CN103595284A - Modular multi-level current converter passivity modeling and control method - Google Patents

Abstract

The invention discloses a modular multi-level current converter passivity modeling and control method which mainly comprises the following steps: step 1, a modular multi-level current converter passivity mathematic model is established, and an equalization state-space equation within a switching period is obtained; step 2, a modular multi-level current converter energy forming method algorithm model based on the equalization state-space equation is established, and a passive system from an input state variable Xi to an output state variable X is defined; step 3, a current converter damping injection algorithm model is established; step 4, a current converter control model based on all module switching functions is established. The modular multi-level current converter passivity modeling and control method has the advantages that stabilized and balanced control over capacitance and voltages on the direct current sides of upper bridge arms and lower bridges arms and quick tracking control over currents on the alternating current sides of all the bridges arms can be realized rapidly, the defects of a traditional modular multi-level current converter control strategy are overcome, and a feasible means is provided for the design of a control strategy of a flexible direct current transmission system.

Description

Modularization multi-level converter passivity modeling and control method

Technical field

The invention belongs to Power System Flexible power transmission and distribution technical field, relate to a kind of modeling and control method of modularization multi-level converter, be specifically related to a kind of modularization multi-level converter modeling and control method based on Passivity Theory.

Background technology

The development experience of technology of transmission of electricity from direct current to interchange, then the change of technique coexisting to alternating current-direct current.Technology of HVDC based Voltage Source Converter based on voltage source converter, can make the problems of current AC-HVDC field face be readily solved, and for power transmission mode, changing and build following intelligent grid provides brand-new solution.Because full-controlled switch device (as insulated gate bipolar transistor (IGBT) etc.) is withstand voltage still relatively low, flexible DC power transmission system based on two level or three level need adopt the direct serial connection technology of switching device to adapt to high voltage occasion, but can bring thus, device is all pressed, electromagnetic interference, and the series of problems such as switching loss that cause of higher switching frequency.Along with the continuous lifting of electric pressure and capacity requirement, these defects embody more and more significantly, become the bottleneck that restriction two level or three Level Technology are difficult to go beyond itself.

Based on an above-mentioned difficult problem, at the calendar year 2001 R.Marquart of university of Munich, Germany Federal Defence Forces and A.Lesnicar, modularization multi-level converter topological structure has been proposed jointly, general half-bridge or the full-bridge inverter cascading topological structure of adopting, be convenient to modularized design, be easy to the lifting of electric pressure and the upgrading of capacity, switching frequency and the switch stress of power electronic device significantly reduce, and harmonic wave of output voltage content and total voltage aberration rate greatly reduce.Fig. 1 shows a kind of modularization multi-level converter of phase structure.Wherein go up brachium pontis and lower brachium pontis is comprised of two half-bridge modules respectively, each half-bridge consists of two IGBT, two anti-paralleled diodes, DC bus capacitor and DC side equivalent parallel resistance four parts.Wherein, C _ukand C _dk(k=1,2) are respectively the dc-link capacitance of k module of upper and lower brachium pontis, R _ukand R _dkbe respectively the equivalent parallel resistance at k module DC bus capacitor two ends of upper and lower brachium pontis, T _{uk, j}and T _{dk, j}(k=1,2, j=1,2) are respectively j IGBT of k module of upper and lower brachium pontis, D _{uk, j}and D _{dk, j}(k=1,2, j=1,2) are respectively j anti-paralleled diode of k module of upper and lower brachium pontis; V _dfor direct current network voltage, u _vfor the voltage with multiple levels of modularization multi-level converter output, i _uand i _dbe respectively upper and lower brachium pontis electric current; L _gand R _gthe inductance and the equivalent resistance that represent respectively AC network side, v _gfor ac grid voltage.The proposition of this technology and application, promoted the on-road efficiency of flexible DC power transmission engineering, promoted the development of Technology of HVDC based Voltage Source Converter and engineering to promote.

Because the submodule quantity of connecting in each brachium pontis of modularization multi-level converter is more, it is large that the data volume of valve control system required processing within each cycle causes very greatly controlling difficulty, and difficulty is controlled in the equilibrium that has increased submodule capacitance voltage.If unbalanced situation appears in the energy distribution between brachium pontis, the stability of submodule inside is destroyed, and then causes current waveform to distort.Yet, most of scholar will be based on two level or three-level converter voltage, electric current and power control strategy and controller parameter method for designing for the modeling and control of modularization multi-level converter, causing controlling poor effect or effect is to be at least worth discussion.

Summary of the invention

The object of the invention is to overcome existing voltage, electric current and power control strategy and controller method based on two level or three-level converter is applied to the undesirable deficiency of effect that modularization multi-level converter is obtained, propose a kind of modularization multi-level converter passivity modeling and control method.

Technical scheme of the present invention is: modularization multi-level converter passivity modeling and control method, comprises the steps:

S1, set up modularization multi-level converter passivity Mathematical Modeling, ask for the equalization state space equation in a switch periods;

S2, the modularization multi-level converter Energy shaping algorithm model of foundation based on equalization state space equation, definition is from input state variable ξ to the passive system output state variable X;

S3, set up converter damping and inject algorithm model, design damping matrix W is to guarantee the stable control of each DC capacitor voltage of modularization multi-level converter and the rapid track and control of ac-side current; And extract the switch function of each module in the upper and lower brachium pontis of multilevel converter based on Passive Control Algorithm;

S4, build the converter control model based on each module switch function: relatively DC capacitor voltage reference value and measured value, and carry out outer voltage control according to damping matrix W parameter; Meanwhile, according to similar approach, ac-side current is carried out to current inner loop control; Then switch function and the triangular carrier relatively obtaining also forms pwm pulse control signal tracking to the control of DC capacitor voltage and ac-side current in order to realization of each switch of modularization multi-level converter.

Further, the detailed process of the modularization multi-level converter of above-mentioned steps S1 based on phase structure is as follows: in the modularization multi-level converter of phase structure, upper brachium pontis and lower brachium pontis are comprised of two half-bridge modules respectively, and each half-bridge consists of two IGBT, two anti-paralleled diodes, DC bus capacitor and DC side equivalent parallel resistance four parts; Wherein, C _ukand C _dk, k=1 or 2, is respectively the dc-link capacitance of k module of upper and lower brachium pontis, R _ukand R _dkbe respectively the equivalent parallel resistance at k module DC bus capacitor two ends of upper and lower brachium pontis, T _{uk, j}and T _{dk, j}, k=1 or 2, j=1 or 2, be respectively j IGBT of k module of upper and lower brachium pontis, D _{uk, j}and D _{dk, j}, k=1 or 2, j=1 or 2, be respectively j anti-paralleled diode of k module of upper and lower brachium pontis; V _dfor direct current network voltage, u _vfor the voltage with multiple levels of modularization multi-level converter output, i _uand i _dbe respectively upper and lower brachium pontis electric current; L _gand R _gthe inductance and the equivalent resistance that represent respectively AC network side, v _gfor ac grid voltage;

Based on Kirchhoff's law, set up the differential equation of the upper and lower brachium pontis of modularization multi-level converter:

$L_e\frac{d{i}_u}{\mathrm{dt}}+R_e{i}_u+m_{u,1^{u}c,u1}+m_{u,2^{u}c,\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="HDA0000423940580000011.png"\; state="\{\{state\}\}">u</figure-callout>}2}=\frac{V_d}{2}-u_v---\left(1\right)$

$L_e\frac{d{i}_d}{\mathrm{dt}}+R_e{i}_d+m_{d,1^{u}c,d1}+m_{d,2^{u}c,\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="HDA0000423940580000011.png"\; state="\{\{state\}\}">d</figure-callout>}2}=\frac{{\mathrm{<figure-callout\; id="2"\; label="V\; d"\; filenames="HDA0000423940580000011.png"\; state="\{\{state\}\}">V</figure-callout>}}_d}{2}+u_v---\left(2\right)$

Wherein, m _u,kand m _d,k, k=1 or 2 represents respectively the switch function of k module of upper and lower brachium pontis; u _{c, uk}and u _{c, dk}, k=1 or 2 represents respectively k module DC capacitor voltage of upper and lower brachium pontis; L _eand R _ethe inductance and the equivalent resistance that represent respectively each brachium pontis; i _uand i _drepresent respectively upper and lower brachium pontis electric current; V _dfor direct current network voltage, u _vfor the voltage with multiple levels of modularization multi-level converter output, the i.e. voltage of brachium pontis mid point;

Based on Kirchhoff's law, the differential equation of setting up each unit DC side of upper and lower brachium pontis is as follows:

$C_{u1}\frac{d{u}_{c,u1}}{\mathrm{dt}}+\frac{u_{c,u1}}{R_{u1}}-m_{u,1}{i}_u=0---\left(3\right)$

$C_{u2}\frac{d{u}_{c,u2}}{\mathrm{dt}}+\frac{u_{c,u2}}{R_{u2}}-m_{u,2}{i}_u=0---\left(4\right)$

$C_{d1}\frac{d{u}_{c,d1}}{\mathrm{dt}}+\frac{u_{c,d1}}{R_{d1}}-m_{d,1}{i}_d=0---\left(5\right)$

$C_{d2}\frac{d{u}_{c,\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="HDA0000423940580000011.png"\; state="\{\{state\}\}">d</figure-callout>}2}}{\mathrm{dt}}+\frac{u_{c,d2}}{R_{d2}}-m_{d,2}{i}_d=0---\left(6\right)$

Wherein, C _ukand C _dk, k=1 or 2 is respectively the dc-link capacitance of k module of upper and lower brachium pontis, R _ukand R _dkbe respectively the equivalent parallel resistance at k module DC bus capacitor two ends of upper and lower brachium pontis;

For the ease of the derivation of equation, formula (1)～(6) are rewritten into following matrix differential equation form:

$D\stackrel{\&CenterDot;}{z}+\mathrm{Rz}+m_{u,1}{M}_{u1}z+m_{u,2}{M}_{u2}z+m_{d,1}{M}_{d1}z+m_{d,2}{M}_{d2}z=\mathrm{\&xi;}---\left(7\right)$

The input vector that wherein ξ is system, state variable z and coefficient matrix D, R, M _u1, M _u2, M _d1, M _d2be respectively:

$\mathrm{\&xi;}={[\frac{V_d}{2}-u_v,\frac{{\mathrm{<figure-callout\; id="2"\; label="V\; d"\; filenames="HDA0000423940580000011.png"\; state="\{\{state\}\}">V</figure-callout>}}_d}{2}+u_v,\mathrm{0,0,0,0}]}^T$

z=[i _u,i _d,u _c,u1,u _c,u2,u _c,d1,u _c,d2] ^T

D=diag{L _e,L _e,C _u1,C _u2,C _d1,C _d2}

$R=\mathrm{diag}\{R_e,R_e,\frac{1}{R_{u1}},\frac{1}{R_{u2}},\frac{1}{R_{d1}},\frac{1}{R_{d2}}\}$

$M_{u1}=\left[\begin{array}{cccccc}0& 0& 1& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\\ -1& 0& 0& 0& 0& \text{0}\\ 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& \text{0}\\ 0& 0& 0& 0& 0& 0\end{array}\right],$ $M_{u2}=\left[\begin{array}{cccccc}0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\\ -1& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\end{array}\right]$

$M_{d1}=\left[\begin{array}{cccccc}0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 1& \text{0}\\ 0& 0& 0& 0& 0& 0\\ 0& -1& 0& 0& 0& \text{0}\\ 0& 0& 0& 0& 0& 0\end{array}\right],$ ${\mathrm{<figure-callout\; id="2"\; label="M\; d"\; filenames="HDA0000423940580000011.png"\; state="\{\{state\}\}">M</figure-callout>}}_d=\left[\begin{array}{cccccc}0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 1\\ 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\\ 0& -1& 0& 0& 0& 0\end{array}\right]$

Due to coefficient matrix M _u1, M _u2, M _d1, M _d2be antisymmetric matrix, all meet z ^tm _hz=0, wherein h gets respectively u ₁, u ₂, d ₁and d ₂one of, therefore, the energy function E of modularization multi-level converter can be expressed as:

$E=\frac{1}{2}{z}^T\mathrm{Dz},D=D^T>0---\left(8\right)$

Similarly, modularization multi-level converter dissipation energy E _discan be expressed as:

$E_{\mathrm{dis}}=\frac{1}{2}{z}^T\mathrm{Rz},R=R^T>0---\left(9\right)$

Adopt equalization method at a control cycle, to average processing to state variable, equation (7) can be rewritten as:

$D\stackrel{\&CenterDot;}{X}+\mathrm{RX}+s_{u,1}{M}_{u1}X+s_{u,2}{M}_{u2}X+s_{d,1}{M}_{d1}X+s_{d,2}{M}_{d2}X=\mathrm{\&xi;}---\left(10\right)$

Wherein, X be state variable z at the mean value of a switch periods, be expressed as:

$X={[{\stackrel{\&OverBar;}{i}}_u,{\stackrel{\&OverBar;}{i}}_d,{\stackrel{\&OverBar;}{u}}_{c,u1}.{\stackrel{\&OverBar;}{u}}_{c,u2},{\stackrel{\&OverBar;}{u}}_{c,d1},{\stackrel{\&OverBar;}{u}}_{c,d2}]}^T---\left(11\right)$

Wherein, each element of X is respectively each element of state variable z at the mean value of a switch periods.Similarly, s _u,kand s _d,k, k=1 or 2 is respectively the equalization switch function of upper and lower each module of brachium pontis in a switch periods.

Further, the detailed process of above-mentioned steps S2 is as follows:

The energy function E of modularization multi-level converter based on equation (10) is:

$E=\frac{1}{2}{X}^T\mathrm{DX},D=D^T>0---\left(12\right)$

Ask for the single order differential of energy function

for:

$\stackrel{\&CenterDot;}{E}=\frac{1}{2}{X}^{T}D\stackrel{\&CenterDot;}{X}=X^T[-\mathrm{RX}-s_{u,1}{M}_{u1}X-s_{u,2}{M}_{u2}X-s_{d,1}{M}_{d1}X-s_{d,2}{M}_{d2}X+\mathrm{\&xi;}]---\left(13\right)$

Due to coefficient matrix M _u1, M _u2, M _d1, M _d2be antisymmetric matrix, all meet X ^tm _hx=0, wherein h gets respectively u ₁, u ₂, d ₁and d ₂one of, therefore, simplified style (13) is:

$\stackrel{\&CenterDot;}{E}=\frac{1}{2}{X}^{T}D\stackrel{\&CenterDot;}{X}=-X^T\mathrm{RX}+X^T\mathrm{\&xi;}---\left(14\right)$

At [t ₀, t ₁] in the time period, formula (14) is asked for to integration and obtains:

$E\left(t_1\right)-E\left(t_0\right)=-{\&Integral;}_{t_0}^{t1}\left(X^T\mathrm{RX}\right)\mathrm{dt}+{\&Integral;}_{t_0}^{t1}\left(X^T\mathrm{\&xi;}\right)\mathrm{dt}---\left(15\right)$

Equation (15) left side is [t ₀, t ₁] gross energy that stores of time period internal mold blocking multilevel converter, equation the right expression formula

for the energy that modularization multi-level converter dissipates, equation the right expression formula

for the energy of electrical network to modularization multi-level converter injection; The principle of controlling according to passivity, equation (15) has defined one from input ξ to the passive system output X; If input ξ=0, (14) formula can be reduced to:

$\stackrel{\&CenterDot;}{E}=-x^T\mathrm{Rx}<0---\left(16\right).$

Further, the detailed process of described step S3 is as follows:

Suppose the state variable X of expectation _dfor: $X_d={[i_u^{*},i_d^{*},u_{c,u1}^{*},u_{c,\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="HDA0000423940580000011.png"\; state="\{\{state\}\}">u</figure-callout>}2}^{*},u_{c,d1}^{*},u_{c,\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="HDA0000423940580000011.png"\; state="\{\{state\}\}">d</figure-callout>}2}^{*}]}^T---\left(17\right)$

Wherein, with the variable of asterisk, represent the desired value of relevant variable, X _dfor the desired value to dependent variable in state variable X;

Departure vector Δ X is defined as:

ΔX=X _d-X （18）

Using Δ X as new state variable, in conjunction with formula (10) and (18), the equalization state space equation of modularization multi-level converter is rewritten as:

$\mathrm{D\&Delta;}\stackrel{\&CenterDot;}{X}+\mathrm{R\&Delta;X}+s_{u,1}{M}_{u1}\mathrm{\&Delta;X}+s_{u,2}{M}_{u2}\mathrm{\&Delta;X}+s_{d,1}{M}_{d1}\mathrm{\&Delta;X}+s_{d,2}{\mathrm{<figure-callout\; id="2"\; label="M\; d"\; filenames="HDA0000423940580000011.png"\; state="\{\{state\}\}">M</figure-callout>}}_d\mathrm{\&Delta;X}=\mathrm{\&eta;}---\left(19\right)$

Wherein, equivalent control input vector η expression formula is:

$\mathrm{\&eta;}=-\mathrm{\&xi;}+\{D{\stackrel{\&CenterDot;}{X}}_d+R{X}_d+s_{u,1}{M}_{u1}{X}_d+s_{u,2}{M}_{u2}{X}_d+s_{d,1}{M}_{d1}{X}_d+s_{d,2}{M}_{d2}{X}_d\}---\left(20\right)$

Because state space equation (19) and (10) have identical structure, so the energy function E of modularization multi-level converter departure vector Δ X _efor:

$E_e=\frac{1}{2}\mathrm{\&Delta;}{X}^T\mathrm{D\&Delta;X},D=D^T>0---\left(21\right)$

Single order differential is asked in the left and right two ends of formula (21), obtains:

${\stackrel{\&CenterDot;}{E}}_e=-\mathrm{\&Delta;}{X}^T\mathrm{R\&Delta;X}+\mathrm{\&Delta;}{X}^T\mathrm{\&eta;}---\left(22\right)$

Formula (22) has defined a passive system from equivalent control inputs vector η to error vector Δ X.

Further, in order to guarantee the stable control of modularization multi-level converter DC voltage and the quick tracking of ac-side current, introduce damping matrix W, obtain following expression:

η=-WΔX （23）

By formula (23) substitution formula (22), obtain:

${\stackrel{\&CenterDot;}{E}}_e=-\mathrm{\&Delta;}{X}^T(R+W)\mathrm{\&Delta;X}---\left(24\right)$

If known matrix R+W is symmetric positive definite matrix,

permanent establishment, shows energy function E _ewill converge to balance point Δ X=0, convergence rate is determined by the parameter of matrix R+W.

Further, consider that R is a diagonal matrix, for simplicity, W is designed to diagonal matrix, its expression formula is as follows:

W=diag{w ₁,w ₂,w ₃,w ₄,w ₅,w ₆} （25）

Wherein, diag{} represents diagonal matrix, i=1 ..., 6 o'clock w _ifor W entry of a matrix element; In conjunction with formula (1), (2), (17), (18) and (19), the passivity control algolithm of deriving modularization multi-level converter is as follows:

$s_{u,1}=\frac{1}{2u_{c,u1}^{*}}(-L_e\frac{d{\stackrel{\&OverBar;}{i}}_u}{\mathrm{dt}}-R_e{\stackrel{\&OverBar;}{i}}_u+\frac{V_d}{2}-u_v-w_1\mathrm{\&Delta;}{x}_1),\mathrm{\&Delta;}{x}_1=i_u^{*}-{\stackrel{\&OverBar;}{i}}_u---\left(26\right)$

$s_{u,2}=\frac{1}{2u_{c,\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="HDA0000423940580000011.png"\; state="\{\{state\}\}">u</figure-callout>}2}^{*}}(-L_e\frac{d{\stackrel{\&OverBar;}{i}}_u}{\mathrm{dt}}-R_e{\stackrel{\&OverBar;}{i}}_u+\frac{V_d}{2}-u_v-w_1\mathrm{\&Delta;}{x}_1),\mathrm{\&Delta;}{x}_1=i_u^{*}-{\stackrel{\&OverBar;}{i}}_u---\left(27\right)$

$s_{d,1}=\frac{1}{2u_{c,d1}^{*}}(-L_e\frac{d{\stackrel{\&OverBar;}{i}}_d}{\mathrm{dt}}-R_e{\stackrel{\&OverBar;}{i}}_d+\frac{{\mathrm{<figure-callout\; id="2"\; label="V\; d"\; filenames="HDA0000423940580000011.png"\; state="\{\{state\}\}">V</figure-callout>}}_d}{2}+u_v-{\mathrm{<figure-callout\; id="2"\; label="w"\; filenames="HDA0000423940580000011.png"\; state="\{\{state\}\}">w</figure-callout>}}_2\mathrm{\&Delta;}{x}_2),\mathrm{\&Delta;}{x}_2=i_d^{*}-{\stackrel{\&OverBar;}{i}}_d---\left(28\right)$

$s_{d,2}=\frac{1}{2u_{c,\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="HDA0000423940580000011.png"\; state="\{\{state\}\}">d</figure-callout>}2}^{*}}(-L_e\frac{d{\stackrel{\&OverBar;}{i}}_d}{\mathrm{dt}}-R_e{\stackrel{\&OverBar;}{i}}_d+\frac{{\mathrm{<figure-callout\; id="2"\; label="V\; d"\; filenames="HDA0000423940580000011.png"\; state="\{\{state\}\}">V</figure-callout>}}_d}{2}+u_v-{\mathrm{<figure-callout\; id="2"\; label="w"\; filenames="HDA0000423940580000011.png"\; state="\{\{state\}\}">w</figure-callout>}}_2\mathrm{\&Delta;}{x}_2),\mathrm{\&Delta;}{x}_2=i_d^{*}-{\stackrel{\&OverBar;}{i}}_d---\left(29\right)$

The differential equation of each module DC side of upper brachium pontis is:

$C_{u1}\frac{d{\stackrel{\&OverBar;}{u}}_{c,u1}}{\mathrm{dt}}+\frac{{\stackrel{\&OverBar;}{u}}_{c,u1}}{R_{u1}}=s_{u,1}{i}_u^{*}-w_3\mathrm{\&Delta;}{x}_3,\mathrm{\&Delta;}{x}_3=u_{c,u1}^{*}-{\stackrel{\&OverBar;}{u}}_{c,u1}---\left(30\right)$

$C_{u2}\frac{d{\stackrel{\&OverBar;}{u}}_{c,\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="HDA0000423940580000011.png"\; state="\{\{state\}\}">u</figure-callout>}2}}{\mathrm{dt}}+\frac{{\stackrel{\&OverBar;}{u}}_{c,u2}}{{\mathrm{<figure-callout\; id="2"\; label="R\; u"\; filenames="HDA0000423940580000011.png"\; state="\{\{state\}\}">R</figure-callout>}}_u}=s_{u,2}{i}_u^{*}-w_4\mathrm{\&Delta;}{x}_4,\mathrm{\&Delta;}{x}_4=u_{c,\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="HDA0000423940580000011.png"\; state="\{\{state\}\}">u</figure-callout>}2}^{*}-{\stackrel{\&OverBar;}{u}}_{c,u2}---\left(31\right)$

The differential equation of lower each module DC side of brachium pontis is:

$C_{d1}\frac{d{\stackrel{\&OverBar;}{u}}_{c,d1}}{\mathrm{dt}}+\frac{{\stackrel{\&OverBar;}{u}}_{c,d1}}{R_{d1}}=s_{d,1}{i}_d^{*}-w_5\mathrm{\&Delta;}{x}_5,\mathrm{\&Delta;}{x}_5=u_{c,d1}^{*}-{\stackrel{\&OverBar;}{u}}_{c,d1}---\left(32\right)$

$C_{d2}\frac{d{\stackrel{\&OverBar;}{u}}_{c,\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="HDA0000423940580000011.png"\; state="\{\{state\}\}">d</figure-callout>}2}}{\mathrm{dt}}+\frac{{\stackrel{\&OverBar;}{u}}_{c,d2}}{{\mathrm{<figure-callout\; id="2"\; label="R\; d"\; filenames="HDA0000423940580000011.png"\; state="\{\{state\}\}">R</figure-callout>}}_d}=s_{d,2}{i}_d^{*}-w_6\mathrm{\&Delta;}{x}_6,\mathrm{\&Delta;}{x}_6=u_{c,\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="HDA0000423940580000011.png"\; state="\{\{state\}\}">d</figure-callout>}2}^{*}-{\stackrel{\&OverBar;}{u}}_{c,d2}---\left(33\right).$

Further, w ₁and w ₂span be [0.2,2], w ₃～w ₆span be [50,200].

Further, described step S4 is specially:

Based on formula (26)～(33), build the converter control model based on each module switch function: compare DC capacitor voltage reference value and measured value, and carry out outer voltage control according to damping matrix W parameter; Meanwhile, according to similar approach, ac-side current is carried out to current inner loop control; Then switch function and the triangular carrier relatively obtaining also forms pwm pulse control signal tracking to the control of DC capacitor voltage and ac-side current in order to realization of each switch of modularization multi-level converter.

Beneficial effect of the present invention: modularization multi-level converter passivity modeling and control method of the present invention can realize the stable equilibrium control of each brachium pontis DC capacitor voltage up and down and the rapid track and control of ac-side current fast.Overcome the deficiency of traditional modular multilevel converter control strategy, the correlation theory of controlling by introducing passivity, sets up modularization multi-level converter passivity Mathematical Modeling, asks for an equalization state space equation in switch periods; By setting up the algorithm model of modularization multi-level converter Energy shaping method, define the passive system between an input and output; Then damping matrix reasonable in design, set up the algorithm model that modularization multi-level converter damping is injected, guarantee the stable control of each DC capacitor voltage of modularization multi-level converter and the rapid track and control of ac-side current, derive the multilevel converter switch function based on Passive Control Algorithm, thereby realized the whole control flow of modularization multi-level converter.Overcome traditional control method and controlled the shortcoming that parameter is many, amount of calculation is large, consumes resources is large.This control method is fallen under operational mode in reference current sudden change and ac grid voltage, all can realize quickly and accurately DC voltage equilibrium and alternating current follows the tracks of fast, stability is high, tracking velocity is fast, effectively verified that damping based on passivity method injects the feasibility of algorithm, for the control strategy design of flexible DC power transmission system provides feasible means.

Accompanying drawing explanation

Fig. 1 is the topological schematic diagram of modularization multi-level converter;

Fig. 2 is the structured flowchart of modularization multi-level converter passivity modeling and control method;

Fig. 3 is that the amplitude of active current reference value in specific embodiment is suddenlyd change from 100A at t=0.1s to 200A process, the output voltage of modularization multi-level converter, current waveform and upper and lower brachium pontis current waveform;

Fig. 4 is that the amplitude of active current reference value in specific embodiment is suddenlyd change from 100A at t=0.1s to 200A process, the switch function of modularization multi-level converter and each module dc-link capacitance voltage waveform;

Fig. 5 is that in specific embodiment, active current reference value is 100A, and ac grid voltage occurs in 60% voltage falling process between 0.1s～0.2s, the output voltage of modularization multi-level converter, current waveform and upper and lower brachium pontis current waveform;

Fig. 6 is that in specific embodiment, active current reference value is 100A, and ac grid voltage occurs in 60% voltage falling process between 0.1s～0.2s, the switch function of modularization multi-level converter and each module dc-link capacitance voltage waveform.

Embodiment

Below in conjunction with accompanying drawing, embodiments of the invention are elaborated: the present embodiment is implemented take technical solution of the present invention under prerequisite, provided detailed execution mode and concrete operating process, but protection scope of the present invention is not limited to following embodiment.

As shown in Figure 1, modularization multi-level converter is connected between direct current network and AC network, and wherein, direct current network is in series by the DC power supply of two 2250V, the tie point ground connection of two DC power supply, AC network frequency is that 50Hz, voltage peak are 1600V.The upper and lower brachium pontis of modularization multi-level converter is comprised of two half-bridge modules respectively, and each half-bridge consists of two IGBT, two anti-paralleled diodes, DC bus capacitor and DC side equivalent parallel resistance four parts.Wherein, V _dfor direct current network voltage, u _vvoltage with multiple levels for converter output; i _uand i _dbe respectively upper and lower brachium pontis AC output current, L _eand R _ethe inductance value and the equivalent resistance thereof that represent respectively each brachium pontis; u _vfor the voltage with multiple levels of converter output, the i.e. voltage of brachium pontis mid point; C _ukand C _dk(k=1,2) is respectively the dc-link capacitance of k module of upper and lower brachium pontis, R _ukand R _dkbe respectively the equivalent parallel resistance at k module DC bus capacitor two ends of upper and lower brachium pontis; T _{uk, j}and T _{dk, j}(k=1,2, j=1,2) are respectively j IGBT of k module of upper and lower brachium pontis, D _{uk, j}and D _{dk, j}(k=1,2, j=1,2) are respectively j anti-paralleled diode of k module of upper and lower brachium pontis; L _gand R _gthe inductance value and the equivalent resistance thereof that represent respectively AC network side, v _gfor ac grid voltage.

The modularization multi-level converter passivity modeling and control method of the present embodiment, comprises the steps:

S1, set up modularization multi-level converter passivity Mathematical Modeling, ask for the equalization state space equation in a switch periods;

S2, the modularization multi-level converter Energy shaping algorithm model of foundation based on equalization state space equation, main by energy function and the first derivative thereof of derivation multilevel converter, definition is from input state variable ξ to the passive system output state variable X;

S3, set up converter damping and inject algorithm model, design damping matrix W is to guarantee the stable control of each DC capacitor voltage of modularization multi-level converter and the rapid track and control of ac-side current; And extract the switch function of each module in the upper and lower brachium pontis of multilevel converter based on Passive Control Algorithm;

S4, build the converter control model based on each module switch function: relatively DC capacitor voltage reference value and measured value, and carry out outer voltage control according to damping matrix W parameter; Meanwhile, according to similar approach, ac-side current is carried out to current inner loop control; Then switch function and the triangular carrier relatively obtaining also forms pwm pulse control signal tracking to the control of DC capacitor voltage and ac-side current in order to realization of each switch of modularization multi-level converter.

The modularization multi-level converter of phase structure of take is below described further the modeling and control method of the present embodiment as example, the detailed process of the modularization multi-level converter of the above-mentioned steps S1 of the modularization multi-level converter based on phase structure based on phase structure is as follows: wherein in the modularization multi-level converter of phase structure, upper brachium pontis and lower brachium pontis are comprised of two half-bridge modules respectively, and each half-bridge consists of two IGBT, two anti-paralleled diodes, DC bus capacitor and DC side equivalent parallel resistance four parts; Wherein, C _ukand C _dk, k=1 or 2, is respectively the dc-link capacitance of k module of upper and lower brachium pontis, R _ukand R _dkbe respectively the equivalent parallel resistance at k module DC bus capacitor two ends of upper and lower brachium pontis, T _{uk, j}and T _{dk, j}, k=1 or 2, j=1 or 2, be respectively j IGBT of k module of upper and lower brachium pontis, D _{uk, j}and D _{dk, j}, k=1 or 2, j=1 or 2, be respectively j anti-paralleled diode of k module of upper and lower brachium pontis; V _dfor direct current network voltage, u _vfor the voltage with multiple levels of modularization multi-level converter output, i _uand i _dbe respectively upper and lower brachium pontis electric current; L _gand R _gthe inductance and the equivalent resistance that represent respectively AC network side, v _gfor ac grid voltage;

Based on Kirchhoff's law, set up the differential equation of the upper and lower brachium pontis of modularization multi-level converter:

$L_e\frac{d{i}_u}{\mathrm{dt}}+R_e{i}_u+m_{u,1}{u}_{c,u1}+m_{u,2}{u}_{c,\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="HDA0000423940580000011.png"\; state="\{\{state\}\}">u</figure-callout>}2}=\frac{V_d}{2}-u_v---\left(1\right)$

$L_e\frac{d{i}_d}{\mathrm{dt}}+R_e{i}_d+m_{d,1}{u}_{c,d1}+m_{d,2}{u}_{c,\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="HDA0000423940580000011.png"\; state="\{\{state\}\}">d</figure-callout>}2}=\frac{{\mathrm{<figure-callout\; id="2"\; label="V\; d"\; filenames="HDA0000423940580000011.png"\; state="\{\{state\}\}">V</figure-callout>}}_d}{2}+u_v---\left(2\right)$

Wherein, m _u,kand m _d,k, k=1 or 2 represents respectively the switch function of k module of upper and lower brachium pontis; u _{c, uk}and u _{c, dk}, k=1 or 2 represents respectively k module DC capacitor voltage of upper and lower brachium pontis; L _eand R _ethe inductance and the equivalent resistance that represent respectively each brachium pontis; i _uand i _drepresent respectively upper and lower brachium pontis electric current; V _dfor direct current network voltage, u _vfor the voltage with multiple levels of modularization multi-level converter output, the i.e. voltage of brachium pontis mid point.

Based on Kirchhoff's law, the differential equation of setting up each unit DC side of upper and lower brachium pontis is as follows:

$C_{u1}\frac{d{u}_{c,u1}}{\mathrm{dt}}+\frac{u_{c,u1}}{R_{u1}}-m_{u,1}{i}_u=0---\left(3\right)$

$C_{u2}\frac{d{u}_{c,\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="HDA0000423940580000011.png"\; state="\{\{state\}\}">u</figure-callout>}2}}{\mathrm{dt}}+\frac{u_{c,u2}}{R_{u2}}-m_{u,2}{i}_u=0---\left(4\right)$

$C_{d1}\frac{d{u}_{c,d1}}{\mathrm{dt}}+\frac{u_{c,d1}}{R_{d1}}-m_{d,1}{i}_d=0---\left(5\right)$

$C_{d2}\frac{d{u}_{c,\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="HDA0000423940580000011.png"\; state="\{\{state\}\}">d</figure-callout>}2}}{\mathrm{dt}}+\frac{u_{c,d2}}{R_{d2}}-m_{d,2}{i}_d=0---\left(6\right)$

Wherein, C _ukand C _dk, k=1 or 2 is respectively the dc-link capacitance of k module of upper and lower brachium pontis, R _ukand R _dkbe respectively the equivalent parallel resistance at k module DC bus capacitor two ends of upper and lower brachium pontis;

For the ease of the derivation of equation, formula (1)～(6) are rewritten into following matrix differential equation form:

$D\stackrel{\&CenterDot;}{z}+\mathrm{Rz}+m_{u,1}{M}_{u1}z+m_{u,2}{M}_{u2}z+m_{d,1}{M}_{d1}z+m_{d,2}{M}_{d2}z=\mathrm{\&xi;}---\left(7\right)$

The input vector that wherein ξ is system, state variable z and coefficient matrix D, R, M _u1, M _u2, M _d1, M _d2be respectively:

$\mathrm{\&xi;}={[\frac{V_d}{2}-u_v,\frac{{\mathrm{<figure-callout\; id="2"\; label="V\; d"\; filenames="HDA0000423940580000011.png"\; state="\{\{state\}\}">V</figure-callout>}}_d}{2}+u_v,\mathrm{0,0,0,0}]}^T$

z=[i _u,i _d,u _c,u1,u _c,u2,u _c,d1,u _c,d2] ^T

D=diag{L _e,L _e,C _u1,C _u2,C _d1,C _d2}

$R=\mathrm{diag}\{R_e,R_e,\frac{1}{R_{u1}},\frac{1}{{\mathrm{<figure-callout\; id="2"\; label="R\; u"\; filenames="HDA0000423940580000011.png"\; state="\{\{state\}\}">R</figure-callout>}}_u},\frac{1}{R_{d1}},\frac{1}{R_{d2}}\}$

$M_{u1}=\left[\begin{array}{cccccc}0& 0& 1& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\\ -1& 0& 0& 0& 0& \text{0}\\ 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& \text{0}\\ 0& 0& 0& 0& 0& 0\end{array}\right],$ ${\mathrm{<figure-callout\; id="2"\; label="M\; u"\; filenames="HDA0000423940580000011.png"\; state="\{\{state\}\}">M</figure-callout>}}_u=\left[\begin{array}{cccccc}0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\\ -1& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\end{array}\right]$

$M_{d1}=\left[\begin{array}{cccccc}0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 1& \text{0}\\ 0& 0& 0& 0& 0& 0\\ 0& -1& 0& 0& 0& \text{0}\\ 0& 0& 0& 0& 0& 0\end{array}\right],$ ${\mathrm{<figure-callout\; id="2"\; label="M\; d"\; filenames="HDA0000423940580000011.png"\; state="\{\{state\}\}">M</figure-callout>}}_d=\left[\begin{array}{cccccc}0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 1\\ 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\\ 0& -1& 0& 0& 0& 0\end{array}\right]$

From above-mentioned derivation, find out coefficient matrix M _u1, M _u2, M _d1, M _d2be antisymmetric matrix, all meet z ^tm _hz=0(h=u ₁, u ₂, d ₁, d ₂).Therefore, the energy function E of modularization multi-level converter can be expressed as:

$E=\frac{1}{2}{z}^T\mathrm{Dz},D=D^T>0---\left(8\right)$

Similarly, modularization multi-level converter dissipation energy E _discan be expressed as:

$E_{\mathrm{dis}}=\frac{1}{2}{z}^T\mathrm{Rz},R=R^T>0---\left(9\right)$

From equation (7), find out switch function m _{u, 1}, m _{u, 2}, m _{d, 1}, m _{d, 2}=0,1}, causes governing equation discontinuous, and what consider again the employing of this control system is high-speed pulse width modulated method, therefore can adopt equalization method at a control cycle, to average processing to state variable, and equation (7) can be rewritten as:

$D\stackrel{\&CenterDot;}{X}+\mathrm{RX}+s_{u,1}{M}_{u1}X+s_{u,2}{M}_{u2}X+s_{d,1}{M}_{d1}X+s_{d,2}{M}_{d2}X=\mathrm{\&xi;}---\left(10\right)$

Wherein, X be state variable z at the mean value of a switch periods, be expressed as:

$X={[{\stackrel{\&OverBar;}{i}}_u,{\stackrel{\&OverBar;}{i}}_d,{\stackrel{\&OverBar;}{u}}_{c,u1},{\stackrel{\&OverBar;}{u}}_{c,\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="HDA0000423940580000011.png"\; state="\{\{state\}\}">u</figure-callout>}2},{\stackrel{\&OverBar;}{u}}_{c,d1},{\stackrel{\&OverBar;}{u}}_{c,d2}]}^T---\left(11\right)$

Wherein, each element of X is respectively each element of state variable z at the mean value of a switch periods.Similarly, s _u,kand s _d,k, k=1 or 2 is respectively the equalization switch function of upper and lower each module of brachium pontis in a switch periods.

The detailed process of above-mentioned steps S2 is as follows:

The energy function E of modularization multi-level converter based on equation (10) is:

$E=\frac{1}{2}{X}^T\mathrm{DX},D=D^T>0---\left(12\right)$

Ask for the single order differential of energy function for:

$\stackrel{\&CenterDot;}{E}=\frac{1}{2}{X}^{T}D\stackrel{\&CenterDot;}{X}=X^T[-\mathrm{RX}-s_{u,1}{M}_{u1}X-s_{u,2}{M}_{u2}X-s_{d,1}{M}_{d1}X-s_{d,2}{M}_{d2}X+\mathrm{\&xi;}]---\left(13\right)$

Due to coefficient matrix M _u1, M _u2, M _d1, M _d2be antisymmetric matrix, all meet X ^tm _hx=0, wherein h gets respectively u ₁, u ₂, d ₁and d ₂one of, therefore, simplified style (13) is:

$\stackrel{\&CenterDot;}{E}=\frac{1}{2}{X}^{T}D\stackrel{\&CenterDot;}{X}=-X^T\mathrm{RX}+X^T\mathrm{\&xi;}---\left(14\right)$

At [t ₀, t ₁] in the time period, formula (14) is asked for to integration and obtains:

$E\left(t_1\right)-E\left(t_0\right)=-{\&Integral;}_{t_0}^{t1}\left(X^T\mathrm{RX}\right)\mathrm{dt}+{\&Integral;}_{t_0}^{t1}\left(X^T\mathrm{\&xi;}\right)\mathrm{dt}---\left(15\right)$

Equation (15) left side is [t ₀, t ₁] gross energy that stores of time period internal mold blocking multilevel converter, equation the right expression formula

for the energy that modularization multi-level converter dissipates, equation the right expression formula for the energy of electrical network to modularization multi-level converter injection; The principle of controlling according to passivity, equation (15) has defined one from input ξ to the passive system output X; If input ξ=0, (14) formula can be reduced to:

$\stackrel{\&CenterDot;}{E}=-x^T\mathrm{Rx}<0---\left(16\right).$

Formula (12) and (16) show, energy function E is being for just, the first derivative of energy function E when input ξ=0

be less than zero, show that energy function E decays to zero in time gradually, system is progressive stable.

The detailed process of described step S3 is as follows:

Suppose the state variable X of expectation _dfor: $X_d=[i_u^{*},i_d^{*},u_{c,u1}^{*},u_{c,\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="HDA0000423940580000011.png"\; state="\{\{state\}\}">u</figure-callout>}2}^{*},u_{c,d1}^{*},u_{c,\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="HDA0000423940580000011.png"\; state="\{\{state\}\}">d</figure-callout>}2}^{*}{]}^T---\left(17\right)$

Wherein, X _dfor the desired value to dependent variable in state variable X;

Departure vector Δ X is defined as:

ΔX=X _d-X （18）

Using Δ X as new state variable, in conjunction with formula (10) and (18), the equalization state space equation of modularization multi-level converter is rewritten as:

$\mathrm{D\&Delta;}\stackrel{\&CenterDot;}{X}+\mathrm{R\&Delta;X}+s_{u,1}{M}_{u1}\mathrm{\&Delta;X}+s_{u,2}{\mathrm{<figure-callout\; id="2"\; label="M\; u"\; filenames="HDA0000423940580000011.png"\; state="\{\{state\}\}">M</figure-callout>}}_u\mathrm{\&Delta;X}+s_{d,1}{M}_{d1}\mathrm{\&Delta;X}+s_{d,2}{\mathrm{<figure-callout\; id="2"\; label="M\; d"\; filenames="HDA0000423940580000011.png"\; state="\{\{state\}\}">M</figure-callout>}}_d\mathrm{\&Delta;X}=\mathrm{\&eta;}---\left(19\right)$

Wherein, equivalent control input vector η expression formula is:

$\mathrm{\&eta;}=-\mathrm{\&xi;}+\{D{\stackrel{\&CenterDot;}{X}}_d+R{X}_d+s_{u,1}{M}_{u1}{X}_d+s_{u,2}{M}_{u2}{X}_d+s_{d,1}{M}_{d1}{X}_d+s_{d,2}{M}_{d2}{X}_d\}---\left(20\right)$

In conjunction with above-mentioned derivation, learn, state space equation (19) and (10) have identical structure, so the energy function E of modularization multi-level converter departure vector Δ X _efor:

$E_e=\frac{1}{2}\mathrm{\&Delta;}{X}^T\mathrm{D\&Delta;X},D=D^T>0---\left(21\right)$

Single order differential is asked in the left and right two ends of formula (21), obtains:

${\stackrel{\&CenterDot;}{E}}_e=-\mathrm{\&Delta;}{X}^T\mathrm{R\&Delta;X}+\mathrm{\&Delta;}{X}^T\mathrm{\&eta;}---\left(22\right)$

Be similar to the derivation of formula (14) and (15), formula (22) has defined a passive system from equivalent control inputs vector η to error vector Δ X.If η=0, the energy function E of departure vector Δ X _esingle order differential show that state variable X will finally converge to desired value X _d.

In order to guarantee the stable control of modularization multi-level converter DC voltage and the quick tracking of ac-side current, introduce damping matrix W, obtain following expression:

η=-WΔX （23）

By formula (23) substitution formula (22), obtain:

${\stackrel{\&CenterDot;}{E}}_e=-\mathrm{\&Delta;}{X}^T(R+W)\mathrm{\&Delta;X}---\left(24\right)$

If known matrix R+W is symmetric positive definite matrix,

permanent establishment, shows energy function E _ewill converge to balance point Δ X=0, convergence rate is determined by the parameter of matrix R+W.

Consider that R is a diagonal matrix, for simplicity, W is designed to diagonal matrix, its expression formula is as follows:

W=diag{w ₁,w ₂,w ₃,w ₄,w ₅,w ₆} （25）

Wherein, diag{} represents diagonal matrix, i=1 ..., 6 o'clock w _ifor W entry of a matrix element; In conjunction with formula (1), (2), (17), (18) and (19), the passivity control algolithm of deriving modularization multi-level converter is as follows:

$s_{u,1}=\frac{1}{2u_{c,u1}^{*}}(-L_e\frac{d{\stackrel{\&OverBar;}{i}}_u}{\mathrm{dt}}-R_e{\stackrel{\&OverBar;}{i}}_u+\frac{V_d}{2}-u_v-w_1\mathrm{\&Delta;}{x}_1),\mathrm{\&Delta;}{x}_1=i_u^{*}-{\stackrel{\&OverBar;}{i}}_u---\left(26\right)$

$s_{u,2}=\frac{1}{2u_{c,\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="HDA0000423940580000011.png"\; state="\{\{state\}\}">u</figure-callout>}2}^{*}}(-L_e\frac{d{\stackrel{\&OverBar;}{i}}_u}{\mathrm{dt}}-R_e{\stackrel{\&OverBar;}{i}}_u+\frac{V_d}{2}-u_v-w_1\mathrm{\&Delta;}{x}_1),\mathrm{\&Delta;}{x}_1=i_u^{*}-{\stackrel{\&OverBar;}{i}}_u---\left(27\right)$

$s_{d,1}=\frac{1}{2u_{c,d1}^{*}}(-L_e\frac{d{\stackrel{\&OverBar;}{i}}_d}{\mathrm{dt}}-R_e{\stackrel{\&OverBar;}{i}}_d+\frac{{\mathrm{<figure-callout\; id="2"\; label="V\; d"\; filenames="HDA0000423940580000011.png"\; state="\{\{state\}\}">V</figure-callout>}}_d}{2}+u_v-{\mathrm{<figure-callout\; id="2"\; label="w"\; filenames="HDA0000423940580000011.png"\; state="\{\{state\}\}">w</figure-callout>}}_2\mathrm{\&Delta;}{x}_2),\mathrm{\&Delta;}{x}_2=i_d^{*}-{\stackrel{\&OverBar;}{i}}_d---\left(28\right)$

$s_{d,2}=\frac{1}{2u_{c,\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="HDA0000423940580000011.png"\; state="\{\{state\}\}">d</figure-callout>}2}^{*}}(-L_e\frac{d{\stackrel{\&OverBar;}{i}}_d}{\mathrm{dt}}-R_e{\stackrel{\&OverBar;}{i}}_d+\frac{{\mathrm{<figure-callout\; id="2"\; label="V\; d"\; filenames="HDA0000423940580000011.png"\; state="\{\{state\}\}">V</figure-callout>}}_d}{2}+u_v-{\mathrm{<figure-callout\; id="2"\; label="w"\; filenames="HDA0000423940580000011.png"\; state="\{\{state\}\}">w</figure-callout>}}_2\mathrm{\&Delta;}{x}_2),\mathrm{\&Delta;}{x}_2=i_d^{*}-{\stackrel{\&OverBar;}{i}}_d---\left(29\right)$

The differential equation of each module DC side of upper brachium pontis is:

$C_{u1}\frac{d{\stackrel{\&OverBar;}{u}}_{c,u1}}{\mathrm{dt}}+\frac{{\stackrel{\&OverBar;}{u}}_{c,u1}}{R_{u1}}=s_{u,1}{i}_u^{*}-w_3\mathrm{\&Delta;}{x}_3,\mathrm{\&Delta;}{x}_3=u_{c,u1}^{*}-{\stackrel{\&OverBar;}{u}}_{c,u1}---\left(30\right)$

$C_{u2}\frac{d{\stackrel{\&OverBar;}{u}}_{c,\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="HDA0000423940580000011.png"\; state="\{\{state\}\}">u</figure-callout>}2}}{\mathrm{dt}}+\frac{{\stackrel{\&OverBar;}{u}}_{c,u2}}{{\mathrm{<figure-callout\; id="2"\; label="R\; u"\; filenames="HDA0000423940580000011.png"\; state="\{\{state\}\}">R</figure-callout>}}_u}=s_{u,2}{i}_u^{*}-w_4\mathrm{\&Delta;}{x}_4,\mathrm{\&Delta;}{x}_4=u_{c,\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="HDA0000423940580000011.png"\; state="\{\{state\}\}">u</figure-callout>}2}^{*}-{\stackrel{\&OverBar;}{u}}_{c,u2}---\left(31\right)$

The differential equation of lower each module DC side of brachium pontis is:

$C_{d1}\frac{d{\stackrel{\&OverBar;}{u}}_{c,d1}}{\mathrm{dt}}+\frac{{\stackrel{\&OverBar;}{u}}_{c,d1}}{R_{d1}}=s_{d,1}{i}_d^{*}-w_5\mathrm{\&Delta;}{x}_5,\mathrm{\&Delta;}{x}_5=u_{c,d1}^{*}-{\stackrel{\&OverBar;}{u}}_{c,d1}---\left(32\right)$

$C_{d2}\frac{d{\stackrel{\&OverBar;}{u}}_{c,\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="HDA0000423940580000011.png"\; state="\{\{state\}\}">d</figure-callout>}2}}{\mathrm{dt}}+\frac{{\stackrel{\&OverBar;}{u}}_{c,d2}}{{\mathrm{<figure-callout\; id="2"\; label="R\; d"\; filenames="HDA0000423940580000011.png"\; state="\{\{state\}\}">R</figure-callout>}}_d}=s_{d,2}{i}_d^{*}-w_6\mathrm{\&Delta;}{x}_6,\mathrm{\&Delta;}{x}_6=u_{c,\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="HDA0000423940580000011.png"\; state="\{\{state\}\}">d</figure-callout>}2}^{*}-{\stackrel{\&OverBar;}{u}}_{c,d2}---\left(33\right).$

In diagonal matrix W, each element w _i(i=1 .., 6) choose the convergence that can have influence on passivity control algolithm, w _iparameter more convergence rate is faster, but stability margin reduces; Otherwise, w _ithe less convergence rate of parameter is slower, and stability margin improves.Therefore, w ₁and w ₂span be preferably [0.2,2], w ₃～w ₆span be preferably [50,200].

Described step S4 builds the converter control model based on each module switch function based on formula (26)～(33): compare DC capacitor voltage reference value and measured value, and carry out outer voltage control according to damping matrix W parameter; Meanwhile, according to similar approach, ac-side current is carried out to current inner loop control; Then switch function and the triangular carrier relatively obtaining also forms pwm pulse control signal tracking to the control of DC capacitor voltage and ac-side current in order to realization of each switch of modularization multi-level converter.

As shown in Figure 2, according to main circuit topology figure, complete each electric parameters (i _u, i _d, u _{c, u1}, u _{c, u2}, u _{c, d1}, u _{c, d2}) collection; Set up the passivity Mathematical Modeling of modularization multi-level converter, ask for the equalization state space equation of each control variables in a switch periods, form in order to ensure the stable control of each DC capacitor voltage of modularization multi-level converter and the rapid track and control of ac-side current, setting up on the basis of the algorithm model based on Energy shaping method, introduce damping and inject matrix, design rational damping matrix parameter w ₁～w ₆, then in conjunction with the reference value of each control variables, derive the switch function s of each module switch element of upper and lower brachium pontis _u1, s _u2, s _d1, s _d2; The triangular carrier signal of switch function and high frequency compares the most at last, forms the PWM modulation signal of each switch, and the block diagram of realizing modularization multi-level converter passivity modeling and control method builds.

Fig. 3 and Fig. 4 are the response wave shape figure that the amplitude of active current reference value is suddenlyd change from 100A to 200A ruuning situation at t=0.1s.In Fig. 3, u _vvoltage with multiple levels for modularization multi-level converter output; i _ufor brachium pontis electric current on modularization multi-level converter; i _dfor brachium pontis electric current under modularization multi-level converter; i _lalternating current for modularization multi-level converter output.In Fig. 4, s _{u, 1}, s _{u, 2}switch function for each module of brachium pontis on modularization multi-level converter; s _{d, 1}, s _{d, 2}switch function for each module of brachium pontis under modularization multi-level converter; u _{c, u1}and u _{c, u2}dc-link capacitance voltage for each module of brachium pontis on modularization multi-level converter; u _{c, d1}and u _{c, d2}dc-link capacitance voltage for each module of brachium pontis under modularization multi-level converter.

As can be seen from Figure 3, converter output voltage u _vbe five level, upper brachium pontis current i _uwith lower brachium pontis current i _dsingle spin-echo, modularization multi-level converter outputs to AC network v _gcurrent i _lwith active current reference value i _{l, ref}unanimously, when t=0.1s, its amplitude is suddenlyd change to 200A from 100A, and the response time is 10ms; As can be seen from Figure 4, at i _{l, ref}before and after saltus step, the switch function s of each module of brachium pontis on modularization multi-level converter _{u, 1}and s _{u, 2}waveform overlaps completely, the switch function s of lower each module of brachium pontis _{d, 1}and s _{d, 2}waveform overlaps completely, and the single spin-echo of upper and lower brachium pontis switch function waveform; The dc-link capacitance voltage u of upper each module of brachium pontis _{c, u1}and u _{c, u2}waveform overlaps completely, the dc-link capacitance voltage u of lower each module of brachium pontis _{c, d1}and u _{c, d2}waveform overlaps completely, at active current reference value i _{l, ref}before and after saltus step, dc-link capacitance voltage is all stabilized in set point, and the single spin-echo of upper and lower brachium pontis dc-link capacitance voltage waveform.

Fig. 5 and Fig. 6 are that modularization multi-level converter is at ac grid voltage v _gfall the response wave shape figure in 60% situation.

In Fig. 5, u _vvoltage with multiple levels for modularization multi-level converter output; i _ufor brachium pontis electric current on modularization multi-level converter; i _dfor brachium pontis electric current under modularization multi-level converter; i _lalternating current for modularization multi-level converter output.In Fig. 6, s _{u, 1}, s _{u, 2}switch function for each module of brachium pontis on modularization multi-level converter; s _{d, 1}, s _{d, 2}switch function for each module of brachium pontis under modularization multi-level converter; u _{c, u1}and u _{c, u2}dc-link capacitance voltage for each module of brachium pontis on modularization multi-level converter; u _{c, d1}and u _{c, d2}dc-link capacitance voltage for each module of brachium pontis under modularization multi-level converter.As can be seen from Figure 5, when t<0.1s, converter output voltage u _vbe five level; When 0.1s<t<0.2s, v _gfall 60%, converter output voltage u _vbe three level; When t>0.2s, converter output voltage u _vbe five level.In whole process, upper brachium pontis current i _uwith lower brachium pontis current i _dsingle spin-echo, alternating current i _lin ac grid voltage falling process, remain unchanged.As can be seen from Figure 6, when 0.1s<t<0.2s, the switch function s of upper and lower each module of brachium pontis _{u, 1}, s _{u, 2}, s _{d, 1}, s _{d, 2}the amplitude of waveform falls 60%; The switch function s of upper each module of brachium pontis _{u, 1}, s _{u, 2}waveform is at ac grid voltage v _gin falling process, overlap completely, the switch function s of lower each module of brachium pontis _{d, 1}, s _{d, 2}waveform is at ac grid voltage v _gin falling process, overlap completely, and the single spin-echo of upper and lower brachium pontis switch function waveform; The dc-link capacitance voltage u of upper each module of brachium pontis _{c, u1}, u _{c, u2}waveform overlaps completely, the dc-link capacitance voltage u of lower each module of brachium pontis _{c, d1}, u _{c, d2}waveform overlaps completely; At ac grid voltage v _gbefore and after falling, the dc-link capacitance voltage of modularization multi-level converter is all stabilized in set point, and the single spin-echo of upper and lower brachium pontis dc-link capacitance voltage waveform.

From the dynamic response oscillogram of Fig. 3～Fig. 6, find out, passivity modeling and control method is applied in modularization multi-level converter, when falling, current break, line voltage all can realize rapidly the rapid track and control of DC voltage equilibrium and alternating current, there is the control effect that stability is strong, tracking velocity is fast, the feasibility of this control method is not limited to the operating mode of mentioning in the embodiment of the present invention simultaneously, can extensively be generalized to the controlling unit of the modularization multi-level converter of flexible DC power transmission system.

The foregoing is only the specific embodiment of the present invention, one skilled in the art will appreciate that in the disclosed technical scope of the present invention, can carry out various modifications, replacement and change to the present invention.Therefore the present invention should not limited by above-mentioned example, and should limit with the protection range of claims.

Claims (7)

1. modularization multi-level converter passivity modeling and control method, comprises the steps:

S1, set up modularization multi-level converter passivity Mathematical Modeling, ask for the equalization state space equation in a switch periods;

S2, the modularization multi-level converter Energy shaping algorithm model of foundation based on equalization state space equation, definition is from input state variable ξ to the passive system output state variable X;

S3, set up converter damping and inject algorithm model, design damping matrix W is to guarantee the stable control of each DC capacitor voltage of modularization multi-level converter and the rapid track and control of ac-side current; And extract the switch function of each module in the upper and lower brachium pontis of multilevel converter based on Passive Control Algorithm;

S4, build the converter control model based on each module switch function: relatively DC capacitor voltage reference value and measured value, and carry out outer voltage control according to damping matrix W parameter; Meanwhile, according to similar approach, ac-side current is carried out to current inner loop control; Then switch function and the triangular carrier relatively obtaining also forms pwm pulse control signal tracking to the control of DC capacitor voltage and ac-side current in order to realization of each switch of modularization multi-level converter.

2. passivity modeling and control method according to claim 1, it is characterized in that, step S1 sets up the specifically modularization multi-level converter based on phase structure of modularization multi-level converter passivity Mathematical Modeling, process is as follows: in the modularization multi-level converter of phase structure, upper brachium pontis and lower brachium pontis are comprised of two half-bridge modules respectively, and each half-bridge consists of two IGBT, two anti-paralleled diodes, DC bus capacitor and DC side equivalent parallel resistance four parts; Wherein, C _ukand C _dk, k=1 or 2, is respectively the dc-link capacitance of k module of upper and lower brachium pontis, R _ukand R _dkbe respectively the equivalent parallel resistance at k module DC bus capacitor two ends of upper and lower brachium pontis, T _{uk, j}and T _{dk, j}, k=1 or 2, j=1 or 2, be respectively j IGBT of k module of upper and lower brachium pontis, D _{uk, j}and D _{dk, j}, k=1 or 2, j=1 or 2, be respectively j anti-paralleled diode of k module of upper and lower brachium pontis; V _dfor direct current network voltage, u _vfor the voltage with multiple levels of modularization multi-level converter output, i _uand i _dbe respectively upper and lower brachium pontis electric current; L _gand R _gthe inductance and the equivalent resistance that represent respectively AC network side, v _gfor ac grid voltage;

Based on Kirchhoff's law, set up the differential equation of the upper and lower brachium pontis of modularization multi-level converter:

$L_e\frac{d{i}_u}{\mathrm{dt}}+R_e{i}_u+m_{u,1^{u}c,u1}+m_{u,2^{u}c,u2}=\frac{V_d}{2}-u_v---\left(1\right)$

$L_e\frac{d{i}_d}{\mathrm{dt}}+R_e{i}_d+m_{d,1^{u}c,d1}+m_{d,2^{u}c,d2}=\frac{V_d}{2}{+u}_v---\left(2\right)$

Wherein, m _u,kand m _d,k, k=1 or 2 represents respectively the switch function of k module of upper and lower brachium pontis; u _{c, uk}and u _{c, dk}, k=1 or 2 represents respectively k module DC capacitor voltage of upper and lower brachium pontis; L _eand R _ethe inductance and the equivalent resistance that represent respectively each brachium pontis; i _uand i _drepresent respectively upper and lower brachium pontis electric current; V _dfor direct current network voltage, u _vfor the voltage with multiple levels of modularization multi-level converter output, the i.e. voltage of brachium pontis mid point;

Based on Kirchhoff's law, the differential equation of setting up each unit DC side of upper and lower brachium pontis is as follows:

$C_{u1}\frac{d{u}_{c,u1}}{\mathrm{dt}}+\frac{u_{c,u1}}{R_{u1}}-m_{u,1}{i}_u=0---\left(3\right)$

$C_{u2}\frac{d{u}_{c,u2}}{\mathrm{dt}}+\frac{u_{c,u2}}{R_{u2}}-m_{u,2}{i}_u=0---\left(4\right)$

$C_{d1}\frac{d{u}_{c,d1}}{\mathrm{dt}}+\frac{u_{c,d1}}{R_{d1}}-m_{d,1}{i}_d=0---\left(5\right)$

$C_{d2}\frac{d{u}_{c,d2}}{\mathrm{dt}}+\frac{u_{c,d2}}{R_{d2}}-m_{d,2}{i}_d=0---\left(6\right)$

Wherein, C _ukand C _dk, k=1 or 2 is respectively the dc-link capacitance of k module of upper and lower brachium pontis, R _ukand R _dkbe respectively the equivalent parallel resistance at k module DC bus capacitor two ends of upper and lower brachium pontis;

Formula (1)～(6) are rewritten into following matrix differential equation form:

$D\stackrel{\&CenterDot;}{z}+\mathrm{Rz}+m_{u,1}{M}_{u1}z+m_{u,2}{M}_{u{2}^z}+m_{d,1}{M}_{d{1}^z}+m_{d,2}{M}_{d{2}^z}=\mathrm{\&xi;}---\left(7\right)$

The input vector that wherein ξ is system, state variable z and coefficient matrix D, R, M _u1, M _u2, M _d1, M _d2be respectively:

$\mathrm{\&xi;}={[\frac{V_d}{2}-u_v,\frac{V_d}{2}+u_v,\mathrm{0,0,0,0}]}^T$

z=[i _u,i _d,u _c,u1,u _c,u2,u _c,d1,u _c,d2] ^T

D=diag{L _e,L _e,C _u1,C _u2,C _d1,C _d2}

$R=\mathrm{diag}\{R_e,R_e,\frac{1}{R_{u1}},\frac{1}{R_{u2}},\frac{1}{R_{d1}},\frac{1}{R_{d2}}\}$

$M_{u1}=\left[\begin{array}{cccccc}0& 0& 1& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\\ -1& 0& 0& 0& 0& \text{0}\\ 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& \text{0}\\ 0& 0& 0& 0& 0& 0\end{array}\right],$ $M_{u2}=\left[\begin{array}{cccccc}0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\\ -1& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\end{array}\right]$

$M_{d1}=\left[\begin{array}{cccccc}0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 1& \text{0}\\ 0& 0& 0& 0& 0& 0\\ 0& -1& 0& 0& 0& \text{0}\\ 0& 0& 0& 0& 0& 0\end{array}\right],$ $M_{d2}=\left[\begin{array}{cccccc}0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 1\\ 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\\ 0& -1& 0& 0& 0& 0\end{array}\right]$

Due to coefficient matrix M _u1, M _u2, M _d1, M _d2be antisymmetric matrix, all meet z ^tm _hz=0, wherein h gets respectively u ₁, u ₂, d ₁and d ₂one of, the energy function E of modularization multi-level converter is expressed as:

$E=\frac{1}{2}{z}^T\mathrm{Dz},D=D^T>0---\left(8\right)$

Modularization multi-level converter dissipation energy E _disbe expressed as:

$E_{\mathrm{dis}}=\frac{1}{2}{z}^T\mathrm{Rz},R=R^T>0---\left(9\right)$

Adopt equalization method at a control cycle, to average processing to state variable, equation (7) can be rewritten as:

$D\stackrel{\&CenterDot;}{X}+\mathrm{RX}+s_{u,1}{M}_{u1}X+s_{u,2}{M}_{u2}X+s_{d,1}{M}_{d1}X+s_{d,2}{M}_{d2}X=\mathrm{\&xi;}---\left(10\right)$

Wherein, X be state variable z at the mean value of a switch periods, be expressed as:

$X={[{\stackrel{\&OverBar;}{i}}_u,{\stackrel{\&OverBar;}{i}}_d,{\stackrel{\&OverBar;}{u}}_{c,u1},{\stackrel{\&OverBar;}{u}}_{c,u2},{\stackrel{\&OverBar;}{u}}_{c,d1},{\stackrel{\&OverBar;}{u}}_{c,d2}]}^T---\left(11\right)$

Wherein, each element of X is respectively each element of state variable z at the mean value of a switch periods; s _u,kand s _d,kbe respectively the equalization switch function of k module of upper and lower brachium pontis in a switch periods.

3. passivity modeling and control method according to claim 2, is characterized in that, the detailed process of step S2 is as follows:

The energy function E of modularization multi-level converter based on equation (10) is:

$E=\frac{1}{2}{X}^T\mathrm{DX},D=D^T>0---\left(12\right)$

Ask for the single order differential of energy function

for:

$\stackrel{\&CenterDot;}{E}=\frac{1}{2}{X}^{T}D\stackrel{\&CenterDot;}{X}=X^T[-\mathrm{RX}-s_{u,1}{M}_{u1}X-s_{u,2}{M}_{u2}X-s_{d,1}{M}_{d1}X-s_{d,2}{M}_{d2}X+\mathrm{\&xi;}]---\left(13\right)$

Due to coefficient matrix M _u1, M _u2, M _d1, M _d2be antisymmetric matrix, all meet X ^tm _hx=0, wherein h gets respectively u ₁, u ₂, d ₁and d ₂one of, simplified style (13) is:

$\stackrel{\&CenterDot;}{E}=\frac{1}{2}{X}^{T}D\stackrel{\&CenterDot;}{X}=-X^T\mathrm{RX}+X^T\mathrm{\&xi;}---\left(14\right)$

At [t ₀, t ₁] in the time period, formula (14) is asked for to integration and obtains:

$E\left(t_1\right)-E\left(t_0\right)=-{\&Integral;}_{t_0}^{t1}\left(X^T\mathrm{RX}\right)\mathrm{dt}+{\&Integral;}_{t_0}^{t1}\left(X^T\mathrm{\&xi;}\right)\mathrm{dt}---\left(15\right)$

Equation (15) left side is [t ₀, t ₁] gross energy that stores of time period internal mold blocking multilevel converter, equation the right expression formula for the energy that modularization multi-level converter dissipates, equation the right expression formula

for the energy of electrical network to modularization multi-level converter injection; The principle of controlling according to passivity, equation (15) has defined one from input ξ to the passive system output X; If input ξ=0, (14) formula can be reduced to:

$\stackrel{\&CenterDot;}{E}=-x^T\mathrm{Rx}<0---\left(16\right).$

4. passivity modeling and control method according to claim 2, is characterized in that, the detailed process of described step S3 is as follows:

Suppose the state variable X of expectation _dfor: $X_d={[i_u^{*},i_d^{*},u_{c,u1}^{*},u_{c,u2}^{*},u_{c,d1}^{*},u_{c,d2}^{*}]}^T---\left(17\right)$

Wherein, X _dfor the desired value to dependent variable in state variable X;

Departure vector Δ X is defined as:

ΔX=X _d-X （18）

Using Δ X as new state variable, in conjunction with formula (10) and (18), the equalization state space equation of modularization multi-level converter is rewritten as:

$\mathrm{D\&Delta;}\stackrel{\&CenterDot;}{X}+\mathrm{R\&Delta;X}+s_{u,1}{M}_{u1}\mathrm{\&Delta;X}+s_{u,2}{M}_{u2}\mathrm{\&Delta;X}+s_{d,1}{M}_{d1}\mathrm{\&Delta;X}+s_{d,2}{M}_{d2}\mathrm{\&Delta;X}=\mathrm{\&eta;}---\left(19\right)$

Wherein, equivalent control input vector η expression formula is:

$\mathrm{\&eta;}=-\mathrm{\&xi;}+\{D{\stackrel{\&CenterDot;}{X}}_d+R{X}_d+s_{u,1}{M}_{u1}{X}_d+s_{u,2}{M}_{u2}{X}_d+s_{d,1}{M}_{d1}{X}_d+s_{d,2}{M}_{d2}{X}_d\}---\left(20\right)$

The energy function E of modularization multi-level converter departure vector Δ X _efor:

$E_e=\frac{1}{2}\mathrm{\&Delta;}{X}^T\mathrm{D\&Delta;X},D=D^T>0---\left(21\right)$

Single order differential is asked in the left and right two ends of formula (21), obtains:

${\stackrel{\&CenterDot;}{E}}_e=-\mathrm{\&Delta;}{X}^T\mathrm{R\&Delta;X}+\mathrm{\&Delta;}{X}^T\mathrm{\&eta;}---\left(22\right)$

Formula (22) has defined a passive system from equivalent control inputs vector η to error vector Δ X.

5. passivity modeling and control method according to claim 4, is characterized in that, introduces damping matrix W, obtains following expression:

η=-WΔX （23）

By formula (23) substitution formula (22), obtain:

${\stackrel{\&CenterDot;}{E}}_e=-\mathrm{\&Delta;}{X}^T(R+W)\mathrm{\&Delta;X}---\left(24\right)$

If known matrix R+W is symmetric positive definite matrix,

permanent establishment, shows energy function E _ewill converge to balance point Δ X=0, convergence rate is determined by the parameter of matrix R+W;

W is designed to diagonal matrix, and its expression formula is as follows:

W=diag{w ₁,w ₂,w ₃,w ₄,w ₅,w ₆} （25）

Wherein, diag{} represents diagonal matrix, i=1 ..., 6 o'clock w _ifor W entry of a matrix element; In conjunction with formula (1), (2), (17), (18) and (19), the passivity control algolithm of deriving modularization multi-level converter is as follows:

$s_{u,1}=\frac{1}{2u_{c,u1}^{*}}(-L_e\frac{d{\stackrel{\&OverBar;}{i}}_u}{\mathrm{dt}}-R_e{\stackrel{\&OverBar;}{i}}_u+\frac{V_d}{2}-u_v-w_1\mathrm{\&Delta;}{x}_1),\mathrm{\&Delta;}{x}_1=i_u^{*}-{\stackrel{\&OverBar;}{i}}_u---\left(26\right)$

$s_{u,2}=\frac{1}{2u_{c,u2}^{*}}(-L_e\frac{d{\stackrel{\&OverBar;}{i}}_u}{\mathrm{dt}}-R_e{\stackrel{\&OverBar;}{i}}_u+\frac{V_d}{2}-u_v-w_1\mathrm{\&Delta;}{x}_1),\mathrm{\&Delta;}{x}_1=i_u^{*}-{\stackrel{\&OverBar;}{i}}_u---\left(27\right)$

$s_{d,1}=\frac{1}{2u_{c,d1}^{*}}(-L_e\frac{d{\stackrel{\&OverBar;}{i}}_d}{\mathrm{dt}}-R_e{\stackrel{\&OverBar;}{i}}_d+\frac{V_d}{2}-u_v-w_2\mathrm{\&Delta;}{x}_2),\mathrm{\&Delta;}{x}_2=i_d^{*}-{\stackrel{\&OverBar;}{i}}_d---\left(28\right)$

$s_{d,2}=\frac{1}{2u_{c,d2}^{*}}(-L_e\frac{d{\stackrel{\&OverBar;}{i}}_d}{\mathrm{dt}}-R_e{\stackrel{\&OverBar;}{i}}_d+\frac{V_d}{2}-u_v-w_2\mathrm{\&Delta;}{x}_2),\mathrm{\&Delta;}{x}_2=i_d^{*}-{\stackrel{\&OverBar;}{i}}_d---\left(29\right)$

The differential equation of each module DC side of upper brachium pontis is:

$C_{u1}\frac{d{\stackrel{\&OverBar;}{u}}_{c,u1}}{\mathrm{dt}}+\frac{{\stackrel{\&OverBar;}{u}}_{c,u1}}{R_{u1}}=s_{u,1}{i}_u^{*}-w_3\mathrm{\&Delta;}{x}_3,\mathrm{\&Delta;}{x}_3=u_{c,u1}^{*}-{\stackrel{\&OverBar;}{u}}_{c,u1}---\left(30\right)$

$C_{u2}\frac{d{\stackrel{\&OverBar;}{u}}_{c,u2}}{\mathrm{dt}}+\frac{{\stackrel{\&OverBar;}{u}}_{c,u2}}{R_{u2}}=s_{u,2}{i}_u^{*}-w_4\mathrm{\&Delta;}{x}_4,\mathrm{\&Delta;}{x}_4=u_{c,u2}^{*}-{\stackrel{\&OverBar;}{u}}_{c,u2}---\left(31\right)$

The differential equation of lower each module DC side of brachium pontis is:

$C_{d1}\frac{d{\stackrel{\&OverBar;}{u}}_{c,d1}}{\mathrm{dt}}+\frac{{\stackrel{\&OverBar;}{u}}_{c,d1}}{R_{d1}}=s_{d,1}{i}_d^{*}-w_5\mathrm{\&Delta;}{x}_5,\mathrm{\&Delta;}{x}_5=u_{c,d1}^{*}-{\stackrel{\&OverBar;}{u}}_{c,d1}---\left(32\right)$

$C_{d2}\frac{d{\stackrel{\&OverBar;}{u}}_{c,d2}}{\mathrm{dt}}+\frac{{\stackrel{\&OverBar;}{u}}_{c,d2}}{R_{d2}}=s_{d,2}{i}_d^{*}-w_6\mathrm{\&Delta;}{x}_6,\mathrm{\&Delta;}{x}_6=u_{c,d2}^{*}-{\stackrel{\&OverBar;}{u}}_{c,d2}---\left(33\right).$

6. passivity modeling and control method according to claim 5, is characterized in that w ₁and w ₂span be [0.2,2], w ₃～w ₆span be [50,200].

7. passivity modeling and control method according to claim 5, is characterized in that, described step S4 is specially:

Based on formula (26)～(33), build the converter control model based on each module switch function: compare DC capacitor voltage reference value and measured value, and carry out outer voltage control according to damping matrix W parameter; Meanwhile, according to similar approach, ac-side current is carried out to current inner loop control; Then switch function and the triangular carrier relatively obtaining also forms pwm pulse control signal tracking to the control of DC capacitor voltage and ac-side current in order to realization of each switch of modularization multi-level converter.

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