JP2013219902A - State estimation method for electric power system - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a weighted state estimation method for an electric power system in which a weight is set to a proper value.SOLUTION: There is provided a state estimation method for an electric power system that uses a weighted least square method, and determines a weight minimizing the difference between an estimated value determined by state estimation for a certain state amount of the electric power system and a measured value (or a calculated value of load-flow calculation) of the electric power system.

Description

  The present invention relates to a power system state estimation method using a weighted least square method, and relates to a state estimation method in which an appropriate weight is determined by an optimization method.

  In general, power system state values such as voltage amplitude (V) and phase (θ) of each node are calculated from observations of power, current, voltage, etc. at nodes (busbars) and branches (impedance elements) of the power system. And a monitoring system is in operation. The observation values of the power system include measurement errors of measuring instruments, errors due to delays during transmission or transmission troubles, and the like. Conventionally, a technique called state estimation has been applied as a technique for removing the error and estimating the state value of the power system (Patent Document 1).

The state estimation is a method of calculating a state value x (for example, voltage amplitude, phase, etc.) of the power system by a weighted least square method using an observed value z (for example, power, current, voltage, etc.).
The observation vector z is defined below.

Here, m is the number of observation values, x is the state value vector of the power system, n is the number of state values, h is a function vector obtained by removing the observation error from the observation value, and e is the observation error vector.
Elements z _{1 to} z _m of the observed value vector z are measured values of power (active power, reactive power), current, voltage (voltage amplitude (V), phase (θ)), and the like.

Elements x _{1 to} x _n of the state value vector x are physical quantities such as voltage (voltage amplitude (V), phase (θ)) that are to be estimated by the power system.
Function vector h ₁ to h _m represents the relationship between the observed value z and a state value x, which is a nonlinear function derived from the circuit equation.

Element e ₁ to e _m of the observation error vector represents the error included in each observation.
The state estimation method of the power system using the weighted least square method is to obtain a solution of the estimated value x by minimizing an objective function J (x) shown in the following two equations.

  However, R is a weighting matrix as shown in Equation 3, for example.

Elements w _{1 to} w _m of the weight matrix R are set in order to take into account the difference in accuracy of each measured value (observed value), and generally the variance σ _i ² with respect to the observed value z _i is used. The non-target element may not be 0. In that case, the weight matrix R is a covariance matrix of each measurement value.

  A solution x obtained by minimizing the objective function of the two equations satisfies the following equation.

Here, H is δh (x) / δx.
When Taylor expansion is performed on δh (x) / δx and the terms up to the first order are taken into consideration, the following equation holds for x.

Here, k is the number of iterations with 0 as an initial value.
An appropriate initial value is given to x ⁰ (for example, if the voltage is 1, the amplitude is 1 and the phase angle is 0), and iterative calculation is performed until x converges, thereby estimating the state value of the power system. it can.

However, in order to perform state estimation, it is necessary to set each element of the three weight matrices R. Conventionally, it has been necessary to obtain the value of variance σ _i ² by trial and error in consideration of the error of the measurement value and the convergence of the numerical calculation, and there has been a problem such as being troublesome.

In order to solve the problem, Patent Document 2 proposes a method of automatically calculating weights using a Jacobian element reflecting the connection state of the system (branch impedance magnitude).
In Patent Document 3, an element w of the weight matrix R is treated as an optimization variable, and the weight value is changed by alternately solving the optimization problem related to the least square method of state estimation and the weight w. Discloses a method of detecting defect data (defect measurement value) based on the size of. According to this method, it is not necessary to set a weight and state estimation can be performed.

JP-A-6-327155 JP-A-63-73831 JP 61-231837 A

  However, the invention described in Patent Document 2 is a weight setting method based on the connection state of the system (configuration of power supply, load, etc.), and does not consider actually measured observation data etc. There is a problem with high accuracy.

  The invention described in Patent Document 3 aims to detect defective data by changing the weight value, and evaluates whether the weight value itself is an appropriate value for state estimation. I do not have a mechanism to do. In the invention described in Patent Document 3, since the parameter α is added to the newly set objective function, adjustment of the weight is not necessary, but the parameter α must be appropriately adjusted by some method.

  This invention solves said subject and sets the weight in the weighted state estimation method of an electric power system to an appropriate value.

  The present invention according to claim 1, which solves the above-mentioned problem, is a power system state estimation method using a weighted least squares method, and measures an estimated value obtained by state estimation for a certain state quantity of the power system. A power system state estimation method characterized by calculating a difference from an obtained measurement value and obtaining a weight that minimizes the difference.

  The present invention according to claim 4 that solves the above-described problem is a power system state estimation method that uses a weighted least square method, and includes an estimated value obtained by state estimation for a certain state quantity of the power system and a power flow calculation. A power system state estimation method characterized in that a weight that minimizes a difference from a calculated value is obtained.

  According to the state estimation method of the present invention, it is possible to perform state estimation by setting weights to appropriate values without trial and error.

It is a system block diagram which implement | achieves a state estimation method. It is a flowchart (Example 1) which shows the calculation procedure of a state estimation. It is a flowchart (Example 2) which shows the calculation procedure of a state estimation. 10 is a flowchart (third embodiment) illustrating a calculation procedure of state estimation. It is a state quantity transition image figure of the state estimation process of this invention.

  Hereinafter, based on FIG. 1, the system configuration and the outline | summary for implement | achieving the state estimation method in one Embodiment of this invention are demonstrated. FIG. 1 shows a system configuration for realizing the state estimation method.

  In FIG. 1, 100 is a power system, 200 is a system for realizing a state estimation method, 10 is an observation value collection unit, 20 is a state estimation unit, 30 is a power flow calculation unit, 40 is an objective function creation unit, and 50 is optimal. The conversion execution unit 60 is an output unit.

  The state estimation method of the present invention is characterized by the difference between the estimated value calculated by the state estimating unit 20 and the measured value measured by the observation value collecting unit 10 (or the calculated value calculated by the tidal current calculating unit 30). The weight R is determined so as to minimize the difference.

The processing flow of the first embodiment will be described with reference to FIG.
In step S11, the observed value collection unit 10 measures the state values (power, current, voltage (amplitude, phase)) of the power system 100 at m measurement points from time t0 to time t1. Is the power system observation value z ^t (z ₁ ^{t to} z _m ^t : m observation values at time t).

In step S12, the observation value acquisition unit 10, the state value of the power system 100 (physical quantity corresponding to the later-described power system measurements ^{x t),} to the time t0 to t1, measured at measurement point n points, power System measurement value y ^t (y ₁ ^{t to} y _n ^t : n measurement values at time t).

In step S13, the objective function creating section 40 creates a power system estimates x ^t and power system measurements y ^t, the objective function F to be minimized with respect to the weight R and (R) as equation (6).

Note that ‖ ベ ク ト ル represents the norm of the vector. The norm here refers to converting a vector into a scalar as in the expansion of equation (6). Further, x ^{t0 to} x ^t1 (estimated value vector x at time t) are assumed to be estimated values obtained by state estimation at each time in step S14 described later.

  In step S14, the optimization execution unit 50 solves the objective function F (R) for the weighting matrix R that is an optimization variable by using some kind of optimization method. As an optimization method, since the objective function F (R) is a nonlinear function, for example, an optimization method called a metaheuristic such as nonlinear programming or a genetic algorithm can be considered. In step S14, state estimation and objective function calculation are repeated until the convergence condition of the optimization method is satisfied.

In the repetitive calculation, the estimated value x when the weight R is changed is obtained by using the power system observation value z ^t and the weight R at each time as input, and the power system estimated value x ^t (x ₁ ^{t from} time t0 to t1). ˜x _n ^t : n estimated values at time t). By substituting the estimated value x obtained by the state estimation into the objective function F (R), an evaluation value when the weight R is changed is obtained.

  The weight R may be set to a different value for each time. In that case, each weight R can be obtained by having different weights R at all times and using all the weights R as optimization variables. Further, if the weight R at a certain time is obtained in the state estimation before the previous time, the weight R is fixed to the obtained value, and the weight R for which the value has not been obtained (the weight R at the latest time). ) May be the optimization variables.

Finally, in step S15, the output unit 60 outputs the optimum solution R obtained in step S14 and the estimated value when the state estimation is performed with the weight R, and the process ends.
In the above, the optimization has been described for the estimated value and the measured value from time t0 to t1, but the data obtained up to the current time can be obtained by performing the optimization from time t0 to the current time. It is possible to estimate the state along the operation that is closer to real time.

  The optimum solution R that minimizes the objective function F (R) described above is obtained by summing the difference between the measured value and estimated value of each state quantity as shown in FIG. ).

  The first embodiment of the present invention evaluates whether the weight R is an appropriate value in estimating the state by taking the difference between the measured value and the estimated value of each state quantity as described above. By determining the weight R so as to be minimized, it is possible to set the most appropriate weight R in estimating the state.

In the first embodiment, the measured value y is used to create the objective function F (R). However, the second embodiment is different in that the calculated value obtained by the power flow calculation is used.
The processing flow of the second embodiment will be described below with reference to FIG.

In step S21, the observation value collection unit 10 measures the state values (power, current, voltage (amplitude, phase)) of the power system 100 at m measurement points from time t0 to time t1. Is the power system observation value z ^t (z ₁ ^{t to} z _m ^t : m observation values at time t).

In step S22, the power flow calculation unit 30 uses the power system observation value z ^{t as} input, obtains a physical quantity corresponding to the power system estimated value x ^t from the power flow calculation, and calculates the calculated value to the power system calculation value w ^t (w ₁ ^t ˜w _n ^t : n calculated values at time t).

In step S23, the objective function creating section 40 creates a power system estimates x ^t and power system calculated value w ^t, the objective function F (R) should be minimized for weight R as Equation 7.

Note that x ^{t0 to} x ^t1 (estimated value vector x at time t) are estimated values obtained by state estimation at each time in step S24 described later.
In step S24, the optimization execution unit 50 solves the objective function F (R) for the weighting matrix R that is an optimization variable by using some optimization technique. Details are the same as in the first embodiment.

Finally, in step S25, the output unit 60 outputs the optimum solution R obtained in step S24 and the estimated value when the state estimation is performed with the weight R, and the state estimation is terminated.
Obtaining the optimal solution R that minimizes the objective function F (R) described above is an image that reduces the difference between the calculated value and the estimated value obtained by the power flow calculation of each state quantity.

  The second embodiment of the present invention evaluates whether the weight R is an appropriate value in estimating the state by taking the difference between the calculated value of each state quantity and the estimated value as described above, and calculates the difference. By determining the weight R so as to be minimized, it is possible to set the most appropriate weight R in estimating the state.

  In the second embodiment, since the measurement value corresponding to the estimated value, which is the data necessary in the first embodiment, is not used, the present invention is executed even when the measurement value corresponding to the physical quantity of the estimated value is not obtained. Can do.

  In the third embodiment, for the purpose of reducing the influence of bad data and improving the accuracy of state estimation, the bad data is estimated from the information obtained by the state estimation, and the bad data is excluded from the observed values. State estimation was performed. The bad data is not an error but a measured value obtained by measurement failure, and a measured value (observed value) having a clearly incorrect value.

The process flow of the third embodiment will be described below with reference to FIG.
In step S31, the observed value collection unit 10 measures the state values (power, current, voltage (amplitude, phase)) of the power system 100 at m measurement points from time t0 to time t1, and the measured values. Is the power system observation value z ^t (z ₁ ^{t to} z _m ^t : m observation values at time t).

In step S32, the observation value acquisition unit 10, the state value of the power system 100 (physical quantity corresponding to the later-described power system measurements ^{x t),} to the time t0 to t1, measured at measurement point n points, power System measurement value y ^t (y ₁ ^{t to} y _n ^t : n measurement values at time t).

In step S33, the objective function creating section 40 creates a power system estimates x ^t and power system measurements y ^t, the objective function F to be minimized with respect to the weight R and (R) as Formula 8.

Note that x ^{t0 to} x ^t1 (estimated value vector x at time t) are estimated values obtained by state estimation at each time in step S34 described later.
In step S34, the optimization execution unit 50 solves the objective function F (R) for the weighting matrix R that is an optimization variable by using some optimization technique. The details are substantially the same as in the first embodiment, but in the third embodiment, when performing state estimation at a certain time, the bat data estimated from the previous state estimation information is removed from the power system observation value z ^t , Perform state estimation. When the bad data is removed from the observed values, the weights related to the bad data, the function vector h, and the size of the Jacobian H are reduced, so that each update is performed.

Finally, in step S35, the output unit 60 outputs the estimated value when the state estimation is performed with the optimum solution R and the weight R obtained in step S34, and the state estimation ends.
The third embodiment of the present invention evaluates whether the weight R is an appropriate value in estimating the state by taking the difference between the measured value and the estimated value of each state quantity as described above. By determining the weight R so as to be minimized, it is possible to set the most appropriate weight R in estimating the state. In the third embodiment of the present invention, more accurate state estimation can be performed by using a value excluding bad data as an observation value used in state estimation.

  Embodiments 1 to 3 of the present invention are examples in which the present invention is applied to power system state estimation using the weighted least squares method, but the present invention is not limited to the weighted least squares method, but for each measurement value. It can be applied to a method for estimating a state using weights. For example, when the weight matrix R is a covariance matrix, it is conceivable to solve the state estimation using an extended matrix method or linear programming, but the present invention can also be applied to the determination of the weight in that case.

DESCRIPTION OF SYMBOLS 10 Observation value collection part 20 State estimation part 30 Power flow calculation part 40 Objective function creation part 50 Optimization execution part 60 Output part 100 Power system 200 The system for implement | achieving a state estimation method

Claims (6)

A power system state estimation method using a weighted calculation method,
A power system characterized by calculating a difference between an estimated value obtained by state estimation of a state quantity of the power system and a measured value obtained by measuring the state quantity, and obtaining a weight that minimizes the difference. State estimation method. A power system state estimation method using a weighted calculation method,
Calculate the difference between the estimated value obtained by state estimation of the state quantity of the power system and the measured value obtained by measuring the state quantity for a plurality of times at the time within a predetermined time, and minimize the sum of the differences. A power system state estimation method characterized by obtaining a weight such as A power system state estimation method using a weighted calculation method,
A method for estimating a state of a power system, characterized in that a weight that minimizes a difference between an estimated value obtained by state estimation of the state quantity of the power system and a calculated value obtained by calculating the state quantity by power flow calculation is obtained. A power system state estimation method using a weighted calculation method,
Calculate the difference between the estimated value obtained from the state estimation of the power system by state estimation and the calculated value obtained from the tidal current calculation for multiple times at the time within a predetermined time, and minimize the sum of the differences. A power system state estimation method characterized by obtaining a weight such as   5. The power system state estimation method according to claim 1, wherein the weighted calculation method is a weighted least square method. 6. It is the state estimation method of the electric power system as described in any one of Claims 1-5,
A state estimation method for a power system characterized by using observed values excluding bad data specified by state estimation when obtaining the estimated value.

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