CN117977593A - Power distribution network dynamic state estimation method and system based on self-adaptive member filtering - Google Patents

Abstract

The invention discloses a power distribution network dynamic state estimation method based on self-adaptive member filtering, which comprises the following steps: 1. collecting power distribution parameters and measurement information; 2. establishing a dynamic state estimation model by considering unknown but bounded noise, transforming the mixed measurement data, linearizing the measurement function, and establishing a linear dynamic state estimation model by combining a linear state prediction equation; 3. time updating, namely determining a priori estimated ellipsoid containing the current time state ellipsoid according to the last time state ellipsoid and a system state equation; 4. the method comprises the steps of adaptively detecting bad data, defining an adaptive detection threshold value, and identifying and eliminating the bad data in measurement; 5. and measuring and correcting, namely determining a posterior estimated ellipsoid comprising a priori estimated ellipsoid at the current moment and a measured updated ellipsoid by using a measuring function and a measured value correction state predicted value. The invention can realize high-precision dynamic state estimation in a noise unknown but bounded environment, can effectively identify and reject bad data when the measurement set contains the bad data, and has very important significance for making a power system operation plan and preventing power system accidents.

Description

Power distribution network dynamic state estimation method and system based on self-adaptive member filtering

Technical Field

The invention relates to the field of power distribution network state estimation, in particular to a power distribution network dynamic state estimation method and system based on self-adaptive member filtering.

Background

The random and fluctuation of the operation of the distribution network is aggravated by the rising of the grid-connected scale of the distributed power supply, the unknown but bounded characteristics of the system noise are increasingly highlighted, the accurate modeling is more difficult, and the distribution management system faces the challenge of comprehensively and accurately monitoring and sensing the operation state of the system. The accurate dynamic state estimation based on the existing measurement system has very important significance for making an operation plan of the power system and preventing accidents of the power system. The development of advanced measurement technology makes the power distribution network measurement set be composed of data from different measurement systems for a long time, however, the existence of sampling period differences of multi-source measurement data makes the probability that all kinds of real-time measurement are collected at the same time smaller, and in most cases, only one or two kinds of measurement can be obtained. Under the measuring environment, the estimation result obtained by the static state estimation method based on the measuring data at the current moment is difficult to reflect the actual state of the power distribution network, and the dynamic state estimation method combines prior state prediction and posterior measurement correction, so that the system is considerable under the environment with insufficient measurement, and the utilization rate of state estimation frequency and high-frequency measurement is improved. Therefore, research on a dynamic state estimation method integrating multi-source measurement data is important for tracking the running state of a system.

The current dynamic state estimation algorithm is mainly Kalman filtering based on Gaussian noise assumption and derived algorithms thereof, such as extended Kalman filtering, self-adaptive Kalman filtering and the like. These methods have good estimation accuracy in a preset noise environment, however, in an actual power grid where only boundary information of noise can be obtained, the state estimation performance will be greatly reduced. For this reason, the crew filtering algorithm based on unknown but bounded noise hypothesis is favored by researchers and is gradually applied to power systems, such as crew filtering, crew filtering algorithm based on double-layer optimization, crew filtering method based on event triggering mechanism, and the like. However, most current power system state estimation algorithms based on crew filtering ignore situations where the measurement set contains bad data, which will cause the estimation result to deviate from the true value.

Disclosure of Invention

In order to overcome the defects in the prior art, the invention provides a power distribution network dynamic state estimation method based on self-adaptive member filtering. In order to accurately track the system state of the power distribution network in the environment with unknown noise but limited noise, bad measurement is effectively filtered, and an accurate data basis is provided for situation awareness and operation planning of the power distribution network.

The invention solves the technical problems by the following technical means:

a power distribution network dynamic state estimation method based on self-adaptive member filtering comprises the following steps:

Step1, collecting parameter information and measurement data of a power distribution network;

Step 2, transforming the mixed measurement data, linearizing the measurement function, and establishing a linear dynamic state estimation model by combining a linear state prediction equation;

step 3, updating the filtering time of the gatherer; determining a priori estimated ellipsoid containing the state ellipsoid at the current moment according to the state ellipsoid at the previous moment and a system state equation;

Step 4, self-adaptive detection of bad data, defining a self-adaptive detection threshold value to identify and reject the bad data in measurement; the method comprises the following steps:

And 4.1, calculating a self-adaptive detection threshold of the bad data at the moment k, wherein the calculation formula is as follows:

Wherein: σ _ε,k is the equivalent measured noise standard deviation, L _w is the sliding window length,/>Is the average value of measurement values in a sliding window,/>For the variance of the absolute value sequence of the difference between the measurements in the sliding window, the formula is calculated as follows:

wherein: For i time measurement value,/> For the absolute value of the difference between i-1 measurement and i measurement in the sliding window,/>For sliding window interior/>Is the average value of (2);

Step 4.2, bad data identification, comparing the absolute value of the measured difference with the self-adaptive detection threshold If the absolute value of the measured difference is smaller than/>The measurement data is determined to be good; if the absolute value of the measured difference exceeds/>Identifying it as bad data;

Step 4.3, replacing bad data, if the measurement z _k+1 at the time of k+1 is identified as the bad data, assigning the average value of the rest measurements in the sliding window to z _k+1, wherein the average value is represented by the following formula:

And 5, measuring and correcting, namely determining a posterior estimated ellipsoid comprising a prior estimated ellipsoid at the current moment and a measurement updated ellipsoid by using a measuring function and a measured value correction state predicted value, and estimating the dynamic state of the power distribution network by using the posterior estimated ellipsoid.

Further, the specific implementation process of the step 1 is as follows:

step 1.1, collecting information such as topology of a power distribution network, line parameters and the like;

step 1.2, collecting system measurement data, and establishing an original measurement set, wherein the following formula is as follows:

z⁰＝[U_i,θ_i,I_ij,θ_ij,P_ij,Q_ij,P_i,Q_i]^T

Wherein, U _i、θ_i is the magnitude and phase angle measurement of the voltage phasor measurement of the node I, I _ij、θ_ij is the magnitude and phase angle measurement of the current phasor measurement of the branch ij, P _ij、Q_ij is the active and reactive measurement of the branch ij, and P _i、Q_i is the active and reactive injection power measurement of the node I.

Further, the specific implementation process of the step 2 is as follows:

Step 2.1, linear transformation of multi-source measurement;

Step 2.1.1, setting state variables as real part and imaginary part phasors of node voltages, wherein the following formula is as follows:

x＝[e_i,f_i]^T

Wherein: e _i is the real part phasor of the node voltage, and f _i is the imaginary part phasor of the node voltage;

Step 2.1.2, converting bus voltage phasors into a real part and an imaginary part of equivalent voltage, wherein the real part and the imaginary part are represented by the following formula:

Wherein: e _i、f_i is the measurement of the real part and the imaginary part of the voltage of the equivalent node i respectively;

step 2.1.3, converting the branch current phasors into a real part and an imaginary part of an equivalent branch current, wherein the real part and the imaginary part are represented by the following formula:

wherein: measuring the real part and the imaginary part of the current of the equivalent branch ij respectively;

Step 2.1.4, converting the branch active power and reactive power into a real part and an imaginary part of an equivalent branch current, wherein the real part and the imaginary part are represented by the following formula:

wherein: measuring the real part and the imaginary part of the equivalent current of the branch ik respectively;

step 2.1.5, converting the node injection power into a real part and an imaginary part of an equivalent node injection current, wherein the real part and the imaginary part are represented by the following formula:

wherein: measuring the real part and the imaginary part of the equivalent injection current of the node i respectively;

step 2.2, constructing a dynamic state estimation model based on an ellipsoid set;

step 2.2.1, establishing a prediction equation, wherein the following formula is as follows:

x_k+1＝F_kx_k+w_k

wherein: x _k+1、x_k is the state variable at k+1 and k times, respectively; f _k is a state transition matrix at k time; w _k is process noise;

Step 2.2.2, establishing a measurement equation, wherein the following formula is as follows:

z_k＝H_kx_k+v_k

Wherein: z _k is a measurement variable at time k; h _k is a measurement matrix at k time; v _k is measurement noise;

step 2.2.3, establishing an ellipsoidal collection model of process noise and measurement noise, wherein the ellipsoidal collection model has the following formula:

wherein: w _k and V _k are process noise and metrology noise ellipsoids sets respectively, For a given real positive definite matrix, the shape matrices of W _k and V _k are represented, respectively;

Step 2.3, setting the current time k=0, stopping estimation time k _max, adopting an ellipsoid set as a shape of a state quantity feasible set, and setting an initial set of system state variables, wherein the initial set of system state variables is represented by the following formula:

Wherein: x ₀ is the initial state of the device, Is an estimated value of x ₀, which represents the center of an ellipsoid,/>For a given real positive definite matrix, an ellipsoidal shape matrix is represented.

Further, the specific implementation process of the step 3 is as follows:

step 3.1, constructing an ellipsoid set of the state variable at the moment k, wherein the ellipsoid set of the state variable at the moment k is represented by the following formula:

wherein: A posterior estimate of x _k, representing the center of the ellipsoid,/> For a given real positive definite matrix, representing an ellipsoidal shape matrix;

And 3.2, constructing a state variable priori estimated ellipsoid set at the moment k+1, wherein the state variable priori estimated ellipsoid set is represented by the following formula:

wherein: For a priori estimate of x _k+1, represent the center of the ellipsoid,/> For a given real positive definite matrix, representing an ellipsoidal shape matrix;

Step 3.3, constructing an ellipsoid set of the state transition matrix at the moment k, and calculating the center and shape matrix of the ellipsoid set, wherein the formula is as follows:

wherein: f _k＝{F_kx_k:x_k∈EL_k is the set of k moment state transition matrix ellipsoids, Is the center of an ellipsoid, and Q _fk is an ellipsoid shape matrix;

and 3.4, calculating the center and shape matrix of the state variable priori estimated ellipsoid set at the time of k+1, wherein the center and shape matrix are represented by the following formula:

wherein: tr (Q) is the sum of squares of the lengths of the half axes of the ellipsoid Q, and represents the size of the ellipsoid shape matrix.

Further, the specific implementation process of the step 5 is as follows:

and 5.1, constructing a k+1 moment state variable posterior estimated ellipsoid set, wherein the following formula is as follows:

wherein: is an estimated value of x _k+1, which represents the center of an ellipsoid,/> For a given real positive definite matrix, representing an ellipsoidal shape matrix;

and 5.2, constructing a measurement update ellipsoid set according to a measurement equation, wherein the measurement update ellipsoid set is represented by the following formula:

Wherein: z _k+1 is a measurement update ellipsoid at time k+1;

and 5.3, constructing a measurement update ellipsoid set according to a measurement equation, wherein the measurement update ellipsoid set is represented by the following formula:

Wherein: z _k+1 is a measurement update ellipsoid at time k+1;

step 5.4, constructing a meeting Is a minimum ellipsoid of (1), as follows:

Wherein: for any 0.ltoreq.ρ _k+1.ltoreq.1, the above formula holds;

step 5.5, rewriting the above formula:

Wherein: delta _k+1 is more than or equal to 0 and less than or equal to 1, As intermediate variables, if you get/>Then a measurement calibration ellipsoid EL _k+1 can be obtained;

And 5.6, solving the center and shape matrix of the k+1 moment state variable posterior estimated ellipsoid set according to a measurement correction iteration formula, wherein the following formula is as follows:

wherein: the optimal value of the parameter ρ _k+1 is obtained by solving equation (29):

Step 5.7, judging whether the state estimation calculation is stopped, if k is smaller than k _max, making k=k+1, and continuing to calculate in the step three; otherwise, the calculation is ended.

The invention also discloses a power distribution network dynamic state estimation system based on the self-adaptive member filtering, which is applied to the method and comprises the following steps:

The data acquisition module is used for acquiring the parameter information and the measurement data of the power distribution network;

the data conversion module is used for converting the mixed measurement data, linearizing the measurement function and establishing a linear dynamic state estimation model by combining a linear state prediction equation;

The member collection filtering module is used for updating the member collection filtering time; determining a priori estimated ellipsoid containing the state ellipsoid at the current moment according to the state ellipsoid at the previous moment and a system state equation;

the bad data self-adaptive detection module is used for self-adaptively detecting bad data, defining a self-adaptive detection threshold value and identifying and eliminating the bad data in measurement; the method comprises the following steps:

And 4.1, calculating a self-adaptive detection threshold of the bad data at the moment k, wherein the calculation formula is as follows:

Wherein: σ _ε,k is the equivalent measured noise standard deviation, L _w is the sliding window length,/>Is the average value of measurement values in a sliding window,/>For the variance of the absolute value sequence of the difference between the measurements in the sliding window, the formula is calculated as follows:

wherein: For i time measurement value,/> For the absolute value of the difference between i-1 measurement and i measurement in the sliding window,/>For sliding window interior/>Is the average value of (2);

Step 4.2, bad data identification, comparing the absolute value of the measured difference with the self-adaptive detection threshold If the absolute value of the measured difference is smaller than/>The measurement data is determined to be good; if the absolute value of the measured difference exceeds/>Identifying it as bad data;

Step 4.3, replacing bad data, if the measurement z _k+1 at the time of k+1 is identified as the bad data, assigning the average value of the rest measurements in the sliding window to z _k+1, wherein the average value is represented by the following formula:

and the measurement correction module is used for measuring and correcting, utilizing a measurement function and a measurement value to correct a state predicted value, determining a posterior estimated ellipsoid comprising a prior estimated ellipsoid at the current moment and a measurement updated ellipsoid, and utilizing the posterior estimated ellipsoid to estimate the dynamic state of the power distribution network.

Further, the specific implementation process of the data acquisition module is as follows:

step 1.1, collecting information such as topology of a power distribution network, line parameters and the like;

step 1.2, collecting system measurement data, and establishing an original measurement set, wherein the following formula is as follows:

z⁰＝[U_i,θ_i,I_ij,θ_ij,P_ij,Q_ij,P_i,Q_i]^T

Wherein, U _i、θ_i is the magnitude and phase angle measurement of the voltage phasor measurement of the node I, I _ij、θ_ij is the magnitude and phase angle measurement of the current phasor measurement of the branch ij, P _ij、Q_ij is the active and reactive measurement of the branch ij, and P _i、Q_i is the active and reactive injection power measurement of the node I.

Further, the specific implementation process of the data transformation module is as follows:

Step 2.1, linear transformation of multi-source measurement;

Step 2.1.1, setting state variables as real part and imaginary part phasors of node voltages, wherein the following formula is as follows:

x＝[e_i,f_i]^T

Wherein: e _i is the real part phasor of the node voltage, and f _i is the imaginary part phasor of the node voltage;

Step 2.1.2, converting bus voltage phasors into a real part and an imaginary part of equivalent voltage, wherein the real part and the imaginary part are represented by the following formula:

Wherein: e _i、f_i is the measurement of the real part and the imaginary part of the voltage of the equivalent node i respectively;

step 2.1.3, converting the branch current phasors into a real part and an imaginary part of an equivalent branch current, wherein the real part and the imaginary part are represented by the following formula:

wherein: measuring the real part and the imaginary part of the current of the equivalent branch ij respectively;

Step 2.1.4, converting the branch active power and reactive power into a real part and an imaginary part of an equivalent branch current, wherein the real part and the imaginary part are represented by the following formula:

wherein: measuring the real part and the imaginary part of the equivalent current of the branch ik respectively;

step 2.1.5, converting the node injection power into a real part and an imaginary part of an equivalent node injection current, wherein the real part and the imaginary part are represented by the following formula:

wherein: measuring the real part and the imaginary part of the equivalent injection current of the node i respectively;

step 2.2, constructing a dynamic state estimation model based on an ellipsoid set;

step 2.2.1, establishing a prediction equation, wherein the following formula is as follows:

x_k+1＝F_kx_k+w_k

wherein: x _k+1、x_k is the state variable at k+1 and k times, respectively; f _k is a state transition matrix at k time; w _k is process noise;

Step 2.2.2, establishing a measurement equation, wherein the following formula is as follows:

z_k＝H_kx_k+v_k

Wherein: z _k is a measurement variable at time k; h _k is a measurement matrix at k time; v _k is measurement noise;

step 2.2.3, establishing an ellipsoidal collection model of process noise and measurement noise, wherein the ellipsoidal collection model has the following formula:

wherein: w _k and V _k are process noise and metrology noise ellipsoids sets respectively, For a given real positive definite matrix, the shape matrices of W _k and V _k are represented, respectively;

Step 2.3, setting the current time k=0, stopping estimation time k _max, adopting an ellipsoid set as a shape of a state quantity feasible set, and setting an initial set of system state variables, wherein the initial set of system state variables is represented by the following formula:

Wherein: x ₀ is the initial state of the device, Is an estimated value of x ₀, which represents the center of an ellipsoid,/>For a given real positive definite matrix, an ellipsoidal shape matrix is represented.

Further, the member filtering module specifically performs the following steps:

step 3.1, constructing an ellipsoid set of the state variable at the moment k, wherein the ellipsoid set of the state variable at the moment k is represented by the following formula:

wherein: A posterior estimate of x _k, representing the center of the ellipsoid,/> For a given real positive definite matrix, representing an ellipsoidal shape matrix;

And 3.2, constructing a state variable priori estimated ellipsoid set at the moment k+1, wherein the state variable priori estimated ellipsoid set is represented by the following formula:

wherein: For a priori estimate of x _k+1, represent the center of the ellipsoid,/> For a given real positive definite matrix, representing an ellipsoidal shape matrix;

Step 3.3, constructing an ellipsoid set of the state transition matrix at the moment k, and calculating the center and shape matrix of the ellipsoid set, wherein the formula is as follows:

wherein: f _k＝{F_kx_k:x_k∈EL_k is the set of k moment state transition matrix ellipsoids, Is the center of an ellipsoid, and Q _fk is an ellipsoid shape matrix;

and 3.4, calculating the center and shape matrix of the state variable priori estimated ellipsoid set at the time of k+1, wherein the center and shape matrix are represented by the following formula:

wherein: tr (Q) is the sum of squares of the lengths of the half axes of the ellipsoid Q, and represents the size of the ellipsoid shape matrix.

Further, the specific implementation process of the measurement correction module is as follows:

and 5.1, constructing a k+1 moment state variable posterior estimated ellipsoid set, wherein the following formula is as follows:

wherein: is an estimated value of x _k+1, which represents the center of an ellipsoid,/> For a given real positive definite matrix, representing an ellipsoidal shape matrix;

and 5.2, constructing a measurement update ellipsoid set according to a measurement equation, wherein the measurement update ellipsoid set is represented by the following formula:

Wherein: z _k+1 is a measurement update ellipsoid at time k+1;

and 5.3, constructing a measurement update ellipsoid set according to a measurement equation, wherein the measurement update ellipsoid set is represented by the following formula:

Wherein: z _k+1 is a measurement update ellipsoid at time k+1;

step 5.4, constructing a meeting Is a minimum ellipsoid of (1), as follows:

Wherein: for any 0.ltoreq.ρ _k+1.ltoreq.1, the above formula holds;

step 5.5, rewriting the above formula:

Wherein: delta _k+1 is more than or equal to 0 and less than or equal to 1, As intermediate variables, if you get/>Then a measurement calibration ellipsoid EL _k+1 can be obtained;

And 5.6, solving the center and shape matrix of the k+1 moment state variable posterior estimated ellipsoid set according to a measurement correction iteration formula, wherein the following formula is as follows:

wherein: the optimal value of the parameter ρ _k+1 is obtained by solving equation (29):

Step 5.7, judging whether the state estimation calculation is stopped, if k is smaller than k _max, making k=k+1, and continuing to calculate in the step three; otherwise, the calculation is ended.

The invention has the advantages that:

1. Aiming at the problems of incompatibility of multisource measurement data forms and high complexity of solving a nonlinear state estimation model, the multisource measurement set is simplified into the measurement set only comprising voltage and current phasors through linear transformation, the measurement function is linearized, a linear dynamic state estimation model is established by combining a state prediction equation, and the state estimation calculation complexity of a nonlinear power system is reduced.

2. Aiming at the problem that the performance of the traditional dynamic state estimation algorithm based on Gaussian noise assumption is greatly reduced in an unknown but bounded noise environment, the adaptive set member filtering algorithm is adopted to solve the dynamic state estimation model, so that high-precision dynamic state estimation can be realized, the problem that a system is not considerable due to insufficient measurement of a low-frequency measurement sampling gap is solved, and the utilization rate of high-frequency measurement is improved.

3. Aiming at the problem that the collection member filtering method is difficult to monitor bad measurement data, the method introduces a bad data self-adaptive detection threshold value to carry out self-adaptive pre-screening on the measurement data, and filters bad measurement. When the measurement set contains bad data, the algorithm can adaptively adjust the detection threshold according to the measurement sequence, can effectively filter the bad data, and improves the robustness of state estimation.

Drawings

FIG. 1 is a flow chart of a dynamic state estimation model solution based on adaptive member filtering in accordance with the present invention.

Detailed Description

For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions in the embodiments of the present invention will be clearly and completely described in the following in conjunction with the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.

Example 1

In this embodiment, a dynamic state estimation method of a power distribution network based on adaptive member filtering firstly provides a multi-source measurement linear transformation strategy for various measurement data form differences, and simplifies a multi-type measurement set into a measurement set only including voltage and current phasors; secondly, linearizing the measurement function, and establishing a dynamic state estimation model based on an ellipsoid set by combining a linear state prediction equation; and then, solving the provided dynamic state estimation model by adopting an adaptive set member filtering method algorithm considering bad data detection, and solving state quantities at different moments through time updating, bad data adaptive detection and measurement correction iteration. Specifically, the method comprises the following steps:

Step one, collecting parameter information and measurement data of a power distribution network;

step 1.1, collecting information such as topology of a power distribution network, line parameters and the like;

Step 1.2, collecting system measurement data, and establishing an original measurement set, as shown in formula (1):

z⁰＝[U_i,θ_i,I_ij,θ_ij,P_ij,Q_ij,P_i,Q_i]^T

In the formula (1), U _i、θ_i is the amplitude and phase angle measurement of the voltage phasor measurement of the node I, I _ij、θ_ij is the amplitude and phase angle measurement of the current phasor measurement of the branch ij, P _ij、Q_ij is the active and reactive measurement of the branch ij, and P _i、Q_i is the active and reactive injection power measurement of the node I;

Step two, establishing a dynamic state estimation model considering unknown but bounded noise;

Step 2.1, linear transformation of multi-source measurement;

step 2.1.1, setting state variables as real and imaginary phasors of node voltages, as in formula (2):

x＝[e_i,f_i]^T

In the formula (2): e _i is the real part phasor of the node voltage, and f _i is the imaginary part phasor of the node voltage;

Step 2.1.2, converting the bus voltage phasor into a real part and an imaginary part of an equivalent voltage, as in formula (3):

In the formula (3): e _i、f_i is the measurement of the real part and the imaginary part of the voltage of the equivalent node i respectively;

Step 2.1.3, converting the branch current phasors into real and imaginary parts of equivalent branch current, as in formula (4):

In the formula (4): measuring the real part and the imaginary part of the current of the equivalent branch ij respectively;

step 2.1.4, converting the branch active power and reactive power into the real part and the imaginary part of the equivalent branch current, as shown in formula (5):

In formula (5): measuring the real part and the imaginary part of the equivalent current of the branch ik respectively;

step 2.1.5, converting the node injection power into real and imaginary parts of the equivalent node injection current, as in equation (6):

In formula (6): measuring the real part and the imaginary part of the equivalent injection current of the node i respectively;

step 2.2, constructing a dynamic state estimation model based on an ellipsoid set;

step 2.2.1, establishing a prediction equation, and predicting the state quantity at the current moment according to the posterior state quantity at the previous moment, wherein the state quantity at the current moment is shown as a formula (7):

x_k+1＝F_kx_k+w_k

In the formula (7): x _k+1、x_k is the state variable at k+1 and k times, respectively; f _k is a state transition matrix at k time; w _k is process noise;

Step 2.2.2, a measurement equation is established, and the state quantity at the current moment is calculated through the measurement quantity at the current moment, as shown in the formula (8):

z_k＝H_kx_k+v_k

In formula (8): z _k is a measurement variable at time k; h _k is a measurement matrix at k time; v _k is measurement noise;

Step 2.2.3, establishing an ellipsoidal set model of process noise and measurement noise, as shown in the formula (9) and the formula (10):

In the formula (9) and the formula (10): w _k and V _k are process noise and metrology noise ellipsoids sets respectively, For a given real positive definite matrix, the shape matrices of W _k and V _k are represented, respectively;

Step 2.3, setting the current time k=0, stopping estimating time k _max, adopting an ellipsoid set as a shape of a state quantity feasible set, and setting an initial set of system state variables, as shown in formula (11):

In the formula (11): x ₀ is the initial state of the device, Is an estimated value of x ₀, which represents the center of an ellipsoid,/>For a given real positive definite matrix, representing an ellipsoidal shape matrix;

Step three, updating the filtering time of the gatherer;

and determining a priori estimated ellipsoid containing the state ellipsoid at the current moment according to the state ellipsoid at the previous moment and the predictive equation.

Step 3.1, constructing an ellipsoid set of state variables at the moment k, as shown in a formula (12):

In the formula (12): A posterior estimate of x _k, representing the center of the ellipsoid,/> For a given real positive definite matrix, representing an ellipsoidal shape matrix;

step 3.2, constructing a state variable priori estimated ellipsoid set at the moment k+1, as shown in formula (13):

in the formula (13): For a priori estimate of x _k+1, represent the center of the ellipsoid,/> For a given real positive definite matrix, representing an ellipsoidal shape matrix;

step 3.3, constructing an ellipsoid set of the state transition matrix at the moment k, and calculating the center and shape matrix of the ellipsoid set, as shown in formula (14):

In formula (14): f _k＝{F_kx_k:x_k∈EL_k is the set of k moment state transition matrix ellipsoids, Is the center of an ellipsoid, and Q _fk is an ellipsoid shape matrix;

step 3.4, calculating the center and shape matrix of the state variable priori estimated ellipsoid set at the time of k+1, as shown in the formula (15):

In formula (15): tr (Q) is the sum of squares of the lengths of the half axes of the ellipsoid Q and represents the size of the ellipsoid shape matrix;

step four, adaptive detection of the filtering bad data of the gatherer;

According to the characteristic that bad data and normal data have weak correlation in time, an adaptive detection mechanism is introduced to identify and replace the bad data in measurement.

The basic idea of the establishment of the bad data self-adaptive detection threshold is as follows: when the power system operates normally, the absolute value |z _k-z_k-1 | of the measurement difference between the k moment and the k-1 moment can be considered to only contain noise signals because the measurement value of the adjacent sampling moment changes very little; when bad data exists at the moment k, the noise signal is contained in the z _k-z_k-1, and based on the abrupt signal, the bad data can be identified by comparing the self-adaptive detection threshold value with the measurement difference value.

Step 4.1, calculating a self-adaptive detection threshold value of the bad data at the moment k, wherein a calculation formula is shown as a formula (16):

in formula (16): σ _ε,k is the equivalent measured noise standard deviation, L _w is the sliding window length,/>Is the average value of measurement values in a sliding window,/>For the variance of the absolute value sequence of the difference between the measurements in the sliding window, the calculation formulas are shown as formula (17) and formula (18): /(I)

In the formula (17) and the formula (18): For i time measurement value,/> For the absolute value of the difference between i-1 measurement and i measurement in the sliding window,/>For sliding window interior/>Is the average value of (2);

In formula (18): And/> The calculation formula is as follows:

Step 4.2, bad data identification, comparing the absolute value of the measured difference with the self-adaptive detection threshold If the absolute value of the measured difference is smaller than/>The measurement data is determined to be good; if the absolute value of the measured difference exceeds/>Identifying it as bad data;

The analysis formulas (16) - (18) can obtain that the absolute value of the measured difference between adjacent moments only contains noise signals when no bad data exists, The numerical value is smaller, the detection threshold value/>The numerical value is higher, and the absolute value of the measured difference value can be ensured to be/>In the range, thereby judging that the measurement data is good; in the presence of bad data, a measured difference absolute value comprising a sudden change signal and a noise signal is generated,/>Value rise, detection threshold/>Decreasing the value so that the absolute value of the measured difference exceeds/>Range, thereby identifying it as bad data.

Step 4.3, replacing bad data, if the measurement z _k+1 at the time of k+1 is identified as the bad data, assigning the average value of the rest measurements in the sliding window to z _k+1, as shown in formula (19):

fifthly, filtering measurement and correction of the personnel;

and determining a minimum ellipsoid comprising the current time priori estimated ellipsoid and the measured updated ellipsoid according to the current time measurement value and the measurement function.

Step 5.1, constructing a k+1 moment state variable posterior estimated ellipsoid set, as shown in formula (20):

In the formula (20): is an estimated value of x _k+1, which represents the center of an ellipsoid,/> For a given real positive definite matrix, representing an ellipsoidal shape matrix;

Step 5.2, constructing a measurement update ellipsoid set according to a measurement equation, as shown in formula (21):

in the formula (21): z _k+1 is a measurement update ellipsoid at time k+1;

step 5.3, constructing a measurement update ellipsoid set according to a measurement equation, as shown in formula (22):

/>

In formula (22): z _k+1 is a measurement update ellipsoid at time k+1;

step 5.4, constructing a meeting Is the minimum ellipsoid of formula (23):

In formula (23): the above equation holds true for any 0.ltoreq.ρ _k+1.ltoreq.1.

Step 5.5, formula (23) is formula (24):

in formula (24): delta _k+1 is more than or equal to 0 and less than or equal to 1, As intermediate variables, if you get/>Then a measurement calibration ellipsoid EL _k+1 can be obtained;

Step 5.6, solving the center and shape matrix of the k+1 moment state variable posterior estimated ellipsoid set according to the measurement correction iterative formula, as shown in formulas (25) to (28):

in formula (27): the optimal value of the parameter ρ _k+1 is obtained by solving equation (29):

Step 5.7, judging whether the state estimation calculation is stopped, if k is smaller than k _max, making k=k+1, and continuing to calculate in the step three; otherwise, the calculation is ended.

In summary, the present invention firstly performs linear transformation on multi-source measurement, and simplifies the multi-type measurement set into a measurement set only including voltage and current phasors; then linearizing the measurement function and establishing a dynamic state estimation model by combining a linear state prediction equation; and finally, solving the provided dynamic state estimation model by adopting an adaptive set member filtering method algorithm considering bad data detection, and solving state quantities at different moments through time updating, bad data adaptive detection and measurement correction iteration.

Example 2

The embodiment discloses a power distribution network dynamic state estimation system based on self-adaptive member filtering, which is applied to the method and comprises the following steps:

The data acquisition module is used for acquiring the parameter information and the measurement data of the power distribution network;

the data conversion module is used for converting the mixed measurement data, linearizing the measurement function and establishing a linear dynamic state estimation model by combining a linear state prediction equation;

The member collection filtering module is used for updating the member collection filtering time; determining a priori estimated ellipsoid containing the state ellipsoid at the current moment according to the state ellipsoid at the previous moment and a system state equation;

The bad data self-adaptive detection module is used for self-adaptively detecting bad data, defining a self-adaptive detection threshold value and identifying and eliminating the bad data in measurement;

and the measurement correction module is used for measuring and correcting, utilizing a measurement function and a measurement value to correct a state predicted value, determining a posterior estimated ellipsoid comprising a prior estimated ellipsoid at the current moment and a measurement updated ellipsoid, and utilizing the posterior estimated ellipsoid to estimate the dynamic state of the power distribution network.

The above-described respective modules perform the respective steps in embodiment 1, and are not described in detail herein.

The above embodiments are only for illustrating the technical solution of the present invention, and are not limiting; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims (10)

1. The power distribution network dynamic state estimation method based on the adaptive member filtering is characterized by comprising the following steps of:

Step1, collecting parameter information and measurement data of a power distribution network;

Step 2, transforming the mixed measurement data, linearizing the measurement function, and establishing a linear dynamic state estimation model by combining a linear state prediction equation;

step 3, updating the filtering time of the gatherer; determining a priori estimated ellipsoid containing the state ellipsoid at the current moment according to the state ellipsoid at the previous moment and a system state equation;

Step 4, self-adaptive detection of bad data, defining a self-adaptive detection threshold value to identify and reject the bad data in measurement; the method comprises the following steps:

And 4.1, calculating a self-adaptive detection threshold of the bad data at the moment k, wherein the calculation formula is as follows:

Wherein: σ _ε,k is the equivalent measured noise standard deviation, L _w is the sliding window length,/>Is the average value of measurement values in a sliding window,/>For the variance of the absolute value sequence of the difference between the measurements in the sliding window, the formula is calculated as follows:

wherein: For i time measurement value,/> For the absolute value of the difference between the i-1 moment measurement and the i moment measurement in the sliding window,For sliding window interior/>Is the average value of (2);

Step 4.2, bad data identification, comparing the absolute value of the measured difference with the self-adaptive detection threshold If the absolute value of the measured difference is smaller than/>The measurement data is determined to be good; if the absolute value of the measured difference exceeds/>Identifying it as bad data;

Step 4.3, replacing bad data, if the measurement z _k+1 at the time of k+1 is identified as the bad data, assigning the average value of the rest measurements in the sliding window to z _k+1, wherein the average value is represented by the following formula:

And 5, measuring and correcting, namely determining a posterior estimated ellipsoid comprising a prior estimated ellipsoid at the current moment and a measurement updated ellipsoid by using a measuring function and a measured value correction state predicted value, and estimating the dynamic state of the power distribution network by using the posterior estimated ellipsoid.

2. The method for estimating the dynamic state of the power distribution network based on the adaptive member filtering according to claim 1, wherein the specific implementation process of the step 1 is as follows:

step 1.1, collecting information such as topology of a power distribution network, line parameters and the like;

step 1.2, collecting system measurement data, and establishing an original measurement set, wherein the following formula is as follows:

z⁰＝[U_i,θ_i,I_ij,θ_ij,P_ij,Q_ij,P_i,Q_i]^T

Wherein, U _i、θ_i is the magnitude and phase angle measurement of the voltage phasor measurement of the node I, I _ij、θ_ij is the magnitude and phase angle measurement of the current phasor measurement of the branch ij, P _ij、Q_ij is the active and reactive measurement of the branch ij, and P _i、Q_i is the active and reactive injection power measurement of the node I.

3. The method for estimating the dynamic state of the power distribution network based on the adaptive member filtering according to claim 1, wherein the specific implementation process of the step 2 is as follows:

Step 2.1, linear transformation of multi-source measurement;

Step 2.1.1, setting state variables as real part and imaginary part phasors of node voltages, wherein the following formula is as follows:

x＝[e_i,f_i]^T

Wherein: e _i is the real part phasor of the node voltage, and f _i is the imaginary part phasor of the node voltage;

Step 2.1.2, converting bus voltage phasors into a real part and an imaginary part of equivalent voltage, wherein the real part and the imaginary part are represented by the following formula:

Wherein: e _i、f_i is the measurement of the real part and the imaginary part of the voltage of the equivalent node i respectively;

step 2.1.3, converting the branch current phasors into a real part and an imaginary part of an equivalent branch current, wherein the real part and the imaginary part are represented by the following formula:

wherein: measuring the real part and the imaginary part of the current of the equivalent branch ij respectively;

Step 2.1.4, converting the branch active power and reactive power into a real part and an imaginary part of an equivalent branch current, wherein the real part and the imaginary part are represented by the following formula:

wherein: measuring the real part and the imaginary part of the equivalent current of the branch ik respectively;

step 2.1.5, converting the node injection power into a real part and an imaginary part of an equivalent node injection current, wherein the real part and the imaginary part are represented by the following formula:

wherein: measuring the real part and the imaginary part of the equivalent injection current of the node i respectively;

step 2.2, constructing a dynamic state estimation model based on an ellipsoid set;

step 2.2.1, establishing a prediction equation, wherein the following formula is as follows:

x_k+1＝F_kx_k+w_k

wherein: x _k+1、x_k is the state variable at k+1 and k times, respectively; f _k is a state transition matrix at k time; w _k is process noise;

Step 2.2.2, establishing a measurement equation, wherein the following formula is as follows:

z_k＝H_kx_k+v_k

Wherein: z _k is a measurement variable at time k; h _k is a measurement matrix at k time; v _k is measurement noise;

step 2.2.3, establishing an ellipsoidal collection model of process noise and measurement noise, wherein the ellipsoidal collection model has the following formula:

wherein: w _k and V _k are process noise and metrology noise ellipsoids sets respectively, For a given real positive definite matrix, the shape matrices of W _k and V _k are represented, respectively;

Step 2.3, setting the current time k=0, stopping estimation time k _max, adopting an ellipsoid set as a shape of a state quantity feasible set, and setting an initial set of system state variables, wherein the initial set of system state variables is represented by the following formula:

Wherein: x ₀ is the initial state of the device, Is an estimated value of x ₀, which represents the center of an ellipsoid,/>For a given real positive definite matrix, an ellipsoidal shape matrix is represented.

4. A method for estimating a dynamic state of a power distribution network based on adaptive member filtering according to any one of claims 1 to 3, wherein the step 3 is specifically performed as follows:

step 3.1, constructing an ellipsoid set of the state variable at the moment k, wherein the ellipsoid set of the state variable at the moment k is represented by the following formula:

wherein: A posterior estimate of x _k, representing the center of the ellipsoid,/> For a given real positive definite matrix, representing an ellipsoidal shape matrix;

And 3.2, constructing a state variable priori estimated ellipsoid set at the moment k+1, wherein the state variable priori estimated ellipsoid set is represented by the following formula:

wherein: For a priori estimate of x _k+1, represent the center of the ellipsoid,/> For a given real positive definite matrix, representing an ellipsoidal shape matrix;

Step 3.3, constructing an ellipsoid set of the state transition matrix at the moment k, and calculating the center and shape matrix of the ellipsoid set, wherein the formula is as follows:

wherein: f _k＝{F_kx_k:x_k∈EL_k is the set of k moment state transition matrix ellipsoids, Is the center of an ellipsoid, and Q _fk is an ellipsoid shape matrix;

and 3.4, calculating the center and shape matrix of the state variable priori estimated ellipsoid set at the time of k+1, wherein the center and shape matrix are represented by the following formula:

wherein: tr (Q) is the sum of squares of the lengths of the half axes of the ellipsoid Q, and represents the size of the ellipsoid shape matrix.

5. A method for estimating a dynamic state of a power distribution network based on adaptive member filtering according to any one of claims 1 to 3, wherein the specific implementation procedure of step 5 is as follows:

and 5.1, constructing a k+1 moment state variable posterior estimated ellipsoid set, wherein the following formula is as follows:

wherein: is an estimated value of x _k+1, which represents the center of an ellipsoid,/> For a given real positive definite matrix, representing an ellipsoidal shape matrix;

and 5.2, constructing a measurement update ellipsoid set according to a measurement equation, wherein the measurement update ellipsoid set is represented by the following formula:

Wherein: z _k+1 is a measurement update ellipsoid at time k+1;

and 5.3, constructing a measurement update ellipsoid set according to a measurement equation, wherein the measurement update ellipsoid set is represented by the following formula:

Wherein: z _k+1 is a measurement update ellipsoid at time k+1;

step 5.4, constructing a meeting Is a minimum ellipsoid of (1), as follows:

Wherein: for any 0.ltoreq.ρ _k+1.ltoreq.1, the above formula holds;

step 5.5, rewriting the above formula:

Wherein: delta _k+1 is more than or equal to 0 and less than or equal to 1, As intermediate variables, if you get/>Then a measurement calibration ellipsoid EL _k+1 can be obtained;

And 5.6, solving the center and shape matrix of the k+1 moment state variable posterior estimated ellipsoid set according to a measurement correction iteration formula, wherein the following formula is as follows:

wherein: the optimal value of the parameter ρ _k+1 is obtained by solving equation (29):

Step 5.7, judging whether the state estimation calculation is stopped, if k is smaller than k _max, making k=k+1, and continuing to calculate in the step three; otherwise, the calculation is ended.

6. A power distribution network dynamic state estimation system based on adaptive member-set filtering, comprising:

The data acquisition module is used for acquiring the parameter information and the measurement data of the power distribution network;

the data conversion module is used for converting the mixed measurement data, linearizing the measurement function and establishing a linear dynamic state estimation model by combining a linear state prediction equation;

The member collection filtering module is used for updating the member collection filtering time; determining a priori estimated ellipsoid containing the state ellipsoid at the current moment according to the state ellipsoid at the previous moment and a system state equation;

the bad data self-adaptive detection module is used for self-adaptively detecting bad data, defining a self-adaptive detection threshold value and identifying and eliminating the bad data in measurement; the method comprises the following steps:

And 4.1, calculating a self-adaptive detection threshold of the bad data at the moment k, wherein the calculation formula is as follows:

Wherein: σ _ε,k is the equivalent measured noise standard deviation, L _w is the sliding window length,/>Is the average value of measurement values in a sliding window,/>For the variance of the absolute value sequence of the difference between the measurements in the sliding window, the formula is calculated as follows:

wherein: For i time measurement value,/> For the absolute value of the difference between the i-1 moment measurement and the i moment measurement in the sliding window,For sliding window interior/>Is the average value of (2);

Step 4.2, bad data identification, comparing the absolute value of the measured difference with the self-adaptive detection threshold If the absolute value of the measured difference is smaller than/>The measurement data is determined to be good; if the absolute value of the measured difference exceeds/>Identifying it as bad data;

Step 4.3, replacing bad data, if the measurement z _k+1 at the time of k+1 is identified as the bad data, assigning the average value of the rest measurements in the sliding window to z _k+1, wherein the average value is represented by the following formula:

and the measurement correction module is used for measuring and correcting, utilizing a measurement function and a measurement value to correct a state predicted value, determining a posterior estimated ellipsoid comprising a prior estimated ellipsoid at the current moment and a measurement updated ellipsoid, and utilizing the posterior estimated ellipsoid to estimate the dynamic state of the power distribution network.

7. The adaptive member filtering-based power distribution network dynamic state estimation system of claim 6, wherein the data acquisition module specifically performs the following steps:

step 1.1, collecting information such as topology of a power distribution network, line parameters and the like;

step 1.2, collecting system measurement data, and establishing an original measurement set, wherein the following formula is as follows:

z⁰＝[U_i,θ_i,I_ij,θ_ij,P_ij,Q_ij,P_i,Q_i]^T

Wherein, U _i、θ_i is the magnitude and phase angle measurement of the voltage phasor measurement of the node I, I _ij、θ_ij is the magnitude and phase angle measurement of the current phasor measurement of the branch ij, P _ij、Q_ij is the active and reactive measurement of the branch ij, and P _i、Q_i is the active and reactive injection power measurement of the node I.

8. The adaptive member filtering-based power distribution network dynamic state estimation system of claim 6, wherein the data transformation module specifically performs the following steps:

Step 2.1, linear transformation of multi-source measurement;

Step 2.1.1, setting state variables as real part and imaginary part phasors of node voltages, wherein the following formula is as follows:

x＝[e_i,f_i]^T

Wherein: e _i is the real part phasor of the node voltage, and f _i is the imaginary part phasor of the node voltage;

Step 2.1.2, converting bus voltage phasors into a real part and an imaginary part of equivalent voltage, wherein the real part and the imaginary part are represented by the following formula:

Wherein: e _i、f_i is the measurement of the real part and the imaginary part of the voltage of the equivalent node i respectively;

step 2.1.3, converting the branch current phasors into a real part and an imaginary part of an equivalent branch current, wherein the real part and the imaginary part are represented by the following formula:

wherein: measuring the real part and the imaginary part of the current of the equivalent branch ij respectively;

Step 2.1.4, converting the branch active power and reactive power into a real part and an imaginary part of an equivalent branch current, wherein the real part and the imaginary part are represented by the following formula:

wherein: measuring the real part and the imaginary part of the equivalent current of the branch ik respectively;

step 2.1.5, converting the node injection power into a real part and an imaginary part of an equivalent node injection current, wherein the real part and the imaginary part are represented by the following formula:

wherein: measuring the real part and the imaginary part of the equivalent injection current of the node i respectively;

step 2.2, constructing a dynamic state estimation model based on an ellipsoid set;

step 2.2.1, establishing a prediction equation, wherein the following formula is as follows:

x_k+1＝F_kx_k+w_k

wherein: x _k+1、x_k is the state variable at k+1 and k times, respectively; f _k is a state transition matrix at k time; w _k is process noise;

Step 2.2.2, establishing a measurement equation, wherein the following formula is as follows:

z_k＝H_kx_k+v_k

Wherein: z _k is a measurement variable at time k; h _k is a measurement matrix at k time; v _k is measurement noise;

step 2.2.3, establishing an ellipsoidal collection model of process noise and measurement noise, wherein the ellipsoidal collection model has the following formula:

wherein: w _k and V _k are process noise and metrology noise ellipsoids sets respectively, For a given real positive definite matrix, the shape matrices of W _k and V _k are represented, respectively;

Step 2.3, setting the current time k=0, stopping estimation time k _max, adopting an ellipsoid set as a shape of a state quantity feasible set, and setting an initial set of system state variables, wherein the initial set of system state variables is represented by the following formula:

Wherein: x ₀ is the initial state of the device, Is an estimated value of x ₀, which represents the center of an ellipsoid,/>For a given real positive definite matrix, an ellipsoidal shape matrix is represented.

9. The power distribution network dynamic state estimation system based on adaptive member filtering according to any one of claims 6 to 8, wherein the member filtering module specifically performs the following steps:

step 3.1, constructing an ellipsoid set of the state variable at the moment k, wherein the ellipsoid set of the state variable at the moment k is represented by the following formula:

wherein: A posterior estimate of x _k, representing the center of the ellipsoid,/> For a given real positive definite matrix, representing an ellipsoidal shape matrix;

And 3.2, constructing a state variable priori estimated ellipsoid set at the moment k+1, wherein the state variable priori estimated ellipsoid set is represented by the following formula:

wherein: For a priori estimate of x _k+1, represent the center of the ellipsoid,/> For a given real positive definite matrix, representing an ellipsoidal shape matrix;

Step 3.3, constructing an ellipsoid set of the state transition matrix at the moment k, and calculating the center and shape matrix of the ellipsoid set, wherein the formula is as follows:

wherein: f _k＝{F_kx_k:x_k∈EL_k is the set of k moment state transition matrix ellipsoids, Is the center of an ellipsoid, and Q _fk is an ellipsoid shape matrix;

and 3.4, calculating the center and shape matrix of the state variable priori estimated ellipsoid set at the time of k+1, wherein the center and shape matrix are represented by the following formula:

wherein: tr (Q) is the sum of squares of the lengths of the half axes of the ellipsoid Q, and represents the size of the ellipsoid shape matrix.

10. The power distribution network dynamic state estimation system based on adaptive member filtering according to any one of claims 6 to 8, wherein the measurement correction module specifically performs the following steps:

and 5.1, constructing a k+1 moment state variable posterior estimated ellipsoid set, wherein the following formula is as follows:

wherein: is an estimated value of x _k+1, which represents the center of an ellipsoid,/> For a given real positive definite matrix, representing an ellipsoidal shape matrix;

and 5.2, constructing a measurement update ellipsoid set according to a measurement equation, wherein the measurement update ellipsoid set is represented by the following formula:

Wherein: z _k+1 is a measurement update ellipsoid at time k+1;

and 5.3, constructing a measurement update ellipsoid set according to a measurement equation, wherein the measurement update ellipsoid set is represented by the following formula:

Wherein: z _k+1 is a measurement update ellipsoid at time k+1;

step 5.4, constructing a meeting Is a minimum ellipsoid of (1), as follows:

Wherein: for any 0.ltoreq.ρ _k+1.ltoreq.1, the above formula holds;

step 5.5, rewriting the above formula:

Wherein: delta _k+1 is more than or equal to 0 and less than or equal to 1, As intermediate variables, if you get/>Then a measurement calibration ellipsoid EL _k+1 can be obtained;

And 5.6, solving the center and shape matrix of the k+1 moment state variable posterior estimated ellipsoid set according to a measurement correction iteration formula, wherein the following formula is as follows:

wherein: the optimal value of the parameter ρ _k+1 is obtained by solving equation (29):

Step 5.7, judging whether the state estimation calculation is stopped, if k is smaller than k _max, making k=k+1, and continuing to calculate in the step three; otherwise, the calculation is ended.