CN101702521B - State estimation method for electric power system considering influences of multi-balancing machine - Google Patents

Abstract

The invention discloses a state estimation method for an electric power system considering the influences of a multi-balancing machine. The method comprises the following steps of: firstly, according to the needs of the system, setting a group of multi-balancing machines for commonly sharing the imbalanced power of the system; secondly, deriving a computational formula of a measurement vector according to the setting of the multi-balancing machines, solving a Jacobian matrix of the measurement vector with respect to a quantity of state, and estimating the state of the system by using a least squares estimation criteria . Because the influences the multi-balancing machine is considered, the imbalanced power of the system is commonly shared by setting a group of multi-balancing machines, and the result of the state estimation accords with the practical situation better. In addition, the method can realize the state estimation considering the influences of the multi-balancing machine only by slightly amending the measurement function and the Jacobian matrix parts of the prior state estimation software. The invention has definite physical meaning, is convenient to realize in the traditional state estimation software and satisfies the requirements of engineering on the estimation precision.

Description

The power system state estimation method of considering influences of multi-balancing machine

Technical field

Invention relates to a kind of power system state estimation method of considering influences of multi-balancing machine, belongs to power system operation and control technology field.

Background technology

State estimation claims filtering again, and it utilizes the redundancy of real-time measurement system to improve data precision, gets rid of the caused error message of random disturbances automatically, the running status of estimation or forecast system.Along with the enforcement, the rapid implementation of electricity market of transferring electricity from the west to the east, ultra high voltage, remote, alternating current-direct current mix technology of transmission of electricity and develop in China's electrical network rapidly, and the automatization level at power system dispatching center also needs progressively to improve.Important component part as modern large-scale power system control centres at different levels EMS (EMS), state estimation provides the information of reliable and complete system running state for EMS, and set up the required database of various advanced applied software with these data, be described as " heart " of application software, so state estimation is the basis of aspects such as power system operation, control and security evaluation.

In conventional state estimation, a balance node only is set usually, corresponding balancing machine, in order to the imbalance power in the balance sysmte, but this does not conform to the actual conditions of electric power system.Because in practical power systems, when less imbalance power appearred in system, imbalance power had the generator of capacity nargin and all load bases meritorious frequency characteristic coefficient separately to distribute jointly by all, just primary frequency modulation; When bigger imbalance power appearred in system, imbalance power can also utilize the generating set with frequency modulation frequency modulation ability to carry out frequency modulation frequency modulation except regulating by primary frequency modulation.Therefore, when system's imbalance power hour, adopt the conventional method for estimating state that a balancing generator is set can not produce too much influence to system running state; And when system's imbalance power was big, it was unsuitable adopting the conventional method for estimating state that a balancing generator only is set, and it is bigger that the system running state that obtains thus might depart from virtual condition.The method for estimating state of considering influences of multi-balancing machine has then remedied above shortcoming, and it bears system's imbalance power jointly by one group of balancing generator group is set, and the state estimation result is more tallied with the actual situation.At present, this notion of multi-balancing machine is more common in the electric power system tide calculating, and bibliographical information is not seen in the Power system state estimation research under the multi-balancing machine as yet.

Summary of the invention

Technical problem to be solved by this invention is that the balance that the setting at interconnected network list balancing machine has been difficult to satisfy imbalance power requires this defective that a kind of power system state estimation method of considering influences of multi-balancing machine is provided.

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

The present invention is the power system state estimation method of considering influences of multi-balancing machine, it is characterized in that may further comprise the steps:

(1) obtains the network parameter of electric power system, comprising: the branch road of transmission line number, headend node and endpoint node numbering, series resistance, series reactance, shunt conductance, shunt susceptance, transformer voltage ratio and impedance;

(2) initialization comprises: quantity of state is provided with initial value, the optimization of node order, forms node admittance matrix, threshold value is set, storage allocation;

(3) input telemetry z comprises voltage magnitude, generator active power, generator reactive power, load active power, reactive load power, circuit head end active power, circuit head end reactive power, line end active power and line end reactive power;

(4) electric power system has n node, node n wherein ..., the generator at n-m place is formed the balancing machine group, bears the imbalance power of electric power system;

(5) the iterations k=1 of recovery iteration count;

(6) by existing quantity of state x ^(k), calculate the calculated value h (x of each measurement amount according to following formula ^(k));

The node i voltage magnitude is V _i=v _i:

The node i injecting power:

$\left\{\begin{array}{c}{P}_i=v_i\underset{j=1}{\overset{n-m-1}{\mathrm{\Σ}}}{v}_j(G_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}}+B_{\mathrm{ij}}{\sin \mathrm{\θ}}_{\mathrm{ij}})+v_i\underset{j=n-m}{\overset{n}{\mathrm{\Σ}}}{v}_j(G_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}}+B_{\mathrm{ij}}{\sin \mathrm{\θ}}_{\mathrm{ij}})\\ Q_i=v_i\underset{j=1}{\overset{n-m-1}{\mathrm{\Σ}}}{v}_j(G_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}})+v_i\underset{j=n-m}{\overset{n}{\mathrm{\Σ}}}{v}_j(G_{\mathrm{ij}}{\sin \mathrm{\θ}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}})\end{array}\right.,$

Circuit i-j goes up top power:

$\left\{\begin{array}{c}{P}_{\mathrm{ij}}=v_i^{2}g-v_i{v}_{j}g\cos {\mathrm{\θ}}_{\mathrm{ij}}-v_i{v}_{j}b{\sin \mathrm{\θ}}_{\mathrm{ij}}\\ Q_{\mathrm{ij}}=-v_i^2(b+y_c)-v_i{v}_{j}g\sin {\mathrm{\θ}}_{\mathrm{ij}}+v_i{v}_{j}b\cos {\mathrm{\θ}}_{\mathrm{ij}}\end{array}\right.,$

Circuit i-j goes up terminal power:

$\left\{\begin{array}{c}{P}_{\mathrm{ji}}=v_j^{2}g-v_i{v}_{j}g\cos {\mathrm{\θ}}_{\mathrm{ij}}+v_i{v}_{j}b{\sin \mathrm{\θ}}_{\mathrm{ij}}\\ Q_{\mathrm{ji}}=-v_j^2(b+y_c)+v_i{v}_{j}g\sin {\mathrm{\θ}}_{\mathrm{ij}}+v_i{v}_{j}b\cos {\mathrm{\θ}}_{\mathrm{ij}}\end{array}\right.,$

Transformer lines i-j goes up top power:

$\left\{\begin{array}{c}{P}_{\mathrm{ij}}=-\frac{1}{K}{v}_i{v}_j{b}_T{\sin \mathrm{\θ}}_{\mathrm{ij}}\\ Q_{\mathrm{ij}}=-\frac{1}{K^2}{v}_i^2{b}_T+\frac{1}{K}{v}_i{v}_j{b}_T{\cos \mathrm{\θ}}_{\mathrm{ij}}\end{array}\right.,$

Transformer lines i-j goes up terminal power:

$\left\{\begin{array}{c}{P}_{\mathrm{ji}}=\frac{1}{K}{v}_i{v}_j{b}_T\sin {\mathrm{\θ}}_{\mathrm{ij}}\\ Q_{\mathrm{ji}}=-v_j^2{b}_T+\frac{1}{K}{v}_i{v}_j{b}_T\cos {\mathrm{\θ}}_{\mathrm{ij}}\end{array}\right.,$

V in the formula _i, v _jBe respectively the voltage magnitude of node i, node j; θ _IjPhase difference of voltage for node i and node j; G _Ij, B _IjReal part and imaginary part for admittance matrix; G, b, y _cThe electricity that is respectively circuit is led, susceptance, ground connection susceptance; K is the non-standard no-load voltage ratio of transformer; b _TSusceptance for the survey of transformer standard; P, Q represent the active power and the reactive power of generator respectively; I, j=1,2 ..., n-m-1, i, j, m, n are the natural number greater than zero, m＜n;

(7) carry out differentiate about quantity of state respectively to step (6) is various, obtain the Jacobian matrix H (x of measurement amount ^(k)):

The node injecting power:

$\left\{\begin{array}{c}\frac{{\∂P}_i}{\∂v_i}=\underset{j=n-m}{\overset{n}{\mathrm{\Σ}}}{v}_j(G_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}})+\underset{\underset{j\≠i}{j=1}}{\overset{n-m-1}{\mathrm{\Σ}}}{v}_j(G_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}}+B_{\mathrm{ij}}{\sin \mathrm{\θ}}_{\mathrm{ij}})+2G_{\mathrm{ii}}{v}_i\\ \frac{{\∂P}_i}{{\∂\mathrm{\θ}}_i}=v_i\underset{j=n-m}{\overset{n}{\mathrm{\Σ}}}{v}_j(-G_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}}+B_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}})+v_i\underset{\underset{j\≠i}{j=1}}{\overset{n-m-1}{\mathrm{\Σ}}}{v}_j(-G_{\mathrm{ij}}{\sin \mathrm{\θ}}_{\mathrm{ij}}+B_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}})\end{array}\right.$

(i＝1，2，…，n-m-1)

$\left\{\begin{array}{c}\frac{{\∂P}_i}{{\∂v}_j}=v_i(G_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}})\\ \frac{{\∂P}_i}{{\∂\mathrm{\θ}}_j}=v_i{v}_j(G_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}}-B_{\mathrm{ij}}{\cos \mathrm{\θ}}_{\mathrm{ij}})\end{array}\right.$

(j＝1，2，…，n-m-1)

$\left\{\begin{array}{c}\frac{{\∂Q}_i}{\∂v_i}=\underset{j=n-m}{\overset{n}{\mathrm{\Σ}}}{v}_j(G_{\mathrm{ij}}s{\mathrm{in\θ}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}})+\underset{\underset{j\≠i}{j=1}}{\overset{n-m-1}{\mathrm{\Σ}}}{v}_j(G_{\mathrm{ij}}s{\mathrm{in\θ}}_{\mathrm{ij}}-B_{\mathrm{ij}}{\cos \mathrm{\θ}}_{\mathrm{ij}})-2B_{\mathrm{ii}}{v}_i\\ \frac{{\∂Q}_i}{{\∂\mathrm{\θ}}_i}=v_i\underset{j=n-m}{\overset{n}{\mathrm{\Σ}}}{v}_j(G_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}})+v_i\underset{\underset{j\≠i}{j=1}}{\overset{n-m-1}{\mathrm{\Σ}}}{v}_j(G_{\mathrm{ij}}{\cos \mathrm{\θ}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}})\end{array}\right.$

(i＝1，2，…，n-m-1)

$\left\{\begin{array}{c}\frac{{\∂Q}_i}{{\∂v}_j}=v_i(G_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}})\\ \frac{{\∂Q}_i}{{\∂\mathrm{\θ}}_j}={-v}_i{v}_j(G_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}}+B_{\mathrm{ij}}{\sin \mathrm{\θ}}_{\mathrm{ij}})\end{array}\right.$

(j＝1，2，…，n-m-1)

Top power on the circuit i-j

$\left\{\begin{array}{c}\frac{{\∂P}_{\mathrm{ij}}}{{\∂v}_i}={2v}_{i}g-v_{j}g\cos {\mathrm{\θ}}_{\mathrm{ij}}-v_{j}b\sin {\mathrm{\θ}}_{\mathrm{ij}}\\ \frac{{\∂P}_{\mathrm{ij}}}{{\∂\mathrm{\θ}}_i}=v_i{v}_{j}g\sin {\mathrm{\θ}}_{\mathrm{ij}}-v_i{v}_{j}b\cos {\mathrm{\θ}}_{\mathrm{ij}}\end{array}\right.$

(i＝1，2，…，n-m-1)

$\left\{\begin{array}{c}\frac{{\∂P}_{\mathrm{ij}}}{{\∂v}_j}=-v_{i}g\cos {\mathrm{\θ}}_{\mathrm{ij}}-v_{i}b\sin {\mathrm{\θ}}_{\mathrm{ij}}\\ \frac{{\∂P}_{\mathrm{ij}}}{{\∂\mathrm{\θ}}_j}=-v_i{v}_{j}g\sin {\mathrm{\θ}}_{\mathrm{ij}}+v_i{v}_{j}b\cos {\mathrm{\θ}}_{\mathrm{ij}}\end{array}\right.$

(j＝1，2，…，n-m-1)

$\left\{\begin{array}{c}\frac{{\∂Q}_{\mathrm{ij}}}{{\∂v}_i}={-2v}_i(b+y_c)-v_{j}g\sin {\mathrm{\θ}}_{\mathrm{ij}}+v_{j}b\cos {\mathrm{\θ}}_{\mathrm{ij}}\\ \frac{{\∂Q}_{\mathrm{ij}}}{{\∂\mathrm{\θ}}_i}={-v}_i{v}_{j}g\cos {\mathrm{\θ}}_{\mathrm{ij}}-v_i{v}_{j}b\sin {\mathrm{\θ}}_{\mathrm{ij}}\end{array}\right.$

(i＝1，2，…，n-m-1)

$\left\{\begin{array}{c}\frac{{\∂Q}_{\mathrm{ij}}}{{\∂v}_j}=-v_{i}g\sin {\mathrm{\θ}}_{\mathrm{ij}}+v_{i}b\cos {\mathrm{\θ}}_{\mathrm{ij}}\\ \frac{{\∂Q}_{\mathrm{ij}}}{{\∂\mathrm{\θ}}_j}=v_i{v}_{j}g\cos {\mathrm{\θ}}_{\mathrm{ij}}+v_i{v}_{j}b\sin {\mathrm{\θ}}_{\mathrm{ij}}\end{array}\right.$

(j＝1，2，…，n-m-1)

(8) ask for the state correction

Choose

And the correction quantity of state obtains

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

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

Wherein, x is the 2n-1 dimension state variable of electric power system;

It is the estimated value of quantity of state; Z is a telemetry for the measuring value vector; H (x) is the nonlinear function of x; H (x) is for measuring the Jacobian matrix of function; R ^-1For measuring the weight matrices of vector; T is for changeing the order symbol; (k) expression iteration sequence number;

(9) when

Less than the convergence of setting, done state is estimated, carries out the k+1 time estimation otherwise return step (6).

The power system state estimation method of the considering influences of multi-balancing machine that the present invention proposes, by being set, one group of balancing generator group bears the imbalance power of system jointly, make the result of state estimation more tally with the actual situation, and only need the standing state Estimation Software is just measured function and the Jacobian matrix part is revised slightly, can realize the state estimation of considering influences of multi-balancing machine, explicit physical meaning, be convenient on existing state estimation software, realize, and satisfy the requirement of engineering estimated accuracy.

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.

Fig. 3: applied two the little example systems of the method for estimating state of the considering influences of multi-balancing machine that the present invention proposes, wherein: figure (a) is the IEEE-14 node system, figure (b) is the IEEE-30 node system.

Embodiment

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

The Xu Huaipi of Massachusetts Institute Technology in 1969 people such as (F.C.Schweppe) has proposed the rudimentary algorithm of Power system state estimation---and state estimation algorithm (WLS) is taken advantage of in basic weighting two, and its basic thought is to be the method for estimation of objective criteria with measurement amount and the quadratic sum minimum that measures the difference of estimated value.This method is simple with its model, and good convergence, the characteristics that estimated quality is high have obtained using widely.This paper has proposed the power system state estimation method of considering influences of multi-balancing machine just on the basis of WLS algorithm.

As shown in Figure 1, 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 obtains by remote measurement, and it is artificial the setting that sub-fraction is also arranged; The measurement function of h (x) for being set up by basic circuit laws such as kirchhoffs; X is a system state variables; V is for measuring random error, supposes that it obeys that average is zero, variance is σ ²Normal distribution.Setting up departments system has a n node, with node voltage amplitude and voltage phase angle as state variable, node n ..., what the generator at n-m place met balancing machine chooses requirement (promptly the generator as balancing machine should have bigger adjusting surplus), the Compositional balance unit, then ${\stackrel{\·}{V}}_n=v_n\∠0,$ ${\stackrel{\·}{V}}_{n-1}=v_{n-1}\∠{\mathrm{\θ}}_{n-1},$

${\stackrel{\·}{V}}_{n-m}\∠{\mathrm{\θ}}_{n-m}.$

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 magnitude of node measures V _i, measurement equation is shown below:

The node injecting power:

$\left\{\begin{array}{c}{P}_i=v_i\underset{j=1}{\overset{n-m-1}{\mathrm{\Σ}}}{v}_j(G_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}})+v_i\underset{j=n-m}{\overset{n}{\mathrm{\Σ}}}{v}_j(G_{\mathrm{ij}}{\cos \mathrm{\θ}}_{\mathrm{ij}}+B_{\mathrm{ij}}{\sin \mathrm{\θ}}_{\mathrm{ij}})\\ Q_i=v_i\underset{j=1}{\overset{n-m-1}{\mathrm{\Σ}}}{v}_j(G_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}}-B_{\mathrm{ij}}{\cos \mathrm{\θ}}_{\mathrm{ij}})+v_i\underset{j=n-m}{\overset{n}{\mathrm{\Σ}}}{v}_j(G_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}}-B_{\mathrm{ij}}{\cos \mathrm{\θ}}_{\mathrm{ij}})\end{array}\right.$

Circuit i-j goes up top power:

$\left\{\begin{array}{c}{P}_{\mathrm{ij}}=v_i^{2}g-v_i{v}_{j}g\cos {\mathrm{\θ}}_{\mathrm{ij}}-v_i{v}_{j}b\sin {\mathrm{\θ}}_{\mathrm{ij}}\\ Q_{\mathrm{ij}}=-v_i^2(b+y_c)-v_i{v}_{j}g\sin {\mathrm{\θ}}_{\mathrm{ij}}+v_i{v}_{j}b\cos {\mathrm{\θ}}_{\mathrm{ij}}\end{array}\right.$

Circuit i-j goes up terminal power:

$\left\{\begin{array}{c}{P}_{\mathrm{ji}}=v_j^{2}g-v_i{v}_{j}g\cos {\mathrm{\θ}}_{\mathrm{ij}}+v_i{v}_{j}b\sin {\mathrm{\θ}}_{\mathrm{ij}}\\ Q_{\mathrm{ji}}=-v_j^2(b+y_c)+v_i{v}_{j}g\sin {\mathrm{\θ}}_{\mathrm{ij}}+v_i{v}_{j}b\cos {\mathrm{\θ}}_{\mathrm{ij}}\end{array}\right.$

Transformer lines i-j goes up top power:

$\left\{\begin{array}{c}{P}_{\mathrm{ij}}=-\frac{1}{K}{v}_i{v}_j{b}_T\sin {\mathrm{\θ}}_{\mathrm{ij}}\\ Q_{\mathrm{ij}}=-\frac{1}{K^2}{v}_i^2{b}_T+\frac{1}{K}{v}_i{v}_j{b}_T\cos {\mathrm{\θ}}_{\mathrm{ij}}\end{array}\right.$

Transformer lines i-j goes up terminal power:

$\left\{\begin{array}{c}{P}_{\mathrm{ji}}=\frac{1}{K}{v}_i{v}_j{b}_T\sin {\mathrm{\θ}}_{\mathrm{ij}}\\ Q_{\mathrm{ji}}=-v_j^2{b}_T+\frac{1}{K}{v}_i{v}_j{b}_T\cos {\mathrm{\θ}}_{\mathrm{ij}}\end{array}\right.$

The node i voltage magnitude:

V _i＝v _i，i、j＝1，2，…，n-m-1

In the above-mentioned measurement equation, v _i, v _jBe respectively the voltage magnitude of node i, node j; θ _IjPhase difference of voltage for node i and node j; G _Ij, B _IjReal part and imaginary part for admittance matrix; G, b, y _cFor the electricity of circuit is led, susceptance, ground connection susceptance; K is the non-standard no-load voltage ratio of transformer; b _TSusceptance for the survey of transformer standard.

After the given measurement vector z, the state estimation problem is asked exactly and is made target function

J(x)＝[z-h(x)] ^TR ^-1[z-h(x)]

The value of the x that reaches hour.Wherein, R is with σ _i ²Be the error in measurement variance battle array of diagonal element, in state estimation, get its inverse matrix for measuring the weight matrices of vector.

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

In order to ask for

At first will be with h (x) linearisation.Make x ₀Be a certain approximation of x, at x ₀Near h (x) is carried out Taylor expansion, and after ignoring the above higher order term of secondary, obtain:

h(x)≈h(x ₀)+H(x ₀)Δx

In the formula, Δ x=x-x ₀, $H\left(x_0\right)=\frac{\∂h\left(x\right)}{\∂x}{|}_{x=x_0}.$

With the top power on node injecting power and the circuit i-j is example, and the corresponding element of Jacobian matrix H (x) that measures vector is:

The node injecting power

$\left\{\begin{array}{c}\frac{{\∂P}_i}{\∂v_i}=\underset{j=n-m}{\overset{n}{\mathrm{\Σ}}}{v}_j(G_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}})+\underset{\underset{j\≠i}{j=1}}{\overset{n-m-1}{\mathrm{\Σ}}}{v}_j(G_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}}+B_{\mathrm{ij}}{\sin \mathrm{\θ}}_{\mathrm{ij}})+2G_{\mathrm{ii}}{v}_i\\ \frac{{\∂P}_i}{{\∂\mathrm{\θ}}_i}=v_i\underset{j=n-m}{\overset{n}{\mathrm{\Σ}}}{v}_j(-G_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}}+B_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}})+v_i\underset{\underset{j\≠i}{j=1}}{\overset{n-m-1}{\mathrm{\Σ}}}{v}_j(-G_{\mathrm{ij}}{\sin \mathrm{\θ}}_{\mathrm{ij}}+B_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}})\end{array}\right.$

(i＝1，2，…，n-m-1)

$\left\{\begin{array}{c}\frac{{\∂P}_i}{{\∂v}_j}=v_i(G_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}})\\ \frac{{\∂P}_i}{{\∂\mathrm{\θ}}_j}=v_i{v}_j(G_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}}-B_{\mathrm{ij}}{\cos \mathrm{\θ}}_{\mathrm{ij}})\end{array}\right.$

(j＝1，2，…，n-m-1)

$\left\{\begin{array}{c}\frac{{\∂Q}_i}{\∂v_i}=\underset{j=n-m}{\overset{n}{\mathrm{\Σ}}}{v}_j(G_{\mathrm{ij}}s{\mathrm{in\θ}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}})+\underset{\underset{j\≠i}{j=1}}{\overset{n-m-1}{\mathrm{\Σ}}}{v}_j(G_{\mathrm{ij}}s{\mathrm{in\θ}}_{\mathrm{ij}}-B_{\mathrm{ij}}{\cos \mathrm{\θ}}_{\mathrm{ij}})-2B_{\mathrm{ii}}{v}_i\\ \frac{{\∂Q}_i}{{\∂\mathrm{\θ}}_i}=v_i\underset{j=n-m}{\overset{n}{\mathrm{\Σ}}}{v}_j(G_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}})+v_i\underset{\underset{j\≠i}{j=1}}{\overset{n-m-1}{\mathrm{\Σ}}}{v}_j(G_{\mathrm{ij}}{\cos \mathrm{\θ}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}})\end{array}\right.$

(i＝1，2，…，n-m-1)

$\left\{\begin{array}{c}\frac{{\∂Q}_i}{{\∂v}_j}=v_i(G_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}})\\ \frac{{\∂Q}_i}{{\∂\mathrm{\θ}}_j}={-v}_i{v}_j(G_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}}+B_{\mathrm{ij}}{\sin \mathrm{\θ}}_{\mathrm{ij}})\end{array}\right.$

(j＝1，2，…，n-m-1)

Top power on the circuit i-j

$\left\{\begin{array}{c}\frac{{\∂P}_{\mathrm{ij}}}{{\∂v}_i}={2v}_{i}g-v_{j}g\cos {\mathrm{\θ}}_{\mathrm{ij}}-v_{j}b\sin {\mathrm{\θ}}_{\mathrm{ij}}\\ \frac{{\∂P}_{\mathrm{ij}}}{{\∂\mathrm{\θ}}_i}=v_i{v}_{j}g\sin {\mathrm{\θ}}_{\mathrm{ij}}-v_i{v}_{j}b\cos {\mathrm{\θ}}_{\mathrm{ij}}\end{array}\right.$

(i＝1，2，…，n-m-1)

$\left\{\begin{array}{c}\frac{{\∂P}_{\mathrm{ij}}}{{\∂v}_j}=-v_{i}g\cos {\mathrm{\θ}}_{\mathrm{ij}}-v_{i}b\sin {\mathrm{\θ}}_{\mathrm{ij}}\\ \frac{{\∂P}_{\mathrm{ij}}}{{\∂\mathrm{\θ}}_j}=-v_i{v}_{j}g\sin {\mathrm{\θ}}_{\mathrm{ij}}+v_i{v}_{j}b\cos {\mathrm{\θ}}_{\mathrm{ij}}\end{array}\right.$

(j＝1，2，…，n-m-1)

$\left\{\begin{array}{c}\frac{{\∂Q}_{\mathrm{ij}}}{{\∂v}_i}={-2v}_i(b+y_c)-v_{j}g\sin {\mathrm{\θ}}_{\mathrm{ij}}+v_{j}b\cos {\mathrm{\θ}}_{\mathrm{ij}}\\ \frac{{\∂Q}_{\mathrm{ij}}}{{\∂\mathrm{\θ}}_i}={-v}_i{v}_{j}g\cos {\mathrm{\θ}}_{\mathrm{ij}}-v_i{v}_{j}b\sin {\mathrm{\θ}}_{\mathrm{ij}}\end{array}\right.$

(i＝1，2，…，n-m-1)

$\left\{\begin{array}{c}\frac{{\∂Q}_{\mathrm{ij}}}{{\∂v}_j}=-v_{i}g\sin {\mathrm{\θ}}_{\mathrm{ij}}+v_{i}b\cos {\mathrm{\θ}}_{\mathrm{ij}}\\ \frac{{\∂Q}_{\mathrm{ij}}}{{\∂\mathrm{\θ}}_j}=v_i{v}_{j}g\cos {\mathrm{\θ}}_{\mathrm{ij}}+v_i{v}_{j}b\sin {\mathrm{\θ}}_{\mathrm{ij}}\end{array}\right.$

(j＝1，2，…，n-m-1)

This shows that m+1 balance node arranged in the system, Jacobian matrix will reduce 2 (m+1) rank.

With the linearized expression substitution target function of h (x), behind mathematical induction, this target function can utilize the following formula iterative:

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

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

(k) expression iteration sequence number in the formula.

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.

Introduce two embodiment of the present invention below:

Embodiment one:

The present invention adopts the standard example of the IEEE-14 node shown in Fig. 3 (a), with regard to single balancing machine and multi-balancing machine example has been carried out emulation respectively, and system parameters is as shown in table 1, and simulation result is as shown in table 2:

Table 1 system parameter table

Type	Balance node	Redundancy
				1	1	2.15
2	1，2	2.33
			3	1，2，3，8	2.80

Table 2 simulation result table

Class1

Type

2

Type 3

J	0.002062	0.002155	0.002232
				EMI	0.010031	0.010031	0.010031
EEI	0.007070	0.006931	0.006748
				EMO	0.008536	0.008536	0.008536
EEO	0.006031	0.005902	0.005736

Embodiment two:

The present invention adopts the standard example of the IEEE-30 node shown in Fig. 3 (b), with regard to single balancing machine and multi-balancing machine example has been carried out emulation respectively, and system parameters is as shown in table 3, and simulation result is as shown in table 4:

Table 3 system parameter table

Type	Balance node	Redundancy
				1	1	2.07
2	1，2，5	2.22
			3	1，2，5，8，11	2.40

Table 4 simulation result table

	Class1	Type	2	Type 3
					J	0.003482	0.003665	0.003681
EMI	0.008891	0.008891	0.008891
				EEI	0.006351	0.006212	0.006164
EMO	0.007513	0.007513	0.007513
				EEO	0.005251	0.005130	0.005087

Wherein, $\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{\left[\frac{z_i-h_i\left(\hat{x}\right)}{{\mathrm{\σ}}_i}\right]}^2$

$\mathrm{EMI}={\left[\frac{1}{m}\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{\left({\mathrm{EM}}_i\right)}^2\right]}^{\frac{1}{2}},$ $\mathrm{EEI}=[\frac{1}{m}\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{\left({\mathrm{EE}}_i\right)}^2{]}^{\frac{1}{2}}$

$\mathrm{EMO}={\left[\frac{1}{m}\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{({\mathrm{EM}}_i/{\mathrm{\σ}}_i)}^2\right]}^{\frac{1}{2}},$ $\mathrm{EEO}={\left[\frac{1}{m}\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{({\mathrm{EE}}_i/{\mathrm{\σ}}_i)}^2\right]}^{\frac{1}{2}}$

In the formula, EM _i=MEA _i-MTR _iBe measure error; EE _i=EST _i-MTR _iBe evaluated error; MEA _iIt is the measuring value of i measurement amount; EST _iIt is the estimated value of i measurement amount; MTR _iThe true value of i measurement amount.

The inventive method has following advantage, on the one hand, can learn from simulation result, compares conventional single balancing machine method for estimating state, and it is high that the computational accuracy of multi-balancing machine method for estimating state is wanted, and estimated result meets the virtual condition of electric power system more; On the other hand, the structure of group method has clear physical meaning, has protected the state estimation program of existing maturation, only partly revises at measurement vector and Jacobian matrix thereof, and is very little to the modification of standing state Estimation Software, realizes easily.

Claims (1)

1. the power system state estimation method of a considering influences of multi-balancing machine is characterized in that may further comprise the steps:

(1) obtains the network parameter of electric power system, comprising: the branch road of transmission line number, headend node and endpoint node numbering, series resistance, series reactance, shunt conductance, shunt susceptance, transformer voltage ratio and impedance;

(2) initialization comprises: quantity of state is provided with initial value, the optimization of node order, forms node admittance matrix, threshold value is set, storage allocation;

(3) input telemetry z comprises voltage magnitude, generator active power, generator reactive power, load active power, reactive load power, circuit head end active power, circuit head end reactive power, line end active power and line end reactive power;

(4) electric power system has n node, node n wherein ..., the generator at n-m place is formed the balancing machine group, bears the imbalance power of electric power system;

(5) the iterations k=1 of recovery iteration count;

(6) by existing quantity of state x ^(k), calculate the calculated value h (x of each measurement amount according to following formula ^(k));

The node i voltage magnitude is V _i=v _i:

The node i injecting power:

$\left\{\begin{array}{c}{P}_i=v_i\underset{j=1}{\overset{n-m-1}{\mathrm{\Σ}}}{v}_j(G_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}})+v_i\underset{j=n-m}{\overset{n}{\mathrm{\Σ}}}{v}_j(G_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}})\\ Q_i=v_i\underset{j=1}{\overset{n-m-1}{\mathrm{\Σ}}}{v}_j(G_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}})+v_i\underset{j=n-m}{\overset{n}{\mathrm{\Σ}}}{v}_j(G_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}})\end{array}\right.,$

Circuit i-j goes up top power:

$\left\{\begin{array}{c}{P}_{\mathrm{ij}}=v_i^{2}g-v_i{v}_{j}g\cos {\mathrm{\θ}}_{\mathrm{ij}}-v_i{v}_{j}b\sin {\mathrm{\θ}}_{\mathrm{ij}}\\ Q_{\mathrm{ij}}=-v_i^2(b+y_c)-v_i{v}_{j}g\sin {\mathrm{\θ}}_{\mathrm{ij}}+v_i{v}_{j}b\cos {\mathrm{\θ}}_{\mathrm{ij}}\end{array}\right.,$

Circuit i-j goes up terminal power:

$\left\{\begin{array}{c}{P}_{\mathrm{ji}}=v_j^{2}g-v_i{v}_{j}g\cos {\mathrm{\θ}}_{\mathrm{ij}}+v_i{v}_{j}b\sin {\mathrm{\θ}}_{\mathrm{ij}}\\ Q_{\mathrm{ji}}=-v_j^2(b+y_c)+v_i{v}_{j}g\sin {\mathrm{\θ}}_{\mathrm{ij}}+v_i{v}_{j}b\cos {\mathrm{\θ}}_{\mathrm{ij}}\end{array}\right.,$

Transformer lines i-j goes up top power:

$\left\{\begin{array}{c}{P}_{\mathrm{ij}}=-\frac{1}{K}{v}_i{v}_j{b}_T\sin {\mathrm{\θ}}_{\mathrm{ij}}\\ Q_{\mathrm{ij}}=-\frac{1}{K^2}{v}_i^2{b}_T+\frac{1}{K}{v}_i{v}_j{b}_T\cos {\mathrm{\θ}}_{\mathrm{ij}}\end{array}\right.,$

Transformer lines i-j goes up terminal power:

$\left\{\begin{array}{c}{P}_{\mathrm{ji}}=\frac{1}{K}{v}_i{v}_j{b}_T\sin {\mathrm{\θ}}_{\mathrm{ij}}\\ Q_{\mathrm{ji}}=-v_j^2{b}_T+\frac{1}{K}{v}_i{v}_j{b}_T\cos {\mathrm{\θ}}_{\mathrm{ij}}\end{array}\right.,$

V in the formula _i, v _jBe respectively the voltage magnitude of node i, node j; θ _IjPhase difference of voltage for node i and node j; G _Ij, B _IjReal part and imaginary part for admittance matrix; G, b, y _cThe electricity that is respectively circuit is led, susceptance, ground connection susceptance; K is the non-standard no-load voltage ratio of transformer; b _TSusceptance for the survey of transformer standard; P, Q represent the active power and the reactive power of generator respectively; I, j=1,2 ..., n-m-1, i, j, m, n are the natural number greater than zero, m＜n;

(7) carry out differentiate about quantity of state respectively to step (6) is various, obtain the Jacobian matrix H (x of measurement amount ^(k)):

The node injecting power:

$\left\{\begin{array}{c}\frac{\∂P_i}{\∂v_i}=\underset{j=n-m}{\overset{n}{\mathrm{\Σ}}}{v}_j(G_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}})+\underset{j\≠i}{\overset{n-m-1}{\underset{j=1}{\mathrm{\Σ}}}}{v}_j(G_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}})+2G_{\mathrm{ii}}{v}_i\\ \frac{{\∂P}_i}{\∂{\mathrm{\θ}}_i}=v_i\underset{j=n-m}{\overset{n}{\mathrm{\Σ}}}{v}_j(-G_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}}+B_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}})+v_i\underset{j\≠i}{\overset{n-m-1}{\underset{j=1}{\mathrm{\Σ}}}}{v}_j(-G_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}}+B_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}})\end{array}\right.$

(i＝1，2，…，n-m-1)

$\left\{\begin{array}{c}\frac{\∂P_i}{\∂v_j}=v_i(G_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}})\\ \frac{\∂P_i}{\∂{\mathrm{\θ}}_j}=v_i{v}_j(G_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}})\end{array}\right.$

(j＝1，2，…，n-m-1)

$\left\{\begin{array}{c}\frac{\∂Q_i}{\∂v_i}=\underset{j=n-m}{\overset{n}{\mathrm{\Σ}}}{v}_j(G_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}})+\underset{j\≠i}{\overset{n-m-1}{\underset{j=1}{\mathrm{\Σ}}}}{v}_j(G_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}})-2B_{\mathrm{ii}}{v}_i\\ \frac{{\∂Q}_i}{\∂{\mathrm{\θ}}_i}=v_i\underset{j=n-m}{\overset{n}{\mathrm{\Σ}}}{v}_j(G_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}})+v_i\underset{j\≠i}{\overset{n-m-1}{\underset{j=1}{\mathrm{\Σ}}}}{v}_j(G_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}})\end{array}\right.$

(i＝1，2，…，n-m-1)

$\left\{\begin{array}{c}\frac{\∂Q_i}{\∂v_j}=v_i(G_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}})\\ \frac{\∂Q_i}{\∂{\mathrm{\θ}}_j}={-v}_i{v}_j(G_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}})\end{array}\right.$

(j＝1，2，…，n-m-1)

Top power on the circuit i-j

$\left\{\begin{array}{c}\frac{\∂P_{\mathrm{ij}}}{\∂v_i}=2v_{i}g-v_{j}g\cos {\mathrm{\θ}}_{\mathrm{ij}}-v_{j}b\sin {\mathrm{\θ}}_{\mathrm{ij}}\\ \frac{\∂P_{\mathrm{ij}}}{\∂{\mathrm{\θ}}_i}=v_i{v}_{j}g\sin {\mathrm{\θ}}_{\mathrm{ij}}-v_i{v}_{j}b\cos {\mathrm{\θ}}_{\mathrm{ij}}\end{array}\right.$

(i＝1，2，…，n-m-1)

$\left\{\begin{array}{c}\frac{\∂P_{\mathrm{ij}}}{\∂v_j}=-v_{i}g\cos {\mathrm{\θ}}_{\mathrm{ij}}-v_{i}b\sin {\mathrm{\θ}}_{\mathrm{ij}}\\ \frac{\∂P_{\mathrm{ij}}}{\∂{\mathrm{\θ}}_j}=-v_i{v}_{j}g\sin {\mathrm{\θ}}_{\mathrm{ij}}+v_i{v}_{j}b\cos {\mathrm{\θ}}_{\mathrm{ij}}\end{array}\right.$

(j＝1，2，…，n-m-1)

$\left\{\begin{array}{c}\frac{\∂Q_{\mathrm{ij}}}{\∂v_i}=-2v_i(b+y_c)-v_{j}g\sin {\mathrm{\θ}}_{\mathrm{ij}}+v_{j}b\cos {\mathrm{\θ}}_{\mathrm{ij}}\\ \frac{\∂Q_{\mathrm{ij}}}{\∂{\mathrm{\θ}}_i}=-v_i{v}_{j}g\cos {\mathrm{\θ}}_{\mathrm{ij}}-v_i{v}_{j}b\sin {\mathrm{\θ}}_{\mathrm{ij}}\end{array}\right.$

(i＝1，2，…，n-m-1)

$\left\{\begin{array}{c}\frac{\∂Q_{\mathrm{ij}}}{\∂v_j}=-v_{i}g\sin {\mathrm{\θ}}_{\mathrm{ij}}+v_{i}b\cos {\mathrm{\θ}}_{\mathrm{ij}}\\ \frac{\∂Q_{\mathrm{ij}}}{\∂{\mathrm{\θ}}_j}=v_i{v}_{j}g\cos {\mathrm{\θ}}_{\mathrm{ij}}+v_i{v}_{j}b\sin {\mathrm{\θ}}_{\mathrm{ij}}\end{array}\right.$

(j＝1，2，…，n-m-1)

(8) ask for the state correction

Choose

And the correction quantity of state obtains

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

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

Wherein, x is the 2n-1 dimension state variable of electric power system; It is the estimated value of quantity of state; Z is a telemetry for the measuring value vector; H (x) is the nonlinear function of x; H (x) is for measuring the Jacobian matrix of function; R ^-1For measuring the weight matrices of vector; T is for changeing the order symbol; (k) expression iteration sequence number;

(9) when

Less than the convergence of setting, done state is estimated, carries out the k+1 time estimation otherwise return step (6).

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