CN103595284B - Modularization multi-level converter passivity modeling and control method - Google Patents

Abstract

Modularization multi-level converter passivity modeling and control method of the present invention mainly comprises step: S1, set up modularization multi-level converter passivity Mathematical Modeling, asks for the equalization state space equation in a switch periods; S2, set up modularization multi-level converter Energy shaping algorithm model based on equalization state space equation, define from the passive system input state variable ξ to output state variable X; S3, set up converter damping inject algorithm model.S4, build converter control model based on each module switch function.Beneficial effect is to 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, for the control strategy design of flexible direct current power transmission system provides feasible means.

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 to the change of technique that alternating current-direct current coexists.Based on the Technology of HVDC based Voltage Source Converter of voltage source converter, the problems of current AC-HVDC field face can be made to be readily solved, change for power transmission mode and build following intelligent grid and provide brand-new solution.Because full-controlled switch device (as insulated gate bipolar transistor (IGBT) etc.) is withstand voltage still relatively low, flexible direct current 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 device be brought thus all to press, electromagnetic interference, and the series of problems such as the switching loss that causes of higher switching frequency.Along with the continuous lifting of electric pressure and capacity requirement, these defects embody more and more significant, become the bottleneck that restriction two level or three level technology itself are difficult to go beyond.

Based on an above-mentioned difficult problem, jointly modular multi-level converter topological structure is proposed at calendar year 2001 university of Munich, Germany Federal Defence Forces R.Marquart and A.Lesnicar, general employing half-bridge or full-bridge inverter cascading topological structure, be convenient to modularized design, be easy to the upgrading of the lifting of electric pressure and 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 made up of two half-bridge modules respectively, each half-bridge is made up 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 a upper and lower brachium pontis kth module, R _ukand R _dkbe respectively the equivalent parallel resistance at a upper and lower brachium pontis kth module DC bus capacitor two ends, T _{uk, j}and T _{dk, j}(k=1,2, j=1,2) are respectively jth IGBT, the D of a upper and lower brachium pontis kth module _{uk, j}and D _{dk, j}(k=1,2, j=1,2) are respectively a jth anti-paralleled diode of a upper and lower brachium pontis kth module; V _dfor direct current network voltage, u _vfor the voltage with multiple levels that modularization multi-level converter exports, i _uand i _dbe respectively upper and lower bridge arm current; L _gand R _grepresent inductance and the equivalent resistance of AC network side respectively, v _gfor ac grid voltage.The proposition of this technology and application, improve the on-road efficiency of flexible DC power transmission engineering, and the development and the engineering that facilitate Technology of HVDC based Voltage Source Converter are promoted.

Because the submodule quantity of connecting in each brachium pontis of modularization multi-level converter is more, the data volume of valve control system required process within each cycle causes very greatly controlling difficulty greatly, adds the Balance route difficulty of submodule capacitor voltage.If unbalanced situation appears in the energy distribution between brachium pontis, the stability of submodule inside will be destroyed, and then cause current waveform to distort.But, major part scholar will be used in the modeling and control of modularization multi-level converter based on the voltage of two level or three-level converter, electric current and power control strategy and controller parameter method for designing, causes the not good or effect of control effects to be at least be worth discussion.

Summary of the invention

The object of the invention is to overcome and the existing voltage based on two level or three-level converter, electric current and power control strategy and controller method be applied to the undesirable deficiency of effect that modularization multi-level converter obtains, 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, set up modularization multi-level converter Energy shaping algorithm model based on equalization state space equation, define from the passive system input state variable ξ to output state variable X;

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

S4, build 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, current inner loop control is carried out to ac-side current; Then compare the switch function of acquisition and triangular carrier and the pwm pulse control signal forming each switch of modularization multi-level converter in order to realize the tracking of control to DC capacitor voltage and ac-side current.

Further, above-mentioned steps S1 is as follows based on the detailed process of the modularization multi-level converter of phase structure: in the modularization multi-level converter of phase structure, upper brachium pontis and lower brachium pontis are made up of two half-bridge modules respectively, and each half-bridge is made up 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 a upper and lower brachium pontis kth module, R _ukand R _dkbe respectively the equivalent parallel resistance at a upper and lower brachium pontis kth module DC bus capacitor two ends, T _{uk, j}and T _{dk, j}, k=1 or 2, j=1 or 2, be respectively jth IGBT, the D of a upper and lower brachium pontis kth module _{uk, j}and D _{dk, j}, k=1 or 2, j=1 or 2, be respectively a jth anti-paralleled diode of a upper and lower brachium pontis kth module; V _dfor direct current network voltage, u _vfor the voltage with multiple levels that modularization multi-level converter exports, i _uand i _dbe respectively upper and lower bridge arm current; L _gand R _grepresent inductance and the equivalent resistance of AC network side respectively, v _gfor ac grid voltage;

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

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

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

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

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

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

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

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

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

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

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

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

Wherein ξ is the input vector of system, state variable z and coefficient matrix D, R, M _u1, M _u2, M _d1, M _d2be respectively:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Ask for the first differential of energy function for:

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

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

$\stackrel{\·}{E}=\frac{1}{2}{X}^{T}D\stackrel{\·}{X}=-X^T\mathrm{RX}+X^T\mathrm{\ξ}---\left(14\right)$

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

$E\left(t_1\right)-E\left(t_0\right)=-{\∫}_{t_0}^{t1}\left(X^T\mathrm{RX}\right)\mathrm{dt}+{\∫}_{t_0}^{t1}\left(X^T\mathrm{\ξ}\right)\mathrm{dt}---\left(15\right)$

Equation (15) left side is [t ₀, t ₁] time period internal mold blocking multilevel converter store gross energy, expression formula on the right of equation for the energy that modularization multi-level converter dissipates, expression formula on the right of equation for the energy that electrical network injects to modularization multi-level converter; According to the principle of passive coherent locating, equation (15) defines one from input ξ to the passive system exported X; If input ξ=0, then (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 expected _dfor: $X_d={[i_u^{*},i_d^{*},u_{c,u1}^{*},u_{c,u2}^{*},u_{c,d1}^{*},u_{c,d2}^{*}]}^T---\left(17\right)$

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

Departure vector Δ X is defined as:

ΔX=X _d-X （18）

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

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

Wherein, equivalent control input vector η expression formula is:

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

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

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

First differential is asked for formula (21) left and right two ends, to obtain final product:

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

Formula (22) defines the passive system of the vector of the control inputs from an equivalence η to error vector Δ X.

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

η=-WΔX （23）

Formula (23) is substituted into formula (22), to obtain final product:

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

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

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

W=diag{w ₁,w ₂,w ₃,w ₄,w ₅,w ₆} （25）

Wherein, diag{} represents diagonal matrix, i=1 ..., w when 6 _ifor W entry of a matrix element; In conjunction with formula (1), (2), (17), (18) and (19), the passive coherent locating algorithm deriving modularization multi-level converter is as follows:

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

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

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

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

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

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

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

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

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

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

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

Further, described step S4 is specially:

Build 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, current inner loop control is carried out to ac-side current; Then compare the switch function of acquisition and triangular carrier and the pwm pulse control signal forming each switch of modularization multi-level converter in order to realize the tracking of control to DC capacitor voltage and ac-side current.

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, by introducing the correlation theory of passive coherent locating, setting up modularization multi-level converter passivity Mathematical Modeling, asking for the equalization state space equation in a switch periods; By setting up the algorithm model of modularization multi-level converter Energy shaping method, define the passive system between a constrained input; Then damping matrix reasonable in design, set up the algorithm model that modularization multi-level converter damping is injected, guarantee the stability contorting 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, thus achieve the whole control flow of modularization multi-level converter.Overcome the shortcoming that traditional control method controling parameters is many, amount of calculation is large, consumes resources is large.This control method is under operational mode is fallen in reference current sudden change and ac grid voltage, all can realize the balanced and alternating current of DC voltage quickly and accurately to follow the tracks of fast, stability is high, tracking velocity is fast, effectively demonstrate the feasibility of the damping injection algorithm based on passivity-based method, for the control strategy design of flexible direct current 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 to 200A process at t=0.1s from 100A, the output voltage of modularization multi-level converter, current waveform and upper and lower bridge arm current waveform;

Fig. 4 is that the amplitude of active current reference value in specific embodiment is suddenlyd change to 200A process at t=0.1s from 100A, 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 the Voltage Drop process of 60% between 0.1s ~ 0.2s, the output voltage of modularization multi-level converter, current waveform and upper and lower bridge arm current waveform;

Fig. 6 is that in specific embodiment, active current reference value is 100A, and ac grid voltage occurs in the Voltage Drop process of 60% 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 under premised on technical solution of the present invention, give 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 50Hz, voltage peak is 1600V.The upper and lower brachium pontis of modularization multi-level converter is made up of two half-bridge modules respectively, and each half-bridge is made up 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 _vfor the voltage with multiple levels that converter exports; i _uand i _dbe respectively upper and lower brachium pontis AC output current, L _eand R _erepresent inductance value and the equivalent resistance thereof of each brachium pontis respectively; u _vfor the voltage with multiple levels that converter exports, i.e. the voltage of brachium pontis mid point; C _ukand C _dk(k=1,2) is respectively the dc-link capacitance of a upper and lower brachium pontis kth module, R _ukand R _dkbe respectively the equivalent parallel resistance at a upper and lower brachium pontis kth module DC bus capacitor two ends; T _{uk, j}and T _{dk, j}(k=1,2, j=1,2) are respectively jth IGBT, the D of a upper and lower brachium pontis kth module _{uk, j}and D _{dk, j}(k=1,2, j=1,2) are respectively a jth anti-paralleled diode of a upper and lower brachium pontis kth module; L _gand R _grepresent inductance value and the equivalent resistance thereof of AC network side respectively, 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, set up modularization multi-level converter Energy shaping algorithm model based on equalization state space equation, mainly through energy function and the first derivative thereof of derivation multilevel converter, define from the passive system input state variable ξ to output state variable X;

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

S4, build 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, current inner loop control is carried out to ac-side current; Then compare the switch function of acquisition and triangular carrier and the pwm pulse control signal forming each switch of modularization multi-level converter in order to realize the tracking of control to DC capacitor voltage and ac-side current.

Be described further for the modeling and control method of the modularization multi-level converter of phase structure to the present embodiment below, above-mentioned steps S1 based on the modularization multi-level converter of phase structure is as follows based on the detailed process of the modularization multi-level converter of phase structure: in the modularization multi-level converter of wherein phase structure, upper brachium pontis and lower brachium pontis are made up of two half-bridge modules respectively, and each half-bridge is made up 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 a upper and lower brachium pontis kth module, R _ukand R _dkbe respectively the equivalent parallel resistance at a upper and lower brachium pontis kth module DC bus capacitor two ends, T _{uk, j}and T _{dk, j}, k=1 or 2, j=1 or 2, be respectively jth IGBT, the D of a upper and lower brachium pontis kth module _{uk, j}and D _{dk, j}, k=1 or 2, j=1 or 2, be respectively a jth anti-paralleled diode of a upper and lower brachium pontis kth module; V _dfor direct current network voltage, u _vfor the voltage with multiple levels that modularization multi-level converter exports, i _uand i _dbe respectively upper and lower bridge arm current; L _gand R _grepresent inductance and the equivalent resistance of AC network side respectively, v _gfor ac grid voltage;

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

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

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

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

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

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

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

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

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

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

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

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

Wherein ξ is the input vector of system, state variable z and coefficient matrix D, R, M _u1, M _u2, M _d1, M _d2be respectively:

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

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

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

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

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

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

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

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

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

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

Find out from equation (7), switch function m _{u, 1}, m _{u, 2}, m _{d, 1}, m _{d, 2}=0,1}, causes governing equation discontinuous, and what consider again that this control system adopts is high-speed pulse width modulation methods, and averaging method therefore can be adopted to average process to state variable at a control cycle, and namely 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 is the mean value of state variable z a switch periods, is 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 the mean value of each element of state variable z a switch periods.Similarly, s _u,kand s _d,k, k=1 or 2 is respectively the equalization switch function of each module of upper and lower brachium pontis in a switch periods.

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

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

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

Ask for the first 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 u respectively ₁, u ₂, d ₁and d ₂one of, therefore, simplified style (13) is:

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

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

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

Equation (15) left side is [t ₀, t ₁] time period internal mold blocking multilevel converter store gross energy, expression formula on the right of equation for the energy that modularization multi-level converter dissipates, expression formula on the right of equation for the energy that electrical network injects to modularization multi-level converter; According to the principle of passive coherent locating, equation (15) defines one from input ξ to the passive system exported X; If input ξ=0, then (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 just, the first derivative of energy function E when inputting ξ=0 be less than zero, show that energy function E decays to zero in time gradually, namely system is asymptotically stability.

The detailed process of described step S3 is as follows:

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

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

Departure vector Δ X is defined as:

ΔX=X _d-X （18）

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

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

Wherein, equivalent control input vector η expression formula is:

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

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

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

First differential is asked for formula (21) left and right two ends, to obtain final product:

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

Be similar to the derivation of formula (14) and (15), formula (22) defines the passive system of the vector of the control inputs from an equivalence η to error vector Δ X.If η=0, then the energy function E of departure vector Δ X _efirst differential show that state variable X finally will converge to desired value X _d.

In order to the quick tracking of the stability contorting and ac-side current that ensure modularization multi-level converter DC voltage, introduce damping matrix W, obtain following expression:

η=-WΔX （23）

Formula (23) is substituted into formula (22), to obtain final product:

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

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

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

W=diag{w ₁,w ₂,w ₃,w ₄,w ₅,w ₆} （25）

Wherein, diag{} represents diagonal matrix, i=1 ..., w when 6 _ifor W entry of a matrix element; In conjunction with formula (1), (2), (17), (18) and (19), the passive coherent locating algorithm deriving modularization multi-level converter is as follows:

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

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

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

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

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

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

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

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

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

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

In diagonal matrix W, each element w _ichoosing of (i=1 .., 6) can have influence on passive coherent locating convergence, w _ithe larger then convergence rate of parameter is faster, but stability margin reduces; Otherwise, w _ithe less then convergence rate of parameter is slower, and stability margin improves.Therefore, w ₁and w ₂span be preferably [0.2,2], w ₃~ w ₆span be preferably [50,200].

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

As shown in Figure 2, each electric parameters (i is completed according to main circuit topology figure _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, namely formed in order to ensure the stability contorting 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 based on the algorithm model of Energy shaping method, introduce damping and inject matrix, design rational damping matrix parameter w ₁~ w ₆, then in conjunction with the reference value of each control variables, derive the switch function s of each module switch element of upper and lower brachium pontis _u1, s _u2, s _d1, s _d2; The triangle 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 namely realizing modularization multi-level converter passivity modeling and control method builds.

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

As can be seen from Figure 3, inverter output voltage u _vbe five level, upper bridge arm current i _uwith lower bridge arm current i _dphase place contrary, 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 each module of lower brachium pontis _{d, 1}and s _{d, 2}waveform overlaps completely, and the phase place of upper and lower brachium pontis switch function waveform is contrary; The dc-link capacitance voltage u of each module of upper brachium pontis _{c, u1}and u _{c, u2}waveform overlaps completely, the dc-link capacitance voltage u of each module of lower 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 phase place of upper and lower brachium pontis dc-link capacitance voltage waveform is contrary.

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

In Fig. 5, u _vfor the voltage with multiple levels that modularization multi-level converter exports; i _ufor bridge arm current on modularization multi-level converter; i _dfor bridge arm current under modularization multi-level converter; i _lfor the alternating current that modularization multi-level converter exports.In Fig. 6, s _{u, 1}, s _{u, 2}for the switch function of each module of brachium pontis on modularization multi-level converter; s _{d, 1}, s _{d, 2}for the switch function of each module of brachium pontis under modularization multi-level converter; u _{c, u1}and u _{c, u2}for the dc-link capacitance voltage of each module of brachium pontis on modularization multi-level converter; u _{c, d1}and u _{c, d2}for the dc-link capacitance voltage of each module of brachium pontis under modularization multi-level converter.As can be seen from Figure 5, as t<0.1s, inverter output voltage u _vbe five level; As 0.1s<t<0.2s, v _gfall 60%, inverter output voltage u _vfor three level; As t>0.2s, inverter output voltage u _vbe five level.In whole process, upper bridge arm current i _uwith lower bridge arm current i _dphase place contrary, alternating current i _lremain unchanged in ac grid voltage falling process.As can be seen from Figure 6, as 0.1s<t<0.2s, the switch function s of each module of upper and lower brachium pontis _{u, 1}, s _{u, 2}, s _{d, 1}, s _{d, 2}the amplitude of waveform falls 60%; The switch function s of each module of upper brachium pontis _{u, 1}, s _{u, 2}waveform is at ac grid voltage v _goverlap completely in falling process, the switch function s of each module of lower brachium pontis _{d, 1}, s _{d, 2}waveform is at ac grid voltage v _goverlap completely in falling process, and the phase place of upper and lower brachium pontis switch function waveform is contrary; The dc-link capacitance voltage u of each module of upper brachium pontis _{c, u1}, u _{c, u2}waveform overlaps completely, the dc-link capacitance voltage u of each module of lower 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 phase place of upper and lower brachium pontis dc-link capacitance voltage waveform is contrary.

Find out from the dynamic response oscillogram of Fig. 3 ~ Fig. 6, by passivity modeling and control approach application in modularization multi-level converter, the rapid track and control of DC voltage equilibrium and alternating current all can be realized rapidly when current break, grid voltage sags, there is the control effects that stability is strong, tracking velocity is fast, the feasibility of this control method is not limited to the operating mode mentioned in the embodiment of the present invention simultaneously, extensively can be generalized to the controlling unit of the modularization multi-level converter of flexible direct current power transmission system.

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

Claims (7)

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

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

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

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

S4, build 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, compare ac-side current reference value and measured value, and carry out current inner loop control according to damping matrix W parameter; Then compare the switch function of acquisition and triangular carrier and the pwm pulse control signal forming each switch of modularization multi-level converter in order to realize the tracking of control to DC capacitor voltage and ac-side current.

2. passivity modeling and control method according to claim 1, it is characterized in that, step S1 sets up modularization multi-level converter passivity Mathematical Modeling specifically based on the modularization multi-level converter of phase structure, process is as follows: in the modularization multi-level converter of phase structure, upper brachium pontis and lower brachium pontis are made up of two half-bridge modules respectively, and each half-bridge is made up 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 a upper and lower brachium pontis kth module, R _ukand R _dkbe respectively the equivalent parallel resistance at a upper and lower brachium pontis kth module DC bus capacitor two ends, T _{uk, j}and T _{dk, j}, k=1 or 2, j=1 or 2, be respectively jth IGBT, the D of a upper and lower brachium pontis kth module _{uk, j}and D _{dk, j}, k=1 or 2, j=1 or 2, be respectively a jth anti-paralleled diode of a upper and lower brachium pontis kth module; V _dfor direct current network voltage, u _vfor the voltage with multiple levels that modularization multi-level converter exports, i _uand i _dbe respectively upper and lower bridge arm current; L _gand R _grepresent inductance and the equivalent resistance of AC network side respectively, 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:

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

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

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

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

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

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

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

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

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

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

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

Wherein ξ is the input vector of system, state variable z and coefficient matrix D, R, M _u1, M _u2, M _d1, M _d2be respectively:

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

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

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

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

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

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

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

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

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

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

Adopt averaging method to average process to state variable at a control cycle, namely 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 is the mean value of state variable z a switch periods, is 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 the mean value of each element of state variable z a switch periods; s _u,kand s _d,kbe respectively the equalization switch function of a upper and lower brachium pontis kth module in a switch periods.

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

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

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

Ask for the first 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 u respectively ₁, u ₂, d ₁and d ₂one of, simplified style (13) is:

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

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

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

Equation (15) left side is [t ₀, t ₁] time period internal mold blocking multilevel converter store gross energy, expression formula on the right of equation for the energy that modularization multi-level converter dissipates, expression formula on the right of equation for the energy that electrical network injects to modularization multi-level converter; According to the principle of passive coherent locating, equation (15) defines one from input ξ to the passive system exported X; If input ξ=0, then (14) formula can be reduced to:

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

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

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

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

Departure vector Δ X is defined as:

ΔX＝X _d-X (18)

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

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

Wherein, equivalent control input vector η expression formula is:

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

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

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

First differential is asked for formula (21) left and right two ends, to obtain final product:

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

Formula (22) defines the passive system of the vector of the control inputs from an equivalence η to error vector Δ X.

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

η＝-WΔX (23)

Formula (23) is substituted into formula (22), to obtain final product:

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

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

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

W＝diag{w ₁,w ₂,w ₃,w ₄,w ₅,w ₆} (25)

Wherein, diag{} represents diagonal matrix, i=1 ..., w when 6 _ifor W entry of a matrix element; In conjunction with formula (1), (2), (17), (18) and (19), the passive coherent locating algorithm deriving modularization multi-level converter is as follows:

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

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

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

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

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

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

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

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

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

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

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

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

Build 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, compare ac-side current reference value and measured value, and carry out current inner loop control according to damping matrix W parameter; Then compare the switch function of acquisition and triangular carrier and the pwm pulse control signal forming each switch of modularization multi-level converter in order to realize the tracking of control to DC capacitor voltage and ac-side current.