CN107370150A - The Power system state estimation Bad data processing method measured based on synchronized phasor - Google Patents

The Power system state estimation Bad data processing method measured based on synchronized phasor Download PDF

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CN107370150A
CN107370150A CN201710795550.0A CN201710795550A CN107370150A CN 107370150 A CN107370150 A CN 107370150A CN 201710795550 A CN201710795550 A CN 201710795550A CN 107370150 A CN107370150 A CN 107370150A
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mrow
msup
msub
measurement
bad data
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CN107370150B (en
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林俊杰
周华锋
陆超
姚海成
苏寅生
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Tsinghua University
China Southern Power Grid Co Ltd
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Tsinghua University
China Southern Power Grid Co Ltd
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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
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • 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
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E40/00—Technologies for an efficient electrical power generation, transmission or distribution
    • Y02E40/70—Smart grids as climate change mitigation technology in the energy generation sector
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E60/00—Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y04—INFORMATION OR COMMUNICATION TECHNOLOGIES HAVING AN IMPACT ON OTHER TECHNOLOGY AREAS
    • Y04S—SYSTEMS INTEGRATING TECHNOLOGIES RELATED TO POWER NETWORK OPERATION, COMMUNICATION OR INFORMATION TECHNOLOGIES FOR IMPROVING THE ELECTRICAL POWER GENERATION, TRANSMISSION, DISTRIBUTION, MANAGEMENT OR USAGE, i.e. SMART GRIDS
    • Y04S10/00—Systems supporting electrical power generation, transmission or distribution
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y04—INFORMATION OR COMMUNICATION TECHNOLOGIES HAVING AN IMPACT ON OTHER TECHNOLOGY AREAS
    • Y04S—SYSTEMS INTEGRATING TECHNOLOGIES RELATED TO POWER NETWORK OPERATION, COMMUNICATION OR INFORMATION TECHNOLOGIES FOR IMPROVING THE ELECTRICAL POWER GENERATION, TRANSMISSION, DISTRIBUTION, MANAGEMENT OR USAGE, i.e. SMART GRIDS
    • Y04S10/00—Systems supporting electrical power generation, transmission or distribution
    • Y04S10/22—Flexible AC transmission systems [FACTS] or power factor or reactive power compensating or correcting units

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  • Engineering & Computer Science (AREA)
  • Power Engineering (AREA)
  • Other Investigation Or Analysis Of Materials By Electrical Means (AREA)
  • Remote Monitoring And Control Of Power-Distribution Networks (AREA)

Abstract

The present invention proposes a kind of Power system state estimation Bad data processing method measured based on synchronized phasor, belongs to Power system state estimation field.The measuring value of the fully synchronized phasor measurement units of discontinuity surface establishes measurement collection when this method obtains one, power network, obtains representing the measurement equation of linear relationship between measurement collection and quantity of state；The state estimator of power system is obtained by power system linear state estimation；Calculate the estimate and measurement residual vector of measurement collection；Using residual vector is measured, calculate measurement and concentrate bad data index and bad data judgment threshold corresponding to each measuring value；When the bad data index of all measuring values is respectively less than its corresponding bad data judgment threshold, show no bad data, output power system state estimation amount, Bad data processing terminates.The present invention carries out the detection of bad data by using the actual measurement error of measurement residual error estimation, and method is simple and reliable, and the degree of accuracy is high, there is higher practical value.

Description

The Power system state estimation Bad data processing method measured based on synchronized phasor
Technical field
The invention belongs to Power system state estimation field, relates generally to a kind of power system measured based on synchronized phasor State estimation Bad data processing method.
Background technology
Synchronous phasor measurement unit (Phasor Measurement Unit, PMU) is the power network measurement apparatus of a new generation, Compared to traditional measurement apparatus, PMU synchronisms are more preferable, refreshing frequency is higher and can provide the phasor data of electrical quantity.In recent years Come, as phasor measurement unit is quickly arranged in power network, substantial amounts of PMU metric data provides for Electrical power system analysis and computing New data.But for relative active power measures, the precision of PMU phase angle metric data not enough, and due to network communication Interrupt, measuring apparatus failure situations such as, the measurement data of substantial deviation actual value is there may be in PMU metric data, i.e., it is bad Data.
The Bad data processing technology of power system at present is mostly to be directed to traditional measurement data, is lacked to PMU data Specific aim method.Under full PMU measurements, the measurement equation of Power system state estimation is linear, thus can direct solution most A young waiter in a wineshop or an inn multiplies solution or state estimation, but because least square method lacks robustness, so need in measurement data not Good data are handled.After Bad data processing includes state estimation pre-treatment, and (rear) is handled during state estimation, state Main method before estimation has measurement mutation method etc., and the method simply after state estimation has residual method, method of maximum surplus error Deng.
Conventional residual discrimination method is using weighted residual or residual as characteristic value, is examined using the hypothesis of probability theory Test, a threshold value is determined according to certain confidence level, the two-valued function that " either-or " is then carried out to measurement amount judges. But residual error is larger can not to be equal to that measurement error is larger, therefore these method reliabilities are general completely, it is possible that misjudgement or The situation that person fails to judge, and the situation of how related bad data can not be handled.
The content of the invention
The purpose of the present invention is to overcome the weak point of prior art, proposes a kind of to measure based on synchronous phasor measurement Power system state estimation Bad data processing method.Present invention utilizes the synchro measure phase for being just widely used in power network now Measurement, the detection of bad data is carried out using the actual measurement error of residual error estimation is measured, method is simple and reliable, the degree of accuracy Height, there is higher practical value.
The Power system state estimation Bad data processing method proposed by the present invention measured based on synchronized phasor, its feature It is, comprises the following steps：
1) measuring value of the fully synchronized phasor measurement units of discontinuity surface when obtaining one, power network, the amount of voltage phasor is included Measured value and electric current phasor measuring value, establish measurement collection Y；Measurement collection Y is one complex vector located, when measurement collects all measurements in Y When value is synchronized phasor, according to power network physical model, measurement integrates as linear relationship between Y and quantity of state X, and measurement equation is write as Matrix form as shown in formula (1)：
Y=AX+ ε (1)
Wherein, A is node-branch admittance matrix；Assuming that the number of synchronous phasor measurement unit measuring value is in measurement collection Y M, quantity of state X state number are n, then order rank (A)=n, ε is measurement error vector；
2) power system linear state estimation is carried out, the state estimation of power system is solved using weighted least-squares method Amount, shown in expression formula such as formula (2)：
Xe=(AHWCWLSA)-1AHWCWLSY (2)
Wherein, WCWLSIt is m × m rank weight matrix, is real diagonal matrix；
3) the state estimator X obtained according to step 2)eThe estimate Y of measurement collection is calculated with measurement equation formula (1)eAnd survey Measure residual vector r；
Measure the estimate Y of collectioneExpression formula is as follows：
Ye=AXe (3)
Residual vector r is measured, expression formula is as follows：
R=Y-Ye (4)
Meanwhile measure residual vector r and be expressed as：
WhereinFor residual sensitivity matrix, YTThe true value of measurement collection is represented, I represents unit Matrix；
According to formula (5), the expression formula of measurement error vector is updated to：
Wherein δYRepresent evaluated error vector；
4) bad data index R corresponding to i-th of measuring value in measurement collection Y is calculatedi, i=1,2 ... ..., m, expression formula is as follows：
Wherein,<,>Represent point multiplication operation vectorial in complex vector space, []iI-th row of representing matrix [], δYi, riPoint δ is not representedYWith r i-th of component；
The bad data judgment threshold corresponding to i-th of measuring value is calculated, expression formula is as follows：
Wherein, kiRepresent safety factor, aiAnd biThe amplitude maximum error in measurement and phase angle of i-th of measuring value are represented respectively Maximum error in measurement, ZiRepresent the amplitude of i-th of measuring value；
5) repeat step 4), the bad data indexs and its correspondingly of all synchronized phase measurement quantity of units measured values is calculated Bad data judgment threshold, and judged：
If the bad data index R of all synchronized phase measurement quantity of units measured valuesiRespectively less than its corresponding bad data Judgment threshold, then illustrate there is no bad data in the measurement collection Y used in this state estimation, the electricity that output step 2) is calculated Force system state estimator, Bad data processing terminate；Otherwise by all RiIndex exceedes its corresponding bad data judgment threshold Measuring value be labeled as suspicious data, into step 6)；
6) by all suspicious datas that step 5) obtains according to its corresponding RiThe order of index from big to small is arranged, By corresponding RiThe maximum suspicious data of index is labeled as bad data, and bad data is collected in Y from measurement and rejected；
7) step 2) is returned to, the new measurement collection obtained by step 6) processing re-starts POWER SYSTEM STATE and estimated Meter, when not having bad data until measuring concentration, output power system state estimation amount, Bad data processing terminates.
The features of the present invention and beneficial effect are：
The Power system state estimation Bad data processing method proposed by the present invention measured based on synchronized phasor, by right The residual sum error of state estimation is analyzed, it is proposed that after a kind of new Power Network Status Estimation at raw data detection and identification Reason technology.
The detection method of the present invention is simple and reliable, by relation between measurement collection residual sum error after Power Network Status Estimation Analysis, be derived by measurement collection residual error approximate evaluation value, and accordingly construction detection measurement whether integrate as bad data Bad data index R, can effectively pick out bad data.Method by once rejecting again, measurement can be handled and concentrated All bad datas, including how related bad data.
Embodiment
The Power system state estimation Bad data processing method proposed by the present invention measured based on synchronized phasor, is tied below It is as follows to close specific embodiment further description.
The Power system state estimation Bad data processing method proposed by the present invention measured based on synchronized phasor, including with Lower step：
1) whole PMU of discontinuity surface measuring value when obtaining one, power network by emulating or surveying, including voltage phasor And current phasor data, establish measurement collection Y.Measurement collection Y is one complex vector located, is when measurement collects all measuring values in Y During synchronized phasor, according to power network physical model, measurement integrates as linear relationship between Y and quantity of state X, measurement equation can be write as Under matrix form：
Y=AX+ ε (1)
Wherein, A is node-branch admittance matrix, it is assumed that measurement integrates the number of PMU measuring values in Y as m, quantity of state X shape State number is n, then order rank (A)=n, and element therein is plural number, and ε is measurement error vector.
2) power system linear state estimation is carried out, the state estimation of power system is solved using weighted least-squares method Amount, shown in expression formula such as formula (2)：
Xe=(AHWCWLSA)-1AHWCWLSY (2)
Wherein, WCWLSIt is m × m rank weight matrix, is real diagonal matrix.
3) the state estimator X obtained according to step 2)eThe estimate Y of PMU measurement collection is calculated with measurement equation formula (1)eWith Measure residual vector r；The estimate Y of PMU measurement collectioneExpression formula is as follows：
Ye=AXe (3)
PMU measurement collection residual vector r, expression formula are as follows：
R=Y-Ye (4)
The residual vector r of PMU measurements simultaneously can also be expressed as：
WhereinFor residual sensitivity matrix, YTThe true value of measurement collection is represented, I represents unit Matrix.
According to formula (5), PMU measurement error vectors ε can be rearranged as：
Wherein δYRepresent evaluated error vector；
To formula (6) both sides Modulus of access, it is as follows that error of absolute method of measurement vector expression can be obtained：
| ε |=| r |+| δY| (7)
Error of absolute method of measurement vector is understood by above formula | ε | the mould vector of two components, i.e. residual error can be decomposed into | r |=S | ε | and vector | δY|=(I-S) | ε |, can prove that the two vectorial inner products are zero, the two vectors are mutually orthogonal.Cause This residual vector r is a measurement error vector ε part, can estimate measurement error vector ε by residual vector r.
4) according to above-mentioned conclusion, define and calculate in measurement collection Y corresponding to i-th (i=1,2 ... ..., m) individual measuring value Bad data index Ri, expression formula is as follows：
Wherein,<,>Represent point multiplication operation vectorial in complex vector space, []iI-th row of representing matrix [], δYi, riPoint δ is not representedYWith r i-th of component.
The bad data judgment threshold corresponding to i-th of measuring value is further calculated, expression formula is as follows：
Wherein, kiSafety factor is represented, 1 is typically taken, when known measuring condition is more severe, can suitably increase kiValue, aiAnd biThe amplitude maximum error in measurement and phase angle maximum error in measurement of i-th of measuring value, Z are represented respectivelyiRepresent i-th of measurement The amplitude of value.
5) repeat step 4), the bad data index and its corresponding bad data that all PMU measuring values are calculated are sentenced Disconnected threshold value, and judged：
If the bad data index R of all PMU measuring valuesiRespectively less than its corresponding bad data judgment threshold, then say There is no bad data in the bright this time measurement collection Y used in state estimation, the POWER SYSTEM STATE that output step 2) is calculated is estimated Metering, Bad data processing terminate；Otherwise by all RiIndex exceedes the measuring value mark of its corresponding bad data judgment threshold For suspicious data, into step 6).
6) by all suspicious datas that step 5) obtains according to its corresponding RiThe order of index from big to small is arranged, By corresponding RiThe maximum suspicious data of index is labeled as bad data, and bad data is collected in Y from measurement and rejected.
7) step 2) is returned to, handling obtained new measurement collection by step 6) re-starts state estimation, until When measurement concentration does not have bad data, output power system state estimation amount, Bad data processing terminates.

Claims (1)

  1. A kind of 1. Power system state estimation Bad data processing method measured based on synchronized phasor, it is characterised in that including Following steps：
    1) measuring value of the fully synchronized phasor measurement units of discontinuity surface when obtaining one, power network, the measuring value of voltage phasor is included With electric current phasor measuring value, measurement collection Y is established；Measurement collection Y is one complex vector located, when all measuring values that measurement collects in Y are equal For synchronized phasor when, according to power network physical model, measurement integrates as linear relationship between Y and quantity of state X, and measurement equation is write as such as formula (1) matrix form shown in：
    Y=AX+ ε (1)
    Wherein, A is node-branch admittance matrix；Assuming that measurement integrates the number of synchronous phasor measurement unit measuring value in Y as m, shape State amount X state number is n, then order rank (A)=n, ε is measurement error vector；
    2) power system linear state estimation is carried out, the state estimator of power system, table are solved using weighted least-squares method Up to formula such as formula (2) Suo Shi：
    Xe=(AHWCWLSA)-1AHWCWLSY (2)
    Wherein, WCWLSIt is m × m rank weight matrix, is real diagonal matrix；
    3) the state estimator X obtained according to step 2)eThe estimate Y of measurement collection is calculated with measurement equation formula (1)eIt is residual with measuring Difference vector r；
    Measure the estimate Y of collectioneExpression formula is as follows：
    Ye=AXe (3)
    Residual vector r is measured, expression formula is as follows：
    R=Y-Ye (4)
    Meanwhile measure residual vector r and be expressed as：
    <mrow> <mtable> <mtr> <mtd> <mrow> <mi>r</mi> <mo>=</mo> <mi>Y</mi> <mo>-</mo> <msub> <mi>Y</mi> <mi>e</mi> </msub> <mo>=</mo> <msub> <mi>T</mi> <mi>T</mi> </msub> <mo>+</mo> <mi>&amp;epsiv;</mi> <mo>-</mo> <mo>&amp;lsqb;</mo> <msub> <mi>Y</mi> <mi>T</mi> </msub> <mo>+</mo> <mi>A</mi> <msup> <mrow> <mo>(</mo> <msup> <mi>A</mi> <mi>H</mi> </msup> <mover> <mi>W</mi> <mo>&amp;OverBar;</mo> </mover> <mi>A</mi> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <msup> <mi>A</mi> <mi>H</mi> </msup> <mover> <mi>W</mi> <mo>&amp;OverBar;</mo> </mover> <mi>&amp;epsiv;</mi> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <mi>&amp;epsiv;</mi> <mo>-</mo> <mi>A</mi> <msup> <mrow> <mo>(</mo> <msup> <mi>A</mi> <mi>H</mi> </msup> <mover> <mi>W</mi> <mo>&amp;OverBar;</mo> </mover> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <msup> <mi>A</mi> <mi>H</mi> </msup> <mover> <mi>W</mi> <mo>&amp;OverBar;</mo> </mover> <mi>&amp;epsiv;</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <mo>&amp;lsqb;</mo> <mi>I</mi> <mo>-</mo> <mi>A</mi> <msup> <mrow> <mo>(</mo> <msup> <mi>A</mi> <mi>H</mi> </msup> <mover> <mi>W</mi> <mo>&amp;OverBar;</mo> </mover> <mi>A</mi> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <msup> <mi>A</mi> <mi>H</mi> </msup> <mover> <mi>W</mi> <mo>&amp;OverBar;</mo> </mover> <mo>&amp;rsqb;</mo> <mi>&amp;epsiv;</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <mi>S</mi> <mi>&amp;epsiv;</mi> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>
    WhereinFor residual sensitivity matrix, YTThe true value of measurement collection is represented, I represents unit matrix；
    According to formula (5), the expression formula of measurement error vector is updated to：
    <mrow> <mi>&amp;epsiv;</mi> <mo>=</mo> <mi>r</mi> <mo>+</mo> <mi>A</mi> <msup> <mrow> <mo>(</mo> <msup> <mi>A</mi> <mi>H</mi> </msup> <mover> <mi>W</mi> <mo>&amp;OverBar;</mo> </mover> <mi>A</mi> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <msup> <mi>A</mi> <mi>H</mi> </msup> <mover> <mi>W</mi> <mo>&amp;OverBar;</mo> </mover> <mi>&amp;epsiv;</mi> <mo>=</mo> <mi>r</mi> <mo>+</mo> <msub> <mi>&amp;delta;</mi> <mi>Y</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>
    Wherein δYRepresent evaluated error vector；
    4) bad data index R corresponding to i-th of measuring value in measurement collection Y is calculatedi, i=1,2 ... ..., m, expression formula is as follows：
    <mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>R</mi> <mi>i</mi> </msub> <mo>=</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>+</mo> <mfrac> <mrow> <mo>&lt;</mo> <msub> <mi>&amp;delta;</mi> <mrow> <mi>Y</mi> <mi>i</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;delta;</mi> <mrow> <mi>Y</mi> <mi>i</mi> </mrow> </msub> <mo>&gt;</mo> </mrow> <mrow> <mo>&lt;</mo> <msub> <mi>r</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>r</mi> <mi>i</mi> </msub> <mo>&gt;</mo> </mrow> </mfrac> <mo>)</mo> </mrow> <mo>|</mo> <msub> <mi>r</mi> <mi>i</mi> </msub> <mo>|</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>+</mo> <mfrac> <mrow> <msubsup> <mrow> <mo>&amp;lsqb;</mo> <mi>A</mi> <msup> <mrow> <mo>(</mo> <msup> <mi>A</mi> <mi>H</mi> </msup> <mi>W</mi> <mi>A</mi> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <msup> <mi>A</mi> <mi>H</mi> </msup> <mi>W</mi> <mo>&amp;rsqb;</mo> </mrow> <mi>i</mi> <mi>H</mi> </msubsup> <mi>W</mi> <msub> <mrow> <mo>&amp;lsqb;</mo> <mi>A</mi> <msup> <mrow> <mo>(</mo> <msup> <mi>A</mi> <mi>H</mi> </msup> <mi>W</mi> <mi>A</mi> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <msup> <mi>A</mi> <mi>H</mi> </msup> <mi>W</mi> <mo>&amp;rsqb;</mo> </mrow> <mi>i</mi> </msub> </mrow> <mrow> <msubsup> <mrow> <mo>&amp;lsqb;</mo> <mi>I</mi> <mo>-</mo> <mi>A</mi> <msup> <mrow> <mo>(</mo> <msup> <mi>A</mi> <mi>H</mi> </msup> <mi>W</mi> <mi>A</mi> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <msup> <mi>A</mi> <mi>H</mi> </msup> <mi>W</mi> <mo>&amp;rsqb;</mo> </mrow> <mi>i</mi> <mi>H</mi> </msubsup> <mi>W</mi> <msub> <mrow> <mo>&amp;lsqb;</mo> <mi>I</mi> <mo>-</mo> <mi>A</mi> <msup> <mrow> <mo>(</mo> <msup> <mi>A</mi> <mi>H</mi> </msup> <mi>W</mi> <mi>A</mi> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <msup> <mi>A</mi> <mi>H</mi> </msup> <mi>W</mi> <mo>&amp;rsqb;</mo> </mrow> <mi>i</mi> </msub> </mrow> </mfrac> <mo>)</mo> </mrow> <mo>|</mo> <msub> <mi>r</mi> <mi>i</mi> </msub> <mo>|</mo> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow>
    Wherein,<,>Represent point multiplication operation vectorial in complex vector space, []iI-th row of representing matrix [], δYi, riTable respectively Show δYWith r i-th of component；
    The bad data judgment threshold corresponding to i-th of measuring value is calculated, expression formula is as follows：
    <mrow> <msub> <mi>&amp;eta;</mi> <mi>i</mi> </msub> <mo>=</mo> <msub> <mi>k</mi> <mi>i</mi> </msub> <msqrt> <mrow> <mn>2</mn> <mrow> <mo>(</mo> <msubsup> <mi>Z</mi> <mi>i</mi> <mn>2</mn> </msubsup> <mo>+</mo> <msub> <mi>a</mi> <mi>i</mi> </msub> <msub> <mi>Z</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>cosb</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msubsup> <mi>a</mi> <mi>i</mi> <mn>2</mn> </msubsup> </mrow> </msqrt> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow>
    Wherein, kiRepresent safety factor, aiAnd biThe amplitude maximum error in measurement and phase angle maximum of i-th of measuring value are represented respectively Error in measurement, ZiRepresent the amplitude of i-th of measuring value；
    5) repeat step 4), be calculated all synchronized phase measurement quantity of units measured values bad data index and its it is corresponding not Good data judgment threshold, and judged：
    If the bad data index R of all synchronized phase measurement quantity of units measured valuesiRespectively less than its corresponding bad data judges threshold Value, then illustrate do not have bad data in the measurement collection Y used in this state estimation, the power system that output step 2) is calculated State estimator, Bad data processing terminate；Otherwise by all RiIndex exceedes the measurement of its corresponding bad data judgment threshold Value is labeled as suspicious data, into step 6)；
    6) by all suspicious datas that step 5) obtains according to its corresponding RiThe order of index from big to small is arranged, will be right The R answerediThe maximum suspicious data of index is labeled as bad data, and bad data is collected in Y from measurement and rejected；
    7) step 2) is returned to, handling obtained new measurement collection by step 6) re-starts Power system state estimation, When not having bad data until measuring concentration, output power system state estimation amount, Bad data processing terminates.
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