CN110008638A - A kind of dynamic state estimator method based on adaptive EnKF technology - Google Patents
A kind of dynamic state estimator method based on adaptive EnKF technology Download PDFInfo
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Abstract
The invention discloses a kind of dynamic state estimator methods based on adaptive EnKF technology, for the dynamic state estimator under electric system generator unknown system noise operating condition.The present invention in EnKF by introducing the Sage-Husa noise statistics estimators device of improved fading memory exponent, it is capable of the mean value and variance of dynamic estimation correction time-varying system noise, inhibit influence of the unknown system noise to precision of state estimation, realizes the accurate estimation of operation state of generator.The present invention is because considering Practical Project background, and simple and convenient, engineering application value with higher.
Description
Technical field
It is the invention belongs to Power System Analysis and monitoring technical field, in particular to a kind of based on adaptive EnKF technology
Dynamic state estimator method.
Background technique
State estimation is also referred to as filtering, and data precision is improved using the redundancy of real-time measurement system, removal
Random noise in measuring value realizes POWER SYSTEM STATE accurate measurements.In general, Power system state estimation can be divided into
The estimation of two classes, i.e. static state and dynamic state estimator.Wherein, static state estimation is applied more mature at present, can be obtained
Status information when systematic steady state is run.But static state estimation has ignored the dynamic characteristic of system, cannot achieve system
State on_line monitoring.For the defect for making up static state estimation, dynamic state estimator device comes into being, and passes through model and measurement
Amount carries out once-through operation, obtains state estimation and predicted value；Since dynamic state estimator can be to the shape of system subsequent time
State amount is predicted, and is not required to iteration, compared with static state estimation advantageously.
Currently, Electrical Power System Dynamic state estimation mainly based on EKF and its improved method, is such as included in non-linear Kalman
Filtering, adaptive prediction dynamic state estimator, smooth increasing plane fuzzy control dynamic state estimator etc..These above-mentioned methods are one
Determine the result that state estimation is improved in degree.However, it is worth noting that these methods assume that the variance of system noise is
Constant；And in practical power systems, the statistical property of system noise is difficult accurately to obtain and is dynamic change.So false
Determining system noise covariance matrix is constant, and the system noise covariance matrix value and true value that will cause setting mismatch, from
And dynamic state estimator is seriously affected as a result, reducing precision of state estimation.
Summary of the invention
Goal of the invention: in order to overcome the deficiencies in the prior art, the present invention provides a kind of based on adaptive EnKF skill
The dynamic state estimator method of art can reduce influence of the unknown system noise to dynamic state estimator, overcome traditional filtering side
Deficiency existing for method promotes generator dynamic state estimator precision, provides solid data letter for the safe and stable operation of power grid
Breath.
Technical solution: to achieve the above object, the present invention provides a kind of dynamical state based on adaptive EnKF technology and estimates
Meter method, which comprises the steps of:
(1) dynamic state estimator model is established；
(2) initialization filtering initial value is carried out with adaptive EnKF technology；
(3) k moment measuring value z is obtainedk；
(4) the status predication value at k moment is calculatedWith measurement predictor
(5) the measurement predicting covariance at k moment is calculatedWith quantity of state test cross Cross-covariance
(6) the filtering gain K at k moment is calculatedkAnd state estimation
(7) the system noise covariance matrix Q at k moment is calculatedk；
(8) according to step (3) to (7) foundation time series to electric system generator state dynamic estimation, until k+1 >
State estimation iteration stopping when N, output state estimated result, otherwise return step (3) continues to calculate.
Further, dynamic state estimator is established in the step (1) specific step is as follows:
The state equation and measurement equation of generator dynamic state estimator, general type can indicate are as follows:
F () indicates that Generator Status equation, h () indicate that measurement equation, x, u, z respectively correspond the change of expression state in formula
Amount controls variable and measures vector；Subscript k and k+1 indicate the moment, and w indicates system noise, and v is to measure noise, it is assumed that the two point
Do not meet w~N (0, Q), the Gaussian Profile of v~N (0, R), wherein Q and R respectively indicates system noise and measures what noise met
Covariance matrix, w are mutually indepedent and unrelated with state variable with v.
Further, the specific step of initialization filtering initial value is carried out in the step (2) with adaptive EnKF technology
It is rapid as follows:
Setting carries out the initial value of state estimation with adaptive EnKF technology, includes state estimation initial valueWherein m indicates total number of samples；System noise and the covariance matrix initial value for measuring noise satisfaction
Q0And R0, noise estimator forgetting factor parameter b and maximum estimated moment N.
Further, the status predication value at k moment is calculated in the step (4)With measurement predictorSpecific steps
It is as follows:
It predicts to walk with adaptive EnKF, calculates k moment status predication valueWith measurement predictorCalculation formula is as follows
Subscript i is ith sample value in formula, and subscript k and k-1 indicate the moment；WithRespectively indicate status predication value and
The sampling of estimated value；It is according to k-1 moment system noise covariance matrix Qk-1The noise figure of generation samples,Expression amount
Survey the sampling of predicted value.
Further, the measurement predicting covariance at k moment is calculated in the step (5)It is mutual with quantity of state test cross
Covariance matrixSpecific step is as follows:
Calculation formula difference is as follows
The transposition operation of subscript T representing matrix in formula.
Further, the filtering gain K at k moment is calculated in the step (6)kAnd state estimationSpecific steps such as
Under:
According to k moment measurement information zk, update and walk according to adaptive EnKF, calculate the filtering gain K at k momentkEstimate with state
EvaluationSpecific formula for calculation is as follows
Subscript () in formula-1The inversion operation of representing matrix,It is to measure noise covariance matrix R according to the k momentkIt generates
Noise figure sampling,Indicate the sampling of state estimation.
Further, the system noise covariance matrix Q at k moment is calculated in the step (7)kSpecific step is as follows:
Using fading memory exponent Sage-Husa noise covariance estimator, dynamic corrections update k moment system noise
Sound covariance matrix Qk, the form of system noise covariance estimator is as follows
dk-1=(1-b)/(1-bk)
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.
The utility model has the advantages that compared with the prior art, the present invention has the following advantages:
The present invention in EnKF by introducing the Sage-Husa noise statistics estimators of improved fading memory exponent
Device is capable of the mean value and variance of dynamic estimation correction time-varying system noise, inhibits unknown system noise to precision of state estimation
It influences, realizes the accurate estimation of operation state of generator.The present invention can reduce unknown system noise to dynamic state estimator
It influences, overcomes deficiency existing for traditional filtering method.
Detailed description of the invention
Fig. 1 is flow chart of the method for the present invention；
Fig. 2 is 10 machine of IEEE, 39 node system structure chart in specific embodiment；
Fig. 3 is estimated using EnKF methodology and the method for the present invention to the dynamic of generator's power and angle and angular speed in specific embodiment
Count comparative result figure；
Fig. 4 is to utilize EnKF methodology and the method for the present invention to the dynamic estimation of generator transient internal voltage in specific embodiment
Comparative result figure.
Specific embodiment
The present invention will be further explained with reference to the accompanying drawing.
As shown in Figure 1, estimating with the method for the present invention embodiment test macro dynamic variable, it includes following steps
It is rapid:
(1) dynamic state estimator model foundation
The state equation and measurement equation of generator dynamic state estimator, general type can indicate are as follows:
F () indicates that Generator Status equation, h () indicate that measurement equation, x, u, z respectively correspond the change of expression state in formula
Amount controls variable and measures vector；Subscript k and k+1 indicate the moment, and w indicates system noise, and v is to measure noise, generally assume that two
Person meets w~N (0, Q) respectively, the Gaussian Profile of v~N (0, R), and wherein Q and R respectively indicates system noise and measures noise and expires
The covariance matrix of foot, w are mutually indepedent and unrelated with state variable with v.
(2) setting carries out the initial value of state estimation with adaptive EnKF technology, includes state estimation initial valueWherein m indicates total number of samples, system noise and the covariance matrix initial value for measuring noise satisfaction
Q0And R0, noise estimator forgetting factor parameter b and maximum estimated moment N；
(3) k moment measuring value z is obtainedk；
(4) with adaptive EnKF prediction step, k moment status predication value is calculatedWith measurement predictorCalculation formula
It is as follows
Subscript i is ith sample value in formula, and subscript k and k-1 indicate the moment；WithRespectively indicate status predication value
With the sampling of estimated value；It is according to k-1 moment system noise covariance matrix Qk-1The noise figure of generation samples,It indicates
The sampling of measurement predictor.
(5) the measurement predicting covariance at k moment is calculatedWith quantity of state test cross Cross-covarianceIt calculates public
Formula difference is as follows
The transposition operation of subscript T representing matrix in formula.
(6) according to k moment measurement information zk, update and walk according to adaptive EnKF, calculate the filtering gain K at k momentkAnd shape
State estimated valueSpecific formula for calculation is as follows
Subscript () in formula-1The inversion operation of representing matrix,It is to measure noise covariance matrix R according to the k momentkIt generates
Noise figure sampling,Indicate the sampling of state estimation.
(7) using fading memory exponent Sage-Husa noise covariance estimator, the dynamic corrections update k moment is
Unite noise covariance matrix Qk, the form of noise covariance estimator is as follows
dk-1=(1-b)/(1-bk)
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.
(8) step is calculated according to time series to electric system generator state dynamic estimation, until k+ according to (2)-(7)
State estimation iteration stopping when 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'qAnd 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；xdAnd x'dRespectively indicate generator d axis synchronous reactance and transient state reactance, xq
And 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 the validity and reality of the dynamic state estimator method proposed by the invention based on adaptive EnKF technology
With property, the present embodiment chooses 10 machine of IEEE, 39 node system as test macro, and system structure is shown in Fig. 2.It is verified in algorithm
When, the state variable of the generator G2 using in system takes into account the effect of governor as estimation object, wherein generator
Using quadravalence model.Generator inertia time parameter is 30.3, damping factor 2, and assumes the node 16- in 20 cycle
Three-phase metallic short circuit failure occurs for 21 branch of node, and failure continued for 6 periods (sampling period 0.02s) and 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.450 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 450, m=20.The initial value of state variable chooses the quiescent value of last moment, the initial association of system noise when estimation
Anti- arranged in matrix is Q0=10-6I4×4, the initial covariance matrix for measuring noise is set as R0=10-6I4×4。
To above-described embodiment system, the EnKF algorithm (ginseng of related parameter values and the method for the present invention needed for it is used respectively
Number initial values it is identical) and adaptive EnKF methodology proposed by the present invention tested.
Two kinds of distinct methods are as shown in Figure 3 and Figure 4 to the state variable dynamic estimation result of generator G2, can obviously see
Out the method that is mentioned of the present invention due to can dynamic corrections adjustment system noise covariance matrix, inhibit system noise covariance square
Influence of the battle array dynamic change to state estimation, can more accurately track the dynamical state variation of generator, and estimated accuracy is remote
Higher than EnKF methodology, it can be seen that the mentioned method of the present invention has better applicability.
Claims (7)
1. a kind of dynamic state estimator method based on adaptive EnKF technology, which comprises the steps of:
(1) dynamic state estimator model is established；
(2) initialization filtering initial value is carried out with adaptive EnKF technology；
(3) k moment measuring value z is obtainedk；
(4) the status predication value at k moment is calculatedWith measurement predictor
(5) the measurement predicting covariance at k moment is calculatedWith quantity of state test cross Cross-covariance
(6) the filtering gain K at k moment is calculatedkAnd state estimation
(7) the system noise covariance matrix Q at k moment is calculatedk；
(8) according to step (3) to (7) foundation time series to electric system generator state dynamic estimation, until when k+1 > N
State estimation iteration stopping, output state estimated result, otherwise return step (3) continues to calculate.
2. a kind of dynamic state estimator method based on adaptive EnKF technology according to claim 1, which is characterized in that
Establishing dynamic state estimator in the step (1), specific step is as follows:
The state equation and measurement equation of generator dynamic state estimator, general type can indicate are as follows:
F () indicates that Generator Status equation, h () indicate that measurement equation, x, u, z respectively correspond expression state variable in formula,
It controls variable and measures vector；Subscript k and k+1 indicate the moment, and w indicates system noise, and v is to measure noise, it is assumed that the two difference
Meet w~N (0, Q), the Gaussian Profile of v~N (0, R), wherein Q and R respectively indicates system noise and measures the association that noise meets
Variance matrix, w are mutually indepedent and unrelated with state variable with v.
3. a kind of dynamic state estimator method based on adaptive EnKF technology according to claim 1, which is characterized in that
Initialization is carried out with adaptive EnKF technology in the step (2) to filter initial value specific step is as follows:
Setting carries out the initial value of state estimation with adaptive EnKF technology, includes state estimation initial valueWherein m indicates total number of samples；System noise and the covariance matrix initial value for measuring noise satisfaction
Q0And R0, noise estimator forgetting factor parameter b and maximum estimated moment N.
4. a kind of dynamic state estimator method based on adaptive EnKF technology according to claim 1, which is characterized in that
The status predication value at k moment is calculated in the step (4)With measurement predictorSpecific step is as follows:
It predicts to walk with adaptive EnKF, calculates k moment status predication valueWith measurement predictorCalculation formula is as follows
Subscript i is ith sample value in formula, and subscript k and k-1 indicate the moment；WithRespectively indicate status predication value and estimation
The sampling of value；It is according to k-1 moment system noise covariance matrix Qk-1The noise figure of generation samples,It indicates to measure pre-
The sampling of measured value.
5. a kind of dynamic state estimator method based on adaptive EnKF technology according to claim 1, which is characterized in that
The measurement predicting covariance at k moment is calculated in the step (5)With quantity of state test cross Cross-covarianceTool
Steps are as follows for body:
Calculation formula difference is as follows
The transposition operation of subscript T representing matrix in formula.
6. a kind of dynamic state estimator method based on adaptive EnKF technology according to claim 1, which is characterized in that
The filtering gain K at k moment is calculated in the step (6)kAnd state estimationSpecific step is as follows:
According to k moment measurement information zk, update and walk according to adaptive EnKF, calculate the filtering gain K at k momentkAnd state estimationSpecific formula for calculation is as follows
Subscript () in formula-1The inversion operation of representing matrix,It is to measure noise covariance matrix R according to the k momentkWhat is generated makes an uproar
The sampling of sound value,Indicate the sampling of state estimation.
7. a kind of dynamic state estimator method based on adaptive EnKF technology according to claim 1, which is characterized in that
The system noise covariance matrix Q at k moment is calculated in the step (7)kSpecific step is as follows:
Using fading memory exponent Sage-Husa noise covariance estimator, dynamic corrections update k moment system noise association
Variance matrix Qk, the form of system noise covariance estimator is as follows
dk-1=(1-b)/(1-bk)
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.
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