201210017819X100002DEST_PATH_IMAGE010
Matched curve
Figure DEST_PATH_IMAGE011
Usually obtained by least square method or generalized extended algorithm,
Figure 201210017819X100002DEST_PATH_IMAGE012
Usually get 1～3.The method of above two kinds of initial estimates, in each integration step state variable and operation variable change hour, effect still can.But, when variable change is larger, will significantly increase iterations, sometimes not even convergence.The second estimation algorithm particularly, sometimes even poorer than first method effect.
Along with the continuous expansion of electric power system scale, the fault that may occur also becomes increasingly complex, and causes that thus system loses the loss of stablizing and causing also more serious.This just can carry out dynamic security analysis, implement safety and stability prevention and control and emergency control electric power system rapidly in the urgent need to us, and everything all is to be calculated as the basis with Fast numerical integration transient stability.In the transient stability computational process, the good predict of each integration step initial value is one of key technology that realizes the fast transient stability Calculation.
Summary of the invention
The present invention seeks in order to solve in the electric power system transient stability simulation process, the initial discreet value of generator node voltage is inaccurate, so that the iterative number of times increases, amount of calculation is large, computational speed can not satisfy the shortcoming of the online calculation requirement of electric power system, invented in a kind of electrical power system transient computational process, can dope more exactly the method for the initial discreet value of each integration step generator node voltage, reduce so that the iterations in each integration step of power system transient simulation when calculating can have significantly, and then significantly improve simulation velocity.
The present invention seeks to be achieved through the following technical solutions: a kind of generator node voltage Forecasting Methodology for electric power system transient stability emulation is characterized in that comprising the steps:
Step 1: according to
Figure 428276DEST_PATH_IMAGE001
The time etching system in each generator node voltage and Injection Current, be calculated as follows the corresponding whole external system Equivalent admittance of each generator:
Figure 201210017819X100002DEST_PATH_IMAGE013
(
Figure 201210017819X100002DEST_PATH_IMAGE014
Be the generator number of units)
In the formula,
Figure 201210017819X100002DEST_PATH_IMAGE015
Be respectively
Figure 332647DEST_PATH_IMAGE001
Constantly the
Figure 201210017819X100002DEST_PATH_IMAGE016
Real part, the imaginary part of the real part of platform generator node voltage, imaginary part and node Injection Current;
Figure 201210017819X100002DEST_PATH_IMAGE017
Expression
Figure 867138DEST_PATH_IMAGE001
Constantly with the
Figure 681510DEST_PATH_IMAGE016
The whole external system Equivalent admittance that generator joins;
Step 2: use explicit integration scheme, by
Figure 566290DEST_PATH_IMAGE001
Moment state variable
Figure 833323DEST_PATH_IMAGE002
With the operation variable Value is calculated The initial estimate of state variable constantly
Figure 819100DEST_PATH_IMAGE007
Obtain the initial estimate of each generator's power and angle and each electromotive force
Figure 201210017819X100002DEST_PATH_IMAGE018
The generator built-in potential
Figure 201210017819X100002DEST_PATH_IMAGE019
Different and different according to the selected model of generator, their corresponding value is referring to table 1;
Step 3: be calculated as follows
Figure 635746DEST_PATH_IMAGE004
Each generator of moment generator node admittance corresponding with the state variable initial estimate:
Figure 201210017819X100002DEST_PATH_IMAGE021
In the formula,
Figure 201210017819X100002DEST_PATH_IMAGE022
Expression is resistance in the generator,
Figure 201210017819X100002DEST_PATH_IMAGE023
,
Figure 201210017819X100002DEST_PATH_IMAGE024
, ,
Figure 201210017819X100002DEST_PATH_IMAGE026
What represent is that the admittance relevant with the generator built-in potential exists Initial discreet value constantly,
Figure 201210017819X100002DEST_PATH_IMAGE027
,
Figure 201210017819X100002DEST_PATH_IMAGE028
,
Figure 201210017819X100002DEST_PATH_IMAGE029
,
Figure 272974DEST_PATH_IMAGE029
What represent is that the admittance relevant with the generator node voltage exists
Figure 765135DEST_PATH_IMAGE004
Initial discreet value constantly,
Figure 201210017819X100002DEST_PATH_IMAGE030
,
Figure 201210017819X100002DEST_PATH_IMAGE031
Represent respectively each generator
Figure 201210017819X100002DEST_PATH_IMAGE032
Axle and The reactance of axle, along with the used model of generator is different and different, their corresponding value can see Table 1.
Table 1 motor model and the parameter table of comparisons
Figure 201210017819X100002DEST_PATH_IMAGE034
In the table 1
Figure 201210017819X100002DEST_PATH_IMAGE035
What represent is generator transient state reactance after-potential,
Figure 201210017819X100002DEST_PATH_IMAGE036
,
Figure 201210017819X100002DEST_PATH_IMAGE037
,
Figure 201210017819X100002DEST_PATH_IMAGE038
, Represent respectively generator
Figure 321275DEST_PATH_IMAGE032
Axle,
Figure 658715DEST_PATH_IMAGE033
The transient internal voltage of axle and time transient potential,
Figure 201210017819X100002DEST_PATH_IMAGE040
What represent is generator
Figure 364503DEST_PATH_IMAGE033
The axle synchronous reactance,
Figure 201210017819X100002DEST_PATH_IMAGE041
,
Figure 201210017819X100002DEST_PATH_IMAGE042
,
Figure 201210017819X100002DEST_PATH_IMAGE043
,
Figure 201210017819X100002DEST_PATH_IMAGE044
Represent respectively generator Axle,
Figure 615542DEST_PATH_IMAGE033
Transient state reactance and the subtranient reactance of axle.
Step 4: be calculated as follows
Figure 694356DEST_PATH_IMAGE004
The initial estimate of each generator node voltage of the moment
Figure 201210017819X100002DEST_PATH_IMAGE045
In the formula
Figure DEST_PATH_IMAGE046
Represent respectively
Figure 319897DEST_PATH_IMAGE016
The platform generator exists Real part, the imaginary part of moment node voltage initial estimate; The inventive method is Single-step Prediction, namely only uses The voltage of generator node and relevant generator state variable just can dope next integration step more exactly constantly
Figure 987005DEST_PATH_IMAGE004
Generator node voltage constantly.
The inventive method when prediction generator node voltage just according to the generator node voltage before the prediction constantly, but integrated application generator node voltage and relevant generator state variables before the prediction constantly.
The inventive method is when each generator node voltage of prediction, regard one by one whole electric power system as a generating set and an external system that represents with Equivalent admittance links, namely one by one whole complication system is become the single system that the system equivalent admittance forms outside a power supply and the generator.
The inventive method is in prediction during each generator node voltage, approximately thinks that the Equivalent admittance with the whole external system of each generator electric remains unchanged in the step at an integration.
The present invention only needs according to following simple forecast formula
Figure DEST_PATH_IMAGE047
Just can dope more exactly the generator node voltage.
The invention has the beneficial effects as follows: a generator node voltage Forecasting Methodology foundation
Figure 401806DEST_PATH_IMAGE001
State variable constantly and operation variate-value just can be obtained more rapidly
Figure 406671DEST_PATH_IMAGE004
The constantly discreet value of generator node voltage can reduce the iterations of network algebra equation solution in the transient stability emulation effectively, improves the speed of power system transient simulation.
Description of drawings
Fig. 1 is flow chart of the present invention;
Fig. 2 is the equivalent schematic diagram of the present invention;
Fig. 3 is the equivalent schematic diagram of unit corresponding to system.
Embodiment
The invention will be further described below in conjunction with accompanying drawing.
A kind of generator node voltage Forecasting Methodology for electric power system transient stability emulation that the present invention proposes may further comprise the steps:
Step 1: according to
Figure 844605DEST_PATH_IMAGE001
The time etching system in each generator node voltage and Injection Current, be calculated as follows the corresponding whole external system Equivalent admittance of each generator:
Figure DEST_PATH_IMAGE048
(
Figure 327539DEST_PATH_IMAGE014
Be the generator number of units)
In the formula,
Figure DEST_PATH_IMAGE049
Be respectively
Figure 862426DEST_PATH_IMAGE001
Constantly the Real part, the imaginary part of the real part of platform generator node voltage, imaginary part and node Injection Current;
Figure DEST_PATH_IMAGE050
Expression
Figure 963423DEST_PATH_IMAGE001
Constantly with the
Figure 250048DEST_PATH_IMAGE016
The whole external system Equivalent admittance that generator joins;
Step 2: use explicit integration scheme, by
Figure 311545DEST_PATH_IMAGE001
Moment state variable With the operation variable
Figure DEST_PATH_IMAGE051
Value is calculated
Figure 124267DEST_PATH_IMAGE004
The initial estimate of state variable constantly
Figure DEST_PATH_IMAGE052
Obtain the initial estimate of each generator's power and angle and each electromotive force The generator built-in potential
Figure DEST_PATH_IMAGE054
Different and different according to the selected model of generator, their corresponding value is referring to table 1;
Step 3: be calculated as follows
Figure 276900DEST_PATH_IMAGE004
Each generator of moment generator node admittance corresponding with the state variable initial estimate:
Figure DEST_PATH_IMAGE055
In the formula, Expression is resistance in the generator,
Figure DEST_PATH_IMAGE057
,
Figure DEST_PATH_IMAGE058
,
Figure DEST_PATH_IMAGE059
, What represent is that the admittance relevant with the generator built-in potential exists
Figure 897423DEST_PATH_IMAGE004
Initial discreet value constantly,
Figure DEST_PATH_IMAGE061
,
Figure DEST_PATH_IMAGE062
,
Figure DEST_PATH_IMAGE063
,
Figure 924809DEST_PATH_IMAGE063
What represent is that the admittance relevant with the generator node voltage exists
Figure 490920DEST_PATH_IMAGE004
Initial discreet value constantly,
Figure DEST_PATH_IMAGE064
,
Figure DEST_PATH_IMAGE065
Represent respectively each generator
Figure 917222DEST_PATH_IMAGE032
Axle and
Figure 340113DEST_PATH_IMAGE033
The reactance of axle, along with the used model of generator is different and different, their corresponding value can see Table 1.
Table 1 motor model and the parameter table of comparisons
Figure DEST_PATH_IMAGE066
In the table 1
Figure 727232DEST_PATH_IMAGE035
What represent is generator transient state reactance after-potential,
Figure 159350DEST_PATH_IMAGE036
,
Figure 49946DEST_PATH_IMAGE037
,
Figure 909317DEST_PATH_IMAGE038
,
Figure 518153DEST_PATH_IMAGE039
Represent respectively generator
Figure 753963DEST_PATH_IMAGE032
Axle,
Figure 764644DEST_PATH_IMAGE033
The transient internal voltage of axle and time transient potential,
Figure 797846DEST_PATH_IMAGE040
What represent is generator The axle synchronous reactance,
Figure 667899DEST_PATH_IMAGE041
,
Figure 533087DEST_PATH_IMAGE042
,
Figure 734261DEST_PATH_IMAGE043
,
Figure 317689DEST_PATH_IMAGE044
Represent respectively generator
Figure 629722DEST_PATH_IMAGE032
Axle,
Figure 614996DEST_PATH_IMAGE033
Transient state reactance and the subtranient reactance of axle.
Step 4: be calculated as follows
Figure 987071DEST_PATH_IMAGE004
The initial estimate of each generator node voltage of the moment
Figure 57795DEST_PATH_IMAGE045
In the formula
Figure 173519DEST_PATH_IMAGE046
Represent respectively
Figure 13299DEST_PATH_IMAGE016
The platform generator exists
Figure 556276DEST_PATH_IMAGE004
Real part, the imaginary part of moment node voltage initial estimate;
The inventive method is Single-step Prediction, namely only uses
Figure 848717DEST_PATH_IMAGE001
The voltage of generator node and relevant generator state variable just can dope next integration step more exactly constantly Generator node voltage constantly.
The inventive method when prediction generator node voltage just according to the generator node voltage before the prediction constantly, but integrated application generator node voltage and relevant generator state variables before the prediction constantly.
The inventive method is when each generator node voltage of prediction, regard one by one whole electric power system as a generating set and an external system that represents with Equivalent admittance links, namely one by one whole complication system is become the single system that the system equivalent admittance forms outside a power supply and the generator.
The inventive method is in prediction during each generator node voltage, approximately thinks that the Equivalent admittance with the whole external system of each generator electric remains unchanged in the step at an integration.
The present invention only needs according to following simple forecast formula
Figure 462418DEST_PATH_IMAGE045
Just can dope more exactly the generator node voltage.
Below introduce in detail the detailed process of the inventive method.
As shown in Figure 2 whole electric power system is regarded as a generating set one by one and an external system that represents with Equivalent admittance links, i.e. whole electric power system can be expressed as respectively equivalent circuit shown in Figure 3.Then The moment all can be tried to achieve with voltage and the Injection Current of each generator node by (1) formula with the Equivalent admittance of the whole external system of each generator electric:
Figure DEST_PATH_IMAGE067
(1)
In the formula, Be respectively
Figure 682068DEST_PATH_IMAGE001
Constantly the Real part, the imaginary part of the real part of platform generator node voltage, imaginary part and node Injection Current;
Figure 381220DEST_PATH_IMAGE050
Expression
Figure 648253DEST_PATH_IMAGE001
Constantly with the
Figure 909470DEST_PATH_IMAGE016
The whole external system Equivalent admittance that generator joins;
Use explicit integration scheme, by
Figure 312770DEST_PATH_IMAGE001
Moment state variable With the operation variable Value is calculated The initial estimate of state variable constantly
Figure 711073DEST_PATH_IMAGE052
Obtain the initial estimate of each generator's power and angle and each electromotive force
Figure 203234DEST_PATH_IMAGE053
The generator built-in potential
Figure 241597DEST_PATH_IMAGE054
According to the difference of the selected model of generator and difference.
Figure 782300DEST_PATH_IMAGE004
The constantly discreet value of the Injection Current of generator node can be shown at this state variable of constantly estimating and the voltmeter of estimating with generator:
Figure DEST_PATH_IMAGE068
（2）
In the formula (2)
Figure 315236DEST_PATH_IMAGE004
Moment generator
Figure DEST_PATH_IMAGE069
Internal impedance under the coordinate transforms to
Figure DEST_PATH_IMAGE070
Admittance under the coordinate ,
Figure DEST_PATH_IMAGE072
But formula (3), formula (4) are asked for:
Figure 775036DEST_PATH_IMAGE055
（3）
Figure 566275DEST_PATH_IMAGE056
（4）
Simultaneously
Figure 707406DEST_PATH_IMAGE004
The constantly discreet value of each generator node Injection Current also estimating with the external system Equivalent admittance of available this moment generator node voltage is tried to achieve:
Figure DEST_PATH_IMAGE073
（5）
Suppose that each generator exists
Figure 267701DEST_PATH_IMAGE001
Constantly with
Figure 836085DEST_PATH_IMAGE004
The Equivalent admittance approximately equal of valve system is waited in the outside constantly, namely has:
Figure DEST_PATH_IMAGE074
（6）
Then by (2)～(6) Shi Kede The voltage of estimating of every generator node is constantly:
Figure 997125DEST_PATH_IMAGE045
（7）
Each generator exists in the transient stability simulation process like this
Figure 349609DEST_PATH_IMAGE004
The constantly voltage discreet value of each generator node, can try to achieve as follows:
1.According to
Figure 419721DEST_PATH_IMAGE001
The time etching system in each generator node voltage and Injection Current, calculate the corresponding whole external system Equivalent admittance of each generator by (1) formula
Figure 857655DEST_PATH_IMAGE050
2.Use explicit integration scheme, by Moment state variable With the operation variable
Figure 723346DEST_PATH_IMAGE051
Value is calculated
Figure 648577DEST_PATH_IMAGE004
The initial estimate of state variable constantly
Figure 935202DEST_PATH_IMAGE052
Obtain the initial estimate of each generator's power and angle and each electromotive force
Figure 262278DEST_PATH_IMAGE053
By calculating suc as formula (3), formula (4)
Figure 608945DEST_PATH_IMAGE004
Each generator of moment generator node admittance corresponding with the state variable initial estimate:
Figure 83789DEST_PATH_IMAGE071
,
4.Calculate by formula (7)
Figure 908526DEST_PATH_IMAGE004
The predicted value of each generator node voltage of the moment.
Below be an embodiment of the inventive method, carry out emulation experiment with East China 529 machines 3918 systems and make embodiment, further specify as follows: all generators all adopt in the test macro
Figure DEST_PATH_IMAGE076
Constant model, load adopts the constant impedance model, and iteration error is
Figure DEST_PATH_IMAGE077
The generator node voltage Forecasting Methodology that this paper is proposed is used for implicit expression trapezoidal integration transient stability simulation calculation, and with the calculated value that adopts the preceding integration step as this integration initial estimate in step, namely get
Figure DEST_PATH_IMAGE078
Method compare.
Suppose near the SNQ node of the SNQ--SSJ branch road of East China 529 machines, 3918 node systems three phase short circuit fault occurs, continue 0.3s fault time after, with the faulty line excision, simulation time is 3 seconds.
The amount of calculation of table 1. pair two kinds of algorithms compares.As can be seen from Table 1, the number of times that adopts the present invention to predict that the generator node voltage can make transient emulation find the solution network equation reduces 52%～117%, and the CPU time saves 30%～44%, has reduced significantly the amount of calculation of transient stability emulation.
Figure DEST_PATH_IMAGE079
。

Claims (5)

1. be used for the generator node voltage Forecasting Methodology of electric power system transient stability emulation, it is characterized in that comprising the steps:
Step 1: each generator node voltage and Injection Current in the etching system during according to t are calculated as follows the corresponding whole external system Equivalent admittance of each generator:
Figure FDA00003528094300011
I=1,2 ... N G, N wherein GBe the generator number of units
In the formula, V XGi(t), V YGi(t), I XGi(t), I YGi(t) be respectively t constantly real part, the imaginary part of real part, imaginary part and the node Injection Current of i platform generator node voltage; G Gi(t), B Gi(t) represent the whole external system Equivalent admittance that the t moment and i platform generator join;
Step 2: use explicit integration scheme, by the value of t moment state variable x (t) and operation variable y (t), calculate the initial estimate x of t+h state variable constantly [0](t+h); Obtain the initial estimate of each generator's power and angle
Figure FDA00003528094300012
Initial estimate with built-in potential The generator built-in potential
Figure FDA00003528094300014
Different and different according to the selected model of generator, their corresponding value is referring to table 1;
Step 3: be calculated as follows constantly each generator generator node admittance corresponding with the state variable initial estimate of t+h:
Figure FDA00003528094300021
Figure FDA00003528094300022
Figure FDA00003528094300023
Figure FDA00003528094300024
Figure FDA00003528094300025
Figure FDA00003528094300026
Figure FDA00003528094300027
Figure FDA00003528094300028
In the formula, R AiExpression is resistance in the generator, Expression be the admittance relevant with the generator built-in potential in the t+h initial discreet value in the moment,
Figure FDA000035280943000210
Expression be the admittance relevant with the generator node voltage in the t+h initial discreet value in the moment,
Figure FDA000035280943000212
Represent respectively the reactance of each generator d axle and q axle, along with the used model of generator is different and different, their corresponding value can see Table 1;
Table 1 motor model and the parameter table of comparisons
Figure FDA000035280943000213
Figure FDA00003528094300031
What E' represented in the table 1 is generator transient state reactance after-potential, E' d, E' q, E " d, E " qThe transient internal voltage and the inferior transient potential that represent respectively generator d axle, q axle, X qWhat represent is generator q axle synchronous reactance, X' d, X' q, X " d, X " qThe transient state reactance and the subtranient reactance that represent respectively generator d axle, q axle;
Step 4: be calculated as follows the constantly initial estimate of each generator node voltage of t+h
Figure FDA00003528094300032
In the formula
Figure FDA00003528094300033
Represent that respectively i platform generator is in real part, the imaginary part of t+h moment node voltage initial estimate.
2. the generator node voltage Forecasting Methodology for electric power system transient stability emulation according to claim 1, it is characterized in that: the method is Single-step Prediction, and voltage and the relevant state variable of generator of generator node just can dope next integration step t+h generator node voltage constantly more exactly constantly namely only to use t.
3. the generator node voltage Forecasting Methodology for electric power system transient stability emulation according to claim 1, it is characterized in that: the method when prediction generator node voltage just according to the generator node voltage before the prediction constantly, but integrated application generator node voltage and relevant generator state variables before the prediction constantly.
4. the generator node voltage Forecasting Methodology for electric power system transient stability emulation according to claim 1, it is characterized in that: the method is when each generator node voltage of prediction, regarding one by one whole electric power system as a generating set and an external system that represents with Equivalent admittance links, namely is the single system that the system equivalent admittance forms outside a power supply and the generator one by one with whole complication system equivalence.
5. the generator node voltage Forecasting Methodology for electric power system transient stability emulation according to claim 1, it is characterized in that: the method is in prediction during each generator node voltage, thinks that the Equivalent admittance with the whole external system of each generator electric remains unchanged in the step at an integration.
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