Method for designing distributed communication topology of micro-grid based on network mirroring and global propagation rates

Abstract

A method for designing a distributed communication topology of a micro-grid based on network mirroring and global propagation rates includes the following steps: first, determining the communication connectivity of distributed directed networks in the micro-grid; next, obtaining, for connected directed communication networks, mirror networks thereof based on a mirroring operation, and selecting an optimal distributed directed communication topology corresponding to a maximum performance indicator based on algebraic connectivity and communication costs; solving, for the optimized distributed communication topology, pinned distributed generation sets corresponding to different pinning numbers based on global propagation rates and out-degrees; and finally, establishing a distributed secondary voltage control of the micro-grid based on the optimal distributed communication network and pinned nodes of the micro-grid, to achieve accurate reactive power sharing and average voltage restoration.

Claims

1. A method for designing a distributed communication topology of a micro-grid based on a network mirroring and global propagation rates, used to implement information interaction in a droop operation mode of an islanded micro-grid, comprising the following steps: step A, determining a connectivity of all distributed directed communication networks in the micro-grid, selecting connected distributed directed communication networks as candidate communication networks, and then proceeding to step B; step B, obtaining mirror networks of the candidate communication networks based on a mirroring operation, obtaining an algebraic connectivity and a communication cost corresponding to each mirror network of the mirror networks, selecting an optimal distributed directed communication topology corresponding to a maximum performance indicator to obtain an optimal distributed directed communication network, and then proceeding to step C; step C, solving, for the optimal distributed directed communication topology obtained in step B, pinned distributed generation sets corresponding to different pinning numbers based on the global propagation rates and out-degrees, and then proceeding to step D; and step D, establishing a distributed secondary voltage control of the micro-grid based on the optimal distributed directed communication network and the pinned distributed generation sets of the micro-grid, to achieve accurate reactive power sharing and average voltage restoration; wherein in step C, for each candidate pinned set comprising (k+1) distributed generations, an objective function value is calculated based on a sum of the global propagation rates and an out-degree of the each candidate pinned set, and a candidate pinned set corresponding to a maximum objective function value is selected as an optimal pinned distributed generation set with a pinning number (k+1); for the each candidate pinned set, according to the following formula: $\begin{array}{cc}f\left(P_{k+1}\right)=\mathrm{deg}\left(P_{k+1}\right)+\underset{j\in I_{k+1}}{.Math.}\underset{\stackrel{.fwdarw.}{d}\left(P_{k+1}\right)}{.Math.}\frac{1}{l\left(P_{k+1},j\right)}& \mathrm{formula}\left(10\right)\end{array}$ the objective function value ƒ(P.sub.k+1) corresponding to the each candidate pinned set is calculated; wherein deg(P.sub.k+1) represents the out-degree of the each candidate pinned set, l(P.sub.k+1, j) represents a length of a communication path from the each candidate pinned set to an unpinned distributed generation j, and when there are multiple communication paths, a shorter path is preferred.

2. The method for designing the distributed communication topology of the micro-grid based on the network mirroring and global propagation rates according to claim 1, wherein in step A, the connected distributed directed communication networks are selected from the all distributed directed communication networks in the micro-grid according to steps A01 and A02 below as the candidate communication networks of the micro-grid: step A01, for the distributed communication topology, introducing a corresponding connectivity matrix as shown in the following formula:
RC=A+A.sup.2+ . . . +A.sup.n  formula (1) wherein RC represents the corresponding connectivity matrix of the distributed communication topology; □ represents an adjacency matrix of the distributed directed communication topology, and the □ is composed of connecting elements between distributed generations, □=[a.sub.ij]; + represents a Boolean sum of the adjacency matrix, and a.sub.ij represents a direct communication connectivity from a j-th distributed generation to an i-th distributed generation in the micro-grid; and step A02, obtaining RC=[r.sub.ij] based on formula (1), wherein r.sub.ij represents a communication connectivity from the j-th distributed generation to the i-th distributed generation in the micro-grid, r.sub.ij=1 indicates that the communication connectivity presents from the j-th distributed generation to the i-th distributed generation in the micro-grid, and r.sub.ij=0 indicates that the communication connectivity does not present from the j-th distributed generation to the i-th distributed generation in the micro-grid; if all non-diagonal elements r.sub.ij in RC are equal to 1, the distributed directed communication network is a connected network; and if some non-diagonal elements r.sub.ij in RC are equal to 0, the distributed directed communication network is an unconnected network.

3. The method for designing the distributed communication topology of the micro-grid based on the network mirroring and global propagation rates according to claim 1, wherein in step B, an undirected mirror counterpart of each candidate communication network is obtained based on the mirroring operation according to steps B01 and B02 below: step B01, based on a graph theory, using a directed graph G=(□, E, □) to represent a topology of the each candidate communication network, wherein □ is a set of distributed generation nodes, E represents a set of communication links in the distributed directed communication network, and □ □ represents a direct connectivity in the distributed directed communication network; and step B02, for the each candidate communication network represented by the directed graph, according to the following formula: $\begin{array}{cc}\{\begin{array}{c}\hat{E}=\mathrm{EU}\\ \hat{A}=\left[{\hat{a}}_{\mathrm{ij}}\right],{\hat{a}}_{\mathrm{ij}}={\hat{a}}_{\mathrm{ji}}=\left(a_{\mathrm{ij}}+a_{\mathrm{ji}}\right)/2\\ \hat{G}=M\left(G\right)=\left(V,\hat{E},\hat{A}\right)\end{array}& \mathrm{formula}\left(2\right)\end{array}$ obtaining the undirected mirror counterpart Ĝ corresponding to the each candidate communication network; wherein {hacek over (E)} is a set of communication links obtained by reversing all information transfer directions in a directed communication topology.

4. The method for designing the distributed communication topology of the micro-grid based on the network mirroring and the global propagation rates according to claim 1, wherein in step B, for the each mirror network, according to the following formula: $\begin{array}{cc}{\lambda }_2\left(L\left(\hat{G}\right)\right)=\underset{\underset{1^{T}x=0}{x\ne 0}}{\min }\frac{x^{T}L\left(\hat{G}\right)x}{{.Math.x.Math.}^2}& \mathrm{formula}\left(3\right)\end{array}$ the algebraic connectivity λ.sub.2(L(Ĝ)) corresponding to the each mirror network is obtained; wherein x represents a state variable of each distributed generation, and L(Ĝ) is a Laplacian matrix of the undirected mirror graph Ĝ, and the L(Ĝ) is obtained according to the following formula:
L(Ĝ)=½(L+L.sup.T)=Δ−½(A+A.sup.T)={circumflex over (Δ)}−Â  formula (4) wherein L is a Laplacian matrix of the directed graph G, Δ is a diagonal matrix, and a diagonal element Δ.sub.ii of the Δ represents an out-degree of the distributed generation i in a directed communication topology; in the meantime, for the each mirror network, according to the following formula:
Length=Σ.sub.i,j=1.sup.n sgn(â.sub.ij)  formula (5) the communication cost corresponding to the each mirror network is obtained.

5. The method for designing the distributed communication topology of the micro-grid based on the network mirroring and the global propagation rates according to claim 1, wherein in step B, for each candidate topology meetings a specified convergence performance requirement, a performance indicator is calculated based on a weighted sum of the algebraic connectivity and the communication cost, and a candidate directed distributed communication topology corresponding to the maximum performance indicator is selected as the optimal distributed directed communication topology of the micro-grid; aiming at the each candidate topology meeting the specified convergence performance requirement, for each candidate directed distributed topology, according to the following formula:
J(L)=γ.sub.1λ.sub.2(L(Ĝ))+γ.sub.2Length  formula (6) the performance indicator J(L) corresponding to the each candidate topology is obtained, and the candidate directed distributed topology corresponding to the maximum performance indicator is selected as the optimal distributed directed communication topology of the micro-grid, wherein λ.sub.2(L(Ĝ)) represents the algebraic connectivity corresponding to the each candidate topology, and Length represents the communication cost corresponding to the each candidate topology.

6. The method for designing the distributed communication topology of the micro-grid based on the network mirroring and the global propagation rates according to claim 1, wherein in step C, for a pinned set comprising k distributed generations and one distributed generation in an unpinned set, according to the following formula: $\begin{array}{cc}\{\begin{array}{c}{P}_{k+1}=P_k.Math.\left\{i\right\}\\ I_{k+1}=I_k\square \left\{i\right\}\end{array}& \mathrm{formula}\left(7\right)\end{array}$ a candidate pinned set comprising (k+1) distributed generations and a corresponding unpinned set are obtained; wherein □.sub.k represents the pinned set comprising k distributed generations, □.sub.k represents the unpinned set corresponding to the pinned set □.sub.k comprising k distributed generations, and i represents one distributed generation in the unpinned set.

7. The method for designing the distributed communication topology of the micro-grid based on the network mirroring and the global propagation rates according to claim 1, wherein in step C, for a candidate pinned set comprising (k+1) distributed generations, according to the following formula: $\begin{array}{cc}\underset{i\in P_{k+1}}{.Math.}\underset{j\in I_{k+1}}{.Math.}\frac{1}{l\left(i,j\right)}{|}_{\stackrel{.fwdarw.}{d}\left(i\right)}& \mathrm{formula}\left(8\right)\end{array}$ the global propagation rate corresponding to each candidate pinned set is obtained; where l(i, j)|.sub.{right arrow over (d)}(i) represents a length of a shortest communication path from a distributed generation i to a distributed generation j; in the meantime, for the candidate pinned set comprising (k+1) distributed generations, according to the following formula: $\begin{array}{cc}\mathrm{deg}\left(P_{k+1}\right)=\underset{j\in P_{k+1}}{.Math.}\underset{i\in I_{k+1}}{.Math.}{a}_{\mathrm{ij}}& \mathrm{formula}\left(9\right)\end{array}$ the out-degree corresponding to the each candidate pinned set is obtained.

8. The method for designing the distributed communication topology of the micro-grid based on the network mirroring and the global propagation rates according to claim 1, wherein in step C, a pinned distributed generation set □.sub.0 is initialized to an empty set, a corresponding unpinned distributed generation set □.sub.0 is a set of all distributed generations in the communication network, the above operations are cycled with a number of the distributed generations in the pinned set increased each time, and the pinned distributed generation sets corresponding to the different pinning numbers are solved.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 is the flowchart of the method for designing the distributed communication topology of the micro-grid based on network mirroring and global propagation rates according to the present invention;

(2) FIG. 2 is the micro-grid simulation system used in an embodiment of the present invention;

(3) FIG. 3A is the diagram of a G.sub.1 type distributed communication topology used in the micro-grid according to an embodiment of the present invention;

(4) FIG. 3B is the diagram of a G.sub.2 type distributed communication topology used in the micro-grid according to an embodiment of the present invention;

(5) FIG. 3C is the diagram of a G.sub.3 type distributed communication topology used in the micro-grid according to an embodiment of the present invention;

(6) FIG. 3D is the diagram of a G.sub.4 type distributed communication topology used in the micro-grid according to an embodiment of the present invention;

(7) FIG. 3E is the diagram of a G.sub.5 type distributed communication topology used in the micro-grid according to an embodiment of the present invention;

(8) FIG. 3F is the diagram of a G.sub.6 type distributed communication topology used in the micro-grid according to an embodiment of the present invention;

(9) FIG. 3G is the diagram of a G.sub.7 type distributed communication topology used in the micro-grid according to an embodiment of the present invention;

(10) FIG. 3H is the diagram of a G.sub.8 type distributed communication topology used in the micro-grid according to an embodiment of the present invention;

(11) FIG. 4A is the control effect diagram of output reactive power of the micro-grid using the G.sub.1 type communication topology;

(12) FIG. 4B is the control effect diagram of output voltage of the micro-grid using the G.sub.1 type communication topology;

(13) FIG. 5A is the control effect diagram of output reactive power of the micro-grid using the G.sub.4 type communication topology;

(14) FIG. 5B is the control effect diagram of output voltage of the micro-grid using the G.sub.4 type communication topology;

(15) FIG. 6A is the control effect diagram of output reactive power of the micro-grid using the G.sub.7 type communication topology;

(16) FIG. 6B is the control effect diagram of output voltage of the micro-grid using the G.sub.7 type communication topology;

(17) FIG. 7A is the control effect diagram of output reactive power of the micro-grid appointing DG.sub.5 as the pinned node under the G.sub.7 type communication topology;

(18) FIG. 7B is the control effect diagram of output voltage of the micro-grid appointing DG.sub.5 as the pinned node under the G.sub.7 type communication topology;

(19) FIG. 8A is the control effect diagram of output reactive power of the micro-grid appointing DG.sub.2 as the pinned node under the G.sub.7 type communication topology; and

(20) FIG. 8B is the control effect diagram of output voltage of the micro-grid appointing DG.sub.2 as the pinned node under the G.sub.7 type communication topology.

DETAILED DESCRIPTION OF THE EMBODIMENTS

(21) The specific embodiments of the present invention will be further described in detail below in conjunction with the accompanying drawings.

(22) The present invention provides a method for designing the distributed communication topology of the micro-grid based on network mirroring and global propagation rates, which is used to implement information interaction in the droop operation mode of an islanded micro-grid. In practical applications, as shown in FIG. 1, the method specifically includes the following steps:

(23) Step A, the connectivity of all distributed directed communication networks in the micro-grid are determined, connected directed communication networks are selected as candidate communication networks, and then step B is proceeded.

(24) In step A above, the connected distributed directed communication networks are selected from all the distributed directed communication networks in the micro-grid according to steps A01 and A02 below as the candidate communication networks of the micro-grid:

(25) Step A01, for a distributed communication topology, the corresponding connectivity matrix as shown in the following formula is introduced:
RC=A+A.sup.2+ . . . +A″  formula(1)

(26) Where RC represents the connectivity matrix of the distributed communication topology; A represents an adjacency matrix of the distributed directed communication topology, and the A is composed of connecting elements between distributed generations, A=[a.sub.ij]; + represents the Boolean sum of the adjacency matrix, and a.sub.ij represents the direct communication connectivity from a j-th distributed generation to an i-th distributed generation in the micro-grid.

(27) Step A02, RC=[r.sub.ij] is obtained based on formula (1), where r.sub.ij represents a communication connectivity from the j-th distributed generation to the i-th distributed generation in the micro-grid, r.sub.ij=1 indicates that the communication connectivity presents from the j-th distributed generation to the i-th distributed generation in the micro-grid, and r.sub.ij=0 indicates that the communication connectivity does not present from the j-th distributed generation to the i-th distributed generation in the micro-grid; if all non-diagonal elements r.sub.ij in RC are equal to 1, the distributed directed communication network is a connected network; and if some non-diagonal elements r.sub.ij in RC are equal to 0, the distributed directed communication network is an unconnected network.

(28) Step B, mirror networks of the candidate communication networks are obtained based on a mirroring operation, an algebraic connectivity and a communication cost corresponding to each mirror network are obtained, an optimal distributed directed communication topology corresponding to a maximum performance indicator is selected to obtain an optimal distributed directed communication network, and then step C is proceeded.

(29) In step B above, an undirected mirror counterpart of each candidate directed communication network is obtained based on the mirroring operation according to steps B01 and B02 below:

(30) Step B01, based on the graph theory, a directed graph G=(ζ, E, A) is used to represent the topology of each candidate communication network, where ζ is a set of distributed generation nodes, E represents a set of communication links in the distributed directed communication network, and A represents a direct connectivity in the distributed directed communication network

(31) Step B02, for each candidate communication network represented by the directed graph, according to the following formula:

(32) $\begin{array}{cc}\{\begin{array}{c}\hat{E}=\mathrm{EU}\\ \hat{A}=\left[{\hat{a}}_{\mathrm{ij}}\right],{\hat{a}}_{\mathrm{ij}}={\hat{a}}_{\mathrm{ji}}=\left(a_{\mathrm{ij}}+a_{\mathrm{ji}}\right)/2\\ \hat{G}=M\left(G\right)=\left(V,\hat{E},\hat{A}\right)\end{array}& \mathrm{formula}\left(2\right)\end{array}$

(33) the undirected mirror counterpart Ĝ corresponding to each candidate communication network is obtained; where {hacek over (E)} is a set of communication links obtained by reversing all information transfer directions in the directed communication topology.

(34) For each mirror network, according to the following formula:

(35) $\begin{array}{cc}{\lambda }_2\left(L\left(\hat{G}\right)\right)=\underset{\underset{1^{T}x=0}{x\ne 0}}{\min }\frac{x^{T}L\left(\hat{G}\right)x}{{.Math.x.Math.}^2}& \mathrm{formula}\left(3\right)\end{array}$

(36) the algebraic connectivity λ.sub.2(L(Ĝ)) corresponding to each mirror network is obtained; where x represents a state variable of each distributed generation, and L(Ĝ) is a Laplacian matrix of the undirected mirror graph Ĝ, and the L(Ĝ) can be obtained according to the following formula:
L(Ĝ)=½(L+L.sup.T)=Δ−½(A+A.sup.T)={circumflex over (Δ)}−Â  formula (4)

(37) where L is a Laplacian matrix of the directed graph G, Δ is a diagonal matrix, and its diagonal element Δ.sub.ii represents an out-degree of the distributed generation i in the directed communication topology.

(38) For each mirror network, according to the following formula:
Length=Σ.sub.i,j=1.sup.n sgn(â.sub.ij)  formula (5)

(39) the communication cost corresponding to each mirror network is obtained.

(40) The higher the algebraic connectivity is, the better the network convergence performance will be, meanwhile, on the premise that the specified convergence indicator is met, the shorter the communication link is, the lower the communication cost will be. Therefore, based on the algebraic connectivity and communication cost introduced above, for each candidate topology that meets the specified convergence performance requirement, the following formula is used to calculate a performance indicator based on a weighted sum of the algebraic connectivity and the communication cost.
J(L)=γ.sub.1λ.sub.2(L(Ĝ))+γ.sub.2Length  formula (6)

(41) After the performance indicator J(L) corresponding to each candidate topology is obtained, the candidate directed distributed topology corresponding to the maximum performance indicator is selected as the optimal distributed directed communication topology of the micro-grid, and then step C is proceeded; where λ.sub.2 (L(Ĝ)) represents the algebraic connectivity corresponding to the candidate topology, and Length represents the communication cost corresponding to the candidate topology.

(42) Step C, for the optimal communication topology obtained in step B, pinned distributed generation sets corresponding to different pinning numbers are solved based on global propagation rates and out-degrees, and then step D is proceeded.

(43) In step C above, for a pinned set including k distributed generations and one distributed generation in the corresponding unpinned set, according to the following formula:

(44) $\begin{array}{cc}\{\begin{array}{c}{P}_{k+1}=P_k.Math.\left\{i\right\}\\ I_{k+1}=I_k\left\{i\right\}\end{array}& \mathrm{formula}\left(7\right)\end{array}$

(45) a candidate pinned set including (k+1) distributed generations and a corresponding unpinned set are obtained; where Π.sub.k represents the pinned set including k distributed generations, I.sub.k represents the unpinned set corresponding to the pinned set Π.sub.k which comprises k distributed generations, and i represents one distributed generation in the unpinned set.

(46) For each candidate pinned set including (k+1) distributed generations, according to the following formula:

(47) 0$\begin{array}{cc}\underset{i\in P_{k+1}}{.Math.}\underset{j\in I_{k+1}}{.Math.}\frac{1}{l\left(i,j\right)}{|}_{\stackrel{.fwdarw.}{d}\left(i\right)}& \mathrm{formula}\left(8\right)\end{array}$

(48) the global propagation rate corresponding to each candidate pinned set is obtained; where l(i, j)|.sub.{right arrow over (d)}(i) represents the length of the shortest communication path from the distributed generation i to the distributed generation j.

(49) For each candidate pinned set including (k+1) distributed generations, according to the following formula:

(50) $\begin{array}{cc}\mathrm{deg}\left(P_{k+1}\right)=\underset{j\in P_{k+1}}{.Math.}\underset{i\in I_{k+1}}{.Math.}{a}_{\mathrm{ij}}& \mathrm{formula}\left(9\right)\end{array}$

(51) the out-degree corresponding to each candidate pinned set is obtained.

(52) The larger the out-degree and global propagation rate of the pinned set is, the better the corresponding network convergence performance will be, so for each candidate pinned set including (k+1) distributed generations, an objective function value is calculated based on a sum of the global propagation rate and an out-degree of the pinned set according to the following formula.

(53) $\begin{array}{cc}f\left(P_{k+1}\right)=\mathrm{deg}\left(P_{k+1}\right)+\underset{j\in I_{k+1}}{.Math.}\underset{\stackrel{.fwdarw.}{d}\left(P_{k+1}\right)}{.Math.}\frac{1}{l\left(P_{k+1},j\right)}& \mathrm{formula}\left(10\right)\end{array}$

(54) After the objective function value ƒ(P.sub.k+1) corresponding to each candidate pinned set is obtained, the candidate pinned set corresponding to the maximum objective function value is selected as the optimal pinned distributed generation set with a pinning number (k+1). and then step D is proceeded; where deg(P.sub.k+1) represents the out-degree of the candidate pinned set, l(P.sub.k+1, j) represents the length of the communication path from the candidate pinned set to the unpinned distributed generation j, and when there are multiple communication paths, a shorter path is preferred.

(55) Step D, a distributed secondary voltage control of the micro-grid is established based on the optimal distributed directed communication network and pinned distributed generation set of the micro-grid, to achieve accurate reactive power sharing and average voltage restoration.

(56) Based on the optimal distributed directed communication network and pinned distributed generation set obtained in the above steps, the local controller of each distributed generation in the micro-grid adopts droop control, and a distributed secondary voltage control of the micro-grid is established based on the theory of pinning consensus, to achieve accurate reactive power sharing and average voltage restoration.

(57) The control process of the i-th pinned distributed generation is shown in formula (11):

(58) $\begin{array}{cc}\{\begin{array}{c}\Delta {\stackrel{.}{Q}}_{\mathrm{refi}}=\underset{j\in N_i}{.Math.}{w}_{\mathrm{ij}}\left(\Delta Q_{\mathrm{refj}}-\Delta Q_{\mathrm{refi}}\right)-d_i\left(\Delta Q_{\mathrm{refi}}-\Delta Q_c\right)\\ Q_{\mathrm{DGi}}^{\min }\le \left(\Delta Q_{\mathrm{refj}}+Q_{\mathrm{DGi}}\right)\le Q_{\mathrm{DGi}}^{\max }\end{array}& \left(11\right)\end{array}$

(59) In the formula, i=1, 2, . . . , n, j=1, 2, . . . , n; ΔQ.sub.ref,i represents a reactive power increment of the i-th distributed generation; ΔQ.sub.refj represents a reactive power increment of the j-th distributed generation; ΔQ.sub.c represents a preset consensus convergence equilibrium based on pinning voltage control; w.sub.ij represents a communication coupling weight between the i-th distributed generation and the j-th distributed generation; if the i-th distributed generation communicates with the j-th distributed generation, w.sub.ij≠0, otherwise, w.sub.ij=0. N.sub.i represents a set of neighbor nodes of node i; and d.sub.i represents a pinning control gain.

(60) The above designed technical solution is applied to practice, and the simulation system is shown in FIG. 2. The micro-grid consists of 5 distributed generations, DG.sub.1, DG.sub.2 and DG.sub.3 are connected to voltage bus 1 through their respective connection impedances, and a local load is connected to DG.sub.3; DG.sub.4 and DG.sub.5 are connected to voltage bus 2 through their respective connection impedances, and a local load is connected to DG4. The rated active and reactive power capacities of the 5 distributed generations are equal, and the impedance type loads are adopted in the system. Communication topologies are designed and selected according to the method for designing a distributed communication topology of a micro-grid in the embodiment of the present invention, and a simulation model of the micro-grid is built based on a MATLAB/Simulink platform to simulate the control effect under each communication topology so as to verify the effectiveness of the method proposed in the present invention.

(61) FIGS. 3A to 3H show diagrams of 8 distributed communication topologies that satisfy topology connectivity in this embodiment. FIG. 3A is the diagram of a G.sub.1 type communication topology used in the embodiment of the present invention; FIG. 3B is the diagram of a G.sub.2 type communication topology used in the embodiment of the present invention; FIG. 3C is the diagram of a G.sub.3 type communication topology used in the embodiment of the present invention; FIG. 3D is the diagram of a G.sub.4 type communication topology used in the embodiment of the present invention; FIG. 3E is the diagram of a G.sub.5 type communication topology used in the embodiment of the present invention; FIG. 3F is the diagram of a G.sub.6 type communication topology used in the embodiment of the present invention; FIG. 3G is the diagram of a G.sub.7 type communication topology used in the embodiment of the present invention; and FIG. 3H is the diagram of a G.sub.8 type communication topology used in the embodiment of the present invention. According to the distributed communication topology optimization performance indicators proposed in the present invention, the algebraic connectivity and the number of links of the 8 topologies are shown in Table 1 below. G.sub.1, G.sub.3, and G.sub.7 are selected as example topologies for simulation. It can be seen that the distributed communication topology G.sub.7 corresponds to the optimal dynamic convergence, followed by G.sub.3, and G.sub.1 corresponds to the poor dynamic convergence.

(62) TABLE-US-00001 TABLE 1 Pattern Connectivity Number of links G.sub.1 0.7753 8 G.sub.2 0.8820 8 G.sub.3 1 9 G.sub.4 1.1044 9 G.sub.5 1.09 10 G.sub.6 1.5 10 G.sub.7 1.2192 11 G.sub.8 1.6044 11

(63) FIGS. 4A and 4B show the simulation results of the micro-grid in this embodiment using the G.sub.1 communication topology. Each distributed generation operates in a droop control mode at the beginning, secondary voltage control is activated at 0.3 second, and the load increases at 2.5 seconds. The simulation results are shown in FIGS. 4A and 4B. FIG. 4A is the curve of reactive power output by each distributed generation in the micro-grid, the abscissa represents time in units of seconds, and the ordinate represents reactive power in units of var. As shown in FIG. 4A, the reactive power sharing between distributed generations is not ideal initially under the effect of droop control, however, after 0.3 second, the reactive power tends to be gradually equally allocated under the effect of secondary control, and the system is stable at about 2.5 seconds. Then, the load of the system increases at 2.5 seconds and the reactive power output by each distributed generation increases, whereas the system is stable at about 5 seconds and achieves power equipartition again. FIG. 4B is the curve of voltage output by each distributed generation in the micro-grid, the abscissa represents time in units of seconds, and the ordinate represents output voltage in units of volts. It can be seen from FIG. 4B that the output voltages of the distributed generations deviate from the rated value initially under the effect of droop control, correspondingly, the average output voltage is lower than the rated value, whereas the output voltage increases after 0.3 second under the effect of secondary control so that the average output voltage of the micro-grid reaches the rated value, the system is stable at about 2.5 seconds. Then, the output voltages of the distributed generations decrease due to the increase of system load at 2.5 seconds, and the system is stable again at about 5 seconds, with the average output voltage increasing to the rated value.

(64) FIGS. 5A and 5B show the simulation results of the micro-grid in this embodiment using the G.sub.2 communication topology. Each distributed generation operates in a droop control mode at the beginning, and secondary voltage control is activated at 0.3 second. The simulation results are shown in FIGS. 5A and 5B. FIG. 5A is the curve of reactive power output by each distributed generation in the micro-grid, the abscissa represents time in units of seconds, and the ordinate represents reactive power in units of var. As shown in FIG. 5A, the reactive power sharing between distributed generations is not ideal initially under the effect of droop control, however, after 0.3 second, the reactive power tends to be gradually equally allocated under the effect of secondary control, and the system is stable at about 1.7 seconds. Then, the load of the system increases at 2.5 seconds and the reactive power output by each distributed generation increases, whereas the system is stable at about 3.8 seconds and achieves power equipartition again. FIG. 5B is the curve of voltage output by each distributed generation in the micro-grid, the abscissa represents time in units of seconds, and the ordinate represents output voltage in units of volts. It can be seen from FIG. 5B that the output voltages of the distributed generations deviate from the rated value initially under the effect of droop control, correspondingly, the average output voltage is lower than the rated value, whereas the output voltage increases after 0.3 second under the effect of secondary control so that the average output voltage of the micro-grid reaches the rated value, the system is stable at about 1.7 seconds. Then, the output voltages of the distributed generations decrease due to the increase of system load at 2.5 seconds, and the system is stable again at about 3.8 seconds, with the average output voltage increasing to the rated value.

(65) FIGS. 6A and 6B show the simulation results of the micro-grid in this embodiment using a distributed all-pass communication topology. Each distributed generation operates in a droop control mode at the beginning, and secondary voltage control is activated at 0.3 second. The simulation results are shown in FIGS. 6A and 6B. FIG. 6A is the curve of reactive power output by each distributed generation in the micro-grid, the abscissa represents time in units of seconds, and the ordinate represents reactive power in units of var. As shown in FIG. 6A, the reactive power sharing of the distributed generations is not ideal initially under the effect of droop control, however, after 0.3 second, the reactive power tends to be gradually equally allocated under the effect of secondary control, and the system is stable at about 0.8 second. Then, the load of the system increases at 2.5 seconds and the reactive power output by each distributed generation increases, whereas the system is stable at about 3 seconds and achieves power equipartition again. FIG. 6B is the curve of voltage output by each distributed generation in the micro-grid, the abscissa represents time in units of seconds, and the ordinate represents output voltage in units of volts. It can be seen from FIG. 6B that the output voltages of the distributed generations deviate from the rated value initially under the effect of droop control, correspondingly, the average output voltage is lower than the rated value, whereas the output voltage increases after 0.3 second under the effect of secondary control so that the average output voltage of the micro-grid reaches the rated value, the system is stable at about 0.8 second. Then, the output voltages of the distributed generations decrease due to the increase of system load at 2.5 seconds, and the system is stable again at about 3 seconds, with the average output voltage increasing to the rated value.

(66) From FIGS. 4A, 4B, 5A, 5B, 6A and 6B, it can be seen that the G.sub.7 type communication topology can achieve the optimal convergence performance, followed by the G.sub.3 type topology, and the G.sub.1 type topology is the worst, which is consistent with the analysis results of the method for designing the distributed communication topology of the micro-grid based on network mirroring proposed in the present invention.

(67) As for the selection of pinning nodes, the value of objective function corresponding to each single pinning node is calculated as f(DG.sub.2)=9.75>f(DG.sub.5)=9.5>f(DG.sub.1)=6.67>f(DG.sub.4)=6.37>f(DG.sub.3)=3.5. It indicates that the pinned node DG.sub.2 corresponds to the optimal dynamic convergence, followed by the pinned nodes DG.sub.5, DG.sub.1, and DG.sub.4, and the pinned node DG.sub.3 corresponds to a poor dynamic convergence.

(68) FIGS. 7A and 7B show the simulation results of the micro-grid in this embodiment appointing the DG.sub.3 as the pinned node under the G.sub.7 type distributed communication topology. Each distributed generation operates in the droop control mode at the beginning, secondary voltage control is activated at 0.3 second, and the load increases at 2.5 seconds. The simulation results are shown in FIGS. 7A and 7B. FIG. 7A is the curve of reactive power output by each distributed generation in the micro-grid, the abscissa represents time in units of seconds, and the ordinate represents reactive power in units of var. As shown in FIG. 7A, the reactive power sharing of the distributed generations is not ideal initially under the effect of droop control, however, after 0.3 second, the reactive power tends to be gradually equally allocated under the effect of secondary control, and the system is stable at about 2.5 seconds. Then, the load of the system increases at 2.5 seconds and the reactive power output by each distributed generation increases, whereas the system is stable at about 5 seconds and achieves power equipartition again. FIG. 7B is the curve of voltage output by each distributed generation in the micro-grid, the abscissa represents time in units of seconds, and the ordinate represents output voltage in units of volts. It can be seen from FIG. 7B that the output voltages of the distributed generations deviate from a rated value initially under the effect of droop control, correspondingly, the average output voltage is lower than the rated value, whereas the output voltage increases after 0.3 second under the effect of secondary control so that the average output voltage of the micro-grid reaches the rated value, the system is stable at about 2.5 seconds. Then, the output voltages of the distributed generations decrease due to the increase of system load at 2.5 seconds, and the system is stable again at about 5 seconds, with the average output voltage increasing to the rated value.

(69) FIGS. 8A and 8B show the simulation results of the micro-grid in this embodiment appointing DG.sub.2 as the pinned node under the G.sub.7 type distributed communication topology. Each distributed generation operates in a droop control mode at the beginning, secondary voltage control is activated at 0.3 second, and the load increases at 2.5 seconds. The simulation results are shown in FIGS. 8A and 8B. FIG. 8A is the curve of reactive power output by each distributed generation in the micro-grid, the abscissa represents time in units of seconds, and the ordinate represents reactive power in units of var. As shown in FIG. 8A, the reactive power sharing of the distributed generations is not ideal initially under the effect of droop control, however, after 0.3 second, the reactive power tends to be gradually equally allocated under the effect of secondary control, and the system is stable at about 2 seconds. Then, the load of the system increases at 2.5 seconds and the reactive power output by each distributed generation increases, whereas the system is stable at about 4 seconds and achieves power equipartition again. FIG. 8B is the curve of voltage output by each distributed generation in the micro-grid, the abscissa represents time in units of seconds, and the ordinate represents output voltage in units of volts. It can be seen from FIG. 8B that the output voltages of the distributed generations deviate from the rated value initially under the effect of droop control, correspondingly, the average output voltage is lower than the rated value, whereas the output voltage increases after 0.3 second under the effect of secondary control so that the average output voltage of the micro-grid reaches the rated value, the system is stable at about 2 seconds. Then, the output voltages of the distributed generations decrease due to the increase of system load at 2.5 seconds, and the system is stable again at about 4 seconds, with the average output voltage increasing to the rated value.

(70) According to the method for designing the distributed communication topology of the micro-grid based on network mirroring and global propagation rates proposed by the present invention, the algebraic connectivity of directed distributed communication topologies is associated with the connectivity in graph theory, thereby an optimization indicator considering the dynamic convergence performance of secondary control under the limitation of certain communication cost is established to provide guidance for the design of directed distributed communication topologies; further, on account of that the convergence performance of the pinned node is associated with the global propagation rate, an optimization design indicator considering the out-degree of the pinned node and the global propagation rate is established to provide guidance for the design of pinned nodes. In view of the research gap that the existing distributed secondary control technologies have not investigated the design of directed communication topologies and pinned nodes, the present invention proposes a distributed communication topology design method. As an important part of the secondary control strategy, the method optimizes the control effects of reactive power sharing and average voltage restoration of distributed generations, which in turn improves the dynamic operation performance of the micro-grid effectively.

(71) The embodiments of the present invention are described in detail above with reference to the accompanying drawings, however, the present invention is not limited to the above-mentioned embodiments. Various changes can be made without departing from the purpose of the present invention within the scope of knowledge possessed by those ordinary technicians in this field.