High-precision MMC-HVDC harmonic stability calculation method considering time lag characteristic

Abstract

The invention provides a high-precision MMC-HVDC harmonic stability calculation method considering a time lag characteristic. By establishing a multi-time scale harmonic coupling model, a dynamic interaction process of an MMC internal control link is accurately described, and the influence of key time delay parameters such as communication delay and a sampling period on the system stability is quantified. The harmonic stability of the MMC-HVDC power transmission system is accurately analyzed, and the stable operation of the MMC-HVDC power transmission system is guaranteed. The method has remarkable advantages in the aspects of stability evaluation precision and fault prevention capability.

Description

Technical Field

[0001] This invention relates to the field of high voltage direct current transmission technology, specifically to a high-precision MMC-HVDC harmonic stability calculation method that considers time delay characteristics. Background Technology

[0002] With the rapid development of new energy power systems, the high proportion of power electronic equipment connected to the grid has resulted in low inertia and weak damping characteristics, leading to fundamental differences in the dynamic characteristics of the system compared to traditional power grids. The wide-frequency coupling effect between the MMC and the AC grid has been significantly enhanced, resulting in increasingly prominent harmonic stability issues.

[0003] In practical engineering, harmonic oscillations caused by time delays have become a significant challenge to the stable operation of flexible DC transmission systems. Most existing inventions neglect or simplify time delays and fail to quantify the impact of time delay factors such as communication delays and sampling periods on system stability. This results in insufficient accuracy in high-frequency modeling, potentially leading to erroneous stability analyses and unexpected performance results.

[0004] Therefore, to address the above problems, this invention proposes a high-precision MMC-HVDC harmonic stability calculation method that considers time delay characteristics. Summary of the Invention

[0005] In view of this, the present invention proposes a high-precision method for calculating the harmonic stability of MMC-HVDC based on time delay characteristics. Based on eigenvalues ​​and eigenvectors, the harmonic stability of the MMC-HVDC system is analyzed to ensure the stable operation of the MMC-HVDC system.

[0006] A high-precision MMC-HVDC harmonic stability calculation method considering time delay characteristics is applied to high-voltage direct current transmission systems. The method includes:

[0007] Establish the harmonic state-space equations for the electrical components of the MMC-HVDC system;

[0008] Establish the harmonic state-space equations for the control section of the MMC-HVDC system;

[0009] Establish the time-delay harmonic state-space equations for the MMC-HVDC system;

[0010] Linearize the harmonic state-space equations for time delay;

[0011] By eliminating intermediate variables, the equations for harmonic stability mode analysis are obtained;

[0012] Based on infinitesimal theory, the time delay interval is discretized to obtain the characteristic equation;

[0013] The characteristic equation matrix is ​​translated and the delay interval is scaled, and the eigenvalues ​​and eigenvectors are solved iteratively.

[0014] Filter out false feature values;

[0015] Harmonic stability discrimination based on time-delay stability margin;

[0016] Furthermore, the harmonic state-space equations for the electrical components of the MMC-HVDC system are established, specifically including:

[0017] Establish the harmonic state-space equations for the converter and transmission line of the MMC-HVDC system.

[0018] Furthermore, the harmonic state-space equations for the control section of the MMC-HVDC system are established, specifically including:

[0019] Establish the harmonic state-space equations for the sending and receiving control sections of the MMC-HVDC system.

[0020] Furthermore, the time-delay harmonic state-space equations of the MMC-HVDC system are established, specifically including:

[0021] The sampling delay, communication delay, and hardware delay, which are difficult to measure, are modeled using the lumped delay equivalence method, so that the total delay effect can be approximated as the sum of the delays of each component.

[0022] Concentrating the total time delay at the output of the entire MMC control, the corresponding bridge arm insertion index is as follows:

[0023]

[0024] Where τ s For the total time delay, ε τs =diag[...e jωlτs e 0τs e jωlτs …].

[0025] Furthermore, the harmonic state equation for the time delay is linearized as follows:

[0026]

[0027] Where x(t) is the state vector, u(t) is the control input, w(t) is the disturbance feedback term, and S T Represents the time delay operator, t d For time delay, C0(t), C r (t) is the derivative matrix of the system equations with respect to the state variables, B0(t), D0(t), D τ (t) is the derivative matrix of the system equation with respect to the input variables, B0(t), D1(t), D τ1The derivative matrix of (t) and the delayed variable.

[0028] Eliminating intermediate variables yields the equations for harmonic stability mode analysis, specifically including:

[0029] Setting u(t) = 0 to the harmonic stable mode analysis equation, we get:

[0030]

[0031] Solve for z(t): z(t) = C r x(t)+D r1 w(t).

[0032] Substitute w(t) = S T z(tt d From this, we get: w(t) = S T [C r x(tt d )+D r1 w(tt d )).

[0033] Let D r1 =0, the equation simplifies to: w(t) = S T C r x(tt d ).

[0034] Substituting w(t) into the first equation, we get...

[0035] After simplification, the harmonic stability mode analysis equation is obtained as follows:

[0036] in:

[0037] Furthermore, based on infinitesimal theory, the time delay interval is discretized to obtain the characteristic equation, which specifically includes:

[0038] Select the time delay interval [-t] for the harmonic stable mode analysis equation dd [0], and discretize the interval into a finite number of N+1 points.

[0039] Interpolate these points using a known function:

[0040] Among them l r (θ) is a known Lagrange basis function, x t (θ r ) is an unknown coefficient.

[0041] Taking the derivative of the polynomial interpolation, the derivative is expressed as:

[0042] The characteristic equation is obtained by using discrete interval interpolation and differentiation of the harmonic stability mode analysis equation:

[0043]

[0044] Furthermore, the characteristic equation matrix is ​​translated and scaled over the time delay interval, and the eigenvalues ​​and eigenvectors are solved iteratively, specifically including:

[0045] Characteristic equation A N x N =λx N Replace λ with λ+α. Shift all eigenvalues ​​near 0 to the right.

[0046] For time delay interval scaling, divide all times by the maximum delay, i.e., change the time unit to the maximum delay equal to 1, and let u = t / τ. max .

[0047] The eigenvalues ​​are obtained by solving on the translated and scaled matrix.

[0048] Furthermore, filtering out spurious feature values ​​specifically includes:

[0049] False eigenvalues ​​appear near 0, and their position shifts when the truncation order is changed. False eigenvalues ​​that change with the truncation order and are near 0 will be excluded.

[0050] Furthermore, stability is determined based on time-delay stability margin, specifically including:

[0051] Set an initial time delay value Ttd and select an appropriate step size ΔT. Gradually increase the time delay value and use the bisection method to quickly locate the critical time delay value. Check if all eigenvalues ​​are located on the left half of the complex plane. If all eigenvalues ​​corresponding to a certain time delay value are located on the left side of the imaginary axis for the first time, then that value is the maximum allowable time delay for the system to satisfy the stability condition.

[0052] The stability of a system is determined based on the time-delay stability margin. When the system time delay exceeds the time-delay stability margin, the system will experience harmonic instability.

[0053] The present invention has the following advantages over the prior art:

[0054] This invention proposes a harmonic stability analysis method for MMC-HVDC that simultaneously considers interaction and time-delay characteristics. By establishing a multi-time-scale harmonic coupling model, the dynamic interaction process of the internal control links of the MMC is accurately characterized, and the impact of key time-delay parameters such as communication delay and sampling period on system stability is quantified. This allows for precise evaluation of the harmonic stability of the MMC-HVDC transmission system, ensuring its stable operation. This method has significant advantages in terms of stability assessment accuracy and fault prevention capabilities. Attached Figure Description

[0055] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the structures shown in these drawings without creative effort.

[0056] Figure 1 This is a flowchart of the MMC-HVDC harmonic stability assessment process of the present invention, which is shown in the abstract figure.

[0057] Figure 2 This is a schematic diagram of the MMC-HVDC system considered in this invention.

[0058] Figure 3 The waveform diagram for time-delay stability in Embodiment 1 of the present invention is shown in the time-domain simulation.

[0059] Figure 4 This is a distribution diagram of the characteristic roots of time-delay stability in Embodiment 1 of the present invention.

[0060] Figure 5 This is a time-domain simulation waveform diagram of time-delay instability in Embodiment 1 of the present invention.

[0061] Figure 6 This is a distribution diagram of the characteristic roots of time-delay instability in Embodiment 1 of the present invention. Detailed Implementation

[0062] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are some embodiments of the present invention, but not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0063] Example 1:

[0064] S1. Establish the harmonic state-space equations for the electrical components of the MMC-HVDC system, specifically including:

[0065] S11, the MMV-HVDC system of this embodiment is as follows: Figure 2 As shown, the harmonic state-space equations of its converter are established as follows:

[0066]

[0067] in and For the upper and lower bridge arm currents, For transformer current, and The voltage across the capacitor. and The insertion index of the upper and lower bridge arms is N = diag[…jω…0…-jω…].

[0068] S12. Establish the harmonic state-space equation for the line, as follows:

[0069]

[0070] Among them, R d L d C d It is the Topulitz matrix composed of parameters from the exact π model.

[0071] S2. Establish the harmonic state-space equations for the control section of the MMC-HVDC system, specifically including:

[0072] S21. Establish the state-space equation for the outer loop control harmonics of the MMC-HVDC system at the sending end, as follows:

[0073]

[0074] Among them, u dc DC voltage, u dcref i is the DC voltage reference value. derf 0 and k are the current reference values ​​for the inner current loop. DC_iout and k DC_pout These are the outer loop PI control parameters.

[0075] S22. Establish the state-space equation for the inner loop control harmonics of the MMC-HVDC system at the sending end, as follows:

[0076]

[0077] Where i d and i q For the d-axis and q-axis currents, k DC_iin and k DC_pinThese are the parameters for the inner-loop PI control.

[0078] S23. Establish the state-space equation for the outer loop control harmonics of the MMC-HVDC system at the receiving end, as follows:

[0079]

[0080] Among them, u gd and u gq For AC d-axis and q-axis voltages, u gdref and u gqref i is the AC voltage reference value. dref and i qref k is the current reference value for the inner current loop. AC_iout and k AC_pout These are the outer loop PI control parameters.

[0081] S24. Establish the state-space equation for the inner loop control harmonics of the MMC-HVDC system at the receiving end, as follows:

[0082]

[0083] Among them, i d and i q For the d-axis and q-axis currents, k AC_iin and k AC_pin For the inner loop PI control parameters, Γ(ω)=diag[…ω…ω…ω].

[0084] S25. Establish the phase-locked loop harmonic state-space equation of the MMC-HVDC system, as follows:

[0085]

[0086] The deviation angle can be expressed as δθ PLL =atan2(v gq ,v gd ). k PLL_i and k PLL_p These are PI control parameters.

[0087] S3. Establish the time-delay harmonic state-space equations for the MMC-HVDC system, specifically including:

[0088] S31. The sampling delay T1, communication delay T2 and hardware delay T3 are modeled using the lumped delay equivalence method. The total delay effect can be approximated as the sum of the delays of each component.

[0089] S32. The total time delay is concentrated at the output of the entire MMC control, corresponding to the bridge arm insertion index as follows:

[0090]

[0091] S4. Further, the harmonic state equation for the time delay is linearized as follows:

[0092]

[0093] Where x(t) is the state vector, u(t) is the control input, w(t) is the disturbance feedback term, and S T Represents the time delay operator, t d For time delay, C0(t), C τ (t) represents the coefficients of the system equations with respect to the state variables, B0(t), D0(t), D τ (t) represents the coefficients of the system equations with respect to the input variables, B0(t), D1(t), D τ1 (t) and the coefficients of the delayed variable.

[0094] S5. Eliminating intermediate variables yields the equations for harmonic stability mode analysis, specifically including:

[0095] S51. By setting u(t) = 0 to the harmonic stable mode analysis equation, we obtain:

[0096]

[0097] S52. Solve for z(t): z(t) = C t x(t)+D r1 w(t).

[0098] S53, Substitute w(t) = S T z(tt d From this, we get: w(t) = S T [C r x(tt d )+D r1 w(tt d )).

[0099] S54, Order D r1 =0, the equation simplifies to: w(t) = S T C r x(tt d ).

[0100] S55. Substituting w(t) into the first equation, we get...

[0101] S56. After simplification, the harmonic stability mode analysis equation is obtained as follows:

[0102] in:

[0103] S6. Further, based on infinitesimal theory, the time delay interval is discretized to obtain the characteristic equation, which specifically includes:

[0104] S61. Select the time delay interval [-t] for the harmonic stable mode analysis equation. dd [0], and discretize the interval into a finite number of N+1 points.

[0105] S62. Interpolate these points using a known function:

[0106] S63, where l r (θ) is a known Lagrange basis function, x t (θ r ) is an unknown coefficient.

[0107] S64. Take the derivative of the polynomial interpolation, which is expressed as:

[0108] S65. The characteristic equation is obtained by using discrete interval interpolation and differentiation on the harmonic stable mode analysis equation:

[0109]

[0110] S7. The characteristic equation matrix is ​​shifted and the delay interval is scaled. The eigenvalues ​​and eigenvectors are then iteratively solved, specifically including:

[0111] S71, the characteristic equation A N x N =λx N Replace λ with λ+α. Shift all eigenvalues ​​near 0 to the right.

[0112] S72. For time delay interval scaling, divide all times by the maximum delay, i.e., change the time unit to the maximum delay equal to 1, and let u = t / τ. max .

[0113] S73. Solving for eigenvalues ​​on the translated and scaled matrix.

[0114] S8. Further, filter out false feature values, specifically including:

[0115] False eigenvalues ​​appear near 0, and their position shifts when the truncation order is changed. False eigenvalues ​​that change with the truncation order and are near 0 will be excluded.

[0116] S9. Furthermore, stability determination is based on time-delay stability margin, specifically including:

[0117] S91. Set an initial time delay value Ttd and select an appropriate step size ΔT. Gradually increase the time delay value and use the bisection method to quickly locate the critical time delay value. Check if all eigenvalues ​​are located on the left half of the complex plane. If all eigenvalues ​​corresponding to a certain time delay value are located on the left side of the imaginary axis for the first time, then that value is the maximum allowable time delay for the system to meet the stability condition.

[0118] S92. Based on the time delay stability margin, the system stability is judged. When the system time delay exceeds the time delay stability margin, the system will experience harmonic instability.

[0119] The time-delay stability margin obtained according to the method described in this paper indicates that the system is stable when the system time delay is less than its time-delay stability margin. Figure 3 The figure shows the time-domain simulation waveform of the system from 1s to 2s. The characteristic root distribution diagram obtained according to this method is as follows. Figure 4 As shown, its characteristic roots do not appear on the left half-axis, indicating the system is in a stable state, and the judgment is correct. When the system time delay is greater than its time delay stability margin, as... Figure 5 The figure shows the time-domain simulation waveform of the system from 1s to 2s. The system is unstable, and the time-domain waveform oscillates. Its eigenvalue distribution is shown below. Figure 6 As shown, the characteristic root appears on the left half-axis, indicating that the system is in an unstable state, which is a correct judgment.

[0120] Those skilled in the art will understand that all or part of the steps in the methods of the above embodiments can be implemented by a program instructing related hardware, and the corresponding program can be stored in a computer-readable storage medium.

[0121] It should be noted that although the method operations of the above embodiments are described in a specific order in the accompanying drawings, this does not require or imply that these operations must be performed in that specific order, or that all the operations shown must be performed to achieve the desired result. On the contrary, the order of execution of the described steps may be changed. Additionally or alternatively, certain steps may be omitted, multiple steps may be combined into one step, and / or one step may be broken down into multiple steps.

Claims

1. This invention proposes a high-precision method for calculating the harmonic stability of an MMC-HVDC system based on time-delay characteristics. It analyzes the harmonic stability of the MMC-HVDC system based on eigenvalues ​​and eigenvectors, ensuring the stable operation of the MMC-HVDC system. Its features include: The method includes: Establish the harmonic state-space equations for the electrical components of the MMC-HVDC system; Establish the harmonic state-space equations for the control section of the MMC-HVDC system; Establish the time-delay harmonic state-space equations for the MMC-HVDC system; Linearize the harmonic state-space equations for time delay; By eliminating intermediate variables, the equations for harmonic stability mode analysis are obtained; Based on infinitesimal theory, the time delay interval is discretized to obtain the characteristic equation; The eigenvalues ​​are iteratively solved by translating and scaling the delay interval of the characteristic equation matrix; Filter out false feature values; Harmonic stability discrimination based on time-delay stability margin.

2. The high-precision MMC-HVDC harmonic stability calculation method for calculating time delay characteristics according to claim 1, characterized in that, Establish the time-delay harmonic state-space equations for the MMC-HVDC system, specifically including: Furthermore, the time-delay harmonic state-space equations of the MMC-HVDC system are established, specifically including: The sampling delay, communication delay, and hardware delay, which are difficult to measure, are modeled using the lumped delay equivalence method, so that the total delay effect can be approximated as the sum of the delays of each component. Concentrating the total time delay at the output of the entire MMC control, the corresponding bridge arm insertion index is as follows: Where τ s For the total time delay, ε τs =diag[...e jωlτs e 0τs e jωlτs ...).

3. The high-precision MMC-HVDC harmonic stability calculation method for calculating time delay characteristics according to claim 1, characterized in that, Eliminating intermediate variables yields the equations for harmonic stability mode analysis, specifically including: Setting u(t) = 0 to the harmonic stable mode analysis equation, we get: Solve for z(t): z(t) = C r x(t) + D r1 w(t). Substitute w(t) = S T z(tt d ),have to: Let D r1 =0, the equation simplifies to: w(t) = S T C r x(tt d ). Substituting w(t) into the first equation, we get... After simplification, the harmonic stability mode analysis equation is obtained as follows: Where: A0 = AN, A d =B1S T C r .

4. The high-precision MMC-HVDC harmonic stability calculation method for calculating time delay characteristics according to claim 1, characterized in that, Based on infinitesimal theory, the time delay interval is discretized to obtain the characteristic equation, which specifically includes: Select the time delay interval for the harmonic stable mode analysis equation The interval is then discretized into a finite number of N+1 points. Interpolate these points using a known function: Among them l r (θ) is a known Lagrange basis function, x t (θ r ) is an unknown coefficient. Taking the derivative of the polynomial interpolation, the derivative is expressed as: The characteristic equation is obtained by using discrete interval interpolation and differentiation of the harmonic stability mode analysis equation:

5. The high-precision MMC-HVDC harmonic stability calculation method for calculating time delay characteristics according to claim 1, characterized in that, The characteristic equation matrix is ​​translated and scaled over time delay intervals, and the eigenvalues ​​and eigenvectors are iteratively solved, specifically including: Characteristic equation A N x N =λx N Replace λ with λ+α. Shift all eigenvalues ​​near 0 to the right. For time delay interval scaling, divide all times by the maximum delay, i.e., change the time unit to the maximum delay equal to 1, and let u = t / τ. max . The eigenvalues ​​are obtained by solving on the translated and scaled matrix.

6. The high-precision MMC-HVDC harmonic stability calculation method for calculating time delay characteristics according to claim 1, characterized in that, The characteristic equation matrix is ​​translated and scaled over time delay intervals, and the eigenvalues ​​and eigenvectors are iteratively solved, specifically including: Characteristic equation A N x N =λx N Replace λ with λ+α. Shift all eigenvalues ​​near 0 to the right. For time delay interval scaling, divide all times by the maximum delay, i.e., change the time unit to the maximum delay equal to 1, and let u = t / τ. max . The eigenvalues ​​are obtained by solving on the translated and scaled matrix.

7. The high-precision MMC-HVDC harmonic stability calculation method for calculating time delay characteristics according to claim 1, characterized in that, Filtering out spurious feature values ​​specifically includes: False eigenvalues ​​appear near 0, and their positions shift with changing the truncation order. False eigenvalues ​​that change with the truncation order and are near 0 will be excluded.

8. The high-precision MMC-HVDC harmonic stability calculation method for calculating time delay characteristics according to claim 1, characterized in that, Stability assessment based on time-delay stability margin specifically includes: Set an initial time delay value Ttd and select an appropriate step size ΔT. Gradually increase the time delay value and use the bisection method to quickly locate the critical time delay value. Check if all eigenvalues ​​are located on the left half of the complex plane. If all eigenvalues ​​corresponding to a certain time delay value are located on the left side of the imaginary axis for the first time, then that value is the maximum allowable time delay for the system to satisfy the stability condition. The stability of a system is determined based on the time-delay stability margin. When the system time delay exceeds the time-delay stability margin, the system will experience harmonic instability.

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