CN103995199A - Method for detecting interaction degree of DFACTS devices in power distribution system based on singular value decomposition method - Google Patents

Abstract

The invention provides a method for detecting the interaction degree of DFACTS devices in a power distribution system based on a singular value decomposition method, and relates to the field of detection of the interaction degree of the DFACTS devices in the power distribution system. The method solves the problem that in actual industrial production application, a method for detecting the interaction degree of the DFACTS devices in the power distribution system in real time does not exist. The method for detecting the interaction degree of the DFACTS devices in the power distribution system based on the singular value decomposition method includes the steps that according to a transfer function of a researched system, singular value decomposition is conducted on a system transfer function matrix, singular values, a left singular matrix and a right singular matrix of the system transfer function matrix are respectively acquired, and on the basis, parameters and the condition number of the interaction degree are calculated, so that the interaction degree of the DFACTS devices is acquired according to the parameters and the condition number of the interaction degree. The method is suitable for detecting the interaction degree of the DFACTS devices in the power distribution system.

Description

Reciprocal effect degree detection method between DFACTS device in distribution system based on singular value decomposition method

Technical field

The present invention relates in distribution system reciprocal effect degree detection field between DFACTS device.

Background technology

Along with coming into operation in a large number of sensitive load in distribution system, user has proposed the more requirement of Gao Gengyan to the high-quality quality of power supply especially quality of voltage.DFACTS technology claims again custom power (Custom Power) technology, is the application in distribution system of Power Electronic Technique and modern control technology, has become the powerful that improves power distribution system quality of electric power at present.As the Distribution Network Static Reactive Compensator (DSVC) of one of DFACTS technological core device can comprehensive regulation voltage fluctuation and flicker, the power quality problem such as voltage falls, three-phase imbalance, being most widely used in distribution system.Increasing along with the DSVC device coming into operation in distribution system, the reciprocal effect degree problem between a plurality of DSVC controllers will cause people's extensive concern day by day.

In recent years, existing many scholars have done large quantity research for the reciprocal effect degree between a plurality of FACTS controllers.Mainly contain nonlinear time-domain simulation method, normal form (NF) method, relative gain matrix (RGA) method, NI method, the method based on Gramian etc.Research shows, between same type and dissimilar many FACTS devices, really has reciprocal effect degree, may cause controller performance to worsen when serious, even causes system unstability.Usually, DFACTS device can be interpreted as to the scaled down version of FACTS device, its principle, structure are all identical, function is also similar, reciprocal effect degree problem between DFACTS controller should draw attention, in the paper of having published " many flat Distribution Network Static Reactive Compensator cross-impact analyses based on SVD method ", mentioned the reciprocal effect degree problem between two DFACTS controllers has been detected, yet, at present for the also rarely seen research both at home and abroad of the reciprocal effect degree problem between a plurality of DFACTS controllers.

Summary of the invention

The present invention is in order to solve in actual industrial production application, also do not have to occur in distribution system between a plurality of DFACTS devices reciprocal effect degree carry out the problem of the method that detects in real time, reciprocal effect degree detection method between DFACTS device has been proposed in the distribution system based on singular value decomposition method.

In distribution system based on singular value decomposition method, between DFACTS device, reciprocal effect degree detection method comprises the following steps:

Step 1, foundation contain the differential algebraic equations group of the controller of each DFACTS device in distribution system;

Step 2, according to the differential algebraic equations group of step 1, obtain state-space model, and this state-space model is converted to transport function form, thereby obtain the transfer function matrix G (s) of distribution system;

Step 3, the transfer function matrix G (s) obtaining in step 2 is carried out to svd, obtain singular value, left singular matrix Z (s) and the right singular matrix V (s) of transfer function matrix G (s);

Step 4, according to the singular value of transfer function matrix G (s), transfer function matrix G (s), left singular matrix Z (s) and right singular matrix V (s), obtain reciprocal effect degree parameter θ and conditional number κ between DFACTS device, and obtain reciprocal effect degree situation between each DFACTS device according to reciprocal effect degree parameter θ and conditional number κ between DFACTS device.

According to the singular value of transfer function matrix G (s), transfer function matrix G (s), left singular matrix Z (s) and right singular matrix V (s), obtain reciprocal effect degree parameter θ between DFACTS device, and according to the process that reciprocal effect degree parameter θ between DFACTS device obtains reciprocal effect degree between DFACTS device be:

Distribution system for m input m output, is decomposed into transfer function matrix G (s):

$G\left(s\right)=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{\mathrm{\σ}}_i\left(s\right)z_i\left(s\right)v_i{\left(s\right)}^T=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{\mathrm{\σ}}_i\left(s\right)W_i\left(s\right),$

P output quantity of distribution system for l gain is:

$g_{\mathrm{pl}}\left(s\right)=\frac{y_p\left(s\right)}{u_l\left(s\right)}=\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&sigma;}}_i\left(s\right)<W_i\left(s\right),E_{\mathrm{pl}}>,$

Wherein, $<W_i\left(s\right),E_{\mathrm{pl}},>\&equiv;({\left(e_p^m\right)}^T\&CenterDot;z_i\left(s\right))\&CenterDot;(v_i^T\left(s\right)\&CenterDot;\left(e_i^m\right)),$ with be unit vector,

Calculate:

θ _i＝arccos|<W _i(s),E _pl>|，

Between DFACTS device, reciprocal effect degree parameter θ is:

$\mathrm{\&theta;}=\arccos {\left[\frac{\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&sigma;}}_i^2{\cos }^2{\mathrm{\&theta;}}_i}{\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&sigma;}}_i^2}\right]}^{1/2},$

When θ=0, cos θ=1 o'clock, does not have reciprocal effect degree between expression DFACTS device, when be cos θ=0 o'clock, represent vectorial quadrature, now between DFACTS device, reciprocal effect degree is maximum.

According to the singular value of transfer function matrix G (s), transfer function matrix G (s), left singular matrix Z (s) and right singular matrix V (s), obtain conditional number κ, and according to the process of reciprocal effect degree situation between conditional number κ acquisition DFACTS device be:

According to κ=σ ₁/ σ _mobtain the value of conditional number κ, wherein, σ ₁for the maximum singular value of transfer function matrix G (s), σ _mminimum singular value for transfer function matrix G (s);

According to the value of conditional number κ, can obtain reciprocal effect degree situation between DFACTS device, the value of conditional number κ is larger, and between DFACTS device, reciprocal effect degree is larger, and the value of conditional number κ is less, and between DFACTS device, reciprocal effect degree is less.

Beneficial effect: in the distribution system based on singular value decomposition method that the present invention proposes, between DFACTS device, reciprocal effect degree detection method is according to the transport function of institute's Study system, ssystem transfer function matrix is carried out to svd, ask for respectively its singular value and left and right singular matrix, and calculate on this basis reciprocal effect degree parameter and conditional number, thereby according to the situation of reciprocal effect degree between reciprocal effect degree parameter and conditional number acquisition DFACTS device, make can understand in time the situation of reciprocal effect degree between DFACTS device in actual industrial production application, and the reciprocal effect degree that the method goes between a plurality of DFACTS devices detects.

Accompanying drawing explanation

Fig. 1 is the infinitely great distribution system of single induction motor load that contains two DSVC;

Fig. 2 is for carrying out the oscillogram of time-domain-simulation to the infinitely great distribution system of single induction motor load of the independent design of two DSVC;

Fig. 3 is not for to consider in the situation of circuit equivalent resistance, when electrical distance is far away, and the control design sketch of two DSVC when the infinitely great distribution system of the single induction motor load that contains two DSVC is carried out to time-domain-simulation;

Fig. 4 is not for to consider in the situation of circuit equivalent resistance, when electrical distance is nearer, and the control design sketch of two DSVC when the infinitely great distribution system of the single induction motor load that contains two DSVC is carried out to time-domain-simulation.

Embodiment

In the distribution system based on singular value decomposition method described in embodiment one, this embodiment, between DFACTS device, reciprocal effect degree detection method comprises the following steps:

Step 1, foundation contain the differential algebraic equations group of the controller of each DFACTS device in distribution system;

Step 2, according to the differential algebraic equations group of step 1, obtain state-space model, and this state-space model is converted to transport function form, thereby obtain the transfer function matrix G (s) of distribution system;

Step 3, the transfer function matrix G (s) obtaining in step 2 is carried out to svd, obtain singular value, left singular matrix Z (s) and the right singular matrix V (s) of transfer function matrix G (s);

Step 4, according to the singular value of transfer function matrix G (s), transfer function matrix G (s), left singular matrix Z (s) and right singular matrix V (s), obtain reciprocal effect degree parameter θ and conditional number κ between DFACTS device, and obtain reciprocal effect degree situation between each DFACTS device according to reciprocal effect degree parameter θ and conditional number κ between DFACTS device.

In present embodiment, in step 3, transfer function matrix G (s) is carried out to svd and be defined as there is unitary matrix Z ∈ C ^{m * n}with V ∈ C ^{m * n}, make $A=Z\left(\begin{array}{cc}\mathrm{\&Gamma;}& 0\\ 0& 0\end{array}\right)V^T,$ The singular value that wherein Γ is matrix A.

In the distribution system based on singular value decomposition method described in embodiment two, this embodiment and embodiment one, between DFACTS device, the difference of reciprocal effect degree detection method is, the state-space model obtaining according to differential algebraic equations group in step 2 is: $\left\{\begin{array}{c}\mathrm{\&Delta;}\stackrel{.}{x}=\mathrm{A\&Delta;x}+\mathrm{B\&Delta;u}\\ \mathrm{\&Delta;y}=\mathrm{C\&Delta;v}+\mathrm{D\&Delta;u}\end{array}\right.,$ Wherein, A, B, C, D are matrix of coefficients, expression is carried out differentiate to △ x, and △ x is state variable, and △ y is output variable, and △ u is input variable.

In the distribution system based on singular value decomposition method described in embodiment three, this embodiment and embodiment one or two, between DFACTS device, the difference of reciprocal effect degree detection method is, the transfer function matrix G (s) of the distribution system obtaining in step 2 is: G (s)=C (sI-A) ^-1b+D, wherein, I is unit matrix.

In the distribution system based on singular value decomposition method described in embodiment four, this embodiment and embodiment one or two, between DFACTS device, the difference of reciprocal effect degree detection method is, the result of in step 3, transfer function matrix G (s) being carried out to svd is G (s)=Z (s) Λ (s) V (s) ^t, wherein, Λ (s)=diag (σ ₁(s), σ ₂(s) ..., σ _r(s), 0 ..., 0).

In the distribution system based on singular value decomposition method described in embodiment five, this embodiment and embodiment one, between DFACTS device, the difference of reciprocal effect degree detection method is, singular value Γ=diag (σ of transfer function matrix G (s) ₁, σ ₂..., σ _r), left singular matrix Z (s)=(z ₁, z ₂..., z _r... z _m), right singular matrix V (s)=(v ₁, v ₂..., v _r... v _n), wherein, m>=r, n>=r, and m, n and r are positive integer.

In the distribution system based on singular value decomposition method described in embodiment six, this embodiment and embodiment one, between DFACTS device, the difference of reciprocal effect degree detection method is, in step 4, according to the singular value of transfer function matrix G (s), transfer function matrix G (s), left singular matrix Z (s) and right singular matrix V (s), obtain reciprocal effect degree parameter θ between DFACTS device, and according to the process that reciprocal effect degree parameter θ between DFACTS device obtains reciprocal effect degree between DFACTS device be:

Distribution system for m input m output, is decomposed into transfer function matrix G (s):

$G\left(s\right)=\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&sigma;}}_i\left(s\right)z_i\left(s\right)v_i{\left(s\right)}^T=\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&sigma;}}_i\left(s\right)W_i\left(s\right),$

P output quantity of distribution system for l gain is:

$g_{\mathrm{pl}}\left(s\right)=\frac{y_p\left(s\right)}{u_l\left(s\right)}=\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&sigma;}}_i\left(s\right)<W_i\left(s\right),E_{\mathrm{pl}}>,$

Wherein, $<W_i\left(s\right),E_{\mathrm{pl}},>\&equiv;({\left(e_p^m\right)}^T\&CenterDot;z_i\left(s\right))\&CenterDot;(v_i^T\left(s\right)\&CenterDot;\left(e_i^m\right)),$ with be unit vector,

Calculate:

θ _i＝arccos|<W _i(s),E _pl>|，

Between DFACTS device, reciprocal effect degree parameter θ is:

$\mathrm{\&theta;}=\arccos {\left[\frac{\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&sigma;}}_i^2{\cos }^2{\mathrm{\&theta;}}_i}{\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&sigma;}}_i^2}\right]}^{1/2},$

When θ=0, cos θ=1 o'clock, does not have reciprocal effect degree between expression DFACTS device, when be cos θ=0 o'clock, represent vectorial quadrature, now between DFACTS device, reciprocal effect degree is maximum.

In the distribution system based on singular value decomposition method described in embodiment seven, this embodiment and embodiment one, between DFACTS device, the difference of reciprocal effect degree detection method is, according to the singular value of transfer function matrix G (s), transfer function matrix G (s), left singular matrix Z (s) and right singular matrix V (s), obtain conditional number κ, and according to the process of reciprocal effect degree situation between conditional number κ acquisition DFACTS device be:

According to κ=σ ₁/ σ _mobtain the value of conditional number κ, wherein, σ ₁for the maximum singular value of transfer function matrix G (s), σ _mminimum singular value for transfer function matrix G (s);

According to the value of conditional number κ, can obtain reciprocal effect degree situation between DFACTS device, the value of conditional number κ is larger, and between DFACTS device, reciprocal effect degree is larger, and the value of conditional number κ is less, and between DFACTS device, reciprocal effect degree is less.

Figure 1 shows that the infinitely great distribution system of the single induction motor load that contains two DSVC, in system, DSVC1 is arranged on node M place, and DSVC2 is arranged on node N place, is respectively used to maintain the busbar voltage of installation place, and systematic parameter perunit value is X ₁=X ₂=0.3, X ₃=0.2, V _e=1.0, motor parameter perunit value is as shown in the table:

, in table: R _sfor the resistance of stator winding, R _rfor the resistance of rotor winding, X _sfor the leakage reactance of stator winding, X _rfor the leakage reactance of rotor winding, T _ifor rotor inertia time constant, X _mfor excitation reactance, a is the constant moment of force of induction motor mechanical force moment, the load mechanical property index that ρ is motor, S ₀for rotor slippage; For the reciprocal effect degree of different electrical distances between two DSVC, guaranteeing systematic parameter and circuit resulting impedance X _Σin constant situation, change the electrical distance X between two DSVC, when X is got to 0.1-0.5, calculate respectively the value of reciprocal effect degree parameter θ and conditional number κ between DFACTS device, as shown in the table:

According to the data shown in upper table, when electrical distance between two DSVC is larger, between the DFACTS device of calculating gained, the value of reciprocal effect degree parameter θ and conditional number κ is less, represent that the reciprocal effect degree between two DSVC is less, along with reducing of electrical distance, between the DFACTS device of calculating gained, the value of reciprocal effect degree parameter θ and conditional number κ is larger, represents that the reciprocal effect degree between two DSVC strengthens gradually, that is, the electrical distance between controller affects the degree of reciprocal effect degree.

In order to verify the validity of reciprocal effect degree detection method between DFACTS device proposed by the invention, the distribution system shown in Fig. 1 is carried out to time-domain-simulation, for following two kinds of situations, respectively this distribution system is carried out to emulation:

Situation 1, two DSVC design separately, when t=0.5s, by the reference voltage V of DSVC _refby 1.0pu and 1.01pu, increase to respectively 1.03pu and 1.04pu, make voltage generation step, simulation result as shown in Figure 2.

Situation 2, do not consider in the situation of circuit equivalent resistance, guarantee other parameter constants of distribution system, while getting between two DSVC different electrical distance, the simulation process that the situation of carrying out 1 is identical, obtain the control design sketch of two DSVC, as shown in Figure 3 and Figure 4, and corresponding peak to peak value is calculated, result is as shown in the table:

In sum, there is the problem of reciprocal effect degree in two DSVC really, and when between two DSVC, electrical distance is larger, between controller, a little less than coupling, node voltage fluctuation is less, reaches very soon stationary value, can follow preferably reference voltage and complete step, reciprocal effect degree is less; Along with reducing of electrical distance, voltage fluctuation Shaoxing opera is strong, illustrates that coupling strengthens, and between controller, reciprocal effect degree is also stronger, simulation result is consistent with result of calculation, has verified the validity of reciprocal effect degree detection method between DFACTS device proposed by the invention.

Claims (7)

1. reciprocal effect degree detection method between DFACTS device in the distribution system based on singular value decomposition method, is characterized in that, it comprises the following steps:

Step 1, foundation contain the differential algebraic equations group of the controller of each DFACTS device in distribution system;

Step 2, according to the differential algebraic equations group of step 1, obtain state-space model, and this state-space model is converted to transport function form, thereby obtain the transfer function matrix G (s) of distribution system;

Step 3, the transfer function matrix G (s) obtaining in step 2 is carried out to svd, obtain singular value, left singular matrix Z (s) and the right singular matrix V (s) of transfer function matrix G (s);

Step 4, according to the singular value of transfer function matrix G (s), transfer function matrix G (s), left singular matrix Z (s) and right singular matrix V (s), obtain reciprocal effect degree parameter θ and conditional number κ between DFACTS device, and obtain reciprocal effect degree testing result between each DFACTS device according to reciprocal effect degree parameter θ and conditional number κ between DFACTS device.

2. reciprocal effect degree detection method between DFACTS device in the distribution system based on singular value decomposition method according to claim 1, is characterized in that, the state-space model obtaining according to differential algebraic equations group in step 2 is: wherein, A, B, C, D are matrix of coefficients, expression is carried out differentiate to △ x, and △ x is state variable, and △ y is output variable, and △ u is input variable.

3. reciprocal effect degree detection method between DFACTS device in the distribution system based on singular value decomposition method according to claim 1 and 2, it is characterized in that, the transfer function matrix G (s) of the distribution system obtaining in step 2 is: G (s)=C (sI-A) ^-1b+D, wherein, I is unit matrix.

4. reciprocal effect degree detection method between DFACTS device in the distribution system based on singular value decomposition method according to claim 1 and 2, it is characterized in that, the result of in step 3, transfer function matrix G (s) being carried out to svd is G (s)=Z (s) Λ (s) V (s) ^t, wherein, Λ (s)=diag (σ ₁(s), σ ₂(s) ..., σ _r(s), 0 ..., 0).

5. reciprocal effect degree detection method between DFACTS device in the distribution system based on singular value decomposition method according to claim 1, is characterized in that, the singular value of transfer function matrix G (s) is diag (σ ₁, σ ₂..., σ _r), left singular matrix Z (s)=(z ₁, z ₂..., z _r... z _m), right singular matrix V (s)=(v ₁, v ₂..., v _r... v _n), wherein, m>=r, n>=r, and m, n and r are positive integer.

6. reciprocal effect degree detection method between DFACTS device in the distribution system based on singular value decomposition method according to claim 1, it is characterized in that, in step 4, according to the singular value of transfer function matrix G (s), transfer function matrix G (s), left singular matrix Z (s) and right singular matrix V (s), obtain reciprocal effect degree parameter θ between DFACTS device, and according to the process that reciprocal effect degree parameter θ between DFACTS device obtains reciprocal effect degree between DFACTS device be:

Distribution system for m input m output, is decomposed into transfer function matrix G (s):

$G\left(s\right)=\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&sigma;}}_i\left(s\right)z_i\left(s\right)v_i{\left(s\right)}^T=\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&sigma;}}_i\left(s\right)W_i\left(s\right),$

P output quantity of distribution system for l gain is:

$g_{\mathrm{pl}}\left(s\right)=\frac{y_p\left(s\right)}{u_l\left(s\right)}=\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&sigma;}}_i\left(s\right)<W_i\left(s\right),E_{\mathrm{pl}}>,$

Wherein, $<W_i\left(s\right),E_{\mathrm{pl}},>\&equiv;({\left(e_p^m\right)}^T\&CenterDot;z_i\left(s\right))\&CenterDot;(v_i^T\left(s\right)\&CenterDot;\left(e_i^m\right)),$ with be unit vector,

Calculate:

θ _i＝arccos|<W _i(s),E _pl>|，

Between DFACTS device, reciprocal effect degree parameter θ is:

$\mathrm{\&theta;}=\arccos {\left[\frac{\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&sigma;}}_i^2{\cos }^2{\mathrm{\&theta;}}_i}{\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&sigma;}}_i^2}\right]}^{1/2},$

When θ=0, cos θ=1 o'clock, does not have reciprocal effect degree between expression DFACTS device, when be cos θ=0 o'clock, represent vectorial quadrature, now between DFACTS device, reciprocal effect degree is maximum.

7. reciprocal effect degree detection method between DFACTS device in the distribution system based on singular value decomposition method according to claim 1, it is characterized in that, according to the singular value of transfer function matrix G (s), transfer function matrix G (s), left singular matrix Z (s) and right singular matrix V (s), obtain conditional number κ, and according to the process of reciprocal effect degree situation between conditional number κ acquisition DFACTS device be:

According to κ=σ ₁/ σ _mobtain the value of conditional number κ, wherein, σ ₁for the maximum singular value of transfer function matrix G (s), σ _mminimum singular value for transfer function matrix G (s);

According to the value of conditional number κ, can obtain reciprocal effect degree situation between DFACTS device, the value of conditional number κ is larger, and between DFACTS device, reciprocal effect degree is larger, and the value of conditional number κ is less, and between DFACTS device, reciprocal effect degree is less.