Direct-driven wind turbine generator grid-connected low-frequency oscillation damping characteristic analysis and early warning method

Abstract

The invention discloses a direct-driven wind turbine generator grid-connected low-frequency oscillation damping characteristic analysis and early warning method, and belongs to the field of wind power grid-connected system stability operation control. According to the method, a direct-driven wind turbine generator full-order grid-connected mathematical model is constructed, and dominant factors of low-frequency oscillation are identified according to the direct-driven wind turbine generator full-order grid-connected mathematical model; a wind turbine generator grid-connected order reduction model capable of accurately retaining oscillation characteristics is constructed, a direct-driven wind turbine generator damping torque model is constructed according to the order reduction model, and a damping coupling relation between damping paths and a system negative damping forming mechanism under different power grid strengths, operation conditions and control parameters are quantitatively analyzed from the damping angle. A low-frequency oscillation coupling factor induction mechanism is researched, a controller parameter stable operation domain is described, the wind power integration stability is discriminated according to the stable operation domain, and a theoretical basis is provided for early warning of grid-connected low-frequency oscillation instability of a wind turbine generator. The effectiveness and applicability of the analysis method are verified through simulation examples.

Description

Technical Field

[0001] The present invention belongs to the field of wind power grid-connected system stability operation control, and in particular relates to a direct-drive wind turbine grid-connected low-frequency oscillation damping characteristic analysis and early warning method. Background Art

[0002] Wind power generation is connected to the grid through power electronic conversion technology. As the penetration of wind power continues to increase, the dynamic behavior of the power system will gradually evolve from being dominated by synchronous machines to being dominated by power electronic equipment, and the dynamic behavior of the system will undergo fundamental changes. Compared with traditional synchronous generators, the multi-time scale response and weak support capabilities of power electronic equipment have seriously deteriorated the operational stability of wind power grid-connected systems and derived many new stability problems. Among them, oscillation problems frequently occur in wind power grid-connected projects at home and abroad, causing a large number of wind turbines to be disconnected from the grid, and even inducing shaft torsional vibration of conventional generators hundreds of kilometers away. The oscillation problem should not be underestimated. Oscillation has multi-band characteristics, mainly manifested in low-frequency bands and sub-synchronous bands. There are few existing studies on low-frequency oscillations, and the analysis results are often only for a single scenario or a single operating condition. Therefore, it is necessary to quantitatively analyze the low-frequency oscillation mechanism of multi-factor coupling, characterize the controller parameter adjustment range to maintain stable operation of the system under different external operating conditions, and provide practical guidance value for actual wind power grid connection. Summary of the invention

[0003] The purpose of the present invention is to identify the dominant factors of low-frequency oscillations, construct a reduced-order model that accurately retains the dominant factors, analyze the coupling relationship between the damping paths based on the damping torque analysis method, quantitatively analyze the negative damping formation mechanism under different grid strengths, operating conditions and controller parameters, analyze the low-frequency oscillation mechanism of multi-factor coupling, characterize the stable operation domain of wind turbines, and provide a strong reference for the early warning of low-frequency oscillation instability of direct-drive wind turbines connected to the grid.

[0004] To achieve the above object, the present invention proposes a method for analyzing and warning the low-frequency oscillation damping characteristics of a direct-drive wind turbine connected to the grid. The specific technical scheme of the method is as follows:

[0005] Step S1: construct a full-order grid-connected mathematical model of a direct-drive wind turbine, which includes four parts: a main circuit model, a control system model, a phase-locked loop model, and a power grid model; the main circuit model dynamics include the DC capacitor voltage dynamics and the AC filter inductor dynamics; the control link adopts a dual closed-loop control strategy of DC voltage outer loop control and AC current inner loop control; the power grid model includes a line impedance dynamic model;

[0006] Step S2: identifying the dominant factors of low-frequency oscillation based on the full-order grid-connected mathematical model of the direct-drive wind turbine generator set, and constructing a reduced-order model under the system DC voltage time scale;

[0007] Step S3: converting the reduced-order model of the system DC voltage time scale into a multi-loop damping torque model based on the dynamic characteristics of the DC voltage;

[0008] Step S4: quantitatively analyzing the relationship between each damping circuit and the internal operating condition of the wind turbine generator set, the relationship between each damping circuit and the external operating condition of the wind turbine generator set, and the coupling relationship between each damping circuit according to the multi-circuit damping torque model;

[0009] Step S5: clarifying the stability index of the multi-loop damping torque model, and analyzing the damping characteristics of the direct-drive wind turbine grid-connected system based on the stability index;

[0010] Step S6: characterize the stable operation domain of control parameters for avoiding low-frequency oscillation of the system under different external operating conditions of wind turbines, and provide a theoretical reference for early warning of low-frequency oscillation instability of wind power grid connection.

[0011] Furthermore, the full-order grid-connected mathematical model of the direct-drive wind turbine in step S1 is based on the topological structure of the direct-drive wind turbine; the main circuit model:

[0012]

[0013] In the formula, C represents the DC capacitance value, ω represents the oscillation angular frequency, and L f represents the filter inductance, u dc Represents the DC capacitor voltage; i d 、i q Respectively represent the d-axis and q-axis components of the converter output current; e d 、e q They represent the d-axis and q-axis components of the converter port voltage respectively; u td 、u tq Respectively represent the d-axis and q-axis components of the grid-connected point voltage; P in , P out They represent the injected power and delivered power of wind turbines respectively;

[0014] Control system model:

[0015]

[0016] In the formula, k p1 , k p2 , k p4 They represent the proportionality coefficients of the voltage outer loop, the active current inner loop, and the reactive current inner loop respectively; k i1 , k i2 , k i4 They represent the integral coefficients of the voltage outer loop, active current inner loop and reactive current inner loop respectively; u dcref 、i qrefThey represent the expected values ​​of the DC side capacitor voltage and reactive current respectively; x1, x2, x3 represent the indirect state variables of the voltage outer loop, current active inner loop, and current reactive outer loop control links respectively; e d 、e q They represent the d-axis and q-axis components of the converter port voltage respectively.

[0017] Phase-locked loop model:

[0018]

[0019] In the formula, k pp and k ip They represent the proportional coefficient and integral coefficient of the phase-locked loop control link, ω0 represents the reference angular frequency, u tq represents the q-axis component of the grid-connected point voltage in the control coordinate system, x pll It represents the intermediate variable of the phase-locked loop control link, and s is the Laplace transform complex variable;

[0020] Mathematical model of power grid:

[0021]

[0022] Where, L g is the line inductance, i x 、i y They are respectively represented as the x-axis and y-axis components of the line current in the main circuit coordinate system; u gx 、u gy They are respectively represented as the grid voltage u g The x and y axis components in the main circuit coordinate system; u tx 、u ty They are respectively expressed as the x-axis and y-axis components of the grid connection point voltage in the main circuit coordinate system; the d-axis and q-axis components of the grid voltage, grid connection point voltage and wind turbine output current in the control coordinate system and the x-axis and y-axis components in the main circuit coordinate system satisfy the following relationship:

[0023]

[0024] Formulas (1)-(6) are combined, and the state space equation is linearized at the equilibrium point to obtain the small signal state space model of the system. The model contains 8 state variables, including 3 main circuit state variables Δi d , Δi q , Δu dc And the five control link state variables Δx1, Δx2, Δx3, Δx pll , Δθ pll .

[0025] Furthermore, the process of identifying the dominant factors of low-frequency oscillation according to the full-order grid-connected mathematical model of the direct-drive wind turbine generator set and constructing a reduced-order model on the system DC voltage time scale in step S2 is as follows:

[0026] The following conditions are set: 1) The machine side is equivalent to a controlled current source; 2) The current inner loop control bandwidth is much higher than the voltage outer loop and phase-locked loop bandwidth, that is, before the DC voltage outer loop and phase-locked loop control action, the current has tracked the reference value; Based on the set conditions, the system reduced-order model includes four parts: main circuit model, control system model, phase-locked loop model and power grid model. The construction of the main circuit model, phase-locked loop model and power grid model is the same as that of the full-order system. The difference is that the control system ignores the current inner loop control, as follows:

[0027]

[0028] The construction of the phase-locked loop model and the power grid model is the same as that of the full-order system. Based on formulas (3)-(7), the small signal state space model of the reduced-order system is as follows:

[0029]

[0030] In the formula, i dc0 is the initial current of the DC capacitor, i d0 is the initial value of the d-axis current of the converter output current, u td0 is the initial value of the d-axis component of the grid-connected point voltage, u tdc0 is the initial value of the DC capacitor voltage.

[0031] Further, in step S3, the process of converting the reduced-order model of the system DC voltage time scale into a multi-loop damping torque model based on the DC voltage dynamic characteristics is as follows:

[0032] Relative density of ΔP and Δu dc The relationship is similar to the relationship between the second-order rotor motion equation ΔP and Δω:

[0033]

[0034]

[0035] Other control links are analogous to the damping link and the synchronization link:

[0036]

[0037] ΔP out2 =i d0 Δu td (12)

[0038] Δu td =-i d0 ωLg Δθ pll (13)

[0039]

[0040] Based on formula (9)-formula (15), the multi-loop damping torque model contains three damping loops, and the damping coefficient and synchronization coefficient of each loop are:

[0041]

[0042] By adding up all the feedback links, the total damping coefficient and synchronization coefficient of the system can be obtained as follows:

[0043]

[0044] Where D0, D1, and D2 represent the damping coefficients of each circuit respectively, K0, K1, and K2 represent the synchronization coefficients of each circuit respectively, and D and K represent the total damping and total equivalent synchronization coefficient of the system respectively.

[0045] Furthermore, the direct-drive wind turbine grid-connected low-frequency oscillation damping characteristic analysis and early warning method, step S4 specifically includes:

[0046] Let s = jω s Substituting into each damping loop formula (16)-formula (19), we can get

[0047]

[0048] In the formula, ω s is the oscillation frequency under different grid strengths, wind turbine operating conditions and control parameters; Im and Re represent the real and imaginary parts of the complex number, respectively.

[0049] Loop G dc0 Damping D0 presents negative damping characteristics, which is determined only by the working conditions of the wind turbine. As the working conditions increase, the negative damping characteristics increase, and the system stability decreases. dc1 Damping D1 presents positive damping characteristics. The damping is determined by the outer loop proportional coefficient and is not affected by the grid strength and working conditions. dc2 The damping of damping D2 is affected by the grid strength, wind turbine operating conditions, and control parameter conditions, and presents a negative damping characteristic. Under low operating conditions and strong grids, the magnitude of the negative damping coefficient is very small and can be almost ignored. However, as the wind turbine operating conditions increase and the grid strength weakens, the magnitude of the negative damping coefficient gradually increases, and the rate of increase is negatively correlated with the grid strength and positively correlated with the operating conditions.

[0050] There is a loop G between each damping loop dc0 and loop G dc2The coupling relationship with the wind turbine operating conditions shows that the negative damping of the two circuits increases with the increase of wind turbine operating conditions, and they are equally affected by the wind turbine operating conditions. dc1 and loop G dc2 Coupling relationship with the outer loop proportional coefficient, loop G dc1 The positive damping coefficient is positively correlated with the outer loop proportional coefficient, while the loop G dc2 The negative damping coefficient is negatively correlated with the voltage outer loop proportional coefficient, that is, the outer loop proportional coefficient has a mutual constraint on the two damping loops. Within the same proportional coefficient variation range, loop G dc1 The increase in positive damping ΔD1 is greater than loop G dc2 The negative damping increases by ΔD2, that is, increasing the outer loop proportional coefficient, and the overall positive damping of the system shows an increasing trend.

[0051] Furthermore, the direct-drive wind turbine grid-connected low-frequency oscillation damping characteristic analysis and early warning method, step S5 specifically includes:

[0052] According to formula (19), D and K represent the total equivalent damping coefficient and the total equivalent synchronization coefficient of the model respectively, and the stability index is defined as follows:

[0053]

[0054] The influence of grid strength and working conditions on equivalent synchronization coefficient:

[0055] The synchronization coefficient K of the damping torque model under different working conditions and grid strengths shows an increasing trend with the decrease of wind turbine working conditions and SCR, and its value deviates far from K = 0 and is always greater than zero. Therefore, in the process of stability analysis and stability margin division, the influence of the synchronization coefficient in the stability index is not considered for the time being;

[0056] The influence of grid strength and working conditions on the total damping of the system:

[0057] Based on the stability index formula (21), the influence of grid strength and wind turbine operating conditions on the total damping of the system is quantitatively evaluated. As the wind turbine operating conditions increase and the grid strength decreases, the system damping shows a downward trend, and the stability decreases. In addition, the system has negative damping in weak grid SCR≤2.6 and high operating conditions, that is, the system is unstable. The operating conditions and grid strength corresponding to the critical instability point, i.e., D=0, are shown as follows:

[0058] When SCR=1.4, P in =1.17MW, the total system damping D=0. As the wind turbine operating conditions increase, the total system damping D<0, resulting in low-frequency oscillation instability.

[0059] When SCR=2, P in=1.36MW, the total system damping D=0. As the wind turbine operating conditions increase, the total system damping D<0, resulting in low-frequency oscillation instability.

[0060] When SCR=2.6, P in =1.48MW, the total system damping D=0. As the wind turbine operating conditions increase, the total system damping D<0, resulting in low-frequency oscillation instability.

[0061] When the grid strength is weaker than the critical instability point or the operating condition is greater than the critical instability point, the system damping is negative and low-frequency oscillation instability occurs; therefore, as the operating condition of the wind turbine increases, the system damping decreases and the stability decreases; as the grid strength decreases, the stable operating condition range of the wind turbine increases and the stability increases.

[0062] Specifically, the direct-drive wind turbine grid-connected low-frequency oscillation damping characteristic analysis and early warning method, step S6 describes the stable operation domain of the control parameters of the system to avoid low-frequency oscillation under different wind turbine external operating conditions:

[0063] When SCR = 2, the outer ring proportional coefficient k p1 When k > 2.9, the system remains stable in the full range of operating conditions; p1 <0.5, at P in In the higher operating range of >0.8MW, the system damping is always negative;

[0064] When SCR = 1.4, the outer ring proportional coefficient k p1 >3.5, the system remains stable in the full range of operating conditions; p1 <0.45, at P in >0.8MW In the higher operating range, the system damping is always negative;

[0065] As the operating conditions of SCR and wind turbines decrease, the stable operating area of ​​the proportional coefficient becomes smaller; and to ensure stable operation, the outer loop proportional coefficient should be appropriately increased; that is, increasing the outer loop proportional coefficient improves the stability of the system under high operating conditions and weak power grid conditions;

[0066] When SCR = 2, the outer loop integral coefficient k i1 When k > 160, the system can remain stable in the full range of working conditions; i1 When <75, in >0.8MW high operating range, the system damping is always negative;

[0067] When SCR = 1.4, the outer loop integral coefficient k i1 >242, the system can remain stable in the full range of operating conditions; i1 When <80, in >0.8MW In the higher operating range, the system damping is always negative;

[0068] As the SCR and wind turbine operating conditions decrease, k i1 The stable operating domain is reduced. In order to ensure the stable operation of the system, the integral coefficient is increased, that is, the outer loop integral coefficient is increased to improve the stability of the system under high operating conditions and weak power grid conditions.

[0069] Through the above design scheme, the present invention can bring the following beneficial effects: the present invention aims at the low-frequency oscillation problem caused by the direct-drive wind turbine grid connection, identifies the dominant factors of low-frequency oscillation, constructs a wind turbine grid connection reduced-order model that can accurately retain the oscillation characteristics, constructs a multi-loop damping torque model of the direct-drive wind turbine based on the reduced-order model, quantitatively analyzes the damping coupling relationship between the damping paths and the system negative damping formation mechanism under different grid strengths, operating conditions and control parameters from the damping perspective, studies the induction mechanism of low-frequency oscillation coupling factors and characterizes the stable operation domain of controller parameters, and judges the stability of wind power grid connection based on the stable operation domain, providing a theoretical basis for the early warning of low-frequency oscillation instability of wind turbine grid connection. The effectiveness and applicability of the proposed analysis method are verified by simulation examples. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] The accompanying drawings herein are used to provide a further understanding of the present invention and constitute a part of the present application. The exemplary embodiments of the present invention and their descriptions are used to understand the present invention and do not constitute improper limitations of the present invention. In the accompanying drawings:

[0071] Figure 1 This is a schematic diagram of the structure of the converter control system on the grid side of the direct-drive wind turbine;

[0072] Figure 2(a) is a diagram of the phase-locked loop control structure;

[0073] Figure 2(b) is a schematic diagram of the phase-locked loop control principle;

[0074] Figure 3 is the participation factor of the dominant low-frequency oscillation eigenvalue;

[0075] Figure 4 This is a schematic diagram of the reduced-order model structure of a direct-drive wind turbine;

[0076] Figure 5 It is the multi-circuit damping torque model of direct-drive wind turbine;

[0077] Figure 6(a) shows the oscillation frequency under different operating conditions and grid strength;

[0078] Figure 6(b) shows the oscillation frequency under different outer loop proportional coefficients and integral coefficients;

[0079] Figure 7(a) is the characteristic curve of the damping coefficient D1 at different outer ring proportional coefficients;

[0080] Figure 7(b) is the characteristic curve of the damping coefficient D2 under different outer loop integral coefficients;

[0081] Figure 7(c) shows the characteristic curve of the damping coefficient D2 under different outer ring proportional coefficients;

[0082] Figure 7(d) shows the characteristic curve of the damping coefficient D2 under different grid strengths;

[0083] Figure 8 It is the comparison curve of the damping characteristics of the coupled damping loop as the coupling factor changes;

[0084] Fig. 9 The variation of system synchronization coefficient with working conditions under different power grid strengths;

[0085] Fig.10 The variation of system damping coefficient with working conditions under different power grid strengths;

[0086] Fig.11 The system damping changes with working conditions under different proportional control parameters;

[0087] Fig.12 It is the stable adjustment range of proportional control parameters under different grid strengths and working conditions;

[0088] Fig.13 The system damping changes with working conditions under different integral control parameters;

[0089] Fig.14 It is the stable adjustment range of integral control parameters under different grid strengths and working conditions;

[0090] FIG15( a ) is a simulation curve of system power and DC side capacitor voltage when the external power is switched from 1.1MW to 1.2MW when SCR=1.4;

[0091] FIG15( b ) is a simulation curve of system power and DC side capacitor voltage when the external power is switched from 1.3 MW to 1.4 MW when SCR=2;

[0092] FIG15( c ) is a simulation curve of system power and DC side capacitor voltage when the external power is switched from 1.4 MW to 1.5 MW when SCR=2.6;

[0093] FIG15( d ) is a simulation curve diagram of system power and DC side capacitor voltage in the full operating range when SCR=3.2;

[0094] Figure 16(a) shows the p1 =2.1, SCR=2, the system power and DC side capacitor voltage simulation curves in the full operating range;

[0095] Figure 16(b) shows kp1 When switching from 0.7 to 0.95 and SCR=2, the system power and DC side capacitor voltage simulation curves are shown when the external power is 0.9MW;

[0096] Figure 16(c) shows the p1 =3.6, SCR = 1.4, the system power and DC side capacitor voltage simulation curves in the full operating range;

[0097] Figure 16(d) shows the k when SCR = 1.4 and the external power is switched from 0.6MW to 0.9MW. p1 Simulation curves of system power and DC side capacitor voltage when the values ​​are 0.8, 0.95, and 1.1;

[0098] Figure 17(a) shows the i1 =160, SCR=2, the system power and DC side capacitor voltage simulation curve within the full operating range;

[0099] Figure 17(b) shows the k when SCR=2 and the external power is switched from 0.6MW to 0.9MW. i1 The simulation curves of system power and DC side capacitor voltage when the values ​​are equal to 78 and 104;

[0100] Figure 17(c) shows the p1 =239, SCR=1.4, the system power and DC side capacitor voltage simulation curves in the full operating range;

[0101] Figure 17(d) shows the k when SCR = 1.4 and the external power is switched from 0.6MW to 0.9MW. p1 The simulation curves of system power and DC side capacitor voltage when it is equal to 86, 104, and 120;

[0102] Fig.18 This is a flow chart of the low-frequency oscillation early warning method for direct-drive wind turbines connected to the grid;

[0103] Fig.19 This is a process flow chart for the analysis of low-frequency oscillation damping characteristics and early warning methods for direct-drive wind turbines connected to the grid. DETAILED DESCRIPTION

[0104] In order to better understand the purpose, structure and function of the present invention, the following is a further detailed description of a direct-drive wind turbine grid-connected low-frequency oscillation damping characteristic analysis and early warning method of the present invention in conjunction with the accompanying drawings.

[0105] See also Fig.18 and Fig.19As shown, firstly, a full-order grid-connected mathematical model of direct-drive wind turbines is constructed, which includes four parts: main circuit model, control system model, phase-locked loop model and power grid model; according to the mathematical model, the dominant factors of low-frequency oscillation are identified, and a reduced-order model under the system DC voltage time scale is constructed; based on the dynamic characteristics of DC voltage (i.e., the expression of external power increment), the reduced-order model is constructed as a multi-loop damping torque model; according to the multi-loop damping torque model, the relationship between each damping loop and the internal operating conditions of the wind turbine, each damping loop and the external operating conditions of the wind turbine, and the coupling relationship between each damping loop are quantitatively analyzed; the stability index of the multi-loop damping torque model is clarified, and the damping characteristics of the grid-connected system of direct-drive wind turbines with external operating conditions are analyzed according to the stability index; the stable adjustment domain of the control parameters to avoid low-frequency oscillations in the system under different external operating conditions is characterized. Specifically, it includes:

[0106] 1) Mathematical model of full-order grid-connected direct-drive wind turbines

[0107] The full-order grid-connected mathematical model of direct-drive wind turbines consists of four parts: main circuit model, control system model, phase-locked loop model and power grid model;

[0108] Main circuit model:

[0109]

[0110] In the formula, C represents the DC capacitance value, ω represents the oscillation angular frequency, and L f represents the filter inductance, u dc Represents the DC capacitor voltage; i d 、i q Respectively represent the d-axis and q-axis components of the converter output current; e d 、e q They represent the d-axis and q-axis components of the converter port voltage respectively; u td 、u tq Respectively represent the d-axis and q-axis components of the grid-connected point voltage; P in , P out They represent the injected power and delivered power of wind turbines respectively;

[0111] Control system model:

[0112] The structure of the direct-drive wind turbine grid-side converter control system is as follows: Figure 1 As shown in the figure, the system DC voltage dynamic deviation value generates the expected value of active current through the outer loop controller. To achieve unity power factor power generation, the expected value of reactive current is set to 0. Under the constraints of the main circuit dynamic equation, the active current deviation generates the expected value of the converter terminal voltage d-axis component e through the PI controller. d The reactive current deviation is generated by the PI controller to generate the expected value of the converter terminal voltage q-axis component e q, the active / reactive current is regulated by controlling the voltage. The state model of the control link is as follows:

[0113] Control system model:

[0114]

[0115] In the formula, k p1 , k p2 , k p4 They represent the proportionality coefficients of the voltage outer loop, the active current inner loop, and the reactive current inner loop respectively; k i1 , k i2 , k i4 They represent the integral coefficients of the voltage outer loop, active current inner loop and reactive current inner loop respectively; u dcref 、i qref They represent the expected values ​​of the DC side capacitor voltage and reactive current respectively; x1, x2, x3 represent the indirect state variables of the voltage outer loop, current active inner loop, and current reactive outer loop control links respectively; e d 、e q They represent the d-axis and q-axis components of the converter port voltage respectively.

[0116] The phase-locked loop (PLL) is used to synchronize the output of the grid-connected converter with the AC power grid. Its control structure and principle are shown in Figure 2(a) and Figure 2(b). In steady state, the d-axis of the phase-locked loop coincides with the voltage vector of the grid-connected point (i.e., u tq = 0), when the phase-locked loop d-axis deviates from the grid-connected point voltage vector, u tq The offset is used as the PI controller input to generate the angular frequency deviation to achieve synchronous rotation of the phase-locked loop and the grid-connected point voltage vector. That is, by tracking the grid-connected point voltage phase θ, the phase angle θ of the control system coordinate system is given. pll , x / y is defined as the grid coordinate system and is determined by the grid connection point voltage phase angle θ; d / q is the control system coordinate system, which is determined by the phase-locked loop output phase angle θ pll The PLL mathematical model is shown in equation (3) and equation (4).

[0117]

[0118] In the formula, k pp and k ip They represent the proportional coefficient and integral coefficient of the phase-locked loop control link, ω0 represents the reference angular frequency, u tq represents the q-axis component of the grid-connected point voltage in the control coordinate system, x pll represents the intermediate variable of the phase-locked loop control link, s is the Laplace transform complex variable; the relationship between the x / y axis component of the electrical quantity F in the power grid coordinate system and the d / q axis component in the control system coordinate system is:

[0119]

[0120] Among them, f d 、f q Represents the d-axis and q-axis components of the system electrical quantity F in the control system coordinate system; f x 、f y Represents the x-axis and y-axis components of the system electrical quantity F in the grid coordinate system;

[0121] Mathematical model of power grid:

[0122]

[0123] Where, L g is the line inductance, i x 、i y They are respectively represented as the x-axis and y-axis components of the line current in the main circuit coordinate system; u gx 、u gy They are respectively represented as the grid voltage u g The x-axis and y-axis components in the main circuit coordinate system; u tx 、u ty They are respectively expressed as the x-axis and y-axis components of the grid connection point voltage in the main circuit coordinate system; the d-axis and q-axis components of the grid voltage, grid connection point voltage and wind turbine output current in the control coordinate system and the x-axis and y-axis components in the main circuit coordinate system satisfy the following relationship:

[0124]

[0125] Formulas (1)-(6) are combined, and the state space equation is linearized at the equilibrium point to obtain the small signal state space model of the system. The model contains 8 state variables, including 3 main circuit state variables Δi d , Δi q , Δu dc And the five control link state variables Δx1, Δx2, Δx3, Δx pll , Δθ pll .

[0126] 2) Identification of dominant factors and model reduction

[0127] According to the electrical parameters and control parameters shown in Table 1 and Table 2, the system is SCR = 2, P in The characteristic values ​​when =1.2MW are shown in Table 2.

[0128] Table 1 System electrical parameters

[0129]

[0130] Table 2 System control parameters

[0131]

[0132] Table 3 System characteristic values

[0133]

[0134] The system eigenvalues ​​include two high-frequency oscillation modes λ 5 / 6 , 7 / 8 and two low frequency oscillation modes λ 1 / 2 , 3 / 4 , where λ 1 / 2 is the dominant eigenvalue of low-frequency oscillation. In order to identify the dominant factors affecting the low-frequency oscillation mode, For λ 1 / 2 The participation factor is analyzed, where v i is the i-th eigenvector, and x is the state variable. The participation factor of the dominant low-frequency oscillation mode eigenvalue is as follows: Figure 3 As shown. For the eigenvalue λ 1 / 2 The dominant oscillation mode is mainly affected by the voltage outer loop control, and is also affected by the phase-locked loop control link, but the influence is smaller. The current inner loop control has almost no effect on λ 1 / 2 The influence of is almost 0, and it is mainly affected by the voltage outer loop.

[0135] In order to analyze the mechanism of the dominant factors on low-frequency oscillation, the full-order grid-connected model of wind turbines is reduced.

[0136] The set conditions are as follows: 1) The machine side is equivalent to a controlled current source; 2) The current inner loop control bandwidth is much higher than the voltage outer loop and phase-locked loop bandwidth, that is, before the DC voltage outer loop and phase-locked loop control action, the current has tracked the reference value. Based on the set conditions, the system reduced-order model is as follows Figure 4 As shown, it includes four parts: main circuit model, control system model, phase-locked loop model and power grid model. The construction of the main circuit model, phase-locked loop model and power grid model is the same as that of the full-order system. The difference is that the control system ignores the current inner loop control, as follows:

[0137]

[0138] The construction of the phase-locked loop model and the power grid model is the same as that of the full-order system. Based on formulas (3)-(7), the small signal state space model of the reduced-order system is as follows:

[0139]

[0140] In the formula, i dc0 is the initial current of the DC capacitor, i d0 is the initial value of the d-axis current of the converter output current, u td0 is the initial value of the d-axis component of the grid-connected point voltage, u tdc0is the initial value of the DC capacitor voltage.

[0141] To ensure that the simplified model can accurately retain the low-frequency oscillation characteristics of the full-order model, based on the electrical and control parameters in Tables 1 and 2, SCR = 2, P in =1.2MW, the eigenvalues ​​of the reduced-order model are calculated, as shown in Table 4. Comparing Tables 3 and 4, it can be seen that the eigenvalues ​​of the reduced-order model and the full-order model that dominate the low-frequency oscillation are the same, that is, the simplified model and the full-order model have the same low-frequency oscillation mode. Next, a damping torque model of DC voltage scale is constructed based on the simplified model to analyze the low-frequency oscillation mechanism of the system.

[0142] Table 4 Eigenvalues ​​of the reduced-order model

[0143]

[0144] 3) Construction of multi-loop damping torque model

[0145] Analogizing the DC capacitor dynamics to the second-order rotor dynamics:

[0146]

[0147]

[0148] The other control links are analogous to the damping link and the synchronization link:

[0149]

[0150] ΔP out2 =i d0 Δu td (12)

[0151] Δu td =-i d0 ωL g Δθ pll (13)

[0152]

[0153] Let G pll =k pp +k ip / s,J=u td0 , establish as Figure 5 The multi-loop damping torque model shown in FIG. 1 uses the DC voltage dynamics as the forward loop. The model contains three damping loops, and the transfer function of each feedback link is:

[0154]

[0155] By adding up all the feedback links, the total damping coefficient and synchronization coefficient of the system can be obtained as follows:

[0156]

[0157] Where D0, D1, and D2 represent the damping coefficients of each circuit respectively, K0, K1, and K2 represent the synchronization coefficients of each circuit respectively, and D and K represent the total damping and total equivalent synchronization coefficient of the system respectively.

[0158] 4) Analysis of damping characteristics and coupling effects of each circuit

[0159] Oscillation frequencyω s The changes of operating conditions, grid strength and control parameters are shown in Figure 6(a) and Figure 6(b). s Substituting each damping loop into formulas (16) to (19), we can obtain the damping characteristics of each loop.

[0160]

[0161] In the formula, ω s is the oscillation frequency under different grid strengths, wind turbine operating conditions and control parameters. Im and Re represent the real and imaginary parts of the complex number, respectively.

[0162] According to formula (19), D and K represent the total equivalent damping coefficient and the total equivalent synchronization coefficient of the model respectively, and the stability index is defined as follows:

[0163]

[0164] From formula (21), we can know that path G d1 It presents a positive damping characteristic and is only affected by the outer loop proportional control parameter. The damping coefficient increases with the increase of the outer loop proportional coefficient. d1 The curve of the damping characteristics changing with the outer loop proportional coefficient is shown in Figure 7(a). d0 It has a negative damping characteristic, which is determined only by the working condition of the wind turbine. As the working condition increases, the negative damping characteristic increases, and the system stability decreases. Path G d0 The curve of the damping characteristics changing with the working condition is shown in Figure 7(b); loop G d2 The damping of is affected by the combined effects of the grid strength and the wind turbine operating conditions, and presents a negative damping characteristic. Under low operating conditions and strong grids, the magnitude of the negative damping coefficient is very small (almost negligible), but as the wind turbine operating conditions increase and the grid strength weakens, the magnitude of the negative damping coefficient gradually increases (and the rate of increase is negatively correlated with the grid strength and positively correlated with the operating conditions). d2 The variation of damping characteristics with grid strength and operating conditions is shown in Figure 7(c) and Figure 7(d).

[0165] According to the above analysis, the influencing factors of the damping of each loop are quite different and there is a coupling relationship.d0 and G d2 Both are affected by the working conditions of the wind turbine. The damping characteristic curve shows that the damping of the two circuits is affected by the working conditions of the wind turbine in the same trend, that is, with the change of working conditions, the damping of the two circuits shows a cooperative relationship, and with the increase of working conditions, this cooperative relationship provides more negative damping, and the system stability decreases. Similarly, loop G d1 and G d2 Both are affected by the outer loop proportional coefficient, loop G d1 The positive damping coefficient is positively correlated with the outer loop proportional coefficient, while the loop G d2 The negative damping coefficient is negatively correlated with the voltage outer loop proportional coefficient, that is, the outer loop proportional coefficient has a competitive effect on the damping of the two paths. p1 Increase, its G d1 The mechanism of the loop contributes to the stability of the system, and in G d2 The mechanism of action is not conducive to the stability of the system. To clarify this contradictory relationship, the loop G within the same outer loop proportional coefficient variation range is compared. d1 and G d2 The damping characteristic curve is as follows: Figure 8 As shown, loop G d1 The increase in positive damping ΔD1 is greater than loop G d2 The negative damping increases by ΔD2, that is, increasing the outer loop proportional coefficient, and the overall positive damping of the system shows an increasing trend. Fig. 9 The variation of system synchronization coefficient with working conditions under different power grid strengths; Fig.10 The variation of system damping coefficient with working conditions under different power grid strengths; Fig.11 The system damping changes with working conditions under different proportional control parameters; Fig.12 It is the stable adjustment range of proportional control parameters under different grid strengths and working conditions; Fig.13 The system damping changes with working conditions under different integral control parameters; Fig.14 It is the stable adjustment range of integral control parameters under different grid strengths and working conditions.

[0166] 5) Specific example: A PSCAD simulation model of a direct-drive wind turbine grid-connected system is built. Based on the electrical parameters and control parameters in Tables 1 and 2, the low-frequency oscillation characteristics of the system affected by the coupling effects of multiple factors of the external and internal operating conditions of the wind turbine are analyzed and verified.

[0167] Through the above damping characteristics analysis, it can be seen that when SCR = 1.4, when P in When SCR is 1.17MW, the system damping is always less than 0. The simulation results in Figure 15(a) show that when SCR = 1.4, the system will experience low-frequency oscillation instability when the external power is switched from 1.1MW to 1.2MW in 5 seconds, and the oscillation frequency is 2.8Hz; when SCR = 2, when P inWhen SCR = 2, the system damping is always less than 0 when the external power is switched from 1.3MW to 1.4MW in 5 seconds. The simulation results in Figure 15(b) show that when SCR = 2, the system becomes unstable due to low-frequency oscillation, and the oscillation frequency is 3.1Hz. When SCR = 2.6, when P in When SCR is greater than 1.48MW, the system damping is always less than 0. The simulation results in Figure 15(c) show that when SCR=2.6, the external power is switched from 1.4MW to 1.5MW in 5 seconds, and the system becomes unstable due to low-frequency oscillation, with an oscillation frequency of 3.2Hz. When SCR≥3.2, the system can remain stable in the full range of operating conditions. The simulation results in Figure 15(d) show that when SCR=3.2, the system external power is gradually increased from 0.5MW to 1.5MW. In the full range of operating conditions, the system power is in a decaying oscillation and can operate stably.

[0168] From the damping characteristics analysis, we know that when SCR = 2, the outer loop proportional coefficient k p1 When k > 2.04, the system remains stable in the full range of working conditions. The results in Figure 16(a) show that p1 =2.1, the system power output is gradually increased from 0.5MW to 1.5MW. In the full range of operating conditions, the system power is in a decaying oscillation and can operate stably. p1 <2.04, in the higher working range (P in >0.8MW) system damping is always negative. The results in Figure 16(b) show that when P in =0.6MW, k p1 =0.7, the system runs stably, and at 5 seconds P in When the system increases to 0.9MW, low-frequency oscillation instability occurs, and the oscillation frequency is 3.5Hz. At 9 seconds, k p1 When it increases to 0.95, the system changes from low-frequency oscillation to attenuated oscillation, and the system becomes stable.

[0169] When SCR=1.4, the outer ring proportional coefficient k p1 When k > 3.59, the system remains stable in the full range of working conditions. The results in Figure 16(c) show that p1 =3.6, the system output power is gradually increased from 0.5MW to 1.5MW, and the system can operate stably in the full range of operating conditions; p1 <0.84, in the higher working range (P in >0.8MW) system damping is always negative. The results in Figure 16(d) show that when P in =0.6MW, k p1 =0.8, the system runs stably, and at 5 seconds P in When the system increases to 0.9MW, low-frequency oscillation instability occurs, and the oscillation frequency is 3.5Hz. At 7 seconds, kp1 Switching to 0.95, the system still oscillates at a low frequency. At 9 seconds, k p1 Switching to 1.1, the system power shows attenuated oscillation and remains stable. As the SCR decreases and the operating conditions increase, k should be increased within the stable operating range. p1 , which can improve system stability.

[0170] From the damping characteristics analysis, we know that when SCR = 2, the outer loop integral coefficient k i1 When k > 165, the system remains stable in the full range of operating conditions. The results in Figure 17(a) show that i1 =170, the system power output is gradually increased from 0.5MW to 1.5MW. In the full range of operating conditions, the system power shows attenuated oscillation and can operate stably. i1 <78.2, in the higher working range (P in >0.8MW) system damping is always negative. The results in Figure 17(b) show that when P in =0.6MW, k i1 =78, the system runs stably, and at 5 seconds P in When the system increases to 0.9MW, low-frequency oscillation instability occurs, and the oscillation frequency is 3.1Hz. At 9 seconds, k i1 When it increases to 104, the system changes from low-frequency oscillation to attenuated oscillation, and the system becomes stable.

[0171] When SCR=1.4, the outer loop integral coefficient k i1 When k > 238, the system remains stable in the full range of working conditions. The results in Figure 17(c) show that i1 =239, the system power output is gradually increased from 0.5MW to 1.5MW. In the full range of operating conditions, the system power shows attenuated oscillation and can operate stably. i1 <86.5, in the higher working range (P in >0.8MW) system damping is always negative. The results in Figure 17(d) show that when P in =0.6MW, k i1 =86, the system runs stably, and at 5 seconds P in When the system increases to 0.9MW, low-frequency oscillation instability occurs, and the oscillation frequency is 3.3Hz. At 7 seconds, k i1 Switching to 104, the system still oscillates at a low frequency of 3.6 Hz. At 9 seconds, k i1 Switching to 120, the system power shows attenuated oscillation and remains stable. As the SCR decreases and the operating conditions increase, k should be increased within the stable operating area. i1 , which can improve system stability.

[0172] In summary, as the operating conditions of wind turbines increase and the strength of the power grid decreases, the risk of low-frequency oscillation instability increases. From an engineering practice perspective, even if the wind power plant can achieve stable operation under all operating conditions under the set control parameters, as the strength of the power grid decreases, the operating conditions, control links, and the interaction between the operating conditions will cause the system to exhibit negative damping characteristics, resulting in low-frequency oscillation instability. At this time, the control parameters are no longer applicable. The analysis of the damping characteristics and coupling effects of each circuit in 4) above shows that increasing the proportional coefficient and the integral coefficient can avoid the system's low-frequency oscillation instability to a certain extent. Based on the constructed stable operation domain, a parameter adjustment reference is provided for the wind turbine grid connection to ensure that the wind turbine can maintain a stable operation system under different operating conditions and power grid strengths, and an effective early warning is provided for low-frequency oscillation instability. The early warning mechanism is as follows: Fig.19 As shown, under the proposed wind turbine operating conditions and grid strength, the stability of the system is judged based on whether the wind turbine control parameters are in the stable operating area, and a reference is given to parameter adjustment. The key lies in the accuracy of the stable operating domain characterization.

Claims

1. A method for analyzing and warning the low-frequency oscillation damping characteristics of a direct-drive wind turbine connected to the grid, characterized in that: The method comprises the following steps: Step S1: construct a full-order grid-connected mathematical model of a direct-drive wind turbine, which includes four parts: a main circuit model, a control system model, a phase-locked loop model, and a power grid model; the main circuit model dynamics include the DC capacitor voltage dynamics and the AC filter inductor dynamics; the control link adopts a dual closed-loop control strategy of DC voltage outer loop control and AC current inner loop control; the power grid model includes a line impedance dynamic model; Step S2: identifying the dominant factors of low-frequency oscillation based on the full-order grid-connected mathematical model of the direct-drive wind turbine generator set, and constructing a reduced-order model under the system DC voltage time scale; Step S3: converting the reduced-order model of the system DC voltage time scale into a multi-loop damping torque model based on the dynamic characteristics of the DC voltage; Step S4: quantitatively analyzing the relationship between each damping circuit and the internal operating condition of the wind turbine generator set, the relationship between each damping circuit and the external operating condition of the wind turbine generator set, and the coupling relationship between each damping circuit according to the multi-circuit damping torque model; Step S5: clarifying the stability index of the multi-loop damping torque model, and analyzing the damping characteristics of the direct-drive wind turbine grid-connected system based on the stability index; Step S6: characterize the stable operation domain of control parameters for avoiding low-frequency oscillation of the system under different external operating conditions of wind turbines, and provide a theoretical reference for early warning of low-frequency oscillation instability of wind power grid connection.

2. The method for analyzing and warning the low-frequency oscillation damping characteristics of direct-drive wind turbines connected to the grid according to claim 1 is characterized in that: The full-order grid-connected mathematical model of the direct-drive wind turbine in step S1 is based on the topological structure of the direct-drive wind turbine; the main circuit model: In the formula, C represents the DC capacitance value, ω represents the oscillation angular frequency, and L f represents the filter inductance, u dc Represents the DC capacitor voltage; i d 、i q Respectively represent the d-axis and q-axis components of the converter output current; e d 、e q They represent the d-axis and q-axis components of the converter port voltage respectively; u td 、u tq Respectively represent the d-axis and q-axis components of the grid-connected point voltage; P in , P out They represent the injected power and delivered power of wind turbines respectively; Control system model: In the formula, k p1 , k p2 , k p4 They represent the proportionality coefficients of the voltage outer loop, the active current inner loop, and the reactive current inner loop respectively; k i1 , k i2 , k i4 They represent the integral coefficients of the voltage outer loop, active current inner loop and reactive current inner loop respectively; u dcref 、i qref They represent the expected values ​​of the DC side capacitor voltage and reactive current respectively; x1, x2, x3 represent the indirect state variables of the voltage outer loop, current active inner loop, and current reactive outer loop control links respectively; e d 、e q They represent the d-axis and q-axis components of the converter port voltage respectively; Phase-locked loop model: In the formula, k pp and k ip They represent the proportional coefficient and integral coefficient of the phase-locked loop control link, ω0 represents the reference angular frequency, u tq represents the q-axis component of the grid-connected point voltage in the control coordinate system, x pll represents the intermediate variable of the phase-locked loop control link, and s is the Laplace transform complex variable; Mathematical model of power grid: Where, L g is the line inductance, i x 、i y They are respectively represented as the x-axis and y-axis components of the line current in the main circuit coordinate system; u gx 、u gy They are respectively represented as the grid voltage u g The x-axis and y-axis components in the main circuit coordinate system; u tx 、u ty They are respectively expressed as the x-axis and y-axis components of the grid connection point voltage in the main circuit coordinate system; the d-axis and q-axis components of the grid voltage, grid connection point voltage and wind turbine output current in the control coordinate system and the x-axis and y-axis components in the main circuit coordinate system satisfy the following relationship: Formulas (1)-(6) are combined, and the state space equation is linearized at the equilibrium point to obtain the small signal state space model of the system. The model contains 8 state variables, including 3 main circuit state variables Δi d , Δi q , Δu dc And the five control link state variables Δx1, Δx2, Δx3, Δx pll , Δθ pll .

3. The method for analyzing and warning the low-frequency oscillation damping characteristics of direct-drive wind turbines connected to the grid according to claim 2 is characterized in that: The process of identifying the dominant factors of low-frequency oscillation according to the full-order grid-connected mathematical model of the direct-drive wind turbine generator set and constructing a reduced-order model on the system DC voltage time scale in step S2 is as follows: The following conditions are set: 1) The machine side is equivalent to a controlled current source; 2) The current inner loop control bandwidth is much higher than the voltage outer loop and phase-locked loop bandwidth, that is, before the DC voltage outer loop and phase-locked loop control action, the current has tracked the reference value; Based on the set conditions, the system reduced-order model includes four parts: main circuit model, control system model, phase-locked loop model and power grid model. The construction of the main circuit model, phase-locked loop model and power grid model is the same as that of the full-order system. The difference is that the control system ignores the current inner loop control, as follows: The construction of the phase-locked loop model and the power grid model is the same as that of the full-order system. Based on formulas (3)-(7), the small signal state space model of the reduced-order system is as follows: In the formula, i dc0 is the initial current of the DC capacitor, i d0 is the initial value of the d-axis current of the converter output current, u td0 is the initial value of the d-axis component of the grid-connected point voltage, u tdc0 is the initial value of the DC capacitor voltage.

4. The method for analyzing and warning the low-frequency oscillation damping characteristics of direct-drive wind turbines connected to the grid according to claim 3 is characterized in that: In step S3, the process of converting the reduced-order model of the system DC voltage time scale into a multi-loop damping torque model based on the DC voltage dynamic characteristics is as follows: Relative density of ΔP and Δu dc The relationship is similar to the relationship between the second-order rotor motion equation ΔP and Δω: Other control links are analogous to the damping link and the synchronization link: ΔP out2 =i d0 Δu td (12) Thu td =-i d0 ωL g Dth pll (13) Based on formula (9)-formula (15), the multi-loop damping torque model contains three damping loops, and the damping coefficient and synchronization coefficient of each loop are: By adding up all the feedback links, the total damping coefficient and synchronization coefficient of the system can be obtained as follows: Where D0, D1, and D2 represent the damping coefficients of each circuit respectively, K0, K1, and K2 represent the synchronization coefficients of each circuit respectively, and D and K represent the total damping and total equivalent synchronization coefficient of the system respectively.

5. The method for analyzing and warning the low-frequency oscillation damping characteristics of direct-drive wind turbines connected to the grid according to claim 4 is characterized in that: Step S4 specifically includes: Let s = jω s Substituting into each damping loop formula (16)-formula (19), we can obtain: In the formula, ω s is the oscillation frequency under different grid strengths, wind turbine operating conditions, and control parameters; Im and Re represent the real and imaginary parts of the complex number, respectively; Loop G dc0 Damping D0 presents negative damping characteristics, which is determined only by the working conditions of the wind turbine. As the working conditions increase, the negative damping characteristics increase, and the system stability decreases. dc1 Damping D1 presents positive damping characteristics. The damping is determined by the outer loop proportional coefficient and is not affected by the grid strength and working conditions. dc2 The damping of damping D2 is affected by the combined effects of grid strength, wind turbine operating conditions, and control parameter operating conditions, and presents a negative damping characteristic. Under low operating conditions and strong grids, the magnitude of the negative damping coefficient is very small and can be almost ignored. However, as the wind turbine operating conditions increase and the grid strength weakens, the magnitude of the negative damping coefficient gradually increases, and the rate of increase is negatively correlated with the grid strength and positively correlated with the operating conditions. There is a loop G between each damping loop dc0 and loop G dc2 The coupling relationship with the wind turbine operating conditions shows that the negative damping of the two circuits increases with the increase of wind turbine operating conditions, and they are equally affected by the wind turbine operating conditions. dc1 and loop G dc2 Coupling relationship with the outer loop proportional coefficient, loop G dc1 The positive damping coefficient is positively correlated with the outer loop proportional coefficient, while the loop G dc2 The negative damping coefficient is negatively correlated with the voltage outer loop proportional coefficient, that is, the outer loop proportional coefficient has a mutual constraint on the two damping loops. Within the same proportional coefficient variation range, loop G dc1 The increase in positive damping ΔD1 is greater than loop G dc2 The negative damping increases by ΔD2, that is, increasing the outer loop proportional coefficient, and the overall positive damping of the system shows an increasing trend.

6. The method for analyzing and warning the low-frequency oscillation damping characteristics of direct-drive wind turbines connected to the grid according to claim 5 is characterized in that: Step S5 specifically includes: According to formula (19), D and K represent the total equivalent damping coefficient and the total equivalent synchronization coefficient of the model respectively, and the stability index is defined as follows: The influence of grid strength and working conditions on equivalent synchronization coefficient: The synchronization coefficient K of the damping torque model under different working conditions and grid strengths shows an increasing trend with the decrease of wind turbine working conditions and SCR, and its value deviates far from K = 0 and is always greater than zero. Therefore, in the process of stability analysis and stability margin division, the influence of the synchronization coefficient in the stability index is not considered for the time being; The influence of grid strength and working conditions on the total damping of the system: Based on the stability index formula (21), the influence of grid strength and wind turbine operating conditions on the total damping of the system is quantitatively evaluated. As the wind turbine operating conditions increase and the grid strength decreases, the system damping shows a downward trend, and the stability decreases. In addition, the system has negative damping in weak grid SCR≤2.6 and high operating conditions, that is, the system is unstable. The operating conditions and grid strength corresponding to the critical instability point, i.e., D=0, are shown as follows: When SCR=1.4, P in =1.17MW, the total system damping D=0. As the wind turbine operating conditions increase, the total system damping D<0, resulting in low-frequency oscillation instability. When SCR=2, P in =1.36MW, the total system damping D=0. As the wind turbine operating conditions increase, the total system damping D<0, resulting in low-frequency oscillation instability. When SCR=2.6, P in =1.48MW, the total system damping D=0. As the wind turbine operating conditions increase, the total system damping D<0, resulting in low-frequency oscillation instability. When the grid strength is weaker than the critical instability point or the operating condition is greater than the critical instability point, the system damping is negative and low-frequency oscillation instability occurs; therefore, as the operating condition of the wind turbine increases, the system damping decreases and the stability decreases; as the grid strength decreases, the stable operating condition range of the wind turbine increases and the stability increases.

7. The method for analyzing and warning the low-frequency oscillation damping characteristics of direct-drive wind turbines connected to the grid according to claim 6 is characterized in that: In step S6, the control parameter stable operation domain for avoiding low-frequency oscillation of the system under different wind turbine external operating conditions is described as follows: When SCR = 2, the outer ring proportional coefficient k p1 When k > 2.9, the system remains stable in the full range of operating conditions; p1 <0.5, at P in In the higher operating range of >0.8MW, the system damping is always negative; When SCR = 1.4, the outer ring proportional coefficient k p1 >3.5, the system remains stable in the full range of operating conditions; p1 When P in >0.8MW In the higher operating range, the system damping is always negative; As the operating conditions of SCR and wind turbines decrease, the stable operating area of ​​the proportional coefficient becomes smaller; and to ensure stable operation, the outer loop proportional coefficient should be appropriately increased; that is, increasing the outer loop proportional coefficient improves the stability of the system under high operating conditions and weak power grid conditions; When SCR = 2, the outer loop integral coefficient k i1 When k > 160, the system can remain stable in the full range of working conditions; i1 When <75, in >0.8MW high operating range, the system damping is always negative; When SCR = 1.4, the outer loop integral coefficient k i1 >242, the system can remain stable in the full range of operating conditions; i1 When <80, in >0.8MW In the higher operating range, the system damping is always negative; As the SCR and wind turbine operating conditions decrease, k i1 The stable operating domain is reduced. In order to ensure the stable operation of the system, the integral coefficient is increased, that is, the outer loop integral coefficient is increased to improve the stability of the system under high operating conditions and weak power grid conditions.

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