CN106972949A - A kind of fractional order network system situation method of estimation based on adaptive equalization technology - Google Patents

Abstract

The invention discloses a kind of fractional order network system situation method of estimation based on adaptive equalization technology, for solving state estimation problem of the fractional order network system in the case of random loss occurs for measurement signal data.The present invention's comprises the following steps that：(1) based on binary system Bernoulli Jacob's distribution variable, the characteristics of occurring random loss with reference to metric data establishes meter and surveys the fractional order network system model that data random loss occurs for signal.(2) based on innovation sequence, it is proposed that can be used for the adaptive equalization technology that dynamic compensation value surveys signal packet loss.(3) on the basis of above-mentioned steps, with reference to traditional linear fractional rank kalman filter method, give available for the fractional order network system situation method of estimation in the case of measurement signal data random loss.Sample calculation analysis indicates the inventive method validity and practicality.

Description

A kind of fractional order network system situation method of estimation based on adaptive equalization technology

Technical field

The present invention relates to a kind of fractional order network system situation method of estimation based on adaptive equalization technology, belong to network Network analysis and control technology field.

Background technology

The analysis of network system is with control for ensureing that network system security stable operation has great importance.In recent years Come, with the development and progress of measurement technology so that carrying out real time on-line monitoring and control to network system becomes possibility. In existing research, by means of the real-time measurement information acquired in phasor measurement unit, by designing dynamic state estimator, It is to realize the main path that network system is analyzed with control in real time.

Generally, measured first by phasor measurement unit, obtain field measurement data, then pass through information Transmission channel passes to control centre, it is however noted that, in the transmitting procedure of measurement information, metric data can not can be kept away The situation for the generation data random loss exempted from, so, it must count and measure when carrying out the dynamic estimator design of network system The situation of packet loss occurs for signal.

Fractional order network system is widely used in each in recent years due to can more accurately describe the structure of system Field, is such as used in power system network, more accurate node voltage in power system and electric current can be carried out pre- Survey and estimate.At present, in existing research, it is directed to linear fractional rank network system metric data and occurs asking for random loss Topic, related researcher proposes some and measures compensation data technology, but the validity of these methods, which is built upon measurement, makes an uproar Known to sound and system noise covariance matrix in condition, and in the practical application of engineering, these conditions are not often not Know.Based on this, the present invention devises a kind of fractional order network system situation method of estimation based on adaptive equalization technology, should Method, which can not only be realized, dynamically to be compensated packet loss metric data, and can be expired with dynamic access system noise and measurement noise The covariance matrix of foot, therefore the inventive method has more preferable engineering practicability.Finally, actual fractional order network system is calculated Example test demonstrates the validity and practicality of the inventive method.

The content of the invention

Goal of the invention：For problems of the prior art, the present invention provides a kind of based on adaptive equalization technology Fractional order network system situation method of estimation.

Technical scheme：A kind of fractional order network system situation method of estimation based on adaptive equalization technology, including it is as follows Part：

1) the linear fractional rank network system model of meter and metric data random loss

On the premise of assuming that each phasor measurement unit each works independently, with binary system Bernoulli Jacob distribution variable side Method, is modeled to the Discrete Linear fractional order network system in the case of meter and measurement signal data random loss, and model is System EQUATION x_k+1And output equationIt can be respectively depicted as：

Δ^γx_k+1=A_dx_k+Bu_k+w_k

In formula：Δ^γFor fractional order operator, γ=[n₁,n₂…n_p]^TFor fractional order order, x_k+1Represent the state at k+1 moment Vector (dimension is p), A_dFor sytem matrix, B is control matrix, u_kFor input variable,Represent the output vector (dimension at k moment For m),Be meet Bernoulli Jacob distribution binary system scalar, its value be 0 or 1, expect be respectively with varianceC is output matrix, w_kFor the system noise value at k moment,Measured in respectively each phasor measurement unit Noise figure is surveyed, and is hadSystem noise and measurement both noises are separate unrelated, are met Average is 0, and covariance matrix is respectively Q_kAnd R_k, and γ in formula_jCalculation formula be defined as follows

N >=0 is fractional order order in formula, and j >=0 is represented not in the same time.

2) the adaptive equalization technology of metric data packet loss

Generally, the output variable tieed up for m, the covariance matrix that its measurement noise is met can be described as：

In formulaFor the constant value (and it is often assumed that for be known) at k moment, and when meter and measurement signal During random loss, the k momentValue withIn the presence of following relation

From analyzing, whenWhen packet loss occurs for metric data, σ → ∞ in formula now measures what noise was met Covariance matrix R_kIt can change, and then the meter of the influence filtering gain related to measuring noise and evaluated error covariance Calculate.

Based on this, the present invention proposes system noise and measurement noise covariance matrix Q under metric data packet loss situation_k, R_k Method for dynamic estimation, and then realize the dynamic compensation to packet loss metric data, its specific implementation step is as follows：

(1) innovation sequence is calculated, calculation formula is as follows

In formulaIt is the measuring value at k moment in the case of meter and data packetloss,It is the state estimation at k moment.

(2) when it is L to take moving window size, innovation sequence s in calculation window_kAverage value, i.e., new breath Matrix C_vk, its Calculation formula is as follows

(3) on the basis of previous step, noise covariance matrix Q is asked for_k, R_kDynamic estimation value, calculation formula is as follows

Q_k=G_kC_vkG_k ^T

G in formula_kIt is the filtering gain at k moment,It is the evaluated error covariance matrix at k moment, Ξ_kIt is defined as follows

3) on the basis of above-mentioned, then it can be believed by following Generalized fractional kalman filter method counting and measuring The linear fractional rank network state of number packet loss is estimated that comprise the following steps that, this method is successively according to such as in a computer What lower step was realized：

(1) the related initial value of setting filtering, such as state estimation initial valueState estimation error covarianceSystem noise The initial value of sound and measurement 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；It is (specific Step is shown in the adaptive equalization technology segment of metric data packet loss)

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

In formula ()^TTo seek the transposition of matrix.

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

C represents output matrix in formula, ()^-1To ask inverse of a matrix computing.

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

I is the unit matrix of correspondence dimension in formula.

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

(8) then iteration stopping, output estimation result as k+1 ＞ N；Conversely, then repeating our department (2)-(7) step by step, enter The state estimation of row subsequent time.

Brief description of the drawings

Fig. 1 is the method flow diagram of the embodiment of the present invention；

Fig. 2 is state estimation result figure of the embodiment using traditional fractional order kalman filter method, and (a) is fractional order card Kalman Filtering algorithm state estimated result, (b) is fractional order Kalman filtering algorithm state estimation result；

Fig. 3 is evaluated error figure of the embodiment using traditional fractional order kalman filter method, and (a) is fractional order Kalman Filtering algorithm state estimation error, (b) is fractional order Kalman filtering algorithm state estimation error；

Fig. 4 is the state estimation result figure that embodiment uses the inventive method, and (a) is the inventive method state estimation knot Really, (b) is the inventive method state estimation result；

Fig. 5 is the state estimation Error Graph that embodiment uses the inventive method, and (a) misses for the inventive method state estimation Difference, (b) is the inventive method state estimation error.

Embodiment

With reference to specific embodiment, the present invention is furture elucidated, it should be understood that these embodiments are merely to illustrate the present invention Rather than limitation the scope of the present invention, after the present invention has been read, various equivalences of the those skilled in the art to the present invention The modification of form falls within the application appended claims limited range.

As shown in figure 1, the fractional order network system situation method of estimation based on adaptive equalization technology, including such as bottom Point：

1) the linear fractional rank network system model of meter and metric data random loss

On the premise of assuming that each phasor measurement unit each works independently, with binary system Bernoulli Jacob distribution variable side Method, is modeled to the Discrete Linear fractional order network system in the case of meter and measurement signal data random loss, and model is System EQUATION x_k+1And output equationIt can be respectively depicted as：

Δ^γx_k+1=A_dx_k+Bu_k+w_k

In formula：Δ^γFor fractional order operator, γ=[n₁,n₂…n_p]^TFor fractional order order, x_k+1Represent the state at k+1 moment Vector (dimension is p), A_dFor sytem matrix, B is control matrix, u_kFor input variable,Represent the output vector (dimension at k moment For m),Be meet Bernoulli Jacob distribution binary system scalar, its value be 0 or 1, expect be respectively with varianceC is output matrix, w_kFor the system noise value at k moment,Measured in respectively each phasor measurement unit Noise figure is surveyed, and is hadSystem noise and measurement both noises are separate unrelated, are met Average is 0, and covariance matrix is respectively Q_kAnd R_k, and γ in formula_jCalculation formula be defined as follows

N >=0 is fractional order order in formula, and j >=0 is represented not in the same time.

2) the adaptive equalization technology of metric data packet loss

Generally, the output variable tieed up for m, the covariance matrix that its measurement noise is met can be described as：

In formulaFor the constant value (and it is often assumed that for be known) at k moment, and when meter and measurement signal During random loss, the k momentValue withIn the presence of following relation

From analyzing, whenWhen packet loss occurs for metric data, σ → ∞ in formula now measures what noise was met Covariance matrix R_kIt can change, and then the meter of the influence filtering gain related to measuring noise and evaluated error covariance Calculate.

Based on this, the present invention proposes system noise and measurement noise covariance matrix Q under metric data packet loss situation_k, R_k Method for dynamic estimation, and then realize the dynamic compensation to packet loss metric data, its specific implementation step is as follows：

(2) innovation sequence is calculated, calculation formula is as follows

In formulaIt is the measuring value at k moment in the case of meter and data packetloss,It is the state estimation at k moment.

(2) when it is L to take moving window size, innovation sequence s in calculation window_kAverage value, i.e., new breath Matrix C_vk, its Calculation formula is as follows

(3) on the basis of previous step, noise covariance matrix Q is asked for_k, R_kDynamic estimation value, calculation formula is as follows

Q_k=G_kC_vkG_k ^T

G in formula_kIt is the filtering gain at k moment,It is the evaluated error covariance matrix at k moment, Ξ_kIt is defined as follows

3) on the basis of above-mentioned, then it can be believed by following Generalized fractional kalman filter method counting and measuring The linear fractional rank network state of number packet loss is estimated, comprises the following steps that

(1) the related initial value of setting filtering, such as state estimation initial valueState estimation error covarianceSystem The initial value of noise and measurement 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 computing.

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

I is the unit matrix of correspondence dimension in formula.

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

(8) then iteration stopping, output estimation result as k+1 ＞ N；Conversely, then repeating our department (2)-(7) step by step, enter The state estimation of row subsequent time.

In order to verify the validity and practicality of the inventive method, it is described below in fractional order network system research extensively One fractional order network system of application, it is specific as follows

y_k=[0.1 0.3] x_k+v_k

Formula mid-score rank order n₁=0.7, n₂=1.2, the random loss rate of phasor measurement unit metric data is 0.3, is Unite noise w_kWith measurement noise v_kThe covariance matrix met is respectively

With the inventive method to the non-linear fractional order network of embodiment carry out state estimation when, state estimation it is initial Value x₀=[0 0]^T；Greatest iteration estimates moment N=150, adaptive equalization technology moving window value L=10, Initial state estimation Error co-variance matrixWith control input variable u_kRespectively

Above-described embodiment measurement signal data occurs the linear fractional rank network system of packet loss, respectively with traditional point Number rank Kalman filtering algorithm (related parameter values needed for it are identical with the initial parameter values of the inventive method), and base of the present invention System state variables is estimated in the fractional order network system situation method of estimation of adaptive equalization technology.Using traditional Fractional order Kalman filtering algorithm state estimation result is as shown in Fig. 2 evaluated error is as shown in Figure 3；Using the bright method of this law State estimation result is as shown in figure 4, evaluated error is as shown in Figure 5.

Complex chart 2 and the test result shown in Fig. 3, it can be deduced that such as draw a conclusion：Because metric data is in transmission channel Can occur data random loss, so, traditional fractional order Kalman filtering method for estimating state can not be realized in such cases System mode accurately estimate.

Complex chart 4 and the test result shown in Fig. 5, it can be deduced that such as draw a conclusion：The present invention is based on adaptive equalization technology Fractional order network system situation method of estimation can realize the packet loss of metric data is dynamically compensated, and then complete paired systems shape The accurate tracking and estimation of state.

Claims (1)

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

(1) the related initial value of setting filtering, 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

${\tilde{x}}_{k+1}=A_d{\hat{x}}_k+{\mathrm{Bu}}_k-\underset{j=1}{\overset{k+1}{\Σ}}{(-1)}^j{\mathrm{\γ}}_j{\hat{x}}_{k+1-j}$

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；(specific steps See the adaptive equalization technology segment of metric data packet loss)

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

${\tilde{P}}_{k+1}=(A_d+{\mathrm{\γ}}_1){\hat{P}}_k{(A_d+{\mathrm{\γ}}_1)}^T+Q_k+\underset{j=2}{\overset{k+1}{\Σ}}{\mathrm{\γ}}_j{P}_{k+1-j}{\mathrm{\γ}}_j^T$

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

$G_{k+1}={\tilde{P}}_{k+1}{C}^T{(C{\tilde{P}}_{k+1}{C}^T+R_{k+1})}^{-1}$

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

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

${\hat{P}}_{k+1}=(I-G_{k+1}C){\tilde{P}}_{k+1}$

I is the unit matrix of correspondence dimension in formula.

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

${\hat{x}}_{k+1}={\tilde{x}}_{k+1}+G_{k+1}\[y_{k+1}^s-C{\tilde{x}}_{k+1}\]$

(8) then iteration stopping, output estimation result as k+1 ＞ N；Conversely, our department (2)-(7) step by step are then repeated, under progress The state estimation at one moment.