CN103995199A - Method for detecting interaction degree of DFACTS devices in power distribution system based on singular value decomposition method - Google Patents
Method for detecting interaction degree of DFACTS devices in power distribution system based on singular value decomposition method Download PDFInfo
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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
Technical Field
The invention relates to the field of detection of interaction influence degree between DFACTS devices in a power distribution system.
Background
With the large investment of sensitive loads in power distribution systems, users have put higher and tighter demands on high quality power quality, especially voltage quality. The DFACTS technology is also called customer Power (Custom Power) technology, is an application of Power electronic technology and modern control technology in a Power distribution system, and has become a powerful tool for improving the Power quality of the Power distribution system at present. A static var compensator (DSVC) of a power distribution network, which is one of core devices of the DFACTS technology, can comprehensively solve the problems of voltage fluctuation, flicker, voltage drop, three-phase imbalance and other electric energy quality, and is most widely applied to a power distribution system. With the increasing number of DSVC devices put into use in power distribution systems, the problem of the interaction influence degree among a plurality of DSVC controllers will attract more and more attention.
In recent years, a lot of studies have been made by many scholars on the influence of interaction among a plurality of FACTS controllers. Mainly, there are a nonlinear time domain simulation method, a canonical form (NF) method, a relative gain matrix (RGA) method, an NI method, a Gramian-based method, and the like. Studies have shown that there is a certain degree of interaction between multiple FACTS devices of the same type and different types, which may lead to degraded controller performance and even system instability when severe. Generally, the DFACTS device can be understood as a reduced version of a FACTS device, the principle and the structure of the device are the same, the function of the device is similar, the problem of the interaction influence degree between DFACTS controllers is emphasized, the published paper, "interaction influence analysis of multiple flat distribution network static var compensators based on the SVD method" refers to detection of the interaction influence degree between two DFACTS controllers, however, the problem of the interaction influence degree between multiple DFACTS controllers is rarely studied at home and abroad at present.
Disclosure of Invention
The invention provides a method for detecting interaction influence degrees among DFACTS devices in a power distribution system based on a singular value decomposition method, which aims to solve the problem that no method for detecting interaction influence degrees among a plurality of DFACTS devices in the power distribution system in real time exists in practical industrial production application.
The method for detecting the interaction influence degree between DFACTS devices in the power distribution system based on the singular value decomposition method comprises the following steps:
step one, establishing a differential algebraic equation set of a controller containing each DFACTS device in a power distribution system;
step two, obtaining a state space model according to the differential algebraic equation set in the step one, and converting the state space model into a transfer function form, thereby obtaining a transfer function matrix G(s) of the power distribution system;
performing singular value decomposition on the transfer function matrix G(s) obtained in the step two to obtain singular values of the transfer function matrix G(s), a left singular matrix Z(s) and a right singular matrix V(s);
and step four, obtaining the interaction influence degree parameter theta and the condition number kappa between the DFACTS devices according to the singular values of the transfer function matrix G(s), the left singular matrix Z(s) and the right singular matrix V(s), and obtaining the interaction influence degree condition between the DFACTS devices according to the interaction influence degree parameter theta and the condition number kappa between the DFACTS devices.
Obtaining a parameter theta of the interactive influence degree among the DFACTS devices according to the transfer function matrix G(s), the singular values of the transfer function matrix G(s), the left singular matrix Z(s) and the right singular matrix V(s), and obtaining the interactive influence degree among the DFACTS devices according to the parameter theta of the interactive influence degree among the DFACTS devices:
for an m-input m-output power distribution system, the transfer function matrix g(s) is decomposed into:
the p output of the power distribution system for the l gain is:
wherein, <math>
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and (3) calculating:
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then the interaction influence degree parameter θ between the DFACTS devices is:
when theta is 0, namely cos theta is 1, the DFACTS device shows no interactive influence degree, and when theta is 0, cos theta is 1That is, when cos θ is 0, the vectors are orthogonal, and the interaction influence degree between DFACTS devices is the largest.
Obtaining a condition number kappa according to singular values of a transfer function matrix G(s), a left singular matrix Z(s) and a right singular matrix V(s), and obtaining the interactive influence degree condition between DFACTS devices according to the condition number kappa, wherein the process comprises the following steps:
according to κ ═ σ1/σmObtaining a value of a condition number k, where σ1Is the maximum singular value, σ, of the transfer function matrix G(s)mIs the minimum singular value of the transfer function matrix g(s);
the interaction influence degree condition between the DFACTS devices can be obtained according to the value of the condition number kappa, namely the interaction influence degree between the DFACTS devices is larger when the value of the condition number kappa is larger, and the interaction influence degree between the DFACTS devices is smaller when the value of the condition number kappa is smaller.
Has the advantages that: the method for detecting the interaction influence degree among the DFACTS devices in the power distribution system based on the singular value decomposition method is characterized in that the singular value decomposition is carried out on a system transfer function matrix according to a transfer function of a researched system, the singular value and the left and right singular matrixes are respectively obtained, and the interaction influence degree parameter and the condition number are calculated on the basis, so that the interaction influence degree among the DFACTS devices is obtained according to the interaction influence degree parameter and the condition number, the interaction influence degree among the DFACTS devices can be known in time in the practical industrial production application, and the method can be suitable for detecting the interaction influence degree among a plurality of DFACTS devices.
Drawings
FIG. 1 is a single induction motor load infinite power distribution system having two DSVCs;
FIG. 2 is a waveform diagram of a time domain simulation of a single induction motor load infinite power distribution system with two DSVCs individually designed;
FIG. 3 is a diagram showing the control effect of two DSVCs when performing time domain simulation on a single-induction-motor load infinite power distribution system having two DSVCs when the electrical distance is long, without considering the line equivalent resistance;
fig. 4 is a diagram showing the control effect of two DSVCs when a single induction motor load infinite power distribution system including the two DSVCs is subjected to time domain simulation when the electrical distance is short without considering the line equivalent resistance.
Detailed Description
In a first specific embodiment, a method for detecting an interaction influence degree between DFACTS devices in a power distribution system based on a singular value decomposition method according to the first specific embodiment includes the following steps:
step one, establishing a differential algebraic equation set of a controller containing each DFACTS device in a power distribution system;
step two, obtaining a state space model according to the differential algebraic equation set in the step one, and converting the state space model into a transfer function form, thereby obtaining a transfer function matrix G(s) of the power distribution system;
performing singular value decomposition on the transfer function matrix G(s) obtained in the step two to obtain singular values of the transfer function matrix G(s), a left singular matrix Z(s) and a right singular matrix V(s);
and step four, obtaining the interaction influence degree parameter theta and the condition number kappa between the DFACTS devices according to the singular values of the transfer function matrix G(s), the left singular matrix Z(s) and the right singular matrix V(s), and obtaining the interaction influence degree condition between the DFACTS devices according to the interaction influence degree parameter theta and the condition number kappa between the DFACTS devices.
In this embodiment, the singular value decomposition of the transfer function matrix G(s) in step three is defined asThe existence of a unitary matrix Z ∈ Cm×nAnd V ∈ Cm×nSo that <math>
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The difference between the second embodiment, the present embodiment and the first embodiment of the method for detecting the interaction influence degree between DFACTS devices in the power distribution system based on the singular value decomposition method is that the state space model obtained according to the differential algebraic equation system in the second step is: <math>
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In a third embodiment, the difference between this embodiment and the method for detecting the interaction influence degree between DFACTS devices in the power distribution system based on the singular value decomposition method in the first or second embodiment is that the transfer function matrix g(s) of the power distribution system obtained in the second step is: g(s) ═ C (sI-a)-1B + D, wherein I is an identity matrix.
A fourth specific embodiment, which is different from the first or second specific embodiment in the method for detecting the interaction influence degree between DFACTS devices in the power distribution system based on the singular value decomposition method, is that in the third step, the result of performing the singular value decomposition on the transfer function matrix g(s) is g(s) ═ z(s) Λ(s) v(s)TWherein Λ(s) ═ diag (σ)1(s),σ2(s),...,σr(s),0,...,0)。
A fifth embodiment is different from the method for detecting the interaction influence degree between DFACTS devices in the power distribution system based on the singular value decomposition method described in the first embodiment in that the singular value Γ ═ diag (σ) of the transfer function matrix g(s)1,σ2,...,σr) Left singular matrix z(s) ═ z1,z2,...,zr,...zm) Right singular matrix v(s) ═ v (v)1,v2,...,vr,...vn) Wherein m is more than or equal to r, n is more than or equal to r, and m, n and r are positive integers.
A sixth specific embodiment, a difference between the present specific embodiment and the first specific embodiment of the method for detecting the interaction influence degree between DFACTS devices in the power distribution system based on the singular value decomposition method is that, in the fourth step, the process of obtaining the interaction influence degree parameter θ between the DFACTS devices according to the transfer function matrix g(s), the singular value of the transfer function matrix g(s), the left singular matrix z(s), and the right singular matrix v(s) and obtaining the interaction influence degree parameter θ between the DFACTS devices according to the interaction influence degree parameter θ between the DFACTS devices is as follows:
for an m-input m-output power distribution system, the transfer function matrix g(s) is decomposed into:
the p output of the power distribution system for the l gain is:
wherein, <math>
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and (3) calculating:
θi＝arccos|<Wi(s),Epl>|，
then the interaction influence degree parameter θ between the DFACTS devices is:
when theta is 0, namely cos theta is 1, the DFACTS device shows no interactive influence degree, and when theta is 0, cos theta is 1That is, when cos θ is 0, the vectors are orthogonal, and the interaction influence degree between DFACTS devices is the largest.
A seventh specific embodiment, the difference between the present specific embodiment and the first specific embodiment of the method for detecting the interaction influence degree between DFACTS devices in the power distribution system based on the singular value decomposition method, is that the process of obtaining the condition number κ according to the transfer function matrix g(s), the singular value of the transfer function matrix g(s), the left singular matrix z(s), and the right singular matrix v(s), and obtaining the interaction influence degree between the DFACTS devices according to the condition number κ, includes:
according to κ ═ σ1/σmObtaining a value of a condition number k, where σ1Is the maximum singular value, σ, of the transfer function matrix G(s)mIs the minimum singular value of the transfer function matrix g(s);
the interaction influence degree condition between the DFACTS devices can be obtained according to the value of the condition number kappa, namely the interaction influence degree between the DFACTS devices is larger when the value of the condition number kappa is larger, and the interaction influence degree between the DFACTS devices is smaller when the value of the condition number kappa is smaller.
FIG. 1 shows a single induction motor negative having two DSVCsIn the load-infinity power distribution system, DSVC1 is installed at a node M, DSVC2 is installed at a node N and is respectively used for maintaining the bus voltage at the installation position, and the per unit value of a system parameter is X1＝X2＝0.3，X3＝0.2，Ve1.0, the per unit values of the motor parameters are shown in the following table:
in the table: rsIs the resistance of the stator winding, RrIs the resistance of the rotor winding, XsIs leakage reactance of stator winding, XrFor leakage reactance of rotor winding, TiIs the rotor inertia time constant, XmFor the excitation reactance, a is the constant moment of the mechanical moment of the induction motor, ρ is the load mechanical characteristic index of the motor, S0Is the rotor slip; the interaction influence degree aiming at different electrical distances between two DSVCs, namely, the system parameters and the total line impedance X are ensuredΣUnder the condition of no change, the electrical distance X between two DSVCs is changed, and the values of the interaction degree parameter theta and the condition number kappa between the DFACTS devices are respectively calculated when the value of X is 0.1-0.5, as shown in the following table:
according to the data shown in the table, when the electrical distance between the two DSVCs is large, the smaller the values of the calculated interaction influence parameter θ and the condition number κ between the two DSVCs devices are, the smaller the interaction influence between the two DSVCs is, and as the electrical distance decreases, the larger the values of the calculated interaction influence parameter θ and the condition number κ between the DFACTS devices are, the larger the interaction influence between the two DSVCs is, that is, the degree to which the electrical distance between the controllers affects the interaction influence is.
In order to verify the effectiveness of the method for detecting the interaction influence degree between DFACTS devices, the time domain simulation is performed on the power distribution system shown in fig. 1, and the power distribution system is simulated respectively according to the following two conditions:
case 1, two DSVCs are designed independently, and when t is 0.5s, the reference voltage V of the DSVC is setrefThe voltages are stepped from 1.0pu and 1.01pu to 1.03pu and 1.04pu, respectively, and the simulation result is shown in fig. 2.
Case 2, without considering the equivalent resistance of the line, ensuring that other parameters of the power distribution system are unchanged, and when different electrical distances between two DSVCs are taken, performing the same simulation process as in case 1 to obtain control effect graphs of the two DSVCs, as shown in fig. 3 and 4, and calculating corresponding maximum voltage fluctuation values, the results are shown in the following table:
in conclusion, the two DSVCs really have the problem of interaction influence degree, when the electrical distance between the two DSVCs is large, the coupling between the controllers is weak, the node voltage fluctuation is small, the node voltage quickly reaches a stable value, the step can be completed well along with the reference voltage, and the interaction influence degree is small; along with the reduction of the electrical distance, the more violent the voltage fluctuation is, the stronger the coupling effect is, the stronger the interaction influence degree between the controllers is, the simulation result is consistent with the calculation result, and the effectiveness of the method for detecting the interaction influence degree between the DFACTS devices provided by the invention is verified.
Claims (7)
1. The method for detecting the interaction influence degree between DFACTS devices in the power distribution system based on the singular value decomposition method is characterized by comprising the following steps:
step one, establishing a differential algebraic equation set of a controller containing each DFACTS device in a power distribution system;
step two, obtaining a state space model according to the differential algebraic equation set in the step one, and converting the state space model into a transfer function form, thereby obtaining a transfer function matrix G(s) of the power distribution system;
performing singular value decomposition on the transfer function matrix G(s) obtained in the step two to obtain singular values of the transfer function matrix G(s), a left singular matrix Z(s) and a right singular matrix V(s);
and step four, obtaining an interaction influence parameter theta and a condition number kappa between the DFACTS devices according to singular values of the transfer function matrix G(s), the left singular matrix Z(s) and the right singular matrix V(s), and obtaining an interaction influence detection result between each DFACTS device according to the interaction influence parameter theta and the condition number kappa between the DFACTS devices.
2. The method for detecting the interaction influence degree between DFACTS devices in the power distribution system based on the singular value decomposition method as claimed in claim 1, wherein the state space model obtained according to the differential algebraic equation system in the step two is:wherein A, B, C, D is a matrix of coefficients,the expression is derived for Δ x, which is the state variable, Δ y is the output variable, and Δ u is the input variable.
3. The method for detecting the interaction influence degree between DFACTS devices in the power distribution system based on the singular value decomposition method according to claim 1 or 2, wherein the transfer function matrix G(s) of the power distribution system obtained in the second step is: g(s) ═ C (sI-a)-1B + D, wherein I is an identity matrix.
4. The method for detecting interaction influence degree between DFACTS devices in power distribution system based on singular value decomposition method as claimed in claim 1 or 2, wherein the result of singular value decomposition of transfer function matrix G(s) in step three is G(s) -Z(s) Λ(s) V(s)TWherein Λ(s) ═ diag (σ)1(s),σ2(s),...,σr(s),0,...,0)。
5. The method of claim 1, wherein the singular value of the transfer function matrix g(s) is diag (σ), and the method of detecting the interaction between DFACTS devices in the power distribution system is based on the singular value decomposition method1,σ2,...,σr) Left singular matrix z(s) ═ z1,z2,...,zr,...zm) Right singular matrix v(s) ═ v (v)1,v2,...,vr,...vn) Wherein m is more than or equal to r, n is more than or equal to r, and m, n and r are positive integers.
6. The method for detecting the interaction influence degree between the DFACTS devices in the power distribution system based on the singular value decomposition method according to claim 1, wherein the step four includes obtaining the interaction influence degree parameter θ between the DFACTS devices according to the singular value of the transfer function matrix g(s), the left singular matrix z(s), and the right singular matrix v(s), and the step of obtaining the interaction influence degree between the DFACTS devices according to the interaction influence degree parameter θ between the DFACTS devices includes:
for an m-input m-output power distribution system, the transfer function matrix g(s) is decomposed into:
the p output of the power distribution system for the l gain is:
wherein, <math>
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and (3) calculating:
θi＝arccos|<Wi(s),Epl>|，
then the interaction influence degree parameter θ between the DFACTS devices is:
when theta is 0, namely cos theta is 1, the DFACTS device shows no interactive influence degree, and when theta is 0, cos theta is 1That is, when cos θ is 0, the vectors are orthogonal, and the interaction influence degree between DFACTS devices is the largest.
7. The method for detecting the interaction influence degree between DFACTS devices in the power distribution system based on the singular value decomposition method as claimed in claim 1, wherein the process for obtaining the condition number κ according to the transfer function matrix g(s), the singular values of the transfer function matrix g(s), the left singular matrix z(s), and the right singular matrix v(s), and obtaining the interaction influence degree between the DFACTS devices according to the condition number κ comprises:
according to κ ═ σ1/σmObtaining a value of a condition number k, where σ1Is the maximum singular value, σ, of the transfer function matrix G(s)mIs the minimum singular value of the transfer function matrix g(s);
the interaction influence degree condition between the DFACTS devices can be obtained according to the value of the condition number kappa, namely the interaction influence degree between the DFACTS devices is larger when the value of the condition number kappa is larger, and the interaction influence degree between the DFACTS devices is smaller when the value of the condition number kappa is smaller.
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| CN201410218832.0A Pending CN103995199A (en) | 2014-05-22 | 2014-05-22 | Method for detecting interaction degree of DFACTS devices in power distribution system based on singular value decomposition method |
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| CN109390966A (en) * | 2018-12-25 | 2019-02-26 | 四川大学 | A kind of more direct current control method for coordinating based on singular value decomposition |
| CN109635456A (en) * | 2018-12-17 | 2019-04-16 | 广西电网有限责任公司电力科学研究院 | A kind of harmonic resonance analysis method based on H ∞theory |
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| CN109635456A (en) * | 2018-12-17 | 2019-04-16 | 广西电网有限责任公司电力科学研究院 | A kind of harmonic resonance analysis method based on H ∞theory |
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