CN103390251B - The measurement weight method to set up of a kind of Power system state estimation - Google Patents

Abstract

The present invention discloses the measurement weight method to set up of a kind of Power system state estimation, it is proposed that to be considered measurement error and measurement type when arranging weight simultaneously, in tradition by variances sigma²The weighted basis arranged reciprocal is multiplied by a type factor k again_w, the present invention is divided into 3 types measurement, respectively voltage magnitude measurement, branch power measurement, node injecting power measurement. Through test of many times, the type factor k of voltage measurement_wSpan is 0.8��1.2; The type factor k of node injecting power measurement_wIt is taken as 2.5��3.5; The type factor k of branch power measurement_wIt is taken as 8.5��11.5. Implement example and show that the measurement weight method to set up that the present invention proposes can significantly improve the precision of Power system state estimation. To IEEE30 system, when each measurement all exists 1% error, adopting the inventive method to arrange measurement weight, precision can improve 4.9%.

Description

The measurement weight method to set up of a kind of Power system state estimation

Technical field

The present invention relates to the method for estimating state of a kind of power system, particularly the measurement weight method to set up of a kind of weighted least-squares method state estimation.

Background technology

State estimation is the important component part of energy management system (EMS), and along with the increasing year by year of electrical network scale, the automatization level of power system is more and more higher. In order to ensure economy and the security of Operation of Electric Systems, require that the electric power dispatching system of modernization can grasp the running status of power system reality accurately, rapidly, comprehensively, the operation trend of analysis and prediction power system also can in time to the various problems occurred in running, propose treatment process, formulate next step operation scheme.

In order to monitor the running status of power system, each plant stand (power station and substation) in power system is all equipped with measuring unit to obtain the real time data of various electric parameters, and these are called as the real time data measuring data and are sent to grid dispatching center by various means of communication. But directly judge that POWER SYSTEM STATE is obviously requirement irrational, that can not meet dispatching of power netwoks by measurement data, because measuring data have following two shortcomings:

(1) data are measured not comprehensive. Measure all data that data do not comprise electrical network, only acquire the part data of electrical network.

(2) measure data and there is error. The real time data that grid dispatching center obtains is come in by the telemechanical installation transmission such as sensor, umformer, and data gathering, conversion and each link that communicates have error, and there is interference in various degree, and thus these data are not completely reliably.

Owing to there is above shortcoming, measuring data can not directly use, it is necessary to processing treatment, mends neat not enough data, reduces error effect, could use. The process of this processing treatment is exactly state estimation.

Weighted least-squares method is basic, the most the most frequently used algorithm of state estimation, and method of least squares is exactly make objective function obtain mnm. according to least square criterion.

The principle of weighted least-squares method state estimation is as follows:

The power system measurement equation group is made to be

Z=h (x) (1)

In formula, z is that m ties up measurement vector; X is that n ties up state variables vector (being made up of node voltage amplitude and voltage phase angle); H (x) is the calculated value functional vector of m dimension measurement.

Owing to the number m of measurement equation is greater than state variables number n, i.e. m > n, equation is generally without separating, namely do not exist and meet all non trivial solution in formula (1). Need to find one group of state variables, make the weighted residual of equation minimum.

The objective function is made to be

$J\left(x\right)={(z-h\left(x\right))}^T{R}^{-1}(z-h\left(x\right))=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{R}_i^{-1}{(z_i-h_i\left(x\right))}^2---\left(2\right)$

In formula, R^-1Represent measurement weight matrix; z_i-h_iX () is called the residual error of i-th measurement.

H (x) in formula (2) represents the calculated value of measurement by state variables, is nonlinear function. Measurement comprises branch road wattful power measurement, branch road wattless power measurement, and node injects meritorious power measurement amount, node injects wattless power measurement, node voltage amplitude measurement.

Traditional measurement weight method to set up is generally the variance inverse that selected amount is measured is weighted value, namely

$R_i^{-1}=1/{\mathrm{\σ}}_i^2---\left(3\right)$

In formula,It it is the variance of i-th measurement.

Method of least squares to be made objective function J (x) minimum exactly. Partially leading of J (x) be zero is the prerequisite asking for J (x) extreme value, namely

$\frac{\mathrm{dJ}\left(x\right)}{\mathrm{dx}}=-{2H}^T\left(x\right)R^{-1}(z-h\left(x\right))---\left(4\right)$

In formula, H (x) is measurement Jacobian matrix, is made up of by the partial derivative of x calculated value function h (x) of measurement.

Formula (4) is a Nonlinear System of Equations, it is possible to solve by newton's method.

Make f (x)=H^T(x)R^-1(z-h (x))=0, by x at x₀Carry out Taylor expansion near point, and it is taken to linear item,

$f\left(x_0\right)+\frac{\∂f\left(x\right)}{{\∂x}^T}{|}_{x_0}\mathrm{\Δx}=0---\left(5\right)$

In formula,

$\frac{\∂f\left(x\right)}{{\∂x}^T}=\frac{\∂}{{\∂x}^T}\left[H^T\left(x\right)R^{-1}(z-h\left(x\right))\right]\≈{-H}^T\left(x\right)R^{-1}H\left(x\right)---\left(6\right)$

Formula (6) substitutes into formula (5), obtains the normal equation of state estimation

H^TR^-1H �� x=H^TR^-1(z-h(x))(7)

In formula, equation coefficient part H^TR^-1H is called information matrix.

Separate normal equation,

$\mathrm{\Δx}={\left[H^T{R}^{-1}H\right]}^{-1}{H}^T{R}^{-1}(z-h\left(x\right)){|}_{x=x_0}---\left(8\right)$

With �� x to initial value x₀Revising, obtaining x is

X=x₀+��x(9)

Launch owing to f (x) to be done first order Taylor, work as x₀Time very close to the true value of x, first order Taylor launches could be enough accurate, but in fact is difficult to get enough close to the initial value x of x true value₀, progressively revise x make it approach the true value of x so should iterate. Iterative formula is

x^(k+1)=x^(k)+��x^(k)(10)

��x^(k)=[H^T(x^(k))R^-1H(x^(k))]^-1H^T(x^(k))R^-1(z-h(x^(k)))(11)

Iterated revision is carried out by formula (10) and formula (11), untilTill (�� is convergence precision), what at this moment obtain is exactly best estimate, makes objective function J (x^(k)) obtain minimum value.

As shown in Figure 1, weighted least-squares method state estimation comprises the following steps:

Step 1: read network data and measure data z;

Step 2: voltage initial value is set by flat startup, namely all node voltage amplitude are 1.0, and voltage phase angle is 0.0;

Step 3: make iteration number of times k=1;

Step 4: the calculated value function that calculated amount is measured is to the Jacobian matrix H (x of the partial derivative of x^(k)), the calculated value function h (x of measurement^(k)), information matrix H^TR^-1H, equation right-hand-side vector H^TR^-1(z-h(x^(k)));

Step 5: separate normal equation (H^TR^-1H)��x=H^TR^-1(z-h(x^(k))) seek �� x^(k)And max | �� x_i|;

Step 6: judge max | �� x_i| whether being less than convergence precision ��, if being not less than ��, then going to step 7; Otherwise terminate;

Step 7: make x^(k+1)=x^(k)+��x^(k), k=k+1, return step 4.

In above-mentioned method of calculation, it is very big that the weight of measurement arranges the impact that state estimation calculates precision, the inverse that traditional measurement weight method to set up is generally selected amount Measurement Variance is weighted value, finds that the influence degree of state estimation is had a great difference by the dissimilar measurement that error is identical in practice. Do not consider when weight is set that the impact of precision of state estimation must be affected the precision of state estimation by measurement type.

Summary of the invention

For solving the problems referred to above that prior art exists, the present invention to be designed the measurement weight method to set up of a kind of Power system state estimation, to improve the precision of state estimation.

In order to realize above-mentioned purpose, the technical scheme of the present invention is as follows: the measurement weight method to set up of a kind of Power system state estimation, comprises the following steps:

A, reading measure data z;

B, current sequence number i=1 is set;

C, whether be voltage magnitude measurement, if not being that voltage magnitude measurement goes to step E if judging current measurement;

D, the type factor arranging current measurement are k_wi=a, gets a=0.8��1.2;

E, whether be node injecting power measurement, if not being that node injecting power measurement goes to step G if judging current measurement;

F, the type factor arranging current measurement are k_wi=b, gets b=2.5��3.5;

G, whether be branch power measurement, if not being that branch power measurement goes to step I if judging current measurement;

H, the type factor arranging current measurement are k_wi=c, gets c=8.5��11.5;

I, current measurement weight is set it is

J, make i=i+1;

K, judge i and whether it is greater than measurement number m, if i is not more than m, then go to step C; Otherwise terminate.

Compared with prior art, the present invention has following useful effect:

The present invention proposes and when weight is set, to be considered measurement error and measurement type simultaneously, in tradition by variances sigma²The weighted basis arranged reciprocal is multiplied by a type factor k again_w, it is revised as by formula (3)

$R_i^{-1}=k_{\mathrm{wi}}/{\mathrm{\σ}}_i^2$

The present invention is divided into 3 types measurement, respectively voltage magnitude measurement, branch power measurement, node injecting power measurement. Through test of many times, the type factor k of voltage measurement_wSpan is 0.8��1.2; The type factor k of node injecting power measurement_wIt is taken as 2.5��3.5; The type factor k of branch power measurement_wIt is taken as 8.5��11.5. Implement example and show that the amount amount weight method to set up that the present invention proposes can significantly improve the precision of Power system state estimation. To IEEE30 system, when each measurement all exists 1% error, adopting the inventive method to arrange measurement weight, precision can improve 4.9%; When there is 5% error, adopting the inventive method to arrange measurement weight, precision can improve 6.2%. Measurement error is more big, and the amplitude that the inventive method improves precision is more big.

Accompanying drawing explanation

The present invention has 3, accompanying drawing, wherein:

Fig. 1 is the weighted least-squares method state estimation schema of prior art.

Fig. 2 is the measurement weight setting procedure figure of the present invention.

The measurement weight that Fig. 3 is the present invention arranges example IEEE30 system wiring figure.

Embodiment

Below in conjunction with accompanying drawing, the present invention is further described.

Adopt the algorithm shown in Fig. 1-2 that the IEEE30 system shown in Fig. 3 is carried out state estimation. It is the true value of measurement and the true value of quantity of state taking calculation of tidal current during calculating, adopts 2 kinds of methods to carry out state estimation for 5 kinds of operating modes respectively. During calculating, the type factor of measurement all gets typical case value, i.e. a=1, b=3, c=10.

5 kinds of operating modes are as follows respectively:

Operating mode 1: all measurement increase the 1% of respective measurement, namely all there is 1% error in all measurement;

Operating mode 2: all measurement increase the 2% of respective measurement;

Operating mode 3: all measurement increase the 3% of respective measurement;

Operating mode 4: all measurement increase the 4% of respective measurement;

Operating mode 5: all measurement increase the 5% of respective measurement.

2 kinds of methods are as follows respectively:

Method 1: traditional is reciprocal as weight using measurement variance;

Method 2: be multiplied by the type factor as weight using measurement variance inverse with what the present invention proposed.

Calculation result is such as following table, and in table, state estimation total error is state estimation sum of the squares of errors, namely

Wherein z_0iIt it is the true value of i-th measurement; h_iX () is called the calculated value of i-th measurement. Precision increase rate in method 1 state estimation total error be benchmark, calculation result is in table 1.

Table 1 state estimation result table

From upper table, adopting the measurement weight method to set up that the present invention proposes, the precision of state estimation significantly improves, and measurement error is more big, and it is more big that the inventive method improves precision of state estimation amplitude.

The present invention can adopt any a kind of programming language and programming environment to realize, such as C language, C++, FORTRAN, Delphi etc. Development environment can adopt VisualC++, BorlandC++Builder, VisualFORTRAN etc.

Claims (1)

1. the measurement weight method to set up of a Power system state estimation, it is characterised in that: comprise the following steps:

A, reading measure data z;

B, current sequence number i=1 is set;

C, whether be voltage magnitude measurement, if not being that voltage magnitude measurement goes to step E if judging current measurement;

D, the type factor arranging current measurement are k_wi=a, gets a=0.8��1.2;

E, whether be node injecting power measurement, if not being that node injecting power measurement goes to step G if judging current measurement;

F, the type factor arranging current measurement are k_wi=b, gets b=2.5��3.5;

G, whether be branch power measurement, if not being that branch power measurement goes to step I if judging current measurement;

H, the type factor arranging current measurement are k_wi=c, gets c=8.5��11.5;

I, current measurement weight is set it isIn formula,It it is the variance of i-th measurement;

J, make i=i+1;

K, judge i and whether it is greater than measurement number m, if i is not more than m, then go to step C; Otherwise terminate.