CN115800271A - Power distribution system parameter correction method and system based on adaptive Kalman filtering - Google Patents

Power distribution system parameter correction method and system based on adaptive Kalman filtering Download PDF

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CN115800271A
CN115800271A CN202310048743.5A CN202310048743A CN115800271A CN 115800271 A CN115800271 A CN 115800271A CN 202310048743 A CN202310048743 A CN 202310048743A CN 115800271 A CN115800271 A CN 115800271A
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covariance
value
calculating
kalman filtering
distribution system
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CN115800271B (en
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祖国强
黄旭
丁琪
李治
晋萃萃
张春晖
魏然
贺春
冯郁竹
徐智
吴俣
张军
邱巧红
魏炜
季文文
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State Grid Corp of China SGCC
State Grid Tianjin Electric Power Co Ltd
Electric Power Research Institute of State Grid Tianjin Electric Power Co Ltd
Chengdong Power Supply Co of State Grid Tianjin Electric Power Co Ltd
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State Grid Corp of China SGCC
State Grid Tianjin Electric Power Co Ltd
Electric Power Research Institute of State Grid Tianjin Electric Power Co Ltd
Chengdong Power Supply Co of State Grid Tianjin Electric Power Co Ltd
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Abstract

The invention provides a power distribution system parameter correction method and system based on 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 power distribution system based on adaptive Kalman filtering; calculating a predicted value and covariance of system parameters at a certain moment based on a state equation and a measurement equation; calculating residual errors and covariance thereof according to the predicted values and the covariance thereof; calculating the mahalanobis distance according to the residual error and the covariance thereof; performing self-adaptive correction on the residual error according to the Mahalanobis distance; then, calculating Kalman filtering gain through the residual error and the covariance thereof; and calculating the posterior state estimation value according to the Kalman filtering gain. The invention improves the observability and the calculation capability of the medium-voltage distribution network.

Description

Power distribution system parameter correction method and system based on adaptive Kalman filtering
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 adaptive Kalman filtering.
Background
With the development of society and the improvement of people's living standard, 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 which is an important component of the power system is directly oriented to the terminal users, and whether the medium-voltage distribution system is perfected or not is directly related to the power utilization reliability and the power utilization quality of the majority of users. In conventional power flow calculations for medium-voltage power distribution systems, 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 different seasons and different times, and the traditional approximate processing influences the observability and the computing capacity of the medium-voltage distribution network. Therefore, how to improve the observable capability of the medium-voltage distribution network and ensure the operation safety and the power supply reliability of the power grid becomes a problem to be solved urgently.
Disclosure of Invention
In order to solve 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 power distribution system based on adaptive Kalman filtering;
calculating a predicted value and covariance of system parameters at a certain moment based on a state equation and a measurement equation;
calculating residual errors and covariance thereof according to the predicted values, the covariance thereof and the measured values;
calculating the Mahalanobis distance according to the residual error and the covariance thereof, and performing self-adaptive correction on the residual error according to the Mahalanobis distance, wherein the self-adaptive correction 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 the covariance thereof through a self-adaptive factor;
determining whether the corresponding measurement value is a wild value or not according to the Mahalanobis distance, if so, abandoning the wild value, and replacing the measurement value with a predicted value to recalculate the residual error and the covariance thereof;
then, calculating Kalman filtering gain according to the latest residual error and the covariance thereof;
and calculating the posterior state estimation value according to the Kalman filtering gain.
Further, establishing an adaptive kalman filter-based state equation and measurement equation for the medium voltage power distribution system parameters includes:
establishing a state equation and a measurement equation of the added noise:
Figure SMS_1
(10)
Figure SMS_6
a state variable representing a parameter of the system,
Figure SMS_10
indicating the previous moment of time, i.e.
Figure SMS_14
The state of the system parameter at the time of day,
Figure SMS_3
is a matrix of state transitions that is,
Figure SMS_9
，
Figure SMS_13
is zero mean and covariance of
Figure SMS_19
White gaussian noise;
Figure SMS_5
the measured value is expressed as a measurement value,
Figure SMS_15
is a measurement matrix, which is a matrix of measurements,
Figure SMS_21
，
Figure SMS_25
represents the voltage amplitude of the line current inflow terminal at the time k,
Figure SMS_7
representing the current flowing through the line at time k,
Figure SMS_12
representing the current at the line current inflow terminal at time k-1,
Figure SMS_18
representing the magnitude of the terminal voltage at the line current inflow at time k-1,
Figure SMS_23
representing the voltage amplitude of the incoming terminal of the line current at the moment k-2;
Figure SMS_20
is zero mean and covariance of
Figure SMS_24
The white gaussian noise of (a) is,
Figure SMS_26
in order to add extra noise to the sound,
Figure SMS_27
for measuring outliers, wherein
Figure SMS_2
Compliance parameter of
Figure SMS_11
The distribution of the Bernoulli effect of (A),
Figure SMS_17
,
Figure SMS_22
in the form of a function of the unit pulse,
Figure SMS_4
compliance parameter of
Figure SMS_8
The distribution of the Bernoulli effect of (A),
Figure SMS_16
；
wherein the system parameters comprise line parameters and/or transformer parameters.
Further, the step of calculating the predicted value and the covariance of the certain time line parameter includes: obtaining initial values and covariance of line parameters of a medium voltage distribution system
Figure SMS_28
And
Figure SMS_29
，
calculated by the following formula:
Figure SMS_30
(11)
Figure SMS_31
(12)
known initial value
Figure SMS_32
And its covariance
Figure SMS_33
Calculating the value and covariance of the state variable at the next moment, calculating the value and covariance of the state variable at the later moment by the value and covariance of the state variable at the next moment, and continuously iterating to obtain
Figure SMS_34
Prediction value of system parameters of medium-voltage distribution system at moment
Figure SMS_35
And its covariance
Figure SMS_36
。
Further, a residual is calculated
Figure SMS_37
And its covariance
Figure SMS_38
The formula (c) is as follows:
Figure SMS_39
(13)
Figure SMS_40
(14)。
further, calculating the mahalanobis distance from the residual and its covariance comprises:
Figure SMS_41
(15)
wherein, (r) represents the r-th element, (r, r) represents the r-th row, r-th column element.
Further, if the Mahalanobis distance is in the specified confidence interval, which indicates that uncertain noise occurs in the measurement, the residual error and the covariance thereof are updated through a self-adaptive factor;
adaptive factor
Figure SMS_42
And its updated residual covariance
Figure SMS_43
The calculation formula of (a) is as follows:
Figure SMS_44
(16)
Figure SMS_45
(17)
wherein ,
Figure SMS_47
representing the lower bound of the assigned confidence interval,
Figure SMS_51
is the residual covariance before the update,
Figure SMS_55
for the purpose of the updated residual covariance,
Figure SMS_48
as a vector
Figure SMS_52
To (1) a
Figure SMS_56
The number of the elements is one,
Figure SMS_58
as a vector
Figure SMS_49
To (1) a
Figure SMS_53
The number of the elements is one,
Figure SMS_57
、
Figure SMS_59
、
Figure SMS_46
is a matrix
Figure SMS_50
On the diagonal line of the first
Figure SMS_54
And (4) each element.
Further, calculating the kalman filter gain by the residual and its covariance includes:
if no uncertain noise appears, the Kalman filtering gain of the parameters of the medium-voltage power distribution system
Figure SMS_60
The calculation formula of (a) is as follows:
Figure SMS_61
(18)
if uncertain noise occurs, then:
Figure SMS_62
(19)。
further, the posterior state estimation value
Figure SMS_63
And its covariance
Figure SMS_64
The calculation formula of (a) is as follows:
Figure SMS_65
(20)
Figure SMS_66
(21) 。
further, 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 is discarded, and the predicted value is adopted for replacement.
The invention also provides a power distribution system parameter correction system based on adaptive Kalman filtering, which comprises:
a model determination unit to: establishing a state equation and a measurement equation of system parameters of the medium-voltage power distribution system based on adaptive Kalman filtering;
a prediction unit to: calculating a predicted value and covariance of system parameters at a certain moment based on a state equation and a measurement equation;
a residual calculation unit for: calculating residual errors and covariance thereof according to the predicted values and the covariance thereof;
the residual error correction unit is used for calculating the 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, 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 the covariance thereof through a self-adaptive factor;
determining whether the corresponding measured value is a wild value according to the Mahalanobis distance, if so, abandoning the wild value, and recalculating the residual error and the covariance thereof by replacing the measured value with the predicted value;
a gain calculation unit to: calculating Kalman filtering gain according to the residual error determined by the residual error correction unit and the covariance thereof;
an estimated value calculation unit configured to: and calculating the posterior state estimation value according to the Kalman filtering gain.
According to the power distribution system parameter correction method and system based on the adaptive Kalman filtering, model and noise statistical characteristics of a large amount of measured data can be estimated and corrected through the adaptive Kalman filtering, parameters of the medium-voltage power distribution system are estimated through a large amount of historical data, changed new parameter values are obtained, and observability and calculation capacity of a 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 will 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 used in the description of the embodiments or the prior art will be briefly introduced below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without creative efforts.
Fig. 1 shows a schematic diagram of an equivalent circuit structure of a line of a medium voltage distribution system according to an embodiment of the invention;
FIG. 2 illustrates a schematic diagram of an equivalent circuit configuration of a medium voltage distribution system transformer in accordance with an embodiment of the present invention;
FIG. 3 shows a flow chart of a method for on-line correction of parameters of a medium voltage distribution system according to an embodiment of the invention;
fig. 4 shows a schematic structural diagram of a medium voltage distribution system parameter online correction system according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention provides a power distribution system parameter correction method based on adaptive Kalman filtering, which can be used for on-line correction of medium-voltage power distribution system parameters. The method utilizes a large amount of historical measurement data recorded in the power grid to correct parameters, and utilizes a hypothesis testing method to respectively judge and process wild values and uncertain noises in measurement information. Compared with the existing calculation method using unchanged system parameters, the method can consider the condition that the parameters of the medium-voltage distribution network change along with different seasons and time at any 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 as figure 1. The equivalent resistance R and the equivalent reactance X of the circuit are connected in series, and the voltages at two ends of the circuit are respectively
Figure SMS_67
The current flowing into the line is
Figure SMS_68
The current in the line is I. The equivalent capacitance to ground of both ends of the line (the grounding points are GND1 and GND2 respectively) is C.
The equivalent circuit structure of the transformer of the medium voltage distribution system 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 excitation part is represented by a parallel branch formed by connecting a conductance G and a capacitor C in parallel, one end of the parallel branch is grounded, and the other end of the parallel branch is used as a current inflow end of the circuit structure.Other properties of transformers
Figure SMS_81
、
Figure SMS_70
、
Figure SMS_76
A gate (pi) equivalent circuit representation is formed, wherein,
Figure SMS_73
，
Figure SMS_75
，
Figure SMS_74
, wherein ,
Figure SMS_80
one end is grounded and the other end is connected with
Figure SMS_79
Is connected to the current inflow terminal of the power supply,
Figure SMS_83
one end is grounded and the other end is connected with
Figure SMS_69
Is connected to the current outflow end. Wherein Z represents impedance and is composed of equivalent resistance R and equivalent reactance X which are connected in series. The voltages at the two ends of the line are respectively
Figure SMS_77
The current flowing into the line at the head end is
Figure SMS_72
Is flowed through
Figure SMS_78
Is I, flows through
Figure SMS_82
With a current of
Figure SMS_84
The current of the excitation part is
Figure SMS_71
。
A flow chart of the on-line correction of the parameters of the medium voltage distribution system based on the adaptive kalman filter is shown in fig. 3.
The method comprises the following steps:
step 1: establishing medium voltage distribution system parameters
Figure SMS_85
And provides (can be directly obtained according to the system parameter performance) the process noise covariance
Figure SMS_86
Measuring the noise covariance
Figure SMS_87
；
In the embodiment of the invention, the system parameters comprise line parameters and/or transformer parameters, and the processing logics of the self-adaptive Kalman filtering-based power distribution system parameter correction method for the two parameters are the same, so that the parameters can be corrected in an all-around and multi-angle manner, and the accuracy of power grid observation and calculation is improved.
The establishment of a state equation and a measurement equation 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 equation of state is established as follows:
Figure SMS_88
(1)
wherein ,
Figure SMS_89
in the form of a discrete time series of,
Figure SMS_90
indicating the state of the system parameter at time k,
Figure SMS_91
representing the state of the system parameter at the previous instant, i.e. at instant k-1,
Figure SMS_92
is a matrix of state transitions that is,
Figure SMS_93
. For line parameters, state variables
Figure SMS_94
。
A measurement equation is established below, and for the line parameters, the equivalent reactance is set
Figure SMS_95
A voltage across the terminals of
Figure SMS_96
In the continuous-time domain, according to kirchhoff's law:
is easy to know
Figure SMS_97
(2)
Figure SMS_98
(3)
Figure SMS_99
(4)
Figure SMS_100
Representing the magnitude of the terminal voltage at the line current outlet at time t,
Figure SMS_101
representing the magnitude of the terminal voltage at which line current flows at time t,
Figure SMS_102
represents the equivalent reactance at time t
Figure SMS_103
The voltage of the two ends is applied,
Figure SMS_104
representing the current flowing through the line at time t,
Figure SMS_105
and represents the current of the line current inflow end at the time t. Since the sample points are discrete, it is necessary to cross-domain the continuous time domain to the discrete time domain:
Figure SMS_106
(5)
Figure SMS_107
(6)
Figure SMS_108
(7)
wherein ,
Figure SMS_111
are all continuous time functions, sampled (in discrete time domain) as
Figure SMS_114
Abbreviated as
Figure SMS_116
，
Figure SMS_110
Is the sampling time. That is to say that the temperature of the molten steel,
Figure SMS_113
represents the current of the line current inflow terminal at the time k,
Figure SMS_115
representing the current at the line current inflow terminal at time k-1,
Figure SMS_117
indicating the k-1 timeThe down-line current flows into the terminal voltage magnitude,
Figure SMS_109
representing the terminal voltage magnitude of the line current inflow at time k,
Figure SMS_112
representing the voltage amplitude of the current outlet end of the line at the moment k;
substituting (4), (5) and (6) into (1) to obtain:
Figure SMS_118
Figure SMS_119
Figure SMS_120
(8)
after finishing, the method can obtain:
Figure SMS_121
(9)
Figure SMS_122
t is transformer transformation ratio, impedance
Figure SMS_123
J represents the imaginary part of the complex number,
Figure SMS_124
；
Figure SMS_125
Figure SMS_126
(2) And establishing a measurement equation and a state equation with noise influence as a system parameter correction model of the adaptive Kalman filtering.
Respectively adding noise interference on a state equation and a measurement equation to obtain:
Figure SMS_127
(10)
Figure SMS_145
is zero mean and covariance of
Figure SMS_130
White gaussian noise. Measured value
Figure SMS_139
,
Figure SMS_143
Respectively the voltage amplitudes at the beginning and end of the line (of the system),
Figure SMS_149
is a measurement matrix, which is a matrix of measurements,
Figure SMS_144
，
Figure SMS_148
representing the magnitude of the terminal voltage of the line current flowing in at time k-2.
Figure SMS_132
Is zero mean and covariance of
Figure SMS_136
The white gaussian noise of (a) is,
Figure SMS_128
in order to add extra noise to the sound,
Figure SMS_134
for measuring outliers, wherein
Figure SMS_131
Compliance parameter of
Figure SMS_135
The distribution of the Bernoulli effect of (A),
Figure SMS_141
,
Figure SMS_147
a constant of large magnitude, illustratively,
Figure SMS_133
in the range of 100-1000 f,
Figure SMS_137
in the form of a function of the unit pulse,
Figure SMS_140
compliance parameter is
Figure SMS_146
The distribution of the Bernoulli effect of (1),
Figure SMS_129
the initial values and the covariances of the system parameters of the medium-voltage distribution system are respectively
Figure SMS_138
And
Figure SMS_142
。
and 2, step: calculating a system parameter modification model (namely formula (10)) based on the adaptive Kalman filtering
Figure SMS_150
Prediction value of system parameters of medium-voltage distribution system at moment
Figure SMS_151
And its covariance
Figure SMS_152
And initial value of the state variable
Figure SMS_153
And its covariance
Figure SMS_154
；
The predicted value and its covariance calculation formula are as follows:
Figure SMS_155
(11)
Figure SMS_156
(12)
known initial value
Figure SMS_157
And its covariance
Figure SMS_158
Calculating the value and covariance of the state variable at the next moment, calculating the value and covariance of the state variable at the later moment according to the value and covariance of the state variable at the next moment, and continuously iterating to obtain
Figure SMS_159
Prediction value of system parameters of medium-voltage distribution system at moment
Figure SMS_160
And its covariance
Figure SMS_161
. Initial value
Figure SMS_162
And its covariance
Figure SMS_163
Is obtained by consulting known standards for the cable used, i.e. the value of the cable as a result of factory testing.
And step 3: measuring matrix obtained by using current value and load power obtained by measuring device and using distribution network three-phase power flow algorithm and state estimation
Figure SMS_164
And calculating the residual error
Figure SMS_165
And covariance
Figure SMS_166
；
Calculating residual error
Figure SMS_167
And its covariance
Figure SMS_168
The formula of (1) is as follows:
Figure SMS_169
(13)
Figure SMS_170
(14)
and 4, step 4: calculating the Mahalanobis distance by the obtained residual error
Figure SMS_171
If at all
Figure SMS_172
Then go to step 5; otherwise, go to step 6;
using residual errors
Figure SMS_173
And its covariance
Figure SMS_174
The formula for calculating the mahalanobis distance is as follows:
Figure SMS_175
(15)
wherein, (r) represents the r-th element, (r, r) represents the r-th row, r-th column element;
and 5: comparison
Figure SMS_176
And
Figure SMS_177
size of (1), if
Figure SMS_178
If so, the corresponding measurement value is regarded as uncertain noise, and the adaptive factor is calculated
Figure SMS_179
And updating the prior residual, calculating the covariance of the updated residual
Figure SMS_180
Then, go to step 7; otherwise, go to step 7 directly;
the judgment and processing method of the outlier and the uncertain noise is explained as follows: calculating the Mahalanobis distance of the residual
Figure SMS_181
If, if
Figure SMS_182
If so, the measurement outliers are eliminated and the predicted values (obtained from equation (11)) are used to replace the posterior state estimated values (used in equation (20)); it should be noted that, 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 is equivalent to replacing the posterior state estimation value with the predicted value. If it is
Figure SMS_183
Then, it is regarded that the uncertainty noise is present at this time. Adaptive factor
Figure SMS_184
And its updated residual covariance
Figure SMS_185
The calculation formula of (c) is as follows:
Figure SMS_186
(16)
Figure SMS_187
(17)
wherein ,
Figure SMS_189
、
Figure SMS_195
the lower and upper bounds of the confidence interval are shown, illustratively, as 0 and 1, respectively.
Figure SMS_199
Is the residual covariance before the update,
Figure SMS_190
for the purpose of the updated residual covariance,
Figure SMS_194
is a vector
Figure SMS_198
To (1) a
Figure SMS_202
The number of the elements is one,
Figure SMS_188
is a vector
Figure SMS_192
To (1) a
Figure SMS_196
The number of the elements is one,
Figure SMS_200
、
Figure SMS_191
、
Figure SMS_193
is a matrix
Figure SMS_197
On the diagonal line of the first
Figure SMS_201
And (4) each element.
The invention judges the outlier and the uncertain noise through the Mahalanobis distance and carries out corresponding processing, thereby realizing the adaptive correction of the parameters.
Step 6: the measured value is regarded as a wild value, discarded, and the predicted value obtained in the step 2 is used for replacing the posterior state estimated value, and the step 7 is carried out;
and 7: kalman filtering gain for calculating parameters related to medium voltage distribution system
Figure SMS_203
；
Kalman filter gain of medium voltage distribution system parameters
Figure SMS_204
The calculation formula of (c) is as follows:
Figure SMS_205
(18)
if uncertain noise occurs, then:
Figure SMS_206
(19)。
and 8: by using
Figure SMS_207
Is calculated to obtain
Figure SMS_208
Posterior state estimation of temporal system parameters
Figure SMS_209
And its covariance
Figure SMS_210
(matrix) and
Figure SMS_211
as a correction to system parametersAnd (6) obtaining the result.
Of medium-voltage distribution systems
Figure SMS_212
Posterior state estimation of temporal system parameters
Figure SMS_213
And its covariance
Figure SMS_214
The calculation formula of (c) is as follows:
Figure SMS_215
(20)
Figure SMS_216
(21)
based on the same inventive concept, an embodiment of the present invention further provides a power distribution system parameter correction system based on adaptive kalman filtering, as shown in fig. 4, including:
a model determination unit to: establishing a state equation and a measurement equation of system parameters of the medium-voltage power distribution system based on adaptive Kalman filtering;
a prediction unit to: calculating a predicted value and covariance of system parameters at a certain moment based on a state equation and a measurement equation;
a residual calculation unit for: calculating residual errors and covariance thereof according to the predicted values and the covariance thereof;
the residual error correction unit is used for calculating the Mahalanobis distance according to the residual error and the covariance thereof and performing 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 the covariance thereof through a self-adaptive factor;
determining whether the corresponding measurement value is a wild value or not according to the Mahalanobis distance, if so, abandoning the wild value, and replacing the measurement value with a predicted value to recalculate the residual error and the covariance thereof;
a gain calculation unit to: calculating Kalman filtering gain according to the residual error determined by the residual error correction unit and the covariance thereof;
an estimated value calculation unit configured to: and calculating the 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 specified confidence interval or not, if so, considering the corresponding measurement value as a wild value and abandoning the wild value, and in the estimation value calculation unit, adopting the predicted value to replace the posterior state estimation value; and judging whether the Mahalanobis distance is in the specified confidence interval, if so, indicating that uncertain noise appears in the measurement, and updating the residual error and the covariance thereof through a self-adaptive factor.
The specific implementation of each unit of the power distribution system parameter correction system based on the adaptive Kalman filtering can be obtained according to the power distribution system parameter correction method based on the adaptive Kalman filtering in the embodiment of the invention, and the detailed description is omitted.
Although the present invention has been described in detail with reference to the foregoing embodiments, it should be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.

Claims (10)

1. A power distribution system parameter correction method based on adaptive Kalman filtering is characterized by comprising the following steps:
establishing a state equation and a measurement equation of system parameters of the medium-voltage power distribution system based on adaptive Kalman filtering;
calculating a predicted value and covariance of system parameters at a certain moment based on a state equation and a measurement equation;
calculating residual errors and covariance thereof according to the predicted values, the covariance thereof and the measured values;
calculating the Mahalanobis distance according to the residual error and the covariance thereof, and performing self-adaptive correction on the residual error according to the Mahalanobis distance, wherein the self-adaptive correction 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 the covariance thereof through a self-adaptive factor;
determining whether the corresponding measured value is a wild value according to the Mahalanobis distance, if so, abandoning the wild value, and recalculating the residual error and the covariance thereof by replacing the measured value with the predicted value;
then, calculating Kalman filtering gain according to the latest residual error and the covariance thereof;
and calculating the posterior state estimation value according to the Kalman filtering gain.
2. The adaptive kalman filter-based power distribution system parameter modification method according to claim 1, wherein establishing the adaptive kalman filter-based state equation and measurement equation for the medium voltage power distribution system parameter comprises:
establishing a state equation and a measurement equation of the added noise:
Figure QLYQS_1
(10)
Figure QLYQS_6
a state variable representing a parameter of the system,
Figure QLYQS_13
indicating the previous moment, i.e.
Figure QLYQS_17
The state of the system parameter at the time of day,
Figure QLYQS_4
is a matrix of state transitions that is,
Figure QLYQS_9
，
Figure QLYQS_14
is zero mean and covariance of
Figure QLYQS_18
White gaussian noise;
Figure QLYQS_7
the measured value is expressed as a measurement value,
Figure QLYQS_10
is a measurement matrix, which is a matrix of measurements,
Figure QLYQS_15
，
Figure QLYQS_19
represents the voltage amplitude at the line current inflow terminal at time k,
Figure QLYQS_21
representing the current flowing through the line at time k,
Figure QLYQS_24
representing the current at the line current inflow terminal at time k-1,
Figure QLYQS_25
representing the magnitude of the terminal voltage at the line current inflow at time k-1,
Figure QLYQS_27
representing the voltage amplitude of the incoming terminal of the line current at the moment k-2;
Figure QLYQS_3
is zero mean and covariance of
Figure QLYQS_11
The white gaussian noise of (a) is,
Figure QLYQS_16
in order to add extra noise to the sound,
Figure QLYQS_20
for measuring outliersIn which
Figure QLYQS_2
Compliance parameter is
Figure QLYQS_8
The distribution of the Bernoulli effect of (1),
Figure QLYQS_23
,
Figure QLYQS_26
is a function of the unit pulse and is,
Figure QLYQS_5
compliance parameter of
Figure QLYQS_12
The distribution of the Bernoulli effect of (A),
Figure QLYQS_22
；
wherein the system parameters comprise line parameters and/or transformer parameters.
3. The adaptive Kalman filtering-based power distribution system parameter correction method of claim 2, wherein calculating the predicted value of a certain time line parameter and its covariance comprises: obtaining initial values and covariance of line parameters of a medium voltage distribution system
Figure QLYQS_28
And
Figure QLYQS_29
，
calculated by the following formula:
Figure QLYQS_30
(11)
Figure QLYQS_31
(12)
known initial value
Figure QLYQS_32
And its covariance
Figure QLYQS_33
Calculating the value and covariance of the state variable at the next moment, calculating the value and covariance of the state variable at the later moment according to the value and covariance of the state variable at the next moment, and continuously iterating to obtain
Figure QLYQS_34
Prediction value of system parameters of medium-voltage distribution system at moment
Figure QLYQS_35
And its covariance
Figure QLYQS_36
。
4. The adaptive Kalman filtering based power distribution system parameter correction method according to claim 3, characterized in that a residual error is calculated
Figure QLYQS_37
And its covariance
Figure QLYQS_38
The formula of (1) is as follows:
Figure QLYQS_39
(13)
Figure QLYQS_40
(14)。
5. the adaptive Kalman filtering-based power distribution system parameter correction method of claim 4, wherein calculating the Mahalanobis distance from the residual and its covariance comprises:
Figure QLYQS_41
(15)
where (r) denotes the r-th element, (r, r) denotes the r-th row, r-th column element.
6. The adaptive Kalman filtering based power distribution system parameter modification method of claim 5,
if the Mahalanobis distance is in the specified confidence interval, which indicates that uncertain noise occurs in the measurement, updating the residual error and the covariance thereof through a self-adaptive factor;
adaptive factor
Figure QLYQS_42
And its updated residual covariance
Figure QLYQS_43
The calculation formula of (a) is as follows:
Figure QLYQS_44
(16)
Figure QLYQS_45
(17)
wherein ,
Figure QLYQS_48
representing the lower bound of the assigned confidence interval,
Figure QLYQS_51
is the residual covariance before the update,
Figure QLYQS_55
as updated remainsThe difference of the covariance of the difference,
Figure QLYQS_49
as a vector
Figure QLYQS_53
To (1) a
Figure QLYQS_57
The number of the elements is one,
Figure QLYQS_59
is a vector
Figure QLYQS_46
To (1) a
Figure QLYQS_50
The number of the elements is one,
Figure QLYQS_54
、
Figure QLYQS_58
、
Figure QLYQS_47
is a matrix
Figure QLYQS_52
On the diagonal line of the first
Figure QLYQS_56
And (4) each element.
7. The adaptive Kalman filtering based power distribution system parameter modification method of claim 6, wherein calculating Kalman filtering gain through a residual and its covariance comprises:
if no uncertain noise appears, the Kalman filtering gain of the parameters of the medium-voltage distribution system
Figure QLYQS_60
The calculation formula of (c) is as follows:
Figure QLYQS_61
(18)
if uncertain noise is present:
Figure QLYQS_62
(19)。
8. the adaptive Kalman filtering based power distribution system parameter correction method of claim 1, characterized in that a posteriori state estimates
Figure QLYQS_63
And its covariance
Figure QLYQS_64
The calculation formula of (a) is as follows:
Figure QLYQS_65
(20)
Figure QLYQS_66
(21) 。
9. the adaptive Kalman filtering based power distribution system parameter modification method according to any one of claims 6-8,
and 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 is discarded, and the predicted value is adopted for replacement.
10. A power distribution system parameter correction system based on adaptive Kalman filtering is characterized by comprising:
a model determination unit to: establishing a state equation and a measurement equation of system parameters of the medium-voltage power distribution system based on adaptive Kalman filtering;
a prediction unit to: calculating a predicted value and covariance of system parameters at a certain moment based on a state equation and a measurement equation;
a residual calculation unit for: calculating residual errors and covariance thereof according to the predicted values and the covariance thereof;
the residual error correction unit is used for calculating the Mahalanobis distance according to the residual error and the covariance thereof and performing 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 the covariance thereof through a self-adaptive factor;
determining whether the corresponding measurement value is a wild value or not according to the Mahalanobis distance, if so, abandoning the wild value, and replacing the measurement value with a predicted value to recalculate the residual error and the covariance thereof;
a gain calculation unit to: calculating Kalman filtering gain according to the residual error determined by the residual error correction unit and the covariance thereof;
an estimated value calculation unit configured to: and calculating the posterior state estimation value according to the Kalman filtering gain.
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CN110530365A (en) * 2019-08-05 2019-12-03 浙江工业大学 A kind of estimation method of human posture based on adaptive Kalman filter

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