METHOD AND SYSTEM FOR DYNAMIC STABILITY CONTROL OF POWER SYSTEMS WITH RENEWABLE ENERGY

Abstract

A dynamic stability control method for power systems with renewable energy, in which a non-linear system of a grid-forming inverter corresponding to a renewable energy power system is created. An external subsystem corresponding to the grid-forming inverter is constructed based on a Lie derivative. According to the external subsystem, a linear sliding surface corresponding to the external subsystem is constructed, and a dynamic stability control unit corresponding to the external subsystem is generated based on sliding mode control. A first instruction data corresponding to the dynamic stability control unit is generated to control dynamic stability of the renewable energy power system in real time. The voltage instruction value of the grid-forming inverter is modified to improve the dynamic stability of the renewable energy power system. A system for implementing such method is also provided.

Claims

1. A method for dynamic stability control of a renewable energy power system, comprising: (1) creating a non-linear system of a grid-forming inverter corresponding to the renewable energy power system; and constructing an external subsystem corresponding to the grid-forming inverter based on a Lie derivative; (2) constructing a linear sliding surface corresponding to the external subsystem; and generating a dynamic stability control unit corresponding to the external subsystem based on sliding mode control; and (3) generating a first instruction data corresponding to the dynamic stability control unit, and according to the first instruction data, controlling dynamic stability of the renewable energy power system in real time; wherein the first instruction data is a voltage instruction value data.

2. The method of claim 1, wherein in step (1), the non-linear system is created through steps of: creating at least three control loops corresponding to the non-linear system of the grid-forming inverter, wherein the at least three control loops comprise a virtual synchronization loop, a current inner loop and an outer loop; constructing an inner loop current controller corresponding to the current inner loop and an outer loop controller corresponding to the outer loop; and obtaining a voltage reference value data and a power angle variation data corresponding to the grid-forming inverter, and constructing a non-linear single-input single-output (SISO) model corresponding to the grid-forming inverter.

3. The method of claim 1, wherein step (1) further comprises: constructing a positive sequence and fundamental frequency model corresponding to the non-linear system of the grid-forming inverter, wherein the positive sequence and fundamental frequency model is expressed as: $\begin{array}{cc}\{\begin{array}{c}\frac{{\mathrm{di}}_{\mathrm{sd}}}{\mathrm{dt}}=\frac{1}{L_{\mathrm{arm}}}\left(-u_{\mathrm{sd}}+v_d+L_{\mathrm{arm}}{i}_{\mathrm{sq}}-R_{\mathrm{arm}}{i}_{\mathrm{sd}}\right)\\ \frac{{\mathrm{di}}_{\mathrm{sq}}}{\mathrm{dt}}=\frac{1}{L_{\mathrm{arm}}}\left(-u_{\mathrm{sq}}+v_q+L_{\mathrm{arm}}{i}_{\mathrm{sd}}-R_{\mathrm{arm}}{i}_{\mathrm{sq}}\right)\end{array};& \left(1\right)\end{array}$ wherein v.sub.d denotes a d-axis output of an inner loop controller, and v.sub.q denotes a q-axis output of the inner loop controller; R.sub.arm denotes a resistance of a bridge arm, and L.sub.arm denotes an inductance of the bridge arm; u.sub.sd denotes a d-axis component of a bus voltage, and u.sub.sq denote a q-axis component of the bus voltage; i.sub.sd denotes a d-axis component of an output current of the grid-forming inverter, and i.sub.sq denotes a q-axis component of the output current of the grid-forming inverter; and denotes a fundamental frequency of the grid-forming inverter.

4. The method of claim 2, wherein the non-linear SISO model is expressed as: $\begin{array}{cc}\begin{array}{cc}\{\begin{array}{c}\stackrel{.}{x}=f+\mathrm{gu}\\ y=h\left(x\right)\end{array},& \{\begin{array}{c}x={\left[,,i_{\mathrm{sd}},i_{\mathrm{sq}},M_{\mathrm{id}},M_{\mathrm{iq}},M_{\mathrm{Us}},M_{\mathrm{uq}}\right]}^T\\ f=\left[\begin{array}{c}{}_0\\ -\frac{1}{2H_m}{P}_s-\frac{D_m}{2H_m}\\ \frac{1}{L_{\mathrm{arm}}}\left[-k_{\mathrm{pid}}{k}_{\mathrm{pUs}}{u}_{\mathrm{sd}}-\left(k_{\mathrm{pid}}+R_{\mathrm{arm}}\right)i_{\mathrm{sd}}+M_{\mathrm{id}}+k_{\mathrm{pid}}{M}_{\mathrm{Us}}\right]\\ \frac{1}{L_{\mathrm{arm}}}\left[-k_{\mathrm{pid}}{k}_{\mathrm{pup}}{u}_{\mathrm{sq}}-\left(k_{\mathrm{piq}}+R_{\mathrm{arm}}\right)i_{\mathrm{sq}}+M_{\mathrm{iq}}+k_{\mathrm{piq}}{M}_{\mathrm{uq}}\right]\\ -k_{\mathrm{iid}}{k}_{\mathrm{pUs}}{u}_{\mathrm{sd}}-k_{\mathrm{iid}}{i}_{\mathrm{sd}}+k_{\mathrm{iid}}{M}_{\mathrm{Us}}\\ -k_{\mathrm{iiq}}{k}_{\mathrm{pup}}{u}_{\mathrm{sq}}-k_{\mathrm{iiq}}{i}_{\mathrm{sq}}+k_{\mathrm{iiq}}{M}_{\mathrm{uq}}\\ -k_{\mathrm{iUs}}{u}_{\mathrm{sd}}-k_{\mathrm{iUs}}{U}_{\mathrm{sref}}\\ -k_{\mathrm{iuq}}{u}_{\mathrm{sq}}\end{array}\right]\\ \begin{array}{c}g=\left[0,0,\frac{k_{\mathrm{pid}}{K}_{\mathrm{pUs}}}{L_{\mathrm{arm}}},0,k_{\mathrm{iid}},k_{\mathrm{pUs}},0,k_{\mathrm{iUs}},0\right]\\ h=\\ u=U_{\mathrm{sref}}\end{array}\end{array}\end{array};& \left(2\right)\end{array}$ wherein denotes a rotating speed of the grid-forming inverter, and denotes a power angle variation of the grid-forming inverter; i.sub.sd denotes a d-axis component of an output current of the grid-forming inverter, and i.sub.sq denotes a q-axis component of the output current of the grid-forming inverter; M.sub.id denotes an integral variable of a d-axis part of the inner loop current controller, and M.sub.iq denotes an integral variable of a q-axis part of the inner loop current controller; M.sub.Us denotes an integral variable of a d-axis part of the outer loop controller, and M.sub.uq denotes an integral variable of a q-axis part of the outer loop controller; .sub.0 denotes a reference frequency; H.sub.m denotes an inertia coefficient of the grid-forming inverter, and D.sub.m denotes a damping coefficient of the grid-forming inverter; P.sub.s denotes a power variation of the grid-forming inverter; Ram denotes a resistance of a bridge arm, and L.sub.arm denotes an inductance of the bridge arm; k.sub.pid denotes a proportional coefficient of the d-axis part of the inner loop current controller, and k.sub.iid denotes an integral coefficient of the d-axis part of the inner loop current controller; k.sub.piq denotes a proportional coefficient of the q-axis part of the inner loop current controller, and k.sub.iiq denotes an integral coefficient of the q-axis part of the inner loop current controller; u denotes an input signal; U.sub.sref denotes a bus voltage reference value of the grid-forming inverter; k.sub.pus denotes a proportional coefficient of the d-axis part of the outer loop controller, and k.sub.iUs denotes an integral coefficient of the d-axis part of the outer loop controller; k.sub.puq denotes a proportional coefficient of the q-axis part of the outer loop controller, and k.sub.iuq denotes an integral coefficient of the q-axis part of the outer loop controller; u.sub.sd denotes ad-axis component of inverter-based generator (IBG) bus voltage, and u.sub.sq denotes a q-axis component of the IBG bus voltage; and y denotes an output signal.

5. The method of claim 1, wherein step (2) further comprises: generating a hybrid reaching law corresponding to the linear sliding surface based on the linear sliding surface; and according to the hybrid reaching law, generating an input signal data of the grid-forming inverter corresponding to the non-linear system of the grid-forming inverter.

6. The method of claim 1, further comprising: after step (3), generating a fault data corresponding to the renewable energy power system; and verifying the dynamic stability of the renewable energy power system in real time based on the fault data.

7. A system for implementing the method of claim 1, comprising: a creation unit; a data construction unit; and a data generation unit; wherein the creation unit is configured for creating the non-linear system of the grid-forming inverter corresponding to the renewable energy power system, and constructing the external subsystem corresponding to the grid-forming inverter based on the Lie derivative; the data construction unit is configured for constructing the linear sliding surface corresponding to the external subsystem, and generating the dynamic stability control unit corresponding to the external subsystem based on sliding mode control; and the data generation unit is configured for generating the first instruction data corresponding to the dynamic stability control unit, and controlling the dynamic stability of the renewable energy power system in real time according to the first instruction data; wherein the first instruction data is the voltage instruction value data.

8. The system of claim 7, wherein the creation unit comprises: a first creation module; a second creation module; and a third creation module; wherein the first creation module is configured for creating at least three control loops corresponding to the non-linear system of the grid-forming inverter; wherein the at least three control loops comprise a virtual synchronization loop, a current inner loop and an outer loop; the second creation module is configured for constructing an inner loop current controller corresponding to the current inner loop, and an outer loop controller corresponding to the outer loop; and the third creation module is configured for obtaining a voltage reference value data and a power angle variation data corresponding to the grid-forming inverter, and constructing a non-linear SISO model corresponding to the grid-forming inverter.

9. The system of claim 7, wherein the data construction unit comprises: a first generation module; and a second generation module; wherein the first generation module is configured for generating a hybrid reaching law corresponding to the linear sliding surface based on the linear sliding surface; the second generation module is configured for generating an input signal data of the grid-forming inverter corresponding to the non-linear system of the grid-forming inverter according to the hybrid reaching law.

10. The system of claim 7, further comprising: a generation and verification module; wherein the generation and verification module is configured for generating a fault data corresponding to the renewable energy power system, and verifying the dynamic stability of the renewable energy power system in real time based on the fault data.

11. The system of claim 8, wherein the creation unit further comprises: a fourth creation module; wherein the fourth creation module is configured for constructing a positive sequence and fundamental frequency model corresponding to the non-linear system of the grid-forming inverter, wherein the positive sequence and fundamental frequency model is expressed as: $\begin{array}{cc}\{\begin{array}{c}\frac{{\mathrm{di}}_{\mathrm{sd}}}{\mathrm{dt}}=\frac{1}{L_{\mathrm{arm}}}\left(-u_{\mathrm{sd}}+v_d+L_{\mathrm{arm}}{i}_{\mathrm{sq}}-R_{\mathrm{arm}}{i}_{\mathrm{sd}}\right)\\ \frac{{\mathrm{di}}_{\mathrm{sq}}}{\mathrm{dt}}=\frac{1}{L_{\mathrm{arm}}}\left(-u_{\mathrm{sq}}+v_q+L_{\mathrm{arm}}{i}_{\mathrm{sd}}-R_{\mathrm{arm}}{i}_{\mathrm{sq}}\right)\end{array};& \left(1\right)\end{array}$ wherein v.sub.d denotes a d-axis output of an inner loop controller, and v.sub.q denotes a q-axis output of the inner loop controller; R.sub.arm denotes a resistance of a bridge arm, and L.sub.arm denotes an inductance of the bridge arm; u.sub.sd denotes a d-axis component of a bus voltage, and u.sub.sq denote a q-axis component of the bus voltage; i.sub.sd denotes a d-axis component of an output current of the grid-forming inverter, and i.sub.sq denotes a q-axis component of the output current of the grid-forming inverter; and denotes a fundamental frequency of the grid-forming inverter.

12. The system of claim 8, wherein the non-linear SISO model is expressed as: $\begin{array}{cc}\begin{array}{cc}\{\begin{array}{c}\stackrel{.}{x}=f+\mathrm{gu}\\ y=h\left(x\right)\end{array},& \{\begin{array}{c}x={\left[,,i_{\mathrm{sd}},i_{\mathrm{sq}},M_{\mathrm{id}},M_{\mathrm{iq}},M_{\mathrm{Us}},M_{\mathrm{uq}}\right]}^T\\ f=\left[\begin{array}{c}{}_0\\ -\frac{1}{2H_m}{P}_s-\frac{D_m}{2H_m}\\ \frac{1}{L_{\mathrm{arm}}}\left[-k_{\mathrm{pid}}{k}_{\mathrm{pUs}}{u}_{\mathrm{sd}}-\left(k_{\mathrm{pid}}+R_{\mathrm{arm}}\right)i_{\mathrm{sd}}+M_{\mathrm{id}}+k_{\mathrm{pid}}{M}_{\mathrm{Us}}\right]\\ \frac{1}{L_{\mathrm{arm}}}\left[-k_{\mathrm{pid}}{k}_{\mathrm{pup}}{u}_{\mathrm{sq}}-\left(k_{\mathrm{piq}}+R_{\mathrm{arm}}\right)i_{\mathrm{sq}}+M_{\mathrm{iq}}+k_{\mathrm{piq}}{M}_{\mathrm{uq}}\right]\\ -k_{\mathrm{iid}}{k}_{\mathrm{pUs}}{u}_{\mathrm{sd}}-k_{\mathrm{iid}}{i}_{\mathrm{sd}}+k_{\mathrm{iid}}{M}_{\mathrm{Us}}\\ -k_{\mathrm{iiq}}{k}_{\mathrm{pup}}{u}_{\mathrm{sq}}-k_{\mathrm{iiq}}{i}_{\mathrm{sq}}+k_{\mathrm{iiq}}{M}_{\mathrm{uq}}\\ -k_{\mathrm{iUs}}{u}_{\mathrm{sd}}-k_{\mathrm{iUs}}{U}_{\mathrm{sref}}\\ -k_{\mathrm{iuq}}{u}_{\mathrm{sq}}\end{array}\right]\\ \begin{array}{c}g=\left[0,0,\frac{k_{\mathrm{pid}}{K}_{\mathrm{pUs}}}{L_{\mathrm{arm}}},0,k_{\mathrm{iid}},k_{\mathrm{pUs}},0,k_{\mathrm{iUs}},0\right]\\ h=\\ u=U_{\mathrm{sref}}\end{array}\end{array}\end{array};& \left(2\right)\end{array}$ wherein denotes a rotating speed of the grid-forming inverter, and denotes a power angle variation of the grid-forming inverter; i.sub.sd denotes a d-axis component of an output current of the grid-forming inverter, and i.sub.sq denotes a q-axis component of the output current of the grid-forming inverter; M.sub.id denotes an integral variable of a d-axis part of the inner loop current controller, and M.sub.iq denotes an integral variable of a q-axis part of the inner loop current controller; M.sub.Us denotes an integral variable of a d-axis part of the outer loop controller, and M.sub.uq denotes an integral variable of a q-axis part of the outer loop controller; .sub.0 denotes a reference frequency; H.sub.m denotes an inertia coefficient of the grid-forming inverter, and D.sub.m denotes a damping coefficient of the grid-forming inverter; P.sub.s denotes a power variation of the grid-forming inverter; R.sub.arm denotes the resistance of the bridge arm, and L.sub.arm denotes the inductance of the bridge arm; k.sub.pid denotes a proportional coefficient of the d-axis part of the inner loop current controller, and k.sub.iid denotes an integral coefficient of the d-axis part of the inner loop current controller; k.sub.piq denotes a proportional coefficient of the q-axis part of the inner loop current controller, and k.sub.iiq denotes an integral coefficient of the q-axis part of the inner loop current controller; u denotes an input signal; U.sub.sref denotes a bus voltage reference value of the grid-forming inverter; k.sub.pus denotes a proportional coefficient of the d-axis part of the outer loop controller, and k.sub.iUs denotes an integral coefficient of the d-axis part of the outer loop controller; k.sub.puq denotes a proportional coefficient of the q-axis part of the outer loop controller, and k.sub.iuq denotes an integral coefficient of the q-axis part of the outer loop controller; u.sub.sd denotes a d-axis component of inverter-based generation (IBG) bus voltage, and u.sub.sq denotes a q-axis component of the IBG output voltage; and y denotes an output signal.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0056] To illustrate the technical solutions of the embodiments of this application more clearly, the accompanying drawings required in the description of the embodiments will be briefly introduced below. It is obvious that the following accompanying drawings only show some embodiments of this application, and for those of ordinary skill in the art, other accompanying drawings can also be obtained according to these drawings without making creative effort.

[0057] FIG. 1 is a schematic diagram of an inverter model of a method for dynamic stability control of a renewable energy power system according to an embodiment of the present disclosure.

[0058] FIG. 2 is a schematic diagram of an IEEE 11-bus system with 100% renewable energy of the dynamic stability control method according to an embodiment of the present disclosure.

[0059] FIG. 3 is a schematic diagram of an oscillation phenomenon of the renewable energy power system before an application of the dynamic stability control method according to an embodiment of the present disclosure.

[0060] FIG. 4 is a schematic diagram of stability results after the application of the method according to an embodiment of the present disclosure.

[0061] FIG. 5 is a flow chart of the method according to an embodiment of the present disclosure.

[0062] FIG. 6 is a schematic diagram of an architecture of the method according to an embodiment of the present disclosure.

[0063] The realization of the objects, functional characteristics and advantages of the present disclosure will be further described combined with the embodiments with reference to the accompanying drawings.

DETAILED DESCRIPTION OF EMBODIMENTS

[0064] In order to illustrate the objects, technical solutions and advantages of embodiments of this application more clearly, the embodiments of this application will be further described below with reference to the accompanying drawings. Those of ordinary skill in the art can easily understand other advantages and functions of this application from the disclosure of this description.

[0065] This application can also be implemented or applied by other different specific embodiments. In addition, various details in this description can be modified and changed based on different perspectives and applications without departing from the spirit of the present disclosure.

[0066] It should be noted that the terms, such as up, down, left, right, front, rear and other directional indications used herein, are only used for illustrating relative position relationship and motion between components in a specific state (as shown in the accompanying drawings). If the specific state changes, the directional indication accordingly changes.

[0067] In addition, the terms first and second are only used for distinguishment rather than indicating or implying the relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined with first or second may explicitly or implicitly indicates the inclusion of at least one of such features. Besides, technical solutions of individual embodiments can be combined with each other as long as the combined solution can be implemented by those skilled in the art. When a combination of the technical solutions is contradictory or cannot be realized, it should be considered that such a combination does not exist, and is not within the scope of the present disclosure.

[0068] This application will be further described below with reference to the accompanying drawings. Referring to FIGS. 1-5, this application provides a method for dynamic stability control of a renewable energy power system, and the method includes the following steps.

[0069] (S1) A non-linear system of a grid-forming inverter corresponding to the renewable energy power system is created, and an external subsystem corresponding to the grid-forming inverter is constructed based on a Lie derivative.

[0070] (S2) A linear sliding surface corresponding to the external subsystem is constructed, and a dynamic stability control unit corresponding to the external subsystem is generated based on a sliding mode control.

[0071] (S3) A first instruction data corresponding to the dynamic stability control unit is generated, and according to the first instruction data, dynamic stability of the renewable energy power system is controlled in real time, where the first instruction data is a voltage instruction value data.

[0072] In an embodiment, in step (S1), the non-linear system is created through the following steps.

[0073] (S11) At least three control loops corresponding to the non-linear system of the grid-forming inverter are created, where the at least three control loops include a virtual synchronization loop, a current inner loop and an outer loop.

[0074] (S12) An inner loop current controller corresponding to the current inner loop and an outer loop controller corresponding to the outer loop are constructed.

[0075] (S13) A voltage reference value data and a power angle variation data corresponding to the grid-forming inverter are obtained, and a non-linear single-input single-output (SISO) model corresponding to the grid-forming inverter is constructed.

[0076] In an embodiment, step (S1) further includes the following steps.

[0077] (S14) A positive sequence and fundamental frequency model corresponding to the non-linear system of the grid-forming inverter is constructed, where the positive sequence and fundamental frequency model is expressed as:

[00005]$\begin{array}{cc}\{\begin{array}{c}\frac{{\mathrm{di}}_{\mathrm{sd}}}{\mathrm{dt}}=\frac{1}{L_{\mathrm{arm}}}\left(-u_{\mathrm{sd}}+v_d+L_{\mathrm{arm}}{i}_{\mathrm{sq}}-R_{\mathrm{arm}}{i}_{\mathrm{sd}}\right)\\ \frac{{\mathrm{di}}_{\mathrm{sq}}}{\mathrm{dt}}=\frac{1}{L_{\mathrm{arm}}}\left(-u_{\mathrm{sq}}+v_q-L_{\mathrm{arm}}{i}_{\mathrm{sd}}-R_{\mathrm{arm}}{i}_{\mathrm{sq}}\right)\end{array};& \left(1\right)\end{array}$ [0078] where v.sub.d denotes a d-axis output of an inner loop controller, and v.sub.q denotes a q-axis output of the inner loop controller; R.sub.arm denotes a resistance of a bridge arm, and L.sub.arm denotes an inductance of the bridge arm; u.sub.sd denotes a d-axis component of a bus voltage, and u.sub.sq denote a q-axis component of the bus voltage; i.sub.sd denotes a d-axis component of an output current of the grid-forming inverter, and i.sub.sq denotes a q-axis component of the output current of the grid-forming inverter; and denotes a fundamental frequency of the grid-forming inverter.

[0079] The non-linear SISO model is expressed as:

[00006]$\begin{array}{cc}\{\begin{array}{c}\stackrel{}{x}=f+gu\\ y=h\left(x\right)\end{array},\{\begin{array}{c}x={\left[,,i_{\mathrm{sd}},i_{\mathrm{sq}},M_{\mathrm{id}},M_{\mathrm{iq}},M_{\mathrm{Us}},M_{\mathrm{uq}}\right]}^T\\ f=\left[\begin{array}{c}{}_0\\ -\frac{1}{2H_m}{P}_s-\frac{D_m}{2H_m}\\ \frac{1}{L_{\mathrm{arm}}}\left[-k_{\mathrm{pid}}{k}_{\mathrm{pUs}}{u}_{\mathrm{sd}}-\left(k_{\mathrm{pid}}+R_{\mathrm{arm}}\right)i_{\mathrm{sd}}+M_{\mathrm{id}}+k_{\mathrm{pid}}{M}_{\mathrm{Us}}\right]\\ \frac{1}{L_{\mathrm{arm}}}\left[-k_{\mathrm{pid}}{k}_{\mathrm{puq}}{u}_{\mathrm{sq}}-\left(k_{\mathrm{piq}}+R_{\mathrm{arm}}\right)i_{\mathrm{sq}}+M_{\mathrm{iq}}+k_{\mathrm{piq}}{M}_{\mathrm{uq}}\right]\\ -k_{\mathrm{iid}}{k}_{\mathrm{pUs}}{u}_{\mathrm{sd}}-k_{\mathrm{iid}}{i}_{\mathrm{sd}}+k_{\mathrm{iid}}{M}_{\mathrm{Us}}\\ -k_{\mathrm{iiq}}{k}_{\mathrm{puq}}{u}_{\mathrm{sq}}-k_{\mathrm{iiq}}{i}_{\mathrm{sq}}+k_{\mathrm{iiq}}{M}_{\mathrm{uq}}\\ -k_{\mathrm{iUs}}{u}_{\mathrm{sd}}-k_{\mathrm{iUs}}{U}_{\mathrm{sref}}\\ -k_{\mathrm{iuq}}{u}_{\mathrm{sq}}\end{array}\right]\\ g=\left[0,0,\frac{k_{\mathrm{pid}}{k}_{\mathrm{pUs}}}{L_{\mathrm{arm}}},0,k_{\mathrm{iid}}{k}_{\mathrm{pUs}},0,k_{\mathrm{iUs}},0\right]\\ h=\\ u=U_{\mathrm{sref}}\end{array};& \left(2\right)\end{array}$ [0080] where denotes a rotating speed of the grid-forming inverter, and denotes a power angle variation of the grid-forming inverter; i.sub.sd denotes a d-axis component of an output current of the grid-forming inverter, and i.sub.sq denotes a q-axis component of the output current of the grid-forming inverter; M.sub.id denotes an integral variable of a d-axis part of the inner loop current controller, and M.sub.iq denotes an integral variable of a q-axis part of the inner loop current controller; M.sub.Us denotes an integral variable of a d-axis part of the outer loop controller, and M.sub.uq denotes an integral variable of a q-axis part of the outer loop controller; .sub.0 denotes a reference frequency; H.sub.m denotes an inertia coefficient of the grid-forming inverter, and D.sub.m denotes a damping coefficient of the grid-forming inverter; P.sub.s denotes a power variation of the grid-forming inverter; R.sub.arm denotes the resistance of the bridge arm, and L.sub.arm denotes the inductance of the bridge arm; k.sub.pid denotes a proportional coefficient of the d-axis part of the inner loop current controller, and k.sub.iid denotes an integral coefficient of the d-axis part of the inner loop current controller; k.sub.piq denotes a proportional coefficient of the q-axis part of the inner loop current controller, and k.sub.iiq denotes an integral coefficient of the q-axis part of the inner loop current controller; u denotes an input signal; U.sub.sref denotes a bus voltage reference value of the grid-forming inverter; k.sub.pUs denotes a proportional coefficient of a d-axis part of the outer loop controller, and k.sub.iUs denotes an integral coefficient of the d-axis part of the outer loop controller; k.sub.puq denotes a proportional coefficient of the q-axis part of the outer loop controller, and k.sub.iuq denotes an integral coefficient of the q-axis part of the outer loop controller; u.sub.sd denotes a d-axis component of inverter-based generation (IBG) bus voltage, and u.sub.sq denotes a q-axis component of the IBG output voltage; and y denotes an output signal.

[0081] In an embodiment, step (S2) includes the following steps.

[0082] (S21) A hybrid reaching law corresponding to the linear sliding surface is generated based on the linear sliding surface.

[0083] (S22) According to the hybrid reaching law, an input signal data of the grid-forming inverter corresponding to the non-linear system of the grid-forming inverter is generated.

[0084] In an embodiment, the method further includes the following step.

[0085] (S40) After step (S3), a fault data corresponding to the renewable energy power system is generated, and the dynamic stability of the renewable energy power system is verified in real time based on the fault data.

[0086] In an embodiment, this application provides a method for dynamic stability control of a 100% renewable energy power system including the following steps. First, an external subsystem model of the grid-forming inverter is obtained through input-output linearization, and expressions of the external subsystem are derived by using the Lie derivative, so that a hybrid reaching law of the sliding surface is proposed. In addition, this application further provides a dynamic stability controller of the grid-forming inverter based on the hybrid reaching law of the sliding surface.

[0087] The method for dynamic stability control of a 100% renewable energy power system includes the following steps.

[0088] (1) A non-linear system standard form of the grid-forming inverter is derived.

[0089] (2) The expressions of the external subsystem are derived by using the Lie derivative.

[0090] (3) The hybrid reaching law of the sliding surface is proposed.

[0091] (4) The dynamic stability controller of the grid-forming inverter is obtained based on the sliding mode control.

[0092] In step (1), the non-linear system standard form of the grid-forming inverter is obtained by the following formulas:

[00007]$\begin{array}{cc}\{\begin{array}{c}\stackrel{}{x}=f+gu\\ y=h\left(x\right)\end{array},\{\begin{array}{c}x={\left[,,i_{\mathrm{sd}},i_{\mathrm{sq}},M_{\mathrm{id}},M_{\mathrm{iq}},M_{\mathrm{Us}},M_{\mathrm{uq}}\right]}^T\\ f=\left[\begin{array}{c}{}_0\\ -\frac{1}{2H_m}{P}_s-\frac{D_m}{2H_m}\\ \frac{1}{L_{\mathrm{arm}}}\left[-k_{\mathrm{pid}}{k}_{\mathrm{pUs}}{u}_{\mathrm{sd}}-\left(k_{\mathrm{pid}}+R_{\mathrm{arm}}\right)i_{\mathrm{sd}}+M_{\mathrm{id}}+k_{\mathrm{pid}}{M}_{\mathrm{Us}}\right]\\ \frac{1}{L_{\mathrm{arm}}}\left[-k_{\mathrm{pid}}{k}_{\mathrm{puq}}{u}_{\mathrm{sq}}-\left(k_{\mathrm{piq}}+R_{\mathrm{arm}}\right)i_{\mathrm{sq}}+M_{\mathrm{iq}}+k_{\mathrm{piq}}{M}_{\mathrm{uq}}\right]\\ -k_{\mathrm{iid}}{k}_{\mathrm{pUs}}{u}_{\mathrm{sd}}-k_{\mathrm{iid}}{i}_{\mathrm{sd}}+k_{\mathrm{iid}}{M}_{\mathrm{Us}}\\ -k_{\mathrm{iiq}}{k}_{\mathrm{puq}}{u}_{\mathrm{sq}}-k_{\mathrm{iiq}}{i}_{\mathrm{sq}}+k_{\mathrm{iiq}}{M}_{\mathrm{uq}}\\ -k_{\mathrm{iUs}}{u}_{\mathrm{sd}}-k_{\mathrm{iUs}}{U}_{\mathrm{sref}}\\ -k_{\mathrm{iuq}}{u}_{\mathrm{sq}}\end{array}\right]\\ g=\left[0,0,\frac{k_{\mathrm{pid}}{k}_{\mathrm{pUs}}}{L_{\mathrm{arm}}},0,k_{\mathrm{iid}}{k}_{\mathrm{pUs}},0,k_{\mathrm{iUs}},0\right]\\ h=\\ u=U_{\mathrm{sref}}\end{array};& \left(2\right)\end{array}$ [0093] where denotes the rotating speed of the grid-forming inverter, and denotes the power angle variation of the grid-forming inverter; i.sub.sd denotes the d-axis component of the output current of the grid-forming inverter, and i.sub.sq denotes the q-axis component of the output current of the grid-forming inverter; M.sub.id denotes the integral variable of the d-axis part of the inner loop current controller, and M.sub.iq denotes the integral variable of the q-axis part of the inner loop current controller; M.sub.Us denotes the integral variable of the d-axis part of the outer loop controller, and M.sub.uq denotes the integral variable of the q-axis part of the outer loop controller; .sub.0 denotes the reference frequency; H.sub.m denotes the inertia coefficient of the grid-forming inverter, and D.sub.m denotes the damping coefficient of the grid-forming inverter; P.sub.s denotes the power variation of the grid-forming inverter; R.sub.arm denotes the resistance of the bridge arm, and L.sub.arm denotes the inductance of the bridge arm; k.sub.pid denotes the proportional coefficient of the d-axis part of the inner loop current controller, and k.sub.iid denotes the integral coefficient of the d-axis part of the inner loop current controller; k.sub.piq denotes the proportional coefficient of the q-axis part of the inner loop current controller, and k.sub.iiq denotes the integral coefficient of the q-axis part of the inner loop current controller; u denotes the input signal; U.sub.sref denotes the bus voltage reference value of the grid-forming inverter; k.sub.pUs denotes the proportional coefficient of the d-axis part of the outer loop controller, and k.sub.iUs denotes the integral coefficient of the d-axis part of the outer loop controller; k.sub.puq denotes the proportional coefficient of the q-axis part of the outer loop controller, and k.sub.iuq denotes the integral coefficient of the q-axis part of the outer loop controller; u.sub.sd denotes the d-axis component of IBG bus voltage, and u.sub.sq denotes the q-axis component of the IBG output voltage; and y denotes the output signal.

[0094] In step (2), the expressions of the external subsystem are obtained by the following formulas:

[00008]$\begin{array}{cc}\{\begin{array}{c}{\stackrel{}{}}_1={}_2\\ {\stackrel{}{}}_2={}_3\\ {\stackrel{}{}}_3=L_f^{3}y+L_g{L}_f^{2}y{U}_{\mathrm{sref}}\end{array};& \left(3\right)\end{array}$ [0095] where .sub.i denotes an external subsystem variable; L.sub.f.sup.3y denotes a third Lie derivative of the output signal y with respect to a system function f; L.sub.gL.sub.f.sup.2y denotes a third Lie derivative of the output signal y with respect to an input function g.

[0096] In step (3), the hybrid reaching law of the sliding surface is proposed by the following formulas:

[00009]$\begin{array}{cc}\stackrel{.}{v}=-k{.Math.v.Math.}^{}v-{.Math.v.Math.}^{}sat\left(v\right);v={}_1{}_1+{}_2{}_2+{}_3;\mathrm{sat}\left(v\right)=\{\begin{array}{cc}\mathrm{sign}\left(v\right),& .Math.v.Math.>\\ \frac{v}{},& .Math.v.Math.\end{array};& \left(4\right)\end{array}$ [0097] where .sub.1 denotes a constant coefficient, and .sub.2 denotes a constant coefficient; v denotes the sliding surface; >1, 0<<1, and , , k and are constant coefficients; sat( ) denotes a saturation function; denotes a thickness of a boundary layer, and 0<<1; when |v|>, a power term would accelerate the system to approach the sliding mode; when |v|<, the saturation function is controlled by adopting linear feedback in the boundary layer, so as to achieve smooth transition and weaken system buffeting.

[0098] In the step (4), the dynamic stability controller of the grid-forming inverter is obtained by the following formula:

[00010]$\begin{array}{cc}{U}_{\mathrm{sref}}=\frac{-k{.Math.v.Math.}^{}v-{.Math.v.Math.}^{}sat\left(v\right)-{}_1{}_2-{}_2{}_3-L_f^{3}y}{L_g{L}_f^{2}y}.& \left(5\right)\end{array}$

[0099] In other words, the technical solutions of the present disclosure provide the method for dynamic stability control of the renewable energy power systems, including the following steps.

[0100] (1) The non-linear system standard form of the grid-forming inverter is derived as follows.

[0101] A model of the grid-forming inverter is shown in FIG. 1, and the dynamic stability controller of the grid-forming inverter includes three control loops, which are the virtual synchronization loop, the inner loop and the outer loop. In the FIG. 1, P.sub.s denotes an actual value of an active power output, and P.sub.sref denotes a reference value of the active power output; U.sub.s denote a bus voltage actual value, and U.sub.sref denotes the bus voltage reference value; and u.sub.sq denotes a q-axis component of the bus voltage.

[0102] The positive sequence and fundamental frequency model of the grid-forming inverter is constructed as follows:

[00011]$\begin{array}{cc}\{\begin{array}{c}\frac{{\mathrm{di}}_{\mathrm{sd}}}{\mathrm{dt}}=\frac{1}{L_{\mathrm{arm}}}\left(-u_{\mathrm{sd}}+v_d+L_{\mathrm{arm}}{i}_{\mathrm{sq}}-R_{\mathrm{arm}}{i}_{\mathrm{sd}}\right)\\ \frac{{\mathrm{di}}_{\mathrm{sq}}}{\mathrm{dt}}=\frac{1}{L_{\mathrm{arm}}}\left(-u_{\mathrm{sq}}+v_q-L_{\mathrm{arm}}{i}_{\mathrm{sd}}-R_{\mathrm{arm}}{i}_{\mathrm{sq}}\right)\end{array};& \left(1\right)\end{array}$ [0103] where v.sub.d denotes the d-axis output of the inner loop controller, and v.sub.q denotes the q-axis output of the inner loop controller; R.sub.arm denotes the resistance of the bridge arm, and L.sub.arm denotes the inductance of the bridge arm; u.sub.sd denotes the d-axis component of the bus voltage, and u.sub.sq denote the q-axis component of the bus voltage; i.sub.sd denotes the d-axis component of the output current of the grid-forming inverter, and i.sub.sq denotes the q-axis component of the output current of the grid-forming inverter; and denotes the fundamental frequency of the grid-forming inverter.

[0104] A modulation process is ignored, and a model of the inner loop controller of the grid-forming inverter is expressed as:

[00012]$\begin{array}{cc}\{\begin{array}{c}{v}_d=u_{\mathrm{sd}}-L_{\mathrm{arm}}{i}_{\mathrm{sq}}+\left[k_{\mathrm{pid}}\left(i_{\mathrm{sdref}}-i_{\mathrm{sd}}\right)+M_{\mathrm{id}}\right]\\ v_q=u_{\mathrm{sq}}+L_{\mathrm{arm}}{i}_{\mathrm{sd}}+\left[k_{\mathrm{piq}}\left(i_{\mathrm{sqref}}-i_{\mathrm{sq}}\right)+M_{\mathrm{iq}}\right]\end{array};\mathrm{and}& \left(6\right)\end{array}$$\begin{array}{cc}\{\begin{array}{c}\frac{{\mathrm{dM}}_{\mathrm{id}}}{\mathrm{dt}}=k_{\mathrm{iid}}\left(i_{\mathrm{sdref}}-i_{\mathrm{sd}}\right)\\ \frac{{\mathrm{dM}}_{\mathrm{iq}}}{\mathrm{dt}}=k_{\mathrm{iiq}}\left(i_{\mathrm{sqref}}-i_{\mathrm{sq}}\right)\end{array};& \left(7\right)\end{array}$ [0105] where M.sub.id denotes the integral variable of the d-axis part of the inner loop current controller, and M.sub.iq denotes the integral variable of the q-axis part of the inner loop current controller; k.sub.pid denotes the proportional coefficient of the d-axis part of the inner loop current controller, and k.sub.iid denotes the integral coefficient of the d-axis part of the inner loop current controller; k.sub.piq denotes the proportional coefficient of the q-axis part of the inner loop current controller, and k.sub.iiq denotes the integral coefficient of the q-axis part of the inner loop current controller; and i.sub.sdref denotes a d-axis part of the current reference, and i.sub.sqref denotes q-axis current reference.

[0106] A model of the outer loop controller of the grid-forming inverter is expressed as:

[00013]$\begin{array}{cc}\{\begin{array}{c}{i}_{\mathrm{sdref}}=\left(U_{\mathrm{sref}}-u_{\mathrm{sd}}\right)k_{\mathrm{pUs}}+M_{\mathrm{Us}}\\ i_{\mathrm{sqref}}=-u_{\mathrm{sq}}{k}_{\mathrm{puq}}+M_{\mathrm{Uq}}\end{array};\mathrm{and}& \left(8\right)\end{array}$$\begin{array}{cc}\{\begin{array}{c}\frac{{\mathrm{dM}}_{\mathrm{Us}}}{\mathrm{dt}}=k_{\mathrm{iUs}}\left(U_{\mathrm{sref}}-u_{\mathrm{sd}}\right)\\ \frac{{\mathrm{dM}}_{uq}}{\mathrm{dt}}=-k_{\mathrm{iuq}}{u}_{\mathrm{sq}}\end{array};& \left(9\right)\end{array}$ [0107] where U.sub.sref denotes the bus voltage reference value of the grid-forming inverter; k.sub.pUs denotes the proportional coefficient of the d-axis part of the outer loop controller, and k.sub.iUs denotes the integral coefficient of the d-axis part of the outer loop controller; k.sub.puq denotes the proportional coefficient of the q-axis part of the outer loop controller, and k.sub.iuq denotes the integral coefficient of the q-axis part of the outer loop controller; and M.sub.Us denotes the integral variable of the d-axis part of the outer loop controller, and M.sub.uq denotes the integral variable of the q-axis part of the outer loop controller.

[0108] The output voltage reference value of the grid-forming inverter U.sub.sref is selected as an input, and the power angle variation is selected as an output, and the non-linear SISO model is expressed as:

[00014]$\begin{array}{cc}\{\begin{array}{c}\stackrel{}{x}=f+gu\\ y=h\left(x\right)\end{array},\{\begin{array}{c}x={\left[,,i_{\mathrm{sd}},i_{\mathrm{sq}},M_{\mathrm{id}},M_{\mathrm{iq}},M_{\mathrm{Us}},M_{\mathrm{uq}}\right]}^T\\ f=\left[\begin{array}{c}{}_0\\ -\frac{1}{2H_m}{P}_s-\frac{D_m}{2H_m}\\ \frac{1}{L_{\mathrm{arm}}}\left[-k_{\mathrm{pid}}{k}_{\mathrm{pUs}}{u}_{\mathrm{sd}}-\left(k_{\mathrm{pid}}+R_{\mathrm{arm}}\right)i_{\mathrm{sd}}+M_{\mathrm{id}}+k_{\mathrm{pid}}{M}_{\mathrm{Us}}\right]\\ \frac{1}{L_{\mathrm{arm}}}\left[-k_{\mathrm{pid}}{k}_{\mathrm{puq}}{u}_{\mathrm{sq}}-\left(k_{\mathrm{piq}}+R_{\mathrm{arm}}\right)i_{\mathrm{sq}}+M_{\mathrm{iq}}+k_{\mathrm{piq}}{M}_{\mathrm{uq}}\right]\\ -k_{\mathrm{iid}}{k}_{\mathrm{pUs}}{u}_{\mathrm{sd}}-k_{\mathrm{iid}}{i}_{\mathrm{sd}}+k_{\mathrm{iid}}{M}_{\mathrm{Us}}\\ -k_{\mathrm{iiq}}{k}_{\mathrm{puq}}{u}_{\mathrm{sq}}-k_{\mathrm{iiq}}{i}_{\mathrm{sq}}+k_{\mathrm{iiq}}{M}_{\mathrm{uq}}\\ -k_{\mathrm{iUs}}{u}_{\mathrm{sd}}-k_{\mathrm{iUs}}{U}_{\mathrm{sref}}\\ -k_{\mathrm{iuq}}{u}_{\mathrm{sq}}\end{array}\right]\\ g=\left[0,0,\frac{k_{\mathrm{pid}}{k}_{\mathrm{pUs}}}{L_{\mathrm{arm}}},0,k_{\mathrm{iid}}{k}_{\mathrm{pUs}},0,k_{\mathrm{iUs}},0\right]\\ h=\\ u=U_{\mathrm{sref}}\end{array};& \left(2\right)\end{array}$

[0109] (2) The expressions of the external subsystem are derived by using the Lie derivative.

[0110] The output signal y is written as a Lie derivative form as:

[00015]$\begin{array}{cc}\stackrel{.}{y}=L_{f}y+L_{g}y{U}_{\mathrm{sref}}.& \left(10\right)\end{array}$

[0111] Since L.sub.gy=0, a second Lie derivative of the output signal y is:

[00016]$\begin{array}{cc}\stackrel{.Math.}{y}=L_f^{2}y+L_g{L}_f{\mathrm{yU}}_{\mathrm{sref}}.& \left(11\right)\end{array}$

[0112] Here, L.sub.gL.sub.fy is still 0, and a third Lie derivative of the output signal y is derived as:

[00017]$\begin{array}{cc}\stackrel{...}{y}=L_f^{3}h\left(x\right)+L_g{L}_f^{2}h\left(x\right)U_{\mathrm{sref}}.& \left(12\right)\end{array}$

[0113] Here, L.sub.gL.sub.f.sup.2h(x) is no longer 0, and a third-order external subsystem of an original system is obtained by using an input-output linearization method, and is expressed as:

[00018]$\begin{array}{cc}\{\begin{array}{c}{\stackrel{}{}}_1={}_2\\ {\stackrel{}{}}_2={}_3\\ {\stackrel{}{}}_3=L_f^{3}y+L_g{L}_f^{2}y{U}_{\mathrm{sref}}\end{array};& \left(3\right)\end{array}$ [0114] where .sub.i denotes the external subsystem variable and is expressed as:

[00019]$\begin{array}{cc}\{\begin{array}{c}{}_1=\\ {}_2={}_0\\ {}_3=-\frac{{}_0}{2H_m}{P}_s-{}_0\frac{D_m}{2H_m}\end{array};& \left(13\right)\end{array}$$\begin{array}{cc}{L}_f^{3}y=\frac{L_f^{2}y}{}\frac{}{t}+\frac{L_f^{2}y}{}\frac{}{t}+\frac{L_f^{2}y}{i_{sd}}\frac{i_{sd}}{t}+\frac{L_f^{2}y}{i_{sq}}\frac{i_{sq}}{t}+\frac{L_f^{2}y}{i_{sd}^2}\frac{i_{sd}}{t}+\frac{L_f^{2}y}{i_{sq}^2}\frac{i_{sq}}{t}& \left(14\right)\end{array}$$\mathrm{and}$$\begin{array}{cc}{L}_g{L}_f^{2}y=\frac{L_f^{2}y}{i_{\mathrm{sd}}}\frac{k_{\mathrm{pid}}{k}_{\mathrm{pUs}}}{L_{\mathrm{arm}}};& \left(15\right)\end{array}$$\mathrm{where}\mathrm{terms}\mathrm{above}\mathrm{are}\mathrm{expressed}\mathrm{as}:$$\begin{array}{cc}\frac{L_f^{2}f\left(x\right)}{}=-\frac{{}_0}{2H_m}\frac{P_s}{};& \left(16\right)\end{array}$$\begin{array}{cc}\frac{L_f^{2}y}{}=-\frac{D_m}{2H_m};& \left(17\right)\end{array}$$\begin{array}{cc}\frac{L_f^{2}h\left(x\right)}{i_{sd}}=-\frac{{}_0}{2H_m}\frac{P_s}{i_{sd}};& \left(18\right)\end{array}$$\begin{array}{cc}\frac{L_f^{2}y}{i_{sq}}=-\frac{{}_0}{2H_m}\frac{P_s}{i_{sq}};& \left(19\right)\end{array}$$\begin{array}{cc}\begin{array}{c}\frac{P_s}{i_{\mathrm{sd}}}=U_{\inf }\cos {}_s+2R_s{i}_{\mathrm{sd}}\\ \frac{P_s}{i_{\mathrm{sq}}}=-U_{\inf }\sin {}_s+2R_s{i}_{\mathrm{sq}}\end{array};\mathrm{and}& \left(20\right)-\left(21\right)\end{array}$ [0115] an expression of L.sub.f.sup.2y is expressed as:

[00020]$\begin{array}{cc}{L}_f^{2}y=-\frac{{}_o}{2H_m}{P}_s-\frac{D_m}{2H_m}.& \left(22\right)\end{array}$

[0116] The hybrid reaching law of the sliding surface is proposed.

[0117] In view of the third-order external subsystem, the linear sliding surface is expressed as:

[00021]$\begin{array}{cc}={}_1{}_1+{}_2{}_2+{}_3& \left(23\right)\end{array}$ [0118] .sub.1 tends to 0 after a system trajectory approaches the sliding surface, where v=0 on the sliding surface, and the system moves on the sliding surface and satisfies:

[00022]$\begin{array}{cc}{\stackrel{.Math.}{}}_1+{}_2{\stackrel{.}{}}_1+{}_1{}_1=0.& \left(24\right)\end{array}$

[0119] A natural frequency and a damping coefficient of .sub.1 motion are expressed as:

[00023]$\begin{array}{cc}\{\begin{array}{c}{}_n=\sqrt{{}_1}\\ =\frac{{}_2}{2\sqrt{{}_1}}\end{array};& \left(25\right)\end{array}$ [0120] where .sub.n denotes the natural frequency when .sub.1 is moving on the sliding surface; g denotes the damping coefficient when .sub.1 is moving on the sliding surface; and .sub.1 and .sub.2 can be determined by using selecting the natural frequency and the damping coefficient.

[0121] A derivative of v satisfies:

[00024]$\begin{array}{cc}\stackrel{.}{}={}_1{}_2+{}_2{}_3+L_f^{3}y+L_g{L}_f^2{\mathrm{yU}}_{\mathrm{sref}}.& \left(26\right)\end{array}$

[0122] To ensure that the system trajectory reaches the sliding surface faster and ensure a motion smoothness near the sliding surface, a new hybrid reaching law is proposed as:

[00025]$\begin{array}{cc}=-k{.Math..Math.}^{}-{.Math..Math.}^{}\mathrm{sat}\left(\right);& \left(27\right)\end{array}$ [0123] where , , k and are constant coefficients, >1, and 0<<1.

[0124] sat( ) denotes the saturation function, and is expressed as:

[00026]$\begin{array}{cc}\mathrm{sat}\left(\right)=\{\begin{array}{cc}\mathrm{sign}\left(\right),& .Math..Math.>\\ \frac{}{},& .Math..Math.\end{array};& \left(28\right)\end{array}$ [0125] where denotes the thickness of the boundary layer, and 0<<1; when |v|>, the power term would accelerate the system to approach the sliding mode; when |v|<, the saturation function is controlled by adopting linear feedback in the boundary layer, so as to achieve smooth transition and weaken system buffeting.

[0126] (4) The dynamic stability controller of the grid-forming inverter is obtained based on the sliding mode control.

[0127] According to the derivative of v and the hybrid reaching law, their relationship is expressed as:

[00027]$\begin{array}{cc}{}_1{}_2+{}_2{}_3+L_f^{3}y+L_g{L}_f^2{\mathrm{yU}}_{\mathrm{sref}}=-k{.Math..Math.}^{}-{.Math..Math.}^{}\mathrm{sat}\left(\right);& \left(29\right)\end{array}$

[0128] According to the hybrid reaching law, the input signal data of the grid-forming inverter is expressed as:

[00028]$\begin{array}{cc}{U}_{\mathrm{sref}}=\frac{-k{.Math..Math.}^{}-{.Math..Math.}^{}\mathrm{sat}\left(\right)-{}_1{}_2-{}_2{}_3-L_f^3\left(x\right)}{L_g{L}_f^{2}h\left(x\right)}.& \left(5\right)\end{array}$

[0129] (5) Verification is performed.

[0130] The verification is performed in a modified Institute of Electrical and Electronics Engineers (IEEE) 11-bus system, where each of original four synchronous generators are replaced with the grid-forming inverter, and an original output are constant, and a tie line between two areas has doubled in size. A topological structure of the modified IEEE 11-bus system is shown in FIG. 2. Before the dynamic stability control method is applied, a small disturbance is applied to obtain response curves of individual grid-forming inverters as shown in FIG. 3. As observed from FIG. 3, individual units of the modified IEEE 11-bus system oscillate and are in dynamic instability. After applying the dynamic stability control method, a same fault is applied to obtain response curves of individual grid-forming inverters as shown in FIG. 4. As observed from comparison between the FIG. 3 with FIG. 4, the method for dynamic stability control can effectively improve a dynamic stability of the 100% renewable energy power system.

[0131] In order to realize the objects above, this application also provides a dynamic stability control system for power systems with renewable energy as shown in FIG. 6.

[0132] The dynamic stability control system is applied on the dynamic stability control method, and includes a creation unit, a data construction unit and a data generation unit.

[0133] The creation unit is configured for creating the non-linear system of the grid-forming inverter corresponding to the renewable energy power system, and constructing the external subsystem corresponding to the grid-forming inverter based on the Lie derivative.

[0134] The data construction unit is configured for constructing the linear sliding surface corresponding to the external subsystem, and generating the dynamic stability control unit corresponding to the external subsystem based on the sliding mode control.

[0135] The data generation unit is configured for generating the first instruction data corresponding to the dynamic stability control unit, and controlling the dynamic stability of the renewable energy power system in real time, where the first instruction data is the voltage instruction value data.

[0136] In an embodiment, the creation unit includes a first creation module, a second creation module and a third creation module.

[0137] The first creation module is configured for creating at least three control loops corresponding to the non-linear system of the grid-forming inverter, where the at least three control loops include the virtual synchronization loop, the current inner loop and the outer loop.

[0138] The second creation module is configured for constructing the inner loop current controller corresponding to the inner loop and the outer loop controller corresponding to the outer loop based on the at least three control loops.

[0139] The third creation module is configured for respectively selecting and obtaining the voltage reference value data and the power angle variation data corresponding to the grid-forming inverter, and constructing the non-linear SISO model corresponding to the grid-forming inverter.

[0140] In an embodiment, the data construction unit further includes a first generation module and a second generation module.

[0141] The first generation module is configured for generating the hybrid reaching law corresponding to the linear sliding surface based on the linear sliding surface.

[0142] The second generation module is configured for generating the input signal data of the grid-forming inverter corresponding to the non-linear system of the grid-forming inverter according to the hybrid reaching law.

[0143] In an embodiment, the control system further includes a generation and verification module. The generation and verification module is configured for generating the fault data corresponding to the renewable energy power system, and verifying the dynamic stability of the renewable energy power system in real time based on the fault data.

[0144] The creation unit further includes a fourth creation module. The fourth creation module is configured for constructing the positive sequence and fundamental frequency model corresponding to the non-linear system of the grid-forming inverter. The positive sequence and fundamental frequency model is expressed as:

[00029]$\begin{array}{cc}\{\begin{array}{c}\frac{{\mathrm{di}}_{\mathrm{sd}}}{\mathrm{dt}}=\frac{1}{L_{\mathrm{arm}}}\left(-u_{\mathrm{sd}}+v_d+L_{\mathrm{arm}}{i}_{\mathrm{sq}}-R_{\mathrm{arm}}{i}_{\mathrm{sd}}\right)\\ \frac{{\mathrm{di}}_{\mathrm{sq}}}{\mathrm{dt}}=\frac{1}{L_{\mathrm{arm}}}\left(-u_{\mathrm{sq}}+v_q+L_{\mathrm{arm}}{i}_{\mathrm{sd}}-R_{\mathrm{arm}}{i}_{\mathrm{sq}}\right)\end{array};& \left(1\right)\end{array}$ [0145] where v.sub.d denotes the d-axis output of the inner loop controller, and v.sub.q denotes the q-axis output of the inner loop controller; R.sub.arm denotes the resistance of the bridge arm, and L.sub.arm denotes the inductance of the bridge arm; u.sub.sd denotes the d-axis component of the bus voltage, and u.sub.sq denote the q-axis component of the bus voltage; i.sub.sd denotes the d-axis component of the output current of the grid-forming inverter, and i.sub.sq denotes the q-axis component of the output current of the grid-forming inverter; and denotes the fundamental frequency of the grid-forming inverter.

[0146] In the third creation module, the non-linear SISO model is expressed as:

[00030]$\begin{array}{cc}\begin{array}{cc}\{\begin{array}{c}\stackrel{.}{x}=f+\mathrm{gu}\\ y=h\left(x\right)\end{array},& \{\begin{array}{c}x={\left[,,i_{\mathrm{sd}},i_{\mathrm{sq}},M_{\mathrm{id}},M_{\mathrm{iq}},M_{\mathrm{Us}},M_{\mathrm{uq}}\right]}^T\\ f=\left[\begin{array}{c}{}_0\\ -\frac{1}{2H_m}{P}_s-\frac{D_m}{2H_m}\\ \frac{1}{L_{\mathrm{arm}}}\left[-k_{\mathrm{pid}}{k}_{\mathrm{pUs}}{u}_{\mathrm{sd}}-\left(k_{\mathrm{pid}}+R_{\mathrm{arm}}\right)i_{\mathrm{sd}}+M_{\mathrm{id}}+k_{\mathrm{pid}}{M}_{\mathrm{Us}}\right]\\ \frac{1}{L_{\mathrm{arm}}}\left[-k_{\mathrm{pid}}{k}_{\mathrm{pup}}{u}_{\mathrm{sq}}-\left(k_{\mathrm{piq}}+R_{\mathrm{arm}}\right)i_{\mathrm{sq}}+M_{\mathrm{iq}}+k_{\mathrm{piq}}{M}_{\mathrm{uq}}\right]\\ -k_{\mathrm{iid}}{k}_{\mathrm{pUs}}{u}_{\mathrm{sd}}-k_{\mathrm{iid}}{i}_{\mathrm{sd}}+k_{\mathrm{iid}}{M}_{\mathrm{Us}}\\ -k_{\mathrm{iiq}}{k}_{\mathrm{pup}}{u}_{\mathrm{sq}}-k_{\mathrm{iiq}}{i}_{\mathrm{sq}}+k_{\mathrm{iiq}}{M}_{\mathrm{uq}}\\ -k_{\mathrm{iUs}}{u}_{\mathrm{sd}}-k_{\mathrm{iUs}}{U}_{\mathrm{sref}}\\ -k_{\mathrm{iuq}}{u}_{\mathrm{sq}}\end{array}\right]\\ \begin{array}{c}g=\left[0,0,\frac{k_{\mathrm{pid}}{K}_{\mathrm{pUs}}}{L_{\mathrm{arm}}},0,k_{\mathrm{iid}},k_{\mathrm{pUs}},0,k_{\mathrm{iUs}},0\right]\\ h=\\ u=U_{\mathrm{sref}}\end{array}\end{array}\end{array};& \left(2\right)\end{array}$ [0147] where denotes the rotating speed of the grid-forming inverter, and denotes the power angle variation of the grid-forming inverter; i.sub.sd denotes the d-axis component of the output current of the grid-forming inverter, and i.sub.sq denotes the q-axis component of the output current of the grid-forming inverter; M.sub.id denotes the integral variable of the d-axis part of the inner loop current controller, and M.sub.iq denotes the integral variable of the q-axis part of the inner loop current controller; M.sub.Us denotes the integral variable of the d-axis part of the outer loop controller, and M.sub.uq denotes the integral variable of the q-axis part of the outer loop controller; .sub.0 denotes the reference frequency; H.sub.m denotes the inertia coefficient of the grid-forming inverter, and D.sub.m denotes the damping coefficient of the grid-forming inverter; P.sub.s denotes the power variation of the grid-forming inverter; R.sub.arm denotes the resistance of the bridge arm, and L.sub.arm denotes the inductance of the bridge arm; k.sub.pid denotes the proportional coefficient of the d-axis part of the inner loop current controller, and k.sub.iid denotes the integral coefficient of the d-axis part of the inner loop current controller; k.sub.piq denotes the proportional coefficient of the q-axis part of the inner loop current controller, and k.sub.iiq denotes the integral coefficient of the q-axis part of the inner loop current controller; u denotes the input signal; Usref denotes the bus voltage reference value of the grid-forming inverter; k.sub.pUs denotes the proportional coefficient of the d-axis part of the outer loop controller, and k.sub.iUs denotes the integral coefficient of the d-axis part of the outer loop controller; k.sub.puq denotes the proportional coefficient of the q-axis part of the outer loop controller, and k.sub.iuq denotes the integral coefficient of the q-axis part of the outer loop controller; u.sub.sd denotes the d-axis component of IBG bus voltage, and u.sub.sq denotes the q-axis component of the IBG output voltage; and y denotes the output signal.

[0148] In the embodiments of the present disclosure, method steps involved in the dynamic stability control method for the renewable energy power system have specifically described above, that is, function modules of the dynamic stability control system, which are configured for realizing steps or sub-steps in the embodiments of the method, will not described herein.

[0149] This application, through the method above, creates the non-linear system of the grid-forming inverter corresponding to the renewable energy power system, and constructs the external subsystem corresponding to the grid-forming inverter based on the Lie derivative; constructs the linear sliding surface corresponding to the grid-forming inverter according to the external subsystem, and generates the dynamic stability control unit corresponding to the grid-forming inverter based on the sliding mode control; and generates and obtains the first instruction data corresponding to the dynamic stability control unit, and controls the dynamic stability of the renewable energy power system in real time according to the first instruction data; where the first instruction data is the voltage instruction value data. In addition, the voltage instruction value of the grid-forming inverter is modified to improve the dynamic stability of the renewable energy power system.

[0150] Through technical solutions of the present disclosure, the external subsystem of the renewable energy power system is constructed, and the analytical expression of the inverter voltage control signal is derived based on the sliding mode control method, so as to improve the dynamic stability of the system by modifying the voltage command value of the inverter. In other words, the technical solutions of this application consider dynamic stability problems of the 100% renewable energy power system and provides the method for dynamic stability control of the 100% renewable energy power system, where obtained results can effectively improve the dynamic stability of the 100% renewable energy power system during operation process, promote realization of the power systems with 100% renewable energy, and ensure safe and stable operation of the system.

[0151] Described above are only some embodiments of this application, which are specific and detailed, and are not intended to limit this application. It should be noted that various modifications and improvements made by those of ordinary skill in the art without departing the spirit of the present disclosure shall fall within the scope of this application defined by the appended claims.