CN115800271B - Power distribution system parameter correction method and system based on self-adaptive Kalman filtering - Google Patents
Power distribution system parameter correction method and system based on self-adaptive Kalman filtering Download PDFInfo
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Abstract
The invention provides a power distribution system parameter correction method and system based on self-adaptive Kalman filtering, wherein the method comprises the following steps: establishing a state equation and a measurement equation of system parameters of the medium-voltage distribution system based on the self-adaptive Kalman filtering; calculating a predicted value and covariance of a system parameter at a certain moment based on the state equation and the measurement equation; calculating residual errors and covariance thereof according to the predicted values and covariance thereof; calculating a mahalanobis distance according to the residual error and the covariance; carrying out self-adaptive correction on the residual error according to the mahalanobis distance; then, calculating Kalman filtering gain through residual error and covariance thereof; and calculating a posterior state estimation value according to the Kalman filtering gain. The invention improves the observability and the computing capability of the medium-voltage distribution network.
Description
Technical Field
The invention belongs to the field of situation awareness of medium-voltage power distribution systems, and particularly relates to a power distribution system parameter correction method and system based on self-adaptive Kalman filtering.
Background
Along with the development of society and the improvement of the living standard of people, the requirements on the power supply reliability and the power supply quality of a power system are higher and higher. The medium voltage distribution system as an important component of the power system is directly oriented to end users, and the perfection of the medium voltage distribution system is directly related to the electricity reliability and the electricity quality of the vast users. In the conventional calculation of the power flow for a medium-voltage power distribution system, the parameters of the medium-voltage power distribution system are generally approximated unchanged. In fact, the parameters of the medium voltage distribution system change at any time according to seasons and time, and the observability and the computing capacity of the medium voltage distribution network are affected by the traditional approximation process. Therefore, how to improve the observability of the medium-voltage distribution network and ensure the operation safety and the power supply reliability of the power network becomes a problem to be solved urgently.
Disclosure of Invention
In view of the above problems, the present invention provides a power distribution system parameter correction method based on adaptive kalman filtering, including:
establishing a state equation and a measurement equation of system parameters of the medium-voltage distribution system based on the self-adaptive Kalman filtering;
calculating a predicted value and covariance of a system parameter at a certain moment based on the state equation and the measurement equation;
calculating residual errors and covariance thereof according to the predicted values and the covariance and the measured values;
calculating a mahalanobis distance according to the residual error and the covariance thereof, and carrying out self-adaptive correction on the residual error according to the mahalanobis distance, wherein the method comprises the following steps:
determining whether the corresponding measurement value is uncertain noise according to the mahalanobis distance, and if so, updating the residual error and covariance thereof through the self-adaptive factor;
determining whether the corresponding measured value is a wild value according to the Marsh distance, if so, discarding the wild value, and recalculating residual errors and covariance thereof by replacing the measured value with a predicted value;
then, calculating Kalman filtering gain through the latest residual error and covariance thereof;
and calculating a posterior state estimation value according to the Kalman filtering gain.
Further, establishing a state equation and a measurement equation of the system parameters of the medium-voltage distribution system based on the adaptive Kalman filtering comprises:
establishing a state equation and a measurement equation of added noise:
Wherein the system parameters include line parameters and/or transformer parameters.
Further, calculating the predicted value and covariance of the line parameter at a certain moment includes: obtaining initial values and covariance of line parameters of medium-voltage distribution system
and />
，
Calculated by the following formula:
knowing the initial value
And covariance + ->
The value and the covariance of the state variable at the next moment are obtained, then the value and the covariance of the state variable at the later moment are obtained through the value and the covariance of the state variable at the next moment, and iteration is continuously carried out to obtain +.>
Predicted value of system parameter of time medium voltage distribution system>
And covariance + ->
。
Further, calculate the residual
And covariance + ->
The formula of (2) is as follows:
further, calculating the mahalanobis distance from the residual and its covariance includes:
wherein (r) represents the r-th element, (r, r) represents the r-th row, and the r-th column of elements.
Further, if the mahalanobis distance is within the specified confidence interval, indicating that uncertain noise appears in measurement, updating the residual error and covariance thereof by the self-adaptive factor;
adaptive factor
And its updated residual covariance->
The calculation formula of (2) is as follows: />
wherein ,
indicating that the lower boundary of the assigned confidence interval, < ->
Is the residual covariance before the update,
for the updated residual covariance +.>
For vector->
Is>
Element(s)>
Is vector quantity
Is>
Element(s)>
、/>
、/>
For matrix->
Diagonal->
The elements.
Further, calculating the kalman filter gain from the residual and its covariance includes:
kalman filtering gain of medium voltage distribution system parameters without occurrence of uncertain noise
The calculation formula of (2) is as follows:
if uncertain noise occurs, then:
further, posterior state estimation
And covariance + ->
Computing means of (a)The formula is as follows:
further, if the mahalanobis distance is greater than the upper limit of the specified confidence interval, the corresponding measured value is considered to be a wild value and discarded, and the predicted value is adopted instead.
The invention also provides a distribution system parameter correction system based on the self-adaptive Kalman filtering, which comprises:
a model determination unit configured to: establishing a state equation and a measurement equation of system parameters of the medium-voltage distribution system based on the self-adaptive Kalman filtering;
a prediction unit for: calculating a predicted value and covariance of a system parameter at a certain moment based on the state equation and the measurement equation;
a residual calculation unit for: calculating residual errors and covariance thereof according to the predicted values and covariance thereof;
the residual error correction unit is used for calculating a mahalanobis distance according to the residual error and covariance thereof, and carrying out self-adaptive correction on the residual error according to the mahalanobis distance, and comprises the following steps:
determining whether the corresponding measurement value is uncertain noise according to the mahalanobis distance, and if so, updating the residual error and covariance thereof through the self-adaptive factor;
determining whether the corresponding measured value is a wild value according to the Marsh distance, if so, discarding the wild value, and recalculating residual errors and covariance thereof by replacing the measured value with a predicted value;
gain calculation unit for: calculating a Kalman filtering gain by using the residual error and the covariance determined by the residual error correction unit;
an estimated value calculation unit configured to: and calculating a posterior state estimation value according to the Kalman filtering gain.
According to the power distribution system parameter correction method and system based on the self-adaptive Kalman filtering, the self-adaptive Kalman filtering can utilize a large amount of measured value data to estimate and correct the model and noise statistics characteristics, and a large amount of historical data is used for estimating the parameters of the medium-voltage power distribution system to obtain a changed new parameter value, so that the observability and the computing capacity of the medium-voltage power distribution network are improved.
Additional features and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. The objectives and other advantages of the invention may be realized and attained by the structure particularly pointed out in the written description and claims hereof as well as the appended drawings.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, and it is obvious that the drawings in the following description are some embodiments of the present invention, and other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
Fig. 1 shows a schematic diagram of an equivalent circuit structure of a medium voltage distribution system line according to an embodiment of the present invention;
fig. 2 is a schematic diagram showing an equivalent circuit structure of a transformer of a medium-voltage distribution system according to an embodiment of the present invention;
FIG. 3 illustrates a flow chart of a method for on-line correction of parameters of a medium voltage power distribution system in accordance with an embodiment of the present invention;
fig. 4 shows a schematic structural diagram of an on-line parameter correction system for a medium voltage distribution system according to an embodiment of the present invention.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments of the present invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The invention provides a power distribution system parameter correction method based on self-adaptive Kalman filtering, which can be used for on-line correction of medium-voltage power distribution system parameters. The method corrects parameters by utilizing a large amount of historical measurement data recorded in the power grid, and judges and processes the outlier and the uncertainty noise existing in the measurement information by utilizing a hypothesis testing method. Compared with the existing calculation by using unchanged system parameters, the method can consider the condition that the parameters of the medium-voltage distribution system change at any time along with the difference of seasons and time, and improves the observability and the calculation capability of the medium-voltage distribution network.
In the embodiment of the invention, the equivalent circuit structure of the medium voltage distribution system circuit is shown in figure 1. The equivalent resistance R and the equivalent reactance X of the circuit are connected in series, and the voltages at the two ends of the circuit are respectively
The current flowing into the line is +.>
The current in the line is I. The equivalent capacitance to ground at both ends of the line (ground points GND1 and GND2 respectively) is C.
The equivalent circuit structure of the medium voltage distribution system transformer is shown in fig. 2. The equivalent circuit structure comprises an excitation part and a gate-type equivalent circuit which are connected in series. The transformation ratio of the transformer is T. The exciting section is represented by a parallel branch formed by connecting a conductance G and a capacitance C in parallel, one end of the parallel branch is grounded, and the other end is used as a current inflow end of the circuit structure. Other performance uses of transformers
、/>
、/>
Constitution ofGate (n-type) equivalent circuit representation, wherein->
，/>
，
, wherein ,/>
One end is grounded, the other end is connected with->
Is connected with the current inflow end of (a)>
One end is grounded, the other end is connected with->
Is connected to the current outlet terminal of the (c). Wherein Z represents impedance and consists of an equivalent resistor R and an equivalent reactor X which are connected in series. The voltages at the two ends of the line are respectively->
The current flowing into the line at the head end is +.>
Flow through->
The current of (2) is I, flow->
Is +.>
The current of the excitation part is +.>
。
An on-line correction flow chart of the medium voltage distribution system parameters based on the adaptive Kalman filtering is shown in figure 3.
The method comprises the following steps:
step 1: establishing system parameters of medium voltage distribution system
State equation and measurement equation based on adaptive Kalman filtering, and gives (can be directly obtained according to the system parameter performance) the process noise covariance +.>
Measurement noise covariance->
；
In the embodiment of the invention, the system parameters comprise line parameters and/or transformer parameters, and the processing logic of the two parameters is the same by the power distribution system parameter correction method based on the self-adaptive Kalman filtering, so that the parameters can be corrected in an omnibearing and multi-angle manner, and the accuracy of power grid observation and calculation is improved.
The establishment of state equations and measurement equations of system parameters of the medium-voltage distribution system is divided into the following two parts:
(1) Establishing a state equation and a measurement equation without noise interference
The state equation is established as follows:
wherein ,
discrete time series>
Representing the state of the system parameter at time k +.>
Representing the state of the system parameter at the previous instant, i.e. at time k-1 +.>
Is a state transition matrix, ">
. For line parameters, state variables ∈ ->
。
The measurement equation is established below, and equivalent reactance is set for the line parameters
The voltage at two ends is +>
In the continuous time domain, according to kirchhoff's law:
easily-known
(2)
wherein ,
are all continuous time functions, and are sampled (in discrete time domain) as
Abbreviated as +.>
，/>
Is the sampling time. I.e.)>
Represents the current at the line current inflow at time k, < >>
Representing the current at the line current inflow at time k-1,
represents the line current inflow terminal voltage amplitude at time k-1,/->
Representing the line at time kCurrent inflow terminal voltage amplitude, ">
Representing the voltage amplitude of the line current outflow end at the moment k;
substituting (4), (5) and (6) into (1) to obtain:
the preparation method comprises the following steps of:
t is transformer transformation ratio, impedance
J represents the imaginary part of the complex number, < ->
；
(2) And (3) establishing a measurement equation and a state equation with noise influence as a system parameter correction model of the adaptive Kalman filtering.
Adding noise interference to a state equation and a measurement equation respectively to obtain:
Step 2: system parameter correction model (namely formula (10)) based on adaptive Kalman filtering and calculation
Predicted value of system parameter of time medium voltage distribution system>
And covariance + ->
And the initial value of the state variable +.>
And covariance +.>
；
The predicted value and covariance calculation formula are as follows:
knowing the initial value
And covariance + ->
The value and the covariance of the state variable at the next moment are obtained, then the value and the covariance of the state variable at the later moment are obtained through the value and the covariance of the state variable at the next moment, and iteration is continuously carried out to obtain +.>
Predicted value of system parameter of time medium voltage distribution system>
And covariance + ->
. Initial value->
And covariance + ->
Is obtained by consulting a standard for the known cable used, i.e. the value obtained by subjecting the cable to a factory test.
Step 3: measuring matrix obtained by using current value and load power obtained by measuring device, distribution network three-phase tide algorithm and state estimation
And calculates the residual +.>
Covariance->
；
Calculating residual errors
And covariance + ->
The formula of (2) is as follows:
step 4: calculation of the mahalanobis distance from the resulting residual
If->
Then go to step 5; otherwise, go to step 6;
utilizing residual errors
And covariance + ->
The calculated mahalanobis distance is calculated as follows:
wherein (r) represents an r-th element, (r, r) represents an r-th row, and an r-th column of elements;
step 5: comparison of
and />
The size of (1)>
The corresponding measurement value is regarded as uncertain noise, and the adaptive factor is calculated>
And updating the prior residual, calculating the updated residual covariance +.>
Then, go to step 7; otherwise, directly turning to the step 7;
judging and processing modes of the outlier and the uncertainty noise are as follows: calculation of the Marshall distance of the residual
If (if)
Then the measurement outlier is considered to appear, is removed and is replaced by a predicted value (obtained by the formula (11)) to replace the posterior state estimation value (used in the formula (20)); when the outlier appears, the covariance is recalculated by using the predicted value instead of the outlier, the covariance is 0, and the kalman filter gain is 0 according to the subsequent calculation, which corresponds to replacing the posterior state estimation value by the predicted value. If->
Then it is considered that uncertainty noise is present at this time. Adaptive factor->
And its updated residual covariance->
The calculation formula of (2) is as follows: />
wherein ,
、/>
the lower and upper boundaries of the confidence interval are represented, illustratively by values of 0 and 1, respectively.
Is the residual covariance before update, +.>
For the updated residual covariance +.>
For vector->
Is>
Element(s)>
For vector->
Is>
Element(s)>
、/>
、
For matrix->
Diagonal->
The elements.
The invention judges the wild value and the uncertain noise through the mahalanobis distance and carries out corresponding processing, thereby realizing the self-adaptive correction of the parameters.
Step 6: taking the measured value as an outlier, discarding, replacing the posterior state estimation value with the predicted value obtained in the step 2, and turning to the step 7;
step 7: kalman filtering gain for calculating parameters of medium voltage distribution system
；
Kalman filtering gain for medium voltage distribution system parameters
The calculation formula of (2) is as follows:
if uncertain noise occurs, then:
step 8: by means of
Calculated->
Posterior state estimation value of time-of-day system parameters +.>
And covariance + ->
(matrix) and will->
As a result of the correction of system parameters.
Medium voltage power distribution system
Posterior state estimation value of time-of-day system parameters +.>
And covariance + ->
The calculation formula of (2) is as follows:
based on the same inventive concept, the embodiment of the invention also provides a power distribution system parameter correction system based on adaptive Kalman filtering, as shown in fig. 4, comprising:
a model determination unit configured to: establishing a state equation and a measurement equation of system parameters of the medium-voltage distribution system based on the self-adaptive Kalman filtering;
a prediction unit for: calculating a predicted value and covariance of a system parameter at a certain moment based on the state equation and the measurement equation;
a residual calculation unit for: calculating residual errors and covariance thereof according to the predicted values and covariance thereof;
the residual error correction unit is used for calculating a mahalanobis distance according to the residual error and covariance thereof, and carrying out self-adaptive correction on the residual error according to the mahalanobis distance, and comprises the following steps of;
determining whether the corresponding measurement value is uncertain noise according to the mahalanobis distance, and if so, updating the residual error and covariance thereof through the self-adaptive factor;
determining whether the corresponding measured value is a wild value according to the Marsh distance, if so, discarding the wild value, and recalculating residual errors and covariance thereof by replacing the measured value with a predicted value;
gain calculation unit for: calculating a Kalman filtering gain by using the residual error and the covariance determined by the residual error correction unit;
an estimated value calculation unit configured to: and calculating a posterior state estimation value according to the Kalman filtering gain.
The residual error correction unit is used for judging whether the mahalanobis distance is larger than the upper limit value of the appointed confidence interval, if so, the corresponding measured value is considered to be a wild value and is discarded, and the predicted value is adopted to replace the posterior state estimated value in the estimated value calculation unit; and judging whether the Marsh distance is within a specified confidence interval, if so, updating the residual error and covariance thereof through the self-adaptive factor, wherein the uncertainty noise appears in measurement.
Each unit specific implementation of the distribution system parameter correction system based on the adaptive Kalman filter can be obtained according to the distribution system parameter correction method based on the adaptive Kalman filter according to the embodiment of the invention, and the description is omitted.
Although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present invention.
Claims (10)
1. The power distribution system parameter correction method based on the adaptive Kalman filtering is characterized by comprising the following steps of:
establishing a state equation and a measurement equation of system parameters of the medium-voltage distribution system based on the self-adaptive Kalman filtering;
calculating a predicted value and covariance of a system parameter at a certain moment based on the state equation and the measurement equation;
calculating residual errors and covariance thereof according to the predicted values and the covariance and the measured values;
calculating a mahalanobis distance according to the residual error and the covariance thereof, and carrying out self-adaptive correction on the residual error according to the mahalanobis distance, wherein the method comprises the following steps:
determining whether the corresponding measurement value is uncertain noise according to the mahalanobis distance, and if so, updating the residual error and covariance thereof through the self-adaptive factor;
determining whether the corresponding measured value is a wild value according to the Marsh distance, if so, discarding the wild value, and recalculating residual errors and covariance thereof by replacing the measured value with a predicted value;
then, calculating Kalman filtering gain through the latest residual error and covariance thereof;
calculating a posterior state estimation value according to the Kalman filtering gain;
wherein the system parameters include line parameters;
in the equivalent circuit structure of the medium-voltage distribution system circuit, an equivalent resistor R and an equivalent reactance X are connected in series, and voltages at two ends of the circuit are respectively
The current flowing into the line is +.>
The current in the circuit is I, and the equivalent capacitance to the ground at the two ends of the circuit is C; the state equation and the measurement equation based on the adaptive Kalman filtering for establishing the system parameters of the medium-voltage distribution system comprise:
establishing a state equation and a measurement equation of added noise:
2. The adaptive Kalman filtering-based power distribution system parameter modification method of claim 1, wherein the system parameters further comprise transformer parameters,
for transformer parameters, the equivalent circuit structure of the transformer of the medium-voltage distribution system comprises an excitation part and a gate-type equivalent circuit, the transformation ratio of the transformer is T, the excitation part is represented by a parallel branch formed by connecting a conductance G and a capacitance C in parallel, one end of the parallel branch is grounded, the other end of the parallel branch is used as a current inflow end of the circuit structure, and other performances of the transformer are used
、/>
、/>
A gate-type equivalent circuit representation is constructed, wherein +.>
，/>
，/>
, wherein ,/>
One end is grounded, the other end is connected with->
Is connected with the current inflow end of (a)>
One end is grounded, the other end is connected with->
Wherein Z represents impedance and consists of an equivalent resistor R and an equivalent reactor X which are connected in series, and voltages at two ends of the line are respectively +.>
The current flowing into the line at the head end is +.>
Flow through->
The current of (2) is I, flow->
Is +.>
The current of the excitation part is +.>
，/>
Is connected with the current inflow end of the equivalent circuit structure of the transformer, +.>
The current outflow end of the transformer equivalent circuit structure;
in the state equation and the measurement equation,
3. the adaptive kalman filter based power distribution system parameter correction method according to claim 2, wherein calculating the predicted value of the system parameter and the covariance thereof at a certain moment comprises: obtaining initial values and covariance of system parameters of a medium voltage distribution system
and />
，
Calculated by the following formula:
knowing the initial value
And covariance + ->
Continuously iterating to obtain ++>
Predicted value of system parameter of time medium voltage distribution system>
And covariance + ->
，/>
and />
The posterior state estimates and covariance of the k-1 time are obtained.
4. The adaptive kalman filter based power distribution system parameter correction method according to claim 3, wherein residual error is calculated
And covariance + ->
The formula of (2) is as follows:
5. the adaptive kalman filter based power distribution system parameter correction method according to claim 4, wherein calculating the mahalanobis distance based on the residual error and its covariance comprises:
where (r) represents the r-th element, (r, r) represents the r-th row, and the r-th column.
6. The adaptive Kalman filtering-based power distribution system parameter modification method of claim 5, wherein,
if the mahalanobis distance is within the specified confidence interval, indicating that uncertain noise appears in measurement, updating the residual error and covariance thereof through the self-adaptive factor;
adaptive factor
And its updated residual covariance->
The calculation formula of (2) is as follows:
wherein ,
representing the lower boundary of the specified confidence interval, +.>
Is the residual covariance before update, +.>
For the updated residual covariance +.>
For vector->
Is>
Element(s)>
、
、/>
Respectively is matrix->
and />
Diagonal->
The elements.
7. The adaptive kalman filter based power distribution system parameter correction method according to claim 6, wherein calculating the kalman filter gain by the latest residual and covariance thereof includes:
kalman filtering gain of medium voltage distribution system parameters without occurrence of uncertain noise
The calculation formula of (2) is as follows:
if uncertain noise occurs, then:
8. the adaptive kalman filter based power distribution system parameter correction method according to claim 7, wherein the posterior state estimation value
And covariance + ->
The calculation formula of (2) is as follows:
9. an adaptive kalman filter based power distribution system parameter correction method as in any of the claims 6-8, wherein,
if the mahalanobis distance is greater than the upper limit value of the specified confidence interval, the corresponding measurement value is considered as a wild value and discarded, and the predicted value is adopted for replacement.
10. An adaptive kalman filter-based power distribution system parameter correction system, comprising:
a model determination unit configured to: establishing a state equation and a measurement equation of system parameters of the medium-voltage distribution system based on the self-adaptive Kalman filtering;
a prediction unit for: calculating a predicted value and covariance of a system parameter at a certain moment based on the state equation and the measurement equation;
a residual calculation unit for: calculating residual errors and covariance thereof according to the predicted values and covariance thereof;
the residual error correction unit is used for calculating a mahalanobis distance according to the residual error and covariance thereof, and carrying out self-adaptive correction on the residual error according to the mahalanobis distance, and comprises the following steps:
determining whether the corresponding measurement value is uncertain noise according to the mahalanobis distance, and if so, updating the residual error and covariance thereof through the self-adaptive factor;
determining whether the corresponding measured value is a wild value according to the Marsh distance, if so, discarding the wild value, and recalculating residual errors and covariance thereof by replacing the measured value with a predicted value;
gain calculation unit for: calculating a Kalman filtering gain by using the residual error and the covariance determined by the residual error correction unit;
an estimated value calculation unit configured to: calculating a posterior state estimation value according to the Kalman filtering gain;
wherein the system parameters include line parameters;
in the equivalent circuit structure of the medium-voltage distribution system circuit, an equivalent resistor R and an equivalent reactance X are connected in series, and voltages at two ends of the circuit are respectively
The current flowing into the line is +.>
The current in the line is IThe equivalent capacitance to ground at the two ends of the circuit is C; the state equation and the measurement equation based on the adaptive Kalman filtering for establishing the system parameters of the medium-voltage distribution system comprise:
establishing a state equation and a measurement equation of added noise:
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