CN109950903A - A kind of dynamic state estimator method counted and noise statistics are unknown - Google Patents
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Abstract
The invention discloses a kind of dynamic state estimator methods that meter and noise statistics are unknown, for realizing the accurate estimation of electric system generator dynamic state variables.This method is in traditional Unscented kalman filtering algorithm (unscented Kalman filter, UKF under frame), the system noise based on innovative information sequence is established respectively and measures noise statistics estimator, dynamically can adjust with update the system noise and measure the covariance matrix of noise satisfaction according to environmental change.Mentioned method (adaptive unscented Kalman filter, AUKF) can effectively solve traditional UKF method because noise matrix setting it is improper caused by state estimation degradation problem, promoted dynamic state estimator device precision of state estimation.The algorithm is because of meter and Practical Project background, and simple and convenient easy to implement, engineering application value with higher.
Description
Technical field
The present invention relates to a kind of dynamic state estimator methods that meter and noise statistics are unknown, belong to Power System Analysis
And monitoring technical field.
Background technique
Accurate state estimation is of great significance for the analysis of electric system with stability contorting.State estimation is generally divided
For two classes, one kind is static estimation, and another kind of is dynamic state estimator.Static state estimation utilizes a certain moment section redundancy
Measurement information realizes the estimation of the system moment state variable.Although static state estimated accuracy is higher, it has ignored electric power
The dynamic characteristic of system.Therefore, the real-time online that static state estimation can not be applied to POWER SYSTEM STATE is estimated.In order to adapt to
The demand of electric system on-line monitoring, the dynamic state estimator method for having estimation and forecast function obtain researcher in recent years
Extensive concern.
Currently, dynamic state estimator device has gradually been applied to the state estimation of electric system generator.The state of use is estimated
Meter method specifically includes that Kalman filtering, Extended Kalman filter, volume Kalman filtering, Unscented kalman filtering etc..It is above-mentioned
These methods improve dynamic state estimator precision to a certain extent.However, it is worth noting that these methods are assumed mostly
System noise and the covariance matrix for measuring noise satisfaction are constant；And in practical power systems, system and measurement noise
Statistical property is difficult accurately to obtain in advance, and noise covariance matrix setting is closely related with the performance of dynamic state estimator device.
So, by degradation mode estimator performance, reducing state estimation essence if system and measurement noise covariance matrix setting are improper
Degree even results in state estimator failure.
Summary of the invention
Goal of the invention: present invention seek to address that improper draw is arranged for system and measurement noise in existing dynamic state estimator device
The degradation problem risen promotes generator dynamic state estimator precision, provides solid number for the safe and stable operation of power grid
It is believed that breath.
The invention discloses a kind of dynamic state estimator methods that meter and noise statistics are unknown, send out for electric system
Motor dynamics state estimation, includes the following steps:
S1: according to generator quadravalence dynamical equation, Generator Status estimation equation is established, and constructs and obtains generator dynamic
The state equation and measurement equation of state estimation:
In formula, f () indicates that Generator Status equation, h () indicate that measurement equation, x, u, z respectively correspond expression state
Variable controls variable and measures vector；Subscript k-1 and k indicate the moment, and w indicates system noise, and v is to measure noise, both for
White Gaussian noise, the mean value met are 0, and corresponding covariance matrix is respectively Q and R, w and v is mutually indepedent and and state
Variable is unrelated；
S2: based on state estimation known to the k-1 momentUsing Unscented transform technology generate the k moment several
Sigma state samples；
S3: it is walked using the status predication of adaptive Unscented kalman filtering, calculates the Generator Status predicted value at k moment
With status predication error co-variance matrix
S4: being based on generator measurement equation, calculates the generator measurement predictor at k momentError association side is predicted with measuring
Poor matrix
S5: the cross-covariance matrix P between status predication value and measurement predictor is calculatedxz,k；
S6: based on adaptive Unscented kalman filtering filtering step, the filtering gain at k moment is obtained；
S7: the measurement information value z at k moment is utilizedk, to status predication valueIt is modified update, state estimation is calculated
Error co-variance matrix
S8: it is based on innovative information valueDynamic corrections update k moment system noise covariance matrix QkWith measurement noise
Covariance matrix Rk；
S9: according to S2-S8 according to measurement information value zkTo electric system generator state dynamic estimation, until k+1 > N, N
State estimation iteration stopping when for the maximum estimated moment, output state estimated result.
Further, 2n+1 Sigma state samples of k moment are generated in S2
In formula, n indicates Generator Status predictor dimension,For state estimation error association side known to the k-1 moment
Poor matrix,It indicates to carry out matrix Cholesky decomposition operation, κ indicates scale parameter.
Further, the Generator Status predicted value at the k moment in S3With status predication error co-variance matrixTable
Show as follows:
In formula,Indicate Sigma state samplesCorrespondence point value after the propagation of Generator Status equation, Qk-1It indicates
The covariance matrix that k-1 moment system noise meets, WlFor the weighted value corresponding to Sigma state samples:
Further, in S4, k moment generator measurement predictorWith measurement predicting covariance matrixIt indicates
Are as follows:
In formula,Indicate correspondence point value of the status predication point after measurement equation is propagated, Rk-1It indicates that the k-1 moment measures to make an uproar
The covariance matrix that sound meets.
Further, in S5, cross-covariance matrix Pxz,kIt indicates are as follows:
Further, in S6, the filtering gain K at k momentkIt indicates are as follows:
Further, in S7, the measurement information value z at k momentk, to status predication valueIt is modified update, and calculates shape
State evaluated error covariance matrixIts calculation formula is:
Further, in S8, dynamic corrections update k moment system noise covariance matrix QkWith measurement noise covariance square
Battle array Rk, calculation formula is as follows:
dk-1=(1-b)/(1-bk) (16)
In formula, b indicates forgetting factor, dk-1For k-1 moment system noise covariance matrix estimator adjustment parameter, diag
() is building diagonal matrix symbol, and exp is indicated using natural constant as the exponential function at bottom.
The utility model has the advantages that a kind of meter of the invention and the unknown dynamic state estimator method of noise statistics, in traditional nothing
Under the frame of mark Kalman filtering algorithm, the system noise based on innovative information sequence is established respectively and measures noise statistics
Estimator, the covariance matrix that can meet according to the adjustment of environmental change dynamic and update the system noise and measurement noise, overcomes
Traditional UKF method because noise matrix setting it is improper caused by state estimation degradation problem, promote dynamic state estimator device
Precision of state estimation.The algorithm has fully considered the actual application background of generator dynamic state estimator, and simple and convenient is easy to
Implement, engineering application value with higher.
Detailed description of the invention
Fig. 1 is flow chart of the method for the present invention；
Fig. 2 is 39 node system structure chart of IEEE10 machine；
Fig. 3 is to utilize tradition UKF method and the method for the present invention to the dynamic estimation result pair of generator's power and angle and angular speed
Than；
Fig. 4 is to utilize tradition UKF method and the method for the present invention to the dynamic estimation Comparative result of generator transient internal voltage；
Fig. 5 is to be compared using tradition UKF method and the method for the present invention to Generator Status estimated result error.
Specific embodiment
The present invention is further explained with reference to the accompanying drawings and examples.
As shown in Figure 1, estimating with the method for the present invention embodiment test macro dynamic variable, including walk as follows
It is rapid:
Step 1: Generator Status estimates model foundation:
The state equation and measurement equation of generator dynamic state estimator, general type can indicate are as follows:
In formula, f () indicates that Generator Status equation, h () indicate that measurement equation, x, u, z respectively correspond expression state
Variable controls variable and measures vector；Subscript k-1 and k indicate the moment, and w indicates system noise, and v is to measure noise, both for
White Gaussian noise, the mean value met are 0, and corresponding covariance matrix is respectively Q and R, w and v is mutually indepedent and and state
Variable is unrelated.
Step 2: the initial parameter value of adaptive Unscented kalman filtering method designed by the setting present invention includes setting
Initial time state variable valueState estimation error co-variance matrixControl variable value u0It is taken as steady-state operation value, scale
Parameter κ；The initial covariance matrix Q that setting system noise and measurement noise are met0, R0And maximum estimated moment N；
Step 3: based on state estimation known to the k-1 momentK moment 2n+1 are generated using Unscented transform technology
Sigma state samplesWherein n indicates Generator Status predictor dimension, and calculation formula is as follows:
In formula,For state estimation error co-variance matrix known to the k-1 moment,It indicates to carry out matrix
Cholesky decomposition operation, κ ∈ [10-4, 1] and indicate scale parameter.
Step 4: it is walked using the status predication of adaptive Unscented kalman filtering, calculates the status predication value at k momentWith
Status predication error co-variance matrixSolution formula is as follows
In formula,Indicate Sigma state samplesCorrespondence point value after the propagation of Generator Status equation, subscript T table
Show the transposition operation of matrix, Qk-1Indicate the covariance matrix that k-1 moment system noise meets, WlTo be adopted corresponding to Sigma state
The weighted value of sampling point, calculation formula are as follows
Step 5: function is measured based on generator, calculates k moment generator measurement predictorIt is assisted with prediction error is measured
Variance matrixCalculation formula is
In formula,Indicate correspondence point value of the status predication point after measurement equation is propagated, Rk-1Indicate that the k-1 moment measures mistake
Poor covariance matrix.
Step 6: calculating status predication and measures the cross-covariance matrix P between predictionxz,k, calculation formula is
Step 7: based on designed adaptive Unscented kalman filtering filtering step, the filtering gain K at k moment is calculatedk, meter
Calculating formula is
Subscript () in formula-1The inversion operation of representing matrix.
Step 8: the measurement information value z at k moment is utilizedk, to status predication valueIt is modified update, and calculates state and estimates
Count error co-variance matrixIts calculation formula is
The transposition operation of subscript T representing matrix in formula.
Step 9: it is based on innovative information valueDynamic corrections update k moment system noise covariance matrix QkAnd measurement
Noise covariance matrix Rk, calculation formula is as follows
dk-1=(1-b)/(1-bk) (16)
B indicates forgetting factor, and 0 < b < 1 in formula, and when the variation degree of system mode is bigger, the value of b is bigger；
dk-1For k-1 moment system noise covariance matrix estimator adjustment parameter, diag () is building diagonal matrix symbol, exp table
Show the exponential function using natural constant the bottom of as.
Step 10: it is dynamic to electric system generator state according to measurement information time series that step is calculated according to (2)-(9)
State estimation, until state estimation iteration stopping when k+1 > N, output state estimated result.
Embodiment:
(a) model foundation
According to generator quadravalence dynamical equation, the Generator Status estimation equation of building is as follows:
In formula: δ indicates generator's power and angle, rad；ω and ω0Respectively angular rate and synchronous rotational speed, pu；e′qWith e 'dPoint
Not Biao Shi generator q axis and d axis transient internal voltage；H indicates generator inertia constant, TmAnd TeRespectively indicate generator mechanical
Power and electromagnetic power, wherein Te=Pe/ω；KDIndicate damping factor, EfdFor stator excitation voltage；T′d0With T 'q0Indicate power generation
Open circuit time constant of the machine machine under d-q coordinate system；xdWith x 'dRespectively indicate generator d axis synchronous reactance and transient state reactance, xq
With x 'qRespectively generator q axis synchronous reactance and transient state reactance；idAnd iqRespectively indicate the stator current of generator d axis and q axis.
When carrying out dynamic estimation to electric system generator dynamic variable, state estimation vector is x=(δ, ω, e 'q,e′d)T；
Choose the electric current i of generator mechanical power, stator excitation voltage and stator R axis and I axisR,iIFor dominant vector, i.e. u=(Tm,
Efd,iR,iI)T；Choose the voltage e of the absolute generator rotor angle of generator, generator angular speed and generator unit stator R axis and I axisR,eIAs
Measuring value, i.e. measurement vector are
Z=(δ, ω, eR,eI)T
Wherein the absolute generator rotor angle of generator and angular speed can directly measure acquisition by PMU measurement equipment, be under this situation
System meets controllability.
(b) embodiment is analyzed
In order to verify meter and noise statistics proposed by the invention unknown dynamic state estimator method validity and reality
With property, the present embodiment chooses 39 node system of IEEE10 machine as test macro, and system structure is shown in Fig. 2.It is verified in algorithm
When, the state variable of the generator G9 using in system is as estimation object, and wherein generator uses quadravalence model.Generator G9's is used
Property time parameter be 34.5, damping factor 2, d axis and q axis open circuit transient time-constant be respectively 4.79 and 1.96.For simulation
Generator transient characteristic, it is assumed that in 20 cycle, three-phase metallic short circuit failure, failure occur for 21 branch of node 16- node
Continued for 6 periods (sampling period 0.02s) disappears afterwards.
With the simulation PMU data acquisition of BPA software, obtains generator and run true value.Metric data value is folded by true value
Random noise is added to be formed.500 cycles (1 cycle is 0.02s) measuring value carries out algorithm before the present invention takes when carrying out emulation experiment
Verifying, i.e. N are 500.The initial value of state variable chooses the quiescent value of last moment when estimation.It is assumed that system noise and measurement noise
Statistical property is unknown, i.e., its value is set as follows: system noise initially defences arranged in matrix jointly as Q0=10-5I4×4, measure noise
Initial covariance matrix is set as R0=10-4I4×4, and the true value of the two is respectively Q0=10-6I4×4And R0=10-6I4×4。
In order to compare and analyze to the estimated result between algorithms of different, the present invention uses average absolute evaluated error
MAE is as performance comparison between index progress algorithm.
MAE (k) is the average value of the sum of absolute error of each state variable estimated result of k moment generator, x in formulai,kFor
The true value (BPA data) of i-th of quantity of state of k moment,Estimated value, N are corresponded to for itsFor total state variable number.
Be utilized respectively traditional Unscented kalman filtering algorithm (UKF) (related parameter values and the method for the present invention needed for it
Initial parameter values are identical) and adaptive Unscented kalman filtering method (AUKF) proposed by the present invention tested.
The state estimation result of generator G9 is respectively such as Fig. 3, shown in Fig. 4.Fig. 5 further provides UKF and AUKF method shape
The mean absolute error of state estimated result compares.It can be seen that from the state estimation result in figure in initial system noise association side
In the case of poor matrix and measurement noise covariance matrix setting improperly, AUKF method designed by the present invention still can be accurate
Generator state variables are tracked, there is higher precision of state estimation compared with UKF.
State estimation result confirms the adaptive Unscented kalman filtering method that is mentioned of the present invention due to being capable of base in figure
In innovative information sequence dynamic corrections and more new system and noise covariance matrix is measured, is overcome because of system noise covariance matrix
Improper caused estimator performance decline is set, generator dynamic state estimator precision is effectively promoted.I.e. the method for the present invention can
The demand of electric system generator dynamic state estimator is better met, realizes the accurate measurements of Electrical Power System Dynamic state.
Claims (8)
1. a kind of dynamic state estimator method counted and noise statistics are unknown, estimates for electric system generator dynamical state
Meter, which comprises the steps of:
S1: according to generator quadravalence dynamical equation, Generator Status estimation equation is established, and constructs and obtains generator dynamical state
The state equation and measurement equation of estimation:
In formula, f () indicates that Generator Status equation, h () indicate that measurement equation, x, u, z respectively correspond expression state variable,
It controls variable and measures vector；Subscript k-1 and k indicate the moment, and w indicates system noise, and v is to measure noise, both for Gauss
White noise, the mean value met are 0, and corresponding covariance matrix is respectively Q and R, w and v is mutually indepedent and and state variable
It is unrelated；
S2: based on state estimation known to the k-1 momentSeveral Sigma states of k moment are generated using Unscented transform technology
Sampled point；
S3: it is walked using the status predication of adaptive Unscented kalman filtering, calculates the Generator Status predicted value at k momentAnd shape
State predicting covariance matrix
S4: being based on generator measurement equation, calculates the generator measurement predictor at k momentWith measurement predicting covariance square
Battle array
S5: the cross-covariance matrix P between status predication value and measurement predictor is calculatedxz,k；
S6: based on adaptive Unscented kalman filtering filtering step, the filtering gain at k moment is obtained；
S7: the measurement information value z at k moment is utilizedk, to status predication valueIt is modified update and obtains state estimation, calculate
To state estimation error co-variance matrix
S8: it is based on innovative information valueDynamic corrections update k moment system noise covariance matrix QkWith measurement noise association side
Poor matrix Rk；
S9: according to S2-S8 according to measurement information value zkTo electric system generator state dynamic estimation, until k+1 > N, N are most
State estimation iteration stopping when the big estimation moment, output state estimated result.
2. a kind of dynamic state estimator method counted and noise statistics are unknown according to claim 1, feature exist
In: 2n+1 Sigma state samples of k moment are generated in S2
In formula, n indicates Generator Status predictor dimension,For state estimation error covariance square known to the k-1 moment
Battle array,It indicates to carry out matrix Cholesky decomposition operation, κ indicates scale parameter.
3. a kind of dynamic state estimator method counted and noise statistics are unknown according to claim 2, feature exist
In: the Generator Status predicted value at the k moment in S3With status predication error co-variance matrixIt is expressed as follows:
In formula,Indicate Sigma state samplesCorrespondence point value after the propagation of Generator Status equation, Qk-1When indicating k-1
The covariance matrix that etching system noise meets, WlFor the weighted value corresponding to Sigma state samples:
4. a kind of dynamic state estimator method counted and noise statistics are unknown according to claim 3, feature exist
In: in S4, k moment generator measurement predictorWith measurement predicting covariance matrixIt indicates are as follows:
In formula,Indicate correspondence point value of the status predication point after measurement equation is propagated, Rk-1It is full to indicate that the k-1 moment measures noise
The covariance matrix of foot.
5. a kind of dynamic state estimator method counted and noise statistics are unknown according to claim 4, feature exist
In: in S5, cross-covariance matrix Pxz,kIt indicates are as follows:
6. a kind of dynamic state estimator method counted and noise statistics are unknown according to claim 5, feature exist
In: in S6, the filtering gain K at k momentkIt indicates are as follows:
7. a kind of dynamic state estimator method counted and noise statistics are unknown according to claim 6, feature exist
In: in S7, the measurement information value z at k momentk, to status predication valueIt is modified update, obtains state estimation, and calculate
State estimation error co-variance matrixIts calculation formula is:
8. a kind of dynamic state estimator method counted and noise statistics are unknown according to claim 7, feature exist
In: in S8, dynamic corrections update k moment system noise covariance matrix QkWith measurement noise covariance matrix Rk, calculation formula is such as
Under:
dk-1=(1-b)/(1-bk) (16)
In formula, b indicates forgetting factor, dk-1For k-1 moment system noise covariance matrix estimator adjustment parameter, diag ()
To construct diagonal matrix symbol, exp is indicated using natural constant as the exponential function at bottom.
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