CN107016489A - A kind of electric power system robust state estimation method and device - Google Patents
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Abstract
The embodiment of the present invention provides a kind of electric power system robust state estimation method and device based on piecewise nonlinear weight function, and method includes building the bus admittance matrix of power system, measurement measurement equation and zero injection equality constraint；The Jacobian matrix and measurement residual error of power system are calculated, the weight of each measurement is obtained；State variable is updated, and judges whether iterative algorithm reaches convergence threshold, if then obtaining the node voltage amplitude and phase of final power system.The present invention carries out bad data detection and identification and state estimation simultaneously, while state estimation is calculated, can change measurement weight, bad data weight is constantly reduced in iteration, suppress the influence that bad data is brought, effectively reduce amount of calculation, improve operating efficiency；And directly bring the residual error of measurement into segmentation nonlinear weight function, it is to avoid and the calculating of standardized residual, calculating speed can be greatly promoted, the calculating time is saved, is very suitable for engineer applied.
Description
Technical field
The present invention relates to Power system state estimation technology, and in particular to a kind of electric power based on piecewise nonlinear weight function
System robust state estimation method and device.
Background technology
What traditional Power system state estimation was most widely used is weighted least square algorithm, the letter of its model
Single, computational methods are convenient, and it is minimum and unbiased to obtain variance in the case where error in measurement obeys the hypothesis of preferable normal distribution
Estimated result.
But power system measurement in, in addition to random error and systematic error, also inevitably exist some with
The bad data that true value differs greatly, these bad datas can bring serious harmful effect to estimated result.It is mixed in measurement number
Bad data in can make the estimated result of weighted least-squares method lose reliability and accuracy.Estimate to improve presence
The accuracy and practicality of result are counted, is typically the detection that bad data is added after state estimation procedure in actual applications
With identification link, go to examine bad data using methods such as residual tests.However, this mode needs state estimation and umber of defectives
According to the multiple circular test of two links of detection and identification, its workload is huge, and the calculating time is long, and due to residual test method
Itself intrinsic defect, identification reliability is not high enough.
Existing robust state estimation method includes weighting least absolute value (Weighted least absolute
Absolute, WLAV) and weighting least absolute value robust state estimation based on substitution of variable interior point method etc., its solution procedure is answered
It is miscellaneous, it is computationally intensive, it is impossible to be applied in the real-time estimation of large-scale power system.
The content of the invention
In order to overcome the above-mentioned deficiencies of the prior art, the present invention provides a kind of power train based on piecewise nonlinear weight function
Robust state estimation method of uniting and device, gather network parameter and SCADA system parameter first, and according to the network parameter of collection
Bus admittance matrix, measurement measurement equation and zero injection equality constraint are determined with SCADA system parameter；Then with node electricity
Pressure amplitude value and phase are that state variable calculates Jacobian matrix and measurement residual error, and are obtained respectively by piecewise nonlinear weight function
The weight of measurement；State variable is updated finally by Newton iteration method, and carries out convergence judgement, and then obtains state estimation knot
Really.The present invention can meet computational efficiency requirement, but also with good robustness.
In order to realize foregoing invention purpose, the present invention is adopted the following technical scheme that：
The present invention provides a kind of electric power system robust state estimation method based on piecewise nonlinear weight function, methods described
Including：
According to the network parameter of data acquisition and supervisor control the SCADA power system collected and node and branch
Road operational factor, builds the bus admittance matrix, measurement measurement equation and zero injection equality constraint of power system；
Node voltage amplitude and phase using power system is as state variable, and the node of the power system according to structure
The Jacobian matrix and measurement that admittance matrix, measurement measurement equation and zero injection equality constraint calculate power system are residual
Difference, and obtain by piecewise nonlinear weight function the weight of each measurement；
State variable is updated by iterative algorithm, and judges whether iterative algorithm reaches receipts according to the correction of state variable
Threshold value is held back, if then obtaining the node voltage amplitude and phase of final power system.
The network parameter and SCADA system parameter according to collection determines bus admittance matrix, measurement equation and zero
Injection equality constraint includes：
The bus admittance matrix is expressed as：
Wherein, YiiRepresent the diagonal entry of bus admittance matrix, YijRepresent the non-diagonal line element of bus admittance matrix
Element, yijRepresent the branch impedance z between node i and node jijInverse.
The network parameter and SCADA system parameter according to collection determines bus admittance matrix, measurement measurement equation
And zero injection equality constraint include：
The measurement measurement equation is expressed as：
Z=h (x)+r
Wherein, z represents measurement measuring value, and r represents measurement residual error, and x represents state variable, and h (x) calculates for measurement
Equation, it includes node power measurement equation, circuit branch road power measurement equation and transformer branch power measurement equation；
Wherein, node power measurement equation is expressed as：
Wherein, PiThe active power injected for node i, QiThe reactive power injected for node i, viFor the voltage amplitude of node i
Value, vjFor node j voltage magnitude, θiFor the voltage phase angle for node i, θjFor node j voltage phase angle, θijTo represent node i
With node j phase difference of voltage, GijFor the transconductance in bus admittance matrix between corresponding node i and j, BijFor node admittance
Mutual susceptance in matrix between corresponding node i and j, N is node total number；
The circuit branch road power measurement equation is expressed as：
Wherein, PijFor the active power of circuit branch road node side, QijFor the reactive power of circuit branch road node side, ycFor line
Road branch road susceptance over the ground；
The transformer branch power measurement equation is expressed as：
Wherein, Pij' be transformer branch node i side active power, Qij' be transformer branch node i side idle work(
Rate, Pji' be transformer branch node j sides active power, Qji' be transformer branch node j sides reactive power, K is transformation
The non-standard no-load voltage ratio of device, bTFor the susceptance of transformer standard side, node i side is standard side, and no-load voltage ratio is 1；Node j sides are non-standard
Side, no-load voltage ratio is K.
The network parameter and SCADA system parameter according to collection determines bus admittance matrix, measurement equation and zero
Injection equality constraint includes：
The zero injection equality constraint is expressed as：
C (x)=0
Wherein, c (x) is the measurement equation of zero injection node, represents that node injection active and reactive power is zero.
The amplitude and phase using data acquisition and the node voltage of supervisor control as state variable, and according to
Bus admittance matrix, measurement measurement equation and the zero injection equality constraint of the power system of structure calculate the refined of power system
Include than matrix and measurement residual error：
Jacobian matrix is comprising m measurement accounting equation to the local derviation of n state variable, and it is expressed as：
Wherein, H (x) represents Jacobian matrix, and it is m × n matrix；hm(x) m-th of measurement accounting equation, x are representedn
Represent n-th of state variable；
For node voltage amplitude, its Jacobi's element representation is：
Active power and reactive power are injected for node, its Jacobi's element representation is：
Wherein, GiiFor the self-conductance of node i, BiiIt is node i from susceptance；
For circuit branch road active power and reactive power and transformer branch active power and reactive power, its it is refined can
It is than element representation：
Represent that measurement is indexed with l, l=1,2 ..., m, then l-th of measurement residual error rlIt is expressed as：
rl=zl-hl(xk)
Wherein, zlRepresent l-th of measurement measuring value；xkRepresent k-th of state variable, k=1,2 ..., n；hl(xk) table
Show l-th of measurement accounting equation.
The piecewise nonlinear weight function is expressed as：
Wherein, w (rl) represent l-th of measurement piecewise nonlinear weight function, a be bad data detection threshold value；
Pass through w (rl) obtain the weight R of l-th of measurementl, it is expressed as：
Wherein,For the initial weight of l-th of measurement, andσlFor the standard deviation of l-th of measurement.
It is described that state variable is updated by iterative algorithm, and judge whether iterative algorithm reaches according to the correction of state variable
To convergence threshold, include if then obtaining the node voltage amplitude and phase of final power system：
The correction of state variable is obtained using Newton iteration method, is had：
Wherein, t represents iterations, Δ x(t)The correction of state variable during for the t times iteration, T represents transposition, x(t)For
State variable during the t times iteration, x(t+1)State variable during for the t+1 times iteration, h (x(t)) be the t times iteration when state
The corresponding measurement accounting equation of variable, H (x(t)) be the t time iteration when the corresponding Jacobian matrix of state variable, R for measurement
The weight matrix of amount, and R=[R1,R2,…,Rl,…,Rm]T；
According to obtained Δ x(t)Update state variable x；
Carry out convergence judgement, if meet max (| Δ x(t)|) ＜ εx, then show convergence, terminate iterative calculation, output state
Assessment result；Otherwise iteration count plus one, re-start iterative calculation, wherein εxRepresent convergence threshold.
The present invention also provides a kind of power system robust condition estimating device based on piecewise nonlinear weight function, the dress
Put including：
Module is built, for joining according to the network of data acquisition and supervisor control the SCADA power system collected
Number and node and branch road operational factor, build the bus admittance matrix, measurement measurement equation and zero injection of power system
Equality constraint；
Computing module, for using the node voltage amplitude and phase of power system as state variable, and according to structure
Bus admittance matrix, measurement measurement equation and the zero injection equality constraint of power system calculate the Jacobean matrix of power system
Battle array and measurement residual error, and obtain by piecewise nonlinear weight function the weight of each measurement；
Judge module, for updating state variable by iterative algorithm, and judges iteration according to the correction of state variable
Whether algorithm reaches convergence threshold, if then obtaining the node voltage amplitude and phase of final power system.
It is described structure module specifically for：
The bus admittance matrix is expressed as：
Wherein, YiiRepresent the diagonal entry of bus admittance matrix, YijRepresent the non-diagonal line element of bus admittance matrix
Element, yijRepresent the branch impedance z between node i and node jijInverse.
It is described structure module specifically for：
The measurement measurement equation is expressed as：
Z=h (x)+r
Wherein, z represents measurement measuring value, and r represents measurement residual error, and x represents state variable, and h (x) calculates for measurement
Equation, it includes node power measurement equation, circuit branch road power measurement equation and transformer branch power measurement equation；
Wherein, node power measurement equation is expressed as：
Wherein, PiThe active power injected for node i, QiThe reactive power injected for node i, viFor the voltage amplitude of node i
Value, vjFor node j voltage magnitude, θiFor the voltage phase angle for node i, θjFor node j voltage phase angle, θijTo represent node i
With node j phase difference of voltage, GijFor the transconductance in bus admittance matrix between corresponding node i and j, BijFor node admittance
Mutual susceptance in matrix between corresponding node i and j, N is node total number；
The circuit branch road power measurement equation is expressed as：
Wherein, PijFor the active power of circuit branch road node side, QijFor the reactive power of circuit branch road node side, ycFor line
Road branch road susceptance over the ground；
The transformer branch power measurement equation is expressed as：
Wherein, Pij' be transformer branch node i side active power, Qij' be transformer branch node i side idle work(
Rate, Pji' be transformer branch node j sides active power, Qji' be transformer branch node j sides reactive power, K is transformation
The non-standard no-load voltage ratio of device, bTFor the susceptance of transformer standard side, node i side is standard side, and no-load voltage ratio is 1；Node j sides are non-standard
Side, no-load voltage ratio is K.
It is described structure module specifically for：
The zero injection equality constraint is expressed as：
C (x)=0
Wherein, c (x) is the measurement equation of zero injection node, represents that node injection active and reactive power is zero.
The computing module specifically for：
Jacobian matrix is comprising m measurement accounting equation to the local derviation of n state variable, and it is expressed as：
Wherein, H (x) represents Jacobian matrix, and it is m × n matrix；hm(x) m-th of measurement accounting equation, x are representedn
Represent n-th of state variable；
For node voltage amplitude, its Jacobi's element representation is：
Active power and reactive power are injected for node, its Jacobi's element representation is：
Wherein, GiiFor the self-conductance of node i, BiiIt is node i from susceptance；
For circuit branch road active power and reactive power and transformer branch active power and reactive power, its it is refined can
It is than element representation：
Represent that measurement is indexed with l, l=1,2 ..., m, then l-th of measurement residual error rlIt is expressed as：
rl=zl-hl(xk)
Wherein, zlRepresent l-th of measurement measuring value；xkRepresent k-th of state variable, k=1,2 ..., n；hl(xk) table
Show l-th of measurement accounting equation；
The piecewise nonlinear weight function is expressed as：
Wherein, w (rl) represent l-th of measurement piecewise nonlinear weight function, a be bad data detection threshold value；
Pass through w (rl) obtain the weight R of l-th of measurementl, it is expressed as：
Wherein,For the initial weight of l-th of measurement, andσlFor the standard deviation of l-th of measurement.
The judge module specifically for：
The correction of state variable is obtained using Newton iteration method, is had：
Wherein, t represents iterations, Δ x(t)The correction of state variable during for the t times iteration, T represents transposition, x(t)For
State variable during the t times iteration, x(t+1)State variable during for the t+1 times iteration, h (x(t)) be the t times iteration when shape
The corresponding measurement accounting equation of state variable, H (x(t)) be the t time iteration when the corresponding Jacobian matrix of state variable, R for measure
The weight matrix of measurement, and R=[R1,R2,…,Rl,…,Rm]T；
According to obtained Δ x(t)Update state variable x；
Carry out convergence judgement, if meet max (| Δ x(t)|) ＜ εx, then show convergence, terminate iterative calculation, output state
Assessment result；Otherwise iteration count plus one, re-start iterative calculation, wherein εxRepresent convergence threshold.
Compared with immediate prior art, the technical scheme that the present invention is provided has the advantages that：
The present invention carries out bad data detection and identification and state estimation simultaneously, while state estimation is calculated, energy
Enough change measurement weight, bad data weight is constantly reduced in iteration, suppress the influence that bad data is brought, can be effective
Reduction amount of calculation, improve operating efficiency；
Compared with the weight function assignment of prior art, the present invention directly brings the residual error of measurement into segmentation nonlinear weight letter
Number, it is to avoid the calculating of standardized residual, can greatly promote calculating speed, save the calculating time, be very suitable for engineer applied；
The present invention uses piecewise nonlinear weight function, for measurement of the residual error within detection threshold value, maintains it to weigh
Weight, and the measurement for residual error beyond detection threshold value, reduce its weight, closer to zero by Exponential Type Weights function
And be not equal to zero, can effectively exclude bad data it is excessive when, correspondence neutral element is excessive and nonsingular matrix occur in matrix
Situation so that state estimation can effectively restrain, and greatly improve numerical stability when bad data and error in measurement coexist
Property.
Brief description of the drawings
Fig. 1 is the electric power system robust state estimation method flow based on piecewise nonlinear weight function in the embodiment of the present invention
Figure.
Embodiment
The present invention is described in further detail below in conjunction with the accompanying drawings.
The embodiment of the present invention provides a kind of electric power system robust state estimation method based on piecewise nonlinear weight function, such as
Shown in Fig. 1, this method detailed process is as follows：
S101：According to the network parameter of data acquisition and supervisor control the SCADA power system collected and section
(node includes node voltage amplitude, node injecting power and Branch Power Flow with branch road operational factor to be believed point with branch road operational factor
Breath), build the bus admittance matrix, measurement measurement equation and zero injection equality constraint of power system；
S102：The node voltage amplitude and phase of power system be as state variable using in S101, and according to the electricity of structure
Bus admittance matrix, measurement measurement equation and the zero injection equality constraint of Force system calculate the Jacobian matrix of power system
With measurement residual error, and the weight of each measurement is obtained by piecewise nonlinear weight function；
S103：State variable in S102 is updated by iterative algorithm, and judges that iteration is calculated according to the correction of state variable
Whether method reaches convergence threshold, if then obtaining the node voltage amplitude and phase of final power system.
In above-mentioned S101, according to the network parameter of data acquisition and supervisor control the SCADA power system collected
The node of sum and branch road operational factor, build bus admittance matrix, measurement measurement equation and zero injection of power system etc.
Formula constraint is specific as follows：
1) bus admittance matrix is expressed as：
Wherein, YiiRepresent the diagonal entry of bus admittance matrix, YijRepresent the non-diagonal line element of bus admittance matrix
Element, yijRepresent the branch impedance z between node i and node jijInverse.
2) according to the network parameter of collection and SCADA system parameter determine bus admittance matrix, measurement measurement equation with
And zero injection equality constraint include：
Measurement measurement equation is expressed as：
Z=h (x)+r
Wherein, z represents measurement measuring value, and r represents measurement residual error, and x represents state variable, and h (x) calculates for measurement
Equation, it includes node power measurement equation, circuit branch road power measurement equation and transformer branch power measurement equation；
Wherein, node power measurement equation is expressed as：
Wherein, PiThe active power injected for node i, QiThe reactive power injected for node i, viFor the voltage amplitude of node i
Value, vjFor node j voltage magnitude, θiFor the voltage phase angle for node i, θjFor node j voltage phase angle, θijTo represent node i
With node j phase difference of voltage, GijFor the transconductance in bus admittance matrix between corresponding node i and j, BijFor node admittance
Mutual susceptance in matrix between corresponding node i and j, N is node total number；
Circuit branch road power measurement equation is expressed as：
Wherein, PijFor the active power of circuit branch road node side, QijFor the reactive power of circuit branch road node side, ycFor line
Road branch road susceptance over the ground；
Transformer branch power measurement equation is expressed as：
Wherein, Pij' be transformer branch node i side active power, Qij' be transformer branch node i side idle work(
Rate, Pji' be transformer branch node j sides active power, Qji' be transformer branch node j sides reactive power, K is transformation
The non-standard no-load voltage ratio of device, bTFor the susceptance of transformer standard side, node i side is standard side, and no-load voltage ratio is 1；Node j sides are non-standard
Side, no-load voltage ratio is K.
3) zero injection equality constraint is expressed as：
C (x)=0
Wherein, c (x) is the measurement equation of zero injection node, represents that node injection active and reactive power is zero.
State variable includes node voltage amplitude and node voltage phase place, and measurement includes node voltage amplitude, node and noted
Enter active power, node injection reactive power, circuit branch road active power, circuit branch road reactive power, transformer branch active
Power and transformer branch reactive power.
In above-mentioned S102, the node voltage amplitude and phase of power system are as state variable using in S101, and according to structure
Bus admittance matrix, measurement measurement equation and the zero injection equality constraint for the power system built calculate the refined of power system can
Than matrix and measurement residual error, and the weight detailed process for obtaining each measurement by piecewise nonlinear weight function is as follows：
(1) Jacobian matrix is comprising m measurement accounting equation to the local derviation of n state variable, and it is expressed as：
Wherein, H (x) represents Jacobian matrix, and it is m × n matrix；hm(x) m-th of measurement accounting equation, x are representedn
Represent n-th of state variable；
1) for node voltage amplitude, its Jacobi's element representation is：
2) active power and reactive power are injected for node, its Jacobi's element representation is：
Wherein, GiiFor the self-conductance of node i, BiiIt is node i from susceptance；
3) for circuit branch road active power and reactive power and transformer branch active power and reactive power, its is refined
It is than element representation：
(2) represent that measurement is indexed with l, l=1,2 ..., m, then l-th of measurement residual error rlIt is expressed as：
rl=zl-hl(xk)
Wherein, zlRepresent l-th of measurement measuring value；xkRepresent k-th of state variable, k=1,2 ..., n；hl(xk) table
Show l-th of measurement accounting equation；
(3) piecewise nonlinear weight function is expressed as：
Wherein, w (rl) represent l-th of measurement piecewise nonlinear weight function, a be bad data detection threshold value；
(4) w (r are passed throughl) obtain the weight R of l-th of measurementl, it is expressed as：
Wherein,For the initial weight of l-th of measurement, andσlFor the standard deviation of l-th of measurement.
In above-mentioned S103, the state variable in S102 is updated by iterative algorithm, and sentence according to the correction of state variable
Whether disconnected iterative algorithm reaches convergence threshold, if the node voltage amplitude and phase that then obtain final power system are specifically wrapped
Include process as follows：
(1) correction of state variable is obtained using Newton iteration method, is had：
Wherein, t represents iterations, and the correction of state variable when Δ x (t) is the t times iteration, T represents transposition, x(t)
State variable during for the t times iteration, x(t+1)State variable during for the t+1 times iteration, h (x(t)) be the t times iteration when shape
The corresponding measurement accounting equation of state variable, H (x(t)) be the t time iteration when the corresponding Jacobian matrix of state variable, R for measure
The weight matrix of measurement, and R=[R1,R2,…,Rl,…,Rm]T；
(2) according to obtained Δ x(t)Update state variable x；
(3) carry out convergence judgement, if meet max (| Δ x(t)|) ＜ εx, then show convergence, terminate iterative calculation, export shape
State assessment result；Otherwise iteration count plus one, re-start iterative calculation, wherein εxRepresent convergence threshold.
The embodiment of the present invention also provides a kind of power system robust state estimation based on piecewise nonlinear weight function simultaneously
Device, the device includes building module, computing module and judge module, and concrete function is as follows：
Module is built, for joining according to the network of data acquisition and supervisor control the SCADA power system collected
Number and node and branch road operational factor, build the bus admittance matrix, measurement measurement equation and zero injection of power system
Equality constraint；
Computing module, for using the node voltage amplitude and phase of power system as state variable, and according to structure
Bus admittance matrix, measurement measurement equation and the zero injection equality constraint of power system calculate the Jacobean matrix of power system
Battle array and measurement residual error, and obtain by piecewise nonlinear weight function the weight of each measurement；
Judge module, for updating state variable by iterative algorithm, and judges iteration according to the correction of state variable
Whether algorithm reaches convergence threshold, if then obtaining the node voltage amplitude and phase of final power system.
The bus admittance matrix that above-mentioned structure module is determined is expressed as：
Wherein, YiiRepresent the diagonal entry of bus admittance matrix, YijRepresent the non-diagonal line element of bus admittance matrix
Element, yijRepresent the branch impedance z between node i and node jijInverse.
The measurement measurement equation that above-mentioned structure module is determined is expressed as：
Z=h (x)+r
Wherein, z represents measurement measuring value, and r represents measurement residual error, and x represents state variable, and h (x) calculates for measurement
Equation, it includes node power measurement equation, circuit branch road power measurement equation and transformer branch power measurement equation；
Wherein, node power measurement equation is expressed as：
Wherein, PiThe active power injected for node i, QiThe reactive power injected for node i, viFor the voltage amplitude of node i
Value, vjFor node j voltage magnitude, θiFor the voltage phase angle for node i, θjFor node j voltage phase angle, θijTo represent node i
With node j phase difference of voltage, GijFor the transconductance in bus admittance matrix between corresponding node i and j, BijFor node admittance
Mutual susceptance in matrix between corresponding node i and j, N is node total number；
Wherein, circuit branch road power measurement equation is expressed as：
Wherein, PijFor the active power of circuit branch road node side, QijFor the reactive power of circuit branch road node side, ycFor line
Road branch road susceptance over the ground；
Wherein, transformer branch power measurement equation is expressed as：
Wherein, Pij' be transformer branch node i side active power, Qij' be transformer branch node i side idle work(
Rate, Pji' be transformer branch node j sides active power, Qji' be transformer branch node j sides reactive power, K is transformation
The non-standard no-load voltage ratio of device, bTFor the susceptance of transformer standard side, node i side is standard side, and no-load voltage ratio is 1；Node j sides are non-standard
Side, no-load voltage ratio is K.
The zero injection equality constraint that above-mentioned structure module is determined is expressed as：
C (x)=0
Wherein, c (x) is the measurement equation of zero injection node, represents that node injection active and reactive power is zero.
State variable includes node voltage amplitude and node voltage phase place, and the measurement includes node voltage amplitude, section
Point injection active power, node injection reactive power, circuit branch road active power, circuit branch road reactive power, transformer branch
Active power and transformer branch reactive power.
Above-mentioned computing module is using the node voltage amplitude and phase of power system as state variable, and according to structure
Bus admittance matrix, measurement measurement equation and the zero injection equality constraint of power system calculate the Jacobean matrix of power system
Battle array and measurement residual error, and the weight detailed process for obtaining each measurement by piecewise nonlinear weight function is as follows：
Jacobian matrix is comprising m measurement accounting equation to the local derviation of n state variable, and it is expressed as：
Wherein, H (x) represents Jacobian matrix, and it is m × n matrix；hm(x) m-th of measurement accounting equation, x are representedn
Represent n-th of state variable；
For node voltage amplitude, its Jacobi's element representation is：
Active power and reactive power are injected for node, its Jacobi's element representation is：
Wherein, GiiFor the self-conductance of node i, BiiIt is node i from susceptance；
For circuit branch road active power and reactive power and transformer branch active power and reactive power, its it is refined can
It is than element representation：
Represent that measurement is indexed with l, l=1,2 ..., m, then l-th of measurement residual error rlIt is expressed as：
rl=zl-hl(xk)
Wherein, zlRepresent l-th of measurement measuring value；xkRepresent k-th of state variable, k=1,2 ..., n；hl(xk) table
Show l-th of measurement accounting equation；
Piecewise nonlinear weight function is expressed as：
Wherein, w (rl) represent l-th of measurement piecewise nonlinear weight function, a be bad data detection threshold value；
Pass through w (rl) obtain the weight R of l-th of measurementl, it is expressed as：
Wherein,For the initial weight of l-th of measurement, andσlFor the standard deviation of l-th of measurement.
Above-mentioned judge module updates state variable by iterative algorithm, and judges iteration according to the correction of state variable
Whether algorithm reaches convergence threshold, if then obtaining the node voltage amplitude and phase detailed process of final power system such as
Under：
(1) correction of state variable is obtained using Newton iteration method, is had：
Wherein, t represents iterations, Δ x(t)The correction of state variable during for the t times iteration, T represents transposition, x(t)For
State variable during the t times iteration, x(t+1)State variable during for the t+1 times iteration, h (x(t)) be the t times iteration when state
The corresponding measurement accounting equation of variable, H (x(t)) be the t time iteration when the corresponding Jacobian matrix of state variable, R for measurement
The weight matrix of amount, and R=[R1,R2,…,Rl,…,Rm]T；
(2) according to obtained Δ x(t)Update state variable x；
(3) carry out convergence judgement, if meet max (| Δ x(t)|) ＜ εx, then show convergence, terminate iterative calculation, export shape
State assessment result；Otherwise iteration count plus one, re-start iterative calculation, wherein εxRepresent convergence threshold.
The embodiment of the present invention is first when iterative calculation is proceeded by, and each measurement weights use the initial value of setting, profit
Initial value is tried to achieve with weighted least-squares method；Secondly weight is updated with piecewise nonlinear weight function amount of calculation according to measurement residuals, entered
Row measures the weights that measurement is changed before the iteration that weights change with residual error, each iteration, by calculating iterative equation more new state
Amount, and made comparisons with convergence criterion, until convergence, obtains state estimation result.
It should be understood by those skilled in the art that, embodiments herein can be provided as method, system or computer program
Product.Therefore, the application can be using the reality in terms of complete hardware embodiment, complete software embodiment or combination software and hardware
Apply the form of example.Moreover, the application can be used in one or more computers for wherein including computer usable program code
The computer program production that usable storage medium is implemented on (including but is not limited to magnetic disk storage, CD-ROM, optical memory etc.)
The form of product.
The application is the flow with reference to method, equipment (system) and computer program product according to the embodiment of the present application
Figure and/or block diagram are described.It should be understood that can be by every first-class in computer program instructions implementation process figure and/or block diagram
Journey and/or the flow in square frame and flow chart and/or block diagram and/or the combination of square frame.These computer programs can be provided
The processor of all-purpose computer, special-purpose computer, Embedded Processor or other programmable data processing devices is instructed to produce
A raw machine so that produced by the instruction of computer or the computing device of other programmable data processing devices for real
The device for the function of being specified in present one flow of flow chart or one square frame of multiple flows and/or block diagram or multiple square frames.
These computer program instructions, which may be alternatively stored in, can guide computer or other programmable data processing devices with spy
Determine in the computer-readable memory that mode works so that the instruction being stored in the computer-readable memory, which is produced, to be included referring to
Make the manufacture of device, the command device realize in one flow of flow chart or multiple flows and/or one square frame of block diagram or
The function of being specified in multiple square frames.
These computer program instructions can be also loaded into computer or other programmable data processing devices so that in meter
Series of operation steps is performed on calculation machine or other programmable devices to produce computer implemented processing, thus in computer or
The instruction performed on other programmable devices is provided for realizing in one flow of flow chart or multiple flows and/or block diagram one
The step of function of being specified in individual square frame or multiple square frames.
Claims (14)
1. a kind of electric power system robust state estimation method, it is characterised in that methods described includes：
According to the network parameter of data acquisition and supervisor control the SCADA power system collected and node transported with branch road
Row parameter, builds the bus admittance matrix, measurement measurement equation and zero injection equality constraint of power system；
Node voltage amplitude and phase using power system is as state variable, and the node admittance of the power system according to structure
Matrix, measurement measurement equation and zero injection equality constraint calculate the Jacobian matrix and measurement residual error of power system, and
The weight of each measurement is obtained by piecewise nonlinear weight function；
State variable is updated by iterative algorithm, and judges whether iterative algorithm reaches convergence threshold according to the correction of state variable
Value, if then obtaining the node voltage amplitude and phase of final power system.
2. electric power system robust state estimation method according to claim 1, it is characterised in that the bus admittance matrix
It is expressed as：
Wherein, YiiRepresent the diagonal entry of bus admittance matrix, YijRepresent the off diagonal element of bus admittance matrix, yij
Represent the branch impedance z between node i and node jijInverse.
3. electric power system robust state estimation method according to claim 1, it is characterised in that the measurement amount measurement side
Journey is expressed as：
Z=h (x)+r
Wherein, z represents measurement measuring value, and r represents measurement residual error, and x represents state variable, and h (x) is measurement calculating side
Journey, it includes node power measurement equation, circuit branch road power measurement equation and transformer branch power measurement equation；
Wherein, node power measurement equation is expressed as：
Wherein, PiThe active power injected for node i, QiThe reactive power injected for node i, viFor the voltage magnitude of node i, vj
For node j voltage magnitude, θiFor the voltage phase angle for node i, θjFor node j voltage phase angle, θijTo represent node i and section
Point j phase difference of voltage, GijFor the transconductance in bus admittance matrix between corresponding node i and j, BijFor bus admittance matrix
Mutual susceptance between middle corresponding node i and j, N is node total number；
The circuit branch road power measurement equation is expressed as：
Wherein, PijFor the active power of circuit branch road node side, QijFor the reactive power of circuit branch road node side, ycFor circuit branch
Road susceptance over the ground；
The transformer branch power measurement equation is expressed as：
Wherein, Pij' be transformer branch node i side active power, Qij' be transformer branch node i side reactive power,
Pji' be transformer branch node j sides active power, Qji' be transformer branch node j sides reactive power, K is transformer
Non-standard no-load voltage ratio, bTFor the susceptance of transformer standard side, node i side is standard side, and no-load voltage ratio is 1；Node j sides are non-standard side,
No-load voltage ratio is K.
4. electric power system robust state estimation method according to claim 1, it is characterised in that the zero injection equation is about
Beam is expressed as：
C (x)=0
Wherein, c (x) is the measurement equation of zero injection node, represents that node injection active and reactive power is zero.
5. electric power system robust state estimation method according to claim 3, it is characterised in that it is described with data acquisition with
The amplitude and phase of the node voltage of supervisor control are as state variable, and the node admittance of the power system according to structure
Matrix, measurement measurement equation and zero injection equality constraint calculate the Jacobian matrix and measurement residual error bag of power system
Include：
Jacobian matrix is comprising m measurement accounting equation to the local derviation of n state variable, and it is expressed as：
Wherein, H (x) represents Jacobian matrix, and it is m × n matrix；hm(x) m-th of measurement accounting equation, x are representednRepresent
N-th of state variable；
For node voltage amplitude, its Jacobi's element representation is：
Active power and reactive power are injected for node, its Jacobi's element representation is：
Wherein, GiiFor the self-conductance of node i, BiiIt is node i from susceptance；
For circuit branch road active power and reactive power and transformer branch active power and reactive power, its Jacobi member
Element is expressed as：
Represent that measurement is indexed with l, l=1,2 ..., m, then l-th of measurement residual error rlIt is expressed as：
rl=zl-hl(xk)
Wherein, zlRepresent l-th of measurement measuring value；xkRepresent k-th of state variable, k=1,2 ..., n；hl(xk) represent l
Individual measurement accounting equation.
6. electric power system robust state estimation method according to claim 5, it is characterised in that described by being segmented non-thread
The weight that property weight function obtains each measurement includes：
The piecewise nonlinear weight function is expressed as：
Wherein, w (rl) represent l-th of measurement piecewise nonlinear weight function, a be bad data detection threshold value；
Pass through w (rl) obtain the weight R of l-th of measurementl, it is expressed as：
Wherein,For the initial weight of l-th of measurement, andσlFor the standard deviation of l-th of measurement.
7. electric power system robust state estimation method according to claim 6, it is characterised in that described to pass through iterative algorithm
State variable is updated, and judges whether iterative algorithm reaches convergence threshold according to the correction of state variable, if then obtaining most
The node voltage amplitude and phase of whole power system include：
The correction of state variable is obtained using Newton iteration method, is had：
Wherein, t represents iterations, Δ x(t)The correction of state variable during for the t times iteration, T represents transposition, x(t)For t
State variable during secondary iteration, x(t+1)State variable during for the t+1 times iteration, h (x(t)) be the t time iteration when state change
Measure corresponding measurement accounting equation, H (x(t)) be the t times iteration when the corresponding Jacobian matrix of state variable, R is measurement
Weight matrix, and R=[R1,R2,…,Rl,…,Rm]T；
According to obtained Δ x(t)Update state variable x；
Carry out convergence judgement, if meet max (| Δ x(t)|) ＜ εx, then show convergence, terminate iterative calculation, output state assesses knot
Really；Otherwise iteration count plus one, re-start iterative calculation, wherein εxRepresent convergence threshold.
8. a kind of power system robust condition estimating device, it is characterised in that described device includes：
Build module, for the network parameter according to data acquisition and supervisor control the SCADA power system collected and
Node and branch road operational factor, build the bus admittance matrix, measurement measurement equation and zero injection equation of power system
Constraint；
Computing module, for using the node voltage amplitude and phase of power system as state variable, and according to the electric power of structure
The bus admittance matrix of system, measurement measurement equation and zero injection equality constraint calculate power system Jacobian matrix and
Measurement residual error, and obtain by piecewise nonlinear weight function the weight of each measurement；
Judge module, for updating state variable by iterative algorithm, and judges iterative algorithm according to the correction of state variable
Whether convergence threshold is reached, if then obtaining the node voltage amplitude and phase of final power system.
9. power system robust condition estimating device according to claim 8, it is characterised in that the structure module is specific
For：
The bus admittance matrix is expressed as：
Wherein, YiiRepresent the diagonal entry of bus admittance matrix, YijRepresent the off diagonal element of bus admittance matrix, yij
Represent the branch impedance z between node i and node jijInverse.
10. power system robust condition estimating device according to claim 8, it is characterised in that the structure module tool
Body is used for：
The measurement measurement equation is expressed as：
Z=h (x)+r
Wherein, z represents measurement measuring value, and r represents measurement residual error, and x represents state variable, and h (x) is measurement calculating side
Journey, it includes node power measurement equation, circuit branch road power measurement equation and transformer branch power measurement equation；
Wherein, node power measurement equation is expressed as：
Wherein, PiThe active power injected for node i, QiThe reactive power injected for node i, viFor the voltage magnitude of node i, vj
For node j voltage magnitude, θiFor the voltage phase angle for node i, θjFor node j voltage phase angle, θijTo represent node i and section
Point j phase difference of voltage, GijFor the transconductance in bus admittance matrix between corresponding node i and j, BijFor bus admittance matrix
Mutual susceptance between middle corresponding node i and j, N is node total number；
The circuit branch road power measurement equation is expressed as：
Wherein, PijFor the active power of circuit branch road node side, QijFor the reactive power of circuit branch road node side, ycFor circuit branch
Road susceptance over the ground；
The transformer branch power measurement equation is expressed as：
Wherein, Pij' be transformer branch node i side active power, Qij' be transformer branch node i side reactive power,
Pji' be transformer branch node j sides active power, Qji' be transformer branch node j sides reactive power, K is transformer
Non-standard no-load voltage ratio, bTFor the susceptance of transformer standard side, node i side is standard side, and no-load voltage ratio is 1；Node j sides are non-standard side,
No-load voltage ratio is K.
11. power system robust condition estimating device according to claim 8, it is characterised in that the structure module tool
Body is used for：
The zero injection equality constraint is expressed as：
C (x)=0
Wherein, c (x) is the measurement equation of zero injection node, represents that node injection active and reactive power is zero.
12. power system robust condition estimating device according to claim 10, it is characterised in that the computing module tool
Body is used for：
Jacobian matrix is comprising m measurement accounting equation to the local derviation of n state variable, and it is expressed as：
Wherein, H (x) represents Jacobian matrix, and it is m × n matrix；hm(x) m-th of measurement accounting equation, x are representednRepresent
N-th of state variable；
For node voltage amplitude, its Jacobi's element representation is：
Active power and reactive power are injected for node, its Jacobi's element representation is：
Wherein, GiiFor the self-conductance of node i, BiiIt is node i from susceptance；
For circuit branch road active power and reactive power and transformer branch active power and reactive power, its Jacobi member
Element is expressed as：
Represent that measurement is indexed with l, l=1,2 ..., m, then l-th of measurement residual error rlIt is expressed as：
rl=zl-hl(xk)
Wherein, zlRepresent l-th of measurement measuring value；xkRepresent k-th of state variable, k=1,2 ..., n；hl(xk) represent l
Individual measurement accounting equation.
13. power system robust condition estimating device according to claim 12, it is characterised in that the piecewise nonlinear
Weight function is expressed as：
Wherein, w (rl) represent l-th of measurement piecewise nonlinear weight function, a be bad data detection threshold value；
Pass through w (rl) obtain the weight R of l-th of measurementl, it is expressed as：
Wherein,For the initial weight of l-th of measurement, andσlFor the standard deviation of l-th of measurement.
14. power system robust condition estimating device according to claim 13, it is characterised in that the judge module tool
Body is used for：
The correction of state variable is obtained using Newton iteration method, is had：
Wherein, t represents iterations, Δ x(t)The correction of state variable during for the t times iteration, T represents transposition, x(t)For t
State variable during secondary iteration, x(t+1)State variable during for the t+1 times iteration, h (x(t)) be the t time iteration when state change
Measure corresponding measurement accounting equation, H (x(t)) be the t times iteration when the corresponding Jacobian matrix of state variable, R is measurement
Weight matrix, and R=[R1,R2,…,Rl,…,Rm]T；
According to obtained Δ x(t)Update state variable x；
Carry out convergence judgement, if meet max (| Δ x(t)|) ＜ εx, then show convergence, terminate iterative calculation, output state assesses knot
Really；Otherwise iteration count plus one, re-start iterative calculation, wherein εxRepresent convergence threshold.
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| CN113255959A (en) * | 2021-04-09 | 2021-08-13 | 广东电网有限责任公司电力调度控制中心 | Power system dynamic state estimation method and system |
| CN113139288A (en) * | 2021-04-21 | 2021-07-20 | 广东电网有限责任公司广州供电局 | Power distribution network distributed robust state estimation method and device based on GPU (graphics processing Unit) secondary acceleration |
| CN115470736A (en) * | 2022-09-29 | 2022-12-13 | 长沙学院 | Power system dynamic behavior modeling method adaptive to variable working condition operation of energy storage power station |
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