KR101219545B1 - Optimized parameter estimation method for power system - Google Patents

Abstract

PURPOSE: A parameter estimation method applied with a power system optimizing method is provided to enhance data integrity in analyzing data of a power system, and estimate real-time parameters only with the available measured data. CONSTITUTION: Voltage data and current data on a power transmission line are measured to create an admittance matrix. A target function is set by the measured data and the admittance matrix and variables of the target function are supposed. The WLS(Weighted Least-Squares) estimation method is applied about the variables, and the gradients of the gain matrix are obtained. As the Jacobian matrix of the gain matrix is calculated to the Hessian matrix, corrected amount of the variables is calculated. Convergence of parameter estimates is examined. [Reference numerals] (AA) Start; (BB) Reading measured data; (CC) Constructing admittance matrix; (DD) Defining a purpose function, supposing variable z; (EE) Calculating Gradient G(z); (FF) Calculating a Hessian matrix; (GG) Calculating variable correction rates; (HH) End; (II) Modifying each variable value

Description

Optimized parameter estimation method for power system

The present invention relates to a parameter estimation method using an optimization technique in a power system, and more particularly, by calculating inversely a parameter that changes according to physical changes, environmental factors, and the structure of a line to find an accurate parameter value. The present invention relates to a parameter estimation method using an optimization technique in a power system that can analyze data of a power system and improve data integrity.

Recently, various methods for stable operation of power systems have been developed by calculating accurate parameter values in power systems.

Patent No. 10-656381 shows that the conventional power mode estimation method using a fixed section selection method for selecting an arbitrary section is difficult to accurately estimate the power mode according to the interval or noise. Since there are many differences from the original solution, in order to solve this problem, a linear predictive polynomial according to the variable interval selection including at least one variable among sampling multiples, number of sections and time intervals is constructed to estimate the abnormality of the power mode. Disclosed is a method for automatically estimating power mode using a variable interval.

However, in the power mode estimation method, the error of interpreting the result of a specific section into the entire section without selecting the entire section still exists, and in particular, it was impossible to estimate a state that changes every moment because the parameter of the real time was not reflected. .

State estimation is a process of assigning a value to an unknown system state variable based on a system's measured value according to some criteria. From a power system perspective, the measured value of the voltage, current, and power measured at various points in the system and the system This is a technique for estimating the state of a currently operating system using a model.

State estimation is necessary to extend the capabilities of Supervisory Control and Data Acquisition (SCADA) systems and to increase the reliability and stability of other application functions within Energy Management Systems (EMS).

In addition, status estimation identifies the current operating status of the system, facilitating accurate and efficient monitoring of operational constraints such as transmission line data or bus voltage data and providing a reliable real-time database of events.

Currently used weighted least squares (WLS) state estimation has the advantage of relatively simple program implementation, but is sensitive to poor data including errors in SCADA measurement equipment and errors in communication equipment and errors in noise. The disadvantage is that problems can arise.

The performance and accuracy of applications such as economic dispatch, assumed accident analysis, automatic power generation control, safety analysis, and online tidal calculations used for stable and economical operation of the system significantly affect the quality of the data used in the calculation. Will receive.

The measured values (constants) currently used in the WLS state estimation are line power flow, bus power injections, bus voltage magnitudes and line current flow. magnitudes).

Among the above constants, power is a value produced by voltage and current, and its accuracy is relatively inferior compared to the measurement of voltage and current magnitude. Therefore, constants should be used with more weight on the most accurate voltage magnitude, followed by the correct current magnitude.

에서 이득행렬에 역(inverse)을 하는 부분이 있는데, 일반적으로 측정 자코비안 행렬인 H는 희소행렬이므로

를 하게 되면 완전 행렬(full matrix)이 되며, 완전 행렬(full matrix)의 역(inverse)을 구하는 것은 사실상 불가능하다.Also, gain matrix during WLS state estimation

There is an inverse of the gain matrix in. In general, the measured Jacobian matrix H is sparse.

Is a full matrix, and it is virtually impossible to find the inverse of a full matrix.

If we use the sparity technique to compensate for this, the measurement Jacobian H must be a square matrix, and eventually we need to subtract some of the variables to form a square.

Parameter estimation refers to providing accurate data of a system by estimating real-time parameters using only available measurement data and finding and removing data including errors.

The main function of state estimation is to build an accurate database of current systems by filtering errors from the measurement data and estimating the state of the system, provided that observability and system topology are accurate.

However, the data provided by SCADA may contain errors in the measurement or transmission process, and the real-time tidal calculations calculated using this data may be inaccurate. Therefore, parameter estimation is essential because the accuracy of parameter data and measurement data is key.

However, in the conventional method of parameter estimation of Merrill and Schweppe, the system parameter is estimated by adding the system parameter as a new state vector to the state vector used in the state estimation and performing the state estimation.

However, this parameter estimation method requires a large margin of measurement data, and the addition of a new state vector makes the calculation of the state estimation very complicated, the calculation time is long, and the bad data is included in the measurement data. The problem is that estimation is almost impossible.

In addition, the Debs parameter estimation method of the prior art estimates a parameter by applying a cyclic algorithm using a Kalman filter. In this method, the parameter is treated as a constant and used for calculation. However, in the actual system, the system's parameters may change over time, so the proposed algorithm lacks validity. If applied to a large system, convergence problems occur.

The magnetic and mutual admittance values of the current tracks are given by the formula. However, this method has an error as an estimated value using only a geometric model without applying physical changes or environmental factors.

Conventional magnetic and mutual impedance is given by Equation 1 and magnetic impedance is given by Equation 2, respectively.

(earth resistivity)=100[Ohm]이며, GMR_i는 Geometric mean radius of conductor i in feet이고,

는 컨덕터 i와 j 사이의 거리이다. Where f (frequency) = 60 Hz,

(earth resistivity) = 100 [Ohm], GMR _i is Geometric mean radius of conductor i in feet,

Is the distance between conductors i and j.

FIG. 1 illustrates a three-phase circuit in which a general neutral point is grounded. The circuit formed of ABCN may be expressed by Equation 3 by applying Kirchhoff's Voltage Law.

Equation 3 is expressed in an exploded form as follows.

이고, here,

ego,

이다.

to be.

이 된다. 이를 상기 수학식 4에 대입하면 수학식 5와 같이 표현할 수 있다.In Figure 1, the neutral N is grounded

. Substituting this in Equation 4 may be expressed as Equation 5.

에 대해 정리하면 수학식 6과 같이 된다.Equation 5 above

When summarized as in equation (6).

Substituting Equation 6 into Equation 5 results in Equation 7.

를

로 대치시키면 수학식 8과 같다.Of Equation 7

To

If replaced with Equation (8).

Therefore, the final phase impedance to which Kron's reduction is applied is shown in Equation (9).

When the equation 9 is converted into p.u. units, it becomes a raw impedance matrix as shown in Equation 10, and thus the final raw impedance matrix is shown in Equation 11.

The current parameter used in the algae analysis is using the above equation (11). Therefore, the analysis results may be inaccurate when the algae analysis is used because the parameter contains an error. Thus parameter estimation is essential for the accuracy of the parameter.

Accordingly, an object of the present invention is to improve data integrity in interpreting data of a power system by inversely calculating and estimating a parameter that changes according to an environment and a line structure through a state estimation algorithm for finding an accurate parameter value of a power system. It is to provide a parameter estimation method applying the optimization technique in the power system that can be made.

)의 그래디언트(Gradient)를 구하는 단계와, 상기 이득행렬의 자코비안 행렬(H)을 헤시안 행렬로 계산하고, 변수의 수정량을 계산하는 단계와, 계통 운용 및 제어를 위해 계통 파라미터의 상태를 파악하는 파라미터 추정의 수렴 여부를 확인하는 단계로 이루어진 것을 특징으로 한다.The parameter estimation method applying the optimization technique in the power system according to the present invention for achieving the object of the present invention comprises the steps of reading the measurement data of the voltage and current measured on the transmission line to form an admittance matrix, Setting an objective function using measured data and admittance, assuming a variable z of the objective function, and gain matrix G (z) = during estimation of the weighted least squares (WLS) state for the variable z. (

Calculating the gradient of the gradient, calculating the Jacobian matrix H of the gain matrix as the Hessian matrix, calculating the correction amount of the variable, and calculating the state of the system parameter for system operation and control. It is characterized in that it comprises a step of confirming whether or not the converged parameter estimation to grasp.

In this case, the step of confirming whether or not the parameter estimation is converged may include performing a G (z) calculation, a Hessian matrix calculation, and a variable correction amount by modifying a value of each variable when the parameter estimation does not converge to a true value. And later reconfirming whether or not the parameter estimation has converged.

The objective function may be defined using voltage and current of each phase, magnetic and mutual admittance of the line, and shunt admittance.

으로 수정하는 것을 특징으로 한다.In addition, after the conversion to a form containing a constraint using a Lagrangian function for the optimization of the objective function to obtain the optimal condition equation, and applying the Newton-Raphson method to the optimum condition equation

It is characterized by modifying.

으로 구하는 것을 특징으로 한다.Meanwhile, the variable correction amount is based on the modified optimal conditional expression.

It is characterized by obtaining.

으로부터 반복적으로 구하는 것을 특징으로 한다.The value of the variable is

It is characterized in that it is repeatedly obtained from.

On the other hand, the step of confirming whether or not the convergence of the parameter estimation for identifying the state of the system parameters for the system operation and control, fixing the admittance calculated in the parameter estimation to a constant, the phase angle of the voltage using an optimization technique Estimating the state of the phase difference.

Here, the step of fixing the admittance calculated in the parameter estimation to a constant, and estimating the state of the phase difference by using the optimization technique of the phase angle of the voltage, the voltage phase angle of one of the bus bars of both ends is calculated by fixing to 0 It is characterized by further comprising the step of obtaining the phase difference between the phases of both ends.

으로 수정하고, 각 행렬과 벡터를 계산하여 변수의 수정량(

)을 계산하는 단계와, 상기 변수의 수정량을 보정한 보정식(

)을 반복 계산하여 결과값을 추정하는 단계로 이루어진 것을 특징으로 한다.In addition, fixing the admittance calculated in the parameter estimation to a constant, and estimating the state of the phase difference using the optimization technique of the phase angle of the voltage, setting the objective function of the parameter estimation using the equal constraint conditions, Assuming the function (z) of the function, and specifying the phase of the slack busbar as 0 when applying the phase difference to the overall system analysis, and calculating the phase angle of the entire system based on the slack busbar by accumulating the phase difference In order to optimize the objective function, a Lagrangian function is used to convert the form into a form including constraints, and then the optimum conditional equation is obtained.

And calculate the amount of correction of the variable by calculating each matrix and vector

) And a correction equation correcting the correction amount of the variable (

It is characterized in that it consists of a step of repeatedly calculating the estimated value.

The parameter value for minimizing the objective function is representative of a parameter value of the current system.

According to the parameter estimation method applying the optimization technique in the power system as described above, through the parameter estimation algorithm for finding the correct parameter value of the power system by calculating the estimated parameter that changes according to the environment and the structure of the line inversely The data integrity can be improved in interpreting the data, and the convergence of the parameter estimation is always guaranteed even when the real time parameter is estimated only with the available measurement data and an error is included.

1 is a diagram illustrating a three-phase circuit with a general neutral point grounded;
2 is a diagram of a three-phase medium-distance power transmission equivalent circuit applied to an embodiment of the present invention;
3 is a flowchart illustrating a parameter estimation method applying an optimization technique in a power system according to an embodiment of the present invention.

While the invention is susceptible to various modifications and alternative forms, specific embodiments thereof are shown by way of example in the drawings and will herein be described in detail. It should be understood, however, that the invention is not intended to be limited to the particular embodiments, but includes all modifications, equivalents, and alternatives falling within the spirit and scope of the invention. Like reference numerals are used for like elements in describing each drawing.

Unless defined otherwise, all terms used herein, including technical or scientific terms, have the same meaning as commonly understood by one of ordinary skill in the art. Terms such as those defined in the commonly used dictionaries should be construed as having meanings consistent with the meanings in the context of the related art and shall not be construed in ideal or excessively formal meanings unless expressly defined in this application. Do not.

The present invention can be embodied as computer readable codes on a computer readable recording medium. The computer-readable recording medium includes all kinds of recording devices in which data that can be read by a computer system is stored. Examples of computer-readable recording media include ROM, RAM, CD-ROM, magnetic tape, floppy disk, optical data storage device, and the like, and are also implemented in the form of a carrier wave (for example, transmission over the Internet). It also includes. The computer readable recording medium can also be distributed over network coupled computer systems so that the computer readable code is stored and executed in a distributed fashion.

Hereinafter, with reference to the accompanying drawings, it will be described in detail a preferred embodiment of the present invention.

The impedance of the transmission and distribution lines used for power system analysis is calculated from the line type and length of the line, but the mutual inductance between the live lines cannot be applied accurately. This is because the mutual inductance between tracks changes from time to time depending on the surrounding environment of the track.

In addition, since the measurement technique also removes and measures the current flowing in the corresponding line, it is different from the mutual inductance between the lines in the live state and the error is large. Using the measured current and voltage, an optimization technique is used to estimate the line parameters.

In addition, reactive power control such as switched shunt and FACTS is used for stable operation and increased efficiency of the power system. In order to operate the reactive power control device, information of various power systems such as voltage, current phase angle, and grid frequency is required.

Among the information of the power system, there are a parameter obtained by measuring a fixed value such as a line impedance, an absolute value of voltage, current, and the like, and a value obtained by calculation. In AC systems, voltage and current are complex numbers, but the measured values are absolute values and only scalar values can be obtained. Therefore, we need a value to calculate this as a complex number, which is the phase difference.

 The phase difference is obtained through a PMU, etc., but this is performed under the premise that the times of the measuring devices at both ends are exactly the same by measuring the frequencies of both ends and confirming the phase difference through time comparison.

Therefore, in the parameter estimation method using the optimization technique in the power system of the present invention, the state of the phase difference is estimated through the optimization technique based on the value calculated in the parameter estimation.

Referring to FIGS. 2 and 3, first, magnetic and mutual admittances and shunt admittances of a line are obtained by using voltage magnitudes of each phase and current magnitudes of each phase measured on a transmission line, and an admittance matrix is configured.

 When the equation is developed based on FIG. 2, Equation 12 may be defined as Equation 12, and Equation 13 and Equation 14 may be defined.

이고, 이를 정리하면 수학식 16과 같이 표현할 수 있다.In the model defined in Equations 13 to 15, N is grounded.

In summary, this can be expressed as Equation 16.

에 대해 정리하면 수학식 17과 같이 되고,이를 대입하면 수학식 18과 같이 정리된다.This

If we sum up, we get as in equation (17).

를

로 대치시키면 수학식 19와 같이 된다. In Equation 18

To

Replace with Eq. (19).

Therefore, the final phase impedance to which Kron's reduction is applied can be expressed by Equation 20.

When the above Equation 20 is converted into p.u. units, it is as shown in Equation 21, and when it is expressed as an admittance matrix, it can be expressed as Equation 22.

, 각 상의 전류 크기

이고, 기존의 파라미터 rqkt은 선로의 자기 및 상호 어드미턴스

, 션트(Shunt) 어드미턴스

이다. 구해야할 변수는 각 상의 전압

, 각 상의 전류

, 선로의 자기 및 상호 어드미턴스

, 션트 어드미턴스

가 된다. As shown in Figure 2, the value measured in the three-phase medium-distance transmission line, that is, the constant is the voltage magnitude of each phase

Current magnitude of each phase

The existing parameter rqkt is the magnetic and mutual admittance of the line

, Shunt admittance

to be. The variable to get is the voltage of each phase

Current of each phase

, Magnetic and mutual admittance of the track

, Shunt admittance

.

과 관련된 모선 방정식은 계산에서 제외된다. 여기서, 슬랙 모선의 위상각

은 0으로 고정시킨다.And, as shown in the constants and variables in the parameter estimation of Table 1 below, the phase angle of the slack bus bar knowing the value of the voltage value to be obtained

The busbar equation associated with is excluded from the calculation. Where the phase angle of the slack busbar

Is fixed to zero.

의

=0이므로

으로써

은 실수부로만 이루어진 형태가 된다. therefore,

of

= 0

As

Is a form of real numbers only.

The busbar equation for the three-phase medium-distance transmission line of FIG. 2 may be expressed as shown in Table 2.

Simplification of Table 2 is given by Equation 23.

Where [] = diagonal matrix

는 자기 및 상호 어드미턴스 벡터이고,

는 션트 어드미턴스 벡터이다.

Is the magnetic and mutual admittance vector,

Is the shunt admittance vector.

The voltage magnitude of each phase of the bus and the magnitude of the current of each phase, the magnetic and mutual admittances of the line, and the deviation between the calculated value and the measured value of the shunt admittance can be mathematically modeled as in Equation 24 below.

Based on Equation 13, an objective function of parameter estimation using an equal sign constraint is defined as in Equation 14, and assumes a variable z. A parameter value for minimizing the objective function represents a parameter value of a current system.

If this is applied to the model defined above, it can be expressed as Equation 25.

,

,

의 세트수이다.Where j is

,

,

The number of sets.

의 형태, 즉 전류 및 전압 크기의 자승 형태로 표현한다.Since the value measured in Equation 14 is the magnitude of current and voltage, the expression of the objective function is

In the form of, that is, the square of the current and voltage magnitude.

The optimization problem of Equation 25 may be converted into an extended form including a constraint as shown in Equation 26 using a Lagrangian function.

Equation 24 and Equation 26 are completely equivalent, and the solution of Equation 26 becomes the solution of Equation 24.

,

,

,

에 대해서는 라그랑지안 함수를 최소화시키고, 라그랑지안 슬랙변수

에 대해서는 라그랑지안 하무를 최대화시키는 것을 목적으로 한다. Here, the Lagrangian function of Equation 26 is a variable,

,

,

,

Minimize the Lagrangian function for

For the purpose of maximizing Lagrangian Hamu.

Therefore, since the maximum value and the minimum value of Equation 27 exist at the poles of the function, the partial differential value of each variable should be 0 for the value of the variable for the above purpose. That is, the optimum conditional expression is shown in Equation 28.

The value of the variable satisfying equation (28) is the solution to the given optimization problem. The existence of a solution that satisfies this optimal condition equation simultaneously is a necessary and sufficient condition for a given optimization problem to have a solution.

파트의 최적 조건식은 모선 방정식과 완전히 같은 형태를 가지는 비선형 방정식임을 알 수 있다.In order to solve the given optimization problem, Equation 28 must be solved. However, in Equation 28

It can be seen that the optimal conditional expression of the part is a nonlinear equation that has exactly the same shape as the mother bus equation.

Therefore, since the optimal conditional equation is a nonlinear system of equations, the Newton-Raphson method, which is mainly used to find a function value by computer, should be applied.

By applying the Newton-Rapson method to modify the given optimal condition equation can be expressed as

,

,here,

,

,

The Jacobian matrix H is composed of Hessian matrices, so the Hessian matrix is calculated.

The correction amount of the variable may be obtained from Equation 29 as shown in Equation 30, and the value of each variable may be repeatedly obtained from Equation 31.

Knowing the status of the power system is essential to economical grid operation, so the role of parameter estimation is very important. In addition, the size and complexity of the power system has greatly increased the importance of grid control for power system operation, and the accuracy of measurement data and parameter data is a key factor in accurately estimating the current operating status of the system.

Therefore, the parameter estimation method applying the optimal technique according to the embodiment of the present invention defines the objective function using the voltage, current, line magnetic admittance, mutual admittance, and shunt admittance of each phase of a three-phase transmission line, The equations for all elements are newly derived using these measurement functions to estimate the real-time parameters using only the available measurement data, and the parameter estimation using the optimization technique converges to the true value even when errors are included.

Therefore, the parameter estimation method applying the optimal technique according to the embodiment of the present invention can always ensure the convergence degree of the parameter estimation for grasping the state of the system parameter for system operation and control.

Meanwhile, the phase can be obtained by fixing the admittance calculated in the parameter estimation to a constant and calculating the phase angle of the voltage using an optimization technique. However, the phase has a meaning as a phase difference, and the voltage phase angle of one of the bus bars at both ends is fixed to 0 to calculate the phase difference between the phases at both ends.

We define the objective function of parameter estimation using equal constraints and assume the variable z. The parameter value that minimizes the objective function represents the parameter value of the current system.

 If this is applied to the model defined above, it can be expressed as Equation 33, and it can be expressed as Equation 34 using Lagrangian function.

 When the phase difference thus obtained is applied to the entire system analysis, as shown in Equation 35, the phase of the slack bus bar is set to 0, and the phase difference is accumulated based on this, and the phase angle of the entire system based on the slack bus bar can be obtained.

 Thus, the value of the satisfying variable is the solution to a given optimization problem. The existence of a solution that satisfies this optimal condition equation simultaneously is a necessary and sufficient condition for a given optimization problem to have a solution.

파트의 최적 조건식은 모선 방정식과 완전히 같은 형태를 가지는 비선형 방정식임을 알 수 있다.To solve this optimization problem, we need to solve the above equation. By the way,

It can be seen that the optimal conditional expression of the part is a nonlinear equation that has exactly the same shape as the mother bus equation.

Therefore, since the optimal conditional equation is a nonlinear simultaneous equation, the Newton-Raphson method, which is mainly used to find a function value by computer, should be applied.

 Applying the Newton-Rapson method can be expressed by the following equation (36).

In Equation 36, each vector and matrix are represented by Equation 37 below.

When the correction value is calculated by calculating the matrix and the vector of Equation 37, Equation 38 is obtained.

It will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined in the appended claims. It will be possible.

Claims (10)

Constructing an admittance matrix by reading measured data of voltage and current measured on a transmission line,
Setting an objective function using the measured data and admittance, and assuming a variable z of the objective function;
Gain matrix G (z) = (of estimated weighted least squares (WLS) states for the variable z.

To get the gradient of),
Calculating the Jacobian matrix H of the gain matrix as a Hessian matrix, calculating a correction amount of a variable,
A parameter estimation method using an optimization technique in a power system, characterized in that the step of verifying the convergence of parameter estimation for identifying the state of the system parameters for grid operation and control. The method of claim 1,
Determining whether the parameter estimates converge,
Modifying the value of each variable if the parameter estimate does not converge to a true value, and reconfirming whether the parameter estimate has converged after re-performing the G (z) calculation, the Hessian matrix calculation, and the variable correction amount calculation. A parameter estimation method using an optimization technique in a power system. The method of claim 1,
The objective function is a parameter estimation method using an optimization technique in a power system, characterized in that the voltage and current of each phase, the magnetic and mutual admittance of the line, the shunt admittance. The method of claim 3,
For the optimization of the objective function, the Lagrangian function is converted into a form including constraints, and then the optimum conditional equation is obtained.

Parameter estimation method applying an optimization technique in the power system, characterized in that for modifying. 5. The method of claim 4,
The variable correction amount is based on the modified optimal condition equation.

Parameter estimation method using an optimization technique in the power system, characterized in that obtained by. The method of claim 5,
The value of this variable

Parameter estimation method using an optimization technique in the power system, characterized in that it is repeatedly obtained from. The method of claim 1,
Determining whether or not convergence of the parameter estimation for identifying the state of the system parameters for the system operation and control,
And fixing the admittance calculated in the parameter estimation to a constant, and estimating the state of the phase difference by using an optimization technique of the phase angle of the voltage. The method of claim 7, wherein
The step of fixing the admittance calculated in the parameter estimation to a constant, and estimating the state of the phase difference by using the optimization technique of the phase angle of the voltage, by calculating the voltage phase angle of one of the bus bars of both ends by calculating fixed to 0 A method for estimating a parameter applying an optimization technique in a power system, characterized by further comprising the step of obtaining a phase difference of a phase. The method of claim 7, wherein
Fixing the admittance calculated in the parameter estimation to a constant, and estimating the state of the phase difference by using an optimization technique of the phase angle of the voltage,
Setting an objective function of parameter estimation using equal constraints, and assuming a variable z of the objective function;
When the phase difference is applied to the entire system analysis, the phase of the slack bus bar is set to 0, and the phase difference is accumulated based on this, and the phase angle of the entire system based on the slack bus bar is calculated.
For the optimization of the objective function, the Lagrangian function is converted into a form including constraints, and then an optimum conditional equation is obtained.

And calculate the amount of correction of the variable by calculating each matrix and vector

),
A correction formula for correcting the correction amount of the variable (

And estimating the resultant value by iterative calculation. 10. The method of claim 9,
And a parameter value for minimizing the objective function represents a parameter value of a current system.

Images