CN104778367A - On-line wide-area Thevenin equivalent parameter calculation method based on single state section - Google Patents

Abstract

The invention discloses an on-line wide-area Thevenin equivalent parameter calculation method based on a single state section, which includes the following steps: equivalent impedance processing is carried out on the load of a current-state load node; an original system node admittance matrix is corrected, so that an equivalent impedance-processed system admittance matrix is obtained; a node voltage equation of the equivalent impedance-processed current-state load node is calculated; the open-circuit voltage of the load node is calculated, moreover, the open-circuit voltage is used as Thevenin equivalent potential, consequently, all the Thevenin equivalent parameters of the studied load node are obtained, and a criterion of voltage stability is obtained. The on-line wide-area Thevenin equivalent parameter calculation method based on the single state section has the following advantages: initial values and assumed conditions do not need to be chosen, the problem that the deviation of Thevenin equivalent parameter calculation is great when disturbance takes place in a conventional system based on the local-area quantity calculation method is solved, the obtained Thevenin parameters are more accurate, moreover, the calculation load is little, the robustness is good, and the on-line wide-area Thevenin equivalent parameter calculation method based on the single state section can be adapted to the different operating condition modes of a power grid.

Description

Based on the wide area Thevenin's equivalence parameter on-line calculation method of a single state section

Technical field

The present invention relates to the voltage stabilization on-line analysis technical field of electric system based on Thevenin's equivalence, particularly relate to a kind of wide area Thevenin's equivalence parameter on-line calculation method based on a single state section.

Background technology

Along with the expansion of Power System Interconnection scale, the quick growth of electricity needs, Operation of Electric Systems point is more and more close to stability limit.The research of in-service monitoring Network Voltage Stability causes Chinese scholars extensive concern and attention.Based on the voltage stabilization on-line analysis of Thevenin's equivalence, because its method clear concept, principle be simple etc., advantage makes it to become the important research direction in one, voltage stabilization field.

The Thevenin's equivalence parameter quick and precisely assessing critical load node directly determines the method and is applied in on-Line Voltage Stability Monitoring and the feasibility in control and validity.Chinese scholars just realizes Voltage Stability Analysis based on local measurement raising Thevenin's equivalence parameter computational accuracy and proposes multiple method, as Z-V space supply side characteristic method, expansion PV curve follow the tracks of the method etc. estimating Thevenin's equivalence parameter, but the basis of algorithm is all Thevenin's equivalence parameter constant in hypothesis metric data window.The actual conditions of this precondition and system cloud gray model also misfit, by analysis parameter drift and time become problem, find to utilize least square fitting that the situation of numerical value instability occurs to there will be in compared with large disturbances situation at electrical network.

The Thevenin's equivalence parameter identification method measured based on local achieves significant progress, but parameter time varying and drifting problem when the non-linear enhancing of electrical network or two adjacent region datas change very close to time, still can affect the Thevenin's equivalence parameter identification precision based on continuous system state section local metric data.Bring larger randomness and undulatory property along with the regenerative resources such as wind-powered electricity generation photovoltaic access on a large scale to system cloud gray model, this problem will be more outstanding.Along with the popularization of PMU, WAMS reaches its maturity, and the Thevenin's equivalence parameter that the triangular web state profile data based on overall situation measurement solves load bus becomes new Research Thinking, and common method has:

(1) node of the whole network is divided into power supply, contact and load bus three class, be the feature of zero according to contact node Injection Current, the nodal voltage equation of the whole network is transformed to the Thevenin's equivalence form of multinode multiple branch circuit, again to the Impedance Matrix diagonalization after conversion, realize internodal decoupling zero conversion, obtain the single supply single spur track Thevenin's equivalence parameter of load bus.

(2) propose coupled single-ended mouth network concept, achieve and calculate based on the Thevenin's equivalence under a single state section, but under load increase nonlinear situation, the method result of calculation is estimated on the low side to load margin, calculate in accuracy and have much room for improvement.

(3) PMU real-time measurement data are utilized to be coupled between processing node, to improve load margin computational accuracy by the coupling of local node reactive response factor pair System Reactive Power response factor.But be difficult to quantize different internodal coupling association, effective quantum chemical method cannot be carried out to the out-of-limit situation of generator reactive.

All need in above method solution procedure to invert to admittance battle array, add matrix and the coupling processing of follow-up relative complex, the calculation amount for line computation for Iarge-scale system is still larger.More wish in practical implementation quick and precisely to calculate on equivalent parameters basis under a single state section, can according to load prediction, quantize each node load change and each regulation measure on the impact of Thevenin's equivalence parameter under to-be, to obtain security information in advance, for the optimization realizing prevention and control creates conditions.

Summary of the invention

Object of the present invention is exactly that propose the wide area Thevenin's equivalence parameter on-line calculation method based on a single state section, the method calculated amount is little, reliable and stable in order to solve the problem, and can complete the quick calculating paying close attention to node equivalent parameters online.

To achieve these goals, the present invention adopts following technical scheme:

Based on the wide area Thevenin's equivalence parameter on-line calculation method of a single state section, comprise the following steps:

(1) equiva lent impedance process is done to the load of current state load bus;

(2) correcting process is done to original system bus admittance matrix, obtain the system admittance matrix after equiva lent impedance process;

(3) load impedance at current state load bus place is disconnected, according to the bus admittance matrix revising later admittance matrix calculating open-circuit voltage;

(4) nodal voltage equation of current state load bus after equiva lent impedance process is calculated;

(5) according to revised admittance matrix and nodal voltage equation, the open-circuit voltage of calculated load node, and using described open-circuit voltage as Thevenin's equivalence electromotive force, and then obtain study the whole parameter of Thevenin's equivalence of load bus, obtain the criterion of voltage stabilization.

The concrete grammar of described step (1) is:

If system PV and balance node number sum are m, PQ nodes is r, total nodes is n; Under wide area measurement condition, each node voltage amplitude of system, phase place and active reactive power are known, under calculating moment system state section, all PV nodes and balance node are all considered as ideal voltage source, for the PQ node of on-load, its load all by the power of this node and voltage, can calculate an equivalent load impedance.

The concrete grammar of described step (2) is:

If the original admittance matrix of system is Y ₀, Y ₀middle element is as follows:

$Y_0=\left(\begin{array}{ccccc}{Y}_{11}& ...& Y_{1i}& ...& Y_{1n}\\ .& & .& & .\\ .& & .& & .\\ .& & .& & .\\ Y_{i1}& ...& Y_{\mathrm{ii}}& ...& Y_{\mathrm{in}}\\ .& & .& & .\\ .& & .& & .\\ .& & .& & .\\ Y_{n1}& ...& Y_{\mathrm{ni}}& ...& Y_{\mathrm{nn}}\end{array}\right);$

Element Y in matrix _ijtransadmittance between representation node i and node j, Y _iithe self-admittance of representation node i; Load impedance is integrated into system admittance matrix Y ₀, only need revise the admittance battle array Y corresponding with load bus ₀diagonal element, all the other elements are constant;

$a_{\mathrm{ii}}=Y_{\mathrm{ii}}+\frac{1}{Z_{\mathrm{Li}}},i\∈(\mathrm{1,2,3}...r)$

Then revised admittance matrix is:

$Y_1=\left(\begin{array}{ccccc}{a}_{11}& ...& a_{1r}& ...& a_{1n}\\ .& & .& & .\\ .& & .& & .\\ .& & .& & .\\ a_{r1}& ...& a_{\mathrm{rr}}& ...& a_{\mathrm{rn}}\\ .& & .& & .\\ .& & .& & .\\ .& & .& & .\\ a_{n1}& ...& a_{\mathrm{nr}}& ...& a_{\mathrm{nn}}\end{array}\right)=\left(\begin{array}{ccccc}{a}_{11}& ...& Y_{1r}& ...& Y_{1n}\\ .& & .& & .\\ .& & .& & .\\ .& & .& & .\\ Y_{r1}& ...& a_{\mathrm{rr}}& ...& Y_{\mathrm{rn}}\\ .& & .& & .\\ .& & .& & .\\ .& & .& & .\\ Y_{n1}& ...& Y_{\mathrm{nr}}& ...& Y_{\mathrm{nn}}\end{array}\right);$

Wherein, r is PQ nodes, Z _libe the equiva lent impedance of i-th PQ node, represent the admittance value of load impedance.

The concrete grammar of described step (3) is:

Current state load bus self-admittance a in later admittance matrix will be revised _iideduct load impedance, namely form the bus admittance matrix Y calculating open-circuit voltage.

The bus admittance matrix Y of open-circuit voltage is specially:

$Y=\left(\begin{array}{ccccc}{b}_{11}& ...& b_{1r}& ...& b_{1n}\\ .& & .& & .\\ .& & .& & .\\ .& & .& & .\\ b_{r1}& ...& b_{\mathrm{rr}}& ...& b_{\mathrm{rn}}\\ .& & .& & .\\ .& & .& & .\\ .& & .& & .\\ b_{n1}& ...& b_{\mathrm{nr}}& ...& b_{\mathrm{nn}}\end{array}\right)=\left(\begin{array}{ccccc}{b}_{11}& ...& a_{1r}& ...& a_{1n}\\ .& & .& & .\\ .& & .& & .\\ .& & .& & .\\ a_{r1}& ...& a_{\mathrm{rr}}& ...& a_{\mathrm{rn}}\\ .& & .& & .\\ .& & .& & .\\ .& & .& & .\\ a_{n1}& ...& a_{\mathrm{nr}}& ...& a_{\mathrm{nn}}\end{array}\right)$

Wherein, for the node i of open-circuit voltage to be asked, its corresponding self-admittance should be represent the admittance value of load impedance, a _iirepresent and revise r diagonal entry before in later admittance matrix.

The concrete grammar of described step (4) is:

When solving i node open-circuit voltage, node voltage vector $\stackrel{\·}{U}=\left(\begin{array}{c}{\stackrel{\·}{U}}_1\\ .\\ .\\ .\\ {\stackrel{\·}{U}}_{\mathrm{iopen}}\\ .\\ .\\ .\\ {\stackrel{\·}{U}}_n\end{array}\right)$ In, PQ node voltage phasor is amount to be asked, and PV node and balance node voltage phasor are known quantity; After adopting node load equivalent impedance, node Injection Current vector $\stackrel{\·}{I}=\left(\begin{array}{c}{\stackrel{\·}{I}}_1\\ .\\ .\\ .\\ {\stackrel{\·}{I}}_i\\ .\\ .\\ .\\ {\stackrel{\·}{I}}_n\end{array}\right)$ In be 0, draw according to nodal voltage equation

$\left(\begin{array}{ccc}{b}_{11}...& b_{1i}...& b_{1n}\\ .& .& .\\ .& .& .\\ .& .& .\\ b_{i1}...& b_{\mathrm{ii}}...& b_{\mathrm{in}}\\ .& .& .\\ .& .& .\\ .& .& .\\ b_{r1}...& b_{\mathrm{ri}}...& b_{\mathrm{rn}}\\ b_{(r+1)1}...& b_{(r+1)i}...& b_{(r+1)n}\\ .& .& .\\ .& .& .\\ .& .& .\\ b_{(n-1)1}...& b_{(n-1)i}...& b_{(n-1)n}\\ b_{n1}...& b_{\mathrm{ni}}...& b_{\mathrm{nn}}\end{array}\right)\left(\begin{array}{c}{\stackrel{\·}{U}}_1\\ .\\ .\\ .\\ {\stackrel{\·}{U}}_{\mathrm{iopen}}\\ .\\ .\\ .\\ {\stackrel{\·}{U}}_r\\ {\stackrel{\·}{U}}_{r+1}\\ .\\ .\\ .\\ {\stackrel{\·}{U}}_{n-1}\\ {\stackrel{\·}{U}}_n\end{array}\right)=\left(\begin{array}{c}0\\ .\\ .\\ .\\ 0\\ .\\ .\\ .\\ 0\\ {\stackrel{\·}{I}}_{r+1}\\ .\\ .\\ .\\ {\stackrel{\·}{I}}_{n-1}\\ {\stackrel{\·}{I}}_n\end{array}\right);$

In formula: bus admittance matrix and voltage vector middle element be known quantity; represent the voltage of PQ node 1 to r, representing the open-circuit voltage of i-th PQ node, is amount to be asked, represent the Injection Current of PV and balance node.

In described nodal voltage equation,

Order $A=\left(\begin{array}{ccccc}{b}_{11}& ...& b_{1i}& ...& b_{1n}\\ .& & .& & .\\ .& & .& & .\\ .& & .& & .\\ b_{i1}& ...& b_{\mathrm{ii}}& ...& b_{\mathrm{in}}\\ .& & .& & .\\ .& & .& & .\\ .& & .& & .\\ b_{r1}& ...& b_{\mathrm{ri}}& ...& b_{\mathrm{rr}}\end{array}\right),U=\left(\begin{array}{c}{\stackrel{\·}{U}}_1\\ .\\ .\\ .\\ {\stackrel{\·}{U}}_{\mathrm{iopen}}\\ .\\ .\\ .\\ {\stackrel{\·}{U}}_r\end{array}\right),B=\left(\begin{array}{c}{b}_{1(r+1)}{\stackrel{\·}{U}}_{(r+1)}+......b_{1n}{\stackrel{\·}{U}}_n\\ b_{2(r+1)}{\stackrel{\·}{U}}_{(r+1)}+......b_{2n}{\stackrel{\·}{U}}_n\\ .\\ .\\ .\\ .\\ .\\ .\\ b_{r(r+1)}{\stackrel{\·}{U}}_{(r+1)}+......b_{\mathrm{rn}}{\stackrel{\·}{U}}_n\end{array}\right);$

Then nodal voltage equation can be write as following matrix form:

AU＝-B

Utilize Gaussian elimination method to solve above-mentioned equation, solve i Nodes open-circuit voltage be Thevenin's equivalence electromotive force

Due to the sparse property of admittance battle array, utilizing in gaussian elimination solution procedure, be upper triangular matrix by coefficient matrices A abbreviation, and owing to only needing the open-circuit voltage of computing node i, therefore arrive in backward steps , without the need to whole unknown quantity is all solved; Solving the equivalent parameters of other nodes as needed, only need again revise admittance battle array Y ₁, form new nodal voltage equation, again utilize gaussian elimination to solve.

The concrete grammar of described step (5) is:

Utilize Gaussian elimination method solution node voltage equation, i Nodes open-circuit voltage can be solved

According to the load fluctuation of each node of load prediction gained, take into account various regulation measure quantum chemical method and go out to-be section information, the change of each node equivalent parameters can be calculated fast, realize accurately estimating the equivalent parameters under to-be.

The invention has the beneficial effects as follows:

The correctness of the method and validity by simulation example analysis verification.The method does not need to select initial value and assumed condition, solve the existing problem larger based on Thevenin's equivalence parameter calculation deviation during the generation disturbance of local measurement algorithmic system inside, the Dai Weinan parameter that the coupled single-ended mouth method based on wide area measurement of comparing calculates is more accurate, and calculated amount is little, robustness is good, can adapt to the different operating condition mode of electrical network.

In ultra-short term accurately, taking into account various regulation measure can the state of rapid Estimation system in future, Prediction System state section Information base can provide online Prediction comparatively accurately to Thevenin's equivalence Parameters variation track by institute of the present invention extracting method, is optimization based theoretical and the argin of preventive control measure.Institute's extracting method is also applicable to the variation issue of the Thevenin's equivalence parameter analyzed in the medium-term and long-term process of electric system simultaneously, for regulation and control center utilizes Thevenin's equivalence model analysis on-Line Voltage stability to provide useful reference, has good application on site prospect.

Accompanying drawing explanation

Fig. 1 (a) is the electric system schematic diagram before equivalence;

Fig. 1 (b) is the electric system schematic diagram after equivalence;

Fig. 2 is the system schematic after load is equivalent to impedance;

Fig. 3 is the open-circuit voltage system schematic of node i

Fig. 4 is embodiment of the present invention IEEE3 machine 9 node system structural drawing;

Fig. 5 is the contrast of embodiment of the present invention voltage magnitude deviation;

Fig. 6 is embodiment of the present invention New England 10 machine 39 node system structural drawing;

Fig. 7 is the contrast of embodiment of the present invention node 29 voltage magnitude.

Embodiment:

Below in conjunction with accompanying drawing and embodiment, the present invention will be further described:

One, based on the basic thought of the wide area Thevenin's equivalence of a single state section

Thevenin's equivalence is with a certain node for object, with this node equivalent network of observing to system side of port over the ground.Electric system (for load 1) as shown in Fig. 1 (a), a period of time in office discontinuity surface, the electric system of any complexity all can be regarded as the equivalent electromotive force E to any node _ththrough an equivalent impedance Z _thto the equivalent network that this node is powered, as shown in Fig. 1 (b), load 1 corresponding node.

If system PV and balance node number sum are m, PQ nodes is r, total nodes is n.Under wide area measurement condition, each node voltage amplitude of system, phase place and active reactive power are known, under calculating moment system state section, all PV nodes and balance node are all considered as ideal voltage source, for the PQ node of on-load, its load all by the power of this node and voltage, can calculate an equivalent load impedance, namely for load bus i, its equiva lent impedance is:

$Z_{\mathrm{Li}}={\stackrel{\·}{U}}_i/{\stackrel{\·}{I}}_i={\stackrel{\·}{U}}_i\frac{{\stackrel{\·}{U}}_i^{*}}{P_i-j{Q}_i}=\frac{U_i^2}{P_i-j{Q}_i}---\left(1\right)$

In formula p _iand Q _ibe respectively the voltage of node i, electric current phasor and meritorious, reactive power.

Equiva lent impedance herein not processes the load of PQ node by constant-impedance model, only for the load Equivalent Calculation of current state, when system running state changes, this equiva lent impedance is change.After equivalence, system as shown in Figure 2.

When system after equivalent process asks for certain load bus Thevenin's equivalence parameter, E can be calculated according to the definition of the Thevenin's equivalence electromotive force i.e. open-circuit voltage of this node _thi, then ask for its equivalent impedance Z according to formula (2) _thi.

${\stackrel{\·}{E}}_{\mathrm{thi}}={\stackrel{\·}{U}}_i+{\stackrel{\·}{I}}_i{Z}_{\mathrm{thi}};{\stackrel{\·}{I}}_i={\left(\frac{{\tilde{S}}_i}{{\stackrel{\·}{U}}_i}\right)}^{*}=\frac{P_i-j{Q}_i}{{\stackrel{\·}{U}}_i^{*}}---\left(2\right)$

Two, wide area Thevenin's equivalence potential calculation method

The bus admittance matrix of Fig. 2 system can obtain by carrying out correction to origin node admittance matrix.If the original admittance matrix of system is Y ₀, Y ₀middle element is as follows

$Y_0=\left(\begin{array}{ccccc}{Y}_{11}& ...& Y_{1i}& ...& Y_{1n}\\ .& & .& & .\\ .& & .& & .\\ .& & .& & .\\ Y_{i1}& ...& Y_{\mathrm{ii}}& ...& Y_{\mathrm{in}}\\ .& & .& & .\\ .& & .& & .\\ .& & .& & .\\ Y_{n1}& ...& Y_{\mathrm{ni}}& ...& Y_{\mathrm{nn}}\end{array}\right)$

Element Y in matrix _ijtransadmittance between representation node i and node j, Y _iithe self-admittance of representation node i; Element implication below in matrix is identical therewith;

Load impedance is integrated into the diagonal element that system admittance matrix only need revise the admittance battle array corresponding with load bus.

$a_{\mathrm{ii}}=Y_{\mathrm{ii}}+\frac{1}{Z_{\mathrm{Li}}},(i\∈(\mathrm{1,2,3}...r))---\left(3\right)$

Then revised admittance matrix is

$Y_1=\left(\begin{array}{ccccc}{a}_{11}& ...& a_{1i}& ...& a_{1n}\\ .& & .& & .\\ .& & .& & .\\ .& & .& & .\\ a_{r1}& ...& a_{\mathrm{rr}}& ...& a_{\mathrm{rn}}\\ .& & .& & .\\ .& & .& & .\\ .& & .& & .\\ a_{n1}& ...& a_{\mathrm{ni}}& ...& a_{\mathrm{nn}}\end{array}\right)---\left(4\right)$

When solving the Thevenin's equivalence parameter at load bus i place, only need the load impedance at disconnected node i place, solve its open-circuit voltage and be Thevenin's equivalence electromotive force.

After the equiva lent impedance disconnection of node i load, system architecture as shown in Figure 3.

As long as by Y ₁middle i node self-admittance a _iideduct load impedance such as formula shown in (5), the bus admittance matrix of calculating open-circuit voltage can be formed such as formula the admittance matrix Y shown in (6).

$b_{\mathrm{ii}}=a_{\mathrm{ii}}-\frac{1}{Z_{\mathrm{Li}}}---\left(5\right)$

$Y=\left(\begin{array}{ccccc}{b}_{11}& ...& b_{1i}& ...& b_{1n}\\ .& & .& & .\\ .& & .& & .\\ .& & .& & .\\ b_{r1}& ...& b_{\mathrm{rr}}& ...& b_{\mathrm{rn}}\\ .& & .& & .\\ .& & .& & .\\ .& & .& & .\\ b_{n1}& ...& b_{\mathrm{ni}}& ...& b_{\mathrm{nn}}\end{array}\right)---\left(6\right)$

Except b _iioutward, Y and Y ₁element all identical.

When solving i node open-circuit voltage, node voltage vector $\stackrel{\·}{U}=\left(\begin{array}{c}{\stackrel{\·}{U}}_1\\ .\\ .\\ .\\ {\stackrel{\·}{U}}_{\mathrm{iopen}}\\ .\\ .\\ .\\ {\stackrel{\·}{U}}_n\end{array}\right)$ In, PQ node voltage phasor is amount to be asked, and PV node and balance node voltage phasor are known quantity.After adopting node load equivalent impedance, node Injection Current vector $\stackrel{\·}{I}=\left(\begin{array}{c}{\stackrel{\·}{I}}_1\\ .\\ .\\ .\\ {\stackrel{\·}{I}}_i\\ .\\ .\\ .\\ {\stackrel{\·}{I}}_n\end{array}\right)$ In be 0, can draw according to nodal voltage equation

$\left(\begin{array}{ccc}{b}_{11}...& b_{1i}...& b_{1n}\\ .& .& .\\ .& .& .\\ .& .& .\\ b_{i1}...& b_{\mathrm{ii}}...& b_{\mathrm{in}}\\ .& .& .\\ .& .& .\\ .& .& .\\ b_{r1}...& b_{\mathrm{ri}}...& b_{\mathrm{rn}}\\ b_{(r+1)1}...& b_{(r+1)i}...& b_{(r+1)n}\\ .& .& .\\ .& .& .\\ .& .& .\\ b_{(n-1)1}...& b_{(n-1)i}...& b_{(n-1)n}\\ b_{n1}...& b_{\mathrm{ni}}...& b_{\mathrm{nn}}\end{array}\right)\left(\begin{array}{c}{\stackrel{\·}{U}}_1\\ .\\ .\\ .\\ {\stackrel{\·}{U}}_{\mathrm{iopen}}\\ .\\ .\\ .\\ {\stackrel{\·}{U}}_r\\ {\stackrel{\·}{U}}_{r+1}\\ .\\ .\\ .\\ {\stackrel{\·}{U}}_{n-1}\\ {\stackrel{\·}{U}}_n\end{array}\right)=\left(\begin{array}{c}0\\ .\\ .\\ .\\ 0\\ .\\ .\\ .\\ 0\\ {\stackrel{\·}{I}}_{r+1}\\ .\\ .\\ .\\ {\stackrel{\·}{I}}_{n-1}\\ {\stackrel{\·}{I}}_n\end{array}\right)---\left(7\right)$

In formula: bus admittance matrix and voltage vector middle element be known quantity.

According to above nodal voltage equation, the system of equations of r equation composition can be obtained such as formula shown in (8):

Order $A=\left(\begin{array}{ccccc}{b}_{11}& ...& b_{1i}& ...& b_{1n}\\ .& & .& & .\\ .& & .& & .\\ .& & .& & .\\ b_{i1}& ...& b_{\mathrm{ii}}& ...& b_{\mathrm{in}}\\ .& & .& & .\\ .& & .& & .\\ .& & .& & .\\ b_{r1}& ...& b_{\mathrm{ri}}& ...& b_{\mathrm{rr}}\end{array}\right),U=\left(\begin{array}{c}{\stackrel{\·}{U}}_1\\ .\\ .\\ .\\ {\stackrel{\·}{U}}_{\mathrm{iopen}}\\ .\\ .\\ .\\ {\stackrel{\·}{U}}_r\end{array}\right),$

$B=\left(\begin{array}{c}{b}_{1(r+1)}{\stackrel{\·}{U}}_{(r+1)}+......b_{1n}{\stackrel{\·}{U}}_n\\ b_{2(r+1)}{\stackrel{\·}{U}}_{(r+1)}+......b_{2n}{\stackrel{\·}{U}}_n\\ .\\ .\\ .\\ .\\ .\\ .\\ b_{r(r+1)}{\stackrel{\·}{U}}_{(r+1)}+......b_{\mathrm{rn}}{\stackrel{\·}{U}}_n\end{array}\right)$

Then formula (8) can be write as following matrix form

AU＝-B (9)

Utilize Gaussian elimination method solving equation (9), i Nodes open-circuit voltage can be solved be Thevenin's equivalence electromotive force due to the sparse property of admittance battle array, utilizing in gaussian elimination solution procedure, be that the calculated amount of upper triangular matrix is less by coefficient matrices A abbreviation, and owing to only needing the open-circuit voltage of computing node i, therefore arrive in backward steps , also without the need to whole unknown quantity is all solved, accelerate solving speed further.Solving the equivalent parameters of other nodes as needed, only need again revise admittance battle array Y ₁, form the equation shown in formula (9), again utilize gaussian elimination to solve.

Thevenin's equivalence parameter comprises equivalent electromotive force and equivalent impedance.The object obtaining whole parameter goes for different voltage stability criterion.Voltage stability criterion based on Thevenin's equivalence comprises based on voltage and impedance comparison two type, if only try to achieve Thevenin's equivalence electromotive force to be only applicable to voltage criterion, therefore also demand gets impedance parameter.After obtaining equivalent electromotive force, the method asking for equivalent impedance is as you know.

Three, simulation example analysis

Simulation calculation is carried out, the correctness of analysis verification we bright institute extracting method and validity for IEEE-9 node and New England 10 machine 39 node system.Accuracy Verification is calculated for Thevenin's equivalence parameter, using calculation of tidal current as system running state profile data in example, between the voltage after being fluctuated by actual Load flow calculation gained voltage and two node system calculated loads after applying this node Thevenin's equivalence after the fluctuation of contrast node load, extent carrys out the quality of parameter of measurement identification result by mistake.It is more accurate that equivalent parameters calculates, and the deviation that after load fluctuation, two node systems of actual this node voltage amplitude of trend gained and Thevenin's equivalence calculate between gained voltage magnitude is less.

What improve is at present based on the fresh approach that local measures based on total differential Thevenin's equivalence parameter tracking algorithm, there is good adaptability for internal system change in equivalence course, therefore select the method and traditional least square method to contrast with institute of the present invention extracting method on IEEE3 machine 9 node system; And contrast equivalent for load bus for coupled single-ended mouth network method with based on triangular web state profile data for New England 10 machine 39 node system.Result shows, no matter institute of the present invention extracting method is in calculating accuracy or is all better than previous methods in calculated amount.

3.1IEEE-9 node analogue system example

IEEE3 machine 9 node system structure as shown in Figure 4.Suppose known t1 and t5 moment system load flow profile data, and between adjacent two moment trend sections, each PQ node load all has the random fluctuation in a big way, PV node meritorious is exerted oneself and to be changed with load fluctuation equal proportion.According to improve based on total differential Thevenin's equivalence parameter tracking algorithm, first calculate Thevenin's equivalence initial value, then the accounting equation substituting into improvement tries to achieve the Thevenin's equivalence parameter of PQ node.For node 6, according to principle of least square method, the voltage phasor of application t1 and t5 moment node 6 and meritorious, reactive power, can calculate the Thevenin's equivalence parameter E in t5 moment _th61, Z _th61.According to institute of the present invention extracting method, the Thevenin's equivalence parameter E of the trend profile data computing node 6 in t5 moment directly can be utilized _th63, Z _th63.

For contrasting the accuracy of t5 moment two groups of equivalent parameters, keep other node condition constant, the load of node 6 adds the random perturbation in one group of 30 ± 35% scope on the basis of t5 moment load.The load of disturbance posterior nodal point 6 is S _6m=P _6m+ jQ _6m(m=1,2 ..., 30).By S _6msubstitute into t5 moment IEEE3 machine 9 node system and carry out the voltage magnitude of Load flow calculation acquisition node 6 as standard value.Again by S _6msubstitute in two node systems of node 6 after Thevenin's equivalence, E is respectively to equivalent parameters _th61, Z _th61and E _th62, Z _th62and E _th63, Z _th63two node systems carry out Load flow calculation obtain voltage magnitude, contrast with standard value, result is as shown in Figure 5.

In figure, voltage 1 is standard value, voltage 2 is for calculating gained voltage magnitude under institute extracting method Dai Weinan parameter of the present invention, voltage 3 is the voltage magnitude under traditional least square method calculating parameter, voltage 4 for improve based on the voltage magnitude under total differential Thevenin's equivalence parameter tracking algorithm parameters obtained.Visible in figure, the comparing traditional least square method based on total differential Thevenin's equivalence parameter tracking algorithm and had certain improvement of improvement, but the inventive method calculates with actual calculation of tidal current deviation less, and relatively above-mentioned two kinds of methods are more accurate.For further illustrating the contrast of equivalent effect, calculate average error and the maximum error of three kinds of methods.The average error of institute of the present invention extracting method is 0.0741%, and maximum error is 0.1217%; The average error of least square method is 0.8248%, and maximum error is 1.4323%; The average error based on total differential Thevenin's equivalence parameter tracking algorithm improved is 0.5605%, and maximum error is 0.9799%.As can be seen here, the method that institute of the present invention extracting method measures based on local relatively has higher accuracy.

3.2New England10 machine 39 node analogue system example

New England10 machine 39 node system structure as shown in Figure 6.For comparing institute of the present invention extracting method and the effect based on triangular web state profile data by load bus equivalence being coupled single-ended mouth network method, New England 10 machine 39 node system carries out simulation analysis.In control methods and 4.1, thinking is similar.First be the Thevenin's equivalence parameter E that coupled single-ended mouth network method distinguishes calculated load node i based on a trend profile data by load bus equivalence by the inventive method with based on triangular web state profile data _thi1, Z _thi1with E _thi2, Z _thi2.Then keep other node condition constant, the load of node i adds one group of random perturbation in totally 20 ± 35% scope on the basis of original load.The load of disturbance posterior nodal point i is S _im=P _im+ jQ _im(m=1,2 ..., 20).By S _imi node load as New England 10 machine 39 node system carries out Load flow calculation and obtains the voltage magnitude of node i as standard value.Again by S _imrespectively as the load of two node systems of node i after Thevenin's equivalence, E is respectively to equivalent parameters _thi1, Z _thi1and E _thi2, Z _thi2two node systems carry out Load flow calculation obtain voltage magnitude, try to achieve the relative error number percent with standard value, the comparing result of node 29 is as shown in Figure 7.

In figure, voltage magnitude 1 is standard value, voltage magnitude 2 calculates gained load bus voltage magnitude for adopting the inventive method Thevenin's equivalence parameter, two node Load flow calculation load bus voltage magnitudes of voltage magnitude 3 be employing based on triangular web state profile data by load bus equivalence be coupled single-ended mouth network method gained Thevenin's equivalence parameter.By in figure shown in curve, in load random variation process, the equivalent parameters accuracy that the inventive method calculates is higher than being coupled single-ended mouth network method based on triangular web state profile data by load bus equivalence.

Finally contrast according to above-mentioned thinking the node that each load is non-vanishing, on each node, the parameter computational accuracy of institute of the present invention extracting method is all higher than being coupled single-ended mouth network method based on triangular web state profile data by load bus equivalence.

Relatively from calculated amount, if calculate separately the Thevenin's equivalence parameter of a certain node, computing time needed for the inventive method is than based on triangular web state profile data by load bus equivalence being the little order of magnitude of coupled single-ended mouth network method, if need the equivalent parameters calculating whole load bus, then both computing times are suitable, and scale and the load bus number of its concrete time and system are closely related.With regard to this simulation example, computing platform is HP Z600 workstation, and CPU is two four core Xeon E5504, and dominant frequency 2G, internal memory 4G, software platform is MatLab, and trend instrument is open source software PSAT.The Thevenin's equivalence parameter temporal calculating whole load non-zero node is 5 to 6 milliseconds, meets the needs of online real-time application completely.

By reference to the accompanying drawings the specific embodiment of the present invention is described although above-mentioned; but not limiting the scope of the invention; one of ordinary skill in the art should be understood that; on the basis of technical scheme of the present invention, those skilled in the art do not need to pay various amendment or distortion that creative work can make still within protection scope of the present invention.

Claims (10)

1., based on the wide area Thevenin's equivalence parameter on-line calculation method of a single state section, it is characterized in that, comprise the following steps:

(1) equiva lent impedance process is done to the load of current state load bus;

(2) correcting process is done to original system bus admittance matrix, obtain the system admittance matrix after equiva lent impedance process;

(3) load impedance at current state load bus place is disconnected, according to the bus admittance matrix revising later admittance matrix calculating open-circuit voltage;

(4) nodal voltage equation of current state load bus after equiva lent impedance process is calculated;

(5) according to revised admittance matrix and nodal voltage equation, the open-circuit voltage of calculated load node, and using described open-circuit voltage as Thevenin's equivalence electromotive force, and then obtain study the whole parameter of Thevenin's equivalence of load bus, obtain the criterion of voltage stabilization.

2., as claimed in claim 1 based on the wide area Thevenin's equivalence parameter on-line calculation method of a single state section, it is characterized in that, the concrete grammar of described step (1) is:

If system PV and balance node number sum are m, PQ nodes is r, total nodes is n; Under wide area measurement condition, each node voltage amplitude of system, phase place and active reactive power are known, under calculating moment system state section, all PV nodes and balance node are all considered as ideal voltage source, for the PQ node of on-load, its load all by the power of this node and voltage, can calculate an equivalent load impedance.

3., as claimed in claim 1 based on the wide area Thevenin's equivalence parameter on-line calculation method of a single state section, it is characterized in that, the concrete grammar of described step (2) is:

If the original admittance matrix of system is Y ₀, Y ₀middle element is as follows:

$Y_0=\left(\begin{array}{ccccc}{Y}_{11}& ...& Y_{1i}& ...& Y_{1n}\\ .& & .& & .\\ .& & .& & .\\ .& & .& & .\\ Y_{i1}& ...& Y_{\mathrm{ii}}& ...& Y_{\mathrm{in}}\\ .& & .& & .\\ .& & .& & .\\ .& & .& & .\\ Y_{n1}& ...& Y_{\mathrm{ni}}& ...& Y_{\mathrm{nn}}\end{array}\right);$

Element Y in matrix _ijtransadmittance between representation node i and node j, Y _iithe self-admittance of representation node i;

Load impedance is integrated into system admittance matrix Y ₀, only need revise the admittance battle array Y corresponding with load bus ₀diagonal element, all the other elements are constant;

$a_{\mathrm{ii}}=Y_{\mathrm{ii}}+\frac{1}{Z_{\mathrm{Li}}},i\∈(\mathrm{1,2,3}...r)$

Then revised admittance matrix is:

$Y_1=\left(\begin{array}{ccccc}{a}_{11}& ...& a_{1r}& ...& a_{1n}\\ .& & .& & .\\ .& & .& & .\\ .& & .& & .\\ a_{r1}& ...& a_{\mathrm{rr}}& ...& a_{\mathrm{rn}}\\ .& & .& & .\\ .& & .& & .\\ .& & .& & .\\ a_{n1}& ...& a_{\mathrm{nr}}& ...& a_{\mathrm{nn}}\end{array}\right)=\left(\begin{array}{ccccc}{a}_{11}& ...& Y_{1r}& ...& Y_{1n}\\ .& & .& & .\\ .& & .& & .\\ .& & .& & .\\ Y_{r1}& ...& a_{\mathrm{rr}}& ...& Y_{\mathrm{rn}}\\ .& & .& & .\\ .& & .& & .\\ .& & .& & .\\ Y_{n1}& ...& Y_{\mathrm{nr}}& ...& Y_{\mathrm{nn}}\end{array}\right);$

Wherein, r is PQ nodes, Z _libe the equiva lent impedance of i-th PQ node, represent the admittance value of load impedance.

4., as claimed in claim 1 based on the wide area Thevenin's equivalence parameter on-line calculation method of a single state section, it is characterized in that, the concrete grammar of described step (3) is:

Current state load bus self-admittance a in later admittance matrix will be revised _iideduct load impedance, namely form the bus admittance matrix Y calculating open-circuit voltage.

5., as claimed in claim 4 based on the wide area Thevenin's equivalence parameter on-line calculation method of a single state section, it is characterized in that, the bus admittance matrix Y of open-circuit voltage is specially:

$Y=\left(\begin{array}{ccccc}{b}_{11}& ...& b_{1r}& ...& b_{1n}\\ .& & .& & .\\ .& & .& & .\\ .& & .& & .\\ b_{r1}& ..& b_{\mathrm{rr}}& ...& b_{\mathrm{rn}}\\ .& & .& & .\\ .& & .& & .\\ .& & .& & .\\ b_{n1}& ...& b_{\mathrm{nr}}& ...& b_{\mathrm{nn}}\end{array}\right)=\left(\begin{array}{ccccc}{b}_{11}& ...& a_{1r}& ...& a_{1n}\\ .& & .& & .\\ .& & .& & .\\ .& & .& & .\\ a_{r1}& ...& b_{\mathrm{rr}}& ...& a_{\mathrm{rn}}\\ .& & .& & .\\ .& & .& & .\\ .& & .& & .\\ a_{n1}& ...& a_{\mathrm{nr}}& ...& a_{\mathrm{nn}}\end{array}\right);$

Wherein, for the node i of open-circuit voltage to be asked, its corresponding self-admittance should be represent the admittance value of load impedance, a _iirepresent and revise r diagonal entry before in later admittance matrix.

6., as claimed in claim 1 based on the wide area Thevenin's equivalence parameter on-line calculation method of a single state section, it is characterized in that, the concrete grammar of described step (4) is:

When solving i node open-circuit voltage, node voltage vector $\stackrel{.}{U}=\left(\begin{array}{c}{\stackrel{.}{U}}_1\\ .\\ .\\ .\\ {\stackrel{.}{U}}_{\mathrm{iopen}}\\ .\\ .\\ .\\ {\stackrel{.}{U}}_n\end{array}\right)$ In, PQ node voltage phasor is amount to be asked, and PV node and balance node voltage phasor are known quantity; After adopting node load equivalent impedance, node Injection Current vector $\stackrel{.}{I}=\left(\begin{array}{c}{\stackrel{.}{I}}_1\\ .\\ .\\ .\\ {\stackrel{.}{I}}_i\\ .\\ .\\ .\\ {\stackrel{.}{I}}_n\end{array}\right)$ In be 0, draw according to nodal voltage equation

In formula: bus admittance matrix and voltage vector middle element be known quantity; represent the voltage of PQ node 1 to r, representing the open-circuit voltage of i-th PQ node, is amount to be asked, represent the Injection Current of PV and balance node.

7., as claimed in claim 6 based on the wide area Thevenin's equivalence parameter on-line calculation method of a single state section, it is characterized in that, in described nodal voltage equation,

Order $A=\left(\begin{array}{ccccc}{b}_{11}& ...& b_{1i}& ...& b_{1n}\\ .& & .& & .\\ .& & .& & .\\ .& & .& & .\\ b_{i1}& ...& b_{\mathrm{ii}}& ...& b_{\mathrm{in}}\\ .& & .& & .\\ .& & .& & .\\ .& & .& & .\\ b_{r1}& ...& b_{r1}& ...& b_{\mathrm{rr}}\end{array}\right),U=\left(\begin{array}{c}{\stackrel{.}{U}}_1\\ .\\ .\\ .\\ {\stackrel{.}{U}}_{\mathrm{iopen}}\\ .\\ .\\ .\\ {\stackrel{.}{U}}_r\end{array}\right),B=\left(\begin{array}{c}{b}_{1(r+1)}{\stackrel{.}{U}}_{(r+1)}+......b_{1n}{\stackrel{.}{U}}_n\\ b_{2(r+1)}{\stackrel{.}{U}}_{(r+1)}+......b_{2n}{\stackrel{.}{U}}_n\\ .\\ .\\ .\\ .\\ .\\ .\\ b_{r(r+1)}{\stackrel{.}{U}}_{(r+1)}+......b_{\mathrm{rn}}{\stackrel{.}{U}}_n\end{array}\right);$

Then nodal voltage equation can be write as following matrix form:

AU＝-B

Utilize Gaussian elimination method to solve above-mentioned equation, solve i Nodes open-circuit voltage be Thevenin's equivalence electromotive force ${\stackrel{\·}{E}}_{\mathrm{thi}}.$

8. as claimed in claim 6 based on the wide area Thevenin's equivalence parameter on-line calculation method of a single state section, it is characterized in that, due to the sparse property of admittance battle array, utilizing in gaussian elimination solution procedure, be upper triangular matrix by coefficient matrices A abbreviation, and owing to only needing the open-circuit voltage of computing node i, therefore arrive in backward steps , without the need to whole unknown quantity is all solved; Solving the equivalent parameters of other nodes as needed, only need again revise admittance battle array Y ₁, form new nodal voltage equation, again utilize gaussian elimination to solve.

9., as claimed in claim 1 based on the wide area Thevenin's equivalence parameter on-line calculation method of a single state section, it is characterized in that, the concrete grammar of described step (5) is:

Utilize Gaussian elimination method solution node voltage equation, i Nodes open-circuit voltage can be solved

10. as claimed in claim 1 based on the wide area Thevenin's equivalence parameter on-line calculation method of a single state section, it is characterized in that, according to the load fluctuation of each node of load prediction gained, take into account various regulation measure quantum chemical method and go out to-be section information, the change of each node equivalent parameters can be calculated fast, realize accurately estimating the equivalent parameters under to-be.