JPH0716289B2 - Power system state estimation method - Google Patents

Description

Description: TECHNICAL FIELD The present invention relates to a power system state estimation method, and more particularly to a method suitable for power system state estimation with large impedance variations.

[Conventional technology]

As shown in FIG. 6, this kind of state estimation is performed by using the least squares method, and the state estimation solution is the following (1).
It can be obtained by finding x that minimizes the objective function J (α) of the expression.

^{J (x) = (y-} f (x) T w (y-f (x)) ...
(1) y: Observed value vector x: Bus voltage vector f: Non-linear function vector showing the relation between y and x Jacobian of f (χ) Let H be the solution as follows.

In step 100, an initial value x ₀ of x is given with k = 0. Next, in step 101, the Jacobian H is created.
Next, in step 102, the following simultaneous linear equations are solved and Δ
Find X.

(H ^T WH) · Δx = (H ^T W) (y−f (xk) ... (2) In step 103, it is determined whether | Δx | is smaller than ε, and if | Δx | <ε The process is terminated, and if not, X _{K + 1} = x _K + Δx, K = K + 1 and the process returns to step 101. ε: convergence determination constant Here, the weight w is a value obtained from the accuracy of the measuring instrument.
The weight should be expressed by the following equation theoretically, where a is the absolute error of the attached measuring instrument.

w = K · a ² (K is a constant) (3) However, with this theoretically obtained value, the non-linear calculation may not converge due to incorrect calculation of the numerical calculation. It was sought by trial and error while considering the convergence of the. For systems with extremely large variations in impedance, the Institute of Electrical Engineers of Japan PE-85-
As described in 39, “Method for estimating the state of a power system densely packed in a small area”, the system is divided into a transformer with a relatively large impedance and a transmission line with a relatively small impedance. Divide into one system mainly consisting of transmission lines (hereinafter referred to as the intermediate system) excluding radial ones such as load transformers, and multiple systems consisting of radial transformers. Then, the method of state estimation in the anti-radiation system is used. However, even in this method, the weight is also a manual input, and a theory for determining the weight has not been proposed.

[Problems to be solved by the invention]

In the above prior art, the method for determining the weight is not formulated, the weight is a manual input for each observation value, and the weight must be determined by thinking and error based on past experience.

An object of the present invention is to provide a state estimation method for a power system that solves the above-mentioned problems by formulating weights and surely converging even in a system in which the variation in inherance is large.

[Means for solving problems]

According to the present invention, there is a possibility that a large amount of tidal current does not flow in a place with a large impedance, and a large amount of tidal current may flow in a place with a small impedance. Focusing on the point that the absolute error is small, the above object is achieved by making the weight large for the flow of the branch having a large impedance and small for the flow of the branch having a small impedance.

That is, the present invention which has achieved the above-mentioned object gives a weight to an observation value such as a power flow observed at a plurality of points of an electric power system, and based on the weighted observation value and the connection state of the electric power system, the electric power A method for estimating the state of a power system that estimates the total power flow of a system using a weighted least squares method, characterized in that the weight given to each observation value is determined based on the Jacobian element. Is.

[Action]

The present invention does not determine the weight given to the observation value based on the error of the observation value, but determines the weight by focusing on reducing the dispersion of the elements of the matrix,
The numerical properties of the matrix have been improved, and the nonlinear calculation can be easily converged even in the system where the variation of the impedance of the branch is large.

〔Example〕

 Embodiments of the present invention will be described below with reference to the drawings.

FIG. 1 is a block diagram of state estimation.

FIG. 2 shows an example of a system in which impedance variation is large.

In FIG. 1, 1 is a power system, 2 is a system reduction unit, 3 is a Jacobian creation unit, 4 is an estimation calculation unit, 5 is a batho data determination unit, 6
Is an output device, and 7 is a weight determining unit.

An example of the power system 1 of FIG. 1 is shown in FIG. In FIG. 2, only the reactance is considered as the impedance of the branch, and only the effective flow is considered as the tidal current. In Fig. 2, the tidal current flowing through the branch 8 with a large impedance (P ₁₄ ) and the tidal current flowing through the branch 9 with a small impedance (P ₂₃ )
Is expressed by the following formula.

e _i : real part of voltage at node i f _i : imaginary part of voltage at node i X _i j: reactance of branch connecting node i and node j Now, the operation of the embodiment shown in FIG. 1 will be described.

The open / closed state of the switch is taken into the system contracting unit 2 online from the power system 1, and the nodes connected by the zero impedance branch are contracted into one node. The reduced system is input to the Jacobian creation unit 3 together with the observed values such as the bus voltage and the line power flow, and the Jacobian is created here.

Here, the element of Jacobian is Therefore, the one related to the branch power flow with a large impedance becomes small, and the one related to the branch power flow with a small impedance becomes large (the same property holds for the term differentiated by the real part of the voltage). The created Jacobian is input to the estimation calculation unit 4, where a gain matrix is created, and iterative calculation is performed with the Jacobian creation unit.

On the other hand, the weight determining section 7 creates weights by the method represented by the following expression (10).

If h _ki is an element of H, K is an observed value, and i is a node, the weight W _k is Thus, the weight W _k becomes larger for the tidal current of the branch with a large impedance, and smaller for the tidal current of the branch with a smaller impedance, which is the same as the property of the weight.

On the other hand, considering the numerical properties of the gain matrix G = H ^T WH in a system with a large variation in impedance, the elements G _ij of the gain matrix are Therefore, if all the weights W _k are 1.0, the size of G _ij is h
Influenced by the square of the size of _ki , h _ki is proportional to the inverse ratio of impedance, so if the ratio of impedance is 1:10 ³ , the size of the gain matrix element is 10 ⁶ :
The element of the gain matrix for the one with a large impedance is almost equal to 0 in the numerical calculation.
Therefore, the nodes in the system of FIG. 2 are considered to be separated from other nodes, and the gain matrix G becomes irregular.

However, when the weight given by the equation (10) is used and n = 1, Given that the size of the Jacobian element h _ki does not change much even if i changes when k is constant, G _{ij in} Eq. (12) is not affected by impedance variations. , The numerical property of the gain matrix G becomes very good. The above explanation is for the case of n = 1 in the equation (10), but the observed value of a general electric power system is not only the power flow of the branch but also the node injection power. There are also voltage and so on,
The value of n may be adjusted according to each system for which the state is estimated.

The weight determining unit 7 creates the weight as described above and outputs it to the estimation calculating unit 4. When the nonlinear calculation of the estimation calculation unit 4 is completed, the result is output to the bad data determination unit 5. Here, the bad data is detected, and if the bad data exists, the bad data is corrected and the process returns to the Jacobian creator 3. If the bad data does not exist, the result is output to the output device 6 such as a CRT.

The above is an example of the system to which the present invention is applied to automatically calculate the weights.

Below, a comparison of the numerical characteristics of the matrix when the present invention is applied and when it is not applied will be made using the example of the system of FIG.

In FIG. 2, if the reactance of the branch 8 having a large impedance is 0.75, the reactance of the branch 9 having a small impedance is 1 × 10 ^−4, and the initial value of the node voltage is (1.0,0.0), the Jacobian ((6 ) -Equation (9)) is shown in Fig. 3, and the gain matrix (Eq. (1
Equation 1) is obtained as shown in Fig. 4. In this case, the magnitudes of the elements in the first row and the first column of the gain matrix are smaller than the others, and are numerically close to irregular.

On the other hand, FIG. 5 shows the gain matrix calculated using the equation (12) when the present invention is applied. In this case, the sizes of the elements of the gain matrix are uniform, and the gain matrix is sufficiently regular. It has become a line. This example is (10)
This is the case where n = 1 in the equation.

Since the gain matrix of FIG. 6 is sufficiently regular, it is possible to solve the equation (2).

〔The invention's effect〕

As described above, according to the present invention, since the formalized weights are automatically calculated, not only the conventional manual input becomes unnecessary, but also the largest interrogation than the conventional one can be achieved. Since the method for determining the weight, which has been obtained through trial and error over time, has been formulated, the weight adjustment effort for state estimation is significantly reduced. Further, according to the present invention, a system with large variation in impedance, which cannot be estimated unless it is conventionally divided into an intermediate system and a radiation state system (the maximum and minimum ratios of impedance are about 10 ³ to 10 ^4). ), Batch calculation is also possible, which has the effect of greatly expanding the system to which state estimation can be applied.

[Brief description of drawings]

FIG. 1 is a block diagram showing an apparatus for realizing a state estimation method of a power system according to the present invention, FIG. 2 is a system diagram showing an example of a system in which impedance variation is large, and FIG. 3 is an explanation showing a concrete example of Jacobian. FIG. 4 is an explanatory diagram showing an example of a conventional gain matrix, FIG. 5 is an explanatory diagram showing an example of a gain matrix when the present invention is applied, and FIG. 6 is a conventional state theory. It is a flow chart shown for explaining. 1 ... Power system, 2 ... System reduction unit, 3 ... Jacobian creation unit, 4 ... Estimate calculation unit, 5 ... Bad data determination unit, 6 ... Output device, 7 ... Weight determination unit.

Claims (1)

[Claims] 1. An observation value of a power flow observed at a plurality of points in a power system is weighted, and based on the weighted observation value and the connection state of the power system, the entire power flow of the power system is determined. In the state designating method of the power system for estimating by using the weighted least squares method, the weight given to each observation value is set so that the variation in the size of the elements of the matrix is reduced and the numerical properties are improved. A method of estimating the state of a power system, which is characterized in that it is calculated based on the elements of.