Stable control method and system for strong interaction of new energy power system

Abstract

The present application relates to a kind of new energy power system strong interaction stability control method, belong to power system stability and control technical field, solve the problem of low reliability caused by the fact that the transient stability control strategy in the prior art cannot effectively improve the transient stability of wind farm system.The outlet voltage and current of each wind turbine at the time of fault occurrence are collected;Based on the outlet voltage and current of each wind turbine, the inductive energy, machine network energy, inter-machine energy of direct-drive wind farm and the storage energy after disturbance of the DC voltage outer loop subsystem, phase-locked loop link subsystem and filter line d-axis subsystem of each wind turbine are obtained, and then the system storage energy of direct-drive wind farm is obtained;Based on each control parameter, and taking the minimum value of the system storage energy of direct-drive wind farm as the objective function constraint condition, a multi-control parameter collaborative optimization model is established, the optimal solution of the multi-control parameter collaborative optimization model is solved to obtain the specific value of each control parameter, and the stability control of direct-drive wind farm is realized.

Description

Technical Field

[0001] This invention relates to the field of power system stability and control technology, and in particular to a method and system for stabilizing and controlling strong interactions in a new energy power system. Background Technology

[0002] As the share of new energy power systems, such as wind power, in my country's energy structure continues to increase, the high efficiency and high reliability of wind farms have become important goals for wind energy development. In recent years, power systems both domestically and internationally have experienced numerous wind turbine disconnection accidents caused by large-scale disturbances due to faults. For example, in October 2009, a fault occurred at a doubly-fed induction generator (DFIG) wind farm in Texas, USA, where the crowbar protection device burned out due to overcurrent, ultimately leading to a large-scale wind turbine disconnection accident. In August 2019, a large-scale power outage occurred in the UK, with offshore wind turbines experiencing successive trips, triggering a chain reaction of faults and causing power outages in some areas, affecting more than one million people. Therefore, research on transient stability control strategies for new energy power systems has significant application value. Currently, research on transient stability control strategies for new energy power systems does not fully consider the impact of control system parameters on the transient stability of the new energy power system. This results in transient stability control strategies that often fail to effectively improve the transient stability of wind farm systems and have low reliability. Summary of the Invention

[0003] Based on the above analysis, the embodiments of the present invention aim to provide a strong interaction stability control method and system for new energy power systems, in order to solve the problem of low reliability caused by the inability of existing transient stability control strategies to effectively improve the transient stability of wind farm systems.

[0004] On one hand, embodiments of the present invention provide a method for stabilizing a new energy power system with strong interaction, comprising the following steps:

[0005] When a fault occurs in a direct-drive wind farm in a new energy power system, the output voltage and current of each wind turbine are collected at the moment the fault occurs.

[0006] Based on the outlet voltage and current of each wind turbine, the induced energy, grid energy, and inter-turbine energy of the direct-drive wind farm are obtained, as well as the stored energy after disturbance of the DC voltage outer loop subsystem, phase-locked loop subsystem, and filter line d-axis subsystem of each wind turbine, and thus the system stored energy of the direct-drive wind farm is obtained.

[0007] Based on the selected control parameters, and with the objective function constraint of minimizing the system storage energy of the direct-drive wind farm, a multi-control parameter collaborative optimization model is established. The optimal solution of the multi-control parameter collaborative optimization model is solved to obtain the specific values ​​of each control parameter. Based on the specific values ​​of each control parameter, the stability control of the direct-drive wind farm is realized.

[0008] Furthermore, the gain coefficient k of the phase-locked loop proportional element for each wind turbine is selected. ipθ Gain coefficient k of the integral element iIθ DC voltage outer loop proportional element gain coefficient k ipu Gain coefficient k of the integral element iIu And the distance L from each wind turbine to the grid connection bus of the wind farm i As control parameters; the multi-control parameter collaborative optimization model is expressed as:

[0009]

[0010] In the formula, W 存储 Let W' represent the system stored energy of a direct-drive wind farm, f represent a function of the control parameters, and W' represent the energy stored in the system. idc 、W′ iθ 、W′ id1 Let k represent the rate of change of stored energy after disturbance in the DC voltage outer loop subsystem, phase-locked loop subsystem, and filter circuit d-axis subsystem of the i-th wind turbine, respectively. ipumin k ipumax These represent the lower and upper limits of the gain coefficient of the outer loop proportional element of the DC voltage of the i-th wind turbine in a direct-drive wind farm, respectively; k ipθmin k ipθmax These represent the lower and upper limits of the gain coefficient of the phase-locked loop proportional element of the i-th wind turbine in a direct-drive wind farm, respectively; k iIumin k iIumax Let k represent the lower and upper limits of the gain coefficient of the outer loop integral element of the DC voltage of the i-th wind turbine in a direct-drive wind farm, respectively. iIθmin k iIθmax represents the lower and upper limits of the gain coefficient of the phase-locked loop integral element of the i-th wind turbine in a direct-drive wind farm, respectively; n represents the total number of wind turbines in the direct-drive wind farm.

[0011] Furthermore, the system stored energy W of the direct-drive wind farm 存储 Represented as:

[0012]

[0013] in,

[0014]

[0015]

[0016] In the formula, L T The inductance r represents the transformer at the output of the transmission line of a direct-drive wind farm. l l l These represent the resistance and inductance per unit length from the wind turbine outlet to the grid-connected bus, respectively, k.iIq U represents the integral coefficient of the reactive power of the i-th wind turbine in the outer loop. s The voltage at the grid connection point, Δu md , Δu mq Represent the d-axis and q-axis voltage transient components at the fault point of the transmission line of a direct-drive wind farm, respectively; C represents the DC bus capacitance between the machine-side converter and the grid-side converter; R li L li Let Y and R represent the resistance and inductance from the sampling point of the phase-locked loop (PLL) on the transmission line corresponding to the i-th wind turbine to the fault point, respectively. f L f Representing the filter resistor and inductor of the grid-side converter, respectively, t represents time, k jpθ k jIθ Let represent the gain coefficients of the proportional and integral elements of the phase-locked loop for the j-th wind turbine, respectively.

[0017] Furthermore, the rate of change of stored energy W′ after disturbance of the DC voltage outer loop subsystem of the i-th wind turbine idc Represented as:

[0018]

[0019] The rate of change of stored energy W′ after disturbance of the phase-locked loop subsystem of the i-th wind turbine iθ Represented as:

[0020]

[0021] in,

[0022] Furthermore, the rate of change of stored energy W′ after disturbance of the filter line d-axis subsystem of the i-th wind turbine id1 Represented as:

[0023]

[0024] Furthermore, the optimal solution of the multi-control parameter collaborative optimization model is obtained as the specific value of each control parameter through the following method:

[0025] S41. Obtain the initial values ​​of each control parameter at the time of the fault occurrence. Based on the outlet voltage and current of each wind turbine at the time of the fault occurrence and the initial values ​​of each control parameter, obtain the initial value of the system's stored energy and use the initial values ​​of each control parameter as the initial solution. Use the initial solution as the current solution for iteration.

[0026] S42. Based on the current solution, randomly select the solution change amount to generate a new solution. The new solution must satisfy the multi-control parameter collaborative optimization model. If it does not satisfy the model, reselect the solution change amount to generate a new solution until the multi-control parameter collaborative optimization model is satisfied and a new solution is obtained.

[0027] S43. Based on the voltage and current at the outlet of each wind turbine in the direct-drive wind farm during the fault and the new solution, the system stored energy of the current iteration is obtained, and then the system stored energy difference with the system stored energy of the previous iteration is obtained.

[0028] S44. Determine whether the new solutions generated in continuous iterations with a set threshold for the number of iterations do not satisfy the requirement that the difference in system storage energy is less than 0.

[0029] If so, then the last solution that satisfies the storage energy difference being greater than 0 is taken as the optimal solution;

[0030] Otherwise, if the difference in system storage energy is less than 0, the new solution obtained in this iteration will be used as the current solution for the next iteration, and the process will return to step S42 for the next iteration.

[0031] If the energy difference in the system storage is not less than 0, then the current solution at this iteration is used as the current solution for the next iteration, and the process returns to step S42 for the next iteration.

[0032] Furthermore, the number threshold is set to 10.

[0033] On the other hand, embodiments of the present invention provide a strong interaction stability control system for a new energy power system, comprising:

[0034] The data acquisition module is used to collect the output voltage and current of each wind turbine at the moment of the fault when a fault occurs in a direct-drive wind farm in the new energy power system.

[0035] The system storage energy calculation module is used to obtain the induced energy, grid energy, and inter-unit energy of the direct-drive wind farm based on the outlet voltage and current of each wind turbine, as well as the stored energy after disturbance of the DC voltage outer loop subsystem, phase-locked loop subsystem, and filter line d-axis subsystem of each wind turbine, and then obtain the system storage energy of the direct-drive wind farm.

[0036] The stability control module is used to establish a multi-control parameter collaborative optimization model based on the selected control parameters and with the objective function constraint of minimizing the system storage energy of the direct-drive wind farm. The optimal solution of the multi-control parameter collaborative optimization model is solved to obtain the specific values ​​of each control parameter, and the stability control of the direct-drive wind farm is realized based on the specific values ​​of each control parameter.

[0037] Furthermore, the gain coefficient k of the phase-locked loop proportional element for each wind turbine is selected in the stability control module. ipθGain coefficient k of the integral element iIθ DC voltage outer loop proportional element gain coefficient k ipu Gain coefficient k of the integral element iIu And the distance L from each wind turbine to the grid connection bus of the wind farm i As control parameters; the multi-control parameter collaborative optimization model is expressed as:

[0038]

[0039] In the formula, W 存储 Let W' represent the system stored energy of a direct-drive wind farm, f represent a function of the control parameters, and W' represent the energy stored in the system. idc 、W′ iθ 、W′ id1 Let k represent the rate of change of stored energy after disturbance in the DC voltage outer loop subsystem, phase-locked loop subsystem, and filter circuit d-axis subsystem of the i-th wind turbine, respectively. ipumin k ipumax These represent the lower and upper limits of the gain coefficient of the outer loop proportional element of the DC voltage of the i-th wind turbine in a direct-drive wind farm, respectively; k ipθmin k ipθmax These represent the lower and upper limits of the gain coefficient of the phase-locked loop proportional element of the i-th wind turbine in a direct-drive wind farm, respectively; k iIu min k iIu max Let k represent the lower and upper limits of the gain coefficient of the outer loop integral element of the DC voltage of the i-th wind turbine in a direct-drive wind farm, respectively. iIθmin k iIθmax represents the lower and upper limits of the gain coefficient of the phase-locked loop integral element of the i-th wind turbine in a direct-drive wind farm, respectively; n represents the total number of wind turbines in the direct-drive wind farm.

[0040] Compared with the prior art, the present invention can achieve at least one of the following beneficial effects:

[0041] This invention provides a method and system for stable control of a new energy power system under strong interaction. It obtains the system stored energy of a direct-drive wind farm by collecting the outlet voltage and current of each wind turbine at the moment of a fault. Based on selected control parameters and with the minimum system stored energy of the direct-drive wind farm as the objective function constraint, a multi-control parameter collaborative optimization model is established. The optimal solution of the multi-control parameter collaborative optimization model is solved to obtain the specific values ​​of each control parameter. Based on these specific values, the stability control of the direct-drive wind farm is achieved, effectively improving the transient stability control under strong interaction of the new energy power system and enhancing the reliability of the stability control.

[0042] In this invention, the above-described technical solutions can be combined with each other to achieve more preferred combinations. Other features and advantages of this invention will be set forth in the following description, and some advantages may become apparent from the description or be learned by practicing the invention. The objects and other advantages of this invention can be realized and obtained from what is particularly pointed out in the description and drawings. Attached Figure Description

[0043] The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Throughout the drawings, the same reference numerals denote the same parts.

[0044] Figure 1 A flowchart illustrating the strong interaction stability control method for a new energy power system provided in Embodiment 1 of the present invention;

[0045] Figure 2 This is a schematic diagram of the direct-drive wind farm grid connection system provided in Embodiment 3 of the present invention;

[0046] Figure 3 The graphs show the power angle response curves of PMSG1-3 after optimization with and without the parameters provided in Embodiment 3 of the present invention.

[0047] Figure 4 The transient energy of the outer loop voltage of PMSG1-3 before and after parameter optimization of the direct-drive wind farm provided in Embodiment 3 of the present invention;

[0048] Figure 5 The transient energy of PMSG1-3 phase-locked loop and filter line before and after parameter optimization of the direct-drive wind farm provided in Embodiment 1 of the present invention. Detailed Implementation

[0049] Preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings, which form part of this application and are used together with the embodiments of the present invention to illustrate the principles of the present invention, but are not intended to limit the scope of the present invention.

[0050] Example 1

[0051] A specific embodiment of the present invention discloses a method for stabilizing a new energy power system with strong interaction, such as... Figure 1 As shown, it includes the following steps:

[0052] S1. When a fault occurs in a direct-drive wind farm in the new energy power system, collect the output voltage and current of each wind turbine at the moment the fault occurs.

[0053] Specifically, voltage and current data at the outlet of each wind turbine in the direct-drive wind farm system are measured using voltage and current transformers.

[0054] S2. Based on the outlet voltage and current of each wind turbine, the induced energy, grid energy, and inter-turbine energy of the direct-drive wind farm are obtained, as well as the stored energy after disturbance of the DC voltage outer loop subsystem, phase-locked loop subsystem, and filter line d-axis subsystem of each wind turbine, and then the system stored energy of the direct-drive wind farm is obtained.

[0055] S3. Based on the selected control parameters, and with the objective function constraint of minimizing the system storage energy of the direct-drive wind farm, establish a multi-control parameter collaborative optimization model. Solve the optimal solution of the multi-control parameter collaborative optimization model to obtain the specific values ​​of each control parameter. Based on the specific values ​​of each control parameter, realize the stability control of the direct-drive wind farm.

[0056] During implementation, the gain coefficient k of the phase-locked loop proportional element for each wind turbine is selected. ipθ Gain coefficient k of the integral element iIθ DC voltage outer loop proportional element gain coefficient k ipu Gain coefficient k of the integral element iIu And the distance L from each wind turbine to the grid connection bus of the wind farm i As control parameters; the multi-control parameter collaborative optimization model is expressed as:

[0057]

[0058] In the formula, W 存储 Let W' represent the system stored energy of a direct-drive wind farm, f represent a function of the control parameters, and W' represent the energy stored in the system. idc 、W′ iθ 、W′ id1 Let k represent the rate of change of stored energy after disturbance in the DC voltage outer loop subsystem, phase-locked loop subsystem, and filter circuit d-axis subsystem of the i-th wind turbine, respectively. ipu min k ipu max These represent the lower and upper limits of the gain coefficient of the outer loop proportional element of the DC voltage of the i-th wind turbine in a direct-drive wind farm, respectively; k ipθmin k ipθmax These represent the lower and upper limits of the gain coefficient of the phase-locked loop proportional element of the i-th wind turbine in a direct-drive wind farm, respectively; k iIu min k iIu max Let k represent the lower and upper limits of the gain coefficient of the outer loop integral element of the DC voltage of the i-th wind turbine in a direct-drive wind farm, respectively. iIθmin k iIθmax represents the lower and upper limits of the gain coefficient of the phase-locked loop integral element of the i-th wind turbine in a direct-drive wind farm, respectively; n represents the total number of wind turbines in the direct-drive wind farm.

[0059] In practical implementation, the system stored energy W of the direct-drive wind farm 存储 Represented as:

[0060]

[0061] in,

[0062]

[0063] In the formula, L T The inductance r represents the transformer at the output of the transmission line of a direct-drive wind farm. l l l These represent the resistance and inductance per unit length from the wind turbine outlet to the grid-connected bus, respectively, k. iIq U represents the integral coefficient of the reactive power of the i-th wind turbine in the outer loop. s The voltage at the grid connection point, Δu md , Δu mq Represent the d-axis and q-axis voltage transient components at the fault point of the transmission line of a direct-drive wind farm, respectively; C represents the DC bus capacitance between the machine-side converter and the grid-side converter; R li L li Let Y and R represent the resistance and inductance from the sampling point of the phase-locked loop (PLL) on the transmission line corresponding to the i-th wind turbine to the fault point, respectively. f L f Representing the filter resistor and inductor of the grid-side converter, respectively, t represents time, k jpθ k jIθ Let represent the gain coefficients of the proportional and integral elements of the phase-locked loop for the j-th wind turbine, respectively.

[0064] Specifically, the rate of change of stored energy W′ after disturbance of the DC voltage outer loop subsystem of the i-th wind turbine. idc Represented as:

[0065]

[0066] Specifically, the rate of change of stored energy W′ after disturbance of the phase-locked loop subsystem of the i-th wind turbine. iθ Represented as:

[0067]

[0068] in,

[0069] Specifically, the rate of change of stored energy W′ after disturbance of the filter circuit d-axis subsystem of the i-th wind turbine. id1 Represented as:

[0070]

[0071] Preferably, the optimal solution of the multi-control parameter collaborative optimization model is obtained as the specific value of each control parameter through the following method:

[0072] S41. Obtain the initial values ​​of each control parameter at the time of the fault occurrence. Based on the outlet voltage and current of each wind turbine at the time of the fault occurrence and the initial values ​​of each control parameter, obtain the initial value of the system's stored energy and use the initial values ​​of each control parameter as the initial solution. Use the initial solution as the current solution for iteration.

[0073] S42. Based on the current solution, randomly select the solution change amount to generate a new solution. The new solution must satisfy the multi-control parameter collaborative optimization model. If it does not satisfy the model, reselect the solution change amount to generate a new solution until the multi-control parameter collaborative optimization model is satisfied and a new solution is obtained.

[0074] S43. Based on the voltage and current at the outlet of each wind turbine in the direct-drive wind farm during the fault and the new solution, the system stored energy of the current iteration is obtained, and then the system stored energy difference with the system stored energy of the previous iteration is obtained.

[0075] S44. Determine whether the new solutions generated in continuous iterations with a set threshold for the number of iterations do not satisfy the requirement that the difference in system storage energy is less than 0.

[0076] If so, then the last solution that satisfies the storage energy difference being greater than 0 is taken as the optimal solution;

[0077] Otherwise, if the difference in system storage energy is less than 0, the new solution obtained in this iteration will be used as the current solution for the next iteration, and the process will return to step S42 for the next iteration.

[0078] If the energy difference in the system storage is not less than 0, then the current solution at this iteration is used as the current solution for the next iteration, and the process returns to step S42 for the next iteration.

[0079] Specifically, the number threshold is set to 10.

[0080] To facilitate a better understanding of the formation process of the solution in this embodiment by those skilled in the art, the working principle of a strong interaction stability control method for a new energy power system provided in this embodiment is explained below:

[0081] For the direct-drive wind farm transmission system in the new energy power system, based on the voltage and current components of the physical components and control links in the direct-drive wind farm transmission system, the system can be divided into 6 subsystems, namely the transmission line d / q axis, the filter line d / q axis, the DC voltage outer loop link, and the phase-locked loop link subsystem.

[0082] In the entire grid-connected system of a direct-drive wind farm, the system stored energy W of the entire direct-drive wind farm is... 存储 The following equation holds true:

[0083]

[0084] In the formula, W 感应 This represents induced energy, which is the energy of the wind turbine itself; W 机网 This represents grid-connected energy, specifically the energy exchanged between the wind turbine and the power grid; W 机间 The energy between turbines represents the energy exchanged between the turbines within the wind farm; n is the total number of turbines in the direct-drive wind farm; W idc W iθ W id1 These represent the stored energy of the DC voltage outer loop subsystem, phase-locked loop subsystem, and filter line d-axis subsystem of the i-th wind turbine after disturbance, respectively.

[0085] According to Lyapunov's second method, the rate of change of system stored energy reflects the speed at which transient energy accumulates or dissipates in the corresponding system per unit time. When the rate of change of system stored energy is positive, the system accumulates transient energy, which is detrimental to system stability; conversely, the system dissipates transient energy, which is beneficial to system stability. Based on the specific transient energy transmission path, it can be seen that the transient energy of the filter circuit d-axis subsystem, the DC voltage outer loop subsystem, and the phase-locked loop subsystem is detrimental to system stability. The specific derivation is given below:

[0086] The DC voltage outer loop parameters mainly affect the stored energy of the DC voltage outer loop subsystem. The stored energy W of the DC voltage outer loop subsystem of the i-th wind turbine after being disturbed is... idc ,have:

[0087]

[0088] in,

[0089]

[0090] In the formula, W1 and W2 are the transient energy generated by the interaction between the transient component of the DC-side voltage of the wind turbine grid-side converter and the transient component of the DC voltage outer loop, respectively; W3 is the transient energy generated by the interaction between the transient component of the DC-side voltage of the wind turbine grid-side converter and the transient component of the d-axis current of the transmission line; W4 and W5 are the transient energy generated by the interaction between the transient component of the DC-side voltage of the wind turbine grid-side converter and the transient components of the current transmitted from the machine-side converter to the DC bus and the transient components of the current transmitted from the DC bus to the grid-side converter, respectively; W6 is the transient energy generated by the interaction of the internal links of the DC voltage outer loop; C represents the DC bus capacitance between the machine-side converter and the grid-side converter; Δu idc Let Δi be the transient voltage component of the DC bus capacitor between the turbine side and the grid side converter of the i-th wind turbine. ifd Let Δi be the transient component of the d-axis current of the wind turbine. g Δi represents the transient current component transmitted from the DC bus to the grid-side converter. sThis refers to the transient current component transmitted from the machine-side converter to the DC bus. This is the reference value for the outer loop DC voltage of the direct-drive fan; k ipu k ipu These represent the gain coefficients of the proportional and integral elements of the outer loop of the DC voltage for the i-th wind turbine, respectively; k ipθ k iIθ These are the gain coefficients of the proportional and integral elements of the phase-locked loop for the i-th wind turbine, respectively; k iIq Let be the integral coefficient of the reactive power of the i-th wind turbine in the outer loop. R is the reference value for the outer loop DC voltage of the direct-drive fan. li L li U represents the resistance and inductance from the sampling point of the phase-locked loop of the i-th wind turbine to the fault point on the transmission line corresponding to the i-th wind turbine, respectively. s t represents the voltage at the grid connection point, and t represents time.

[0091] Substituting equation (3) into equation (2), we get:

[0092]

[0093] Then W can be obtained under the combined action of the DC voltage outer loop and the phase-locked loop. idc The specific expression is:

[0094]

[0095] Differentiating the above equation using Lyapunov's second method yields:

[0096]

[0097] Equation (6) yields the rate of change of stored energy in the outer loop subsystem of DC voltage for each wind turbine after a disturbance. This rate of change reflects the speed at which transient energy accumulates or dissipates in the corresponding system per unit time. When the rate of change of stored energy is positive, the corresponding system accumulates transient energy, which is detrimental to system stability; conversely, the system dissipates transient energy, which is beneficial to system stability. If the rate of change of stored energy increases, the system will accumulate more transient energy within the same fault duration, causing the system to become unstable more quickly. Since in practical engineering, the phase-locked loop k... iIθ / k ipθ The outer loop voltage k is greater than the DC voltage. iIu / k ipu Substituting this into the rate of change of stored energy, it is easy to see that the coefficient of the rate of change of stored energy in the DC voltage outer loop subsystem is positive, indicating that the stored energy in the DC voltage outer loop subsystem will continuously increase over time, which is not conducive to the stability of the entire system.

[0098] At the same time, regarding equation (6) with respect to kipu Find the partial derivative, using the first variable x1 to represent k. ipu ,have to:

[0099]

[0100] It can be seen that increasing the DC voltage outer loop proportional coefficient will slow down the growth rate of stored energy and the energy accumulation rate in the DC voltage outer loop subsystem, which is more conducive to the transient stability of the system. Conversely, decreasing the DC voltage outer loop proportional coefficient will speed up the growth rate of stored energy and the energy accumulation rate in the DC voltage outer loop subsystem, which is less conducive to the transient stability of the system.

[0101] Similarly, find the rate of change of stored energy with respect to k. iIu The partial derivative of k is represented by the second variable x2. iIu Then we have:

[0102]

[0103] In summary, increasing the DC voltage outer loop proportional coefficient will slow down the growth rate and energy accumulation rate of the stored energy in the DC voltage outer loop subsystem, which is more conducive to the transient stability of the system. Conversely, decreasing the DC voltage outer loop proportional coefficient will speed up the growth rate and energy accumulation rate of the stored energy in the DC voltage outer loop subsystem, which is less conducive to the transient stability of the system.

[0104] The phase-locked loop (PLL) parameters also affect the stored energy of the DC voltage outer loop subsystem, PLL subsystem, and filter line d-axis subsystem of each wind turbine in the wind farm. The stored energy W of the PLL subsystem of the i-th wind turbine after being disturbed is... iθ The expression is:

[0105]

[0106] in,

[0107]

[0108]

[0109]

[0110] In the formula, Δu fq The transient q-axis voltage component of the phase-locked loop sampling point of the wind turbine, where Y is a constant less than 0, and W θ1 and W θ2 It is the transient energy generated by the interaction between the q-axis voltage transient component at the sampling point of the wind turbine phase-locked loop and the phase-locked loop components, W θ3 It is the transient energy generated by the interaction between the transient components of the phase-locked loop voltage and its phase angle; Δθ pllThis refers to the transient phase angle component of the phase-locked loop output affected by the fault.

[0111] Considering W θ1 The order of magnitude is much larger than W θ2 and W θ3 Applying Lyapunov's second method to differentiate equation (9) yields:

[0112]

[0113] Equation (10) represents the rate of change of stored energy of the phase-locked loop subsystem of the i-th wind turbine after being disturbed. As can be seen from Equation (10), the sign of the rate of change of stored energy of the phase-locked loop subsystem is determined by the coefficient in front of it. The coefficient in front of the rate of change of stored energy of the phase-locked loop subsystem is positive, indicating that the stored energy of the phase-locked loop subsystem will increase continuously over time, which is not conducive to the stability of the entire system.

[0114] Similarly, the stored energy W of the d-axis subsystem of the filter line after being disturbed is obtained. id1 The specific expression is:

[0115]

[0116] Where, ω pll =ω0+Δω;

[0117] In the formula, W i1d W i2d and W i3d These represent the transient energy generated by the interaction between the transient component of the d-axis current of the filter line and the transient component of the d-axis voltage at the fan port, the interaction between the transient component of the d-axis current of the filter line and the transient component of the d-axis voltage at the fan phase-locked loop sampling point, and the interaction between the transient component of the d-axis current of the filter line and the transient component of the q-axis current of the filter line, respectively; R f L f These are the filter resistor and inductor of the grid-side converter, respectively, Δv fd and Δi fd These are the transient components of the d-axis voltage and current at the fan port, ω. pll ω0 is the output angular frequency of the phase-locked loop after the fault, ω0 is the power frequency angular velocity, and Δω is the transient component of the phase-locked loop angular frequency after being disturbed.

[0118] Differentiating equation (11) using Lyapunov's second method yields:

[0119]

[0120] Equation (12) represents the rate of change of stored energy of the d-axis subsystem of the filter line of the i-th wind turbine after being disturbed. Analyzing equation (12), it can be seen that the sign of the rate of change of the total stored energy of the d-axis subsystem of the filter line after being disturbed is determined by the coefficient preceding it. Since k iIθ / k ipθ Less than R f / L f Substituting this into the coefficient analysis of the rate of change of stored energy, we can see that the rate of change of total stored energy of the d-axis subsystem of the filter line after being disturbed is greater than 0. Therefore, the stored energy of the d-axis subsystem of the filter line after being disturbed will continue to increase over time, which is not conducive to the stability of the entire system.

[0121] Similar to the analysis of the influence of DC voltage outer loop parameters on the transient energy of the wind turbine, it is easy to see that when a system fault occurs, the influence of the phase-locked loop control parameters on the rate of change of stored energy is k. ipθ The larger or k iIθ The smaller the value, the slower the accumulation rate of stored energy in the DC voltage outer loop subsystem, phase-locked loop subsystem, and filter line d-axis subsystem of each wind turbine in the wind farm, which is more conducive to the transient stability of the system. However, the phase-locked loop control parameters of the wind turbines in the wind farm will not change the transmission direction of stored energy in the three subsystems, but will affect the accumulation rate of transient stored energy.

[0122] In summary, the transient energy storage of the DC voltage outer loop subsystem, the phase-locked loop subsystem, and the d-axis subsystem of the filter circuit is detrimental to system stability, and the DC voltage outer loop control parameter k... iIu / k ipu Phase-locked loop control parameter k iIθ / k ipθ This is a key parameter affecting energy storage; therefore, the gain coefficient k of the phase-locked loop proportional element of each wind turbine is selected. ipθ Gain coefficient k of the integral element iIθ DC voltage outer loop proportional element gain coefficient k ipu Gain coefficient k of the integral element iIu As a control parameter.

[0123] Based on the composition of a direct-drive wind farm, the inductive energy, grid energy, and inter-unit energy of the direct-drive wind farm can be obtained, specifically:

[0124] The inductive energy W of the i-th wind turbine in a direct-drive wind farm i感应 for:

[0125]

[0126] In the formula, Δu di , Δu qi Let Δi be the transient voltage components along the d-axis and q-axis of the i-th wind turbine. qi , Δidi Let ΔU represent the transient current components along the d-axis and q-axis of the i-th wind turbine. s L represents the change in voltage at the grid connection point. T This refers to the inductance of the transformer at the output of the power transmission line of a direct-drive wind farm.

[0127] Therefore, the induced energy W of the direct-drive wind farm can be obtained. 感应 , is represented as:

[0128]

[0129] When a wind farm has n wind turbines, the coupling energy W between the wind farm and the power grid 机网 for:

[0130]

[0131] In the formula, Δu md and Δu mq These are the transient voltage components along the d-axis and q-axis at the fault point of the wind farm's transmission line, respectively.

[0132] The coupling energy W between the i-th and j-th wind turbines in the wind farm i-j机间 for:

[0133]

[0134] Similarly, the inter-machine coupling energy W generated by the interaction between the transient current component of the j-th wind turbine and the transient current component of the i-th wind turbine in the wind farm is... j-i机间 Transient energy will also be transferred from the j-th wind turbine to the i-th wind turbine in the wind farm. Therefore, the inter-machine coupling energy W transferred from the i-th wind turbine to the j-th wind turbine in the wind farm... i-j机间 The inter-machine coupling energy W transferred from the j-th wind turbine to the i-th wind turbine in the wind farm j-i机间 They will cancel each other out, and the final result will be the coupling energy W between the i-th wind turbine and the other wind turbines in the wind farm. i机间 The specific expression is:

[0135]

[0136] When a wind farm has n wind turbines, the inter-turbine coupling energy is W. 机间 The specific expression is:

[0137]

[0138] Therefore, according to equation (1), the system stored energy of a direct-drive wind farm can be expressed as:

[0139]

[0140] In the formula, L ir represents the distance from the i-th wind turbine to the grid connection bus. l and l l These represent the resistance and inductance per unit length from the fan outlet to the grid-connected bus, respectively.

[0141] According to Lyapunov's second method, the rate of change of stored energy reflects the speed at which transient energy accumulates or dissipates in the system per unit time. When the rate of change of stored energy is positive, the system accumulates transient energy, which is detrimental to system stability; conversely, the system dissipates transient energy, which is beneficial to system stability.

[0142] Therefore, with the goal of minimizing the system storage energy of a direct-drive wind farm, and considering the parameters that affect the storage energy, the optimization objective function is obtained as follows:

[0143]

[0144] Considering the impact of the distance between the wind turbine and the grid bus on the system's energy storage, the control parameter is selected as (k). ipθ k iIθ k ipu k iIu L i When the control parameters change, the stored energy of the new direct-drive wind farm is obtained. when When the stored energy of the wind farm decreases, it indicates that the wind farm's energy storage is reduced, which is beneficial to the transient stability of the wind farm system. Therefore, it can be concluded that when the stored energy of the wind farm decreases, (k ipθ k iIθ k ipu k iIu L i The conditions that need to be met are:

[0145]

[0146] Furthermore, as the above analysis shows, when a fault occurs at the output of the power transmission line of a direct-drive wind farm, the stored energy in the DC voltage outer loop, phase-locked loop, and filter circuit of each wind turbine will continuously increase over time, which is detrimental to the transient stability of the wind farm. Simultaneously, the control parameter (k) ipθ k iIθ k ipu k iIu L i When the control parameter (k) changes, it will have different effects on the rate of change of stored energy in the three stages mentioned above, thereby affecting the transient stability of the system, i.e., the control parameter (k). ipθ k iIθ k ipu k iIu L iWhen the parameters change, the parameter constraints that must be satisfied to ensure the influence of the parameters are as follows:

[0147]

[0148] In the formula, the superscript * on the parameter indicates the variable obtained after the control parameter is changed.

[0149] In summary, a constrained multi-control parameter collaborative optimization control model is constructed, which is expressed as:

[0150]

[0151] In the formula, W 存储 Let W' represent the system stored energy of a direct-drive wind farm, f represent a function of the control parameters, and W' represent the energy stored in the system. idc 、W′ iθ 、W′ id1 Let k represent the rate of change of stored energy after disturbance in the DC voltage outer loop subsystem, phase-locked loop subsystem, and filter circuit d-axis subsystem of the i-th wind turbine, respectively. ipu min k ipu max These represent the lower and upper limits of the gain coefficient of the outer loop proportional element of the DC voltage of the i-th wind turbine in a direct-drive wind farm, respectively; k ipθmin k ipθmax These represent the lower and upper limits of the gain coefficient of the phase-locked loop proportional element of the i-th wind turbine in a direct-drive wind farm, respectively; k iIu min k iIu max Let k represent the lower and upper limits of the gain coefficient of the outer loop integral element of the DC voltage of the i-th wind turbine in a direct-drive wind farm, respectively. iIθmin k iIθmax represents the lower and upper limits of the gain coefficient of the phase-locked loop integral element of the i-th wind turbine in a direct-drive wind farm, respectively; n represents the total number of wind turbines in the direct-drive wind farm.

[0152] During implementation, the optimal solution of the multi-control parameter collaborative optimization model is obtained as the specific value of each control parameter through the following methods:

[0153] S41. Obtain the initial values ​​of each control parameter at the time of the fault occurrence. Based on the outlet voltage and current of each wind turbine at the time of the fault occurrence and the initial values ​​of each control parameter, obtain the initial value of the system's stored energy and use the initial values ​​of each control parameter as the initial solution. Use the initial solution as the current solution for iteration.

[0154] S42. Based on the current solution, randomly select the solution change amount to generate a new solution. The new solution must satisfy the multi-control parameter collaborative optimization model. If it does not satisfy the model, reselect the solution change amount to generate a new solution until the multi-control parameter collaborative optimization model is satisfied and a new solution is obtained. Among them, the solution change amount is selected based on the parameter constraint condition, i.e., equation (22). The solution change amount is added to the current solution in the current iteration to obtain a new solution.

[0155] S43. Based on the voltage and current at the outlet of each wind turbine in the direct-drive wind farm during the fault and the new solution, the system stored energy of the current iteration is obtained, and then the system stored energy difference with the system stored energy of the previous iteration is obtained.

[0156] S44. Determine whether the new solutions generated in continuous iterations with a set threshold for the number of iterations do not satisfy the requirement that the difference in system storage energy is less than 0.

[0157] If so, then the last new solution that satisfies the storage energy difference being greater than 0 is taken as the optimal solution; that is, the last optimal solution taken is the last new solution that satisfies the storage energy difference being greater than 0 in the historical iteration process.

[0158] Otherwise, if the difference in system storage energy is less than 0, the new solution obtained in this iteration will be used as the current solution for the next iteration, and the process will return to step S42 for the next iteration.

[0159] If the energy difference in the system storage is not less than 0, then the current solution at this iteration is used as the current solution for the next iteration, and the process returns to step S42 for the next iteration.

[0160] Specifically, the number threshold is set to 10.

[0161] Compared with existing technologies, this embodiment provides a stable control method for strong interaction in a new energy power system. It obtains the system stored energy of the direct-drive wind farm by collecting the outlet voltage and current of each wind turbine at the moment of a fault. Then, based on selected control parameters and with the minimum system stored energy of the direct-drive wind farm as the objective function constraint, a multi-control parameter collaborative optimization model is established. The optimal solution of the multi-control parameter collaborative optimization model is solved to obtain the specific values ​​of each control parameter. Based on these specific values, the stability control of the direct-drive wind farm is achieved, effectively improving the transient stability control under strong interaction in the new energy power system and enhancing the reliability of the stability control.

[0162] Example 2

[0163] A specific embodiment of the present invention discloses a strong interaction stability control system for a new energy power system, comprising:

[0164] The data acquisition module is used to collect the output voltage and current of each wind turbine at the moment of the fault when a fault occurs in a direct-drive wind farm in the new energy power system.

[0165] The system storage energy calculation module is used to obtain the induced energy, grid energy, and inter-unit energy of the direct-drive wind farm based on the outlet voltage and current of each wind turbine, as well as the stored energy after disturbance of the DC voltage outer loop subsystem, phase-locked loop subsystem, and filter line d-axis subsystem of each wind turbine, and then obtain the system storage energy of the direct-drive wind farm.

[0166] The stability control module is used to establish a multi-control parameter collaborative optimization model based on the selected control parameters and with the objective function constraint of minimizing the system storage energy of the direct-drive wind farm. The optimal solution of the multi-control parameter collaborative optimization model is solved to obtain the specific values ​​of each control parameter, and the stability control of the direct-drive wind farm is realized based on the specific values ​​of each control parameter.

[0167] During implementation, the gain coefficient k of the phase-locked loop proportional element of each wind turbine is selected in the stability control module. ipθ Gain coefficient k of the integral element iIθ DC voltage outer loop proportional element gain coefficient k ipu Gain coefficient k of the integral element iIu And the distance L from each wind turbine to the grid connection bus of the wind farm i As control parameters, the multi-control parameter collaborative optimization model is expressed as:

[0168]

[0169] In the formula, W 存储 Let W' represent the system stored energy of a direct-drive wind farm, f represent a function of the control parameters, and W' represent the energy stored in the system. idc 、W′ iθ 、W′ id1 Let k represent the rate of change of stored energy after disturbance in the DC voltage outer loop subsystem, phase-locked loop subsystem, and filter circuit d-axis subsystem of the i-th wind turbine, respectively. ipu min k ipu max These represent the lower and upper limits of the gain coefficient of the outer loop proportional element of the DC voltage of the i-th wind turbine in a direct-drive wind farm, respectively; k ipθmin k ipθmax These represent the lower and upper limits of the gain coefficient of the phase-locked loop proportional element of the i-th wind turbine in a direct-drive wind farm, respectively; k iIu min k iIu max Let k represent the lower and upper limits of the gain coefficient of the outer loop integral element of the DC voltage of the i-th wind turbine in a direct-drive wind farm, respectively. iIθmin k iIθmax represents the lower and upper limits of the gain coefficient of the phase-locked loop integral element of the i-th wind turbine in a direct-drive wind farm, respectively; n represents the total number of wind turbines in the direct-drive wind farm.

[0170] It should be noted that the system embodiments described above are based on the same principles, and their related aspects can be referenced from each other to achieve the same technical effects.

[0171] Example 3

[0172] To verify the effectiveness of the strong interaction stability control method and system for new energy power systems provided in Embodiments 1 and 2 of this invention, a specific embodiment is provided: based on Figure 2 The structure diagram of the grid-connected direct-drive wind farm system is shown. A simulation model of the direct-drive wind farm system was built on the MATLAB / Simulink platform. The direct-drive wind farm system model adopts a 3-machine system.

[0173] Before optimization, the control parameters of PMSG1-3 in the wind farm were all set as follows: k pθ =1p.u.,k Iθ =1p.u.,k pu =1p.u.,k Iu =1p.u., L=1p.u., under the premise of satisfying the constraints, the simulated annealing algorithm is used to optimize the objective function. After optimization, the parameters of PMSG1-3 in the wind farm are: PMSG1: k pθ =1.42pu,k Iθ =0.9pu,k pu =2.68 pu, k Iu =0.91pu; PMSG2:k pθ =1.03 pu, k Iθ =0.98pu,k pu =1.62 pu, k Iu =0.93pu; PMSG3:k pθ =1.1pu,k Iθ =1p.u.,k pu =1.18pu,k Iu =0.96 pu. The power angle curves of each wind turbine before and after optimization of control and line parameters in a direct-drive wind farm (using the grid bus voltage as a reference voltage) are shown below. Figure 3 After optimizing the wind farm parameters using the simulated annealing algorithm, the transient response time of PMSG1-3 in the wind farm after a fault is significantly shortened compared to before optimization, and the transient change in power angle is significantly reduced. The power angle response characteristics of the wind farm are significantly improved. The parameter co-optimization strategy proposed in this chapter can achieve the effect of improving the power angle stability of the wind farm.

[0174] Comparison of transient energy curves for each wind turbine before and after optimization of control and line parameters in a direct-drive wind farm. Figure 4 and Figure 5As shown.

[0175] Figure 4 and Figure 5 The solid line represents the PMSG1-3 transient energy curve before optimization, and the dashed line represents the PMSG1-3 transient energy curve after optimization. Figure 4 and Figure 5 It can be seen that after optimizing the wind farm parameters using the simulated annealing algorithm, the transient energy of PMSG1-3 in the wind farm after the fault occurs is significantly reduced compared with that before optimization. At the same time, the accumulation rate of transient energy is reduced compared with that before optimization, and the transient stability of the wind farm is significantly improved. The methods and systems proposed in Examples 1 and 2 can achieve the effect of improving the transient stability of the wind farm.

[0176] Those skilled in the art will understand that all or part of the processes of the methods described in the above embodiments can be implemented by a computer program instructing related hardware, and the program can be stored in a computer-readable storage medium. The computer-readable storage medium may be a disk, optical disk, read-only memory, or random access memory, etc.

[0177] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for stable control of strong interaction in a new energy power system, characterized in that, Includes the following steps: When a fault occurs in a direct-drive wind farm in a new energy power system, the output voltage and current of each wind turbine are collected at the moment the fault occurs. Based on the outlet voltage and current of each wind turbine, the induced energy, grid energy, and inter-turbine energy of the direct-drive wind farm are obtained, as well as the DC voltage outer loop subsystem, phase-locked loop subsystem, and filter circuit of each wind turbine. d The stored energy after the axle system is disturbed is then used to obtain the system stored energy of the direct-drive wind farm; Based on the selected control parameters, and with the objective function constraint of minimizing the system storage energy of the direct-drive wind farm, a multi-control parameter collaborative optimization model is established. The optimal solution of the multi-control parameter collaborative optimization model is solved to obtain the specific values ​​of each control parameter. Based on the specific values ​​of each control parameter, the stability control of the direct-drive wind farm is realized. Among them, the gain coefficient of the phase-locked loop proportional element of each wind turbine is selected. Integral gain coefficient DC voltage outer loop proportional element gain coefficient Integral gain coefficient And the distance from each wind turbine to the grid connection bus of the wind farm As control parameters; the multi-control parameter collaborative optimization model is expressed as: ； In the formula, This refers to the system's stored energy in a direct-drive wind farm. Represents a function relating to each control parameter. , , They represent the first i The DC voltage outer loop subsystem, phase-locked loop subsystem, and filter circuit of the typhoon generator d The rate of change of stored energy in the axle system after disturbance. , These represent the first direct-drive wind farm. i The lower and upper limits of the gain coefficient of the outer loop proportional element of the DC voltage of the typhoon generator; , These represent the first direct-drive wind farm. i The lower and upper limits of the gain coefficient of the proportional element in the phase-locked loop of a typhoon generator; , These represent the first direct-drive wind farm. i The lower and upper limits of the gain coefficient of the outer loop integral stage of the DC voltage of a typhoon generator. , These represent the first direct-drive wind farm. i The lower and upper limits of the gain coefficient of the phase-locked loop integral element of a typhoon generator; n This indicates the total number of wind turbines in a direct-drive wind farm.

2. The method for strong interaction stability control of new energy power systems according to claim 1, characterized in that, The system energy storage of the direct-drive wind farm Represented as: ； in, ， ， In the formula, This represents the inductance of the transformer at the output of the transmission line of a direct-drive wind farm. , These represent the resistance and inductance per unit length from the fan outlet to the grid-connected bus, respectively. Indicates the first i The integral coefficient of the reactive power outer loop of the typhoon turbine. Indicates the voltage at the grid connection point. , These represent the fault points of the transmission lines of the direct-drive wind farm. d shaft and q The transient voltage component of the axis, This represents the DC bus capacitance between the generator-side converter and the grid-side converter. , They represent the first i The resistance and inductance from the sampling point of the phase-locked loop (PLL) of the typhoon turbine to the fault point on the corresponding transmission line, where Y represents a constant less than 0. , These represent the filter resistor and inductor of the grid-side converter, respectively. t Indicates time, , They represent the first j The gain coefficients of the proportional and integral elements of the phase-locked loop in a typhoon generator.

3. The method for strong interaction stability control of a new energy power system according to claim 2, characterized in that, The first i Rate of change of stored energy after disturbance of the DC voltage outer loop subsystem of the typhoon Represented as: 。 4. The method for strong interaction stability control of new energy power systems according to claim 2, characterized in that, The first i The rate of change of stored energy in the phase-locked loop subsystem of a typhoon generator after disturbance Represented as: ； in, .

5. The method for strong interaction stability control of new energy power systems according to claim 2, characterized in that, The first i Filtering circuit of typhoon generator d Rate of change of stored energy after disturbance of axion system Represented as: 。 6. The method for strong interaction stability control of a new energy power system according to claim 2, characterized in that, The optimal solution of the multi-control parameter collaborative optimization model is obtained as the specific value of each control parameter through the following method: S41. Obtain the initial values ​​of each control parameter at the time of the fault occurrence, obtain the initial value of the system's stored energy based on the outlet voltage and current of each wind turbine at the time of the fault occurrence and the initial values ​​of each control parameter, and use the initial values ​​of each control parameter as the initial solution. Iterate using the initial solution as the current solution; S42. Based on the current solution, randomly select the solution change amount to generate a new solution. The new solution must satisfy the multi-control parameter collaborative optimization model. If it does not satisfy the model, reselect the solution change amount to generate a new solution until the multi-control parameter collaborative optimization model is satisfied and a new solution is obtained. S43. Based on the voltage and current at the outlet of each wind turbine in the direct-drive wind farm during the fault and the new solution, the system stored energy of the current iteration is obtained, and then the system stored energy difference with the system stored energy of the previous iteration is obtained. S44. Determine whether the new solutions generated in continuous iterations with a set threshold for the number of iterations do not satisfy the requirement that the difference in system storage energy is less than 0. If so, then the last new solution that satisfies the storage energy difference being greater than 0 is taken as the optimal solution; Otherwise, if the difference in system storage energy is less than 0, the new solution obtained in this iteration will be used as the current solution for the next iteration, and the process will return to step S42 for the next iteration. If the energy difference stored in the system is not less than 0, then the current solution at this iteration is used as the current solution for the next iteration, and the process returns to step S42 for the next iteration.

7. The method for strong interaction stability control of a new energy power system according to claim 6, characterized in that, The threshold for the number of times is set to 10.

8. A strong interaction stability control system for a new energy power system, characterized in that, include: The data acquisition module is used to collect the output voltage and current of each wind turbine at the moment of the fault when a fault occurs in a direct-drive wind farm in the new energy power system. The system stores energy calculation modules to obtain the induced energy, grid energy, and inter-unit energy of the direct-drive wind farm based on the outlet voltage and current of each wind turbine, as well as the DC voltage outer loop subsystem, phase-locked loop subsystem, and filter circuit of each wind turbine. d The stored energy after the axle system is disturbed is then used to obtain the system stored energy of the direct-drive wind farm; The stability control module is used to establish a multi-control parameter collaborative optimization model based on the selected control parameters and with the objective function constraint of minimizing the system storage energy of the direct-drive wind farm. The optimal solution of the multi-control parameter collaborative optimization model is solved to obtain the specific values ​​of each control parameter, and the stability control of the direct-drive wind farm is realized based on the specific values ​​of each control parameter. In the stability control module, the gain coefficient of the phase-locked loop proportional element of each wind turbine is selected. Integral gain coefficient DC voltage outer loop proportional element gain coefficient Integral gain coefficient And the distance from each wind turbine to the grid connection bus of the wind farm As control parameters; the multi-control parameter collaborative optimization model is expressed as: ； In the formula, This refers to the system's stored energy in a direct-drive wind farm. Represents a function relating to each control parameter. , , They represent the first i The DC voltage outer loop subsystem, phase-locked loop subsystem, and filter circuit of the typhoon generator d The rate of change of stored energy in the axle system after disturbance. , These represent the first direct-drive wind farm. i The lower and upper limits of the gain coefficient of the outer loop proportional element of the DC voltage of the typhoon generator; , These represent the first direct-drive wind farm. i The lower and upper limits of the gain coefficient of the proportional element in the phase-locked loop of a typhoon generator; , These represent the first direct-drive wind farm. i The lower and upper limits of the gain coefficient of the outer loop integral stage of the DC voltage of a typhoon generator. , These represent the first direct-drive wind farm. i The lower and upper limits of the gain coefficient of the phase-locked loop integral element of a typhoon generator; n This indicates the total number of wind turbines in a direct-drive wind farm.

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