CN108574291A - One kind being based on Ensemble Kalman Filter generator dynamic state estimator method - Google Patents
One kind being based on Ensemble Kalman Filter generator dynamic state estimator method Download PDFInfo
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/24—Arrangements for preventing or reducing oscillations of power in networks
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Abstract
The present invention provides one kind being based on Ensemble Kalman Filter generator dynamic state estimator method, variation characteristic and generator itself for electric system electromechanics transient process it is non-linear, the selection of sampled point in linearisation and Unscented transform of the present invention without state equation, but use the error covariance in set statistical thinking estimation Kalman filter equation, the probability density function of virtual condition is approached, estimated accuracy is also improved while reducing computation complexity.In the present invention in order to which Ensemble Kalman Filter obtains preferable estimated result in generator dynamic state estimator, consider the estimated accuracy of filtering and calculates the time according to the suitable set sizes of the complexity of state equation selection, and it is added to offset appropriate on the basis of original state average value, its effect filtered increases in filtering accuracy and compared to direct set of applications Kalman filtering on the estimation time.
Description
Technical field
The present invention relates to a kind of method for estimating state of electric system, and in particular to a kind of dynamic state estimator method.
Background technology
In recent years, it is based on the synchronized phasor of Wide Area Measurement System (wide-area measurement systems, WAMS)
Measuring unit (phasor measurement unit, PMU) is had been widely used due to the synchronism of its high sampling rate and data
In the dynamic state estimator of electric system electromechanics transient process.But often there is error in measurement and bad number in the data that PMU is measured
According to influencing the formulation of electric power system control strategy.Dynamic state estimator can not only reduce the influence of error in measurement and noise, also
Corresponding control strategy can be formulated with the variation of forecasting system future state, ensure the safe and stable operation of power grid.
Currently, for generator dynamic state estimator, common method includes mainly Extended Kalman filter (EKF), nothing
Mark Kalman filtering (UKF) etc..State equation is launched into Taylor series and omits second order and the above item, linearization procedure by EKF
It can lead to larger truncated error, the estimation of mistake is may result in nonlinearity system；UKF passes through Unscented transform
(unscented transform, UT) approximatively obtains the statistical property after nonlinear change, needs to select quantity of parameters, right
The flexibility that parameter is chosen is poor, using there are limitations.
Invention content
Goal of the invention：It is an object of the invention to propose it is a kind of reduce computation complexity and improve estimated accuracy based on
Ensemble Kalman Filter generator dynamic state estimator method.
Technical solution：The present invention provides one kind being based on Ensemble Kalman Filter generator dynamic state estimator method, packet
Include following steps：
(1) parameter information of estimation generator unit needed for obtaining, including time inertia constant, damped coefficient, synchronous turn
Speed, rated power and the total unit number of generator；
(2) setting estimation time span, setting set member number, setting Set Status variable initial value, initialization system mould
Type noise variance matrix, setting measure varivance matrix；
(3) original state of generator's power and angle and angular rate is obtained by known priori, original state passes through
Monte Carlo method productive set number of members is the initial sets of q, which reacts the error statistics feelings of original state
Condition, and add on the basis of initial sets the initial sets X that appropriate deviation d is filtered0：
Each element in setIndicate one group of state variable；
(4) prediction step：Calculate each set member+1 moment of kth predicted state valueWith predicted state average value
In formula, f () is state transition function, ukInput quantity is controlled for the k moment,For i-th of set member's of k moment
Process noise,For the analysis state value of i-th of set member of k moment,For the prediction shape of i-th of set member of k+1 moment
State value,For k+1 moment predicted state average values, q is set member's number；
(5) due to time of day xkIt is unknown, approximate error covariance matrix is come by using set member, and calculate k+1
The kalman gain matrix at moment：
In formula, h () is to measure function,For the prediction measuring value of i-th of set member of k+1 moment,For k+1 when
Prediction measuring value average value is carved,For k+1 moment state set error matrixes,Aggregate error matrix is measured for the k+1 moment,For k+1 moment state variable with measure variable covariance matrix,Variable is measured for the k+1 moment and measures the association of variable
Variance matrix,For k+1 moment kalman gain matrix；
(6) analysis step：Tracking is iterated to each member in set, the calculating k+1 moment analyzes state valueWith
Analysis state average value
In formula, yk+1For the actual value of k+1 moment measuring values,For the measurement noise of i-th of set member of k+1 moment,State average value, that is, state estimation is analyzed for the k+1 moment；
(7) judge whether to reach estimation time span, if so, output result；If it is not, then return to step (4) continues.
Advantageous effect：Non-linear, this hair of variation characteristic and generator itself for electric system electromechanics transient process
Bright carried Ensemble Kalman Filter to generator carry out dynamic state estimator during, without state equation linearisation and
The selection of sampled point in Unscented transform, but the error covariance in set statistical thinking estimation Kalman filter equation is used,
The probability density function of virtual condition is approached, estimated accuracy is also improved while reducing computation complexity.It is in the present invention
Ensemble Kalman Filter obtains preferable estimated result in generator dynamic state estimator, consider filtering estimated accuracy and
The time is calculated according to the suitable set sizes of the complexity of state equation selection, and is added on the basis of original state average value
Offset appropriate is added, the effect of filtering is compared to direct set of applications Kalman filtering, in filtering accuracy and estimation time
On increase.The present invention shows that the present invention proposes that the filtering accuracy of method is better than by ieee standard numerical testing
Extended Kalman filter and Unscented kalman filtering device.
Description of the drawings
Fig. 1 is the method for the present invention flow chart；
Fig. 2 is IEEE9 standard test system figures；
Fig. 3 is embodiment using the method for the present invention and EKF and UKF filter result comparison diagrams；Wherein, (a) is 1 work(of generator
Angular motion state estimation curve (b) is 1 generator rotor angle dynamic estimation curve partial enlarged view of generator；
Fig. 4 is embodiment using the method for the present invention and EKF and UKF filter result comparison diagrams；Wherein, (a) is 1 electricity of generator
Angular speed dynamic estimation curve (b) is 1 angular rate dynamic estimation curve partial enlarged view of generator.
Specific implementation mode
Technical solution of the present invention is described in detail below, but protection scope of the present invention is not limited to the implementation
Example.
1, generator dynamic state estimator model
Due in practical power systems accident process, it is difficult to obtain grid topology and system busbar voltage amplitude in real time
Value and phase angle, so general choose the generator amature generator rotor angle and angular rate that will not be mutated and obey the constraint of the rotor differential equation
As state variable.Therefore, select the classical second-order model of synchronous generator, concrete form as follows herein：
In formula, δ is generator amature generator rotor angle (radian)；ω is generator angular rate (perunit value)；ω0It is electromechanical for power generation
The initial value (perunit value) of angular speed；T is the time (second)；TmAnd TeThe machine torque and electricity being respectively added on generator amature
Magnetic torque (perunit value)；PmAnd PeThe mechanical output and electromagnetic power (perunit value) being respectively added on generator amature；TJFor hair
Rotor inertia time constant；D is damped coefficient.
Write (1) formula as state equation：
The unit of δ is degree in formula.
The state variable of generator dynamic state estimator is x=[δ ω]TIf the mechanical output and electromagnetism of known generators
Power, input quantity are selected as u=[Pm Pe]T。
δ and ω can directly be measured by PMU, therefore be had：
In formula, y is to measure variable, and C is observing matrix.
2, error analysis
Process noise is mostly derived from model parameter, generator amature inertia time constant TJWith the inaccuracy of damped coefficient D
Property, generator electromagnetic power PeError in measurement and prime mover input mechanical output PmVariation.Without loss of generality, systematic procedure
Noise variance matrix is selected as：
Q=diag (0,0.0004Pe+0.0001) (4)
Measure the error in measurement that noise is mostly derived from PMU.In the ideal case, cause the error in measurement of generator rotor angle that can reach
1~2 °, the standard deviation of the direct error in measurement of angular rate is selected as 0.001 (perunit value, famous value are 0.05~0.06Hz), does not lose
Generality, system measurements noise variance matrix are selected as：
R=diag (22,10-6) (5)
3, Ensemble Kalman Filter method for dynamic estimation
On the basis of establishing state-space model, the present invention is using Ensemble Kalman Filter to generator electromechanical transient mistake
Journey correlated variables carries out dynamic estimation, as shown in Figure 1, its specific implementation steps is as follows：
(1) parameter information of estimation generator unit needed for obtaining, including：Time inertia constant, damped coefficient, synchronization turn
Speed, rated power and the total unit number of generator etc.；
(2) program initialization, including initialization system plant noise variance matrix, setting measure varivance matrix, setting
Estimate time span, setting set member's number；
(3) original state of generator's power and angle and angular rate is obtained by known priori, original state passes through
Monte Carlo method productive set number of members is the initial sets of q, which reacts the error statistics feelings of original state
Condition, and add on the basis of initial sets the initial sets X that appropriate deviation d is filtered0：
(4) prediction step：Calculate each set member+1 moment of kth predicted state valueWith predicted state average valueCalculation formula is as follows：
In formula, f () is state transition function, ukInput quantity is controlled for the k moment,For i-th of set member's of k moment
Process noise,For the analysis state value of i-th of set member of k moment,For the prediction shape of i-th of set member of k+1 moment
State value,For k+1 moment predicted state average values, q is set member's number；
(5) due to time of day xkIt is unknown, approximate error covariance matrix is come by using set member, when calculating k+1
The kalman gain matrix at quarter, calculation formula are as follows：
In formula, subscript T represents the transposition of matrix, and subscript -1 represents inverse of a matrix, and h () is to measure function,For k+1
The prediction measuring value of i-th of set member of moment,Measuring value average value is predicted for the k+1 moment,For k+1 moment state sets
Error matrix is closed,Aggregate error matrix is measured for the k+1 moment,For k+1 moment state variable and the association side for measuring variable
Poor matrix,Variable is measured for the k+1 moment and measures the covariance matrix of variable,For k+1 moment kalman gain squares
Battle array；
(6) analysis step：Tracking is iterated to each member in set, the calculating k+1 moment analyzes state valueWith
Analysis state average valueCalculation formula is as follows：
In formula, yk+1For the actual value of k+1 moment measuring values,For the measurement noise of i-th of set member of k+1 moment,State average value, that is, state estimation is analyzed for the k+1 moment；
(7) judge whether to reach estimation time span, if so, output is as a result, exit the program；If it is not, then return to step
(4) continue.
The example of the present invention is described below：
The example that the present invention tests is IEEE9 node modular systems, as shown in Fig. 2, 1~9 node is tie point, G1 in figure
~G3 is generator.IEEE9 nodes metric data is obtained by BPA emulation true value addition random noises, and generator is used when emulation
Classical second-order model simultaneously takes into account the effect of governor, and assumes that (1 cycle is 0.02s, i.e. electric system in the 40th cycle
The cycle of operation) when, three-phase metallic short circuit occurs for 8 branch head end of interior joint 4- nodes, and short trouble disappears when 58 cycle.
In order to make the estimated result between each algorithm more more obvious, mean square error (mean is used herein
Squared error, MSE) as the comparison between index progress algorithm performance, it is defined as follows：
In formula,Represent the filter value of k moment state variables, xkRepresent actual value (the BPA numbers of k moment state variables
According to), n is sampling period number.
To above-described embodiment system, tested respectively with EKF, UKF and the method for the present invention.As space is limited, of the invention
The dynamic estimation filter curve of generator 1 in IEEE9 node systems is only provided, generator 2 is similar with 3 result of generator.
Shown in the dynamic estimation result such as Fig. 3 (a) of three kinds of distinct methods to 1 generator rotor angle of generator, Fig. 3 (b) gives power generation
The partial enlarged view of 1 generator rotor angle estimated result of machine, it can be clearly seen that the method applied in the present invention can be tracked more accurately
The generator rotor angle state change of generator.
Shown in the dynamic estimation result such as Fig. 4 (a) of three kinds of distinct methods to 1 angular rate of generator, Fig. 4 (b) gives
The partial enlarged view of 1 angular rate estimated result of generator.Equally, it is analyzed by the Comparative result to Fig. 4 (a) He Fig. 4 (b),
The angular rate variation of generator can more accurately be estimated by showing the used method of the present invention.
In order to analyze superiority of the method for the present invention compared with EKF and UKF methods comprehensively, table 1 gives algorithms of different to IEEE9
The means square error data of 3 generator dynamic estimation results in node system：
The mean square error of generator estimated result under 1 algorithms of different of table
As can be seen from the table, the performance indicator of the used method of the present invention is superior to EKF and UKF.
To sum up, it can be deduced that such as draw a conclusion：It is of the present invention to be based on Ensemble Kalman Filter generator dynamical state
Method of estimation has more accurate estimated accuracy compared with EKF and UKF.
Claims (1)
1. one kind being based on Ensemble Kalman Filter generator dynamic state estimator method, it is characterised in that：Include the following steps：
(1) parameter information of estimation generator unit needed for obtaining, including time inertia constant, damped coefficient, synchronous rotational speed, volume
Determine power and the total unit number of generator；
(2) setting estimation time span, setting set member number, setting Set Status variable initial value, initialization system model are made an uproar
Sound variance matrix, setting measure varivance matrix；
(3) original state of generator's power and angle and angular rate is obtained by known priori, original state passes through Monte
Carlo method productive set number of members is the initial sets of q, which reacts the error statistics situation of original state, and
And the initial sets X that appropriate deviation d is filtered is added on the basis of initial sets0：
Each element in setIndicate one group of state variable；
(4) prediction step：Calculate each set member+1 moment of kth predicted state valueWith predicted state average value
In formula, f () is state transition function, ukInput quantity is controlled for the k moment,For the process of i-th of set member of k moment
Noise,For the analysis state value of i-th of set member of k moment,For the predicted state of i-th of set member of k+1 moment
Value,For k+1 moment predicted state average values, q is set member's number；
(5) due to time of day xkIt is unknown, approximate error covariance matrix is come by using set member, and calculate the k+1 moment
Kalman gain matrix：
In formula, h () is to measure function,For the prediction measuring value of i-th of set member of k+1 moment,It is pre- for the k+1 moment
Measured value average value is measured,For k+1 moment state set error matrixes,Aggregate error matrix is measured for the k+1 moment,
For k+1 moment state variable with measure variable covariance matrix,Variable is measured for the k+1 moment and measures the association side of variable
Poor matrix,For k+1 moment kalman gain matrix；
(6) analysis step：Tracking is iterated to each member in set, the calculating k+1 moment analyzes state valueAnd analysis
State average value
In formula, yk+1For the actual value of k+1 moment measuring values,For the measurement noise of i-th of set member of k+1 moment,For k
+ 1 moment analyzed state average value, that is, state estimation；
(7) judge whether to reach estimation time span, if so, output result；If it is not, then return to step (4) continues.
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| CN109754013A (en) * | 2018-12-31 | 2019-05-14 | 浙江大学 | A kind of electric system hybrid measurement fusion method based on Unscented kalman filtering |
| CN110008638A (en) * | 2019-04-23 | 2019-07-12 | 河海大学 | A kind of dynamic state estimator method based on adaptive EnKF technology |
| CN110032812A (en) * | 2019-04-18 | 2019-07-19 | 河海大学 | A kind of dynamic state estimator method based on adaptive volume Kalman filtering |
| CN110112770A (en) * | 2019-04-17 | 2019-08-09 | 河海大学 | A kind of generator dynamic state estimator method based on adaptive H ∞ volume Kalman filtering |
| CN110133400A (en) * | 2019-05-10 | 2019-08-16 | 青岛大学 | A kind of dynamic power system method for detecting abnormality merging recursive state estimation |
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| CN111272867A (en) * | 2019-12-25 | 2020-06-12 | 浙江大学 | Method for detecting compactness of grouting body in steel bar sleeve connecting structure |
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| CN109638811A (en) * | 2018-11-13 | 2019-04-16 | 天津大学 | Distribution network voltage power sensitivity robust estimation method based on model equivalence |
| CN109638811B (en) * | 2018-11-13 | 2022-03-08 | 天津大学 | Power distribution network voltage power sensitivity robust estimation method based on model equivalence |
| CN109412653A (en) * | 2018-11-16 | 2019-03-01 | 福州大学 | A kind of equalization methods making full use of channel multi-path characteristic |
| CN109754013B (en) * | 2018-12-31 | 2021-09-10 | 浙江大学 | Electric power system hybrid measurement fusion method based on unscented Kalman filtering |
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| CN110112770A (en) * | 2019-04-17 | 2019-08-09 | 河海大学 | A kind of generator dynamic state estimator method based on adaptive H ∞ volume Kalman filtering |
| CN110032812A (en) * | 2019-04-18 | 2019-07-19 | 河海大学 | A kind of dynamic state estimator method based on adaptive volume Kalman filtering |
| CN110008638A (en) * | 2019-04-23 | 2019-07-12 | 河海大学 | A kind of dynamic state estimator method based on adaptive EnKF technology |
| CN110133400A (en) * | 2019-05-10 | 2019-08-16 | 青岛大学 | A kind of dynamic power system method for detecting abnormality merging recursive state estimation |
| CN110133400B (en) * | 2019-05-10 | 2021-07-09 | 青岛大学 | Dynamic power system anomaly detection method fused with recursion state estimation |
| CN110289989A (en) * | 2019-05-27 | 2019-09-27 | 东南大学 | A kind of distributed state estimation method based on volume Kalman filtering algorithm |
| CN110749835A (en) * | 2019-10-09 | 2020-02-04 | 三峡大学 | Power transmission line fault positioning method based on Kalman filter |
| CN111272867A (en) * | 2019-12-25 | 2020-06-12 | 浙江大学 | Method for detecting compactness of grouting body in steel bar sleeve connecting structure |
| CN111123131A (en) * | 2020-01-02 | 2020-05-08 | 江苏方天电力技术有限公司 | Lithium battery state of charge estimation method based on ensemble Kalman filtering |
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