CN105760346A - Method for identifying parameters of proportional-integral controller of conventional direct-current power transmission system - Google Patents

Abstract

The invention relates to a method for identifying parameters of a proportional-integral controller of a conventional direct-current power transmission system, belonging to the technical field of power-grid simulation. The method comprises the following steps: acquiring an input signal time sequence and an output signal time sequence of the proportional-integral controller from the conventional direct-current power transmission system to construct a measurement equation; carrying out primary solving by utilizing an optimization method, using the obtained result as a new initial value, reducing an auxiliary coefficient for recalculation, repeating the step till the coefficient is less than a set value, thus obtaining a final parameter identification result. The method has the beneficial effects that under the condition of noise in the acquired input and output signals of the proportional-integral controller, the parameters of the proportional-integral controller can be still accurately identified. The method has the advantages of accurate and automatic elimination of influences of measurement errors; and the practical effect of the engineering is satisfactory.

Description

A kind of pi controller parameter identification method of customary DC transmission system

Technical field

The present invention relates to the pi controller parameter identification method of a kind of customary DC transmission system, belong to grid simulation technical field.

Background technology

Electric system simulation is one of important method of research power system characteristic.Electric system simulation comprises two key factors, phantom and model parameter.Wherein model parameter can not directly obtain sometimes, it is necessary to is calculated by indirectly means and obtains, it is simply that parameter identification.

Pi controller (PI controller) is the controller of a kind of classics, has a wide range of applications, in the control field particularly in customary DC transmission system in power system.The input signal x of pi controller and output signal y meets relationship below:

$x(K_p+\frac{K_i}{s})=y$

Wherein s is Laplace operator, K_pAnd K_iThe parameter of pi controller.The input signal x of passing ratio integral controller and output signal y, utilizes the parameter identification method can its parameter K of identification_pAnd K_i.Owing to there being a large amount of harmonic wave in customary DC transmission system, the input/output signal of acquired pi controller contains noise and error, and this just requires that parameter identification method has the ability that stronger elimination measurement error affects.The existing parameter identification method based on least square, when measured value has appreciable error, is generally not capable of accurate recognition and goes out parameter.

Summary of the invention

It is an object of the invention to contain noise and error problem for the input/output signal solving to obtain, it is proposed to the pi controller parameter identification method of a kind of customary DC transmission system, the method has the advantage automatically eliminating measurement error impact；Engineering practice good results.

The present invention proposes the pi controller parameter identification method of a kind of customary DC transmission system, it is characterised in that the method comprises the following steps:

(1) obtaining input signal time sequence x (i) and output signal time sequences y (i) of pi controller from customary DC transmission system, seasonal effect in time series interval is Δ t, i=1,2 ..., N, N is positive integer；

(2) according to the input of aforementioned proportion integral controller, the output following measurement equation of signal time sequence construct:

Ax=b,

In formula: A, B are respectively for inputting signal coefficient matrix, output signal coefficient matrix, and x is the parameter matrix of pi controller, and wherein coefficient matrices A is constituted in such a way by inputting signal time sequence x (i):

$A=\left[\begin{array}{cc}x\left(2\right)-x\left(1\right)& \frac{x\left(2\right)+x\left(1\right)}{2}\mathrm{\Δ}t\\ x\left(3\right)-x\left(2\right)& \frac{x\left(3\right)+x\left(2\right)}{2}\mathrm{\Δ}t\\ .& .\\ .& .\\ .& .\\ x\left(N\right)-x(N-1)& \frac{x\left(N\right)+x(N-1)}{2}\mathrm{\Δ}t\end{array}\right],$

Coefficient matrix B is constituted in such a way by exporting signal time sequences y (i):

$b=\left[\begin{array}{c}y\left(2\right)-y\left(1\right)\\ y\left(3\right)-y\left(2\right)\\ .\\ .\\ .\\ y\left(N\right)-y(N-1)\end{array}\right],$

X is following matrix:

X=[K_pK_i]^T,

K_pAnd K_iFor the parameter of pi controller, [*]^TThe transposition of representing matrix；

(3) taking auxiliary coefficient σ isThe initial value of x is [11]^T；

(4) carry out an optimization, specifically include:

(4-1) intermediate variable matrix W is calculated:

W is the diagonal matrix on N-1 rank, its i-th diagonal element W_iiTry to achieve in such a way:

$W_{ii}=\frac{1}{{\mathrm{\σ}}^2}\exp (-{\left(\frac{b_i-A_{i}x}{\sqrt{2}\mathrm{\σ}}\right)}^2),$

Wherein A_iAnd b_iBeing the coefficient matrices A and i-th row of b that obtain in (2nd) step, exp represents with the e index being the end, i=1,2 ..., N-1；

(4-2) extra large gloomy matrix Q is calculated:

$Q=-A^{T}W\[I-diag\left\{\frac{{(b-Ax)}^2}{{\mathrm{\σ}}^2}\right\}\]A,$

Wherein I is the unit matrix on N-1 rank, and diag{*} represents a column matrix is changed into diagonal matrix；

(4-3) the renewal amount Δ x of x is calculated:

Δ x=-Q^-1A^TW(b-Ax)；

(4-4) size according to sum (abs (Δ x)) differentiates, wherein abs (*) represents matrix all elements is taken absolute value, sum (*) represent matrix all elements taken and；

If sum (abs (Δ x)) > tol, wherein tol is that set threshold value tol is taken as 1e-6, then the value updating x is:

X=x+ Δ x,

And come back to (4-1) step and be calculated,

If sum (abs (Δ x))≤tol, then optimization this time terminates, and the value of current x is exactly this result solved；

(5) factor sigma is updated in such a way:

$\mathrm{\σ}=\mathrm{\σ}/\sqrt[5]{100},$

IfThen taking σ is the value after updating, and the value of the x (4th) step finally given is as new initial value, comes back to the beginning of (4th) step,

IfThen calculating and terminate, now the result of x is:

$x^{*}={\left[\begin{array}{cc}{K}_p^{*}& K_i^{*}\end{array}\right]}^T;$

(6) parameter identification result obtaining final pi controller isWith

The feature of the present invention and beneficial effect:

There is substantial amounts of harmonic wave in customary DC transmission system, the input/output signal of acquired pi controller contains noise and error.The existing parameter identification method based on least square, when measured value has appreciable error, is generally not capable of accurate recognition and goes out the parameter of pi controller.The present invention proposes the pi controller parameter identification method of a kind of customary DC transmission system, in the noisy situation of input/output signal of acquired pi controller, still is able to the parameter of accurate recognition pi controller.

The advantage of elimination measurement error accurate, automatic that this method has impact；Engineering practice good results.

Detailed description of the invention

The pi controller parameter identification method of the customary DC transmission system that the present invention proposes is further described below in conjunction with the embodiments:

The pi controller parameter identification method of the customary DC transmission system that the present invention proposes, comprises the following steps:

(1) from customary DC transmission system, obtain input signal time sequence x (the i) (i=1 of pi controller, 2, ..., N) and output signal time sequences y (i) (i=1,2, ..., N) N is any positive integer (being generally taken as 100-200), seasonal effect in time series interval is Δ t (being generally 50us)；

(2) according to the input of aforementioned proportion integral controller, the output following measurement equation of signal time sequence construct:

Ax=b,

In formula: A, B are respectively for inputting signal coefficient matrix, output signal coefficient matrix, and x is the parameter matrix of pi controller, and wherein coefficient matrices A is constituted in such a way by inputting signal time sequence x (i):

$A=\left[\begin{array}{cc}x\left(2\right)-x\left(1\right)& \frac{x\left(2\right)+x\left(1\right)}{2}\mathrm{\Δ}t\\ x\left(3\right)-x\left(2\right)& \frac{x\left(3\right)+x\left(2\right)}{2}\mathrm{\Δ}t\\ .& .\\ .& .\\ .& .\\ x\left(N\right)-x(N-1)& \frac{x\left(N\right)+x(N-1)}{2}\mathrm{\Δ}t\end{array}\right],$

Coefficient matrix B is constituted in such a way by exporting signal time sequences y (i):

$b=\left[\begin{array}{c}y\left(2\right)-y\left(1\right)\\ y\left(3\right)-y\left(2\right)\\ .\\ .\\ .\\ y\left(N\right)-y(N-1)\end{array}\right]$

X is following matrix:

X=[K_pK_i]^T,

K_pAnd K_iFor the intrinsic parameter of pi controller, [*]^TThe transposition of representing matrix；

(3) taking auxiliary coefficient σ isThe initial value of x is [11]^T；

(4) carry out an optimization, specifically include:

(4-1) intermediate variable matrix W is calculated:

W is the diagonal matrix on N-1 rank, its i-th diagonal element W_ii(i=1,2 ..., N-1) try to achieve in such a way:

$W_{ii}=\frac{1}{{\mathrm{\σ}}^2}\exp (-{\left(\frac{b_i-A_{i}x}{\sqrt{2}\mathrm{\σ}}\right)}^2),$

Wherein A_iAnd b_iBeing i-th row of coefficient matrices A and the b obtained in (2nd) step, exp represents with the e index being the end；

(4-2) extra large gloomy matrix Q is calculated:

$Q=-A^{T}W\[I-diag\left\{\frac{{(b-Ax)}^2}{{\mathrm{\σ}}^2}\right\}\]A,$

Wherein I is the unit matrix on N-1 rank, and diag{*} represents a column matrix is changed into diagonal matrix；

(4-3) the renewal amount Δ x of x is calculated:

Δ x=-Q^-1A^TW(b-Ax)；

(4-4) size according to sum (abs (Δ x)) differentiates, wherein abs (*) represents matrix all elements is taken absolute value, sum (*) represent matrix all elements taken and:

If sum (abs (Δ x)) > tol, wherein tol is set threshold value (being usually taken to be 1e-6), then the value updating x is:

X=x+ Δ x,

And come back to (4-1) step and be calculated；

If sum (abs (Δ x))≤tol, then optimization this time terminates, and the value of current x is exactly this result solved；

(5) auxiliary coefficient σ is updated in such a way:

$\mathrm{\σ}=\mathrm{\σ}/\sqrt[5]{100},$

IfThen taking σ is the value after updating, and the value of the x (4th) step finally given is as new initial value, comes back to the beginning of (4th) step,

IfThen calculating and terminate, now the result of x is:

$x^{*}={\left[\begin{array}{cc}{K}_p^{*}& K_i^{*}\end{array}\right]}^T;$

(6) parameter identification result obtaining final pi controller isWith

Claims (1)

1. the pi controller parameter identification method of customary DC transmission system, it is characterised in that the method comprises the following steps:

(1) obtain input signal time sequence x (i) and output signal time sequences y (i) of pi controller from actual electric network, seasonal effect in time series interval is Δ t, i=1,2 ..., N, N is positive integer；

(2) according to the input of aforementioned proportion integral controller, the output following measurement equation of signal time sequence construct:

Ax=b,

In formula: A, B are respectively for inputting signal coefficient matrix, output signal coefficient matrix, and x is the parameter matrix of pi controller, and wherein coefficient matrices A is constituted in such a way by inputting signal time sequence x (i):

$A=\left[\begin{array}{cc}x\left(2\right)-x\left(1\right)& \frac{x\left(2\right)+x\left(1\right)}{2}\mathrm{\Δ}t\\ x\left(3\right)-x\left(2\right)& \frac{x\left(3\right)+x\left(2\right)}{2}\mathrm{\Δ}t\\ .& .\\ .& .\\ .& .\\ x\left(N\right)-x(N-1)& \frac{x\left(N\right)+x(N-1)}{2}\mathrm{\Δ}t\end{array}\right],$

Coefficient matrix B is constituted in such a way by exporting signal time sequences y (i):

$b=\left[\begin{array}{c}y\left(2\right)-y\left(1\right)\\ y\left(3\right)-y\left(2\right)\\ .\\ .\\ .\\ y\left(N\right)-y(N-1)\end{array}\right],$

X is following matrix:

X=[K_pK_i]^T,

K_pAnd K_iFor the parameter of pi controller, [*]^TThe transposition of representing matrix；

(3) taking auxiliary coefficient σ isThe initial value of x is [11]^T；

(4) carry out an optimization, specifically include:

(4-1) intermediate variable matrix W is calculated:

W is the diagonal matrix on N-1 rank, its i-th diagonal element W_iiTry to achieve in such a way:

$W_{ii}=\frac{1}{{\mathrm{\σ}}^2}\exp (-{\left(\frac{b_i-A_{i}x}{\sqrt{2}\mathrm{\σ}}\right)}^2),$

Wherein A_iAnd b_iBeing the coefficient matrices A and i-th row of b that obtain in (2nd) step, exp represents with the e index being the end, i=1,2 ..., N-1；

(4-2) extra large gloomy matrix Q is calculated:

$Q=-A^{T}W\[I-diag\left\{\frac{{(b-Ax)}^2}{{\mathrm{\σ}}^2}\right\}\]A,$

Wherein I is the unit matrix on N-1 rank, and diag{*} represents a column matrix is changed into diagonal matrix；

(4-3) the renewal amount Δ x of x is calculated:

Δ x=-Q^-1A^TW(b-Ax)；

(4-4) size according to sum (abs (Δ x)) differentiates, wherein abs (*) represents matrix all elements is taken absolute value, sum (*) represent matrix all elements taken and；

If sum (abs (Δ x)) > tol, wherein tol is that set threshold value tol is taken as 1e-6, then the value updating x is:

X=x+ Δ x,

And come back to (4-1) step and be calculated,

If sum (abs (Δ x))≤tol, then optimization this time terminates, and the value of current x is exactly this result solved；

(5) factor sigma is updated in such a way:

$\mathrm{\σ}=\mathrm{\σ}/\sqrt[5]{100},$

IfThen taking σ is the value after updating, and the value of the x (4th) step finally given is as new initial value, comes back to the beginning of (4th) step,

IfThen calculating and terminate, now the result of x is:

$x^{*}={\left[\begin{array}{cc}{K}_p^{*}& K_i^{*}\end{array}\right]}^T;$

(6) parameter identification result obtaining final pi controller isWith