CN102427229A - Zero-injection-constraint electric power system state estimation method based on modified Newton method - Google Patents

Abstract

The invention, which belongs to an electric power system scheduling automation and electric power system simulation technology field, relates to a zero-injection-constraint electric power system state estimation method based on a modified Newton method. The method is characterized by: establishing a state estimation model; carrying out an iterative solution to the state estimation model according to the common Newton method; in the each iteration, correcting a state variable of a nonzero injection node according to a calculation result of the common Newton method; however, acquiring the state variable of the zero injection node by using a relationship between the zero injection node state variable established by the zero injection equality constraint and the nonzero injection node state variable and not by taking the calculation result of the common Newton method. A whole calculating process of the invention is similar to a traditional state estimation calculating flow. Realization is convenient. Simultaneously, an injection power of the zero injection node can be guaranteed to be zero. The state estimation result strictly satisfies a trend equation.

Description

Band zero based on modified newton method injects the power system state estimation method of constraint

Technical field

The present invention relates to a kind of band zero and inject the power state method of estimation of constraint, belong to dispatching automation of electric power systems and electric system simulation technical field based on modified newton method.

Background technology

Power system state estimation is the key foundation module of electric power system EMS.In the electric power system of reality, there are many zero injection nodes that generator does not articulate load yet that neither articulate.In the result of calculation of Power system state estimation; The node injecting power of these zero injection nodes should strictness be 0; Otherwise; The result of calculation of Power system state estimation can not strictness satisfy power flow equation, and this will cause the result of calculation of Power system state estimation and the result of calculation of dispatcher's trend that deviation is arranged, and bring very big inconvenience for other ADVANCED APPLICATIONS of electric power system.

The common practices that node is injected in processing at present zero is the very big zero node power puppet of injecting of weight to be set measure, and is less with the injecting power of zero injection node in the Guarantee Status estimated result.This is a kind of approximate method, can't make that the injecting power strictness of zero injection node is 0.In fact, at present both at home and abroad zero to inject the bigger problem of node injecting power quite serious, the research advantages of simplicity and high efficiency can guarantee zero inject node the injecting power strictness be that 0 Power system state estimation method for solving is extremely important.

Summary of the invention

The objective of the invention is to propose a kind of band zero and inject the power state method of estimation of constraint based on modified newton method; The method that can use the present invention to propose is found the solution the Power system state estimation model that contains zero injection equality constraint, satisfies power flow equation fully with the Guarantee Status estimated result.

The band zero based on modified newton method that the present invention proposes injects the power system state estimation method of constraint, and this method may further comprise the steps:

(1) set up a power state estimation model that contains equality constraint:

min J(x)

s.t. c(x)＝0

Equality constraint is: making the node injecting power of zero injection node is 0; With c (x)=0 expression, wherein x is the power system state variable, adopts polar coordinate representation; Comprise that zero injects the voltage magnitude and the phase angle of node and non-zero injection node, J (x) is the target function of Power system state estimation;

(2), form electric power system present node admittance matrix, and calculate following coefficient matrix F according to electric power system current topological structure and network parameter

$F=-{\left[\begin{array}{cc}{B}_{\mathrm{zz}}& G_{\mathrm{zz}}\\ G_{\mathrm{zz}}& -B_{\mathrm{zz}}\end{array}\right]}^{-1}\left[\begin{array}{cc}{B}_{\mathrm{zn}}& G_{\mathrm{zn}}\\ G_{\mathrm{zn}}& -B_{\mathrm{zn}}\end{array}\right]$

Matrix G wherein _ZzAnd B _ZzBe respectively the real part and the imaginary part of the diagonal angle submatrix that zero injection node is corresponding in the node admittance matrix, battle array G _ZnAnd B _ZnBe respectively in the node admittance matrix zero inject node and non-zero injection node intersect non-diagonal angle submatrix corresponding real part and imaginary part;

(3) the calculating initial value that Power system state estimation is set is x ⁽⁰⁾, and iterations k=0 is set;

(4) the k time iteration obtain POWER SYSTEM STATE variable x ^(k), with x ^(k)In zero inject the state variable subvector of node and the state variable subvector of non-zero injection node is designated as respectively With

(5) it is constant to keep non-zero to inject node subvector

, calculates consideration zero and injects the following with the zero injection corresponding state variable subvector of node

computing formula of constraint:

${\tilde{x}}_z^{\left(k\right)}=\mathrm{\ΦF}{\mathrm{\Φ}}^{-1}{x}_n^{\left(k\right)}$

Wherein matrix F is the result of calculation of step (2), and Φ is in the plural theory, and the plural number of representing with rectangular coordinate arrives the conversion mapping with the plural number of polar coordinate representation; Φ ^-1The inverse mapping of expression Φ, the expression formula of Φ is:

$U=\sqrt{{\mathrm{<figure-callout\; id="2"\; label="e"\; filenames="HDA0000099732250000011.png,HDA0000099732250000012.png"\; state="\{\{state\}\}">e</figure-callout>}}^2+{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA0000099732250000011.png,HDA0000099732250000012.png"\; state="\{\{state\}\}">f</figure-callout>}}^2}$

$\mathrm{\&theta;}=\arctan \left(\frac{e}{f}\right)$

Φ ^-1Expression formula be:

e＝Ucosθ

f＝Usinθ

E wherein, f are the real part and the imaginary parts of the node voltage represented with rectangular coordinate, and U, θ are with the amplitude of the node voltage of polar coordinate representation and phase angle;

(6) according to above-mentioned iteration

With

Use Newton method to calculate the state variable correction amount x of the k time iteration ^(k)

The correction of the POWER SYSTEM STATE variable of (7) the k time iteration is Δ x ^(k), with Δ x ^(k)In zero inject the state variable of node correction and the correction of the state variable of non-zero injection node be designated as respectively

With

(8) convergence precision of setting Power system state estimation is ε; if

then Power system state estimation convergence; Calculate and finish; If

then makes

k=k+1, carry out step (4).

The band zero based on modified newton method that the present invention proposes injects restrained condition and estimates derivation algorithm, and its advantage is:

1, the inventive method can satisfy power flow equation by the Guarantee Status estimated result fully, and result of calculation does not have the power amount of unbalance, and state estimation result and dispatcher's trend result are in full accord.

2, the computational speed of the inventive method is suitable with existing big method of weighting state estimation program, but the result of calculation of big method of weighting state estimation can not satisfy power flow equation fully.The computational speed of the inventive method can the strictness of Guarantee Status estimated result satisfies the method for power flow equation faster than existing other far away.

3, the numerical stability of the inventive method is better than existing any state estimation solution, restrains very reliable.

4, the inventive method and present widely used traditional state estimation algorithm compatibility are very good, and only needing very little program to change can realize, implements easily.

Description of drawings

Fig. 1 is the sketch map of IEEE 9 node systems among the embodiment of the inventive method.

Fig. 2 is the contrast sketch map of the convergence curve of the inventive method and the traditional big method of weighting.

Embodiment

The band zero based on modified newton method that the present invention proposes injects the power system state estimation method of constraint, may further comprise the steps:

(1) set up a power state estimation model that contains equality constraint:

min J(x)

s.t. c(x)＝0

Equality constraint is: making the node injecting power of zero injection node is 0; With c (x)=0 expression, wherein x is the power system state variable, adopts polar coordinate representation; Comprise that zero injects the voltage magnitude and the phase angle of node and non-zero injection node, J (x) is the target function of Power system state estimation;

(2), form electric power system present node admittance matrix, and calculate following coefficient matrix F according to electric power system current topological structure and network parameter

$F=-{\left[\begin{array}{cc}{B}_{\mathrm{zz}}& G_{\mathrm{zz}}\\ G_{\mathrm{zz}}& -B_{\mathrm{zz}}\end{array}\right]}^{-1}\left[\begin{array}{cc}{B}_{\mathrm{zn}}& G_{\mathrm{zn}}\\ G_{\mathrm{zn}}& -B_{\mathrm{zn}}\end{array}\right]$

Matrix G wherein _ZzAnd B _ZzBe respectively the real part and the imaginary part of the diagonal angle submatrix that zero injection node is corresponding in the node admittance matrix, battle array G _ZnAnd B _ZnBe respectively in the node admittance matrix zero inject node and non-zero injection node intersect non-diagonal angle submatrix corresponding real part and imaginary part.

(3) the calculating initial value that Power system state estimation is set is x ⁽⁰⁾, and iterations k=0 is set;

(4) the k time iteration obtain POWER SYSTEM STATE variable x ^(k), with x ^(k)In zero inject the state variable subvector of node and the state variable subvector of non-zero injection node is designated as respectively

With

(5) it is constant to keep non-zero to inject node subvector

, and the zero injection corresponding state variable subvector of node computing formula that constraint is injected in calculating consideration zero is following:

${\tilde{x}}_z^{\left(k\right)}=\mathrm{\&Phi;F}{\mathrm{\&Phi;}}^{-1}{x}_n^{\left(k\right)}$

Wherein matrix F is the result of calculation of step (2).Φ is in the plural theory, and the plural number of representing with rectangular coordinate arrives the conversion mapping with the plural number of polar coordinate representation; Φ ^-1The inverse mapping of expression Φ.The expression formula of Φ is:

$U=\sqrt{{\mathrm{<figure-callout\; id="2"\; label="e"\; filenames="HDA0000099732250000011.png,HDA0000099732250000012.png"\; state="\{\{state\}\}">e</figure-callout>}}^2+{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA0000099732250000011.png,HDA0000099732250000012.png"\; state="\{\{state\}\}">f</figure-callout>}}^2}$

$\mathrm{\&theta;}=\arctan \left(\frac{e}{f}\right)$

Φ ^-1Expression formula be:

e＝Ucosθ

f＝Usinθ

E wherein, f are the real part and the imaginary parts of the node voltage represented with rectangular coordinate, and U, θ are with the amplitude of the node voltage of polar coordinate representation and phase angle;

(6) according to above-mentioned iteration

With

Use Newton method to calculate the state variable correction amount x of the k time iteration ^(k)

The correction of the POWER SYSTEM STATE variable of (7) the k time iteration is Δ x ^(k), with Δ x ^(k)In zero inject the state variable of node correction and the correction of the state variable of non-zero injection node be designated as respectively

With

(8) convergence precision of setting Power system state estimation is ε; if

then Power system state estimation convergence; Calculate and finish; If

then makes

k k+1, carry out step (4).Wherein ε is the artificial convergence precision of setting, and gets 0.0001 usually.

Below introduce the embodiment of inventive method:

IEEE 9 node systems with like Fig. 1 are example, and 4,7,9th, zero injects node among Fig. 1, and all the other 6 nodes are that non-zero injects node.The error in measurement of on the basis that the true trend of this system distributes, adding normal distribution; Measure for power measurement and voltage, the standard deviation of error in measurement gets 0.09 and 0.009 respectively.The state estimation model adopts least-squares estimation.The power system state estimation method that the band zero based on modified newton method that proposes with the present invention below injects constraint is found the solution the state estimation problem of this system.

(1) equality constraint is: making the node injecting power of zero injection node is 0; With c (x)=0 expression, wherein x is the power system state variable, adopts polar coordinate representation; Comprise that zero injects the voltage magnitude and the phase angle of node and non-zero injection node, J (x) is the target function of Power system state estimation.Present embodiment adopts least-squares estimation.Then estimation model is:

min $J\left(x\right)=\frac{1}{2}\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{(z_i-h_i\left(x\right))}^2$

s.t c(x)＝0

Wherein, z _iBe the real-time measurement values of i number measurement, h _i(x) be the real-time measurement equation of i number measurement, m is for measuring number.

(2) the formation admittance matrix Y of system is following:

$Y=\left[\begin{array}{ccccccccc}-j17.36& & & j17.36& & & & & \\ & -j16& & & & & j16& & \\ & & -j17.06& & & & & & j17.06\\ j17.36& & & 3.31-j39.31& -1.37+j11.60& -1.94+j10.51& & & \\ & & & -1.37+j11.60& 2.55-j17.33& & -1.18+j5.98& & \\ & & & -1.94+j10.51& & 3.22-j15.84& & & -1.28+j5.59\\ & j16& & & -1.18+j5.98& & 2.80-j35.44& -1.62+j13.70& \\ & & & & & & -1.62+j13.70& 2.77-j23.30& -1.15+j9.78\\ & & j17.06& & & -1.28+j5.59& & -1.15+j9.78& 2.43-j32.15\end{array}\right]$

Its numerical value of element of not indicating numerical value in the above matrix is 0.Because node the 4,7, the 9th, zero injects node, and all the other nodes are that non-zero injects node, then can take out matrix G _Zz, B _Zz, G _ZnAnd B _ZnFor:

According to the result of calculation of above matrix, can calculate coefficient matrix:

$F=-{\left[\begin{array}{cc}{B}_{\mathrm{zz}}& G_{\mathrm{zz}}\\ G_{\mathrm{zz}}& -B_{\mathrm{zz}}\end{array}\right]}^{-1}\left[\begin{array}{cc}{B}_{\mathrm{zn}}& G_{\mathrm{zn}}\\ G_{\mathrm{zn}}& -B_{\mathrm{zn}}\end{array}\right]$

$=\left[\begin{array}{cccccccccccc}0.438& & & 0.296& 0.270& & 0.037& & & -0.009& -0.026& \\ & 0.448& & 0.170& & 0.388& & 0.035& & -0.02& & -0.015\\ & & 0.527& & 0.176& 0.305& & & 0.04& & -0.026& -0.013\\ -0.037& & & 0.009& 0.026& & 0.438& & & 0.296& 0.269& \\ & -0.036& & 0.020& & 0.015& & 0.448& & 0.170& & 0.387\\ & & -0.04& & 0.026& 0.012& & & 0.528& & 0.175& 0.305\end{array}\right]$

(3) the calculating initial value that Power system state estimation is set is x ⁽⁰⁾, and iterations k=0 is set; In the present embodiment, the initial value of voltage magnitude is taken as according to measurement:

U ⁽⁰⁾=[1.04 1.025 1.025 1.0258 0.9956 1.0127 1.0258 1.0159 1.0324] ^TVoltage phase angle adopts flat the startup, that is:

θ ⁽⁰⁾＝[000000000] ^T

(4) the k time iteration obtain POWER SYSTEM STATE variable x ^(k), with x ^(k)In zero inject the state variable subvector of node and the state variable subvector of non-zero injection node is designated as respectively With

Here $x_z^{\left(k\right)}={\left[\begin{array}{ccc}{x}_4^{\left(k\right)}& x_7^{\left(k\right)}& x_9^{\left(k\right)}\end{array}\right]}^T;$ $x_n^{\left(k\right)}={\left[\begin{array}{cccccc}{x}_1^{\left(k\right)}& x_2^{\left(k\right)}& x_3^{\left(k\right)}& x_5^{\left(k\right)}& x_6^{\left(k\right)}& x_8^{\left(k\right)}\end{array}\right]}^T,$ Subscript T representes transposition.

(5) it is constant to keep non-zero to inject node subvector

, and the zero injection corresponding state variable subvector of node computing formula that constraint is injected in calculating consideration zero is following:

${\tilde{x}}_z^{\left(k\right)}=\mathrm{\&Phi;F}{\mathrm{\&Phi;}}^{-1}{x}_n^{\left(k\right)}$

Wherein Φ is that plural number is theoretical, and the plural number of representing with rectangular coordinate arrives the conversion mapping with the plural number of polar coordinate representation; Φ ^-1The inverse mapping of expression Φ.The expression formula of Φ is:

$U=\sqrt{e^2+{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA0000099732250000011.png,HDA0000099732250000012.png"\; state="\{\{state\}\}">f</figure-callout>}}^2}$

$\mathrm{\&theta;}=\arctan \left(\frac{e}{f}\right)$

Φ ^-1Expression formula be:

e＝Ucosθ

f＝Usinθ

E wherein, f are the real part and the imaginary parts of the node voltage represented with rectangular coordinate, and U, θ are with the amplitude of the node voltage of polar coordinate representation and phase angle.

In the present embodiment, at first calculate

and establish intermediate variable:

$x_{\mathrm{efn}}^{\left(k\right)}={\mathrm{\&Phi;}}^{-1}{x}_n^{\left(k\right)}$

The physical meaning of

is to inject the node state variable with the non-zero that rectangular coordinate is represented.

e ₁＝U ₁cosθ ₁＝1.04?f ₁＝U ₁sinθ ₁＝0

e ₂＝U ₂cosθ ₂＝1.025?f ₂＝U ₂sinθ ₂＝0

$x_{\mathrm{efn}}^{\left(k\right)}={\left[\begin{array}{cccccccccccc}{e}_1& e_2& e_3& e_5& e_6& e_8& f_1& f_2& f_3& f_5& f_6& f_8\end{array}\right]}^T$

Establish intermediate variable again

$x_{\mathrm{efz}}^{\left(k\right)}={\mathrm{Fx}}_{\mathrm{efn}}^{\left(k\right)}$

The physical meaning of

is the zero injection node state variable of representing with rectangular coordinate.

$x_{\mathrm{efz}}^{\left(k\right)}={\left[\begin{array}{cccccc}{e}_4& e_7& e_9& f_4& f_7& f_9\end{array}\right]}^T$

The results of calculation of first step iteration

is:

$x_{\mathrm{efz}}^{\left(k\right)}={\left[\begin{array}{cccccc}1.0235& 1.0226& 1.0286& -0.0016& -0.0013& -0.0012\end{array}\right]}^T$

Utilize the plural number represented with rectangular coordinate to calculate again and consider that zero injects zero of constraint and injects the corresponding state variable subvector of node

computational methods and be to conversion mapping Φ with the plural number of polar coordinate representation:

${\mathrm{<figure-callout\; id="4"\; label="U"\; filenames="HDA0000099732250000011.png,HDA0000099732250000012.png"\; state="\{\{state\}\}">U</figure-callout>}}_4=\sqrt{{\mathrm{<figure-callout\; id="4"\; label="e"\; filenames="HDA0000099732250000011.png,HDA0000099732250000012.png"\; state="\{\{state\}\}">e</figure-callout>}}_4^2+{\mathrm{<figure-callout\; id="4"\; label="f"\; filenames="HDA0000099732250000011.png,HDA0000099732250000012.png"\; state="\{\{state\}\}">f</figure-callout>}}_4^2}=1.0235$ ${\mathrm{\&theta;}}_4=\arctan \left(\frac{f_4}{e_4}\right)=-0.0015\mathrm{rad}$

${\mathrm{<figure-callout\; id="7"\; label="U"\; filenames="HDA0000099732250000011.png"\; state="\{\{state\}\}">U</figure-callout>}}_7=\sqrt{{\mathrm{<figure-callout\; id="7"\; label="e"\; filenames="HDA0000099732250000011.png"\; state="\{\{state\}\}">e</figure-callout>}}_7^2+{\mathrm{<figure-callout\; id="7"\; label="f"\; filenames="HDA0000099732250000011.png"\; state="\{\{state\}\}">f</figure-callout>}}_7^2}=1.0226$ ${\mathrm{\&theta;}}_7=\arctan \left(\frac{f_7}{e_7}\right)=-0.0012\mathrm{rad}$

${\mathrm{<figure-callout\; id="9"\; label="U"\; filenames="HDA0000099732250000011.png"\; state="\{\{state\}\}">U</figure-callout>}}_9=\sqrt{{\mathrm{<figure-callout\; id="9"\; label="e"\; filenames="HDA0000099732250000011.png"\; state="\{\{state\}\}">e</figure-callout>}}_9^2+{\mathrm{<figure-callout\; id="9"\; label="f"\; filenames="HDA0000099732250000011.png"\; state="\{\{state\}\}">f</figure-callout>}}_9^2}=1.0286$ ${\mathrm{\&theta;}}_9=\arctan \left(\frac{f_9}{e_9}\right)=-0.0011\mathrm{rad}$

${\tilde{x}}_z^{\left(k\right)}={\left[\begin{array}{cccccc}{U}_4& U_7& {\mathrm{<figure-callout\; id="9"\; label="U"\; filenames="HDA0000099732250000011.png"\; state="\{\{state\}\}">U</figure-callout>}}_9& {\mathrm{\&theta;}}_4& {\mathrm{\&theta;}}_7& {\mathrm{\&theta;}}_9\end{array}\right]}^T$

$={\left[\begin{array}{cccccc}1.0235& 1.0226& 1.0286& -0.0015& -0.0012& -0.0011\end{array}\right]}^T$

(6) according to above-mentioned iteration

With

Use Newton method to calculate the state variable correction amount x of the k time iteration ^(k)Present embodiment adopts least-squares estimation, Δ x ^(k)Computing formula be:

Δx ^(k)＝(H ^TWH) ^-1H ^TWr

Wherein H is the measurement Jacobian matrix of state estimation, and subscript T representes transposition.W is for measuring weight matrix; R is for measuring residual vector; For i number measurement,

arranged

(7) utilize and the identical method of step (4), Δ x ^(k)In zero inject the state variable of node correction and the correction of the state variable of non-zero injection node be designated as respectively

With

(8) convergence precision of setting Power system state estimation is ε; if then Power system state estimation convergence; Calculate and finish; If

then makes

k=k+1, return step (4); ε gets 0.0001 among this embodiment

4 convergences of iteration.The result of calculation of result of calculation and traditional authority weighing method (zero inject measure weight is taken as common power and measures 10 times) is relatively like following table:

The contrast of the convergence curve of the method for the present invention and the traditional big method of weighting is as shown in Figure 2.In Fig. 2, abscissa is an iterations, and ordinate is the peaked common logarithm of state variable correction in each iteration.Can find out that the modified newton method state estimation convergence that the present invention proposes is suitable with traditional big method of weighting, convergence is reliable.On the other hand, modified newton method of the present invention can guarantee that zero injection constraint is strict satisfied, and traditional big method of weighting can't be accomplished this point.

Claims (1)

1. the band zero based on modified newton method injects the power system state estimation method of constraint, it is characterized in that this method may further comprise the steps:

(1) set up a power state estimation model that contains equality constraint:

min J(x)

s.t. c(x)＝0

Equality constraint is: making the node injecting power of zero injection node is 0; With c (x)=0 expression, wherein x is the power system state variable, adopts polar coordinate representation; Comprise that zero injects the voltage magnitude and the phase angle of node and non-zero injection node, J (x) is the target function of Power system state estimation;

(2), form electric power system present node admittance matrix, and calculate following coefficient matrix F according to electric power system current topological structure and network parameter

$F=-{\left[\begin{array}{cc}{B}_{\mathrm{zz}}& G_{\mathrm{zz}}\\ G_{\mathrm{zz}}& -B_{\mathrm{zz}}\end{array}\right]}^{-1}\left[\begin{array}{cc}{B}_{\mathrm{zn}}& G_{\mathrm{zn}}\\ G_{\mathrm{zn}}& -B_{\mathrm{zn}}\end{array}\right]$

Matrix G wherein _ZzAnd B _ZzBe respectively the real part and the imaginary part of the diagonal angle submatrix that zero injection node is corresponding in the node admittance matrix, battle array G _ZnAnd B _ZnBe respectively in the node admittance matrix zero inject node and non-zero injection node intersect non-diagonal angle submatrix corresponding real part and imaginary part;

(3) the calculating initial value that Power system state estimation is set is x ⁽⁰⁾, and iterations k=0 is set;

(4) the k time iteration obtain POWER SYSTEM STATE variable x ^(k), with x ^(k)In zero inject the state variable subvector of node and the state variable subvector of non-zero injection node is designated as respectively With

(5) it is constant to keep non-zero to inject node subvector

, calculates consideration zero and injects the following with the zero injection corresponding state variable subvector of node

computing formula of constraint:

${\tilde{x}}_z^{\left(k\right)}=\mathrm{\&Phi;F}{\mathrm{\&Phi;}}^{-1}{x}_n^{\left(k\right)}$

Wherein matrix F is the result of calculation of step (2), and Φ is in the plural theory, and the plural number of representing with rectangular coordinate arrives the conversion mapping with the plural number of polar coordinate representation; Φ ^-1The inverse mapping of expression Φ, the expression formula of Φ is:

$U=\sqrt{e^2+f^2}$

$\mathrm{\&theta;}=\arctan \left(\frac{e}{f}\right)$

Φ ^-1Expression formula be:

e＝Ucosθ

f＝Usinθ

E wherein, f are the real part and the imaginary parts of the node voltage represented with rectangular coordinate, and U, θ are with the amplitude of the node voltage of polar coordinate representation and phase angle;

(6) according to above-mentioned iteration

With

Use Newton method to calculate the state variable correction amount x of the k time iteration ^(k)

The correction of the POWER SYSTEM STATE variable of (7) the k time iteration is Δ x ^(k), with Δ x ^(k)In zero inject the state variable of node correction and the correction of the state variable of non-zero injection node be designated as respectively

With

(8) convergence precision of setting Power system state estimation is ε; if

then Power system state estimation convergence; Calculate and finish; If

then makes

k=k+1, carry out step (4).

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