CN103123664B - A kind of dynamic model of modular multi-level convector modeling method - Google Patents

Abstract

The present invention provides a kind of dynamic model of modular multi-level convector modeling method, said method comprising the steps of: brachium pontis single submodule cycle by cycle switch average model and upper brachium pontis single submodule small-signal alternate model in foundation；Brachium pontis cycle by cycle switch average model and upper brachium pontis small-signal alternate model in foundation；Set up lower brachium pontis cycle by cycle switch average model and lower brachium pontis small-signal alternate model；Set up modularization multi-level converter cycle by cycle switch average model and modularization multi-level converter small-signal model.The mould set up is changed multilevel converter dynamic model soon and is easy to the dynamic property to modularization multi-level converter and Frequency Response is analyzed, it is simple to designs for Unit Level control strategy, and achieves the description to internal quantity of state.

Description

Modeling method for dynamic model of modular multilevel converter

Technical Field

The invention belongs to the technical field of power transmission of power systems, and particularly relates to a modeling method for a dynamic model of a modular multilevel converter.

Background

In 2002, r.marquart and a.leinicar, the university of defense, united states, munich, germany, have proposed a novel modular multilevel voltage source type converter. A17-level 2MW prototype was successfully developed in 2004. In 2009, the international large grid conference B4.48 working group formally named it as a Modular Multilevel Converter (MMC). The topological structure forms the converter valve by serially connecting the sub-modules, has high modularization degree, small harmonic distortion and low switching loss, is suitable for application in high-voltage and high-power occasions, has wide application prospect, and can be used for various flexible direct-current power transmission and flexible alternating-current power transmission devices such as flexible direct-current power transmission, unified power flow controllers, line-to-line power flow controllers, convertible static compensators and the like. In 2010, the first modular multilevel converter dc transmission project was networked with submarine dc cables between pittsburgh and san francisco, california, usa, solving the problem of tension in local transmission corridors and enhancing the safety stability and reliability of the system.

A mathematical model of the power electronic device based on the modular multilevel converter is the basis for researching corresponding control strategies. Because the main circuit package is a nonlinear, alternating current-direct current hybrid and high-frequency power frequency hybrid complex system comprising a switching element and an energy storage element, model description has certain difficulty, and common modeling methods comprise a topology modeling method and an output modeling method. The model built by the topology modeling method directly reflects the circuit topology structure, and the complexity is obviously increased along with the increase of the number of the switching devices; the output modeling method generally equates the device to a controlled source or impedance form, and the modeling is relatively simple, but ignores the state information of the internal elements of the device and is not beneficial to the characteristic analysis in the device. Thus, both methods have limitations in their application.

Disclosure of Invention

In order to overcome the defects of the prior art, the invention provides a modeling method for a dynamic model of a modular multilevel converter, wherein the established dynamic model of the modular multilevel converter is convenient for analyzing the dynamic performance and the frequency response characteristic of the modular multilevel converter, is convenient for designing a device-level control strategy, and realizes the description of internal state quantity.

In order to achieve the purpose of the invention, the invention adopts the following technical scheme:

a method for modeling a dynamic model of a modular multilevel converter, the method comprising the steps of:

step 1: establishing an upper bridge arm single sub-module switching period average model and an upper bridge arm single sub-module small signal alternating current model;

step 2: establishing an upper bridge arm switching period average model and an upper bridge arm small signal alternating current model;

and step 3: establishing a lower bridge arm switching period average model and a lower bridge arm small signal alternating-current model;

and 4, step 4: and establishing a modular multilevel converter switching period average model and a modular multilevel converter small signal model.

The modular multilevel converter comprises three pairs of bridge arms, each pair of bridge arms comprises an upper bridge arm and a lower bridge arm, the upper bridge arm and the lower bridge arm respectively comprise N sub-modules and reactors which are sequentially connected in series, and the three pairs of bridge arms are connected in parallel to lead out a common direct current end.

The step 1 comprises the following steps:

step 1-1: establishing a switching period average model of a single sub-module of an upper bridge arm;

step 1-2: and establishing a small signal alternating-current model of a single submodule of the upper bridge arm.

In step 1-1, the equation of a single submodule of the upper bridge arm is as follows:

$\left\{\begin{array}{c}{u}_{p1}=S_p{u}_{d1p}\\ i_{d1p}=S_p{i}_p\end{array}\right.---\left(1\right)$

$\left\{\begin{array}{c}\frac{{\mathrm{di}}_p}{\mathrm{dt}}=\frac{1}{L_1}({{-u}_1}^{\′}+S_p{u}_{d1p}-R_s^{\′}{i}_p)\\ \frac{{\mathrm{du}}_{d1p}}{\mathrm{dt}}=\frac{1}{C}(-S_p{i}_p-\frac{u_{d1p}}{R_1})\end{array}\right.---\left(2\right)$

wherein u is_p1For a single submodule output voltage u of the upper bridge arm_d1pFor a single sub-module DC voltage of the upper bridge arm, i_d1pIs as followsDirect discharge current of single submodule of bridge arm, i_pOutputting current for a single submodule of an upper bridge arm; s_pRepresenting the switching function, S_p∈[0，1]，S_p1 denotes that the IGBT connected in parallel with the ac output of the submodule is switched off, the other IGBT is switched on, S_pWhen the voltage is equal to 0, the IGBT connected with the alternating current output end of the submodule in parallel is turned on, and the other IGBT is turned off;

L₁for a single sub-module inductance of the upper bridge arm, L₁＝L/N，U_d1p＝U_dN, L is bridge arm reactance, U_dFor common DC bus voltage, C for individual sub-module support capacitors, u₁'is the sum of the output voltage of a single submodule and the reactive voltage drop of a bridge arm, R'_sIs an equivalent series resistance, R, of a submodule series reactor₁A loss equivalent resistance of a main circuit of the submodule;

averaging the switching cycles of (2) to obtain:

$\left\{\begin{array}{c}\frac{d{<i_p>}_{T_s}}{\mathrm{dt}}=\frac{1}{L_1}(-{<{u_1}^{\&prime;}>}_{T_s}+{<S_p{u}_{d1p}>}_{T_s}-R_s^{\&prime;}{<i_p>}_{T_s})\\ \frac{d{<u_{d1p}>}_{T_s}}{\mathrm{dt}}=\frac{1}{C}(-{<S_p{i}_p>}_{T_s}-\frac{{<u_{d1p}>}_{T_s}}{R_1})\end{array}\right.---\left(3\right)$

wherein, T_sWhich is indicative of the switching period of the switch,represents u₁In the switching period T_sThe average value of the values of (a) to (b),denotes S_pu_d1pIn the switching period T_sThe average value of the values of (a) to (b),represents i_pIn the switching period T_sThe average value of the values of (a) to (b),denotes S_pi_pIn the switching period T_sThe average value of the values of (a) to (b),represents u_d1pIn the switching period T_sAverage value of (d); suppose that in the switching period T_sInner, u_d1pAnd i_pThe following approximation can be obtained with little variation:

${<S_p{u}_{d1p}>}_{T_s}\&ap;{<S_p>}_{T_s}{<u_{d1p}>}_{T_s}=d_p{<u_{d1p}>}_{T_s}---\left(4\right)$

${<S_p{i}_p>}_{T_s}\&ap;{<S_p>}_{T_s}{<i_p>}_{T_s}=d_p{<i_p>}_{T_s}---\left(5\right)$

wherein d is_pIs the switching signal duty cycle;

substituting (4) and (5) into (3) to obtain an average model of the switching period of a single submodule of the upper bridge arm as follows:

$\left\{\begin{array}{c}\frac{d{<i_p>}_{T_s}}{\mathrm{dt}}=\frac{1}{L_1}(-{<{u_1}^{\&prime;}>}_{T_s}+d_p{<u_{d1p}>}_{T_s}-R_s^{\&prime;}{<i_p>}_{T_s})\\ \frac{d{<u_{d1p}>}_{T_s}}{\mathrm{dt}}=-\frac{1}{C}(d_p{<i_p>}_{T_s}+\frac{{<u_{d1p}>}_{T_s}}{R_1})\end{array}\right.---\left(6\right).$

in the switching period average model of the single submodule of the upper bridge arm, a controlled voltage source at the AC sideR′_sAnd L₁Sequentially connected in series, controlled voltage sourceThe positive electrode is used as the positive electrode of the output end of the equivalent switch period model of the single submodule of the upper bridge arm, L₁Not with R'_sOne end of the connection is used as the cathode of the output end of the equivalent switch period model of the single sub-module of the upper bridge arm; controlled current source on the direct current sideR₁And C are connected in parallel with each other.

In the step 1-2 of the step,

order:

${<{u_1}^{\&prime;}>}_{T_s}={U_1}^{\&prime;}+{{\tilde{u}}_1}^{\&prime;}$

${<i_p>}_{T_s}=I_p+{\tilde{i}}_p$ (7)

${<u_{d1p}>}_{T_s}=U_{d1p}+{\tilde{u}}_{d1p}$

d_p＝D_p+d_p

in the formula of U₁′，I_p，U_d1p，D_pIs a static working point, and the working point is,d_pis the disturbance quantity; substituting (7) into (6) to obtain

$\left\{\begin{array}{c}\frac{d(I_p+{\tilde{i}}_p)}{\mathrm{dt}}=\frac{1}{L_1}(-{U_1}^{\&prime;}-{\tilde{u}}_1^{\&prime;}+(D_1+d_p)(U_{d1p}+{\tilde{u}}_{d1p})-R_s^{\&prime;}(I_p+{\tilde{i}}_p))\\ \frac{d(U_{d1p}+{\tilde{u}}_{d1p})}{\mathrm{dt}}=\frac{1}{C}(-(D_p+d_p)(I_p+{\tilde{i}}_p)-\frac{U_{d1p}+{\tilde{u}}_{d1p}}{R_1})\end{array}\right.---\left(8\right)$

The following relationship exists due to the static operating points:

$\frac{d{I}_p}{\mathrm{dt}}=0$

$\frac{{\mathrm{dU}}_{d1p}}{\mathrm{dt}}=0---\left(9\right)$

U₁′＝U_d/2-u_s＝D_pU_d1p-R_sI_p

$D_p{I}_p=\frac{U_{d1p}}{R_1}$

wherein u is_sIs the system voltage;

according to the step (8), neglecting high-order terms, obtaining the small signal alternating-current model of the single submodule of the upper bridge arm as follows:

$\left\{\begin{array}{c}\frac{d{\tilde{i}}_p}{\mathrm{dt}}=\frac{1}{L_1}(-{{\tilde{u}}_1}^{\&prime;}+d_p{U}_{d1p}+D_p{\tilde{u}}_{d1p}-R_s^{\&prime;}{\tilde{i}}_p)\\ \frac{d{\tilde{u}}_{d1p}}{\mathrm{dt}}=\frac{1}{C}(-D_p{\tilde{i}}_p-d_p{I}_p-\frac{{\tilde{u}}_{d1p}}{R_1})\end{array}\right.---\left(10\right).$

the upper bridge arm single sub-module small signal alternating-current model comprises an upper bridge arm single sub-module controlled source type small signal alternating-current model and an upper bridge arm single sub-module transfer function block diagram type small signal alternating-current model.

In the controlled source type small-signal alternating-current model of the single submodule of the upper bridge arm, a controlled voltage source d at the alternating-current side_pU_d1pControlled voltage sourceR′_sAnd L₁Sequentially connected in series; controlled voltage source d_pU_d1pThe positive electrode is used as the positive electrode of the output end of the small-signal alternating-current model of the single submodule of the upper bridge arm, L₁Not with R'_sOne end of the connection is used as the negative electrode of the output end of the small signal alternating-current model of the single submodule of the upper bridge arm; controlled current source on the direct current sideControlled current source d_pI_p、R₁And C are connected in parallel with each other; in the upper bridge arm single sub-module transfer function block diagram type small signal alternating current model, an input signal d_p(s) by a proportion link U_d1pGenerated signal, -u₁'(s) and an output signal u_dlp(s) by a proportional element D_pThe generated feedback signal enters an adder 1, and the signal generated by the adder 1 passes through a proportional-integral elementObtain a signal i_p(s) the signal i_p(s) by a proportional segment D_pGenerated signal and input signal d_p(s) by a proportional procedure I_pThe generated signal enters an adder 2, and the signal generated by the adder 2 takes the negative sum and outputs a signal u_dlp(s) via a proportional linkThe generated feedback signal is taken to be negative and enters an adder 3, and the adder 3 generates a signalThe number is subjected to a proportion linkGenerating an output signal u_dlp(s)。

The step 2 comprises the following steps:

step 2-1: the method comprises the following steps of establishing an upper bridge arm switching period average model:

$\left\{\begin{array}{c}\frac{d{<i_p>}_{T_s}}{\mathrm{dt}}=\frac{1}{L}(-{<u_1>}_{T_s}+\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}\left(d_{\mathrm{pj}}{<u_{\mathrm{dj}p}>}_{T_s}\right)-R_s{<i_p>}_{T_s})\\ \frac{d{<u_{\mathrm{djp}}>}_{T_s}}{\mathrm{dt}}=\frac{1}{C}(-d_{\mathrm{pj}}{<i_p>}_{T_s}-\frac{{<u_{\mathrm{djp}}>}_{T_s}}{R_j}),j=\mathrm{1,2},...N\end{array}\right.---\left(11\right)$

wherein R is_jRepresenting the equivalent loss resistance, R, of the sub-module_sFor equivalent series resistance of bridge arm series reactor, d_pjAnd u_djpRespectively representing the equivalent duty ratio and the direct current side voltage of the jth sub-module of the upper bridge arm,represents u_djpIn the switching period T_sAverage value of (d);

step 2-2: establishing an upper bridge arm small signal alternating current model as follows:

$\left\{\begin{array}{c}{<i_p>}_{T_s}=I_p+{\tilde{i}}_p\\ {<u_1>}_{T_s}=U_1+{\tilde{u}}_1\\ {<u_{\mathrm{djp}}>}_{T_s}=U_{\mathrm{djp}}+{\tilde{u}}_{\mathrm{djp}},j=\mathrm{1,2},...,N\\ d_{\mathrm{pj}}=D_{\mathrm{pj}}+d_{\mathrm{pj}},j=\mathrm{1,2},...,N\end{array}\right.---\left(12\right)$

in the formula I_p，U₁，U_djp，D_pjIs a static operating point;for the disturbance quantity, the static working points of the upper bridge arm have the following relations:

$\frac{{\mathrm{dI}}_p}{\mathrm{dt}}=0$

$\frac{{\mathrm{dU}}_{\mathrm{djp}}}{\mathrm{dt}}=0$ (13)

$U_1=U_d/2-u_s=\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}{D}_{\mathrm{pj}}{U}_{\mathrm{djp}}-R_s{I}_p$

$D_{\mathrm{pj}}{I}_p=\frac{U_{\mathrm{djp}}}{R_j}$

the (12) is brought into the (11), and the upper bridge arm small signal alternating current model obtained according to the (13) is

$\left\{\begin{array}{c}\frac{d{\tilde{i}}_p}{\mathrm{dt}}=\frac{1}{L}(-{\tilde{u}}_1+\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}(d_{\mathrm{pj}}{U}_{\mathrm{djp}}+D_{\mathrm{pj}}{\tilde{u}}_{\mathrm{djp}})-R_s{\tilde{i}}_p)\\ \frac{d{\tilde{u}}_{\mathrm{djp}}}{\mathrm{dt}}=\frac{1}{C}(-D_{\mathrm{pj}}{\tilde{i}}_p-d_{\mathrm{pj}}{I}_p-\frac{{\tilde{u}}_{\mathrm{djp}}}{R_j}),j=\mathrm{1,2},...,N\end{array}\right.---\left(14\right)$

In the upper bridge arm switch period average model, the controlled voltage source of each sub-module switch period average model on the AC sideR_sAnd L are connected in series in sequence and controlled by a voltage sourceThe positive electrode is used as the positive electrode of the output end of the upper bridge arm switch period average model, and L is not equal to R_sOne end of the connection is used as the output end cathode of the upper bridge arm switching period average model; controlled current source of switch period average model of each submodule on direct current sideR_jAnd C are connected in parallel with each other.

The upper bridge arm small signal alternating current model comprises an upper bridge arm controlled source type small signal alternating current model and an upper bridge arm transfer function block diagram type small signal alternating current model;

in the upper bridge arm controlled source form small signal alternating current model, the controlled voltage source d of each sub-module small signal alternating current model at the alternating current side_pjU_djpControlled voltage sourceR_sAnd L are connected in series in sequence; controlled voltage source d_pNU_dNpThe positive electrode is used as the positive electrode of the output end of the upper bridge arm small signal alternating current model, and L is not equal to R_sOne end of the connection is used as the negative electrode of the output end of the upper bridge arm small signal alternating current model; controlled current source of small-signal alternating-current model of each submodule on direct-current sideControlled current source d_pjI_p、R_jAnd C are respectively connected in parallel;

in the upper bridge arm transfer function block diagram type small signal alternating current model, N input signals d_pj(s) passing through corresponding N proportional links U_djpGenerated signal and input signal-u₁(s) enter adder 1'; the signal generated by the adder 1' and the corresponding N output signals u_djp(s) by a proportional element D_pjThe generated feedback signal enters an adder 2'; the signal generated by the adder 2' passes through a proportional integral elementObtain a signal i_p(s) the signal i_p(s) by N proportional steps D_pjRespectively generated N signals and corresponding N input signals d_pj(s) by a proportional procedure I_pThe resulting signals go to corresponding N adders 3 j'The signals generated by the N adders 3 j' take the negative sum of the corresponding N output signals u_djp(s) via a proportional linkThe resulting feedback signal takes the negative of the N adders 4 j. The signals generated by the N adders 4j pass through the corresponding N proportion linksGenerating N output signals u_djp(s)。

Assuming that parameters of each submodule of an upper bridge arm are symmetrical, and the parameters comprise:

d_p1＝d_p2＝...＝d_pN＝d_p(15)

u_d1p＝u_d2p＝...＝u_dNp＝u_dp(16)

getStatic working point of upper bridge arm small signal alternating current model is changed into

$\frac{{\mathrm{dI}}_p}{\mathrm{dt}}=0,\frac{{\mathrm{dU}}_{\mathrm{dp}}}{\mathrm{dt}}=0$

D_pI_p＝U_dp/R

NU_dp＝U_d(18)

U₁＝U_d/2-u_s＝ND_pU_dp-R_sI_p

D_p≈(U_d/2-u_s)/NU_dp＝1/2-u_s/NU_dp

Thus obtaining a simplified upper bridge arm small signal alternating-current model of

$\left\{\begin{array}{c}\frac{d{\tilde{i}}_p}{\mathrm{dt}}=\frac{1}{L}(-{\tilde{u}}_1+({\mathrm{Nd}}_p{U}_{\mathrm{dp}}+{\mathrm{ND}}_p{\tilde{u}}_{\mathrm{dp}})-R_s{\tilde{i}}_p)\\ \frac{d{\tilde{u}}_{\mathrm{dp}}}{\mathrm{dt}}=\frac{1}{C}(-D_p{\tilde{i}}_p-d_p{I}_p-\frac{{\tilde{u}}_{\mathrm{dp}}}{R})\end{array}\right.---\left(19\right)$

Wherein R represents the loss equivalent resistance of the bridge arm main circuit.

The simplified upper bridge arm small signal alternating current model comprises a simplified upper bridge arm controlled source form small signal alternating current model and a simplified upper bridge arm transfer function block diagram form small signal alternating current model.

In the simplified upper bridge arm controlled source form small signal alternating current model, the alternating current side is controlledVoltage source Nd_pU_dpControlled voltage sourceR_sAnd L are connected in series in sequence and controlled by a voltage source Nd_pU_dpThe positive electrode is used as the positive electrode of the output end of the simplified upper bridge arm controlled source type small signal alternating current model, and L is not equal to R_sOne end of the connection is used as the cathode of the output end of the simplified upper bridge arm controlled source type small signal alternating current model; controlled current source on the direct current sideControlled current source d_pI_pR and C are connected in parallel; in the simplified upper bridge arm transfer function block diagram type small signal alternating current model, an input signal d_p(s) by the proportional link NU_dpGenerated signal and input signal-u₁(s) into adder 1 ', adder 1' generates a signal and an output signal u_dp(s) pass ratio Link ND_pThe generated feedback signal enters an adder 2 ', and the signal generated by the adder 2' passes through a proportional-integral elementObtain a signal i_p(s), signal i_p(s) by a proportional segment D_pGenerated signal and input signal d_p(s) by a proportional procedure I_pThe resulting signal enters an adder 3 ', the signal produced by the adder 3' takes the negative of the sum output signal u_dp(s) via a proportional linkThe generated feedback signal is taken as negative and enters an adder 4, and the signal generated by the adder 4 passes through a proportion linkGenerating an output signal u_dp(s)。

The step 3 comprises the following steps:

step 3-1: establishing a switching period average model of a single sub-module of a lower bridge arm and a small signal alternating-current model of the single sub-module of the lower bridge arm;

step 3-2: establishing a lower bridge arm switching period average model;

$\left\{\begin{array}{c}\frac{d{<i_n>}_{T_s}}{\mathrm{dt}}=\frac{1}{L}({<u_2>}_{T_s}-\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}\left(d_{\mathrm{nj}}{<u_{\mathrm{djn}}>}_{T_s}\right)+R_s{<i_n>}_{T_s})\\ \frac{d{<u_{\mathrm{djn}}>}_{T_s}}{\mathrm{dt}}=\frac{1}{C}(d_{\mathrm{nj}}{<i_n>}_{T_s}+\frac{{<u_{\mathrm{djn}}>}_{T_s}}{R_j}),j=\mathrm{1,2},...N\end{array}\right.---\left(20\right)$

wherein d is_njAnd u_djnRespectively representing the equivalent duty ratio and the direct-current side voltage of the jth sub-module of the lower bridge arm,represents u_djnIn the switching period T_sAverage value of (d);

step 3-3: a lower bridge arm small signal alternating current model;

$\left\{\begin{array}{c}{u}_1=U_d/2-u_s\\ u_2=U_d/2+u_s\end{array}\right.---\left(21\right)$

and has the following components:

d_n1＝d_n2＝...＝d_nN＝d_n(22)

u_d1n＝u_d2n＝...u_dNn＝u_dn(23)

get $u_{\mathrm{dn}}=\frac{1}{N}\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}{u}_{\mathrm{djn}},$ Can obtain the product

D_n≈(U_d/2+u_s)/NU_dn＝1/2+u_s/NU_dn＝1/2+u_s/U_d(24)

D_nIs a static operating point;

thus obtaining a simplified lower bridge arm small signal alternating-current model of

$\left\{\begin{array}{c}\frac{d{\tilde{i}}_n}{\mathrm{dt}}=\frac{1}{L}({\tilde{u}}_2-({\mathrm{Nd}}_n{U}_{\mathrm{dn}}+{\mathrm{ND}}_n{\tilde{u}}_{\mathrm{dn}})-R_s{\tilde{i}}_n)\\ \frac{d{\tilde{u}}_{\mathrm{dn}}}{\mathrm{dt}}=\frac{1}{C}(D_n{\tilde{i}}_n+d_n{I}_n-\frac{{\tilde{u}}_{\mathrm{dn}}}{R})\end{array}\right.---\left(25\right).$

In the lower bridge arm switch period average model, the controlled voltage source of each sub-module switch period average model on the AC sideR_sAnd L are connected in series in sequence and controlled by a voltage sourceThe positive electrode is used as the positive electrode of the output end of the lower bridge arm switch period average model, and L is not equal to R_sOne end of the connection is used as the output end cathode of the lower bridge arm switching period average model; controlled current source of single sub-module switch period average model on direct current sideR_jAnd C are connected in parallel with each other.

The lower bridge arm small signal alternating current model comprises a simplified lower bridge arm controlled source form small signal alternating current model and a simplified lower bridge arm transfer function block diagram form small signal alternating current model;

l, R on the AC side in the simplified lower bridge arm controlled source form small signal AC model_sControlled voltage source Nd_nU_dnAnd a controlled voltage sourceAre sequentially connected in series, L is not connected with R_sOne end of the connection is used as the positive electrode of the output end of the simplified lower bridge arm controlled source type small signal alternating current model, and the controlled voltage sourceThe negative electrode is used as the negative electrode of the output end of the simplified lower bridge arm controlled source type small signal alternating current model; controlled current source on the direct current sideControlled current source d_nI_nR and C are connected in parallel;

in the simplified lower bridge arm transfer function block diagram type small signal alternating current model, an input signal d_n(s) by the proportional link NU_dnThe resulting signal is negated and the input signal u is summed₂(s) into adder 1'; output signal u_dn(s) pass ratio Link ND_nThe generated feedback signal is taken as negative and the signal generated by the adder 1 ' is fed into the adder 2 ', and the signal generated by the adder 2 ' is passed through a proportional-integral elementObtain a signal i_n(s), signal i_n(s) the signal generated by the proportional element Dn and the input signal d_n(s) by a proportional procedure I_nThe resulting signal enters the adder 3' ", and the output signal u_dn(s) via a proportional linkThe generated feedback signal is taken as the negative of the signal generated by the adder 3 ' ″ and fed into the adder 4 ' ″, and the signal generated by the adder 4 ' ″ passes through the proportional elementGenerating an output signal u_dn(s)。

The step 4 comprises the following steps:

step 4-1: the method comprises the following steps of establishing a switching period average model of an upper bridge arm and a lower bridge arm of the modular multilevel converter as follows:

$\left\{\begin{array}{c}\frac{d\stackrel{\&RightArrow;}{i_p}}{\mathrm{dt}}=\frac{1}{L}(-\stackrel{\&RightArrow;}{u_1}+{\mathrm{ND}}_p\stackrel{\&RightArrow;}{u_{\mathrm{dp}}}-R_s\stackrel{\&RightArrow;}{i_p})\\ \frac{d\stackrel{\&RightArrow;}{u_{\mathrm{dp}}}}{\mathrm{dt}}=-\frac{1}{C}{D}_p\stackrel{\&RightArrow;}{i_p}-\frac{\stackrel{\&RightArrow;}{u_{\mathrm{dp}}}}{\mathrm{RC}}\end{array}\right.---\left(26\right)$

$\left\{\begin{array}{c}\frac{d\stackrel{\&RightArrow;}{i_n}}{\mathrm{dt}}=\frac{1}{L}(\stackrel{\&RightArrow;}{u_2}-{\mathrm{ND}}_n\stackrel{\&RightArrow;}{u_{\mathrm{dn}}}-R_s\stackrel{\&RightArrow;}{i_n})\\ \frac{d\stackrel{\&RightArrow;}{u_{\mathrm{dn}}}}{\mathrm{dt}}=\frac{1}{C}{D}_n\stackrel{\&RightArrow;}{i_n}-\frac{\stackrel{\&RightArrow;}{u_{\mathrm{dn}}}}{\mathrm{RC}}\end{array}\right.---\left(27\right)$

$\left\{\begin{array}{c}\stackrel{\&RightArrow;}{i_s}=\stackrel{\&RightArrow;}{i_p}+\stackrel{\&RightArrow;}{i_n}\\ {<i_d>}_{\mathrm{Ts}}=\left[\begin{array}{ccc}1& 1& 1\end{array}\right]\stackrel{\&RightArrow;}{i_p}=-\left[\begin{array}{ccc}1& 1& 1\end{array}\right]\stackrel{\&RightArrow;}{i_n}\end{array}\right.---\left(28\right)$

wherein, $\stackrel{\&RightArrow;}{i_p}={\left[\begin{array}{ccc}{<i_{\mathrm{pa}}>}_{T_s}& {<i_{\mathrm{pb}}>}_{T_s}& {<i_{\mathrm{pc}}>}_{T_s}\end{array}\right]}^T,$ $\stackrel{\&RightArrow;}{u_1}={\left[\begin{array}{ccc}{<u_{1a}>}_{T_s}& {<u_{1b}>}_{T_s}& {<u_{1c}>}_{T_s}\end{array}\right]}^T,$

D_p＝diag[d_pad_pbd_pc]， ${\stackrel{\&RightArrow;}{u_{\mathrm{dp}}}}^T={\left[\begin{array}{ccc}{<u_{\mathrm{dap}}>}_{T_s}& {<u_{\mathrm{dbp}}>}_{T_s}& {<u_{\mathrm{dcp}}>}_{T_s}\end{array}\right]}^T,$

$\stackrel{\&RightArrow;}{i_n}={\left[\begin{array}{ccc}{<i_{\mathrm{na}}>}_{T_s}& {<i_{\mathrm{nb}}>}_{T_s}& {<i_{\mathrm{nc}}>}_{T_s}\end{array}\right]}^T,$ $\stackrel{\&RightArrow;}{u_2}={\left[\begin{array}{ccc}{<u_{2a}>}_{T_s}& {<u_{2b}>}_{T_s}& {<u_{2c}>}_{T_s}\end{array}\right]}^T,$

D_n＝diag[d_nad_nbd_nc]， ${\stackrel{\&RightArrow;}{u_{\mathrm{dn}}}}^T={\left[\begin{array}{ccc}{<u_{\mathrm{dan}}>}_{T_s}& {<u_{\mathrm{dbn}}>}_{T_s}& {<u_{\mathrm{dcn}}>}_{T_s}\end{array}\right]}^T,$

${\stackrel{\&RightArrow;}{i_s}}^T={\left[\begin{array}{ccc}{<i_{\mathrm{sa}}>}_{T_s}& {<i_{\mathrm{sb}}>}_{T_s}& {<i_{\mathrm{sc}}>}_{T_s}\end{array}\right]}^T,$ the corner mark p represents an upper bridge arm module, and the corner mark n represents a lower bridge arm module;

wherein, $\stackrel{\&RightArrow;}{u_1}=\left[\begin{array}{c}{<u_{1a}>}_{T_s}\\ {<u_{1b}>}_{T_s}\\ {<u_{1c}>}_{T_s}\end{array}\right]=\frac{{<U_d>}_{\mathrm{Ts}}}{2}\left[\begin{array}{c}1\\ 1\\ 1\end{array}\right]-\left[\begin{array}{c}{<u_{a0}>}_{T_s}\\ {<u_{b0}>}_{T_s}\\ {<u_{c0}>}_{T_s}\end{array}\right]=\frac{{<U_d>}_{\mathrm{Ts}}}{2}\left[\begin{array}{c}1\\ 1\\ 1\end{array}\right]-\left[\begin{array}{c}{<u_{\mathrm{sa}}>}_{T_s}\\ {<u_{\mathrm{sb}}>}_{T_s}\\ {<u_{\mathrm{sc}}>}_{T_s}\end{array}\right]-{<u_{N0}>}_{T_s}\left[\begin{array}{c}1\\ 1\\ 1\end{array}\right]---\left(29\right)$

$\stackrel{\&RightArrow;}{u_2}=\left[\begin{array}{c}{<u_{2a}>}_{T_s}\\ {<u_{2b}>}_{T_s}\\ {<u_{2c}>}_{T_s}\end{array}\right]=\frac{{<U_d>}_{\mathrm{Ts}}}{2}\left[\begin{array}{c}1\\ 1\\ 1\end{array}\right]+\left[\begin{array}{c}{<u_{a0}>}_{T_s}\\ {<u_{b0}>}_{T_s}\\ {<u_{c0}>}_{T_s}\end{array}\right]=\frac{{<U_d>}_{\mathrm{Ts}}}{2}\left[\begin{array}{c}1\\ 1\\ 1\end{array}\right]+\left[\begin{array}{c}{<u_{\mathrm{sa}}>}_{T_s}\\ {<u_{\mathrm{sb}}>}_{T_s}\\ {<u_{\mathrm{sc}}>}_{T_s}\end{array}\right]+{<u_{N0}>}_{T_s}\left[\begin{array}{c}1\\ 1\\ 1\end{array}\right]---\left(30\right)$

u_N0is the AC side common mode voltage;

step 4-2: a small signal alternating current model of the modular multilevel converter;

the static operating points of the modular multilevel converter are as follows:

$\left\{\begin{array}{c}\frac{{\mathrm{dI}}_{\mathrm{pi}}}{\mathrm{dt}}=0,\frac{{\mathrm{dU}}_{\mathrm{dip}}}{\mathrm{dt}}=0\\ {\mathrm{NU}}_{\mathrm{dip}}=U_d\\ -U_d/2+u_{\mathrm{si}}+u_{N0}+D_{\mathrm{pi}}{\mathrm{NU}}_{\mathrm{dip}}-R_s{I}_{\mathrm{pi}}\text{=0}\end{array}\right.i=a,b,c---\left(31\right)$

$\left\{\begin{array}{c}\frac{{\mathrm{dI}}_{\mathrm{ni}}}{\mathrm{dt}}=0,\frac{{\mathrm{dU}}_{\mathrm{din}}}{\mathrm{dt}}=0\\ {\mathrm{NU}}_{\mathrm{din}}=U_d\\ U_d/2+u_{\mathrm{si}}+u_{N0}-D_{\mathrm{ni}}{\mathrm{NU}}_{\mathrm{din}}-R_s{I}_{\mathrm{ni}}\text{=0}\end{array}\right.i=a,b,c---\left(32\right)$

obtaining small signal alternating current models of an upper bridge arm and a lower bridge arm of the modular multilevel converter:

$\left\{\begin{array}{cc}\frac{d{\tilde{i}}_{\mathrm{pi}}}{\mathrm{dt}}=\frac{1}{L}(-\frac{{\tilde{u}}_d}{2}+{\tilde{u}}_{\mathrm{si}}+{\tilde{u}}_{N0}+{\mathrm{ND}}_{\mathrm{pi}}{\tilde{u}}_{\mathrm{dpi}}+N{\tilde{d}}_{\mathrm{pi}}{U}_{\mathrm{dpi}}-R_s{\tilde{i}}_{\mathrm{pi}})& \\ \frac{d{\tilde{u}}_{\mathrm{dpi}}}{\mathrm{dt}}=-\frac{1}{C}(D_{\mathrm{pi}}{\tilde{i}}_{\mathrm{pi}}+{\tilde{d}}_{\mathrm{pi}}{I}_{\mathrm{pi}})-\frac{{\tilde{u}}_{\mathrm{dpi}}}{\mathrm{RC}}& i=a,b,c\end{array}\right.---\left(33\right)$

$\left\{\begin{array}{cc}\frac{d{\tilde{i}}_{\mathrm{ni}}}{\mathrm{dt}}=\frac{1}{L}(\frac{{\tilde{u}}_d}{2}+{\tilde{u}}_{\mathrm{si}}+{\tilde{u}}_{N0}-{\mathrm{ND}}_{\mathrm{ni}}{\tilde{u}}_{\mathrm{dni}}-N{\tilde{d}}_{\mathrm{ni}}{U}_{\mathrm{dni}}-R_s{\tilde{i}}_{\mathrm{ni}})& \\ \frac{d{\tilde{u}}_{\mathrm{dni}}}{\mathrm{dt}}=\frac{1}{C}(D_{\mathrm{ni}}{\tilde{i}}_{\mathrm{ni}}+{\tilde{d}}_{\mathrm{ni}}{I}_{\mathrm{ni}})-\frac{{\tilde{u}}_{\mathrm{dni}}}{\mathrm{RC}}& i=a,b,c\end{array}\right.---\left(34\right)$

$\left\{\begin{array}{c}{\tilde{i}}_{\mathrm{si}}={\tilde{i}}_{\mathrm{pi}}+{\tilde{i}}_{\mathrm{ni}}\\ {\tilde{i}}_d=\underset{i=a,b,c}{\mathrm{\&Sigma;}}{\tilde{i}}_{\mathrm{pi}}=-\underset{i=a,b,c}{\mathrm{\&Sigma;}}{\tilde{i}}_{\mathrm{ni}}\end{array}\right.---\left(35\right).$

in the modular multilevel converter upper bridge arm switching period average model, an upper bridge arm controlled voltage source Nd_pi<u_dip>T_s、R_sAnd L are connected in series in sequence, and the upper bridge arm is controlled by a current source d_pi<i_pi>T_sR and C are connected in parallel; l, R in the average model of the switching period of the lower bridge arm of the modular multilevel converter_sAnd a lower bridge arm controlled voltage source Nd_ni<u_din>T_sSerially connected, controlled current source d_ni<i_ni>T_sAnd R and C are mutually connected in parallel to form a lower bridge arm equivalent switching period average model.

In the small-signal alternating current model of the modular multilevel converter, a signal i_pi(s) and signal i_ni(s) entering an adder to generate a signal i_si(s), signalSignal-u_si(s) and signal-u_N0(s) entering an adder to generate a signal u_1i(s), signalSignal u_si(s) sum signal u_N0(s) entering an adder to generate a signal u_2i(s)；

In the modular multilevel converter upper bridge arm small signal alternating current model, an input signal d_pi(s) by the proportional link NU_dipGenerated signal and input signal-u_1i(s) into an adder A, the signal generated by adder A and the output signal u_dip(s) pass ratio Link ND_piThe generated feedback signal enters an adder B, and the signal generated by the adder B passes through a proportional-integral linkObtain a signal i_pi(s), signal i_pi(s) by a proportional segment D_piGenerated signal and input signal d_pi(s) by a proportional procedure I_piThe generated signal enters an adder C, and the signal generated by the adder C takes the negative sum and outputs a signal u_dip(s) via a proportional linkThe generated feedback signal is taken as negative and enters an adder D, and the signal generated by the adder D passes through a proportion linkGenerating an output signal u_dip(s)；

In the modular multilevel converter lower bridge arm small signal alternating current model, an input signal d_ni(s) by the proportional link NU_dinThe resulting signal is negated and the input signal u is summed_2i(s) into an adder E, outputting the signal u_din(s) pass ratio Link ND_niThe generated feedback signal is taken as the negative sum, the signal generated by the adder E enters the adder F, and the signal generated by the adder F passes through a proportional-integral linkObtain a signal i_ni(s), signal i_ni(s) by a proportional segment D_niGenerated signal and input signal d_ni(s) by a proportional procedure I_mThe resulting signal enters adder G, which outputs signal u_din(s) via a proportional linkThe generated feedback signal is taken as the negative sum, the signal generated by the adder G enters the adder H, and the signal generated by the adder H passes through a proportion linkGenerating an output signal u_din(s)。

Compared with the prior art, the invention has the beneficial effects that:

1. the dynamic model of the modular multilevel converter lays a solid foundation for characteristic analysis and control strategies of power electronic devices such as a unified power flow controller and flexible direct-current transmission;

2. the dynamic model of the modular multilevel converter is convenient to analyze with the dynamic performance of the modular multilevel converter;

3. the dynamic model of the modular multilevel converter is convenient for analyzing the frequency response of the modular multilevel converter;

4. the dynamic model of the modular multilevel converter is convenient for the design of a device-level control strategy;

5. the dynamic model of the modular multilevel converter realizes the description of the internal state quantity of the model;

6. the modeling method is simple, reliable and easy to implement.

Drawings

FIG. 1 is a schematic diagram of a dynamic model main circuit topology of a modular multilevel converter;

FIG. 2 is a schematic diagram of a sub-module main circuit;

FIG. 3 is an equivalent circuit diagram of a single submodule of an upper bridge arm;

FIG. 4 is a diagram of an average switching period model of a single submodule of an upper bridge arm;

FIG. 5 is a diagram of an upper bridge arm single sub-module controlled source type small signal alternating current model;

FIG. 6 is a block diagram of a small signal alternating current model in the form of an upper bridge arm single sub-module transfer function;

FIG. 7 is a diagram of an upper arm switching period averaging model;

FIG. 8 is a diagram of an upper arm controlled source form small signal alternating current model;

FIG. 9 is a block diagram of a small signal AC model of the upper arm transfer function;

FIG. 10 is a simplified upper arm controlled source form small signal AC model diagram;

FIG. 11 is a simplified upper arm transfer function block diagram representation of a small signal AC model;

FIG. 12 is a simplified lower arm controlled source form small signal AC model diagram;

FIG. 13 is a simplified lower leg transfer function block diagram version of the small signal AC model;

fig. 14 is a diagram of a switching period averaging model of a modular multilevel converter;

fig. 15 is a small-signal ac model diagram of a modular multilevel converter.

Detailed Description

The present invention will be described in further detail with reference to the accompanying drawings.

A method for modeling a dynamic model of a modular multilevel converter, the method comprising the steps of:

step 1: establishing an upper bridge arm single sub-module switching period average model and an upper bridge arm single sub-module small signal alternating current model;

step 2: establishing an upper bridge arm switching period average model and an upper bridge arm small signal alternating current model;

and step 3: establishing a lower bridge arm switching period average model and a lower bridge arm small signal alternating-current model;

and 4, step 4: and establishing a modular multilevel converter switching period average model and a modular multilevel converter small signal model.

As shown in fig. 1-2, the modular multilevel converter includes three pairs of bridge arms, each pair of bridge arms includes an upper bridge arm and a lower bridge arm, each of the upper bridge arm and the lower bridge arm includes N sub-modules and reactors connected in series, and the three pairs of bridge arms are connected in parallel to lead out a common direct current terminal.

The step 1 comprises the following steps:

step 1-1: establishing a switching period average model of a single sub-module of an upper bridge arm;

step 1-2: and establishing a small signal alternating-current model of a single submodule of the upper bridge arm.

In step 1-1, as shown in fig. 3, the equation of a single submodule of the upper bridge arm is:

$\left\{\begin{array}{c}{u}_{p1}=S_p{u}_{d1p}\\ i_{d1p}=S_p{i}_p\end{array}\right.---\left(1\right)$

$\left\{\begin{array}{c}\frac{{\mathrm{di}}_p}{\mathrm{dt}}=\frac{1}{L_1}({{-u}_1}^{\&prime;}+S_p{u}_{d1p}-R_s^{\&prime;}{i}_p)\\ \frac{{\mathrm{du}}_{d1p}}{\mathrm{dt}}=\frac{1}{C}(-S_p{i}_p-\frac{u_{d1p}}{R_1})\end{array}\right.---\left(2\right)$

wherein u is_p1For a single submodule output voltage u of the upper bridge arm_d1pFor a single sub-module DC voltage of the upper bridge arm, i_d1pFor a direct discharge current of a single submodule of the upper bridge arm, i_pOutputting current for a single submodule of an upper bridge arm; s_pRepresenting the switching function, S_p∈[0，1]，S_l1 means that the IGB2 connected in parallel with the ac output of the submodule is switched off, the IGBT1 is switched on, and S is_p0 denotes the AC output with submodule andthe IGBT2 of the pair is turned on, and the IGBT1 is turned off;

L₁for a single sub-module inductance of the upper bridge arm, L₁＝L/N，U_d1p＝U_dN, L is bridge arm reactance, U_dFor common DC bus voltage, C for individual sub-module support capacitors, u₁'is the sum of the output voltage of a single submodule and the reactive voltage drop of a bridge arm, R'_sIs an equivalent series resistance, R, of a submodule series reactor₁A loss equivalent resistance of a main circuit of the submodule;

averaging the switching cycles of (2) to obtain:

$\left\{\begin{array}{c}\frac{d{<i_p>}_{T_s}}{\mathrm{dt}}=\frac{1}{L_1}(-{<{u_1}^{\&prime;}>}_{T_s}+{<S_p{u}_{d1p}>}_{T_s}-R_s^{\&prime;}{<i_p>}_{T_s})\\ \frac{d{<u_{d1p}>}_{T_s}}{\mathrm{dt}}=\frac{1}{C}(-{<S_p{i}_p>}_{T_s}-\frac{{<u_{d1p}>}_{T_s}}{R_1})\end{array}\right.---\left(3\right)$

wherein, T_sWhich is indicative of the switching period of the switch,represents u₁In the switching period T_sThe average value of the values of (a) to (b),denotes S_pu′_d1pIn the switching period T_sThe average value of the values of (a) to (b),represents i_pIn the switching period T_sThe average value of the values of (a) to (b),denotes S_pi_pIn the switching period T_sThe average value of the values of (a) to (b),represents u_d1pIn the switching period T_sAverage value of (d); suppose that in the switching period T_sInner, u_d1pAnd i_pThe following approximation can be obtained with little variation:

${<S_p{u}_{d1p}>}_{T_s}\&ap;{<S_p>}_{T_s}{<u_{d1p}>}_{T_s}=d_p{<u_{d1p}>}_{T_s}---\left(4\right)$

${<S_p{i}_p>}_{T_s}\&ap;{<S_p>}_{T_s}{<i_p>}_{T_s}=d_p{<i_p>}_{T_s}---\left(5\right)$

wherein d is_pIs the switching signal duty cycle;

substituting (4) and (5) into (3) to obtain an average model of the switching period of a single submodule of the upper bridge arm as follows:

$\left\{\begin{array}{c}\frac{d{<i_p>}_{T_s}}{\mathrm{dt}}=\frac{1}{L_1}(-{<{u_1}^{\&prime;}>}_{T_s}+d_p{<u_{d1p}>}_{T_s}-R_s^{\&prime;}{<i_p>}_{T_s})\\ \frac{d{<u_{d1p}>}_{T_s}}{\mathrm{dt}}=-\frac{1}{C}(d_p{<i_p>}_{T_s}+\frac{{<u_{d1p}>}_{T_s}}{R_1})\end{array}\right.---\left(6\right).$

referring to fig. 4, in the switching period averaging model of the single submodule of the upper bridge arm, the controlled voltage source on the alternating current sideR′_sAnd L₁Sequentially connected in series, controlled voltage sourceThe positive electrode is used as the positive electrode of the output end of the equivalent switch period model of the single submodule of the upper bridge arm, L₁Not with R'_sOne end of the connection is used as the cathode of the output end of the equivalent switch period model of the single sub-module of the upper bridge arm; controlled current source on the direct current sideR₁And C are connected in parallel with each other.

In the step 1-2 of the step,

order:

${<{u_1}^{\&prime;}>}_{T_s}={U_1}^{\&prime;}+{{\tilde{u}}_1}^{\&prime;}$

${<i_p>}_{T_s}=I_p+{\tilde{i}}_p$ (7)

${<u_{d1p}>}_{T_s}=U_{d1p}+{\tilde{u}}_{d1p}$

d_p＝D_p+d_p

in the formula of U₁′，I_p，U_d1p，D_pIs a static working point, and the working point is,d_pis the disturbance quantity; substituting (7) into (6) to obtain

$\left\{\begin{array}{c}\frac{d(I_p+{\tilde{i}}_p)}{\mathrm{dt}}=\frac{1}{L_1}(-{U_1}^{\&prime;}-{\tilde{u}}_1^{\&prime;}+(D_1+d_p)(U_{d1p}+{\tilde{u}}_{d1p})-R_s^{\&prime;}(I_p+{\tilde{i}}_p))\\ \frac{d(U_{d1p}+{\tilde{u}}_{d1p})}{\mathrm{dt}}=\frac{1}{C}(-(D_p+d_p)(I_p+{\tilde{i}}_p)-\frac{U_{d1p}+{\tilde{u}}_{d1p}}{R_1})\end{array}\right.---\left(8\right)$

The following relationship exists due to the static operating points:

$\frac{{\mathrm{dI}}_p}{\mathrm{dt}}=0$

$\frac{{\mathrm{dU}}_{d1p}}{\mathrm{dt}}=0---\left(9\right)$

U₁′＝U_d/2-u_s＝D_pU_d1p-R_sI_p

$D_p{I}_p=\frac{U_{d1p}}{R_1}$

wherein u is_sIs the system voltage;

according to the step (8), neglecting high-order terms, obtaining the small signal alternating-current model of the single submodule of the upper bridge arm as follows:

$\left\{\begin{array}{c}\frac{d{\tilde{i}}_p}{\mathrm{dt}}=\frac{1}{L_1}(-{{\tilde{u}}_1}^{\&prime;}+d_p{U}_{d1p}+D_p{\tilde{u}}_{d1p}-R_s^{\&prime;}{\tilde{i}}_p)\\ \frac{d{\tilde{u}}_{d1p}}{\mathrm{dt}}=\frac{1}{C}(-D_p{\tilde{i}}_p-d_p{I}_p-\frac{{\tilde{u}}_{d1p}}{R_1})\end{array}\right.---\left(10\right).$

the upper bridge arm single sub-module small signal alternating-current model comprises an upper bridge arm single sub-module controlled source type small signal alternating-current model and an upper bridge arm single sub-module transfer function block diagram type small signal alternating-current model.

As shown in fig. 5, the single submodule controlled source form small signal of the upper bridge armIn the AC model, the controlled voltage source d on the AC side_pU_d1pControlled voltage sourceR′_sAnd L₁Sequentially connected in series; controlled voltage source d_pU_d1pThe positive electrode is used as the positive electrode of the output end of the small-signal alternating-current model of the single submodule of the upper bridge arm, L₁Not with R'_sOne end of the connection is used as the negative electrode of the output end of the small signal alternating-current model of the single submodule of the upper bridge arm; controlled current source on the direct current sideControlled current source d_pI_p、R₁And C are connected in parallel with each other; as shown in fig. 6, in the small-signal alternating-current model in the form of the transfer function block diagram of the single sub-module of the upper bridge arm, 3 adders are an adder 1, an adder 2 and an adder 3 from left to right in sequence, and an input signal d_p(s) by a proportion link U_d1pGenerated signal, -u₁'(s) and an output signal u_dlp(s) by a proportional element D_pThe generated feedback signal enters an adder 1, and the signal generated by the adder 1 passes through a proportional-integral elementObtain a signal i_p(s) the signal i_p(s) by a proportional segment D_pGenerated signal and input signal d_p(s) by a proportional procedure I_pThe generated signal enters an adder 2, and the signal generated by the adder 2 takes the negative sum and outputs a signal u_dp(s) via a proportional linkThe generated feedback signal is taken as negative and enters an adder 3, and the signal generated by the adder 3 passes through a proportion linkGenerating an output signal u_dlp(s)。

The step 2 comprises the following steps:

step 2-1: the method comprises the following steps of establishing an upper bridge arm switching period average model:

$\left\{\begin{array}{c}\frac{d{<i_p>}_{T_s}}{\mathrm{dt}}=\frac{1}{L}(-{<u_1>}_{T_s}+\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}\left(d_{\mathrm{pj}}{<u_{\mathrm{dj}p}>}_{T_s}\right)-R_s{<i_p>}_{T_s})\\ \frac{d{<u_{\mathrm{djp}}>}_{T_s}}{\mathrm{dt}}=\frac{1}{C}(-d_{\mathrm{pj}}{<i_p>}_{T_s}-\frac{{<u_{\mathrm{djp}}>}_{T_s}}{R_j}),j=\mathrm{1,2},...N\end{array}\right.---\left(11\right)$

wherein R is_jRepresenting the equivalent loss resistance, R, of the sub-module_sFor equivalent series resistance of bridge arm series reactor, d_pjAnd u_djpRespectively representing the equivalent duty ratio and the direct current side voltage of the jth sub-module of the upper bridge arm,represents u_djpIn the switching period T_sAverage value of (d);

step 2-2: establishing an upper bridge arm small signal alternating current model as follows:

$\left\{\begin{array}{c}{<i_p>}_{T_s}=I_p+{\tilde{i}}_p\\ {<u_1>}_{T_s}=U_1+{\tilde{u}}_1\\ {<u_{\mathrm{djp}}>}_{T_s}=U_{\mathrm{djp}}+{\tilde{u}}_{\mathrm{djp}},j=\mathrm{1,2},...,N\\ d_{\mathrm{pj}}=D_{\mathrm{pj}}+d_{\mathrm{pj}},j=\mathrm{1,2},...,N\end{array}\right.---\left(12\right)$

in the formula I_p，U₁，U_djp，D_pjIs a static operating point;d_pjfor the disturbance quantity, the static working points of the upper bridge arm have the following relations:

$\frac{{\mathrm{dI}}_p}{\mathrm{dt}}=0$

$\frac{{\mathrm{dU}}_{\mathrm{djp}}}{\mathrm{dt}}=0$ (13)

$U_1=U_d/2-u_s=\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}{D}_{\mathrm{pj}}{U}_{\mathrm{djp}}-R_s{I}_p$

$D_{\mathrm{pj}}{I}_p=\frac{U_{\mathrm{djp}}}{R_j}$

the (12) is brought into the (11), and the upper bridge arm small signal alternating current model obtained according to the (13) is

$\left\{\begin{array}{c}\frac{d{\tilde{i}}_p}{\mathrm{dt}}=\frac{1}{L}(-{\tilde{u}}_1+\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}(d_{\mathrm{pj}}{U}_{\mathrm{djp}}+D_{\mathrm{pj}}{\tilde{u}}_{\mathrm{djp}})-R_s{\tilde{i}}_p)\\ \frac{d{\tilde{u}}_{\mathrm{djp}}}{\mathrm{dt}}=\frac{1}{C}(-D_{\mathrm{pj}}{\tilde{i}}_p-d_{\mathrm{pj}}{I}_p-\frac{{\tilde{u}}_{\mathrm{djp}}}{R_j}),j=\mathrm{1,2},...,N\end{array}\right.---\left(14\right)$

Referring to fig. 7, in the upper bridge arm switching period average model, the controlled voltage source of each sub-module switching period average model on the ac sideR_sAnd L are connected in series in sequence and controlled by a voltage sourceThe positive electrode is used as the positive electrode of the output end of the upper bridge arm switch period average model, and L is not equal to R_sOne end of the connection is used as the output end cathode of the upper bridge arm switching period average model; controlled current source of switch period average model of each submodule on direct current sideR_jAnd C are connected in parallel with each other.

The upper bridge arm small signal alternating current model comprises an upper bridge arm controlled source type small signal alternating current model and an upper bridge arm transfer function block diagram type small signal alternating current model;

referring to fig. 8, in the upper bridge arm controlled source type small signal alternating current model, the controlled voltage source d of the small signal alternating current model of each sub-module at the alternating current side_pjU_djpControlled voltage sourceR_sAnd L are connected in series in sequence; controlled voltage source d_pNU_dNpThe positive electrode is used as the positive electrode of the output end of the upper bridge arm small signal alternating current model, and L is not equal to R_sOne end of the connection is used as the negative electrode of the output end of the upper bridge arm small signal alternating current model; controlled current source of small-signal alternating-current model of each submodule on direct-current sideControlled current source d_pjI_p、R_jAnd C are respectively connected in parallel;

as shown in fig. 9, in the small-signal ac model in the upper arm transfer function block diagram form, 4 adders sequentially include an adder 1 ', an adder 2', an adder 3 ', and an adder 4' from left to right, and N input signals d_pj(s) passing through corresponding N proportional links U_djpGenerated signal and input signal-u₁(s) enter adder 1'; the signal generated by the adder 1' and the corresponding N output signals u_djp(s) by a proportional element D_pjThe generated feedback signal enters an adder 2'; the signal generated by the adder 2' passes through a proportional integral elementObtain a signal i_p(s) the signal i_p(s) by N proportional steps D_pjRespectively generated N signals and corresponding N input signals d_pj(s) by a proportional procedure I_pThe generated signals enter corresponding N adders 3j ', the signals generated by the N adders 3 j' take the negative sum and the corresponding N output signals u_djp(s) via a proportional linkThe resulting feedback signal takes the negative of the N adders 4 j. The signals generated by the N adders 4j pass through the corresponding N proportion linksGenerating N output signals u_djp(s)。

Assuming that parameters of each submodule of an upper bridge arm are symmetrical, and the parameters comprise:

d_p1＝d_p2＝...＝d_pN＝d_p(15)

u_d1p＝u_d2p＝…＝u_dNp＝u_dp(16)

getStatic working point of upper bridge arm small signal alternating current model is changed into

$\frac{{\mathrm{dI}}_p}{\mathrm{dt}}=0,\frac{{\mathrm{dU}}_{\mathrm{dp}}}{\mathrm{dt}}=0$

D_pI_p＝U_dp/R

NU_dp＝U_d(18)

U₁＝U_d/2-u_s＝ND_pU_dp-R_sI_p

D_p≈(U_d/2-u_s)/NU_dp＝1/2-u_s/NU_dp

Thus obtaining a simplified upper bridge arm small signal alternating-current model of

$\left\{\begin{array}{c}\frac{d{\tilde{i}}_p}{\mathrm{dt}}=\frac{1}{L}(-{\tilde{u}}_1+({\mathrm{Nd}}_p{U}_{\mathrm{dp}}+{\mathrm{ND}}_p{\tilde{u}}_{\mathrm{dp}})-R_s{\tilde{i}}_p)\\ \frac{d{\tilde{u}}_{\mathrm{dp}}}{\mathrm{dt}}=\frac{1}{C}(-D_p{\tilde{i}}_p-d_p{I}_p-\frac{{\tilde{u}}_{\mathrm{dp}}}{R})\end{array}\right.---\left(19\right)$

Wherein R represents the loss equivalent resistance of the bridge arm main circuit.

The simplified upper bridge arm small signal alternating current model comprises a simplified upper bridge arm controlled source form small signal alternating current model and a simplified upper bridge arm transfer function block diagram form small signal alternating current model.

In the simplified upper bridge arm controlled source form small-signal alternating current model, as shown in fig. 10, the controlled voltage source Nd on the alternating current side_pU_dpControlled voltage sourceR_sAnd L are connected in series in sequence and controlled by a voltage source Nd_pU_dpThe positive electrode is used as the positive electrode of the output end of the simplified upper bridge arm controlled source type small signal alternating current model, and L is not equal to R_sOne end of the connection is used as the cathode of the output end of the simplified upper bridge arm controlled source type small signal alternating current model; controlled current source on the direct current sideControlled current source d_pI_pR and C are connected in parallel;

in the simplified upper arm transfer function block diagram form small signal ac model, 4 adders are adder 1 ", adder 2", adder 3 "and adder 4" from left to right, and input signal d is shown in fig. 11_p(s) by the proportional link NU_dpGenerated signal and input signal-u₁(s) into adder 1 ', adder 1' generates a signal and an output signal u_dp(s) pass ratio Link ND_pThe generated feedback signal enters an adder 2 ', and the signal generated by the adder 2' passes through a proportional-integral elementObtain a signal i_p(s), signal i_p(s) by a proportional segment D_pGenerated signal and input signal d_p(s) by a proportional procedure I_pThe resulting signal enters an adder 3 ', the signal produced by the adder 3' takes the negative of the sum output signal u_dp(s) via a proportional linkThe generated feedback signal is taken as negative and enters an adder 4, and the signal generated by the adder 4 passes through a proportion linkGenerating an output signal u_dp(s)。

The step 3 comprises the following steps:

step 3-1: establishing a switching period average model of a single sub-module of a lower bridge arm and a small signal alternating-current model of the single sub-module of the lower bridge arm;

step 3-2: establishing a lower bridge arm switching period average model;

$\left\{\begin{array}{c}\frac{d{<i_n>}_{T_s}}{\mathrm{dt}}=\frac{1}{L}({<u_2>}_{T_s}-\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}\left(d_{\mathrm{nj}}{<u_{\mathrm{djn}}>}_{T_s}\right)+R_s{<i_n>}_{T_s})\\ \frac{d{<u_{\mathrm{djn}}>}_{T_s}}{\mathrm{dt}}=\frac{1}{C}(d_{\mathrm{nj}}{<i_n>}_{T_s}+\frac{{<u_{\mathrm{djn}}>}_{T_s}}{R_j}),j=\mathrm{1,2},...N\end{array}\right.---\left(20\right)$

wherein d is_njAnd u_djnRespectively representing the equivalent duty ratio and the direct-current side voltage of the jth sub-module of the lower bridge arm,represents u_djnIn the switching period T_sAverage value of (d);

step 3-3: a lower bridge arm small signal alternating current model;

$\left\{\begin{array}{c}{u}_1=U_d/2-u_s\\ u_2=U_d/2+u_s\end{array}\right.---\left(21\right)$

and has the following components:

d_n1＝d_n2＝...＝d_nN＝d_n(22)

u_d1n＝u_d2n＝...u_dNn＝u_dn(23)

get $u_{\mathrm{dn}}=\frac{1}{N}\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}{u}_{\mathrm{djn}},$ Can obtain the product

D_n≈(U_d/2+u_s)/NU_dn＝1/2+u_s/NU_dn＝1/2+u_s/U_d(24)

D_nIs a static operating point;

thus obtaining a simplified lower bridge arm small signal alternating-current model of

$\left\{\begin{array}{c}\frac{d{\tilde{i}}_n}{\mathrm{dt}}=\frac{1}{L}({\tilde{u}}_2-({\mathrm{Nd}}_n{U}_{\mathrm{dn}}+{\mathrm{ND}}_n{\tilde{u}}_{\mathrm{dn}})-R_s{\tilde{i}}_n)\\ \frac{d{\tilde{u}}_{\mathrm{dn}}}{\mathrm{dt}}=\frac{1}{C}(D_n{\tilde{i}}_n+d_n{I}_n-\frac{{\tilde{u}}_{\mathrm{dn}}}{R})\end{array}\right.---\left(25\right).$

In the lower bridge arm switch period average model, the controlled voltage source of each sub-module switch period average model on the AC sideR_sAnd L are connected in series in sequence and controlled by a voltage sourceThe positive electrode is used as the positive electrode of the output end of the lower bridge arm switch period average model, and L is not equal to R_sOne end of the connection is used as the output end cathode of the lower bridge arm switching period average model; controlled current source of single sub-module switch period average model on direct current sideR_jAnd C are connected in parallel with each other.

The lower bridge arm small signal alternating current model comprises a simplified lower bridge arm controlled source form small signal alternating current model and a simplified lower bridge arm transfer function block diagram form small signal alternating current model;

in the simplified lower bridge arm controlled source form small signal alternating current model, L, R on the alternating current side is shown in FIG. 12_sControlled voltage source Nd_nU_dnAnd a controlled voltage sourceAre sequentially connected in series, L is not connected with R_sOne end of the connection is used as the positive electrode of the output end of the simplified lower bridge arm controlled source type small signal alternating current model, and the controlled voltage sourceThe negative electrode is used as the negative electrode of the output end of the simplified lower bridge arm controlled source type small signal alternating current model; controlled current source on the direct current sideControlled current source d_nI_nR and C are connected in parallel;

in the simplified lower arm transfer function block diagram form small signal ac model, 4 adders are sequentially an adder 1 '", an adder 2'", an adder 3 '"and an adder 4'" from left to right, and an input signal d is shown in fig. 13_n(s) by the proportional link NU_dnThe resulting signal is negated and the input signal u is summed₂(s) into adder 1'; output signal u_dn(s) pass ratio Link ND_nThe generated feedback signal is taken as negative and the signal generated by the adder 1 ' is fed into the adder 2 ', and the signal generated by the adder 2 ' is passed through a proportional-integral elementObtain a signal i_n(s), signal i_n(s) by a proportional segment D_nGenerated signal and input signal d_n(s) by a proportional procedure I_nThe resulting signal enters the adder 3' ", and the output signal u_dn(s) via a proportional linkThe generated feedback signal is taken as the negative of the signal generated by the adder 3 ' ″ and fed into the adder 4 ' ″, and the signal generated by the adder 4 ' ″ passes through the proportional elementGenerating an output signal u_dn(s)。

The step 4 comprises the following steps:

step 4-1: the method comprises the following steps of establishing a switching period average model of an upper bridge arm and a lower bridge arm of the modular multilevel converter as follows:

$\left\{\begin{array}{c}\frac{d\stackrel{\&RightArrow;}{i_p}}{\mathrm{dt}}=\frac{1}{L}(-\stackrel{\&RightArrow;}{u_1}+{\mathrm{ND}}_p\stackrel{\&RightArrow;}{u_{\mathrm{dp}}}-R_s\stackrel{\&RightArrow;}{i_p})\\ \frac{d\stackrel{\&RightArrow;}{u_{\mathrm{dp}}}}{\mathrm{dt}}=-\frac{1}{C}{D}_p\stackrel{\&RightArrow;}{i_p}-\frac{\stackrel{\&RightArrow;}{u_{\mathrm{dp}}}}{\mathrm{RC}}\end{array}\right.---\left(26\right)$

$\left\{\begin{array}{c}\frac{d\stackrel{\&RightArrow;}{i_n}}{\mathrm{dt}}=\frac{1}{L}(\stackrel{\&RightArrow;}{u_2}-{\mathrm{ND}}_n\stackrel{\&RightArrow;}{u_{\mathrm{dn}}}-R_s\stackrel{\&RightArrow;}{i_n})\\ \frac{d\stackrel{\&RightArrow;}{u_{\mathrm{dn}}}}{\mathrm{dt}}=\frac{1}{C}{D}_n\stackrel{\&RightArrow;}{i_n}-\frac{\stackrel{\&RightArrow;}{u_{\mathrm{dn}}}}{\mathrm{RC}}\end{array}\right.---\left(27\right)$

$\left\{\begin{array}{c}\stackrel{\&RightArrow;}{i_s}=\stackrel{\&RightArrow;}{i_p}+\stackrel{\&RightArrow;}{i_n}\\ {<i_d>}_{\mathrm{Ts}}=\left[\begin{array}{ccc}1& 1& 1\end{array}\right]\stackrel{\&RightArrow;}{i_p}=-\left[\begin{array}{ccc}1& 1& 1\end{array}\right]\stackrel{\&RightArrow;}{i_n}\end{array}\right.---\left(28\right)$

wherein, $\stackrel{\&RightArrow;}{i_p}={\left[\begin{array}{ccc}{<i_{\mathrm{pa}}>}_{T_s}& {<i_{\mathrm{pb}}>}_{T_s}& {<i_{\mathrm{pc}}>}_{T_s}\end{array}\right]}^T,$ $\stackrel{\&RightArrow;}{u_1}={\left[\begin{array}{ccc}{<u_{1a}>}_{T_s}& {<u_{1b}>}_{T_s}& {<u_{1c}>}_{T_s}\end{array}\right]}^T,$

D_p＝diag[d_pad_pbd_pc]， ${\stackrel{\&RightArrow;}{u_{\mathrm{dp}}}}^T={\left[\begin{array}{ccc}{<u_{\mathrm{dap}}>}_{T_s}& {<u_{\mathrm{dbp}}>}_{T_s}& {<u_{\mathrm{dcp}}>}_{T_s}\end{array}\right]}^T,$

$\stackrel{\&RightArrow;}{i_n}={\left[\begin{array}{ccc}{<i_{\mathrm{na}}>}_{T_s}& {<i_{\mathrm{nb}}>}_{T_s}& {<i_{\mathrm{nc}}>}_{T_s}\end{array}\right]}^T,$ $\stackrel{\&RightArrow;}{u_2}={\left[\begin{array}{ccc}{<u_{2a}>}_{T_s}& {<u_{2b}>}_{T_s}& {<u_{2c}>}_{T_s}\end{array}\right]}^T,$

D_n＝diag[d_nad_nbd_nc]， ${\stackrel{\&RightArrow;}{u_{\mathrm{dn}}}}^T={\left[\begin{array}{ccc}{<u_{\mathrm{dan}}>}_{T_s}& {<u_{\mathrm{dbn}}>}_{T_s}& {<u_{\mathrm{dcn}}>}_{T_s}\end{array}\right]}^T,$

the corner mark p represents an upper bridge arm module, and the corner mark n represents a lower bridge arm module; wherein, $\stackrel{\&RightArrow;}{u_1}=\left[\begin{array}{c}{<u_{1a}>}_{T_s}\\ {<u_{1b}>}_{T_s}\\ {<u_{1c}>}_{T_s}\end{array}\right]=\frac{{<U_d>}_{\mathrm{Ts}}}{2}\left[\begin{array}{c}1\\ 1\\ 1\end{array}\right]-\left[\begin{array}{c}{<u_{a0}>}_{T_s}\\ {<u_{b0}>}_{T_s}\\ {<u_{c0}>}_{T_s}\end{array}\right]=\frac{{<U_d>}_{\mathrm{Ts}}}{2}\left[\begin{array}{c}1\\ 1\\ 1\end{array}\right]-\left[\begin{array}{c}{<u_{\mathrm{sa}}>}_{T_s}\\ {<u_{\mathrm{sb}}>}_{T_s}\\ {<u_{\mathrm{sc}}>}_{T_s}\end{array}\right]-{<u_{N0}>}_{T_s}\left[\begin{array}{c}1\\ 1\\ 1\end{array}\right]---\left(29\right)$

$\stackrel{\&RightArrow;}{u_2}=\left[\begin{array}{c}{<u_{2a}>}_{T_s}\\ {<u_{2b}>}_{T_s}\\ {<u_{2c}>}_{T_s}\end{array}\right]=\frac{{<U_d>}_{\mathrm{Ts}}}{2}\left[\begin{array}{c}1\\ 1\\ 1\end{array}\right]+\left[\begin{array}{c}{<u_{a0}>}_{T_s}\\ {<u_{b0}>}_{T_s}\\ {<u_{c0}>}_{T_s}\end{array}\right]=\frac{{<U_d>}_{\mathrm{Ts}}}{2}\left[\begin{array}{c}1\\ 1\\ 1\end{array}\right]+\left[\begin{array}{c}{<u_{\mathrm{sa}}>}_{T_s}\\ {<u_{\mathrm{sb}}>}_{T_s}\\ {<u_{\mathrm{sc}}>}_{T_s}\end{array}\right]+{<u_{N0}>}_{T_s}\left[\begin{array}{c}1\\ 1\\ 1\end{array}\right]---\left(30\right)$

u_N0is the AC side common mode voltage;

step 4-2: a small signal alternating current model of the modular multilevel converter;

the static operating points of the modular multilevel converter are as follows:

$\left\{\begin{array}{c}\frac{{\mathrm{dI}}_{\mathrm{pi}}}{\mathrm{dt}}=0,\frac{{\mathrm{dU}}_{\mathrm{dip}}}{\mathrm{dt}}=0\\ {\mathrm{NU}}_{\mathrm{dip}}=U_d\\ -U_d/2+u_{\mathrm{si}}+u_{N0}+D_{\mathrm{pi}}{\mathrm{NU}}_{\mathrm{dip}}-R_s{I}_{\mathrm{pi}}\text{=0}\end{array}\right.,i=a,b,c---\left(31\right)$

$\left\{\begin{array}{c}\frac{{\mathrm{dI}}_{\mathrm{ni}}}{\mathrm{dt}}=0,\frac{{\mathrm{dU}}_{\mathrm{din}}}{\mathrm{dt}}=0\\ {\mathrm{NU}}_{\mathrm{din}}=U_d\\ U_d/2+u_{\mathrm{si}}+u_{N0}-D_{\mathrm{ni}}{\mathrm{NU}}_{\mathrm{din}}-R_s{I}_{\mathrm{ni}}\text{=0}\end{array}\right.i=a,b,c---\left(32\right)$

obtaining small signal alternating current models of an upper bridge arm and a lower bridge arm of the modular multilevel converter:

$\left\{\begin{array}{cc}\frac{d{\tilde{i}}_{\mathrm{pi}}}{\mathrm{dt}}=\frac{1}{L}(-\frac{{\tilde{u}}_d}{2}+{\tilde{u}}_{\mathrm{si}}+{\tilde{u}}_{N0}+{\mathrm{ND}}_{\mathrm{pi}}{u}_{\mathrm{dpi}}+N{\tilde{d}}_{\mathrm{pi}}{U}_{\mathrm{dpi}}-R_s{\tilde{i}}_{\mathrm{pi}})& \\ \frac{d{\tilde{u}}_{\mathrm{dpi}}}{\mathrm{dt}}=-\frac{1}{C}(D_{\mathrm{pi}}{\tilde{i}}_{\mathrm{pi}}+{\tilde{d}}_{\mathrm{pi}}{I}_{\mathrm{pi}})-\frac{{\tilde{u}}_{\mathrm{dpi}}}{\mathrm{RC}}& i=a,b,c\end{array}\right.---\left(33\right)$

$\left\{\begin{array}{cc}\frac{d{\tilde{i}}_{\mathrm{ni}}}{\mathrm{dt}}=\frac{1}{L}(\frac{{\tilde{u}}_d}{2}+{\tilde{u}}_{\mathrm{si}}+{\tilde{u}}_{N0}-{\mathrm{ND}}_{\mathrm{ni}}{\tilde{u}}_{\mathrm{dni}}-N{\tilde{d}}_{\mathrm{ni}}{U}_{\mathrm{dni}}-R_s{\tilde{i}}_{\mathrm{ni}})& \\ \frac{d{\tilde{u}}_{\mathrm{dni}}}{\mathrm{dt}}=\frac{1}{C}(D_{\mathrm{ni}}{\tilde{i}}_{\mathrm{ni}}+{\tilde{d}}_{\mathrm{ni}}{I}_{\mathrm{ni}})-\frac{{\tilde{u}}_{\mathrm{dni}}}{\mathrm{RC}}& i=a,b,c\end{array}\right.---\left(34\right)$

$\left\{\begin{array}{c}{\tilde{i}}_{\mathrm{si}}={\tilde{i}}_{\mathrm{pi}}+{\tilde{i}}_{\mathrm{ni}}\\ {\tilde{i}}_d=\underset{i=a,b,c}{\mathrm{\&Sigma;}}{\tilde{i}}_{\mathrm{pi}}=-\underset{i=a,b,c}{\mathrm{\&Sigma;}}{\tilde{i}}_{\mathrm{ni}}\end{array}\right.---\left(35\right).$

in the switching period averaging model of the upper arm of the modular multilevel converter, as shown in fig. 14, the upper arm controlled voltage source Nd_pi<u_dip>_Ts、R_sAnd L are connected in series in sequence, and the upper bridge arm is controlled by a current source d_pi<i_pi>_TsR and C are connected in parallel; under the modular multilevel converterL, R in bridge arm switching period average model_sAnd a lower bridge arm controlled voltage source Nd_ni<u_din>_TsSerially connected, controlled current source d_ni<i_ni>_TsAnd R and C are mutually connected in parallel to form a lower bridge arm equivalent switching period average model.

In the small-signal alternating current model of the modular multilevel converter, as shown in FIG. 15, a signal i_pi(s) and signal i_ni(s) entering an adder to generate a signal i_si(s), signalSignal-u_si(s) and signal-u_N0(s) entering an adder to generate a signal u_1i(s), signalSignal u_si(s) sum signal u_N0(s) entering an adder to generate a signal u_2i(s)；

In the modular multilevel converter upper bridge arm small signal alternating current model, 4 adders are an adder A, an adder B, an adder C and an adder D from left to right in sequence, and an input signal D_pi(s) by the proportional link NU_dipGenerated signal and input signal-u_1i(s) into an adder A, the signal generated by adder A and the output signal u_dip(s) pass ratio Link ND_piThe generated feedback signal enters an adder B, and the signal generated by the adder B passes through a proportional-integral linkObtain a signal i_pi(s), signal i_pi(s) by a proportional segment D_piGenerated signal and input signal d_pi(s) by a proportional procedure I_piThe generated signal enters an adder C, and the signal generated by the adder C takes the negative sum and outputs a signal u_dip(s) via a proportional linkGenerated feedbackThe signal is taken as negative and enters an adder D, and the signal generated by the adder D passes through a proportion linkGenerating an output signal u_dip(s)；

In the modular multilevel converter lower bridge arm small signal alternating current model, an input signal d_ni(s) by the proportional link NU_dinThe resulting signal is negated and the input signal u is summed_2i(s) into an adder E, outputting the signal u_din(s) pass ratio Link ND_niThe generated feedback signal is taken as the negative sum, the signal generated by the adder E enters the adder F, and the signal generated by the adder F passes through a proportional-integral linkObtain a signal i_ni(s), signal i_ni(s) by a proportional segment D_niGenerated signal and input signal d_ni(s) by a proportional procedure I_mThe resulting signal enters adder G, which outputs signal u_din(s) via a proportional linkThe generated feedback signal is taken as the negative sum, the signal generated by the adder G enters the adder H, and the signal generated by the adder H passes through a proportion linkGenerating an output signal u_din(s)。

Finally, it should be noted that: the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting the same, and although the present invention is described in detail with reference to the above embodiments, those of ordinary skill in the art should understand that: modifications and equivalents may be made to the embodiments of the invention without departing from the spirit and scope of the invention, which is to be covered by the claims.

Claims (14)

1. A modeling method for a dynamic model of a modular multilevel converter is characterized by comprising the following steps: the method comprises the following steps:

step 1: establishing an upper bridge arm single sub-module switching period average model and an upper bridge arm single sub-module small signal alternating current model;

step 2: establishing an upper bridge arm switching period average model and an upper bridge arm small signal alternating current model;

and step 3: establishing a lower bridge arm switching period average model and a lower bridge arm small signal alternating-current model;

and 4, step 4: establishing a modular multilevel converter switching period average model and a modular multilevel converter small signal model;

the step 1 comprises the following steps:

step 1-1: establishing a switching period average model of a single sub-module of an upper bridge arm;

step 1-2: establishing a small signal alternating-current model of a single submodule of an upper bridge arm;

in step 1-1, the equation of a single submodule of the upper bridge arm is as follows:

$\left\{\begin{array}{c}{u}_{p1}=S_p{u}_{d1p}\\ i_{d1p}=S_p{i}_p\end{array}\right.---\left(1\right)$

$\left\{\begin{array}{c}\frac{{\mathrm{di}}_p}{dt}=\frac{1}{L_1}(-{u_1}^{\&prime;}+S_p{u}_{d1p}-R_s^{\&prime;}{i}_p)\\ \frac{{\mathrm{du}}_{d1p}}{dt}=\frac{1}{C}(-S_p{i}_p-\frac{u_{d1p}}{R_1})\end{array}\right.---\left(2\right)$

wherein u is_p1For a single submodule output voltage u of the upper bridge arm_d1pFor a single sub-module DC voltage of the upper bridge arm, i_d1pFor a direct discharge current of a single submodule of the upper bridge arm, i_pOutputting current for a single submodule of an upper bridge arm; s_pRepresenting the switching function, S_p∈[0，1]，S_p1 denotes that the IGBT connected in parallel with the ac output of the submodule is switched off, the other IGBT is switched on, S_pWhen the voltage is equal to 0, the IGBT connected with the alternating current output end of the submodule in parallel is turned on, and the other IGBT is turned off;

L₁for a single sub-module inductance of the upper bridge arm, L₁＝L/N，U_d1p＝U_dN, L is bridge arm reactance, U_dFor common DC bus voltage, C for individual sub-module support capacitors, u₁'is the sum of the output voltage of a single submodule and the reactive voltage drop of a bridge arm, R'_sIs an equivalent series resistance, R, of a submodule series reactor₁Equivalent electricity for loss of main circuit of sub-moduleBlocking;

averaging the switching cycles of (2) to obtain:

$\left\{\begin{array}{c}\frac{d<i_p{>}_{T_s}}{dt}=\frac{1}{L_1}(-<{u_1}^{\&prime;}{>}_{T_s}+<S_p{u}_{d1p}{>}_{T_s}-R_s^{\&prime;}<i_p{>}_{T_s})\\ \frac{d<u_{d1p}{>}_{T_s}}{dt}=\frac{1}{C}(-<S_p{i}_p{>}_{T_s}-\frac{<u_{d1p}{>}_{T_s}}{R_1})\end{array}\right.---\left(3\right)$

wherein, T_sWhich is indicative of the switching period of the switch,represents u₁In a switching period T_sThe average value of the values of (a) to (b),denotes S_pu_d1pIn the switching period T_sThe average value of the values of (a) to (b),represents i_pIn the switching period T_sThe average value of the values of (a) to (b),denotes S_pi_pIn the switching period T_sThe average value of the values of (a) to (b),represents u_d1pIn the switching period T_sAverage value of (d);

suppose that in the switching period T_sInner, u_d1pAnd i_pThe following approximation can be obtained with little variation:

$<S_p{u}_{d1p}{>}_{T_s}\&ap;<S_p{>}_{T_s}<u_{d1p}{>}_{T_s}=d_p<u_{d1p}{>}_{T_s}---\left(4\right)$

$<S_p{i}_p{>}_{T_s}\&ap;<S_p{>}_{T_s}<i_p{>}_{T_s}=d_p<i_p{>}_{T_s}---\left(5\right)$

wherein d is_pIs the switching signal duty cycle;

substituting (4) and (5) into (3) to obtain an average model of the switching period of a single submodule of the upper bridge arm as follows:

$\left\{\begin{array}{c}\frac{d<i_p{>}_{T_s}}{dt}=\frac{1}{L_1}(-<{u_1}^{\&prime;}{>}_{T_s}+d_p<u_{d1p}{>}_{T_s}-R_s^{\&prime;}<i_p{>}_{T_s})\\ \frac{d<u_{d1p}{>}_{T_s}}{dt}=-\frac{1}{C}(d_p<i_p{>}_{T_s}+\frac{<u_{d1p}{>}_{T_s}}{R_1})\end{array}\right.---\left(6\right);$

in the switching period average model of the single submodule of the upper bridge arm, a controlled voltage source at the AC sideR′_sAnd L₁Sequentially connected in series, controlled voltage sourceThe positive electrode is used as the positive electrode of the output end of the equivalent switch period model of the single submodule of the upper bridge arm, L₁Not with R'_sOne end of the connection is used as the cathode of the output end of the equivalent switch period model of the single sub-module of the upper bridge arm; controlled current source on the direct current sideR₁And C are connected in parallel with each other;

in the step 1-2, the step of the method,

order:

$\begin{array}{c}<{u_1}^{\&prime;}{>}_{T_s}={U_1}^{\&prime;}+{{\tilde{u}}_1}^{\&prime;}\\ <i_p{>}_{T_s}=I_p+{\tilde{i}}_p\\ <u_{d1p}{>}_{T_s}=U_{d1p}+{\tilde{u}}_{d1p}\\ d_p=D_p+{\tilde{d}}_p\end{array}---\left(7\right)$

in the formula of U₁′,I_p,U_d1p,D_pIs a static working point, and the working point is,is the disturbance quantity; substituting (7) into (6) to obtain

$\left\{\begin{array}{c}\frac{d(I_p+{\tilde{i}}_p)}{dt}=\frac{1}{L_1}(-{U_1}^{\&prime;}-{{\tilde{u}}_1}^{\&prime;}+(D_p+d_p\left)\right(U_{d1p}+{\tilde{u}}_{d1p})-R_s^{\&prime;}(I_p+{\tilde{i}}_p\left)\right)\\ \frac{d(U_{d1p}+{\tilde{u}}_{d1p})}{dt}=\frac{1}{C}(-(D_p+d_p\left)\right(I_p+{\tilde{i}}_p)-\frac{U_{d1p}+{\tilde{u}}_{d1p}}{R_1})\end{array}\right.---\left(8\right)$

The following relationship exists due to the static operating points:

$\begin{array}{c}\frac{{\mathrm{dI}}_p}{dt}=0\\ \frac{{\mathrm{dU}}_{d1p}}{dt}=0\\ {U_1}^{\&prime;}=U_d/2-u_s=D_p{U}_{d1p}-R_s{I}_p\\ D_p{I}_p=\frac{U_{d1p}}{R_1}\end{array}---\left(9\right)$

wherein u is_sIs the system voltage;

according to the step (8), neglecting high-order terms, obtaining the small signal alternating-current model of the single submodule of the upper bridge arm as follows:

$\left\{\begin{array}{c}\frac{d{\tilde{i}}_p}{dt}=\frac{1}{L_1}(-{{\tilde{u}}_1}^{\&prime;}+d_p{U}_{d1p}+D_p{\tilde{u}}_{d1p}-R_s^{\&prime;}{\tilde{i}}_p)\\ \frac{d{\tilde{u}}_{d1p}}{dt}=\frac{1}{C}\left(-D_p{\tilde{i}}_p-d_p{I}_p-\frac{{\tilde{u}}_{d1p}}{R_1}\right)\end{array}\right.---\left(10\right);$

the upper bridge arm single sub-module small signal alternating-current model comprises an upper bridge arm single sub-module controlled source type small signal alternating-current model and an upper bridge arm single sub-module transfer function block diagram type small signal alternating-current model;

in the controlled source type small-signal alternating-current model of the single submodule of the upper bridge arm, a controlled voltage source d at the alternating-current side_pU_d1pControlled voltage sourceR′_sAnd L₁Sequentially connected in series; controlled voltage source d_pU_d1pThe positive electrode is used as the positive electrode of the output end of the small-signal alternating-current model of the single submodule of the upper bridge arm, L₁Not with R'_sOne end of the connection is used as the negative electrode of the output end of the small signal alternating-current model of the single submodule of the upper bridge arm; controlled current source on the direct current sideControlled current source d_pI_p、R₁And C are connected in parallel with each other; in the upper bridge arm single sub-module transfer function block diagram type small signal alternating current model, an input signal d_p(s) by a proportion link U_d1pGenerated signal, -u₁'(s) and an output signal u_dlp(s) by a proportional element D_pThe generated feedback signal enters an adder 1, and the signal generated by the adder 1 passes through a proportional-integral elementObtain a signal i_p(s) the signal i_p(s) warpOver-proportional link D_pGenerated signal and input signal d_p(s) by a proportional procedure I_pThe generated signal enters an adder 2, and the signal generated by the adder 2 takes the negative sum and outputs a signal u_dlp(s) via a proportional linkThe generated feedback signal is taken as negative and enters an adder 3, and the signal generated by the adder 3 passes through a proportion linkGenerating an output signal u_dlp(s)。

2. The modeling method for the dynamic model of the modular multilevel converter according to claim 1, wherein: the modular multilevel converter comprises three pairs of bridge arms, each pair of bridge arms comprises an upper bridge arm and a lower bridge arm, the upper bridge arm and the lower bridge arm respectively comprise N sub-modules and reactors which are sequentially connected in series, and the three pairs of bridge arms are connected in parallel to lead out a common direct current end.

3. The modeling method for the dynamic model of the modular multilevel converter according to claim 1, wherein: the step 2 comprises the following steps:

step 2-1: the method comprises the following steps of establishing an upper bridge arm switching period average model:

$\left\{\begin{array}{c}\frac{d<i_p{>}_{T_s}}{dt}=\frac{1}{L}(-<u_1{>}_{T_s}+\underset{j=1}{\overset{N}{\&Sigma;}}(d_{pj}<u_{djp}{>}_{T_s})-R_s<i_p{>}_{T_s})\\ \frac{d<u_{djp}{>}_{T_s}}{dt}=\frac{1}{C}(-d_{pj}<i_p{>}_{T_s}-\frac{<u_{djp}{>}_{T_s}}{R_j}),j=1,2,...N\end{array}\right.---\left(11\right)$

wherein R is_jRepresenting the equivalent loss resistance, R, of the sub-module_sFor equivalent series resistance of bridge arm series reactor, d_pjAnd u_djpRespectively representing the equivalent duty ratio and the direct current side voltage of the jth sub-module of the upper bridge arm,represents u_djpIn the switching period T_sAverage value of (d);

step 2-2: establishing an upper bridge arm small signal alternating current model as follows:

$\left\{\begin{array}{c}<i_p{>}_{T_s}=I_p+{\tilde{i}}_p\\ <u_1{>}_{T_s}=U_1+{\tilde{u}}_1\\ <u_{djp}{>}_{T_s}=U_{djp}+{\tilde{u}}_{djp},j=1,2,...,N\\ d_{pj}=D_{pj}+{\tilde{d}}_{pj},j=1,2,...,N\end{array}\right.---\left(12\right)$

in the formula I_p,U₁,U_djp,D_pjIs a static operating point;for the disturbance quantity, the static working points of the upper bridge arm have the following relations:

$\begin{array}{c}\frac{{\mathrm{dI}}_p}{dt}=0\\ \frac{{\mathrm{dU}}_{djp}}{dt}=0\\ U_1=U_d/2-u_s=\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}{D}_{pj}{U}_{djp}-R_s{I}_p\\ D_{pj}{I}_p=\frac{U_{djp}}{R_j}\end{array}---\left(13\right)$

the (12) is brought into the (11), and the upper bridge arm small signal alternating current model obtained according to the (13) is

$\left\{\begin{array}{c}\frac{d{\tilde{i}}_p}{dt}=\frac{1}{L}(-{\tilde{u}}_1+\underset{j=1}{\overset{N}{\&Sigma;}}(d_{pj}{U}_{djp}+D_{pj}{\tilde{u}}_{djp})-R_s{\tilde{i}}_p)\\ \frac{d{\tilde{u}}_{djp}}{dt}=\frac{1}{C}(-D_{pj}{\tilde{i}}_p-d_{pj}{I}_p-\frac{{\tilde{u}}_{djp}}{R_j}),j=1,2,...,N\end{array}\right.---\left(14\right).$

4. The modeling method for the dynamic model of the modular multilevel converter according to claim 3, wherein: in the upper bridge arm switch period average model, the controlled voltage source of each sub-module switch period average model on the AC sideR_sAnd L are connected in series in sequence and controlled by a voltage sourceThe positive electrode is used as the positive electrode of the output end of the upper bridge arm switch period average model, and L is not equal to R_sOne end of the connection is used as the output end cathode of the upper bridge arm switching period average model; controlled current source of switch period average model of each submodule on direct current sideR_jAnd C are connected in parallel with each other.

5. The modeling method for the dynamic model of the modular multilevel converter according to claim 3, wherein: the upper bridge arm small signal alternating current model comprises an upper bridge arm controlled source type small signal alternating current model and an upper bridge arm transfer function block diagram type small signal alternating current model;

in the upper bridge arm controlled source form small signal alternating current model, the controlled voltage source d of each sub-module small signal alternating current model at the alternating current side_pjU_djpControlled voltage sourceR_sAnd L are connected in series in sequence; controlled voltage source d_pNU_dNpThe positive electrode is used as the positive electrode of the output end of the upper bridge arm small signal alternating current model, and L is not equal to R_sOne end of the connection is used as the output end negative of the upper bridge arm small signal alternating current modelA pole; controlled current source of small-signal alternating-current model of each submodule on direct-current sideControlled current source d_pjI_p、R_jAnd C are respectively connected in parallel;

in the upper bridge arm transfer function block diagram type small signal alternating current model, N input signals d_pj(s) passing through corresponding N proportional links U_djpGenerated signal and input signal-u₁(s) enter adder 1'; the signal generated by the adder 1' and the corresponding N output signals u_djp(s) by a proportional element D_pjThe generated feedback signal enters an adder 2'; the signal generated by the adder 2' passes through a proportional integral elementObtain a signal i_p(s) the signal i_p(s) by N proportional steps D_pjRespectively generated N signals and corresponding N input signals d_pj(s) by a proportional procedure I_pThe generated signals enter corresponding N adders 3j ', the signals generated by the N adders 3 j' take the negative sum and the corresponding N output signals u_djp(s) via a proportional linkThe generated feedback signal is taken as negative and enters N adders 4j, and the signals generated by the N adders 4j pass through corresponding N proportion linksGenerating N output signals u_djp(s)。

6. The modeling method for the dynamic model of the modular multilevel converter according to claim 5, wherein: assuming that parameters of each submodule of an upper bridge arm are symmetrical, and the parameters comprise:

d_p1＝d_p2＝...＝d_pN＝d_p(15)

u_d1p＝u_d2p＝…＝u_dNp＝u_dp(16)

getStatic working point of upper bridge arm small signal alternating current model is changed into

$\begin{array}{c}\frac{{\mathrm{dI}}_p}{dt}=0,\frac{{\mathrm{dU}}_{dp}}{dt}=0\\ D_p{I}_p=U_{dp}/R\\ {\mathrm{NU}}_{dp}=U_d\\ U_1=U_d/2-u_s={\mathrm{ND}}_p{U}_{dp}-R_s{I}_p\\ D_p\&ap;\left(U_d/2-u_s\right)/{\mathrm{NU}}_{dp}=1/2-u_s/{\mathrm{NU}}_{dp}\end{array}---\left(18\right)$

Thus obtaining a simplified upper bridge arm small signal alternating-current model of

$\left\{\begin{array}{c}\frac{d{\tilde{i}}_p}{dt}=\frac{1}{L}(-{\tilde{u}}_1+({\mathrm{Nd}}_p{U}_{dp}+{\mathrm{ND}}_p{\tilde{u}}_{dp})-R_s{\tilde{i}}_p)\\ \frac{d{\tilde{u}}_{dp}}{dt}=\frac{1}{C}(-D_p{\tilde{i}}_p-d_p{I}_p-\frac{{\tilde{u}}_{dp}}{R})\end{array}\right.---\left(19\right)$

Wherein R represents the loss equivalent resistance of the bridge arm main circuit.

7. The modeling method for the dynamic model of the modular multilevel converter according to claim 6, wherein: the simplified upper bridge arm small signal alternating current model comprises a simplified upper bridge arm controlled source form small signal alternating current model and a simplified upper bridge arm transfer function block diagram form small signal alternating current model.

8. The modeling method for the dynamic model of the modular multilevel converter according to claim 7, wherein: in the simplified upper bridge arm controlled source form small signal alternating current model, a controlled voltage source Nd at an alternating current side_pU_dpControlled voltage sourceR_sAnd L are connected in series in sequence and controlled by a voltage source Nd_pU_dpThe positive electrode is used as the positive electrode of the output end of the simplified upper bridge arm controlled source type small signal alternating current model, and L is not equal to R_sOne end of the connection is used as the cathode of the output end of the simplified upper bridge arm controlled source type small signal alternating current model; controlled current source on the direct current sideControlled current source d_pI_pR and C are connected in parallel; in the simplified upper bridge arm transfer function block diagram type small signal alternating current model, an input signal d_p(s) by the proportional link NU_dpGenerated signal and input signal-u₁(s) into adder 1 ', adder 1' generates a signal and an output signal u_dp(s) pass ratio Link ND_pThe generated feedback signal enters an adder 2 ', and the signal generated by the adder 2' passes through a proportional-integral elementObtain a signal i_p(s), signal i_p(s) by a proportional segment D_pGenerated signal and input signal d_p(s) by a proportional procedure I_pThe resulting signal enters an adder 3 ', the signal produced by the adder 3' takes the negative of the sum output signal u_dp(s) via a proportional linkThe generated feedback signal is taken as negative and enters an adder 4, and the signal generated by the adder 4 passes through a proportion linkGenerating an output signal u_dp(s)。

9. The modeling method for the dynamic model of the modular multilevel converter according to claim 1, wherein: the step 3 comprises the following steps:

step 3-1: establishing a switching period average model of a single sub-module of a lower bridge arm and a small signal alternating-current model of the single sub-module of the lower bridge arm;

step 3-2: establishing a lower bridge arm switching period average model;

$\left\{\begin{array}{c}\frac{d<i_n{>}_{T_s}}{dt}=\frac{1}{L}\left(<u_2{>}_{T_s}-\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}\left(d_{nj}<u_{djn}{>}_{T_s}\right)+R_s<i_n{>}_{T_s}\right)\\ \frac{d<u_{djn}{>}_{T_s}}{dt}=\frac{1}{C}\left(d_{nj}<i_n{>}_{T_s}+\frac{<u_{djn}{>}_{T_s}}{R_j}\right),j=1,2,...N\end{array}\right.---\left(20\right)$

wherein d is_njAnd u_djnRespectively representing the equivalent duty ratio and the direct-current side voltage of the jth sub-module of the lower bridge arm,represents u_djnIn the switching period T_sAverage value of (d);

step 3-3: a lower bridge arm small signal alternating current model;

$\left\{\begin{array}{c}{u}_1=U_d/2-u_s\\ u_2=U_d/2+u_s\end{array}\right.---\left(21\right)$

and has the following components:

d_n1＝d_n2＝...＝d_nN＝d_n(22)

u_d1n＝u_d2n＝...u_dNn＝u_dn(23)

getCan obtain the product

D_n≈(U_d/2+u_s)/NU_dn＝1/2+u_s/NU_dn＝1/2+u_s/U_d(24)

D_nIs a static operating point;

thus obtaining a simplified lower bridge arm small signal alternating-current model of

$\left\{\begin{array}{c}\frac{d{\tilde{i}}_n}{dt}=\frac{1}{L}({\tilde{u}}_2-({\mathrm{Nd}}_n{U}_{dn}+{\mathrm{ND}}_n{\tilde{u}}_{dn})-R_s{\tilde{i}}_n)\\ \frac{d{\tilde{u}}_{dn}}{dt}=\frac{1}{C}(D_n{\tilde{i}}_n+d_n{I}_n-\frac{{\tilde{u}}_{dn}}{R})\end{array}\right.---\left(25\right).$

10. The modeling method for the dynamic model of the modular multilevel converter according to claim 9, wherein: in the lower bridge arm switch period average model, the controlled voltage source of each sub-module switch period average model on the AC sideR_sAnd L are connected in series in sequence and controlled by a voltage sourceThe positive electrode is used as the positive electrode of the output end of the lower bridge arm switch period average model, and L is not equal to R_sOne end of the connection is used as the output end cathode of the lower bridge arm switching period average model; controlled current source of single sub-module switch period average model on direct current sideR_jAnd C are connected in parallel with each other.

11. The modeling method for the dynamic model of the modular multilevel converter according to claim 9, wherein: the lower bridge arm small signal alternating current model comprises a simplified lower bridge arm controlled source form small signal alternating current model and a simplified lower bridge arm transfer function block diagram form small signal alternating current model;

l, R on the AC side in the simplified lower bridge arm controlled source form small signal AC model_sControlled voltage source Nd_nU_dnAnd a controlled voltage sourceAre sequentially connected in series, L is not connected with R_sOne end of the connection is used as the positive electrode of the output end of the simplified lower bridge arm controlled source type small signal alternating current modelControlled voltage sourceThe negative electrode is used as the negative electrode of the output end of the simplified lower bridge arm controlled source type small signal alternating current model; controlled current source on the direct current sideControlled current source d_nI_nR and C are connected in parallel;

in the simplified lower bridge arm transfer function block diagram type small signal alternating current model, an input signal d_n(s) by the proportional link NU_dnThe resulting signal is negated and the input signal u is summed₂(s) into adder 1'; output signal u_dn(s) pass ratio Link ND_nThe generated feedback signal is taken as negative and the signal generated by the adder 1 ' is fed into the adder 2 ', and the signal generated by the adder 2 ' is passed through a proportional-integral elementObtain a signal i_n(s), signal i_n(s) by a proportional segment D_nGenerated signal and input signal d_n(s) by a proportional procedure I_nThe resulting signal enters the adder 3' ", and the output signal u_dn(s) via a proportional linkThe generated feedback signal is taken as the negative of the signal generated by the adder 3 ' ″ and fed into the adder 4 ' ″, and the signal generated by the adder 4 ' ″ passes through the proportional elementGenerating an output signal u_dn(s)。

12. The modeling method for the dynamic model of the modular multilevel converter according to claim 1, wherein: the step 4 comprises the following steps:

step 4-1: the method comprises the following steps of establishing a switching period average model of an upper bridge arm and a lower bridge arm of the modular multilevel converter as follows:

$\left\{\begin{array}{c}\stackrel{\&RightArrow;}{i_s}=\stackrel{\&RightArrow;}{i_p}+\stackrel{\&RightArrow;}{i_n}\\ <i_d{>}_{Ts}=\left[\begin{array}{ccc}1& 1& 1\end{array}\right]\stackrel{\&RightArrow;}{i_p}=-\left[\begin{array}{ccc}1& 1& 1\end{array}\right]\stackrel{\&RightArrow;}{i_n}\end{array}\right.---\left(28\right)$

wherein,

$\stackrel{\&RightArrow;}{i_n}={\left[\begin{array}{ccc}<i_{na}{>}_{T_s}& <i_{nb}{>}_{T_s}& <i_{nc}{>}_{T_s}\end{array}\right]}^T,\stackrel{\&RightArrow;}{u_2}={\left[\begin{array}{ccc}<u_{2a}{>}_{T_s}& <u_{2b}{>}_{T_s}& <u_{2c}{>}_{T_s}\end{array}\right]}^T,$

the corner mark p represents an upper bridge arm module, and the corner mark n represents a lower bridge arm module;

wherein,

$\stackrel{\&RightArrow;}{u_2}=\left[\begin{array}{c}<u_{2a}{>}_{T_s}\\ <u_{2b}{>}_{T_s}\\ <u_{2c}{>}_{T_s}\end{array}\right]=\frac{<U_d{>}_{Ts}}{2}\left[\begin{array}{c}1\\ 1\\ 1\end{array}\right]+\left[\begin{array}{c}<u_{a0}{>}_{T_s}\\ <u_{b0}{>}_{T_s}\\ <u_{c0}{>}_{T_s}\end{array}\right]=\frac{<U_d{>}_{Ts}}{2}\left[\begin{array}{c}1\\ 1\\ 1\end{array}\right]+\left[\begin{array}{c}<u_{sa}{>}_{T_s}\\ <u_{sb}{>}_{T_s}\\ <u_{sc}{>}_{T_s}\end{array}\right]+<u_{N0}{>}_{T_s}\left[\begin{array}{c}1\\ 1\\ 1\end{array}\right]---\left(30\right)$

u_N0is the AC side common mode voltage;

step 4-2: a small signal alternating current model of the modular multilevel converter;

the static operating points of the modular multilevel converter are as follows:

$\left\{\begin{array}{c}\frac{{\mathrm{dI}}_{pi}}{dt}=0,\frac{{\mathrm{dU}}_{dip}}{dt}=0\\ {\mathrm{NU}}_{dip}=U_d\\ -U_d/2+u_{si}+u_{N0}+D_{pi}{\mathrm{NU}}_{dip}-R_s{I}_{pi}=0\end{array}\right.,i=a,b,c---\left(31\right)$

$\left\{\begin{array}{c}\frac{{\mathrm{dI}}_{ni}}{dt}=0,\frac{{\mathrm{dU}}_{din}}{dt}=0\\ {\mathrm{NU}}_{din}=U_d\\ U_d/2+u_{si}+u_{N0}-D_{ni}{\mathrm{NU}}_{din}-R_s{I}_{ni}=0\end{array}\right.,i=a,b,c---\left(32\right)$

obtaining small signal alternating current models of an upper bridge arm and a lower bridge arm of the modular multilevel converter:

$\left\{\begin{array}{c}\frac{d{\tilde{i}}_{pi}}{dt}=\frac{1}{L}(-\frac{{\tilde{u}}_d}{2}+{\tilde{u}}_{si}+{\tilde{u}}_{N0}+{\mathrm{ND}}_{pi}{\tilde{u}}_{dip}+N{\tilde{d}}_{pi}{U}_{dip}-R_s{\tilde{i}}_{pi})\\ \begin{array}{cc}\frac{d{\tilde{u}}_{dip}}{dt}=-\frac{1}{C}(D_{pi}{\tilde{i}}_{pi}+{\tilde{d}}_{pi}{I}_{pi})-\frac{{\tilde{u}}_{dip}}{RC}& i=a,b,c\end{array}\end{array}\right.---\left(33\right)$

$\left\{\begin{array}{c}\frac{d{\tilde{i}}_{ni}}{dt}=\frac{1}{L}(\frac{{\tilde{u}}_d}{2}+{\tilde{u}}_{si}+{\tilde{u}}_{N0}-{\mathrm{ND}}_{ni}{\tilde{u}}_{din}-N{\tilde{d}}_{ni}{U}_{din}-R_s{\tilde{i}}_{ni})\\ \begin{array}{cc}\frac{d{\tilde{u}}_{din}}{dt}=\frac{1}{C}(D_{ni}{\tilde{i}}_{ni}+{\tilde{d}}_{ni}{I}_{ni})-\frac{{\tilde{u}}_{din}}{RC}& i=a,b,c\end{array}\end{array}\right.---\left(34\right)$

$\left\{\begin{array}{c}{\tilde{i}}_{si}={\tilde{i}}_{pi}+{\tilde{i}}_{ni}\\ {\tilde{i}}_d=\underset{i=a,b,c}{\mathrm{\&Sigma;}}{\tilde{i}}_{pi}=-\underset{i=a,b,c}{\mathrm{\&Sigma;}}{\tilde{i}}_{ni}\end{array}\right.---\left(35\right).$

13. the modeling method for the dynamic model of the modular multilevel converter according to claim 12, wherein: in the modular multilevel converter upper bridge arm switching period average model, an upper bridge arm controlled voltage source Nd_pi<u_dip>_Ts、R_sAnd L are connected in series in sequence, and the upper bridge arm is controlled by a current source d_pi<i_pi>_TsR and C are connected in parallel; l, R in the average model of the switching period of the lower bridge arm of the modular multilevel converter_sAnd a lower bridge arm controlled voltage source Nd_ni<u_din>_TsSerially connected and controlled current sourced_ni<i_ni>_TsAnd R and C are mutually connected in parallel to form a lower bridge arm equivalent switching period average model.

14. The modeling method for the dynamic model of the modular multilevel converter according to claim 12, wherein: in the small-signal alternating current model of the modular multilevel converter, a signal i_pi(s) and signal i_ni(s) entering an adder to generate a signal i_si(s), signalSignal-u_si(s) and signal-u_N0(s) entering an adder to generate a signal u_1i(s), signalSignal u_si(s) sum signal u_N0(s) entering an adder to generate a signal u_2i(s)；

In the modular multilevel converter upper bridge arm small signal alternating current model, an input signal d_pi(s) by the proportional link NU_dipGenerated signal and input signal-u_1i(s) into an adder A, the signal generated by adder A and the output signal u_dip(s) pass ratio Link ND_piThe generated feedback signal enters an adder B, and the signal generated by the adder B passes through a proportional-integral linkObtain a signal i_pi(s), signal i_pi(s) by a proportional segment D_piGenerated signal and input signal d_pi(s) by a proportional procedure I_piThe generated signal enters an adder C, and the signal generated by the adder C takes the negative sum and outputs a signal u_dip(s) via a proportional linkThe generated feedback signal is taken as negative and enters an adder D, and the signal generated by the adder D passes through a proportion linkGenerating an output signal u_dip(s)；

In the modular multilevel converter lower bridge arm small signal alternating current model, an input signal d_ni(s) by the proportional link NU_dinThe resulting signal is negated and the input signal u is summed_2i(s) into an adder E, outputting the signal u_din(s) pass ratio Link ND_niThe generated feedback signal is taken as the negative sum, the signal generated by the adder E enters the adder F, and the signal generated by the adder F passes through a proportional-integral linkObtain a signal i_ni(s), signal i_ni(s) by a proportional segment D_niGenerated signal and input signal d_ni(s) by a proportional procedure I_niThe resulting signal enters adder G, which outputs signal u_din(s) via a proportional linkThe generated feedback signal is taken as the negative sum, the signal generated by the adder G enters the adder H, and the signal generated by the adder H passes through a proportion linkGenerating an output signal u_din(s)。