CN113076658A - PMU amplitude data recovery method considering synchronization errors at two ends of line - Google Patents

Abstract

This patent has proposed a PMU amplitude data recovery method of considering circuit both ends synchronous error, and this method can accurately resume PMU data, guarantees the accuracy of PMU data application. Firstly, analyzing the quality problem in actual measurement PMU data, secondly, establishing a data recovery model, calculating recovery coefficients by using historical data, then sequentially recovering the voltage amplitude, the active power, the reactive power and the current amplitude, and finally recovering the problems in the actual measurement example and displaying the recovery result, wherein the method has higher precision.

Description

PMU amplitude data recovery method considering synchronization errors at two ends of line

Technical Field

The invention relates to the field of operation control protection of an electric power system, in particular to a PMU amplitude data recovery method considering synchronous errors at two ends of a line

Background

The synchronous Phasor Measurement Unit (PMU) is used as the eye of a power grid and can provide voltage phasor, current phasor, active power, reactive power and frequency for a control center. And has many applications including power system control, state estimation, stability evaluation, and fault detection, among others. Therefore, the data quality of PMUs is very important.

However, due to measurement system failure, device aging, communication channel blockage, even network attack, etc., abnormal data and even data loss may occur, which seriously affects various applications based on PMU data, and therefore, abnormal data needs to be corrected and recovered, and currently, data recovery methods of PMU can be divided into two categories: 1) recovery methods based on single PMU data. 2) A method for recovery based on multiple PMU data.

The recovery method based on single PMU data mainly comprises interpolation, low-rank matrix decomposition and the like, but the method is only suitable for a small amount (less than 30 time slices) of continuous data loss and is not suitable for a large amount (more than 100 time slices) of continuous data loss.

The second method is based on the power system state estimation of a plurality of nodes or a line model of two nodes, and can effectively recover a large amount of abnormal data which are continuously lost, but most of the existing methods rely on line parameters to recover the data, and in the actual operation of a line, the line parameters often deviate from an off-line value due to changes of weather, temperature, equipment aging and the like, so that the accuracy of a recovery result is low. In addition, most methods in the second category do not take into account the synchronization problem that may exist in PMU data, and thus the second category still has problems.

In summary, in consideration of the problems that the PMU data may have abnormal data and the existing methods have, it is necessary to develop a method for recovering a large amount of consecutive PMU data effectively, and consider the synchronization problem at both ends of the line and the situation that the true value of the line parameter is unknown during the recovery process.

Disclosure of Invention

The method is suitable for the situation that the true value of the line parameter is unknown, and has high practicability. The technical scheme of the invention is as follows:

step 1: obtaining historical actual measurement PMU data without abnormal data and PMU data containing abnormal data;

step 2: calculating a recovery coefficient based on historical measured data;

and step 3: and recovering the abnormal data based on the recovery coefficient.

Drawings

In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on the drawings without creative efforts.

FIG. 1 shows a situation where data loss occurs in actual PMU data;

FIG. 2 is a PI type equivalent model diagram of the line parameters;

fig. 3 is a flowchart of a PMU amplitude data recovery method according to an embodiment of the present invention;

fig. 4 is a diagram of recovery of lost data.

Detailed Description

Step 1: firstly, obtaining PMU data at two ends of a line under a plurality of working conditions, and ensuring that the PMU has no abnormal data as historical data; further, PMU data containing abnormal data is obtained

Step 2: calculating a restitution coefficient based on historical measured data

Based on the PI equivalent model of the line in fig. 2, the line voltage has the following relationship according to the voltage drop across the line:

wherein the content of the first and second substances,

in addition, according to the balance of active power and reactive power at two ends of the line, the method can obtain,

S′_m＝P′_m+jQ′_m＝P_m+jQ_m+jU_m ²B/2 (5)

further, based on the active and reactive power balance equations (3) - (5) and the voltage drop equations (1) - (2), the following equations can be obtained:

for equations (6) - (8), the left side of the equation can be taken from historical PMU data, while the right side term of the equation is the product of PMU magnitude data and coefficients consisting of line parameters.

In a short time profile, the line parameters remain unchanged, so the recovery coefficient can be considered constant. And, once the PMU data at one end is known, the PMU data at the other end can be recovered.

However, due to different working conditions, sag, ambient temperature, etc., the line parameters may change, and the true value of the coefficient is unknown, so that the solution of the recovery coefficient is needed first.

Further, Eq. (6) can be written as

z_U＝x_Ua_U (9)

Wherein the content of the first and second substances,

similarly, equation (7) can be written as,

z_P＝x_Pa_P (11)

wherein the content of the first and second substances,

z_P＝[P_m+P_n]

the formula (8) can be written as,

z_Q＝x_Qa_Q (13)

wherein

For the history data (9), (11) and (13) at time k, it can be stated that,

z_U,k＝x_U,ka_U (15)

z_P,k＝x_P,ka_P (16)

z_Q,k＝x_Q,ka_Q (17)

therefore, to obtain the restitution coefficient, a_U,a_PAnd a_QAt least historical data under 4 different power flow conditions are needed, and assuming that the historical data comprises data of l time sections, the following linear relation can be obtained,

Z_U＝X_Ua_U (18)

Z_P＝X_Pa_P (19)

Z_Q＝X_Qa_Q (20)

wherein the content of the first and second substances,

the recovery coefficients may therefore be obtained based on a least squares method, i.e.,

by the method, the recovery coefficient can be obtained, and data recovery is further carried out.

And step 3: and recovering the abnormal data based on the recovery coefficient.

First, assuming that the data to be recovered is the j time of the n terminal, the voltage and the active power can be recovered first by the equations (25) and (26), that is, the voltage and the active power are recovered

P_nr,j＝a_Px_P,j-P_m,j (26)

Wherein, U_nr,j,P_nr,jIs the recovered voltage amplitude and active power.

Further, reactive power may be restored, i.e.,

Q_nr,j＝a_Qx_Q,j-Q_m,j (27)

wherein Q is_nr,jIs the reactive power after recovery. It should be noted that U must be restored first_n,jThen to Q_nr,jRecovery is performed because

Is x_Q,jA part of (a).

Finally, the current magnitude data is restored based on the restored voltage magnitude, active power and reactive power, i.e.,

based on the above process, n-end data can be corrected.

The process according to the invention is demonstrated below by way of example.

In this embodiment, PMU data of a certain actually measured 500kV is recovered in China, where the line parameters are R ═ 0.5 Ω, X ═ 5.6 Ω, and B ═ 1.07664 × 10^-4S，

By applying the method, the PMU lost data at the n terminal in fig. 1 is recovered, and the error of the recovery result is shown in the following table,

relative error of recovery result

As can be seen from the above table, the relative error of the recovery result is small, indicating that the method is effective.

In conclusion, the PMU amplitude data recovery method considering the synchronous errors at the two ends of the line is feasible and has engineering application value.

It is noted that those skilled in the art will recognize that embodiments of the present invention are not described in detail herein.

The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (4)

1. A PMU amplitude data recovery method considering synchronization errors at two ends of a line is characterized by comprising the following steps:

step 1: obtaining historical actual measurement PMU data without abnormal data and PMU data containing abnormal data;

step 2: calculating a recovery coefficient based on historical measured data;

and step 3: and recovering the abnormal data based on the recovery coefficient.

2. The method for restoring the PMU amplitude data considering the synchronization error at two ends of the line according to claim 1, characterized in that in step 1, the PMU amplitude data obtained from the historical measurement without abnormal data and the PMU data containing abnormal data are obtained.

3. The method for restoring the PMU amplitude data considering the synchronous errors at the two ends of the line according to claim 1, characterized in that the relationship between the amplitude data at the two ends of the line is deduced based on the PI-type equivalent model of the transmission line, and the recovery coefficient is calculated based on the historical measured data, the specific calculation process is as follows,

voltage recovery coefficient model:

z_U＝x_Ua_U (1)

wherein the content of the first and second substances,

active power recovery coefficient model:

z_P＝x_Pa_P (3)

wherein the content of the first and second substances,

reactive power recovery coefficient model

z_Q＝x_Qa_Q (5)

Wherein

As for the history data (1), (3) and (5) at the time k, it can be expressed that,

z_U,k＝x_U,ka_U (7)

z_P,k＝x_P,ka_P (8)

z_Q,k＝x_Q,ka_Q (9)

therefore, to obtain recoveryCoefficient of a_U,a_PAnd a_QAt least historical data under 4 different power flow conditions are needed, and assuming that the historical data comprises data of l time sections, the following linear relation can be obtained,

Z_U＝X_Ua_U (10)

Z_P＝X_Pa_P (11)

Z_Q＝X_Qa_Q (12)

wherein the content of the first and second substances,

the recovery coefficients may therefore be obtained based on a least squares method, i.e.,

a_U＝(X_U ^TX_U)^-1X_U ^TZ_U (14)

a_P＝(X_P ^TX_P)^-1X_P ^TZ_P (15)

a_Q＝(X_Q ^TX_Q)^-1X_Q ^TZ_Q (16)

by the method, the recovery coefficient can be obtained, and data recovery is further carried out.

4. The method for restoring the PMU amplitude data considering the synchronization error of the two ends of the line according to claim 1, characterized in that: based on the recovery coefficients calculated in step 2 and the data recovery model, the abnormal data can be recovered, the recovery process is as follows,

first, assuming that data to be recovered is at time j of the n terminal, the voltage and active power can be recovered first by equations (17) and (18), i.e., the voltage and active power can be recovered

P_nr,j＝a_Px_P,j-P_m,j (18)

Wherein, U_nr,j,P_nr,jIs the recovered voltage amplitude and active power, and further, reactive power can be recovered, i.e.,

Q_nr,j＝a_Qx_Q,j-Q_m,j (19)

wherein Q is_nr,jIs the reactive power after recovery, and it should be noted that U must be recovered first_n,jThen to Q_nr,jRecovery is performed because

Is x_Q,jA part of (a) of (b),

finally, the current magnitude data is restored based on the restored voltage magnitude, active power and reactive power, i.e.,

based on the above process, n-end data can be corrected.

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