CN104240036A - Transient voltage stability quantitative evaluation method based on equivalent impedance of critical system - Google Patents

Abstract

The invention relates to a transient voltage stability quantitative evaluation method based on equivalent impedance of a critical system. The transient voltage stability quantitative evaluation method based on equivalent impedance of the critical system comprises the following steps of selecting a monitoring bus when a system fails; gaining an equivalent impedance curve and an equivalent potential curve of the system by using the monitoring bus and gaining a state variable and an algebra variable of a direct-current or load dynamic model at the monitoring bus during clearing of fault; establishing an equivalent system model; gaining an equivalent impedance curve of the critical system; and calculating a transient voltage stability quantitative evaluation index of the system. Dynamic response characteristics of a direct-current element, a load and the like are sufficiently considered, and transient voltage stability quantitative evaluation is realized. The transient voltage stability quantitative evaluation method can be used for on-line analysis control and off-line simulation analysis of a power system, and facilitates running of an alternating-current to direct-current system; analyzing workers can determine stability of transient voltage, identify weak nodes and timely take effective measures; and the safe and stable running level of a large power grid is improved.

Description

A kind of Transient Voltage Stability quantitative estimation method based on critical system equiva lent impedance

Technical field

The present invention relates to a kind of appraisal procedure, specifically relate to a kind of Transient Voltage Stability quantitative estimation method based on critical system equiva lent impedance.

Background technology

Along with economy and social development, installed capacity and load level constantly increase, and electrical network scale constantly expands, system operating point more and more close to stability limit, so there is the risk of whole system generation collapse of voltage.Transient Voltage Stability problem relative complex, stability assessment method and discriminant criterion are study hotspots always.What Transient Voltage Stability was the most frequently used is time-domain-simulation method, although the method can accurately take into account element dynamic perfromance, can only provide system and whether stablize conclusion, cannot provide degree of stability information.And in existing Transient Voltage Stability appraisal procedure, lack effective quantitative estimation method.

The PMU of Electrical Power System Dynamic behavior can be monitored, for voltage stabilization on-line monitoring provides new tool.Utilizing PMU measurement and Dai Weinan equivalent model to carry out voltage stabilization on-line monitoring, is one of them important research direction.But owing to there is the differential equation in dynamic load model, be difficult to form comparatively accurate quantitative evaluation index according to single or multiple section.

Summary of the invention

For the deficiencies in the prior art, the object of this invention is to provide a kind of Transient Voltage Stability quantitative estimation method based on critical system equiva lent impedance, the method can take into full account the dynamic response characteristic of the element such as direct current, load, realizes the quantitative evaluation of Transient Voltage Stability.The present invention can apply to electric system on-line analysis control and off-line simulation analysis, be beneficial to that ac and dc systems runs, analyst carries out Enhancement of Transient Voltage Stability differentiation and weak node identification, take effective measures in time, improve the safe and stable operation level of bulk power grid.

The object of the invention is to adopt following technical proposals to realize:

The invention provides a kind of Transient Voltage Stability quantitative estimation method based on critical system equiva lent impedance, its improvements are, described method comprises the steps:

Step 1: when electric system is broken down, chooses monitoring bus;

Step 2: the initial equiva lent impedance curve of system and the equivalent potential curve of asking for monitoring bus;

Step 3: ask for monitoring bus place direct current or Dynamic Load Model at the state variable in fault clearance moment and algebraic variable;

Step 4: set up equivalent system model;

Step 5: ask for critical system equiva lent impedance curve;

Step 6: according to initial equiva lent impedance curve and critical system equiva lent impedance curve, calculates Transient Voltage Stability in Electric Power System quantitative evaluation index.

Further, in described step 1, the monitoring bus chosen is change of current bus or the load bus of direct current.

Further, described step 2 comprises following situation:

Situation 2-1: under offline mode, carries out time-domain-simulation to the whole network, and the admittance battle array according to each emulation moment determines electric system equiva lent impedance and equivalent potential;

If the node serial number monitoring bus is i;

In t, the network equation of electric system is:

$Y_t{\stackrel{\·}{U}}_t={\stackrel{\·}{I}}_t---\left(1\right);$

Wherein, Y _tfor the admittance matrix of t system; for the Injection Current vector of each node of t system; for the voltage vector of each node of t system;

The impedance matrix Z of system _tfor:

$Z_t=Y_t^{-1}---\left(2\right);$

Then system equiva lent impedance Z _eqfor:

Z _eq＝Z _tii (3)；

Wherein, Z _tiifor Z _ti-th row diagonal element;

System equivalent potential for:

${\stackrel{\·}{E}}_{\mathrm{eq}}={\stackrel{\·}{U}}_{\mathrm{ti}}+{\stackrel{\·}{I}}_{\mathrm{ti}}{Z}_{\mathrm{eq}}---\left(4\right);$

Wherein, be the voltage of i-th bus, for flowing out the electric current of i-th bus;

Situation 2-2: under online mode, according to the voltage and current value at the monitoring bus place that phasor measurement unit PMU measures, certainty annuity equiva lent impedance and equivalent potential;

If the voltage and current that t phasor measurement unit PMU measures (inflow direct current or load are just) is respectively with system equiva lent impedance and equivalent potential are respectively and Z _eq', then have:

${{\stackrel{\·}{E}}_{\mathrm{eq}}}^{\′}={{\stackrel{\·}{U}}_{\mathrm{ti}}}^{\′}+{{\stackrel{\·}{I}}_{\mathrm{ti}}}^{\′}{Z_{\mathrm{eq}}}^{\′}---\left(5\right);$

The phasor measurement unit PMU choosing multiple adjacent moment measures, and takes least square method, Kalman filtering method, based on total differential Thevenin's equivalence parameter tracking algorithm certainty annuity equiva lent impedance and equivalent potential.

Further, described step 3 comprises following situation:

Situation 3-1: under offline mode, according to time-domain simulation results, direct read failure removes state variable and the algebraic variable of moment monitoring bus place direct current or Dynamic Load Model;

Situation 3-2: under online mode, according to before fault to the fault clearance moment continuously many group phasor measurement unit PMU to measure and the dynamic model of direct current or load calculates its state variable and algebraic variable;

Before fault, direct current or load are in stable state, and the derivative of state variable is zero, calculate state variable and algebraic variable according to direct current or Dynamic Load Model parameter and PMU measuration meter;

In fault, because direct current or load busbar voltage and Injection Current PMU directly measure; Emulate to the fault clearance moment and obtain state variable and the algebraic variable of this moment direct current or Dynamic Load Model.

Further, in described step 4, the system equivalent model at monitoring bus place is spliced with direct current or load equivalent model, sets up equivalent system model.

Further, in described step 5, continuous increase system equiva lent impedance, carries out time-domain-simulation to equivalent system, until electric system neutrality, obtains critical system equiva lent impedance curve.

Further, in described step 6, according to initial equiva lent impedance curve and critical system equiva lent impedance curve, calculate Transient Voltage Stability in Electric Power System quantitative evaluation index k _tVSI:

$k_{\mathrm{TVSI}}=1-\frac{\left|Z_{\mathrm{eqmean}}\right|}{\left|Z_{\mathrm{eqcrit}\_\mathrm{mean}}\right|}---\left(6\right);$

$Z_{\mathrm{eqmean}}=\frac{1}{t_2-{t_1}^{(+)}}{\∫}_{{t_1}^{(+)}}^{t_2}{Z}_{\mathrm{eq}}\left(t\right)\mathrm{dt}---\left(7\right);$

$Z_{\mathrm{eqcrit}\_\mathrm{mean}}=\frac{1}{t_2{{-t}_1}^{(+)}}{\∫}_{{t_1}^{(+)}}^{t_2}{Z}_{\mathrm{eqcrit}}\left(t\right)\mathrm{dt}---\left(8\right);$

Wherein, Z _eqt starter system equiva lent impedance that () is t, Z _eqcritt critical system equiva lent impedance that () is t, t ₁ ⁽⁺⁾for moment after fault clearance, t ₂for time-domain-simulation finish time;

Work as k _tVSIduring >0, power system stability; Work as k _tVSIwhen=0, electric system neutrality.

Compared with the prior art, the invention has the beneficial effects as follows:

1. the Transient Voltage Stability quantitative estimation method of critical system equiva lent impedance provided by the invention, can take into full account the dynamic response characteristic of the element such as direct current, load, realizes the quantitative evaluation of Transient Voltage Stability.

2. the present invention can apply to electric system on-line analysis control and off-line simulation analysis, be beneficial to that ac and dc systems runs, analyst carries out Enhancement of Transient Voltage Stability differentiation and weak node identification, take effective measures in time, improve the safe and stable operation level of bulk power grid.

Accompanying drawing explanation

Fig. 1 is system schematic in embodiment provided by the invention; Wherein: bus 1 is the infinitely great generator of sending end, line bus 2-bus 3 is double back 500kV line, and bus 4 is load (load model is 60% motor+40% constant-impedance), and bus 5 is receiving end unit, bus 6 is DC inversion side current conversion station, and bus 7 is DC rectifier side current conversion station;

Fig. 2 is fault afterload busbar voltage curve map in embodiment provided by the invention;

Fig. 3 is fault afterload current curve diagram in embodiment provided by the invention;

Fig. 4 is post-fault system equivalent potential curve map in embodiment provided by the invention;

Fig. 5 is post-fault system equiva lent impedance curve map in embodiment provided by the invention;

Fig. 6 is critical system equiva lent impedance curve map after fault in embodiment provided by the invention;

Fig. 7 is the Transient Voltage Stability quantitative estimation method process flow diagram based on critical system equiva lent impedance provided by the invention.

Embodiment

Below in conjunction with accompanying drawing, the specific embodiment of the present invention is described in further detail.

Transient Voltage Stability quantitative estimation method based on critical system equiva lent impedance provided by the invention, by the system equivalent model that monitoring bus is seen into, with direct current or the Dynamic Load Model splicing in fault clearance moment, set up equivalent system model, by carrying out time-domain-simulation to equivalent system, ask for critical system equiva lent impedance, and then computing system Transient Voltage Stability quantitative evaluation index.Concrete steps as shown in a flowchart of fig. 7, comprise the steps:

Step 1: when electric system is broken down, selects monitoring bus; The monitoring bus chosen can think the change of current bus of direct current, also can be load bus.

Step 2: ask for the system equiva lent impedance curve (being called " starter system equiva lent impedance curve ") seen into of monitoring bus and equivalent potential curve;

Comprise the following two kinds situation:

Situation 2-1: under offline mode, carries out time-domain-simulation to the whole network, according to admittance battle array computing system equiva lent impedance and the equivalent potential in each emulation moment;

Without loss of generality, if the node serial number monitoring bus is i.

In t, the network equation of electric system is:

$Y_t{\stackrel{\·}{U}}_t={\stackrel{\·}{I}}_t---\left(1\right);$

Wherein, Y _tfor the admittance matrix of t electric system; for the Injection Current vector of each node of t electric system; for the voltage vector of each node of t electric system.

The impedance matrix Z of electric system _tfor:

$Z_t=Y_t^{-1}---\left(2\right);$

Then electric system equiva lent impedance Z _eqfor:

Z _eq＝Z _tii (3)；

Wherein, Z _tiifor Z _ti-th row diagonal element.

Electric system equivalent potential for:

${\stackrel{\·}{E}}_{\mathrm{eq}}={\stackrel{\·}{U}}_{\mathrm{ti}}+{\stackrel{\·}{I}}_{\mathrm{ti}}{Z}_{\mathrm{eq}}---\left(4\right);$

Wherein, be ithe voltage of individual bus, for flowing out the electric current of i-th bus.

Situation 2-2: under online mode, according to voltage, the current value at the monitoring bus place that PMU (phasor measurement unit) measures, estimating system equiva lent impedance and equivalent potential;

Without loss of generality, if the voltage of t PMU measurement, electric current (inflow direct current or load are just) are system equiva lent impedance, equivalent potential are z _eq', then have:

${{\stackrel{\·}{E}}_{\mathrm{eq}}}^{\′}={{\stackrel{\·}{U}}_{\mathrm{ti}}}^{\′}+{{\stackrel{\·}{I}}_{\mathrm{ti}}}^{\′}{Z_{\mathrm{eq}}}^{\′}---\left(5\right);$

The PMU choosing multiple adjacent moment measures, and multiple method can be taked to estimate electric system equiva lent impedance and equivalent potential, as descended most square law, Kalman filtering method, based on total differential Thevenin's equivalence parameter tracking algorithm etc.

The electric system equiva lent impedance curve that step 2 obtains is starter system equiva lent impedance curve.

Step 3: ask for monitoring bus place direct current or Dynamic Load Model at the state variable in fault clearance moment and algebraic variable;

Comprise the following two kinds situation:

Situation 3-1: under offline mode, according to time-domain simulation results, direct read failure removes state variable and the algebraic variable of moment monitoring bus place direct current or Dynamic Load Model.

Situation 3-2: under online mode, according to before fault to the fault clearance moment continuously many group PMU to measure and the dynamic model of direct current or load calculates its state variable and algebraic variable.

Before fault, direct current or load are in stable state, and the derivative of state variable is zero, measure can be easy to calculate state variable and algebraic variable according to its dynamic model parameters and PMU.

In fault, because the busbar voltage of direct current or load and Injection Current directly can measure with PMU, therefore just can carry out time-domain-simulation to direct current or Dynamic Load Model without the need to carrying out network calculations; Emulate to the fault clearance moment and just can obtain state variable and the algebraic variable of this moment direct current or load model.

Step 4: the electric system equivalent model at monitoring bus place is spliced with direct current or load equivalent model, sets up equivalent system model;

Step 5: constantly increase system equiva lent impedance, carries out time-domain-simulation to equivalent system, asks for critical system equiva lent impedance curve;

Step 6: according to initial and critical system equiva lent impedance curve, computing system Transient Voltage Stability quantitative evaluation index.

System transient modelling voltage stabilization quantitative evaluation index k _tVSI:

$k_{\mathrm{TVSI}}=1-\frac{\left|Z_{\mathrm{eqmean}}\right|}{\left|Z_{\mathrm{eqcrit}\_\mathrm{mean}}\right|}---\left(6\right);$

$Z_{\mathrm{eqmean}}=\frac{1}{t_2-{t_1}^{(+)}}{\∫}_{{t_1}^{(+)}}^{t_2}{Z}_{\mathrm{eq}}\left(t\right)\mathrm{dt}---\left(7\right);$

$Z_{\mathrm{eqcrit}\_\mathrm{mean}}=\frac{1}{t_2{{-t}_1}^{(+)}}{\∫}_{{t_1}^{(+)}}^{t_2}{Z}_{\mathrm{eqcrit}}\left(t\right)\mathrm{dt}---\left(8\right);$

Wherein, Z _eqt starter system equiva lent impedance that () is t, Z _eqcritt critical system equiva lent impedance that () is t, t ₁ ⁽⁺⁾for moment after fault clearance, t ₂for time-domain-simulation finish time.

Work as k _tVSIduring >0, system stability; Work as k _tVSIwhen=0, system neutrality.

Embodiment

For electric system shown in Fig. 1.Wherein, bus 1 is the infinitely great generator of sending end, and line bus 2-bus 3 is double back 500kV line, bus 4 is load (load model is 60% motor+40% constant-impedance), bus 5 is receiving end unit, and bus 6 is DC inversion side current conversion station, and bus 7 is DC rectifier side current conversion station.Be 1500MW by end load, it is 0 that line bus 2-bus 3 trend is gained merit, and DC power is 800MW.During 1s, there is three phase short circuit fault, fault clearance after 1.1s in bus 3 side in double loop bus 2-bus 3.Load busbar voltage and load current curve are as shown in Figure 2 and Figure 3.

The first step: after fault occurs, select load bus 4 for monitoring bus, by time-domain-simulation, calculate system equivalent potential, the equiva lent impedance in each moment, result as shown in Figure 4, Figure 5.

Second step: direct read failure removes state variable and the algebraic variable of moment load from time-domain simulation results, itself and system equivalent parameters is spliced, composition equivalent system.

3rd step: increase system equiva lent impedance, carry out time-domain-simulation to equivalent system, until system neutrality, can obtain system critical impedance curve, result as shown in Figure 6.

4th step: computing system Transient Voltage Stability quantitative evaluation index, can obtain stability margin index is 0.3469.

Finally should be noted that: above embodiment is only in order to illustrate that technical scheme of the present invention is not intended to limit; although with reference to above-described embodiment to invention has been detailed description; those of ordinary skill in the field still can modify to the specific embodiment of the present invention or equivalent replacement; these do not depart from any amendment of spirit and scope of the invention or equivalent replacement, are all applying within the claims of the present invention awaited the reply.

Claims (7)

1. based on a Transient Voltage Stability quantitative estimation method for critical system equiva lent impedance, it is characterized in that, described method comprises the steps:

Step 1: choose monitoring bus when electric system is broken down;

Step 2: the initial equiva lent impedance curve of system and the equivalent potential curve of asking for monitoring bus;

Step 3: ask for monitoring bus place direct current or Dynamic Load Model at the state variable in fault clearance moment and algebraic variable;

Step 4: set up equivalent system model;

Step 5: ask for critical system equiva lent impedance curve;

Step 6: according to initial equiva lent impedance curve and critical system equiva lent impedance curve, calculates Transient Voltage Stability in Electric Power System quantitative evaluation index.

2. Transient Voltage Stability quantitative estimation method as claimed in claim 1, it is characterized in that, in described step 1, the monitoring bus chosen is change of current bus or the load bus of direct current.

3. Transient Voltage Stability quantitative estimation method as claimed in claim 1, it is characterized in that, described step 2 comprises the step under following off-line and online mode:

Under offline mode: carry out time-domain-simulation to the whole network, the admittance battle array according to each emulation moment determines electric system equiva lent impedance and equivalent potential;

If the node serial number monitoring bus is i;

In t, the network equation of electric system is:

$Y_t{\stackrel{\·}{U}}_t={\stackrel{\·}{I}}_t---\left(1\right);$

Wherein, Y _tfor the admittance matrix of t system; for the Injection Current vector of each node of t system; for the voltage vector of each node of t system;

The impedance matrix Z of system _tfor:

$Z_t=Y_t^{-1}---\left(2\right);$

Then system equiva lent impedance Z _eqfor:

Z _eq＝Z _tii (3)；

Wherein, Z _tiifor Z _ti-th row diagonal element;

System equivalent potential for:

${\stackrel{\·}{E}}_{\mathrm{eq}}={\stackrel{\·}{U}}_{\mathrm{ti}}+{\stackrel{\·}{I}}_{\mathrm{ti}}{Z}_{\mathrm{eq}}---\left(4\right);$

Wherein, be the voltage of i-th bus, for flowing out the electric current of i-th bus;

Under online mode: according to the voltage and current value at the monitoring bus place that phasor measurement unit PMU measures, certainty annuity equiva lent impedance and equivalent potential;

If the voltage and current that t phasor measurement unit PMU measures (inflow direct current or load are just) is respectively with system equiva lent impedance and equivalent potential are respectively and Z _eq', then have:

${{\stackrel{\·}{E}}_{\mathrm{eq}}}^{\′}={{\stackrel{\·}{U}}_{\mathrm{ti}}}^{\′}+{{\stackrel{\·}{I}}_{\mathrm{ti}}}^{\′}{Z_{\mathrm{eq}}}^{\′}---\left(5\right);$

The phasor measurement unit PMU choosing multiple adjacent moment measures, and takes least square method, Kalman filtering method, based on total differential Thevenin's equivalence parameter tracking algorithm certainty annuity equiva lent impedance and equivalent potential.

4. Transient Voltage Stability quantitative estimation method as claimed in claim 1, it is characterized in that, described step 3 comprises the step under following off-line and online mode:

Under offline mode: according to time-domain simulation results, direct read failure removes state variable and the algebraic variable of moment monitoring bus place direct current or Dynamic Load Model;

Under online mode: according to before fault to the fault clearance moment continuously many group phasor measurement unit PMU to measure and the dynamic model of direct current or load calculates its state variable and algebraic variable;

Before fault, direct current or load are in stable state, and the derivative of state variable is zero, calculate state variable and algebraic variable according to direct current or Dynamic Load Model parameter and PMU measuration meter;

In fault, because direct current or load busbar voltage and Injection Current PMU directly measure; Emulate to the fault clearance moment and obtain state variable and the algebraic variable of this moment direct current or Dynamic Load Model.

5. Transient Voltage Stability quantitative estimation method as claimed in claim 1, is characterized in that, in described step 4, is spliced by the system equivalent model at monitoring bus place, set up equivalent system model with direct current or load equivalent model.

6. Transient Voltage Stability quantitative estimation method as claimed in claim 1, it is characterized in that, in described step 5, continuous increase system equiva lent impedance, carries out time-domain-simulation to equivalent system, until electric system neutrality, obtains critical system equiva lent impedance curve.

7. Transient Voltage Stability quantitative estimation method as claimed in claim 1, is characterized in that, in described step 6, according to initial equiva lent impedance curve and critical system equiva lent impedance curve, calculates Transient Voltage Stability in Electric Power System quantitative evaluation index k _tVSI:

$k_{\mathrm{TVSI}}=1-\frac{\left|Z_{\mathrm{eqmean}}\right|}{\left|Z_{\mathrm{eqcrit}\_\mathrm{mean}}\right|}---\left(6\right);$

$Z_{\mathrm{eqmean}}=\frac{1}{t_2-{t_1}^{(+)}}{\∫}_{{t_1}^{(+)}}^{t_2}{Z}_{\mathrm{eq}}\left(t\right)\mathrm{dt}---\left(7\right);$

$Z_{\mathrm{eqcrit}\_\mathrm{mean}}=\frac{1}{t_2{{-t}_1}^{(+)}}{\∫}_{{t_1}^{(+)}}^{t_2}{Z}_{\mathrm{eqcrit}}\left(t\right)\mathrm{dt}---\left(8\right);$

Wherein, Z _eqt starter system equiva lent impedance that () is t, Z _eqcritt critical system equiva lent impedance that () is t, t ₁ ⁽⁺⁾for moment after fault clearance, t ₂for time-domain-simulation finish time;

Work as k _tVSIduring >0, power system stability; Work as k _tVSIwhen=0, electric system neutrality.