A Stability Analysis Method for Doubly-Fed Wind Turbine Grid-Connected System Based on Gale Circle Theorem

Abstract

The present invention discloses a stability analysis method for a doubly-fed wind turbine grid-connected system based on the Gale circle theorem. The method comprises the following steps: calculating the equivalent front-stage output impedance and the equivalent rear-stage input admittance of the doubly-fed wind turbine grid-connected system, obtaining the overall transfer function of the system and obtaining the rate matrix of the doubly-fed wind turbine grid-connected system; setting a restricted area to limit the distribution of the eigenvalues ​​of the rate matrix; deriving and calculating the distance between the center of the Gale circle and the restricted area and the radius of the Gale circle, taking the difference as a stability criterion, and then determining the stability of the system. Based on the method of the present invention, the influence mechanism of different physical / control parameters on the stability of the doubly-fed wind turbine grid-connected system under weak power grid conditions can be effectively analyzed, and then the design of the loop parameters of the doubly-fed wind turbine control system can be guided, and its conservatism is smaller than the existing improved sum-norm, IFRC criterion, etc.

Description

Technical Field

[0001] The invention belongs to the field of research on grid-connected stability of doubly-fed wind turbine generators, and specifically is a stability criterion for a grid-connected doubly-fed wind turbine system based on the Gale circle theorem, and can perform stability analysis on the grid-connected doubly-fed wind turbine system. Background Art

[0002] In order to cope with the crisis of traditional fossil energy and the resulting environmental pollution, the development and utilization of new energy has become a consensus among countries around the world. Among them, wind power generation, after nearly two decades of development practice, has become one of the most recognized new energy forms with the most commercial prospects. Among various types of grid-connected wind turbine equipment, doubly-fed wind turbines have long occupied more than 2 / 3 of the wind turbine market due to their advantages such as small excitation converter capacity, low cost, and high operating efficiency. Due to the reverse distribution characteristics of my country's wind power resources and power loads, most wind turbines are connected to the end of the power grid. Considering the impedance factors of long transmission lines under wind power development modes such as large-scale centralized development and long-distance transmission, low short-circuit ratio has become the main form of wind turbine access to the power grid. Under low short-circuit ratio power grids, the stability of doubly-fed wind turbine grid-connected systems has become a research focus.

[0003] The doubly-fed wind turbine grid-connected system is a typical multiple-input multiple-output (MIMO) system. Traditional stability analysis methods for single-input single-output (SISO) systems, such as the Nyquist criterion and the Middlebrook criterion, are no longer applicable. For MIMO systems, the state space method is usually used. However, the state space method requires multiple listing of state variables under different operating conditions, and the calculation of the eigenvalues ​​and damping ratios of each state variable and the participation factor of each link to analyze the grid-connected stability.

[0004] The impedance analysis method only needs to establish the input impedance model of the grid-connected equipment once to analyze the stability of the grid-connected system under different steady-state operating points. Therefore, Belkhayat et al. extended the impedance stability criterion of the SISO system to the MIMO system, but it is more conservative. Mu Xiuqing et al. proposed an improved sum-norm criterion based on the sum-norm and conducted a conservative analysis on it. Ge Xinglai et al. established an improved stability criterion (IFRC) based on the restricted area with x=-1 as the boundary, which further improved the effectiveness of the stability analysis, but it is still more conservative. How to reduce the conservatism of the stability criterion is the key to the stability judgment of the impedance method.

[0005] Therefore, it is urgent to propose a stability criterion for MIMO cascade systems that can further reduce the conservatism of stability analysis. Summary of the invention

[0006] The purpose of the present invention is to provide a stability analysis method for a doubly-fed wind turbine grid-connected system based on the Gale circle theorem in view of the deficiencies in the prior art. The present invention uses the impedance feedback matrix of the MIMO cascade system, sets a restricted area and divides the complex plane, calculates the distance between the center of the Gale circle and the restricted area and the radius of the Gale circle, and takes the difference as a stability criterion; the present invention can simply and effectively analyze the stability of a doubly-fed wind turbine grid-connected system under a low short-circuit ratio power grid, has lower conservatism, and improves the accuracy of stability analysis.

[0007] The object of the present invention is achieved through the following technical solution: A stability analysis method for a doubly-fed wind turbine grid-connected system based on the Gale circle theorem, comprising the following steps:

[0008] (1) Calculate the equivalent front-stage output impedance and equivalent rear-stage input admittance of the doubly fed wind turbine grid-connected system, obtain the overall transfer function of the system and obtain the impedance feedback matrix L of the doubly fed wind turbine grid-connected system DFIG ;

[0009] (2) A restricted zone is set to limit the distribution of the eigenvalues ​​of the return rate matrix. The distance between the center of the Gale circle and the restricted zone and the radius of the Gale circle are derived and calculated. The difference is taken as the stability criterion to determine the stability of the system.

[0010] Further, step (1) comprises:

[0011] (1.1) Obtain the equivalent front-stage output impedance of the doubly-fed wind turbine grid-connected system and obtain:

[0012]

[0013] Among them, R line and L line is the resistance and inductance of the weak grid, ω s is the grid angular frequency, D is the differential operator;

[0014] (1.2) Calculate the equivalent input admittance of the doubly fed wind turbine grid-connected system and obtain:

[0015]

[0016] Among them, G rr , G rs , G ss , G sr is the transfer function matrix of stator voltage, rotor voltage, stator current and rotor current of the doubly fed wind turbine, G pis , G pir , G pur G is the transfer function matrix of the grid voltage disturbance added to the stator current, rotor current and rotor voltage through the phase-locked loop. rcc is the current loop controller, G d1 , Gd2 is the current decoupling term;

[0017] (1.3) Obtain the impedance response matrix of the doubly fed wind turbine grid-connected system and obtain:

[0018]

[0019] Among them, Z L is the equivalent output impedance of the front stage, Y DFIG is the equivalent input admittance of the subsequent stage, and the element of the impedance feedback matrix is ​​L dd , L dq , L qd , L qq .

[0020] Further, step (2) comprises:

[0021] (2.1) Set the restricted area:

[0022] PA={L||Im(L)|<-tan(π / 180)·(Re(L)+1)} (10)

[0023] Among them, L is the main diagonal element of the impedance return matrix, that is, L dd , L qq ;

[0024] (2.2) Based on the relationship between the center of the Gale circle and the forbidden area, the complex plane is divided into four regions, and we get:

[0025] Sec I={L||Im(L)|≤tan(π / 2-π / 180)·(Re(L)+1)} (11)

[0026] Sec II={L|Re(L)≥-1}∩{L||Im(L)|>tan(π / 2-π / 180)·(Re(L)+1)} (12)

[0027] Sec III={L|Re(L)<-1}∩{L||Im(L)|≥-tan(π / 180)·(Re(L)+1)} (13)

[0028] Sec IV={L||Im(L)|<-tan(π / 180)·(Re(L)+1)} (14)

[0029] Among them, SecⅠ, SecⅡ, SecⅢ, and SecⅣ are four regions;

[0030] (2.3) The distance from the center of the Gale circle to the restricted area is derived and the difference between it and the radius of the Gale circle is taken as the stability criterion, and we get:

[0031]

[0032]

[0033] θ dd =arctan(|Im(L dd )| / |Re(L dd )+1|),θ qq =arctan(|Im(L qq )| / |Re(L qq )+1|)

[0034]

[0035] Among them, L dd , L dq , L qd , L qq is the element of the impedance feedback matrix, s represents the complex frequency domain;

[0036] (2.4) When W(s) and H(s) are both less than 0, the system is in a small signal stable state, otherwise the system is in a small signal unstable state.

[0037] The beneficial effects of the present invention are as follows: the present invention is applicable to stability analysis of all MIMO cascade systems; the present invention further narrows the restricted area, and divides the complex plane according to the restricted area, establishes a more detailed stability criterion, reduces conservatism, and makes stability analysis more accurate; the present invention provides a method for stability analysis of a doubly-fed wind turbine grid-connected system under weak power grid conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 This is the structural block diagram of the overall input admittance of the doubly-fed wind turbine;

[0039] Figure 2 The Gale circle and restricted area diagram of the return rate matrix;

[0040] Figure 3 It is a schematic diagram of complex plane partition based on restricted area;

[0041] Figure 4 The graphs of the stability criterion W(s) and H(s) under different short-circuit ratios; (a) is when the short-circuit ratio is 5, (b) is when the short-circuit ratio is 3, and (c) is when the short-circuit ratio is 2;

[0042] Figure 5 The simulation results of the voltage and current of the double-fed wind turbine grid-connected under different short-circuit ratios are shown in Figure 1. (a) is the voltage, and (b) is the current.

[0043] Figure 6The W(s) and H(s) curves of stability criteria under different current loop proportional coefficients; (a) is when the current loop proportional coefficient is 1.5, (b) is when the current loop proportional coefficient is 2.2, and (c) is when the current loop proportional coefficient is 3;

[0044] Figure 7 The simulation results of the voltage and current of the doubly fed wind turbine grid-connected under different current loop proportional coefficients are shown in Figure 1; (a) is the voltage and (b) is the current. DETAILED DESCRIPTION

[0045] In order to describe the present invention in more detail, the present invention is further illustrated below with reference to the accompanying drawings and specific implementation examples.

[0046] The programming environment of the embodiment of the present invention is set as MATLAB / Simulink. Taking a DFIG with a capacity of 3.0MW and a rated voltage of 690V as an example, the model is built using the motor convention. The implementation method first normalizes the parameters in the fan and measurement module. The parameters of the DFIG are as follows: stator resistance R s =0.013pu, rotor resistance R r =0.024pu, stator inductance L s =0.239pu, rotor inductance L r =0.213pu, stator-rotor mutual inductance L m =3.99pu, pole pair number p=3. Specifically includes the following steps:

[0047] The present invention provides a stability analysis method for a doubly-fed wind turbine grid-connected system based on the Gale circle theorem, which calculates the equivalent front-stage output impedance and equivalent rear-stage input admittance of the doubly-fed wind turbine grid-connected system, obtains the overall transfer function of the system and obtains the rate matrix of the doubly-fed wind turbine grid-connected system, sets a restricted area to limit the distribution of characteristic values ​​of the rate matrix, derives and calculates the distance between the center of the Gale circle and the restricted area and the radius of the Gale circle, and takes the difference as a stability criterion, so as to judge the stability of the doubly-fed wind turbine grid-connected system under weak power grid conditions. Specifically, the following steps are included:

[0048] (1) Impedance return matrix L based on the doubly fed wind turbine grid-connected system DFIG The solution steps include:

[0049] (1.1) Equivalent front-stage output impedance Z of the doubly-fed wind turbine grid-connected system L for:

[0050]

[0051] Among them, R line and L line is the resistance and inductance of the weak grid, ω s is the grid angular frequency, and D is the differential operator.

[0052] (1.2) Figure 1 As shown in the figure, according to the transfer function matrix of the stator voltage, rotor voltage, stator current and rotor current of the doubly fed wind turbine, the grid voltage disturbance is added to the transfer function matrix of the stator current, rotor current and rotor voltage through the phase-locked loop, the current loop transfer function matrix, and the current decoupling term transfer function matrix, the equivalent subsequent input admittance Y of the doubly fed wind turbine grid-connected system is obtained. DFIG :

[0053]

[0054] Among them, E is the second-order unit matrix; G rr , G rs , G ss , G sr is the transfer function matrix of stator voltage, rotor voltage, stator current and rotor current of the doubly fed wind turbine, G pis , G pir , G pur G is the transfer function matrix of the grid voltage disturbance added to the stator current, rotor current and rotor voltage through the phase-locked loop, rcc is the current loop controller, G d1 is the rotor dq axis current decoupling term, G d2 is the stator and rotor current decoupling term. Figure 1 middle, is the rotor current command value, which is a constant. Therefore, when the small disturbance impedance model is established, its small disturbance is 0.

[0055] The transfer function matrix of the stator voltage, rotor voltage, stator current and rotor current of the doubly fed wind turbine, the transfer function matrix of the grid voltage disturbance added to the stator current, rotor current and rotor voltage through the phase-locked loop, the current loop transfer function matrix, and the current decoupling term transfer function matrix are shown in formulas (3) to (8):

[0056]

[0057]

[0058]

[0059]

[0060]

[0061]

[0062]

[0063]

[0064] a s =K1L m (ω slip ω s L m R s -DK s )+(R r +DL r )

[0065] b s =-K1L m (Dω s L m R s +ω slip K s )+ω slip L r

[0066] c s =K1L m [D(R s +DL s )+ω slip ω s L s ]

[0067] d s =K1L m [-ω slip (R s +DL s )+Dω s L s ]

[0068] Among them, U sd , U sq They are stator voltage U s The d-axis component and q-axis component of I sd ,I sq They are stator current I s The d-axis component and q-axis component of U rd , U rq They are the rotor voltage U r The d-axis component and q-axis component of I rd ,I rq They are the rotor current I r The d-axis component and q-axis component of the grid; the superscript b represents the grid dq coordinate system. s is the differential operator, R s is the stator resistance, R r is the rotor resistance, L s is the stator inductance, L r is the rotor inductance, L m is the stator-rotor mutual inductance, ω s is the grid angular frequency, ωslip is the slip angular frequency.

[0069]

[0070]

[0071]

[0072]

[0073]

[0074]

[0075]

[0076] Among them, k p_pll k is the phase-locked loop proportional coefficient, i_pll is the phase-locked loop integral coefficient; the superscript c represents the control dq coordinate system.

[0077]

[0078]

[0079]

[0080]

[0081] Among them, k p_rcc is the current loop proportionality coefficient, k i_rcc is the current loop integration coefficient.

[0082] (1.3) The equivalent front-stage output impedance Z of the doubly-fed wind turbine grid-connected system obtained according to step (1.1) L , the equivalent subsequent input admittance Y of the doubly fed wind turbine grid-connected system obtained in step (1.2) DFIG , the system's return rate matrix L can be calculated DFIG ,Right now:

[0083]

[0084] Among them, L dd , L dq , L qd , L qq are the elements of the impedance return matrix.

[0085] (2) The derivation steps of the stability criterion based on the Gale circle theorem include:

[0086] (2.1) Figure 2 As shown, the restricted area PA:

[0087] PA={L||Im(L)|<-tan(π / 180)·(Re(L)+1)} (10)

[0088] Among them, L is the main diagonal element of the impedance return matrix, that is, L dd , L qq Im means taking the imaginary part, and Re means taking the real part.

[0089] (2.2) Figure 3 As shown, the expressions of the four regions are calculated:

[0090] Sec I={L||Im(L)|≤tan(π / 2-π / 180)·(Re(L)+1)} (11)

[0091] Sec II={L|Re(L)≥-1}∩{L||Im(L)|>tan(π / 2-π / 180)·(Re(L)+1)} (12)

[0092] Sec III={L|Re(L)<-1}∩{L||Im(L)|≥-tan(π / 180)·(Re(L)+1)} (13)

[0093] Sec IV={L||Im(L)|<-tan(π / 180)·(Re(L)+1)} (14)

[0094] Among them, SecⅠ, SecⅡ, SecⅢ and SecⅣ are four regions.

[0095] (2.3) Calculate the distance from the center of the Gale circle to the restricted area, and take the difference between it and the radius of the Gale circle as the stability criterion, and we can get:

[0096]

[0097]

[0098] θ dd =arctan(|Im(L dd )| / |Re(L dd )+1|)

[0099] θ qq =arctan(|Im(L qq )| / |Re(L qq )+1|)

[0100]

[0101]

[0102] Where s represents the complex frequency domain, L dd , L dq , L qd , L qq are the elements of the impedance return matrix.

[0103] The specific derivation steps of the stability criterion are as follows:

[0104] For SecⅠ, the distance from the center of the Gale circle to the restricted area is the distance from L to (-1,0):

[0105] D1(s)=l λ1 (17)

[0106] D2(s)=l λ2 (18)

[0107]

[0108]

[0109] As long as the center of the Gale circle falls within SecⅠ, we can compare D1(s) and |L dq |, D2(s) and |L qd | to determine the stability. Therefore, the stability judgment expression is:

[0110]

[0111] For SecⅡ, the distance from the center of the Gale circle to the restricted area is the distance from the restricted area boundary Im(L) = -tan(π / 180)·(Re(L)+1). By deducing from geometric relationships, the distance expression can be obtained as:

[0112] D1(s)=l λ1 ·sin(π / 180+θ dd ) (20)

[0113] D2(s)=l λ2 ·sin(π / 180+θ qq ) (twenty one)

[0114] θ dd =arctan(|Im(L dd )| / |Re(L dd )+1|)

[0115] θ qq =arctan(|Im(L qq )| / |Re(L qq )+1|)

[0116] Similar to SecⅠ, the stability judgment expression, namely D1(s) and |L dq |, D2(s) and |L qd The numerical difference of | is:

[0117]

[0118] For SecⅢ, it is similar to the previous two, so we can directly write its stability judgment expression:

[0119]

[0120] For SecⅣ, if the center of the Gale circle falls on SecⅣ, the eigenvalue trajectory of the rate matrix is ​​likely to be around the point (-1,0). In this case, the system is unstable by default, so you only need to ensure that W(s) or H(s) is less than zero. In the region SecⅣ, θ dd <π / 180,θ qq <π / 180. Therefore, W(s) and H(s) in the SecⅢ region must be less than zero when applied in SecⅣ. In addition, the continuity of the W(s) curve can be guaranteed by using the stability judgment expression of SecⅢ instead of any constant less than zero.

[0121] (2.4) Within the required frequency band, when W(s) and H(s) are both greater than 0, the system is in a small signal stable state, otherwise the system is in a small signal unstable state.

[0122] Figure 4 (a) is the stability criterion W(s) and H(s) curves when the short-circuit ratio is equal to 5. Figure 4 (b) is the stability criterion W(s) and H(s) curves when the short-circuit ratio is equal to 3. Figure 4 (c) is the stability criterion W(s) and H(s) curves when the short-circuit ratio is equal to 2. Figure 4 It can be seen that when the short-circuit ratio is 5, W(s) and H(s) are greater than 0 in the entire frequency band, and the system is stable; when the short-circuit ratio is 3, the system is critically stable; when the short-circuit ratio is 2, there is a frequency point less than 0 in the H(s) curve, and the system is unstable.

[0123] Figure 5 (a) is the three-phase voltage U of the doubly fed wind turbine connected to the grid under different short-circuit ratios s (U sa , U sb , U sc ) simulation results. Figure 5 (b) is the three-phase current I of the doubly fed wind turbine connected to the grid under different short-circuit ratios s (I sa ,I sb ,Isc ) simulation results. Figure 5 It can be seen that within 1 to 1.6 seconds, the short-circuit ratio SCR is 4, at which time the system is stable with small disturbances; within 1.6 to 2 seconds, the short-circuit ratio SCR is 2, the system is unstable, and the stator voltage and current show obvious oscillations. Figure 4 The conclusions of the theoretical analysis correspond.

[0124] Figure 6 (a) is the stability criterion W(s) and H(s) curves when the current loop proportional coefficient is 1.5. Figure 6 (b) is the stability criterion W(s) and H(s) curves when the current loop proportional coefficient is 2.2. Figure 6 (c) is the stability criterion W(s) and H(s) curves when the current loop proportional coefficient is 3. Figure 6 It can be seen that as the current loop proportional coefficient increases from 1.5 to 3, the H(s) curve gradually intersects with the zero line, indicating that the DFIG system changes from a stable state to an unstable state.

[0125] Figure 7 (a) is the three-phase voltage U of the doubly-fed wind turbine connected to the grid under different current loop proportional coefficients s (U sa , U sb , U sc ) simulation results. Figure 7 (b) is the three-phase current I of the doubly fed wind turbine connected to the grid under different current loop proportional coefficients s (I sa ,I sb ,I sc ) simulation results. Figure 7 It can be seen that within 1 to 1.6 seconds, the current loop proportional coefficient is 1.5, at this time the grid and current present a three-phase sinusoidal state; within 1.6 to 2 seconds, the current loop proportional coefficient is 3, the grid voltage oscillates, the grid current presents a non-sinusoidal state, and the system becomes unstable during this process. Figure 6 The conclusions of the theoretical analysis correspond.

[0126] In summary, the present invention is based on the impedance feedback matrix of the doubly-fed wind turbine grid-connected system, and uses the Gale circle theorem to estimate the eigenvalues ​​of the feedback matrix, sets the distribution of the eigenvalues ​​limited by the restricted area, and divides the complex plane into four areas according to the distance relationship between the center of the Gale circle and the restricted area, and derives and calculates the distance between the center of the Gale circle and the restricted area and the radius of the Gale circle, respectively, and takes the difference to obtain a stability analysis method for the doubly-fed wind turbine grid-connected system with further reduced conservatism. Based on the method of the present invention, the influence of different physical / control parameters on the stability of the doubly-fed wind turbine grid-connected system under weak power grid conditions can be effectively analyzed, and then the optimal design of the loop parameters of the doubly-fed wind turbine control system can be guided, and the conservatism is smaller than the existing improved sum-norm, IFRC criterion, etc. The criterion of the present invention is also applicable to the stability analysis of general MIMO cascade systems.

Claims

1. A stability analysis method for a doubly-fed wind turbine grid-connected system based on the Gale circle theorem, characterized in that: The steps include: (1) Calculate the equivalent front-stage output impedance and equivalent rear-stage input admittance of the doubly fed wind turbine grid-connected system, obtain the overall transfer function of the system and obtain the impedance feedback matrix L of the doubly fed wind turbine grid-connected system DFIG ; (1.1) Obtain the equivalent front-stage output impedance of the doubly-fed wind turbine grid-connected system and obtain: Among them, R line and L line is the resistance and inductance of the weak grid, ω s is the grid angular frequency, D is the differential operator; (1.2) Calculate the equivalent input admittance of the doubly fed wind turbine grid-connected system and obtain: Among them, G rr , G rs , G ss , G sr is the transfer function matrix of stator voltage, rotor voltage, stator current and rotor current of the doubly fed wind turbine, G pis , G pir , G pur G is the transfer function matrix of the grid voltage disturbance added to the stator current, rotor current and rotor voltage through the phase-locked loop. rcc is the current loop controller, G d1 , G d2 is the current decoupling term; (1.3) Obtain the impedance response matrix of the doubly fed wind turbine grid-connected system and obtain: Among them, Z L is the equivalent output impedance of the front stage, Y DFIG is the equivalent input admittance of the subsequent stage, and the element of the impedance feedback matrix is ​​L dd , L dq , L qd , L qq ; (2) Setting a restricted zone to limit the distribution of the eigenvalues ​​of the return rate matrix, deriving and calculating the distance between the center of the Gale circle and the restricted zone and the radius of the Gale circle, taking the difference as the stability criterion, and then determining the stability of the system; (2.1) Set the restricted area: PA={L||Im(L)|<-tan(π / 180)·(Re(L)+1)} (10) Among them, L is the main diagonal element of the impedance return matrix, that is, L dd , L qq ; (2.2) Based on the relationship between the center of the Gale circle and the forbidden area, the complex plane is divided into four regions, and we get: Sec I={L||Im(L)|≤tan(π / 2-π / 180)·(Re(L)+1)} (11) SecII={L|Re(L)≥-1}∩{L||Im(L)|>tan(π / 2-π / 180)·(Re(L)+1)} (12) Sec III={L|Re(L)<-1}∩{L||Im(L)|≥-tan(π / 180)·(Re(L)+1)} (13) Sec IV={L||Im(L)|<-tan(π / 180)·(Re(L)+1)} (14) Among them, SecⅠ, SecⅡ, SecⅢ, and SecⅣ are four regions; (2.3) The distance from the center of the Gale circle to the restricted area is derived and the difference between it and the radius of the Gale circle is taken as the stability criterion, and we get: θ dd =arctan(|Im(L dd )| / |Re(L dd )+1|),θ qq =arctan(|Im(L qq )| / |Re(L qq )+1|) Among them, L dd , L dq , L qd , L qq is the element of the impedance feedback matrix, s represents the complex frequency domain; (2.4) When W(s) and H(s) are both less than 0, the system is in a small signal stable state, otherwise the system is in a small signal unstable state.

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