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

Abstract

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

Description

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

Technical field

The invention belongs to power system technical field of electric power transmission, be specifically related to a kind of dynamic model of modular multi-level convector Modeling method.

Background technology

2002, R.Marquart and A.Lesnicar of university of Munich, Germany Federal Defence Forces proposed novel jointly Modular multilevel voltage source converter.Within 2004, succeed in developing 17 level 2MW model machines.2009, international conference on large HV electric systems B4.48 working group formally by its named modularization multi-level converter (modular multilevel converter, MMC).This topological structure passes through submodule converter valve in series, and the degree of modularity is high, and harmonic distortion is little, and switching loss is low, suitable Close the application of high-tension high-power occasion, have broad application prospects, can be used for flexible DC power transmission, Unified Power Flow control The multiple flexible DC power transmission such as flow controller, convertible static compensator, flexible AC transmission device between device, line.2010 Year, Section 1 modularization multi-level converter DC transmission engineering is between the Pittsburgh and San Francisco of California, USA Subsea DC cable networking, solve the nervous problem in transmission of electricity corridor, locality and strengthen security and stability and the reliability of system.

Power electronic equipment mathematical model based on modularization multi-level converter is the basis studying corresponding control strategy. Because main circuit bag is containing switch element, non-linear, the alternating current-direct current mixing of energy-storage travelling wave tube, the complication system of high frequency power frequency mixing, Model describes tool and acquires a certain degree of difficulty, and usual modeling method includes topology model construction method and output modeling two kinds.Topology model construction method institute Established model directly reflects circuit topological structure, and complexity dramatically increases with the increase of switching device quantity；Output modeling Device is generally equivalent to controlled source or impedance manner, and institute's established model is relatively easy, but have ignored the state of device inner member Information, is unfavorable for the specificity analysis within device.Thus the application of both approaches is respectively provided with limitation.

Summary of the invention

In order to overcome above-mentioned the deficiencies in the prior art, the present invention provides a kind of dynamic model of modular multi-level convector to build Mould method, the dynamic model of modular multi-level convector of foundation is easy to the dynamic property to modularization multi-level converter and frequency Ring characteristic to be analyzed, it is simple to design for Unit Level control strategy, and achieve the description to internal quantity of state.

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

A kind of dynamic model of modular multi-level convector modeling method, said method comprising the steps of:

Step 1: in foundation, brachium pontis single submodule cycle by cycle switch average model and upper brachium pontis single submodule small-signal are handed over Flow model；

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 the little letter of modularization multi-level converter Number model.

Described modularization multi-level converter includes that three pairs of brachium pontis, every pair of brachium pontis include brachium pontis and lower brachium pontis, described on Brachium pontis and lower brachium pontis all include that public direct-current end drawn by N number of submodule being sequentially connected in series and reactor, three pairs of brachium pontis parallel connections.

Described step 1 comprises the following steps:

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

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

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

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

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

Wherein, u_p1For upper brachium pontis single submodule output voltage, u_d1pFor upper brachium pontis single submodule DC voltage, i_d1pFor Upper brachium pontis single submodule direct-current discharge electric current, i_pElectric current is exported for the single submodule of upper brachium pontis；S_pRepresent switch function, S_p∈ [0,1], S_p=1 represents the IGBT cut-off in parallel with submodule ac output end, and another IGBT turns on, S_p=0 represents and submodule The IGBT conducting that block ac output end is in parallel, another IGBT ends；

L₁For upper brachium pontis single submodule inductance, L₁=L/N, U_d1p=U_d/ N, L are brachium pontis reactance, U_dFemale for public direct-current Line voltage, C is single submodule Support Capacitor, u₁' for single submodule output voltage and brachium pontis reactance pressure drop sum, R '_sFor son Block coupled in series reactor equivalent series resistance, R₁Equivalent resistance is lost for submodule main circuit；

(2) are asked switch periods averagely:

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

Wherein, T_sRepresent switch periods,Represent u₁In switch periods T_sInterior meansigma methods,Represent S_pu_d1p In switch periods T_sInterior meansigma methods,Represent i_pIn switch periods T_sInterior meansigma methods,Represent S_pi_pIn switch week Phase T_sInterior meansigma methods,Represent u_d1pIn switch periods T_sInterior meansigma methods；Assuming that in switch periods T_sIn, u_d1pAnd i_pBecome Change the least, can be able to lower aprons 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_pFor switching signal dutycycle；

(4) and (5) are brought into (3), obtain brachium pontis single submodule cycle by cycle switch average model 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 described upper brachium pontis single submodule cycle by cycle switch average model, the controlled voltage source of ACR′_s And L₁It is sequentially connected in series, controlled voltage sourcePositive pole is as the output of upper brachium pontis single submodule equivalent switch periodic model Rectify pole, L₁Not with R '_sThe one end connected is as the negative pole of output end of upper brachium pontis single submodule equivalent switch periodic model；Directly The controlled current source of stream sideR₁Parallel with one another with C.

In described step step 1-2,

Order:

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

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

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

d_p=D_p+d_p

In formula, U₁', I_p, U_d1p, D_pFor quiescent point,d_pFor disturbance quantity；(7) substitution (6) can be obtained

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

Owing to there is following relation in quiescent point:

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

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

U₁'=U_d/2-u_s=D_pU_d1p-R_sI_p

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

Wherein, u_sFor system voltage；

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

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

Described upper brachium pontis single submodule small-signal alternate model includes the brachium pontis single submodule little letter of controlled source form Number AC model and upper brachium pontis single submodule transmission function block diagram form small-signal alternate model.

In described upper brachium pontis single submodule controlled source form small-signal alternate model, the controlled voltage source of AC d_pU_d1p, controlled voltage sourceR′_sAnd L₁It is sequentially connected in series；Controlled voltage source d_pU_d1pPositive pole is as the single submodule of upper brachium pontis The output head anode of small-signal alternate model, L₁Not with R '_sThe one end connected exchanges mould as upper brachium pontis single submodule small-signal The negative pole of output end of type；The controlled current source of DC sideControlled current source d_pI_p、R₁Parallel with one another with C；Described upper brachium pontis In single submodule transmission function block diagram form small-signal alternate model, input signal d_pS () is through proportional component U_d1pProduce Signal ,-u₁' (s) and output signal u_dlp(s) passing ratio link D_pProduce feedback signal enter adder 1, described in add The signal passing ratio integral element that musical instruments used in a Buddhist or Taoist mass 1 producesObtain signal i_p(s), described signal i_pS () is through proportional component D_pThe signal produced and input signal d_pS () is through proportional component I_pThe signal produced enters adder 2, and described adder 2 produces Signal take negative and output signal u_dlpS () is through proportional componentThe feedback signal produced takes and negative enters adder 3, described in add The signal that musical instruments used in a Buddhist or Taoist mass 3 produces is through proportional componentProduce output signal u_dlp(s)。

Described step 2 comprises the following steps:

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

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

Wherein, R_jRepresent the equivalent loss resistance of submodule, R_sFor brachium pontis current-limiting reactor equivalent series resistance, d_pjWith u_djpRepresent equivalent dutycycle and the DC voltage of upper brachium pontis jth submodule respectively,Represent u_djpIn switch periods T_s Interior meansigma methods；

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

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

In formula, I_p, U₁, U_djp, D_pjFor quiescent point；For 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)

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

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

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

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

In described upper brachium pontis cycle by cycle switch average model, each submodule cycle by cycle switch average model of AC controlled Voltage sourceR_sIt is sequentially connected in series with L, controlled voltage sourcePositive pole is as upper brachium pontis cycle by cycle switch average model Output head anode, L not with R_sThe one end connected is as the negative pole of output end of upper brachium pontis cycle by cycle switch average model；DC side The controlled current source of each submodule cycle by cycle switch average modelR_jParallel with one another with C.

Described upper brachium pontis small-signal alternate model includes that brachium pontis controlled source form small-signal alternate model and upper brachium pontis pass Delivery function block diagram form small-signal alternate model；

In described upper brachium pontis controlled source form small-signal alternate model, AC each submodule small-signal alternate model Controlled voltage source d_pjU_djp, controlled voltage sourceR_sIt is sequentially connected in series with L；Controlled voltage source d_pNU_dNpPositive pole is as upper brachium pontis The output head anode of small-signal alternate model, L not with R_sThe one end connected is as the outfan of upper brachium pontis small-signal alternate model Negative pole；The controlled current source of the small-signal alternate model of each submodule of DC sideControlled current source d_pjI_p、R_jDivide with C The most parallel with one another；

In described upper brachium pontis transmission function block diagram form small-signal alternate model, N number of input signal d_pjS () is through correspondence N number of proportional component U_djpThe signal produced and input signal-u₁S () enters adder 1 '；The signal and right that adder 1 ' produces N number of output signal u answered_djp(s) passing ratio link D_pjThe feedback signal produced enters adder 2 '；Adder 2 ' produces Signal passing ratio integral elementObtain signal i_p(s), described signal i_pS () is through N number of proportional component D_pjProduce respectively Raw N number of signal and corresponding N number of input signal d_pjS () is through proportional component I_pThe signal produced enters corresponding N number of addition The signal that device 3j ', N number of adder 3j ' produce takes negative and corresponding N number of output signal u_djpS () is through proportional componentProduce Feedback signal takes N number of adder 4j of negative entrance.The signal that N number of adder 4j produces is through corresponding N number of proportional componentProduce N number of output signal u_djp(s)。

Assume 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)

TakeThe 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)

U₁=U_d/2-u_s=ND_pU_dp-R_sI_p

D_p≈(U_d/2-u_s)/NU_dp=1/2-u_s/NU_dp

Then being simplified brachium pontis small-signal alternate model is

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

Wherein, R represents that brachium pontis main circuit is lost equivalent resistance.

In simplification, brachium pontis small-signal alternate model includes simplifying upper brachium pontis controlled source form small-signal alternate model and simplification Upper brachium pontis transmission function block diagram 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 sourceR_sIt is sequentially connected in series with L, controlled voltage source Nd_pU_dpPositive pole is as simplifying upper brachium pontis controlled source form small-signal The output head anode of AC model, L not with R_sThe one end connected is as simplifying upper brachium pontis controlled source form small-signal alternate model Negative pole of output end；The controlled current source of DC sideControlled current source d_pI_p, R and C parallel with one another；Brachium pontis in described simplification In transmission function block diagram form small-signal alternate model, input signal d_pS () is through proportional component NU_dpThe signal and defeated produced Enter signal-u₁S () enters adder 1 ", adder 1 " signal produced and output signal u_dp(s) passing ratio link ND_pProduce Feedback signal enter the signal passing ratio integral element that adder 2 ", adder 2 " producesObtain signal i_p(s), Signal i_pS () is through proportional component D_pThe signal produced and input signal d_pS () is through proportional component I_pThe signal produced enters and adds Musical instruments used in a Buddhist or Taoist mass 3 ", " signal produced takes negative and output signal u to adder 3_dpS () is through proportional componentThe feedback signal produced takes negative Entering adder 4, the signal that adder 4 produces is through proportional componentProduce output signal u_dp(s)。

Step 3 comprises the following steps:

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

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

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

Wherein, d_njAnd u_djnRepresent equivalent dutycycle and the DC voltage of lower brachium pontis jth submodule respectively, Represent u_djnIn switch periods T_sInterior meansigma methods；

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

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

And have:

d_n1=d_n2=...=d_nN=d_n (22)

u_d1n=u_d2n=... u_dNn=u_dn (23)

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

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

D_nFor quiescent point；

Then being simplified lower brachium pontis small-signal alternate model is

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

In described lower brachium pontis cycle by cycle switch average model, each submodule cycle by cycle switch average model of AC controlled Voltage sourceR_sIt is sequentially connected in series with L, controlled voltage sourcePositive pole is as lower brachium pontis cycle by cycle switch average model Output head anode, L not with R_sThe one end connected is as the negative pole of output end of lower brachium pontis cycle by cycle switch average model；DC side The controlled current source of single submodule cycle by cycle switch average modelR_jParallel with one another with C.

Described lower brachium pontis small-signal alternate model includes simplifying lower brachium pontis controlled source form small-signal alternate model and simplification Lower brachium pontis transmission function block diagram form small-signal alternate model；

Under described simplification in brachium pontis controlled source form small-signal alternate model, L, R of AC_s, controlled voltage source Nd_nU_dn And controlled voltage sourceBe sequentially connected in series, L not with R_sThe one end connected is handed over as simplifying lower brachium pontis controlled source form small-signal The output head anode of flow model, controlled voltage sourceNegative pole is as simplifying lower brachium pontis controlled source form small-signal alternate model Negative pole of output end；The controlled current source of DC sideControlled current source d_nI_n, R and C parallel with one another；

Under described simplification in brachium pontis transmission function block diagram form small-signal alternate model, input signal d_n(s) through than Example link NU_dnThe signal produced takes negative and input signal u₂S () enters adder 1 " '；Output signal u_dn(s) passing ratio link ND_nThe feedback signal produced take negative and adder 1 " ' produce signal enter adder 2 " ', " ' the signal that produces leads to adder 2 Cross proportional integral linkObtain signal i_n(s), signal i_nS signal that () produces through proportional component Dn and input signal d_nS () is through proportional component I_nThe signal produced enters adder 3 " ', output signal u_dnS () is through proportional componentProduce is anti- Feedback signal take negative and adder 3 " ' produce signal enter adder 4 " ', " ' the signal that produces is through proportional component for adder 4Produce output signal u_dn(s)。

Described step 4 comprises the following steps:

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

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

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

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

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

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

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

D_n=diag [d_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 that bridge arm module, footmark n represent lower bridge arm module；

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

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

u_N0For AC common-mode voltage；

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

Modularization multi-level converter quiescent point has a 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 modularization multi-level converter upper and lower brachium pontis small-signal alternate model:

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

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

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

On described modularization multi-level converter in brachium pontis cycle by cycle switch average model, upper brachium pontis controlled voltage source Nd_pi< u_dip>T_s、R_sIt is sequentially connected in series with L, upper brachium pontis controlled current source d_pi<i_pi>T_s, R and C parallel with one another；Described modular multilevel changes Under stream device in brachium pontis cycle by cycle switch average model, L, R_sWith lower brachium pontis controlled voltage source Nd_ni<u_din>T_sIt is sequentially connected in series, controlled electricity Stream source d_ni<i_ni>T_s, R and C parallel with one another, constitute 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_niS () enters addition Device produces signal i_si(s), signalSignal-u_si(s) and signal-u_N0S () enters adder and produces signal u_1i(s), letter NumberSignal u_si(s) and signal u_N0S () enters adder and produces signal u_2i(s)；

On described modularization multi-level converter in brachium pontis small-signal alternate model, input signal d_piS () is through ratio ring Joint NU_dipThe signal produced and input signal-u_1iS () enters adder A, the signal of adder A generation and output signal u_dip(s) Passing ratio link ND_piThe feedback signal produced enters adder B, the signal passing ratio integral element that adder B producesObtain signal i_pi(s), signal i_piS () is through proportional component D_piThe signal produced and input signal d_pi(s) through than Example link I_piThe signal produced enters adder C, and the signal that adder C produces takes negative and output signal u_dipS () is through ratio ring JointThe feedback signal produced takes negative adder D that enters, and the signal of adder D generation is through proportional componentProduce output signal u_dip(s)；

Under described modularization multi-level converter in brachium pontis small-signal alternate model, input signal d_niS () is through ratio ring Joint NU_dinThe signal produced takes negative and input signal u_2iS () enters adder E, output signal u_din(s) passing ratio link ND_ni The feedback signal produced takes negative and the generation of adder E signal and enters adder F, and the signal passing ratio that adder F produces amasss Divide linkObtain signal i_ni(s), signal i_niS () is through proportional component D_niThe signal produced and input signal d_ni(s) Through proportional component I_mThe signal produced enters adder G, output signal u_dinS () is through proportional componentThe feedback signal produced Taking negative and the generation of adder G signal and enter adder H, the signal that adder H produces is through proportional componentProduce output letter Number u_din(s)。

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

1. this dynamic model of modular multi-level convector is the power electronics such as THE UPFC, flexible DC power transmission Specificity analysis and the control strategy of device have established solid foundation；

2. the dynamic property that this this dynamic model of modular multi-level convector is easy to modularization multi-level converter is entered Row is analyzed；

3. this dynamic model of modular multi-level convector is easy to the frequency to modularization multi-level converter and is carried out accordingly Analyze；

4. this dynamic model of modular multi-level convector is easy to the design for Unit Level control strategy；

5. this dynamic model of modular multi-level convector achieves the description to model internal state amount；

6. this modeling method is simple and reliable, easily performs.

Accompanying drawing explanation

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

Fig. 2 is submodule main circuit schematic diagram；

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

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

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

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

Figure 10 is to simplify upper brachium pontis controlled source form small-signal alternate model figure；

Figure 11 is to simplify upper brachium pontis transmission function block diagram form small-signal alternate model figure；

Figure 12 is to simplify lower brachium pontis controlled source form small-signal alternate model figure；

Figure 13 is to simplify lower brachium pontis transmission function block diagram 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.

Detailed description of the invention

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

A kind of dynamic model of modular multi-level convector modeling method, said method comprising the steps of:

Step 1: in foundation, brachium pontis single submodule cycle by cycle switch average model and upper brachium pontis single submodule small-signal are handed over Flow model；

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 the little letter of modularization multi-level converter Number model.

Such as Fig. 1-Fig. 2, described modularization multi-level converter includes that three pairs of brachium pontis, every pair of brachium pontis include brachium pontis and Xia Qiao Arm, described upper brachium pontis and lower brachium pontis all include N number of submodule being sequentially connected in series and reactor, and three pairs of brachium pontis parallel connection extractions are public directly Stream end.

Described step 1 comprises the following steps:

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

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

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

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

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

Wherein, u_p1For upper brachium pontis single submodule output voltage, u_d1pFor upper brachium pontis single submodule DC voltage, i_d1pFor Upper brachium pontis single submodule direct-current discharge electric current, i_pElectric current is exported for the single submodule of upper brachium pontis；S_pRepresent switch function, S_p∈ [0,1], S_l=1 represents the IGB2 cut-off in parallel with submodule ac output end, and IGBT1 turns on, S_p=0 represents and submodule friendship The IGBT2 conducting that stream outfan is in parallel, IGBT1 ends；

L₁For upper brachium pontis single submodule inductance, L₁=L/N, U_d1p=U_d/ N, L are brachium pontis reactance, U_dFemale for public direct-current Line voltage, C is single submodule Support Capacitor, u₁' for single submodule output voltage and brachium pontis reactance pressure drop sum, R '_sFor son Block coupled in series reactor equivalent series resistance, R₁Equivalent resistance is lost for submodule main circuit；

(2) are asked switch periods averagely:

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

Wherein, T_sRepresent switch periods,Represent u₁In switch periods T_sInterior meansigma methods,Represent S_pu′_d1pIn switch periods T_sInterior meansigma methods,Represent i_pIn switch periods T_sInterior meansigma methods,Represent S_pi_p? Switch periods T_sInterior meansigma methods,Represent u_d1pIn switch periods T_sInterior meansigma methods；Assuming that in switch periods T_sIn, u_d1pAnd i_pVary less, can be able to lower aprons 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_pFor switching signal dutycycle；

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

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

Such as Fig. 4, in described upper brachium pontis single submodule cycle by cycle switch average model, the controlled voltage source of ACR′_sAnd L₁It is sequentially connected in series, controlled voltage sourcePositive pole is as upper brachium pontis single submodule equivalent switch week The output head anode of phase model, L₁Not with R '_sDefeated as upper brachium pontis single submodule equivalent switch periodic model of one end connected Go out to hold negative pole；The controlled current source of DC sideR₁Parallel with one another with C.

In described step step 1-2,

Order:

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

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

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

d_p=D_p+d_p

In formula, U₁', I_p, U_d1p, D_pFor quiescent point,d_pFor disturbance quantity；(7) substitution (6) can be obtained

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

Owing to there is following relation in quiescent point:

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

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

U₁'=U_d/2-u_s=D_pU_d1p-R_sI_p

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

Wherein, u_sFor system voltage；

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

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

Described upper brachium pontis single submodule small-signal alternate model includes the brachium pontis single submodule little letter of controlled source form Number AC model and upper brachium pontis single submodule transmission function block diagram form small-signal alternate model.

Such as Fig. 5, in described upper brachium pontis single submodule controlled source form small-signal alternate model, the controlled voltage of AC Source d_pU_d1p, controlled voltage sourceR′_sAnd L₁It is sequentially connected in series；Controlled voltage source d_pU_d1pPositive pole is as the single submodule of upper brachium pontis The output head anode of block small-signal alternate model, L₁Not with R '_sThe one end connected exchanges as upper brachium pontis single submodule small-signal The negative pole of output end of model；The controlled current source of DC sideControlled current source d_pI_p、R₁Parallel with one another with C；Such as Fig. 6, institute Stating in brachium pontis single submodule transmission function block diagram form small-signal alternate model, 3 adders are followed successively by from left to right Adder 1, adder 2 and adder 3, input signal d_pS () is through proportional component U_d1pThe signal of generation ,-u₁' (s) and defeated Go out signal u_dlp(s) passing ratio link D_pThe feedback signal produced enters adder 1, and the signal that described adder 1 produces passes through Proportional integral linkObtain signal i_p(s), described signal i_pS () is through proportional component D_pThe signal produced and input letter Number d_pS () is through proportional component I_pThe signal produced enters adder 2, and the signal that described adder 2 produces takes negative and output signal u_dpS () is through proportional componentThe feedback signal produced takes and negative enters adder 3, the signal that described adder 3 produces through than Example linkProduce output signal u_dlp(s)。

Described step 2 comprises the following steps:

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

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

Wherein, R_jRepresent the equivalent loss resistance of submodule, R_sFor brachium pontis current-limiting reactor equivalent series resistance, d_pjWith u_djpRepresent equivalent dutycycle and the DC voltage of upper brachium pontis jth submodule respectively,Represent u_djpIn switch periods T_s Interior meansigma methods；

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

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

In formula, I_p, U₁, U_djp, D_pjFor quiescent point；d_pjFor 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)

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

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

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

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

Such as Fig. 7, in described upper brachium pontis cycle by cycle switch average model, each submodule cycle by cycle switch average model of AC Controlled voltage sourceR_sIt is sequentially connected in series with L, controlled voltage sourcePositive pole is put down as upper brachium pontis switch periods All output head anodes of model, L not with R_sThe one end connected is as the negative pole of output end of upper brachium pontis cycle by cycle switch average model；Directly The controlled current source of each submodule cycle by cycle switch average model of stream sideR_jParallel with one another with C.

Described upper brachium pontis small-signal alternate model includes that brachium pontis controlled source form small-signal alternate model and upper brachium pontis pass Delivery function block diagram form small-signal alternate model；

Such as Fig. 8, in described upper brachium pontis controlled source form small-signal alternate model, AC each submodule small-signal exchanges The controlled voltage source d of model_pjU_djp, controlled voltage sourceR_sIt is sequentially connected in series with L；Controlled voltage source d_pNU_dNpPositive pole conduct The output head anode of upper brachium pontis small-signal alternate model, L not with R_sThe one end connected is as upper brachium pontis small-signal alternate model Negative pole of output end；The controlled current source of the small-signal alternate model of each submodule of DC sideControlled current source d_pjI_p、R_j The most parallel with one another with C；

Such as Fig. 9, in described upper brachium pontis transmission function block diagram form small-signal alternate model, 4 adders are from left to right It is followed successively by adder 1 ', adder 2 ', adder 3 ' and adder 4 ', N number of input signal d_pjS () is through corresponding N number of ratio Link U_djpThe signal produced and input signal-u₁S () enters adder 1 '；The signal that adder 1 ' produces is N number of defeated with correspondence Go out signal u_djp(s) passing ratio link D_pjThe feedback signal produced enters adder 2 '；Adder 2 ' produce signal by than Example integral elementObtain signal i_p(s), described signal i_pS () is through N number of proportional component D_pjThe N number of signal produced respectively With corresponding N number of input signal d_pjS () is through proportional component I_pThe signal produced enters corresponding N number of adder 3j ', N number of adds The signal that musical instruments used in a Buddhist or Taoist mass 3j ' produces takes negative and corresponding N number of output signal u_djpS () is through proportional componentThe feedback signal produced takes N number of adder 4j of negative entrance.The signal that N number of adder 4j produces is through corresponding N number of proportional componentProduce N number of output letter Number u_djp(s)。

Assume 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)

TakeThe 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)

U₁=U_d/2-u_s=ND_pU_dp-R_sI_p

D_p≈(U_d/2-u_s)/NU_dp=1/2-u_s/NU_dp

Then being simplified brachium pontis small-signal alternate model is

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

Wherein, R represents that brachium pontis main circuit is lost equivalent resistance.

In simplification, brachium pontis small-signal alternate model includes simplifying upper brachium pontis controlled source form small-signal alternate model and simplification Upper brachium pontis transmission function block diagram form small-signal alternate model.

Such as Figure 10, in described simplification in brachium pontis controlled source form small-signal alternate model, the controlled voltage source of AC Nd_pU_dp, controlled voltage sourceR_sIt is sequentially connected in series with L, controlled voltage source Nd_pU_dpPositive pole is as simplifying upper brachium pontis controlled source The output head anode of form small-signal alternate model, L not with R_sThe one end connected is as simplifying the upper brachium pontis little letter of controlled source form The negative pole of output end of number AC model；The controlled current source of DC sideControlled current source d_pI_p, R and C parallel with one another；

Such as Figure 11, in described simplification in brachium pontis transmission function block diagram form small-signal alternate model, 4 adders are from a left side Adder 1 ", adder 2 ", adder 3 " and adder 4 ", input signal d it is followed successively by the right side_pS () is through proportional component NU_dpProduce Raw signal and input signal-u₁S () enters adder 1 ", adder 1 " signal produced and output signal u_dp(s) by than Example link ND_pThe feedback signal produced enters adder 2 ", adder 2 " the signal passing ratio integral element produced Obtain signal i_p(s), signal i_pS () is through proportional component D_pThe signal produced and input signal d_pS () is through proportional component I_pProduce Raw signal enters adder 3 ", " signal produced takes negative and output signal u to adder 3_dpS () is through proportional componentProduce Feedback signal take and negative enter adder 4, the signal that adder 4 produces is through proportional componentProduce output signal u_dp(s)。

Step 3 comprises the following steps:

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

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

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

Wherein, d_njAnd u_djnRepresent equivalent dutycycle and the DC voltage of lower brachium pontis jth submodule respectively, Represent u_djnIn switch periods T_sInterior meansigma methods；

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

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

And have:

d_n1=d_n2=...=d_nN=d_n (22)

u_d1n=u_d2n=... u_dNn=u_dn (23)

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

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

D_nFor quiescent point；

Then being simplified lower brachium pontis small-signal alternate model is

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

In described lower brachium pontis cycle by cycle switch average model, each submodule cycle by cycle switch average model of AC controlled Voltage sourceR_sIt is sequentially connected in series with L, controlled voltage sourcePositive pole is as lower brachium pontis cycle by cycle switch average model Output head anode, L not with R_sThe one end connected is as the negative pole of output end of lower brachium pontis cycle by cycle switch average model；DC side The controlled current source of single submodule cycle by cycle switch average modelR_jParallel with one another with C.

Described lower brachium pontis small-signal alternate model includes simplifying lower brachium pontis controlled source form small-signal alternate model and simplification Lower brachium pontis transmission function block diagram form small-signal alternate model；

Such as Figure 12, under described simplification in brachium pontis controlled source form small-signal alternate model, L, R of AC_s, controlled voltage Source Nd_nU_dnAnd controlled voltage sourceBe sequentially connected in series, L not with R_sThe one end connected is little as simplifying lower brachium pontis controlled source form The output head anode of signal communication model, controlled voltage sourceNegative pole is handed over as simplifying lower brachium pontis controlled source form small-signal The negative pole of output end of flow model；The controlled current source of DC sideControlled current source d_nI_n, R and C parallel with one another；

Such as Figure 13, under described simplification in brachium pontis transmission function block diagram form small-signal alternate model, 4 adders are from a left side Be followed successively by the right side adder 1 " ', adder 2 " ', adder 3 " ' and adder 4 " ', input signal d_nS () is through proportional component NU_dnThe signal produced takes negative and input signal u₂S () enters adder 1 " '；Output signal u_dn(s) passing ratio link ND_nProduce Raw feedback signal take negative and adder 1 " ' produce signal enter adder 2 " ', adder 2 " ' the signal that produces by than Example integral elementObtain signal i_n(s), signal i_nS () is through proportional component D_nThe signal produced and input signal d_n(s) Through proportional component I_nThe signal produced enters adder 3 " ', output signal u_dnS () is through proportional componentThe feedback letter produced Number take negative and adder 3 " ' produce signal enter adder 4 " ', " ' the signal that produces is through proportional component for adder 4Produce Raw output signal u_dn(s)。

Described step 4 comprises the following steps:

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

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

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

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

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

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

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

D_n=diag [d_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 that bridge arm module, footmark n represent lower bridge arm module；Its In, $\stackrel{\&RightArrow;}{u_1}=\left[\begin{array}{c}{<u_{1a}>}_{T_s}\\ {<u_{1b}>}_{T_s}\\ {<u_{1c}>}_{T_s}\end{array}\right]=\frac{{<U_d>}_{\mathrm{Ts}}}{2}\left[\begin{array}{c}1\\ 1\\ 1\end{array}\right]-\left[\begin{array}{c}{<u_{a0}>}_{T_s}\\ {<u_{b0}>}_{T_s}\\ {<u_{c0}>}_{T_s}\end{array}\right]=\frac{{<U_d>}_{\mathrm{Ts}}}{2}\left[\begin{array}{c}1\\ 1\\ 1\end{array}\right]-\left[\begin{array}{c}{<u_{\mathrm{sa}}>}_{T_s}\\ {<u_{\mathrm{sb}}>}_{T_s}\\ {<u_{\mathrm{sc}}>}_{T_s}\end{array}\right]-{<u_{N0}>}_{T_s}\left[\begin{array}{c}1\\ 1\\ 1\end{array}\right]---\left(29\right)$

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

u_N0For AC common-mode voltage；

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

Modularization multi-level converter quiescent point has a 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 modularization multi-level converter upper and lower brachium pontis small-signal alternate model:

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

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

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

Such as Figure 14, on described modularization multi-level converter in brachium pontis cycle by cycle switch average model, upper brachium pontis controlled voltage Source Nd_pi<u_dip>_Ts、R_sIt is sequentially connected in series with L, upper brachium pontis controlled current source d_pi<i_pi>_Ts, R and C parallel with one another；Described modularity is many Under level converter in brachium pontis cycle by cycle switch average model, L, R_sWith lower brachium pontis controlled voltage source Nd_ni<u_din>_TsIt is sequentially connected in series, is subject to Control current source d_ni<i_ni>_Ts, R and C parallel with one another, constitute lower bridge arm equivalent cycle by cycle switch average model.

Such as Figure 15, in described modularization multi-level converter small-signal alternate model, signal i_pi(s) and signal i_niS () enters Enter adder and produce signal i_si(s), signalSignal-u_si(s) and signal-u_N0S () enters adder and produces signal u_1i (s), signalSignal u_si(s) and signal u_N0S () enters adder and produces signal u_2i(s)；

On described modularization multi-level converter in brachium pontis small-signal alternate model, 4 adders are followed successively by from left to right Adder A, adder B, adder C and adder D, input signal d_piS () is through proportional component NU_dipThe signal and defeated produced Enter signal-u_1iS () enters adder A, the signal of adder A generation and output signal u_dip(s) passing ratio link ND_piProduce Feedback signal enter adder B, adder B produce signal passing ratio integral elementObtain signal i_pi(s), Signal i_piS () is through proportional component D_piThe signal produced and input signal d_piS () is through proportional component I_piThe signal produced enters Adder C, the signal that adder C produces takes negative and output signal u_dipS () is through proportional componentThe feedback signal produced takes negative Entering adder D, the signal that adder D produces is through proportional componentProduce output signal u_dip(s)；

Under described modularization multi-level converter in brachium pontis small-signal alternate model, input signal d_niS () is through ratio ring Joint NU_dinThe signal produced takes negative and input signal u_2iS () enters adder E, output signal u_din(s) passing ratio link ND_ni The feedback signal produced takes negative and the generation of adder E signal and enters adder F, and the signal passing ratio that adder F produces amasss Divide linkObtain signal i_ni(s), signal i_niS () is through proportional component D_niThe signal produced and input signal d_ni(s) Through proportional component I_mThe signal produced enters adder G, output signal u_dinS () is through proportional componentThe feedback signal produced Taking negative and the generation of adder G signal and enter adder H, the signal that adder H produces is through proportional componentProduce output letter Number u_din(s)。

Finally should be noted that: above example is only in order to illustrate that technical scheme is not intended to limit, to the greatest extent The present invention has been described in detail by pipe with reference to above-described embodiment, and those of ordinary skill in the field are it is understood that still The detailed description of the invention of the present invention can be modified or equivalent, and any without departing from spirit and scope of the invention Amendment or equivalent, it all should be contained in the middle of scope of the presently claimed invention.

Claims (14)

1. a dynamic model of modular multi-level convector modeling method, it is characterised in that: said method comprising the steps of:

Step 1: in foundation, brachium pontis single submodule cycle by cycle switch average model submodule single with upper brachium pontis small-signal exchanges mould Type；

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 mould Type；

Described step 1 comprises the following steps:

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

Step 1-2: brachium pontis single submodule small-signal alternate model in foundation；

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

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

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

Wherein, u_p1For upper brachium pontis single submodule output voltage, u_d1pFor upper brachium pontis single submodule DC voltage, i_d1pFor upper bridge Arm single submodule direct-current discharge electric current, i_pElectric current is exported for the single submodule of upper brachium pontis；S_pRepresent switch function, S_p∈ [0, 1], S_p=1 represents the IGBT cut-off in parallel with submodule ac output end, and another IGBT turns on, S_p=0 represents and submodule The IGBT conducting that ac output end is in parallel, another IGBT ends；

L₁For upper brachium pontis single submodule inductance, L₁=L/N, U_d1p=U_d/ N, L are brachium pontis reactance, U_dFor common DC bus electricity Pressure, C is single submodule Support Capacitor, u₁' for single submodule output voltage and brachium pontis reactance pressure drop sum, R '_sFor submodule Current-limiting reactor equivalent series resistance, R₁Equivalent resistance is lost for submodule main circuit；

(2) are asked switch periods averagely:

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

Wherein, T_sRepresent switch periods,Represent u₁' in switch periods T_sInterior meansigma methods,Represent S_pu_d1p? Switch periods T_sInterior meansigma methods,Represent i_pIn switch periods T_sInterior meansigma methods,Represent S_pi_pIn switch periods T_sInterior meansigma methods,Represent u_d1pIn switch periods T_sInterior meansigma methods；

Assuming that in switch periods T_sIn, u_d1pAnd i_pVary less, can be able to lower aprons 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_pFor switching signal dutycycle；

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

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

In described upper brachium pontis single submodule cycle by cycle switch average model, the controlled voltage source of ACR′_sAnd L₁ It is sequentially connected in series, controlled voltage sourcePositive pole is rectified as the output of upper brachium pontis single submodule equivalent switch periodic model Pole, L₁Not with R '_sThe one end connected is as the negative pole of output end of upper brachium pontis single submodule equivalent switch periodic model；DC side Controlled current sourceR₁Parallel with one another with C；

In described step 1-2,

Order:

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

In formula, U₁′,I_p,U_d1p,D_pFor quiescent point,For disturbance quantity；(7) substitution (6) can be obtained

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

Owing to there is following relation in quiescent point:

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

Wherein, u_sFor system voltage；

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

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

Described upper brachium pontis single submodule small-signal alternate model includes that brachium pontis single submodule controlled source form small-signal is handed over Flow model and upper brachium pontis single submodule transmission function block diagram form small-signal alternate model；

In described upper brachium pontis single submodule controlled source form small-signal alternate model, the controlled voltage source d of AC_pU_d1p, be subject to Control voltage sourceR′_sAnd L₁It is sequentially connected in series；Controlled voltage source d_pU_d1pPositive pole is handed over as upper brachium pontis single submodule small-signal The output head anode of flow model, L₁Not with R '_sThe one end connected is as the output of upper brachium pontis single submodule small-signal alternate model End negative pole；The controlled current source of DC sideControlled current source d_pI_p、R₁Parallel with one another with C；The described single submodule of upper brachium pontis In block transmission function block diagram form small-signal alternate model, input signal d_pS () is through proportional component U_d1pProduce signal ,- u₁' (s) and output signal u_dlp(s) passing ratio link D_pThe feedback signal produced enters adder 1, and described adder 1 is produced Raw signal passing ratio integral elementObtain signal i_p(s), described signal i_pS () is through proportional component D_pProduce Signal and input signal d_pS () is through proportional component I_pThe signal produced enters adder 2, and the signal that described adder 2 produces takes Bear and output signal u_dlpS () is through proportional componentThe feedback signal produced takes negative entrance adder 3, and described adder 3 produces Signal through proportional componentProduce output signal u_dlp(s)。

Dynamic model of modular multi-level convector modeling method the most according to claim 1, it is characterised in that: described mould Massing multilevel converter includes that three pairs of brachium pontis, every pair of brachium pontis include that brachium pontis and lower brachium pontis, described upper brachium pontis and lower brachium pontis are equal Including N number of submodule being sequentially connected in series and reactor, public direct-current end is drawn in three pairs of brachium pontis parallel connections.

Dynamic model of modular multi-level convector modeling method the most according to claim 1, it is characterised in that: described step Rapid 2 comprise the following steps:

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

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

Wherein, R_jRepresent the equivalent loss resistance of submodule, R_sFor brachium pontis current-limiting reactor equivalent series resistance, d_pjAnd u_djpRespectively The equivalent dutycycle of brachium pontis jth submodule and DC voltage in expression,Represent u_djpIn switch periods T_sInterior is flat Average；

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

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

In formula, I_p,U₁,U_djp,D_pjFor quiescent point；For disturbance quantity, each quiescent point of upper brachium pontis has following Relation:

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

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

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

Dynamic model of modular multi-level convector modeling method the most according to claim 3, it is characterised in that: on described In brachium pontis cycle by cycle switch average model, the controlled voltage source of each submodule cycle by cycle switch average model of ACR_sIt is sequentially connected in series with L, controlled voltage sourcePositive pole is defeated as upper brachium pontis cycle by cycle switch average model Go out proper pole, L not with R_sThe one end connected is as the negative pole of output end of upper brachium pontis cycle by cycle switch average model；DC side each The controlled current source of submodule cycle by cycle switch average modelR_jParallel with one another with C.

Dynamic model of modular multi-level convector modeling method the most according to claim 3, it is characterised in that: on described Brachium pontis small-signal alternate model includes brachium pontis controlled source form small-signal alternate model and upper brachium pontis transmission function block figure Formula small-signal alternate model；

In described upper brachium pontis controlled source form small-signal alternate model, AC each submodule small-signal alternate model controlled Voltage source d_pjU_djp, controlled voltage sourceR_sIt is sequentially connected in series with L；Controlled voltage source d_pNU_dNpPositive pole is as the little letter of upper brachium pontis The output head anode of number AC model, L not with R_sThe one end connected 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 sideControlled current source d_pjI_p、R_jWith C the most mutually In parallel；

In described upper brachium pontis transmission function block diagram form small-signal alternate model, N number of input signal d_pjS () is through corresponding N Individual proportional component U_djpThe signal produced and input signal-u₁S () enters adder 1 '；The signal of adder 1 ' generation and correspondence N number of output signal u_djp(s) passing ratio link D_pjThe feedback signal produced enters adder 2 '；The letter that adder 2 ' produces Number passing ratio integral elementObtain signal i_p(s), described signal i_pS () is through N number of proportional component D_pjProduce respectively N number of signal and corresponding N number of input signal d_pjS () is through proportional component I_pThe signal produced enters corresponding N number of adder The signal that 3j ', N number of adder 3j ' produce takes negative and corresponding N number of output signal u_djpS () is through proportional componentProduce Feedback signal takes N number of adder 4j of negative entrance, and the signal that N number of adder 4j produces is through corresponding N number of proportional componentProduce N number of output signal u_djp(s)。

Dynamic model of modular multi-level convector modeling method the most according to claim 5, it is characterised in that: on assuming Each submodule parameter of brachium pontis is symmetrical, and has:

d_p1=d_p2=...=d_pN=d_p (15)

u_d1p=u_d2p=...=u_dNp=u_dp (16)

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

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

Then being simplified brachium pontis small-signal alternate model is

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

Wherein, R represents that brachium pontis main circuit is lost equivalent resistance.

Dynamic model of modular multi-level convector modeling method the most according to claim 6, it is characterised in that: in simplification Brachium pontis small-signal alternate model includes simplifying upper brachium pontis controlled source form small-signal alternate model and simplifying upper brachium pontis transmission function Block diagram form small-signal alternate model.

Dynamic model of modular multi-level convector modeling method the most according to claim 7, it is characterised in that: described letter In change in brachium pontis controlled source form small-signal alternate model, the controlled voltage source Nd of AC_pU_dp, controlled voltage source R_sIt is sequentially connected in series with L, controlled voltage source Nd_pU_dpPositive pole is as the output simplifying upper brachium pontis controlled source form small-signal alternate model Rectify pole, L not with R_sThe one end connected is as the negative pole of output end simplifying upper brachium pontis controlled source form small-signal alternate model；Directly The controlled current source of stream sideControlled current source d_pI_p, R and C parallel with one another；Brachium pontis transmission function block diagram in described simplification In form small-signal alternate model, input signal d_pS () is through proportional component NU_dpThe signal produced and input signal-u₁S () enters Enter adder 1 ", adder 1 " signal produced and output signal u_dp(s) passing ratio link ND_pThe feedback signal produced enters Adder 2 ", adder 2 " the signal passing ratio integral element producedObtain signal i_p(s), signal i_pS () passes through Proportional component D_pThe signal produced and input signal d_pS () is through proportional component I_pThe signal produced enters adder 3 ", adder 3 " signal produced takes negative and output signal u_dpS () is through proportional componentThe feedback signal produced takes negative entrance adder 4, adds The signal that musical instruments used in a Buddhist or Taoist mass 4 produces is through proportional componentProduce output signal u_dp(s)。

Dynamic model of modular multi-level convector modeling method the most according to claim 1, it is characterised in that: step 3 Comprise the following steps:

Step 3-1: set up lower brachium pontis single submodule cycle by cycle switch average model and exchange with lower brachium pontis single submodel small-signal Model；

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

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

Wherein, d_njAnd u_djnRepresent equivalent dutycycle and the DC voltage of lower brachium pontis jth submodule respectively,Represent u_djnIn switch periods T_sInterior meansigma methods；

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

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

And have:

d_n1=d_n2=...=d_nN=d_n (22)

u_d1n=u_d2n=... u_dNn=u_dn (23)

TakeCan obtain

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

D_nFor quiescent point；

Then being simplified lower brachium pontis small-signal alternate model is

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

Dynamic model of modular multi-level convector modeling method the most according to claim 9, it is characterised in that: described In lower brachium pontis cycle by cycle switch average model, the controlled voltage source of each submodule cycle by cycle switch average model of ACR_sIt is sequentially connected in series with L, controlled voltage sourcePositive pole is as the output of lower brachium pontis cycle by cycle switch average model Rectify pole, L not with R_sThe one end connected is as the negative pole of output end of lower brachium pontis cycle by cycle switch average model；The single son of DC side The controlled current source of module switch period average modelR_jParallel with one another with C.

11. dynamic model of modular multi-level convector modeling methods according to claim 9, it is characterised in that: described Lower brachium pontis small-signal alternate model includes simplifying lower brachium pontis controlled source form small-signal alternate model and simplifying lower brachium pontis transmission letter Number block diagram form small-signal alternate model；

Under described simplification in brachium pontis controlled source form small-signal alternate model, L, R of AC_s, controlled voltage source Nd_nU_dnBe subject to Control voltage sourceBe sequentially connected in series, L not with R_sThe one end connected is as simplifying lower brachium pontis controlled source form small-signal exchange mould The output head anode of type, controlled voltage sourceNegative pole is as simplifying the defeated of lower brachium pontis controlled source form small-signal alternate model Go out to hold negative pole；The controlled current source of DC sideControlled current source d_nI_n, R and C parallel with one another；

Under described simplification in brachium pontis transmission function block diagram form small-signal alternate model, input signal d_nS () is through proportional component NU_dnThe signal produced takes negative and input signal u₂S () enters adder 1 " '；Output signal u_dn(s) passing ratio link ND_nProduce Raw feedback signal take negative and adder 1 " ' produce signal enter adder 2 " ', adder 2 " ' the signal that produces by than Example integral elementObtain signal i_n(s), signal i_nS () is through proportional component D_nThe signal produced and input signal d_n(s) Through proportional component I_nThe signal produced enters adder 3 " ', output signal u_dnS () is through proportional componentThe feedback letter produced Number take negative and adder 3 " ' produce signal enter adder 4 " ', " ' the signal that produces is through proportional component for adder 4Produce Raw output signal u_dn(s)。

12. dynamic model of modular multi-level convector modeling methods according to claim 1, it is characterised in that: described Step 4 comprises the following steps:

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

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

Wherein,

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

Footmark p represents that bridge arm module, footmark n represent lower bridge arm module；

Wherein,

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

u_N0For AC common-mode voltage；

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

Modularization multi-level converter quiescent point has a following relation:

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

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

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

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

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

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

13. dynamic model of modular multi-level convector modeling methods according to claim 12, it is characterised in that: described On modularization multi-level converter in brachium pontis cycle by cycle switch average model, upper brachium pontis controlled voltage source Nd_pi<u_dip>_Ts、R_sDepend on L Secondary series connection, upper brachium pontis controlled current source d_pi<i_pi>_Ts, R and C parallel with one another；Brachium pontis switch under described modularization multi-level converter In period average model, L, R_sWith lower brachium pontis controlled voltage source Nd_ni<u_din>_TsIt is sequentially connected in series, controlled current source d_ni<i_ni>_Ts, R and C is parallel with one another, constitutes lower bridge arm equivalent cycle by cycle switch average model.

14. dynamic model of modular multi-level convector modeling methods according to claim 12, it is characterised in that: described In modularization multi-level converter small-signal alternate model, signal i_pi(s) and signal i_niS () enters adder and produces signal i_si (s), signalSignal-u_si(s) and signal-u_N0S () enters adder and produces signal u_1i(s), signalLetter Number u_si(s) and signal u_N0S () enters adder and produces signal u_2i(s)；

On described modularization multi-level converter in brachium pontis small-signal alternate model, input signal d_piS () is through proportional component NU_dipThe signal produced and input signal-u_1iS () enters adder A, the signal of adder A generation and output signal u_dipS () leads to Cross proportional component ND_piThe feedback signal produced enters adder B, the signal passing ratio integral element that adder B producesObtain signal i_pi(s), signal i_piS () is through proportional component D_piThe signal produced and input signal d_pi(s) through than Example link I_piThe signal produced enters adder C, and the signal that adder C produces takes negative and output signal u_dipS () is through ratio ring JointThe feedback signal produced takes negative adder D that enters, and the signal of adder D generation is through proportional componentProduce output letter Number u_dip(s)；

Under described modularization multi-level converter in brachium pontis small-signal alternate model, input signal d_niS () is through proportional component NU_din The signal produced takes negative and input signal u_2iS () enters adder E, output signal u_din(s) passing ratio link ND_niProduce is anti- Feedback signal takes negative and the generation of adder E signal and enters adder F, the signal passing ratio integral element that adder F producesObtain signal i_ni(s), signal i_niS () is through proportional component D_niThe signal produced and input signal d_niS () is through ratio Link I_niThe signal produced enters adder G, output signal u_dinS () is through proportional componentThe feedback signal produced takes negative and adds The signal that musical instruments used in a Buddhist or Taoist mass G produces enters adder H, and the signal that adder H produces is through proportional componentProduce output signal u_din(s)。