CN103474992A - Real-time on-line identification criterion of electric system node voltage steady state - Google Patents

Abstract

The invention discloses a real-time on-line identification criterion method of an electric system node voltage steady state. After a PMU conducts sampling every time, a voltage stabilization discrimination result is computed in real time, where each discrimination comprises the following steps that 1), data collection and processing are conducted; 2) tracking calculation is conducted on Thevenin equivalent parameters; (3) according to a simple power network obtained through the present Thevenin equivalent parameters, a differential state equation of a node voltage dynamic trajectory is computed and described; (4) a voltage steady state on-line identification criterion of a node to be analyzed is obtained. The real-time on-line identification criterion method of the electric system node voltage steady state achieves voltage steady state on-line identification of the node to be analyzed is obtained by means of PMU measurement data.

Description

The real-time online identification criterion of Electric Power System Node Voltage stable state

Technical field

The invention belongs to voltage stability and differentiate field, be specifically related to a kind of real-time online identification criterion of the stable state of the node voltage for electric power system.

Background technology

The voltage stability problem is that operation produces a large class key issue of significant impact to power system stability.But because the voltage stability problem of system can only be embodied by each node voltage unstability in system, therefore the stability status identification difficulty of node voltage is large, even and adopt existing Voltage Instability basis for estimation, almost after voltage collapses fully, could judge Voltage Instability, and can't be in advance in best control, implement corresponding Voltage Stability Control strategy opportunity.Although in recent decades, Chinese scholars are focused on the research to the Voltage Stability Analysis method, have proposed stable analysis theories and the practical methods of multiple voltage, and due to the complexity of Voltage-stabilizing Problems, the research of relevant Voltage-stabilizing Problems is still in development.

Along with phasor measurement unit (PMU) and wide area measurement technology (WideArea Measurement System, WAMS) extensive use in electric power system, measurement by the voltage and current vector to the part important node, according to the system real-time running state, system Dai Weinan equivalent parameters is carried out to the real-time online tracking, for the analysis of voltage stabilization provides extremely beneficial condition.If can utilize the WAMS technology, system is carried out to real-time Dai Weinan equivalence, will be greatly simplify the complexity of calculating, become possibility thereby make voltage stabilization state to each node in electric power system carry out dynamic on-line identification.Once and realize the dynamic on-line identification to the voltage stabilization state of each node in electric power system, the unstability trend of reliable criterion for identification voltage can be provided, just can before the complete unstability of node voltage, take corresponding stability control strategy based on this, this stability to each node voltage in the increase system, thus the security and stability tool that further increases system is of great significance.

Summary of the invention

The invention provides a kind of based on phasor measurement unit (PMU) and wide area measurement technology (WAMS), can instruct electric power system to take effective Voltage Stability Control strategy, improve the node voltage stable state real-time online identification criterion of power system safety and stability.

Voltage stabilization state on-line identification criterion proposed by the invention, along the disturbed track of the node voltage measured by PMU in essence, each PMU sampling time section at disturbed track, the primary voltage differential equation is carried out to dynamic linearisation, and obtain dynamically the singular point after linearisation, when the dynamic singular point type of trying to achieve is saddle point, decision-making system voltage has unsure state.

Electric Power System Node Voltage stable state real-time online identification criterion of the present invention calculates in real time a voltage stability distinguishing result in each PMU sampling process, and each differentiation comprises the steps:

1) data acquisition and processing (DAP): obtain amplitude, the phase angle of voltage and current of the node to be analyzed of PMU Real-time Collection, and active power and the reactive power of node output, and data are processed accordingly;

2) tracking of Dai Weinan equivalent parameters is calculated: the Dai Weinan equivalent parameters calculated according to last PMU sampling, and this sampling node voltage and the current data that obtain, calculate this sampling node Dai Weinan equivalent parameters;

3) calculate the differential state equation of description node voltage dynamic trajectory: the simple electric power networks obtained according to this sampling Dai Weinan equivalence, calculate the differential state equation group of node to be observed, that is after real-time Dai Weinan equivalence the mathematical description of node voltage dynamic trajectory to be observed;

4) calculating voltage stable state on-line identification criterion: according to the mathematical description equation of the node voltage dynamic trajectory to be observed calculated in step 3), whether decision-making system exists dynamic singular point.When there is not dynamic singular point in decision-making system, think that now criterion lost efficacy, the voltage stabilization situation is not decision making within this step sampling period, and provide the criterion disablement signal; When there is dynamic singular point in decision-making system, the mathematical description equation of the node voltage dynamic trajectory to be observed that calculates in step 3) is retained to the dynamic linear processing of track nonlinear characteristic, and the characteristic value of calculating lienarized equation Jacobian matrix, can judge according to the situation of this characteristic value real part the stability state of this sampling step length interior nodes voltage: if the characteristic value real part for just, predicate node voltage has unstable trend; If the characteristic value real part is negative, the predicate node voltage stabilization;

In step 1) of the present invention, the concrete grammar of node relevant data acquisition to be analyzed and processing is:

Obtain the real-time sampling data of node PMU to be analyzed, the amplitude, the phase angle that comprise node voltage and electric current, and active power and the reactive power of node output, and take electric current as reference vector, even the electric current phase angle is 0, thereby calculate the voltage phase angle under this reference system, for using in calculation procedure after this.

The step 2 of the inventive method), in, the concrete steps that real-time tracking calculates the Dai Weinan equivalent parameters are:

21) node voltage that utilizes this PMU sampling to obtain and amplitude, the phase angle of electric current, and amplitude and the angle values of the equivalent electromotive force of Dai Weinan last time estimated after the PMU sampling, calculate the predicted value of this equivalent impedance;

22) the equivalent impedance numerical value doped according to this sampling and the front equivalent impedance numerical value that once sampling calculates, calculate the equivalent electromotive force of this Dai Weinan with respect to previous correction, and then calculation obtains the equivalent electromotive force of this Dai Weinan;

23) utilize step 22) in the equivalent electromotive force of Dai Weinan of this sampling of calculating and amplitude, the phase angle of node voltage and electric current, calculate the numerical value of this equivalent impedance.

In step 3) of the present invention, the concrete grammar that calculates the differential state equation of description node voltage dynamic trajectory is:

The simple electric power networks obtained for the Dai Weinan equivalence, can obtain this network and express formula containing active power and the reactive power of node voltage amplitude to be analyzed and phase angle, the differential state equation group that two expression formulas were asked local derviation to derive to obtain node voltage to the time, that is the nonlinear second-order system of node voltage dynamic trajectory to be observed described, by PMU sampling in step 1) and the node related data and the step 2 that after processing, obtain) in this equation group of Dai Weinan equivalent parameters substitution of this sampling of calculating, important differential state equation while having obtained analysis node voltage stability in step after this.

In step 4) of the present invention, the concrete grammar of calculating voltage stable state on-line identification criterion is:

41) according to the differential state equation of the description node voltage dynamic trajectory calculated in step 3), whether decision-making system exists dynamic singular point.When there is not dynamic singular point in decision-making system, think that now criterion lost efficacy, within this step sampling period, the voltage stabilization situation is not decision making, provide the criterion disablement signal, get back to the judgement that step 1) is prepared next step sampling period; When there is dynamic singular point in decision-making system, continue step 42) to 44) calculating.

42) Taylor expansion is carried out in the differential state equation of the description node voltage dynamic trajectory that calculates in step 3), ignore higher order term, can obtain the differential state equation and describe the linearization of nonlinear system system; 43) consider when initial point is node, focus and saddle point, non linear system is rough system in the initial point field, it is the qualitative variation that the variation of system in the initial point field is unlikely to cause the wire of system, can be in step 42) changed on the basis of the linearized system that obtains, thus obtain the dynamic linear equation of node non-linear voltage track to be analyzed in this sampling period;

44) solution procedure 43) in the characteristic value of the dynamic linear equation Jacobian matrix that obtains, can carry out according to the situation of characteristic value real part the stability state of decision node voltage: if the characteristic value real part for just, predicate node voltage has unstable trend; If the characteristic value real part is negative, the predicate node voltage stabilization.

Compared with prior art, the present invention has the following advantages:

(1) institute of the present invention extracting method is the disturbed track along system, according to the dynamic saddle point occurred in track, comes decision-making system voltage to have unsure state.And in the disturbed track of system, comprised in real system and actual disturbance that sometimes become and impact non-linear factor, dynamic behaviour that can the disturbed real process of complete reflection system.

(2) owing to introducing the real-time equivalent method of Dai Weinan, make this criterion data used PMU data based on node to be determined fully, as long as obtain in real time voltage, the current data of Nodes PMU, can carry out equivalence to system in real time and form the voltage derivative equation, and in real time this node voltage stable state be carried out to identification based on the voltage dynamic trajectory.Therefore it is easy that this criterion has access, the advantage that independence is strong;

(3) the dynamic electric voltage differential equation that the Dai Weinan equivalence of this criterion based on retaining the substitutional resistance parameter forms afterwards, the type of the dynamic singular point of employing based on disturbed track is as the identification foundation, there is ripe stable theory support, thereby guaranteed the accuracy of voltage stabilization state on-line identification criterion result, and this criterion is applicable in electric power system under any disturbance type, the voltage stabilization situation identification of any node;

(4) this criterion method is simple, independence is strong, be convenient to modularization and embed various systems, can accomplish, with the frequency of PMU sampling, the voltage stabilization situation of place node is carried out to real-time on-line identification, not gathered by the PMU of system scale and other nodes or the impact of the voltage stabilization state on-line identification criterion of other Nodes;

(5) section unified time based on the PMU data acquisition due to this criterion, a plurality of nodes result that the independent utility criterion draws respectively can be fully utilized, and then be able to real-time analysis and go out inner link and the instability Mechanism that each node voltage has unstability trend in succession, therefore this criterion possesses the ability of each node voltage unstability inner link of certain exposing system and mechanism, and then can provide real-time control reference information for the control measure of prevention Voltage Instability.

The accompanying drawing explanation

Fig. 1 is flow chart of the present invention.

Fig. 2 is node Dai Weinan equivalent circuit schematic diagram.

Fig. 3 follows the tracks of the flow chart that calculates the Dai Weinan equivalent parameters in the present invention.

Fig. 4 is simulation example of the present invention 3 machine 10 node systems used.

Fig. 5 is each node voltage and stability criteria curve in example one of the present invention.

Fig. 6 is each node voltage and stability criteria curve in example two of the present invention.

Fig. 7 is each node voltage and stability criteria curve in example three of the present invention.

Fig. 8 is N7 and N9 node voltage curve under situation I and II in example four of the present invention.

Embodiment

Below in conjunction with accompanying drawing, technical scheme of the present invention is described further.The real-time online identification criterion flow process of overall Electric Power System Node Voltage stable state as shown in Figure 1.

1) obtain the voltage and current data of the node to be analyzed of PMU Real-time Collection, and carry out the data processing.

The application of PMU in electric power system is more and more extensive, and its sample frequency commonly used is 50Hz, and sampling step length is very little, is conducive to Real-Time Monitoring Electric Power System Node Voltage stability of the present invention, and provides rational basis for the linearization procedure in the present invention.Amplitude, the phase angle of the voltage and current of the node to be analyzed that Real-time Obtaining PMU sampling of the present invention obtains, and active power and the reactive power of output, and hypothesis electric current phase angle is 0, set up and take the vector space that current vector is reference vector, and then obtain the voltage vector U of node to be analyzed in this sampling _m∠ ψ _m, current vector I _m0 ° of ∠, active power of output P _lwith output reactive power Q _l.Each voltage stabilization criterion is calculated the data that need this this sampled data and last sampling.

2) utilize the data of this sampling, the data of sampling last time and the Dai Weinan equivalent parameters that last time, sampling calculated, real-time tracking calculates the Dai Weinan equivalent parameters of this sampling, and method flow as shown in Figure 3.

21) node Dai Weinan equivalent circuit is shown in Fig. 2, wherein voltage vector U _m∠ ψ _m, current vector I _m0 ° of ∠, active power of output P _lwith output reactive power Q _l, by the PMU acquisition of sampling, be all known quantity, the Dai Weinan equivalent parameters comprises the equivalent electromotive force E of Dai Weinan _th∠ δ, Dai Weinan equivalent impedance R _th+ jX _th, be amount to be asked;

22) use owing to after this sampling, following the tracks of the process need that calculates the Dai Weinan equivalent parameters Dai Weinan equivalent parameters that last time, sampling calculated, therefore the initial time come into operation in criterion, need to choose rational Dai Weinan equivalent parameters initial value, the acquiring method of its initial value is as follows:

${\mathrm{\&delta;}}^0=\frac{1}{2}\&CenterDot;[{\mathrm{\&psi;}}_{\mathrm{<figure-callout\; id="1"\; label="m"\; filenames="131008141721.png,131008141733.png"\; state="\{\{state\}\}">m</figure-callout>}}^1+\arctan \left(\frac{\cos {\mathrm{\&psi;}}_{\mathrm{<figure-callout\; id="1"\; label="m"\; filenames="131008141721.png,131008141733.png"\; state="\{\{state\}\}">m</figure-callout>}}^1}{1+\sin {\mathrm{\&psi;}}_m^1}\right)---\left(1\right)$

${\mathrm{<figure-callout\; id="0"\; label="E\; th"\; filenames="131008141737.png,131008141745.png"\; state="\{\{state\}\}">E</figure-callout>}}_{\mathrm{th}}^{}=\frac{{\mathrm{<figure-callout\; id="1"\; label="U\; m"\; filenames="131008141721.png,131008141733.png"\; state="\{\{state\}\}">U</figure-callout>}}_m^{}\&CenterDot;\cos {\mathrm{\&psi;}}_{\mathrm{<figure-callout\; id="1"\; label="m"\; filenames="131008141721.png,131008141733.png"\; state="\{\{state\}\}">m</figure-callout>}}^1}{\cos {\mathrm{\&delta;}}^0}---\left(2\right)$

${\mathrm{<figure-callout\; id="0"\; label="R\; th"\; filenames="131008141737.png,131008141745.png"\; state="\{\{state\}\}">R</figure-callout>}}_{\mathrm{th}}^{}=\frac{{\mathrm{<figure-callout\; id="0"\; label="E\; th"\; filenames="131008141737.png,131008141745.png"\; state="\{\{state\}\}">E</figure-callout>}}_{\mathrm{th}}^{}\&CenterDot;\cos {\mathrm{\&delta;}}^0-{\mathrm{<figure-callout\; id="1"\; label="U\; m"\; filenames="131008141721.png,131008141733.png"\; state="\{\{state\}\}">U</figure-callout>}}_m^{}\&CenterDot;\cos {\mathrm{\&psi;}}_m^1}{I_m^1}---\left(3\right)$

${\mathrm{<figure-callout\; id="0"\; label="X\; th"\; filenames="131008141737.png,131008141745.png"\; state="\{\{state\}\}">X</figure-callout>}}_{\mathrm{th}}^{}=\frac{{\mathrm{<figure-callout\; id="0"\; label="E\; th"\; filenames="131008141737.png,131008141745.png"\; state="\{\{state\}\}">E</figure-callout>}}_{\mathrm{th}}^{}\&CenterDot;\sin {\mathrm{\&delta;}}^0-{\mathrm{<figure-callout\; id="1"\; label="U\; m"\; filenames="131008141721.png,131008141733.png"\; state="\{\{state\}\}">U</figure-callout>}}_m^{}\&CenterDot;\sin {\mathrm{\&psi;}}_m^1}{I_m^1}---\left(4\right)$

Wherein, footmark " 1 " means sampling for the first time, the initial time that criterion comes into operation;

23) utilize this PMU sampling to obtain

with

value, and estimate after front PMU sampling

and δ ^i-1value calculates the predicted value of this equivalent impedance according to following formula and

$R_{\mathrm{th}}^i{}_{*}=\frac{{E_{\mathrm{th}}}^{i-1}\&CenterDot;\cos {\mathrm{\&delta;}}^{i-1}-U_m^i\&CenterDot;\cos {\mathrm{\&psi;}}_m^i}{I_m^i}---\left(5\right)$

$X_{\mathrm{th}}^i{}_{*}=\frac{E_{\mathrm{th}}^{i-1}\&CenterDot;\sin {\mathrm{\&delta;}}^{i-1}-U_m^i\&CenterDot;\sin {\mathrm{\&psi;}}_m^i}{I_m^i}---\left(6\right)$

Wherein footmark i means the i time sampling;

24) calculate the equivalent electromotive force of Dai Weinan after this sampling

.

At first calculate intermediate variable Dif and ρ:

$\mathrm{Dif}=\left|Z_{\mathrm{th}}^i{}_{*}\right|-\left|Z_{\mathrm{th}}^{i-1}\right|=\sqrt{{\left(R_{\mathrm{th}}^i{}_{*}\right)}^2+{\left(X_{\mathrm{th}}^i{}_{*}\right)}^2}-\sqrt{{\left(R_{\mathrm{th}}^{i-1}\right)}^2+{\left(X_{\mathrm{th}}^{i-1}\right)}^2}---\left(7\right)$

$\mathrm{\&rho;}=\left|\arctan \left(\frac{X_{\mathrm{th}}^i{}_{*}-X_{\mathrm{th}}^{i-1}}{R_{\mathrm{th}}^i{}_{*}-R_{\mathrm{th}}^{i-1}}\right)\right|---\left(8\right)$

And then try to achieve after this sampling the equivalent electromotive force of Dai Weinan with respect to the correction of sampling last time:

If $\frac{U_m^i}{I_m^i}>\frac{U_m^{i-1}}{I_m^{i-1}},$ And Dif>0, $\stackrel{\&RightArrow;}{{\mathrm{\&Delta;E}}_{\mathrm{th}}}=-\mathrm{\&mu;}\&angle;\mathrm{\&rho;};$

If $\frac{U_m^i}{I_m^i}>\frac{U_m^{i-1}}{I_m^{i-1}},$ And Dif<0, $\stackrel{\&RightArrow;}{{\mathrm{\&Delta;E}}_{\mathrm{th}}}=\mathrm{\&mu;}\&angle;\mathrm{\&rho;};$

If $\frac{U_m^i}{I_m^i}<\frac{U_m^{i-1}}{I_m^{i-1}},$ And Dif>0, $\stackrel{\&RightArrow;}{{\mathrm{\&Delta;E}}_{\mathrm{th}}}=\mathrm{\&mu;}\&angle;\mathrm{\&rho;};$

If $\frac{U_m^i}{I_m^i}<\frac{U_m^{i-1}}{I_m^{i-1}},$ And Dif<0, $\stackrel{\&RightArrow;}{{\mathrm{\&Delta;E}}_{\mathrm{th}}}=-\mathrm{\&mu;}\&angle;\mathrm{\&rho;};$

If $\frac{U_m^i}{I_m^i}=\frac{U_m^{i-1}}{I_m^{i-1}},$ $\stackrel{\&RightArrow;}{{\mathrm{\&Delta;E}}_{\mathrm{th}}}=0;$

Thus, can obtain the equivalent electromotive force of Dai Weinan after this sampling according to following formula

and phase angle δ ⁱ:

$\stackrel{\&RightArrow;}{E_{\mathrm{th}}^i}=\stackrel{\&RightArrow;}{E_{\mathrm{th}}^{i-1}}+\stackrel{\&RightArrow;}{{\mathrm{\&Delta;E}}_{\mathrm{th}}}---\left(9\right)$

25) utilize this PMU sampling to obtain with value, and step 24) in this estimates

and δ ⁱbe worth, calculate this equivalent impedance value according to following formula and

$R_{\mathrm{th}}^i=\frac{{E_{\mathrm{th}}}^i\&CenterDot;\cos {\mathrm{\&delta;}}^i-U_m^i\&CenterDot;\cos {\mathrm{\&psi;}}_m^i}{I_m^i}---\left(10\right)$

$X_{\mathrm{th}}^i=\frac{E_{\mathrm{th}}^i\&CenterDot;\sin {\mathrm{\&delta;}}^i-U_m^i\&CenterDot;\sin {\mathrm{\&psi;}}_m^i}{I_m^i}---\left(11\right)$

So far, obtained the tracking result of calculation of the rear Dai Weinan equivalent parameters of this sampling, what deserves to be explained is, step 24) value of the amplitude μ of medium value electromotive force correction, the online equivalent tracking effect of Dai Weinan will directly be affected, its value is too small will cause equivalent tracking velocity excessively slow, thereby can't meet the tracking to large disturbance situation, causes the hysteresis of subsequent voltage unstability judgement; And its value is excessive, can cause equivalent parameters to produce vibration because of overshoot, and then affect the precision of subsequent voltage stable state identification, its value generally should be less than 0.5.Based on the great many of experiments experience, the μ value is 0.05 o'clock, and Dai Weinan online equivalent tracking velocity and precision can reach good balance, can meet the requirement of subsequent voltage stable state on-line identification.

3) node data to be analyzed and the step 2 of utilizing step 1) to gather) follow the tracks of the Dai Weinan equivalent parameters calculated, calculate the differential state equation of description node voltage dynamic trajectory.

The differential state equation of description node voltage dynamic trajectory is as follows:

${\stackrel{.}{U}}_m=\frac{B\&CenterDot;F-D\&CenterDot;E}{B\&CenterDot;C-D\&CenterDot;A}\&CenterDot;\stackrel{.}{\mathrm{\&delta;}}=F_1---\left(12a\right)$

${\stackrel{.}{\mathrm{\&psi;}}}_m=\frac{A\&CenterDot;F-C\&CenterDot;E}{A\&CenterDot;D-C\&CenterDot;B}\&CenterDot;\stackrel{.}{\mathrm{\&delta;}}=F_2---\left(12b\right)$

Wherein,

$A=-\frac{\&PartialD;P_L}{\&PartialD;U_m}+E_{\mathrm{th}}\&CenterDot;G_{\mathrm{th}}\&CenterDot;\cos ({\mathrm{\&psi;}}_m-\mathrm{\&delta;})+E_{\mathrm{th}}\&CenterDot;B_{\mathrm{th}}\&CenterDot;\sin ({\mathrm{\&psi;}}_m-\mathrm{\&delta;})-2\&CenterDot;U_m\&CenterDot;G_{\mathrm{th}}---\left(13a\right)$

$B=-\frac{\&PartialD;P_L}{\&PartialD;{\mathrm{\&psi;}}_m}-U_m\&CenterDot;E_{\mathrm{th}}\&CenterDot;G_{\mathrm{th}}\&CenterDot;\sin ({\mathrm{\&psi;}}_m-\mathrm{\&delta;})+U_m\&CenterDot;E_{\mathrm{th}}\&CenterDot;B_{\mathrm{th}}\&CenterDot;\cos ({\mathrm{\&psi;}}_m-\mathrm{\&delta;})---\left(13b\right)$

$C=-\frac{\&PartialD;Q_L}{\&PartialD;U_m}-E_{\mathrm{th}}\&CenterDot;B_{\mathrm{th}}\&CenterDot;\cos ({\mathrm{\&psi;}}_m-\mathrm{\&delta;})+E_{\mathrm{th}}\&CenterDot;G_{\mathrm{th}}\&CenterDot;\sin ({\mathrm{\&psi;}}_m-\mathrm{\&delta;})+2\&CenterDot;U_n\&CenterDot;B_{\mathrm{th}}---\left(13c\right)$

$D=-\frac{\&PartialD;Q_L}{\&PartialD;{\mathrm{\&psi;}}_m}+U_m\&CenterDot;E_{\mathrm{th}}\&CenterDot;B_{\mathrm{th}}\&CenterDot;\sin ({\mathrm{\&psi;}}_m-\mathrm{\&delta;})+U_m\&CenterDot;E_{\mathrm{th}}\&CenterDot;G_{\mathrm{th}}\&CenterDot;\cos ({\mathrm{\&psi;}}_m-\mathrm{\&delta;})---\left(13d\right)$

$E=\frac{\&PartialD;P_L}{\&PartialD;\mathrm{\&delta;}}-U_m\&CenterDot;E_{\mathrm{th}}\&CenterDot;G_{\mathrm{th}}\&CenterDot;\sin ({\mathrm{\&psi;}}_m-\mathrm{\&delta;})+U_m\&CenterDot;E_{\mathrm{th}}\&CenterDot;B_{\mathrm{th}}\&CenterDot;\cos ({\mathrm{\&psi;}}_m-\mathrm{\&delta;})---\left(13e\right)$

$F=\frac{\&PartialD;Q_L}{\&PartialD;\mathrm{\&delta;}}+U_m\&CenterDot;E_{\mathrm{th}}\&CenterDot;B_{\mathrm{th}}\&CenterDot;\sin ({\mathrm{\&psi;}}_m-\mathrm{\&delta;})+U_m\&CenterDot;E_{\mathrm{th}}\&CenterDot;G_{\mathrm{th}}\&CenterDot;\cos ({\mathrm{\&psi;}}_m-\mathrm{\&delta;})---\left(13f\right)$

In formula (13), $G_{\mathrm{th}}=\frac{R_{\mathrm{<figure-callout\; id="2"\; label="th\; R\; th"\; filenames="131008141733.png,131008141745.png"\; state="\{\{state\}\}">th</figure-callout>}}}{R_{\mathrm{th}}^{}},B_{\mathrm{th}}=\frac{-X_{\mathrm{<figure-callout\; id="2"\; label="th\; R\; th"\; filenames="131008141733.png,131008141745.png"\; state="\{\{state\}\}">th</figure-callout>}}}{R_{\mathrm{th}}^{}}$

The wherein voltage vector U that sampling in step 1) is obtained _m∠ ψ _m, current vector I _m0 ° of ∠, active power of output P _lwith output reactive power Q _l, and step 2) the middle equivalent electromotive force E of the Dai Weinan calculated that follows the tracks of _th∠ δ, Dai Weinan equivalent impedance R _th+ jX _thsubstitution formula (12), can be regarded as to obtain the differential state equation of description node voltage dynamic trajectory.

In step 3), the concrete derivation of differential state equation is as follows:

Simple electric power networks shown in Fig. 2 based on obtaining according to Dai Weinan equivalence in real time, can write out following meritorious and reactive power and express formula:

$\begin{array}{c}{S}_P=-P_L+U_m\&CenterDot;E_{\mathrm{th}}\&CenterDot;G_{\mathrm{th}}\&CenterDot;\cos ({\mathrm{\&psi;}}_m-\mathrm{\&delta;})+\\ U_m\&CenterDot;E_{\mathrm{th}}\&CenterDot;B_{\mathrm{th}}\&CenterDot;\sin ({\mathrm{\&psi;}}_m-\mathrm{\&delta;})-{\mathrm{<figure-callout\; id="2"\; label="U\; m"\; filenames="131008141733.png,131008141745.png"\; state="\{\{state\}\}">U</figure-callout>}}_m^{}\&CenterDot;G_{\mathrm{th}}=0\end{array}---\left(14a\right)$

$\begin{array}{c}{S}_Q=-Q_L-U_m\&CenterDot;E_{\mathrm{th}}\&CenterDot;B_{\mathrm{th}}\&CenterDot;\cos ({\mathrm{\&psi;}}_m-\mathrm{\&delta;})+\\ U_m\&CenterDot;E_{\mathrm{th}}\&CenterDot;G_{\mathrm{th}}\&CenterDot;\sin ({\mathrm{\&psi;}}_m-\mathrm{\&delta;})+{\mathrm{<figure-callout\; id="2"\; label="U\; m"\; filenames="131008141733.png,131008141745.png"\; state="\{\{state\}\}">U</figure-callout>}}_m^{}\&CenterDot;B_{\mathrm{th}}=0\end{array}---\left(14b\right)$

Formula (14) is asked to local derviation to time t, can obtain:

$\frac{\&PartialD;S_P}{\&PartialD;t}=\frac{\&PartialD;S_P}{\&PartialD;U_m}\&CenterDot;{\stackrel{.}{U}}_m+\frac{\&PartialD;S_P}{\&PartialD;{\mathrm{\&psi;}}_m}\&CenterDot;{\stackrel{.}{\mathrm{\&psi;}}}_m+\frac{\&PartialD;S_P}{\&PartialD;\mathrm{\&delta;}}\&CenterDot;\stackrel{.}{\mathrm{\&delta;}}=0---\left(15a\right)$

$\frac{\&PartialD;S_Q}{\&PartialD;t}=\frac{\&PartialD;S_Q}{\&PartialD;U_m}\&CenterDot;{\stackrel{.}{U}}_m+\frac{\&PartialD;S_Q}{\&PartialD;{\mathrm{\&psi;}}_m}\&CenterDot;{\stackrel{.}{\mathrm{\&psi;}}}_m+\frac{\&PartialD;S_Q}{\&PartialD;\mathrm{\&delta;}}\&CenterDot;\stackrel{.}{\mathrm{\&delta;}}=0---\left(15b\right)$

Each expression formula in formula (13), in formula (15), can be obtained to equation

$\left[\begin{array}{cc}A& B\\ C& D\end{array}\right]\&CenterDot;\left[\begin{array}{c}{\stackrel{.}{U}}_m\\ {\stackrel{.}{\mathrm{\&psi;}}}_m\end{array}\right]=\left[\begin{array}{c}E\\ F\end{array}\right]\&CenterDot;\stackrel{.}{\mathrm{\&delta;}}---\left(16\right)$

Solve an equation (16) can obtain the differential state equation of the description node voltage dynamic trajectory that formula (12) means, that is after real-time Dai Weinan equivalence the mathematical description of node voltage dynamic trajectory to be observed.

4) according to the mathematical description equation of the node voltage dynamic trajectory to be observed calculated in step 3), whether decision-making system exists dynamic singular point.When there is not dynamic singular point in decision-making system, think that now criterion lost efficacy, the voltage stabilization situation is not decision making within this step sampling period, and provide the criterion disablement signal; When there is dynamic singular point in decision-making system, calculate node voltage stable state on-line identification criterion to be analyzed, this criterion has retained the nonlinear characteristic of node voltage track.

To the non-linear voltage track of the node to be analyzed that forms in step 3), equation (12) carries out dynamic linearisation according to the following formula

$\left[\begin{array}{c}{\stackrel{.}{U}}_m\\ {\stackrel{.}{\mathrm{\&psi;}}}_m\end{array}\right]=\left[\begin{array}{cc}\frac{\&PartialD;{\mathrm{<figure-callout\; id="1"\; label="F"\; filenames="131008141721.png,131008141733.png"\; state="\{\{state\}\}">F</figure-callout>}}_1}{\&PartialD;U_m}& \frac{\&PartialD;{\mathrm{<figure-callout\; id="1"\; label="F"\; filenames="131008141721.png,131008141733.png"\; state="\{\{state\}\}">F</figure-callout>}}_1}{\&PartialD;{\mathrm{\&psi;}}_m}\\ \frac{\&PartialD;{\mathrm{<figure-callout\; id="2"\; label="F"\; filenames="131008141733.png,131008141745.png"\; state="\{\{state\}\}">F</figure-callout>}}_2}{\&PartialD;U_m}& \frac{\&PartialD;{\mathrm{<figure-callout\; id="2"\; label="F"\; filenames="131008141733.png,131008141745.png"\; state="\{\{state\}\}">F</figure-callout>}}_2}{\&PartialD;{\mathrm{\&psi;}}_m}\end{array}\right]\&CenterDot;\left[\begin{array}{c}\mathrm{\&Delta;}{U}_m\\ \mathrm{\&Delta;}{\mathrm{\&psi;}}_m\end{array}\right]---\left(17\right)$

Solve the characteristic value of formula (17) Jacobian matrix, carry out the stability state of decision node voltage according to the situation that solves the characteristic value real part: if the characteristic value real part for just, predicate node voltage has unstable trend; If the characteristic value real part is negative, the predicate node voltage stabilization.So far obtained the voltage stabilization real-time online identification criterion of the rear node to be analyzed of this sampling.

Need the mathematical description equation according to the node voltage dynamic trajectory to be observed calculated in step 3) in step 4), whether decision-making system exists the reason of dynamic singular point to be: when system is subject to violent disturbance and system configuration generation great variety, this time etching system do not have equilibrium state.The singular point that now the disturbed track of system is carried out obtaining after dynamic linear in the sampling step length of PMU does not exist yet.And criterion that the present invention carries must exist under the prerequisite of singular point satisfied, could be according to the character judgement voltage stabilization state of characteristic value.Therefore before the result of determination that provides the voltage stabilization state, need decision-making system whether to have dynamic singular point.Whether decision-making system exists the method for dynamic singular point as follows:

In step 3), obtained the nonlinear second-order system of the description node voltage dynamic trajectory to be observed shown in formula (12), that is:

${\stackrel{.}{U}}_m=F_1(U_m,{\mathrm{\&psi;}}_m)---\left(18a\right)$

${\stackrel{.}{\mathrm{\&psi;}}}_m=F_2(U_m,{\mathrm{\&psi;}}_m)---\left(18b\right)$

Its poised state, singular point is:

F ₁(U _m,ψ _m)＝0 （19a）

F ₂(U _m,ψ _m)＝0 （19b）

Therefore can be by verification formula (19a) and (19b) whether set up, whether decision-making system exists dynamic singular point.While when formula (19a) and (19b) setting up, there is dynamic singular point in decision-making system; Otherwise there is not dynamic singular point in decision-making system.

In step 4), the differential state equation of non-linear voltage track is carried out to the method for dynamic linear as follows:

Because the stability of linear system is only relevant with the structure and parameter of system itself, therefore, for linear system, can utilize the Liapunov first method, by the root of solving system characteristic equation, just can make the judgement of stability.But for non linear system, its stability is also relevant with the size of the initial condition of system and external disturbance, and the concept of system features root is non-existent.The present invention proposes a kind of dynamic linear method that retains the voltage trace nonlinear characteristic:

Suppose that this second-order system has an isolated singularity can move to this isolated singularity to initial point by coordinate transform:

$\mathrm{\&xi;}=U_m-{\stackrel{\&OverBar;}{U}}_m,\mathrm{\&eta;}={\mathrm{\&psi;}}_m-{\stackrel{\&OverBar;}{\mathrm{\&psi;}}}_m---\left(20\right)$

Relational expression (18a) and (18b) can turn to:

$\stackrel{.}{\mathrm{\&xi;}}=F_1(\mathrm{\&xi;}+{\stackrel{\&OverBar;}{U}}_m,\mathrm{\&eta;}+{\stackrel{\&OverBar;}{\mathrm{\&psi;}}}_m)={{\mathrm{<figure-callout\; id="1"\; label="F"\; filenames="131008141721.png,131008141733.png"\; state="\{\{state\}\}">F</figure-callout>}}_1}^{\&prime;}(\mathrm{\&xi;},\mathrm{\&eta;})---\left(21a\right)$

$\stackrel{.}{\mathrm{\&eta;}}=F_2(\mathrm{\&xi;}+{\stackrel{\&OverBar;}{U}}_m,\mathrm{\&eta;}+{\stackrel{\&OverBar;}{\mathrm{\&psi;}}}_m)={{\mathrm{<figure-callout\; id="2"\; label="F"\; filenames="131008141733.png,131008141745.png"\; state="\{\{state\}\}">F</figure-callout>}}_2}^{\&prime;}(\mathrm{\&xi;},\mathrm{\&eta;})---\left(21b\right)$

Must have:

${{\mathrm{<figure-callout\; id="1"\; label="F"\; filenames="131008141721.png,131008141733.png"\; state="\{\{state\}\}">F</figure-callout>}}_1}^{\&prime;}\left(\mathrm{0,0}\right)=F_1({\stackrel{\&OverBar;}{U}}_m,{\stackrel{\&OverBar;}{\mathrm{\&psi;}}}_m)=0---\left(22a\right)$

${{\mathrm{<figure-callout\; id="2"\; label="F"\; filenames="131008141733.png,131008141745.png"\; state="\{\{state\}\}">F</figure-callout>}}_2}^{\&prime;}\left(\mathrm{0,0}\right)=F_2({\stackrel{\&OverBar;}{U}}_m,{\stackrel{\&OverBar;}{\mathrm{\&psi;}}}_m)=0---\left(22b\right)$

By formula (18a) and (18b) right-hand member carry out Taylor expansion and can obtain:

${\stackrel{.}{U}}_m=\frac{\&PartialD;{\mathrm{<figure-callout\; id="1"\; label="F"\; filenames="131008141721.png,131008141733.png"\; state="\{\{state\}\}">F</figure-callout>}}_1}{\&PartialD;U_m}\&CenterDot;U_m+\frac{\&PartialD;{\mathrm{<figure-callout\; id="1"\; label="F"\; filenames="131008141721.png,131008141733.png"\; state="\{\{state\}\}">F</figure-callout>}}_1}{\&PartialD;{\mathrm{\&psi;}}_m}\&CenterDot;{\mathrm{\&psi;}}_m+h_1(U_m,{\mathrm{\&psi;}}_m)---\left(23a\right)$

${\stackrel{.}{\mathrm{\&psi;}}}_m=\frac{\&PartialD;{\mathrm{<figure-callout\; id="2"\; label="F"\; filenames="131008141733.png,131008141745.png"\; state="\{\{state\}\}">F</figure-callout>}}_2}{\&PartialD;U_m}\&CenterDot;U_m+\frac{\&PartialD;{\mathrm{<figure-callout\; id="2"\; label="F"\; filenames="131008141733.png,131008141745.png"\; state="\{\{state\}\}">F</figure-callout>}}_2}{\&PartialD;{\mathrm{\&psi;}}_m}\&CenterDot;{\mathrm{\&psi;}}_m+h_2(U_m,{\mathrm{\&psi;}}_m)---\left(23b\right)$

H wherein ₁and h ₂u _mand ψ _mhigh-order term, constant term by formula (22a) and (22b) known perseverance be zero, can obtain thus by (18a) and (18b) describing the linearization of nonlinear system system:

${\stackrel{.}{U}}_m=\frac{\&PartialD;{\mathrm{<figure-callout\; id="1"\; label="F"\; filenames="131008141721.png,131008141733.png"\; state="\{\{state\}\}">F</figure-callout>}}_1}{\&PartialD;U_m}\&CenterDot;U_m+\frac{\&PartialD;{\mathrm{<figure-callout\; id="1"\; label="F"\; filenames="131008141721.png,131008141733.png"\; state="\{\{state\}\}">F</figure-callout>}}_1}{\&PartialD;{\mathrm{\&psi;}}_m}\&CenterDot;{\mathrm{\&psi;}}_m---\left(24a\right)$

${\stackrel{.}{\mathrm{\&psi;}}}_m=\frac{\&PartialD;{\mathrm{<figure-callout\; id="2"\; label="F"\; filenames="131008141733.png,131008141745.png"\; state="\{\{state\}\}">F</figure-callout>}}_2}{\&PartialD;U_m}\&CenterDot;U_m+\frac{\&PartialD;{\mathrm{<figure-callout\; id="2"\; label="F"\; filenames="131008141733.png,131008141745.png"\; state="\{\{state\}\}">F</figure-callout>}}_2}{\&PartialD;{\mathrm{\&psi;}}_m}\&CenterDot;{\mathrm{\&psi;}}_m---\left(24b\right)$

Owing to having ignored the higher order term in the non linear system, must consider that the singular point type of initial point of non linear system is whether identical with its singular point type of linearized system, whether can produce distortion.Owing to when initial point being node, focus and saddle point, non linear system is rough system in the initial point field, i.e. the variation of system in the initial point field is unlikely to cause the qualitative variation of the wire of system.This is explanation just, as long as can guarantee only to obtain the phasor of singular point in the small neighbourhood of non linear system singular point, and so in this small neighbourhood scope, just can be according to the former nonlinear system stability of singular point type decision by obtaining after the non linear system linearisation.And the minimum sampling step length of PMU has just guaranteed only to obtain in the small neighbourhood of non linear system singular point the phasor of singular point, so the time can be according to the former nonlinear system stability of singular point type identification by obtaining after the non linear system linearisation.

Based on this principle, can be within the sampling period of each PMU, the non-linear voltage track for the treatment of observer nodes carries out dynamic linearisation according to the following formula, and then obtains the lienarized equation shown in formula (17).And dynamically solve the characteristic value of Jacobian matrix in formula (17), this characteristic value is the voltage trace characteristic value of node to be analyzed in this sampling step length.Thus, can judge according to the situation of this characteristic value real part the stability state of this sampling step length interior nodes voltage: if the characteristic value real part for just, predicate node voltage has unstable trend; If the characteristic value real part is negative, the predicate node voltage stabilization.The circular that solves the characteristic value of Jacobian matrix in formula (17) in step 4) is as follows:

In formula (12)

, and the equivalent rotating speed of the valve systems such as ω sign Dai Weinan, and can think that in less integration step ω is a constant.Therefore formula (17) can be designated as:

$\left[\begin{array}{c}{\stackrel{.}{U}}_m\\ {\stackrel{.}{\mathrm{\&psi;}}}_m\end{array}\right]=\mathrm{\&omega;}\&CenterDot;\left[\begin{array}{cc}\frac{\&PartialD;{\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="131008141721.png,131008141733.png"\; state="\{\{state\}\}">f</figure-callout>}}_1}{\&PartialD;U_m}& \frac{\&PartialD;{\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="131008141721.png,131008141733.png"\; state="\{\{state\}\}">f</figure-callout>}}_1}{\&PartialD;{\mathrm{\&psi;}}_m}\\ \frac{\&PartialD;{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="131008141733.png,131008141745.png"\; state="\{\{state\}\}">f</figure-callout>}}_2}{\&PartialD;U_m}& \frac{\&PartialD;{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="131008141733.png,131008141745.png"\; state="\{\{state\}\}">f</figure-callout>}}_2}{\&PartialD;{\mathrm{\&psi;}}_m}\end{array}\right]\&CenterDot;\left[\begin{array}{c}\mathrm{\&Delta;}{U}_m\\ \mathrm{\&Delta;}{\mathrm{\&psi;}}_m\end{array}\right]---\left(25\right)$

Wherein:

${\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="131008141721.png,131008141733.png"\; state="\{\{state\}\}">f</figure-callout>}}_1=\frac{B\&CenterDot;F-D\&CenterDot;E}{B\&CenterDot;C-D\&CenterDot;A}---\left(26a\right)$

${\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="131008141733.png,131008141745.png"\; state="\{\{state\}\}">f</figure-callout>}}_2=\frac{A\&CenterDot;F-C\&CenterDot;E}{A\&CenterDot;D-C\&CenterDot;B}---\left(26b\right)$

In the middle Jacobian matrix of formula (25), the mathematical derivation of each element is as follows:

$\begin{array}{c}\frac{\&PartialD;{\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="131008141721.png,131008141733.png"\; state="\{\{state\}\}">f</figure-callout>}}_1}{\&PartialD;U_m}=\frac{1}{B\&CenterDot;C-D\&CenterDot;A}\&CenterDot;(\frac{\&PartialD;B}{\&PartialD;U_m}\&CenterDot;F+\frac{\&PartialD;F}{\&PartialD;U_m}\&CenterDot;B-\frac{\&PartialD;D}{\&PartialD;U_m}\&CenterDot;E-\frac{\&PartialD;E}{\&PartialD;U_m}\&CenterDot;D)\\ -\frac{B\&CenterDot;F-D\&CenterDot;E}{{(B\&CenterDot;C-D\&CenterDot;A)}^2}\&CenterDot;(\frac{\&PartialD;B}{\&PartialD;U_m}\&CenterDot;C+\frac{\&PartialD;C}{\&PartialD;U_m}\&CenterDot;B-\frac{\&PartialD;D}{\&PartialD;U_m}\&CenterDot;A-\frac{\&PartialD;A}{\&PartialD;U_m}\&CenterDot;D)\end{array}---\left(27a\right)$

$\begin{array}{c}\frac{\&PartialD;{\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="131008141721.png,131008141733.png"\; state="\{\{state\}\}">f</figure-callout>}}_1}{\&PartialD;{\mathrm{\&psi;}}_m}=\frac{1}{B\&CenterDot;C-D\&CenterDot;A}\&CenterDot;(\frac{\&PartialD;B}{\&PartialD;{\mathrm{\&psi;}}_m}\&CenterDot;F+\frac{\&PartialD;F}{\&PartialD;{\mathrm{\&psi;}}_m}\&CenterDot;B-\frac{\&PartialD;D}{\&PartialD;{\mathrm{\&psi;}}_m}\&CenterDot;E-\frac{\&PartialD;E}{\&PartialD;{\mathrm{\&psi;}}_m}\&CenterDot;D)\\ -\frac{B\&CenterDot;F-D\&CenterDot;E}{{(B\&CenterDot;C-D\&CenterDot;A)}^2}\&CenterDot;(\frac{\&PartialD;B}{\&PartialD;{\mathrm{\&psi;}}_m}\&CenterDot;C+\frac{\&PartialD;C}{\&PartialD;{\mathrm{\&psi;}}_m}\&CenterDot;B-\frac{\&PartialD;D}{\&PartialD;{\mathrm{\&psi;}}_m}\&CenterDot;A-\frac{\&PartialD;A}{\&PartialD;{\mathrm{\&psi;}}_m}\&CenterDot;D)\end{array}---27b)$

$\begin{array}{c}\frac{\&PartialD;{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="131008141733.png,131008141745.png"\; state="\{\{state\}\}">f</figure-callout>}}_2}{\&PartialD;U_m}=\frac{1}{A\&CenterDot;D-C\&CenterDot;B}\&CenterDot;(\frac{\&PartialD;A}{\&PartialD;U_m}\&CenterDot;F+\frac{\&PartialD;F}{\&PartialD;U_m}\&CenterDot;A-\frac{\&PartialD;C}{\&PartialD;U_m}\&CenterDot;E-\frac{\&PartialD;E}{\&PartialD;U_m}\&CenterDot;C)\\ -\frac{A\&CenterDot;F-C\&CenterDot;E}{{(A\&CenterDot;D-C\&CenterDot;B)}^2}\&CenterDot;(\frac{\&PartialD;A}{\&PartialD;U_m}\&CenterDot;D+\frac{\&PartialD;D}{\&PartialD;U_m}\&CenterDot;A-\frac{\&PartialD;C}{\&PartialD;U_m}\&CenterDot;B-\frac{\&PartialD;B}{\&PartialD;U_m}\&CenterDot;C)\end{array}---27c)$

$\begin{array}{c}\frac{\&PartialD;{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="131008141733.png,131008141745.png"\; state="\{\{state\}\}">f</figure-callout>}}_2}{\&PartialD;{\mathrm{\&psi;}}_m}=\frac{1}{A\&CenterDot;D-C\&CenterDot;B}\&CenterDot;(\frac{\&PartialD;A}{\&PartialD;{\mathrm{\&psi;}}_m}\&CenterDot;F+\frac{\&PartialD;F}{\&PartialD;{\mathrm{\&psi;}}_m}\&CenterDot;A-\frac{\&PartialD;C}{\&PartialD;{\mathrm{\&psi;}}_m}\&CenterDot;E-\frac{\&PartialD;E}{\&PartialD;{\mathrm{\&psi;}}_m}\&CenterDot;C)\\ -\frac{A\&CenterDot;F-C\&CenterDot;E}{{(A\&CenterDot;D-C\&CenterDot;B)}^2}\&CenterDot;(\frac{\&PartialD;A}{\&PartialD;{\mathrm{\&psi;}}_m}\&CenterDot;D+\frac{\&PartialD;D}{\&PartialD;{\mathrm{\&psi;}}_m}\&CenterDot;A-\frac{\&PartialD;C}{\&PartialD;{\mathrm{\&psi;}}_m}\&CenterDot;B-\frac{\&PartialD;B}{\&PartialD;{\mathrm{\&psi;}}_m}\&CenterDot;C)\end{array}---\left(27d\right)$

Wherein:

$\frac{\&PartialD;A}{\&PartialD;U_m}=-\frac{{\&PartialD;}^2{P}_L}{\&PartialD;U_m^2}-2\&CenterDot;G_{\mathrm{th}}---\left(28a\right)$

$\frac{\&PartialD;B}{\&PartialD;U_m}=-\frac{{\&PartialD;}^2{P}_L}{\&PartialD;{\mathrm{\&psi;}}_m\&PartialD;U_m}-E_{\mathrm{th}}\&CenterDot;G_{\mathrm{th}}\&CenterDot;\sin ({\mathrm{\&psi;}}_m-\mathrm{\&delta;})+E_{\mathrm{th}}\&CenterDot;B_{\mathrm{th}}\&CenterDot;\cos ({\mathrm{\&psi;}}_m-\mathrm{\&delta;})---\left(28b\right)$

$\frac{\&PartialD;C}{\&PartialD;U_m}=-\frac{{\&PartialD;}^2{Q}_L}{\&PartialD;{\mathrm{<figure-callout\; id="2"\; label="U\; m"\; filenames="131008141733.png,131008141745.png"\; state="\{\{state\}\}">U</figure-callout>}}_m^{}}+2\&CenterDot;B_{\mathrm{th}}---\left(28c\right)$

$\frac{\&PartialD;D}{\&PartialD;U_m}=-\frac{{\&PartialD;}^2{Q}_L}{\&PartialD;{\mathrm{\&psi;}}_m\&PartialD;U_m}+E_{\mathrm{th}}\&CenterDot;B_{\mathrm{th}}\&CenterDot;\sin ({\mathrm{\&psi;}}_m-\mathrm{\&delta;})+E_{\mathrm{th}}\&CenterDot;G_{\mathrm{th}}\&CenterDot;\cos ({\mathrm{\&psi;}}_m-\mathrm{\&delta;})---\left(28d\right)$

$\frac{\&PartialD;E}{\&PartialD;U_m}=-E_{\mathrm{th}}\&CenterDot;G_{\mathrm{th}}\&CenterDot;\sin ({\mathrm{\&psi;}}_m-\mathrm{\&delta;})+E_{\mathrm{th}}\&CenterDot;B_{\mathrm{th}}\&CenterDot;\cos ({\mathrm{\&psi;}}_m-\mathrm{\&delta;})---\left(28e\right)$

$\frac{\&PartialD;F}{\&PartialD;U_m}=E_{\mathrm{th}}\&CenterDot;B_{\mathrm{th}}\&CenterDot;\sin ({\mathrm{\&psi;}}_m-\mathrm{\&delta;})+E_{\mathrm{th}}\&CenterDot;G_{\mathrm{th}}\&CenterDot;\cos ({\mathrm{\&psi;}}_m-\mathrm{\&delta;})---\left(28f\right)$

$\frac{\&PartialD;A}{\&PartialD;{\mathrm{\&psi;}}_m}=-\frac{{\&PartialD;}^2{P}_L}{\&PartialD;U_m\&PartialD;{\mathrm{\&psi;}}_m}-E_{\mathrm{th}}\&CenterDot;G_{\mathrm{th}}\&CenterDot;\sin ({\mathrm{\&psi;}}_m-\mathrm{\&delta;})+E_{\mathrm{th}}\&CenterDot;B_{\mathrm{th}}\&CenterDot;\cos ({\mathrm{\&psi;}}_m-\mathrm{\&delta;})---\left(\text{28g}\right)$

$\frac{\&PartialD;B}{\&PartialD;{\mathrm{\&psi;}}_m}=-\frac{{\&PartialD;}^2{P}_L}{\&PartialD;{\mathrm{\&psi;}}_M^2}-U_m\&CenterDot;E_{\mathrm{th}}\&CenterDot;G_{\mathrm{th}}\&CenterDot;\cos ({\mathrm{\&psi;}}_m-\mathrm{\&delta;})-U_m\&CenterDot;E_{\mathrm{th}}\&CenterDot;B_{\mathrm{th}}\&CenterDot;\sin ({\mathrm{\&psi;}}_m-\mathrm{\&delta;})---\left(28h\right)$

$\frac{\&PartialD;C}{\&PartialD;{\mathrm{\&psi;}}_m}=-\frac{{\&PartialD;}^2{Q}_L}{\&PartialD;U_m\&PartialD;{\mathrm{\&psi;}}_m}+E_{\mathrm{th}}\&CenterDot;B_{\mathrm{th}}\&CenterDot;\sin ({\mathrm{\&psi;}}_m-\mathrm{\&delta;})+E_{\mathrm{th}}\&CenterDot;G_{\mathrm{th}}\&CenterDot;\cos ({\mathrm{\&psi;}}_m-\mathrm{\&delta;})---\left(28i\right)$

$\frac{\&PartialD;D}{\&PartialD;{\mathrm{\&psi;}}_m}=-\frac{{\&PartialD;}^2{Q}_L}{\&PartialD;{\mathrm{\&psi;}}_{\mathrm{<figure-callout\; id="2"\; label="m"\; filenames="131008141733.png,131008141745.png"\; state="\{\{state\}\}">m</figure-callout>}}^2}+U_m\&CenterDot;E_{\mathrm{th}}\&CenterDot;B_{\mathrm{th}}\&CenterDot;\cos ({\mathrm{\&psi;}}_m-\mathrm{\&delta;})-U_m\&CenterDot;E_{\mathrm{th}}\&CenterDot;G_{\mathrm{th}}\&CenterDot;\sin ({\mathrm{\&psi;}}_m-\mathrm{\&delta;})---\left(28j\right)$

$\frac{\&PartialD;E}{\&PartialD;{\mathrm{\&psi;}}_m}=-U_m\&CenterDot;E_{\mathrm{th}}\&CenterDot;G_{\mathrm{th}}\&CenterDot;\cos ({\mathrm{\&psi;}}_m-\mathrm{\&delta;})-U_m\&CenterDot;E_{\mathrm{th}}\&CenterDot;B_{\mathrm{th}}\&CenterDot;\sin ({\mathrm{\&psi;}}_m-\mathrm{\&delta;})---\left(28k\right)$

$\frac{\&PartialD;F}{\&PartialD;{\mathrm{\&psi;}}_m}=U_m\&CenterDot;E_{\mathrm{th}}\&CenterDot;B_{\mathrm{th}}\&CenterDot;\cos ({\mathrm{\&psi;}}_m-\mathrm{\&delta;})-U_m\&CenterDot;E_{\mathrm{th}}\&CenterDot;G_{\mathrm{th}}\&CenterDot;\sin ({\mathrm{\&psi;}}_m-\mathrm{\&delta;})---\left(28l\right)$

Therefore in formula (17), the characteristic value of Jacobian matrix is the characteristic value of Jacobian matrix in formula (25), and then can carry out according to the situation that solves the characteristic value real part stability state of decision node voltage.

Below further illustrate a little of the present invention and beneficial effect with four simulation example.

Emulation is carried out in the Summary of Power System Simulation Software PSCAD/EMTDC, and the emulation system for use in carrying is 3 machine 10 node systems shown in Fig. 4.For the actual effect of simulation PMU sampling, treat the voltage of analysis node with the sample frequency (sample frequency commonly used of PMU) of 50Hz, the amplitude of electric current, phase angle and output are meritorious, the idle sampling.

In this analogue system, G1, G2, G3 all adopt detailed generator model, and wherein G1 has larger inertia coeffeicent, therefore node N1 is balance node; L1 adopts detailed high capacity motor group model, and L2 adopts detailed middle-size and small-size motor cluster model, and L3 adopts a Large Electric group of planes and constant-impedance mixed model, and its ratio is different and different with example; C1, C2, C3 are local reactive power compensator, for reactive power compensation on the spot, so that the place node voltage reaches requirement.

Each generator of system and load initial power parameter are as shown in table 1.Verify that four examples of the present invention are all based on this initial launch state.

Example one: apply the present invention to the Voltage Instability that judgement system side no-power vacancy causes

Load L3 adopts 100% induction-motor load, in the situation that G3 output is idle, has power shortage (about 3MVar) and moves.

For ease of being contrasted and follow-up practical application, voltage stabilization state on-line identification criterion has been carried out to modularized processing, only need real-time input PMU to measure the voltage of a certain node obtained, amplitude and the phase-angle data of electric current, the identification result of the real-time formal output with the digital signal amount of the frequency that this voltage stabilization state on-line identification criterion just can PMU be sampled to this node voltage stable state.That is: when solving the real part that obtains node voltage track characteristic value, be that timing judges that this node voltage has the trend of unstability, the warning pulse signal of criterion output high level; Otherwise criterion keeps low level output signal.

Fig. 5 compared respectively the voltage (curve shown in chain-dotted line) of N5, N7, N8, N9 node in the analogue system and according to the simulation PMU sampled data of each node, analyzed after voltage stabilization state on-line identification criterion result (pulse signal shown in solid line).

As can be seen from Figure 5, the voltage stabilization state on-line identification criterion of N5 node provided first the identification result that voltage has unstability trend in the time of 16.10 seconds, now the voltage perunit value of node N5 is 0.988, and criterion continues to provide voltage and has the signal of unstability trend until the total system voltage collapse afterwards; N7 Nodes criterion is within 0.983 o'clock, to start to continue to judge that voltage has unstability trend in the 13.08th second, node voltage amplitude; N8 and N9 Nodes criterion are 0.825 o'clock respectively at the 16.04th second, node voltage amplitude, and the 16.06th second, node voltage amplitude are within 0.708 o'clock, to start to continue to judge that voltage has unstability trend.

Provide first the Voltage Instability trend alarm signal time from voltage stabilization state on-line identification criterion and be not difficult to find out each node phenomenon of unstability in succession: the N7 node is Voltage Instability at first, then N8 and N9 node voltage unstability, the Voltage Instability of last N5 node.Voltage stabilization state on-line identification criterion simultaneously proposed by the invention has very large lead, near the unstability trend of voltage that even correctly picks out when the node voltage perunit value is still 1.0 had to the anticipation of the trend of Voltage Instability.This is to utilize conventional voltage unstability method of discrimination to realize.

Example two: apply the present invention to differentiate the Voltage Instability that the large disturbance of electric power system causes

For further verifying the performance of this voltage stabilization state on-line identification criterion, in example two, load L3 adopts the mixing load of 50% induction-motor load and 50% constant-impedance load, system is in the time of the 30th second, article five, in interconnection, three-phase shortcircuit earth fault occurs at distance N5 node 80% place in a certain interconnection, and excised the fault interconnection in the time of 30.05 seconds, this large disturbance causes the voltage collapse of system.It is pointed out that the situation while being different from microvariations, in the generation moment of large disturbance, system departs from equilibrium state because being subject to external disturbance, and now criterion is in failure state; In like manner, in the moment of excision faulty line, system also can be subject to external disturbance and depart from equilibrium state, and now criterion is also in failure state; After only having external disturbance to cancel, system roll-back is (poised state herein can be stability or unstable equilibrium state) when poised state, and criterion could be recovered effective status.Fig. 6 has compared node voltage and the voltage stabilization state identification result of N5, N7, N8, N9 node.

From Fig. 6, be not difficult to find out, in the situation that large disturbance and existence mix load bus, voltage stabilization state on-line identification criterion of the present invention still can pick out the stable state of node voltage fast and accurately.Although each node voltage of system is plummeted to very low level within the time of 0.5 second, criterion is within the time of 0.24 second, according to voltage in succession the order of unstability provided the judgement of the Voltage Instability trend of each node in the system, and unstability tendency judgement the earliest is to provide within the time of the rear 0.04s of fault generation, this is also the follow-up reserved time enough of Voltage Stability Control measure.

The time that equally from voltage stabilization state on-line identification criterion, picks out Voltage Instability trend be not difficult to find out each node in succession unstability phenomenon and can analyze its internal relation: when three-phase shortcircuit earth fault occurs on the 30th second in the system interconnection, picked out at first and there is unstability trend in the N7 node of 30.04 seconds N8 nodes nearest from the fault point electrical distance and the interconnection other end, in 30.08 seconds from fault point, the node N5 away from is slightly picked out and is had unstability trend afterwards, and large disturbance causes the Voltage Instability of system side node N5 and N8, final induction-motor load node N9 causes a large amount of reactive power vacancy because of the Voltage Instability of system side, picked out and there is unstability trend in 30.24 seconds.

Example three: apply the present invention to differentiate the Voltage Instability that the load bus power shortage causes

Example one, two verified at system side no-power vacancy or system side node voltage unstability and caused the load unstability, finally causes the performance of voltage stabilization state on-line identification criterion under the failure condition of total system voltage collapse; This example will be in the situation that the load unstability causes its performance of system side node unstability checking.

In this example, load L3 adopts the mixing load of 50% induction-motor load and 50% constant-impedance load, in the 30th second, the load of node N10 place motor cluster is increased to 35%, Fig. 7 and compared the node voltage of each node of system and the identification result of voltage stabilization state on-line identification criterion.

From Fig. 7, be not difficult to find out, voltage stabilization state on-line identification criterion still still approaches and has provided the alarm signal that voltage has unstability trend at 1.0 o'clock at the moment, voltage perunit value very early.Simultaneously due to this criterion based on the nonlinear kinetics Theory of Stability and to accurately equivalence in real time of system, its judgement order has also disclosed the inner link of each node voltage unstability from mechanism: the motor load of N10 Nodes increases the power shortage produced and makes the node N9 that is connected with N10 unstability at first, and make the N8 that is connected with N9 and N6 node unstability in succession, cause another load branch circuit N7 node voltage unstability be connected with N6, and finally make the N5 node voltage unstability of interconnection head end.This result and actual Voltage Instability mechanism fit like a glove.

Example four: the node voltage applied the present invention under the stability criteria guidance is controlled

Above example shows, voltage stabilization state on-line identification criterion proposed by the invention can provide the relation information in succession of each node voltage unstability and for voltage control wins the control time, therefore can carry out effective Voltage Stability Control according to the information of criterion.This example is verified this:, on the basis of example three, contrasted following three kinds of situations:

Situation I: do not take any control measure;

Situation II: according to the identification result of voltage stabilization state on-line identification criterion, in 30.02 seconds, at load bus N9, compensate the idle of 180MVar;

Situation II: not according to the identification result of voltage stabilization state on-line identification criterion, in 30.02 seconds, being both the 13.8KV electric pressure and being both the node N7 of load bus, compensate equally 180MVar idle.

Fig. 8 has contrasted in above three kinds of situations, the voltage curve of load bus N7 and N9.

From Fig. 8, be not difficult to find out: in situation II, the voltage of N7 and N9 can again recover stable after reactive power compensation adds; And contrast situation III, add the reactive power compensation of equivalent in the identical moment after, only, because of the node difference of compensation, the voltage of N7 and N9 is compared any measure (situation I) of not taking, though obtained support to a certain degree, finally still continued to fall until collapse.This shows, according to the identification result of voltage stabilization state on-line identification criterion, respective nodes is carried out to stability control, can receive good effect; And if by the identification result of voltage stabilization state on-line identification criterion, do not controlled, even drop into abundant reactive power compensation in the enough time early, the possibility of result does not still reach the purpose of controlling voltage stabilization.

By this example, verified that control has directive function to voltage stabilization state on-line identification criterion proposed by the invention to node voltage.

Table 1 three machine ten node system generators and load initial power parameter

Claims (4)

1. the real-time online identification criterion method of an Electric Power System Node Voltage stable state, is characterized in that, the method comprises the following steps:

1) data acquisition: obtain the phasor measurement unit PMU Sampling Measurement Data of node to be analyzed, and till the PMU data result of determination generation extremely next time that after data are carried out processing accordingly, this sampling of preservation obtains;

2) tracking of Dai Weinan equivalent parameters is calculated: the Dai Weinan equivalent parameters calculated according to last PMU sampling, and this sampling node voltage and the current data that obtain, calculate this sampling node Dai Weinan equivalent parameters;

3) calculate the differential state equation of description node voltage dynamic trajectory: the simple electric power networks obtained according to this sampling Dai Weinan equivalence, calculate the differential state equation group of node to be observed, that is after real-time Dai Weinan equivalence the mathematical description of node voltage dynamic trajectory to be observed;

4) calculating voltage stable state on-line identification criterion: according to the mathematical description equation of the node voltage dynamic trajectory to be observed calculated in step 3), whether decision-making system exists dynamic singular point,

When there is not dynamic singular point in decision-making system, think that now criterion lost efficacy, the voltage stabilization situation is not decision making within this step sampling period, and provide the criterion disablement signal; When there is dynamic singular point in decision-making system, the mathematical description equation of the node voltage dynamic trajectory to be observed that calculates in step 3) is retained to the dynamic linear processing of track nonlinear characteristic, and the characteristic value of calculating lienarized equation Jacobian matrix, can judge according to the situation of this characteristic value real part the stability state of this sampling step length interior nodes voltage: if the characteristic value real part for just, predicate node voltage has unstable trend; If the characteristic value real part is negative, the predicate node voltage stabilization.

2. according to the real-time online identification criterion method of the Electric Power System Node Voltage stable state described in claim 1, it is characterized in that, in described step 1), the particular content of data acquisition is:

Obtain the real-time sampling data of node PMU to be analyzed, the amplitude, the phase angle that comprise node voltage and electric current, and active power and the reactive power of node output, and take electric current as reference vector, even the electric current phase angle is 0, thereby calculate the voltage phase angle under this reference system, for using in calculation procedure after this.

3. according to the real-time online identification criterion method of the Electric Power System Node Voltage stable state described in claim 1, it is characterized in that, in described step 3), calculate specifically the comprising of differential state equation of description node voltage dynamic trajectory:

The simple electric power networks obtained for the Dai Weinan equivalence, can obtain this network and express formula containing active power and the reactive power of node voltage amplitude to be analyzed and phase angle, the differential state equation group that two expression formulas were asked local derviation to derive to obtain node voltage to the time, that is the nonlinear second-order system of node voltage dynamic trajectory to be observed described, by PMU sampling in step 1) and the node related data and the step 2 that after processing, obtain) in this equation group of Dai Weinan equivalent parameters substitution of this sampling of calculating, important differential state equation while having obtained analysis node voltage stability in step after this.

4. according to the real-time online identification criterion method of the Electric Power System Node Voltage stable state described in claim 1, it is characterized in that, in described step 4), the concrete steps of calculating voltage stable state on-line identification criterion are:

41) according to the differential state equation of the description node voltage dynamic trajectory calculated in step 3), whether decision-making system exists dynamic singular point,

When there is not dynamic singular point in decision-making system, think that now criterion lost efficacy, within this step sampling period, the voltage stabilization situation is not decision making, provide the criterion disablement signal, get back to the judgement that step 1) is prepared next step sampling period; When there is dynamic singular point in decision-making system, continue step 42) to 44) calculating;

42) Taylor expansion is carried out in the differential state equation of the description node voltage dynamic trajectory that calculates in step 3), ignore higher order term, can obtain the differential state equation and describe the linearization of nonlinear system system;

43) consider when initial point is node, focus and saddle point, non linear system is rough system in the initial point field, it is the qualitative variation that the variation of system in the initial point field is unlikely to cause the wire of system, can be in step 42) changed on the basis of the linearized system that obtains, thus obtain the dynamic linear equation of node non-linear voltage track to be analyzed in this sampling period;

44) solution procedure 43) in the characteristic value of the dynamic linear equation Jacobian matrix that obtains, can carry out according to the situation of characteristic value real part the stability state of decision node voltage: if the characteristic value real part for just, predicate node voltage has unstable trend; If the characteristic value real part is negative, the predicate node voltage stabilization.

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