MICROGRID DISTRIBUTED SECONDARY CONTROL METHOD AND SYSTEM BASED ON VIRTUAL SYNCHRONOUS MACHINE

Abstract

A microgrid distributed secondary control method and system based on a virtual synchronous machine is applied to the technical field of microgrid control. The microgrid distributed secondary control method includes: designing a microgrid primary control strategy based on the virtual synchronous machine, and establishing a microgrid distributed secondary control model based on the virtual synchronous machine by combining a speed regulator equation of the virtual synchronous machine; considering nonlinear characteristics of the virtual synchronous machine, based on a deterministic equivalence principle, designing a linearized microgrid distributed secondary control strategy based on the virtual synchronous machine; and based on the deterministic equivalence principle and a Lyapunov theory, proving accuracy of frequency recovery of the linearized microgrid distributed secondary control strategy based on the virtual synchronous machine. The method and system provides inertia support, significantly reduces communication and computing resources, and helps the microgrid to operate safely and stably.

Claims

1. A microgrid distributed secondary control method based on a virtual synchronous machine, comprising: step 1: designing a microgrid primary control strategy based on the virtual synchronous machine, and establishing a microgrid distributed secondary control model based on the virtual synchronous machine by combining a speed regulator equation of the virtual synchronous machine; wherein in the step 1, the microgrid distributed secondary control model based on the virtual synchronous machine is as follows: ${\stackrel{}{}}_{\mathrm{.Math.}}\left(t\right)={}_i\left(t\right);$ ${\stackrel{}{}}_{\mathrm{.Math.}}\left(t\right)=\frac{1}{J_i}\left(P_i^{*}-P_i\left(t\right)-D_i\left({}_i\left(t\right)-{}_{ni}\left(t\right)\right)\right)+{}_i\left(t\right)={}_i^{}\left(i\right);$ wherein .sub.i(t) is a phase of a virtual synchronous machine i; .sub.i (t) and .sub.ni (t) are an output frequency and a frequency setting value of the virtual synchronous machine i, respectively; J.sub.i=J.sub.Mi.sub.ni (t) is an improved moment of inertia of the virtual synchronous machine i; D.sub.i=k.sub.i+D.sub.Mi is an improved damping coefficient of the virtual synchronous machine i; J.sub.Mi and D.sub.Mi are a moment of inertia and a damping coefficient of the virtual synchronous machine i, respectively; k.sub.i is an adjustment coefficient; $P_i^{*}$ is a rated active power of the virtual synchronous machine i; P.sub.i(t) is a mechanical output active power of the virtual synchronous machine i; and .sub.i(t) and .sub.i.sup.(t) are an error tracking auxiliary control coefficient and an auxiliary frequency control coefficient of the virtual synchronous machine i, respectively; .sub.ni (t) is as follows: ${}_{ni}\left(t\right)=\left({}_i\left(t\right)+{}_i\left(t\right)-\frac{1}{k_{{}_i}}{}_i^P\left(t\right)\right)\mathrm{dt};$ wherein ${}_i^P\left(i\right)$ is a derivative or quadratic compensation; .sub.i(t) is as follows: ${}_i\left(t\right)=\frac{1}{J_i}\left(P_i^{*}-P_i\left(t\right)-D_i\left({}_i\left(t\right)-{}_{ni}\left(t\right)\right)\right);$ step 2: considering nonlinear characteristics of the virtual synchronous machine, based on a deterministic equivalence principle, designing a linearized microgrid distributed secondary control strategy based on the virtual synchronous machine; wherein in the step 2, the linearized microgrid distributed secondary control strategy based on the virtual synchronous machine is as follows: $z_i\left(t\right)={\stackrel{}{}}_i\left(t\right)-{}_i\left(t\right);$ ${\stackrel{.}{\stackrel{}{}}}_i\left(t\right)={}_i^{\stackrel{}{}}\left(t\right);$ ${}_i\left(t\right)={}_i{z}_i\left(t\right)-{}_i\left(t\right)+{}_i^{\stackrel{}{}}\left(t\right);$ wherein z.sub.i (t) is an estimated error; {circumflex over ()}.sub.i(t) is an estimated value of .sub.i (t); .sub.i(t) is the output frequency of the virtual synchronous machine i; ${}_i^{\stackrel{}{}}\left(t\right)$ is a control variable or reference value tracking; .sub.i(t) is the error tracking auxiliary control coefficient of the virtual synchronous machine i; .sub.i is a first control gain; and .sub.i(t) is as follows: ${}_i\left(t\right)=\frac{1}{J_i}\left(P_i^{*}-P_i\left(t\right)-D_i\left({}_i\left(t\right)-{}_{ni}\left(t\right)\right)\right);$ wherein J.sub.i=J.sub.Mi.sub.ni (t) is the improved moment of inertia of the virtual synchronous machine i; D.sub.i=k.sub.i+D.sub.Mi is the improved damping coefficient of the virtual synchronous machine i, J.sub.Mi and D.sub.Mi are the moment of inertia and the damping coefficient of the virtual synchronous machine i, respectively; k.sub.i is the adjustment coefficient; P.sub.i* is the rated active power of the virtual synchronous machine i; P.sub.i(t) is the mechanical output active power of the virtual synchronous machine i; and .sub.ni(t) is the frequency setting value of the virtual synchronous machine i; ${}_i^{\stackrel{}{}}\left(t\right)$ is as follows: ${}_i^{\stackrel{}{}}\left(t\right)={}_{}{}_i\left(t\right);$ wherein .sub. is a second control gain; and .sub.i(t) is an auxiliary control variable; .sub.i(t) is as follows: ${}_i\left(t\right)=-\underset{j{N}_i}{.Math.}{a}_{\mathrm{ij}}\left({}_i\left(t\right)-{}_j\left(t\right)\right)-g_{i0}\left({}_i\left(t\right)-{}_i^{ref}\right)-{}_i{z}_i\left(t\right);$ wherein N.sub.i is a set of neighbors of the virtual synchronous machine i; .sub.ij is a connection gain; g.sub.i0=I means that the virtual synchronous machine i is connected to a reference value; .sub.i.sup.ref is a frequency reference value; and .sub.i is a consensus control gain; ${}_i^{ref}$ is as follows: ${}_i^{ref}=\underset{t.fwdarw.}{\lim }{}_i\left(t\right);$ wherein i=1, 2, . . . , n; and step 3: based on the deterministic equivalence principle and a Lyapunov theory, proving an accuracy of frequency recovery of the linearized microgrid distributed secondary control strategy based on the virtual synchronous machine.

2. The microgrid distributed secondary control method based on the virtual synchronous machine according to claim 1, wherein in the step 1, the microgrid primary control strategy based on the virtual synchronous machine is as follows: $P_{in}\left(t\right)-P_i\left(t\right)=J_{Mi}{}_{ni}\left(t\right)\frac{d\left({}_i\left(t\right)-{}_{ni}\left(t\right)\right)}{dt}+D_{Mi}\left({}_i\left(t\right)-\stackrel{~}{}\right);$ wherein P.sub.in(t) and P.sub.i(t) are a mechanical input active power and the mechanical output active power of the virtual synchronous machine i, respectively; J.sub.Mi and D.sub.Mi are the moment of inertia and the damping coefficient of the virtual synchronous machine i, respectively; .sub.i(t) and .sub.ni (t) are the output frequency and the frequency setting value of the virtual synchronous machine i, respectively; and {tilde over ()} is a measured angular frequency of the virtual synchronous machine i.

3. The microgrid distributed secondary control method based on the virtual synchronous machine according to claim 1, wherein in the step 1, the speed regulator equation of the virtual synchronous machine is as follows: $k_i\left({}_{ni}\left(t\right)-{}_i\left(t\right)\right)=P_{in}\left(t\right)-P_i^{*};$ wherein k.sub.i is the adjustment coefficient; .sub.i (t) and .sub.ni (t) are the output frequency and the frequency setting value of the virtual synchronous machine i, respectively; P.sub.in(t) is a mechanical input active power of the virtual synchronous machine i; and $P_i^{*}$ is the rated active power of the virtual synchronous machine i.

4. The microgrid distributed secondary control method based on the virtual synchronous machine according to claim 1, wherein the step 3 of, based on the deterministic equivalence principle and the Lyapunov theory, proving the accuracy of frequency recovery of the linearized microgrid distributed secondary control strategy based on the virtual synchronous machine comprises: step 3.1: proving that the frequency with .sub.i(t) approaches a frequency estimate {circumflex over ()}.sub.i(t); and step 3.2: proving that the frequency estimate {circumflex over ()}.sub.i(t) approaches a frequency reference ${}_i^{ref}.$

5. The microgrid distributed secondary control method based on the virtual synchronous machine according to claim 4, wherein in the step 3.1, the proving that the frequency .sub.i(t) approaches the frequency estimate .sub.i(t) comprises: deriving an estimation error z.sub.i (t), as follows: ${\stackrel{}{z}}_i\left(t\right)={\stackrel{.}{\stackrel{}{}}}_t\left(t\right)-{\stackrel{}{}}_i\left(t\right)=-{}_i{z}_i\left(t\right);$ defining a Lyapunov function V.sub.1(t), as follows: $V_1\left(t\right)=\frac{1}{2}{z}^{T}z;$ wherein z=[z.sub.1,z.sub.2, . . . ,z.sub.n].sup.T; and T is the transpose; deriving the lyapunov function V.sub.1(t) to obtain: ${\stackrel{}{V}}_1\left(t\right)=\frac{1}{2}{z}^T\stackrel{}{z}=-0;$ wherein =diag{.sub.i}.Math..sup.NN; $=\mathrm{diag}\left\{z_i^2\right\}.Math.{}^{NN};$ .sub.i is the first control gain; and $z_i^2$ is a parameter form; when .sub.i>0, {dot over (V)}.sub.1(t)<0, and the frequency .sub.i(t) approaches the frequency estimate {circumflex over ()}.sub.i(t).

6. The microgrid distributed secondary control method based on the virtual synchronous machine according to claim 4, wherein in the step 3.2, the proving that the frequency estimate {circumflex over ()}.sub.i(t) approaches the frequency reference ${}_i^{ref}$ comprises: defining .sub.i(t), .sub.i(t), and .sub.i(t), as follows: ${\tilde{n}}_i\left(t\right)=-{}_i{z}_i\left(t\right);$ ${}_i\left(t\right)={}_i\left(t\right)-{}_i^{ref};$ ${}_i\left(t\right)=-\underset{j{N}_i}{.Math.}{a}_{ij}\left({}_i\left(t\right)-{}_j\left(t\right)\right)-g_{i0}\left({}_i\left(t\right)-{}_i^{ref}\right);$ expressing the linearized microgrid distributed secondary control strategy based on the virtual synchronous machine in matrix form, as follows: $={}_{}+{}_{}\tilde{n};$ wherein is in matrix form; =(L+B); L+B is a matrix form of a connection status; and is in matrix form; defining a Lyapunov function V.sub.2(t), as follows: $v_2\left(t\right)=\frac{1}{2}{}^T\left(L+B\right);$ wherein =[.sub.1,.sub.2, . . . ,.sub.N].sup.T; deriving the lyapunov function V.sub.2(t) to obtain: ${\stackrel{}{V}}_2\left(t\right)={}^T\left(L+B\right);$ based on = and (L+B).sup.T=(L+B), obtaining: ${\stackrel{}{V}}_2\left(t\right)=-{}_{}{}^T-{}_{}{}^T\tilde{n};$ scaling {dot over (V)}.sub.2(t), and obtaining: ${\stackrel{}{V}}_2\left(t\right)-\frac{{}_{}}{2}\underset{i=l}{\overset{N}{.Math.}}\left({}_i^2\left(t\right)-{\tilde{n}}_i^2\left(t\right)\right);$ since a convergence parameter .sub.i satisfies ${}_i^2\left(t\right)<{}_i{\tilde{n}}_i^2\left(t\right)$ and .sub.i>1, obtaining: ${\stackrel{}{V}}_2\left(t\right)-\frac{{}_{}}{2}\underset{i=l}{\overset{N}{.Math.}}\left({}_i-l\right){\tilde{n}}_i^2\left(t\right)0;$ wherein {dot over (V)}.sub.2(t) is strictly negative semi-definite, and the frequency estimate {circumflex over ()}.sub.i(t) approaches the frequency reference ${}_i^{\mathrm{ref}}.$

7. A microgrid distributed secondary control system based on a virtual synchronous machine using the microgrid distributed secondary control method based on the virtual synchronous machine according to claim 1, comprising: an establishment module for a microgrid distributed secondary control model based on the virtual synchronous machine, configured to, design a microgrid primary control strategy based on the virtual synchronous machine, and establish the microgrid distributed secondary control model based on the virtual synchronous machine by combining a speed regulator equation of the virtual synchronous machine; a designing module for a linearized microgrid distributed secondary control strategy based on the virtual synchronous machine, configured to, consider nonlinear characteristics of the virtual synchronous machine, and based on a deterministic equivalence principle, design the linearized microgrid distributed secondary control strategy based on the virtual synchronous machine; and a frequency recovery accuracy proof module, configured to, based on the deterministic equivalence principle and a Lyapunov theory, prove an accuracy of frequency recovery of the linearized microgrid distributed secondary control strategy based on the virtual synchronous machine.

8. The microgrid distributed secondary control system based on the virtual synchronous machine according to claim 7, wherein in the step 1 of the microgrid distributed secondary control method based on the virtual synchronous machine, the microgrid primary control strategy based on the virtual synchronous machine is as follows: $P_{\mathrm{in}}\left(t\right)-P_i\left(t\right)=J_{\mathrm{Mi}}{}_{\mathrm{ni}}\left(t\right)\frac{d\left({}_i\left(t\right)-{}_{\mathrm{ni}}\left(t\right)\right)}{\mathrm{dt}}+D_{\mathrm{Mi}}\left({}_i\left(t\right)-\stackrel{~}{}\right);$ wherein P.sub.in(t) and P.sub.i(t) are a mechanical input active power and the mechanical output active power of the virtual synchronous machine i, respectively; J.sub.Mi and D.sub.Mi are the moment of inertia and the damping coefficient of the virtual synchronous machine i, respectively; .sub.i(t) and .sub.ni (t) are the output frequency and the frequency setting value of the virtual synchronous machine i, respectively; and {tilde over ()} is a measured angular frequency of the virtual synchronous machine i.

9. The microgrid distributed secondary control system based on the virtual synchronous machine according to claim 7, wherein in the step 1 of the microgrid distributed secondary control method based on the virtual synchronous machine, the speed regulator equation of the virtual synchronous machine is as follows: $k_i\left({}_{\mathrm{ni}}\left(t\right)-{}_i\left(t\right)\right)=P_{\mathrm{in}}\left(t\right)-P_i^{*};$ wherein k.sub.i is the adjustment coefficient; .sub.i (t) and .sub.ni (t) are the output frequency and the frequency setting value of the virtual synchronous machine i, respectively; P.sub.in(t) is a mechanical input active power of the virtual synchronous machine i; and $P_i^{*}$ is the rated active power of the virtual synchronous machine i.

10. The microgrid distributed secondary control system based on the virtual synchronous machine according to claim 7, wherein in the microgrid distributed secondary control method based on the virtual synchronous machine, the step 3 of, based on the deterministic equivalence principle and the Lyapunov theory, proving the accuracy of frequency recovery of the linearized microgrid distributed secondary control strategy based on the virtual synchronous machine comprises: step 3.1: proving that the frequency .sub.i(t) approaches a frequency estimate {circumflex over ()}.sub.i(t); and step 3.2: proving that the frequency estimate {circumflex over ()}.sub.i(t) approaches a frequency reference ${}_i^{\mathrm{ref}}.$

11. The microgrid distributed secondary control system based on the virtual synchronous machine according to claim 10, wherein in the step 3.1, the proving that the frequency with .sub.i(t) approaches the frequency estimate {circumflex over ()}.sub.i(t) comprises: deriving an estimation error z.sub.i(t), as follows: ${\stackrel{}{z}}_i\left(t\right)={\stackrel{.}{\stackrel{}{}}}_t\left(t\right)-{\stackrel{}{}}_i\left(t\right)=-{}_i{z}_i\left(t\right);$ defining a Lyapunov function V.sub.1(t), as follows: $V_l\left(t\right)=\frac{l}{2}{z}^{T}z;$ wherein z=[z.sub.1,z.sub.2, . . . ,z.sub.n].sup.T; and T is the transpose; deriving the lyapunov function V.sub.1(t) to obtain: ${\stackrel{}{V}}_l\left(t\right)=\frac{l}{2}{z}^T\stackrel{}{z}=-0;$ wherein =diag{.sub.i}.Math..sup.NN; $=\mathrm{diag}\left\{z_i^2\right\}.Math.{}^{NN};$ .sub.i is the first control gain; and $z_i^2$ is a parameter form; when .sub.i>0, {dot over (V)}.sub.1(t)<0, and the frequency .sub.i(t) approaches the frequency estimate {circumflex over ()}.sub.i(t).

12. The microgrid distributed secondary control system based on the virtual synchronous machine according to claim 10, wherein in the step 3.2, the proving that the frequency estimate {circumflex over ()}.sub.i(t) approaches the frequency reference ${}_i^{\mathrm{ref}}$ comprises: defining .sub.i(t), .sub.i(t), and .sub.i(t), as follows: ${\tilde{n}}_i\left(t\right)=-{}_i{z}_i\left(t\right);$ ${}_i\left(t\right)={}_i\left(t\right)-{}_i^{\mathrm{ref}};$ ${}_i\left(t\right)=-\underset{j{N}_i}{.Math.}{a}_{\mathrm{ij}}\left({}_i\left(t\right)-{}_j\left(t\right)\right)-g_{i0}\left({}_i\left(t\right)-{}_i^{\mathrm{ref}}\right);$ expressing the linearized microgrid distributed secondary control strategy based on the virtual synchronous machine in matrix form, as follows: $={}_{}+{}_{}\tilde{n};$ wherein is in matrix form; =(L+B); L+B is a matrix form of a connection status; and is in matrix form; defining a Lyapunov function V.sub.2(t), as follows: $V_2\left(t\right)=\frac{1}{2}{}^T\left(L+B\right);$ wherein =[.sub.1,.sub.2, . . . ,.sub.N].sup.T; deriving the lyapunov function V.sub.2(t) to obtain: ${\stackrel{}{V}}_2\left(t\right)={}^T\left(L+B\right);$ based on = and (L+B).sup.T=(L+B), obtaining: ${\stackrel{}{V}}_2\left(t\right)=-{}_{}{}^T-{}_{}{}^T\tilde{n};$ scaling {dot over (V)}.sub.2(t), and obtaining: ${\stackrel{}{V}}_2\left(t\right)-\frac{{}_{}}{2}\underset{i=1}{\overset{N}{.Math.}}\left({}_i^2\left(t\right)-{\tilde{n}}_i^2\left(t\right)\right);$ since a convergence parameter .sub.i satisfies ${}_i^2\left(t\right)<{}_i{\tilde{n}}_i^2\left(t\right)$ and .sub.i>1, obtaining: ${\stackrel{.}{V}}_2\left(t\right)-\frac{{}_{}}{2}\underset{i=1}{\overset{N}{.Math.}}\left({}_i-1\right){\tilde{n}}_i^2\left(t\right)0;$ wherein {dot over (V)}.sub.2(t) is strictly negative semi-definite, and the frequency estimate {circumflex over ()}.sub.i(t) approaches the frequency reference ${}_i^{\mathrm{ref}}.$

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0054] The patent or application file contains at least one drawing executed in color. Copies of this patent or patent application publication with color drawing(s) will be provided by the Office upon request and payment of the necessary fee.

[0055] To more clearly illustrate technical solutions in embodiments of the present invention or in the prior art, the following briefly introduces accompanying drawings required in the embodiments or the prior art. It is clear that the accompanying drawings in the following descriptions are only embodiments of the present invention, and a person of ordinary skill in the art may still derive other drawings from the accompanying drawings without creative efforts.

[0056] FIG. 1 is a schematic flow chart of a method according to the present invention.

[0057] FIG. 2 is a schematic diagram of a structure of an island microgrid system according to the present invention.

[0058] FIG. 3 is a schematic diagram of frequencies of virtual synchronous machines under a microgrid distributed secondary control strategy based on a virtual synchronous machine according to the present invention.

[0059] FIG. 4 is a schematic diagram of active power of virtual synchronous machines under a microgrid distributed secondary control strategy based on a virtual synchronous machine according to the present invention.

DETAILED DESCRIPTION OF THE EMBODIMENTS

[0060] The following clearly and completely describes the technical solutions in embodiments of the present invention with reference to the accompanying drawings in embodiments of the present invention. It is clear that the described embodiments are merely a part rather than all of embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

Embodiment 1

[0061] Embodiment 1 of the present invention discloses a microgrid distributed secondary control method and system based on a virtual synchronous machine.

[0062] To achieve the above objective, the present invention adopts the following technical solutions.

[0063] A microgrid distributed secondary control method based on a virtual synchronous machine includes: [0064] Step 1: A microgrid primary control strategy based on the virtual synchronous machines is designed, so that inertia support is provided for operation of the microgrid, and rapid balance of the virtual synchronous machines under load change is achieved; a microgrid distributed secondary control model based on the virtual synchronous machines is established by combining with a speed regulator equation of the virtual synchronous machines, so that inertia support is provided for operation of the microgrid, and instantaneous frequency offset is reduced.

[0065] The microgrid primary control strategy based on the virtual synchronous machine is as follows:

[00033]$P_{\mathrm{in}}\left(t\right)-P_i\left(t\right)=J_{\mathrm{Mi}}{}_{\mathrm{ni}}\left(t\right)\frac{d\left({}_i\left(t\right)-{}_{\mathrm{ni}}\left(t\right)\right)}{\mathrm{dt}}+D_{\mathrm{Mi}}\left({}_i\left(t\right)-\stackrel{~}{}\right);$ [0066] wherein P.sub.in(t) and P.sub.i(t) are a mechanical input active power and an output active power of the virtual synchronous machine i, respectively; J.sub.Mi and D.sub.Mi are a moment of inertia and a damping coefficient of the virtual synchronous machine i, respectively; .sub.i (t) and .sub.ni (t) are an output frequency and a frequency setting value of the virtual synchronous machine i, respectively; and {tilde over ()} is a measured angular frequency of the virtual synchronous machine i, {tilde over ()}=.sub.ni(t).

[0067] The speed regulator equation of the virtual synchronous machine is as follows:

[00034]$k_i\left({}_{\mathrm{ni}}\left(t\right)-{}_i\left(t\right)\right)=P_{\mathrm{in}}\left(t\right)-P_i^{*};$ [0068] wherein k.sub.i is an adjustment coefficient; .sub.i (t) and .sub.ni (t) are an output frequency and a frequency setting value of the virtual synchronous machine i, respectively; P.sub.in(t) is a mechanical input active power of the virtual synchronous machine i; and

[00035]$P_i^{*}$ is a rated active power of the virtual synchronous machine i.

[0069] The microgrid distributed secondary control model based on the virtual synchronous machine is as follows:

[00036]${\stackrel{}{}}_{\mathrm{.Math.}}\left(t\right)={}_i\left(t\right);$${\stackrel{}{}}_{\mathrm{.Math.}}\left(t\right)=\frac{1}{J_i}\left(P_i^{*}-P_i\left(t\right)-D_i\left({}_i\left(t\right)-{}_{ni}\left(t\right)\right)\right)+{}_i\left(t\right)={}_i^{}\left(t\right);$ [0070] .sub.i(t) is a phase of a virtual synchronous machine i; .sub.i(t) and .sub.ni (t) are an output frequency and a frequency setting value of the virtual synchronous machine i, respectively; J.sub.i=J.sub.Mi.sub.ni (t) is an improved moment of inertia of the virtual synchronous machine i; D.sub.i=k.sub.i+D.sub.Mi is an improved damping coefficient of the virtual synchronous machine i; J.sub.Mi and D.sub.Mi are a moment of inertia and a damping coefficient of the virtual synchronous machine i, respectively; k.sub.i is an adjustment coefficient;

[00037]$P_i^{*}$

is a rate active power of the virtual synchronous machine i; P.sub.i(t) is a mechanical output active power of the virtual synchronous machine i; .sub.i(t) and .sub.i.sup.(t) are an error tracking auxiliary control coefficient and an auxiliary frequency control coefficient of the virtual synchronous machine i, respectively; [0071] quadratic compensation dP.sub.i(t) is defined as follows:

[00038]${}_i\left(t\right)-{}_{ni}\left(t\right)=\frac{1}{k_{{}_i}}{\mathrm{dP}}_i\left(t\right);$ [0072] the quadratic compensation dP.sub.i(t) is derived as follows:

[00039]${\stackrel{}{}}_i\left(t\right)-{\stackrel{}{}}_{ni}\left(t\right)=\frac{1}{k_{{}_i}}d{\stackrel{}{P}}_i\left(t\right);$

[00040]$d{\stackrel{}{P}}_i\left(t\right)={}_i^P\left(t\right)$

is defined, so that the frequency setting .sub.ni (t) is as follows:

[00041]${}_{ni}\left(t\right)=\left({\stackrel{}{}}_i\left(t\right)-\frac{1}{k_{{}_i}}d{\stackrel{.}{P}}_i\left(t\right)\right)\mathrm{dt}=\left({\stackrel{}{}}_i\left(t\right)-\frac{1}{k_{{}_i}}{}_i^P\left(t\right)\right)\mathrm{dt}=\left({}_i\left(t\right)+{}_i\left(t\right)-\frac{1}{k_{{}_i}}{}_i^P\left(t\right)\right)\mathrm{dt};$ [0073] wherein

[00042]${}_i^P\left(t\right)$ is a derivative or quadratic compensation; [0074] .sub.i(t) is as follows:

[00043]${}_i\left(t\right)=\frac{1}{J_i}\left(P_i^{*}-P_i\left(t\right)-D_i\left({}_i\left(t\right)-{}_{ni}\left(t\right)\right)\right).$

[0075] Step 2: Nonlinear characteristics of the virtual synchronous machine are considered, and based on a deterministic equivalence principle, a linearized microgrid distributed secondary control strategy based on the virtual synchronous machine is designed. Considering the nonlinear characteristics of the virtual synchronous machine, the deterministic equivalence principle is used to achieve the linearization of the virtual synchronous machine. A distributed frequency recovery control strategy of the virtual synchronous machine is designed to restore the frequency of each virtual synchronous machine to the rated reference.

[0076] The secondary frequency control target is to restore the frequency of each virtual synchronous machine to the frequency reference, as follows:

[00044]$\underset{t.fwdarw.}{\lim }{}_i\left(t\right)={}_i^{\mathrm{ref}};$ [0077] wherein i=1, 2, . . . , n;

[00045]${}_i^{\mathrm{ref}}$ is a frequency reference.

[0078] The nonlinear characteristic of the virtual synchronous machine is considered, the linearization of the virtual synchronous machine is achieved d by applying a deterministic equivalence principle, and the linearized microgrid distributed secondary control strategy based on the virtual synchronous machine is as follows:

[00046]$z_i\left(t\right)={\hat{}}_i\left(t\right)-{}_i\left(t\right);$${\stackrel{.}{\hat{}}}_i\left(t\right)={}_i^{\hat{}}\left(t\right);$${}_i\left(t\right)={}_i{z}_i\left(t\right)-{}_i\left(t\right)+{}_i^{\hat{}}\left(t\right);$ [0079] z.sub.i (t) is an estimated error; {circumflex over ()}.sub.i(t) is an estimated value of .sub.i(t); .sub.i(t) is an output frequency of the virtual synchronous machine i;

[00047]${}_i^{\hat{}}\left(t\right)$ is a control variable of reference value tracking; .sub.i(t) is an error tracking auxiliary control coefficient of the virtual synchronous machine i; .sub.i is a control gain; .sub.i(t) is as follows:

[00048]${}_i\left(t\right)=\frac{1}{J_i}\left(P_i^{*}-P_i\left(t\right)-D_i\left({}_i\left(t\right)-{}_{ni}\left(t\right)\right)\right);$ [0080] J.sub.i=J.sub.Mi.sub.ni (t) is an improved moment of inertia of the virtual synchronous machine i; D.sub.i=k.sub.i+D.sub.Mi is an improved damping coefficient of the virtual synchronous machine i, J.sub.Mi and D.sub.Mi are a moment of inertia and a damping coefficient of the virtual synchronous machine i, respectively; k.sub.i is an adjustment coefficient;

[00049]$P_i^{*}$ is a rated active power of the virtual synchronous machine i; P.sub.i(t) is a mechanical output active power of the virtual synchronous machine i; .sub.ni (t) is a frequency setting value of virtual synchronous machine i; [0081] .sub.i.sup.{circumflex over ()}(t) is as follows:

[00050]${}_i^{\hat{}}\left(t\right)={}_{}{}_i\left(t\right);$ [0082] wherein .sub. is a control gain; .sub.i(t) is an auxiliary control variable; [0083] .sub.i(t) is as follows:

[00051]${}_i\left(t\right)=-\underset{j{N}_i}{.Math.}{a}_{\mathrm{ij}}\left({}_i\left(t\right)-{}_j\left(t\right)\right)-g_{i0}\left({}_i\left(t\right)-{}_i^{\mathrm{ref}}\right)-{}_i{z}_i\left(t\right);$ [0084] N.sub.i is a set of neighbors of the virtual synchronous machine i; .sub.ij is a connection gain; g.sub.i0=1 means that the virtual synchronous machine i is connected to a reference value;

[00052]${}_i^{\mathrm{ref}}$ is a frequency reference value; .sub.i is a consensus control gain;

[00053]${}_i^{\mathrm{ref}}$

is as follows:

[00054]${}_i^{\mathrm{ref}}=\underset{t.fwdarw.}{\lim }{}_i\left(t\right);$ [0085] wherein i=1, 2, . . . , n.

[0086] Step 3: Based on the deterministic equivalence principle and a Lyapunov theory, the accuracy of frequency recovery of the linearized microgrid distributed secondary control strategy based on the virtual synchronous machine is proved, so that inertia support is provided.

[0087] The step of, based on the deterministic equivalence principle and a Lyapunov theory, proving accuracy of frequency recovery of the linearized microgrid distributed secondary control strategy based on the virtual synchronous machine, is specifically as follows:

[0088] Step 3.1: Proving that the frequency .sub.i(t) approaches a frequency estimate {circumflex over ()}.sub.i(t). [0089] the proving that the frequency .sub.i(t) approaches a frequency estimate {circumflex over ()}.sub.i(t) is specifically as follows: [0090] deriving an estimation error z.sub.i(t), as follows:

[00055]${\stackrel{.}{z}}_i\left(t\right)={\stackrel{.}{\hat{}}}_t\left(t\right)-{\stackrel{.}{}}_i\left(t\right)=-{}_i{z}_i\left(t\right);$ [0091] defining a Lyapunov function V.sub.1(t), as follows:

[00056]$V_1\left(t\right)=\frac{1}{2}{z}^{T}z;$ [0092] wherein z=[z.sub.1,z.sub.2, . . . ,z.sub.n].sup.T; T is the transpose; [0093] deriving the lyapunov function V.sub.1(t) to obtain:

[00057]${\stackrel{.}{V}}_1\left(t\right)=\frac{1}{2}{z}^T\stackrel{.}{z}=-0;$ [0094] wherein =diag{.sub.i}.Math..sup.NN.

[00058]$=\mathrm{diag}\left\{z_i^2\right\}.Math.{}^{NN};$ .sub.i is a control gain;

[00059]$z_i^2$ is a parameter form for the convenience of writing; [0095] when .sub.i>0, {dot over (V)}.sub.1(t)<0, and the frequency .sub.i(t) approaches the frequency estimate {circumflex over ()}.sub.i(t).

[0096] Step 3.2: Proving that the frequency estimate {circumflex over ()}.sub.i(t) approaches a frequency reference

[00060]${}_i^{\mathrm{ref}}.$

[0097] The proving that the frequency estimate {circumflex over ()}.sub.i(t) approaches a frequency reference

[00061]${}_i^{\mathrm{ref}}$

is specifically as follows: [0098] defining .sub.i(t), .sub.i(t), and .sub.i(t), as follows:

[00062]${\tilde{n}}_i\left(t\right)=-{}_i{z}_i\left(t\right);$${}_i\left(t\right)={}_i\left(t\right)-{}_i^{\mathrm{ref}};$${}_i\left(t\right)=-\underset{j{N}_i}{.Math.}{a}_{\mathrm{ij}}\left({}_i\left(t\right)-{}_j\left(t\right)\right)-g_{i0}\left({}_i\left(t\right)-{}_i^{\mathrm{ref}}\right);$ [0099] expressing the linearized microgrid distributed secondary control strategy based on the virtual synchronous machine in a matrix form, as follows:

[00063]$={}_{}+{}_{}\tilde{n};$ [0100] wherein is in matrix form; =(L+B); L+B is a matrix form of the connection status; is in matrix form; [0101] defining a Lyapunov function V.sub.2(t), as follows:

[00064]$V_2\left(t\right)=\frac{1}{2}{}^T\left(L+B\right);$ [0102] wherein =[.sub.1,.sub.2, . . . ,.sub.N].sup.T; [0103] deriving the lyapunov function V.sub.2(t) to obtain:

[00065]${\stackrel{.}{V}}_2\left(t\right)={}^T\left(L+B\right);$ [0104] based on = and (L+B).sup.T=(L+B), obtaining:

[00066]${\stackrel{.}{V}}_2\left(t\right)=-{}_{}{}^T-{}_{}{}^T\tilde{n};$ [0105] scaling {dot over (V)}.sub.2(t), and obtaining:

[00067]${\stackrel{.}{V}}_2\left(t\right)-\frac{{}_{}}{2}\underset{i=1}{\overset{N}{.Math.}}\left({}_i^2\left(t\right)-{\tilde{n}}_i^2\left(t\right)\right);$ [0106] since a convergence parameter .sub.i satisfies

[00068]${}_i^2\left(t\right)<{}_i{\tilde{n}}_i^2\left(t\right)$ and .sub.i>1, obtaining:

[00069]${\stackrel{.}{V}}_2\left(t\right)-\frac{{}_{}}{2}\underset{i=1}{\overset{N}{.Math.}}\left({}_i-1\right){\tilde{n}}_i^2\left(t\right)0;$ [0107] wherein {dot over (V)}.sub.2(t) is strictly negative semi-definite, and the frequency estimate {circumflex over ()}.sub.i(t) approaches the frequency reference

[00070]${}_i^{ref}.$

Embodiment 2

[0108] Embodiment 2 of the present invention discloses a specific application of the microgrid distributed secondary control method based on the virtual synchronous machine, as follows:

[0109] An island microgrid system is shown in FIG. 2, and the system parameters are shown in Table 1.

TABLE-US-00001 TABLE 1 Parameters of island microgrid system Virtual DG1&2 (10.64 kW) DG3&4 (8.0 kW) synchronous D J D J machine 9.85 0.1692 7.4 0.225 R.sub.c L.sub.c R.sub.c L.sub.c 0.2 3 10.sup.3 0.2 3 10.sup.3 Line Line 1 Line 2 Line 3 R.sub.Line1 L.sub.Line1 R.sub.Line2 L.sub.Line2 R.sub.Line3 L.sub.Line3 0.23 0.318 10.sup.3 0.35 1.847 10.sup.3 0.23 0.318 10.sup.3 Load Load 1 Load 2 P.sub.Load1 Q.sub.Load1 P.sub.load2 Q.sub.Load2 10 10.sup.3 15 10.sup.3 15.6 10.sup.3 7.6 10.sup.3

[0110] To verify the effectiveness of the proposed microgrid distributed secondary control strategy based on the virtual synchronous machine, the simulation process is designed as follows: [0111] 1) t=0 s, the microgrid enters the island operation mode; [0112] 2) t=1.5 s, using the proposed microgrid distributed secondary control strategy based on the virtual synchronous machine; [0113] 3) t=4 s, load 1 increases by 3 kW; [0114] 4) t=6 s, load 1 reduces by 3 kW.

[0115] The total simulation time is 8 s.

[0116] The schematic diagrams of the frequency and active power of each virtual synchronous machine under the microgrid distributed secondary control strategy based on the virtual synchronous machines proposed in the present invention are shown in FIG. 3 and FIG. 4, respectively. It may be seen that, during the period of 0-1.5 s, the output frequency of each virtual synchronous machine is lower than 50 Hz; when t=1.5 s, the microgrid distributed secondary control strategy based on the virtual synchronous machine proposed in the present invention is used, and the frequency of each virtual synchronous machine is accurately restored to 50 Hz, and active power distribution is achieved. This performance verifies the effectiveness of the microgrid distributed secondary control strategy based on the virtual synchronous machines proposed in the present invention.

Embodiment 3

[0117] Embodiment 3 of the present invention discloses a microgrid distributed secondary control system based on a virtual synchronous machine using the microgrid distributed secondary control method based on the virtual synchronous machine, which includes: [0118] an establishment module for a microgrid distributed secondary control model based on a virtual synchronous machine, configured to, design a microgrid primary control strategy based on the virtual synchronous machine, and establish a microgrid distributed secondary control model based on the virtual synchronous machine by combining a speed regulator equation of the virtual synchronous machine; [0119] a designing module for a linearized microgrid distributed secondary control strategy based on a virtual synchronous machine, configured to, consider nonlinear characteristics of the virtual synchronous machine, and based on a deterministic equivalence principle, design a linearized microgrid distributed secondary control strategy based on the virtual synchronous machine; and [0120] a frequency recovery accuracy proof module, configured to, based on the deterministic equivalence principle and a Lyapunov theory, prove accuracy of frequency recovery of the linearized microgrid distributed secondary control strategy based on the virtual synchronous machine.

[0121] The embodiments of the present invention discloses a microgrid distributed secondary control method and system based on a virtual synchronous machine. Based on the construction of a virtual synchronous machine model, the present invention designs a distributed secondary control strategy based on the virtual synchronous machine to provide inertia support for microgrid operation and reduce the frequency change rate and response time under load switching. The present invention designs a distributed control strategy based on the conventional centralized communication strategy, which significantly reduces communication and computing resources. In summary, compared with the conventional centralized secondary control strategy, the present invention provides inertia support, significantly reduces communication and computing resources, and helps the microgrid to operate safely and stably.

[0122] Embodiments in this specification are all described in a progressive manner, for same or similar parts in embodiments, reference may be made to these embodiments, and each embodiment focuses on a difference from other embodiments. The apparatus disclosed in embodiments corresponds to the apparatus disclosed in embodiments, and therefore is briefly described. For related parts, refer to the descriptions of the apparatus.

[0123] The foregoing descriptions of the disclosed embodiments enables a person skilled in the art to implement or use the present invention. The various modifications to the embodiments are clear to a person skilled in the art, and the general principles defined herein may be implemented in another embodiment without departing from the spirit or scope of the present invention. Therefore, the present invention is not limited to the embodiments shown herein, but the present invention needs to conform to the widest range consistent with the principles and novel features disclosed herein.