CN108899910A - A kind of data-driven electric network swim equation the linear calculation method of pair of measurement noise robustness - Google Patents
A kind of data-driven electric network swim equation the linear calculation method of pair of measurement noise robustness Download PDFInfo
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
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Abstract
The present invention relates to a kind of to the data-driven electric network swim equation the linear calculation method for measuring noise robustness, belongs to electric network swim calculating field and data driven technique field.Power grid history data is arranged first；Then the power flow equation parameter of linearisation is solved, includes the solution of power flow equation initial parameter values, parameter coarse regulation, parameter fine control；Finally the calculating of power grid Real-time Power Flow is carried out using the linearisation power flow equation that solution obtains.The present invention linearizes power flow equation using power grid historical metrology data, to the noise robustness in metric data, the precision of electric network swim equation calculation can be improved, reduce the calculation amount during operation of power networks, help to reduce operation of power networks cost, there are wide application scenarios in fields such as the power grid risk assessment calculating for being related to more analysis of uncertainty；This method has fully considered the noise in metric data, situation about being more in line in actual electric network.
Description
Technical field
The present invention relates to a kind of to the data-driven electric network swim equation the linear calculation method for measuring noise robustness, belongs to
Electric network swim calculating field and data driven technique field.
Background technique
Electric network swim analysis and optimization is the basis of Power System Planning, operation, control, however electric network swim equation is non-
Linearly high computation burden and poor constringent challenge are brought to electrical network analysis and optimization algorithm.Especially for be related to compared with
The power grid risk assessment of more analysiss of uncertainty calculates, and is related to the electricity market node electricity price calculating of high real-time calculating,
All have higher requirements to the calculating time of algorithm with computational convergence.Electric network swim equation linearization calculation based on model in the past
Method is difficult to ensure computational accuracy.
Recent literature Liu Y, Zhang N, Wang Y, et al.Data-Driven Power Flow
Linearization:A Regression Approach [J] .IEEE Transactions on Smart Grid, 2018 make
Power flow equation is linearized with data-driven method, this method is linear using the history data metric data of power grid
Change trend.Due to the linearisation power flow equation of the case where being for specific power grid " customization ", this method can be promoted significantly
Linearize the computational accuracy of power flow equation.
But grid measurement data contains noise, document Liu Y, Zhang N, Wang Y, et al.Data-Driven
Power Flow Linearization:A Regression Approach[J].IEEE Transactions on Smart
Grid, method in 2018 precision when metric data contains noise are greatly reduced.It does not research and propose still and makes an uproar to measurement at present
The data-driven electric network swim equation the linear calculation method of sound robust.
It in addition to this, include calling commercial optimization software package Mosek in step involved in this patent.Mosek
It is convex excellent to be to solve for large scale linear programming, mixed integer linear programming, quadratic programming, MINLP model, cone optimization etc.
The business software packet of change.The language such as Mosek and C, C#, Java, Python, Matlab have preferable interaction.In Mosek use
Point method is main optimization algorithm, and concrete principle is shown in document Andersen E D, Andersen K D.The MOSEK
interior point optimizer for linear programming:an implementation of the
homogeneous algorithm[M]//High performance optimization.Springer,Boston,MA,
2000:197-232。
Summary of the invention
The purpose of the present invention is to propose to a kind of to the data-driven electric network swim equation linearization calculation for measuring noise robustness
Method.Power flow equation is linearized using power grid historical metrology data, to the noise robustness in metric data, to improve electricity
Net power flow equation calculate precision, reduce operation of power networks during calculation amount, facilitate reduce operation of power networks cost, be related to
There are wide application scenarios in the fields such as the power grid risk assessment calculating of more analysis of uncertainty.
Data-driven electric network swim equation the linear calculation method proposed by the present invention to measurement noise robustness, including with
Lower step：
(1) metric data in power grid history data is pre-processed, metric data includes node active power
Injection, the injection of node reactive power, node voltage phase angle and node voltage amplitude；Specific step is as follows：
All N number of node divisions of electric system are PQ, PV, V θ node by (1-1), and wherein PQ node on behalf node is active
Power injection and reactive power are injected to the node of known quantity, and PV node represents the injection of node active power and voltage magnitude as
The node for the amount of knowing, V θ node on behalf node voltage amplitude and voltage phase angle are the node of known quantity, according to node type, by power grid
The active power injection of operation, reactive power injection, voltage magnitude and voltage phase angle data are respectively according to PQ, PV, V θ node
Sequence arranges：
Wherein, P indicates that each node active power of power grid injects vector, and P is the dimensional vector of N × 1,Indicate that PQ node is active
Power injects vector PLTransposition,Indicate that PV node active power injects vector PSTransposition,Indicate V θ node wattful power
Rate injects vector PRTransposition, Q indicates that each node reactive power of power grid injects vector, and Q is the dimensional vector of N × 1,Indicate PQ section
Point reactive power injects vector QLTransposition,Indicate that PV node reactive power injects vector QSTransposition,Indicate V θ node
The transposition of reactive power injection vector；V indicates each node voltage amplitude vector of power grid, and V is the dimensional vector of N × 1,Indicate PQ
Node voltage amplitude vector VLTransposition,Indicate PV node voltage magnitude vector VSTransposition,Indicate V θ node voltage width
It is worth vector VRTransposition；θ indicates each node voltage phase angle vector of power grid, and θ is the dimensional vector of N × 1,Indicate PQ node voltage phase
Angular amount θLTransposition,Indicate PV node voltage phase angle vector θSTransposition,Indicate V θ node voltage phase angle vector θRTurn
It sets；
The historical metrology data of electric system different time points as unit of the format in step 1-1, is organized by (1-2)
The form of X matrix and Y matrix：
Wherein, M is the time point number of historical metrology data, and subscript 1...m...M indicates the time of historical metrology data
Point, wherein xmAnd ymIt is all the dimensional vector of 2N × 1, X and Y are 2N × M dimension matrixes；
(2) the power flow equation parameter of linearisation is solved, specific step is as follows：
(2-1) solves the optimization problem in following (3) using interior point method, obtains power flow equation initial parameter values：
In above-mentioned optimization problem, (3a) is objective function, and (3b) (3c) is constraint condition, wherein | | | |FIt indicates
The Frobenius norm of matrix, i.e., to given matrix D,The mark of tr () representing matrix, mark are matrixes
Diagonal element adduction；
In above-mentioned optimization problem, E, F,It is known variables to be asked with C, wherein E is N × N symmetrical matrix,
Element and transposed matrix E i.e. in matrixTThe element of middle same position is equal：E=ET, F is N × N symmetrical matrix, i.e., first in matrix
Element and transposed matrix FTThe element of middle same position is equal：F=FT,It is N × N diagonal matrix： It is N × N diagonal matrix：C is the dimensional vector of N × 1,Represent withFor diagonal element building diagonal matrix,Represent withFor diagonal element
The diagonal matrix of element building,Representative takes matrixThe vector of diagonal element building,Representative takes matrixDiagonally
The vector of member building；
In above-mentioned optimization problem, X, Y, Pmin、Pmax、QminAnd QmaxIt is known quantity, wherein PminAnd PmaxIt goes through respectively
Minimum and maximum active power injection of each node from the moment 1 to T, Q in history dataminAnd QmaxIt is every in historical data respectively
Minimum and maximum reactive power injection of a node from the moment 1 to T, Pmin、Pmax、QminAnd QmaxIt is all the dimensional vector of N × 1；
Above-mentioned optimization problem is solved, and 2N × 2N dimension matrix A is calculated using formula (3b)J'；
(2-2) carries out coarse adjustment to above-mentioned power flow equation parameter, ties up matrix A to 2N × 2N of above-mentioned steps (2-1)J'It carries out more
Newly, include the following steps：
(2-2-1) solves the optimization problem in following (4) using interior point method：
Y-εY=AJ'X+dAJ'X-AJ'εX+C1T (4b)
In optimization problem (4), (4a) is objective function, and (4b)-(4d) is constraint condition, whereinIt indicates to close
In matrix Σ-1Norm, i.e., to given matrix D,Σ-1It is the inverse matrix of Σ, Σ is pair of setting
Angle battle array, diagonal element are the variance of error in measurement： WithRespectively indicate εXAnd εYVariance；
In optimization problem (4), εX、εY、E、F、It is known variables to be asked with C, wherein εXAnd εYAll be 2N ×
M ties up matrix, εXAnd εYRespectively indicate the measurement noise of measurement matrix X and Y, dAJ'It is 2N × 2N dimension matrix, representing matrix AJ'Change
Change amount；
In optimization problem (4), AJ'、Σ、X、Y、Pmin、Pmax、QminAnd QmaxIt is known quantity, wherein AJ'By above-mentioned step
Suddenly (2-1) is calculated, and Σ is the diagonal matrix of setting, and diagonal element is the variance of error in measurement：
WithRespectively indicate εXAnd εYVariance, obtain in the explanation by power grid measurement equipment；
It solves optimization problem (4), calculates dA using formula (4c)J', the dA that is calculated with thisJ'Update matrix AJ'：AJ'
←AJ'+dAJ'；
(2-2-2) is to inequalityJudged, ifIt thens follow the steps
(2-3)；IfThen follow the steps (2-2-1), wherein W is weight matrix：σXAnd σYPoint
The standard deviation of other representing matrix X and matrix Y；It indicates Hadamard operator, calculates the product of two matrix corresponding position elements,
Max | | it indicates to seek the maximum value of element absolute value in matrix, α indicates to stop the threshold parameter of iteration, takes α=0.1；
(2-3) carries out fine tuning to above-mentioned power flow equation parameter, ties up matrix A to 2N × 2N of above-mentioned steps (2-2)J'It carries out more
Newly, include the following steps：
(2-3-1) solves the optimization problem in (5) using interior point method：
Y-εY=AX+dAX-A εX+C1T (5b)
In optimization problem (5), (5a) is objective function, and (5b) is constraint condition, wherein
||·||1The 1- norm of representing matrix, i.e., to given matrix D,dijThe element of representing matrix D the i-th row j column.
In optimization problem (5), εX、εY, dA and C be known variables to be asked, wherein dA is 2N × 2N dimension matrix, is indicated
The variable quantity of matrix A；
In optimization problem (5), A, Σ, X and Y are known quantities, wherein A is the A in above-mentioned steps (2-2)J'；
After solving optimization problem (5), matrix A is updated：A ← A+dA, and record variable C；
(2-3-2) is to inequalityJudged：IfThen follow the steps (3-
1), ifIt executes step (2-3-1)；
(3) the power flow equation parameter obtained according to above-mentioned solution obtains the linearisation power flow equation of power grid, and carries out power grid
Load flow calculation, specific step is as follows：
The node type PQ that is divided in the parameter A and C and above-mentioned steps (1) that (3-1) is obtained according to above-mentioned steps (2),
PV and V θ writes out the linearisation power flow equation of power grid：
Wherein, CiIndicate above-mentioned steps (2-3-1) vector C according to the subvector after (6) arrangement, AijIndicate above-mentioned steps
Submatrix after (2-3-1) matrix A is arranged according to (6) maps formula (6) dependent variable in left side, P when calculating trendR, QS
And QRIt is unknown quantity, PL, PSAnd QLIt is known quantity, for the independent variable on formula (6) mapping right side, θL, θSAnd VLIt is unknown quantity, θR,
VSAnd VRIt is known quantity, and then matrix (6) is write as to the form of following matrix in block form：
Wherein, x2=[θR,VS,VR]TAnd y1=[PL,PS,QL]TIt is known quantity, x1=[θL,θS,VL]TAnd y2=[PR,QS,
QR]TIt is unknown quantity,WithRespectively indicate A in formula (6)ijThe corresponding part of matrix：
(3-2) solves the linearisation power flow equation of above-mentioned steps (3-1) according to the following formula, obtains power grid linearisation power flow equation
Real-time solution：
Wherein x1=[θL,θS,VL]TAnd y2=[PR,QS,QR]TThe solution of the power flow equation as linearized.
Data-driven electric network swim equation the linear calculation method proposed by the present invention to measurement noise robustness, advantage
It is：
1, it considers containing this feature of noise in electrical power system metric data, the present invention measures noise Shandong to electric system
Stick, compared to the data-driven power flow equation the linear calculation method researched and proposed before, the present invention has fully considered power train
The actual conditions of metric data in system.
2, the training data of the method for the present invention is the historical data measured, reflects the true operation shape of particular power system
State, in addition the present invention compares robust to the metric data noise in electric system, therefore the equation after linearisation is with higher
Computational accuracy.
3, what the method for the present invention obtained is the electric network swim accounting equation of linearisation, is asked in direct calculating and as optimization
In the problem of constraint of topic is calculated, calculation amount can be effectively reduced, especially for being related to more analysis of uncertainty
Power grid risk assessment calculate, and be related to the electricity market node electricity price of high real-time calculating and calculate, have more apparent
Advantage.
Detailed description of the invention
Fig. 1 is 300 groups of test result voltage phase angles of IEEE-33 system and amplitude schematic diagram in the embodiment of the present invention.
Specific embodiment
Data-driven electric network swim equation the linear calculation method proposed by the present invention to measurement noise robustness, including with
Lower step：
(1) metric data in power grid history data is pre-processed, metric data includes node active power
Injection, the injection of node reactive power, node voltage phase angle and node voltage amplitude；Specific step is as follows：
All N number of node divisions of electric system are PQ, PV, V θ node by (1-1), and wherein PQ node on behalf node is active
Power injection and reactive power are injected to the node of known quantity, and PV node represents the injection of node active power and voltage magnitude as
The node for the amount of knowing, V θ node on behalf node voltage amplitude and voltage phase angle are the node of known quantity, according to node type, by power grid
The active power injection of operation, reactive power injection, voltage magnitude and voltage phase angle data are respectively according to PQ, PV, V θ node
Sequence arranges：
Wherein, P indicates that each node active power of power grid injects vector, and P is the dimensional vector of N × 1,Indicate that PQ node is active
Power injects vector PLTransposition,Indicate that PV node active power injects vector PSTransposition,Indicate V θ node wattful power
Rate injects vector PRTransposition, Q indicates that each node reactive power of power grid injects vector, and Q is the dimensional vector of N × 1,Indicate PQ section
Point reactive power injects vector QLTransposition,Indicate that PV node reactive power injects vector QSTransposition,Indicate V θ node
The transposition of reactive power injection vector；V indicates each node voltage amplitude vector of power grid, and V is the dimensional vector of N × 1,Indicate PQ
Node voltage amplitude vector VLTransposition,Indicate PV node voltage magnitude vector VSTransposition,Indicate V θ node voltage width
It is worth vector VRTransposition；θ indicates each node voltage phase angle vector of power grid, and θ is the dimensional vector of N × 1,Indicate PQ node voltage phase
Angular amount θLTransposition,Indicate PV node voltage phase angle vector θSTransposition,Indicate V θ node voltage phase angle vector θRTurn
It sets；
The historical metrology data of electric system different time points as unit of the format in step 1-1, is organized by (1-2)
The form of X matrix and Y matrix：
Wherein, M is the time point number of historical metrology data, and subscript 1...m...M indicates the time of historical metrology data
Point, wherein xmAnd ymIt is all the dimensional vector of 2N × 1, X and Y are 2N × M dimension matrixes；It may be noted that record and arrange in step 1
All data are all noise-containing metric data, rather than truthful data.
(2) the power flow equation parameter of linearisation is solved, specific step is as follows：
(2-1) solves the optimization problem in following (3) using interior point method, obtains power flow equation initial parameter values：
In above-mentioned optimization problem, (3a) is objective function, and (3b) (3c) is constraint condition, wherein | | | |FIt indicates
The Frobenius norm of matrix, i.e., to given matrix D,The mark of tr () representing matrix, mark are matrixes
Diagonal element adduction；
In above-mentioned optimization problem, E, F,It is known variables to be asked with C, wherein E is N × N symmetrical matrix,
Element and transposed matrix E i.e. in matrixTThe element of middle same position is equal：E=ET, F is N × N symmetrical matrix, i.e., first in matrix
Element and transposed matrix FTThe element of middle same position is equal：F=FT,It is N × N diagonal matrix： It is N × N diagonal matrix：C is the dimensional vector of N × 1,Represent withFor diagonal element building diagonal matrix,Represent withFor diagonal element
The diagonal matrix of element building,Representative takes matrixThe vector of diagonal element building,Representative takes matrixDiagonally
The vector of member building；
In above-mentioned optimization problem, X, Y, Pmin、Pmax、QminAnd QmaxIt is known quantity, wherein PminAnd PmaxIt goes through respectively
Minimum and maximum active power injection of each node from the moment 1 to T, Q in history dataminAnd QmaxIt is every in historical data respectively
Minimum and maximum reactive power injection of a node from the moment 1 to T, Pmin、Pmax、QminAnd QmaxIt is all the dimensional vector of N × 1；
Above-mentioned optimization problem is solved, and 2N × 2N dimension matrix A is calculated using formula (3b)J'；
(2-2) carries out coarse adjustment to above-mentioned power flow equation parameter, ties up matrix A to 2N × 2N of above-mentioned steps (2-1)J'It carries out more
Newly, include the following steps：
(2-2-1) solves the optimization problem in following (4) using interior point method：
Y-εY=AJ'X+dAJ'X-AJ'εX+C1T (4b)
In optimization problem (4), (4a) is objective function, and (4b)-(4d) is constraint condition, whereinIt indicates to close
In matrix Σ-1Norm, i.e., to given matrix D,Σ-1It is the inverse matrix of Σ, Σ is pair of setting
Angle battle array, diagonal element are the variance of error in measurement： WithRespectively indicate εXAnd εYVariance；
In optimization problem (4), εX、εY、E、F、It is known variables to be asked with C, wherein εXAnd εYAll be 2N ×
M ties up matrix, εXAnd εYRespectively indicate the measurement noise of measurement matrix X and Y, dAJ'It is 2N × 2N dimension matrix, representing matrix AJ'Change
Change amount；
In optimization problem (4), AJ'、Σ、X、Y、Pmin、Pmax、QminAnd QmaxIt is known quantity, wherein AJ'By above-mentioned step
Suddenly (2-1) is calculated, and Σ is the diagonal matrix of setting, and diagonal element is the variance of error in measurement：
WithRespectively indicate εXAnd εYVariance, obtain in the explanation by power grid measurement equipment；
It solves optimization problem (4), calculates dA using formula (4c)J', the dA that is calculated with thisJ'Update matrix AJ'：AJ'
←AJ'+dAJ'；
(2-2-2) is to inequalityJudged, ifIt thens follow the steps
(2-3)；IfThen follow the steps (2-2-1), wherein W is weight matrix：σXAnd σYPoint
The standard deviation of other representing matrix X and matrix Y；It indicates Hadamard operator, calculates the product of two matrix corresponding position elements,
Max | | it indicates to seek the maximum value of element absolute value in matrix, α indicates to stop the threshold parameter of iteration, takes α=0.1；
(2-3) carries out fine tuning to above-mentioned power flow equation parameter, ties up matrix A to 2N × 2N of above-mentioned steps (2-2)J'It carries out more
Newly, include the following steps：
(2-3-1) solves the optimization problem in (5) using interior point method：
Y-εY=AX+dAX-A εX+C1T (5b)
In optimization problem (5), (5a) is objective function, and (5b) is constraint condition, wherein
||·||1The 1- norm of representing matrix, i.e., to given matrix D,dijThe element of representing matrix D the i-th row j column.
In optimization problem (5), εX、εY, dA and C be known variables to be asked, wherein dA is 2N × 2N dimension matrix, is indicated
The variable quantity of matrix A；
In optimization problem (5), A, Σ, X and Y are known quantities, wherein A is the A in above-mentioned steps (2-2)J'；
After solving optimization problem (5), matrix A is updated：A ← A+dA, and record variable C；
(2-3-2) is to inequalityJudged：IfThen follow the steps (3-
1), ifIt executes step (2-3-1)；
(3) the power flow equation parameter obtained according to above-mentioned solution obtains the linearisation power flow equation of power grid, and carries out power grid
Load flow calculation, specific step is as follows：
The node type PQ that is divided in the parameter A and C and above-mentioned steps (1) that (3-1) is obtained according to above-mentioned steps (2),
PV and V θ writes out the linearisation power flow equation of power grid：
Wherein, CiIndicate above-mentioned steps (2-3-1) vector C according to the subvector after (6) arrangement, AijIndicate above-mentioned steps
Submatrix after (2-3-1) matrix A is arranged according to (6) maps formula (6) dependent variable in left side, P when calculating trendR, QS
And QRIt is unknown quantity, PL, PSAnd QLIt is known quantity, for the independent variable on formula (6) mapping right side, θL, θSAnd VLIt is unknown quantity, θR,
VSAnd VRIt is known quantity, and then matrix (6) is write as to the form of following matrix in block form：
Wherein, x2=[θR,VS,VR]TAnd y1=[PL,PS,QL]TIt is known quantity, x1=[θL,θS,VL]TAnd y2=[PR,QS,
QR]TIt is unknown quantity,WithRespectively indicate A in formula (6)ijThe corresponding part of matrix：
(3-2) solves the linearisation power flow equation of above-mentioned steps (3-1) according to the following formula, obtains power grid linearisation power flow equation
Real-time solution：
Wherein x1=[θL,θS,VL]TAnd y2=[PR,QS,QR]TThe solution of the power flow equation as linearized.It may be noted that step
Suddenly grid measurement data involved in (1) and step (2) is all historical data, and the given data in step (3) is new
Electric network data, new electric network data can be the electric network data etc. generated in the case of real-time data of power grid, imagination, according to reality
Depending on application demand.
The embodiment of the method for the present invention is introduced below in conjunction with attached drawing：
The present invention is with Baran M E, Wu F F.Network reconfiguration in distribution
systems for loss reduction and load balancing[J].IEEE Transactions on Power
delivery,1989,4(2):Method proposed by the invention is carried out for IEEE-33 test macro in 1401-1407.
Eyesight verifying.Wherein metric data is made of Monte Carlo with the adduction for measuring noise.Monte Carlo is according to utilization
Matpower software package is calculated under specific primary condition.Wherein active power load data is according to the base in test macro
Value and the multiplier generated at random are thought of as and obtain, and multiplier numerical value is between [0.8-1.2]；Reactive power load data is according to active
Power load values are multiplied with the multiplier generated at random and are obtained, and multiplier numerical value is between [0.15-0.25].Noise is measured according to letter
It makes an uproar and is generated than (Signal to noise ratio, SNR) 40dB, noise Gaussian distributed.Under the definition of signal-to-noise ratio is obeyed
Formula：
Wherein asignal/anoiseRespectively indicate signal/noise root-mean-square amplitude.This example has taken 300 groups of data to be used for altogether
Training, 300 groups of data are for testing.
The linearisation electric network swim equation calculation trend obtained according to the proposed method, and tide is exchanged with accurate
Stream calculation Comparative result, result are as shown in Figure 1.Fig. 1 subgraph (a1) and (b1) describe the calculating error of voltage phase angle, subgraph
(a2) the calculating error of voltage magnitude is described with (b2).Subgraph (a1) and (a2) illustrate 1 group of survey in 300 groups of test results
Test result, horizontal axis indicates node number, error is indicated on the right side of the longitudinal axis, and left side indicates specific evaluation.Subgraph (b1) and (b2) are opened up
The histogram of 300 groups of result mean absolute errors is shown, wherein horizontal axis indicates error, and the longitudinal axis indicates frequency.In all subgraphs,
Calculating error is all indicated with logarithmic coordinates axis.To show beneficial effects of the present invention, compared with the following method in example：
1,Noiseless：It is used without the metric data of noise, uses document Liu Y, Zhang N, Wang Y, et
al.Data-Driven Power Flow Linearization:A Regression Approach[J].IEEE
Transactions on Smart Grid, the power flow equation that the method in 2018 is linearized.This method is considered as
It is " theoretical limit " of the data-driven method under containing noise conditions.
2,M1：Using there is noise-containing metric data, using method of the invention, the power flow equation that is linearized.
3,M2：Utilize document J.Yang, N.Zhang, C.Kang, and Q.Xia, " A State-Independent
Linear Power Flow Model with Accurate Estimation of Voltage Magnitude,"IEEE
The power flow equation that method in Trans.Power Syst., vol.22, pp.3607-3617,2017 is linearized, this side
Method is the representative of traditional power flow equation the linear calculation method based on model.
4,M3：Using noise-containing metric data, document Liu Y, Zhang N, Wang Y, et al.Data- are used
Driven Power Flow Linearization:A Regression Approach[J].IEEE Transactions on
Smart Grid, the power flow equation that the method in 2018 is linearized.
As can be drawn from Figure 1 to draw a conclusion：
1, in the case where 40dB measures noise situations, the error of the error ratio method Noiseless of method M3 is three orders of magnitude greater,
If this illustrates that traditional data-driven method without the special designing to noise robustness, linearizes calculation of tidal current meeting
Very big error is generated in certain noise.
2, method M3 not only low precision, and the calculating error between its different node has significantly compared to other methods
Fluctuation, it means that the difference of the adjacent result of calculated result can generate bigger error, and the calculating of adjacent node difference is accurate right
Tidal current analysis is extremely important.
3, small two orders of magnitude of error of error the ratio method M2 and M3 of method M1, the error of method M1 only ratio method
Noiseless is greatly less than an order of magnitude.This explanation method proposed by the present invention is containing noise is measured, significantly
The computational accuracy of power grid linearisation trend is improved, and linearization accuracy approaches and do not have noisy " theoretical limit ".
4, the error of error the ratio method Noiseless and M3 of method M1 have smaller variance, this illustration method M3 exists
It is showed in difference group calculated result highly stable.
Claims (1)
1. a kind of to the data-driven electric network swim equation the linear calculation method for measuring noise robustness, which is characterized in that the party
Method includes the following steps：
(1) metric data in power grid history data is pre-processed, metric data include node active power injection,
The injection of node reactive power, node voltage phase angle and node voltage amplitude；Specific step is as follows：
All N number of node divisions of electric system are PQ, PV, V θ node, wherein PQ node on behalf node active power by (1-1)
Injection and reactive power are injected to the node of known quantity, and PV node represents the injection of node active power and voltage magnitude as known quantity
Node, V θ node on behalf node voltage amplitude and voltage phase angle are the node of known quantity, according to node type, by operation of power networks
Active power injection, reactive power injection, voltage magnitude and voltage phase angle data are respectively according to the sequence of PQ, PV, V θ node
Arrangement：
Wherein, P indicates that each node active power of power grid injects vector, and P is the dimensional vector of N × 1,Indicate PQ node active power
Inject vector PLTransposition,Indicate that PV node active power injects vector PSTransposition,Indicate V θ node active power note
Incoming vector PRTransposition, Q indicates that each node reactive power of power grid injects vector, and Q is the dimensional vector of N × 1,Indicate PQ node without
Function power injects vector QLTransposition,Indicate that PV node reactive power injects vector QSTransposition,Indicate that V θ node is idle
The transposition of power injection vector；V indicates each node voltage amplitude vector of power grid, and V is the dimensional vector of N × 1,Indicate PQ node
Voltage magnitude vector VLTransposition,Indicate PV node voltage magnitude vector VSTransposition,Indicate V θ node voltage amplitude to
Measure VRTransposition；θ indicates each node voltage phase angle vector of power grid, and θ is the dimensional vector of N × 1,Indicate PQ node voltage phase angle to
Measure θLTransposition,Indicate PV node voltage phase angle vector θSTransposition,Indicate V θ node voltage phase angle vector θRTransposition；
The historical metrology data of electric system different time points as unit of the format in step 1-1, is organized into X square by (1-2)
The form of battle array and Y matrix：
Wherein, M is the time point number of historical metrology data, and subscript 1...m...M indicates the time point of historical metrology data,
Middle xmAnd ymIt is all the dimensional vector of 2N × 1, X and Y are 2N × M dimension matrixes；
(2) the power flow equation parameter of linearisation is solved, specific step is as follows：
(2-1) solves the optimization problem in following (3) using interior point method, obtains power flow equation initial parameter values：
In above-mentioned optimization problem, (3a) is objective function, and (3b) (3c) is constraint condition, wherein | | | |FRepresenting matrix
Frobenius norm, i.e., to given matrix D,The mark of tr () representing matrix, mark are pairs of matrix
Angle element adduction；
In above-mentioned optimization problem, E, F,It is known variables to be asked with C, wherein E is N × N symmetrical matrix, i.e. matrix
Middle element and transposed matrix ETThe element of middle same position is equal：E=ET, F is N × N symmetrical matrix, i.e., in matrix element with turn
Set matrix FTThe element of middle same position is equal：F=FT,It is N × N diagonal matrix： It is N
× N diagonal matrix：C is the dimensional vector of N × 1,Represent withFor diagonal element building diagonal matrix,Represent withFor diagonal element
The diagonal matrix of building,Representative takes matrixThe vector of diagonal element building,Representative takes matrixDiagonal element
The vector of building；
In above-mentioned optimization problem, X, Y, Pmin、Pmax、QminAnd QmaxIt is known quantity, wherein PminAnd PmaxIt is history number respectively
Minimum and maximum active power injection of each node from the moment 1 to T, Q inminAnd QmaxIt is each section in historical data respectively
Minimum and maximum reactive power injection of the point from the moment 1 to T, Pmin、Pmax、QminAnd QmaxIt is all the dimensional vector of N × 1；
Above-mentioned optimization problem is solved, and 2N × 2N dimension matrix A is calculated using formula (3b)J'；
(2-2) carries out coarse adjustment to above-mentioned power flow equation parameter, ties up matrix A to 2N × 2N of above-mentioned steps (2-1)J'It is updated,
Include the following steps：
(2-2-1) solves the optimization problem in following (4) using interior point method：
Y-εY=AJ'X+dAJ'X-AJ'εX+C1T (4b)
In optimization problem (4), (4a) is objective function, and (4b)-(4d) is constraint condition, whereinIt indicates about square
Battle array Σ-1Norm, i.e., to given matrix D,Σ-1It is the inverse matrix of Σ, Σ is the diagonal matrix of setting,
Diagonal element is the variance of error in measurement： WithRespectively indicate εXAnd εYVariance；
In optimization problem (4), εX、εY、E、F、It is known variables to be asked with C, wherein εXAnd εYIt is all 2N × M dimension
Matrix, εXAnd εYRespectively indicate the measurement noise of measurement matrix X and Y, dAJ'It is 2N × 2N dimension matrix, representing matrix AJ'Variation
Amount；
In optimization problem (4), AJ'、Σ、X、Y、Pmin、Pmax、QminAnd QmaxIt is known quantity, wherein AJ'By above-mentioned steps (2-
1) it is calculated, Σ is the diagonal matrix of setting, and diagonal element is the variance of error in measurement： With
Respectively indicate εXAnd εYVariance, obtain in the explanation by power grid measurement equipment；
It solves optimization problem (4), calculates dA using formula (4c)J', the dA that is calculated with thisJ'Update matrix AJ'：AJ'←AJ'
+dAJ'；
(2-2-2) is to inequalityJudged, ifThen follow the steps (2-3)；
IfThen follow the steps (2-2-1), wherein W is weight matrix：σXAnd σYIt respectively indicates
The standard deviation of matrix X and matrix Y；Indicate Hadamard operator, calculate the product of two matrix corresponding position elements, max | |
The maximum value of element absolute value in matrix is sought in expression, and α indicates to stop the threshold parameter of iteration, takes α=0.1；
(2-3) carries out fine tuning to above-mentioned power flow equation parameter, ties up matrix A to 2N × 2N of above-mentioned steps (2-2)J'It is updated,
Include the following steps：
(2-3-1) solves the optimization problem in (5) using interior point method：
Y-εY=AX+dAX-A εX+C1T (5b)
In optimization problem (5), (5a) is objective function, and (5b) is constraint condition, wherein||·
||1The 1- norm of representing matrix, i.e., to given matrix D,dijThe element of representing matrix D the i-th row j column.
In optimization problem (5), εX、εY, dA and C be known variables to be asked, wherein dA is 2N × 2N dimension matrix, representing matrix
The variable quantity of A；
In optimization problem (5), A, Σ, X and Y are known quantities, wherein A is the A in above-mentioned steps (2-2)J'；
After solving optimization problem (5), matrix A is updated：A ← A+dA, and record variable C；
(2-3-2) is to inequalityJudged：If(3-1) is thened follow the steps, ifIt executes step (2-3-1)；
(3) the power flow equation parameter obtained according to above-mentioned solution obtains the linearisation power flow equation of power grid, and carries out electric network swim
It calculates, specific step is as follows：
Node type PQ, PV for being divided in the parameter A and C and above-mentioned steps (1) that (3-1) is obtained according to above-mentioned steps (2) and
V θ writes out the linearisation power flow equation of power grid：
Wherein, CiIndicate above-mentioned steps (2-3-1) vector C according to the subvector after (6) arrangement, AijIndicate above-mentioned steps (2-3-
1) matrix A is according to the submatrix after (6) arrangement, when calculating trend, for the dependent variable in formula (6) mapping left side, PR, QSAnd QR
It is unknown quantity, PL, PSAnd QLIt is known quantity, for the independent variable on formula (6) mapping right side, θL, θSAnd VLIt is unknown quantity, θR, VSWith
VRIt is known quantity, and then matrix (6) is write as to the form of following matrix in block form：
Wherein, x2=[θR,VS,VR]TAnd y1=[PL,PS,QL]TIt is known quantity, x1=[θL,θS,VL]TAnd y2=[PR,QS,QR]TIt is
Unknown quantity,WithRespectively indicate A in formula (6)ijThe corresponding part of matrix：
(3-2) solves the linearisation power flow equation of above-mentioned steps (3-1) according to the following formula, obtains the reality of power grid linearisation power flow equation
Shi Xie：
Wherein x1=[θL,θS,VL]TAnd y2=[PR,QS,QR]TThe solution of the power flow equation as linearized.
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