Direct-drive permanent magnet synchronous wind turbine under weak grid next synchronous oscillation suppression method

Abstract

The patent relates to wind power control technology, in particular to a method for suppressing subsynchronous oscillation of direct-drive permanent magnet synchronous wind turbine under weak power grid. In view of the problem of power generation system instability and power distribution network voltage fluctuation caused by subsynchronous oscillation of direct-drive permanent magnet synchronous wind turbine under weak power grid, an additional damping oscillation suppression method based on uncertainty and disturbance estimator UDE is proposed. First, the virtual synchronous machine technology VSG is adopted for the grid-side converter, and the sequence impedance model of the grid-side converter is established based on the harmonic linearization theory; secondly, an additional damping robust control method based on UDE is proposed for the current loop. The additional damping controller based on UDE replaces the disturbance of grid voltage, active power instruction and other factors with lumped disturbance, which can effectively suppress subsynchronous oscillation and improve the robustness of the system, and has certain adaptability to complex working conditions.

Description

Technical Field

[0001] This patent relates to wind power control technology, specifically to a method for suppressing the next synchronization oscillation of a direct-drive permanent magnet synchronous wind turbine in a weak power grid. Background Technology

[0002] With the continuous growth of wind power installed capacity, the problem of subsynchronous oscillations caused by the interaction between direct-drive wind farms and weak power grids in remote areas has become increasingly prominent in recent years, even affecting the voltage stability of the distribution network. During the interaction between direct-drive permanent magnet synchronous wind turbines and weak power grids, the equivalent capacitive property resonates with the inductive property of the weak power grid, and under negative damping, this resonance diverges, generating subsynchronous oscillations. Compared to the traditional subsynchronous oscillations dominated by shaft dynamics, the oscillation phenomenon in new power systems often begins with small-signal negative damping divergence and ends with nonlinear continuous oscillation, exhibiting a wide oscillation frequency range.

[0003] Existing technologies have conducted extensive research on the grid connection stability and oscillation mechanism of direct-drive wind turbines under weak power grids, and have achieved fruitful results. Reference 1 (“Broadband Oscillation Mechanism and Suppression Method of Direct-Drive Wind Farm Connected to Weak Power Grid (I): Broadband Impedance Characteristics and Oscillation Mechanism Analysis”, Li Guanghui, Proceedings of the CSEE, 2019, No. 39(22), pp. 6547-6562) combined the impedance model of direct-drive permanent magnet synchronous wind turbines in the frequency domain to conduct an in-depth analysis of the subsynchronous oscillation mechanism and characteristics under weak power grids. Among them, the influence of the grid-side converter double closed-loop control parameters and the interaction between the current loop and the phase-locked loop on the subsynchronous oscillation of the system is particularly prominent. References 2 (“Analysis of the Open-Loop Mode Resonance Mechanism of Subsynchronous Oscillation Caused by Phase-Locked Loop in Direct-Drive Wind Power Grid-Connected System, Wang Xubin”, Du Wenjuan, Wang Haifeng, Proceedings of the CSEE, 2018, No. 38(07), pp. 1935-1950) and 3 (“Interaction Model and Mechanism Analysis of Direct-Drive Wind Turbine Units Considering Phase-Locked Loops”, Cao Na, Xin Guifeng, Yu Qun, Electric Power Automation Equipment, 2021, No. 41(08), pp. 89-96) studied the subsynchronous oscillation characteristics dominated by phase-locked loops, focusing on analyzing the influence mechanism of phase-locked loops on subsynchronous oscillations of direct-drive permanent magnet synchronous wind turbine units under weak grid conditions. Reference 4 (“Analysis of the subsynchronous oscillation mechanism of direct-drive converter connected to a weak power grid”, Lü Dianshun, Acta Energiae Solaris Sinica, 2021, No. 42(05), pp. 423-429) used the root locus method to conduct an in-depth study on the subsynchronous oscillation characteristics dominated by the current loop of the grid-side converter. The current loop q-axis exhibits negative resistance characteristics in a specific frequency range, which can easily lead to the risk of subsynchronous oscillation. To avoid the negative damping effect caused by directly using phase-locked loops and to provide inertia support to the system, references 5 (“inverters that mimic synchronous generators”, ZHONG QC, IEEE Transactions on Industrial Electronics, 2011, No. 58(4), pp. 1259-1267) and 6 (“A novel virtual synchronous generator control of pmsg-based wind generation system to enhance transient stability of power system”, Imai H, 2018 IEEE Electronic Power Grid (eGrid), 2018, pp. 1-6) apply grid-type virtual synchronous generator control technology to the grid-side converter of direct-drive permanent magnet synchronous wind turbines.

[0004] Impedance analysis is widely used in the stability analysis of new energy grid connection due to its ease of engineering measurement and simplicity. Among them, sequence impedance modeling provides a clear description of the frequency coupling characteristics in the broadband oscillation of new energy grid connection. This method converts AC signals into DC signals in the frequency domain based on harmonic linearization theory, and can be corrected by impedance measurement. Compared with the dq impedance method, it has the advantages of clear physical meaning and strong adaptability. Reference 7 ("Sequence Impedance Modeling of Virtual Synchronous Generator Considering Frequency Coupling Effect", Du Yan, Journal of Power Supply, 2020, No. 18(06), pp. 42-49) establishes a sequence impedance model based on harmonic linearization theory and conducts an in-depth analysis of the frequency coupling oscillation characteristics under the voltage-current dual closed-loop control mode of virtual synchronous generator. References 8 (“Stability Comparison Analysis of Virtual Synchronous Generators and Traditional Grid-Connected Inverters from the Perspective of Sequence Impedance”, Wu Wenhua, Proceedings of the CSEE, 2019, No. 39(5), pp. 1411-1421) and 9 (“Sequence Impedance Modeling and Stability Analysis of Virtual Synchronous Generators Connected to Weak Grids”, Wu Wenhua, Proceedings of the CSEE, 2019, No. 39(06), pp. 1560-1571) studied the stability of virtual synchronous generator control technology under weak grids and the factors affecting stability through sequence impedance modeling. Reference 10 (“Impedance modeling and stability analysis of VSG controlled grid-connected converters with cascaded inner control loop”, Xu Y, Energies, 2020, No. 13(19), p. 5114) compared the stability of VSG in weak grids with and without voltage-current dual closed-loop modes using Bode plots. Dual closed-loop control is beneficial for improving voltage control accuracy and limiting the amplitude, but its equivalent capacitive and negative damping characteristics make the resonance of the system in a specific frequency range prone to divergence, resulting in subsynchronous oscillations. Reference 11 (“Subsynchronous Oscillation Damping Control Method and Its Adaptability for Direct-Drive Wind Turbines”, Zhou Peipeng, Automation of Electric Power Systems, 2019, No. 43(13), pp. 177-184) proposes a voltage loop additional damping control strategy, which compensates the system voltage through the phase-shift compensation control principle, thereby suppressing the oscillation and achieving good results. However, when the system is subjected to external disturbances or changes in operating conditions, the parameters of the traditional additional damping controller cannot be adjusted in real time, thus affecting the compensation effect.

[0005] UDE control theory is based on robust control theory and is mainly used to address parameter uncertainties and problems caused by external disturbances in control systems. The core idea of ​​this method is to estimate system disturbances using bandpass filters. Compared to active disturbance rejection control, this method eliminates the need for a state observer, resulting in better dynamic performance and robustness. Summary of the Invention

[0006] To enable the system to support inertia, this patented grid-side converter employs virtual synchronous machine control technology and establishes a sequence impedance model for the grid-side converter based on harmonic linearization theory. Based on an in-depth analysis of the impact of introducing a voltage-current dual closed loop on system stability, a mathematical model of an additional damping controller for the current loop based on uncertainty and disturbance estimators is constructed. A method for suppressing secondary synchronization oscillations in weak grids for direct-drive permanent magnet synchronous wind turbines is proposed. The specific technical solution is as follows:

[0007] A method for suppressing secondary synchronization oscillations in weak power grids using direct-drive permanent magnet synchronous wind turbines (PMSMs) is proposed. The PSMs consist of a rotor-side converter, a grid-side converter, and a filter. The grid-side converter employs Virtual Synchronization Generator (VSG) technology and comprises an active power loop, a reactive power loop, and a voltage-current dual closed loop. The active power loop includes an active-frequency component and a mechanical component; the reactive power loop includes a reactive-voltage component and an electrical component. The active power loop generates the voltage phase, the reactive power loop generates the voltage amplitude, and a bridge arm potential signal e is generated. abc The e generated by the power loop abc The mode in which the signal is directly used as the modulation signal for control is called "open-loop mode," while e... abc The mode in which the voltage-current dual closed-loop setpoint is used for control is called "dual closed-loop mode";

[0008] Active power control section: VSG technology introduces a synchronous generator swing equation based on traditional droop control, as shown in equation (1):

[0009]

[0010] In the formula, T m T e These are mechanical torque and electromagnetic torque, respectively. , ;P m P e These are mechanical power and electromagnetic power, respectively; δ, The voltage phase and the rated angular frequency of the power grid are respectively; J and D are the moment of inertia and damping coefficient; VSG controls the output of active power through the active power loop, participates in the primary frequency regulation of the system, and provides inertial support and damping for system oscillations.

[0011] Reactive power control section: The voltage and current relationship of the stator circuit of the VSG simulated synchronous generator is realized through equation (2):

[0012]

[0013] In the formula, e = [e a e b e c ] T The voltage at the midpoint of the inverter bridge arm; u = [u a u b u c ] T i is the output voltage; L =[i La i Lb i Lc ] T For the filter inductor current; L s R and R are the filter inductance and parasitic resistance, respectively;

[0014] Compensation voltage E d E q This is the input of the additional damping controller. By adjusting the control input, the inductor current can be stably tracked with the reference value, thereby achieving the effect of oscillation suppression. Based on the VSG stator voltage and current equation, the inductor current is used as the control variable and the bridge arm potential is used as the control input (voltage compensation). A mathematical model of the additional damping controller based on UDE is established in the inner current loop of the double closed loop.

[0015] Transforming equation (2) into the dq coordinate system yields the first-order state equation of the system:

[0016]

[0017] Further simplification of equation (48) yields the matrix expression:

[0018] (49)

[0019] In the formula: i L =(i Ld i Lq ) T For the control state variable, E = (E d E q ) T For control input, Δd=(Δi) d , Δi q ) T For lumped disturbances, where:

[0020] (50)

[0021] In equation (50), the inductance L in the denominator of the polynomial f Since Δd is not zero, it can be considered bounded.

[0022] Select a suitable control input E to make the inductor current i L Capable of accurately tracking reference input commands i that do not contain oscillating harmonic components Lref change.

[0023] Therefore, the tracking error e=i Lref - i L The following conditions must be met:

[0024] (51)

[0025] In the formula, A m K iL <0,K iL This is the error feedback gain. It eventually converges to 0, therefore the error equation is asymptotically stable.

[0026] By combining equations (49) and (51), we can obtain:

[0027] (52)

[0028] Therefore, the control input E must satisfy:

[0029] (53)

[0030] In the formula, C is the inductor current setpoint; Δd consists of two parts: the uncertainty of the system's internal parameters and the unknown external disturbances of the system, which are called lumped disturbances.

[0031] By selecting an appropriate bandwidth filter to estimate the lumped disturbance, the lumped disturbance based on UDE can be expressed by equation (54):

[0032] (54)

[0033] In the formula, g is the symbol for convolution calculation. f For bandpass filter G f The unit impulse response of G(s) requires that G f (s) Strictly reliable and stable with appropriate bandwidth.

[0034] Replacing Δd in equation (53) with equation (54), we get:

[0035] (55)

[0036] Therefore, the mathematical model of the additional damping controller based on UDE is as follows:

[0037] (56)

[0038] In the formula, G f (s) is g f The Laplace transform; the equation no longer contains uncertainty and unknown perturbation terms;

[0039] Choose a first-order low-pass filter G f (s)=1 / (Ts+1),

[0040] (57)

[0041] In the formula, T is the response time constant. , This represents the upper limit of the lumped disturbance frequency band in the system.

[0042] Substituting equation (57) into equation (47), we get:

[0043] (58)

[0044] Set the reference model parameter C=i Lref Select the cutoff frequency of the first-order low-pass filter. ;K iL The bandwidth of the desired error step response should be less than .

[0045] This invention addresses the subsynchronous oscillation problem caused by the interaction between direct-drive permanent magnet synchronous wind turbines and weak power grids. It proposes an oscillation suppression method for the current loop based on a UDE-based additional damping controller, and draws the following conclusions through time-domain simulation experiments:

[0046] By comparing Bode plots under open-loop and dual-closed-loop conditions, the impact characteristics of negative resistance and capacitance generated in the system at specific frequency bands after introducing dual-closed-loop control were analyzed. A mathematical model of a current-loop additional damping controller based on uncertainty and disturbance estimator was established. By introducing a first-order low-pass filter to estimate lumped disturbances, subsynchronous oscillations were suppressed from the perspective of bandwidth. Simulation results show that the current-loop additional damping control strategy based on UDE has a good suppression effect on subsynchronous oscillations within a certain grid strength range, showing strong adaptability and solving the problem that traditional additional damping controllers must frequently change control parameters. Under step disturbances in grid voltage and active power command, the system can maintain a good subsynchronous oscillation suppression effect, with obvious anti-interference ability and strong system robustness. This oscillation suppression method is of great significance for enhancing the flexible grid-connected operation capability of new energy power generation systems and improving the voltage stability of distribution networks. Attached Figure Description

[0047] Figure 1 This is a schematic diagram of the main topology of a direct-drive wind turbine.

[0048] Figure 2 This is a schematic diagram of the overall framework of the VSG control strategy.

[0049] Figure 3 It is the equivalent circuit diagram of the current frequency domain response.

[0050] Figure 4(a) is the Bode plot of the open-loop sequence impedance; in the figure, the horizontal axis represents frequency and the vertical axis represents amplitude.

[0051] Figure 4(b) is the Bode plot of the open-loop sequence impedance; in the figure, the horizontal axis represents frequency and the vertical axis represents phase.

[0052] Figure 5(a) is the Bode plot of the sequence impedance in the dual closed-loop mode; in the figure, the horizontal axis represents frequency and the vertical axis represents amplitude.

[0053] Figure 5(b) is the Bode plot of the sequence impedance in the dual closed-loop mode; in the figure, the horizontal axis represents frequency and the vertical axis represents phase.

[0054] Figure 6 This is the schematic diagram of the UDE control structure.

[0055] Figure 7 This is a schematic diagram of a traditional additional damping controller structure.

[0056] Figure 8 This is a system control block diagram based on UDE.

[0057] Figure 9(a) shows the power curves under different impedance conditions; in the figure, the horizontal axis represents time in seconds, and the vertical axis represents active power output in megawatts.

[0058] Figure 9(b) shows the power curves under different impedance conditions; in the figure, the horizontal axis represents time in seconds, and the vertical axis represents reactive power output in megawatts.

[0059] Figure 10(a) shows the power curve under voltage step disturbance conditions; in the figure, the horizontal axis represents time in seconds; the vertical axis represents active power output in megawatts.

[0060] Figure 10(b) shows the power curve under voltage step disturbance conditions; in the figure, the horizontal axis represents time in seconds; the vertical axis represents reactive power output in megawatts.

[0061] Figure 11(a) shows the power curve under the active power command step disturbance condition; in the figure, the horizontal axis represents time in seconds; the vertical axis represents active power output in megawatts.

[0062] Figure 11(b) shows the power curve under active power command step disturbance condition; in the figure, the horizontal axis represents time in seconds; the vertical axis represents reactive power output in megawatts. Detailed Implementation

[0063] Main topology and mathematical model of direct-drive wind turbine:

[0064] Direct-drive wind turbine main topology: The direct-drive permanent magnet synchronous wind turbine consists of a rotor-side converter, a grid-side converter, and filters, etc., and its structure is as follows: Figure 1 As shown.

[0065] The grid-side converter of the direct-drive permanent magnet synchronous wind turbine adopts a virtual synchronous machine control strategy with a power outer loop and a voltage-current inner loop. The rotor-side converter, on the other hand, adopts a traditional vector control strategy with dual voltage-current closed loops.

[0066] The basic principle of VSG control technology is to introduce the SG swing equation on the basis of traditional droop control, so that the inverter can simulate the transient characteristics of SG to participate in the frequency and voltage regulation of the system, and provide inertial support to the system, thereby improving the system's operational stability.

[0067] The VSG control strategy simulates the mechanical and electromagnetic characteristics of a SG, and consists of an active power loop, a reactive power loop, and a voltage-current dual closed loop. The active power loop includes an active-frequency component and a mechanical component; the reactive power loop includes a reactive-voltage component and an electrical component. The active power loop generates the voltage phase, the reactive power loop generates the voltage amplitude, and both generate the bridge arm potential signal e. abc Its structure is as follows Figure 2 As shown. This invention generates e from the power loop. abc The mode in which the signal is directly used as the modulation signal for control is called "open-loop mode," while e... abc The mode in which the voltage-current dual closed-loop setpoint is used for control is called "dual closed-loop mode".

[0068] Active power control section: VSG technology introduces the synchronous generator swing equation on the basis of traditional droop control, as shown in equation (1).

[0069] (1)

[0070] In the formula, T m T e These are mechanical torque and electromagnetic torque, respectively. , ;P m P e These are mechanical power and electromagnetic power, respectively; δ, These represent the voltage phase and the grid's rated angular frequency, respectively; J and D represent the moment of inertia and damping coefficient; VSG controls the output of active power through the active power loop, participates in the primary frequency regulation of the system, and provides inertial support and damping for system oscillations.

[0071] Reactive power control section: The voltage and current relationship of the stator circuit of the VSG simulated synchronous generator is realized through equation (2):

[0072] (2)

[0073] In the formula, e = [e a e b e c ] T The voltage at the midpoint of the inverter bridge arm; u = [u a u b u c ] T i is the output voltage; L =[i La i Lb i Lc ] T For the filter inductor current; L s R and R are the filter inductance and parasitic resistance, respectively.

[0074] To achieve reactive power control and simulate the excitation voltage regulation function of a synchronous generator, this part adopts the expression (3).

[0075] (3)

[0076] In the formula, Q e With Q ref For reactive power output value and reactive power setpoint; U n U0 represents the rated peak and actual peak values ​​of the terminal voltage; E represents the peak value of the grid-side inverter arm potential. K q K and K are the reactive power droop coefficient and reactive power adjustment coefficient, respectively.

[0077] VSG sequence impedance modeling and characteristic analysis: When the frequency applied to the converter port is f p When a voltage disturbance component is present, the system will generate a frequency of f. p The current disturbance component, under the frequency coupling effect, generates a frequency of f p -2f0 is the negative-sequence coupled current disturbance component. Its frequency is f. p The current disturbance component with frequency f p The negative-sequence coupled current disturbance components of -2f0 appear in pairs and are symmetrical about the fundamental frequency. Based on the harmonic linearization theory, the three-phase AC output signal of the system is converted into a frequency-domain DC signal, and a sequence impedance model of the grid-side converter is established. The expressions for the A-phase output voltage, output current, and filter inductor current are as follows:

[0078] (4)

[0079] In the formula, V1, I1 and I L These represent the amplitudes of the output fundamental voltage, current, and filter inductor current, respectively; V p I p and I Lp These represent the output voltage, current, and filter inductor current amplitudes at the positive-sequence perturbation frequency, respectively; ω p The sum is the positive-sequence perturbation angular frequency; , and These represent the initial phase angles of the output voltage, current, and filter inductor current at the positive sequence disturbance frequency, respectively; V p2 I p2 and I Lp2 These represent the output voltage, current, and filter inductor current amplitudes at the negative sequence coupling frequency, respectively. , and These represent the initial phase angles of the output voltage, current, and filter inductor current at the negative sequence coupling frequency, respectively; ω p2 It is the negative-sequence coupling angular frequency.

[0080] Equation (4) in the frequency domain is expressed as follows:

[0081] (5)

[0082] In the formula, ; ; ; ; ; ; ; ; .

[0083] Power loop modeling: The potential difference between the VSG arm potential and the terminal voltage can be expressed as:

[0084] (6)

[0085] In the αβ coordinate system, the expressions for the system's output active and reactive power are as follows:

[0086] (7)

[0087] In the formula, , , , These represent the system output voltage and output current in the αβ coordinate system, respectively.

[0088] In the αβ coordinate system, the frequency domain expressions for the system output voltage and output current are as follows:

[0089] (8)

[0090] (9)

[0091] Substituting equations (8) and (9) into (7), and using the frequency domain convolution theorem, ignoring the second harmonic component, we can obtain the frequency domain expressions for active power and reactive power:

[0092] (10)

[0093] (11)

[0094] In the formula, Represents the conjugate expression of a complex number.

[0095] According to equation (1), the expression for the VSG output phase angle can be obtained as follows:

[0096] (12)

[0097] Equation (12) is transformed to the frequency domain using Laplace transform. Then, equation (10) is substituted into equation (12), and the small-signal quadratic term is ignored to obtain the frequency domain expression of the VSG output phase angle:

[0098] (13)

[0099] In the formula, M(s) = 1 / [s*(Js+D)] and θ = θ0 + Δθ. Where ω0t is the voltage fundamental frequency phase, This is the initial phase.

[0100] According to the trigonometric function relationships, we know that:

[0101] (14)

[0102] Transforming equation (14) to the frequency domain using the Laplace transform, we obtain:

[0103] (15)

[0104] (16)

[0105] Equation (3) is transformed to the frequency domain using Laplace transform. Then, equation (11) is substituted into equation (3), and the small-signal quadratic term is ignored to obtain the frequency domain expression for the bridge arm potential amplitude E:

[0106] (17)

[0107] In the formula, N(s) = 1 / Ks.

[0108] Voltage-current dual closed-loop modeling: Voltage outer loop reference command frequency domain expression:

[0109] (18)

[0110] In the formula, v vd v vq The virtual impedance voltage drop is expressed in the frequency domain as shown in equation (19).

[0111] (19)

[0112] The three-phase AC feedback signal is subjected to Park transformation to obtain the voltage and current feedback values ​​in the dq axis coordinate system. The phase is represented by the VSG output phase angle θ, and the Park transformation matrix is ​​shown in equation (20):

[0113] (20)

[0114] Linearizing the Park transformation matrix in equation (20) yields:

[0115] (twenty one)

[0116] In the formula, T(Δθ) is the transformation matrix corresponding to the disturbance component, and T(θ0) is the transformation matrix corresponding to the fundamental frequency component. The matrix expressions are (22) and (23) respectively:

[0117] (twenty two)

[0118] (twenty three)

[0119] The three-phase output voltage of the system is transformed by Park transformation using equation (24) to obtain the voltage signal in the two-phase dq coordinate system.

[0120] (twenty four)

[0121] Equation (24) is transformed using Laplace to obtain the frequency domain expression of the output voltage in the dq coordinate system:

[0122] (25)

[0123] (26)

[0124] Similarly, the frequency domain expression for the inductor current can be obtained:

[0125] (27)

[0126] (28)

[0127] Expression of the modulated wave signal in the dq coordinate system:

[0128] (29)

[0129] in:

[0130] (30)

[0131] The expression for the A-phase bridge arm potential of VSG is:

[0132] (31)

[0133] In the formula, e a V is the voltage of the grid-side inverter bridge arm. dc K is the DC side voltage. m C is the modulation coefficient. a The A-phase modulated signal is obtained by the inverse Park transform of equation (29).

[0134] Figure 3 To ignore the coupling effect on the small-signal current response to frequency disturbances, its expression is:

[0135] (32)

[0136] The frequency domain expression for sequence impedance can be expressed as:

[0137] (33)

[0138] Substituting equation (32) into equation (33) and ignoring the coupling effect, we can obtain the expressions for the positive and negative sequence impedances in the dual closed-loop mode:

[0139]

[0140] in,

[0141] (59)

[0142] Similarly, the positive and negative sequence impedance models in open-loop mode can be obtained:

[0143] (35)

[0144] In the formula, R(s) = (L f C f s 2 +R f C f s+Rc C f s+1) / (R c C f s+1), where E is the fundamental frequency amplitude of the bridge arm potential.

[0145] As shown in Figure 4(b), when the system adopts open-loop control mode, the positive-sequence impedance is inductive within 100Hz, while the negative-sequence impedance gradually changes from capacitive to inductive as the frequency increases. After 100Hz, the positive and negative-sequence impedance curves coincide and remain inductive. However, near 1000Hz, the system becomes capacitive again due to the influence of the output filter capacitor. The phase frequency curves show that the system's positive and negative-sequence impedances are generally inductive in the sub- / super-synchronous frequency band, similar to a synchronous generator, and Figure 4(a) shows no intersection with the weak grid impedance, indicating system stability. Figure 5(b) shows that after introducing the voltage-current dual closed-loop control strategy, the negative-sequence impedance is inductive within 100Hz, while the positive-sequence impedance is generally capacitive. In particular, the positive-sequence impedance exhibits negative resistance + capacitive characteristics in the 20Hz-44Hz range. Figure 5(a) shows that the positive-sequence impedance and weak grid impedance curves intersect at 30Hz, at which point the system loses stability. Therefore, introducing a voltage-current dual closed loop causes the system to exhibit capacitive characteristics and localized negative damping within the subsynchronous frequency range, posing a risk of subsynchronous oscillations. To address this subsynchronous oscillation problem caused by negative damping, this invention proposes an oscillation suppression strategy based on a UDE-based additional damping controller.

[0146] Mathematical modeling based on UDE-based additional damping controller:

[0147] UDE Basic Principles: UDE control theory has significant advantages in solving system oscillation problems caused by parameter uncertainties and external disturbances, exhibiting strong system robustness. A brief introduction to the theoretical principles is given using a first-order linear time-invariant system as an example. Consider a first-order dynamic system:

[0148] (36)

[0149] In the formula, x = (x1, ..., xn)T is the control state variable, u(t) = [u1(t), ..., un(t)]T is the system control input, A is the known state variable coefficient matrix, F is the unknown and uncertain state variable coefficient matrix, B is the control coefficient matrix, and satisfies full column rank; d(t) is the external disturbance.

[0150] By setting a reference model, the closed-loop control system can track the reference model to obtain the desired control performance, the expression of which is:

[0151] (37)

[0152] In the formula, x mc(t) represents the state variables and given variables of the reference model. A m B m This refers to the state variable coefficient matrix and control coefficient matrix of the reference model.

[0153] The purpose of setting up a reference model is to select an appropriate control input u(t) so that the system state variable x asymptotically tracks the reference model state variable x. m This allows the state error to gradually converge to 0. The state error formula is shown in equation (38):

[0154] (38)

[0155] Choose a suitable control input u(t) to make equation (39) hold.

[0156] (39)

[0157] In the formula, the error feedback gain K < 0, A m <0.

[0158] By combining equations (36) and (39), we can obtain:

[0159] (40)

[0160] Control input can be represented as:

[0161] (41)

[0162] In the formula, B + Let B be the pseudo-inverse matrix of B. + =(B T B) -1 B T .

[0163] That is, the final condition must be that equation (42) holds.

[0164] (42)

[0165] If B is invertible, then equation (42) holds; if B is not invertible, it can be achieved by selecting a suitable reference model and error feedback gain.

[0166] Transforming equation (41) to the S-domain using Laplace transform, we get:

[0167] (43)

[0168] According to equation (43), we know that:

[0169] (44)

[0170] The core idea of ​​UDE is to treat uncertainties and disturbances in a system as equivalent to lumped disturbances, and then select a filter with appropriate bandwidth to estimate these lumped disturbances.

[0171] Suppose there exists a filter G with unity gain. f If (s) satisfies strict positive real stability and has suitable bandwidth, then UDE can be expressed as:

[0172] (45)

[0173] Therefore, the control law based on UDE can be expressed as:

[0174] (46)

[0175] Substituting equation (45) into equation (46) yields the final expression for the control law:

[0176] (47)

[0177] The control block diagram based on UDE theory is as follows: Figure 6 As shown.

[0178] Design of an Additional Damping Controller Based on UDE: In power systems, additional damping controllers are frequently used as an effective way to suppress oscillations. Traditional additional damping controllers consist of a gain stage, a DC blocking stage, and a phase compensation stage, such as... Figure 7 As shown, traditional additional damping controllers are difficult to adapt to the complex operating conditions of new power systems due to the need for frequent parameter modifications and poor robustness. To improve the adaptability and robustness of additional damping controllers to complex operating conditions, this paper proposes an oscillation suppression strategy based on a UDE-based additional damping controller.

[0179] Based on the VSG stator voltage and current equations, with inductor current as the control variable and bridge arm potential as the control input (voltage compensation), a mathematical model of an additional damping controller based on UDE is established in the double-closed-loop current inner loop. Transforming equation (2) to the dq coordinate system yields the system's first-order state equation:

[0180] (48)

[0181] Further simplification of equation (48) yields the matrix expression:

[0182] (49)

[0183] In the formula: i L =(i Ld i Lq ) T For the control state variable, E = (Ed E q ) T For control input, Δd=(Δi) d , Δi q ) T For lumped disturbances, where:

[0184] (50)

[0185] In equation (50), the inductance L in the denominator of the polynomial f Since Δd is not zero, it can be considered bounded.

[0186] Select a suitable control input E to make the inductor current i L Capable of accurately tracking reference input commands i that do not contain oscillating harmonic components Lref change.

[0187] Therefore, the tracking error e=i Lref - i L The following conditions must be met:

[0188] (51)

[0189] In the formula, A m K iL <0,K iL This is the error feedback gain. It eventually converges to 0, therefore the error equation is asymptotically stable.

[0190] By combining equations (49) and (51), we can obtain:

[0191] (52)

[0192] Therefore, the control input E must satisfy:

[0193] (53)

[0194] In the formula, C is the inductor current setpoint; Δd consists of two parts: the uncertainty of the system's internal parameters and the unknown external disturbances of the system, which are called lumped disturbances.

[0195] The UDE-based additional damping controller can adjust the control input by changing parameters such as feedback gain, reference model, and filter bandwidth, achieving stable tracking of the inductor current to the reference input command and suppressing oscillations. This method does not require specific models of uncertainties and disturbances, but rather summarizes them as lumped disturbances and selects an appropriate filter to estimate these lumped disturbances. Therefore, the choice of filter has a significant impact on the accuracy of the lumped disturbance estimation.

[0196] By selecting an appropriate bandwidth filter to estimate the lumped disturbance, the lumped disturbance based on UDE can be expressed by equation (54):

[0197] (54)

[0198] In the formula, g is the symbol for convolution calculation. f For bandpass filter G f The unit impulse response of G(s) requires that G f (s) Strictly reliable and stable with appropriate bandwidth.

[0199] Replacing Δd in equation (53) with equation (54), we get:

[0200] (55)

[0201] Therefore, the mathematical model of the additional damping controller based on UDE is as follows:

[0202] (56)

[0203] In the formula, G f (s) is g f The Laplace transform; the formula no longer contains uncertainties and unknown disturbance terms.

[0204] Introducing equation (56) into the double closed-loop current loop, its control structure is as follows: Figure 8 As shown. The closed-loop stability of the UDE-based controller is as follows: when the lumped disturbance Δd is bounded, the filter G... f (s) If the closed-loop system is strictly positive real stable and maintains unity output gain within the Δd frequency band while its gain decays to 0 in other ranges, then the closed-loop system is bounded stable.

[0205] Filter Design: Figure 8 Medium compensation voltage E d E q This is the input of the additional damping controller. By adjusting the control input, the inductor current can be stably tracked with the reference value, thereby achieving the effect of oscillation suppression. In the controller design, the filter is required to have its own bandwidth that can cover the lumped disturbance bandwidth. Within the filter bandwidth range, the filter should maintain unity gain output as much as possible, while outside this range, the gain should be 0. By selecting the filter bandwidth, the information in equation (44) can be preserved relatively completely. By selecting a filter with a suitable bandwidth, equations (45) and (44) are approximately equivalent, thereby realizing the estimation of lumped disturbance. When the system disturbance frequency is within the filter bandwidth range, the system can achieve oscillation suppression within a certain range of grid strength, and has good system robustness.

[0206] Since the uncertainty of system oscillation and external interference are in the low-frequency range, this invention selects a first-order low-pass filter G. f (s)=1 / (Ts+1).

[0207] (57)

[0208] In the formula: T is the response time constant. . This represents the upper limit of the lumped disturbance frequency band in the system.

[0209] Substituting equation (57) into equation (47), we get:

[0210] (58)

[0211] As can be seen from equation (58), the UDE-based control model includes a PI regulator and a derivative element based on the reference model. This control strategy exhibits better dynamic performance due to the addition of the derivative element.

[0212] This invention sets the reference model parameter C=i Lref Select the cutoff frequency of the first-order low-pass filter. K iL The bandwidth of the desired error step response should be less than .

[0213] Table 1 Wind turbine system parameters

[0214]

[0215] Time-domain simulation results:

[0216] Simulation conditions: A grid-connected model of a single 3MW direct-drive permanent magnet synchronous wind turbine was built. The oscillation suppression strategy based on a UDE-based additional damping controller was verified through time-domain simulation. System parameters are shown in Table 1. The time-domain simulation experiment was conducted as follows:

[0217] After the wind turbine is connected to the grid normally, at 0.8s, the grid inductance is switched from the normal value to 0.17mH and 0.22mH respectively to simulate different degrees of weak grid oscillation. At 1.8s, two additional damping controllers are activated respectively. At 3.0s, the grid inductance returns to normal, and the oscillation suppression effect is observed.

[0218] After the wind turbine is successfully connected to the grid, at 0.8s, the grid inductance is switched from its normal value to 0.17mH to simulate weak grid oscillation. At 1.8s, the UDE additional damping controller is put into use, and at the same time, step disturbances are set for the grid voltage and active power command. At 3.0s, the grid inductance returns to normal, and the oscillation suppression effect is observed.

[0219] Simulation results comparison:

[0220] Simulation results of oscillation suppression under different grid strengths: When the grid inductance is set to Z1=0.17mH, the wind turbine output current oscillates at 20Hz, while the active and reactive power oscillate at 30Hz. The parameters of the traditional additional damping controller are calculated and set according to this oscillation frequency, and the short-circuit ratio (SCR) is approximately 3. Figure 9 shows that the system begins to oscillate at 0.8s, and the additional damping controller is activated at 1.8s. The simulation curves show that both active and reactive power achieve good oscillation suppression under the action of the two additional damping controllers, and the convergence speed of oscillation suppression based on the UDE additional damping controller is significantly faster than that of the traditional type.

[0221] When the grid inductance is set to Z2 = 0.22mH, constant-amplitude oscillations occur under traditional additional damping control, and oscillation suppression fails. The oscillation frequency also changes under different grid impedances, while the UDE-based additional damping control maintains good oscillation suppression performance, demonstrating good adaptability. The UDE-based additional damping controller treats external disturbances and uncertainties as lumped disturbances and uses a filter with appropriate bandwidth to estimate these disturbances. When the system disturbance frequency is within the filter bandwidth range, the system can achieve oscillation suppression within a certain grid strength range. This control method is advantageous for adapting to complex operating conditions and solves the problem of frequent parameter changes required by traditional additional damping controllers.

[0222] Simulation results under a step voltage disturbance at the grid: Figure 10 shows that when the grid inductance is cut to 0.17mH at 0.8s, the system oscillates. At 1.8s, the UDE-based additional damping controller is activated, and a 40V (5% of the rated voltage) step voltage disturbance is applied simultaneously. From the active and reactive power waveforms in Figure 10, it can be seen that the system reaches a stable state after a brief adjustment following the disturbance, demonstrating good oscillation suppression. The reactive power, under the influence of the droop coefficient, adjusts the voltage through reactive power, resulting in a certain degree of voltage drop, but its oscillation suppression effect remains significant. The adjustment time required by the UDE-based additional damping controller to bring the system to a stable state under a step voltage disturbance is only a few cycles longer than in the case of no disturbance.

[0223] Simulation results under active power command step disturbance: Figure 11 shows that the system oscillates when the grid inductance is cut off to 0.17mH at 0.8s. At 1.8s, the UDE additional damping controller is switched on, and a 1MW active power command step disturbance is applied simultaneously. As can be seen from the active and reactive power curves in Figure 11, the system reaches a stable state after a brief adjustment under the active power command step disturbance. Although the system output active power exhibits a step response, it still demonstrates good oscillation suppression. At the disturbance removal moment, the system experiences significant oscillations, but quickly converges to a stable state under the action of the UDE additional damping controller, demonstrating good anti-interference capability.

Claims

1. A method for suppressing subsynchronous oscillation of a direct-drive permanent magnet synchronous wind turbine under weak grid, the direct-drive permanent magnet synchronous wind turbine comprising: Rotor-side converter, grid-side converter and filter; The grid-side converter of direct-drive permanent magnet synchronous wind turbine adopts virtual synchronous technology(VSG), which is composed of active loop, reactive loop and voltage-current double closed loop. Active power The active loop comprises an active-frequency part and a mechanical part; the reactive loop comprises a reactive-voltage part and an electrical part; the voltage phase is generated by the active loop, the voltage amplitude is generated by the reactive loop, and the bridge arm potential signal e is generated abc The e generated by the power loop abc The mode of directly controlling e as a modulation signal is called "open loop mode", while the mode of controlling e abc The mode of controlling e as a voltage-current double closed loop given value is called "double closed loop mode"; Active loop control part: VSG technology introduces synchronous generator swing equation on the basis of traditional droop control, as shown in equation(1): （1） In the formula, T m , T e are mechanical torque and electromagnetic torque, respectively, , ; P m , P e are mechanical power and electromagnetic power, respectively; δ, are voltage phase and grid rated angular frequency, respectively; J and D are rotational inertia and damping coefficient; VSG outputs active power through active loop control, participates in system primary frequency modulation, and provides inertia support and damps system oscillation for the system; Reactive loop control part: VSG simulates the relationship between voltage and current of synchronous generator stator circuit, which is realized through equation(2): （2） where e = [e a e b e c ] T is the inverter bridge leg midpoint voltage; u = [u a u b u c ] T is the output terminal voltage; i L = [i La i Lb i Lc ] T is the filter inductance current; L s , R are the filter inductance and parasitic resistance, respectively; characterized in that the compensation voltage E d , E q is the additional damping controller input, by adjusting the control input to achieve stable tracking of the inductor current and the reference value, and then play a role in oscillation suppression effect, based on the VSG stator voltage and current equation, the inductor current as the control variable, the bridge arm potential as the control input voltage compensation, in the current inner loop of double closed loop to establish the mathematical model of additional damping controller based on UDE; The first-order state equation of the system is obtained by transforming equation(2) to dq coordinate system: The matrix expression is obtained by further simplifying equation(48): （49） where: i L = (i Ld , Lq ) T is the controlled state variable, E = (E d , E q ) T is the control input, Δd = (Δi d , Δi q ) T is the lumped disturbance, where: （50） The polynomial in the denominator of the expression (50) f Since d ≠ 0, Δd can be considered to be bounded. The appropriate control input E is selected so that the inductor current i L The reference input command i Lref variation; Thus, the tracking error e = i Lref - i L The following needs to be satisfied: （51） where A m , K iL <0, K iL is the error feedback gain; can eventually converge to 0, so the error equation is asymptotically stable; Equations(49) and(51) are combined to obtain: （52） Therefore, the control input E needs to satisfy: （53） wherein C is the inductor current setpoint; Ad is composed of two parts, the uncertainty of system internal parameters and the unknown external disturbance of the system, which is called lumped disturbance; The appropriate bandwidth filter is selected to estimate the lumped disturbance, which can be expressed by equation(54) based on UDE: （54） wherein is the convolution operator, g f is a bandpass filter G f is the unit impulse response of (s), requiring G f (s) to be strictly positive real stable and have a suitable bandwidth; Substitute Δd in equation(53) with equation(54) to obtain: （55） Therefore, the mathematical model of the additional damping controller based on UDE is: （56） where G f (s) is g f the Laplace transform; where the uncertainty and unknown disturbance terms are no longer included Selecting a first order low pass filter G f (s) = 1 / (Ts+1), （57） where T is a response time constant, , is the upper limit of the lumped disturbance frequency band in the system; Substitute equation(57) into equation The following equation is obtained: （58） Setting reference model parameter C = i Lref , selecting a first-order low-pass filter cutoff frequency ; K iL as the bandwidth of the desired error step response, which is less than .

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