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

Abstract

Translated fromChinese

本发明的模块化多电平换流器无源性建模与控制方法主要包括步骤：S1、建立模块化多电平换流器无源性数学模型，求取在一个开关周期内的平均化状态空间方程；S2、建立基于平均化状态空间方程的模块化多电平换流器能量成型方法算法模型，定义从输入状态变量ξ到输出状态变量X之间的无源系统；S3、建立换流器阻尼注入算法模型。S4、搭建基于各模块开关函数的换流器控制模型。有益效果在于能够快速实现上下各桥臂直流侧电容电压的稳定均衡控制和交流侧电流的快速跟踪控制。克服了传统模块化多电平换流器控制策略的不足，为柔性直流输电系统的控制策略设计提供了可行的手段。

The passivity modeling and control method of the modular multilevel converter of the present invention mainly includes the steps: S1, establishing a passive mathematical model of the modular multilevel converter, and obtaining the averaged value in one switching cycle State space equation; S2. Establish the algorithm model of the energy shaping method of the modular multilevel converter based on the averaged state space equation, and define the passive system between the input state variable ξ and the output state variable X; S3. Establish the converter Flow damper injection algorithm model. S4. Build a converter control model based on the switching functions of each module. The beneficial effect is that the stable and balanced control of the DC side capacitor voltage of the upper and lower bridge arms and the fast tracking control of the AC side current can be quickly realized. It overcomes the shortcomings of the traditional modular multilevel converter control strategy, and provides a feasible means for the control strategy design of the flexible DC 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:

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

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

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:

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

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

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

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

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:

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

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\; 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 u₁, u₂, d₁and d₂one 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 u₁, u₂, d₁and d₂one 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 [t₀, t₁] 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 [t₀, t₁] 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:$X_d={[i_u^{*},i_d^{*},u_{c,u1}^{*},u_{c,\mathrm{<figure-callout\; label="u"\; filenames="HDA0000423940580000011.png"\; state="\{\{state\}\}">u</figure-callout>}2}^{*},u_{c,d1}^{*},u_{c,\mathrm{<figure-callout\; label="d"\; filenames="HDA0000423940580000011.png"\; state="\{\{state\}\}">d</figure-callout>}2}^{*}]}^T---\left(17\right)$

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:

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

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{w₁,w₂,w₃,w₄,w₅,w₆} （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:

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

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

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

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

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

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

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

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

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

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

Further, w₁and w₂span be [0.2,2], w₃～w₆span 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:

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

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

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:

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

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

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

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

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:

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

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}

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

$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\; 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\; 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=u₁, u₂, d₁, d₂).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:

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

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 functionfor:

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

Due to coefficient matrix M_u1, M_u2, M_d1, M_d2be antisymmetric matrix, all meet X^tm_hx=0, wherein h gets respectively u₁, u₂, d₁and d₂one 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 [t₀, t₁] 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 [t₀, t₁] 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 formulafor 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:$X_d=[i_u^{*},i_d^{*},u_{c,u1}^{*},u_{c,\mathrm{<figure-callout\; label="u"\; filenames="HDA0000423940580000011.png"\; state="\{\{state\}\}">u</figure-callout>}2}^{*},u_{c,d1}^{*},u_{c,\mathrm{<figure-callout\; label="d"\; filenames="HDA0000423940580000011.png"\; state="\{\{state\}\}">d</figure-callout>}2}^{*}{]}^T---\left(17\right)$

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:

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

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 differentialshow 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{w₁,w₂,w₃,w₄,w₅,w₆} （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:

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

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

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

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

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

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

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

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

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

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

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, w₁and w₂span be preferably [0.2,2], w₃～w₆span 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, formin 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 w₁～w₆, 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)

Translated fromChinese

1.模块化多电平换流器无源性建模与控制方法，包括如下步骤：1. A passive modeling and control method for a modular multilevel converter, comprising the following steps:S1、建立模块化多电平换流器无源性数学模型，求取在一个开关周期内的平均化状态空间方程；S1. Establish a passive mathematical model of a modular multilevel converter, and obtain an averaged state space equation within a switching cycle;S2、建立基于平均化状态空间方程的模块化多电平换流器能量成型方法算法模型，定义从输入状态变量ξ到输出状态变量X之间的无源系统；S2. Establish the algorithm model of the energy shaping method of the modularized multilevel converter based on the averaged state space equation, and define the passive system between the input state variable ξ and the output state variable X;S3、建立换流器阻尼注入算法模型，设计阻尼矩阵W以确保模块化多电平换流器各直流侧电容电压的稳定控制和交流侧电流的快速跟踪控制；并提取基于无源控制算法的多电平换流器上、下桥臂中各模块的开关函数；S3. Establish the damping injection algorithm model of the converter, and design the damping matrix W to ensure the stable control of the DC side capacitor voltage and the fast tracking control of the AC side current of the modular multilevel converter; and extract the passive control algorithm based The switching function of each module in the upper and lower bridge arms of the multilevel converter;S4、搭建基于各模块开关函数的换流器控制模型：比较直流侧电容电压参考值与实测值，并根据阻尼矩阵W参数进行电压外环控制；同时，按照类似方法对交流侧电流进行电流内环控制；然后比较获得的开关函数与三角载波并形成模块化多电平换流器各开关的PWM脉冲控制信号用以实现对直流侧电容电压的控制和交流侧电流的跟踪。S4. Build a converter control model based on the switching functions of each module: compare the DC side capacitor voltage reference value with the measured value, and perform voltage outer loop control according to the damping matrix W parameter; at the same time, follow a similar method for the AC side current. Then compare the obtained switching function with the triangular carrier wave and form the PWM pulse control signal of each switch of the modular multilevel converter to realize the control of the capacitor voltage on the DC side and the tracking of the current on the AC side.2.根据权利要求1所述的无源性建模与控制方法，其特征在于，步骤S1建立模块化多电平换流器无源性数学模型具体基于单相结构的模块化多电平换流器，过程如下：单相结构的模块化多电平换流器中，上桥臂和下桥臂分别由两个半桥模块组成，每个半桥由两个IGBT、两个反并联二极管、直流侧电容以及直流侧等效并联电阻四部分构成；其中，C_uk和C_dk，k=1或2，分别为上、下桥臂第k个模块的直流母线电容，R_uk和R_dk分别为上、下桥臂第k个模块直流侧电容两端的等效并联电阻，T_uk,j和T_dk,j，k=1或2、j=1或2，分别为上、下桥臂第k个模块的第j个IGBT，D_uk,j和D_dk,j，k=1或2、j=1或2，分别为上、下桥臂第k个模块的第j个反并联二极管；V_d为直流电网电压，u_v为模块化多电平换流器输出的多电平电压，i_u和i_d分别为上、下桥臂电流；L_g和R_g分别表示交流电网侧的电感和等效电阻，v_g为交流电网电压；2. The passivity modeling and control method according to claim 1, characterized in that step S1 establishes a passive mathematical model of a modular multilevel converter based on a modular multilevel converter with a single-phase structure. Converter, the process is as follows: In a single-phase modular multilevel converter, the upper bridge arm and the lower bridge arm are composed of two half-bridge modules, each half-bridge consists of two IGBTs, two anti-parallel diodes , DC side capacitance and DC side equivalent parallel resistance; among them, C_uk and C_dk , k=1 or 2, are the DC bus capacitance of the kth module of the upper and lower bridge arms respectively, R_uk and R_dk are the equivalent parallel resistances at both ends of the DC side capacitor of the kth module of the upper and lower bridge arms respectively, T_uk,j and T_dk,j , k=1 or 2, j=1 or 2, respectively, and are the upper and lower bridge arms The j-th IGBT of the k-th module, D_uk,j and D_dk,j , k=1 or 2, j=1 or 2, are the j-th anti-parallel diodes of the k-th module of the upper and lower bridge arms respectively ; V_d is the DC grid voltage, u_v is the multi-level voltage output by the modular multi-level converter, i_u and i_d are the currents of the upper and lower bridge arms respectively; L_g and R_g are the AC grid side The inductance and equivalent resistance of , v_g is the AC grid voltage;基于基尔霍夫定律，建立模块化多电平换流器上、下桥臂的微分方程：Based on Kirchhoff's law, the differential equations of the upper and lower bridge arms of the modular multilevel converter are established:${\mathrm{<span><span>L</span>L</span>}}_{\mathrm{<span><span>e</span>e</span>}}\frac{\mathrm{<span><span>d</span>d</span>}{\mathrm{<span><span>i</span>i</span>}}_{\mathrm{<span><span>u</span>u</span>}}}{\mathrm{<span><span>dt</span>dt</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>R</span>R</span>}}_{\mathrm{<span><span>e</span>e</span>}}{\mathrm{<span><span>i</span>i</span>}}_{\mathrm{<span><span>u</span>u</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>m</span>m</span>}}_{\mathrm{<span><span>u</span>u</span>}<span><span>,</span>,</span>{\mathrm{<span><span>1</span>1</span>}}^{\mathrm{<span><span>u</span>u</span>}}\mathrm{<span><span>c</span>c</span>}<span><span>,</span>,</span>\mathrm{<span><span>u</span>u</span>}\mathrm{<span><span>1</span>1</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>m</span>m</span>}}_{\mathrm{<span><span>u</span>u</span>}<span><span>,</span>,</span>{\mathrm{<span><span>2</span>2</span>}}^{\mathrm{<span><span>u</span>u</span>}}\mathrm{<span><span>c</span>c</span>}<span><span>,</span>,</span>\mathrm{<span><span>u</span>u</span>}\mathrm{<span><span>2</span>2</span>}}<span><span>=</span>=</span>\frac{{\mathrm{<span><span>V</span>V</span>}}_{\mathrm{<span><span>d</span>d</span>}}}{\mathrm{<span><span>2</span>2</span>}}<span><span>-</span>-</span>{\mathrm{<span><span>u</span>u</span>}}_{\mathrm{<span><span>v</span>v</span>}}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>1</span>1</span>}<span><span>)</span>)</span>$${\mathrm{<span><span>L</span>L</span>}}_{\mathrm{<span><span>e</span>e</span>}}\frac{\mathrm{<span><span>d</span>d</span>}{\mathrm{<span><span>i</span>i</span>}}_{\mathrm{<span><span>d</span>d</span>}}}{\mathrm{<span><span>dt</span>dt</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>R</span>R</span>}}_{\mathrm{<span><span>e</span>e</span>}}{\mathrm{<span><span>i</span>i</span>}}_{\mathrm{<span><span>d</span>d</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>m</span>m</span>}}_{\mathrm{<span><span>d</span>d</span>}<span><span>,</span>,</span>{\mathrm{<span><span>1</span>1</span>}}^{\mathrm{<span><span>u</span>u</span>}}\mathrm{<span><span>c</span>c</span>}<span><span>,</span>,</span>\mathrm{<span><span>d</span>d</span>}\mathrm{<span><span>1</span>1</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>m</span>m</span>}}_{\mathrm{<span><span>d</span>d</span>}<span><span>,</span>,</span>{\mathrm{<span><span>2</span>2</span>}}^{\mathrm{<span><span>u</span>u</span>}}\mathrm{<span><span>c</span>c</span>}<span><span>,</span>,</span>\mathrm{<span><span>d</span>d</span>}\mathrm{<span><span>2</span>2</span>}}<span><span>=</span>=</span>\frac{{\mathrm{<span><span>V</span>V</span>}}_{\mathrm{<span><span>d</span>d</span>}}}{\mathrm{<span><span>2</span>2</span>}}{<span><span>+</span>+</span>\mathrm{<span><span>u</span>u</span>}}_{\mathrm{<span><span>v</span>v</span>}}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>2</span>2</span>}<span><span>)</span>)</span>$其中，m_u,k和m_d,k，k=1或2分别表示上、下桥臂第k个模块的开关函数；u_c,uk和u_c,dk，k=1或2分别表示上、下桥臂第k个模块直流侧电容电压；L_e和R_e分别表示各个桥臂的电感和等效电阻；i_u和i_d分别表示上、下桥臂电流；V_d为直流电网电压，u_v为模块化多电平换流器输出的多电平电压，即桥臂中点的电压；Among them, m_u,k and m_d,k , k=1 or 2 represent the switching function of the kth module of the upper and lower bridge arms respectively; u_c,uk and uc_,dk , k=1 or 2 represent the upper , the DC side capacitor voltage of the kth module of the lower bridge arm; L_e and_Re represent the inductance and equivalent resistance of each bridge arm; i_u and i_d represent the current of the upper and lower bridge arms respectively; V_d is the DC grid voltage ,_uv is the multilevel voltage output by the modular multilevel converter, that is, the voltage at the midpoint of the bridge arm;基于基尔霍夫定律，建立上、下桥臂各单元直流侧的微分方程如下：Based on Kirchhoff's law, the differential equations for the DC side of each unit of the upper and lower bridge arms are established as follows:${\mathrm{<span><span>C</span>C</span>}}_{\mathrm{<span><span>u</span>u</span>}\mathrm{<span><span>1</span>1</span>}}\frac{\mathrm{<span><span>d</span>d</span>}{\mathrm{<span><span>u</span>u</span>}}_{\mathrm{<span><span>c</span>c</span>}<span><span>,</span>,</span>\mathrm{<span><span>u</span>u</span>}\mathrm{<span><span>1</span>1</span>}}}{\mathrm{<span><span>dt</span>dt</span>}}<span><span>+</span>+</span>\frac{{\mathrm{<span><span>u</span>u</span>}}_{\mathrm{<span><span>c</span>c</span>}<span><span>,</span>,</span>\mathrm{<span><span>u</span>u</span>}\mathrm{<span><span>1</span>1</span>}}}{{\mathrm{<span><span>R</span>R</span>}}_{\mathrm{<span><span>u</span>u</span>}\mathrm{<span><span>1</span>1</span>}}}<span><span>-</span>-</span>{\mathrm{<span><span>m</span>m</span>}}_{\mathrm{<span><span>u</span>u</span>}<span><span>,</span>,</span>\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>i</span>i</span>}}_{\mathrm{<span><span>u</span>u</span>}}<span><span>=</span>=</span>\mathrm{<span><span>0</span>0</span>}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>3</span>3</span>}<span><span>)</span>)</span>$${\mathrm{<span><span>C</span>C</span>}}_{\mathrm{<span><span>u</span>u</span>}\mathrm{<span><span>2</span>2</span>}}\frac{\mathrm{<span><span>d</span>d</span>}{\mathrm{<span><span>u</span>u</span>}}_{\mathrm{<span><span>c</span>c</span>}<span><span>,</span>,</span>\mathrm{<span><span>u</span>u</span>}\mathrm{<span><span>2</span>2</span>}}}{\mathrm{<span><span>dt</span>dt</span>}}<span><span>+</span>+</span>\frac{{\mathrm{<span><span>u</span>u</span>}}_{\mathrm{<span><span>c</span>c</span>}<span><span>,</span>,</span>\mathrm{<span><span>u</span>u</span>}\mathrm{<span><span>2</span>2</span>}}}{{\mathrm{<span><span>R</span>R</span>}}_{\mathrm{<span><span>u</span>u</span>}\mathrm{<span><span>2</span>2</span>}}}<span><span>-</span>-</span>{\mathrm{<span><span>m</span>m</span>}}_{\mathrm{<span><span>u</span>u</span>}<span><span>,</span>,</span>\mathrm{<span><span>2</span>2</span>}}{\mathrm{<span><span>i</span>i</span>}}_{\mathrm{<span><span>u</span>u</span>}}<span><span>=</span>=</span>\mathrm{<span><span>0</span>0</span>}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>4</span>4</span>}<span><span>)</span>)</span>$${\mathrm{<span><span>C</span>C</span>}}_{\mathrm{<span><span>d</span>d</span>}\mathrm{<span><span>1</span>1</span>}}\frac{\mathrm{<span><span>d</span>d</span>}{\mathrm{<span><span>u</span>u</span>}}_{\mathrm{<span><span>c</span>c</span>}<span><span>,</span>,</span>\mathrm{<span><span>d</span>d</span>}\mathrm{<span><span>1</span>1</span>}}}{\mathrm{<span><span>dt</span>dt</span>}}<span><span>+</span>+</span>\frac{{\mathrm{<span><span>u</span>u</span>}}_{\mathrm{<span><span>c</span>c</span>}<span><span>,</span>,</span>\mathrm{<span><span>d</span>d</span>}\mathrm{<span><span>1</span>1</span>}}}{{\mathrm{<span><span>R</span>R</span>}}_{\mathrm{<span><span>d</span>d</span>}\mathrm{<span><span>1</span>1</span>}}}<span><span>-</span>-</span>{\mathrm{<span><span>m</span>m</span>}}_{\mathrm{<span><span>d</span>d</span>}<span><span>,</span>,</span>\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>i</span>i</span>}}_{\mathrm{<span><span>d</span>d</span>}}<span><span>=</span>=</span>\mathrm{<span><span>0</span>0</span>}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>5</span>5</span>}<span><span>)</span>)</span>$${\mathrm{<span><span>C</span>C</span>}}_{\mathrm{<span><span>d</span>d</span>}\mathrm{<span><span>2</span>2</span>}}\frac{\mathrm{<span><span>d</span>d</span>}{\mathrm{<span><span>u</span>u</span>}}_{\mathrm{<span><span>c</span>c</span>}<span><span>,</span>,</span>\mathrm{<span><span>d</span>d</span>}\mathrm{<span><span>2</span>2</span>}}}{\mathrm{<span><span>dt</span>dt</span>}}<span><span>+</span>+</span>\frac{{\mathrm{<span><span>u</span>u</span>}}_{\mathrm{<span><span>c</span>c</span>}<span><span>,</span>,</span>\mathrm{<span><span>d</span>d</span>}\mathrm{<span><span>2</span>2</span>}}}{{\mathrm{<span><span>R</span>R</span>}}_{\mathrm{<span><span>d</span>d</span>}\mathrm{<span><span>2</span>2</span>}}}<span><span>-</span>-</span>{\mathrm{<span><span>m</span>m</span>}}_{\mathrm{<span><span>d</span>d</span>}<span><span>,</span>,</span>\mathrm{<span><span>2</span>2</span>}}{\mathrm{<span><span>i</span>i</span>}}_{\mathrm{<span><span>d</span>d</span>}}<span><span>=</span>=</span>\mathrm{<span><span>0</span>0</span>}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>6</span>6</span>}<span><span>)</span>)</span>$其中，C_uk和C_dk，k=1或2分别为上、下桥臂第k个模块的直流母线电容，R_uk和R_dk分别为上、下桥臂第k个模块直流侧电容两端的等效并联电阻；Among them, C_uk and C_dk , k=1 or 2 are the DC bus capacitors of the k-th module of the upper and lower bridge arms respectively, and R_uk and R_dk are the DC bus capacitors of the k-th module of the upper and lower bridge arms respectively. Equivalent parallel resistance;将公式（1）～（6）改写成如下的矩阵微分方程形式：Rewrite formulas (1)-(6) into the following matrix differential equation form:$\mathrm{<span><span>D</span>D.</span>}\stackrel{<span><span>\&CenterDot;</span>\&Center\; Dot;</span>}{\mathrm{<span><span>z</span>z</span>}}<span><span>+</span>+</span>\mathrm{<span><span>Rz</span>Rz</span>}<span><span>+</span>+</span>{\mathrm{<span><span>m</span>m</span>}}_{\mathrm{<span><span>u</span>u</span>}<span><span>,</span>,</span>\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>u</span>u</span>}\mathrm{<span><span>1</span>1</span>}}\mathrm{<span><span>z</span>z</span>}<span><span>+</span>+</span>{\mathrm{<span><span>m</span>m</span>}}_{\mathrm{<span><span>u</span>u</span>}<span><span>,</span>,</span>\mathrm{<span><span>2</span>2</span>}}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>u</span>u</span>}{\mathrm{<span><span>2</span>2</span>}}^{\mathrm{<span><span>z</span>z</span>}}}<span><span>+</span>+</span>{\mathrm{<span><span>m</span>m</span>}}_{\mathrm{<span><span>d</span>d</span>}<span><span>,</span>,</span>\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>d</span>d</span>}{\mathrm{<span><span>1</span>1</span>}}^{\mathrm{<span><span>z</span>z</span>}}}<span><span>+</span>+</span>{\mathrm{<span><span>m</span>m</span>}}_{\mathrm{<span><span>d</span>d</span>}<span><span>,</span>,</span>\mathrm{<span><span>2</span>2</span>}}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>d</span>d</span>}{\mathrm{<span><span>2</span>2</span>}}^{\mathrm{<span><span>z</span>z</span>}}}<span><span>=</span>=</span>\mathrm{<span><span>\&xi;</span>\&xi;</span>}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>7</span>7</span>}<span><span>)</span>)</span>$其中ξ为系统的输入向量，状态变量z及系数矩阵D、R、M_u1、M_u2、M_d1、M_d2分别为：Where ξ is the input vector of the system, the state variable z and the coefficient matrices D, R, M_u1 , M_u2 , M_d1 , M_d2 are respectively:$\mathrm{<span><span>\&xi;</span>\&xi;</span>}<span><span>=</span>=</span>{<span><span>[</span>[</span>\frac{{\mathrm{<span><span>V</span>V</span>}}_{\mathrm{<span><span>d</span>d</span>}}}{\mathrm{<span><span>2</span>2</span>}}<span><span>-</span>-</span>{\mathrm{<span><span>u</span>u</span>}}_{\mathrm{<span><span>v</span>v</span>}}<span><span>,</span>,</span>\frac{{\mathrm{<span><span>V</span>V</span>}}_{\mathrm{<span><span>d</span>d</span>}}}{\mathrm{<span><span>2</span>2</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>u</span>u</span>}}_{\mathrm{<span><span>v</span>v</span>}}<span><span>,</span>,</span>\mathrm{<span><span>0,0,0,0</span>0,0,0,0</span>}<span><span>]</span>]</span>}^{\mathrm{<span><span>T</span>T</span>}}$z=[i_u,i_d,u_c,u1,u_c,u2,u_c,d1,u_c,d2]^Tz=[i_u ,i_d ,u_c,u1 ,u_c,u2 ,u_c,d1 ,u_c,d2 ]^TD=diag{L_e,L_e,C_u1,C_u2,C_d1,C_d2}D=diag{L_e ,L_e ,C_u1 ,C_u2 ,C_d1 ,C_d2 }$\mathrm{<span><span>R</span>R</span>}<span><span>=</span>=</span>\mathrm{<span><span>diag</span>diag</span>}<span><span>\{</span>\{</span>{\mathrm{<span><span>R</span>R</span>}}_{\mathrm{<span><span>e</span>e</span>}}<span><span>,</span>,</span>{\mathrm{<span><span>R</span>R</span>}}_{\mathrm{<span><span>e</span>e</span>}}<span><span>,</span>,</span>\frac{\mathrm{<span><span>1</span>1</span>}}{{\mathrm{<span><span>R</span>R</span>}}_{\mathrm{<span><span>u</span>u</span>}\mathrm{<span><span>1</span>1</span>}}}<span><span>,</span>,</span>\frac{\mathrm{<span><span>1</span>1</span>}}{{\mathrm{<span><span>R</span>R</span>}}_{\mathrm{<span><span>u</span>u</span>}\mathrm{<span><span>2</span>2</span>}}}<span><span>,</span>,</span>\frac{\mathrm{<span><span>1</span>1</span>}}{{\mathrm{<span><span>R</span>R</span>}}_{\mathrm{<span><span>d</span>d</span>}\mathrm{<span><span>1</span>1</span>}}}<span><span>,</span>,</span>\frac{\mathrm{<span><span>1</span>1</span>}}{{\mathrm{<span><span>R</span>R</span>}}_{\mathrm{<span><span>d</span>d</span>}\mathrm{<span><span>2</span>2</span>}}}<span><span>\}</span>\}</span>$${\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>u</span>u</span>}\mathrm{<span><span>1</span>1</span>}}<span><span>=</span>=</span>\left[\begin{array}{cccccc}\mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>1</span>1</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}\\ \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}\\ <span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \text{<span><span>0</span>0</span>}\\ \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}\\ \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \text{<span><span>0</span>0</span>}\\ \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}\end{array}\right]<span><span>,</span>,</span>$${\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>u</span>u</span>}\mathrm{<span><span>2</span>2</span>}}<span><span>=</span>=</span>\left[\begin{array}{cccccc}\mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>1</span>1</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}\\ \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}\\ \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}\\ <span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}\\ \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}\\ \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}\end{array}\right]$${\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>d</span>d</span>}\mathrm{<span><span>1</span>1</span>}}<span><span>=</span>=</span>\left[\begin{array}{cccccc}\mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}\\ \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}\\ \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>1</span>1</span>}& \text{<span><span>0</span>0</span>}\\ \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}\\ \mathrm{<span><span>0</span>0</span>}& <span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \text{<span><span>0</span>0</span>}\\ \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}\end{array}\right]<span><span>,</span>,</span>$${\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>d</span>d</span>}\mathrm{<span><span>2</span>2</span>}}<span><span>=</span>=</span>\left[\begin{array}{cccccc}\mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}\\ \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>1</span>1</span>}\\ \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}\\ \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}\\ \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}\\ \mathrm{<span><span>0</span>0</span>}& <span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}& \mathrm{<span><span>0</span>0</span>}\end{array}\right]$由于系数矩阵M_u1、M_u2、M_d1、M_d2均为反对称矩阵，均满足z^TM_hz=0，其中h分别取u₁、u₂、d₁和d₂之一，模块化多电平换流器的能量函数E表示为：Since the coefficient matrices M_u1 , M_u2 , M_d1 , and M_d2 are all antisymmetric matrices, they all satisfy z^T M_h z=0, where h takes one of u₁ , u₂ , d₁ and d₂ respectively, and the modularization The energy function E of the multilevel converter is expressed as:$\mathrm{<span><span>E</span>E.</span>}<span><span>=</span>=</span>\frac{\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>2</span>2</span>}}{\mathrm{<span><span>z</span>z</span>}}^{\mathrm{<span><span>T</span>T</span>}}\mathrm{<span><span>Dz</span>Z</span>}<span><span>,</span>,</span>\mathrm{<span><span>D</span>D.</span>}<span><span>=</span>=</span>{\mathrm{<span><span>D</span>D.</span>}}^{\mathrm{<span><span>T</span>T</span>}}<span><span>></span>></span>\mathrm{<span><span>0</span>0</span>}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>8</span>8</span>}<span><span>)</span>)</span>$模块化多电平换流器耗散能量E_dis表示为：The dissipated energy E_dis of the modular multilevel converter is expressed as:${\mathrm{<span><span>E</span>E.</span>}}_{\mathrm{<span><span>dis</span>dis</span>}}<span><span>=</span>=</span>\frac{\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>2</span>2</span>}}{\mathrm{<span><span>z</span>z</span>}}^{\mathrm{<span><span>T</span>T</span>}}\mathrm{<span><span>Rz</span>Rz</span>}<span><span>,</span>,</span>\mathrm{<span><span>R</span>R</span>}<span><span>=</span>=</span>{\mathrm{<span><span>R</span>R</span>}}^{\mathrm{<span><span>T</span>T</span>}}<span><span>></span>></span>\mathrm{<span><span>0</span>0</span>}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>9</span>9</span>}<span><span>)</span>)</span>$采用平均化方法对状态变量在一个控制周期进行平均化处理，即方程（7）可改写为：The averaging method is used to average the state variables in one control cycle, that is, equation (7) can be rewritten as:$\mathrm{<span><span>D</span>D.</span>}\stackrel{<span><span>\&CenterDot;</span>\&Center\; Dot;</span>}{\mathrm{<span><span>X</span>x</span>}}<span><span>+</span>+</span>\mathrm{<span><span>RX</span>RX</span>}<span><span>+</span>+</span>{\mathrm{<span><span>s</span>the\; s</span>}}_{\mathrm{<span><span>u</span>u</span>}<span><span>,</span>,</span>\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>u</span>u</span>}\mathrm{<span><span>1</span>1</span>}}\mathrm{<span><span>X</span>x</span>}<span><span>+</span>+</span>{\mathrm{<span><span>s</span>the\; s</span>}}_{\mathrm{<span><span>u</span>u</span>}<span><span>,</span>,</span>\mathrm{<span><span>2</span>2</span>}}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>u</span>u</span>}\mathrm{<span><span>2</span>2</span>}}\mathrm{<span><span>X</span>x</span>}<span><span>+</span>+</span>{\mathrm{<span><span>s</span>the\; s</span>}}_{\mathrm{<span><span>d</span>d</span>}<span><span>,</span>,</span>\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>d</span>d</span>}\mathrm{<span><span>1</span>1</span>}}\mathrm{<span><span>X</span>x</span>}<span><span>+</span>+</span>{\mathrm{<span><span>s</span>the\; s</span>}}_{\mathrm{<span><span>d</span>d</span>}<span><span>,</span>,</span>\mathrm{<span><span>2</span>2</span>}}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>d</span>d</span>}\mathrm{<span><span>2</span>2</span>}}\mathrm{<span><span>X</span>x</span>}<span><span>=</span>=</span>\mathrm{<span><span>\&xi;</span>\&xi;</span>}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>10</span>10</span>}<span><span>)</span>)</span>$其中，X为状态变量z在一个开关周期的平均值，表示为：Among them, X is the average value of the state variable z in a switching cycle, expressed as:$\mathrm{<span><span>X</span>x</span>}<span><span>=</span>=</span>{<span><span>[</span>[</span>{\stackrel{<span><span>\&OverBar;</span>\&OverBar;</span>}{\mathrm{<span><span>i</span>i</span>}}}_{\mathrm{<span><span>u</span>u</span>}}<span><span>,</span>,</span>{\stackrel{<span><span>\&OverBar;</span>\&OverBar;</span>}{\mathrm{<span><span>i</span>i</span>}}}_{\mathrm{<span><span>d</span>d</span>}}<span><span>,</span>,</span>{\stackrel{<span><span>\&OverBar;</span>\&OverBar;</span>}{\mathrm{<span><span>u</span>u</span>}}}_{\mathrm{<span><span>c</span>c</span>}<span><span>,</span>,</span>\mathrm{<span><span>u</span>u</span>}\mathrm{<span><span>1</span>1</span>}}<span><span>,</span>,</span>{\stackrel{<span><span>\&OverBar;</span>\&OverBar;</span>}{\mathrm{<span><span>u</span>u</span>}}}_{\mathrm{<span><span>c</span>c</span>}<span><span>,</span>,</span>\mathrm{<span><span>u</span>u</span>}\mathrm{<span><span>2</span>2</span>}}<span><span>,</span>,</span>{\stackrel{<span><span>\&OverBar;</span>\&OverBar;</span>}{\mathrm{<span><span>u</span>u</span>}}}_{\mathrm{<span><span>c</span>c</span>}<span><span>,</span>,</span>\mathrm{<span><span>d</span>d</span>}\mathrm{<span><span>1</span>1</span>}}<span><span>,</span>,</span>{\stackrel{<span><span>\&OverBar;</span>\&OverBar;</span>}{\mathrm{<span><span>u</span>u</span>}}}_{\mathrm{<span><span>c</span>c</span>}<span><span>,</span>,</span>\mathrm{<span><span>d</span>d</span>}\mathrm{<span><span>2</span>2</span>}}<span><span>]</span>]</span>}^{\mathrm{<span><span>T</span>T</span>}}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>11</span>11</span>}<span><span>)</span>)</span>$其中，X各元素分别为状态变量z各元素在一个开关周期的平均值；s_u,k和s_d,k分别为在一个开关周期内上、下桥臂第k个模块的平均化开关函数。Among them, the elements of X are the average values of the elements of the state variable z in one switching period; s_u,k and s_d,k are the averaged switching functions of the kth module of the upper and lower bridge arms in a switching period, respectively .3.根据权利要求2所述的无源性建模与控制方法，其特征在于，步骤S2的具体过程如下：3. passivity modeling and control method according to claim 2, is characterized in that, the concrete process of step S2 is as follows:模块化多电平换流器基于方程（10）的能量函数E为：The energy function E of the modular multilevel converter based on equation (10) is:$\mathrm{<span><span>E</span>E.</span>}<span><span>=</span>=</span>\frac{\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>2</span>2</span>}}{\mathrm{<span><span>X</span>x</span>}}^{\mathrm{<span><span>T</span>T</span>}}\mathrm{<span><span>DX</span>DX</span>}<span><span>,</span>,</span>\mathrm{<span><span>D</span>D.</span>}<span><span>=</span>=</span>{\mathrm{<span><span>D</span>D.</span>}}^{\mathrm{<span><span>T</span>T</span>}}<span><span>></span>></span>\mathrm{<span><span>0</span>0</span>}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>12</span>12</span>}<span><span>)</span>)</span>$求取能量函数的一阶微分

为：find the first differential of the energy function

for:$\stackrel{<span><span>\&CenterDot;</span>\&Center\; Dot;</span>}{\mathrm{<span><span>E</span>E.</span>}}<span><span>=</span>=</span>\frac{\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>2</span>2</span>}}{\mathrm{<span><span>X</span>x</span>}}^{\mathrm{<span><span>T</span>T</span>}}\mathrm{<span><span>D</span>D.</span>}\stackrel{<span><span>\&CenterDot;</span>\&Center\; Dot;</span>}{\mathrm{<span><span>X</span>x</span>}}<span><span>=</span>=</span>{\mathrm{<span><span>X</span>x</span>}}^{\mathrm{<span><span>T</span>T</span>}}<span><span>[</span>[</span><span><span>-</span>-</span>\mathrm{<span><span>RX</span>RX</span>}<span><span>-</span>-</span>{\mathrm{<span><span>s</span>the\; s</span>}}_{\mathrm{<span><span>u</span>u</span>}<span><span>,</span>,</span>\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>u</span>u</span>}\mathrm{<span><span>1</span>1</span>}}\mathrm{<span><span>X</span>x</span>}<span><span>-</span>-</span>{\mathrm{<span><span>s</span>the\; s</span>}}_{\mathrm{<span><span>u</span>u</span>}<span><span>,</span>,</span>\mathrm{<span><span>2</span>2</span>}}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>u</span>u</span>}\mathrm{<span><span>2</span>2</span>}}\mathrm{<span><span>X</span>x</span>}<span><span>-</span>-</span>{\mathrm{<span><span>s</span>the\; s</span>}}_{\mathrm{<span><span>d</span>d</span>}<span><span>,</span>,</span>\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>d</span>d</span>}\mathrm{<span><span>1</span>1</span>}}\mathrm{<span><span>X</span>x</span>}<span><span>-</span>-</span>{\mathrm{<span><span>s</span>the\; s</span>}}_{\mathrm{<span><span>d</span>d</span>}<span><span>,</span>,</span>\mathrm{<span><span>2</span>2</span>}}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>d</span>d</span>}\mathrm{<span><span>2</span>2</span>}}\mathrm{<span><span>X</span>x</span>}<span><span>+</span>+</span>\mathrm{<span><span>\&xi;</span>\&xi;</span>}<span><span>]</span>]</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>13</span>13</span>}<span><span>)</span>)</span>$由于系数矩阵M_u1、M_u2、M_d1、M_d2均为反对称矩阵，均满足X^TM_hX=0，其中h分别取u₁、u₂、d₁和d₂之一，简化式（13）为：Since the coefficient matrices M_u1 , M_u2 , M_d1 , and M_d2 are all antisymmetric matrices, they all satisfy X^T M_h X=0, where h takes one of u₁ , u₂ , d₁ and d₂ respectively, the simplified formula (13) is:$\stackrel{<span><span>\&CenterDot;</span>\&CenterDot;</span>}{\mathrm{<span><span>E</span>E.</span>}}<span><span>=</span>=</span>\frac{\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>2</span>2</span>}}{\mathrm{<span><span>X</span>x</span>}}^{\mathrm{<span><span>T</span>T</span>}}\mathrm{<span><span>D</span>D.</span>}\stackrel{<span><span>\&CenterDot;</span>\&Center\; Dot;</span>}{\mathrm{<span><span>X</span>x</span>}}<span><span>=</span>=</span><span><span>-</span>-</span>{\mathrm{<span><span>X</span>x</span>}}^{\mathrm{<span><span>T</span>T</span>}}\mathrm{<span><span>RX</span>RX</span>}<span><span>+</span>+</span>{\mathrm{<span><span>X</span>x</span>}}^{\mathrm{<span><span>T</span>T</span>}}\mathrm{<span><span>\&xi;</span>\&xi;</span>}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>14</span>14</span>}<span><span>)</span>)</span>$在[t₀,t₁]时间段内，对式（14）求取积分得：In the time period of [t₀ ,t₁ ], the integral of equation (14) is obtained:$\mathrm{<span><span>E</span>E.</span>}<span><span>(</span>(</span>{\mathrm{<span><span>t</span>t</span>}}_{\mathrm{<span><span>1</span>1</span>}}<span><span>)</span>)</span><span><span>-</span>-</span>\mathrm{<span><span>E</span>E.</span>}<span><span>(</span>(</span>{\mathrm{<span><span>t</span>t</span>}}_{\mathrm{<span><span>0</span>0</span>}}<span><span>)</span>)</span><span><span>=</span>=</span><span><span>-</span>-</span>{<span><span>\&Integral;</span>\&Integral;</span>}_{{\mathrm{<span><span>t</span>t</span>}}_{\mathrm{<span><span>0</span>0</span>}}}^{\mathrm{<span><span>t</span>t</span>}\mathrm{<span><span>1</span>1</span>}}<span><span>(</span>(</span>{\mathrm{<span><span>X</span>x</span>}}^{\mathrm{<span><span>T</span>T</span>}}\mathrm{<span><span>RX</span>RX</span>}<span><span>)</span>)</span>\mathrm{<span><span>dt</span>dt</span>}<span><span>+</span>+</span>{<span><span>\&Integral;</span>\&Integral;</span>}_{{\mathrm{<span><span>t</span>t</span>}}_{\mathrm{<span><span>0</span>0</span>}}}^{\mathrm{<span><span>t</span>t</span>}\mathrm{<span><span>1</span>1</span>}}<span><span>(</span>(</span>{\mathrm{<span><span>X</span>x</span>}}^{\mathrm{<span><span>T</span>T</span>}}\mathrm{<span><span>\&xi;</span>\&xi;</span>}<span><span>)</span>)</span>\mathrm{<span><span>dt</span>dt</span>}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>15</span>15</span>}<span><span>)</span>)</span>$等式（15）左边为[t₀,t₁]时间段内模块化多电平换流器储存的总能量，等式右边表达式为模块化多电平换流器耗散掉的能量，等式右边表达式

为电网向模块化多电平换流器注入的能量；根据无源性控制的原理，等式（15）定义了一个从输入ξ到输出X之间的无源系统；如果输入ξ=0，则（14）式可简化为：The left side of equation (15) is the total energy stored in the modular multilevel converter within the time period [t₀ ,t₁ ], and the right side of the equation is expressed as is the energy dissipated by the modular multilevel converter, the expression on the right side of the equation

is the energy injected into the modular multilevel converter by the grid; according to the principle of passive control, equation (15) defines a passive system from input ξ to output X; if input ξ=0, Then (14) can be simplified as:$\stackrel{<span><span>\&CenterDot;</span>\&CenterDot;</span>}{\mathrm{<span><span>E</span>E.</span>}}<span><span>=</span>=</span><span><span>-</span>-</span>{\mathrm{<span><span>x</span>x</span>}}^{\mathrm{<span><span>T</span>T</span>}}\mathrm{<span><span>Rx</span>Rx</span>}<span><span><</span><</span>\mathrm{<span><span>0</span>0</span>}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>16</span>16</span>}<span><span>)</span>)</span><span><span>.</span>.</span>$4.根据权利要求2所述的无源性建模与控制方法，其特征在于，所述步骤S3的具体过程如下：4. The passive modeling and control method according to claim 2, wherein the specific process of the step S3 is as follows:假设期望的状态变量X_d为：$X_d={[i_u^{*},i_d^{*},u_{c,u1}^{*},u_{c,u2}^{*},u_{c,d1}^{*},u_{c,d2}^{*}]}^T---\left(17\right)$Suppose the desired state variable X_d is:$x_d={[i_u^{*},i_d^{*},u_{c,u1}^{*},u_{c,u2}^{*},u_{c,d1}^{*},u_{c,d2}^{*}]}^T---\left(17\right)$其中，X_d为状态变量X中对应变量的期望值；Among them, X_d is the expected value of the corresponding variable in the state variable X;控制误差向量ΔX定义为：The control error vector ΔX is defined as:ΔX=X_d-X  （18）ΔX=X_d -X (18)将ΔX作为新的状态变量，结合公式（10）和（18）将模块化多电平换流器的平均化状态空间方程改写为：Taking ΔX as a new state variable, combined with formulas (10) and (18), the averaged state space equation of the modular multilevel converter is rewritten as:$\mathrm{<span><span>D\&Delta;</span>D\&Delta;</span>}\stackrel{<span><span>\&CenterDot;</span>\&CenterDot;</span>}{\mathrm{<span><span>X</span>x</span>}}<span><span>+</span>+</span>\mathrm{<span><span>R\&Delta;X</span>R\&Delta;X</span>}<span><span>+</span>+</span>{\mathrm{<span><span>s</span>the\; s</span>}}_{\mathrm{<span><span>u</span>u</span>}<span><span>,</span>,</span>\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>u</span>u</span>}\mathrm{<span><span>1</span>1</span>}}\mathrm{<span><span>\&Delta;X</span>\&Delta;X</span>}<span><span>+</span>+</span>{\mathrm{<span><span>s</span>the\; s</span>}}_{\mathrm{<span><span>u</span>u</span>}<span><span>,</span>,</span>\mathrm{<span><span>2</span>2</span>}}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>u</span>u</span>}\mathrm{<span><span>2</span>2</span>}}\mathrm{<span><span>\&Delta;X</span>\&Delta;X</span>}<span><span>+</span>+</span>{\mathrm{<span><span>s</span>the\; s</span>}}_{\mathrm{<span><span>d</span>d</span>}<span><span>,</span>,</span>\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>d</span>d</span>}\mathrm{<span><span>1</span>1</span>}}\mathrm{<span><span>\&Delta;X</span>\&Delta;X</span>}<span><span>+</span>+</span>{\mathrm{<span><span>s</span>the\; s</span>}}_{\mathrm{<span><span>d</span>d</span>}<span><span>,</span>,</span>\mathrm{<span><span>2</span>2</span>}}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>d</span>d</span>}\mathrm{<span><span>2</span>2</span>}}\mathrm{<span><span>\&Delta;X</span>\&Delta;X</span>}<span><span>=</span>=</span>\mathrm{<span><span>\&eta;</span>\&eta;</span>}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>19</span>19</span>}<span><span>)</span>)</span>$其中，等效控制输入向量η表达式为：Among them, the equivalent control input vector η expression is:$\mathrm{<span><span>\&eta;</span>\&eta;</span>}<span><span>=</span>=</span><span><span>-</span>-</span>\mathrm{<span><span>\&xi;</span>\&xi;</span>}<span><span>+</span>+</span><span><span>\{</span>\{</span>\mathrm{<span><span>D</span>D.</span>}{\stackrel{<span><span>\&CenterDot;</span>\&Center\; Dot;</span>}{\mathrm{<span><span>X</span>x</span>}}}_{\mathrm{<span><span>d</span>d</span>}}<span><span>+</span>+</span>\mathrm{<span><span>R</span>R</span>}{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>d</span>d</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>s</span>the\; s</span>}}_{\mathrm{<span><span>u</span>u</span>}<span><span>,</span>,</span>\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>u</span>u</span>}\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>d</span>d</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>s</span>the\; s</span>}}_{\mathrm{<span><span>u</span>u</span>}<span><span>,</span>,</span>\mathrm{<span><span>2</span>2</span>}}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>u</span>u</span>}\mathrm{<span><span>2</span>2</span>}}{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>d</span>d</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>s</span>the\; s</span>}}_{\mathrm{<span><span>d</span>d</span>}<span><span>,</span>,</span>\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>d</span>d</span>}\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>d</span>d</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>s</span>the\; s</span>}}_{\mathrm{<span><span>d</span>d</span>}<span><span>,</span>,</span>\mathrm{<span><span>2</span>2</span>}}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>d</span>d</span>}\mathrm{<span><span>2</span>2</span>}}{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>d</span>d</span>}}<span><span>\}</span>\}</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>20</span>20</span>}<span><span>)</span>)</span>$模块化多电平换流器控制误差向量ΔX的能量函数E_e为：The energy function E_e of the control error vector ΔX of the modular multilevel converter is:${\mathrm{<span><span>E</span>E.</span>}}_{\mathrm{<span><span>e</span>e</span>}}<span><span>=</span>=</span>\frac{\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>2</span>2</span>}}\mathrm{<span><span>\&Delta;</span>\&Delta;</span>}{\mathrm{<span><span>X</span>x</span>}}^{\mathrm{<span><span>T</span>T</span>}}\mathrm{<span><span>D\&Delta;X</span>D\&Delta;X</span>}<span><span>,</span>,</span>\mathrm{<span><span>D</span>D.</span>}<span><span>=</span>=</span>{\mathrm{<span><span>D</span>D.</span>}}^{\mathrm{<span><span>T</span>T</span>}}<span><span>></span>></span>\mathrm{<span><span>0</span>0</span>}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>21</span>twenty\; one</span>}<span><span>)</span>)</span>$对式（21）左、右两端求取一阶微分，即得：Calculate the first-order differential on the left and right sides of equation (21), that is:${\stackrel{<span><span>\&CenterDot;</span>\&CenterDot;</span>}{\mathrm{<span><span>E</span>E.</span>}}}_{\mathrm{<span><span>e</span>e</span>}}<span><span>=</span>=</span><span><span>-</span>-</span>\mathrm{<span><span>\&Delta;</span>\&Delta;</span>}{\mathrm{<span><span>X</span>x</span>}}^{\mathrm{<span><span>T</span>T</span>}}\mathrm{<span><span>R\&Delta;X</span>R\&Delta;X</span>}<span><span>+</span>+</span>\mathrm{<span><span>\&Delta;</span>\&Delta;</span>}{\mathrm{<span><span>X</span>x</span>}}^{\mathrm{<span><span>T</span>T</span>}}\mathrm{<span><span>\&eta;</span>\&eta;</span>}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>22</span>twenty\; two</span>}<span><span>)</span>)</span>$式（22）定义了一个从等效的控制输入向量η到误差向量ΔX的无源系统。Equation (22) defines a passive system from an equivalent control input vector η to an error vector ΔX.5.根据权利要求4所述的无源性建模与控制方法，其特征在于，引入阻尼矩阵W，得到如下表达式：5. passivity modeling and control method according to claim 4, is characterized in that, introduces damping matrix W, obtains following expression:η=-WΔX  （23）η=-WΔX (23)将式（23）代入式（22），即得：Substituting formula (23) into formula (22), we get:${\stackrel{<span><span>\&CenterDot;</span>\&CenterDot;</span>}{\mathrm{<span><span>E</span>E.</span>}}}_{\mathrm{<span><span>e</span>e</span>}}<span><span>=</span>=</span><span><span>-</span>-</span>\mathrm{<span><span>\&Delta;</span>\&Delta;</span>}{\mathrm{<span><span>X</span>x</span>}}^{\mathrm{<span><span>T</span>T</span>}}<span><span>(</span>(</span>\mathrm{<span><span>R</span>R</span>}<span><span>+</span>+</span>\mathrm{<span><span>W</span>W</span>}<span><span>)</span>)</span>\mathrm{<span><span>\&Delta;X</span>\&Delta;X</span>}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>24</span>twenty\; four</span>}<span><span>)</span>)</span>$可知如果矩阵R+W为对称正定矩阵，则

恒成立，表明能量函数E_e将会收敛到平衡点ΔX=0，收敛速度由矩阵R+W的参数决定；It can be seen that if the matrix R+W is a symmetric positive definite matrix, then

Constantly holds true, indicating that the energy function E_e will converge to the equilibrium point ΔX=0, and the convergence speed is determined by the parameters of the matrix R+W;将W设计成对角矩阵，其表达式如下：Designing W as a diagonal matrix, its expression is as follows:W=diag{w₁,w₂,w₃,w₄,w₅,w₆}  （25）W=diag{w₁ ,w₂ ,w₃ ,w₄ ,w₅ ,w₆ } (25)其中，diag{}表示对角矩阵，i=1,…,6时w_i为W矩阵的元素；结合公式（1）、（2）、（17）、（18）和（19），推导出模块化多电平换流器的无源性控制算法如下：Among them, diag{} represents a diagonal matrix, and when i=1,...,6, w_i is the element of W matrix; combining formulas (1), (2), (17), (18) and (19), it is deduced that The passivity control algorithm of the modular multilevel converter is as follows:${\mathrm{<span><span>s</span>the\; s</span>}}_{\mathrm{<span><span>u</span>u</span>}<span><span>,</span>,</span>\mathrm{<span><span>1</span>1</span>}}<span><span>=</span>=</span>\frac{\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>2</span>2</span>}{\mathrm{<span><span>u</span>u</span>}}_{\mathrm{<span><span>c</span>c</span>}<span><span>,</span>,</span>\mathrm{<span><span>u</span>u</span>}\mathrm{<span><span>1</span>1</span>}}^{<span><span>*</span>*</span>}}<span><span>(</span>(</span><span><span>-</span>-</span>{\mathrm{<span><span>L</span>L</span>}}_{\mathrm{<span><span>e</span>e</span>}}\frac{\mathrm{<span><span>d</span>d</span>}{\stackrel{<span><span>\&OverBar;</span>\&OverBar;</span>}{\mathrm{<span><span>i</span>i</span>}}}_{\mathrm{<span><span>u</span>u</span>}}}{\mathrm{<span><span>dt</span>dt</span>}}<span><span>-</span>-</span>{\mathrm{<span><span>R</span>R</span>}}_{\mathrm{<span><span>e</span>e</span>}}{\stackrel{<span><span>\&OverBar;</span>\&OverBar;</span>}{\mathrm{<span><span>i</span>i</span>}}}_{\mathrm{<span><span>u</span>u</span>}}<span><span>+</span>+</span>\frac{{\mathrm{<span><span>V</span>V</span>}}_{\mathrm{<span><span>d</span>d</span>}}}{\mathrm{<span><span>2</span>2</span>}}<span><span>-</span>-</span>{\mathrm{<span><span>u</span>u</span>}}_{\mathrm{<span><span>v</span>v</span>}}<span><span>-</span>-</span>{\mathrm{<span><span>w</span>w</span>}}_{\mathrm{<span><span>1</span>1</span>}}\mathrm{<span><span>\&Delta;</span>\&Delta;</span>}{\mathrm{<span><span>x</span>x</span>}}_{\mathrm{<span><span>1</span>1</span>}}<span><span>)</span>)</span><span><span>,</span>,</span>\mathrm{<span><span>\&Delta;</span>\&Delta;</span>}{\mathrm{<span><span>x</span>x</span>}}_{\mathrm{<span><span>1</span>1</span>}}<span><span>=</span>=</span>{\mathrm{<span><span>i</span>i</span>}}_{\mathrm{<span><span>u</span>u</span>}}^{<span><span>*</span>*</span>}<span><span>-</span>-</span>{\stackrel{<span><span>\&OverBar;</span>\&OverBar;</span>}{\mathrm{<span><span>i</span>i</span>}}}_{\mathrm{<span><span>u</span>u</span>}}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>26</span>26</span>}<span><span>)</span>)</span>$${\mathrm{<span><span>s</span>the\; s</span>}}_{\mathrm{<span><span>u</span>u</span>}<span><span>,</span>,</span>\mathrm{<span><span>2</span>2</span>}}<span><span>=</span>=</span>\frac{\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>2</span>2</span>}{\mathrm{<span><span>u</span>u</span>}}_{\mathrm{<span><span>c</span>c</span>}<span><span>,</span>,</span>\mathrm{<span><span>u</span>u</span>}\mathrm{<span><span>2</span>2</span>}}^{<span><span>*</span>*</span>}}<span><span>(</span>(</span><span><span>-</span>-</span>{\mathrm{<span><span>L</span>L</span>}}_{\mathrm{<span><span>e</span>e</span>}}\frac{\mathrm{<span><span>d</span>d</span>}{\stackrel{<span><span>\&OverBar;</span>\&OverBar;</span>}{\mathrm{<span><span>i</span>i</span>}}}_{\mathrm{<span><span>u</span>u</span>}}}{\mathrm{<span><span>dt</span>dt</span>}}<span><span>-</span>-</span>{\mathrm{<span><span>R</span>R</span>}}_{\mathrm{<span><span>e</span>e</span>}}{\stackrel{<span><span>\&OverBar;</span>\&OverBar;</span>}{\mathrm{<span><span>i</span>i</span>}}}_{\mathrm{<span><span>u</span>u</span>}}<span><span>+</span>+</span>\frac{{\mathrm{<span><span>V</span>V</span>}}_{\mathrm{<span><span>d</span>d</span>}}}{\mathrm{<span><span>2</span>2</span>}}<span><span>-</span>-</span>{\mathrm{<span><span>u</span>u</span>}}_{\mathrm{<span><span>v</span>v</span>}}<span><span>-</span>-</span>{\mathrm{<span><span>w</span>w</span>}}_{\mathrm{<span><span>1</span>1</span>}}\mathrm{<span><span>\&Delta;</span>\&Delta;</span>}{\mathrm{<span><span>x</span>x</span>}}_{\mathrm{<span><span>1</span>1</span>}}<span><span>)</span>)</span><span><span>,</span>,</span>\mathrm{<span><span>\&Delta;</span>\&Delta;</span>}{\mathrm{<span><span>x</span>x</span>}}_{\mathrm{<span><span>1</span>1</span>}}<span><span>=</span>=</span>{\mathrm{<span><span>i</span>i</span>}}_{\mathrm{<span><span>u</span>u</span>}}^{<span><span>*</span>*</span>}<span><span>-</span>-</span>{\stackrel{<span><span>\&OverBar;</span>\&OverBar;</span>}{\mathrm{<span><span>i</span>i</span>}}}_{\mathrm{<span><span>u</span>u</span>}}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>27</span>27</span>}<span><span>)</span>)</span>$${\mathrm{<span><span>s</span>the\; s</span>}}_{\mathrm{<span><span>d</span>d</span>}<span><span>,</span>,</span>\mathrm{<span><span>1</span>1</span>}}<span><span>=</span>=</span>\frac{\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>2</span>2</span>}{\mathrm{<span><span>u</span>u</span>}}_{\mathrm{<span><span>c</span>c</span>}<span><span>,</span>,</span>\mathrm{<span><span>d</span>d</span>}\mathrm{<span><span>1</span>1</span>}}^{<span><span>*</span>*</span>}}<span><span>(</span>(</span><span><span>-</span>-</span>{\mathrm{<span><span>L</span>L</span>}}_{\mathrm{<span><span>e</span>e</span>}}\frac{\mathrm{<span><span>d</span>d</span>}{\stackrel{<span><span>\&OverBar;</span>\&OverBar;</span>}{\mathrm{<span><span>i</span>i</span>}}}_{\mathrm{<span><span>d</span>d</span>}}}{\mathrm{<span><span>dt</span>dt</span>}}<span><span>-</span>-</span>{\mathrm{<span><span>R</span>R</span>}}_{\mathrm{<span><span>e</span>e</span>}}{\stackrel{<span><span>\&OverBar;</span>\&OverBar;</span>}{\mathrm{<span><span>i</span>i</span>}}}_{\mathrm{<span><span>d</span>d</span>}}<span><span>+</span>+</span>\frac{{\mathrm{<span><span>V</span>V</span>}}_{\mathrm{<span><span>d</span>d</span>}}}{\mathrm{<span><span>2</span>2</span>}}<span><span>-</span>-</span>{\mathrm{<span><span>u</span>u</span>}}_{\mathrm{<span><span>v</span>v</span>}}<span><span>-</span>-</span>{\mathrm{<span><span>w</span>w</span>}}_{\mathrm{<span><span>2</span>2</span>}}\mathrm{<span><span>\&Delta;</span>\&Delta;</span>}{\mathrm{<span><span>x</span>x</span>}}_{\mathrm{<span><span>2</span>2</span>}}<span><span>)</span>)</span><span><span>,</span>,</span>\mathrm{<span><span>\&Delta;</span>\&Delta;</span>}{\mathrm{<span><span>x</span>x</span>}}_{\mathrm{<span><span>2</span>2</span>}}<span><span>=</span>=</span>{\mathrm{<span><span>i</span>i</span>}}_{\mathrm{<span><span>d</span>d</span>}}^{<span><span>*</span>*</span>}<span><span>-</span>-</span>{\stackrel{<span><span>\&OverBar;</span>\&OverBar;</span>}{\mathrm{<span><span>i</span>i</span>}}}_{\mathrm{<span><span>d</span>d</span>}}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>28</span>28</span>}<span><span>)</span>)</span>$${\mathrm{<span><span>s</span>the\; s</span>}}_{\mathrm{<span><span>d</span>d</span>}<span><span>,</span>,</span>\mathrm{<span><span>2</span>2</span>}}<span><span>=</span>=</span>\frac{\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>2</span>2</span>}{\mathrm{<span><span>u</span>u</span>}}_{\mathrm{<span><span>c</span>c</span>}<span><span>,</span>,</span>\mathrm{<span><span>d</span>d</span>}\mathrm{<span><span>2</span>2</span>}}^{<span><span>*</span>*</span>}}<span><span>(</span>(</span><span><span>-</span>-</span>{\mathrm{<span><span>L</span>L</span>}}_{\mathrm{<span><span>e</span>e</span>}}\frac{\mathrm{<span><span>d</span>d</span>}{\stackrel{<span><span>\&OverBar;</span>\&OverBar;</span>}{\mathrm{<span><span>i</span>i</span>}}}_{\mathrm{<span><span>d</span>d</span>}}}{\mathrm{<span><span>dt</span>dt</span>}}<span><span>-</span>-</span>{\mathrm{<span><span>R</span>R</span>}}_{\mathrm{<span><span>e</span>e</span>}}{\stackrel{<span><span>\&OverBar;</span>\&OverBar;</span>}{\mathrm{<span><span>i</span>i</span>}}}_{\mathrm{<span><span>d</span>d</span>}}<span><span>+</span>+</span>\frac{{\mathrm{<span><span>V</span>V</span>}}_{\mathrm{<span><span>d</span>d</span>}}}{\mathrm{<span><span>2</span>2</span>}}<span><span>-</span>-</span>{\mathrm{<span><span>u</span>u</span>}}_{\mathrm{<span><span>v</span>v</span>}}<span><span>-</span>-</span>{\mathrm{<span><span>w</span>w</span>}}_{\mathrm{<span><span>2</span>2</span>}}\mathrm{<span><span>\&Delta;</span>\&Delta;</span>}{\mathrm{<span><span>x</span>x</span>}}_{\mathrm{<span><span>2</span>2</span>}}<span><span>)</span>)</span><span><span>,</span>,</span>\mathrm{<span><span>\&Delta;</span>\&Delta;</span>}{\mathrm{<span><span>x</span>x</span>}}_{\mathrm{<span><span>2</span>2</span>}}<span><span>=</span>=</span>{\mathrm{<span><span>i</span>i</span>}}_{\mathrm{<span><span>d</span>d</span>}}^{<span><span>*</span>*</span>}<span><span>-</span>-</span>{\stackrel{<span><span>\&OverBar;</span>\&OverBar;</span>}{\mathrm{<span><span>i</span>i</span>}}}_{\mathrm{<span><span>d</span>d</span>}}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>29</span>29</span>}<span><span>)</span>)</span>$上桥臂各模块直流侧的微分方程为：The differential equation of the DC side of each module of the upper bridge arm is:${\mathrm{<span><span>C</span>C</span>}}_{\mathrm{<span><span>u</span>u</span>}\mathrm{<span><span>1</span>1</span>}}\frac{\mathrm{<span><span>d</span>d</span>}{\stackrel{<span><span>\&OverBar;</span>\&OverBar;</span>}{\mathrm{<span><span>u</span>u</span>}}}_{\mathrm{<span><span>c</span>c</span>}<span><span>,</span>,</span>\mathrm{<span><span>u</span>u</span>}\mathrm{<span><span>1</span>1</span>}}}{\mathrm{<span><span>dt</span>dt</span>}}<span><span>+</span>+</span>\frac{{\stackrel{<span><span>\&OverBar;</span>\&OverBar;</span>}{\mathrm{<span><span>u</span>u</span>}}}_{\mathrm{<span><span>c</span>c</span>}<span><span>,</span>,</span>\mathrm{<span><span>u</span>u</span>}\mathrm{<span><span>1</span>1</span>}}}{{\mathrm{<span><span>R</span>R</span>}}_{\mathrm{<span><span>u</span>u</span>}\mathrm{<span><span>1</span>1</span>}}}<span><span>=</span>=</span>{\mathrm{<span><span>s</span>the\; s</span>}}_{\mathrm{<span><span>u</span>u</span>}<span><span>,</span>,</span>\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>i</span>i</span>}}_{\mathrm{<span><span>u</span>u</span>}}^{<span><span>*</span>*</span>}<span><span>-</span>-</span>{\mathrm{<span><span>w</span>w</span>}}_{\mathrm{<span><span>3</span>3</span>}}\mathrm{<span><span>\&Delta;</span>\&Delta;</span>}{\mathrm{<span><span>x</span>x</span>}}_{\mathrm{<span><span>3</span>3</span>}}<span><span>,</span>,</span>\mathrm{<span><span>\&Delta;</span>\&Delta;</span>}{\mathrm{<span><span>x</span>x</span>}}_{\mathrm{<span><span>3</span>3</span>}}<span><span>=</span>=</span>{\mathrm{<span><span>u</span>u</span>}}_{\mathrm{<span><span>c</span>c</span>}<span><span>,</span>,</span>\mathrm{<span><span>u</span>u</span>}\mathrm{<span><span>1</span>1</span>}}^{<span><span>*</span>*</span>}<span><span>-</span>-</span>{\stackrel{<span><span>\&OverBar;</span>\&OverBar;</span>}{\mathrm{<span><span>u</span>u</span>}}}_{\mathrm{<span><span>c</span>c</span>}<span><span>,</span>,</span>\mathrm{<span><span>u</span>u</span>}\mathrm{<span><span>1</span>1</span>}}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>30</span>30</span>}<span><span>)</span>)</span>$${\mathrm{<span><span>C</span>C</span>}}_{\mathrm{<span><span>u</span>u</span>}\mathrm{<span><span>2</span>2</span>}}\frac{\mathrm{<span><span>d</span>d</span>}{\stackrel{<span><span>\&OverBar;</span>\&OverBar;</span>}{\mathrm{<span><span>u</span>u</span>}}}_{\mathrm{<span><span>c</span>c</span>}<span><span>,</span>,</span>\mathrm{<span><span>u</span>u</span>}\mathrm{<span><span>2</span>2</span>}}}{\mathrm{<span><span>dt</span>dt</span>}}<span><span>+</span>+</span>\frac{{\stackrel{<span><span>\&OverBar;</span>\&OverBar;</span>}{\mathrm{<span><span>u</span>u</span>}}}_{\mathrm{<span><span>c</span>c</span>}<span><span>,</span>,</span>\mathrm{<span><span>u</span>u</span>}\mathrm{<span><span>2</span>2</span>}}}{{\mathrm{<span><span>R</span>R</span>}}_{\mathrm{<span><span>u</span>u</span>}\mathrm{<span><span>2</span>2</span>}}}<span><span>=</span>=</span>{\mathrm{<span><span>s</span>the\; s</span>}}_{\mathrm{<span><span>u</span>u</span>}<span><span>,</span>,</span>\mathrm{<span><span>2</span>2</span>}}{\mathrm{<span><span>i</span>i</span>}}_{\mathrm{<span><span>u</span>u</span>}}^{<span><span>*</span>*</span>}<span><span>-</span>-</span>{\mathrm{<span><span>w</span>w</span>}}_{\mathrm{<span><span>4</span>4</span>}}\mathrm{<span><span>\&Delta;</span>\&Delta;</span>}{\mathrm{<span><span>x</span>x</span>}}_{\mathrm{<span><span>4</span>4</span>}}<span><span>,</span>,</span>\mathrm{<span><span>\&Delta;</span>\&Delta;</span>}{\mathrm{<span><span>x</span>x</span>}}_{\mathrm{<span><span>4</span>4</span>}}<span><span>=</span>=</span>{\mathrm{<span><span>u</span>u</span>}}_{\mathrm{<span><span>c</span>c</span>}<span><span>,</span>,</span>\mathrm{<span><span>u</span>u</span>}\mathrm{<span><span>2</span>2</span>}}^{<span><span>*</span>*</span>}<span><span>-</span>-</span>{\stackrel{<span><span>\&OverBar;</span>\&OverBar;</span>}{\mathrm{<span><span>u</span>u</span>}}}_{\mathrm{<span><span>c</span>c</span>}<span><span>,</span>,</span>\mathrm{<span><span>u</span>u</span>}\mathrm{<span><span>2</span>2</span>}}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>31</span>31</span>}<span><span>)</span>)</span>$下桥臂各模块直流侧的微分方程为：The differential equation of the DC side of each module of the lower bridge arm is:${\mathrm{<span><span>C</span>C</span>}}_{\mathrm{<span><span>d</span>d</span>}\mathrm{<span><span>1</span>1</span>}}\frac{\mathrm{<span><span>d</span>d</span>}{\stackrel{<span><span>\&OverBar;</span>\&OverBar;</span>}{\mathrm{<span><span>u</span>u</span>}}}_{\mathrm{<span><span>c</span>c</span>}<span><span>,</span>,</span>\mathrm{<span><span>d</span>d</span>}\mathrm{<span><span>1</span>1</span>}}}{\mathrm{<span><span>dt</span>dt</span>}}<span><span>+</span>+</span>\frac{{\stackrel{<span><span>\&OverBar;</span>\&OverBar;</span>}{\mathrm{<span><span>u</span>u</span>}}}_{\mathrm{<span><span>c</span>c</span>}<span><span>,</span>,</span>\mathrm{<span><span>d</span>d</span>}\mathrm{<span><span>1</span>1</span>}}}{{\mathrm{<span><span>R</span>R</span>}}_{\mathrm{<span><span>d</span>d</span>}\mathrm{<span><span>1</span>1</span>}}}<span><span>=</span>=</span>{\mathrm{<span><span>s</span>the\; s</span>}}_{\mathrm{<span><span>d</span>d</span>}<span><span>,</span>,</span>\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>i</span>i</span>}}_{\mathrm{<span><span>d</span>d</span>}}^{<span><span>*</span>*</span>}<span><span>-</span>-</span>{\mathrm{<span><span>w</span>w</span>}}_{\mathrm{<span><span>5</span>5</span>}}\mathrm{<span><span>\&Delta;</span>\&Delta;</span>}{\mathrm{<span><span>x</span>x</span>}}_{\mathrm{<span><span>5</span>5</span>}}<span><span>,</span>,</span>\mathrm{<span><span>\&Delta;</span>\&Delta;</span>}{\mathrm{<span><span>x</span>x</span>}}_{\mathrm{<span><span>5</span>5</span>}}<span><span>=</span>=</span>{\mathrm{<span><span>u</span>u</span>}}_{\mathrm{<span><span>c</span>c</span>}<span><span>,</span>,</span>\mathrm{<span><span>d</span>d</span>}\mathrm{<span><span>1</span>1</span>}}^{<span><span>*</span>*</span>}<span><span>-</span>-</span>{\stackrel{<span><span>\&OverBar;</span>\&OverBar;</span>}{\mathrm{<span><span>u</span>u</span>}}}_{\mathrm{<span><span>c</span>c</span>}<span><span>,</span>,</span>\mathrm{<span><span>d</span>d</span>}\mathrm{<span><span>1</span>1</span>}}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>32</span>32</span>}<span><span>)</span>)</span>$${\mathrm{<span><span>C</span>C</span>}}_{\mathrm{<span><span>d</span>d</span>}\mathrm{<span><span>2</span>2</span>}}\frac{\mathrm{<span><span>d</span>d</span>}{\stackrel{<span><span>\&OverBar;</span>\&OverBar;</span>}{\mathrm{<span><span>u</span>u</span>}}}_{\mathrm{<span><span>c</span>c</span>}<span><span>,</span>,</span>\mathrm{<span><span>d</span>d</span>}\mathrm{<span><span>2</span>2</span>}}}{\mathrm{<span><span>dt</span>dt</span>}}<span><span>+</span>+</span>\frac{{\stackrel{<span><span>\&OverBar;</span>\&OverBar;</span>}{\mathrm{<span><span>u</span>u</span>}}}_{\mathrm{<span><span>c</span>c</span>}<span><span>,</span>,</span>\mathrm{<span><span>d</span>d</span>}\mathrm{<span><span>2</span>2</span>}}}{{\mathrm{<span><span>R</span>R</span>}}_{\mathrm{<span><span>d</span>d</span>}\mathrm{<span><span>2</span>2</span>}}}<span><span>=</span>=</span>{\mathrm{<span><span>s</span>the\; s</span>}}_{\mathrm{<span><span>d</span>d</span>}<span><span>,</span>,</span>\mathrm{<span><span>2</span>2</span>}}{\mathrm{<span><span>i</span>i</span>}}_{\mathrm{<span><span>d</span>d</span>}}^{<span><span>*</span>*</span>}<span><span>-</span>-</span>{\mathrm{<span><span>w</span>w</span>}}_{\mathrm{<span><span>6</span>6</span>}}\mathrm{<span><span>\&Delta;</span>\&Delta;</span>}{\mathrm{<span><span>x</span>x</span>}}_{\mathrm{<span><span>6</span>6</span>}}<span><span>,</span>,</span>\mathrm{<span><span>\&Delta;</span>\&Delta;</span>}{\mathrm{<span><span>x</span>x</span>}}_{\mathrm{<span><span>6</span>6</span>}}<span><span>=</span>=</span>{\mathrm{<span><span>u</span>u</span>}}_{\mathrm{<span><span>c</span>c</span>}<span><span>,</span>,</span>\mathrm{<span><span>d</span>d</span>}\mathrm{<span><span>2</span>2</span>}}^{<span><span>*</span>*</span>}<span><span>-</span>-</span>{\stackrel{<span><span>\&OverBar;</span>\&OverBar;</span>}{\mathrm{<span><span>u</span>u</span>}}}_{\mathrm{<span><span>c</span>c</span>}<span><span>,</span>,</span>\mathrm{<span><span>d</span>d</span>}\mathrm{<span><span>2</span>2</span>}}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>33</span>33</span>}<span><span>)</span>)</span><span><span>.</span>.</span>$6.根据权利要求5所述的无源性建模与控制方法，其特征在于，w₁和w₂的取值范围为[0.2,2]，w₃～w₆的取值范围为[50,200]。6. The passivity modeling and control method according to claim 5, characterized in that, the value range of w₁ and w₂ is [0.2,2], and the value range of w₃ ~ w₆ is [50,200 ].7.根据权利要求5所述的无源性建模与控制方法，其特征在于，所述的步骤S4具体为：7. The passivity modeling and control method according to claim 5, wherein said step S4 is specifically:基于公式（26）～（33）搭建基于各模块开关函数的换流器控制模型：比较直流侧电容电压参考值与实测值，并根据阻尼矩阵W参数进行电压外环控制；同时，按照类似方法对交流侧电流进行电流内环控制；然后比较获得的开关函数与三角载波并形成模块化多电平换流器各开关的PWM脉冲控制信号用以实现对直流侧电容电压的控制和交流侧电流的跟踪。Based on the formulas (26)-(33), the converter control model based on the switching function of each module is built: compare the DC side capacitor voltage reference value with the measured value, and perform voltage outer loop control according to the damping matrix W parameter; at the same time, follow a similar method Perform current inner loop control on the AC side current; then compare the obtained switching function with the triangular carrier wave and form the PWM pulse control signal of each switch of the modular multilevel converter to realize the control of the DC side capacitor voltage and the AC side current tracking.

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