CN102427229B - 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

Power system state estimation method based on the band of modified newton method zero injection-constraint

Technical field

The present invention relates to a kind of power state method of estimation of zero injection-constraint of the band based on modified newton method, belong to dispatching automation of electric power systems and Simulating technique in Electric Power System field.

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, these zero node injecting powers that inject node should be strictly 0, otherwise, the result of calculation of Power system state estimation can not strictly satisfy power flow equation, this will cause the result of calculation of Power system state estimation and the result of calculation of Dispatcher Power Flow that deviation is arranged, and bring very large inconvenience for other senior application of electric power system.

The common practices that node is injected in processing at present zero is the very large 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, and can't make zero injecting power that injects node is strictly 0.In fact, at present both at home and abroad zero to inject the larger problem of node injecting power quite serious, and research can guarantee efficiently that simply zero injecting power that injects node is strictly 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 power state method of estimation of band zero injection-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 power system state estimation method based on band zero injection-constraint of modified newton method that the present invention proposes, the method comprises the following 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 zero node injecting power that injects node is 0, represent with c (x)=0, wherein x is the state variable of electric power system, adopt polar coordinate representation, comprise that zero injects 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) according to electric power system current topological structure and network parameter, form electric power system present node admittance matrix, and calculate following coefficient matrix F

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

Matrix G wherein _zzAnd B _zzRespectively real part and the imaginary part of the diagonal angle submatrix that in node admittance matrix, zero injection node is corresponding, battle array G _znAnd B _znBe respectively in 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 state variable subvector that non-zero injects node is designated as respectively

With

(5) keep non-zero to inject the node subvector

Constant, that calculates method considering zero injection constraint injects the corresponding state variable subvector of node with zero

Computing formula is as follows:

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

Wherein matrix F is the result of calculation of step (2), and Φ is in complex theory, and the plural number that represents with rectangular coordinate shines upon to the conversion of the plural number of using polar coordinate representation; Φ ^-1The inverse mapping of expression Φ, the expression formula of Φ is:

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

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

Φ ^-1Expression formula be:

e＝Ucosθ

f＝Usinθ

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

(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 correction of state variable of node and the correction that non-zero injects the state variable of node is designated as respectively With

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

Power system state estimation convergence is calculated and is finished, if

Order

K=k+1 carries out step (4).

The band zero injection-constraint state estimation derivation algorithm based on modified newton method that the present invention proposes, 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 unbalanced power amount, and state estimation result and Dispatcher Power Flow result are in full accord.

2, the computational speed of the inventive method is suitable with existing large method of weighting state estimation program, but the result of calculation of large method of weighting state estimation can not satisfy power flow equation fully.The computational speed of the inventive method can the Guarantee Status estimated result strictly 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 schematic diagram of IEEE 9 node systems in the embodiment of the inventive method.

Fig. 2 is the contrast schematic diagram of the convergence curve of the inventive method and the traditional large method of weighting.

Embodiment

The power system state estimation method based on band zero injection-constraint of modified newton method that the present invention proposes comprises the following 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 zero node injecting power that injects node is 0, represent with c (x)=0, wherein x is the state variable of electric power system, adopt polar coordinate representation, comprise that zero injects 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) according to electric power system current topological structure and network parameter, form electric power system present node admittance matrix, and calculate following coefficient matrix F

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

Matrix G wherein _zzAnd B _zzRespectively real part and the imaginary part of the diagonal angle submatrix that in node admittance matrix, zero injection node is corresponding, battle array G _znAnd B _znBe respectively in 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 state variable subvector that non-zero injects node is designated as respectively

With

(5) keep non-zero to inject the node subvector

Constant, calculate zero of method considering zero injection constraint and inject the corresponding state variable subvector of node

Computing formula is as follows:

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

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

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

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

Φ ^-1Expression formula be:

e＝Ucosθ

f＝Usinθ

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

(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 correction of state variable of node and the correction that non-zero injects the state variable of node is designated as respectively

With

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

Power system state estimation convergence is calculated and is finished, if

Order

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

Below introduce the embodiment of inventive method:

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

(1) equality constraint is: making the zero node injecting power that injects node is 0, represent with c (x)=0, wherein x is the state variable of electric power system, adopt polar coordinate representation, comprise that zero injects voltage magnitude and the phase angle of node and non-zero injection node, J (x) is the target function of Power system state estimation.The present embodiment adopts least-squares estimation.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 _iThe real-time measurement values of No. i measurement, h _i(x) be the real-time measurement equation of No. i measurement, m is for measuring number.

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

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

Its numerical value of element of not indicating numerical value in above matrix is 0.Due to node 4,7, the 9th, zero injects node, and all the other nodes are that non-zero injects node, 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 state variable subvector that non-zero injects 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 represents transposition.

(5) keep non-zero to inject the node subvector

Constant, calculate zero of method considering zero injection constraint and inject the corresponding state variable subvector of node

Computing formula is as follows:

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

Wherein Φ is complex theory, and the plural number that represents with rectangular coordinate shines upon to the conversion of the plural number of using polar coordinate representation; Φ ^-1The inverse mapping of expression Φ.The expression formula of Φ is:

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

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

Φ ^-1Expression formula be:

e＝Ucosθ

f＝Usinθ

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

In the present embodiment, at first calculate

If intermediate variable:

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

Physical meaning be that the non-zero that represents with rectangular coordinate injects the node state variable.

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 again intermediate variable

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

Physical meaning be zero to inject the node state variable with what rectangular coordinate represented.

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

First step iteration

Results of calculation be:

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

The plural number that recycling represents with rectangular coordinate calculates zero of method considering zero injection constraint to the conversion mapping φ with the plural number of polar coordinate representation and injects the corresponding state variable subvector of node

Computational methods are:

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

$U_7=\sqrt{e_7^2+f_7^2}=1.0226$ ${\mathrm{\&theta;}}_7=\arctan \left(\frac{f_7}{e_7}\right)=-0.0012\mathrm{rad}$

$U_9=\sqrt{e_9^2+f_9^2}=1.0286$ ${\mathrm{\&theta;}}_9=\arctan \left(\frac{f_9}{e_9}\right)=-0.0011\mathrm{rad}$

${\tilde{x}}_z^{\left(k\right)}={\left[\begin{array}{cccccc}{U}_4& U_7& U_9& {\mathrm{\&theta;}}_4& {\mathrm{\&theta;}}_7& {\mathrm{\&theta;}}_9\end{array}\right]}^T$

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

(6) according to above-mentioned iteration

With

Use Newton method to calculate the state variable correction amount x of the k time iteration ^(k)The 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 represents transposition.W is for measuring weight matrix, and r is the measurement residuals vector, for No. i measurement, has

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

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

Power system state estimation convergence is calculated and is finished, if

Order K=k+1 returns to step (4); In this embodiment, ε gets 0.0001

4 convergences of iteration.Comparison of computational results such as the following table of result of calculation and traditional large weight method (zero inject measure weight is taken as common power and measures 10 times):

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

Claims (1)

1. power system state estimation method based on the band of modified newton method zero injection-constraint is characterized in that the method comprises the following 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 zero node injecting power that injects node is 0, represent with c (x)=0, wherein x is the state variable of electric power system, adopt polar coordinate representation, comprise that zero injects 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) according to electric power system current topological structure and network parameter, form electric power system present node admittance matrix, and calculate following coefficient matrix F

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

Matrix G wherein _zzAnd B _zzRespectively real part and the imaginary part of the diagonal angle submatrix that in node admittance matrix, zero injection node is corresponding, battle array G _znAnd B _znBe respectively in 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 state variable subvector that non-zero injects node is designated as respectively

With

(5) keep non-zero to inject the node subvector

Constant, that calculates method considering zero injection constraint injects the corresponding state variable subvector of node with zero

Computing formula is as follows:

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

Wherein matrix F is the result of calculation of step (2), and Φ is in complex theory, and the plural number that represents with rectangular coordinate shines upon to the conversion of the plural number of using 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 real part and the imaginary parts of the node voltage that represents with rectangular coordinate, and U, θ are amplitude and the phase angles with the node voltage of polar coordinate representation;

(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 correction of state variable of node and the correction that non-zero injects the state variable of node is designated as respectively

With

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

Power system state estimation convergence is calculated and is finished, if Order

K=k+1 carries out step (4).

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