CN107565553A - A kind of power distribution network robust dynamic state estimator method based on UKF - Google Patents
A kind of power distribution network robust dynamic state estimator method based on UKF Download PDFInfo
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Abstract
The invention discloses a kind of power distribution network robust dynamic state estimator method based on UKF, index weight function is incorporated into Unscented kalman filtering dynamic state estimator by this method, in the case where system loading mutation causes error in measurement to increase, the dynamic corrections to measuring weight, and then smooth adjustment Kalman filtering gain are realized according to measurement residuals；Simultaneously because the index weight function being introduced into is used in least square method, in order that it is easy to implement in Unscented kalman filtering, specific improved method is given；By using method disclosed by the invention, based under SCADA/PMU Mixed measurements systems, when rough error or system loading mutation be present for measurement, it can effectively strengthen the robustness of algorithm, lift the filtering performance of UKF algorithms, improve precision of state estimation.
Description
Technical field
The present invention relates to a kind of state estimation, and in particular to a kind of power distribution network robust dynamic state estimator side based on UKF
Method.
Background technology
As American-European countries carries out the construction to intelligent grid, China is correspondingly according to the national conditions of oneself, respectively with extra-high
The power transmission network for backbone, the high power distribution network of structure automaticity are pressed as constructive direction.To distribution network automated research and
Development, intelligent power distribution network construction progress is affected, studying high accuracy, dynamic state estimator is outstanding for distribution management system in real time
Its is important.
The electric automobile access power distribution network of a large amount of distributed power sources and part throttle characteristics change greatly, makes the dynamic of distribution more
By force.Grid requirements Distribution Management System improves monitoring and control ability, for this reason, it may be necessary to which state estimation offer is reliable in real time complete
System operation data.The features such as power distribution network three-phase imbalance, the largely presence of short branch road and measure configuration are less, make transmitting electricity
The ripe state estimation algorithm of net application can not be applied in power distribution network, and such as PQ decoupling methods, therefore research is applied to state of electric distribution network
The algorithm of estimation.
Two classes, a kind of static state estimation based on least square method are broadly divided into state of electric distribution network Estimation Study at present
Algorithm, state estimation is carried out with the metric data of discontinuity surface at one, what is often used has based on node voltage, branch current, branch
Road power makes system measurements information and measures the minimum convergence principle of estimate error, it is desirable to measure strict as state variable
Obedience is just distributed very much, and condition is harsh.State model is solved with Newton iteration method.
It is another kind of, it is the dynamic state estimator algorithm based on Kalman filtering, considers multiple measuring time value sections
Metric data carries out state estimation, and good wave filtering effect, calculating speed is fast, and can also predict the system mode of subsequent time.
, can be with one-step prediction, the pseudo- measurement of replenishment system based on two-parameter exponential exponential smoothing in the case that power distribution network measurement is less.
Unscented kalman filtering (Unscented Kalman Filter, UKF) is using linear Kalman filter theory as frame
Frame, sampling Unscented transform technology to nonlinear function linear process, degree of approximation reach quadravalence and more than, applicability is good.And
The algorithm uses sigma point samplings, and without calculating Jacobian matrix, the linearisation for reducing expanded Kalman filtration algorithm misses
Difference, but when having rough error or sudden load change there is also measurement, filtering performance declines, it is also possible to the shortcomings of dissipating.
The content of the invention
Insufficient existing for above-mentioned UKF algorithms in order to solve, the invention provides a kind of power distribution network robust dynamic based on UKF
Method for estimating state, using power distribution network three-phase voltage amplitude and phase angle as state variable, calculated by the symmetric proportional method of sampling
Sigma points and its weights, then carry out parameter identification using two-parameter exponential exponential smoothing and carry out one-step prediction, by measurement side
The quantity of state of Cheng Liyong predictions is asked for measuring prediction, the new breath matrix formed to real-time measurement and measurement predictor, using being carried
The index weight function dynamic corrections gone out, the weight of bad data is adjusted in time, asks for Kalman filtering gain, final updating state
Variable and covariance.Test result indicates that when systems are functioning properly, calculated based on index weight function UKF algorithms and traditional UKF
Method filter effect and time phase difference are little；Be mutated in system loading or when rough error be present, the great decline of UKF algorithm filter effects and
There is the trend of diverging, and index weight function UKF rules do not suffer from this, estimated accuracy is higher, demonstrates the robust of innovatory algorithm
Property and numerical stability.
In order to realize foregoing invention purpose, the present invention takes following technical scheme：
A kind of power distribution network robust dynamic state estimator method based on UKF is provided, the described method comprises the following steps：
Step (1) inputs power distribution network three-phase network parameter, including branch parameters, transformer parameter, load parameter, calculates system
Unite bus admittance matrix Y.
Step (2) is in K=0 moment, the average and covariance of init state variable node voltage.
Step (3) carries out sigma point samplings and corresponding to calculating sampled point according to the state estimation and covariance at K moment
Weights.
Step (4) carries out parameter identification using Holt's two-parameter exponentials exponential smoothing, and it is pre- at the K moment to obtain state variable
Simultaneously measurement predictor is calculated using measurement equation in measured value.
Step (5) by K moment measurement predictor computing systems covariance and cross covariance.
Step (6) is smooth to him according to new breath matrix utilization index weight function, the measurement power of dynamic corrections K moment measuring values
Weight, the error in measurement that upgrades in time covariance matrix.
Step (7) calculates the state and covariance of Kalman filtering gain and more new system.
Step (8) judges whether systematic sampling terminates, if terminating, performs step (7), if not terminating, returns and performs step
(2)。
Step (9) exports the state variable estimate at K+1 moment.
The step (1) is analyzed power distribution network ornamental, generates the bus admittance matrix Y of system.
The average of step (2) the state of electric distribution network variableAnd covarianceAs the initial value of UKF algorithms, wherein p
=abc.
For the step (3) when carrying out sigma point samplings, method mainly has single file sampling, spherical sampling, symmetric proportional to adopt
Sample.Sample mode influences the computational efficiency and numerical stability of state estimation algorithm.Single file sample rate is most fast, numerical stability
Worst, all weight coefficients of spherical sampling are all identical then can be high by state initial value affecting, ratio symmetric sampling method approximation quality.
For the distribution system of n dimensions, using the symmetric proportional method of sampling, 2n+1 sigma point and corresponding weights are calculated；Selection pair
Claim sampling method that there is preferable numerical stability, 2n+1 sigma sampling point set and corresponding weights are obtained by Unscented transform：
Parameter lambda=α2(n+ κ)-n is used for reducing the scale factor of total prediction error, and parameter alpha controls point of sampled point
Cloth state, span [0.0001,1], κ are to ensure that matrix (n+ λ) P is positive semidefinite free parameter, and β >=0 can be higher order term
The weight coefficient that is included of influence, ensure that approximation quality.Formula (3)
In, P is quantity of state covariance matrix,I-th row of representing matrix root.
Calculate the corresponding weights of these sampled points
WmRepresent the weights of quantity of state, WcRepresent the weights of covariance.
The step (4) is identified using two-parameter exponential smoothing parameter method, carries out status predication, calculating speed is fast, precision
In the reasonable scope.
The step (5) asks for the predicted value and prediction covariance of state variable by weighting：
Wherein, Q is service system noise covariance matrix.
The step (6) obtains average and the association side of system by the measurement predictor of sigma point sets by weighted sum
Difference, cross covariance：
The step (7)：In power distribution network metric data, it is understood that there may be rough error, system loading mutation cause metric data
Change is big, introduces exponential weight function pair and newly ceases matrix dynamic corrections, change it is corresponding measure weight, smooth rough error or measure change
Influence to filtering, is implemented as follows：
In order to improve the smooth effect in UKF, modification weight function is negative exponent form：
R'k=Rkexp(-|yk-h(xk)|)
The step (8)：According to the measurement weight calculation measurement variance matrix of amendment, and calculate Kalman filtering gain
The state and covariance of more new system：
Wherein K is Kalman filtering gain matrix.
Compared with prior art, the beneficial effects of the present invention are：
1. this method is realized easily in original algorithm, when rough error be present for system loading mutation, measurement, filter effect
Good, robustness is strong, improves precision of state estimation.
2. numerical stability is strong, good in convergence effect, can effectively solve three-phase imbalance state of electric distribution network estimation problem.
Brief description of the drawings
Fig. 1 is a kind of power distribution network robust dynamic state estimator method flow diagram based on UKF of the present invention；
State estimation when Fig. 2 is system normal operation, inventive algorithm and traditional UKF algorithm comparison results；
Fig. 3 is state estimation comparative result when system loading is mutated.
Embodiment
The invention will be further described with reference to the accompanying drawings and examples, but not as any limitation of the invention.
The implementation steps of the present invention are as follows：
Step (1)：Network connection, branch parameters and the metric data given according to power distribution network, wherein network connection are such as
Accompanying drawing 1, branch parameters are shown in Table one, the ornamental and calculate node admittance matrix of analysis system.
Step (2)：At the sampling K=0 moment, the average and covariance of init state variable node voltage.
Step (3) carries out sigma point samplings and power corresponding to calculating sampled point according to K state estimation and covariance
Value.
Step (4) carries out parameter identification using Holt's two-parameter exponentials exponential smoothing, and it is pre- at the K moment to obtain state variable
Simultaneously measurement predictor is calculated using measurement equation in measured value.
Step (5) by K moment measurement predictor computing systems covariance and cross covariance.
Step (6) is smooth to him according to new breath matrix utilization index weight function, the measurement power of dynamic corrections K moment measuring values
Weight, the error in measurement that upgrades in time covariance matrix.
Step (7) calculates the state and covariance of Kalman filtering gain and more new system.
Step (8) judges whether systematic sampling terminates, if terminating, performs step (7), if not terminating, returns and performs step
(2)。
Step (9) exports the state variable estimate at K+1 moment.
The step (1) is analyzed power distribution network ornamental, generates the bus admittance matrix Y of system.
The average of step (2) the state of electric distribution network variableAnd covarianceAs the initial value of UKF algorithms, wherein p
=abc.
For the step (3) when carrying out sigma point samplings, method mainly has single file sampling, spherical sampling, symmetric proportional to adopt
Sample.Sample mode influences the computational efficiency and numerical stability of state estimation algorithm.Single file sample rate is most fast, numerical stability
Worst, all weight coefficients of spherical sampling are all identical then can be high by state initial value affecting, ratio symmetric sampling method approximation quality.
For the distribution system of n dimensions, using the symmetric proportional method of sampling, 2n+1 sigma point and corresponding weights are calculated；Selection pair
Claim sampling method that there is preferable numerical stability, 2n+1 sigma sampling point set and corresponding weights are obtained by Unscented transform：
Parameter setting：α=0.001, κ=0, β=2.
WmRepresent the weights of quantity of state, WcRepresent the weights of covariance.
The step (4) is identified using two-parameter exponential smoothing parameter method, carries out status predication, calculating speed is fast, precision
In the reasonable scope.
Parameter is arranged to：αH=0.85, βH=0.05
The step (5) asks for the predicted value and prediction covariance of state variable by weighting：
The step (6) obtains average and the association side of system by the measurement predictor of sigma point sets by weighted sum
Difference, cross covariance：
The step (7)：In power distribution network metric data, it is understood that there may be rough error, system loading mutation cause metric data
Change is big, introduces exponential weight function pair and newly ceases matrix dynamic corrections, change it is corresponding measure weight, smooth rough error or measure change
Influence to filtering, is implemented as follows：
In order to improve the smooth effect in UKF, modification weight function is negative exponent form：
R'k=Rk exp(-|yk-h(xk)|)
The step (8)：According to the measurement weight calculation measurement variance matrix of amendment, and calculate Kalman filtering gain
The state and covariance of more new system：
Wherein K is Kalman filtering gain matrix.
With the present invention method to IEEE33 nodes carry out Computer Simulation, define filtering absolute error average value and
Maximum：
Wherein Nbus is system node number, and k is sampling instant, and subscript e and t represent the estimate of quantity of state and true respectively
Value.
The present invention of table 1 and UKF the algorithms phase angle of comparison node voltage and absolute error of amplitude in system normal operation
Average value and maximum.
The present invention of table 2 and UKF the algorithms phase angle of comparison node voltage and absolute error of amplitude when system loading is mutated
Average value and maximum.
As it can be seen from table 1 in distribution network system normal operation, algorithm of the invention and UKF algorithm states estimation essence
Spend it is close, slightly better than UKF algorithms；From table 2 it can be seen that when system loading is mutated, inventive algorithm has higher filtering
Performance, and better numerical value stability.
Certainly, the above is the concrete application example of the present invention, and the present invention also has other embodiments, all using equivalent
The technical scheme that replacement or equivalent transformation are formed, all falls within protection domain of the presently claimed invention.
Claims (9)
- A kind of 1. power distribution network robust dynamic state estimator method based on UKF, it is characterised in that comprise the following steps：(1) power distribution network three-phase network parameter is inputted, including branch parameters, transformer parameter, load parameter, computing system node are led Receive matrix；(2) in K=0 moment, the average and covariance of init state variable node voltage；(3) sigma point samplings are carried out according to the state estimation at K moment and covariance and calculates the corresponding weights of sigma points；(4) parameter identification is carried out using Holt's two-parameter exponentials exponential smoothing, obtains predicted value and profit of the state variable at the K moment Measurement predictor is calculated with measurement equation；(5) by the covariance and cross covariance of K moment measurement predictor computing systems；(6) utilization index weight function is smooth to residual error, the measurement weight of dynamic corrections K moment measuring values, and the measurement that upgrades in time misses Poor covariance matrix；(7) state and covariance of Kalman filtering gain and more new system are calculated；(8) judge whether systematic sampling terminates, if terminating, perform step (9), if not terminating, return and perform step (2)；(9) state variable estimate at K+1 moment is exported.
- 2. the power distribution network robust dynamic state estimator method according to claim 1 based on UKF, it is characterised in that：Step (1) in, power distribution network ornamental is analyzed, generates the bus admittance matrix of system.
- 3. the power distribution network robust dynamic state estimator method according to claim 1 based on UKF, it is characterised in that：Initially Change the average of state of electric distribution network variableAnd covarianceInitial value as UKF algorithms；Computational methods are as follows：<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <msubsup> <mover> <mi>x</mi> <mo>&OverBar;</mo> </mover> <mn>0</mn> <mi>p</mi> </msubsup> <mo>=</mo> <mi>E</mi> <mo>&lsqb;</mo> <msubsup> <mi>x</mi> <mn>0</mn> <mi>p</mi> </msubsup> <mo>&rsqb;</mo> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>P</mi> <mn>0</mn> <mi>p</mi> </msubsup> <mo>=</mo> <mi>E</mi> <mo>&lsqb;</mo> <mo>(</mo> <msubsup> <mover> <mi>x</mi> <mo>&OverBar;</mo> </mover> <mn>0</mn> <mi>P</mi> </msubsup> <mo>-</mo> <msubsup> <mi>x</mi> <mn>0</mn> <mi>p</mi> </msubsup> <mo>)</mo> <msup> <mrow> <mo>(</mo> <mrow> <msubsup> <mover> <mi>x</mi> <mo>&OverBar;</mo> </mover> <mn>0</mn> <mi>P</mi> </msubsup> <mo>-</mo> <msubsup> <mi>x</mi> <mn>0</mn> <mi>p</mi> </msubsup> </mrow> <mo>)</mo> </mrow> <mi>T</mi> </msup> <mo>&rsqb;</mo> </mtd> </mtr> </mtable> </mfenced>Wherein p=abc represents three-phase.
- 4. the power distribution network robust dynamic state estimator method according to claim 1 based on UKF, it is characterised in that：Entering During row sigma point samplings, method includes single file sampling, spherical sampling, symmetric proportional sampling；For the distribution system of n dimensions, using the symmetric proportional method of sampling, 2n+1 sigma point and corresponding weights are calculated：<mrow> <msubsup> <mi>&chi;</mi> <mi>i</mi> <mi>p</mi> </msubsup> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <msup> <mover> <mi>x</mi> <mo>&OverBar;</mo> </mover> <mi>p</mi> </msup> <mo>,</mo> <mi>i</mi> <mo>=</mo> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <msup> <mover> <mi>x</mi> <mo>&OverBar;</mo> </mover> <mi>p</mi> </msup> <mo>+</mo> <msub> <mrow> <mo>&lsqb;</mo> <msqrt> <mrow> <mo>(</mo> <mi>n</mi> <mo>+</mo> <mi>&lambda;</mi> <mo>)</mo> <msub> <mi>P</mi> <mi>x</mi> </msub> </mrow> </msqrt> <mo>&rsqb;</mo> </mrow> <mi>i</mi> </msub> <mo>,</mo> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mo>...</mo> <mo>,</mo> <mi>n</mi> </mtd> </mtr> <mtr> <mtd> <msup> <mover> <mi>x</mi> <mo>&OverBar;</mo> </mover> <mi>p</mi> </msup> <mo>-</mo> <msub> <mrow> <mo>&lsqb;</mo> <msqrt> <mrow> <mo>(</mo> <mi>n</mi> <mo>+</mo> <mi>&lambda;</mi> <mo>)</mo> <msub> <mi>P</mi> <mi>x</mi> </msub> </mrow> </msqrt> <mo>&rsqb;</mo> </mrow> <mi>i</mi> </msub> <mo>,</mo> <mi>i</mi> <mo>=</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo>,</mo> <mo>...</mo> <mo>,</mo> <mn>2</mn> <mi>n</mi> </mtd> </mtr> </mtable> </mfenced> </mrow>Parameter lambda=α2(n+ κ)-n is used for reducing the scale factor of total prediction error, and parameter alpha controls the distribution shape of sampled point State, span [0.0001,1], κ are to ensure that matrix (n+ λ) P is positive semidefinite free parameter, and β >=0 can be the shadow of higher order term The weight coefficient being included is rung, ensure that approximation quality；I-th row of representing matrix root；Calculate the corresponding weights of these sampled points：<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <msubsup> <mi>W</mi> <mn>0</mn> <mi>c</mi> </msubsup> <mo>=</mo> <mi>&lambda;</mi> <mo>/</mo> <mi>n</mi> <mo>+</mo> <mi>&lambda;</mi> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>W</mi> <mn>0</mn> <mi>m</mi> </msubsup> <mo>=</mo> <mi>&lambda;</mi> <mo>/</mo> <mi>n</mi> <mo>+</mo> <mi>&lambda;</mi> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>W</mi> <mi>i</mi> <mi>m</mi> </msubsup> <mo>=</mo> <msubsup> <mi>W</mi> <mi>i</mi> <mi>c</mi> </msubsup> <mo>=</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> <mo>(</mo> <mi>n</mi> <mo>+</mo> <mi>&lambda;</mi> <mo>)</mo> <mo>,</mo> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mo>...</mo> <mo>,</mo> <mn>2</mn> <mi>n</mi> </mtd> </mtr> </mtable> </mfenced>WmRepresent the weights of quantity of state, WcRepresent the weights of covariance.
- 5. the power distribution network robust dynamic state estimator method according to claim 1 based on UKF, it is characterised in that：Utilize Two-parameter exponential smoothing parameter method identifies, carries out status predication, calculating speed is fast, and precision is in the reasonable scope；<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msubsup> <mi>x</mi> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>p</mi> </msubsup> <mo>=</mo> <msub> <mi>s</mi> <mi>k</mi> </msub> <mo>+</mo> <msub> <mi>b</mi> <mi>k</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>s</mi> <mi>k</mi> </msub> <mo>=</mo> <msub> <mi>&alpha;</mi> <mi>H</mi> </msub> <msubsup> <mi>x</mi> <mi>k</mi> <mi>p</mi> </msubsup> <mo>+</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>&alpha;</mi> <mi>H</mi> </msub> <mo>)</mo> </mrow> <msubsup> <mi>x</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> <mi>p</mi> </msubsup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>b</mi> <mi>k</mi> </msub> <mo>=</mo> <msub> <mi>&beta;</mi> <mi>H</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>s</mi> <mi>k</mi> </msub> <mo>-</mo> <msub> <mi>s</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>+</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>&beta;</mi> <mi>H</mi> </msub> <mo>)</mo> </mrow> <msub> <mi>b</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>.</mo> </mrow>
- 6. the power distribution network robust dynamic state estimator method according to claim 1 based on UKF, it is characterised in that：Pass through The predicted value and prediction covariance of state variable are asked in weighting：<mrow> <msubsup> <mover> <mi>x</mi> <mo>&OverBar;</mo> </mover> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>|</mo> <mi>k</mi> </mrow> <mi>p</mi> </msubsup> <mo>=</mo> <munderover> <mo>&Sigma;</mo> <mi>i</mi> <mi>L</mi> </munderover> <msubsup> <mi>W</mi> <mi>i</mi> <mi>m</mi> </msubsup> <msubsup> <mi>&chi;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>|</mo> <mi>k</mi> </mrow> <mi>p</mi> </msubsup> </mrow><mrow> <msubsup> <mi>P</mi> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>|</mo> <mi>k</mi> </mrow> <mi>p</mi> </msubsup> <mo>=</mo> <munderover> <mo>&Sigma;</mo> <mi>i</mi> <mi>L</mi> </munderover> <msubsup> <mi>W</mi> <mi>i</mi> <mi>c</mi> </msubsup> <mrow> <mo>(</mo> <msubsup> <mover> <mi>x</mi> <mo>&OverBar;</mo> </mover> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>|</mo> <mi>k</mi> </mrow> <mi>p</mi> </msubsup> <mo>-</mo> <msubsup> <mi>&chi;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>|</mo> <mi>k</mi> </mrow> <mi>p</mi> </msubsup> <mo>)</mo> </mrow> <mo>*</mo> <msup> <mrow> <mo>(</mo> <msubsup> <mover> <mi>x</mi> <mo>&OverBar;</mo> </mover> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>|</mo> <mi>k</mi> </mrow> <mi>p</mi> </msubsup> <mo>-</mo> <msubsup> <mi>&chi;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>|</mo> <mi>k</mi> </mrow> <mi>p</mi> </msubsup> <mo>)</mo> </mrow> <mi>T</mi> </msup> <mo>+</mo> <msubsup> <mi>Q</mi> <mi>k</mi> <mi>p</mi> </msubsup> </mrow>Wherein, Q is system noise covariance matrix.
- 7. the power distribution network robust dynamic state estimator method according to claim 1 based on UKF, it is characterised in that：By The measurement predictor of sigma point sets, the average and covariance, cross covariance of system are obtained by weighted sum：<mrow> <msubsup> <mover> <mi>z</mi> <mo>&OverBar;</mo> </mover> <mrow> <mi>i</mi> <mo>,</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>p</mi> </msubsup> <mo>=</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mn>2</mn> <mi>n</mi> </mrow> </munderover> <msubsup> <mi>W</mi> <mi>i</mi> <mi>m</mi> </msubsup> <msubsup> <mi>z</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>p</mi> </msubsup> </mrow><mrow> <msubsup> <mi>S</mi> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>p</mi> </msubsup> <mo>=</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mn>2</mn> <mi>n</mi> </mrow> </munderover> <msubsup> <mi>W</mi> <mi>i</mi> <mi>c</mi> </msubsup> <mrow> <mo>(</mo> <msubsup> <mi>z</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>p</mi> </msubsup> <mo>-</mo> <msubsup> <mover> <mi>z</mi> <mo>&OverBar;</mo> </mover> <mrow> <mi>i</mi> <mo>,</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>p</mi> </msubsup> <mo>)</mo> </mrow> <msup> <mrow> <mo>(</mo> <msubsup> <mi>z</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>p</mi> </msubsup> <mo>-</mo> <msubsup> <mover> <mi>z</mi> <mo>&OverBar;</mo> </mover> <mrow> <mi>i</mi> <mo>,</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>p</mi> </msubsup> <mo>)</mo> </mrow> <mi>T</mi> </msup> <mo>+</mo> <msubsup> <mi>R</mi> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>p</mi> </msubsup> </mrow><mrow> <msubsup> <mi>C</mi> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>p</mi> </msubsup> <mo>=</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mn>2</mn> <mi>n</mi> </mrow> </munderover> <msubsup> <mi>W</mi> <mi>i</mi> <mi>c</mi> </msubsup> <mrow> <mo>(</mo> <msubsup> <mi>&chi;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>|</mo> <mi>k</mi> </mrow> <mi>p</mi> </msubsup> <mo>-</mo> <msubsup> <mover> <mi>x</mi> <mo>&OverBar;</mo> </mover> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>|</mo> <mi>k</mi> </mrow> <mi>p</mi> </msubsup> <mo>)</mo> </mrow> <msup> <mrow> <mo>(</mo> <msubsup> <mi>z</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>p</mi> </msubsup> <mo>-</mo> <msubsup> <mover> <mi>z</mi> <mo>&OverBar;</mo> </mover> <mrow> <mi>i</mi> <mo>,</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>p</mi> </msubsup> <mo>)</mo> </mrow> <mi>T</mi> </msup> <mo>.</mo> </mrow>
- 8. the power distribution network robust dynamic state estimator method according to claim 1 based on UKF, it is characterised in that：With In grid measurement data, it is understood that there may be rough error, system loading mutation cause metric data change greatly, it is new to introduce exponential weight function pair Matrix dynamic corrections are ceased, changes corresponding measurement weight, the influence of smooth rough error or measurement change to filtering, is implemented as follows：<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <msub> <mi>r</mi> <mi>i</mi> </msub> <mo>=</mo> <msub> <mi>z</mi> <mi>i</mi> </msub> <mo>-</mo> <mi>h</mi> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>)</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>&rho;</mi> <mn>1</mn> </msub> <mo>(</mo> <msub> <mi>r</mi> <mi>i</mi> </msub> <mo>)</mo> <mo>=</mo> <mfrac> <msub> <mi>w</mi> <mi>i</mi> </msub> <mrow> <mi>exp</mi> <mrow> <mo>(</mo> <mo>|</mo> <msub> <mi>r</mi> <mi>i</mi> </msub> <mo>|</mo> <mo>)</mo> </mrow> </mrow> </mfrac> </mtd> </mtr> </mtable> </mfenced>In order to improve the smooth effect in UKF, modification weight function is negative exponent form：R'k=Rk exp(-|yk-h(xk)|)Corresponding covariance is revised as：<mrow> <msubsup> <mi>S</mi> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>p</mi> </msubsup> <mo>=</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mn>2</mn> <mi>n</mi> </mrow> </munderover> <msubsup> <mi>W</mi> <mi>i</mi> <mi>c</mi> </msubsup> <mrow> <mo>(</mo> <msubsup> <mi>z</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>p</mi> </msubsup> <mo>-</mo> <msubsup> <mover> <mi>z</mi> <mo>&OverBar;</mo> </mover> <mrow> <mi>i</mi> <mo>,</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>p</mi> </msubsup> <mo>)</mo> </mrow> <msup> <mrow> <mo>(</mo> <msubsup> <mi>z</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>p</mi> </msubsup> <mo>-</mo> <msubsup> <mover> <mi>z</mi> <mo>&OverBar;</mo> </mover> <mrow> <mi>i</mi> <mo>,</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>p</mi> </msubsup> <mo>)</mo> </mrow> <mi>T</mi> </msup> <mo>+</mo> <msubsup> <msup> <mi>R</mi> <mo>&prime;</mo> </msup> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>p</mi> </msubsup> <mo>.</mo> </mrow>
- 9. the power distribution network robust dynamic state estimator method according to claim 1 based on UKF, it is characterised in that：According to The measurement weight calculation measurement variance matrix of amendment, and calculate state and the association side of Kalman filtering gain and more new system Difference：<mrow> <msub> <mi>K</mi> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>C</mi> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <msubsup> <mi>S</mi> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mrow><mrow> <msub> <mi>x</mi> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mover> <mi>x</mi> <mo>&OverBar;</mo> </mover> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>|</mo> <mi>k</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>K</mi> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mrow> <mo>(</mo> <msub> <mi>z</mi> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>-</mo> <msub> <mover> <mi>y</mi> <mo>&OverBar;</mo> </mover> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> </mrow><mrow> <msub> <mi>P</mi> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>P</mi> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>|</mo> <mi>k</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>K</mi> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <msub> <mi>S</mi> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <msubsup> <mi>K</mi> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>T</mi> </msubsup> </mrow>Wherein K is Kalman filtering gain matrix.
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