CN101969198A - Method for estimating electrical power system state with consideration of load static property - Google Patents

Abstract

The invention discloses a method for estimating an electrical power system state with the consideration of a load static property, relating to the method for estimating the electric power system state executed on the identified base of a system load model. The method comprises the following steps: firstly, obtaining an algebraic equation changed with the voltage for loading an active power and a reactive power by the identified load static model on a system load node; then, supplementing an injection power measurement of the primary load node by constructing a zero-injection power measurement, and endowing a larger weight; finally, combining with a normal state estimating program for finally accurately estimating the state variable quantity of the system. The method considers the static property of the load node measurement in the state estimating and calculating processes, thereby improving the precision of the state estimation; furthermore, the method is easily combined with an existing state estimating software.

Description

Consider the power system state estimation method of static load characteristic

Technical field

Invention relates to a kind of power system state estimation method of considering static load characteristic, belongs to power system operation and control technology field.

Background technology

In the dispatching patcher in modern times, the senior automation function of computer has become an important ring.EMS (energy manage system, EMS) be modern electric dispatch automated system based on computer, its the most basic change that brings is exactly to rise to the analytic type scheduling by the rule-of-thumb approach scheduling, thereby has improved the fail safe and the economy of power system operation.Along with developing rapidly of electric power system, modern dispatching patcher requires rapidly, accurately and all sidedly to grasp the actual motion state of electric power system, so EMS has obtained using widely.State estimation is the important component part of EMS, its result directly influences the intelligent analysis and the decision-making of dispatching of power netwoks, it is the important ring between telemechanical apparatus and the database, here, it has improved data precision, has filtered bad data, the deficiency of the supplementary point and the project of measurement, guarantee the quality and reliability of electric power system real time data, further improved the level and the function of the senior online application program of electric power system.

In order to determine the safety and economy situation of electric power system, guarantee that the quality of electric power system real time data just becomes the key of the online application level of further raising computer.Along with developing rapidly of electric power system, the load modeling of each load point is more and more accurately with perfect, on this basis, the present invention has utilized the voltage character of load static models to replenish the load bus injecting power and has been applied in the state estimation, in the hope of improving the estimated accuracy of state estimation, and then improve the q﹠r of whole data system.

State estimation is to utilize the redundancy of real-time measurement system to improve data precision, on the measurement amount basis that telemechanical apparatus improves, sets up the target function of a weighted residual quadratic sum, can expect to obtain making the state vector z of target function minimum then.The measurement amount is many more, and the quantity of state that estimates is accurate more; Otherwise, the measurement amount is few more, the error of the quantity of state that estimates is just big more, and in the general quantity examining system, measurement amount variance of estimaion error shows that state estimation can improve the precision of metric data, therefore less than the error in measurement variance, the measurement amount is many more and accurate more, and is good more to the effect as a result of state estimation.In the modern power systems, the research of load model is more and more deep, the load model identification work of the existing load bus of system has been gradually improved and is accurate, the power system state estimation method of considering the load static models is on the basis of the accurate identification of load static models, measure the injecting power measurement that replenishes original load bus by making up zero injecting power, and give bigger weights it.Then, combine with conventional state estimation program, owing in state estimation computational process, when load bus measures, considered its static characteristic, thus finally can estimate the state variable of system more accurately.

Summary of the invention

Technical problem to be solved by this invention is to provide a kind of power system state estimation method based on load voltage static characteristic model at the defective that prior art exists.

The present invention adopts following technical scheme for achieving the above object:

The present invention is characterized in that comprising step down for considering the power system state estimation method of static load characteristic:

(1) reads electric network data among the EMS, comprising: the branch road of transmission line number, headend node and endpoint node numbering, transformer voltage ratio and impedance, series resistance reactance, shunt conductance susceptance;

(2) read the static load characteristic parameter, comprising: load active power, reactive power and relevant voltage performance index during the datum mark steady operation, the static load characteristic model representation is as follows:

Adopt power function model:

$P_i=P_{i0}{\left(\frac{u_i}{u_N}\right)}^{p_U}$

$Q_i=Q_{i0}{\left(\frac{u_i}{u_N}\right)}^{q_U}$

Adopt the quadratic polynomial model:

$P_i=P_{i0}[a_p{\left(\frac{u_i}{u_N}\right)}^2+b_p\left(\frac{u_i}{u_N}\right)+c_p]$

$Q_i=Q_{i0}[a_q{\left(\frac{u_i}{u_N}\right)}^2+b_q\left(\frac{u_i}{u_N}\right)+c_q]$

(3) initialization comprises: to quantity of state initial value, the optimization of node order be set, form node admittance matrix, threshold value be set, storage allocation;

(4) input real-time measurement amount z comprises voltage magnitude, generator active power, generator reactive power, part of nodes (promptly having picked out the node of static load characteristic model) load active power and reactive power, circuit head end active power, circuit head end reactive power, line end active power and line end reactive power;

(5) for the load bus of known its static characteristic parameter, make up zero injecting power measurement equation and replenish original load bus power measurement equation, consider that the zero injection rate measurement of static load characteristic is expressed as follows:

Adopt power function model:

$0=-P_{i0}{\left(\frac{u_i}{u_N}\right)}^{p_U}+\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{u}_i{u}_j(G_{\mathrm{ij}}{\cos \mathrm{\θ}}_{\mathrm{ij}}+B_{\mathrm{ij}}{\sin \mathrm{\θ}}_{\mathrm{ij}})$

$0=-Q_{i0}{\left(\frac{u_i}{u_N}\right)}^{q_U}+\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{u}_i{u}_j(G_{\mathrm{ij}}{\cos \mathrm{\θ}}_{\mathrm{ij}}-B_{\mathrm{ij}}{\sin \mathrm{\θ}}_{\mathrm{ij}})$

Adopt the quadratic polynomial model:

$0={-P}_{i0}[a_p{\left(\frac{u_i}{u_N}\right)}^2+b_p\left(\frac{u_i}{u_N}\right)+c_p]+\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{u}_i{u}_j(G_{\mathrm{ij}}{\cos \mathrm{\θ}}_{\mathrm{ij}}+B_{\mathrm{ij}}{\sin \mathrm{\θ}}_{\mathrm{ij}})$

$0={-Q}_{i0}[a_q{\left(\frac{u_i}{u_N}\right)}^2+b_q\left(\frac{u_i}{u_N}\right)+c_q]+\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{u}_i{u}_j(G_{\mathrm{ij}}{\sin \mathrm{\θ}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}})$

(6) recover iteration count iterations k=1;

(7) calculate the calculated value h (x of each measurement amount by existing quantity of state x (k) ^(l)) and Jacobian matrix H (x ^(l)), the load bus of wherein known load static models zero injection rate is measured calculated value and is:

Adopt power function model:

$h_i\left({x_i}^{\left(l\right)}\right)=-P_{i0}{\left(\frac{u_i^{\left(l\right)}}{u_N}\right)}^{p_U}+\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{u}_i^{\left(l\right)}{u}_j^{\left(l\right)}(G_{\mathrm{ij}}{\cos \mathrm{\θ}}_{\mathrm{ij}}^{\left(l\right)}+B_{\mathrm{ij}}{\sin \mathrm{\θ}}_{\mathrm{ij}}^{\left(l\right)})$

$h_i\left({x_i}^{\left(l\right)}\right)=-Q_{i0}{\left(\frac{u_i^{\left(l\right)}}{u_N}\right)}^{q_U}+\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{u}_i^{\left(l\right)}{u}_j^{\left(l\right)}(G_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}}^{\left(l\right)}-B_{\mathrm{ij}}{\cos \mathrm{\θ}}_{\mathrm{ij}}^{\left(l\right)})$

Adopt the quadratic polynomial model:

$h_i\left(x_i^{\left(l\right)}\right)=-P_{i0}[a_p{\left(\frac{u_i^{\left(l\right)}}{u_N}\right)}^2+b_p\left(\frac{u_i^{\left(l\right)}}{u_N}\right)+c_p]+\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{u}_i^{\left(l\right)}{u}_j^{\left(l\right)}(G_{\mathrm{ij}}{\cos \mathrm{\θ}}_{\mathrm{ij}}^{\left(l\right)}+B_{\mathrm{ij}}{\sin \mathrm{\θ}}_{\mathrm{ij}}^{\left(l\right)})$

$h_i\left(x_i^{\left(l\right)}\right)=-Q_{i0}[a_q{\left(\frac{u_i^{\left(l\right)}}{u_N}\right)}^2+b_q\left(\frac{u_i^{\left(l\right)}}{u_N}\right)+c_q]+\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{u}_i^{\left(l\right)}{u}_j^{\left(l\right)}(G_{\mathrm{ij}}{\sin \mathrm{\θ}}_{\mathrm{ij}}^{\left(l\right)}-B_{\mathrm{ij}}{\cos \mathrm{\θ}}_{\mathrm{ij}}^{\left(l\right)})$

This type of measures, and element is in the corresponding Jacobian matrix:

Adopt power function model:

$\frac{{\∂P}_i}{\∂v_i}=-P_{i0}{p}_U{\left(u_i\right)}^{p_U-1}+\frac{1}{u_i}(G_{\mathrm{ii}}{u}_i^2+P_i)$

$\frac{{\∂Q}_i}{\∂v_i}=-Q_{i0}{q}_U{\left(u_i\right)}^{q_U-1}+\frac{1}{u_i}(-B_{\mathrm{ii}}{u}_i^2+Q_i)$

Adopt the quadratic polynomial model:

$\frac{{\∂P}_i}{{\∂v}_i}=-P_{i0}[2a_p\left(\frac{u_i}{u_N}\right)+b_p]+\frac{1}{u_i}\left(G_{\mathrm{ii}}{u}_i^2{+P}_i\right)$

$\frac{{\∂Q}_i}{{\∂v}_i}=-Q_{i0}[2a_q\left(\frac{u_i}{u_N}\right)+b_q]+\frac{1}{u_i}(-B_{\mathrm{ii}}{u}_i^2{+Q}_i)$

(8) ask for state correction amount x ^(k), choose

And the correction quantity of state obtains x ^(k+1)

$\mathrm{\Δ}{\hat{x}}_1^{\left(k\right)}={\left[H^T\left({\hat{x}}^{\left(k\right)}\right)R^{-1}H\left({\hat{x}}^{\left(k\right)}\right)\right]}^{-1}\×H^T\left({\hat{x}}^{\left(k\right)}\right)R^{-1}[z-h\left({\hat{x}}^{\left(k\right)}\right)]$

${\hat{x}}^{(k+1)}={\hat{x}}^{\left(k\right)}+\mathrm{\Δ}{\hat{x}}^{\left(k\right)}$

(9) judge

Whether less than convergence, if, finish to calculate, carry out the k+1 time estimation otherwise return step (6).

Traditional state estimation utilization is measured and corresponding variance is set up target function, solves to make the quantity of state of target function minimum.Because the measurement amount comprises white Gaussian noise, the inevitable white Gaussian noise that also have of state estimation value in iterative process and last result, and as can be seen by the analysis of state estimation algorithm, state estimation error variance battle array diagonal element is the diagonal element after information matrix is inverted, its diagonal element whatever you like measurement of information matrix increases and increases, the diagonal element of its inverse matrix then decreases, and therefore, the quality of measurement system configuration and what are keys of state estimation effect.

The present invention is on the basis of load modeling identification, the voltage character of load static models have been considered during to the choosing of load power measurement amount, considered the injecting power amount of load point more comprehensively and accurately, utilize accurate voltage character of load static models to replenish the measurement amount that replaces containing random error, at this moment, the load bus injecting power is the performance number of load static models reflection and the zero injecting power of power equation calculated value addition, because it is not containing white Gaussian noise for exact solution, then give bigger weights (10～100 times to the weight of real-time measurement amount) to it, and iterative computation is carried out in substitution, when the iterative Jacobian matrix, need replenish into load model factor for the node of having considered load quiescent voltage characteristic during to self node voltage amplitude differentiate, the Jacobian matrix remainder is constant.The present invention has improved the quality of measurement configuration effectively, and has made the result of state estimation more accurate by having taken into account load voltage static characteristic model.

Description of drawings

Fig. 1: the inventive method flow chart.

Fig. 2: the element equivalent circuit diagram that the present invention adopts, wherein: figure (a) is a circuit ∏ shape equivalent circuit diagram, figure (b) is a transformer ∏ shape equivalent circuit diagram.

Embodiment

Be elaborated below in conjunction with the technical scheme of accompanying drawing to invention:

The real time execution of electric power system and control need the true operating condition of understanding system, because aspects such as measurement and transmission, there is error unavoidably in the living data that obtain, and state estimation can improve the precision of data to a certain extent.From the Xu Huaipi of Massachusetts Institute Technology in 1969 people such as (F.C.Schweppe) the rudimentary algorithm of Power system state estimation having been proposed---since basic weighted least-squares (the weighted least squares WLS) state estimation algorithm, weighted least-squares method becomes the maximum algorithm of application in the Power system state estimation.WLS tries to achieve the weighted residual quadratic sum with the inverse of the variance of measurement amount error as the weight of corresponding residual error (measurement amount and measure the poor of estimated value), and as target function, expectation obtains making the state vector x of target function minimum with this.Therefore, the q﹠r of measurement system configuration is very important to the state estimation result, and the present invention has considered the load static models on the basis of WLS for the measurement system configuration requirement, in the hope of obtaining more accurate estimated result.

Under the condition of given network connection, branch road parameter and measurement system, non-linear measurement equation can be expressed as:

z＝h(x)+v

In the formula, z is a telemetry for the measuring value vector, and the overwhelming majority is the real time data that obtains by remote measurement, and it is the artificial data that are provided with that sub-fraction is also arranged, and is called as pseudo-metric data; H (x) is the true value of measurement amount of hypothesis, the phasor function of being set up by basic circuit laws such as kirchhoffs; X is that n maintains the system state variable; V is an error in measurement, supposes that average is zero, variance is σ ²The normal distribution random vector, it is the m n dimensional vector n.

In Power system state estimation, the type of measurement amount configuration is more than conventional trend, has comprised that not only the injecting power of each node measures P _i, Q _i, can also comprise the power measurement P of branch road _Ij, Q _Ij, P _Ji, Q _JiAnd the voltage of node measures V _iInject meritorious power measurement P with node _i, branch road top active power measures P _IjAnd node voltage measures V _iBe example, measurement equation is shown below:

Node injects active power and reactive power (following all is with polar coordinate representation):

$P_i=\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{u}_i{u}_j(G_{\mathrm{ij}}{\cos \mathrm{\θ}}_{\mathrm{ij}}+B_{\mathrm{ij}}{\sin \mathrm{\θ}}_{\mathrm{ij}})$

$Q_i=\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{u}_i{u}_j(G_{\mathrm{ij}}{\sin \mathrm{\θ}}_{\mathrm{ij}}-B_{\mathrm{ij}}{\cos \mathrm{\θ}}_{\mathrm{ij}})$

In the above-mentioned measurement equation, Y _IjFor the element between corresponding node i and the j in the node admittance battle array, Y is arranged _Ij=G _Ij+ B _Ij, G wherein _IjFor electricity is led, B _IjBe susceptance; P _iAnd Q _iMeritorious and the idle injecting power for node i, its direction dictates: flow into node i for just, flow out node i for negative.

The node i voltage magnitude:

U _i＝U _i

Non-transformer lines i-j goes up top active power and reactive power:

$P_{\mathrm{ij}}=u_i^{2}g-u_i{u}_j{g\cos \mathrm{\θ}}_{\mathrm{ij}}-u_i{u}_j{b\cos \mathrm{\θ}}_{\mathrm{ij}}-u_i{u}_j{b\sin \mathrm{\θ}}_{\mathrm{ij}}$

$Q_{\mathrm{ij}}={-u}_i^2(b+y_c)-u_i{u}_j{g\sin \mathrm{\θ}}_{\mathrm{ij}}+u_i{u}_j{b\cos \mathrm{\θ}}_{\mathrm{ij}}$

Non-transformer branch road i-j goes up terminal active power and reactive power:

$P_{\mathrm{ji}}=u_j^{2}g+u_i{u}_j(-g\cos {\mathrm{\θ}}_{\mathrm{ij}}+{b\sin \mathrm{\θ}}_{\mathrm{ij}})$

$Q_{\mathrm{ji}}=-u_j^2(b+y_c)+u_i{u}_j({g\sin \mathrm{\θ}}_{\mathrm{ij}}+{b\cos \mathrm{\θ}}_{\mathrm{ij}})$

In the above-mentioned measurement equation, y _IjAdmittance value for circuit has R, X, g, b are respectively line resistance, reactance, electricity is led and susceptance.

For the transformer branch road, measurement equation is shown below:

Transformer branch road i-j goes up top active power and reactive power:

$P_{\mathrm{ij}}=-\frac{1}{K}{u}_i{u}_j{b}_T{\sin \mathrm{\θ}}_{\mathrm{ij}}$

$Q_{\mathrm{ij}}=-\frac{1}{K^2}{u}_i^2{b}_T+\frac{1}{K}{u}_i{u}_j{b}_T{\cos \mathrm{\θ}}_{\mathrm{ij}}$

Transformer branch road i-j goes up terminal active power and reactive power:

$P_{\mathrm{ji}}=\frac{1}{K}{u}_i{u}_j{b}_T{\sin \mathrm{\θ}}_{\mathrm{ij}}$

$Q_{\mathrm{ji}}=-b_T{u}_j^2+\frac{1}{K}{u}_i{u}_j{b}_T{\cos \mathrm{\θ}}_{\mathrm{ij}}$

In the above-mentioned transformer branch road measurement equation, K is the non-standard no-load voltage ratio of transformer.J is the standard side, and no-load voltage ratio is 1; I is non-standard side, and no-load voltage ratio is K; b _TSusceptance for transformer standard side (j side) has

X wherein _TReactance for transformer standard side.

Make up zero and inject active power and reactive power equation:

Adopt power function model:

$0=P_i=-P_{i0}{\left(\frac{u_i}{u_N}\right)}^{p_U}+\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{u}_i{u}_j(G_{\mathrm{ij}}{\cos \mathrm{\θ}}_{\mathrm{ij}}+B_{\mathrm{ij}}{\sin \mathrm{\θ}}_{\mathrm{ij}})$

$0-Q_i=-Q_{i0}{\left(\frac{u_i}{u_N}\right)}^{q_U}+\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{u}_i{u}_j(G_{\mathrm{ij}}{\sin \mathrm{\θ}}_{\mathrm{ij}}-B_{\mathrm{ij}}{\cos \mathrm{\θ}}_{\mathrm{ij}})$

Adopt the quadratic polynomial model:

$0=P_i={-P}_{i0}[a_p{\left(\frac{u_i}{u_N}\right)}^2+b_p\left(\frac{u_i}{u_N}\right)+c_p]+\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{u}_i{u}_j(G_{\mathrm{ij}}{\cos \mathrm{\θ}}_{\mathrm{ij}}+B_{\mathrm{ij}}{\sin \mathrm{\θ}}_{\mathrm{ij}})$

$0=Q_i=-Q_{i0}[a_q{\left(\frac{u_i}{u_N}\right)}^2+b_q\left(\frac{u_i}{u_N}\right)+c_q]+\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{u}_i{u}_j(G_{\mathrm{ij}}{\sin \mathrm{\θ}}_{\mathrm{ij}}-B_{\mathrm{ij}}{\cos \mathrm{\θ}}_{\mathrm{ij}})$

In the aforesaid equation, P _I0And Q _I0Load active power and reactive power when being respectively the datum mark steady operation, p _UAnd q _UBe the voltage characteristic index of load meritorious and reactive power, a _p, b _p, c _p(a _q, b _q, c _q) active power (reactive power) that is respectively constant impedance, constant current, firm power load accounts for the percentage of total active power (reactive power), and a is arranged _p+ b _p+ c _p=1 (a _q+ b _q+ c _q=1).This moment, no longer there was random error in load bus injecting power deviation, then Δ P _iWith Δ Q _iIt is zero injecting power.

After the given measurement vector z, the state estimation vector

Be to make target function:

J(x)＝[z-h(x)] ^TR ^-1[z-h(x)]

Reach the value of the x of minimum.Wherein, R ^-1Be with

Inverse be the diagonal matrix of diagonal element, in state estimation, play the meaning heavy to the residual error weighting.

Because h (x) is the nonlinear function of x, so can't directly calculate

In order to ask for

At first h (x) is carried out the linearisation hypothesis, ignores after the above nonlinear terms of secondary, obtain:

h(x)＝h(x ₀)+H(x ₀)Δx

In the formula, Δ x=x-x ₀,

$H\left(x_0\right)=\frac{\∂h\left(x\right)}{\∂x}{|}_{x=x_0}$

The H here (x) is the Jacobian matrix that m * n rank measure vector.

At this moment, target function obtains:

J(x)＝[Δz-H(x ₀)Δx] ^TR ^-1[Δz-H(x ₀)Δx]

Δ z=z-h (x in the formula ₀)

Desire to make the target function minimum,, thereby have its differentiate or expansion prescription:

$\mathrm{\Δ}\tilde{x}=\mathrm{\Σ}\left(x_0\right)H^T\left(x_0\right)R^{-1}\mathrm{\Δz}$

Obtain thus:

$\tilde{x}=x_0+\mathrm{\Δ}\tilde{x}=x_0+\mathrm{\Σ}\left(x_0\right)H^T\left(x_0\right)R^{-1}[z-h\left(x_0\right)]$

When adopting the polar coordinate system expression formula, each measurement amount h _i(x) to quantity of state x _jA partial derivative be calculated as

As follows:

The node voltage amplitude:

$\left\{\begin{array}{c}\frac{{\∂U}_i}{{\∂\mathrm{\ν}}_i}=1\\ \frac{{\∂U}_i}{{\∂\mathrm{\θ}}_i}=0\\ \frac{{\∂U}_i}{{\∂\mathrm{\ν}}_j}=0\\ \frac{{\∂U}_i}{{\∂\mathrm{\θ}}_j}=0\end{array}\right.$

Node injects meritorious and reactive power:

$\left\{\begin{array}{cc}\frac{{\∂P}_i}{\∂u_i}=\frac{1}{u_i}(G_{\mathrm{ii}}{u}_i^2+P_i)& \frac{{\∂O}_i}{{\∂u}_i}=\frac{1}{u_i}(-B_{\mathrm{ii}}{u}_i^2+Q_i)\\ \frac{{\∂P}_i}{{\∂\mathrm{\θ}}_i}=-B_{\mathrm{ii}}{u}_i^2-Q_i& \frac{{\∂Q}_i}{{\∂\mathrm{\θ}}_i}=-G_{\mathrm{ii}}{u}_i^2+P_i\\ \frac{{\∂P}_i}{\∂u_j}=u_i(G_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}})& \frac{{\∂Q}_i}{{\∂u}_j}=u_i(G_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}})\\ \frac{{\∂P}_i}{{\∂\mathrm{\θ}}_j}=u_i{u}_j(G_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}})& \frac{{\∂Q}_i}{{\∂\mathrm{\θ}}_j}=-u_i{u}_j(G_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}})\end{array}\right.$

Top power on the non-transformer branch road i-j:

$\left\{\begin{array}{cc}\frac{{\∂P}_{\mathrm{ij}}}{{\∂u}_i}=2u_{i}g-u_{j}g\cos {\mathrm{\θ}}_{\mathrm{ij}}-u_{j}b\sin {\mathrm{\θ}}_{\mathrm{ij}}& \frac{{\∂O}_{\mathrm{ij}}}{{\∂u}_i}=-2u_i(b+y_c)-u_j(g\sin {\mathrm{\θ}}_{\mathrm{ij}}-b\cos {\mathrm{\θ}}_{\mathrm{ij}})\\ \frac{{\∂P}_{\mathrm{ij}}}{{\∂\mathrm{\θ}}_i}=u_i{u}_j(g\sin {\mathrm{\θ}}_{\mathrm{ij}}-b\cos {\mathrm{\θ}}_{\mathrm{ij}})& \frac{{\∂Q}_{\mathrm{ij}}}{{\∂\mathrm{\θ}}_i}=-u_i{u}_j(g\cos {\mathrm{\θ}}_{\mathrm{ij}}+b\sin {\mathrm{\θ}}_{\mathrm{ij}})\\ \frac{{\∂P}_{\mathrm{ij}}}{{\∂u}_j}=-u_i(g\cos {\mathrm{\θ}}_{\mathrm{ij}}+b\sin {\mathrm{\θ}}_{\mathrm{ij}})& \frac{{\∂Q}_{\mathrm{ij}}}{{\∂u}_j}=-u_i(g\sin {\mathrm{\θ}}_{\mathrm{ij}}-b\cos {\mathrm{\θ}}_{\mathrm{ij}})\\ \frac{{\∂P}_{\mathrm{ij}}}{{\∂\mathrm{\θ}}_j}=-u_i{u}_j(g\sin {\mathrm{\θ}}_{\mathrm{ij}}-b\cos {\mathrm{\θ}}_{\mathrm{ij}})& \frac{{\∂Q}_{\mathrm{ij}}}{{\∂\mathrm{\θ}}_j}=u_i{u}_j(g\cos {\mathrm{\θ}}_{\mathrm{ij}}+b{\sin \mathrm{\θ}}_{\mathrm{ij}})\end{array}\right.$

Terminal power on the non-transformer branch road i-j:

$\left\{\begin{array}{cc}\frac{\∂P_{\mathrm{ji}}}{{\∂u}_i}=u_j(-g\cos {\mathrm{\θ}}_{\mathrm{ij}}+b\sin {\mathrm{\θ}}_{\mathrm{ij}})& \frac{{\∂O}_{\mathrm{ji}}}{{\∂u}_i}=u_j({g\sin \mathrm{\θ}}_{\mathrm{ij}}+b\cos {\mathrm{\θ}}_{\mathrm{ij}})\\ \frac{\∂P_{\mathrm{ji}}}{{\∂\mathrm{\θ}}_i}=u_i{u}_j({g\sin \mathrm{\θ}}_{\mathrm{ij}}+{b\cos \mathrm{\θ}}_{\mathrm{ij}})& \frac{{\∂Q}_{\mathrm{ji}}}{{\∂\mathrm{\θ}}_i}{u}_i{u}_j({g\cos \mathrm{\θ}}_{\mathrm{ij}}-b\sin {\mathrm{\θ}}_{\mathrm{ij}})\\ \frac{{\∂P}_{\mathrm{ji}}}{{\∂u}_j}=2u_{j}g+u_i(-g\cos {\mathrm{\θ}}_{\mathrm{ij}}+b\sin {\mathrm{\θ}}_{\mathrm{ij}})& \frac{{\∂Q}_{\mathrm{ji}}}{{\∂u}_j}=2u_j(b+y_c)+u_i({g\sin \mathrm{\θ}}_{\mathrm{ij}}+b\cos {\mathrm{\θ}}_{\mathrm{ij}})\\ \frac{{\∂P}_{\mathrm{ji}}}{{\∂\mathrm{\θ}}_j}=-u_i{u}_j({g\sin \mathrm{\θ}}_{\mathrm{ij}}+b\cos {\mathrm{\θ}}_{\mathrm{ij}})& \frac{{\∂Q}_{\mathrm{ji}}}{{\∂\mathrm{\θ}}_j}=-u_i{u}_j({g\cos \mathrm{\θ}}_{\mathrm{ij}}-b\sin {\mathrm{\θ}}_{\mathrm{ij}})\end{array}\right.$

Top power on the transformer branch road i-j:

$\left\{\begin{array}{cc}\frac{{\∂P}_{\mathrm{ij}}}{{\∂u}_i}=-\frac{1}{K}{u}_j{b}_T{\sin \mathrm{\θ}}_{\mathrm{ij}}& \frac{{\∂O}_{\mathrm{ij}}}{{\∂u}_i}=-\frac{2}{K^2}{u}_i{b}_T+\frac{1}{K}{u}_j{b}_T\cos {\mathrm{\θ}}_{\mathrm{ij}}\\ \frac{\∂P_{\mathrm{ij}}}{{\∂\mathrm{\θ}}_i}=-\frac{1}{K}{u}_i{u}_j{b}_T\cos {\mathrm{\θ}}_{\mathrm{ij}}& \frac{{\∂Q}_{\mathrm{ij}}}{{\∂\mathrm{\θ}}_i}=-\frac{1}{K}{u}_i{u}_j{b}_T\sin {\mathrm{\θ}}_{\mathrm{ij}}\\ \frac{{\∂P}_{\mathrm{ij}}}{{\∂u}_j}=-\frac{1}{K}{u}_i{b}_T\sin {\mathrm{\θ}}_{\mathrm{ij}}& \frac{\∂Q_{\mathrm{ij}}}{\∂u_j}=\frac{1}{K}{u}_i{b}_T\cos {\mathrm{\θ}}_{\mathrm{ij}}\\ \frac{\∂P_{\mathrm{ij}}}{\∂{\mathrm{\θ}}_j}=\frac{1}{K}{u}_i{u}_j{b}_T\cos {\mathrm{\θ}}_{\mathrm{ij}}& \frac{{\∂Q}_{\mathrm{ij}}}{{\∂\mathrm{\θ}}_j}=\frac{1}{K}{u_i{u}_j{b}_T\sin {\mathrm{\θ}}_{\mathrm{ij}}}_{}\end{array}\right.$

Terminal power on the transformer branch road i-j:

$\left\{\begin{array}{cc}\frac{{\∂P}_{\mathrm{ji}}}{{\∂u}_i}=\frac{1}{K}{u}_j{b}_T{\sin \mathrm{\θ}}_{\mathrm{ij}}& \frac{{\∂O}_{\mathrm{ji}}}{{\∂u}_i}=\frac{1}{K}{u}_j{b}_T\cos {\mathrm{\θ}}_{\mathrm{ij}}\\ \frac{{\∂P}_{\mathrm{ji}}}{\∂{\mathrm{\θ}}_i}=\frac{1}{K}{u}_i{u}_j{b}_T\cos {\mathrm{\θ}}_{\mathrm{ij}}& \frac{{\∂Q}_{\mathrm{ji}}}{{\∂\mathrm{\θ}}_i}=-\frac{1}{K}{u}_i{u}_j{b}_T\sin {\mathrm{\θ}}_{\mathrm{ij}}\\ \frac{{\∂P}_{\mathrm{ji}}}{{\∂u}_j}=\frac{1}{K}{u}_i{b}_T\sin {\mathrm{\θ}}_{\mathrm{ij}}& \frac{{\∂Q}_{\mathrm{ji}}}{{\∂u}_j}=-2b_T{u}_j+\frac{1}{K}{u}_i{b}_T\cos {\mathrm{\θ}}_{\mathrm{ij}}\\ \frac{{\∂P}_{\mathrm{ji}}}{\∂{\mathrm{\θ}}_j}=-\frac{1}{K}{u}_i{u}_j{b}_T\cos {\mathrm{\θ}}_{\mathrm{ij}}& \frac{{\∂Q}_{\mathrm{ji}}}{{\∂\mathrm{\θ}}_j}=\frac{1}{K}{u}_i{u}_j{b}_T\sin {\mathrm{\θ}}_{\mathrm{ij}}\end{array}\right.$

Among the present invention, for the node of setting up load voltage static characteristic model, replenished node injecting power value, its injecting power is as follows to the local derviation computational methods of quantity of state:

Work as i=j, when adopting power function model:

$\left\{\begin{array}{cc}\frac{{\∂P}_i}{{\∂u}_i}=-P_{i0}{p}_U{\left(u_i\right)}^{p_U-1}+\frac{1}{u_i}(G_{\mathrm{ii}}{u}_i^2+P_i)& \frac{{\∂O}_i}{{\∂u}_i}=-Q_{i0}{q}_U{\left(u_i\right)}^{q_U-1}+\frac{1}{u_i}(-B_{\mathrm{ii}}{u}_i^2+Q_i)\\ \frac{{\∂P}_i}{\∂{\mathrm{\θ}}_i}=-B_{\mathrm{ii}}{u}_i^2-Q_i& \frac{{\∂Q}_i}{{\∂\mathrm{\θ}}_i}=-G_{\mathrm{ii}}{u}_i^2+P_i\\ \frac{{\∂P}_i}{{\∂u}_j}=u_i(G_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}})& \frac{{\∂Q}_i}{{\∂u}_j}=u_i(G_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}})\\ \frac{{\∂P}_i}{\∂{\mathrm{\θ}}_j}=u_i{u}_j(G_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}})& \frac{{\∂Q}_i}{{\∂\mathrm{\θ}}_j}=-u_i{u}_j(G_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}})\end{array}\right.$

Adopt the quadratic polynomial model:

$\left\{\begin{array}{cc}\frac{{\∂P}_i}{{\∂u}_i}=-P_{i0}[{2a}_p\left(\frac{u_i}{u_N}\right)+b_p]+\frac{1}{u_i}(G_{\mathrm{ii}}{u}_i^2+P_i)& \frac{{\∂O}_i}{{\∂u}_i}=-Q_{i0}[{2a}_q\left(\frac{u_i}{u_N}\right)+b_q]+\frac{1}{u_i}(-B_{\mathrm{ii}}{u}_i^2+Q_i)\\ \frac{{\∂P}_i}{\∂{\mathrm{\θ}}_i}=-B_{\mathrm{ii}}{u}_i^2-Q_i& \frac{{\∂Q}_i}{{\∂\mathrm{\θ}}_i}=-G_{\mathrm{ii}}{u}_i^2+P_i\\ \frac{{\∂P}_i}{{\∂u}_j}=u_i(G_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}})& \frac{{\∂Q}_i}{{\∂u}_j}=u_i(G_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}})\\ \frac{{\∂P}_i}{\∂{\mathrm{\θ}}_j}=u_i{u}_j(G_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}})& \frac{{\∂Q}_i}{{\∂\mathrm{\θ}}_j}=-u_i{u}_j(G_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}})\end{array}\right.$

Herein, made relevant treatment for the weight based on the node injecting power of load voltage static characteristic model among the present invention, owing to considered static load characteristic, the injecting power of corresponding node is an exact solution, therefore be considered as not existing random error, then set weight gets higher value so that its proportion in target function is outstanding, and the 10-100 that gets all the other measurement amount weights when specifically calculating doubly.

Then, carry out the iteration correction, wherein, when calculating residual error, considered that the residual error of the node of static load characteristic is according to aforementioned formula:

Adopt power function model:

$r_{i,p}^{\left(l\right)}=0-(-P_{i0}{\left(\frac{u_i^{\left(l\right)}}{u_N}\right)}^{p_U}+\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{u}_i^{\left(l\right)}{u}_j^{\left(l\right)}(G_{\mathrm{ij}}\sin {\mathrm{\θ}}_i^{\left(l\right)}-B_{\mathrm{ij}}\cos {\mathrm{\θ}}_i^{\left(l\right)}))$

$r_{i,q}^{\left(l\right)}=0-(-Q_{i0}{\left(\frac{u_i^{\left(l\right)}}{u_N}\right)}^{q_U}+\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{u}_i^{\left(l\right)}{u}_j^{\left(l\right)}(G_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}}^{\left(l\right)}-B_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}}^{\left(l\right)}))$

Adopt the quadratic polynomial model:

$r_{i,p}^{\left(l\right)}=0-(-P_{i0}[a_p{\left(\frac{u_i^{\left(l\right)}}{u_N}\right)}^2+b_p\left(\frac{u_i^{\left(l\right)}}{u_N}\right)+c_p]+\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{u}_i^{\left(l\right)}{u}_j^{\left(l\right)}(G_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}}^{\left(l\right)}-B_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}}^{\left(l\right)}))$

$r_{i,q}^{\left(l\right)}=0-(-Q_{i0}[a_q{\left(\frac{u_i^{\left(l\right)}}{u_N}\right)}^2+b_q\left(\frac{u_i^{\left(l\right)}}{u_N}\right)+c_q]+\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{u}_i^{\left(l\right)}{u}_j^{\left(l\right)}(G_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}}^{\left(l\right)}-B_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}}^{\left(l\right)}))$

Iteration is up to target function J (x ^(l)) less than till the threshold values that sets in advance.

The initial information of state estimation is transmitted the measurement signal of returning from telemetering equipment, measurement signal is the measurement amount that comprises random error, basic weighted least-squares (WLS) method for estimating state is that the inverse of the variance measured of utilization is set up the target function of weighted residual as weight, estimates quantity of state.This method model is simple, good convergence, and the estimated quality height is one of method that is most widely used at present.But this method has certain dependence for the precision of measurement amount, i.e. measurement is accurate more, and estimated result is also accurate more.

The present invention is owing to considered the voltage static characteristic model of load bus, in the measurement amount, replenished load bus zero injecting power, make the precision of measurement amount increase, and when iterative computation, given bigger weight, can make its proportion in target function obvious, therefore also correspondingly improve state estimation result's precision.

As shown in Figure 2, figure (a) is a circuit ∏ shape equivalent circuit diagram, serial connection admittance g+j ' b between node i and the node j, and the output of node i, j is connected in series a ground connection susceptance j ' y respectively _cBack ground connection.

Figure (b) is a transformer ∏ shape equivalent circuit diagram, is connected in series between node i and the node j

One of node i serial connection

Back ground connection, one of the output serial connection of j

Back ground connection.J ' expression imaginary part.

Claims (1)

1. power system state estimation method of considering static load characteristic is characterized in that comprising step down:

(1) reads electric network data among the EMS, comprising: the branch road of transmission line number, headend node and endpoint node numbering, transformer voltage ratio and impedance, series resistance reactance, shunt conductance susceptance;

(2) read the static load characteristic parameter, comprising: load active power, reactive power and relevant voltage performance index during the datum mark steady operation, the static load characteristic model representation is as follows:

Adopt power function model:

$P_i=P_{i0}{\left(\frac{u_i}{u_N}\right)}^{p_U}$

$Q_i=Q_{i0}{\left(\frac{u_i}{u_N}\right)}^{q_U}$

Adopt the quadratic polynomial model:

$P_i=P_{i0}[a_p{\left(\frac{u_i}{u_N}\right)}^2+b_p\left(\frac{u_i}{u_N}\right)+c_p]$

$Q_i=Q_{i0}[a_q{\left(\frac{u_i}{u_N}\right)}^2{+b}_q\left(\frac{u_i}{u_N}\right)+c_q]$

(3) initialization comprises: to quantity of state initial value, the optimization of node order be set, form node admittance matrix, threshold value be set, storage allocation;

(4) input real-time measurement amount z comprises that voltage magnitude, generator active power, generator reactive power, part of nodes have promptly picked out node load active power and reactive power, circuit head end active power, circuit head end reactive power, line end active power and the line end reactive power of static load characteristic model;

(5) for the load bus of known its static characteristic parameter, make up zero injecting power measurement equation and replenish original load bus power measurement equation, consider that the zero injection rate measurement of static load characteristic is expressed as follows:

Adopt power function model:

$0=-P_{i0}{\left(\frac{u_i}{u_N}\right)}^{p_U}+\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{u}_i{u}_j(G_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}})$

$0=-Q_{i0}{\left(\frac{u_i}{u_N}\right)}^{q_U}+\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{u}_i{u}_j(G_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}}-B_{\mathrm{ij}}{\cos \mathrm{\θ}}_{\mathrm{ij}})$

Adopt the quadratic polynomial model:

$0=-P_{i0}[a_p{\left(\frac{u_i}{u_N}\right)}^2+b_p\left(\frac{u_i}{u_N}\right)+c_p]+\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{u}_i{u}_j(G_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}})$

$0=-Q_{i0}[a_q{\left(\frac{u_i}{u_N}\right)}^2+b_q\left(\frac{u_i}{u_N}\right)+c_q]+\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{u}_i{u}_j(G_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}})$

(6) recover iteration count iterations k=1;

(7) by existing quantity of state x ^(k)Calculate the calculated value h (x of each measurement amount ^(l)) and Jacobian matrix H (x ^(l)), the load bus of wherein known load static models zero injection rate is measured calculated value and is:

Adopt power function model:

$h_i\left({x_i}^{\left(l\right)}\right)=-P_{i0}{\left(\frac{u_i^{\left(l\right)}}{u_N}\right)}^{p_U}+\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{u}_i^{\left(l\right)}{u}_j^{\left(l\right)}(G_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}}^{\left(l\right)}+B_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}}^{\left(l\right)})$

$h_i\left({x_i}^{\left(l\right)}\right)=-Q_{i0}{\left(\frac{u_i^{\left(l\right)}}{u_N}\right)}^{q_U}+\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{u}_i^{\left(l\right)}{u}_j^{\left(l\right)}(G_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}}^{\left(l\right)}-B_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}}^{\left(l\right)})$

Adopt the quadratic polynomial model:

$h_i\left(x_i^{\left(l\right)}\right)=-P_{i0}[a_p{\left(\frac{u_i^{\left(l\right)}}{u_N}\right)}^2+b_p\left(\frac{u_i^{\left(l\right)}}{u_N}\right)+c_p]+\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{u}_i^{\left(l\right)}{u}_j^{\left(l\right)}(G_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}}^{\left(l\right)}+B_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}}^{\left(l\right)})$

$h_i\left(x_i^{\left(l\right)}\right)=-Q_{i0}[a_q{\left(\frac{u_i^{\left(l\right)}}{u_N}\right)}^2+b_q\left(\frac{u_i^{\left(l\right)}}{u_N}\right)+c_q]+\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{u}_i^{\left(l\right)}{u}_j^{\left(l\right)}(G_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}}^{\left(l\right)}-B_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}}^{\left(l\right)})$

This type of measures, and element is in the corresponding Jacobian matrix:

Adopt power function model:

$\frac{{\∂P}_i}{{\∂v}_i}=-P_{i0}{p}_U{\left(u_i\right)}^{p_U-1}+\frac{1}{u_i}(G_{\mathrm{ii}}{u}_i^2+P_i)$

$\frac{{\∂Q}_i}{{\∂v}_i}=-Q_{i0}{q}_U{\left(u_i\right)}^{q_U-1}+\frac{1}{u_i}(-B_{\mathrm{ii}}{u}_i^2+Q_i)$

Adopt the quadratic polynomial model:

$\frac{{\∂P}_i}{\∂v_i}=-P_{i0}[2a_p\left(\frac{u_i}{u_N}\right)+b_p]+\frac{1}{u_i}(G_{\mathrm{ii}}{u}_i^2+P_i)$

$\frac{{\∂Q}_i}{\∂v_i}=-Q_{i0}[2a_q\left(\frac{u_i}{u_N}\right)+b_q]+\frac{1}{u_i}(-B_{\mathrm{ii}}{u}_i^2+Q_i)$

(8) ask for state correction amount x ^(k), choose

And the correction quantity of state obtains x ^(k+1)

$\mathrm{\Δ}{\hat{x}}_1^{\left(k\right)}={\left[H^T\left({\hat{x}}^{\left(k\right)}\right)R^{-1}H\left({\hat{x}}^{\left(k\right)}\right)\right]}^{-1}\×H^T\left({\hat{x}}^{\left(k\right)}\right)R^{-1}[z-h\left({\hat{x}}^{\left(k\right)}\right)]$

${\hat{x}}^{(k+1)}={\hat{x}}^{\left(k\right)}+\mathrm{\Δ}{\hat{x}}^{\left(k\right)}$

(9) judge Whether less than convergence, if, finish to calculate, carry out the k+1 time estimation otherwise return step (6).

Images