CN106972949B - A State Estimation Method for Fractional Order Network System Based on Adaptive Compensation Technology - Google Patents

Abstract

The invention discloses a fractional order network system state estimation method based on adaptive compensation technology, which is used to solve the state estimation problem of the fractional order network system in the case of random packet loss in measurement signal data. The specific steps of the present invention are as follows: (1) Based on the binary Bernoulli distribution variable, combined with the characteristics of random packet loss of measurement data, a fractional order network system model is established that takes into account the random packet loss of measurement signal data. (2) Based on the innovation sequence, an adaptive compensation technique that can be used to dynamically compensate the packet loss of the measurement signal is proposed. (3) On the basis of the above steps, combined with the traditional linear fractional-order Kalman filter method, a fractional-order network system state estimation method that can be used in the case of random packet loss of measurement signal data is given. The example analysis shows the effectiveness and practicability of the method of the present invention.

Description

A State Estimation Method for Fractional Order Network System Based on Adaptive Compensation Technology

technical field

The invention relates to a fractional-order network system state estimation method based on self-adaptive compensation technology, belonging to the technical field of network system analysis and control.

Background technique

The analysis and control of the network system is of great significance to ensure the safe and stable operation of the network system. In recent years, with the development and progress of measurement technology, real-time online monitoring and control of network systems has become possible. In the existing research, it is the main way to realize the real-time analysis and control of the network system by designing a dynamic state estimator with the help of the real-time measurement information obtained by the phasor measurement unit.

Under normal circumstances, the measurement is first carried out through the phasor measurement unit, and the on-site measurement data is obtained, and then transmitted to the control center through the information transmission channel. However, it should be noted that during the transmission of the measurement information, the measurement data will be It is inevitable that data will be lost at random. Therefore, when designing the dynamic estimator of the network system, the packet loss of the measurement signal must be taken into account.

The fractional order network system has been widely used in various fields in recent years because it can describe the structure of the system more accurately. For example, it can predict and estimate the node voltage and current in the power system more accurately when used in the power system network. At present, in the existing research, in order to solve the problem of random packet loss in the measurement data of the linear fractional order network system, relevant researchers have proposed some measurement data compensation techniques, but the effectiveness of these methods is based on the measurement noise. and system noise covariance matrix known conditions, but in the practical application of engineering, these conditions are often unknown. Based on this, the present invention designs a fractional-order network system state estimation method based on adaptive compensation technology. This method can not only realize dynamic compensation for packet loss measurement data, but also dynamically obtain the system noise and measurement noise. covariance matrix, so the method of the present invention has better engineering practicability. Finally, the actual fractional order network system example test verifies the effectiveness and practicability of the method of the present invention.

Contents of the invention

Purpose of the invention: Aiming at the problems existing in the prior art, the present invention provides a fractional-order network system state estimation method based on adaptive compensation technology.

Technical solution: A state estimation method for fractional order network systems based on adaptive compensation technology, including the following parts:

1) A linear fractional order network system model considering random packet loss of measurement data

On the premise that each phasor measurement unit works independently, the binary Bernoulli distributed variable method is used to model the discrete linear fractional order network system considering the random packet loss of the measurement signal data. The system of the model Equation x _k+1 and output equation Can be described as:

Δ ^γ x _k+1 ＝A _d x _k +Bu _k +w _k

In the formula: Δ ^γ is a fractional operator, γ=[n ₁ ,n ₂ …n _p ] ^T is a fractional order, x _k+1 represents the state vector (dimension is p) at time k+1, A _d is the system matrix, B is the control matrix, u _k is the input variable, Represents the output vector at time k (dimension m), is a binary scalar conforming to the Bernoulli distribution, its value is 0 or 1, and the expectation and variance are respectively C is the output matrix, w _k is the system noise value at time k, are the measurement noise values in each phasor measurement unit, and have The system noise and the measurement noise are independent and unrelated to each other, and the satisfied mean value is 0, the covariance matrix is Q _k and R _k respectively, and the calculation formula of γ _j in the formula is defined as follows

In the formula, n≥0 is a fractional order, and j≥0 represents different moments.

2) Adaptive compensation technology for measuring data packet loss

In general, for an m-dimensional output variable, the covariance matrix satisfied by its measurement noise can be described as:

In the formula is a constant value at time k (and is often assumed to be known), and when random packet loss of the measurement signal is taken into account, time k The value of There is the following relationship

It can be seen from the analysis that when When packet loss occurs in the measurement data, σ→∞ in the formula, that is, the covariance matrix R _k satisfied by the measurement noise will change at this time, which will affect the calculation of the filter gain and estimation error covariance related to the measurement noise.

Based on this, the present invention proposes a dynamic estimation method of system noise and measurement noise covariance matrix Q _k and R _k in the case of packet loss of measurement data, and then realizes dynamic compensation of packet loss measurement data, and its specific implementation steps as follows:

(1) Calculate the new information sequence, the calculation formula is as follows

In the formula is the measured value at time k in the case of data packet loss, is the state estimate at time k.

(2) When the size of the moving window is L, calculate the average value of the innovation sequence s _k in the window, that is, the innovation matrix C _vk , the calculation formula is as follows

(3) On the basis of the previous step, the dynamic estimation value of the noise covariance matrix Q _k and R _k is obtained, and the calculation formula is as follows

Q _k ＝G _k C _vk G _k ^T

where G _k is the filter gain at time k, is the estimated error covariance matrix at time k, and Ξ _k is defined as follows

3) On the basis of the above, the linear fractional-order network state considering the measurement signal packet loss can be estimated by the following generalized fractional-order Kalman filter method. The specific steps are as follows. The method is followed in turn in the computer as follows Steps to achieve:

(1) Set the initial value related to filtering, such as the initial value of state estimation state estimation error covariance The initial values of the system noise and the measurement covariance matrix are Q _k , R _k , the dynamic estimation window value L, and the maximum iteration time N.

(2) Calculate the state prediction value at k+1 time Calculated as follows

In the formula is the estimated value of the state at time k.

(3) Calculate the noise covariance matrix values Q _k+1 and R _k+ 1 at time k+1 by using adaptive compensation technology; (see the adaptive compensation technology part of measuring data packet loss for specific steps)

(4) Calculate the state prediction error covariance at k+1 time Calculated as follows

In the formula (·) ^T is the transpose of the matrix.

(5) Calculate the generalized Kalman filter gain G _{k+1 at time k+1} , the calculation formula is as follows

In the formula, C represents the output matrix, and (·) ^-1 is the inverse operation of the matrix.

(6) Calculate the estimated error covariance at k+1 time Calculated as follows

where I is the identity matrix of the corresponding dimension.

(7) Calculating the estimated value of the state at k+1 time Calculated as follows

(8) When k+1>N, the iteration stops and the estimation result is output; otherwise, steps (2)-(7) of this part are repeated to estimate the state at the next moment.

Description of drawings

Fig. 1 is the method flowchart of the embodiment of the present invention;

Fig. 2 is the state estimation result figure that the embodiment adopts traditional fractional order Kalman filter method, (a) is the state estimation result of fractional order Kalman filter algorithm, (b) is the state estimation result of fractional order Kalman filter algorithm;

Fig. 3 adopts the estimated error figure of traditional fractional order Kalman filter method for the embodiment, (a) is fractional order Kalman filter algorithm state estimation error, (b) is fractional order Kalman filter algorithm state estimation error;

Fig. 4 is the state estimation result figure that the embodiment adopts the method of the present invention, (a) is the state estimation result of the method of the present invention, (b) is the state estimation result of the method of the present invention;

Fig. 5 is the state estimation error diagram of the embodiment adopting the method of the present invention, (a) is the state estimation error of the method of the present invention, (b) is the state estimation error of the method of the present invention.

Detailed ways

Below in conjunction with specific embodiment, further illustrate the present invention, should be understood that these embodiments are only used to illustrate the present invention and are not intended to limit the scope of the present invention, after having read the present invention, those skilled in the art will understand various equivalent forms of the present invention All modifications fall within the scope defined by the appended claims of this application.

As shown in Figure 1, the fractional order network system state estimation method based on adaptive compensation technology includes the following parts:

1) A linear fractional order network system model considering random packet loss of measurement data

On the premise that each phasor measurement unit works independently, the binary Bernoulli distributed variable method is used to model the discrete linear fractional order network system considering the random packet loss of the measurement signal data. The system of the model Equation x _k+1 and output equation Can be described as:

Δ ^γ x _k+1 ＝A _d x _k +Bu _k +w _k

In the formula: Δ ^γ is a fractional operator, γ=[n ₁ ,n ₂ …n _p ] ^T is a fractional order, x _k+1 represents the state vector (dimension is p) at time k+1, A _d is the system matrix, B is the control matrix, u _k is the input variable, Represents the output vector at time k (dimension m), is a binary scalar conforming to the Bernoulli distribution, its value is 0 or 1, and the expectation and variance are respectively C is the output matrix, w _k is the system noise value at time k, are the measurement noise values in each phasor measurement unit, and have The system noise and the measurement noise are independent and unrelated to each other, and the satisfied mean value is 0, the covariance matrix is Q _k and R _k respectively, and the calculation formula of γ _j in the formula is defined as follows

In the formula, n≥0 is a fractional order, and j≥0 represents different moments.

2) Adaptive compensation technology for measuring data packet loss

In general, for an m-dimensional output variable, the covariance matrix satisfied by its measurement noise can be described as:

In the formula is a constant value at time k (and is often assumed to be known), and when random packet loss of the measurement signal is taken into account, time k The value of There is the following relationship

It can be seen from the analysis that when When packet loss occurs in the measurement data, σ→∞ in the formula, that is, the covariance matrix R _k satisfied by the measurement noise will change at this time, which will affect the calculation of the filter gain and estimation error covariance related to the measurement noise.

Based on this, the present invention proposes a dynamic estimation method of system noise and measurement noise covariance matrix Q _k and R _k in the case of packet loss of measurement data, and then realizes dynamic compensation of packet loss measurement data, and its specific implementation steps as follows:

(2) Calculate the innovation sequence, the calculation formula is as follows

In the formula is the measured value at time k in the case of data packet loss, is the state estimate at time k.

(2) When the size of the moving window is L, calculate the average value of the innovation sequence s _k in the window, that is, the innovation matrix C _vk , the calculation formula is as follows

(3) On the basis of the previous step, the dynamic estimation value of the noise covariance matrix Q _k and R _k is obtained, and the calculation formula is as follows

Q _k ＝G _k C _vk G _k ^T

where G _k is the filter gain at time k, is the estimated error covariance matrix at time k, and Ξ _k is defined as follows

3) On the basis of the above, the linear fractional order network state considering the packet loss of the measurement signal can be estimated by the following generalized fractional order Kalman filter method, the specific steps are as follows

(1) Set the initial value related to filtering, such as the initial value of state estimation state estimation error covariance The initial values of the system noise and the measurement covariance matrix are Q _k , R _k , the dynamic estimation window value L, and the maximum iteration time N.

(2) Calculate the state prediction value at k+1 time Calculated as follows

In the formula is the estimated value of the state at time k.

(3) Utilize the adaptive compensation technique method to calculate the noise covariance matrix values Q _k+1 and R _{k+1 at time k+1} ;

(4) Calculate the state prediction error covariance at k+1 time Calculated as follows

(5) Calculate the generalized Kalman filter gain G _{k+1 at time k+1} , the calculation formula is as follows

In the formula (·) ^-1 is the inverse operation of seeking the matrix.

(6) Calculate the estimated error covariance at k+1 time Calculated as follows

where I is the identity matrix of the corresponding dimension.

(7) Calculating the estimated value of the state at k+1 time Calculated as follows

(8) When k+1>N, the iteration stops and the estimation result is output; otherwise, steps (2)-(7) of this part are repeated to estimate the state at the next moment.

In order to verify the effectiveness and practicability of the method of the present invention, a fractional-order network system widely used in fractional-order network system research is introduced below, specifically as follows

y _k ＝[0.1 0.3]x _k +v _k

In the formula, the fractional order n ₁ =0.7, n ₂ =1.2, the random packet loss rate of the measurement data of the phasor measurement unit is 0.3, and the covariance matrices satisfied by the system noise w _k and the measurement noise v _k are respectively

When using the method of the present invention to estimate the state of the non-linear fractional network of the embodiment, the initial value of state estimation x ₀ =[0 0] ^T ; the maximum iterative estimation time N=150, the adaptive compensation technology moving window value L=10 , the initial state estimation error covariance matrix and the control input variable u _k are respectively

For the linear fractional order network system where packet loss occurs in the measurement signal data of the above-mentioned embodiments, the traditional fractional order Kalman filter algorithm (its required relevant parameter value is the same as the parameter initial value of the method of the present invention) respectively, and the present invention The state estimation method of fractional order network system based on adaptive compensation technology estimates the system state variables. Figure 2 shows the state estimation results using the traditional fractional-order Kalman filter algorithm, and Figure 3 shows the estimation error; Figure 4 shows the state estimation results using this method, and Figure 5 shows the estimation error.

Combining the test results shown in Figure 2 and Figure 3, the following conclusions can be drawn: due to the random data packet loss of the measurement data in the transmission channel, the traditional fractional-order Kalman filter state estimation method cannot achieve this situation An accurate estimation of the system state under .

Combining the test results shown in Figure 4 and Figure 5, the following conclusions can be drawn: the fractional-order network system state estimation method based on the adaptive compensation technology of the present invention can realize dynamic compensation for packet loss of measurement data, and then complete the system state estimation method. accurate tracking and estimation.

Claims (1)

1. a kind of fractional order network system situation estimation method based on adaptive equalization technology, which is characterized in that including as follows Step:

(1) setting filters relevant initial value, such as state estimation initial valueState estimation error covarianceSystem noise and The initial value for measuring covariance matrix is respectively Q_k, R_k, dynamic estimation window value L and greatest iteration moment N；

(2) the status predication value at k+1 moment is calculatedCalculation formula is as follows

In formulaFor the state estimation at k moment；

(3) adaptive equalization technical method is utilized, the noise covariance matrix value Q at k+1 moment is calculated_k+1, R_k+1；

(4) the status predication error covariance at k+1 moment is calculatedCalculation formula is as follows

(5) the general Kalman filtering gain G at k+1 moment is calculated_k+1, calculation formula is as follows

In formula ()^-1To ask inverse of a matrix operation；

(6) the evaluated error covariance at k+1 moment is calculatedCalculation formula is as follows

I is the unit matrix of corresponding dimension in formula；

(7) state estimation at k+1 moment is calculatedCalculation formula is as follows

(8) the then iteration stopping as k+1 > N, output estimation result；Conversely, then repeating our department (2)-(7) step by step, carry out down The state estimation at one moment.