CN102945225A - Solving method of sensitivity of microgrid characteristic solution - Google Patents

Abstract

The invention relates to a solving method of sensitivity of a microgrid characteristic solution. The method includes the following steps of constructing a state matrix of a microgrid system; solving the state matrix of the microgrid system to obtain characteristic values of the microgrid system; classifying the characteristic values of the microgrid system according to the fact that whether the characteristic values are repeated; subjecting repeated characteristic values of the microgrid system to sensitivity calculation of the characteristic values and corresponding characteristic vectors; and subjecting isolated characteristic values of the microgrid system to sensitivity calculation of the characteristic values and the corresponding characteristic vectors. According to the solving method, derivation of complex computational formulas during the solving process of the sensitivity is avoided, or repeated solving of the characteristic values is avoided; simultaneously, basis is provided for integrated study of aspects of the sensitivity, system parameter design and dynamic characteristic analysis; and the method simplifies calculation process of the sensitivity and improves accuracy.

Description

The method for solving of a kind of little electrical network characteristic solution sensitivity

Technical field

The present invention relates to finding the solution of characteristic solution sensitivity, particularly the method for solving of a kind of little electrical network characteristic solution sensitivity.

Background technology

Little electrical network refers to the electric system of being transported to of the autonomy that is comprised of distributed power source, energy storage device, energy conversion device, controllable burden and monitoring and protecting device etc. ^{[1] [2]}There is a large amount of energy conversion devices in little electrical network, and these energy conversion devices lack certain inertia, thereby so that little electrical network is easy to be subject to the impact of various disturbances ^[3], therefore be necessary little electrical network microvariations stability problem is carried out deep research and analysis.In little electrical network microvariations stability analysis, the system features value of little electrical network and proper vector are very important to the sensitivity analysis of control parameter, can play an important role in control parameter designing and all many-sides of the Robust Stability Analysis ^[4]

At present, the method for solving of eigenwert and Method For Calculating Eigenvector Sensitivity mainly is divided into two classes ^{[5] [6]}: analytical method and method of perturbation.Analytic Method is by deriving in detail accurately to the sensitivity solution formula; Method of perturbation is by repeatedly finding the solution the result of calculation of obtaining sensitivity to system features solution problem.

The inventor finds to exist at least in the prior art following shortcoming and defect in realizing process of the present invention:

Analytical method is unfavorable for that the micro-grid system model adds and system extension; Method of perturbation need to be concatenated to form system state matrix and solving system eigenvalue problem, and can't only carry out sensitivity analysis for crucial mode; Thereby affected finding the solution of characteristic solution sensitivity in little electrical network, restricted in little electrical network the raising of improvement, damping ratio and the stability margin of Parameters Optimal Design based on characteristic solution sensitivity, System Small Disturbance stability, analysis of system core mode etc.

Summary of the invention

The invention provides the method for solving of a kind of little electrical network characteristic solution sensitivity, this method has realized only carrying out sensitivity analysis for crucial mode, and has simplified the solution procedure of sensitivity, sees for details hereinafter to describe:

The method for solving of a kind of little electrical network characteristic solution sensitivity said method comprising the steps of:

1) state matrix of structure micro-grid system;

The state matrix of 2) finding the solution micro-grid system obtains the micro-grid system eigenwert; Whether repeat according to eigenwert, the micro-grid system eigenwert is classified;

3) the micro-grid system multiple eigenvalue is carried out eigenwert and corresponding eigenvector sensibility calculating;

4) the micro-grid system isolated eigenvalue is carried out eigenwert and corresponding eigenvector sensibility calculating.

The state matrix of described structure micro-grid system is specially:

1) obtains the original state matrix of micro-grid system;

A _sys=A-BD ^-1C (1)

Wherein, A is that the state equation of little electrical network is to the partial derivative matrix of state variable; B is that the state equation of little electrical network is to the partial derivative matrix of algebraically variable; C is that the algebraic equation of little electrical network is to the partial derivative matrix of state variable; D is that the algebraic equation of little electrical network is to the partial derivative matrix of algebraically variable;

2) the original state matrix of micro-grid system is controlled the perturbation analysis of parameter p;

$A=\underset{i=1}{\overset{N_1}{\mathrm{\Σ}}}{f}_i\left(p\right)\×A_i+\stackrel{\‾}{A}---\left(2\right)$

$B=\underset{i=1}{\overset{N_2}{\mathrm{\Σ}}}{g}_i\left(p\right)\×B_i+\stackrel{\‾}{B}---\left(3\right)$

$C=\underset{i=1}{\overset{N_3}{\mathrm{\Σ}}}{h}_i\left(p\right)\×C_i+\stackrel{\‾}{C}---\left(4\right)$

In the formula, A _i, B _i, C _i,

Be constant matrices; f _i(p), g _i(p), h _i(p) function of representative control parameter p; N ₁, N ₂, N ₃Represent respectively the number of above-mentioned constant matrices;

3) the state matrix A of structure micro-grid system _Sys(p);

$A_{\mathrm{sys}}\left(p\right)={\mathrm{<figure-callout\; id="0"\; label="M"\; filenames="HDA00002436889000022.png"\; state="\{\{state\}\}">M</figure-callout>}}_0+\underset{i=1}{\overset{N_1}{\mathrm{\&Sigma;}}}{f}_i\left(p\right)\&times;M_{1,i}+\underset{i=1}{\overset{N_2}{\mathrm{\&Sigma;}}}{g}_i\left(p\right)\&times;M_{2,i}+\underset{i=1}{\overset{N_3}{\mathrm{\&Sigma;}}}{h}_i\left(p\right)\&times;M_{3,i}+\underset{i=1}{\overset{N_2}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{N_3}{\mathrm{\&Sigma;}}}{g}_i\left(p\right)\&times;h_j\left(p\right)\&times;M_{4,\mathrm{ij}}---\left(5\right)$

In the formula, M ₀, M _{1, i}, M _{2, i}, M _{3, i}, M _{4, ij}As follows respectively, be the constant matrices irrelevant with controlling parameter p;

$\begin{array}{cccc}& {\mathrm{<figure-callout\; id="0"\; label="M"\; filenames="HDA00002436889000022.png"\; state="\{\{state\}\}">M</figure-callout>}}_0=\stackrel{\&OverBar;}{A}-\stackrel{\&OverBar;}{B}{D}^{-1}\stackrel{\&OverBar;}{C}& M_{1,i}=A_i& \\ M_{2,i}=-B_i{D}^{-1}\stackrel{\&OverBar;}{C}& M_{3,i}=-\stackrel{\&OverBar;}{B}{D}^{-1}{C}_i& & M_{4,\mathrm{ij}}=-B_i{D}^{-1}{C}_j\end{array}.$

Described state matrix of finding the solution micro-grid system obtains the micro-grid system eigenwert; Whether repeat according to eigenwert, the micro-grid system eigenwert is classified is specially:

The state matrix of 1) finding the solution micro-grid system obtains the eigenwert of micro-grid system;

$\left\{\begin{array}{c}{A}_{\mathrm{sys}}{v}_i={\mathrm{\&lambda;}}_i{v}_i\\ u_i^T{A}_{\mathrm{sys}}=u_i^T{\mathrm{\&lambda;}}_i\end{array}\right.---\left(6\right)$

In the formula, λ _iBe i eigenwert of micro-grid system, v _i,

Be respectively right proper vector and the left eigenvector corresponding with eigenwert;

2) whether repeat according to eigenwert in the micro-grid system, it is divided into micro-grid system multiple eigenvalue and isolated eigenvalue.

The beneficial effect of technical scheme provided by the invention is: according to the spatial distribution state of system features value, this method is analyzed the perturbed problem of characteristic solution from the angle of isolated eigenvalue and heavy eigenwert respectively, sensitivity solution formula by micro-grid system control parameter has obtained with the sensitivity to control variable of the isolated characteristic solution of Perturbation Method and heavy characteristic solution, and by the little electrical network Example Verification of low pressure validity of the present invention; The present invention has avoided the derivation of complicated calculations formula in the sensitivity solution procedure, and perhaps eigenvalue problem finds the solution repeatedly; The binding that is again simultaneously the aspects such as sensitivity and System Parameter Design, dynamic analysis provides the foundation.

Description of drawings

Fig. 1 is low pressure micro-grid system example;

Fig. 2 is little electrical network eigenwert distribution plan;

The schematic diagram of Matrix perturbation and QR method eigenwert Calculation Comparison when Fig. 3 is Parameter Perturbation;

Fig. 4 is the process flow diagram of the method for solving of a kind of little electrical network characteristic solution sensitivity.

Embodiment

For making the purpose, technical solutions and advantages of the present invention clearer, embodiment of the present invention is described further in detail below in conjunction with accompanying drawing.

In order only to carry out sensitivity analysis for crucial mode, and simplify the solution procedure of sensitivity, the embodiment of the invention provides the method for solving of a kind of little electrical network characteristic solution sensitivity, referring to Fig. 4, sees for details hereinafter and describes:

101: the state matrix that makes up micro-grid system;

This step is specially:

1) obtains the original state matrix of micro-grid system;

A _sys=A-BD ^-1C (2)

Wherein, A is that the state equation of little electrical network is to the partial derivative matrix of state variable; B is that the state equation of little electrical network is to the partial derivative matrix of algebraically variable; C is that the algebraic equation of little electrical network is to the partial derivative matrix of state variable; D is that the algebraic equation of little electrical network is to the partial derivative matrix of algebraically variable.

2) the original state matrix of micro-grid system is controlled the perturbation analysis of parameter p;

By to the perturbation analysis of micro-grid system original state matrix as can be known, the perturbation of control parameter p only can cause matrix A, B, the change of C Partial Elements, and all impacts of uncontrolled parameter p of each element in the matrix D.Be without loss of generality, matrix A, B, C can be expressed as form:

$A=\underset{i=1}{\overset{N_1}{\mathrm{\&Sigma;}}}{f}_i\left(p\right)\&times;A_i+\stackrel{\&OverBar;}{A}---\left(2\right)$

$B=\underset{i=1}{\overset{N_2}{\mathrm{\&Sigma;}}}{g}_i\left(p\right)\&times;B_i+\stackrel{\&OverBar;}{B}---\left(3\right)$

$C=\underset{i=1}{\overset{N_3}{\mathrm{\&Sigma;}}}{h}_i\left(p\right)\&times;C_i+\stackrel{\&OverBar;}{C}---\left(4\right)$

In the formula, A _i, B _i, C _i, Be constant matrices; f _i(p), g _i(p), h _i(p) function of representative control parameter p; N ₁, N ₂, N ₃Represent respectively the number of above-mentioned constant matrices, the concrete value of above-mentioned parameter is definite by the micro-grid system in the practical application, and the embodiment of the invention is not done at this and given unnecessary details.

3) the state matrix A of structure micro-grid system _Sys(p).

Formula (2)-(4) are brought into the original state matrix (1) of micro-grid system, and further after the arrangement, can be controlled parameter p and as the system state matrix of variable be:

$A_{\mathrm{sys}}\left(p\right)={\mathrm{<figure-callout\; id="0"\; label="M"\; filenames="HDA00002436889000022.png"\; state="\{\{state\}\}">M</figure-callout>}}_0+\underset{i=1}{\overset{N_1}{\mathrm{\&Sigma;}}}{f}_i\left(p\right)\&times;M_{1,i}+\underset{i=1}{\overset{N_2}{\mathrm{\&Sigma;}}}{g}_i\left(p\right)\&times;M_{2,i}+\underset{i=1}{\overset{N_3}{\mathrm{\&Sigma;}}}{h}_i\left(p\right)\&times;M_{3,i}+\underset{i=1}{\overset{N_2}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{N_3}{\mathrm{\&Sigma;}}}{g}_i\left(p\right)\&times;h_j\left(p\right)\&times;M_{4,\mathrm{ij}}---\left(5\right)$

In the formula, M ₀, M _{1, i}, M _{2, i}, M _{3, i}, M _{4, ij}As follows respectively, be the constant matrices irrelevant with controlling parameter p.

$\begin{array}{cccc}& {\mathrm{<figure-callout\; id="0"\; label="M"\; filenames="HDA00002436889000022.png"\; state="\{\{state\}\}">M</figure-callout>}}_0=\stackrel{\&OverBar;}{A}-\stackrel{\&OverBar;}{B}{D}^{-1}\stackrel{\&OverBar;}{C}& M_{1,i}=A_i& \\ M_{2,i}=-B_i{D}^{-1}\stackrel{\&OverBar;}{C}& M_{3,i}=-\stackrel{\&OverBar;}{B}{D}^{-1}{C}_i& & M_{4,\mathrm{ij}}=-B_i{D}^{-1}{C}_j\end{array}$

102: the state matrix of finding the solution micro-grid system obtains the micro-grid system eigenwert; Whether repeat according to eigenwert, the micro-grid system eigenwert is classified;

This step is specially:

The state matrix of 1) finding the solution micro-grid system obtains the eigenwert of micro-grid system;

$\left\{\begin{array}{c}{A}_{\mathrm{sys}}{v}_i={\mathrm{\&lambda;}}_i{v}_i\\ u_i^T{A}_{\mathrm{sys}}=u_i^T{\mathrm{\&lambda;}}_i\end{array}\right.---\left(6\right)$

In the formula, λ _iBe i eigenwert of micro-grid system, v _i, Be respectively right proper vector and the left eigenvector corresponding with eigenwert.

2) classification of micro-grid system eigenwert

Whether repeat according to eigenwert in the micro-grid system, it is divided into micro-grid system multiple eigenvalue and isolated eigenvalue.If in micro-grid system, eigenvalue λ _rBe the heavy eigenwert of m (m〉1), all the other are isolated eigenvalue, and then the eigenwert in the micro-grid system can be expressed as form:

Right proper vector and the left eigenvector of its correspondence are respectively:

$\left\{\begin{array}{c}{v}_1,v_2,\&CenterDot;\&CenterDot;\&CenterDot;,v_r^{\left(1\right)},\&CenterDot;\&CenterDot;\&CenterDot;v_r^{\left(m\right)},v_{r+m},\&CenterDot;\&CenterDot;\&CenterDot;v_n\\ {(u_1,u_2,\&CenterDot;\&CenterDot;\&CenterDot;,u_r^{\left(1\right)},\&CenterDot;\&CenterDot;\&CenterDot;u_r^{\left(m\right)},u_{r+m},\&CenterDot;\&CenterDot;\&CenterDot;u_n)}^T\end{array}\right.---\left(8\right)$

103: the micro-grid system multiple eigenvalue is carried out eigenwert and corresponding eigenvector sensibility calculating;

As follows respectively to the sensitivity of control parameter with the corresponding eigenwert of multiple eigenvalue and proper vector that Perturbation is found the solution:

$\frac{{\&PartialD;\mathrm{\&lambda;}}_k}{\&PartialD;p}=\frac{\&PartialD;\left(\mathrm{eig}{\left(U_{r0}^T{\mathrm{\&Delta;A}}_{\mathrm{sys}}{V}_{r0}\right)}_k\right)}{\&PartialD;p}---\left(9\right)$

$\frac{{\&PartialD;x}_k}{\&PartialD;p}=\underset{\underset{l\&NotEqual;r,\&CenterDot;\&CenterDot;\&CenterDot;,r+m-1}{l=1}}{\overset{n}{\mathrm{\&Sigma;}}}\underset{p=1}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_{\mathrm{kp}}\left\{\begin{array}{c}\underset{i=1}{\overset{N_1}{\mathrm{\&Sigma;}}}\frac{{\&PartialD;f}_i\left(p\right)}{\&PartialD;p}\&times;c_{\mathrm{lrp}}^{1,i}\\ +\underset{i=1}{\overset{N_2}{\mathrm{\&Sigma;}}}\frac{{\&PartialD;g}_i\left(p\right)}{\&PartialD;p}\&times;c_{\mathrm{lrp}}^{2,i}\\ +\underset{i=1}{\overset{N_3}{\mathrm{\&Sigma;}}}\frac{{\&PartialD;h}_i\left(p\right)}{\&PartialD;p}\&times;c_{\mathrm{lrp}}^{3,i}\\ +\underset{i=1}{\overset{N_2}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{N_3}{\mathrm{\&Sigma;}}}\frac{\&PartialD;\left(g_i\left(p\right)h_j\left(p\right)\right)}{\&PartialD;p}\&times;c_{\mathrm{lrp}}^{4,\mathrm{ij}}\end{array}\right\}{v}_{l0}---\left(10\right)$

$\frac{{\&PartialD;y}_k^T}{\&PartialD;p}=\underset{\underset{l\&NotEqual;r,\&CenterDot;\&CenterDot;\&CenterDot;,r+m-1}{l=1}}{\overset{n}{\mathrm{\&Sigma;}}}\underset{p=1}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&beta;}}_{\mathrm{kp}}\left\{\begin{array}{c}\underset{i=1}{\overset{N_1}{\mathrm{\&Sigma;}}}\frac{{\&PartialD;f}_i\left(p\right)}{\&PartialD;p}\&times;d_{\mathrm{lrp}}^{1,i}\\ +\underset{i=1}{\overset{N_2}{\mathrm{\&Sigma;}}}\frac{{\&PartialD;g}_i\left(p\right)}{\&PartialD;p}\&times;d_{\mathrm{lrp}}^{2,i}\\ +\underset{i=1}{\overset{N_3}{\mathrm{\&Sigma;}}}\frac{{\&PartialD;h}_i\left(p\right)}{\&PartialD;p}\&times;d_{\mathrm{lrp}}^{3,i}\\ +\underset{i=1}{\overset{N_2}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{N_3}{\mathrm{\&Sigma;}}}\frac{\&PartialD;\left(g_i\left(p\right)h_j\left(p\right)\right)}{\&PartialD;p}\&times;d_{\mathrm{lrp}}^{4,\mathrm{ij}}\end{array}\right\}{v}_{l0}^T---\left(11\right)$

Wherein, in the formula (9) Represent solution matrix Eigenvalue problem, Δ A _SysBe the variable quantity of the micro-grid system state matrix that causes of perturbation of control parameter p,

V _R0Be respectively left eigenvector matrix and right eigenvectors matrix that the corresponding proper vector of multiple eigenvalue forms; The factor alpha that relates in the formula (10) (11) _Kp, β _KpCan in the process of finding the solution formula (9) eigenvalue problem, obtain coefficient

Find the solution as follows:

$c_{\mathrm{lrp}}^{1,i}=\frac{-u_{l0}^T{M}_{1,i}{v}_{r0}^{\left(p\right)}}{{\mathrm{\&lambda;}}_{l0}-{\mathrm{\&lambda;}}_{r0}}$ $d_{\mathrm{lrp}}^{1,i}=\frac{-v_{l0}^T{M}_{1,i}^T{u}_{r0}^{\left(p\right)}}{{\mathrm{\&lambda;}}_{l0}-{\mathrm{\&lambda;}}_{\mathrm{<figure-callout\; id="0"\; label="r"\; filenames="HDA00002436889000022.png"\; state="\{\{state\}\}">r</figure-callout>}0}}$

$c_{\mathrm{lrp}}^{2,i}=\frac{-u_{l0}^T{M}_{2,i}{v}_{r0}^{\left(p\right)}}{{\mathrm{\&lambda;}}_{l0}-{\mathrm{\&lambda;}}_{r0}}$ $d_{\mathrm{lrp}}^{2,i}=\frac{-v_{l0}^T{M}_{2,i}^T{u}_{r0}^{\left(p\right)}}{{\mathrm{\&lambda;}}_{l0}-{\mathrm{\&lambda;}}_{\mathrm{<figure-callout\; id="0"\; label="r"\; filenames="HDA00002436889000022.png"\; state="\{\{state\}\}">r</figure-callout>}0}}$

$c_{\mathrm{lrp}}^{3,i}=\frac{-u_{l0}^T{M}_{3,i}{v}_{r0}^{\left(p\right)}}{{\mathrm{\&lambda;}}_{l0}-{\mathrm{\&lambda;}}_{r0}}$ $d_{\mathrm{lrp}}^{3,i}=\frac{-v_{l0}^T{M}_{3,i}^T{u}_{r0}^{\left(p\right)}}{{\mathrm{\&lambda;}}_{l0}-{\mathrm{\&lambda;}}_{\mathrm{<figure-callout\; id="0"\; label="r"\; filenames="HDA00002436889000022.png"\; state="\{\{state\}\}">r</figure-callout>}0}}$

$c_{\mathrm{lrp}}^{4,\mathrm{ij}}=\frac{-u_{l0}^T{M}_{4,\mathrm{ij}}{v}_{r0}^{\left(p\right)}}{{\mathrm{\&lambda;}}_{l0}-{\mathrm{\&lambda;}}_{r0}}$ $d_{\mathrm{lrp}}^{4,\mathrm{ij}}=\frac{-v_{l0}^T{M}_{4,\mathrm{ij}}^T{u}_{r0}^{\left(p\right)}}{{\mathrm{\&lambda;}}_{l0}-{\mathrm{\&lambda;}}_{\mathrm{<figure-callout\; id="0"\; label="r"\; filenames="HDA00002436889000022.png"\; state="\{\{state\}\}">r</figure-callout>}0}}$

104: the micro-grid system isolated eigenvalue is carried out eigenwert and corresponding eigenvector sensibility calculating.

As follows respectively to the sensitivity of control parameter p with the corresponding eigenwert of isolated eigenvalue and proper vector that Perturbation is found the solution:

$\frac{{\&PartialD;\mathrm{\&lambda;}}_k}{\&PartialD;p}=\underset{i=1}{\overset{N_1}{\mathrm{\&Sigma;}}}\frac{{\&PartialD;f}_i\left(p\right)}{\&PartialD;p}\&times;{\mathrm{\&lambda;}}_{k1}^{1,i}+\underset{i=1}{\overset{N_2}{\mathrm{\&Sigma;}}}\frac{{\&PartialD;g}_i\left(p\right)}{\&PartialD;p}\&times;{\mathrm{\&lambda;}}_{k1}^{2,i}+\underset{i=1}{\overset{N_3}{\mathrm{\&Sigma;}}}\frac{{\&PartialD;h}_i\left(p\right)}{\&PartialD;p}{\mathrm{\&lambda;}}_{k1}^{3,i}+\underset{i=1}{\overset{N_2}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{N_3}{\mathrm{\&Sigma;}}}\frac{\&PartialD;\left(g_i\left(p\right)h_j\left(p\right)\right)}{\&PartialD;p}\&times;{\mathrm{\&lambda;}}_{k1}^{4,\mathrm{ij}}---\left(12\right)$

$\frac{{\&PartialD;v}_k}{\&PartialD;p}=\underset{\underset{l\&NotEqual;k}{l=1}}{\overset{n}{\mathrm{\&Sigma;}}}\left\{\begin{array}{c}\underset{i=1}{\overset{N_1}{\mathrm{\&Sigma;}}}\frac{{\&PartialD;f}_i\left(p\right)}{\&PartialD;p}\&times;a_{\mathrm{lk}}^{1,i}+\underset{i=1}{\overset{N_2}{\mathrm{\&Sigma;}}}\frac{{\&PartialD;g}_i\left(p\right)}{\&PartialD;p}\&times;a_{\mathrm{lk}}^{2,i}\\ +\underset{i=1}{\overset{N_3}{\mathrm{\&Sigma;}}}\frac{{\&PartialD;h}_i\left(p\right)}{\&PartialD;p}\&times;a_{\mathrm{lk}}^{3,i}+\underset{i=1}{\overset{N_2}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{N_3}{\mathrm{\&Sigma;}}}\frac{\&PartialD;\left(g_i\left(p\right)h_j\left(p\right)\right)}{\&PartialD;p}\&times;a_{\mathrm{lk}}^{4,\mathrm{ij}}\end{array}\right\}{v}_{l0}---\left(13\right)$

$\frac{{\&PartialD;u}_k^T}{\&PartialD;p}=\underset{\underset{l\&NotEqual;k}{l=1}}{\overset{n}{\mathrm{\&Sigma;}}}\left\{\begin{array}{c}\underset{i=1}{\overset{N_1}{\mathrm{\&Sigma;}}}\frac{{\&PartialD;f}_i\left(p\right)}{\&PartialD;p}\&times;b_{\mathrm{lk}}^{1,i}+\underset{i=1}{\overset{N_2}{\mathrm{\&Sigma;}}}\frac{{\&PartialD;g}_i\left(p\right)}{\&PartialD;p}\&times;b_{\mathrm{lk}}^{2,i}\\ +\underset{i=1}{\overset{N_3}{\mathrm{\&Sigma;}}}\frac{{\&PartialD;h}_i\left(p\right)}{\&PartialD;p}\&times;b_{\mathrm{lk}}^{3,i}+\underset{i=1}{\overset{N_2}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{N_3}{\mathrm{\&Sigma;}}}\frac{\&PartialD;\left(g_i\left(p\right)h_j\left(p\right)\right)}{\&PartialD;p}\&times;b_{\mathrm{lk}}^{4,\mathrm{ij}}\end{array}\right\}{u}_{l0}^T---\left(14\right)$

In the formula (12)

As follows respectively:

${\mathrm{\&lambda;}}_{k1}^{1,i}=u_{k0}^T{M}_{1,i}{v}_{\mathrm{<figure-callout\; id="0"\; label="k"\; filenames="HDA00002436889000022.png"\; state="\{\{state\}\}">k</figure-callout>}0}$ ${\mathrm{\&lambda;}}_{k1}^{2,i}=u_{k0}^T{M}_{2,i}{v}_{\mathrm{<figure-callout\; id="0"\; label="k"\; filenames="HDA00002436889000022.png"\; state="\{\{state\}\}">k</figure-callout>}0}$

${\mathrm{\&lambda;}}_{k1}^{3,i}=u_{k0}^T{M}_{3,i}{v}_{\mathrm{<figure-callout\; id="0"\; label="k"\; filenames="HDA00002436889000022.png"\; state="\{\{state\}\}">k</figure-callout>}0}$ ${\mathrm{\&lambda;}}_{k1}^{4,\mathrm{ij}}=u_{k0}^T{M}_{4,\mathrm{ij}}{\mathrm{<figure-callout\; id="0"\; label="v\; k"\; filenames="HDA00002436889000022.png"\; state="\{\{state\}\}">v</figure-callout>}}_k$

Undetermined coefficient in the formula (13) (14)

As follows respectively:

$a_{\mathrm{lk}}^{1,i}=\frac{-u_{l0}^T{M}_{1,i}{v}_{\mathrm{<figure-callout\; id="0"\; label="k"\; filenames="HDA00002436889000022.png"\; state="\{\{state\}\}">k</figure-callout>}0}}{{\mathrm{\&lambda;}}_{l0}-{\mathrm{\&lambda;}}_{k0}}$ $b_{\mathrm{lk}}^{1,i}=\frac{-v_{l0}^T{M}_{1,i}^T{u}_{\mathrm{<figure-callout\; id="0"\; label="k"\; filenames="HDA00002436889000022.png"\; state="\{\{state\}\}">k</figure-callout>}0}}{{\mathrm{\&lambda;}}_{l0}-{\mathrm{\&lambda;}}_{\mathrm{<figure-callout\; id="0"\; label="k"\; filenames="HDA00002436889000022.png"\; state="\{\{state\}\}">k</figure-callout>}0}}$

$a_{\mathrm{lk}}^{2,i}=\frac{-u_{l0}^T{M}_{2,i}{v}_{\mathrm{<figure-callout\; id="0"\; label="k"\; filenames="HDA00002436889000022.png"\; state="\{\{state\}\}">k</figure-callout>}0}}{{\mathrm{\&lambda;}}_{l0}-{\mathrm{\&lambda;}}_{k0}}$ $b_{\mathrm{lk}}^{2,i}=\frac{-v_{l0}^T{M}_{2,i}^T{u}_{\mathrm{<figure-callout\; id="0"\; label="k"\; filenames="HDA00002436889000022.png"\; state="\{\{state\}\}">k</figure-callout>}0}}{{\mathrm{\&lambda;}}_{l0}-{\mathrm{\&lambda;}}_{\mathrm{<figure-callout\; id="0"\; label="k"\; filenames="HDA00002436889000022.png"\; state="\{\{state\}\}">k</figure-callout>}0}}$

$a_{\mathrm{lk}}^{3,i}=\frac{-u_{l0}^T{M}_{3,i}{v}_{\mathrm{<figure-callout\; id="0"\; label="k"\; filenames="HDA00002436889000022.png"\; state="\{\{state\}\}">k</figure-callout>}0}}{{\mathrm{\&lambda;}}_{l0}-{\mathrm{\&lambda;}}_{k0}}$ $b_{\mathrm{lk}}^{3,i}=\frac{-v_{l0}^T{M}_{3,i}^T{u}_{\mathrm{<figure-callout\; id="0"\; label="k"\; filenames="HDA00002436889000022.png"\; state="\{\{state\}\}">k</figure-callout>}0}}{{\mathrm{\&lambda;}}_{l0}-{\mathrm{\&lambda;}}_{\mathrm{<figure-callout\; id="0"\; label="k"\; filenames="HDA00002436889000022.png"\; state="\{\{state\}\}">k</figure-callout>}0}}$

$a_{\mathrm{lk}}^{4,\mathrm{ij}}=\frac{-u_{l0}^T{M}_{4,\mathrm{ij}}{\mathrm{<figure-callout\; id="0"\; label="v\; k"\; filenames="HDA00002436889000022.png"\; state="\{\{state\}\}">v</figure-callout>}}_k}{{\mathrm{\&lambda;}}_{l0}-{\mathrm{\&lambda;}}_{k0}}$ $b_{\mathrm{lk}}^{4,\mathrm{ij}}=\frac{-v_{l0}^T{M}_{2,\mathrm{ij}}^T{u}_{\mathrm{<figure-callout\; id="0"\; label="k"\; filenames="HDA00002436889000022.png"\; state="\{\{state\}\}">k</figure-callout>}0}}{{\mathrm{\&lambda;}}_{l0}-{\mathrm{\&lambda;}}_{\mathrm{<figure-callout\; id="0"\; label="k"\; filenames="HDA00002436889000022.png"\; state="\{\{state\}\}">k</figure-callout>}0}}$

Be described in detail below in conjunction with the method for solving of concrete embodiment to the sensitivity of a kind of little electrical network characteristic solution:

In order to realize and to verify the little electrical network characteristic solution sensitivity method for solving based on Matrix Perturbation that this paper proposes, carry out characteristic solution Calculation of Sensitivity and data analysis as an example of low pressure micro-grid system shown in Figure 1 example.But dependency structure and the parameter lists of references [7] such as the circuit in the system, load, distributed power source and control system thereof, the situation of exerting oneself of each node access distributed power source is as shown in table 1 in the system.

The distributed power source of each node of the table 1 access situation of exerting oneself

For the low pressure micro-grid system of studying, under starting condition, carry out successively trend calculating, state initialization, and by QR Algorithm for Solving system features value, as shown in Figure 2.After obtaining the system features solution, the perturbed solution of eigenwert when perturbation occurs calculating parameter, and compare with Exact Solutions is in order to provide the basis for the accurate calculating of sensitivity.What Fig. 3 provided is when+1% perturbation occurs the meritorious droop control coefficient of L17 node accumulator, the Exact Solutions of system features value and the contrast situation between the perturbed solution.

By calculate between Exact Solutions and the perturbed solution related coefficient as can be known, its numerical value is 0.9999, is in close proximity to 1.0, this perturbed solution of having verified eigenwert can match with Exact Solutions preferably, thereby lays a good foundation for the accurate calculating of sensitivity.Choose successively afterwards some parameters of some distributed power sources in the little electrical network of example and inverter control system thereof, computation of characteristic values is to the sensitivity of these control parameters.These perturbation parameters comprise L14 Nodes fuel cell parameters K _Pp, L16 Nodes photovoltaic cell parameter K _P, L17 Nodes accumulator droop control parameter K _i, the definition list of references of these parameters ^[7]The eigenwert of considering the little electrical network of example is more, and table 2 has only provided the Calculation of Sensitivity result of the relative above-mentioned parameter of partial feature value.Consider that analytical method sensitivity numerous and diverse being difficult for of deriving comparatively find the solution, data are respectively to adopt Eigenvalue Sensitivity and the contrast situation thereof of method of perturbation (the correlation parameter disturbance quantity is 1%) and Perturbation Method in the table.

The exact value of table 2 Eigenvalue Sensitivity and the contrast of perturbation value

As known from Table 2, the Eigenvalue Sensitivity of this method (perturbation method) gained can match with method of perturbation result of calculation preferably, and relative error is less, and this has verified validity and the accuracy of Matrix perturbation in Calculation of Sensitivity.And this method can only be carried out sensitivity analysis for crucial mode, has simplified the solution procedure of sensitivity.Similar with the parametric sensitivity computing method of eigenwert, also can utilize the parametric sensitivity of perturbation method calculated characteristics vector.

List of references

[1]R.H.Lasseter,A.Akhil,C.Marnay,J.Stephens,J.Dagle,R.Guttromson,A.Meliopoulous,R.Yinger,and J.Eto,“The CERTS microgrid concept,white paper onintegration of distributed energy resources,”LBNL-50829,California Energy Comm.,Office of Power Technologies-U.S.Dept.Energy,Apr.2002.[Online].Available:http://certs.lbl.gov

[2] Wang Chengshan, Li Peng. development and the challenge of distributed power generation, little electrical network and intelligent distribution network. Automation of Electric Systems, 2010,34 (2): 10-14,23.

[3]E.Barklund,N.Pogaku,M.Prodanovic,C.Hernandez-Aramburo,and T.C.Green,“Energy management in autonomous microgrid using stability-constraineddroop control of inverters,”IEEE Trans.Power Electron.,vol.23,no.5,pp.2346–2352,Sep.2008.

[4]R.H.Lasseter,“Control and design of microgrid components,”PSERC,Tempe,AZ,PSERC Publication 06-03,Jan.2006.

[5] Luo Jian. the theoretical introduction of system sensitivity. Beijing: Science Press, 1990.

[6] Miao Fengxian, Guo Zhizhong. sensitivity method is summarized in Power System Analysis and the application in the control. relay, 2007,35 (15): 72-76.

[7] Peng Ke, Wang Chengshan, Li Yan etc. the little electrical network example of typical mesolow system. Automation of Electric Systems, 2011,35 (18): 31-35.

It will be appreciated by those skilled in the art that accompanying drawing is the schematic diagram of a preferred embodiment, the invention described above embodiment sequence number does not represent the quality of embodiment just to description.

The above only is preferred embodiment of the present invention, and is in order to limit the present invention, within the spirit and principles in the present invention not all, any modification of doing, is equal to replacement, improvement etc., all should be included within protection scope of the present invention.

Claims (3)

1. the method for solving of little electrical network characteristic solution sensitivity is characterized in that, said method comprising the steps of:

1) state matrix of structure micro-grid system;

The state matrix of 2) finding the solution micro-grid system obtains the micro-grid system eigenwert; Whether repeat according to eigenwert, the micro-grid system eigenwert is classified;

3) the micro-grid system multiple eigenvalue is carried out eigenwert and corresponding eigenvector sensibility calculating;

4) the micro-grid system isolated eigenvalue is carried out eigenwert and corresponding eigenvector sensibility calculating.

2. the method for solving of a kind of little electrical network characteristic solution according to claim 1 sensitivity is characterized in that, the state matrix of described structure micro-grid system is specially:

1) obtains the original state matrix of micro-grid system;

A _sys=A-BD ^-1C (1)

Wherein, A is that the state equation of little electrical network is to the partial derivative matrix of state variable; B is that the state equation of little electrical network is to the partial derivative matrix of algebraically variable; C is that the algebraic equation of little electrical network is to the partial derivative matrix of state variable; D is that the algebraic equation of little electrical network is to the partial derivative matrix of algebraically variable;

2) the original state matrix of micro-grid system is controlled the perturbation analysis of parameter p;

$A=\underset{i=1}{\overset{N_1}{\mathrm{\&Sigma;}}}{f}_i\left(p\right)\&times;A_i+\stackrel{\&OverBar;}{A}---\left(2\right)$

$B=\underset{i=1}{\overset{N_2}{\mathrm{\&Sigma;}}}{g}_i\left(p\right)\&times;B_i+\stackrel{\&OverBar;}{B}---\left(3\right)$

$C=\underset{i=1}{\overset{N_3}{\mathrm{\&Sigma;}}}{h}_i\left(p\right)\&times;C_i+\stackrel{\&OverBar;}{C}---\left(4\right)$

In the formula, A _i, B _i, C _i,

Be constant matrices; f _i(p), g _i(p), h _i(p) function of representative control parameter p; N ₁, N ₂, N ₃Represent respectively the number of above-mentioned constant matrices;

3) the state matrix A of structure micro-grid system _Sys(p);

$A_{\mathrm{sys}}\left(p\right)=M_0+\underset{i=1}{\overset{N_1}{\mathrm{\&Sigma;}}}{f}_i\left(p\right)\&times;M_{1,i}+\underset{i=1}{\overset{N_2}{\mathrm{\&Sigma;}}}{g}_i\left(p\right)\&times;M_{2,i}+\underset{i=1}{\overset{N_3}{\mathrm{\&Sigma;}}}{h}_i\left(p\right)\&times;M_{3,i}+\underset{i=1}{\overset{N_2}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{N_3}{\mathrm{\&Sigma;}}}{g}_i\left(p\right)\&times;h_j\left(p\right)\&times;M_{4,\mathrm{ij}}---\left(5\right)$

In the formula, M ₀, M _{1, i}, M _{2, i}, M _{3, i}, M _{4, ij}As follows respectively, be the constant matrices irrelevant with controlling parameter p;

$\begin{array}{cccc}& M_0=\stackrel{\&OverBar;}{A}-\stackrel{\&OverBar;}{B}{D}^{-1}\stackrel{\&OverBar;}{C}& M_{1,i}=A_i& \\ M_{2,i}=-B_i{D}^{-1}\stackrel{\&OverBar;}{C}& M_{3,i}=-\stackrel{\&OverBar;}{B}{D}^{-1}{C}_i& & M_{4,\mathrm{ij}}=-B_i{D}^{-1}{C}_j\end{array}.$

3. the method for solving of a kind of little electrical network characteristic solution according to claim 1 sensitivity is characterized in that, described state matrix of finding the solution micro-grid system obtains the micro-grid system eigenwert; Whether repeat according to eigenwert, the micro-grid system eigenwert is classified is specially:

The state matrix of 1) finding the solution micro-grid system obtains the eigenwert of micro-grid system;

$\left\{\begin{array}{c}{A}_{\mathrm{sys}}{v}_i={\mathrm{\&lambda;}}_i{v}_i\\ u_i^T{A}_{\mathrm{sys}}=u_i^T{\mathrm{\&lambda;}}_i\end{array}\right.---\left(6\right)$

In the formula, λ _iBe i eigenwert of micro-grid system, v _i,

Be respectively right proper vector and the left eigenvector corresponding with eigenwert;

2) whether repeat according to eigenwert in the micro-grid system, it is divided into micro-grid system multiple eigenvalue and isolated eigenvalue.

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