CN103840452B - A kind of bulk power grid method for estimating state introducing PMU measurement information - Google Patents

Abstract

The invention provides a kind of bulk power grid method for estimating state introducing PMU measurement information, comprise the following steps: the algebraically ornamental judging electric power system; Judge the ornamental of PMU measurement information; Carry out the state estimation of bulk power grid.The invention provides a kind of bulk power grid method for estimating state introducing PMU measurement information, based on fast decoupled algorithm for estimating, effectively utilize PMU measurement information, increase and measure redundancy, improve estimated accuracy; And ensure computational efficiency and computational speed, meet the real-time online requirement of electric power system.

Description

Large power grid state estimation method introducing PMU measurement information

Technical Field

The invention relates to a state estimation method, in particular to a large power grid state estimation method introducing PMU measurement information.

Background

The synchronous phasor measurement unit takes the accurate time provided by a Global Positioning System (GPS) as a reference, can realize synchronous measurement of each node of the power system, provides real-time steady-state and dynamic information of each key point of the large-scale interconnected power system in the same reference time frame, improves the observability of the system, and provides a new visual angle and thought for improving the controllability and reliability of the system.

In 1988, the Bonneville Power Agency (BPA) used phasor measurement devices for the first time in the western power coordination consortium (WECC), a prototype WSCC, and conducted indoor and field tests on these prototypes developed by virginia. In 1993, virginia succeeded in developing the first commercially available synchrophasor measurement device worldwide. The IEEE power system relay protection and control committee has set up a special committee, which was pioneered in 1995 to the IEEE1344 standard (IEEE standard for synchronization and phasers for power systems) and was revised in 2005 to IEEE std pc37.118-2005, providing standard basis for details of synchrophasor measurement techniques such as synchrophasor measurement methods, rules of communication interfaces, recommended standards and possible applications.

Related works in China are started from 1994, mainly research, development and batch production are carried out by China institute of Electrical science, each university and equipment manufacturers, and the related works and the power grid companies are respectively and continuously applied to some regional power grids for trial run. In 1995, the first domestic synchronous phasor measurement device was developed by the institute of electrical and scientific research in china and taiwan ohua, and in 1995, two phase angle measurement devices ADX3000 were installed on a 500kV aerial contact line of a southern power grid to monitor the swing of the phase angle of the contact line, which is broadly the first WAMS (wide area monitoring system) in china.

At present, all the WAMS systems of domestic main power grids are put into practical operation, and according to preliminary estimation, more than 1000 sets of synchronous phasor measurement devices are put into power grid operation in China. The functions that WAMS developed or under research and development can expect to implement are mainly of two types:

(1) basic functions including integrating phasor data platforms (collecting and synchronizing data of each PMU, providing standard data interfaces and the like), wide-area dynamic monitoring and analysis, and synchronous disturbance data recording and inversion;

(2) advanced functions comprise monitoring of the running state of the generator, online low-frequency oscillation detection and analysis, identification of a model and parameters thereof, simulation verification, mixed state estimation, online disturbance identification, power angle stability prediction and alarm, dynamic voltage stability monitoring, online decision making in an emergency control framework, wide-area protection, wide-area HVDC damping control and the like.

The application level is basically synchronous with the country in China and the manufacturing level and the production capacity are not inferior to the country in China and the foreign countries in the aspects of standard specification, technical performance, advanced functions, operation management, planning and construction and the like of the WAMS.

At present, the traditional linear estimation is based on least square estimation of a PQ decomposition method, SCADA measurement is used (iterative calculation is carried out), an SCADA system can only provide node injection power, branch load flow, voltage amplitude and current amplitude measurement, the defects of low data precision, poor synchronism and the like exist, and the requirements of a modern large power grid on higher estimation precision and better estimation efficiency are difficult to adapt, so that the traditional state estimation method which only depends on the SCADA measurement needs to be improved.

With the development and application of the WAMS technology, the WAMS measurement data adds a new data source with better quality for state estimation by the characteristics of high measurement accuracy, strict synchronization of data, small data transmission delay and the like, and the WAMS realizes direct measurement of bus voltage and branch current phasor in a wide area range, provides additional measurement data for state estimation in measurement type, and can greatly relieve the difficulties in both state estimation accuracy and calculation workload.

Disclosure of Invention

In order to overcome the defects of the prior art, the invention provides the large power grid state estimation method introducing PMU measurement information, based on a rapid decomposition estimation algorithm, the PMU measurement information is effectively utilized, the measurement redundancy is increased, and the estimation precision is improved; and the calculation efficiency and the calculation speed are ensured, and the real-time online requirement of the power system is met.

In order to achieve the purpose of the invention, the invention adopts the following technical scheme:

the invention provides a large power grid state estimation method introducing PMU measurement information, which comprises the following steps:

step 1: judging the algebraic observability of the power system;

step 2: judging the observability of PMU measurement information;

and step 3: and carrying out state estimation on the large power grid.

In the step 1, for the power system with n nodes and m measurement vector dimensions, if the rank (H) =2n-1 of the linear measurement model coefficient matrix of the power system, that is, H full rank, the power system is considered to be algebraically considerable.

In the step 2, the observability of PMU measurement information is judged according to the algebraic observability of the power system; the following cases are divided:

A. if rank (H) =2n-1 is satisfied, PMU measurement information is completely considerable;

B. if rank (H) is not less than a (2n-1), the PMU measurement information is considerable, wherein a is 0.95-0.9;

C. if rank (H) < a (2n-1) is satisfied, PMU measurement information is small and considerable;

D. if rank (h) =0 is satisfied, PMU measurement information is completely inconspicuous.

In step 3, the state estimation of the large power grid according to the observability of the PMU measurement information is divided into the following cases:

A. if the PMU measurement information is completely observable, linear state estimation is carried out by adopting a rectangular coordinate linear model;

B. if the PMU measurement information is considerable, the SCADA measurement is used for supplementing the region which is not observable by the PMU, and the linear state estimation is carried out;

C. if the PMU measurement information is a little and considerable, carrying out nonlinear state estimation;

D. the PMU measurement information is not objective at all, and the linear estimation introduced into the PMU is not needed.

The specific process of linear state estimation by adopting the rectangular coordinate linear model comprises the following steps:

the real part and the imaginary part of the voltage are used as state quantities, the real part and the imaginary part of the node voltage, the node injection current and the branch current are used as quantity quantities, and then a measurement equation is expressed by a linear equation as follows:

z＝h(x)+v＝Ax+v（1）

wherein z is a measured quantity, x is a state quantity, v is a random error, A is a first order coefficient matrix, h (x) is a calculated value based on the measurement of the state quantity x, and there are $\frac{\&PartialD;h\left(x\right)}{\&PartialD;x}=A,h\left(x\right)=\mathrm{Ax};$

The objective function is expressed as:

J(x)＝[z-Ax]^TR^-1[z-Ax]（2）

wherein R is^-1Is a weight matrix, J (x) is a least squares objective function;

the linear state estimation equation is: ${\hat{x}}^{(n+1)}={\left[\begin{array}{ccc}{A}^T& R^{-1\left(n\right)}& A\end{array}\right]}^T{R}^{-1\left(n\right)}z---\left(3\right)$

wherein R is^-1(n)For the weight matrix calculated for the nth time,the estimated value calculated for the (n + 1) th time;

calculating the deviation of the residualComprises the following steps:

$r_{\max }^{(n+1)}=\max \left\{r\left({\hat{x}}^{(n+1)}\right)\right\}---\left(4\right)$

wherein,is a residual, expressed as:

$r\left({\hat{x}}^{(n+1)}\right)=z-h\left({\hat{x}}^{(n+1)}\right)---\left(5\right)$

wherein,in order to estimate the value according to the state n +1 times,obtaining a measurement calculation value;

because the estimation accuracy of the power system state is greatly influenced by the current measurement accuracy and is less influenced by the voltage measurement, only the residual error with the maximum current is calculated, and the weight of the current measurement is corrected, including

$R^{-1(n+1)}=R_{\mathrm{cor}}^{-1\left(n\right)}---\left(6\right)$

Wherein，Performing a linear estimation on the modified weight matrix corresponding to the maximum value of the residual error until the maximum value is satisfiedAnd isWhereinIn order to correct the amount of the voltage correction,the amount of phase angle correction,_vand_θis a convergence threshold value preset according to the precision; if a measurement has been corrected, the measurement weight is not corrected.

The specific process of utilizing SCADA measurement to supplement the non-observable region of PMU and carrying out linear state estimation comprises the following steps:

using superscript O to represent the observed region for PMU measurements and superscript U to represent the unobservable region for PMU measurements, the node voltage equation can be expressed as:

$\left[\begin{array}{c}{\stackrel{\&CenterDot;}{V}}_i^O\\ {\stackrel{\&CenterDot;}{I}}_i^O\\ {\stackrel{\&CenterDot;}{I}}_{\mathrm{ij}}^O\\ {\stackrel{\&CenterDot;}{V}}_i^U\\ {\stackrel{\&CenterDot;}{I}}_i^U\end{array}\right]=\left[\begin{array}{cc}E& 0\\ Y_i^{\mathrm{OO}}& Y_i^{\mathrm{OU}}\\ Y_{\mathrm{ij}}^{\mathrm{OO}}& Y_{\mathrm{ij}}^{\mathrm{OU}}\\ 0& E\\ Y_i^{\mathrm{UO}}& Y_i^{\mathrm{UU}}\end{array}\right]\left[\begin{array}{c}{\stackrel{\&CenterDot;}{V}}_i^O\\ {\stackrel{\&CenterDot;}{V}}_i^U\end{array}\right]---\left(7\right)$

wherein:andnode voltage matrixes of observable and unobservable areas respectively;andinjecting current matrixes into nodes of observable and unobservable areas respectively; e is an identity matrix;a observable self-admittance matrix is injected for the node,the nodes are injected with observable and unobservable transadmittance matrices,injecting an unvisible and a viewable transadmittance matrix into the node,injecting an unobservable self-admittance matrix for the node;the current matrix can be observed by the branch circuit,the self-admittance matrix is observable for the branch,is a branch observable and unobservable transadmittance matrix;

node injection current matrix of non-observable regionExpressed as:

${\stackrel{\&CenterDot;}{I}}_i^U=\frac{P_i-{\mathrm{jQ}}_i}{{\stackrel{\&CenterDot;}{V}}_i^{*U}}---\left(8\right)$

wherein, P_iAnd Q_iFor the active and reactive power to be injected,is composed ofA conjugate matrix of (a);

node-based equivalent injection admittance matrixExpressed as:

$Y_i^U=\frac{{\stackrel{\&CenterDot;}{I}}_i^U}{{\stackrel{\&CenterDot;}{V}}_i^U}=\frac{P_i-{\mathrm{jQ}}_i}{{\left|{\stackrel{\&CenterDot;}{V}}_i^U\right|}^2}---\left(9\right)$

bringing formula (9) into the following formula

${\stackrel{\&CenterDot;}{I}}_i^U=Y_i^U{\stackrel{\&CenterDot;}{V}}_i^U=Y_i^{\mathrm{UO}}{\stackrel{\&CenterDot;}{V}}_i^O+Y_i^{\mathrm{UU}}{\stackrel{\&CenterDot;}{V}}_i^U---\left(10\right)$

Finishing to obtain:

$0=Y_i^{\mathrm{UO}}{\stackrel{\&CenterDot;}{V}}_i^O+(Y_i^{\mathrm{UU}}-Y_i^U){\stackrel{\&CenterDot;}{V}}_i^U---\left(11\right)$

the modified node current equation is:

$\left[\begin{array}{c}{\stackrel{\&CenterDot;}{V}}_i^O\\ {\stackrel{\&CenterDot;}{I}}_i^O\\ {\stackrel{\&CenterDot;}{I}}_{\mathrm{ij}}^O\\ {\stackrel{\&CenterDot;}{V}}_i^U\\ 0\end{array}\right]=\left[\begin{array}{cc}E& 0\\ Y_i^{\mathrm{OO}}& Y_i^{\mathrm{OU}}\\ Y_{\mathrm{ij}}^{\mathrm{OO}}& Y_{\mathrm{ij}}^{\mathrm{OU}}\\ 0& E\\ Y_i^{\mathrm{UO}}& Y_i^{\mathrm{UU}}-Y_i^U\end{array}\right]\left[\begin{array}{c}{\stackrel{\&CenterDot;}{V}}_i^O\\ {\stackrel{\&CenterDot;}{V}}_i^U\end{array}\right]---\left(12\right)$

taking the node current equation as a linear equation of linear calculation, and carrying out linear state estimation by the formula (3).

In the process of carrying out nonlinear state estimation, PMU voltage measurement information and phase angle measurement information, PMU power measurement information and PMU current measurement information are respectively introduced to carry out nonlinear state estimation.

The specific process of introducing PMU voltage measurement information and phase angle measurement information to carry out nonlinear state estimation comprises the following steps:

1) directly adding a PMU node voltage phasor measurement equation into the nonlinear state estimation, wherein the PMU voltage and phase angle measurement equation is as follows:

$\left\{\begin{array}{c}{V}_i^m=V_i\\ {\mathrm{\&theta;}}_i^m={\mathrm{\&theta;}}_i\end{array}\right.---\left(13\right)$

wherein,andPMU voltage measurement information and phase angle measurement information, V, of node i_iAnd theta_iThe voltage and the phase angle of the node i are shown, the corresponding element of the Jacobian matrix is 1, and other elements are 0;

2) introducing a power phase angle difference;

introducing new quantity measurement theta to large power grid nonlinear state estimation containing PMU phase angle measurement_ijWhere θ between node i and node j_ij＝θ_i-θ_j，θ_jIs the phase angle of node j; then there is

$\left\{\begin{array}{c}\frac{{\mathrm{d\&theta;}}_{\mathrm{ij}}}{{\mathrm{d\&theta;}}_i}=1\\ \frac{{\mathrm{d\&theta;}}_{\mathrm{ij}}}{{\mathrm{d\&theta;}}_j}=-1\end{array}\right.---\left(14\right).$

The specific process of introducing PMU power measurement information to carry out nonlinear state estimation comprises the following steps:

$\left\{\begin{array}{c}{P}_i^m=P_i\\ Q_i^m=Q_i\end{array}\right.---\left(15\right)$

wherein,andactive and reactive power measurement information, P, for node i, respectively_iAnd Q_iRespectively the active power and the reactive power of the node i; according to the types of node injection power and branch power, the corresponding Jacobian matrix coefficient of the PMU power measurement is consistent with the corresponding coefficient of the SCADA measured power quantity.

The specific process of introducing PMU current measurement information to carry out nonlinear state estimation is divided into the following two cases:

1) convert the current magnitude into branch current, having

$\left\{\begin{array}{c}{P}_{\mathrm{ij}}=V_i{I}_i\cos ({\mathrm{\&theta;}}_{\mathrm{ui}}-{\mathrm{\&theta;}}_{\mathrm{Ii}})\\ Q_{\mathrm{ij}}=V_i{I}_i\sin ({\mathrm{\&theta;}}_{\mathrm{ui}}-{\mathrm{\&theta;}}_{\mathrm{Ii}})\end{array}\right.---\left(16\right)$

Wherein, P_ijAnd Q_ijRespectively the active power and reactive power of a branch ij between node I and node j, I_iIs the current at the node i and,andrespectively is a voltage phase angle and a current phase angle of the node i; p_ijAnd Q_ijThe weight of the error is calculated according to the following error transfer formula;

$R_{P_{\mathrm{ij}}}={\left(\frac{{\&PartialD;P}_{\mathrm{ij}}}{{\&PartialD;V}_i}{\mathrm{\&sigma;}}_{V_i}\right)}^2+{\left(\frac{{\&PartialD;P}_{\mathrm{ij}}}{{\&PartialD;I}_i}{\mathrm{\&sigma;}}_{I_i}\right)}^2+{\left(\frac{{\&PartialD;P}_{\mathrm{ij}}}{{\&PartialD;\mathrm{\&theta;}}_{\mathrm{Vi}}}{\mathrm{\&sigma;}}_{{\mathrm{\&theta;}}_{\mathrm{Vi}}}\right)}^2+{\left(\frac{{\&PartialD;P}_{\mathrm{ij}}}{{\&PartialD;\mathrm{\&theta;}}_{\mathrm{Ii}}}{\mathrm{\&sigma;}}_{{\mathrm{\&theta;}}_{\mathrm{Ii}}}\right)}^2---\left(17\right)$

$R_{Q_{\mathrm{ij}}}={\left(\frac{{\&PartialD;Q}_{\mathrm{ij}}}{{\&PartialD;V}_i}{\mathrm{\&sigma;}}_{V_i}\right)}^2+{\left(\frac{{\&PartialD;Q}_{\mathrm{ij}}}{{\&PartialD;I}_i}{\mathrm{\&sigma;}}_{I_i}\right)}^2+{\left(\frac{{\&PartialD;Q}_{\mathrm{ij}}}{{\&PartialD;\mathrm{\&theta;}}_{\mathrm{Vi}}}{\mathrm{\&sigma;}}_{{\mathrm{\&theta;}}_{\mathrm{Vi}}}\right)}^2+{\left(\frac{{\&PartialD;Q}_{\mathrm{ij}}}{{\&PartialD;\mathrm{\&theta;}}_{\mathrm{Ii}}}{\mathrm{\&sigma;}}_{{\mathrm{\&theta;}}_{\mathrm{Ii}}}\right)}^2---\left(18\right)$

wherein,andthe error variance of the equivalent active measurement and the equivalent reactive measurement,andare respectively a voltage amplitude V_iCurrent I_iPhase angle of voltage theta_uiAnd phase angle theta of injected current_IiThe corresponding standard deviation; p_ijAnd Q_ijAre respectively expressed as $R_{P_{\mathrm{ij}}}^{-1}=\frac{1}{R_{P_{\mathrm{ij}}}}$ And $R_{Q_{\mathrm{ij}}}^{-1}=\frac{1}{R_{Q_{\mathrm{ij}}}};$

converting branch current vector of node configured with PMU into adjacent node voltage vector

${\stackrel{\&CenterDot;}{V}}_j=\frac{{\stackrel{\&CenterDot;}{I}}_{\mathrm{ij}}-(Y_{i0}+Y_{\mathrm{ij}}){\stackrel{\&CenterDot;}{V}}_i}{-Y_{\mathrm{ij}}}---\left(19\right)$

Wherein,is the phase voltage at the node j,is the current vector of branch ij, Y_i0Is the capacitance to ground of node i, Y_ijElements of a node admittance matrix;the weight of the error is calculated according to the following error transfer formula;

$R_{{\stackrel{\&CenterDot;}{V}}_j}={\left(\frac{\&PartialD;{\stackrel{\&CenterDot;}{V}}_j}{{\&PartialD;V}_i}{\mathrm{\&sigma;}}_{V_i}\right)}^2+{\left(\frac{\&PartialD;{\stackrel{\&CenterDot;}{V}}_j}{{\&PartialD;\mathrm{\&theta;}}_i}{\mathrm{\&sigma;}}_{{\mathrm{\&theta;}}_i}\right)}^2+{\left(\frac{\&PartialD;{\stackrel{\&CenterDot;}{V}}_j}{{\&PartialD;I}_{\mathrm{ij}}}{\mathrm{\&sigma;}}_{I_{\mathrm{ij}}}\right)}^2+{\left(\frac{\&PartialD;{\stackrel{\&CenterDot;}{V}}_j}{{\&PartialD;\mathrm{\&theta;}}_{\mathrm{ij}}^I}{\mathrm{\&sigma;}}_{{\mathrm{\&theta;}}_{\mathrm{ij}}^I}\right)}^2---\left(20\right)$

wherein,is equal voltage directionThe variance of the error in the metrology is measured,andrespectively a voltage amplitude V_iPhase angle of voltage theta, branch current I_ijPhase angle of sum branch currentThe corresponding standard deviation;is expressed as

2) Constructing a pseudo quantity measurement;

measurement of structural false quantityBy rotation of-theta_iAngle of (A) toTheta of_iThe variable becomes 0, thereby fixing the angle of the i end of the branch ij and constructing the phase angle difference theta_ijUsing theta_ijThe decoupling is performed as follows:

$\begin{array}{c}{\stackrel{\&CenterDot;}{I}}_{\mathrm{ij}.0}={\stackrel{\&CenterDot;}{I}}_{\mathrm{ij}}{e}^{-j{\mathrm{\&theta;}}_i}=[y_{\mathrm{ij}}({\stackrel{\&CenterDot;}{V}}_i-{\stackrel{\&CenterDot;}{V}}_j)+y_{i0}{\stackrel{\&CenterDot;}{V}}_i]e^{-j{\mathrm{\&theta;}}_i}=y_{\mathrm{ij}}(V_i-V_j{e}^{-j{\mathrm{\&theta;}}_{\mathrm{ij}}})+y_{i0}{V}_i\\ =(g+\mathrm{jb})[V_i-V_j(\cos {\mathrm{\&theta;}}_{\mathrm{ij}}-j\sin {\mathrm{\&theta;}}_{\mathrm{ij}})]+j{y}_{\mathrm{ic}}{V}_i\end{array}---\left(21\right)$

wherein,for constructed rotational false quantity measurement, y_ijFor admittance of branch ij, y_i0For the admittance to ground of the i-terminal of the line, y_icThe capacitance reactance to the ground of the branch ij is g and b are respectively the conductance and the susceptance of the branch ij;

will be provided withDecomposition into real partsAnd imaginary partTwo variables of

$\left\{\begin{array}{c}{I}_{\mathrm{ij}.0}^{\mathrm{re}}=g{V}_i-{\mathrm{gV}}_j\cos {\mathrm{\&theta;}}_{\mathrm{ij}}-{\mathrm{bV}}_j\sin {\mathrm{\&theta;}}_{\mathrm{ij}}\\ I_{\mathrm{ij}.0}^{\mathrm{im}}={\mathrm{gV}}_j\sin {\mathrm{\&theta;}}_{\mathrm{ij}}+{\mathrm{bV}}_i-{\mathrm{bV}}_j\cos {\mathrm{\&theta;}}_{\mathrm{ij}}+y_{\mathrm{ic}}{V}_i\end{array}\right.---\left(22\right)$

Derivation of a deviation is obtained by

$\left\{\begin{array}{c}\frac{{\&PartialD;I}_{\mathrm{ij}.0}^{\mathrm{re}}}{{\&PartialD;\mathrm{\&theta;}}_i}={\mathrm{gV}}_j\sin {\mathrm{\&theta;}}_{\mathrm{ij}}-{\mathrm{bV}}_j\cos {\mathrm{\&theta;}}_{\mathrm{ij}}\\ \frac{{\&PartialD;I}_{\mathrm{ij}.0}^{\mathrm{re}}}{{\&PartialD;V}_i}=g\\ \frac{{\&PartialD;I}_{\mathrm{ij}.0}^{\mathrm{im}}}{{\&PartialD;\mathrm{\&theta;}}_i}={\mathrm{gV}}_j\cos {\mathrm{\&theta;}}_{\mathrm{ij}}+{\mathrm{bV}}_j\sin {\mathrm{\&theta;}}_{\mathrm{ij}}\\ \frac{{\&PartialD;I}_{\mathrm{ij}.0}^{\mathrm{im}}}{{\&PartialD;V}_i}=b+y_{\mathrm{ic}}\end{array}\right.---\left(23\right)$

$\left\{\begin{array}{c}\frac{{\&PartialD;I}_{\mathrm{ij}.0}^{\mathrm{re}}}{{\&PartialD;\mathrm{\&theta;}}_j}=-g{V}_j\sin {\mathrm{\&theta;}}_{\mathrm{ij}}+{\mathrm{bV}}_j\cos {\mathrm{\&theta;}}_{\mathrm{ij}}\\ \frac{{\&PartialD;I}_{\mathrm{ij}.0}^{\mathrm{re}}}{{\&PartialD;V}_j}=-g\cos {\mathrm{\&theta;}}_{\mathrm{ij}}-b{\sin \mathrm{\&theta;}}_{\mathrm{ij}}\\ \frac{{\&PartialD;I}_{\mathrm{ij}.0}^{\mathrm{im}}}{{\&PartialD;\mathrm{\&theta;}}_j}=-g{V}_j\cos {\mathrm{\&theta;}}_{\mathrm{ij}}+{\mathrm{bV}}_j\sin {\mathrm{\&theta;}}_{\mathrm{ij}}\\ \frac{{\&PartialD;I}_{\mathrm{ij}.0}^{\mathrm{im}}}{{\&PartialD;V}_j}=g\sin {\mathrm{\&theta;}}_{\mathrm{ij}}-{b\cos \mathrm{\&theta;}}_{\mathrm{ij}}\end{array}\right.---\left(24\right)$

For a high voltage transmission system, r is the line resistance and x is the line reactance, then r is<<x，V_i≈V_j＝V₀In which V is₀Is a reference voltage, θ_ijClose to 0, so there is g<<b，cosθ_ij≈1，sinθ_ijIs approximately equal to 0 and simplified by gsin theta_ij<<bcosθ_ij，|gcosθ_ij±bsinθ_ij|<<|gsinθ_ij±bcosθ_ij；

The equations (20) and (21) are simplified by

$\left\{\begin{array}{c}\frac{{\&PartialD;I}_{\mathrm{ij}.0}^{\mathrm{re}}}{\&PartialD;{\mathrm{\&theta;}}_i}=-b{V}_0\\ \frac{{\&PartialD;I}_{\mathrm{ij}.0}^{\mathrm{re}}}{{\&PartialD;V}_i}=0\\ \frac{{\&PartialD;I}_{\mathrm{ij}.0}^{\mathrm{im}}}{{\&PartialD;\mathrm{\&theta;}}_i}=0\\ \frac{{\&PartialD;I}_{\mathrm{ij}.0}^{\mathrm{im}}}{{\&PartialD;V}_i}=b+y_{\mathrm{ic}}\end{array}\right.---\left(25\right)$

$\left\{\begin{array}{c}\frac{{\&PartialD;I}_{\mathrm{ij}.0}^{\mathrm{re}}}{\&PartialD;{\mathrm{\&theta;}}_j}=b{V}_0\\ \frac{{\&PartialD;I}_{\mathrm{ij}.0}^{\mathrm{re}}}{{\&PartialD;V}_j}=0\\ \frac{{\&PartialD;I}_{\mathrm{ij}.0}^{\mathrm{im}}}{{\&PartialD;\mathrm{\&theta;}}_i}=0\\ \frac{{\&PartialD;I}_{\mathrm{ij}.0}^{\mathrm{im}}}{{\&PartialD;V}_i}=-b\end{array}\right.---\left(26\right)$

The measurement of the rotating pseudo quantity realizes decoupling, has

$\left(\begin{array}{c}\mathrm{\&Delta;}{I}_{\mathrm{ij}.0}^{\mathrm{re}}\\ {\mathrm{\&Delta;I}}_{\mathrm{ij}.0}^{\mathrm{im}}\end{array}\right)=\left(\begin{array}{cc}-B^{\&prime;}& 0\\ 0& B^{\&prime;\&prime;}\end{array}\right)\left(\begin{array}{c}{V}_0\mathrm{\&Delta;\&theta;}\\ \mathrm{\&Delta;v}\end{array}\right)---\left(27\right)$

Wherein B ' and B ' ' are each V₀The coefficient matrixes corresponding to the delta theta and the delta v are constants under the condition that the network topology and the parameters are not changed; Δ θ and Δ v are the phase angle increment and the voltage increment, respectively.

Compared with the prior art, the invention has the beneficial effects that:

A. the configuration proportions of different PMUs in the power grid are analyzed, and different linear or nonlinear algorithms can be flexibly selected according to the observability of the PMUs.

B. The linear estimation is not finished once, but the correction weight is estimated once again according to the residual error value of the first estimation, and the estimation precision is improved to a certain extent through testing.

C. The voltage amplitude and the phase angle are directly introduced to be used as quantity measurement, a larger weight is given to participate in estimation, the method can be directly applied to the existing rapid decomposition state estimation program as long as the method is slightly improved, and when the voltage measurement of the PMU is more accurate, the estimation effect can be obviously improved.

D. The voltage phase angle difference is introduced as the quantity measurement, the effect of the phase angle difference between the nodes is mainly restrained, and the calculation of the Jacobian matrix is simple. Voltage phase angle errors due to common mode factors of PMU measurement equipment or voltage phase angle errors due to different PMU and SCADA selection balance node selections and recalculation can be eliminated.

E. The power measurement is directly introduced, and the method can be directly used for a fast-decomposition state estimation algorithm, directly increase the quantity measurement, improve the redundancy and improve the estimation precision.

F. Introducing the current quantity as a pseudo quantity measurement to participate in estimation by using a rotation method, and only selecting a voltage phase angle as an initial value to participate in iteration at a rotation angle; the precision is irrelevant to the voltage phase angle and only relevant to the original current and current phase angle measurement precision, and the transmission error is small. PQ decoupling can be realized, decoupling conditions are consistent with traditional state estimation, and the method can be fused with traditional rapid decomposition state estimation to realize rapid calculation.

Drawings

FIG. 1 is a flow chart of a large power grid state estimation method incorporating PMU measurement information;

FIG. 2 is a block diagram of a fast decomposition state estimation process with dummy measurements.

Detailed Description

The present invention will be described in further detail with reference to the accompanying drawings.

The invention provides a large power grid state estimation method introducing PMU (phasor measurement unit) measurement information.

The method makes full use of the characteristics and advantages of PMU measurement, and the PMU measurement information participates in state estimation under the conditions that PMU measurement can be observed and cannot be observed, so that PMU measurement in the current power grid can play a role in state estimation, the state estimation precision is improved, and the practical level of state estimation software in the current actual power grid and the future large power grid is improved.

The method can completely utilize PMU measurement information to carry out linear estimation or the system is assembled with a large number of PMU measurements under the condition that the system PMU measurement is observable according to the observability of the system, and can utilize SCADA (Supervisory control and data acquisition, data acquisition and monitoring control system) measurement supplement to carry out linear estimation when only part of nodes are not observable. The linear estimation model of the present invention takes into account the conductance of the ground leg. Since the linear estimation does not require iteration, the accuracy of the model used for estimation is high. The ground leg conductance will have a certain influence on the estimation result if not considered.

In the unobservable case, a measured state estimate of the PUM is introduced on the basis of the PQ decomposition method. The PQ decomposition method has the advantages of simple model, high calculation speed and the like. Aiming at the problem of directly introducing PMU current measurement, the invention innovatively uses a rotary pseudo-measurement method to carry out rotary conversion on the current vector, thereby achieving the aim of introducing the current quantity, increasing the estimation redundancy and improving the estimation precision. The rotating pseudo-measurement method is simple in calculation, can be combined with a PQ decomposition method for calculation, introduces a small measurement transmission error, and has practical value.

1) SCADA: the Supervisory control and DataAcknowledge system is a data acquisition and monitoring control system. The system is the most important subsystem of the EMS, has the advantages of complete information, efficiency improvement, correct control of the system running state, decision acceleration, capability of helping to quickly diagnose the system fault state and the like, and is an indispensable tool for power dispatching.

2) PMU measurement: a synchronous phase angle measurement unit. The grid node voltage vector, power and branch current vector may be measured. The data measurement precision is high, and the acquisition and transmission speed is high.

3) Observability: in the calculation of the power system, if the existing measurement information is utilized, the voltage amplitude and phase angle quantities of all the nodes can be calculated, so that the system state can be completely observable.

4) Algebraic observability: for a power system with n nodes and m measurement vector dimensions, the system can be considered algebraically considerable if the rank (H) =2n-1 of the system linear metrology model, i.e. H full rank.

5) And (3) state estimation: the redundancy of the real-time measurement system is used for improving the data accuracy, automatically eliminating error information caused by interference and estimating or forecasting the running state of the system.

6) PQ decomposition state estimation: and (3) establishing a state estimation algorithm by absorbing the power flow calculation experience (PQ decomposition method) on the basis of a least square method.

7) Rotation pseudo-measurement method: the existing measurement vector is rotated by a certain angle to serve as pseudo measurement information to participate in the state estimation calculation method.

Referring to fig. 1, the present invention provides a large power grid state estimation method introducing PMU measurement information, the method includes the following steps:

step 1: judging the algebraic observability of the power system;

step 2: judging the observability of PMU measurement information;

and step 3: and carrying out state estimation on the large power grid.

The biggest difference between PMU measurement and SCADA measurement is that it can collect the phase angle measurement of voltage and the phase angle measurement of current, and if PMU devices are installed on all nodes of the system and the voltage amplitude and the phase angle measurement of all the nodes are collected, the system is completely observable. However, this is not practical and uneconomical, and it is sufficient to install PMUs on some nodes, because the node equipped with PMUs collects not only the voltage amplitude and phase angle measurements of the node, but also the injected current amplitude and phase angle measurements of the node, and the branch current amplitude and phase angle measurements connected to the node, and the voltage amplitude and phase angle of the connected node can be obtained from the voltage, current amplitude and phase angle measurements of the node, so that PMU equipment installed on each node can provide multiple measurements.

In the step 1, for the power system with n nodes and m measurement vector dimensions, if the rank (H) =2n-1 of the linear measurement model coefficient matrix of the power system, that is, H full rank, the power system is considered to be algebraically considerable.

In the step 2, the observability of PMU measurement information is judged according to the algebraic observability of the power system; the following cases are divided:

A. if rank (H) =2n-1 is satisfied, PMU measurement information is completely considerable;

B. if rank (H) is not less than a (2n-1), the PMU measurement information is considerable, wherein a is 0.95-0.9;

C. if rank (H) < a (2n-1) is satisfied, PMU measurement information is small and considerable;

D. if rank (h) =0 is satisfied, PMU measurement information is completely inconspicuous.

The linear estimation in the literature does not need iterative calculation, and the result can be directly solved. If the measured data has larger bad data, the estimation accuracy is greatly influenced. After the first estimation, the method calculates the maximum residual error between the estimated value and the measured value, if the residual error exceeds a certain value, the weight of the measurement corresponding to the maximum residual error is reduced, and then linear state estimation is performed again, which is equivalent to iterative calculation. The method can be used for many times.

The general linear estimation can control the precision through a convergence condition, and model calculation which neglects the conductance to the ground can be adopted. The PMU-based linearity estimate is computed directly without iteration. Therefore, the requirement on the accuracy of the model is high, and the equivalent conductance of the transformer branch to the ground needs to be considered. The estimation of the state quantities across the transformer branches may be significantly affected if the ground conductance is not considered. Therefore, the state estimation of the large power grid according to the observability of the PMU measurement information in step 3 is divided into the following cases:

A. if the PMU measurement information is completely observable, linear state estimation is carried out by adopting a rectangular coordinate linear model;

B. if the PMU measurement information is considerable, the SCADA measurement is used for supplementing the region which is not observable by the PMU, and the linear state estimation is carried out;

C. if the PMU measurement information is a little and considerable, carrying out nonlinear state estimation;

D. the PMU measurement information is not objective at all, and the linear estimation introduced into the PMU is not needed.

The specific process of linear state estimation by adopting the rectangular coordinate linear model comprises the following steps:

the real part and the imaginary part of the voltage are used as state quantities, the real part and the imaginary part of the node voltage, the node injection current and the branch current are used as quantity quantities, and then a measurement equation is expressed by a linear equation as follows:

z＝h(x)+v＝Ax+v（1）

wherein z is a measured quantity, x is a state quantity, v is a random error, A is a first order coefficient matrix, h (x) is a calculated value based on the measurement of the state quantity x, and there are $\frac{\&PartialD;h\left(x\right)}{\&PartialD;x}=A,h\left(x\right)=\mathrm{Ax};$

The objective function is expressed as:

J(x)＝[z-Ax]^TR^-1[z-Ax]（2）

wherein R is^-1Is a weight matrix, J (x) is a least squares objective function;

the linear state estimation equation is: ${\hat{x}}^{(n+1)}={\left[\begin{array}{ccc}{A}^T& R^{-1\left(n\right)}& A\end{array}\right]}^T{R}^{-1\left(n\right)}z---\left(3\right)$

wherein R is^-1(n)For the weight matrix calculated for the nth time,the estimated value calculated for the (n + 1) th time;

calculating the deviation of the residualComprises the following steps:

$r_{\max }^{(n+1)}=\max \left\{r\left({\hat{x}}^{(n+1)}\right)\right\}---\left(4\right)$

wherein,is a residual, expressed as:

$r\left({\hat{x}}^{(n+1)}\right)=z-h\left({\hat{x}}^{(n+1)}\right)---\left(5\right)$

wherein,according to the n +1 stateThe value of the estimated value is,obtaining a measurement calculation value;

because the estimation accuracy of the power system state is greatly influenced by the current measurement accuracy and is less influenced by the voltage measurement, only the residual error with the maximum current is calculated, and the weight of the current measurement is corrected, including

$R^{-1(n+1)}=R_{\mathrm{cor}}^{-1\left(n\right)}---\left(6\right)$

Wherein,performing a linear estimation on the modified weight matrix corresponding to the maximum value of the residual error until the maximum value is satisfiedAnd isWhereinIn order to correct the amount of the voltage correction,the amount of phase angle correction,_vand_θis a convergence threshold value preset according to the precision; if a measurement has been corrected, the measurement weight is not corrected.

The PMU instrumentation system will be a progressive process, so that, over a considerable period of time, the PMU measurements will still be incompletely observable to the system, in which case the SCADA measurements need to be used to supplement the non-observable areas of the PMU, and the specific process for linear state estimation is:

using superscript O to represent the observed region for PMU measurements and superscript U to represent the unobservable region for PMU measurements, the node voltage equation can be expressed as:

$\left[\begin{array}{c}{\stackrel{\&CenterDot;}{V}}_i^O\\ {\stackrel{\&CenterDot;}{I}}_i^O\\ {\stackrel{\&CenterDot;}{I}}_{\mathrm{ij}}^O\\ {\stackrel{\&CenterDot;}{V}}_i^U\\ {\stackrel{\&CenterDot;}{I}}_i^U\end{array}\right]=\left[\begin{array}{cc}E& 0\\ Y_i^{\mathrm{OO}}& Y_i^{\mathrm{OU}}\\ Y_{\mathrm{ij}}^{\mathrm{OO}}& Y_{\mathrm{ij}}^{\mathrm{OU}}\\ 0& E\\ Y_i^{\mathrm{UO}}& Y_i^{\mathrm{UU}}\end{array}\right]\left[\begin{array}{c}{\stackrel{\&CenterDot;}{V}}_i^O\\ {\stackrel{\&CenterDot;}{V}}_i^U\end{array}\right]---\left(7\right)$

wherein:andnode voltage matrixes of observable and unobservable areas respectively;andinjecting current matrixes into nodes of observable and unobservable areas respectively; e is an identity matrix;a observable self-admittance matrix is injected for the node,the nodes are injected with observable and unobservable transadmittance matrices,the nodes inject the observable and observable transadmittance matrices,injecting an unobservable self-admittance matrix for the node;the current matrix can be observed by the branch circuit,the self-admittance matrix is observable for the branch,is a branch observable and unobservable transadmittance matrix;

the reason that only the node voltage and the node injection current are adopted for the unobservable region is as follows:

1) the injection quantity of the node is a dependent variable determining the system state, the branch current (or power) is only a slave variable describing the system state, and the state of the unobservable region can be completely described by adopting the node voltage and the node injection current;

2) the node voltage and the node injection current of the unobservable region can be conveniently obtained by a state estimation result;

3) after the voltage of the compensation node and the injected current of the node in the non-observable region of the PMU are measured, the complete observability of the system is achieved;

node injection current matrix of non-observable regionExpressed as:

${\stackrel{\&CenterDot;}{I}}_i^U=\frac{P_i-{\mathrm{jQ}}_i}{{\stackrel{\&CenterDot;}{V}}_i^{*U}}---\left(8\right)$

wherein, P_iAnd Q_iFor the active and reactive power to be injected,is composed ofA conjugate matrix of (a);

the real and imaginary parts of the node voltage are used and are determined by the magnitude and phase angle of the voltage.

If the SCADA measurement is used for the unobservable region, the voltage phase angle cannot be obtained, the node injection current cannot be solved, and the node current formula is modified so that the SCADA measurement can be used.

Node-based equivalent injection admittance matrixExpressed as:

$Y_i^U=\frac{{\stackrel{\&CenterDot;}{I}}_i^U}{{\stackrel{\&CenterDot;}{V}}_i^U}=\frac{P_i-{\mathrm{jQ}}_i}{{\left|{\stackrel{\&CenterDot;}{V}}_i^U\right|}^2}---\left(9\right)$

bringing formula (9) into the following formula

${\stackrel{\&CenterDot;}{I}}_i^U=Y_i^U{\stackrel{\&CenterDot;}{V}}_i^U=Y_i^{\mathrm{UO}}{\stackrel{\&CenterDot;}{V}}_i^O+Y_i^{\mathrm{UU}}{\stackrel{\&CenterDot;}{V}}_i^U---\left(10\right)$

Finishing to obtain:

$0=Y_i^{\mathrm{UO}}{\stackrel{\&CenterDot;}{V}}_i^O+(Y_i^{\mathrm{UU}}-Y_i^U){\stackrel{\&CenterDot;}{V}}_i^U---\left(11\right)$

the modified node current equation is:

$\left[\begin{array}{c}{\stackrel{\&CenterDot;}{V}}_i^O\\ {\stackrel{\&CenterDot;}{I}}_i^O\\ {\stackrel{\&CenterDot;}{I}}_{\mathrm{ij}}^O\\ {\stackrel{\&CenterDot;}{V}}_i^U\\ 0\end{array}\right]=\left[\begin{array}{cc}E& 0\\ Y_i^{\mathrm{OO}}& Y_i^{\mathrm{OU}}\\ Y_{\mathrm{ij}}^{\mathrm{OO}}& Y_{\mathrm{ij}}^{\mathrm{OU}}\\ 0& E\\ Y_i^{\mathrm{UO}}& Y_i^{\mathrm{UU}}-Y_i^U\end{array}\right]\left[\begin{array}{c}{\stackrel{\&CenterDot;}{V}}_i^O\\ {\stackrel{\&CenterDot;}{V}}_i^U\end{array}\right]---\left(12\right)$

taking the node current equation as a linear equation of linear calculation, and carrying out linear state estimation by the formula (3).

In the process of carrying out nonlinear state estimation, PMU voltage measurement information and phase angle measurement information, PMU power measurement information and PMU current measurement information are respectively introduced to carry out nonlinear state estimation.

The specific process of introducing PMU voltage measurement information and phase angle measurement information to carry out nonlinear state estimation comprises the following steps:

1) directly adding a PMU node voltage phasor measurement equation into the nonlinear state estimation, wherein the PMU voltage and phase angle measurement equation is as follows:

$\left\{\begin{array}{c}{V}_i^m=V_i\\ {\mathrm{\&theta;}}_i^m={\mathrm{\&theta;}}_i\end{array}\right.---\left(13\right)$

wherein,andPMU voltage measurement information and phase angle measurement information, V, of node i_iAnd theta_iThe voltage and the phase angle of the node i are shown, the corresponding element of the Jacobian matrix is 1, and other elements are 0; the usage of the bus voltage amplitude measurement value in the model is completely the same as that in the traditional state estimation model, when a PMU is configured on a certain bus, 2 equations are added in the measurement equation, 2 rows are added in the measurement Jacobian matrix, and each row only has one nonzero element with the value of 1.

2) Introducing a power phase angle difference;

introducing new quantity measurement theta to large power grid nonlinear state estimation containing PMU phase angle measurement_ijWhere θ between node i and node j_ij＝θ_i-θ_j，θ_jIs the phase angle of node j; then there is

$\left\{\begin{array}{c}\frac{{\mathrm{d\&theta;}}_{\mathrm{ij}}}{{\mathrm{d\&theta;}}_i}=1\\ \frac{{\mathrm{d\&theta;}}_{\mathrm{ij}}}{{\mathrm{d\&theta;}}_j}=-1\end{array}\right.---\left(14\right).$

This modification of the jacobian matrix is very simple and can be used directly in the state estimation. When the method of phase angle difference is adopted, the problem of reference points does not exist,neither direct measurement (or calculation) of the phase angle difference depends on the reference point. Due to theta_ijThe error generated by recalculation due to different balance node selection of PMU and SCADA can be eliminated for the relative phase angle difference between the nodes, and the voltage phase angle error caused by common mode factors of PMU measuring equipment can also be eliminated. Theta_ijThe effect of the phase angle difference between the nodes is mainly constrained.

In the above two methods, the method 1 may be directly used for PMU phase angle measurement with a smaller reduction error or common mode error, and the method 2) is used for phase angle measurement with a larger error.

The specific process of introducing PMU power measurement information to carry out nonlinear state estimation comprises the following steps:

$\left\{\begin{array}{c}{P}_i^m=P_i\\ Q_i^m=Q_i\end{array}\right.---\left(15\right)$

wherein,andactive and reactive power measurement information, P, for node i, respectively_iAnd Q_iAre respectively provided withActive power and reactive power for node i; according to the types of node injection power and branch power, the corresponding Jacobian matrix coefficient of the PMU power measurement is consistent with the corresponding coefficient of the SCADA measured power quantity.

Direct introduction of branchThere are difficulties in that each branch currentIs the phase angle of voltage theta_iAnd theta_jThe current vector varies with the phase angle of the voltage at each node, typically, the phase angle θ of each node_iAnd theta_jThe value cannot be simply considered as 0, and PQ decoupling calculation cannot be used, which brings difficulty to calculation.

The specific process of introducing PMU current measurement information to carry out nonlinear state estimation is divided into the following two cases:

1) convert the current magnitude into branch current, having

$\left\{\begin{array}{c}{P}_{\mathrm{ij}}=V_i{I}_i\cos ({\mathrm{\&theta;}}_{\mathrm{ui}}-{\mathrm{\&theta;}}_{\mathrm{Ii}})\\ Q_{\mathrm{ij}}=V_i{I}_i\sin ({\mathrm{\&theta;}}_{\mathrm{ui}}-{\mathrm{\&theta;}}_{\mathrm{Ii}})\end{array}\right.---\left(16\right)$

Wherein, P_ijAnd Q_ijRespectively the active power and reactive power of a branch ij between node I and node j, I_iIs the current of node i, θ_uiAnd theta_IiRespectively is a voltage phase angle and a current phase angle of the node i; p_ijAnd Q_ijThe weight of the error is calculated according to the following error transfer formula;

$R_{P_{\mathrm{ij}}}={\left(\frac{{\&PartialD;P}_{\mathrm{ij}}}{{\&PartialD;V}_i}{\mathrm{\&sigma;}}_{V_i}\right)}^2+{\left(\frac{{\&PartialD;P}_{\mathrm{ij}}}{{\&PartialD;I}_i}{\mathrm{\&sigma;}}_{I_i}\right)}^2+{\left(\frac{{\&PartialD;P}_{\mathrm{ij}}}{{\&PartialD;\mathrm{\&theta;}}_{\mathrm{Vi}}}{\mathrm{\&sigma;}}_{{\mathrm{\&theta;}}_{\mathrm{Vi}}}\right)}^2+{\left(\frac{{\&PartialD;P}_{\mathrm{ij}}}{{\&PartialD;\mathrm{\&theta;}}_{\mathrm{Ii}}}{\mathrm{\&sigma;}}_{{\mathrm{\&theta;}}_{\mathrm{Ii}}}\right)}^2---\left(17\right)$

$R_{Q_{\mathrm{ij}}}={\left(\frac{{\&PartialD;Q}_{\mathrm{ij}}}{{\&PartialD;V}_i}{\mathrm{\&sigma;}}_{V_i}\right)}^2+{\left(\frac{{\&PartialD;Q}_{\mathrm{ij}}}{{\&PartialD;I}_i}{\mathrm{\&sigma;}}_{I_i}\right)}^2+{\left(\frac{{\&PartialD;Q}_{\mathrm{ij}}}{{\&PartialD;\mathrm{\&theta;}}_{\mathrm{Vi}}}{\mathrm{\&sigma;}}_{{\mathrm{\&theta;}}_{\mathrm{Vi}}}\right)}^2+{\left(\frac{{\&PartialD;Q}_{\mathrm{ij}}}{{\&PartialD;\mathrm{\&theta;}}_{\mathrm{Ii}}}{\mathrm{\&sigma;}}_{{\mathrm{\&theta;}}_{\mathrm{Ii}}}\right)}^2---\left(18\right)$

wherein,andthe error variance of the equivalent active measurement and the equivalent reactive measurement,andare respectively a voltage amplitude V_iCurrent I_iPhase angle of voltage theta_uiAnd phase angle theta of injected current_IiThe corresponding standard deviation; p_ijAnd Q_ijAre respectively expressed as $R_{P_{\mathrm{ij}}}^{-1}=\frac{1}{R_{P_{\mathrm{ij}}}}$ And $R_{Q_{\mathrm{ij}}}^{-1}=\frac{1}{R_{Q_{\mathrm{ij}}}};$

converting branch current vector of node configured with PMU into adjacent node voltage vector

${\stackrel{\&CenterDot;}{V}}_j=\frac{{\stackrel{\&CenterDot;}{I}}_{\mathrm{ij}}-(Y_{i0}+Y_{\mathrm{ij}}){\stackrel{\&CenterDot;}{V}}_i}{-Y_{\mathrm{ij}}}---\left(19\right)$

Wherein,is the phase voltage at the node j,is the current vector of branch ij, Y_i0Is the capacitance to ground of node i, Y_ijElements of a node admittance matrix;the weight of the error is calculated according to the following error transfer formula;

$R_{{\stackrel{\&CenterDot;}{V}}_j}={\left(\frac{\&PartialD;{\stackrel{\&CenterDot;}{V}}_j}{{\&PartialD;V}_i}{\mathrm{\&sigma;}}_{V_i}\right)}^2+{\left(\frac{\&PartialD;{\stackrel{\&CenterDot;}{V}}_j}{{\&PartialD;\mathrm{\&theta;}}_i}{\mathrm{\&sigma;}}_{{\mathrm{\&theta;}}_i}\right)}^2+{\left(\frac{\&PartialD;{\stackrel{\&CenterDot;}{V}}_j}{{\&PartialD;I}_{\mathrm{ij}}}{\mathrm{\&sigma;}}_{I_{\mathrm{ij}}}\right)}^2+{\left(\frac{\&PartialD;{\stackrel{\&CenterDot;}{V}}_j}{{\&PartialD;\mathrm{\&theta;}}_{\mathrm{ij}}^I}{\mathrm{\&sigma;}}_{{\mathrm{\&theta;}}_{\mathrm{ij}}^I}\right)}^2---\left(20\right)$

wherein,is the error variance of the equivalent voltage vector measurement,andrespectively a voltage amplitude V_iPhase angle of voltage theta, branch current I_ijPhase angle of sum branch currentThe corresponding standard deviation;is expressed as

2) Constructing a pseudo quantity measurement;

as shown in FIG. 2, a pseudo-quantity measurement is constructedBy rotation of-theta_iAngle of (A) toTheta of_iThe variable becomes 0, thereby fixing the angle of the i end of the branch ij and constructing the phase angle difference theta_ijUsing theta_ijThe decoupling is performed as follows:

$\begin{array}{c}{\stackrel{\&CenterDot;}{I}}_{\mathrm{ij}.0}={\stackrel{\&CenterDot;}{I}}_{\mathrm{ij}}{e}^{-j{\mathrm{\&theta;}}_i}=[y_{\mathrm{ij}}({\stackrel{\&CenterDot;}{V}}_i-{\stackrel{\&CenterDot;}{V}}_j)+y_{i0}{\stackrel{\&CenterDot;}{V}}_i]e^{-j{\mathrm{\&theta;}}_i}=y_{\mathrm{ij}}(V_i-V_j{e}^{-j{\mathrm{\&theta;}}_{\mathrm{ij}}})+y_{i0}{V}_i\\ =(g+\mathrm{jb})[V_i-V_j(\cos {\mathrm{\&theta;}}_{\mathrm{ij}}-j\sin {\mathrm{\&theta;}}_{\mathrm{ij}})]+j{y}_{\mathrm{ic}}{V}_i\end{array}---\left(21\right)$

wherein,for constructed screwMeasurement of false transfer, y_ijFor admittance of branch ij, y_i0For the admittance to ground of the i-terminal of the line, y_icThe capacitance reactance to the ground of the branch ij is g and b are respectively the conductance and the susceptance of the branch ij;

will be provided withDecomposition into real partsAnd imaginary partTwo variables of

$\left\{\begin{array}{c}{I}_{\mathrm{ij}.0}^{\mathrm{re}}=g{V}_i-{\mathrm{gV}}_j\cos {\mathrm{\&theta;}}_{\mathrm{ij}}-{\mathrm{bV}}_j\sin {\mathrm{\&theta;}}_{\mathrm{ij}}\\ I_{\mathrm{ij}.0}^{\mathrm{im}}={\mathrm{gV}}_j\sin {\mathrm{\&theta;}}_{\mathrm{ij}}+{\mathrm{bV}}_i-{\mathrm{bV}}_j\cos {\mathrm{\&theta;}}_{\mathrm{ij}}+y_{\mathrm{ic}}{V}_i\end{array}\right.---\left(22\right)$

Derivation of a deviation is obtained by

$\left\{\begin{array}{c}\frac{{\&PartialD;I}_{\mathrm{ij}.0}^{\mathrm{re}}}{{\&PartialD;\mathrm{\&theta;}}_i}={\mathrm{gV}}_j\sin {\mathrm{\&theta;}}_{\mathrm{ij}}-{\mathrm{bV}}_j\cos {\mathrm{\&theta;}}_{\mathrm{ij}}\\ \frac{{\&PartialD;I}_{\mathrm{ij}.0}^{\mathrm{re}}}{{\&PartialD;V}_i}=g\\ \frac{{\&PartialD;I}_{\mathrm{ij}.0}^{\mathrm{im}}}{{\&PartialD;\mathrm{\&theta;}}_i}={\mathrm{gV}}_j\cos {\mathrm{\&theta;}}_{\mathrm{ij}}+{\mathrm{bV}}_j\sin {\mathrm{\&theta;}}_{\mathrm{ij}}\\ \frac{{\&PartialD;I}_{\mathrm{ij}.0}^{\mathrm{im}}}{{\&PartialD;V}_i}=b+y_{\mathrm{ic}}\end{array}\right.---\left(23\right)$

$\left\{\begin{array}{c}\frac{{\&PartialD;I}_{\mathrm{ij}.0}^{\mathrm{re}}}{{\&PartialD;\mathrm{\&theta;}}_j}=-g{V}_j\sin {\mathrm{\&theta;}}_{\mathrm{ij}}+{\mathrm{bV}}_j\cos {\mathrm{\&theta;}}_{\mathrm{ij}}\\ \frac{{\&PartialD;I}_{\mathrm{ij}.0}^{\mathrm{re}}}{{\&PartialD;V}_j}=-g\cos {\mathrm{\&theta;}}_{\mathrm{ij}}-b{\sin \mathrm{\&theta;}}_{\mathrm{ij}}\\ \frac{{\&PartialD;I}_{\mathrm{ij}.0}^{\mathrm{im}}}{{\&PartialD;\mathrm{\&theta;}}_j}=-g{V}_j\cos {\mathrm{\&theta;}}_{\mathrm{ij}}+{\mathrm{bV}}_j\sin {\mathrm{\&theta;}}_{\mathrm{ij}}\\ \frac{{\&PartialD;I}_{\mathrm{ij}.0}^{\mathrm{im}}}{{\&PartialD;V}_j}=g\sin {\mathrm{\&theta;}}_{\mathrm{ij}}-{b\cos \mathrm{\&theta;}}_{\mathrm{ij}}\end{array}\right.---\left(24\right)$

For a high voltage transmission system, r is the line resistance and x is the line reactance, then r is<<x，V_i≈V_j＝V₀In which V is₀Is a reference voltage, θ_ijClose to 0, so there is g<<b，cosθ_ij≈1，sinθ_ijIs approximately equal to 0 and simplified by gsin theta_ij<<bcosθ_ij，|gcosθ_ij±bsinθ_ij|<<|gsinθ_ij±bcosθ_ij；

The equations (20) and (21) are simplified by

$\left\{\begin{array}{c}\frac{{\&PartialD;I}_{\mathrm{ij}.0}^{\mathrm{re}}}{\&PartialD;{\mathrm{\&theta;}}_i}=-b{V}_0\\ \frac{{\&PartialD;I}_{\mathrm{ij}.0}^{\mathrm{re}}}{{\&PartialD;V}_i}=0\\ \frac{{\&PartialD;I}_{\mathrm{ij}.0}^{\mathrm{im}}}{{\&PartialD;\mathrm{\&theta;}}_i}=0\\ \frac{{\&PartialD;I}_{\mathrm{ij}.0}^{\mathrm{im}}}{{\&PartialD;V}_i}=b+y_{\mathrm{ic}}\end{array}\right.---\left(25\right)$

$\left\{\begin{array}{c}\frac{{\&PartialD;I}_{\mathrm{ij}.0}^{\mathrm{re}}}{\&PartialD;{\mathrm{\&theta;}}_j}=b{V}_0\\ \frac{{\&PartialD;I}_{\mathrm{ij}.0}^{\mathrm{re}}}{{\&PartialD;V}_j}=0\\ \frac{{\&PartialD;I}_{\mathrm{ij}.0}^{\mathrm{im}}}{{\&PartialD;\mathrm{\&theta;}}_i}=0\\ \frac{{\&PartialD;I}_{\mathrm{ij}.0}^{\mathrm{im}}}{{\&PartialD;V}_i}=-b\end{array}\right.---\left(26\right)$

The measurement of the rotating pseudo quantity realizes decoupling, has

$\left(\begin{array}{c}\mathrm{\&Delta;}{I}_{\mathrm{ij}.0}^{\mathrm{re}}\\ {\mathrm{\&Delta;I}}_{\mathrm{ij}.0}^{\mathrm{im}}\end{array}\right)=\left(\begin{array}{cc}-B^{\&prime;}& 0\\ 0& B^{\&prime;\&prime;}\end{array}\right)\left(\begin{array}{c}{V}_0\mathrm{\&Delta;\&theta;}\\ \mathrm{\&Delta;v}\end{array}\right)---\left(27\right)$

Wherein B ' and B ' ' are each V₀The coefficient matrixes corresponding to the delta theta and the delta v are constants under the condition that the network topology and the parameters are not changed; Δ θ and Δ v are the phase angle increment and the voltage increment, respectively.

Thus, this method can be iteratively computed along with the conventional state estimation PQ decomposition method.

During iteration, if the voltage phase angle of PMUSufficiently accurate, false quantity measurementCan beIf it isNot accurate enough, the first few iterations of the rotation phase angle takingTaking the latest state quantity for each subsequent iterationThus, the measurement of the false quantityEach iteration is changed (only the rotation angle is different), and the calculation amount is small.

In the two methods introduced into the current measurement, when the voltage amplitude and the phase angle measurement have certain errors, the selection method II is more accurate in calculation; when the voltage amplitude is measured accurately and the voltage phase angle measurement error is large, the selection method is simple in programming.

The state estimation method containing the PMU provides a state estimation scheme containing PMU measurement for the power system. The state estimation of the power system is to improve the data accuracy by utilizing the redundancy of a real-time measurement system, automatically eliminate error information caused by random interference and estimate or forecast the running state of the system. According to the scheme, linear estimation directly utilizing the PMU can be provided under the condition that the system PMU is considerable according to the observability of the system; under the condition of invisibility, the state estimation of the measurement of the PUM is introduced to the traditional state estimation method, so that the estimation redundancy is improved, and the accuracy of the state estimation is improved.

Finally, it should be noted that: the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting the same, and although the present invention is described in detail with reference to the above embodiments, those of ordinary skill in the art should understand that: modifications and equivalents may be made to the embodiments of the invention without departing from the spirit and scope of the invention, which is to be covered by the claims.

Claims (8)

1. A large power grid state estimation method introducing PMU measurement information is characterized in that: the method comprises the following steps:

step 1: judging the algebraic observability of the power system;

step 2: judging the observability of PMU measurement information;

and step 3: carrying out state estimation on the large power grid;

in step 3, the state estimation of the large power grid according to the observability of the PMU measurement information is divided into the following cases:

A. if the PMU measurement information is completely observable, linear state estimation is carried out by adopting a rectangular coordinate linear model;

B. if the PMU measurement information is considerable, the SCADA measurement is used for supplementing the region which is not observable by the PMU, and the linear state estimation is carried out;

C. if the PMU measurement information is a little and considerable, carrying out nonlinear state estimation;

D. the PMU measurement information is not observable at all, and the linear estimation introduced into the PMU is not needed;

the specific process of linear state estimation by adopting the rectangular coordinate linear model comprises the following steps:

the real part and the imaginary part of the voltage are used as state quantities, the real part and the imaginary part of the node voltage, the node injection current and the branch current are used as quantity quantities, and then a measurement equation is expressed by a linear equation as follows:

z＝h(x)+v＝Ax+v(1)

wherein z is a measured quantity, x is a state quantity, v is a random error, A is a first order coefficient matrix, h (x) is a calculated value based on the measurement of the state quantity x, and there areh(x)＝Ax；

The objective function is expressed as:

J(x)＝[z-Ax]^TR^-1[z-Ax](2)

wherein R is^-1Is a weight matrix, J (x) is a least squares objective function;

the linear state estimation equation is: ${\hat{x}}^{(n+1)}={\&lsqb;A^T{R}^{-1\left(n\right)}A\&rsqb;}^T{R}^{-1\left(n\right)}z---\left(3\right)$

wherein R is^-1(n)For the weight matrix calculated for the nth time,the estimated value calculated for the (n + 1) th time;

calculating the deviation of the residualComprises the following steps:

$r_{\max }^{(n+1)}=max\left\{r\left({\hat{x}}^{(n+1)}\right)\right\}---\left(4\right)$

wherein,is a residual, expressed as:

$r\left({\hat{x}}^{(n+1)}\right)=z-h\left({\hat{x}}^{(n+1)}\right)---\left(5\right)$

wherein,in order to estimate the value according to the state n +1 times,obtaining a measurement calculation value;

because the estimation accuracy of the power system state is greatly influenced by the current measurement accuracy and is less influenced by the voltage measurement, only the residual error with the maximum current is calculated, and the weight of the current measurement is corrected, including

$R^{-1(n+1)}=R_{cor}^{-1\left(n\right)}---\left(6\right)$

Wherein,the modified weight matrix corresponding to the maximum residual value is measured, and linear estimation is performed again until the maximum residual value is satisfiedAnd isWhereinIn order to correct the amount of the voltage correction,the amount of phase angle correction,_vand_θis a convergence threshold value preset according to the precision; if a measurement has been corrected, the measurement weight is not corrected.

2. The method of claim 1, wherein the method comprises the steps of: in step 1, for a power system with n nodes and m measurement vector dimensions, if the rank (H) of the linear measurement model coefficient matrix of the power system is 2n-1, that is, H full rank, the power system is considered to be algebraically considerable.

3. The method of claim 2, wherein the method comprises the steps of: in the step 2, the observability of PMU measurement information is judged according to the algebraic observability of the power system; the following cases are divided:

A. if rank (H) is satisfied, 2n-1, PMU measurement information is completely considerable;

B. if rank (H) is not less than a (2n-1), the PMU measurement information is considerable, wherein a is 0.95-0.9;

C. if rank (H) < a (2n-1) is satisfied, PMU measurement information is small and considerable;

D. if rank (h) is satisfied, it indicates that PMU measurement information is not observable at all.

4. The method of claim 1, wherein the method comprises the steps of: the specific process of utilizing SCADA measurement to supplement the non-observable region of PMU and carrying out linear state estimation comprises the following steps:

using superscript O to represent the observed region for PMU measurements and superscript U to represent the unobservable region for PMU measurements, the node voltage equation can be expressed as:

$\left[\begin{array}{c}{\stackrel{\&CenterDot;}{V}}_i^O\\ {\stackrel{\&CenterDot;}{I}}_i^O\\ {\stackrel{\&CenterDot;}{I}}_{ij}^O\\ {\stackrel{\&CenterDot;}{V}}_i^U\\ {\stackrel{\&CenterDot;}{I}}_i^U\end{array}\right]=\left[\begin{array}{cc}E& 0\\ Y_i^{OO}& Y_i^{OU}\\ Y_{ij}^{OO}& Y_{ij}^{OU}\\ 0& E\\ Y_i^{UO}& Y_i^{UU}\end{array}\right]\left[\begin{array}{c}{\stackrel{\&CenterDot;}{V}}_i^O\\ {\stackrel{\&CenterDot;}{V}}_i^U\end{array}\right]---\left(7\right)$

wherein:andnode voltage matrixes of observable and unobservable areas respectively;andinjecting current matrixes into nodes of observable and unobservable areas respectively; e is an identity matrix;a observable self-admittance matrix is injected for the node,the nodes are injected with observable and unobservable transadmittance matrices,injecting an unvisible and a viewable transadmittance matrix into the node,injecting an unobservable self-admittance matrix for the node;the current matrix can be observed by the branch circuit,the self-admittance matrix is observable for the branch,is a branch observable and unobservable transadmittance matrix;

node injection current matrix of non-observable regionExpressed as:

${\stackrel{\&CenterDot;}{I}}_i^U=\frac{P_i-{\mathrm{jQ}}_i}{{\stackrel{\&CenterDot;}{V}}_i^{*U}}---\left(8\right)$

wherein, P_iAnd Q_iFor the active and reactive power to be injected,is composed ofA conjugate matrix of (a);

node-based equivalent injection admittance matrixExpressed as:

$Y_i^U=\frac{{\stackrel{\&CenterDot;}{I}}_i^U}{{\stackrel{\&CenterDot;}{V}}_i^U}=\frac{P_i-{\mathrm{jQ}}_i}{{\left|{\stackrel{\&CenterDot;}{V}}_i^U\right|}^2}---\left(9\right)$

bringing formula (9) into the following formula

${\stackrel{\&CenterDot;}{I}}_i^U=Y_i^U{\stackrel{\&CenterDot;}{V}}_i^U=Y_i^{UO}{\stackrel{\&CenterDot;}{V}}_i^O+Y_i^{UU}{\stackrel{\&CenterDot;}{V}}_i^U---\left(10\right)$

Finishing to obtain:

$0=Y_i^{UO}{\stackrel{\&CenterDot;}{V}}_i^O+(Y_i^{UU}-Y_i^U){\stackrel{\&CenterDot;}{V}}_i^U---\left(11\right)$

the modified node current equation is:

$\left[\begin{array}{c}{\stackrel{\&CenterDot;}{V}}_i^O\\ {\stackrel{\&CenterDot;}{I}}_i^O\\ {\stackrel{\&CenterDot;}{I}}_{ij}^O\\ {\stackrel{\&CenterDot;}{V}}_i^U\\ 0\end{array}\right]=\left[\begin{array}{ccc}E& 0& \\ Y_i^{OO}& Y_i^{OU}& \\ Y_{ij}^{OO}& Y_{ij}^{OU}& \\ 0& E& \\ Y_i^{UO}& Y_i^{UU}& -Y_i^U\end{array}\right]\left[\begin{array}{c}{\stackrel{\&CenterDot;}{V}}_i^O\\ {\stackrel{\&CenterDot;}{V}}_i^U\end{array}\right]---\left(12\right)$

taking the node current equation as a linear equation of linear calculation, and carrying out linear state estimation by the formula (3).

5. The method of claim 1, wherein the method comprises the steps of: in the process of carrying out nonlinear state estimation, PMU voltage measurement information and phase angle measurement information, PMU power measurement information and PMU current measurement information are respectively introduced to carry out nonlinear state estimation.

6. The method of claim 5, wherein the PMU measurement information is introduced into the grid state estimation method, and the method further comprises: the specific process of introducing PMU voltage measurement information and phase angle measurement information to carry out nonlinear state estimation comprises the following steps:

1) directly adding a PMU node voltage phasor measurement equation into the nonlinear state estimation, wherein the PMU voltage and phase angle measurement equation is as follows:

$\left\{\begin{array}{c}{V}_i^m=V_i\\ {\mathrm{\&theta;}}_i^m={\mathrm{\&theta;}}_i\end{array}\right.---\left(13\right)$

wherein,andPMU voltage measurement information and phase angle measurement information, V, of node i_iAnd theta_iThe voltage and the phase angle of the node i are shown, the corresponding element of the Jacobian matrix is 1, and other elements are 0;

2) introducing a power phase angle difference;

introducing new quantity measurement theta to large power grid nonlinear state estimation containing PMU phase angle measurement_ijWhere θ between node i and node j_ij＝θ_i-θ_j，θ_jIs the phase angle of node j; then there is

$\left\{\begin{array}{c}\frac{{\mathrm{d\&theta;}}_{ij}}{{\mathrm{d\&theta;}}_i}=1\\ \frac{{\mathrm{d\&theta;}}_{ij}}{{\mathrm{d\&theta;}}_j}=-1\end{array}\right.---\left(14\right).$

7. The method of claim 5, wherein the PMU measurement information is introduced into the grid state estimation method, and the method further comprises: the specific process of introducing PMU power measurement information to carry out nonlinear state estimation comprises the following steps:

$\left\{\begin{array}{c}{P}_i^m=P_i\\ Q_i^m=Q_i\end{array}\right.---\left(15\right)$

wherein,andactive and reactive power measurement information, P, for node i, respectively_iAnd Q_iRespectively the active power and the reactive power of the node i; according to the types of node injection power and branch power, the corresponding Jacobian matrix coefficient of the PMU power measurement is consistent with the corresponding coefficient of the SCADA measured power quantity.

8. The method of claim 5, wherein the PMU measurement information is introduced into the grid state estimation method, and the method further comprises: the specific process of introducing PMU current measurement information to carry out nonlinear state estimation is divided into the following two cases:

1) convert the current magnitude into branch current, having

$\left\{\begin{array}{c}{P}_{ij}=V_i{I}_{i}cos({\mathrm{\&theta;}}_{ui}-{\mathrm{\&theta;}}_{Ii})\\ Q_{ij}=V_i{I}_{i}sin({\mathrm{\&theta;}}_{ui}-{\mathrm{\&theta;}}_{Ii})\end{array}\right.---\left(16\right)$

Wherein, P_ijAnd Q_ijRespectively the active power and reactive power of a branch ij between node I and node j, I_iIs the current of node i, θ_uiAnd theta_IiRespectively is a voltage phase angle and a current phase angle of the node i; p_ijAnd Q_ijIs weighted according to the following errorCalculating a difference transfer formula;

$R_{P_{ij}}={\left(\frac{\&part;P_{ij}}{\&part;V_i}{\mathrm{\&sigma;}}_{V_i}\right)}^2+{\left(\frac{\&part;P_{ij}}{\&part;I_i}{\mathrm{\&sigma;}}_{I_i}\right)}^2+{\left(\frac{\&part;P_{ij}}{\&part;{\mathrm{\&theta;}}_{ui}}{\mathrm{\&sigma;}}_{{\mathrm{\&theta;}}_{ui}}\right)}^2+{\left(\frac{\&part;P_{ij}}{\&part;{\mathrm{\&theta;}}_{Ii}}{\mathrm{\&sigma;}}_{{\mathrm{\&theta;}}_{Ii}}\right)}^2---\left(17\right)$

$R_{Q_{ij}}={\left(\frac{\&part;Q_{ij}}{\&part;V_i}{\mathrm{\&sigma;}}_{V_i}\right)}^2+{\left(\frac{\&part;Q_{ij}}{\&part;I_i}{\mathrm{\&sigma;}}_{I_i}\right)}^2+{\left(\frac{\&part;Q_{ij}}{\&part;{\mathrm{\&theta;}}_{ui}}{\mathrm{\&sigma;}}_{{\mathrm{\&theta;}}_{ui}}\right)}^2+{\left(\frac{\&part;Q_{ij}}{\&part;{\mathrm{\&theta;}}_{Ii}}{\mathrm{\&sigma;}}_{{\mathrm{\&theta;}}_{Ii}}\right)}^2---\left(18\right)$

wherein,andthe error variance of the equivalent active measurement and the equivalent reactive measurement,andare respectively a voltage amplitude V_iCurrent I_iPhase angle of voltage theta_uiAnd phase angle theta of injected current_IiThe corresponding standard deviation; p_ijAnd Q_ijAre respectively expressed as $R_{P_{ij}}^{-1}=\frac{1}{R_{P_{ij}}}$ And $R_{Q_{ij}}^{-1}=\frac{1}{R_{Q_{ij}}};$

converting branch current vector of node configured with PMU into adjacent node voltage vector

${\stackrel{\&CenterDot;}{V}}_j=\frac{{\stackrel{\&CenterDot;}{I}}_{ij}-(Y_{i0}+Y_{ij}){\stackrel{\&CenterDot;}{V}}_i}{-Y_{ij}}---\left(19\right)$

Wherein,is the phase voltage at the node j,is the current vector of branch ij, Y_i0Is the capacitance to ground of node i, Y_ijElements of a node admittance matrix;the weight of the error is calculated according to the following error transfer formula;

$R_{{\stackrel{\&CenterDot;}{V}}_j}={\left(\frac{\&part;{\stackrel{\&CenterDot;}{V}}_j}{\&part;V_i}{\mathrm{\&sigma;}}_{V_i}\right)}^2+{\left(\frac{\&part;{\stackrel{\&CenterDot;}{V}}_j}{\&part;{\mathrm{\&theta;}}_{ui}}{\mathrm{\&sigma;}}_{{\mathrm{\&theta;}}_{ui}}\right)}^2+{\left(\frac{\&part;{\stackrel{\&CenterDot;}{V}}_j}{\&part;I_{ij}}{\mathrm{\&sigma;}}_{I_{ij}}\right)}^2+{\left(\frac{\&part;{\stackrel{\&CenterDot;}{V}}_j}{\&part;{\mathrm{\&theta;}}_{ij}^I}{\mathrm{\&sigma;}}_{{\mathrm{\&theta;}}_{ij}^I}\right)}^2---\left(20\right)$

wherein,is the error variance of the equivalent voltage vector measurement,andrespectively a voltage amplitude V_iPhase angle of voltage theta_uiBranch current I_ijPhase angle of sum branch currentThe corresponding standard deviation;is expressed as

2) Constructing a pseudo quantity measurement;

measurement of structural false quantityBy rotation of-theta_iAngle of (A) toTheta of_iThe variable becomes 0, thereby fixing the angle of the i end of the branch ij and constructing the phase angle difference theta_ijUsing theta_ijThe decoupling is performed as follows:

$\begin{array}{c}{\stackrel{\&CenterDot;}{I}}_{ij.0}={\stackrel{\&CenterDot;}{I}}_{ij}{e}^{-{\mathrm{j\&theta;}}_i}=\&lsqb;y_{ij}({\stackrel{\&CenterDot;}{V}}_i-{\stackrel{\&CenterDot;}{V}}_j)+y_{i0}{\stackrel{\&CenterDot;}{V}}_i\&rsqb;e^{-{\mathrm{j\&theta;}}_i}=y_{ij}(V_i-V_j{e}^{-{\mathrm{j\&theta;}}_{ij}})+y_{i0}{V}_i\\ =(g+jb)\&lsqb;V_i-V_j({\mathrm{cos\&theta;}}_{ij}-{\mathrm{jsin\&theta;}}_{ij})\&rsqb;+{\mathrm{jy}}_{ic}{V}_i\end{array}---\left(21\right)$

wherein,for constructed rotational false quantity measurement, y_ijFor admittance of branch ij, y_i0For the admittance to ground of the i-terminal of the line, y_icThe capacitance reactance to the ground of the branch ij is g and b are respectively the conductance and the susceptance of the branch ij;

will be provided withDecomposition into real partsAnd imaginary partTwo variables of

$\left\{\begin{array}{c}{I}_{ij.0}^{re}={\mathrm{gV}}_i-{\mathrm{gV}}_j{\mathrm{cos\&theta;}}_{ij}-{\mathrm{bV}}_j{\mathrm{sin\&theta;}}_{ij}\\ I_{ij.0}^{im}={\mathrm{gV}}_j{\mathrm{sin\&theta;}}_{ij}+{\mathrm{bV}}_i-{\mathrm{bV}}_j{\mathrm{cos\&theta;}}_{ij}+y_{ic}{V}_i\end{array}\right.---\left(22\right)$

Derivation of a deviation is obtained by

$\left\{\begin{array}{c}\frac{\&part;I_{ij.0}^{re}}{\&part;{\mathrm{\&theta;}}_i}={\mathrm{gV}}_j{\mathrm{sin\&theta;}}_{ij}-{\mathrm{bV}}_j{\mathrm{cos\&theta;}}_{ij}\\ \frac{\&part;I_{ij.0}^{re}}{\&part;V_i}=g\\ \frac{\&part;I_{ij.0}^{im}}{\&part;{\mathrm{\&theta;}}_i}={\mathrm{gV}}_j{\mathrm{cos\&theta;}}_{ij}+{\mathrm{bV}}_j{\mathrm{sin\&theta;}}_{ij}\\ \frac{\&part;I_{ij.0}^{im}}{\&part;V_i}=b+y_{ic}\end{array}\right.---\left(23\right)$

$\left\{\begin{array}{c}\frac{\&part;I_{ij.0}^{re}}{\&part;{\mathrm{\&theta;}}_j}=-{\mathrm{gV}}_j{\mathrm{sin\&theta;}}_{ij}+{\mathrm{bV}}_j{\mathrm{cos\&theta;}}_{ij}\\ \frac{\&part;I_{ij.0}^{re}}{\&part;V_j}=-{\mathrm{gcos\&theta;}}_{ij}-{\mathrm{bsin\&theta;}}_{ij}\\ \frac{\&part;I_{ij.0}^{im}}{\&part;{\mathrm{\&theta;}}_j}=-{\mathrm{gV}}_j{\mathrm{cos\&theta;}}_{ij}+{\mathrm{bV}}_j{\mathrm{sin\&theta;}}_{ij}\\ \frac{\&part;I_{ij.0}^{im}}{\&part;V_j}={\mathrm{gsin\&theta;}}_{ij}-{\mathrm{bcos\&theta;}}_{ij}\end{array}\right.---\left(24\right)$

For a high voltage transmission system, r is the line resistance and x is the line reactance, then r < x, V_i≈V_j＝V₀In which V is₀Is a reference voltage, θ_ijClose to 0, so that g < b, cos θ_ij≈1，sinθ_ijIs approximately equal to 0 and simplified by gsin theta_ij＜＜bcosθ_ij，|gcosθ_ij±bsinθ_ij|＜＜|gsinθ_ij±bcosθ_ij|；

The equations (23) and (24) are simplified by

$\left\{\begin{array}{c}\frac{\&part;I_{ij.0}^{re}}{\&part;{\mathrm{\&theta;}}_i}=-{\mathrm{bV}}_0\\ \frac{\&part;I_{ij.0}^{re}}{\&part;V_i}=0\\ \frac{\&part;I_{ij.0}^{im}}{\&part;{\mathrm{\&theta;}}_i}=0\\ \frac{\&part;I_{ij.0}^{im}}{\&part;V_i}=b+y_{ic}\end{array}\right.---\left(25\right)$

$\left\{\begin{array}{c}\frac{\&part;I_{ij.0}^{re}}{\&part;{\mathrm{\&theta;}}_j}={\mathrm{bV}}_0\\ \frac{\&part;I_{ij.0}^{re}}{\&part;V_j}=0\\ \frac{\&part;I_{ij.0}^{im}}{\&part;{\mathrm{\&theta;}}_i}=0\\ \frac{\&part;I_{ij.0}^{im}}{\&part;V_i}=-b\end{array}\right.---\left(26\right)$

The measurement of the rotating pseudo quantity realizes decoupling, has

$\left(\begin{array}{c}{\mathrm{\&Delta;I}}_{ij.0}^{re}\\ {\mathrm{\&Delta;I}}_{ij.0}^{im}\end{array}\right)=\left(\begin{array}{cc}-B^{\&prime;}& 0\\ 0& B^{\&prime;\&prime;}\end{array}\right)\left(\begin{array}{c}{V}_0\mathrm{\&Delta;}\mathrm{\&theta;}\\ \mathrm{\&Delta;}v\end{array}\right)---\left(27\right)$

Wherein B 'and B' are each V₀The coefficient matrixes corresponding to the delta theta and the delta v are constants under the condition that the network topology and the parameters are not changed; Δ θ and Δ v are the phase angle increment and the voltage increment, respectively.