CN101635457A - Electric network parameter estimation method based on parameter sensitivity of state estimation residual error - Google Patents

Abstract

The invention relates to an electric network parameter estimation method based on the parameter sensitivity of a state estimation residual error, which belongs to the technical field of electric network parameter identification of electric power systems. The electric network parameter estimation method comprises the following steps: deducing the sensitivity of the state estimation residual error for each circuit parameter of an electric network according to an actual electric network model and real-time measuring data; and modifying the circuit parameter on the prior suspicious branch circuit by adopting a linear optimization method, thereby increasing the reliability and the accuracy of application software. The electric network parameter estimation method based on the parameter sensitivity of the state estimation residual error does not have the problems of numerical stability and observation performance and has simple calculation, easy realization and high calculation speed.

Description

A kind of electrical network parameter method of estimation based on state estimation residual error parametric sensitivity

Technical field

The present invention relates to a kind of electrical network parameter method of estimation, belong to electric power system electrical network parameter identification technique field based on state estimation residual error parametric sensitivity.

Background technology

The error of branch road parameter can cause insincere based on the electrical network On-line Control decision-making of EMS (EMS) and security stabilization early warning result.Along with the expansion of scale of power, continue to bring out based on the new application software of EMS network analysis, more and more higher to the reliability and the required precision of the decision-making of EMS software analysis, research practical parameter method of estimation has important practical significance.

In the parameter identification, the application of the estimation of on-load tap-changing transformer no-load voltage ratio in EMS is comparatively ripe, but the practical research of branch impedance parameter Estimation is then less relatively.The most direct method is that the branch road parameter is calculated in state estimation as state variable augmentation, because the differentiate component that measures parameter causes the Jacobian matrix conditional number to rise to easily, so the remarkable variation of the numerical stability of state estimation after the augmentation parameter.

W.-H.E.Liu, F.F.Wu and S.-M.Liu.Estimations of Parameter Errors form MeasurementResiduals in State Estimation.IEEE Tans.on Power Systems, 1992, (7): 81-89. has proposed a kind of improving one's methods, promptly replace suspicious branch road parameter, make state estimation obtain no inclined to one side estimated result with suspicious branch road trend compensation rate.

$\left[\begin{array}{c}{H}^T\\ L^T\end{array}\right]R^{-1}\left[\begin{array}{cc}H& L\end{array}\right]\left[\begin{array}{c}\mathrm{\δ}{x}^{k+1}\\ \mathrm{\δ}{f}^{k+1}\end{array}\right]=\left[\begin{array}{c}{H}^T\\ L^T\end{array}\right]R^{-1}[z-h\left(x^k\right)-L{f}^k]$

x ^k+1＝x ^k+δx ^k+1????f ^k+1＝f ^k+δf ^k+1

$-v_i^2*\mathrm{\Δb}-v_i{v}_j(\mathrm{\Δg}*\sin \mathrm{\θ}-\mathrm{\Δb}*\cos \mathrm{\θ})=f_Q$

$v_i^2*\mathrm{\Δg}-v_i{v}_j(\mathrm{\Δg}*\cos \mathrm{\θ}+\mathrm{\Δb}*\sin \mathrm{\θ})=f_P$

This method is only to improve the numerical stability problem to a certain extent, in using at the scene, and problem such as adopt this method can often occur that the branch road parameter can not be estimated or estimated result is unreasonable, numerical stability is still relatively poor; And this method also exists the local optimum problem and is not well solved.

Summary of the invention

The objective of the invention is to propose a kind of electrical network parameter method of estimation based on state estimation residual error parametric sensitivity, in grid dispatching center, electric network model and real-time measurement data according to reality are derived the sensitivity of state estimation residual error to every line parameter circuit value of electrical network, selected suspicious branch road collection, according to sequential linear programming, revise the parameter of suspicious branch road, thereby improve the reliability and the accuracy of application software.

The electrical network parameter method of estimation based on state estimation residual error parametric sensitivity that the present invention proposes may further comprise the steps:

(1) set up electrical network least square state estimation model, and with quick decomposition method to model solution, obtain state estimation x as a result ^e

Least square state estimation model is:

The residual error target function:

$J(x,a)=\underset{i\∈{\mathrm{\Ω}}_V}{\mathrm{\Σ}}{w}_i^v{(v_i^m-v_i)}^2+\underset{i\∈{\mathrm{\Ω}}_{P_c}}{\mathrm{\Σ}}{w}_i^P{(P_i^m-P_i)}^2+\underset{i\∈{\mathrm{\Ω}}_{Q_c}}{\mathrm{\Σ}}{w}_i^Q{(Q_i^m-Q_i)}^2+\underset{i,j\∈{\mathrm{\Ω}}_{P_F}}{\mathrm{\Σ}}{w}_{\mathrm{ij}}^P{(P_{\mathrm{ij}}^m-P_{\mathrm{ij}})}^2+\underset{i,j\∈{\mathrm{\Ω}}_{Q_F}}{\mathrm{\Σ}}{w}_{\mathrm{ij}}^Q{(Q_{\mathrm{ij}}^m-Q_{\mathrm{ij}})}^2$

Equality constraint:

$P_i=v_i\underset{j\∈{\mathrm{\Ω}}_i}{\mathrm{\Σ}}{v}_j(G_{\mathrm{ij}}\cos ({\mathrm{\θ}}_i-{\mathrm{\θ}}_j)+B_{\mathrm{ij}}\sin ({\mathrm{\θ}}_i-{\mathrm{\θ}}_j))$

$i\∈{\mathrm{\Ω}}_{P_c}$

$Q_i=v_i\underset{j\∈{\mathrm{\Ω}}_i}{\mathrm{\Σ}}{v}_j(G_{\mathrm{ij}}\sin ({\mathrm{\θ}}_i-{\mathrm{\θ}}_j)-B_{\mathrm{ij}}\cos ({\mathrm{\θ}}_i-{\mathrm{\θ}}_j))$

$i{\∈\mathrm{\Ω}}_{Q_c}$

$P_{\mathrm{ij}}=v_i{v}_j(G_{\mathrm{ij}}\cos ({\mathrm{\θ}}_i-{\mathrm{\θ}}_j)+B_{\mathrm{ij}}\sin ({\mathrm{\θ}}_i-{\mathrm{\θ}}_j))-G_{\mathrm{ij}}{v}_i^2/T_{\mathrm{ij}}$

$i,j\∈{\mathrm{\Ω}}_{P_F}$

$Q_{\mathrm{ij}}=v_i{v}_j(G_{\mathrm{ij}}\sin ({\mathrm{\θ}}_i-{\mathrm{\θ}}_j)-B_{\mathrm{ij}}\cos ({\mathrm{\θ}}_i-{\mathrm{\θ}}_j))+v_i^2(B_{\mathrm{ij}}-b_{\mathrm{ij}}/2)/T_{\mathrm{ij}}$

$i,j\∈{\mathrm{\Ω}}_{Q_F}$

Wherein, x is for comprising θ _i, v _i, P _i, Q _i, P _IjAnd Q _IjVariable vector, θ _i, v _i, P _i, Q _i, P _IjAnd Q _IjThe reactive power flow of the idle injection, node i that is respectively meritorious injection, the node i of voltage magnitude, the node i of voltage phase angle, the node i of node i in the electrical network to the meritorious trend of j and node i to j, a is the parameter vector that comprises G, B, b and T, G, B, b and T are respectively the no-load voltage ratio of transformer on imaginary part, branch road direct-to-ground capacitance and the branch road of real part, grid nodes admittance matrix of grid nodes admittance matrix, v _i ^m, P _i ^m, Q _i ^m, P _Ij ^mAnd Q _Ij ^mBe respectively the voltage magnitude measurement of the node i in the electrical network measurement system, the meritorious injection measurement of node i, the idle injection measurement of node i, the reactive power flow measurement that meritorious trend measures and node i arrives j that node i arrives j, w _i ^v, w _i ^P, w _i ^Q, w _Ij ^PAnd w _Ij ^QBe respectively set of node that the value of voltage magnitude weight, the node i of node i measures, comprise set of node that meritorious injection rate surveys, comprise set of node that idle injection measures, comprise the set of node that meritorious tide flow surveys and comprise the set of node that reactive power flow measures;

(2) according to above-mentioned state estimation model and state estimation x as a result ^e, the value of calculating following matrix is respectively:

$F_{x(1\×n)}={\left[{\▿}_{x}J(x^e,a)\right]}^T$

$F_{a(1\×p)}={\left[{\▿}_{a}J(x^e,a)\right]}^T$

$F_{\mathrm{xx}(n\×n)}={\▿}_{\mathrm{xx}}J(x^e,a)+\underset{k=0}{\overset{l}{\mathrm{\Σ}}}{\mathrm{\λ}}_k^{*}{\▿}_{\mathrm{xx}}{c}_k(x^e,a)$

$F_{\mathrm{xa}(n\×p)}={\▿}_{\mathrm{xa}}J(x^e,a)+\underset{k=1}{\overset{l}{\mathrm{\Σ}}}{\mathrm{\λ}}_k^{*}{\▿}_{\mathrm{xa}}{c}_k(x^e,a)$

$C_{x(l\×n)}={\left[{\▿}_{x}c(x^e,a)\right]}^T$

$C_{a(l\×p)}={\left[{\▿}_{a}c(x^e,a)\right]}^T$

Wherein, J (x a) is residual error target function in the above-mentioned state estimation model, c (x a) is equality constraint in the above-mentioned state estimation model, and l is the equality constraint number,

With

Be respectively the x vector is asked first derivative, a vector is asked first derivative, x and a vector are asked second dervative and the x vector is asked second dervative, x is for comprising θ _i, v _i, P _i, Q _i, P _IjAnd Q _IjVariable vector, n is its vectorial dimension, a is the parameter vector that comprises G, B, b and T, p is its vectorial dimension;

(3) according to the value of above-mentioned matrix, calculating parameter sensitivity

Computational process is:

$H_x=\left[\begin{array}{cc}{F}_{\mathrm{xx}}& C_x^T\\ C_x& 0\end{array}\right]$ $H_a=\left[\begin{array}{c}{F}_{\mathrm{xa}}\\ C_a\end{array}\right]$

${\left[\begin{array}{cc}\frac{\∂x}{\∂a}& \frac{\∂\mathrm{\λ}}{\∂a}\end{array}\right]}^T=-H_x^{-1}{H}_a$ $\frac{\∂J}{\∂a}=F_a+F_x\frac{\∂x}{\∂a}$

(4) parametric sensitivity that obtains according to following formula

Calculate actual parameter sensitivity

Calculating residual error J to the sensitivity of line resistance r and reactance x is:

$\frac{\∂J}{\∂r_{\mathrm{ij}}}=\frac{\∂G_{\mathrm{ij}}}{\∂r_{\mathrm{ij}}}(\frac{\∂J}{\∂G_{\mathrm{ij}}}-\frac{\∂J}{\∂G_{\mathrm{ii}}}-\frac{\∂J}{\∂G_{\mathrm{jj}}})+\frac{\∂B_{\mathrm{ij}}}{\∂r_{\mathrm{ij}}}(\frac{\∂J}{\∂B_{\mathrm{ij}}}-\frac{\∂J}{\∂B_{\mathrm{ii}}}-\frac{\∂J}{\∂B_{\mathrm{jj}}})$

$\frac{\∂J}{\∂r_{\mathrm{ij}}}=\frac{\∂G_{\mathrm{ij}}}{\∂r_{\mathrm{ij}}}(\frac{\∂J}{\∂G_{\mathrm{ij}}}+\frac{\∂J}{\∂G_{\mathrm{ii}}}\frac{\∂G_{\mathrm{ii}}}{\∂G_{\mathrm{ij}}}+\frac{\∂J}{\∂G_{\mathrm{jj}}}\frac{\∂G_{\mathrm{jj}}}{\∂G_{\mathrm{ij}}})+\frac{\∂B_{\mathrm{ij}}}{\∂r_{\mathrm{ij}}}(\frac{\∂J}{\∂B_{\mathrm{ij}}}+\frac{\∂J}{\∂B_{\mathrm{ii}}}\frac{\∂B_{\mathrm{ii}}}{\∂B_{\mathrm{ij}}}+\frac{\∂J}{\∂B_{\mathrm{jj}}}\frac{\∂B_{\mathrm{jj}}}{\∂B_{\mathrm{ij}}})$

$=\frac{\∂G_{\mathrm{ij}}}{\∂r_{\mathrm{ij}}}(\frac{\∂J}{\∂G_{\mathrm{ij}}}-\frac{\∂J}{\∂G_{\mathrm{ii}}}-\frac{\∂J}{\∂G_{\mathrm{jj}}})+\frac{\∂B_{\mathrm{ij}}}{\∂r_{\mathrm{ij}}}(\frac{\∂J}{\∂B_{\mathrm{ij}}}-\frac{\∂J}{\∂B_{\mathrm{ii}}}-\frac{\∂J}{\∂B_{\mathrm{jj}}})$

$\frac{\∂J}{\∂x_{\mathrm{ij}}}=\frac{\∂G_{\mathrm{ij}}}{\∂x_{\mathrm{ij}}}(\frac{\∂J}{\∂G_{\mathrm{ij}}}+\frac{\∂J}{\∂G_{\mathrm{ii}}}\frac{\∂G_{\mathrm{ii}}}{\∂G_{\mathrm{ij}}}+\frac{\∂J}{\∂G_{\mathrm{jj}}}\frac{\∂G_{\mathrm{jj}}}{\∂G_{\mathrm{ij}}})+\frac{\∂B_{\mathrm{ij}}}{\∂x_{\mathrm{ij}}}(\frac{\∂J}{\∂B_{\mathrm{ij}}}+\frac{\∂J}{\∂B_{\mathrm{ii}}}\frac{\∂B_{\mathrm{ii}}}{\∂B_{\mathrm{ij}}}+\frac{\∂J}{\∂B_{\mathrm{jj}}}\frac{\∂B_{\mathrm{jj}}}{\∂B_{\mathrm{ij}}})$

$=\frac{\∂G_{\mathrm{ij}}}{\∂x_{\mathrm{ij}}}(\frac{\∂J}{\∂G_{\mathrm{ij}}}-\frac{\∂J}{\∂G_{\mathrm{ii}}}-\frac{\∂J}{\∂G_{\mathrm{jj}}})+\frac{\∂B_{\mathrm{ij}}}{\∂x_{\mathrm{ij}}}(\frac{\∂J}{\∂B_{\mathrm{ij}}}-\frac{\∂J}{\∂B_{\mathrm{ii}}}-\frac{\∂J}{\∂B_{\mathrm{jj}}})$

Calculate residual error J for line charging electric capacity b _IjWith line transformer no-load voltage ratio T _IjSensitivity be:

$\frac{\∂J}{\∂b_{\mathrm{ij}}}=\frac{\∂J}{\∂b_{\mathrm{ij}}}+\frac{\∂J}{\∂B_{\mathrm{ii}}}\frac{\∂B_{\mathrm{ii}}}{\∂b_{\mathrm{ij}}}+\frac{\∂J}{\∂B_{\mathrm{jj}}}\frac{\∂B_{\mathrm{jj}}}{\∂b_{\mathrm{ij}}}=\frac{\∂J}{\∂b_{\mathrm{ij}}}-\frac{\∂J}{\∂B_{\mathrm{ii}}}-\frac{\∂J}{\∂B_{\mathrm{jj}}}$

$\frac{\∂J}{\∂T_{\mathrm{ij}}}=\frac{\∂J}{\∂T_{\mathrm{ij}}}+\frac{\∂J}{\∂G_{\mathrm{jj}}}\frac{\∂G_{\mathrm{jj}}}{\∂T_{\mathrm{ij}}}+\frac{\∂J}{\∂B_{\mathrm{jj}}}\frac{\∂B_{\mathrm{jj}}}{\∂T_{\mathrm{ij}}}+\frac{\∂J}{\∂G_{\mathrm{ij}}}\frac{\∂G_{\mathrm{ij}}}{\∂T_{\mathrm{ij}}}+\frac{\∂J}{\∂B_{\mathrm{ij}}}\frac{\∂B_{\mathrm{ij}}}{\∂T_{\mathrm{ij}}}$

Wherein, u is the actual parameter vector of electrical network, comprises line resistance r _Ij, line reactance x _Ij, line charging electric capacity b _IjWith line transformer no-load voltage ratio T _Ij,

Specifically comprise

With

(4) utilize sequence linear optimization method, electrical network parameter made amendment:

(4-1) determine the suspicious branch road collection ψ of electrical network:

In candidate's branch road, choose the highly sensitive set of fingers of residual error, in this set, choose branch road and enter suspicious branch road collection ψ about the branch road that measures and the state estimation result is bigger than normal;

(4-2) find the solution following linear programming model, obtain the value of actual parameter deviation delta u:

$\min J(x,u^0)+\frac{\∂J}{\∂u}\mathrm{\Δu}$

s.t??Δ u _i≤Δu _i≤Δu _i??i∈ψ

Wherein, u ⁰Be actual electric network parameter initial value, Be actual parameter sensitivity, Δ u _iBe this adjustment amount of i parameter, Δ u _i With Δ u _iBe the step-length restriction of the following mediation rise of i parameter, ψ represents suspicious set of fingers;

(4-3) to the parameter of suspicious branch road, add the value of above-mentioned Δ u, obtain revised electrical network parameter estimated value;

(4-4) repeating step (4-1)-(4-3), till the difference of the state estimation residual error after adjacent twice iteration in front and back is less than 10e-3, electrical network parameter estimated value to the end.

The electrical network parameter method of estimation that the present invention proposes based on state estimation residual error parametric sensitivity, can be applicable to the identification and the estimation of suspicious branch road parameter in the electrical network, the inventive method does not exist numerical stability and observation problem, and can utilize many group historical datas to carry out identification and estimation.Therefore the inventive method has the following advantages:

1, better numerical value stability;

2, accuracy is preferably arranged;

3, calculate simply, realize that easily computational speed is fast.

Description of drawings

Fig. 1 is an IEEE-9 node system of using the inventive method in the example.

Embodiment

The electrical network parameter method of estimation based on state estimation residual error parametric sensitivity that the present invention proposes may further comprise the steps:

(1) set up electrical network least square state estimation model, and with quick decomposition method to model solution, obtain state estimation x as a result ^e

Least square state estimation model is:

The residual error target function:

$J(x,a)=\underset{i\∈{\mathrm{\Ω}}_r}{\mathrm{\Σ}}{w}_i^v{(v_i^m-v_i)}^2+\underset{i\∈{\mathrm{\Ω}}_{P_c}}{\mathrm{\Σ}}{w}_i^P{(P_i^m-P_i)}^2+\underset{i\∈{\mathrm{\Ω}}_{Q_c}}{\mathrm{\Σ}}{w}_i^Q{(Q_i^m-Q_i)}^2+\underset{i,j\∈{\mathrm{\Ω}}_{P_F}}{\mathrm{\Σ}}{w}_{\mathrm{ij}}^P{(P_{\mathrm{ij}}^m-P_{\mathrm{ij}})}^2+\underset{i,j\∈{\mathrm{\Ω}}_{Q_F}}{\mathrm{\Σ}}{w}_{\mathrm{ij}}^Q{(Q_{\mathrm{ij}}^m-Q_{\mathrm{ij}})}^2$

Equality constraint:

$P_i=v_i\underset{j\∈{\mathrm{\Ω}}_i}{\mathrm{\Σ}}{v}_j(G_{\mathrm{ij}}\cos ({\mathrm{\θ}}_i-{\mathrm{\θ}}_j)+B_{\mathrm{ij}}\sin ({\mathrm{\θ}}_i-{\mathrm{\θ}}_j))$

$i\∈{\mathrm{\Ω}}_{P_c}$

$Q_i=v_i\underset{j\∈{\mathrm{\Ω}}_i}{\mathrm{\Σ}}{v}_j(G_{\mathrm{ij}}\sin ({\mathrm{\θ}}_i-{\mathrm{\θ}}_j)-B_{\mathrm{ij}}\cos ({\mathrm{\θ}}_i-{\mathrm{\θ}}_j))$

$i{\∈\mathrm{\Ω}}_{Q_c}$

$P_{\mathrm{ij}}=v_i{v}_j(G_{\mathrm{ij}}\cos ({\mathrm{\θ}}_i-{\mathrm{\θ}}_j)+B_{\mathrm{ij}}\sin ({\mathrm{\θ}}_i-{\mathrm{\θ}}_j))-G_{\mathrm{ij}}{v}_i^2/T_{\mathrm{ij}}$

$i,j\∈{\mathrm{\Ω}}_{P_F}$

$Q_{\mathrm{ij}}=v_i{v}_j(G_{\mathrm{ij}}\sin ({\mathrm{\θ}}_i-{\mathrm{\θ}}_j)-B_{\mathrm{ij}}\cos ({\mathrm{\θ}}_i-{\mathrm{\θ}}_j))+v_i^2(B_{\mathrm{ij}}-b_{\mathrm{ij}}/2)/T_{\mathrm{ij}}$

$i,j\∈{\mathrm{\Ω}}_{Q_F}$

Wherein, x is for comprising θ _i, v _i, P _i, Q _i, P _IjAnd Q _IjVariable vector, θ _i, v _i, P _i, Q _i, P _IjAnd Q _IjThe reactive power flow of the idle injection, node i that is respectively meritorious injection, the node i of voltage magnitude, the node i of voltage phase angle, the node i of node i in the electrical network to the meritorious trend of j and node i to j, a is the parameter vector that comprises G, B, b and T, G, B, b and T are respectively the no-load voltage ratio of transformer on imaginary part, branch road direct-to-ground capacitance and the branch road of real part, grid nodes admittance matrix of grid nodes admittance matrix, v _i ^m, P _i ^m, Q _i ^m, P _Ij ^mAnd Q _Ij ^mBe respectively the voltage magnitude measurement of the node i in the electrical network measurement system, the meritorious injection measurement of node i, the idle injection measurement of node i, the reactive power flow measurement that meritorious trend measures and node i arrives j that node i arrives j, w _i ^v, w _i ^P, w _i ^Q, w _Ij ^PAnd w _Ij ^QThe reactive power flow weight of the idle injection weight, node i that is respectively meritorious injection weight, the node i of voltage magnitude weight, the node i of node i to the meritorious trend weight of j and node i to j, Ω _i, Ω _V, With The set of node of representing respectively to link to each other, comprise set of node that voltage magnitude measures, comprise set of node that meritorious injection rate surveys, comprise set of node that idle injection measures, comprise the set of node that meritorious tide flow surveys and comprise the set of node that reactive power flow measures with node i;

(2) according to above-mentioned state estimation model and state estimation x as a result ^e, the value of calculating following matrix is respectively:

$F_{x(1\×n)}={\left[{\▿}_{x}J(x^e,a)\right]}^T$

$F_{a(1\×p)}={\left[{\▿}_{a}J(x^e,a)\right]}^T$

$F_{\mathrm{xx}(n\×n)}={\▿}_{\mathrm{xx}}J(x^e,a)+\underset{k=1}{\overset{l}{\mathrm{\Σ}}}{\mathrm{\λ}}_k^{*}{\▿}_{\mathrm{xx}}{c}_k(x^e,a)$

$F_{\mathrm{xa}(n\×p)}={\▿}_{\mathrm{xa}}J(x^e,a)+\underset{k=1}{\overset{l}{\mathrm{\Σ}}}{\mathrm{\λ}}_k^{*}{\▿}_{\mathrm{xa}}{c}_k(x^e,a)$

$C_{x(l\×n)}={\left[{\▿}_{x}c(x^e,a)\right]}^T$

$C_{a(l\×p)}={\left[{\▿}_{a}c(x^e,a)\right]}^T$

Wherein, J (x a) is residual error target function in the above-mentioned state estimation model, c (x a) is equality constraint in the above-mentioned state estimation model, and l is the equality constraint number,

With Be respectively the x vector is asked first derivative, a vector is asked first derivative, x and a vector are asked second dervative and the x vector is asked second dervative, x is for comprising θ _i, v _i, P _i, Q _i, P _IjAnd Q _IjVariable vector, n is its vectorial dimension, a is the parameter vector that comprises G, B, b and T, p is its vectorial dimension;

(3) according to the value of above-mentioned matrix, calculating parameter sensitivity

Computational process is:

$H_x=\left[\begin{array}{cc}{F}_{\mathrm{xx}}& C_x^T\\ C_x& 0\end{array}\right]$ $H_a=\left[\begin{array}{c}{F}_{\mathrm{xa}}\\ C_a\end{array}\right]$

${\left[\begin{array}{cc}\frac{\∂x}{\∂a}& \frac{\∂\mathrm{\λ}}{\∂a}\end{array}\right]}^T=-H_x^{-1}{H}_a$ $\frac{\∂J}{\∂a}=F_a+F_x\frac{\∂x}{\∂a}$

(4) parametric sensitivity that obtains according to following formula

Calculate actual parameter sensitivity

Calculating residual error J to the sensitivity of line resistance r and reactance x is:

$\frac{\∂J}{\∂r_{\mathrm{ij}}}=\frac{\∂G_{\mathrm{ij}}}{\∂r_{\mathrm{ij}}}(\frac{\∂J}{\∂G_{\mathrm{ij}}}-\frac{\∂J}{\∂G_{\mathrm{ii}}}-\frac{\∂J}{\∂G_{\mathrm{jj}}})+\frac{\∂B_{\mathrm{ij}}}{\∂r_{\mathrm{ij}}}(\frac{\∂J}{\∂B_{\mathrm{ij}}}-\frac{\∂J}{\∂B_{\mathrm{ii}}}-\frac{\∂J}{\∂B_{\mathrm{jj}}})$

$\frac{\∂J}{\∂x_{\mathrm{ij}}}=\frac{\∂G_{\mathrm{ij}}}{\∂x_{\mathrm{ij}}}(\frac{\∂J}{\∂G_{\mathrm{ij}}}-\frac{\∂J}{\∂G_{\mathrm{ii}}}-\frac{\∂J}{\∂G_{\mathrm{jj}}})+\frac{\∂B_{\mathrm{ij}}}{\∂x_{\mathrm{ij}}}(\frac{\∂J}{\∂B_{\mathrm{ij}}}-\frac{\∂J}{\∂B_{\mathrm{ii}}}-\frac{\∂J}{\∂B_{\mathrm{jj}}})$

Calculate residual error J for line charging electric capacity b _IjWith line transformer no-load voltage ratio T _IjSensitivity be:

$\frac{\∂J}{\∂b_{\mathrm{ij}}}=\frac{\∂J}{\∂b_{\mathrm{ij}}}-\frac{\∂J}{\∂B_{\mathrm{ii}}}-\frac{\∂J}{\∂B_{\mathrm{jj}}}$

$\frac{\∂J}{\∂T_{\mathrm{ij}}}=\frac{\∂J}{\∂T_{\mathrm{ij}}}+\frac{\∂J}{\∂G_{\mathrm{jj}}}\frac{\∂G_{\mathrm{jj}}}{\∂T_{\mathrm{ij}}}+\frac{\∂J}{\∂B_{\mathrm{jj}}}\frac{\∂B_{\mathrm{jj}}}{\∂T_{\mathrm{ij}}}+\frac{\∂J}{\∂G_{\mathrm{ij}}}\frac{\∂G_{\mathrm{ij}}}{\∂T_{\mathrm{ij}}}+\frac{\∂J}{\∂B_{\mathrm{ij}}}\frac{\∂B_{\mathrm{ij}}}{\∂T_{\mathrm{ij}}}$

Wherein, u is the actual parameter vector of electrical network, comprises line resistance r _Ij, line reactance x _Ij, line charging electric capacity b _IjWith line transformer no-load voltage ratio T _Ij,

Specifically comprise

With

(4) utilize sequence linear optimization method, electrical network parameter made amendment:

(4-1) determine the suspicious branch road collection ψ of electrical network:

In candidate's branch road, choose the highly sensitive set of fingers of residual error, in this set, choose branch road and enter suspicious branch road collection ψ about the branch road that measures and the state estimation result is bigger than normal;

(4-2) find the solution following linear programming model, obtain the value of actual parameter deviation delta u:

$\min J(x,u^0)+\frac{\∂J}{\∂u}\mathrm{\Δu}$

s.t??Δ u _i≤Δu _i≤Δu _i??i∈ψ

Wherein, u ⁰Be actual electric network parameter initial value,

Be actual parameter sensitivity, Δ u _iBe this adjustment amount of i parameter, Δ u _i With Δ u _iBe the step-length restriction of the following mediation rise of i parameter, ψ represents suspicious set of fingers;

(4-3) to the parameter of suspicious branch road, add the value of above-mentioned Δ u, obtain revised electrical network parameter estimated value;

(4-4) repeating step (4-1)-(4-3), till the difference of the state estimation residual error after adjacent twice iteration in front and back is less than 10e-3, electrical network parameter estimated value to the end.

Below introduce an embodiment of the inventive method:

IEEE 9 node systems are as shown in Figure 1 designed three examples, are respectively the parameter Estimation situations when line reactance, transformer voltage ratio have the sum of errors both that error is arranged separately.

When (1) only a line reactance has than mistake, the parameter Estimation situation of this method

Suspicious parameter	Actual value	Initial value	Estimated value	Iterations
					Circuit B-3 reactance	??0.17	??0.03	??0.169	??142

When (2) only transformer voltage ratio has than mistake, the parameter Estimation situation of this method

Suspicious parameter	Actual value	Initial value	Estimated value	Iterations
					Transformer 2 no-load voltage ratios	??1.169	??1.3	??1.168	??133

(3) when line parameter circuit value and transformer voltage ratio have than mistake, the parameter Estimation situation of this method

Suspicious parameter set	Actual value	Initial value	Estimated value	Iterations
					Circuit A-1 resistance	??0.01	??0.03	??0.011	??127
Circuit C-2 reactance	??0.072	??0.01	??0.072	??127
					Transformer 3 no-load voltage ratios	??1.052	??1.01	??1.053	??127

Claims (1)

1, a kind of electrical network parameter method of estimation based on state estimation residual error parametric sensitivity is characterized in that this method may further comprise the steps:

(1) set up electrical network least square state estimation model, and with quick decomposition method to model solution, obtain state estimation x as a result ^e:

Least square state estimation model is:

The residual error target function:

$J(x,a)=\underset{i\∈{\mathrm{\Ω}}_i}{\mathrm{\Σ}}{w}_i^v{(v_i^m-v_i)}^2+\underset{i\∈{\mathrm{\Ω}}_{P_c}}{\mathrm{\Σ}}{w}_i^P{(P_i^m-P_i)}^2+\underset{i\∈{\mathrm{\Ω}}_{Q_c}}{\mathrm{\Σ}}{w}_i^Q{(Q_i^m-Q_i)}^2+\underset{i,j\∈{\mathrm{\Ω}}_{P_F}}{\mathrm{\Σ}}{w}_{\mathrm{ij}}^P{(P_{\mathrm{ij}}^m-P_{\mathrm{ij}})}^2+\underset{i,j\∈{\mathrm{\Ω}}_{Q_F}}{\mathrm{\Σ}}{w}_{\mathrm{ij}}^Q{(Q_{\mathrm{ij}}^m-Q_{\mathrm{ij}})}^2$

Equality constraint:

$P_i=v_i\underset{j\∈{\mathrm{\Ω}}_i}{\mathrm{\Σ}}{v}_j(G_{\mathrm{ij}}\cos ({\mathrm{\θ}}_i-{\mathrm{\θ}}_j)+B_{\mathrm{ij}}\sin ({\mathrm{\θ}}_i-{\mathrm{\θ}}_j))$

$i\∈{\mathrm{\Ω}}_{P_c}$

$Q_i=v_i\underset{j\∈{\mathrm{\Ω}}_i}{\mathrm{\Σ}}{v}_j(G_{\mathrm{ij}}\sin ({\mathrm{\θ}}_i-{\mathrm{\θ}}_j)-B_{\mathrm{ij}}\cos ({\mathrm{\θ}}_i-{\mathrm{\θ}}_j))$

$i\∈{\mathrm{\Ω}}_{Q_c}$

$P_{\mathrm{ij}}=v_i{v}_j(G_{\mathrm{ij}}\cos ({\mathrm{\θ}}_i-{\mathrm{\θ}}_j)+B_{\mathrm{ij}}\sin ({\mathrm{\θ}}_i-{\mathrm{\θ}}_j))-G_{\mathrm{ij}}{v}_i^2/T_{\mathrm{ij}}$

$i,j\∈{\mathrm{\Ω}}_{P_F}$

$Q_{\mathrm{ij}}=v_i{v}_j(G_{\mathrm{ij}}\sin ({\mathrm{\θ}}_i-{\mathrm{\θ}}_j)-B_{\mathrm{ij}}\cos ({\mathrm{\θ}}_i-{\mathrm{\θ}}_j))+v_i^2(B_{\mathrm{ij}}-b_{\mathrm{ij}}/2)/T_{\mathrm{ij}}$

$i,j\∈{\mathrm{\Ω}}_{Q_F}$

Wherein, x is for comprising θ _i, v _i, P _i, Q _i, P _IjAnd Q _IjVariable vector, θ _i, v _i, P _i, Q _i, P _IjAnd Q _IjThe reactive power flow of the idle injection, node i that is respectively meritorious injection, the node i of voltage magnitude, the node i of voltage phase angle, the node i of node i in the electrical network to the meritorious trend of j and node i to j, a is the parameter vector that comprises G, B, b and T, G, B, b and T are respectively the no-load voltage ratio of transformer on imaginary part, branch road direct-to-ground capacitance and the branch road of real part, grid nodes admittance matrix of grid nodes admittance matrix, v _i ^m, P _i ^m, Q _i ^m, P _Ij ^mAnd Q _Ij ^mBe respectively the voltage magnitude measurement of the node i in the electrical network measurement system, the meritorious injection measurement of node i, the idle injection measurement of node i, the reactive power flow measurement that meritorious trend measures and node i arrives j that node i arrives j, w _i ^v, w _i ^P, w _i ^Q, w _Ij ^PAnd w _Ij ^QThe reactive power flow weight of the idle injection weight, node i that is respectively meritorious injection weight, the node i of voltage magnitude weight, the node i of node i to the meritorious trend weight of j and node i to j, Ω _i, Ω _V,

With The set of node of representing respectively to link to each other, comprise the meritorious idle injection weight of injecting weight, node i of voltage amplitude, node i reactive power flow weight, Ω to the meritorious trend weight of j and node i to j with node i _i, Ω _V,

With

The set of node of representing respectively to link to each other, comprise set of node that voltage magnitude measures, comprise set of node that meritorious injection rate surveys, comprise set of node that idle injection measures, comprise the set of node that meritorious tide flow surveys and comprise the set of node that reactive power flow measures with node i;

(2) according to above-mentioned state estimation model and state estimation x as a result ^e, the value of calculating following matrix is respectively:

$F_{x(1\×n)}={\left[{\▿}_{x}J(x^e,a)\right]}^T$

$F_{a(1\×p)}={\left[{\▿}_{a}J(x^e,a)\right]}^T$

$F_{\mathrm{xx}(n\×n)}={\▿}_{\mathrm{xx}}J(x^e,a)+\underset{k=1}{\overset{l}{\mathrm{\Σ}}}{\mathrm{\λ}}_k^{*}{\▿}_{\mathrm{xx}}{c}_k(x^e,a)$

$F_{\mathrm{xa}(n\×p)}={\▿}_{\mathrm{xa}}J(x^e,a)+\underset{k=1}{\overset{l}{\mathrm{\Σ}}}{\mathrm{\λ}}_k^{*}{\▿}_{\mathrm{xa}}{c}_k(x^e,a)$

$C_{x(l\×n)}={\left[{\▿}_{x}c(x^e,a)\right]}^T$

$C_{a(l\×p)}={\left[{\▿}_{a}c(x^e,a)\right]}^T$

Wherein, J (x a) is residual error target function in the above-mentioned state estimation model, c (x a) is equality constraint in the above-mentioned state estimation model, and l is the equality constraint number,

With

Be respectively the x vector is asked first derivative, a vector is asked first derivative, x and a vector are asked second dervative and the x vector is asked second dervative, x is for comprising θ _i, v _i, P _i, Q _i, P _IjAnd Q _IjVariable vector, n is its vectorial dimension, a is the parameter vector that comprises G, B, b and T, p is its vectorial dimension;

(3) according to the value of above-mentioned matrix, calculating parameter sensitivity

Computational process is:

$H_x=\left[\begin{array}{cc}{F}_{\mathrm{xx}}& C_x^T\\ C_x& 0\end{array}\right]$ $H_a=\left[\begin{array}{c}{F}_{\mathrm{xa}}\\ C_a\end{array}\right]$

${\left[\begin{array}{cc}\frac{\∂x}{\∂a}& \frac{\∂\mathrm{\λ}}{\∂a}\end{array}\right]}^T=-H_x^{-1}{H}_a$ $\frac{\∂F}{\∂a}=F_a+F_x\frac{\∂x}{\∂a}$

(4) parametric sensitivity that obtains according to following formula

Calculate actual parameter sensitivity

Calculating residual error J to the sensitivity of line resistance r and reactance x is:

$\frac{\∂J}{{\∂x}_{\mathrm{ij}}}=\frac{{\∂G}_{\mathrm{ij}}}{{\∂x}_{\mathrm{ij}}}(\frac{\∂J}{{\∂G}_{\mathrm{ij}}}-\frac{\∂J}{{\∂G}_{\mathrm{ii}}}-\frac{\∂J}{{\∂G}_{\mathrm{jj}}})+\frac{{\∂B}_{\mathrm{ij}}}{{\∂x}_{\mathrm{ij}}}(\frac{\∂J}{{\∂B}_{\mathrm{ij}}}-\frac{\∂J}{{\∂B}_{\mathrm{ii}}}-\frac{\∂J}{{\∂B}_{\mathrm{jj}}})$

Calculate residual error J for line charging electric capacity b _IjWith line transformer no-load voltage ratio T _IjSensitivity be:

$\frac{\∂J}{{\∂b}_{\mathrm{ij}}}=\frac{\∂J}{{\∂b}_{\mathrm{ij}}}-\frac{\∂J}{{\∂B}_{\mathrm{ii}}}-\frac{\∂J}{{\∂B}_{\mathrm{jj}}}$

$\frac{\∂J}{{\∂T}_{\mathrm{ij}}}=\frac{\∂J}{{\∂T}_{\mathrm{ij}}}+\frac{\∂J}{{\∂G}_{\mathrm{jj}}}\frac{{\∂G}_{\mathrm{jj}}}{{\∂T}_{\mathrm{ij}}}+\frac{\∂J}{{\∂B}_{\mathrm{jj}}}\frac{{\∂B}_{\mathrm{jj}}}{{\∂T}_{\mathrm{jj}}}+\frac{\∂J}{{\∂G}_{\mathrm{ij}}}\frac{{\∂G}_{\mathrm{ij}}}{{\∂T}_{\mathrm{ij}}}+\frac{\∂J}{{\∂B}_{\mathrm{ij}}}\frac{{\∂B}_{\mathrm{ij}}}{{\∂T}_{\mathrm{ij}}}$

Wherein, u is the actual parameter vector of electrical network, comprises line resistance r _Ij, line reactance x _Ij, line charging electric capacity b _IjWith line transformer no-load voltage ratio T _Ij,

Specifically comprise With

(4) utilize sequence linear optimization method, electrical network parameter made amendment:

(4-1) determine the suspicious branch road collection ψ of electrical network:

(4-2) find the solution following linear programming model, obtain the value of actual parameter deviation delta u:

$\min J(x,u^0)+\frac{\∂J}{\∂u}\mathrm{\Δu}$

s.t??Δ u _i≤Δu _i≤Δu _i??i∈ψ

Wherein, u ⁰Be actual electric network parameter initial value,

Be actual parameter sensitivity, Δ u _iBe this adjustment amount of i parameter, Δ u _i With Δ u _iBe the step-length restriction of the following mediation rise of i parameter, ψ represents suspicious set of fingers;

(4-3) to the parameter of suspicious branch road, add the value of above-mentioned Δ u, obtain revised electrical network parameter estimated value;

(4-4) repeating step (4-1)-(4-3), till the difference of the state estimation residual error after adjacent twice iteration in front and back is less than 10e-3, electrical network parameter estimated value to the end.

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