CN103123664A - Modeling method for dynamic model of modular multi-level convector - Google Patents

Abstract

The invention provides a modeling method for a dynamic model of a modular multi-level convector. The method comprises the following steps of establishing an upper bridge single submodule switch period average model and an upper bridge arm single submodule small signal communication model; establishing an upper bridge arm switch period average model and an upper bridge arm small signal communication model; establishing a lower bridge arm switch period average model and a lower bridge arm small signal communication model; establishing a lower bridge single submodule switch period average model and a lower bridge arm single submodule small signal communication model; and establishing a modular multi-level convector switch period average module and a modular multi-level convector small signal module. The established dynamic model of the modular multi-level convector facilitates analysis on a dynamic property and a frequency response characteristic of the modular multi-level converter, facilitates cascade control strategy design of the device, and achieves description of internal state quantity.

Description

A kind of modularization multi-level converter dynamic model modeling method

Technical field

The invention belongs to electric system technology of transmission of electricity field, be specifically related to a kind of modularization multi-level converter dynamic model modeling method.

Background technology

2002, the R.Marquart of university of Munich, Germany Federal Defence Forces and A.Lesnicar proposed novel modularized voltage with multiple levels source type transverter jointly.Succeeded in developing 17 level 2MW model machines in 2004.2009, international conference on large HV electric systems B4.48 working group was formally with its called after modularization multi-level converter (modular multilevel converter, MMC).This topological structure is connected by submodule and is consisted of converter valve, the degree of modularity is high, harmonic distortion is little, switching loss is low, be fit to the application of high-tension high-power occasion, have broad application prospects, can be used for multiple flexible DC power transmission, the flexible AC transmission devices such as flow controller, convertible static compensator between flexible DC power transmission, THE UPFC, line.2010, first modularization multi-level converter DC transmission engineering solved the problem of the local corridor anxiety of transmitting electricity and strengthens security of system stability and reliability in the Pittsburgh of California, USA and the seabed direct current cables networking between San Francisco.

Power electronic equipment mathematical model based on modularization multi-level converter is the basis of the corresponding control strategy of research.Because the main circuit bag is that non-linear, the alternating current-direct current that contains on-off element, energy-storage travelling wave tube mixes, the complication system of high frequency power frequency mixing, model description has certain difficulty, and modeling method comprises the topology model construction method and exports two kinds of modelings usually.Topology model construction method institute established model directly reflects circuit topological structure, and complexity significantly increases with the increase of switching device quantity; The output modeling usually will install equivalence and be controlled source or impedance form, and institute's established model is relatively simple, but ignore the status information of device inner member, be unfavorable for the specificity analysis of device inside.Thereby the application of these two kinds of methods all has limitation.

Summary of the invention

In order to overcome above-mentioned the deficiencies in the prior art, the invention provides a kind of modularization multi-level converter dynamic model modeling method, the modularization multi-level converter dynamic model of setting up is convenient to dynamic property and the Frequency Response of modularization multi-level converter are analyzed, be convenient to for the design of device level control strategy, and realized description to inner quantity of state.

In order to realize the foregoing invention purpose, the present invention takes following technical scheme:

A kind of modularization multi-level converter dynamic model modeling method said method comprising the steps of:

Step 1: the single submodule cycle by cycle switch average model of brachium pontis and the single submodule small-signal alternate model of upper brachium pontis in foundation;

Step 2: brachium pontis cycle by cycle switch average model and upper brachium pontis small-signal alternate model in foundation;

Step 3: set up lower brachium pontis cycle by cycle switch average model and lower brachium pontis small-signal alternate model;

Step 4: set up modularization multi-level converter cycle by cycle switch average model and modularization multi-level converter small-signal model.

Described modularization multi-level converter comprises three pairs of brachium pontis, and every pair of brachium pontis comprises brachium pontis and lower brachium pontis, and described upper brachium pontis and lower brachium pontis include N submodule and the reactor of series connection successively, and the public direct-current end is drawn in three pairs of brachium pontis parallel connections.

Described step 1 comprises the following steps:

Step 1-1: the single submodule cycle by cycle switch average model of brachium pontis in foundation;

Step 1-2: the single submodule small-signal alternate model of brachium pontis in foundation.

In described step 1-1, the equation of the single submodule of upper brachium pontis is:

$\left\{\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="u\; p"\; filenames="HSA00000756949100042.png,HSA00000756949100052.png"\; state="\{\{state\}\}">u</figure-callout>}}_p=S_p{u}_{d1p}\\ i_{d1p}=S_p{i}_p\end{array}\right.---\left(1\right)$

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

Wherein, u _p1Be the single submodule output voltage of upper brachium pontis, u _d1pBe the single submodule DC voltage of upper brachium pontis, i _d1pBe the single submodule direct-current discharge of upper brachium pontis electric current, i _pBe the single submodule output current of upper brachium pontis; S _pThe expression switch function, S _p∈ [0,1], S _pThe IGBT cut-off that=1 expression is in parallel with the submodule ac output end, another IGBT conducting, S _p=0 expression IGBT conducting in parallel with the submodule ac output end, another IGBT cut-off;

L ₁Be the single submodule inductance of upper brachium pontis, L ₁=L/N, U _d1p=U _d/ N, L are the brachium pontis reactance, U _dBe common DC bus voltage, C is single submodule Support Capacitor, u ₁' be single submodule output voltage and brachium pontis reactance pressure drop sum, R ' _sBe submodule current-limiting reactor equivalent series resistance, R ₁Be submodule main circuit loss equivalent resistance;

Ask switch periods on average to get to (2):

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

Wherein, T _sThe expression switch periods,

Expression u ₁At switch periods T _sInterior mean value, Expression S _pu _d1pAt switch periods T _sInterior mean value,

Expression i _pAt switch periods T _sInterior mean value,

Expression S _pi _pAt switch periods T _sInterior mean value,

Expression u _d1pAt switch periods T _sInterior mean value; Suppose at switch periods T _sIn, u _d1pAnd i _pChange very littlely, can get following approximation relation:

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

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

Wherein, d _pBe the switching signal dutycycle;

(4) and (5) are brought into (3), get the single submodule cycle by cycle switch average model of brachium pontis 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 single submodule cycle by cycle switch average model of described upper brachium pontis, the controlled voltage source of AC

R′ _sAnd L ₁Series connection successively, controlled voltage source

Anodal output head anode as the single submodule equivalent switch of upper brachium pontis periodic model, L ₁Not with R ' _sAn end that connects is as the negative pole of output end of the single submodule equivalent switch of upper brachium pontis periodic model; The controlled current source of DC side

R ₁Parallel with one another with C.

In described step step 1-2,

Order:

${<{{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HSA00000756949100042.png,HSA00000756949100052.png"\; state="\{\{state\}\}">u</figure-callout>}}_1}^{\&prime;}>}_{T_s}={{\mathrm{<figure-callout\; id="1"\; label="U"\; filenames="HSA00000756949100042.png,HSA00000756949100052.png"\; state="\{\{state\}\}">U</figure-callout>}}_1}^{\&prime;}+{{\tilde{u}}_1}^{\&prime;}$

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

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

d _p＝D _p+d _p

In formula, U ₁', I _p, U _d1p, D _pBe quiescent point,

d _pBe disturbance quantity; (7) substitution (6) can be got

$\left\{\begin{array}{c}\frac{d(I_p+{\tilde{i}}_p)}{\mathrm{dt}}=\frac{1}{L_1}(-{{\mathrm{<figure-callout\; id="1"\; label="U"\; filenames="HSA00000756949100042.png,HSA00000756949100052.png"\; state="\{\{state\}\}">U</figure-callout>}}_1}^{\&prime;}-{\tilde{u}}_1^{\&prime;}+({\mathrm{<figure-callout\; id="1"\; label="D"\; filenames="HSA00000756949100042.png,HSA00000756949100052.png"\; state="\{\{state\}\}">D</figure-callout>}}_1+d_p)(U_{d1p}+{\tilde{u}}_{d1p})-R_s^{\&prime;}(I_p+{\tilde{i}}_p))\\ \frac{d(U_{d1p}+{\tilde{u}}_{d1p})}{\mathrm{dt}}=\frac{1}{C}(-(D_p+d_p)(I_p+{\tilde{i}}_p)-\frac{U_{d1p}+{\tilde{u}}_{d1p}}{R_1})\end{array}\right.---\left(8\right)$

Because there is following relation in quiescent point:

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

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

U ₁′＝U _d/2-u _s＝D _pU _d1p-R _sI _p

$D_p{I}_p=\frac{U_{d1\mathrm{<figure-callout\; id="1"\; label="p\; R"\; filenames="HSA00000756949100042.png,HSA00000756949100052.png"\; state="\{\{state\}\}">p</figure-callout>}}}{R_{}}$

Wherein, u _sBe system voltage;

According to (8), ignore high-order term, get the single submodule small-signal alternate model of brachium pontis 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 single submodule small-signal alternate model of described upper brachium pontis comprises the single submodule controlled source of brachium pontis form small-signal alternate model and the single submodule transport function of upper brachium pontis block scheme form small-signal alternate model.

In the single submodule controlled source of described upper brachium pontis form small-signal alternate model, the controlled voltage source d of AC _pU _d1p, controlled voltage source R′ _sAnd L ₁Series connection successively; Controlled voltage source d _pU _d1pAnodal output head anode as the single submodule small-signal alternate model of upper brachium pontis, L ₁Not with R ' _sAn end that connects is as the negative pole of output end of the single submodule small-signal alternate model of upper brachium pontis; The controlled current source of DC side

Controlled current source d _pI _p, R ₁Parallel with one another with C; In the single submodule transport function of described upper brachium pontis block scheme form small-signal alternate model, input signal d _p(s) through proportional component U _d1pThe signal that produces ,-u ₁' (s) and output signal u _dlp(s) passing ratio link D _pThe feedback signal that produces enters totalizer 1, the signal passing ratio integral element that described totalizer 1 produces

Obtain signal i _p(s), described signal i _p(s) through proportional component D _pThe signal and the input signal d that produce _p(s) through proportional component I _pThe signal that produces enters totalizer 2, and the signal that described totalizer 2 produces is got negative and output signal u _dlp(s) through proportional component

The feedback signal that produces is got the negative totalizer 3 that enters, and the signal that described totalizer 3 produces is through proportional component Produce output signal u _dlp(s).

Described step 2 comprises the following steps:

Step 2-1: in foundation, the brachium pontis cycle by cycle switch average model is:

$\left\{\begin{array}{c}\frac{d{<i_p>}_{T_s}}{\mathrm{dt}}=\frac{1}{L}(-{<{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HSA00000756949100042.png,HSA00000756949100052.png"\; state="\{\{state\}\}">u</figure-callout>}}_1>}_{T_s}+\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}\left(d_{\mathrm{pj}}{<u_{\mathrm{dj}p}>}_{T_s}\right)-R_s{<i_p>}_{T_s})\\ \frac{d{<u_{\mathrm{djp}}>}_{T_s}}{\mathrm{dt}}=\frac{1}{C}(-d_{\mathrm{pj}}{<i_p>}_{T_s}-\frac{{<u_{\mathrm{djp}}>}_{T_s}}{R_j}),j=\mathrm{1,2},...N\end{array}\right.---\left(11\right)$

Wherein, R _jThe equivalent loss resistance of expression submodule, R _sBe brachium pontis current-limiting reactor equivalent series resistance, d _pjAnd u _djpRepresent respectively equivalent dutycycle and the dc voltage of upper j submodule of brachium pontis,

Expression u _djpAt switch periods T _sInterior mean value;

Step 2-2: in foundation, the brachium pontis small-signal alternate model is:

$\left\{\begin{array}{c}{<i_p>}_{T_s}=I_p+{\tilde{i}}_p\\ {<{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HSA00000756949100042.png,HSA00000756949100052.png"\; state="\{\{state\}\}">u</figure-callout>}}_1>}_{T_s}={\mathrm{<figure-callout\; id="1"\; label="U"\; filenames="HSA00000756949100042.png,HSA00000756949100052.png"\; state="\{\{state\}\}">U</figure-callout>}}_1+{\tilde{u}}_1\\ {<u_{\mathrm{djp}}>}_{T_s}=U_{\mathrm{djp}}+{\tilde{u}}_{\mathrm{djp}},j=\mathrm{1,2},...,N\\ d_{\mathrm{pj}}=D_{\mathrm{pj}}+d_{\mathrm{pj}},j=\mathrm{1,2},...,N\end{array}\right.---\left(12\right)$

In formula, I _p, U ₁, U _djp, D _pjBe quiescent point;

Be disturbance quantity, each quiescent point of upper brachium pontis has following relation:

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

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

${\mathrm{<figure-callout\; id="1"\; label="U"\; filenames="HSA00000756949100042.png,HSA00000756949100052.png"\; state="\{\{state\}\}">U</figure-callout>}}_1=U_d/2-u_s=\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}{D}_{\mathrm{pj}}{U}_{\mathrm{djp}}-R_s{I}_p$

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

(12) are brought into (11), obtain upper brachium pontis small-signal alternate model according to (13) and be

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

In described upper brachium pontis cycle by cycle switch average model, the controlled voltage source of each submodule cycle by cycle switch average model of AC R _sConnect successively with L, controlled voltage source

Anodal output head anode as upper brachium pontis cycle by cycle switch average model, L not with R _sAn end that connects is as the negative pole of output end of upper brachium pontis cycle by cycle switch average model; The controlled current source of each submodule cycle by cycle switch average model of DC side

R _jParallel with one another with C.

Described upper brachium pontis small-signal alternate model comprises brachium pontis controlled source form small-signal alternate model and upper brachium pontis transport function block scheme form small-signal alternate model;

In described upper brachium pontis controlled source form small-signal alternate model, the controlled voltage source d of each submodule small-signal alternate model of AC _pjU _djp, controlled voltage source

R _sConnect successively with L; Controlled voltage source d _pNU _dNpAnodal output head anode as upper brachium pontis small-signal alternate model, L not with R _sAn end that connects is as the negative pole of output end of upper brachium pontis small-signal alternate model; The controlled current source of the small-signal alternate model of each submodule of DC side

Controlled current source d _pjI _p, R _jParallel with one another respectively with C;

In described upper brachium pontis transport function block scheme form small-signal alternate model, N input signal d _pj(s) through N corresponding proportional component U _djpThe signal and the input signal-u that produce ₁(s) enter totalizer 1 '; The signal of totalizer 1 ' generation and N corresponding output signal u _djp(s) passing ratio link D _pjThe feedback signal that produces enter totalizer 2 '; The signal passing ratio integral element of totalizer 2 ' generation

Obtain signal i _p(s), described signal i _p(s) through N proportional component D _pjN the signal and N the corresponding input signal d that produce respectively _pj(s) through proportional component I _pThe signal that produces enters N corresponding totalizer 3j ', and the signal of N totalizer 3j ' generation is got N negative and corresponding output signal u _djp(s) through proportional component

The feedback signal that produces is got negative N the totalizer 4j that enter.N N proportional component corresponding to signal process that totalizer 4j produces

Produce N output signal u _djp(s).

Suppose that upper each submodule parameter of brachium pontis is symmetrical, and have:

d _p1＝d _p2＝...＝d _pN＝d _p (15)

u _d1p＝u _d2p＝...＝u _dNp＝u _dp (16)

Get

The quiescent point of upper brachium pontis small-signal alternate model changes 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)

U ₁＝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

So be simplified the brachium pontis small-signal alternate model be

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

Wherein, R represents brachium pontis main circuit loss equivalent resistance.

In simplification, the brachium pontis small-signal alternate model comprises the upper brachium pontis controlled source form small-signal alternate model of simplification and simplifies upper brachium pontis transport function block scheme form small-signal alternate model.

In described simplification in brachium pontis controlled source form small-signal alternate model, the controlled voltage source Nd of AC _pU _dp, controlled voltage source

R _sConnect successively with L, controlled voltage source Nd _pU _dpAnodal output head anode as simplifying upper brachium pontis controlled source form small-signal alternate model, L not with R _sAn end that connects is as the negative pole of output end of simplifying upper brachium pontis controlled source form small-signal alternate model; The controlled current source of DC side

Controlled current source d _pI _p, R and C parallel with one another; In described simplification in brachium pontis transport function block scheme form small-signal alternate model, input signal d _p(s) through proportional component NU _dpThe signal and the input signal-u that produce ₁(s) enter totalizer 1 ", totalizer 1 " signal and the output signal u that produce _dp(s) passing ratio link ND _pThe feedback signal that produces enters totalizer 2 ", totalizer 2 " the signal passing ratio integral element that produces

Obtain signal i _p(s), signal i _p(s) through proportional component D _pThe signal and the input signal d that produce _p(s) through proportional component I _pThe signal that produces enters totalizer 3 ", " signal that produces is got negative and output signal u to totalizer 3 _dp(s) through proportional component

The feedback signal that produces is got the negative totalizer 4 that enters, and the signal that totalizer 4 produces is through proportional component

Produce output signal u _dp(s).

Step 3 comprises the following steps:

Step 3-1: set up the lower single submodule cycle by cycle switch average model of brachium pontis and the single submodel small-signal alternate model of lower brachium pontis;

Step 3-2: set up lower brachium pontis cycle by cycle switch average model;

$\left\{\begin{array}{c}\frac{d{<i_n>}_{T_s}}{\mathrm{dt}}=\frac{1}{L}({<{\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="HSA00000756949100021.png,HSA00000756949100061.png"\; state="\{\{state\}\}">u</figure-callout>}}_2>}_{T_s}-\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}\left(d_{\mathrm{nj}}{<u_{\mathrm{djn}}>}_{T_s}\right)+R_s{<i_n>}_{T_s})\\ \frac{d{<u_{\mathrm{djn}}>}_{T_s}}{\mathrm{dt}}=\frac{1}{C}(d_{\mathrm{nj}}{<i_n>}_{T_s}+\frac{{<u_{\mathrm{djn}}>}_{T_s}}{R_j}),j=\mathrm{1,2},...N\end{array}\right.---\left(20\right)$

Wherein, d _njAnd u _djnRepresent respectively equivalent dutycycle and the dc voltage of lower j submodule of brachium pontis, Expression u _djnAt switch periods T _sInterior mean value;

Step 3-3: lower brachium pontis small-signal alternate model;

$\left\{\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HSA00000756949100042.png,HSA00000756949100052.png"\; state="\{\{state\}\}">u</figure-callout>}}_1=U_d/2-u_s\\ {\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="HSA00000756949100021.png,HSA00000756949100061.png"\; state="\{\{state\}\}">u</figure-callout>}}_2=U_d/2+u_s\end{array}\right.---\left(21\right)$

And have:

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 get

D _n≈(U _d/2+u _s)/NU _dn＝1/2+u _s/NU _dn＝1/2+u _s/U _d (24)

D _nBe quiescent point;

So be simplified lower brachium pontis small-signal alternate model be

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

In described lower brachium pontis cycle by cycle switch average model, the controlled voltage source of each submodule cycle by cycle switch average model of AC R _sConnect successively with L, controlled voltage source

Anodal output head anode as lower brachium pontis cycle by cycle switch average model, L not with R _sAn end that connects is as the negative pole of output end of lower brachium pontis cycle by cycle switch average model; The controlled current source of the single submodule cycle by cycle switch average model of DC side R _jParallel with one another with C.

Described lower brachium pontis small-signal alternate model comprises to be simplified lower brachium pontis controlled source form small-signal alternate model and simplifies lower brachium pontis transport function block scheme form small-signal alternate model;

Under described simplification in brachium pontis controlled source form small-signal alternate model, the L of AC, R _s, controlled voltage source Nd _nU _dnAnd controlled voltage source Successively the series connection, L not with R _sAn end that connects is as the output head anode of simplifying lower brachium pontis controlled source form small-signal alternate model, controlled voltage source Negative pole is as the negative pole of output end of simplifying lower brachium pontis controlled source form small-signal alternate model; The controlled current source of DC side

Controlled current source d _nI _n, R and C parallel with one another;

Under described simplification in brachium pontis transport function block scheme form small-signal alternate model, input signal d _n(s) through proportional component NU _dnThe signal that produces is got negative and input signal u ₂(s) enter totalizer 1 " '; Output signal u _dn(s) passing ratio link ND _nThe feedback signal that produces get negative and totalizer 1 " ' produce signal enter totalizer 2 " ', the totalizer 2 " ' signal passing ratio integral element that produces

Obtain signal i _n(s), signal i _n(s) signal and the input signal d that produce through proportional component Dn _n(s) through proportional component I _nThe signal that produces enters totalizer 3 " ', output signal u _dn(s) through proportional component

The feedback signal that produces get negative and totalizer 3 " ' produce signal enter totalizer 4 " ', " ' the signal that produces is through proportional component for totalizer 4

Produce output signal u _dn(s).

Described step 4 comprises the following steps:

Step 4-1: set up the upper and lower brachium pontis cycle by cycle switch average model of modularization multi-level converter as follows:

$\left\{\begin{array}{c}\frac{d\stackrel{\&RightArrow;}{i_p}}{\mathrm{dt}}=\frac{1}{L}(-\stackrel{\&RightArrow;}{{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HSA00000756949100042.png,HSA00000756949100052.png"\; state="\{\{state\}\}">u</figure-callout>}}_1}+{\mathrm{ND}}_p\stackrel{\&RightArrow;}{u_{\mathrm{dp}}}-R_s\stackrel{\&RightArrow;}{i_p})\\ \frac{d\stackrel{\&RightArrow;}{u_{\mathrm{dp}}}}{\mathrm{dt}}=-\frac{1}{C}{D}_p\stackrel{\&RightArrow;}{i_p}-\frac{\stackrel{\&RightArrow;}{u_{\mathrm{dp}}}}{\mathrm{RC}}\end{array}\right.---\left(26\right)$

$\left\{\begin{array}{c}\frac{d\stackrel{\&RightArrow;}{i_n}}{\mathrm{dt}}=\frac{1}{L}(\stackrel{\&RightArrow;}{{\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="HSA00000756949100021.png,HSA00000756949100061.png"\; state="\{\{state\}\}">u</figure-callout>}}_2}-{\mathrm{ND}}_n\stackrel{\&RightArrow;}{u_{\mathrm{dn}}}-R_s\stackrel{\&RightArrow;}{i_n})\\ \frac{d\stackrel{\&RightArrow;}{u_{\mathrm{dn}}}}{\mathrm{dt}}=\frac{1}{C}{D}_n\stackrel{\&RightArrow;}{i_n}-\frac{\stackrel{\&RightArrow;}{u_{\mathrm{dn}}}}{\mathrm{RC}}\end{array}\right.---\left(27\right)$

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

Wherein, $\stackrel{\&RightArrow;}{i_p}={\left[\begin{array}{ccc}{<i_{\mathrm{pa}}>}_{T_s}& {<i_{\mathrm{pb}}>}_{T_s}& {<i_{\mathrm{pc}}>}_{T_s}\end{array}\right]}^T,$ $\stackrel{\&RightArrow;}{{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HSA00000756949100042.png,HSA00000756949100052.png"\; state="\{\{state\}\}">u</figure-callout>}}_1}={\left[\begin{array}{ccc}{<u_{1a}>}_{T_s}& {<u_{1b}>}_{T_s}& {<u_{1c}>}_{T_s}\end{array}\right]}^T,$

D _p＝diag[d _pa d _pb d _pc]， ${\stackrel{\&RightArrow;}{u_{\mathrm{dp}}}}^T={\left[\begin{array}{ccc}{<u_{\mathrm{dap}}>}_{T_s}& {<u_{\mathrm{dbp}}>}_{T_s}& {<u_{\mathrm{dcp}}>}_{T_s}\end{array}\right]}^T,$

$\stackrel{\&RightArrow;}{i_n}={\left[\begin{array}{ccc}{<i_{\mathrm{na}}>}_{T_s}& {<i_{\mathrm{nb}}>}_{T_s}& {<i_{\mathrm{nc}}>}_{T_s}\end{array}\right]}^T,$ $\stackrel{\&RightArrow;}{{\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="HSA00000756949100021.png,HSA00000756949100061.png"\; state="\{\{state\}\}">u</figure-callout>}}_2}={\left[\begin{array}{ccc}{<u_{2a}>}_{T_s}& {<u_{2b}>}_{T_s}& {<u_{2c}>}_{T_s}\end{array}\right]}^T,$

D _n＝diag[d _na d _nb d _nc]， ${\stackrel{\&RightArrow;}{u_{\mathrm{dn}}}}^T={\left[\begin{array}{ccc}{<u_{\mathrm{dan}}>}_{T_s}& {<u_{\mathrm{dbn}}>}_{T_s}& {<u_{\mathrm{dcn}}>}_{T_s}\end{array}\right]}^T,$

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

Wherein, $\stackrel{\&RightArrow;}{{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HSA00000756949100042.png,HSA00000756949100052.png"\; state="\{\{state\}\}">u</figure-callout>}}_1}=\left[\begin{array}{c}{<u_{1a}>}_{T_s}\\ {<u_{1b}>}_{T_s}\\ {<u_{1c}>}_{T_s}\end{array}\right]=\frac{{<U_d>}_{\mathrm{<figure-callout\; id="2"\; label="Ts"\; filenames="HSA00000756949100021.png,HSA00000756949100061.png"\; state="\{\{state\}\}">Ts</figure-callout>}}}{2}\left[\begin{array}{c}1\\ 1\\ 1\end{array}\right]-\left[\begin{array}{c}{<u_{a0}>}_{T_s}\\ {<u_{b0}>}_{T_s}\\ {<u_{c0}>}_{T_s}\end{array}\right]=\frac{{<U_d>}_{\mathrm{<figure-callout\; id="2"\; label="Ts"\; filenames="HSA00000756949100021.png,HSA00000756949100061.png"\; state="\{\{state\}\}">Ts</figure-callout>}}}{2}\left[\begin{array}{c}1\\ 1\\ 1\end{array}\right]-\left[\begin{array}{c}{<u_{\mathrm{sa}}>}_{T_s}\\ {<u_{\mathrm{sb}}>}_{T_s}\\ {<u_{\mathrm{sc}}>}_{T_s}\end{array}\right]-{<u_{N0}>}_{T_s}\left[\begin{array}{c}1\\ 1\\ 1\end{array}\right]---\left(29\right)$

$\stackrel{\&RightArrow;}{{\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="HSA00000756949100021.png,HSA00000756949100061.png"\; state="\{\{state\}\}">u</figure-callout>}}_2}=\left[\begin{array}{c}{<u_{2a}>}_{T_s}\\ {<u_{2b}>}_{T_s}\\ {<u_{2c}>}_{T_s}\end{array}\right]=\frac{{<U_d>}_{\mathrm{<figure-callout\; id="2"\; label="Ts"\; filenames="HSA00000756949100021.png,HSA00000756949100061.png"\; state="\{\{state\}\}">Ts</figure-callout>}}}{2}\left[\begin{array}{c}1\\ 1\\ 1\end{array}\right]+\left[\begin{array}{c}{<u_{a0}>}_{T_s}\\ {<u_{b0}>}_{T_s}\\ {<u_{c0}>}_{T_s}\end{array}\right]=\frac{{<U_d>}_{\mathrm{<figure-callout\; id="2"\; label="Ts"\; filenames="HSA00000756949100021.png,HSA00000756949100061.png"\; state="\{\{state\}\}">Ts</figure-callout>}}}{2}\left[\begin{array}{c}1\\ 1\\ 1\end{array}\right]+\left[\begin{array}{c}{<u_{\mathrm{sa}}>}_{T_s}\\ {<u_{\mathrm{sb}}>}_{T_s}\\ {<u_{\mathrm{sc}}>}_{T_s}\end{array}\right]+{<u_{N0}>}_{T_s}\left[\begin{array}{c}1\\ 1\\ 1\end{array}\right]---\left(30\right)$

u _N0Be the AC common mode voltage;

Step 4-2: modularization multi-level converter small-signal alternate model;

The modularization multi-level converter quiescent point has following relation:

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

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

Obtain the upper and lower brachium pontis small-signal alternate model of modularization multi-level converter:

$\left\{\begin{array}{cc}\frac{d{\tilde{i}}_{\mathrm{pi}}}{\mathrm{dt}}=\frac{1}{L}(-\frac{{\tilde{u}}_{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="HSA00000756949100021.png,HSA00000756949100061.png"\; state="\{\{state\}\}">d</figure-callout>}}}{2}+{\tilde{u}}_{\mathrm{si}}+{\tilde{u}}_{N0}+{\mathrm{ND}}_{\mathrm{pi}}{\tilde{u}}_{\mathrm{dpi}}+N{\tilde{d}}_{\mathrm{pi}}{U}_{\mathrm{dpi}}-R_s{\tilde{i}}_{\mathrm{pi}})& \\ \frac{d{\tilde{u}}_{\mathrm{dpi}}}{\mathrm{dt}}=-\frac{1}{C}(D_{\mathrm{pi}}{\tilde{i}}_{\mathrm{pi}}+{\tilde{d}}_{\mathrm{pi}}{I}_{\mathrm{pi}})-\frac{{\tilde{u}}_{\mathrm{dpi}}}{\mathrm{RC}}& i=a,b,c\end{array}\right.---\left(33\right)$

$\left\{\begin{array}{cc}\frac{d{\tilde{i}}_{\mathrm{ni}}}{\mathrm{dt}}=\frac{1}{L}(\frac{{\tilde{u}}_{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="HSA00000756949100021.png,HSA00000756949100061.png"\; state="\{\{state\}\}">d</figure-callout>}}}{2}+{\tilde{u}}_{\mathrm{si}}+{\tilde{u}}_{N0}-{\mathrm{ND}}_{\mathrm{ni}}{\tilde{u}}_{\mathrm{dni}}-N{\tilde{d}}_{\mathrm{ni}}{U}_{\mathrm{dni}}-R_s{\tilde{i}}_{\mathrm{ni}})& \\ \frac{d{\tilde{u}}_{\mathrm{dni}}}{\mathrm{dt}}=\frac{1}{C}(D_{\mathrm{ni}}{\tilde{i}}_{\mathrm{ni}}+{\tilde{d}}_{\mathrm{ni}}{I}_{\mathrm{ni}})-\frac{{\tilde{u}}_{\mathrm{dni}}}{\mathrm{RC}}& i=a,b,c\end{array}\right.---\left(34\right)$

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

On described modularization multi-level converter in the brachium pontis cycle by cycle switch average model, upper brachium pontis controlled voltage source Nd _pi＜u _dipT _s, R _sConnect successively with L, upper brachium pontis controlled current source d _pi＜i _piT _s, R and C parallel with one another; Under described modularization multi-level converter in the brachium pontis cycle by cycle switch average model, L, R _sWith lower brachium pontis controlled voltage source Nd _ni＜u _dinT _sSeries connection successively, controlled current source d _ni＜i _niT _s, R and C parallel with one another, consist of lower bridge arm equivalent cycle by cycle switch average model.

In described modularization multi-level converter small-signal alternate model, signal i _pi(s) and signal i _ni(s) enter totalizer and produce signal i _si(s), signal

Signal-u _si(s) and signal-u _N0(s) enter totalizer and produce signal u _1i(s), signal

Signal u _si(s) and signal u _N0(s) enter totalizer and produce signal u _2i(s);

On described modularization multi-level converter in the brachium pontis small-signal alternate model, input signal d _pi(s) through proportional component NU _dipThe signal and the input signal-u that produce _1i(s) enter totalizer A, signal and output signal u that totalizer A produces _dip(s) passing ratio link ND _piThe feedback signal that produces enters totalizer B, the signal passing ratio integral element that totalizer B produces

Obtain signal i _pi(s), signal i _pi(s) through proportional component D _piThe signal and the input signal d that produce _pi(s) through proportional component I _piThe signal that produces enters totalizer C, and the signal that totalizer C produces is got negative and output signal u _dip(s) through proportional component

The feedback signal that produces is got the negative totalizer D that enters, and the signal that totalizer D produces is through proportional component

Produce output signal u _dip(s);

Under described modularization multi-level converter in the brachium pontis small-signal alternate model, input signal d _ni(s) through proportional component NU _dinThe signal that produces is got negative and input signal u _2i(s) enter totalizer E, output signal u _din(s) passing ratio link ND _niThe feedback signal that produces is got signal negative and that totalizer E produces and is entered totalizer F, the signal passing ratio integral element that totalizer F produces

Obtain signal i _ni(s), signal i _ni(s) through proportional component D _niThe signal and the input signal d that produce _ni(s) through proportional component I _mThe signal that produces enters totalizer G, output signal u _din(s) through proportional component The feedback signal that produces is got signal negative and that totalizer G produces and is entered totalizer H, and the signal that totalizer H produces is through proportional component

Produce output signal u _din(s).

Compared with prior art, beneficial effect of the present invention is:

1. this modularization multi-level converter dynamic model is the power electronic equipments such as THE UPFC, flexible DC power transmission specificity analysis and control strategy have been established solid foundation;

2. this this modularization multi-level converter dynamic model is convenient to analyze with the dynamic property of modularization multi-level converter;

3. this modularization multi-level converter dynamic model is convenient to corresponding analysis of frequency to modularization multi-level converter;

4. this modularization multi-level converter dynamic model is convenient to the design for device level control strategy;

5. this modularization multi-level converter dynamic model has been realized the description to model internal state amount;

6. this modeling method is simple and reliable, easily carries out.

Description of drawings

Fig. 1 is a kind of modularization multi-level converter dynamic model main circuit topology figure;

Fig. 2 is submodule main circuit schematic diagram;

Fig. 3 is the single submodule equivalent circuit diagram of upper brachium pontis;

Fig. 4 is the single submodule cycle by cycle switch average model of upper brachium pontis figure;

Fig. 5 is the single submodule controlled source of upper brachium pontis form small-signal alternate model figure;

Fig. 6 is the single submodule transport function of upper brachium pontis block scheme form small-signal alternate model figure;

Fig. 7 is upper brachium pontis cycle by cycle switch average model figure;

Fig. 8 is upper brachium pontis controlled source form small-signal alternate model figure;

Fig. 9 is upper brachium pontis transport function block scheme form small-signal alternate model figure;

Figure 10 simplifies upper brachium pontis controlled source form small-signal alternate model figure;

Figure 11 simplifies upper brachium pontis transport function block scheme form small-signal alternate model figure;

Figure 12 simplifies lower brachium pontis controlled source form small-signal alternate model figure;

Figure 13 simplifies lower brachium pontis transport function block scheme form small-signal alternate model figure;

Figure 14 is modularization multi-level converter cycle by cycle switch average model figure;

Figure 15 is modularization multi-level converter small-signal alternate model figure.

Embodiment

Below in conjunction with accompanying drawing, the present invention is described in further detail.

A kind of modularization multi-level converter dynamic model modeling method said method comprising the steps of:

Step 1: the single submodule cycle by cycle switch average model of brachium pontis and the single submodule small-signal alternate model of upper brachium pontis in foundation;

Step 2: brachium pontis cycle by cycle switch average model and upper brachium pontis small-signal alternate model in foundation;

Step 3: set up lower brachium pontis cycle by cycle switch average model and lower brachium pontis small-signal alternate model;

Step 4: set up modularization multi-level converter cycle by cycle switch average model and modularization multi-level converter small-signal model.

As Fig. 1-Fig. 2, described modularization multi-level converter comprises three pairs of brachium pontis, and every pair of brachium pontis comprises brachium pontis and lower brachium pontis, and described upper brachium pontis and lower brachium pontis include N submodule and the reactor of series connection successively, and the public direct-current end is drawn in three pairs of brachium pontis parallel connections.

Described step 1 comprises the following steps:

Step 1-1: the single submodule cycle by cycle switch average model of brachium pontis in foundation;

Step 1-2: the single submodule small-signal alternate model of brachium pontis in foundation.

In described step 1-1, as Fig. 3, the equation of the single submodule of upper brachium pontis is:

$\left\{\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="u\; p"\; filenames="HSA00000756949100042.png,HSA00000756949100052.png"\; state="\{\{state\}\}">u</figure-callout>}}_p=S_p{u}_{d1p}\\ i_{d1p}=S_p{i}_p\end{array}\right.---\left(1\right)$

$\left\{\begin{array}{c}\frac{{\mathrm{di}}_p}{\mathrm{dt}}=\frac{1}{L_1}({{-\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HSA00000756949100042.png,HSA00000756949100052.png"\; state="\{\{state\}\}">u</figure-callout>}}_1}^{\&prime;}+S_p{u}_{d1p}-R_s^{\&prime;}{i}_p)\\ \frac{{\mathrm{du}}_{d1p}}{\mathrm{dt}}=\frac{1}{C}(-S_p{i}_p-\frac{u_{d1p}}{R_1})\end{array}\right.---\left(2\right)$

Wherein, u _p1Be the single submodule output voltage of upper brachium pontis, u _d1pBe the single submodule DC voltage of upper brachium pontis, i _d1pBe the single submodule direct-current discharge of upper brachium pontis electric current, i _pBe the single submodule output current of upper brachium pontis; S _pThe expression switch function, S _p∈ [0,1], S _lThe IGB2 cut-off that=1 expression is in parallel with the submodule ac output end, IGBT1 conducting, S _p=0 expression IGBT2 conducting in parallel with the submodule ac output end, the IGBT1 cut-off;

L ₁Be the single submodule inductance of upper brachium pontis, L ₁=L/N, U _d1p=U _d/ N, L are the brachium pontis reactance, U _dBe common DC bus voltage, C is single submodule Support Capacitor, u ₁' be single submodule output voltage and brachium pontis reactance pressure drop sum, R ' _sBe submodule current-limiting reactor equivalent series resistance, R ₁Be submodule main circuit loss equivalent resistance;

Ask switch periods on average to get to (2):

$\left\{\begin{array}{c}\frac{d{<i_p>}_{T_s}}{\mathrm{dt}}=\frac{1}{L_1}(-{<{{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HSA00000756949100042.png,HSA00000756949100052.png"\; state="\{\{state\}\}">u</figure-callout>}}_1}^{\&prime;}>}_{T_s}+{<S_p{u}_{d1p}>}_{T_s}-R_s^{\&prime;}{<i_p>}_{T_s})\\ \frac{d{<u_{d1p}>}_{T_s}}{\mathrm{dt}}=\frac{1}{C}(-{<S_p{i}_p>}_{T_s}-\frac{{<u_{d1p}>}_{T_s}}{R_1})\end{array}\right.---\left(3\right)$

Wherein, T _sThe expression switch periods,

Expression u ₁At switch periods T _sInterior mean value,

Expression S _pu′ _d1pAt switch periods T _sInterior mean value,

Expression i _pAt switch periods T _sInterior mean value,

Expression S _pi _pAt switch periods T _sInterior mean value,

Expression u _d1pAt switch periods T _sInterior mean value; Suppose at switch periods T _sIn, u _d1pAnd i _pChange very littlely, can get following approximation relation:

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

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

Wherein, d _pBe the switching signal dutycycle;

(4) and (5) are brought into (3), get the single submodule cycle by cycle switch average model of brachium pontis as follows:

$\left\{\begin{array}{c}\frac{d{<i_p>}_{T_s}}{\mathrm{dt}}=\frac{1}{L_1}(-{<{{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HSA00000756949100042.png,HSA00000756949100052.png"\; state="\{\{state\}\}">u</figure-callout>}}_1}^{\&prime;}>}_{T_s}+d_p{<u_{d1p}>}_{T_s}-R_s^{\&prime;}{<i_p>}_{T_s})\\ \frac{d{<u_{d1p}>}_{T_s}}{\mathrm{dt}}=-\frac{1}{C}(d_p{<i_p>}_{T_s}+\frac{{<u_{d1p}>}_{T_s}}{R_1})\end{array}\right.---\left(6\right).$

As Fig. 4, in the single submodule cycle by cycle switch average model of described upper brachium pontis, the controlled voltage source of AC

R′ _sAnd L ₁Series connection successively, controlled voltage source

Anodal output head anode as the single submodule equivalent switch of upper brachium pontis periodic model, L ₁Not with R ' _sAn end that connects is as the negative pole of output end of the single submodule equivalent switch of upper brachium pontis periodic model; The controlled current source of DC side

R ₁Parallel with one another with C.

In described step step 1-2,

Order:

${<{{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HSA00000756949100042.png,HSA00000756949100052.png"\; state="\{\{state\}\}">u</figure-callout>}}_1}^{\&prime;}>}_{T_s}={{\mathrm{<figure-callout\; id="1"\; label="U"\; filenames="HSA00000756949100042.png,HSA00000756949100052.png"\; state="\{\{state\}\}">U</figure-callout>}}_1}^{\&prime;}+{{\tilde{u}}_1}^{\&prime;}$

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

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

d _p＝D _p+d _p

In formula, U ₁', I _p, U _d1p, D _pBe quiescent point,

d _pBe disturbance quantity; (7) substitution (6) can be got

$\left\{\begin{array}{c}\frac{d(I_p+{\tilde{i}}_p)}{\mathrm{dt}}=\frac{1}{L_1}(-{{\mathrm{<figure-callout\; id="1"\; label="U"\; filenames="HSA00000756949100042.png,HSA00000756949100052.png"\; state="\{\{state\}\}">U</figure-callout>}}_1}^{\&prime;}-{\tilde{u}}_1^{\&prime;}+({\mathrm{<figure-callout\; id="1"\; label="D"\; filenames="HSA00000756949100042.png,HSA00000756949100052.png"\; state="\{\{state\}\}">D</figure-callout>}}_1+d_p)(U_{d1p}+{\tilde{u}}_{d1p})-R_s^{\&prime;}(I_p+{\tilde{i}}_p))\\ \frac{d(U_{d1p}+{\tilde{u}}_{d1p})}{\mathrm{dt}}=\frac{1}{C}(-(D_p+d_p)(I_p+{\tilde{i}}_p)-\frac{U_{d1p}+{\tilde{u}}_{d1p}}{R_1})\end{array}\right.---\left(8\right)$

Because there is following relation in quiescent point:

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

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

U ₁′＝U _d/2-u _s＝D _pU _d1p-R _sI _p

$D_p{I}_p=\frac{U_{d1\mathrm{<figure-callout\; id="1"\; label="p\; R"\; filenames="HSA00000756949100042.png,HSA00000756949100052.png"\; state="\{\{state\}\}">p</figure-callout>}}}{R_{}}$

Wherein, u _sBe system voltage;

According to (8), ignore high-order term, get the single submodule small-signal alternate model of brachium pontis 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 single submodule small-signal alternate model of described upper brachium pontis comprises the single submodule controlled source of brachium pontis form small-signal alternate model and the single submodule transport function of upper brachium pontis block scheme form small-signal alternate model.

As Fig. 5, in the single submodule controlled source of described upper brachium pontis form small-signal alternate model, the controlled voltage source d of AC _pU _d1p, controlled voltage source

R′ _sAnd L ₁Series connection successively; Controlled voltage source d _pU _d1pAnodal output head anode as the single submodule small-signal alternate model of upper brachium pontis, L ₁Not with R ' _sAn end that connects is as the negative pole of output end of the single submodule small-signal alternate model of upper brachium pontis; The controlled current source of DC side

Controlled current source d _pI _p, R ₁Parallel with one another with C; As Fig. 6, in the single submodule transport function of described upper brachium pontis block scheme form small-signal alternate model, 3 totalizers are followed successively by totalizer 1, totalizer 2 and totalizer 3, input signal d from left to right _p(s) through proportional component U _d1pThe signal that produces ,-u ₁' (s) and output signal u _dlp(s) passing ratio link D _pThe feedback signal that produces enters totalizer 1, the signal passing ratio integral element that described totalizer 1 produces Obtain signal i _p(s), described signal i _p(s) through proportional component D _pThe signal and the input signal d that produce _p(s) through proportional component I _pThe signal that produces enters totalizer 2, and the signal that described totalizer 2 produces is got negative and output signal u _dp(s) through proportional component The feedback signal that produces is got the negative totalizer 3 that enters, and the signal that described totalizer 3 produces is through proportional component

Produce output signal u _dlp(s).

Described step 2 comprises the following steps:

Step 2-1: in foundation, the brachium pontis cycle by cycle switch average model is:

$\left\{\begin{array}{c}\frac{d{<i_p>}_{T_s}}{\mathrm{dt}}=\frac{1}{L}(-{<{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HSA00000756949100042.png,HSA00000756949100052.png"\; state="\{\{state\}\}">u</figure-callout>}}_1>}_{T_s}+\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}\left(d_{\mathrm{pj}}{<u_{\mathrm{dj}p}>}_{T_s}\right)-R_s{<i_p>}_{T_s})\\ \frac{d{<u_{\mathrm{djp}}>}_{T_s}}{\mathrm{dt}}=\frac{1}{C}(-d_{\mathrm{pj}}{<i_p>}_{T_s}-\frac{{<u_{\mathrm{djp}}>}_{T_s}}{R_j}),j=\mathrm{1,2},...N\end{array}\right.---\left(11\right)$

Wherein, R _jThe equivalent loss resistance of expression submodule, R _sBe brachium pontis current-limiting reactor equivalent series resistance, d _pjAnd u _djpRepresent respectively equivalent dutycycle and the dc voltage of upper j submodule of brachium pontis, Expression u _djpAt switch periods T _sInterior mean value;

Step 2-2: in foundation, the brachium pontis small-signal alternate model is:

$\left\{\begin{array}{c}{<i_p>}_{T_s}=I_p+{\tilde{i}}_p\\ {<{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HSA00000756949100042.png,HSA00000756949100052.png"\; state="\{\{state\}\}">u</figure-callout>}}_1>}_{T_s}={\mathrm{<figure-callout\; id="1"\; label="U"\; filenames="HSA00000756949100042.png,HSA00000756949100052.png"\; state="\{\{state\}\}">U</figure-callout>}}_1+{\tilde{u}}_1\\ {<u_{\mathrm{djp}}>}_{T_s}=U_{\mathrm{djp}}+{\tilde{u}}_{\mathrm{djp}},j=\mathrm{1,2},...,N\\ d_{\mathrm{pj}}=D_{\mathrm{pj}}+d_{\mathrm{pj}},j=\mathrm{1,2},...,N\end{array}\right.---\left(12\right)$

In formula, I _p, U ₁, U _djp, D _pjBe quiescent point;

d _pjBe disturbance quantity, each quiescent point of upper brachium pontis has following relation:

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

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

${\mathrm{<figure-callout\; id="1"\; label="U"\; filenames="HSA00000756949100042.png,HSA00000756949100052.png"\; state="\{\{state\}\}">U</figure-callout>}}_1=U_d/2-u_s=\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}{D}_{\mathrm{pj}}{U}_{\mathrm{djp}}-R_s{I}_p$

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

(12) are brought into (11), obtain upper brachium pontis small-signal alternate model according to (13) and be

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

As Fig. 7, in described upper brachium pontis cycle by cycle switch average model, the controlled voltage source of each submodule cycle by cycle switch average model of AC

R _sConnect successively with L, controlled voltage source

Anodal output head anode as upper brachium pontis cycle by cycle switch average model, L not with R _sAn end that connects is as the negative pole of output end of upper brachium pontis cycle by cycle switch average model; The controlled current source of each submodule cycle by cycle switch average model of DC side

R _jParallel with one another with C.

Described upper brachium pontis small-signal alternate model comprises brachium pontis controlled source form small-signal alternate model and upper brachium pontis transport function block scheme form small-signal alternate model;

As Fig. 8, in described upper brachium pontis controlled source form small-signal alternate model, the controlled voltage source d of each submodule small-signal alternate model of AC _pjU _djp, controlled voltage source

R _sConnect successively with L; Controlled voltage source d _pNU _dNpAnodal output head anode as upper brachium pontis small-signal alternate model, L not with R _sAn end that connects is as the negative pole of output end of upper brachium pontis small-signal alternate model; The controlled current source of the small-signal alternate model of each submodule of DC side Controlled current source d _pjI _p, R _jParallel with one another respectively with C;

As Fig. 9, in described upper brachium pontis transport function block scheme form small-signal alternate model, 4 totalizers be followed successively by from left to right totalizer 1 ', totalizer 2 ', totalizer 3 ' and totalizer 4 ', N input signal d _pj(s) through N corresponding proportional component U _djpThe signal and the input signal-u that produce ₁(s) enter totalizer 1 '; The signal of totalizer 1 ' generation and N corresponding output signal u _djp(s) passing ratio link D _pjThe feedback signal that produces enter totalizer 2 '; The signal passing ratio integral element of totalizer 2 ' generation

Obtain signal i _p(s), described signal i _p(s) through N proportional component D _pjN the signal and N the corresponding input signal d that produce respectively _pj(s) through proportional component I _pThe signal that produces enters N corresponding totalizer 3j ', and the signal of N totalizer 3j ' generation is got N negative and corresponding output signal u _djp(s) through proportional component

The feedback signal that produces is got negative N the totalizer 4j that enter.N N proportional component corresponding to signal process that totalizer 4j produces

Produce N output signal u _djp(s).

Suppose that upper each submodule parameter of brachium pontis is symmetrical, and have:

d _p1＝d _p2＝...＝d _pN＝d _p (15)

u _d1p＝u _d2p＝…＝u _dNp＝u _dp (16)

Get

The quiescent point of upper brachium pontis small-signal alternate model changes 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)

U ₁＝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

So be simplified the brachium pontis small-signal alternate model be

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

Wherein, R represents brachium pontis main circuit loss equivalent resistance.

In simplification, the brachium pontis small-signal alternate model comprises the upper brachium pontis controlled source form small-signal alternate model of simplification and simplifies upper brachium pontis transport function block scheme form small-signal alternate model.

As Figure 10, in described simplification in brachium pontis controlled source form small-signal alternate model, the controlled voltage source Nd of AC _pU _dp, controlled voltage source R _sConnect successively with L, controlled voltage source Nd _pU _dpAnodal output head anode as simplifying upper brachium pontis controlled source form small-signal alternate model, L not with R _sAn end that connects is as the negative pole of output end of simplifying upper brachium pontis controlled source form small-signal alternate model; The controlled current source of DC side

Controlled current source d _pI _p, R and C parallel with one another;

As Figure 11, in described simplification in brachium pontis transport function block scheme form small-signal alternate model, 4 totalizers are followed successively by totalizer 1 ", totalizer 2 ", totalizer 3 " and totalizer 4 ", input signal d from left to right _p(s) through proportional component NU _dpThe signal and the input signal-u that produce ₁(s) enter totalizer 1 ", totalizer 1 " signal and the output signal u that produce _dp(s) passing ratio link ND _pThe feedback signal that produces enters totalizer 2 ", totalizer 2 " the signal passing ratio integral element that produces Obtain signal i _p(s), signal i _p(s) through proportional component D _pThe signal and the input signal d that produce _p(s) through proportional component I _pThe signal that produces enters totalizer 3 ", " signal that produces is got negative and output signal u to totalizer 3 _dp(s) through proportional component

The feedback signal that produces is got the negative totalizer 4 that enters, and the signal that totalizer 4 produces is through proportional component Produce output signal u _dp(s).

Step 3 comprises the following steps:

Step 3-1: set up the lower single submodule cycle by cycle switch average model of brachium pontis and the single submodel small-signal alternate model of lower brachium pontis;

Step 3-2: set up lower brachium pontis cycle by cycle switch average model;

$\left\{\begin{array}{c}\frac{d{<i_n>}_{T_s}}{\mathrm{dt}}=\frac{1}{L}({<{\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="HSA00000756949100021.png,HSA00000756949100061.png"\; state="\{\{state\}\}">u</figure-callout>}}_2>}_{T_s}-\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}\left(d_{\mathrm{nj}}{<u_{\mathrm{djn}}>}_{T_s}\right)+R_s{<i_n>}_{T_s})\\ \frac{d{<u_{\mathrm{djn}}>}_{T_s}}{\mathrm{dt}}=\frac{1}{C}(d_{\mathrm{nj}}{<i_n>}_{T_s}+\frac{{<u_{\mathrm{djn}}>}_{T_s}}{R_j}),j=\mathrm{1,2},...N\end{array}\right.---\left(20\right)$

Wherein, d _njAnd u _djnRepresent respectively equivalent dutycycle and the dc voltage of lower j submodule of brachium pontis,

Expression u _djnAt switch periods T _sInterior mean value;

Step 3-3: lower brachium pontis small-signal alternate model;

$\left\{\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HSA00000756949100042.png,HSA00000756949100052.png"\; state="\{\{state\}\}">u</figure-callout>}}_1=U_d/2-u_s\\ {\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="HSA00000756949100021.png,HSA00000756949100061.png"\; state="\{\{state\}\}">u</figure-callout>}}_2=U_d/2+u_s\end{array}\right.---\left(21\right)$

And have:

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 get

D _n≈(U _d/2+u _s)/NU _dn＝1/2+u _s/NU _dn＝1/2+u _s/U _d (24)

D _nBe quiescent point;

So be simplified lower brachium pontis small-signal alternate model be

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

In described lower brachium pontis cycle by cycle switch average model, the controlled voltage source of each submodule cycle by cycle switch average model of AC

R _sConnect successively with L, controlled voltage source

Anodal output head anode as lower brachium pontis cycle by cycle switch average model, L not with R _sAn end that connects is as the negative pole of output end of lower brachium pontis cycle by cycle switch average model; The controlled current source of the single submodule cycle by cycle switch average model of DC side

R _jParallel with one another with C.

Described lower brachium pontis small-signal alternate model comprises to be simplified lower brachium pontis controlled source form small-signal alternate model and simplifies lower brachium pontis transport function block scheme form small-signal alternate model;

As Figure 12, under described simplification in brachium pontis controlled source form small-signal alternate model, the L of AC, R _s, controlled voltage source Nd _nU _dnAnd controlled voltage source

Successively the series connection, L not with R _sAn end that connects is as the output head anode of simplifying lower brachium pontis controlled source form small-signal alternate model, controlled voltage source Negative pole is as the negative pole of output end of simplifying lower brachium pontis controlled source form small-signal alternate model; The controlled current source of DC side

Controlled current source d _nI _n, R and C parallel with one another;

As Figure 13, under described simplification in brachium pontis transport function block scheme form small-signal alternate model, 4 totalizers be followed successively by from left to right totalizer 1 " ', totalizer 2 " ', totalizer 3 " ' and totalizer 4 " ', input signal d _n(s) through proportional component NU _dnThe signal that produces is got negative and input signal u ₂(s) enter totalizer 1 " '; Output signal u _dn(s) passing ratio link ND _nThe feedback signal that produces get negative and totalizer 1 " ' produce signal enter totalizer 2 " ', the totalizer 2 " ' signal passing ratio integral element that produces

Obtain signal i _n(s), signal i _n(s) through proportional component D _nThe signal and the input signal d that produce _n(s) through proportional component I _nThe signal that produces enters totalizer 3 " ', output signal u _dn(s) through proportional component

The feedback signal that produces get negative and totalizer 3 " ' produce signal enter totalizer 4 " ', " ' the signal that produces is through proportional component for totalizer 4 Produce output signal u _dn(s).

Described step 4 comprises the following steps:

Step 4-1: set up the upper and lower brachium pontis cycle by cycle switch average model of modularization multi-level converter as follows:

$\left\{\begin{array}{c}\frac{d\stackrel{\&RightArrow;}{i_p}}{\mathrm{dt}}=\frac{1}{L}(-\stackrel{\&RightArrow;}{{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HSA00000756949100042.png,HSA00000756949100052.png"\; state="\{\{state\}\}">u</figure-callout>}}_1}+{\mathrm{ND}}_p\stackrel{\&RightArrow;}{u_{\mathrm{dp}}}-R_s\stackrel{\&RightArrow;}{i_p})\\ \frac{d\stackrel{\&RightArrow;}{u_{\mathrm{dp}}}}{\mathrm{dt}}=-\frac{1}{C}{D}_p\stackrel{\&RightArrow;}{i_p}-\frac{\stackrel{\&RightArrow;}{u_{\mathrm{dp}}}}{\mathrm{RC}}\end{array}\right.---\left(26\right)$

$\left\{\begin{array}{c}\frac{d\stackrel{\&RightArrow;}{i_n}}{\mathrm{dt}}=\frac{1}{L}(\stackrel{\&RightArrow;}{{\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="HSA00000756949100021.png,HSA00000756949100061.png"\; state="\{\{state\}\}">u</figure-callout>}}_2}-{\mathrm{ND}}_n\stackrel{\&RightArrow;}{u_{\mathrm{dn}}}-R_s\stackrel{\&RightArrow;}{i_n})\\ \frac{d\stackrel{\&RightArrow;}{u_{\mathrm{dn}}}}{\mathrm{dt}}=\frac{1}{C}{D}_n\stackrel{\&RightArrow;}{i_n}-\frac{\stackrel{\&RightArrow;}{u_{\mathrm{dn}}}}{\mathrm{RC}}\end{array}\right.---\left(27\right)$

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

Wherein, $\stackrel{\&RightArrow;}{i_p}={\left[\begin{array}{ccc}{<i_{\mathrm{pa}}>}_{T_s}& {<i_{\mathrm{pb}}>}_{T_s}& {<i_{\mathrm{pc}}>}_{T_s}\end{array}\right]}^T,$ $\stackrel{\&RightArrow;}{{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HSA00000756949100042.png,HSA00000756949100052.png"\; state="\{\{state\}\}">u</figure-callout>}}_1}={\left[\begin{array}{ccc}{<u_{1a}>}_{T_s}& {<u_{1b}>}_{T_s}& {<u_{1c}>}_{T_s}\end{array}\right]}^T,$

D _p＝diag[d _pa d _pb d _pc]， ${\stackrel{\&RightArrow;}{u_{\mathrm{dp}}}}^T={\left[\begin{array}{ccc}{<u_{\mathrm{dap}}>}_{T_s}& {<u_{\mathrm{dbp}}>}_{T_s}& {<u_{\mathrm{dcp}}>}_{T_s}\end{array}\right]}^T,$

$\stackrel{\&RightArrow;}{i_n}={\left[\begin{array}{ccc}{<i_{\mathrm{na}}>}_{T_s}& {<i_{\mathrm{nb}}>}_{T_s}& {<i_{\mathrm{nc}}>}_{T_s}\end{array}\right]}^T,$ $\stackrel{\&RightArrow;}{{\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="HSA00000756949100021.png,HSA00000756949100061.png"\; state="\{\{state\}\}">u</figure-callout>}}_2}={\left[\begin{array}{ccc}{<u_{2a}>}_{T_s}& {<u_{2b}>}_{T_s}& {<u_{2c}>}_{T_s}\end{array}\right]}^T,$

D _n＝diag[d _na d _nb d _nc]， ${\stackrel{\&RightArrow;}{u_{\mathrm{dn}}}}^T={\left[\begin{array}{ccc}{<u_{\mathrm{dan}}>}_{T_s}& {<u_{\mathrm{dbn}}>}_{T_s}& {<u_{\mathrm{dcn}}>}_{T_s}\end{array}\right]}^T,$

Footmark p represents bridge arm module, and footmark n represents lower bridge arm module; Wherein, $\stackrel{\&RightArrow;}{{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HSA00000756949100042.png,HSA00000756949100052.png"\; state="\{\{state\}\}">u</figure-callout>}}_1}=\left[\begin{array}{c}{<u_{1a}>}_{T_s}\\ {<u_{1b}>}_{T_s}\\ {<u_{1c}>}_{T_s}\end{array}\right]=\frac{{<U_d>}_{\mathrm{<figure-callout\; id="2"\; label="Ts"\; filenames="HSA00000756949100021.png,HSA00000756949100061.png"\; state="\{\{state\}\}">Ts</figure-callout>}}}{2}\left[\begin{array}{c}1\\ 1\\ 1\end{array}\right]-\left[\begin{array}{c}{<u_{a0}>}_{T_s}\\ {<u_{b0}>}_{T_s}\\ {<u_{c0}>}_{T_s}\end{array}\right]=\frac{{<U_d>}_{\mathrm{<figure-callout\; id="2"\; label="Ts"\; filenames="HSA00000756949100021.png,HSA00000756949100061.png"\; state="\{\{state\}\}">Ts</figure-callout>}}}{2}\left[\begin{array}{c}1\\ 1\\ 1\end{array}\right]-\left[\begin{array}{c}{<u_{\mathrm{sa}}>}_{T_s}\\ {<u_{\mathrm{sb}}>}_{T_s}\\ {<u_{\mathrm{sc}}>}_{T_s}\end{array}\right]-{<u_{N0}>}_{T_s}\left[\begin{array}{c}1\\ 1\\ 1\end{array}\right]---\left(29\right)$

$\stackrel{\&RightArrow;}{{\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="HSA00000756949100021.png,HSA00000756949100061.png"\; state="\{\{state\}\}">u</figure-callout>}}_2}=\left[\begin{array}{c}{<u_{2a}>}_{T_s}\\ {<u_{2b}>}_{T_s}\\ {<u_{2c}>}_{T_s}\end{array}\right]=\frac{{<U_d>}_{\mathrm{<figure-callout\; id="2"\; label="Ts"\; filenames="HSA00000756949100021.png,HSA00000756949100061.png"\; state="\{\{state\}\}">Ts</figure-callout>}}}{2}\left[\begin{array}{c}1\\ 1\\ 1\end{array}\right]+\left[\begin{array}{c}{<u_{a0}>}_{T_s}\\ {<u_{b0}>}_{T_s}\\ {<u_{c0}>}_{T_s}\end{array}\right]=\frac{{<U_d>}_{\mathrm{<figure-callout\; id="2"\; label="Ts"\; filenames="HSA00000756949100021.png,HSA00000756949100061.png"\; state="\{\{state\}\}">Ts</figure-callout>}}}{2}\left[\begin{array}{c}1\\ 1\\ 1\end{array}\right]+\left[\begin{array}{c}{<u_{\mathrm{sa}}>}_{T_s}\\ {<u_{\mathrm{sb}}>}_{T_s}\\ {<u_{\mathrm{sc}}>}_{T_s}\end{array}\right]+{<u_{N0}>}_{T_s}\left[\begin{array}{c}1\\ 1\\ 1\end{array}\right]---\left(30\right)$

u _N0Be the AC common mode voltage;

Step 4-2: modularization multi-level converter small-signal alternate model;

The modularization multi-level converter quiescent point has following relation:

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

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

Obtain the upper and lower brachium pontis small-signal alternate model of modularization multi-level converter:

$\left\{\begin{array}{cc}\frac{d{\tilde{i}}_{\mathrm{pi}}}{\mathrm{dt}}=\frac{1}{L}(-\frac{{\tilde{u}}_{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="HSA00000756949100021.png,HSA00000756949100061.png"\; state="\{\{state\}\}">d</figure-callout>}}}{2}+{\tilde{u}}_{\mathrm{si}}+{\tilde{u}}_{N0}+{\mathrm{ND}}_{\mathrm{pi}}{u}_{\mathrm{dpi}}+N{\tilde{d}}_{\mathrm{pi}}{U}_{\mathrm{dpi}}-R_s{\tilde{i}}_{\mathrm{pi}})& \\ \frac{d{\tilde{u}}_{\mathrm{dpi}}}{\mathrm{dt}}=-\frac{1}{C}(D_{\mathrm{pi}}{\tilde{i}}_{\mathrm{pi}}+{\tilde{d}}_{\mathrm{pi}}{I}_{\mathrm{pi}})-\frac{{\tilde{u}}_{\mathrm{dpi}}}{\mathrm{RC}}& i=a,b,c\end{array}\right.---\left(33\right)$

$\left\{\begin{array}{cc}\frac{d{\tilde{i}}_{\mathrm{ni}}}{\mathrm{dt}}=\frac{1}{L}(\frac{{\tilde{u}}_{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="HSA00000756949100021.png,HSA00000756949100061.png"\; state="\{\{state\}\}">d</figure-callout>}}}{2}+{\tilde{u}}_{\mathrm{si}}+{\tilde{u}}_{N0}-{\mathrm{ND}}_{\mathrm{ni}}{\tilde{u}}_{\mathrm{dni}}-N{\tilde{d}}_{\mathrm{ni}}{U}_{\mathrm{dni}}-R_s{\tilde{i}}_{\mathrm{ni}})& \\ \frac{d{\tilde{u}}_{\mathrm{dni}}}{\mathrm{dt}}=\frac{1}{C}(D_{\mathrm{ni}}{\tilde{i}}_{\mathrm{ni}}+{\tilde{d}}_{\mathrm{ni}}{I}_{\mathrm{ni}})-\frac{{\tilde{u}}_{\mathrm{dni}}}{\mathrm{RC}}& i=a,b,c\end{array}\right.---\left(34\right)$

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

As Figure 14, on described modularization multi-level converter in the brachium pontis cycle by cycle switch average model, upper brachium pontis controlled voltage source Nd _pi＜u _{dip Ts}, R _sConnect successively with L, upper brachium pontis controlled current source d _pi＜i _{pi Ts}, R and C parallel with one another; Under described modularization multi-level converter in the brachium pontis cycle by cycle switch average model, L, R _sWith lower brachium pontis controlled voltage source Nd _ni＜u _{din Ts}Series connection successively, controlled current source d _ni＜i _{ni Ts}, R and C parallel with one another, consist of lower bridge arm equivalent cycle by cycle switch average model.

As Figure 15, in described modularization multi-level converter small-signal alternate model, signal i _pi(s) and signal i _ni(s) enter totalizer and produce signal i _si(s), signal Signal-u _si(s) and signal-u _N0(s) enter totalizer and produce signal u _1i(s), signal

Signal u _si(s) and signal u _N0(s) enter totalizer and produce signal u _2i(s);

On described modularization multi-level converter, in the brachium pontis small-signal alternate model, 4 totalizers are followed successively by totalizer A, totalizer B, totalizer C and totalizer D, input signal d from left to right _pi(s) through proportional component NU _dipThe signal and the input signal-u that produce _1i(s) enter totalizer A, signal and output signal u that totalizer A produces _dip(s) passing ratio link ND _piThe feedback signal that produces enters totalizer B, the signal passing ratio integral element that totalizer B produces

Obtain signal i _pi(s), signal i _pi(s) through proportional component D _piThe signal and the input signal d that produce _pi(s) through proportional component I _piThe signal that produces enters totalizer C, and the signal that totalizer C produces is got negative and output signal u _dip(s) through proportional component

The feedback signal that produces is got the negative totalizer D that enters, and the signal that totalizer D produces is through proportional component

Produce output signal u _dip(s);

Under described modularization multi-level converter in the brachium pontis small-signal alternate model, input signal d _ni(s) through proportional component NU _dinThe signal that produces is got negative and input signal u _2i(s) enter totalizer E, output signal u _din(s) passing ratio link ND _niThe feedback signal that produces is got signal negative and that totalizer E produces and is entered totalizer F, the signal passing ratio integral element that totalizer F produces

Obtain signal i _ni(s), signal i _ni(s) through proportional component D _niThe signal and the input signal d that produce _ni(s) through proportional component I _mThe signal that produces enters totalizer G, output signal u _din(s) through proportional component

The feedback signal that produces is got signal negative and that totalizer G produces and is entered totalizer H, and the signal that totalizer H produces is through proportional component

Produce output signal u _din(s).

Should be noted that at last: above embodiment is only in order to illustrate that technical scheme of the present invention is not intended to limit, although with reference to above-described embodiment, the present invention is had been described in detail, those of ordinary skill in the field are to be understood that: still can modify or be equal to replacement the specific embodiment of the present invention, and do not break away from any modification of spirit and scope of the invention or be equal to replacement, it all should be encompassed in the middle of claim scope of the present invention.

Claims (20)

1. modularization multi-level converter dynamic model modeling method is characterized in that: said method comprising the steps of:

Step 1: the single submodule cycle by cycle switch average model of brachium pontis and the single submodule small-signal alternate model of upper brachium pontis in foundation;

Step 2: brachium pontis cycle by cycle switch average model and upper brachium pontis small-signal alternate model in foundation;

Step 3: set up lower brachium pontis cycle by cycle switch average model and lower brachium pontis small-signal alternate model;

Step 4: set up modularization multi-level converter cycle by cycle switch average model and modularization multi-level converter small-signal model.

2. modularization multi-level converter dynamic model modeling method according to claim 1, it is characterized in that: described modularization multi-level converter comprises three pairs of brachium pontis, every pair of brachium pontis comprises brachium pontis and lower brachium pontis, described upper brachium pontis and lower brachium pontis include N submodule and the reactor of series connection successively, and the public direct-current end is drawn in three pairs of brachium pontis parallel connections.

3. modularization multi-level converter dynamic model modeling method according to claim 1, it is characterized in that: described step 1 comprises the following steps:

Step 1-1: the single submodule cycle by cycle switch average model of brachium pontis in foundation;

Step 1-2: the single submodule small-signal alternate model of brachium pontis in foundation.

4. modularization multi-level converter dynamic model modeling method according to claim 3, it is characterized in that: in described step 1-1, the equation of the single submodule of upper brachium pontis is:

Wherein, u _p1Be the single submodule output voltage of upper brachium pontis, u _d1pBe the single submodule DC voltage of upper brachium pontis, i _d1pBe the single submodule direct-current discharge of upper brachium pontis electric current, i _pBe the single submodule output current of upper brachium pontis; S _pThe expression switch function, S _p∈ [0,1], S _pThe IGBT cut-off that=1 expression is in parallel with the submodule ac output end, another IGBT conducting, S _p=0 expression IGBT conducting in parallel with the submodule ac output end, another IGBT cut-off;

L ₁Be the single submodule inductance of upper brachium pontis, L ₁=L/N, U _d1p=U _d/ N, L are the brachium pontis reactance, U _dBe common DC bus voltage, C is single submodule Support Capacitor, u ₁' be single submodule output voltage and brachium pontis reactance pressure drop sum, R ' _sBe submodule current-limiting reactor equivalent series resistance, R ₁Be submodule main circuit loss equivalent resistance;

Ask switch periods on average to get to (2):

Wherein, T _sThe expression switch periods,

Expression u ₁At switch periods T _sInterior mean value,

Expression S _pu _d1pAt switch periods T _sInterior mean value,

Expression i _pAt switch periods T _sInterior mean value,

Expression S _pi _pAt switch periods T _sInterior mean value,

Expression u _d1pAt switch periods T _sInterior mean value; Suppose at switch periods T _sIn, u _d1pAnd i _pChange very littlely, can get following approximation relation:

Wherein, d _pBe the switching signal dutycycle;

(4) and (5) are brought into (3), get the single submodule cycle by cycle switch average model of brachium pontis as follows:

5. modularization multi-level converter dynamic model modeling method according to claim 4 is characterized in that: in the single submodule cycle by cycle switch average model of described upper brachium pontis, and the controlled voltage source of AC

R′ _sAnd L ₁Series connection successively, controlled voltage source

Anodal output head anode as the single submodule equivalent switch of upper brachium pontis periodic model, L ₁Not with R ' _sAn end that connects is as the negative pole of output end of the single submodule equivalent switch of upper brachium pontis periodic model; The controlled current source of DC side

R ₁Parallel with one another with C.

6. modularization multi-level converter dynamic model modeling method according to claim 3 is characterized in that: in described step 1-2,

Order:

(7)

d _p＝D _p+d _p

In formula, U ₁', I _p, U _d1p, D _pBe quiescent point,

d _pBe disturbance quantity; (7) substitution (6) can be got

Because there is following relation in quiescent point:

U ₁′＝U _d/2-u _s＝D _pU _d1p-R _sI _p

Wherein, u _sBe system voltage;

According to (8), ignore high-order term, get the single submodule small-signal alternate model of brachium pontis as follows:

7. modularization multi-level converter dynamic model modeling method according to claim 6, it is characterized in that: the single submodule small-signal alternate model of described upper brachium pontis comprises the single submodule controlled source of brachium pontis form small-signal alternate model and the single submodule transport function of upper brachium pontis block scheme form small-signal alternate model.

8. modularization multi-level converter dynamic model modeling method according to claim 7 is characterized in that: in the single submodule controlled source of described upper brachium pontis form small-signal alternate model, and the controlled voltage source d of AC _pU _d1p, controlled voltage source

R′ _sAnd L ₁Series connection successively; Controlled voltage source d _pU _d1pAnodal output head anode as the single submodule small-signal alternate model of upper brachium pontis, L ₁Not with R ' _sAn end that connects is as the negative pole of output end of the single submodule small-signal alternate model of upper brachium pontis; The controlled current source of DC side

Controlled current source d _pI _p, R ₁Parallel with one another with C; In the single submodule transport function of described upper brachium pontis block scheme form small-signal alternate model, input signal d _p(s) through proportional component U _d1pThe signal that produces ,-u ₁' (s) and output signal u _dlp(s) passing ratio link D _pThe feedback signal that produces enters totalizer 1, the signal passing ratio integral element that described totalizer 1 produces

Obtain signal i _p(s), described signal i _p(s) through proportional component D _pThe signal and the input signal d that produce _p(s) through proportional component I _pThe signal that produces enters totalizer 2, and the signal that described totalizer 2 produces is got negative and output signal u _dlp(s) through proportional component

The feedback signal that produces is got the negative totalizer 3 that enters, and the signal that described totalizer 3 produces is through proportional component

Produce output signal u _dlp(s).

9. modularization multi-level converter dynamic model modeling method according to claim 1, it is characterized in that: described step 2 comprises the following steps:

Step 2-1: in foundation, the brachium pontis cycle by cycle switch average model is:

Wherein, R _jThe equivalent loss resistance of expression submodule, R _sBe brachium pontis current-limiting reactor equivalent series resistance, d _pjAnd u _djpRepresent respectively equivalent dutycycle and the dc voltage of upper j submodule of brachium pontis, Expression u _djpAt switch periods T _sInterior mean value;

Step 2-2: in foundation, the brachium pontis small-signal alternate model is:

In formula, I _p, U ₁, U _djp, D _pjBe quiescent point;

d _pjBe disturbance quantity, each quiescent point of upper brachium pontis has following relation:

(13)

(12) are brought into (11), obtain upper brachium pontis small-signal alternate model according to (13) and be

。

10. modularization multi-level converter dynamic model modeling method according to claim 9 is characterized in that: in described upper brachium pontis cycle by cycle switch average model, and the controlled voltage source of each submodule cycle by cycle switch average model of AC

R _sConnect successively with L, controlled voltage source

Anodal output head anode as upper brachium pontis cycle by cycle switch average model, L not with R _sAn end that connects is as the negative pole of output end of upper brachium pontis cycle by cycle switch average model; The controlled current source of each submodule cycle by cycle switch average model of DC side R _jParallel with one another with C.

11. modularization multi-level converter dynamic model modeling method according to claim 9 is characterized in that: described upper brachium pontis small-signal alternate model comprises brachium pontis controlled source form small-signal alternate model and upper brachium pontis transport function block scheme form small-signal alternate model;

In described upper brachium pontis controlled source form small-signal alternate model, the controlled voltage source d of each submodule small-signal alternate model of AC _pjU _djp, controlled voltage source

R _sConnect successively with L; Controlled voltage source d _pNU _dNpAnodal output head anode as upper brachium pontis small-signal alternate model, L not with R _sAn end that connects is as the negative pole of output end of upper brachium pontis small-signal alternate model; The controlled current source of the small-signal alternate model of each submodule of DC side

Controlled current source d _pjI _p, R _jParallel with one another respectively with C;

In described upper brachium pontis transport function block scheme form small-signal alternate model, N input signal d _pj(s) through N corresponding proportional component U _djpThe signal and the input signal-u that produce ₁(s) enter totalizer 1 '; The signal of totalizer 1 ' generation and N corresponding output signal u _djp(s) passing ratio link D _pjThe feedback signal that produces enter totalizer 2 '; The signal passing ratio integral element of totalizer 2 ' generation

Obtain signal i _p(s), described signal i _p(s) through N proportional component D _pjN the signal and N the corresponding input signal d that produce respectively _pj(s) through proportional component I _pThe signal that produces enters N corresponding totalizer 3j ', and the signal of N totalizer 3j ' generation is got N negative and corresponding output signal u _djp(s) through proportional component

The feedback signal that produces is got negative N the totalizer 4j that enter.N N proportional component corresponding to signal process that totalizer 4j produces

Produce N output signal u _djp(s).

12. modularization multi-level converter dynamic model modeling method according to claim 11 is characterized in that: suppose that upper each submodule parameter of brachium pontis is symmetrical, and have:

d _p1＝d _p2＝...＝d _pN＝d _p (15)

u _d1p＝u _d2p＝…＝u _dNp＝u _dp (16)

Get

The quiescent point of upper brachium pontis small-signal alternate model changes into

D _pI _p＝U _dp/R

NU _dp＝U _d (18)

U ₁＝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

So be simplified the brachium pontis small-signal alternate model be

Wherein, R represents brachium pontis main circuit loss equivalent resistance.

13. modularization multi-level converter dynamic model modeling method according to claim 12 is characterized in that: in simplification, the brachium pontis small-signal alternate model comprises the upper brachium pontis controlled source form small-signal alternate model of simplification and simplifies upper brachium pontis transport function block scheme form small-signal alternate model.

14. modularization multi-level converter dynamic model modeling method according to claim 13 is characterized in that: in described simplification in brachium pontis controlled source form small-signal alternate model, the controlled voltage source Nd of AC _pU _dp, controlled voltage source

R _sConnect successively with L, controlled voltage source Nd _pU _dpAnodal output head anode as simplifying upper brachium pontis controlled source form small-signal alternate model, L not with R _sAn end that connects is as the negative pole of output end of simplifying upper brachium pontis controlled source form small-signal alternate model; The controlled current source of DC side

Controlled current source d _pI _p, R and C parallel with one another; In described simplification in brachium pontis transport function block scheme form small-signal alternate model, input signal d _p(s) through proportional component NU _dpThe signal and the input signal-u that produce ₁(s) enter totalizer 1 ", totalizer 1 " signal and the output signal u that produce _dp(s) passing ratio link ND _pThe feedback signal that produces enters totalizer 2 ", totalizer 2 " the signal passing ratio integral element that produces Obtain signal i _p(s), signal i _p(s) through proportional component D _pThe signal and the input signal d that produce _p(s) through proportional component I _pThe signal that produces enters totalizer 3 ", " signal that produces is got negative and output signal u to totalizer 3 _dp(s) through proportional component

The feedback signal that produces is got the negative totalizer 4 that enters, and the signal that totalizer 4 produces is through proportional component

Produce output signal u _dp(s).

15. modularization multi-level converter dynamic model modeling method according to claim 1, it is characterized in that: step 3 comprises the following steps:

Step 3-1: set up the lower single submodule cycle by cycle switch average model of brachium pontis and the single submodel small-signal alternate model of lower brachium pontis;

Step 3-2: set up lower brachium pontis cycle by cycle switch average model;

Wherein, d _njAnd u _djnRepresent respectively equivalent dutycycle and the dc voltage of lower j submodule of brachium pontis,

Expression u _djnAt switch periods T _sInterior mean value;

Step 3-3: lower brachium pontis small-signal alternate model;

And have:

d _n1＝d _n2＝...＝d _nN＝d _n (22)

u _d1n＝u _d2n＝...u _dNn＝u _dn (23)

Get

Can get

D _n≈(U _d/2+u _s)/NU _dn＝1/2+u _s/NU _dn＝1/2+u _s/U _d (24)

D _nBe quiescent point;

So be simplified lower brachium pontis small-signal alternate model be

16. modularization multi-level converter dynamic model modeling method according to claim 15 is characterized in that: in described lower brachium pontis cycle by cycle switch average model, the controlled voltage source of each submodule cycle by cycle switch average model of AC R _sConnect successively with L, controlled voltage source

Anodal output head anode as lower brachium pontis cycle by cycle switch average model, L not with R _sAn end that connects is as the negative pole of output end of lower brachium pontis cycle by cycle switch average model; The controlled current source of the single submodule cycle by cycle switch average model of DC side

R _jParallel with one another with C.

17. modularization multi-level converter dynamic model modeling method according to claim 15 is characterized in that: described lower brachium pontis small-signal alternate model comprises to be simplified lower brachium pontis controlled source form small-signal alternate model and simplifies lower brachium pontis transport function block scheme form small-signal alternate model;

Under described simplification in brachium pontis controlled source form small-signal alternate model, the L of AC, R _s, controlled voltage source Nd _nU _dnAnd controlled voltage source

Successively the series connection, L not with R _sAn end that connects is as the output head anode of simplifying lower brachium pontis controlled source form small-signal alternate model, controlled voltage source

Negative pole is as the negative pole of output end of simplifying lower brachium pontis controlled source form small-signal alternate model; The controlled current source of DC side

Controlled current source d _nI _n, R and C parallel with one another;

Under described simplification in brachium pontis transport function block scheme form small-signal alternate model, input signal d _n(s) through proportional component NU _dnThe signal that produces is got negative and input signal u ₂(s) enter totalizer 1 " '; Output signal u _dn(s) passing ratio link N _DnThe feedback signal that produces get negative and totalizer 1 " ' produce signal enter totalizer 2 " ', the totalizer 2 " ' signal passing ratio integral element that produces

Obtain signal i _n(s), signal i _n(s) through proportional component D _nThe signal and the input signal d that produce _n(s) through proportional component I _nThe signal that produces enters totalizer 3 " ', output signal u _dn(s) through proportional component The feedback signal that produces get negative and totalizer 3 " ' produce signal enter totalizer 4 " ', " ' the signal that produces is through proportional component for totalizer 4

Produce output signal u _dn(s).

18. modularization multi-level converter dynamic model modeling method according to claim 1, it is characterized in that: described step 4 comprises the following steps:

Step 4-1: set up the upper and lower brachium pontis cycle by cycle switch average model of modularization multi-level converter as follows:

Wherein,

D _p＝diag[d _pa d _pb d _pc]，

D _n＝diag[d _ba d _nb d _nc]，

Footmark p represents bridge arm module, and footmark n represents lower bridge arm module;

Wherein,

u _N0Be the AC common mode voltage;

Step 4-2: modularization multi-level converter small-signal alternate model;

The modularization multi-level converter quiescent point has following relation:

Obtain the upper and lower brachium pontis small-signal alternate model of modularization multi-level converter:

19. modularization multi-level converter dynamic model modeling method according to claim 18 is characterized in that: on described modularization multi-level converter in the brachium pontis cycle by cycle switch average model, upper brachium pontis controlled voltage source Nd _pi＜u _dipT _s, R _sConnect successively with L, upper brachium pontis controlled current source d _pi＜i _piT _s, R and C parallel with one another; Under described modularization multi-level converter in the brachium pontis cycle by cycle switch average model, L, R _sWith lower brachium pontis controlled voltage source Nd _ni＜u _dinT _sSeries connection successively, controlled current source d _ni＜i _niT _s, R and C parallel with one another, consist of lower bridge arm equivalent cycle by cycle switch average model.

20. modularization multi-level converter dynamic model modeling method according to claim 18 is characterized in that: in described modularization multi-level converter small-signal alternate model, signal i _pi(s) and signal i _ni(s) enter totalizer and produce signal i _si(s), signal

Signal-u _si(s) and signal-u _N0(s) enter totalizer and produce signal u _1i(s), signal

Signal u _si(s) and signal u _N0(s) enter totalizer and produce signal u _2i(s);

On described modularization multi-level converter in the brachium pontis small-signal alternate model, input signal d _pi(s) through proportional component NU _dipThe signal and the input signal-u that produce _1i(s) enter totalizer A, signal and output signal u that totalizer A produces _dip(s) passing ratio link ND _piThe feedback signal that produces enters totalizer B, the signal passing ratio integral element that totalizer B produces

Obtain signal i _pi(s), signal i _pi(s) through proportional component D _piThe signal and the input signal d that produce _pi(s) through proportional component I _piThe signal that produces enters totalizer C, and the signal that totalizer C produces is got negative and output signal u _dip(s) through proportional component The feedback signal that produces is got the negative totalizer D that enters, and the signal that totalizer D produces is through proportional component

Produce output signal u _dip(s);

Under described modularization multi-level converter in the brachium pontis small-signal alternate model, input signal d _pi(s) through proportional component NU _dinThe signal that produces is got negative and input signal u _2i(s) enter totalizer E, output signal u _din(s) passing ratio link ND _niThe feedback signal that produces is got signal negative and that totalizer E produces and is entered totalizer F, the signal passing ratio integral element that totalizer F produces

Obtain signal i _ni(s), signal i _ni(s) through proportional component D _niThe signal and the input signal d that produce _ni(s) through proportional component I _niThe signal that produces enters totalizer G, output signal u _din(s) through proportional component

The feedback signal that produces is got signal negative and that totalizer G produces and is entered totalizer H, and the signal that totalizer H produces is through proportional component

Produce output signal u _din(s).

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