MICROGRID DELAY MARGIN CALCULATION METHOD BASED ON CRITICAL CHARACTERISTIC ROOT TRACKING

Abstract

A microgrid delay margin calculation method based on critical characteristic root tracking includes: establishing a microgrid closed-loop small-signal model with voltage feedback control amount including communication delay based on a static output feedback, so as to obtain a characteristic equation with a transcendental term, performing critical characteristic root locus tracking for the transcendental term of the system characteristic equation, searching for a possible pure virtual characteristic root, and further calculating the maximum delay time in a stable microgrid. The method studies the relationship between the controller parameters and delay margins, thereby guiding the design of the control parameters, effectively improving the stability and dynamic performance of the microgrid.

Claims

1. A microgrid delay margin calculation method based on a critical characteristic root tracking, comprising: establishing an inverter closed-loop small-signal model and a distributed generation closed-loop small-signal model of a voltage feedback control amount comprising a communication delay according to a static feedback output, establishing a microgrid small-signal model consisting of a connection network, a dynamic equation of a load impedance and the distributed generation closed-loop small-signal model, obtaining a characteristic equation with a transcendental term from the microgrid small-signal model, performing the critical characteristic root tracking on the transcendental term, and then determining a delay margin meeting a requirement of a system stability.

2. The microgrid delay margin calculation method based on the critical characteristic root tracking according to claim 1, wherein, the inverter closed-loop small-signal model of the voltage feedback control amount comprising the communication delay established according to the static feedback output is: $\{\begin{array}{c}.Math..Math.{\stackrel{.}{x}}_{\mathrm{inv}}=A_{\mathrm{inv}}.Math..Math..Math.x_{\mathrm{inv}}+B_{\mathrm{inv}}.Math..Math..Math.V_{\mathrm{bDQ}}+B_u.Math..Math..Math.u.Math.\\ .Math..Math.y_{\mathrm{invQ}}=C_{\mathrm{invQ}}.Math..Math..Math.x_{\mathrm{inv}},.Math..Math.y_{\mathrm{invV}}=C_{\mathrm{invV}}.Math..Math..Math.x_{\mathrm{inv}}\end{array},$ x.sub.inv and {dot over (x)}.sub.inv respectively represent a closed-loop small-signal state variable and a change rate of an inverter, x.sub.inv=[x.sub.inv1, x.sub.inv2, . . . , x.sub.invi, . . . , x.sub.invn, .sub.1, .sub.2, . . . , .sub.i, . . . , .sub.n, ].sup.T, x.sub.inv1, x.sub.inv2, x.sub.invi and x.sub.invn respectively represent a closed-loop small-signal state variable of a first distributed generation, a closed-loop small-signal state variable of a second distributed generation, a closed-loop small-signal state variable of an i.sup.th distributed generation and a closed-loop small-signal state variable of an n.sup.th A distributed generation, .sub.1, .sub.2, .sub.i and .sub.n respectively represent a reactive power ancillary small-signal state variable of the first distributed generation, a reactive power ancillary small-signal state variable of the second distributed generation, a reactive power ancillary small-signal state variable of the i.sup.th distributed generation and a reactive power ancillary small-signal state variable of the n.sup.th distributed generation, the reactive power ancillary small-signal state variable .sub.i of the i.sup.th distributed generation is determined by an expression: ${\stackrel{.}{}}_i=\frac{1.Math.\text{/}.Math.n_{\mathrm{Qi}}}{\underset{i=1}{\overset{n}{.Math.}}.Math..Math.1.Math.\text{/}.Math.n_{\mathrm{Qi}}}.Math.\underset{i=1}{\overset{n}{.Math.}}.Math..Math.Q_i-Q_i,$ {dot over ()}.sub.i represents a change rate of the reactive power ancillary small-signal state variable of the i.sup.th distributed generation, Q.sub.i represents a reactive power actually outputted by the i.sup.th distributed generation, n.sub.Qi represents a voltage droop characteristic coefficient of the i.sup.th distributed generation, n represents a number of the distributed generations, represents a voltage ancillary small-signal state variable of the distributed generation, the voltage ancillary small-signal state variable of the distributed generation is determined by an expression: $\stackrel{.}{}=V_i^{*}-\frac{1}{n}.Math.\underset{i=1}{\overset{n}{.Math.}}.Math..Math.V_{\mathrm{odi}},$ {dot over ()} represents a change rate of the voltage ancillary small-signal state variable of the distributed generation, V*.sub.i represents an expected value of an average voltage of the i.sup.th distributed generation, V.sub.odi represents a d-axis component of an output voltage of the i.sup.th distributed generation in a reference coordinate system dq, A.sub.inv represents a state matrix of the distributed generation, V.sub.bDQ represents the small-signal state variable of a bus voltage in a common reference coordinate system DQ, V.sub.bDQ=[V.sub.bDQ1, V.sub.bDQ2, . . . , V.sub.bDQi, . . . , V.sub.bDQm].sup.T, V.sub.bDQ1, V.sub.bDQ2, V.sub.bDQ1 and V.sub.bDQm respectively represent a small-signal state variable of a voltage of a first bus, a small-signal state variable of a voltage of a second bus, a small-signal state variable of a voltage of an l.sup.th bus and a small-signal state of a voltage of an m.sup.th bus in the common reference coordinate system DQ, m represents a number of the buses, B.sub.inv represents an input matrix of the distributed generation to the bus voltage, u represents a secondary voltage small-signal control amount of the distributed generation, u=[u.sub.1, u.sub.2, . . . , u.sub.i, . . . , u.sub.n].sup.T, u.sub.1, u.sub.2, u.sub.i and u.sub.n respectively represent the secondary voltage small-signal control amount of the first distributed generation, the secondary voltage small-signal control amount of the second distributed generation, the secondary voltage small-signal control amount of the i.sup.th distributed generation and the secondary voltage small-signal control amount of the n.sup.th distributed generation, B.sub.u represents an input matrix of the distributed generation to the secondary voltage small-signal control amount, u.sub.i=K.sub.Qiy.sub.invQi(t.sub.i)+K.sub.Viy.sub.invV(t.sub.i), t represents a current time, .sub.i represents a communication delay between a local controller of the i.sup.th distributed generation and a centralized secondary voltage controller of a microgrid, K.sub.Qi and K.sub.Vi respectively represent a reactive power control coefficient of the i.sup.th distributed generation and a voltage control coefficient of the i.sup.th distributed generation, y.sub.invQi represents a reactive power output small-signal state variable of the i.sup.th distributed generation, y.sub.invQ and y.sub.invV respectively represent a reactive power output small-signal state variable of the distributed generation and a voltage output small-signal state variable of the distributed generation, and C.sub.invQ and C.sub.invV respectively represent a reactive power output matrix of the distributed generation and a voltage output matrix of the distributed generation.

3. The microgrid delay margin calculation method based on the critical characteristic root tracking according to claim 2, wherein, the distributed generation closed-loop small-signal model of the voltage feedback control amount comprising the communication delay established according to the static feedback output is: $\{\begin{array}{c}.Math..Math.{\stackrel{.}{x}}_{\mathrm{inv}}=A_{\mathrm{inv}}.Math..Math..Math.x_{\mathrm{inv}}+\underset{i=1}{\overset{n}{.Math.}}.Math..Math.{\stackrel{\_}{A}}_{\mathrm{di}}.Math..Math..Math.x_{\mathrm{inv}}\left(t-{}_i\right)+B_{\mathrm{inv}}.Math..Math..Math.V_{\mathrm{bDQ}}\\ .Math..Math.i_{\mathrm{oDQ}}=C_{\mathrm{invc}}.Math..Math..Math.x_{\mathrm{inv}}.Math.\end{array},$ .sub.di represents a delay state matrix of the i.sup.th distributed generation, .sub.di=[0 . . . B.sub.uiK.sub.QiC.sub.invQi+B.sub.uiK.sub.ViC.sub.invV . . . 0], B.sub.ui represents an input matrix of the i.sup.th distributed generation to the secondary voltage small-signal control amount, C.sub.invQi represents a reactive power output matrix of the i.sup.th distributed generation, i.sub.oDQ represents a small-signal state variable of an output current of the distributed generation in the common reference coordinate system DQ, and C.sub.invQ represents a current output matrix of the distributed generation.

4. The microgrid delay margin calculation method based on the critical characteristic root tracking according to claim 3, wherein, the microgrid small-signal model is $\stackrel{.}{x}=\mathrm{Ax}+\underset{i=1}{\overset{n}{.Math.}}.Math..Math.A_{\mathrm{di}}.Math.x\left(t-{}_i\right),$ x and {dot over (x)} respectively represent a microgrid small-signal state variable and a change rate of the microgrid small-signal state variable, x=[x.sub.inv i.sub.lineDQ .sub.loadDQ].sup.T, i.sub.lineDQ represents a small-signal state variable of a current of a connection line between the plurality of buses connected with the distributed generations in the common reference coordinate system DQ, the small-signal state variable of the current of the connection line between the bus connected with the i.sup.th distributed generation and the bus connected with a jth distributed generation in the common reference coordinate system DQ is: $\{\begin{array}{c}.Math..Math.{\stackrel{.}{i}}_{\mathrm{lineDij}}=-\frac{r_{\mathrm{lineij}}}{L_{\mathrm{lineij}}}.Math..Math..Math.i_{\mathrm{lineDij}}+{}_0.Math..Math..Math.i_{\mathrm{lineQij}}+\frac{1}{L_{\mathrm{lineij}}}.Math.\left(.Math..Math.V_{\mathrm{busDi}}-.Math..Math.V_{\mathrm{busDj}}\right)\\ .Math..Math.{\stackrel{.}{i}}_{\mathrm{lineQij}}=-\frac{r_{\mathrm{lineij}}}{L_{\mathrm{lineij}}}.Math..Math..Math.i_{\mathrm{lineQij}}-{}_0.Math..Math..Math.i_{\mathrm{lineDij}}+\frac{1}{L_{\mathrm{lineij}}}.Math.\left(.Math..Math.V_{\mathrm{busQi}}-.Math..Math.V_{\mathrm{busQj}}\right)\end{array},$ i.sub.lineDij and i.sub.lineDij respectively represent a D-axis small-signal component and a change rate of a current of a connection line ij in the common reference coordinate system DQ, i.sub.lineQij and i.sub.lineQij respectively represent a Q-axis small-signal component and the change rate of the current of the connection line ij in the common reference coordinate system DQ, r.sub.lineij and L.sub.lineij respectively represent a line resistance and a line inductance of the connection line ij, .sub.0 represents a rated angular frequency of a microgrid, V.sub.busDi and V.sub.busQi respectively represent a D-axis component and a Q-axis component of the voltage of the bus connected with the i.sup.th distributed generation in the common reference coordinate system DQ, V.sub.busDj and V.sub.busQj respectively represent the D-axis component and the Q-axis component of the voltage of the bus connected with the j.sup.th distributed generation in the common reference coordinate system DQ, i.sub.loadDQ represents a small-signal state variable of the current of a load connected with the bus in the common reference coordinate system DQ, the small-signal state variable of a current of the load connected with the l.sup.th bus in the common reference coordinate system DQ is: $\{\begin{array}{c}.Math..Math.{\stackrel{.}{i}}_{\mathrm{loadDt}}=-\frac{R_{\mathrm{loadl}}}{L_{\mathrm{loadl}}}.Math..Math..Math.i_{\mathrm{loadDl}}+{}_0.Math..Math..Math.i_{\mathrm{loadQl}}+\frac{1}{L_{\mathrm{loadl}}}.Math..Math..Math.V_{\mathrm{busDl}}\\ .Math..Math.{\stackrel{.}{i}}_{\mathrm{loadQt}}=-\frac{R_{\mathrm{loadl}}}{L_{\mathrm{loadl}}}.Math..Math..Math.i_{\mathrm{loadQl}}-{}_0.Math..Math..Math.i_{\mathrm{loadDl}}+\frac{1}{L_{\mathrm{loadl}}}.Math..Math..Math.V_{\mathrm{busQl}}\end{array},$ i.sub.loadDl and i.sub.loadDl and respectively represent the D-axis component and a change rate of the current of the load connected with the l.sup.th bus in the common reference coordinate system DQ, i.sub.loadQl and i.sub.loadQl respectively represent the Q-axis component and the its change rate of the current of the load connected with the filth bus in the common reference coordinate system DQ, R.sub.loadl and L.sub.loadl respectively represent a load resistance and a load inductance of the load connected with the l.sup.th bus, V.sub.busDl and V.sub.busQl respectively represent the D-axis component and the Q-axis component of the voltage of the l.sup.th bus in the common reference coordinate system DQ, and A.sub.di and .sub.i respectively represent the delay state matrix of the i.sup.th distributed generation and a delay of the i.sup.th distributed generation.

5. The microgrid delay margin calculation method based on the critical characteristic root tracking according to claim 4, wherein, a method for obtaining the characteristic equation with the transcendental term from the microgrid small-signal model comprises as: when a plurality of the delays of the distributed generations are consistent, obtaining a characteristic equation of the microgrid small-signal model: CE.sub.(s, )=det(sIAA.sub.de.sup.s), s represents a time domain complex plane parameter, represents a consistent delay time of each distributed generation of the distributed generations, CE.sub.() represents the characteristic equation of the microgrid small-signal model obtained according to the consistent delay time of the each distributed generation, det() represents a matrix determinant, I represents a unit matrix, A.sub.d represents a delay state matrix of the distributed generation, $A_d=\underset{i=1}{\overset{n}{.Math.}}.Math..Math.A_{\mathrm{di}},$ and e.sup.s represents the transcendental term.

6. The microgrid delay margin calculation method based on the critical characteristic root tracking according to claim 5, wherein, performing the critical characteristic root tracking on the transcendent term to determine the delay margin meeting the requirement of the system stability includes: with a delay time ancillary variable as a variable of the characteristic equation, solving all pure virtual characteristic roots of the characteristic equation within a change cycle of the delay time ancillary variable, and selecting a minimum value as the delay margin meeting the requirement of the system stability from a plurality of critical delay times corresponding to the all pure virtual characteristic roots; wherein the delay time ancillary variable is a product of a distributed generation delay and a virtual characteristic root amplitude.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0018] FIG. 1 shows the flow chart according to an embodiment of the present invention;

[0019] FIG. 2 shows the primary and secondary control block diagrams of a microgrid according to embodiment of the present invention;

[0020] FIG. 3 shows the microgrid simulation system diagram adopted in an embodiment of the present invention;

[0021] FIG. 4 shows the schematic diagram of critical characteristic root locus tracking under a certain set of controller parameters (k.sub.IQ=0.02, k.sub.IV=20);

[0022] FIG. 5 shows the relationship between the controller parameters and system delay margins according to an embodiment of the present invention;

[0023] FIG. 6A shows the influence of three different communication delays on the dynamic performance of average voltage under a certain set of controller parameters (k.sub.IQ=0.02, k.sub.IV=20) according to an embodiment of the present invention;

[0024] FIG. 6B shows the influence of three different communication delays on the dynamic performance of the reactive power of a distributed generation 1 under a certain set of controller parameters (k.sub.IQ=0.02, k.sub.IV=20) according to an embodiment of the present invention;

[0025] FIG. 6C shows the influence of three different communication delays on the dynamic performance of the reactive power of a distributed generation 2 under a certain set of controller parameters (k.sub.IQ=0.02, k.sub.IV=20) according to an embodiment of the present invention;

[0026] FIG. 7A shows the influence of three different communication delays on the dynamic performance of average voltage under a certain set of controller parameters (k.sub.IQ=0.04, k.sub.IV=40) according to an embodiment of the present invention;

[0027] FIG. 7B shows the influence of three different communication delays on the dynamic performance of the reactive power of the distributed generation 1 under a certain set of controller parameters (k.sub.IQ=0.04, k.sub.IV=40) according to an embodiment of the present invention; and

[0028] FIG. 7C shows the influence of three different communication delays on the dynamic performance of the reactive power of the distributed generation 2 under a certain set of controller parameters (k.sub.IQ=0.04, k.sub.IV=40) according to an embodiment of the present invention.

DETAILED DESCRIPTION OF THE EMBODIMENTS

[0029] The following describes the technical solutions of the present invention in detail with reference to accompanying drawings.

[0030] As shown in FIG. 1, the present invention discloses a microgrid delay margin calculation method based on critical characteristic root tracking, which comprises the following steps:

[0031] Step (10): Establish the inverter closed-loop small-signal model with voltage feedback control amount including communication delay based on static output feedback Each distributed generation utilizes the droop control loop in the local controller to set the references of inverter output voltage and frequency, as shown in formula (1):

[00009]$\begin{array}{cc}\{\begin{array}{c}{}_i={}_n-m_{\mathrm{Pi}}.Math.P_i\\ k_{\mathrm{Vi}}.Math.{\stackrel{.}{V}}_{o,\mathrm{mogi}}=V_n-V_{o,\mathrm{mogi}}-n_{\mathrm{Qi}}.Math.Q_i\end{array}.& \mathrm{Formula}.Math..Math.\left(1\right)\end{array}$

[0032] In formula (1), .sub.i represents the local angular frequency of the ith distributed generation; .sub.n represents the reference value of the local angular frequency of the distributed generation, unit: rad/s; m.sub.Pi represents the frequency droop characteristic coefficient of the ith distributed generation, unit: rad/s.Math.W; P represents the output active power of the ith distributed generation, unit: W; k.sub.Vi represents the droop control gain of the ith distributed generation; {dot over (V)}.sub.o,magi represents the change rate of the output voltage of the ith distributed generation, unit: V/s; V.sub.n represents the reference value of the output voltage of the distributed generation, unit: V; V.sub.o,magi represents the output voltage of the ith distributed generation, unit: V; n.sub.Qi represents the voltage droop characteristic coefficient of the ith distributed generation, unit: V/Var; and Q.sub.i represents the output reactive power of the ith distributed generation, unit: Var.

[0033] The output active power P.sub.i and the output reactive power Q.sub.i of the ith distributed generation are obtained by a low-pass filter, as shown in formula (2):

[00010]$\begin{array}{cc}\{\begin{array}{c}{\stackrel{.}{P}}_i=-{}_{\mathrm{ci}}.Math.P_i+{}_{\mathrm{ci}}\left(V_{\mathrm{odi}}.Math.i_{\mathrm{odi}}+V_{\mathrm{oqi}}.Math.i_{\mathrm{oqi}}\right)\\ {\stackrel{.}{Q}}_i=-{}_{\mathrm{ci}}.Math.Q_i+{}_{\mathrm{ci}}\left(V_{\mathrm{oqi}}.Math.i_{\mathrm{odi}}-V_{\mathrm{odi}}.Math.i_{\mathrm{oqi}}\right)\end{array}.& \mathrm{Formula}.Math..Math.\left(2\right)\end{array}$

[0034] In formula (2), {dot over (P)}.sub.i represents the change rate of the output active power of the ith distributed generation, unit: W/s; .sub.ci represents the cutoff frequency of the low-pass filter of the ith distributed generation, unit: rad/s; V.sub.odi represents the d-axis component of the output voltage of the ith distributed generation in the reference coordinate system dq of the ith distributed generation, unit: V; V.sub.oqi represents the q-axis component of the output voltage of the ith distributed generation in the reference coordinate system dq of the ith distributed generation, unit: V; i.sub.odi represents the d-axis component of the output current of the ith distributed generation in the reference coordinate system dq of the ith distributed generation, unit: A; i.sub.oqi represents the q-axis component of the output voltage of the ith distributed generation in the reference coordinate system dq of the ith distributed generation, unit: A; and {dot over (Q)}.sub.i represents the change rate of the output reactive power of the ith distributed generation, unit: Var/s.

[0035] The primary and secondary control block diagrams of the microgrid are shown as FIG. 2, the primary control of each distributed generation makes the q-axis component of the output voltage be 0 by phase-locked loop control, and formula (3) is obtained based on the secondary voltage control of the distributed generation:

[00011]$\begin{array}{cc}\{\begin{array}{c}{k}_{\mathrm{Vi}}.Math.{\stackrel{.}{V}}_{\mathrm{odi}}=V_{\mathrm{ni}}-V_{\mathrm{odi}}-n_{\mathrm{Qi}}.Math.Q_i+u_i\\ V_{\mathrm{oqi}}=0.Math.\end{array}.& \mathrm{Formula}.Math..Math.\left(3\right)\end{array}$

[0036] In formula (3), {dot over (V)}.sub.odi represents the change rate of the d-axis component of the output voltage of the ith distributed generation in the reference coordinate system dq of the ith distributed generation, unit: V/s; V.sub.ni represents the reference value of the output voltage of the ith distributed generation, and u.sub.i represents the secondary voltage control amount, unit: V.

[0037] A dynamic equation for the output current of the distributed generation is shown as formula (4):

[00012]$\begin{array}{cc}\{\begin{array}{c}{\stackrel{.}{i}}_{\mathrm{odi}}=-\frac{R_{\mathrm{ci}}}{L_{\mathrm{ci}}}.Math.i_{\mathrm{odi}}+{}_i.Math.i_{\mathrm{oqi}}+\frac{1}{L_{\mathrm{ci}}}.Math.\left(V_{\mathrm{odi}}-V_{\mathrm{busdi}}\right)\\ {\stackrel{.}{i}}_{\mathrm{oqi}}=-\frac{R_{\mathrm{ci}}}{L_{\mathrm{ci}}}.Math.i_{\mathrm{oqi}}-{}_i.Math.i_{\mathrm{odi}}+\frac{1}{L_{\mathrm{ci}}}.Math.\left(V_{\mathrm{oqi}}-V_{\mathrm{busqi}}\right)\end{array}.& \mathrm{Formula}.Math..Math.\left(4\right)\end{array}$

[0038] In formula (4), i.sub.odi represents the change rate of the d-axis component of the output current of the ith distributed generation in the reference coordinate system dq of the ith distributed generation, unit: A/s; R.sub.ci represents the connection resistance from the ith distributed generation to its connected bus, unit: ; L.sub.ci represents the connection inductance from the ith distributed generation to the connected bus, unit: H; V.sub.busdi represents the d-axis component of the voltage of the bus connected to the ith distributed generation in the reference coordinate system dq of the ith distributed generation; i.sub.oqi represents the change rate of the q-axis component of the output current of the ith distributed generation in the reference coordinate system dq of the ith distributed generation, unit: A/s; and V.sub.busqi represents the q-axis component of the voltage of the bus connected to the ith distributed generation in the reference coordinate system dq of the ith distributed generation, unit: V.

[0039] A model is established for each distributed generation on the basis of the local reference coordinate system dq. In order to establish an integrated microgrid model including a plurality of distributed generations, the reference coordinate system dq of one distributed generation is set as the common reference coordinate system DQ, the output currents of the other distributed generations in their reference coordinate systems dq need to be transformed into the common reference coordinate system, and the transformation equation is shown as formula (5):

[00013]$\begin{array}{cc}\left[\begin{array}{c}{i}_{\mathrm{oDi}}\\ i_{\mathrm{oQi}}\end{array}\right]=T_i\left[\begin{array}{c}{i}_{\mathrm{odi}}\\ i_{\mathrm{oqi}}\end{array}\right].& \mathrm{Formula}.Math..Math.\left(5\right)\end{array}$

[0040] In formula (5), i.sub.oDi represents the D-axis component of the output current of the ith distributed generation in the common reference coordinate system DQ, and i.sub.oQi represents the Q-axis component of the output current of the ith distributed generation in the common reference coordinate system, unit: A; T.sub.i represents the transformation matrix of the output current of the ith distributed generation from the reference coordinate system dq of the ith distributed generation to the common reference coordinate system DQ,

[00014]$T_i=\left[\begin{array}{cc}\cos .Math..Math.{}_i& -\sin .Math..Math.{}_i\\ \sin .Math..Math.{}_i& \cos .Math..Math.{}_i\end{array}\right],$

.sub.i represents the difference between the rotation angle of the reference coordinate system dq of the ith distributed generation and the rotation angle of the common reference coordinate system DQ, unit: degree, and .sub.i can be obtained by formula (6):

{dot over ()}.sub.i=.sub.i.sub.comFormula (6).

[0041] In formula (6), .sub.com represents the angular frequency of the common reference coordinate system DQ; and {dot over ()}.sub.i represents the change rate of .sub.i.

[0042] Formulas (1)-(6) are linearized to obtain an open-loop small-signal model of the ith distributed generation shown as formula (7):

[00015]$\begin{array}{cc}\{\begin{array}{c}.Math..Math.{\stackrel{.}{x}}_{\mathrm{invi}}=A_{\mathrm{invi}}.Math..Math..Math.x_{\mathrm{invi}}+B_{\mathrm{invi}}.Math..Math..Math.V_{\mathrm{bDQi}}+B_{\mathrm{iwcom}}.Math.{}_{\mathrm{com}}+B_{\mathrm{ui}}.Math..Math..Math.u_i\\ .Math..Math.i_{\mathrm{oDQi}}=C_{\mathrm{invci}}.Math..Math..Math.x_{\mathrm{invi}}.Math.\end{array}.& \mathrm{Formula}.Math..Math.\left(7\right)\end{array}$

[0043] In formula (7), {dot over (x)}.sub.invi represents the change rate of the small-signal state variables of the ith distributed generation, {dot over (x)}.sub.invi=[{dot over ()}.sub.i, {dot over (P)}.sub.i, {dot over (Q)}.sub.i, {dot over (V)}.sub.odi, {dot over (i)}.sub.odi, {dot over (i)}.sub.oqi].sup.T; x.sub.invi represents the small-signal state variables of the ith distributed generation, x.sub.invi=[.sub.i, P.sub.i, Q.sub.i, V.sub.odi, i.sub.odi, i.sub.oqi].sup.T; V.sub.bDQi represents the small-signal state variables of the voltage of the bus connected to the ith distributed generation in the common reference coordinate system DQ; V.sub.bDQi=[V.sub.bDi, V.sub.bQi].sup.T, V.sub.bDi represents the D-axis small-signal component of the voltage of the bus connected to the ith distributed generation in the common reference coordinate system DQ, and V.sub.bQi represents the Q-axis small-signal component of the voltage of the bus connected to the ith distributed generation in the common reference coordinate system DQ, unit: V; .sub.com represents the small-signal state variable of the angular frequency of the common reference coordinate system DQ, unit: rad/s; u.sub.i represents the small-signal control amount of the secondary voltage of the ith distributed generation, unit: V; A.sub.invi represents the state matrix of the ith distributed generation; B.sub.invi represents the input matrix of the ith distributed generation to the voltage of the connected bus; B.sub.iwcom represents the input matrix of the ith distributed generation to the angular frequency of the common reference coordinate system; B.sub.ui represents the input matrix of the ith distributed generation to the small-signal control amount of the secondary voltage; i.sub.oDQi represents the small-signal state variables of the output current of the ith distributed generation in the common reference coordinate system DQ, i.sub.oDQi=[i.sub.oDi, i.sub.oQi].sup.T, unit: A; and C.sub.invci represents the output current matrix of the ith distributed generation.

[0044] According to formula (7), V.sub.busDQi and .sub.com serve as disturbance variables of the ith distributed generation, where the reference coordinate system of the first distributed generation is generally selected as the common reference coordinate system DQ, then

.sub.com=[0m.sub.P1 0 0 0 0]x.sub.inv1Formula (8).

[0045] In formula (8), m.sub.P1 represents the frequency droop characteristic coefficient of the first distributed generation, unit: rad/s.Math.W; x.sub.inv1 represents the small-signal state variables of the first distributed generation, x.sub.inv1=[.sub.1, P.sub.i, .sub.Q1, V.sub.od1, i.sub.od1, i.sub.oq1].sup.T.

[0046] According to formula (7) and formula (8), the small-signal model of the system consisting of n distributed generations can be obtained:

[00016]$\begin{array}{cc}\{\begin{array}{c}.Math..Math.{\stackrel{.}{\stackrel{\_}{x}}}_{\mathrm{inv}}={\stackrel{\_}{A}}_{\mathrm{inv}}.Math..Math..Math.{\stackrel{\_}{x}}_{\mathrm{inv}}+{\stackrel{\_}{B}}_{\mathrm{inv}}.Math..Math..Math.V_{\mathrm{bDQ}}+{\stackrel{\_}{B}}_u.Math..Math..Math.u\\ .Math..Math.i_{\mathrm{oDQ}}={\stackrel{\_}{C}}_{\mathrm{invc}}.Math..Math..Math.{\stackrel{\_}{x}}_{\mathrm{inv}}.Math.\end{array}.& \mathrm{Formula}.Math..Math.\left(9\right)\end{array}$

[0047] In formula (9), x.sub.inv=[x.sub.inv1x.sub.inv2 . . . .sub.invn], x.sub.inv1 represents the small-signal state variables of the first distributed generation, x.sub.inv2 represents the small-signal state variables of the second distributed generation, and x.sub.invn represents the small-signal state variables of the nth distributed generation; V.sub.bDQ=[V.sub.bDQ1 V.sub.bDQ2 . . . V.sub.busDQm].sup.T, V.sub.bDQ1=[V.sub.bD1V.sub.bQ1].sup.T, V.sub.BD1 represents the D-axis component of small-signal variable of the voltage of bus 1 in the common reference coordinate system DQ, V.sub.bQ1 represents the Q-axis component of small-signal variable of the voltage of bus 1 in the common reference coordinate system DQ, V.sub.bDQ2=[V.sub.bD2 V.sub.bQ2].sup.T, V.sub.bD2 represents the D-axis component of small-signal variable of the voltage of bus 2 in the common reference coordinate system DQ, V.sub.bQ2 represents the Q-axis component of small-signal variable of the voltage of bus 2 in the common reference coordinate system DQ, V.sub.bDQm=[V.sub.bDm V.sub.bQm].sup.T, V.sub.bDm represents the D-axis component of small-signal variable of the voltage of bus m in the common reference coordinate system DQ, and V.sub.bQm represents the Q-axis component of small-signal variable of the voltage of bus m in the common reference coordinate system DQ; u=[u.sub.1u.sub.2 . . . u.sub.n].sup.T, i.sub.oD1 represents the small-signal control amount of the secondary voltage of the distributed generation 1, u.sub.2 represents the small-signal control amount of the secondary voltage of the distributed generation 2, and u.sub.n represents the small-signal control amount of the secondary voltage of the distributed generation n; i.sub.oDQ=[i.sub.oDQli.sub.oDQ2 . . . i.sub.oDQn].sup.T, i.sub.oDQ1=[i.sub.oD1, i.sub.oQ1].sup.T, i.sub.oD1 represents the D-axis component of small-signal variable of the output current of the first distributed generation in the common reference coordinate system DQ, i.sub.oQ1 represents the Q-axis component of small-signal variable of the output current of the ith distributed generation in the common reference coordinate system DQ, i.sub.oDQ2=[i.sub.oD2, i.sub.oQ2].sup.T, i.sub.oD2 represents the D-axis component of small-signal variable of the output current of the second distributed generation in the common reference coordinate system DQ, and i.sub.oQ2 represents the Q-axis component of small-signal variable of the output current of the second distributed generation in the common reference coordinate system DQ; i.sub.oDQn=[i.sub.oDn, i.sub.oQn].sup.T, i.sub.oDn represents the D-axis component of small-signal variable of the output current of the nth distributed generation in the common reference coordinate system DQ, i.sub.oQn represents the Q-axis component of small-signal variable of the output current of the nth distributed generation in the common reference coordinate system DQ, and .sub.inv represents the state matrix of n distributed generations; B.sub.inv represents the input matrix of n distributed generations to bus voltages; {circumflex over (B)}.sub.n represents the input matrix of the n distributed generations to the small-signal control amount of the secondary voltage; and C.sub.invc represents the current output matrix of the n distributed generations.

[0048] Based on the control requirements of reactive power sharing and voltage recovery, the present invention realizes microgrid voltage control. Reactive power sharing refers to that the output reactive power of each distributed generation is allocated according to the power capacity, voltage recovery refers to that the average output voltage of all the distributed generations is recovered to a rated value, and the following dynamic equation is first defined:

[00017]$\begin{array}{cc}\{\begin{array}{c}{\stackrel{.}{}}_i=Q_i^{*}-Q_i=\frac{1.Math.\text{/}.Math.n_{\mathrm{Qi}}}{\underset{i=1}{\overset{n}{.Math.}}.Math..Math.1.Math.\text{/}.Math.n_{\mathrm{Qi}}}.Math.\underset{i=1}{\overset{n}{.Math.}}.Math..Math.Q_i-Q_i\\ \stackrel{.}{}=V_i^{*}-{\stackrel{\_}{V}}_{\mathrm{od}}=V_i^{*}-\frac{1}{n}.Math.\underset{i=1}{\overset{n}{.Math.}}.Math..Math.V_{\mathrm{odi}}\end{array}.& \mathrm{Formula}.Math..Math.\left(10\right)\end{array}$

[0049] In formula (10), {dot over ()}.sub.i represents the change rate of the small-signal state variable of reactive power ancillary of the ith distributed generation, unit: Var; Q.sub.i: represents the expected output reactive power of the ith distributed generation, unit: Var; n.sub.Qi represents the voltage droop characteristic coefficient of the ith distributed generation, unit: V/Var; represents the change rate of the small-signal state variable for the voltage ancillary of the distributed generation, unit: V; V.sub.od represents the average output voltage of all distributed generations, and V*.sub.i represents the expected average voltage of the ith distributed generation, unit: V.

[0050] Therefore, an inverter closed-loop small-signal model based on output feedback is:

[00018]$\begin{array}{cc}\{\begin{array}{c}.Math..Math.{\stackrel{.}{x}}_{\mathrm{inv}}=A_{\mathrm{inv}}.Math..Math..Math.x_{\mathrm{inv}}+B_{\mathrm{inv}}.Math..Math..Math.V_{\mathrm{bDQ}}+B_u.Math..Math..Math.u.Math.\\ .Math..Math.y_{\mathrm{invQ}}=C_{\mathrm{invQ}}.Math..Math..Math.x_{\mathrm{inv}},.Math..Math.y_{\mathrm{invV}}=C_{\mathrm{invV}}.Math..Math..Math.x_{\mathrm{inv}}\end{array}.& \mathrm{Formula}.Math..Math.\left(11\right)\end{array}$

[0051] In formula (11), x.sub.inv represents the closed-loop small-signal state variables of n inverters, x.sub.inv=[x.sub.invi, x.sub.inv2, . . . , x.sub.invi, . . . , x.sub.invn, .sub.1, .sub.2, . . . , .sub.i, . . . , .sub.n, ].sup.T, .sub.1 small-signal state variable of a reactive power ancillary of the first distributed generation, .sub.2 represents the small-signal state variable of a reactive power ancillary of the second distributed .sub.2 generation, .sub.i represents the small-signal state variable of the reactive power ancillary of the ith distributed generation, .sub.n represents the small-signal state variable of the reactive power ancillary of the nth distributed generation, and represents the small-signal state variable for voltage ancillary of distributed generations; y.sub.invQ represents small-signal state variables of output reactive powers y.sub.invQ=[{dot over ()}.sub.1 .sub.1 {dot over ()}.sub.2 .sub.2 . . . .sub.n .sub.n], {dot over ()}.sub.1 represents the change rate of the small-signal state variable of the reactive power ancillary of the first distributed generation, {dot over ()}.sub.2 represents the change rate of small-signal state variable of the reactive power ancillary of the second distributed generation, and {dot over ()}.sub.n represents the change rate of small-signal state variable of the reactive power ancillary of the nth distributed generation; y.sub.invV represents the small-signal state variables of the output voltage of the distributed generations, y.sub.invV=[{dot over ()}, ].sup.T, and {dot over ()} represents the change rate of small-signal state variable for the voltage ancillary of each distributed generation; C.sub.invQ represents the output matrix of reactive power of distributed generations; and C.sub.invV represents the output matrix of the voltages of distributed generations.

[0052] The control amount of the distributed generation is defined as:

[00019]$\begin{array}{cc}\{\begin{array}{c}.Math..Math.Q_i=k_{\mathrm{PQ}}\left(Q_i^{*}-Q_i\right)+k_{\mathrm{IQ}}.Math..Math.\\ .Math..Math.V_i=k_{\mathrm{PV}}\left(V^{*}-{\stackrel{\_}{V}}_{\mathrm{od}}\right)+k_{\mathrm{IV}}.Math.\end{array}.& \mathrm{Formula}.Math..Math.\left(12\right)\end{array}$

[0053] In formula (12), Q.sub.i represents the reactive power control signal of the ith distributed generation; k.sub.PQ represents the proportional term coefficient in a reactive power proportional-integral controller; k.sub.IQ represents the integral term coefficient in the reactive power proportional-integral controller; V.sub.i represents the average voltage recovery control signal of the ith distributed generation; k.sub.PV represents the proportional term coefficient in the average voltage proportional-integral controller; and k.sub.IV represents the integral term coefficient in the average voltage proportional-integral controller.

[0054] When a communication delay exists between a centralized voltage controller of the microgrid and each distributed generation, a voltage control amount is:

.sub.ui=.sub.Qi(t.sub.i)+.sub.Vi(t.sub.i)=K.sub.Qiy.sub.invQi(t.sub.i)+K.sub.Viy.sub.invV(t.sub.i)Formula (13).

[0055] In formula (13), .sub.i represents the communication delay between the local controller of the ith distributed generation and the centralized secondary voltage controller of the microgrid, unit: s; K.sub.Qi represents the reactive power controller of the ith distributed generation, K.sub.Qi=[k.sub.PQi k.sub.IQi]; and K.sub.Vi represents the voltage controller of the ith distributed generation, K.sub.Vi=[k.sub.PVi k.sub.IVi].

[0056] By reference to formulas (11)-(13), the close-loop small-signal model of n distributed generations are obtained:

[00020]$\begin{array}{cc}\{\begin{array}{c}.Math..Math.{\stackrel{.}{x}}_{\mathrm{inv}}=A_{\mathrm{inv}}.Math..Math..Math.x_{\mathrm{inv}}+\underset{i=1}{\overset{n}{.Math.}}.Math..Math.{\stackrel{\_}{A}}_{\mathrm{di}}.Math..Math..Math.x_{\mathrm{inv}}\left(t-{}_i\right)+B_{\mathrm{inv}}.Math..Math..Math.V_{\mathrm{bDQ}}\\ .Math..Math.i_{\mathrm{oDQ}}=C_{\mathrm{invc}}.Math..Math..Math.x_{\mathrm{inv}}.Math.\end{array}.& \mathrm{Formula}.Math..Math.\left(14\right)\end{array}$

[0057] In formula (14), .sub.dx represents the delayed state matrix of the ith distributed generation,

[0058] .sub.di=[0 . . . B.sub.uiK.sub.QiC.sub.invQi+B.sub.uiK.sub.ViC.sub.invV . . . 0], B.sub.ui represents the input matrix of the ith distributed generation to the small-signal control amount of the secondary voltage, C.sub.invQi represents the output matrix of reactive power of the ith distributed generation, and C.sub.invc represents the output matrix of the current of the distributed generation.

[0059] Step (20) Establish a microgrid small-signal model according to a connection network and a dynamic equation of load impedance

[0060] A current small-signal dynamic equation of a connection line ij between the bus connected to the ith distributed generation and the bus connected to the jth distributed generation in the common reference coordinate system DQ is shown as formula (15):

[00021]$.Math.\mathrm{Formula}.Math..Math.\left(15\right)$$\{\begin{array}{c}.Math..Math.{\stackrel{.}{i}}_{\mathrm{lineDij}}=-\frac{r_{\mathrm{lineij}}}{L_{\mathrm{lineij}}}.Math..Math..Math.i_{\mathrm{lineDij}}+{}_0.Math..Math..Math.i_{\mathrm{lineQij}}+\frac{1}{L_{\mathrm{lineij}}}.Math.\left(.Math..Math.V_{\mathrm{busDi}}-.Math..Math.V_{\mathrm{busDj}}\right)\\ .Math..Math.{\stackrel{.}{i}}_{\mathrm{lineQij}}=-\frac{r_{\mathrm{lineij}}}{L_{\mathrm{lineij}}}.Math..Math..Math.i_{\mathrm{lineQij}}-{}_0.Math..Math..Math.i_{\mathrm{lineDij}}+\frac{1}{L_{\mathrm{lineij}}}.Math.\left(.Math..Math.V_{\mathrm{busQi}}-.Math..Math.V_{\mathrm{busQj}}\right)\end{array}.$

[0061] In formula (15), i.sub.lineDij represents the change rate of a D-axis component of small-signal variable of the current of the ijth connection line in the common reference coordinate system DQ, unit: A/s; r.sub.lineij represents the line resistance of the ijth connection line, unit: ; L.sub.lineij represents the line inductance of the ijth connection line, unit: H; i.sub.lineDij represents the D-axis component of small-signal variable of the current of the ijth connection line in the common reference coordinate system DQ, and i.sub.lineQij represents the Q-axis component of small-signal variable of the current of the ijth connection line in the common reference coordinate system DQ, unit: A; .sub.0 represents the rated angular frequency of the microgrid, unit: rad/s; V.sub.busDi represents the D-axis component of small-signal variable of the voltage of the bus connected to the ith distributed generation in the common reference coordinate system DQ; V.sub.busDj represents the D-axis component of small-signal variable of the voltage of the bus connected to the jth distributed generation in the common reference coordinate system DQ; i.sub.lineQij represents the change rate of the Q-axis component of small-signal variable of the current of the ijth connection line in the common reference coordinate system DQ, unit: A/s; V.sub.busQi represents the Q-axis component of small-signal variable of the voltage of the bus connected to the ith distributed generation in the common reference coordinate system DQ, and V.sub.busQj represents the Q-axis component of small-signal variable of the voltage of the bus connected to the jth distributed generation in the common reference coordinate system DQ, unit: V.

[0062] A current dynamic equation of a load connected to the lth bus in the common reference coordinate system DQ is shown as formula (16):

[00022]$\begin{array}{cc}\{\begin{array}{c}.Math..Math.{\stackrel{.}{i}}_{\mathrm{loadDt}}=-\frac{R_{\mathrm{loadl}}}{L_{\mathrm{loadl}}}.Math..Math..Math.i_{\mathrm{loadDl}}+{}_0.Math..Math..Math.i_{\mathrm{loadQl}}+\frac{1}{L_{\mathrm{loadl}}}.Math..Math..Math.V_{\mathrm{busDl}}\\ .Math..Math.{\stackrel{.}{i}}_{\mathrm{loadQt}}=-\frac{R_{\mathrm{loadl}}}{L_{\mathrm{loadl}}}.Math..Math..Math.i_{\mathrm{loadQl}}-{}_0.Math..Math..Math.i_{\mathrm{loadDl}}+\frac{1}{L_{\mathrm{loadl}}}.Math..Math..Math.V_{\mathrm{busQl}}\end{array}.& \mathrm{Formula}.Math..Math.\left(16\right)\end{array}$

[0063] In formula (16), i.sub.loadD1 represents the change rate of D-axis component of small-signal variable of the current of the load connected to the lth bus in the common reference coordinate system DQ, unit: A/s; R.sub.load1 represents the load resistance of the load connected to the lth bus, unit: ; L.sub.load1 represents the load inductance of the load connected to the lth bus, unit: H; i.sub.loadDl represents the D-axis component of small-signal variable of the current of the load connected to the lth bus in the common reference coordinate system DQ, and i.sub.loadQl represents the Q-axis component of small-signal variable of the current of the load connected to the lth bus in the common reference coordinate system DQ, unit: A; and i.sub.loadQl represents the change rate of Q-axis component of small-signal variable of the current of the load connected to the lth bus in the common reference coordinate system DQ, unit: A/s.

[0064] A small-signal equation of the connection line between the bus connected to the ith distributed generation and the bus connected to the jth distributed generation is set as formula (17):

[00023]$\begin{array}{cc}\{\begin{array}{c}.Math..Math.V_{\mathrm{busDj}}=R_{\mathrm{loadj}}\left(.Math..Math.i_{\mathrm{oDj}}+.Math..Math.i_{\mathrm{lineDij}}-.Math..Math.i_{\mathrm{lineDij}}\right)+L_{\mathrm{loadj}}\left[\left(.Math..Math.i_{\mathrm{oDj}}+.Math..Math.i_{\mathrm{lineDij}}-.Math..Math.i_{\mathrm{lineDij}}\right)-{}_0\left(.Math..Math.i_{\mathrm{oQj}}+.Math..Math.i_{\mathrm{lineQij}}-.Math..Math.i_{\mathrm{lineQij}}\right)\right]\\ .Math..Math.V_{\mathrm{busQj}}=R_{\mathrm{loadj}}\left(.Math..Math.i_{\mathrm{oQj}}+.Math..Math.i_{\mathrm{lineQij}}-.Math..Math.i_{\mathrm{lineQij}}\right)+L_{\mathrm{loadj}}\left[\left(.Math..Math.i_{\mathrm{oQj}}+.Math..Math.i_{\mathrm{lineQij}}-.Math..Math.i_{\mathrm{lineQij}}\right)+{}_0\left(.Math..Math.i_{\mathrm{oDj}}+.Math..Math.i_{\mathrm{lineDij}}-.Math..Math.i_{\mathrm{lineDij}}\right)\right]\end{array}.& \mathrm{Formula}.Math..Math.\left(17\right)\end{array}$

[0065] In formula (17), R.sub.loadj and L.sub.loadj respectively represent the resistance value and the inductance value of a load on the bus connected the jth distributed generation; and i.sub.oDj and i.sub.oQj respectively represent the D-axis component small-signal variable and Q-axis component of small-signal variable of the output current of the jth distributed generation in the common reference coordinate system DQ.

[0066] Formula (17) is substituted into formulas (14)-(16) to obtain the microgrid small-signal model comprising n distributed generations, s branches and p loads:

[00024]$\begin{array}{cc}\stackrel{.}{x}=\mathrm{Ax}+\underset{i=1}{\overset{n}{.Math.}}.Math..Math.A_{\mathrm{di}}.Math.x\left(t-{}_i\right).& \mathrm{Formula}.Math..Math.\left(18\right)\end{array}$

[0067] In formula (18), x represents the microgrid small-signal state variables, x=[x.sub.inv i.sub.lineDQ i.sub.loadDQ].sup.T, i.sub.lineDQ represent the small-signal state variables of the current of the connection lines between the buses connected to the distributed generations in the common reference coordinate system DQ, and i.sub.loadDQ represent the small-signal state variables of the current of the loads connected to the buses in the common reference coordinate system DQ; {dot over (x)} represents the change rate of the microgrid small-signal state variables; A represents the microgrid state matrix; A.sub.di represents the delayed state matrix of the ith distributed generation; and .sub.i represents the delay of the ith distributed generation.

[0068] Step (30) Obtain a characteristic equation with a transcendental term of a microgrid closed-loop small-signal model

[0069] When the delays of all the distributed generations are consistent, a characteristic equation of formula (18) is formula (19):

CE.sub.(s,)=det(sIAA.sub.de.sup.s)Formula (19).

[0070] In formula (19), s represents the parameter of the time domain complex plane; r represents the consistent delay time of each distributed generation, .sub.1=.sub.2= . . . =.sub.n, unit: s; det() represents the matrix determinant; I represents the unit matrix; A.sub.d represents the delayed state matrix of the distributed generation, A.sub.d=.sub.i=1.sup.nA.sub.di; and e.sup.s represents the transcendental term.

[0071] Step (40) Carry out critical characteristic root locus tracking for the transcendental term of the system characteristic equation to calculate the system stability margin For formula (19), if all system characteristic roots are on the left half of a complex plane, the system is stable; if there are characteristic roots on the right half of the complex plane, the system is unstable; and if there are characteristic roots on the left half of the complex plane or the imaginary axis, the system is critically stable. Because the system characteristic roots continuously change along with the delay time , in order to determine the system stability margin Td, that is, the system is stable if r is less than Td, and is unstable if r is greater than Td, the possible pure virtual characteristic roots and the corresponding delay margin need to be determined.

[0072] = is defined and substituted into formula (19), and then,

CE.sub.(s,)=det(sIAA.sub.de.sup.i)Formula (20).

[0073] Where, represents the delay time ancillary variable, and represents the virtual characteristic root amplitude; here, i represents the imaginary unit, and i.sup.2=1. changes within the cycle of [0, 2], so that corresponding characteristic roots of formula (20) are obtained. If there are pure virtual characteristic roots corresponding to certain then a critical delay time is:

.sub.c=.sub.c/abs(.sub.C)Formula (21).

[0074] In the formula, .sub.c represents the delay time ancillary variable for the existence of pure virtual characteristic roots in the system, abs(c) represents the amplitude of the corresponding pure virtual characteristic root, and .sub.c represents the critical delay time.

[0075] When changes within the cycle of [0, 2], there may be a plurality of critical delay times in the system, i.e. .sub.c1, .sub.c2 . . . .sub.cL, and the minimum value .sub.d is selected as the delay margin:

.sub.d=min(.sub.c1 .sub.c2 . . . .sub.cL)Formula (22).

[0076] In the aforementioned embodiment, the common reference coordinate system DQ refers to the reference coordinate system dq of the first distributed generation, and the state variables of the other distributed generations, branch currents and load currents are transformed into the common reference coordinate system DQ by the transformation of coordinates. In step (10), because the proportional term coefficients in the proportional-integral controller of reactive power and the proportional-integral controller of the voltage are small, in practice, the proportional-integral controller of reactive power and the proportional-integral controller of the voltage can be respectively simplified into an integral controller of reactive power and an integral controller of voltage. In step (20), the loads are impedance type loads.

[0077] In the present embodiment, by introducing the microgrid closed-loop small-signal model of signal communication delay time, a system characteristic equation with a transcendental term is established, and thereby the microgrid delay margin calculation method based on critical characteristic root tracking is implemented. Aimed at the conventional microgrid secondary control method which neglects the influence of the communication delay on the dynamic performance of the system, the present embodiment works out a maximum delay time for maintaining the system stable in full consideration of the actual situation that the influence of the communication delay on system stability cannot be neglected due to the low inertia of power electronic interfaced microgrid. By analyzing the relationship between different controller parameters and delay margins, the delay margin calculation method of the present embodiment guides the design of the controllers, thus improving the stability and dynamic performance of the system.

[0078] The block diagram of the microgrid control system in the embodiment of the present invention is shown as FIG. 2. The control block diagram mainly comprises two layers: the first layer is the local controller of each distributed generation, which consists of power calculation, droop control, and a voltage and current double loop; and the second layer is the secondary voltage control layer, which realizes reactive power sharing and average voltage recovery. The centralized secondary voltage controller acquires the output voltage and output reactive power of each distributed generation, works out the secondary voltage control amount of each distributed generation, then sends a control instruction into each local controller. In the process of sending the control instruction, a communication delay exists between the centralized secondary voltage controller and the local controller of each distributed generation, and this delay affects the dynamic performance of the system.

[0079] The following exemplifies an embodiment.

[0080] A simulation system is shown as FIG. 3, a microgrid consists of two distributed generations, two connection lines, and three loads, the load 1 is connected to bus 1, the load 2 is connected to bus 2, and the load 3 is connected to bus 3. In the system, impedance type loads are adopted as the loads. If the capacity ratio of the distributed generation 1 and the distributed generation 2 is 1:1, then corresponding frequency droop coefficient and voltage droop coefficient are designed to make the ratio of the expected output active power and reactive power of two distributed generations be equal to 1:1. Theoretical delay margins of the microgrid under different controller parameters are studied, and a microgrid simulation model is established based on an MATLAB/Simulink platform to simulate and verify the theoretical delay margins.

[0081] FIG. 4 is the schematic diagram of critical characteristic root locus tracking associated with system stability under controller parameters (k.sub.IQ=0.02, k.sub.IV=20). A communication delay ancillary variable change within [0, 2], two pairs of conjugate characteristic roots are closely related to system stability, four critical characteristic roots A(j.sub.c1), A(j.sub.c1), B(j.sub.c2) and B(j.sub.c2) passing through the imaginary axis of a complex plane and corresponding are recorded, and a delay margin d=0.05888 s is worked out according to formula (21) and formula (22).

[0082] FIG. 5 is the relationship between the microgrid delay margin calculated based on critical characteristic root tracking and the controller parameters under the controller parameters (0.005k.sub.IQ0.06, 5k.sub.IV60) in the embodiment of the present invention. It can be known from the drawing that with an increase in the integral coefficient k.sub.IQ of the reactive power controller and the integral coefficient k.sub.IV of the voltage controller, the delay margin of the system decreases. That is, the robust stability of the system reduced. Therefore, when different combinations of controller parameters achieve similar dynamic performance, the delay margin will serve as an additional robust stability index to guide the design of the controller parameters, providing the system with stability and dynamic performance.

[0083] FIG. 6 is the simulation result of a decentralized control method for the influence of three different communication delays on the dynamic performance of the system under a certain set of controller parameters (k.sub.IQ=0.02, k.sub.IV=20) of the microgrid according to the embodiment of the present invention. When the system is started, each distributed generation operates under a droop control mode, and at 0.5 s, secondary voltage control is put into operation. A simulation result is shown as FIG. 6, FIG. 6A is an average voltage curve graph of the distributed generation in the microgrid, the X axis represents time, unit: s, and the Y axis represents average voltage, unit: V. W. As shown in FIG. 6A, at the beginning, under the effect of droop control, a steady-state deviation exists in the average voltage of the distributed generations, and after 0.5 s, under the effect of secondary control, the voltage amplitude increases. It can be known from FIG. 6A that when no communication delay exists in the system, the average voltage is so smooth as to reach a rated value; when the delay time is 53 ms, the voltage curve experiences decreased oscillation and restores; when the delay time is 61 ms, the curve experiences increasing oscillation, and the system is unstable. FIG. 6B is a reactive power output curve graph of the distributed generation 1, unit: s, and the Y axis represents reactive power, unit: Var. It can be known from FIG. 6B that at the beginning, under the effect of droop control, the reactive power sharing effect is not satisfactory (less than the expected output reactive power value of the distributed generation 1), and after 0.5 s, under the effect of secondary control, reactive power output is increased. It can be known from FIG. 6B that when no communication delay exists in the system, the reactive power is so smooth as to reach an expected value; when the delay time is 53 ms, the power curve experiences decreased oscillation and reaches the control target; when the delay time is 61 ms, the curve experiences increasing oscillation, and the system is unstable. Under the effect of secondary control, the reactive power sharing effect of the microgrid is significantly improved. FIG. 6C is a reactive power output curve graph of the distributed generation 2, unit: s, and the Y axis represents reactive power, unit: Var. It can be known from FIG. 6C that at the beginning, under the effect of droop control, the reactive power sharing effect is not satisfactory (higher than an expected output reactive power value of the distributed generation 2), and after 0.5 s, under the effect of secondary control, reactive power output is decreased. It can be known from FIG. 6C that when no communication delay exists in the system, reactive power is so smooth as to reach an expected value; when the delay time is 53 ms, the power curve experiences decreased oscillation and reaches a control target; when the delay time is 61 ms, the curve experiences increasing oscillation, and the system is unstable. It can be known from FIG. 6 that the delay margin of the system under the controller parameters is between 53 ms and 61 ms, and is consistent with a theoretical calculated value.

[0084] FIG. 7 is the simulation result of a decentralized control method for the influence of three communication delays on the dynamic performance of the system under a certain set of controller parameters (k.sub.IQ=0.04, k.sub.IV=40) of the microgrid according to the embodiment of the present invention. When operation is started, each distributed generation operates under a droop control mode, and at 0.5 s, secondary voltage control is put into operation. A simulation result is shown as FIG. 7, FIG. 7A is the average voltage curve graph of the distributed generations in the microgrid, the X axis represents time, unit: s, and the Y axis represents average voltage, unit: V. W. As shown in FIG. 7A, at the beginning, under the effect of droop control, a steady-state deviation exists in the average voltage of the distributed generations, and after 0.5 s, under the effect of secondary control, the voltage amplitude increases. It can be known from FIG. 7A that when no communication delay exists in the system, the average voltage is so smooth as to reach a rated value; when the delay time is 25 ms, the voltage curve experiences decreased oscillation and restores; when the delay time is 33 ms, the oscillation of the curve experiences increasing oscillation, and the system is unstable. FIG. 7B is the reactive power output curve graph of the distributed generation 1, unit: s, and the Y axis represents reactive power, unit: Var. It can be known from FIG. 7B that at the beginning, under the effect of droop control, the reactive power sharing effect is not satisfactory (less than an expected output reactive power value of the distributed generation 1), and after 0.5 s, under the effect of secondary control, reactive power output is increased. It can be known from FIG. 6B that when no communication delay exists in the system, reactive power is so smooth as to reach an expected value; when the delay time is 25 ms, the power curve reaches a control objective due to decreased oscillation; when the delay time is 33 ms, the oscillation of the curve is increased, and the system is unstable. Under the effect of secondary control, the reactive power sharing effect of the microgrid is significantly improved. FIG. 7C is the reactive power output curve graph of the distributed generation 2, unit: s, and the Y axis represents reactive power, unit: Var. It can be known from FIG. 7C that at the beginning, under the effect of droop control, the reactive power sharing effect is not satisfactory (higher than an expected reactive power output value of the distributed generation 2), and after 0.5 s, under the effect of secondary control, reactive power output is decreased. It can be known from FIG. 7C that when no communication delay exists in the system, reactive power is so smooth as to reach an expected value; when the delay time is 25 ms, the power curve experiences decreased oscillation and reaches the control target; when the delay time is 33 ms, the curve experiences increasing oscillation, and the system is unstable. It can be known from FIG. 6 that the delay margin of the system under the controller parameters is between 25 ms and 33 ms, and is consistent with a theoretical calculated value.

[0085] The method of the embodiment of the present invention is a microgrid delay margin calculation method based on critical characteristic root tracking, by which the microgrid closed-loop small-signal model including communication delay is established based on the output feedback method, and the maximum delay time for a stable system, i.e. the delay margin is analyzed. Aimed at the conventional microgrid secondary control method which neglects the influence of communication delay on the dynamic performance of the system, the present embodiment takes the influence of communication delay on system stability into full consideration, and in addition, by studying the relationship between different controller parameters and delay margins, the design of the controllers is guided, thus improving the robust stability and dynamic performance of the microgrid.