Method for suppressing subsynchronous oscillation of new energy through direct current delivery system

Abstract

The invention discloses a method for suppressing subsynchronous oscillation of new energy through a direct current delivery system, which comprises the following steps of: establishing a linearization state space model of the system, and introducing a state feedback gain array on the basis of an original system matrix; after a subsynchronous oscillation mode of the system is obtained by carrying out characteristic value analysis on the system, selecting a dominant factor as system input to change the controllability of the system; a Lyapunov second method is adopted to judge the stability of the uncontrollable part, after the uncontrollable part is judged to be asymptotically stable, a target characteristic value is moved to the left side of a complex plane through a state feedback loop, and a state feedback gain matrix is obtained through calculation; and designing an additional damping controller to obtain a new feedback gain matrix, and realizing subsynchronous oscillation suppression of the new energy through the direct current delivery system. Based on state feedback, the method can change the specific characteristic value of the system, realizes random movement of the characteristic value of the closed-loop system on a complex plane, and is beneficial to improving the stable operation level of the system.

Description

Technical Field

[0001] The present invention relates to the technical field of new energy systems, and in particular to a method for suppressing subsynchronous oscillation of a new energy system via direct current transmission. Background Art

[0002] In recent years, building a new power system has become the development goal of the power industry. my country's wind power, photovoltaic and other new energy sources have developed rapidly, and the grid-connected capacity has continued to grow rapidly, gradually entering a large-scale development stage. my country's western region is rich in wind power, photovoltaic and hydropower resources, and there is an objective demand for large-capacity, long-distance transmission systems to be sent to the central and eastern load centers. The line-commutated-converter based high voltage direct current (LCC-HVDC) has the advantages of mature technology and large capacity, and to a certain extent, it has solved the problem of the reverse distribution of power energy and load centers in the region.

[0003] With the rapid development of new energy and DC transmission projects, a large number of power electronic equipment are connected to the grid, the system is highly power-electronic, and the dynamic stability problem is becoming more and more complex. The new type of subsynchronous oscillation problem caused by this is also becoming more and more complex and prominent. Since new energy units are essentially different from traditional thermal power units in terms of composition structure, control strategy and grid connection mode, their subsynchronous oscillation (SSO) presents new characteristics, the oscillation mechanism is more complex, and the oscillation suppression method is also different. In essence, the oscillation phenomenon of a high proportion of new energy through a DC transmission system is a manifestation of the interaction between new energy units, reactive compensation equipment, synchronous machines, and LCC-HVDC and other diversified equipment through a weak power grid. However, the existing technology has little research on the interaction between new energy units and LCC-HVDC, and even less research on the subsynchronous oscillation suppression method of new energy through a DC transmission system. Summary of the invention

[0004] The purpose of the present invention is to provide a method for suppressing subsynchronous oscillation of a new energy system via a direct current transmission system. The method is based on state feedback, can change specific eigenvalues ​​of the system, and realize arbitrary movement of the eigenvalues ​​of the closed-loop system on the complex plane, which is beneficial to improving the stable operation level of the system.

[0005] The objective of the present invention is achieved through the following technical solutions:

[0006] A method for suppressing subsynchronous oscillation of a new energy source via a direct current transmission system, the method comprising:

[0007] Step 1: Establish a linearized state space model of the system, obtain the matrix parameters corresponding to the system, and introduce the state feedback gain matrix K based on the original system matrix;

[0008] Step 2: After obtaining the subsynchronous oscillation mode of the system by performing eigenvalue analysis on the system, a participation factor analysis is performed to obtain the dominant factor of the subsynchronous oscillation mode, and the dominant factor is selected as the system input to change the controllability of the system;

[0009] Step 3: Use Lyapunov's second method to determine the stability of the uncontrollable part. When the uncontrollable part is determined to be asymptotically stable, move the target eigenvalue to the left of the complex plane through the state feedback loop, and calculate the state feedback gain matrix K.

[0010] Step 4: For the obtained state feedback gain matrix K, on ​​the basis of considering that the state quantity is measurable, the dominant factor of the subsynchronous oscillation mode is used as the state quantity of the feedback signal, and an additional damping controller is designed to obtain a new feedback gain matrix K1 to achieve subsynchronous oscillation suppression of the new energy DC transmission system.

[0011] It can be seen from the technical solution provided by the present invention that this method is based on state feedback, can change the specific eigenvalues ​​of the system, and realize the arbitrary movement of the eigenvalues ​​of the closed-loop system on the complex plane, which is beneficial to improving the stable operation level of the system. It is also applicable to the oscillation suppression problem of other new energy grid-connected systems, and has certain academic research and engineering application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying creative work.

[0013] Figure 1 A schematic flow chart of a method for suppressing subsynchronous oscillation of a new energy source through a direct current transmission system provided by an embodiment of the present invention;

[0014] Figure 2 This is a schematic diagram of the state feedback control structure according to an embodiment of the present invention;

[0015] Figure 3 It is a structural schematic diagram of the additional damping controller according to an embodiment of the present invention;

[0016] Figure 4 The examples of the present invention include those with and without SSDC capacitor voltage U DC Schematic diagram of time domain simulation results;

[0017] Figure 5 The examples of the present invention include those with and without SSDC capacitor voltage U DC Schematic diagram of FFT analysis results. DETAILED DESCRIPTION

[0018] The following is a clear and complete description of the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments, which does not constitute a limitation of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0019] like Figure 1 The figure is a flow chart of a method for suppressing subsynchronous oscillation of a new energy source through a direct current transmission system provided by an embodiment of the present invention, the method comprising:

[0020] Step 1: Establish a linearized state space model of the system, obtain the matrix parameters corresponding to the system, and introduce the state feedback gain matrix K based on the original system matrix;

[0021] In this step, if Figure 2 The figure is a schematic diagram of the state feedback control structure according to an embodiment of the present invention, and the state space model of the linear time-invariant controlled system is described as follows:

[0022]

[0023] In the formula, is the first-order derivative of the n-dimensional state variable x; u is the state linear feedback control rate; y is the m-dimensional output; A, B, C and D are the state matrix, input matrix, output matrix and direct connection matrix corresponding to the system respectively;

[0024] The state linear feedback control rate u is:

[0025] u=Kx+v (2)

[0026] Where v is the reference input; K is the introduced state feedback gain matrix;

[0027] The state space expression of the state feedback closed-loop system is:

[0028]

[0029] The introduction of the state feedback gain matrix K does not increase the dimension of the system, but the eigenvalues ​​of the closed-loop system can be freely changed by selecting the state feedback gain matrix K, so that the system can obtain the required performance.

[0030] Step 2: After obtaining the subsynchronous oscillation mode of the system by performing eigenvalue analysis on the system, a participation factor analysis is performed to obtain the dominant factor of the subsynchronous oscillation mode, and the dominant factor is selected as the system input to change the controllability of the system;

[0031] In this step, the frequency and damping ratio of the oscillation mode are obtained by solving the eigenvalue of the system state matrix A:

[0032] λ i =σ i +jω i (4)

[0033] In the formula, λ i is the characteristic value; σ i is the real part of the eigenvalue, indicating the attenuation characteristics of the system mode, and a negative value indicates stability; ω i is the imaginary part of the eigenvalue, corresponding to the oscillation frequency;

[0034] By analyzing the damping ratio ξ corresponding to the eigenvalue i :

[0035]

[0036] Thereby, low-damped or negatively damped subsynchronous oscillation modes are identified;

[0037] The left and right eigenvectors of the state matrix A are:

[0038]

[0039] In the formula, v i is the right eigenvector of the ith mode, representing the dynamic behavior of the state variable; w i is the left eigenvector of the i-th mode, indicating the sensitivity of the state variable to the mode;

[0040] The participation factor matrix is ​​defined as:

[0041] PF k,i =w k,i v k,i (7)

[0042] In the formula, PF k,i Represents the state variable x k The participation factor for the ith mode; w k,i is the kth component in the left eigenvector; v k,i is the kth component in the right eigenvector; participation factor PF k,i It reflects the contribution of the system's state variables to a specific mode;

[0043] Thus, the dominant state variables of the subsynchronous oscillation mode of the system are obtained. The larger the participation factor, the greater the influence of the state variables on the subsynchronous oscillation mode.

[0044] For example, taking the matching control permanent magnet synchronous generator (MC-PMSG) as an example, the eigenvalue analysis of the MC-PMSG through the LCC-HVDC transmission system shows that it has a subsynchronous oscillation SSO mode with an oscillation frequency of 20.7Hz, and its dominant factors are the DC capacitor voltage and the GSC modulation phase θ p Therefore, SSDC is selected to be installed on the reactive outer loop of grid-side control, and reactive power is selected as system input to change the controllability of the system.

[0045] Step 3: Use Lyapunov's second method to determine the stability of the uncontrollable part. When the uncontrollable part is determined to be asymptotically stable, move the target eigenvalue to the left of the complex plane through the state feedback loop, and calculate the state feedback gain matrix K.

[0046] In this step, the necessary and sufficient condition for arbitrarily configuring the closed-loop poles by using state feedback is that the controlled system is controllable; if the system is not completely controllable, then the system state feedback is stabilizable if and only if the uncontrollable part of the system is asymptotically stable. The meaning of the system state feedback stabilization is that, through appropriate state feedback, all unstable modes of a dynamic system (corresponding to the part where the real part of the eigenvalue is greater than zero) can be moved to the left half plane of the complex plane, so that the system can reach a stable state. Even if the system itself is partially unstable without feedback, state feedback can stabilize it; therefore, when the system is not completely controllable, the system needs to be decomposed into a controllable structure, and the linear transformation is used to obtain the controllable structure of the system. Convert equation (1) to:

[0047]

[0048] In the formula, is the first-order derivative of the controllable state variable; is the first-order derivative of the uncontrollable state variable; is a controllable state variable; is an uncontrollable state variable; is the dynamic matrix of the controllable subsystem; is the dynamic matrix of the uncontrollable subsystem; is the coupling relationship between controllable and uncontrollable subsystems; is the input matrix of the controllable subsystem; is the output matrix of the controllable subsystem; is the output matrix of the uncontrollable subsystem; The state is completely controllable;

[0049] Lyapunov's second method is used to determine the stability of the uncontrollable part. Specifically:

[0050] Linear Steady System The equilibrium state of the origin x e = 0 is asymptotically stable if and only if: for any given positive definite symmetric matrix Q, there is a unique positive definite symmetric matrix P such that:

[0051] A T P+PA=-Q (9)

[0052] All eigenvalues ​​of a positive definite matrix are positive. By calculating the eigenvalues ​​of the matrix P, if all eigenvalues ​​are greater than 0, the matrix P is considered positive definite.

[0053] By judging whether the symmetric matrix P is positive definite, the system stability of the uncontrollable part can be judged.

[0054] For example, the controllable structure of the MC-PMSG transmission system through LCC-HVDC is decomposed, and the dynamic equation of the controllable subsystem after decomposition is:

[0055]

[0056] Lyapunov's second method is used to determine the stability of the uncontrollable part. Taking Q as the unit matrix, the symmetric matrix P is obtained, and the symmetric matrix P is a positive definite symmetric matrix. It can be seen that the uncontrollable part of the system is asymptotically stable.

[0057] Through eigenvalue analysis, it can be seen that the eigenvalue of the system SSO mode is 1.94±130.4i. The eigenvalue corresponding to the SSO mode is shifted left by 2 through the state feedback loop to improve its damping ratio, and then the state feedback gain matrix K is calculated.

[0058] In the specific implementation, considering the inconsistency between the control quantity and the feedback signal phase, the feedback loop should also use a phase shift link to compensate the phase to maximize the control performance.

[0059] Step 4: For the obtained state feedback gain matrix K, on ​​the basis of considering that the state quantity is measurable, the dominant factor of the subsynchronous oscillation mode is used as the state quantity of the feedback signal, and a supplementary subsynchronous damping controller (SSDC) is designed to obtain a new feedback gain matrix K1 to achieve subsynchronous oscillation suppression of the new energy DC transmission system.

[0060] In this step, since it is not realistic to sample and feed back each state quantity in the system in an actual system, the present invention adopts a partial feedback structure to screen out appropriate state quantities as feedback signals.

[0061] For example, since the SSO mode of the MC-PMSG transmission system through LCC-HVDC is composed of the DC capacitor voltage and the GSC modulation phase θ p The DC capacitor voltage and the matching control phase state variables are dominant, and the DC capacitor voltage and the matching control phase state variables are easy to measure, so the DC capacitor voltage and the matching control phase are selected as feedback signals; considering that the control quantity and the feedback signal phase are inconsistent, the present invention uses a lead-lag correction module in the feedback loop to adjust the phase, and in addition, a filtering link and a high-pass filter are also connected in series in the feedback loop. The filtering link is used to filter out the DC capacitor voltage u DC The high-frequency components introduced by the switching devices in the circuit are removed by high-pass filters to avoid steady-state errors, thereby designing an additional damping controller, such as Figure 3 FIG. 1 is a schematic diagram of the structure of the additional damping controller according to an embodiment of the present invention. Figure 3 middle:

[0062] The selected state variable Δx=[Δu dc , Δθ pp ] as the feedback signal, passing through the feedback gain matrix K1 = [18.85, -347419.1]; then passing through the filter to filter out the high-frequency components introduced by the switching device, while preventing the sub-synchronous frequency band from entering the stop band. Its time constant T D Take 0.001s; the isolation link must ensure that the sub-synchronous frequency band is in the passband, and its time constant T w Take 0.1s; finally, through the phase shift link, the control quantity is kept consistent with the phase of the feedback signal, and the time constant T1 is 0.006787 and T2 is 0.00889.

[0063] The following is a simulation of the process of the method described in the embodiment of the present invention using a specific example. A time domain simulation model of the MC-PMSG transmission system via LCC-HVDC is built in PSCAD. Time domain simulation is performed for two working conditions with and without the additional damping controller SSDC, respectively. The total simulation time is set to 5.0s. The wind speed is linearly increased from 10m / s to 10.3m / s within 1.5s to 3.0s, and other system parameters remain unchanged. The MC-PMSG DC capacitor voltage u is obtained under two working conditions with and without SSDC on the MC-PMSG side of the MC-PMSG transmission system via LCC-HVDC. DC Comparison of time domain simulation results and DC capacitor voltage u DC FFT analysis results of time domain simulation waveform.

[0064] like Figure 4The example of the present invention is shown with and without SSDC DC capacitor voltage U DC Schematic diagram of time domain simulation results, such as Figure 5 The example of the present invention is shown with and without SSDC DC capacitor voltage U DC Schematic diagram of FFT analysis results, from Figure 4 It can be seen that after adding the additional damping controller SSDC to the MC-PMSG control link, the wind farm DC capacitor voltage u DC The oscillation weakens. Figure 5 It can be seen that when there is no additional damping controller SSDC, the wind farm DC capacitor voltage u DC There is an obvious subsynchronous component in the wind farm. After adding SSDC, the DC capacitor voltage u DC The subsynchronous component in the signal is reduced and SSO is suppressed. Figure 4 , Figure 5 It shows that the designed additional damping controller SSDC provides positive damping for the oscillation mode, verifying the effectiveness of the additional control.

[0065] It is worth noting that the contents not described in detail in the embodiments of the present invention belong to the prior art known to professional and technical personnel in the field.

[0066] In addition, a person skilled in the art can understand that all or part of the steps in the above-mentioned embodiment method can be implemented by instructing related hardware through a program, and the corresponding program can be stored in a computer-readable storage medium. The above-mentioned storage medium can be a read-only memory, a disk or an optical disk, etc.

[0067] The above is only a preferred specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by any technician familiar with the technical field within the technical scope disclosed in the present invention should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims. The information disclosed in the background technology section of this article is only intended to deepen the understanding of the overall background technology of the present invention, and should not be regarded as an admission or in any form that the information constitutes prior art known to those skilled in the art.

Claims

1. A method for suppressing subsynchronous oscillation of a new energy source via a direct current transmission system, characterized in that: The method comprises: Step 1: Establish a linearized state space model of the system, obtain the matrix parameters corresponding to the system, and introduce the state feedback gain matrix K based on the original system matrix; Step 2: After obtaining the subsynchronous oscillation mode of the system by performing eigenvalue analysis on the system, a participation factor analysis is performed to obtain the dominant factor of the subsynchronous oscillation mode, and the dominant factor is selected as the system input to change the controllability of the system; Step 3: Use Lyapunov's second method to determine the stability of the uncontrollable part. When the uncontrollable part is determined to be asymptotically stable, move the target eigenvalue to the left of the complex plane through the state feedback loop, and calculate the state feedback gain matrix K. Step 4: For the obtained state feedback gain matrix K, on ​​the basis of considering that the state quantity is measurable, the dominant factor of the subsynchronous oscillation mode is used as the state quantity of the feedback signal, and an additional damping controller is designed to obtain a new feedback gain matrix K1 to achieve subsynchronous oscillation suppression of the new energy DC transmission system.

2. The method for suppressing subsynchronous oscillation of a new energy source via a direct current transmission system according to claim 1, characterized in that: In step 1, the state space model of the linear time-invariant controlled system is described as: In the formula, is the first-order derivative of the n-dimensional state variable x; u is the state linear feedback control rate; y is the m-dimensional output; A, B, C and D are the state matrix, input matrix, output matrix and direct connection matrix corresponding to the system respectively; The state linear feedback control rate u is: u=Kx+v (2) Where v is the reference input; K is the introduced state feedback gain matrix; The state space expression of the state feedback closed-loop system is: The introduction of the state feedback gain matrix K does not increase the dimension of the system, but the eigenvalues ​​of the closed-loop system can be freely changed by selecting the state feedback gain matrix K, so that the system can obtain the required performance.

3. The method for suppressing subsynchronous oscillation of a new energy source via a direct current transmission system according to claim 2, characterized in that: In step 2, the frequency and damping ratio of the oscillation mode are obtained by solving the eigenvalue of the system state matrix A: l i =s i +jω i (4) In the formula, λ i is the characteristic value; σ i is the real part of the eigenvalue, indicating the attenuation characteristics of the system mode, and a negative value indicates stability; ω i is the imaginary part of the eigenvalue, corresponding to the oscillation frequency; By analyzing the damping ratio ξ corresponding to the eigenvalue i : Thereby, low-damped or negatively damped subsynchronous oscillation modes are identified; The left and right eigenvectors of the state matrix A are: In the formula, v i is the right eigenvector of the i-th mode, representing the dynamic behavior of the state variables; w i is the left eigenvector of the i-th mode, indicating the sensitivity of the state variable to the mode; The participation factor matrix is ​​defined as: <h2 style=";text-align:left;direction:ltr">PF<h2 style=";text-align:left;direction:ltr"> k,i <h2 style=";text-align:left;direction:ltr"> =w<h2 style=";text-align:left;direction:ltr"> k,i <h2 style=";text-align:left;direction:ltr"> v<h2 style=";text-align:left;direction:ltr"> k,i <h2 style=";text-align:left;direction:ltr"> (7) In the formula, PF k,i Represents the state variable x k The participation factor for the ith mode; w k,i is the kth component in the left eigenvector; v k,i is the kth component in the right eigenvector; participation factor PF k,i It reflects the contribution of the system's state variables to a specific mode; Thus, the dominant state variables of the subsynchronous oscillation mode of the system are obtained. The larger the participation factor, the greater the influence of the state variables on the subsynchronous oscillation mode.

4. The method for suppressing subsynchronous oscillation of a new energy source via a direct current transmission system according to claim 2, characterized in that: In step 3, the necessary and sufficient condition for arbitrarily configuring the closed-loop poles by using state feedback is that the controlled system is controllable; if the system is not completely controllable, the system state feedback can be stabilized if and only if the uncontrollable part of the system is asymptotically stable; therefore, when the system is not completely controllable, the system needs to be decomposed into a controllable structure, and the linear transformation Convert equation (1) to: In the formula, is the first-order derivative of the controllable state variable; is the first-order derivative of the uncontrollable state variable; is a controllable state variable; is an uncontrollable state variable; is the dynamic matrix of the controllable subsystem; is the dynamic matrix of the uncontrollable subsystem; is the coupling relationship between controllable and uncontrollable subsystems; is the input matrix of the controllable subsystem; is the output matrix of the controllable subsystem; is the output matrix of the uncontrollable subsystem; The state is completely controllable; Lyapunov's second method is used to determine the stability of the uncontrollable part. Specifically: Linear Steady System The equilibrium state of the origin x e = 0 is asymptotically stable if and only if: for any given positive definite symmetric matrix Q, there is a unique positive definite symmetric matrix P such that: A T P+PA=-Q (9) All eigenvalues ​​of a positive definite matrix are positive. By calculating the eigenvalues ​​of the matrix P, if all eigenvalues ​​are greater than 0, the matrix P is considered positive definite. By judging whether the symmetric matrix P is positive definite, the system stability of the uncontrollable part can be judged.

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