Stability analysis method based on output impedance model of doubly-fed wind farm grid-connected system

Abstract

The present invention relates to the technical field of grid-connected stability control of renewable energy power generation, and specifically to a stability analysis method based on an output impedance model of a doubly-fed wind farm grid-connected system. The method establishes a doubly-fed wind turbine small-signal output impedance model that considers three parts, namely, a phase-locked loop, a current loop, and a power loop, in a synchronous rotating coordinate system. The doubly-fed wind turbine output impedance model is used to obtain a doubly-fed wind turbine grid-connected small-signal impedance model in a synchronous rotating coordinate system. A power grid small-signal impedance model is established in the synchronous rotating coordinate system. The ratio between the doubly-fed wind turbine output impedance and the power grid impedance is calculated. The stability of the doubly-fed wind farm grid-connected system is judged according to the generalized Nyquist criterion. The method has the beneficial effect that the present invention can be used to analyze the stability of a doubly-fed wind farm grid-connected system, and provides a strong theoretical basis for analyzing sub- / super-synchronous oscillations caused by the connection of large-scale wind farms to the power grid.

Description

Technical Field

[0001] The present invention relates to the technical field of renewable energy power generation grid-connected stability control, and in particular to a stability analysis method based on an output impedance model of a double-fed wind farm grid-connected system. Background Art

[0002] The problem of stable operation of large wind farms connected to the grid is a hot topic of research at home and abroad. Due to the increase in wind power penetration and the fact that most of my country's new energy power plants are located in remote areas, the transmission lines are long, which increases the equivalent electrical impedance and the grid shows a weak grid trend. This will cause the double-fed wind power grid-connected system to interact with the grid and cause serious stability problems.

[0003] The main analysis methods for sub- / super-synchronous oscillations caused by the grid connection of new energy are impedance analysis and modal analysis. Compared with modal analysis, impedance analysis simplifies the complexity of stability analysis due to its clear physical concepts and strong intuitiveness. Its principle is to establish small signal output impedance models of the grid-connected new energy system and the AC power grid respectively, convert the system into a multi-input multi-output system in a synchronous rotating coordinate system, and then perform stability analysis on the system according to the generalized Nyquist criterion.

[0004] The impedance analysis methods of doubly-fed wind turbines proposed so far are mostly based on single-machine analysis, and the impedance analysis methods for multi-machine systems do not make stability analysis of various coefficients and operating conditions in wind farms. Therefore, it is of great significance to propose a method based on the output impedance model of the doubly-fed wind farm grid-connected system that can perform stability analysis of doubly-fed wind farms under different operating conditions. Summary of the invention

[0005] The purpose of the present invention is to overcome the above technical deficiencies and provide a stability analysis method based on the output impedance model of a doubly-fed wind farm grid-connected system. The method establishes a doubly-fed wind turbine small-signal output impedance model that considers three parts: a phase-locked loop, a current loop, and a power loop in a synchronous rotating coordinate system. The doubly-fed wind turbine output impedance model is used to obtain a doubly-fed wind turbine grid-connected small-signal impedance model in a synchronous rotating coordinate system. A power grid small-signal impedance model is established in a synchronous rotating coordinate system. The ratio between the doubly-fed wind turbine output impedance and the power grid impedance is calculated. The stability of the doubly-fed wind turbine grid-connected system is determined according to the generalized Nyquist criterion. The method of the present invention can be used to analyze the stability of a doubly-fed wind turbine grid-connected system and provide a theoretical basis for analyzing sub- / super-synchronous oscillations caused by the integration of large-scale wind farms into the power grid.

[0006] In order to achieve the above object, the specific implementation scheme adopted by the present invention is as follows:

[0007] A stability analysis method based on an output impedance model of a double-fed wind farm grid-connected system comprises the following steps:

[0008] 1) Establish a small signal impedance model of the main circuit of the doubly-fed wind turbine in a synchronous rotating coordinate system;

[0009] 2) Based on the small signal impedance model of the main circuit of the doubly-fed wind turbine generator set, a small signal impedance model considering the current loop, phase-locked loop and power loop is established in a synchronous coordinate system;

[0010] 3) The small signal impedance model of the doubly-fed wind farm in the synchronous coordinate system is obtained through equivalent aggregation;

[0011] 4) Establish a grid impedance model in a synchronous coordinate system;

[0012] 5) The grid-connected doubly-fed wind farm system is equivalent to a multi-input multi-output system. The feedback matrix of the system is obtained, that is, the grid impedance matrix multiplied by the doubly-fed wind farm impedance matrix. According to the generalized Nyquist criterion, the stability of the system can be judged.

[0013] Furthermore, the small signal impedance model of the doubly-fed generator in step 1) is:

[0014] Z dfig =(G iss +G irs G sr +G de G irr G iss K1+G de G irr G sr K2) -1 ·(G de G irr K3+E)

[0015] K1=G ci -G d1

[0016]

[0017]

[0018] Furthermore, in order to obtain the small signal impedance model of the doubly-fed machine in step 1), the relationship between the stator current and the stator voltage needs to be obtained from the grid connection point to the doubly-fed machine side, so it is necessary to add a small signal disturbance to the grid connection point voltage, which is defined as follows:

[0019]

[0020] Among them U sd and U sq are the steady-state operating points of the stator voltage in the synchronous rotating coordinate system.

[0021] Furthermore, the disturbance voltage small signal impedance model of the current loop of the doubly-fed generator in step 2) is:

[0022]

[0023] in:

[0024]

[0025]

[0026]

[0027] Furthermore, the phase-locked loop of the doubly-fed generator in step 2) is mainly used to detect the phase of the three-phase voltage of the power grid and obtain the coordinate transformation angle Δθ of the dq axis coordinate system. PLL , providing a reference for coordinate transformation for the system; its most important manifestation is that when the grid-connected point voltage is disturbed, the disturbance will be introduced into various variables of the system through the phase-locked loop; the relationship between the phase-locked loop dq coordinate system and the system dq coordinate system variables is as follows:

[0028]

[0029] By performing small signal processing on equation (7), we can obtain:

[0030]

[0031] The Δθ PLL The expression is:

[0032]

[0033] in: in is the d-axis component of the static operating point of the stator current in the dq coordinate system, and They are the proportional coefficient and integral coefficient of the phase-locked loop respectively.

[0034] Furthermore, the small signal impedance model of the power loop of the doubly-fed generator in step 2) is:

[0035]

[0036] in:

[0037]

[0038] Furthermore, in step 3), an impedance model of a doubly-fed wind farm having n doubly-fed wind turbines of the same model is obtained through equivalent aggregation:

[0039]

[0040] Furthermore, the output impedance model of the doubly-fed wind farm can be expressed in the form of a second-order matrix:

[0041]

[0042] Where: Z dd , Z dq , Z qd , Z qq Z DFIG The dd, dq, qd, and qq axis components.

[0043] Furthermore, the grid impedance model in step 4) is expressed in the form of a second-order matrix:

[0044]

[0045] The beneficial effects of the present invention are that it can be used to analyze the stability of a doubly-fed wind farm grid-connected system, and provide a basis for improving system stability under different grid strengths, different numbers of wind turbines, and in the design of a doubly-fed wind turbine controller, and provide a strong theoretical basis for sub / supersynchronous oscillations caused by large-scale wind power grid-connected systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 This is the double-fed wind farm grid-connected system of the present invention.

[0047] Figure 2 This is the small signal model of vector control of the doubly-fed wind turbine generator system of the present invention.

[0048] Figure 3 This is a small signal block diagram of the doubly-fed motor of the present invention.

[0049] Figure 4 This is an equivalent MIMO system of the present invention.

[0050] Figure 5 This is the impedance frequency scanning Bode diagram of the present invention.

[0051] Figure 6 It is the characteristic root locus of the rate matrix under different short circuit ratios of the present invention.

[0052] Figure 7 is the terminal voltage and current of the present invention.

[0053] Figure 8 It is the characteristic root matrix of the return rate matrix under different RSC proportional integrals of the present invention.

[0054] Fig. 9 This is the effect of the proportional integral on the stator current of the RSC side of the present invention.

[0055] Fig.10 It is the characteristic root matrix of the rate matrix without using the phase-locked loop proportional integration in the present invention. DETAILED DESCRIPTION

[0056] The structure and beneficial effects of the present invention are further described below in conjunction with the accompanying drawings.

[0057] As shown in the attached figure, a stability analysis method based on the output impedance model of the doubly-fed wind farm grid-connected system uses a small signal disturbance analysis method to establish a small signal output impedance model of the wind turbine considering the current loop, phase-locked loop and power loop through the small signal model of the doubly-fed wind turbine vector control, and then aggregates the equivalent values ​​to obtain the small signal output impedance model of the doubly-fed wind farm, and then establishes the small signal impedance model of the power grid. Figure 1 The figure shows a doubly-fed wind farm grid-connected system.

[0058] The vector control model of the doubly fed wind turbine is as follows: Figure 2 As shown, the specific modeling and analysis process of the double-fed wind farm grid-connected system is as follows;

[0059] 1) Firstly, a small signal impedance model of the main circuit of the doubly-fed wind turbine generator system is established in a synchronous rotating coordinate system;

[0060] 2) Based on the small signal impedance model of the main circuit of the doubly-fed wind turbine generator set, a small signal impedance model considering the current loop, phase-locked loop and power loop is established in a synchronous coordinate system;

[0061] 3) The small signal impedance model of the doubly-fed wind farm in the synchronous coordinate system is obtained through equivalent aggregation;

[0062] 4) Establish a grid impedance model in a synchronous coordinate system;

[0063] 5) The doubly-fed wind farm grid-connected system is equivalent to a multi-input multi-output system, and the system's return matrix is ​​obtained, that is, the grid impedance matrix multiplied by the doubly-fed wind farm impedance matrix. According to the generalized Nyquist criterion, the stability of the system can be determined.

[0064] In order to obtain the small signal impedance model of the doubly-fed generator, the relationship between the stator current and the stator voltage needs to be obtained from the grid-connected point to the doubly-fed generator side. Therefore, it is necessary to add a small signal disturbance to the grid-connected point voltage, which is defined as follows:

[0065]

[0066] Among them U sd and U sqare the steady-state operating points of the stator voltage in the synchronous rotating coordinate system, then the expressions of the stator and rotor current disturbances and the rotor voltage disturbances can be obtained: The expressions of the rotor current disturbances and the stator voltage disturbances are:

[0067]

[0068]

[0069] a=R r +s[L rr -kL m 2 (L ss ω s 2 +LL ss s 2 +R s s)]+L m 2 R s kω2ω s

[0070] b=ω2[L rr -kL m 2 (L ss ω s 2 +L ss s 2 +R s s)]-L m 2 R s kω s s

[0071] c=L m k[L ss (s 2 +ω2ω s )+sR s ]

[0072] d=L m k[L ss ω s s-ω2(R s +L ss s)] (18)

[0073] Where k = 1 / L ss 2 ω s 2 +L ss 2 s 2 +2L ss R s s+Rs 2 , G irs and G irr They are the small signal disturbance transfer functions from stator and rotor voltage to rotor current respectively.

[0074] Similarly, the expressions of rotor current disturbance and stator voltage disturbance can be obtained:

[0075]

[0076]

[0077] Where k1 = L m L ss ω s 2 +L m L ss s 2 +L m R s s, G sr and G iss are the small signal disturbance transfer functions from rotor current and stator voltage to stator current respectively. According to equations (17) and (20), the small signal block diagram of the main circuit of the doubly fed machine can be obtained as follows: Figure 3 shown.

[0078] By Figure 3 It can be obtained that the main circuit output impedance of the doubly fed generator is:

[0079] Z o =(G iss +G sr G irs ) -1 (twenty one)

[0080] The current loop of the doubly-fed machine mainly realizes the decoupling control of the excitation current and the active current. The small signal model of the disturbance voltage passing through the RSC current loop is as follows:

[0081]

[0082] in:

[0083]

[0084]

[0085]

[0086] The phase-locked loop of the doubly-fed generator is mainly used to detect the phase of the three-phase voltage of the power grid and obtain the coordinate transformation angle Δθ of the dq axis coordinate system. PLL, providing a reference for coordinate transformation for the system. Its most important manifestation is that when the grid-connected point voltage is disturbed, the disturbance will be introduced into various variables of the system through the phase-locked loop. The relationship between the phase-locked loop dq coordinate system and the system dq coordinate system variables is as follows:

[0087]

[0088] By performing small signal processing on equation (26), we can obtain:

[0089]

[0090] Δθ is given below PLL The expression is:

[0091]

[0092] in: in is the d-axis component of the static operating point of the stator current in the dq coordinate system, and They are the proportional coefficient and integral coefficient of the phase-locked loop respectively.

[0093] Substituting (28) into (27) and letting x represent different physical quantities, we can obtain the transfer function matrix of the grid-connected voltage winding pair to the stator-rotor current and stator-rotor voltage through the phase-locked loop:

[0094]

[0095]

[0096] The output active and reactive power small signal model of the doubly-fed generator is as follows:

[0097]

[0098] in:

[0099]

[0100] According to Figure 2 The output impedance model of the doubly-fed generator can be obtained as follows:

[0101] Z dfig =(G iss +G irs G sr +G de G irr G iss K1+G de G irr G sr K2) -1 ·(G de Girr K3+E)

[0102] K1=G ci -G d1

[0103]

[0104]

[0105] After equal value aggregation, the impedance model of the doubly-fed wind farm with n doubly-fed wind turbines of the same model is obtained:

[0106]

[0107] Finally, the output impedance model of the doubly fed wind farm can be expressed in the form of a second-order matrix:

[0108]

[0109] Where: Z dd , Z dq , Z qd , Z qq Z DFIG The dd, dq, qd, and qq axis components of the grid impedance model are also in the form of a second-order matrix:

[0110]

[0111] Then the doubly-fed wind farm grid-connected system is equivalent to a multiple-input multiple-output (MIMO) system. The equivalent MIMO system is as follows: Figure 4 As shown. Among them:

[0112] Z sys (s) = Z DFIG (s) (37)

[0113] Then the stability analysis is performed by the generalized Nyquist criterion, and the return rate matrix Z is judged G (s) / Z sys The stability of the closed-loop system can be judged by the sum of the times the Nyquist curve of the (s) eigenvalue circles the point (-1, j0) counterclockwise. The influence of the operating status, grid connection conditions and control system characteristics of the doubly fed wind farm on the system stability can be more vividly observed.

[0114] The frequency scanning results of the output impedance model of the double-fed wind farm are as follows: Figure 5 shown. Figure 5 The gray line in the middle is the calculated output impedance result, and the circle is the simulation test result. The correctness of the established double-fed wind farm output impedance model is verified.

[0115] Figure 6 The root locus diagram of the rate of return matrix under different short-circuit ratios is given. It can be seen from the figure that as the short-circuit ratio gradually decreases, the eigenvalue of the rate of return matrix gradually approaches the point (-1, j0), indicating that the system gradually becomes unstable as the short-circuit ratio decreases.

[0116] Figure 7 The time domain simulation results are given, and it can be seen that the short circuit ratio drops from 3 to 1 in ten seconds. The voltage and current at the machine end diverge and oscillate instably, indicating that the system is in an unstable oscillation state at this time, verifying Figure 6 accuracy.

[0117] The number of wind turbines connected to the grid in a wind farm is different. From the feedback matrix, it can be seen that the more wind turbines connected to the grid, the more equivalent the equivalent inductance of the grid is, which reduces the short-circuit ratio. That is, the more wind turbines connected to the grid, the smaller the short-circuit ratio is, and the easier it is for the system to become unstable and oscillate.

[0118] Figure 8 The root locus diagram of the rate matrix under different rotor-side proportional integral coefficients is given. It can be seen that as the proportional integral decreases, the root locus gradually moves away from the point (-1, j0) and the system tends to be stable. Fig. 9 The stator current waveform under time domain simulation is given. It can be seen that after the proportional integral on the rotor side changes from 0.3 to 0.5 at 10 seconds, the system loses stability briefly and then tends to converge. Figure 8 This is because when the proportional integral is 0.5, the eigenvalue trajectory of the rate matrix just reaches the point (-1, j0), which is just at the boundary of instability.

[0119] from Fig.10 It can be seen that as the proportional integral of the phase-locked loop increases, the eigenvalue trajectory of the system rate matrix gradually bypasses the point (-1, j0). It can be concluded that as the proportional integral of the phase-locked loop increases, the doubly fed wind farm grid-connected system will gradually lose stability and eventually oscillate.

[0120] Through the above simulation examples, it can be seen that the small signal impedance model of the doubly-fed wind farm grid-connected system proposed in the present invention can be used to analyze the stability of the doubly-fed wind farm grid-connected system, and provide a basis for improving the system stability under different grid strengths, different numbers of wind turbines, and in the design of doubly-fed wind turbine controllers, and provide a strong theoretical basis for the sub / super synchronous oscillations caused by large-scale wind power grid-connected systems.

[0121] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A stability analysis method based on the output impedance model of a doubly-fed wind farm grid-connected system, characterized in that: The following steps are involved: 1) Establish a small signal impedance model of the main circuit of the doubly-fed wind turbine in a synchronous rotating coordinate system; 2) Based on the small signal impedance model of the main circuit of the doubly-fed wind turbine generator set, a small signal impedance model considering the current loop, phase-locked loop and power loop is established in a synchronous coordinate system; 3) The small signal impedance model of the doubly-fed wind farm in the synchronous coordinate system is obtained through equivalent aggregation; 4) Establish a grid impedance model in a synchronous coordinate system; 5) The grid-connected doubly-fed wind farm system is equivalent to a multi-input multi-output system. The return matrix of the system is obtained, that is, the grid impedance matrix multiplied by the doubly-fed wind farm impedance matrix. According to the generalized Nyquist criterion, the stability of the system can be judged; The small signal impedance model of the doubly-fed generator in step 1) is: Z dfig =(G iss +G irs G sr +G de G irr G iss K1+G de G irr G sr K2) -1 ·(G de G irr K3+E) K1=G ci -G d1 The disturbance voltage small signal impedance model of the current loop of the doubly-fed generator in step 2) is: in: The phase-locked loop of the doubly-fed motor in step 2) is mainly used to detect the phase of the three-phase voltage of the power grid, obtain the coordinate transformation angle ΔθPLL of the dq axis coordinate system, and provide a coordinate transformation reference for the system; its most important performance is that when the voltage at the grid connection point is disturbed, its disturbance will be introduced into various variables of the system through the phase-locked loop; then the relationship between the phase-locked loop dq coordinate system and the system dq coordinate system variables is as follows: By performing small signal processing on equation (7), we can obtain: The Δθ PLL The expression is: in: in is the d-axis component of the static operating point of the stator current in the dq coordinate system, and They are the proportional coefficient and integral coefficient of the phase-locked loop respectively; The small signal impedance model of the power loop of the doubly-fed generator in step 2) is: in:

2. The stability analysis method based on the output impedance model of the doubly-fed wind farm grid-connected system according to claim 1 is characterized by: In the step 1), in order to obtain the small signal impedance model of the doubly-fed machine, from the grid connection point to the doubly-fed machine side, it is necessary to obtain the relationship between the stator current and the stator voltage, so it is necessary to add a small signal disturbance to the grid connection point voltage, which is defined as follows:

3. The stability analysis method based on the output impedance model of the doubly-fed wind farm grid-connected system according to claim 1 is characterized by: In the step 3), the impedance model of the doubly-fed wind farm having n doubly-fed wind turbines of the same model is obtained through equivalent aggregation:

4. The stability analysis method based on the output impedance model of the doubly-fed wind farm grid-connected system according to claim 1 is characterized by: The output impedance model of the doubly-fed wind farm can be expressed in the form of a second-order matrix: Among them: Zdd, Zdq, Zqd, Zqq are Z DFIG The dd, dq, qd, and qq axis components.

5. A stability analysis method based on the output impedance model of a double-fed wind farm grid-connected system according to claim 1 The method is characterized by: In step 4), the grid impedance model is expressed as a second-order matrix:

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