CN102081684A - Simulation method of double four-quadrant converter - Google Patents

Abstract

The invention relates to a simulation method of a double four-quadrant converter. The double four-quadrant converter comprises a converter and a middle circuit, wherein the converter consists of four parallel branch circuits. The method comprises the following steps of: constructing a corresponding state equation according to different conducting states of switch elements in the four-quadrant converter; constructing a state equation judging module of a simulation model of the double four-quadrant converter by using a Simulink module; constructing an adams resolving module of the simulation model of the double four-quadrant converter by using the Simulink module; and performing simulation calculation by using the double four-quadrant converter. A modeling method has an intuitional principle, simple implementation steps, small real-time calculated amount and more correct and quick simulation, is easy to understand and is beneficial to instantaneity of simulation, and the convergence during zero pulse is effectively ensured.

Description

A kind of dual four quadrant convertor emulation mode

Technical field

The present invention relates to four quadrant convertor emulation field, particularly relate to a kind of dual four quadrant convertor emulation mode.

Background technology

The develop rapidly of, hardware technology soft along with computing machine, Computer Simulation has obtained application more and more widely.At electric and electronic technical field, the appliance computer emulation technology, the deviser the design phase just can observing system static and dynamic performance, seek the optimization of total system structure and parameter, reduce cost to the full extent, reduce testing expenses, shorten the R﹠D cycle, raise the efficiency.

Exchanging transmission is an important directions of China's railway traction power development, and four quadrant convertor is the mains side current transformer of AC transmission electric power locomotive, when traction as rectifier, when regenerative braking as inverter.Four quadrant convertor will guarantee the voltage constant of direct current intermediate link, and AC network side power factor is also wanted harmonic carcellation near 1, makes power network current as far as possible near sinusoidal, is an important electric component on the AC transmission electric power locomotive.Four quadrant convertor is carried out Computer Simulation, have certain help for its R and D.

Referring to Fig. 1, dual four quadrant convertor structure is shown, comprise transformer time limit circuit 11, current transformer 12, intermediate circuit 13 and PWM controller (not shown) composition.

Current transformer 12 is made up of eight branch roads of parallel connection, and the anode of on-off element T11 connects output plus terminal in first branch road, and negative electrode connects the anode of on-off element T12, and the negative electrode of on-off element T12 connects the output negative terminal; The negative electrode of diode D11 connects output plus terminal in second branch road, and anode connects the negative electrode of diode D12, and the anode of diode D12 connects the output negative terminal; The anode of on-off element T13 connects output plus terminal in the 3rd branch road, and negative electrode connects the anode of on-off element T14, and the negative electrode of on-off element T14 connects the output negative terminal; The negative electrode of diode D13 connects output plus terminal in the 4th branch road, and anode connects the negative electrode of diode D14, and the anode of diode D14 connects the output negative terminal; The anode of on-off element T21 connects output plus terminal in the 5th branch road, and negative electrode connects the anode of on-off element T22, and the negative electrode of on-off element T22 connects the output negative terminal; The negative electrode of diode D21 connects output plus terminal in the 6th branch road, and anode connects the negative electrode of diode D22, and the anode of diode D22 connects the output negative terminal; The anode of on-off element T23 connects output plus terminal in the 7th branch road, and negative electrode connects the anode of on-off element T24, and the negative electrode of on-off element T24 connects the output negative terminal; The negative electrode of diode D23 connects output plus terminal in the 8th branch road, and anode connects the negative electrode of diode D24, and the anode of diode D24 connects the output negative terminal.

Transformer time limit 11 circuit comprise the AC power U that is connected transformer time limit _N1, AC power U _N1One end is through the inductance L of series connection _N1And resistance R _N1After, be connected the common port of on-off element T11 and on-off element T12, and the common port of diode D11 and diode D12; AC power U _N1The other end is connected the common port of on-off element T13 and on-off element T14, and the common port of diode D13 and diode D14; Also comprise the AC power U that is connected transformer time limit _N2, AC power U _N2One end is through the inductance L of series connection _N2And resistance R _N2After, be connected the common port of on-off element T21 and on-off element T22, and the common port of diode D21 and diode D22; AC power U _N2The other end is connected the common port of on-off element T23 and on-off element T24, and the common port of diode D23 and diode D24.

Comprise the inductance L that is connected on the positive and negative end of output in the intermediate circuit 13 ₂And resistance R ₂, and the capacitor C that is connected with the positive and negative end of output _dExport the voltage U of positive and negative end output _dThe PWM controller is controlled each on-off element.

In order to set up the four quadrant convertor simulation mathematical model; do not consider the commutation course of on-off element and diode; rectifier cell is regarded as perfect switch, ignore holding circuit wherein, replace the inferior limit leakage inductance and the resistance of transformer respectively with an inductance and resistive element.

In the present emulation technology, four quadrant convertor has following two kinds of methods simulation.

1) utilizes the converter module that carries in the SimPowerSystem module library.

Referring to Fig. 2, the dual four quadrant convertor structure that the SimPowerSystem module is built is shown.This dual four quadrant convertor structural model is slower at the actual emulation medium velocity, can't in time carry out related data and handle.

2) use C language compilation S-Function to realize the function of current transformer model.

Referring to Fig. 3, the dual four quadrant convertor structure that S-Function writes is shown.The current transformer model that uses S-Function to write is slower at the real-time simulation medium velocity, takies the many problems of resource, and particularly under the input control wave of current transformer was zero situation entirely, emulated data result dispersed, and can not restrain.

Summary of the invention

Technical matters to be solved by this invention provides a kind of dual four quadrant convertor emulation mode, and this method emulation is more accurate, fast, and the convergence when effectively having guaranteed zero pulse.

A kind of dual four quadrant convertor emulation mode of the present invention, described four quadrant convertor comprises current transformer and intermediate circuit, current transformer is made up of eight branch roads of parallel connection, the anode of the 11 on-off element (T11) connects output plus terminal in first branch road, negative electrode connects the anode that twelvemo is closed element (T12), and the negative electrode that twelvemo is closed element (T12) connects the output negative terminal; The negative electrode of the 11 diode (D11) connects output plus terminal in second branch road, and anode connects the negative electrode of the 12 diode (D12), and the anode of the 12 diode (D12) connects the output negative terminal; The anode of the 13 on-off element (T13) connects output plus terminal in the 3rd branch road, and negative electrode connects the anode of the 14 on-off element (T14), and the negative electrode of the 14 on-off element (T14) connects the output negative terminal; The negative electrode of the 13 diode (D13) connects output plus terminal in the 4th branch road, and anode connects the negative electrode of the 14 diode (D14), and the anode of the 14 diode (D14) connects the output negative terminal; The anode of the 21 on-off element (T21) connects output plus terminal in the 5th branch road, and negative electrode connects the anode that second twelvemo is closed element (T22), and the negative electrode that second twelvemo is closed element (T22) connects the output negative terminal; The negative electrode of the 21 diode (D21) connects output plus terminal in the 6th branch road, and anode connects the negative electrode of the 22 diode (D22), and the anode of the 22 diode (D22) connects the output negative terminal; The anode of the 23 on-off element (T23) connects output plus terminal in the 7th branch road, and negative electrode connects the anode of the 24 on-off element (T24), and the negative electrode of the 24 on-off element (T24) connects the output negative terminal; The negative electrode of the 23 diode (D23) connects output plus terminal in the 8th branch road, and anode connects the negative electrode of the 24 diode (D24), and the anode of the 24 diode (D24) connects the output negative terminal;

Transformer time limit circuit comprises the first AC power (U that is connected transformer time limit _N1), the first AC power (U _N1) the first inductance (L of an end through connecting _N1) and the first resistance (R _N1) after, be connected the common port that the 11 on-off element (T11) and twelvemo are closed element (T12), and the common port of the 11 diode (D11) and the 12 diode (D12); First AC power (the U _N1) other end is connected the common port of the 13 on-off element (T13) and the 14 on-off element (T14), and the common port of the 13 diode (D13) and the 14 diode (D14); Also comprise the second AC power (U that is connected transformer time limit _N2), AC power (U _N2) the second inductance (L of an end through connecting _N2) and the second resistance (R _N2) after, be connected the common port that the 21 on-off element (T21) and second twelvemo are closed element (T22), and the common port of the 21 diode (D21) and the 22 diode (D22); Second AC power (the U _N2) other end is connected the common port of the 23 on-off element (T23) and the 24 on-off element (T24), and the common port of the 23 diode (D23) and the 24 diode (D24);

Comprise the 3rd inductance (L that is connected on the positive and negative end of output in the intermediate circuit ₂) and the 3rd resistance (R ₂), and the first electric capacity (C that is connected with the positive and negative end of output _d); It is characterized in that this method comprises:

According to the different conducting states of each on-off element in the four quadrant convertor, make up corresponding state equation;

Adopt the Simulink module to build the state equation judge module of dual four quadrant convertor realistic model; Adopt the adams of the dual four quadrant convertor realistic model of Simulink module construction to resolve module;

Utilize dual four quadrant convertor realistic model to carry out simulation calculation.

Preferably, described state equation is specially:

Work as Us1=Us2=+Ud, state equation is:

$\left(\begin{array}{c}{\stackrel{\&CenterDot;}{i}}_{N1}\\ {\stackrel{\&CenterDot;}{i}}_{N2}\\ {\stackrel{\&CenterDot;}{u}}_d\\ {\stackrel{\&CenterDot;}{i}}_2\\ {\stackrel{\&CenterDot;}{u}}_2\end{array}\right)=\left(\begin{array}{ccccc}-{\mathrm{<figure-callout\; id="1"\; label="R\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">R</figure-callout>}}_N/{\mathrm{<figure-callout\; id="1"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& -1/{\mathrm{<figure-callout\; id="1"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& 0\\ 0& -R_{\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">N</figure-callout>}2}/L_{N2}& -1/{\mathrm{<figure-callout\; id="2"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& 0\\ 1/{\mathrm{<figure-callout\; id="1"\; label="C\; d"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">C</figure-callout>}}_d& 1/C_d& 0& -1/{\mathrm{<figure-callout\; id="0"\; label="C\; d"\; filenames="HDA0000036799760000031.png"\; state="\{\{state\}\}">C</figure-callout>}}_d& 0\\ 0& 0& 1/{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_2& 0& -1/{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_2\\ 0& 0& 0& 1/{\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">C</figure-callout>}}_2& 0\end{array}\right)\left(\begin{array}{c}{i}_{N1}\\ i_{N2}\\ u_d\\ i_2\\ u_2\end{array}\right)+\left(\begin{array}{ccc}1/{\mathrm{<figure-callout\; id="1"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& 0\\ 0& 1/{\mathrm{<figure-callout\; id="2"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0\\ 0& 0& -1/{\mathrm{<figure-callout\; id="0"\; label="C\; d"\; filenames="HDA0000036799760000031.png"\; state="\{\{state\}\}">C</figure-callout>}}_d\\ 0& 0& 0\\ 0& 0& 0\end{array}\right)\left(\begin{array}{c}{u}_{N1}\\ u_{N2}\\ i_L\end{array}\right)$

Work as Us1=Us2=-Ud, state equation is:

$\left(\begin{array}{c}{\stackrel{\&CenterDot;}{i}}_{N1}\\ {\stackrel{\&CenterDot;}{i}}_{N2}\\ {\stackrel{\&CenterDot;}{u}}_d\\ {\stackrel{\&CenterDot;}{i}}_2\\ {\stackrel{\&CenterDot;}{u}}_2\end{array}\right)=\left(\begin{array}{ccccc}-{\mathrm{<figure-callout\; id="1"\; label="R\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">R</figure-callout>}}_N/{\mathrm{<figure-callout\; id="1"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& 1/{\mathrm{<figure-callout\; id="1"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& 0\\ 0& -{\mathrm{<figure-callout\; id="2"\; label="R\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">R</figure-callout>}}_N/{\mathrm{<figure-callout\; id="2"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 1/{\mathrm{<figure-callout\; id="2"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& 0\\ -1/C_d& -1/C_d& 0& -1/{\mathrm{<figure-callout\; id="0"\; label="C\; d"\; filenames="HDA0000036799760000031.png"\; state="\{\{state\}\}">C</figure-callout>}}_d& 0\\ 0& 0& 1/{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_2& 0& -1/{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_2\\ 0& 0& 0& 1/{\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">C</figure-callout>}}_2& 0\end{array}\right)\left(\begin{array}{c}{i}_{N1}\\ i_{N2}\\ u_d\\ i_2\\ u_2\end{array}\right)+\left(\begin{array}{ccc}1/{\mathrm{<figure-callout\; id="1"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& 0\\ 0& 1/{\mathrm{<figure-callout\; id="2"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0\\ 0& 0& -1/{\mathrm{<figure-callout\; id="0"\; label="C\; d"\; filenames="HDA0000036799760000031.png"\; state="\{\{state\}\}">C</figure-callout>}}_d\\ 0& 0& 0\\ 0& 0& 0\end{array}\right)\left(\begin{array}{c}{u}_{N1}\\ u_{N2}\\ i_L\end{array}\right)$

Work as Us1=0, Us2=0, state equation is:

$\left(\begin{array}{c}{\stackrel{\&CenterDot;}{i}}_{N1}\\ {\stackrel{\&CenterDot;}{i}}_{N2}\\ {\stackrel{\&CenterDot;}{u}}_d\\ {\stackrel{\&CenterDot;}{i}}_2\\ {\stackrel{\&CenterDot;}{u}}_2\end{array}\right)=\left(\begin{array}{ccccc}-{\mathrm{<figure-callout\; id="1"\; label="R\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">R</figure-callout>}}_N/{\mathrm{<figure-callout\; id="1"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& 0& 0& 0\\ 0& -{\mathrm{<figure-callout\; id="2"\; label="R\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">R</figure-callout>}}_N/{\mathrm{<figure-callout\; id="2"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& 0& 0\\ 0& 0& 0& -1/{\mathrm{<figure-callout\; id="0"\; label="C\; d"\; filenames="HDA0000036799760000031.png"\; state="\{\{state\}\}">C</figure-callout>}}_d& 0\\ 0& 0& 1/{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_2& 0& -1/{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_2\\ 0& 0& 0& 1/{\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">C</figure-callout>}}_2& 0\end{array}\right)\left(\begin{array}{c}{i}_{N1}\\ i_{N2}\\ u_d\\ i_2\\ u_2\end{array}\right)+\left(\begin{array}{ccc}1/{\mathrm{<figure-callout\; id="1"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& 0\\ 0& 1/{\mathrm{<figure-callout\; id="2"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0\\ 0& 0& -1/{\mathrm{<figure-callout\; id="0"\; label="C\; d"\; filenames="HDA0000036799760000031.png"\; state="\{\{state\}\}">C</figure-callout>}}_d\\ 0& 0& 0\\ 0& 0& 0\end{array}\right)\left(\begin{array}{c}{u}_{N1}\\ u_{N2}\\ i_L\end{array}\right)$

Work as Us1=+Ud, Us2=-Ud, state equation is:

$\left(\begin{array}{c}{\stackrel{\&CenterDot;}{i}}_{N1}\\ {\stackrel{\&CenterDot;}{i}}_{N2}\\ {\stackrel{\&CenterDot;}{u}}_d\\ {\stackrel{\&CenterDot;}{i}}_2\\ {\stackrel{\&CenterDot;}{u}}_2\end{array}\right)=\left(\begin{array}{ccccc}-{\mathrm{<figure-callout\; id="1"\; label="R\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">R</figure-callout>}}_N/{\mathrm{<figure-callout\; id="1"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& -1/{\mathrm{<figure-callout\; id="1"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& 0\\ 0& -{\mathrm{<figure-callout\; id="2"\; label="R\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">R</figure-callout>}}_N/{\mathrm{<figure-callout\; id="2"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 1/{\mathrm{<figure-callout\; id="2"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& 0\\ 1/C_d& -1/C_d& 0& -1/{\mathrm{<figure-callout\; id="0"\; label="C\; d"\; filenames="HDA0000036799760000031.png"\; state="\{\{state\}\}">C</figure-callout>}}_d& 0\\ 0& 0& 1/{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_2& 0& -1/{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_2\\ 0& 0& 0& 1/{\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">C</figure-callout>}}_2& 0\end{array}\right)\left(\begin{array}{c}{i}_{N1}\\ i_{N2}\\ u_d\\ i_2\\ u_2\end{array}\right)+\left(\begin{array}{ccc}1/{\mathrm{<figure-callout\; id="1"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& 0\\ 0& 1/{\mathrm{<figure-callout\; id="2"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0\\ 0& 0& -1/{\mathrm{<figure-callout\; id="0"\; label="C\; d"\; filenames="HDA0000036799760000031.png"\; state="\{\{state\}\}">C</figure-callout>}}_d\\ 0& 0& 0\\ 0& 0& 0\end{array}\right)\left(\begin{array}{c}{u}_{N1}\\ u_{N2}\\ i_L\end{array}\right)$

Work as Us1=-Ud, Us2=+Ud, state equation is:

$\left(\begin{array}{c}{\stackrel{\&CenterDot;}{i}}_{N1}\\ {\stackrel{\&CenterDot;}{i}}_{N2}\\ {\stackrel{\&CenterDot;}{u}}_d\\ {\stackrel{\&CenterDot;}{i}}_2\\ {\stackrel{\&CenterDot;}{u}}_2\end{array}\right)=\left(\begin{array}{ccccc}-{\mathrm{<figure-callout\; id="1"\; label="R\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">R</figure-callout>}}_N/{\mathrm{<figure-callout\; id="1"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& 1/{\mathrm{<figure-callout\; id="1"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& 0\\ 0& -{\mathrm{<figure-callout\; id="2"\; label="R\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">R</figure-callout>}}_N/L_{N2}& -1/{\mathrm{<figure-callout\; id="2"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& 0\\ -1/{\mathrm{<figure-callout\; id="1"\; label="C\; d"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">C</figure-callout>}}_d& 1/C_d& 0& -1/{\mathrm{<figure-callout\; id="0"\; label="C\; d"\; filenames="HDA0000036799760000031.png"\; state="\{\{state\}\}">C</figure-callout>}}_d& 0\\ 0& 0& 1/{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_2& 0& -1/{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_2\\ 0& 0& 0& 1/{\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">C</figure-callout>}}_2& 0\end{array}\right)\left(\begin{array}{c}{i}_{N1}\\ i_{N2}\\ u_d\\ i_2\\ u_2\end{array}\right)+\left(\begin{array}{ccc}1/{\mathrm{<figure-callout\; id="1"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& 0\\ 0& 1/{\mathrm{<figure-callout\; id="2"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0\\ 0& 0& -1/{\mathrm{<figure-callout\; id="0"\; label="C\; d"\; filenames="HDA0000036799760000031.png"\; state="\{\{state\}\}">C</figure-callout>}}_d\\ 0& 0& 0\\ 0& 0& 0\end{array}\right)\left(\begin{array}{c}{u}_{N1}\\ u_{N2}\\ i_L\end{array}\right)$

Work as Us1=0, Us2=+Ud, state equation is:

$\left(\begin{array}{c}{\stackrel{\&CenterDot;}{i}}_{N1}\\ {\stackrel{\&CenterDot;}{i}}_{N2}\\ {\stackrel{\&CenterDot;}{u}}_d\\ {\stackrel{\&CenterDot;}{i}}_2\\ {\stackrel{\&CenterDot;}{u}}_2\end{array}\right)=\left(\begin{array}{ccccc}-{\mathrm{<figure-callout\; id="1"\; label="R\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">R</figure-callout>}}_N/{\mathrm{<figure-callout\; id="1"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& 0& 0& 0\\ 0& -{\mathrm{<figure-callout\; id="2"\; label="R\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">R</figure-callout>}}_N/L_{N2}& -1/{\mathrm{<figure-callout\; id="2"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& 0\\ 0& 1/C_d& 0& -1/{\mathrm{<figure-callout\; id="0"\; label="C\; d"\; filenames="HDA0000036799760000031.png"\; state="\{\{state\}\}">C</figure-callout>}}_d& 0\\ 0& 0& 1/{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_2& 0& -1/{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_2\\ 0& 0& 0& 1/{\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">C</figure-callout>}}_2& 0\end{array}\right)\left(\begin{array}{c}{i}_{N1}\\ i_{N2}\\ u_d\\ i_2\\ u_2\end{array}\right)+\left(\begin{array}{ccc}1/{\mathrm{<figure-callout\; id="1"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& 0\\ 0& 1/{\mathrm{<figure-callout\; id="2"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0\\ 0& 0& -1/{\mathrm{<figure-callout\; id="0"\; label="C\; d"\; filenames="HDA0000036799760000031.png"\; state="\{\{state\}\}">C</figure-callout>}}_d\\ 0& 0& 0\\ 0& 0& 0\end{array}\right)\left(\begin{array}{c}{u}_{N1}\\ u_{N2}\\ i_L\end{array}\right)$

Work as Us1=+Ud, Us2=0, state equation is:

$\left(\begin{array}{c}{\stackrel{\&CenterDot;}{i}}_{N1}\\ {\stackrel{\&CenterDot;}{i}}_{N2}\\ {\stackrel{\&CenterDot;}{u}}_d\\ {\stackrel{\&CenterDot;}{i}}_2\\ {\stackrel{\&CenterDot;}{u}}_2\end{array}\right)=\left(\begin{array}{ccccc}-{\mathrm{<figure-callout\; id="1"\; label="R\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">R</figure-callout>}}_N/{\mathrm{<figure-callout\; id="1"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& -1/{\mathrm{<figure-callout\; id="1"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& 0\\ 0& -R_{\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">N</figure-callout>}2}/{\mathrm{<figure-callout\; id="2"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& 0& 0\\ 1/{\mathrm{<figure-callout\; id="0"\; label="C\; d"\; filenames="HDA0000036799760000031.png"\; state="\{\{state\}\}">C</figure-callout>}}_d& 0& 0& -1/{\mathrm{<figure-callout\; id="0"\; label="C\; d"\; filenames="HDA0000036799760000031.png"\; state="\{\{state\}\}">C</figure-callout>}}_d& 0\\ 0& 0& 1/{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_2& 0& -1/{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_2\\ 0& 0& 0& 1/{\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">C</figure-callout>}}_2& 0\end{array}\right)\left(\begin{array}{c}{i}_{N1}\\ i_{N2}\\ u_d\\ i_2\\ u_2\end{array}\right)+\left(\begin{array}{ccc}1/{\mathrm{<figure-callout\; id="1"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& 0\\ 0& 1/{\mathrm{<figure-callout\; id="2"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0\\ 0& 0& -1/{\mathrm{<figure-callout\; id="0"\; label="C\; d"\; filenames="HDA0000036799760000031.png"\; state="\{\{state\}\}">C</figure-callout>}}_d\\ 0& 0& 0\\ 0& 0& 0\end{array}\right)\left(\begin{array}{c}{u}_{N1}\\ u_{N2}\\ i_L\end{array}\right)$

Work as Us1=-Ud, Us2=0, state equation is:

$\left(\begin{array}{c}{\stackrel{\&CenterDot;}{i}}_{N1}\\ {\stackrel{\&CenterDot;}{i}}_{N2}\\ {\stackrel{\&CenterDot;}{u}}_d\\ {\stackrel{\&CenterDot;}{i}}_2\\ {\stackrel{\&CenterDot;}{u}}_2\end{array}\right)=\left(\begin{array}{ccccc}-{\mathrm{<figure-callout\; id="1"\; label="R\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">R</figure-callout>}}_N/{\mathrm{<figure-callout\; id="1"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& 1/{\mathrm{<figure-callout\; id="1"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& 0\\ 0& -{\mathrm{<figure-callout\; id="2"\; label="R\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">R</figure-callout>}}_N/{\mathrm{<figure-callout\; id="2"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& 0& 0\\ -1/{\mathrm{<figure-callout\; id="0"\; label="C\; d"\; filenames="HDA0000036799760000031.png"\; state="\{\{state\}\}">C</figure-callout>}}_d& 0& 0& -1/{\mathrm{<figure-callout\; id="0"\; label="C\; d"\; filenames="HDA0000036799760000031.png"\; state="\{\{state\}\}">C</figure-callout>}}_d& 0\\ 0& 0& 1/{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_2& 0& -1/{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_2\\ 0& 0& 0& 1/{\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">C</figure-callout>}}_2& 0\end{array}\right)\left(\begin{array}{c}{i}_{N1}\\ i_{N2}\\ u_d\\ i_2\\ u_2\end{array}\right)+\left(\begin{array}{ccc}1/{\mathrm{<figure-callout\; id="1"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& 0\\ 0& 1/{\mathrm{<figure-callout\; id="2"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0\\ 0& 0& -1/{\mathrm{<figure-callout\; id="0"\; label="C\; d"\; filenames="HDA0000036799760000031.png"\; state="\{\{state\}\}">C</figure-callout>}}_d\\ 0& 0& 0\\ 0& 0& 0\end{array}\right)\left(\begin{array}{c}{u}_{N1}\\ u_{N2}\\ i_L\end{array}\right)$

Work as Us1=0, Us2=-Ud, state equation is:

$\left(\begin{array}{c}{\stackrel{\&CenterDot;}{i}}_{N1}\\ {\stackrel{\&CenterDot;}{i}}_{N2}\\ {\stackrel{\&CenterDot;}{u}}_d\\ {\stackrel{\&CenterDot;}{i}}_2\\ {\stackrel{\&CenterDot;}{u}}_2\end{array}\right)=\left(\begin{array}{ccccc}-{\mathrm{<figure-callout\; id="1"\; label="R\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">R</figure-callout>}}_N/{\mathrm{<figure-callout\; id="1"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& 0& 0& 0\\ 0& -{\mathrm{<figure-callout\; id="2"\; label="R\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">R</figure-callout>}}_N/{\mathrm{<figure-callout\; id="2"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 1/{\mathrm{<figure-callout\; id="2"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& 0\\ 0& -1/C_d& 0& -1/{\mathrm{<figure-callout\; id="0"\; label="C\; d"\; filenames="HDA0000036799760000031.png"\; state="\{\{state\}\}">C</figure-callout>}}_d& 0\\ 0& 0& 1/{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_2& 0& -1/{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_2\\ 0& 0& 0& 1/{\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">C</figure-callout>}}_2& 0\end{array}\right)\left(\begin{array}{c}{i}_{N1}\\ i_{N2}\\ u_d\\ i_2\\ u_2\end{array}\right)+\left(\begin{array}{ccc}1/{\mathrm{<figure-callout\; id="1"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& 0\\ 0& 1/{\mathrm{<figure-callout\; id="2"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0\\ 0& 0& -1/{\mathrm{<figure-callout\; id="0"\; label="C\; d"\; filenames="HDA0000036799760000031.png"\; state="\{\{state\}\}">C</figure-callout>}}_d\\ 0& 0& 0\\ 0& 0& 0\end{array}\right)\left(\begin{array}{c}{u}_{N1}\\ u_{N2}\\ i_L\end{array}\right)$

Preferably, adopting the adams of the dual four quadrant convertor realistic model of Simulink module construction to resolve module is specially;

Adopt the implicit expression adms formula of four step quadravalences:

$x_{n+1}=x_n+\frac{h}{24}(55f_{n+1}-59f_n+37f_{n-1}-9f_{n-2})$ Formula 11

Because exist algebraic loop can not be applied to real-time simulation in this algorithm, therefore need further conversion.According to

f _N+1=Ax _N+1+ BU _N+1, formula 12

Bring formula 11 into, can get

$x_{n+1}-\frac{h}{24}55{\mathrm{Ax}}_{n+1}=x_n+\frac{h}{24}(55{\mathrm{BU}}_{n+1}-59f_n+37f_{n-1}-9f_{n-2})$ Formula 13

Abbreviation is

$x_{n+1}={(I-\frac{h}{24}55A)}^{-1}(x_n+\frac{h}{24}(55{\mathrm{BU}}_{n+1}-59f_n+37f_{n-1}-9f_{n-2}))$ Formula 14

Utilize formula 14 to make up adams and resolve module.

Compared with prior art, the present invention has the following advantages:

The present invention is according to the different conducting situations of on-off element, and is positive and negative in conjunction with electric current, judges the affiliated situation of state equation, obtains the mathematical model of substance FOUR-QUADRANT CONVERTER SYSTEM, built the realistic model of this model by the Simulink module.This modeling method principle is directly perceived, easy to understand.Use the Simulink module to build, performing step is simple, and calculated amount is little in real time, helps the real-time of emulation.After building the realistic model of FOUR-QUADRANT CONVERTER SYSTEM state equation, convergence when considering the zero pulse state, adopt the adms method to find the solution the differential equation of substance four quadrant convertor model, utilize the adms method to resolve, emulation is more accurate, convergence when having guaranteed zero pulse fast, and effectively.

Description of drawings

In order to be illustrated more clearly in the technical scheme in the embodiment of the invention, to do to introduce simply to the accompanying drawing of required use among prior art and the embodiment below, apparently, accompanying drawing in describing below only is some embodiments of the present invention, for those of ordinary skills, under the prerequisite of not paying creative work, can also obtain other accompanying drawing according to these accompanying drawings.

Fig. 1 is the four quadrant convertor structural representation;

The dual four quadrant convertor structural drawing that Fig. 2 builds for existing SimPowerSystem module;

The dual four quadrant convertor structural drawing that Fig. 3 writes for S-Function;

Fig. 4 is a substance four quadrant convertor emulation mode process flow diagram of the present invention;

Fig. 5 is the simulink block diagram of substance four quadrant convertor of the present invention;

Fig. 6 is a state equation judge module structural representation;

Fig. 7 judges the sub modular structure synoptic diagram for electric current;

Fig. 8 is logic determines and chooser modular structure synoptic diagram;

Fig. 9 is a logic determines sub-module structural representation;

Figure 10 adams resolves the modular structure synoptic diagram;

Figure 11 adams resolves module concrete structure synoptic diagram.

Embodiment

For above-mentioned purpose of the present invention, feature and advantage can be become apparent more, the present invention is further detailed explanation below in conjunction with the drawings and specific embodiments.

The present invention sets up the mathematical model of dual FOUR-QUADRANT CONVERTER SYSTEM according to different conducting situations, the electric current of the converter switches element parameter that inserts situation selection mode equation such as positive and negative, uses the Simulink model to build the emulation that realizes this mathematical model.Convergence when considering the zero pulse state adopts the adms method to find the solution the differential equation of dual four quadrant convertor model, and this calculation method can effectively solve the problem of dispersing, and has the characteristics of high stability, high real-time, high accuracy.

Referring to Fig. 4, the dual four quadrant convertor emulation mode of the present invention flow process is shown, specifically may further comprise the steps.

Step S401, according to the different conducting states of each rectifier cell in the four quadrant convertor, make up corresponding state equation.

Because the rectifier cell under the pwm signal control has different conducting states, corresponding converter system has different main circuit topological structures.Therefore, at first determine the corresponding relation of pwm control signal, current on line side iN and main circuit topological structure, set up the mathematical model of each main circuit structure system then, and then determine the state equation of various pwm control signal correspondences.

Table 1 exemplifies out Ud and inserts Us respectively ₁And Us ₂Situation

According to shown in the table 1, represent that with value 1 on-off element is open-minded, value 0 expression on-off element turn-offs.Further, represent on-off element T11 and T12 switch situation with A1 respectively, because two on-off elements of a brachium pontis can not be open-minded simultaneously, so, make A1=T11-T12, the possible value of A1 is 1,0 and-1, represents that respectively T11 opens with T12 shutoff, T11 shutoff and T12 turn-offs, T11 turn-offs and T12 is open-minded.

Represent on-off element T13 and T14 switch situation with B1, make B1=T13-T14.The possible value of B1 is 1,0 and-1, represents that respectively T13 opens with T14 shutoff, T13 shutoff and T14 turn-offs, T13 turn-offs and T14 is open-minded.

Represent on-off element T21 and T22 switch situation with A2, because two on-off elements of a brachium pontis can not be open-minded simultaneously, so, make A2=T21-T22, the possible value of A1 is 1,0 and-1, represents that respectively T21 opens with T22 shutoff, T21 shutoff and T22 turn-offs, T21 turn-offs and T22 is open-minded.

Represent on-off element T23 and T24 switch situation with B2, make B2=T23-T24.The possible value of B2 is 1,0 and-1, represents that respectively T23 opens with T24 shutoff, T23 shutoff and T24 turn-offs, T23 turn-offs and T24 is open-minded.

System state space under the various pwm signal controls is described as:

(1) works as Us1=Us2=+Ud.

(a)A1＝1，B1＝-1，

Or A1=0, B1=0 and satisfy iN1＞=0,

Or A1=1, B1=0 and satisfy iN1＞=0,

Or A1=0, B1=-1 and satisfy iN1＞=0,

(b)A2＝1，B2＝-1

Or A2=0, B2=0 and satisfy iN2＞=0,

Or A2=1, B2=0 and satisfy iN2＞=0,

Or A2=0, B2=-1 and satisfy iN2＞=0.

When as (a) and (b) setting up simultaneously, state equation below being fit to:

$\left(\begin{array}{c}{\stackrel{\&CenterDot;}{i}}_{N1}\\ {\stackrel{\&CenterDot;}{i}}_{N2}\\ {\stackrel{\&CenterDot;}{u}}_d\\ {\stackrel{\&CenterDot;}{i}}_2\\ {\stackrel{\&CenterDot;}{u}}_2\end{array}\right)=\left(\begin{array}{ccccc}-{\mathrm{<figure-callout\; id="1"\; label="R\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">R</figure-callout>}}_N/{\mathrm{<figure-callout\; id="1"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& -1/{\mathrm{<figure-callout\; id="1"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& 0\\ 0& -{\mathrm{<figure-callout\; id="2"\; label="R\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">R</figure-callout>}}_N/L_{N2}& -1/{\mathrm{<figure-callout\; id="2"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& 0\\ 1/{\mathrm{<figure-callout\; id="1"\; label="C\; d"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">C</figure-callout>}}_d& 1/C_d& 0& -1/{\mathrm{<figure-callout\; id="0"\; label="C\; d"\; filenames="HDA0000036799760000031.png"\; state="\{\{state\}\}">C</figure-callout>}}_d& 0\\ 0& 0& 1/{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_2& 0& -1/{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_2\\ 0& 0& 0& 1/{\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">C</figure-callout>}}_2& 0\end{array}\right)\left(\begin{array}{c}{i}_{N1}\\ i_{N2}\\ u_d\\ i_2\\ {\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">u</figure-callout>}}_2\end{array}\right)+\left(\begin{array}{ccc}1/{\mathrm{<figure-callout\; id="1"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& 0\\ 0& 1/{\mathrm{<figure-callout\; id="2"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0\\ 0& 0& -1/{\mathrm{<figure-callout\; id="0"\; label="C\; d"\; filenames="HDA0000036799760000031.png"\; state="\{\{state\}\}">C</figure-callout>}}_d\\ 0& 0& 0\\ 0& 0& 0\end{array}\right)\left(\begin{array}{c}{u}_{N1}\\ u_{N2}\\ {\mathrm{<figure-callout\; id="1"\; label="i\; L\; Formula"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">i</figure-callout>}}_L& \\ \end{array},\right)$ Formula 1

(2) work as Us1=Us2=-Ud.

(a)A1＝-1，B1＝1，

Or A1=0, B1=0 and satisfy iN1＜0,

Or A1=-1, B1=0 and satisfy iN1＜=0,

Or A1=0, B1=1 and satisfy iN1＜=0,

(b)A2＝-1，B2＝1

Or A2=0, B2=0 and satisfy iN2＜=0,

Or A2=-1, B2=0 and satisfy iN2＜=0,

Or A2=0, B2=1 and satisfy iN2＜=0,

When as (a) and (b) setting up simultaneously, state equation below being fit to:

$\left(\begin{array}{c}{\stackrel{\&CenterDot;}{i}}_{N1}\\ {\stackrel{\&CenterDot;}{i}}_{N2}\\ {\stackrel{\&CenterDot;}{u}}_d\\ {\stackrel{\&CenterDot;}{i}}_2\\ {\stackrel{\&CenterDot;}{u}}_2\end{array}\right)=\left(\begin{array}{ccccc}-{\mathrm{<figure-callout\; id="1"\; label="R\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">R</figure-callout>}}_N/{\mathrm{<figure-callout\; id="1"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& /{\mathrm{<figure-callout\; id="1"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& 0\\ 0& -{\mathrm{<figure-callout\; id="2"\; label="R\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">R</figure-callout>}}_N/{\mathrm{<figure-callout\; id="2"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 1/{\mathrm{<figure-callout\; id="2"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& 0\\ -1/C_d& -1/C_d& 0& -1/{\mathrm{<figure-callout\; id="0"\; label="C\; d"\; filenames="HDA0000036799760000031.png"\; state="\{\{state\}\}">C</figure-callout>}}_d& 0\\ 0& 0& 1/{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_2& 0& -1/{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_2\\ 0& 0& 0& 1/{\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">C</figure-callout>}}_2& 0\end{array}\right)\left(\begin{array}{c}{i}_{N1}\\ i_{N2}\\ u_d\\ i_2\\ {\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">u</figure-callout>}}_2\end{array}\right)+\left(\begin{array}{ccc}1/{\mathrm{<figure-callout\; id="1"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& 0\\ 0& 1/{\mathrm{<figure-callout\; id="2"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0\\ 0& 0& -1/{\mathrm{<figure-callout\; id="0"\; label="C\; d"\; filenames="HDA0000036799760000031.png"\; state="\{\{state\}\}">C</figure-callout>}}_d\\ 0& 0& 0\\ 0& 0& 0\end{array}\right)\left(\begin{array}{c}{u}_{N1}\\ u_{N2}\\ {\mathrm{<figure-callout\; id="2"\; label="i\; L\; Formula"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">i</figure-callout>}}_L& \\ \end{array},\right)$ Formula 2

(3) work as Us1=0, Us2=0.

(a)A1＝-1，B1＝-1，

Or A1=1, B1=1,

Or A1=-1, B1=0 and satisfy iN1＞0,

Or A1=0, B1=1 and satisfy iN1＞0,

Or A1=1, B1=0 and satisfy iN1＜0,

Or A1=0, B1=-1 and satisfy iN1＜0,

(b)A2＝-1，B2＝-1

Or A2=1, B2=1

Or A2=-1, B2=0 and satisfy iN2＞0

Or A2=0, B2=1 and satisfy iN2＞0

Or A2=1, B2=0 and satisfy iN2＜0

Or A2=0, B2=-1 and satisfy iN2＜0

When as (a) and (b) setting up simultaneously, state equation below being fit to:

$\left(\begin{array}{c}{\stackrel{\&CenterDot;}{i}}_{N1}\\ {\stackrel{\&CenterDot;}{i}}_{N2}\\ {\stackrel{\&CenterDot;}{u}}_d\\ {\stackrel{\&CenterDot;}{i}}_2\\ {\stackrel{\&CenterDot;}{u}}_2\end{array}\right)=\left(\begin{array}{ccccc}-{\mathrm{<figure-callout\; id="1"\; label="R\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">R</figure-callout>}}_N/{\mathrm{<figure-callout\; id="1"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& 0& 0& 0\\ 0& -{\mathrm{<figure-callout\; id="2"\; label="R\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">R</figure-callout>}}_N/{\mathrm{<figure-callout\; id="2"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& 0& 0\\ 0& 0& 0& -1/{\mathrm{<figure-callout\; id="0"\; label="C\; d"\; filenames="HDA0000036799760000031.png"\; state="\{\{state\}\}">C</figure-callout>}}_d& 0\\ 0& 0& 1/{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_2& 0& -1/{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_2\\ 0& 0& 0& 1/{\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">C</figure-callout>}}_2& 0\end{array}\right)\left(\begin{array}{c}{i}_{N1}\\ i_{N2}\\ u_d\\ i_2\\ {\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">u</figure-callout>}}_2\end{array}\right)+\left(\begin{array}{ccc}1/{\mathrm{<figure-callout\; id="1"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& 0\\ 0& 1/{\mathrm{<figure-callout\; id="2"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0\\ 0& 0& -1/{\mathrm{<figure-callout\; id="0"\; label="C\; d"\; filenames="HDA0000036799760000031.png"\; state="\{\{state\}\}">C</figure-callout>}}_d\\ 0& 0& 0\\ 0& 0& 0\end{array}\right)\left(\begin{array}{c}{u}_{N1}\\ u_{N2}\\ {\mathrm{<figure-callout\; id="3"\; label="i\; L\; Formula"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">i</figure-callout>}}_L& \\ \end{array},\right)$ Formula 3

(4) work as Us1=+Ud, Us2=-Ud.

(a)A1＝1，B1＝-1，

Or A1=0, B1=0 and satisfy iN1＞=0,

Or A1=1, B1=0 and satisfy iN1＞=0,

Or A1=0, B1=-1 and satisfy iN1＜=0,

(b)A2＝-1，B2＝1

Or A2=0, B2=0 and satisfy iN2＜0

Or A2=-1, B2=0 and satisfy iN2＜=0

Or A2=0, B2=1 and satisfy iN2＜=0

When as (a) and (b) setting up simultaneously, state equation below being fit to:

$\left(\begin{array}{c}{\stackrel{\&CenterDot;}{i}}_{N1}\\ {\stackrel{\&CenterDot;}{i}}_{N2}\\ {\stackrel{\&CenterDot;}{u}}_d\\ {\stackrel{\&CenterDot;}{i}}_2\\ {\stackrel{\&CenterDot;}{u}}_2\end{array}\right)=\left(\begin{array}{ccccc}-{\mathrm{<figure-callout\; id="1"\; label="R\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">R</figure-callout>}}_N/{\mathrm{<figure-callout\; id="1"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& -1/{\mathrm{<figure-callout\; id="1"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& 0\\ 0& -{\mathrm{<figure-callout\; id="2"\; label="R\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">R</figure-callout>}}_N/{\mathrm{<figure-callout\; id="2"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 1/{\mathrm{<figure-callout\; id="2"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& 0\\ 1/C_d& -1/C_d& 0& -1/{\mathrm{<figure-callout\; id="0"\; label="C\; d"\; filenames="HDA0000036799760000031.png"\; state="\{\{state\}\}">C</figure-callout>}}_d& 0\\ 0& 0& 1/{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_2& 0& -1/{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_2\\ 0& 0& 0& 1/{\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">C</figure-callout>}}_2& 0\end{array}\right)\left(\begin{array}{c}{i}_{N1}\\ i_{N2}\\ u_d\\ i_2\\ {\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">u</figure-callout>}}_2\end{array}\right)+\left(\begin{array}{ccc}1/{\mathrm{<figure-callout\; id="1"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& 0\\ 0& 1/{\mathrm{<figure-callout\; id="2"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0\\ 0& 0& -1/{\mathrm{<figure-callout\; id="0"\; label="C\; d"\; filenames="HDA0000036799760000031.png"\; state="\{\{state\}\}">C</figure-callout>}}_d\\ 0& 0& 0\\ 0& 0& 0\end{array}\right)\left(\begin{array}{c}{u}_{N1}\\ u_{N2}\\ {\mathrm{<figure-callout\; id="4"\; label="i\; L\; Formula"\; filenames="HDA0000036799760000032.png,HDA0000036799760000051.png"\; state="\{\{state\}\}">i</figure-callout>}}_L& \\ \end{array},\right)$ Formula 4

(5) work as Us1=-Ud, Us2=+Ud.

(a)A1＝-1，B1＝1，

Or A1=0, B1=0 and satisfy iN1＜=0,

Or A1=-1, B1=0 and satisfy iN1＜=0,

Or A1=0, B1=1 and satisfy iN1＜=0,

(b)A2＝1，B2＝-1

Or A2=0, B2=0 and satisfy iN2＞=0,

Or A2=1, B2=0 and satisfy iN2＞=0,

Or A2=0, B2=-1 and satisfy iN2＞=0

When as (a) and (b) setting up simultaneously, state equation below being fit to:

$\left(\begin{array}{c}{\stackrel{\&CenterDot;}{i}}_{N1}\\ {\stackrel{\&CenterDot;}{i}}_{N2}\\ {\stackrel{\&CenterDot;}{u}}_d\\ {\stackrel{\&CenterDot;}{i}}_2\\ {\stackrel{\&CenterDot;}{u}}_2\end{array}\right)=\left(\begin{array}{ccccc}-{\mathrm{<figure-callout\; id="1"\; label="R\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">R</figure-callout>}}_N/{\mathrm{<figure-callout\; id="1"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& 1/{\mathrm{<figure-callout\; id="1"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& 0\\ 0& -{\mathrm{<figure-callout\; id="2"\; label="R\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">R</figure-callout>}}_N/L_{N2}& -1/{\mathrm{<figure-callout\; id="2"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& 0\\ -1/{\mathrm{<figure-callout\; id="1"\; label="C\; d"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">C</figure-callout>}}_d& 1/C_d& 0& -1/{\mathrm{<figure-callout\; id="0"\; label="C\; d"\; filenames="HDA0000036799760000031.png"\; state="\{\{state\}\}">C</figure-callout>}}_d& 0\\ 0& 0& 1/{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_2& 0& -1/{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_2\\ 0& 0& 0& 1/{\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">C</figure-callout>}}_2& 0\end{array}\right)\left(\begin{array}{c}{i}_{N1}\\ i_{N2}\\ u_d\\ i_2\\ {\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">u</figure-callout>}}_2\end{array}\right)+\left(\begin{array}{ccc}1/{\mathrm{<figure-callout\; id="1"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& 0\\ 0& 1/{\mathrm{<figure-callout\; id="2"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0\\ 0& 0& -1/{\mathrm{<figure-callout\; id="0"\; label="C\; d"\; filenames="HDA0000036799760000031.png"\; state="\{\{state\}\}">C</figure-callout>}}_d\\ 0& 0& 0\\ 0& 0& 0\end{array}\right)\left(\begin{array}{c}{u}_{N1}\\ u_{N2}\\ {\mathrm{<figure-callout\; id="5"\; label="i\; L\; Formula"\; filenames="HDA0000036799760000051.png"\; state="\{\{state\}\}">i</figure-callout>}}_L& \\ \end{array},\right)$ Formula 5

(6) work as Us1=0, Us2=+Ud.

(a)A1＝1，B1＝1，

Or A1=-1, B1=-1,

Or A1=0, B1=1 and satisfy iN1＞0,

Or A1=-1, B1=0 and satisfy iN1＞0

Or A1=1, B1=0 and satisfy iN1＜0,

Or A1=0, B1=-1 and satisfy iN1＜0

(b)A2＝1，B2＝-1，

Or A2=0, B2=0 and satisfy iN2＞=0,

Or A2=1, B2=0 and satisfy iN2＞=0,

Or A2=0, B2=-1 and satisfy iN2＞=0

When as (a) and (b) setting up simultaneously, state equation below being fit to:

$\left(\begin{array}{c}{\stackrel{\&CenterDot;}{i}}_{N1}\\ {\stackrel{\&CenterDot;}{i}}_{N2}\\ {\stackrel{\&CenterDot;}{u}}_d\\ {\stackrel{\&CenterDot;}{i}}_2\\ {\stackrel{\&CenterDot;}{u}}_2\end{array}\right)=\left(\begin{array}{ccccc}-{\mathrm{<figure-callout\; id="1"\; label="R\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">R</figure-callout>}}_N/{\mathrm{<figure-callout\; id="1"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& 0& 0& 0\\ 0& -{\mathrm{<figure-callout\; id="2"\; label="R\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">R</figure-callout>}}_N/L_{N2}& -1/{\mathrm{<figure-callout\; id="2"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& 0\\ 0& 1/C_d& 0& -1/{\mathrm{<figure-callout\; id="0"\; label="C\; d"\; filenames="HDA0000036799760000031.png"\; state="\{\{state\}\}">C</figure-callout>}}_d& 0\\ 0& 0& 1/{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_2& 0& -1/{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_2\\ 0& 0& 0& 1/{\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">C</figure-callout>}}_2& 0\end{array}\right)\left(\begin{array}{c}{i}_{N1}\\ i_{N2}\\ u_d\\ i_2\\ {\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">u</figure-callout>}}_2\end{array}\right)+\left(\begin{array}{ccc}1/{\mathrm{<figure-callout\; id="1"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& 0\\ 0& 1/{\mathrm{<figure-callout\; id="2"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0\\ 0& 0& -1/{\mathrm{<figure-callout\; id="0"\; label="C\; d"\; filenames="HDA0000036799760000031.png"\; state="\{\{state\}\}">C</figure-callout>}}_d\\ 0& 0& 0\\ 0& 0& 0\end{array}\right)\left(\begin{array}{c}{u}_{N1}\\ u_{N2}\\ i_L\end{array}\right)$ Formula 6

(7) work as Us1=+Ud, Us2=0.

(a)A1＝1，B1＝-1，

Or A1=0, B1=0 and satisfy iN1＞=0,

Or A1=1, B1=0 and satisfy iN1＞=0,

Or A1=0, B1=-1 and satisfy iN1＞=0

(b)A2＝1，B2＝1，

Or A2=-1, B2=-1,

Or A2=0, B2=1 and satisfy iN2＞0,

Or A2=-1, B2=0 and satisfy iN2＞0

Or A2=1, B2=0 and satisfy iN2＜0,

Or A2=0, B2=-1 and satisfy iN2＜0 or

When as (a) and (b) setting up simultaneously, state equation below being fit to:

$\left(\begin{array}{c}{\stackrel{\&CenterDot;}{i}}_{N1}\\ {\stackrel{\&CenterDot;}{i}}_{N2}\\ {\stackrel{\&CenterDot;}{u}}_d\\ {\stackrel{\&CenterDot;}{i}}_2\\ {\stackrel{\&CenterDot;}{u}}_2\end{array}\right)=\left(\begin{array}{ccccc}-{\mathrm{<figure-callout\; id="1"\; label="R\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">R</figure-callout>}}_N/{\mathrm{<figure-callout\; id="1"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& -1/{\mathrm{<figure-callout\; id="1"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& 0\\ 0& -{\mathrm{<figure-callout\; id="2"\; label="R\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">R</figure-callout>}}_N/{\mathrm{<figure-callout\; id="2"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& 0& 0\\ 1/{\mathrm{<figure-callout\; id="0"\; label="C\; d"\; filenames="HDA0000036799760000031.png"\; state="\{\{state\}\}">C</figure-callout>}}_d& 0& 0& -1/{\mathrm{<figure-callout\; id="0"\; label="C\; d"\; filenames="HDA0000036799760000031.png"\; state="\{\{state\}\}">C</figure-callout>}}_d& 0\\ 0& 0& 1/{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_2& 0& -1/{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_2\\ 0& 0& 0& 1/{\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">C</figure-callout>}}_2& 0\end{array}\right)\left(\begin{array}{c}{i}_{N1}\\ i_{N2}\\ u_d\\ i_2\\ {\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">u</figure-callout>}}_2\end{array}\right)+\left(\begin{array}{ccc}1/{\mathrm{<figure-callout\; id="1"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& 0\\ 0& 1/{\mathrm{<figure-callout\; id="2"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0\\ 0& 0& -1/{\mathrm{<figure-callout\; id="0"\; label="C\; d"\; filenames="HDA0000036799760000031.png"\; state="\{\{state\}\}">C</figure-callout>}}_d\\ 0& 0& 0\\ 0& 0& 0\end{array}\right)\left(\begin{array}{c}{u}_{N1}\\ u_{N2}\\ i_L\end{array}\right)$ Formula 7

(8) work as Us1=-Ud, Us2=0.

(a)A1＝-1，B1＝1，

Or A1=0, B1=0 and satisfy iN1＜0,

Or A1=-1, B1=0 and satisfy iN1＜=0,

Or A1=0, B1=1 and satisfy iN1＜=0,

(b)A2＝1，B2＝1，

Or A2=-1, B2=-1,

Or A2=0, B2=1 and satisfy iN2＞0,

Or A2=-1, B2=0 and satisfy iN2＞0

Or A2=1, B2=0 and satisfy iN2＜0,

Or A2=0, B2=-1 and satisfy iN2＜0

When as (a) and (b) setting up simultaneously, state equation below being fit to:

$\left(\begin{array}{c}{\stackrel{\&CenterDot;}{i}}_{N1}\\ {\stackrel{\&CenterDot;}{i}}_{N2}\\ {\stackrel{\&CenterDot;}{u}}_d\\ {\stackrel{\&CenterDot;}{i}}_2\\ {\stackrel{\&CenterDot;}{u}}_2\end{array}\right)=\left(\begin{array}{ccccc}-{\mathrm{<figure-callout\; id="1"\; label="R\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">R</figure-callout>}}_N/{\mathrm{<figure-callout\; id="1"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& 1/{\mathrm{<figure-callout\; id="1"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& 0\\ 0& -{\mathrm{<figure-callout\; id="2"\; label="R\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">R</figure-callout>}}_N/{\mathrm{<figure-callout\; id="2"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& 0& 0\\ -1/{\mathrm{<figure-callout\; id="0"\; label="C\; d"\; filenames="HDA0000036799760000031.png"\; state="\{\{state\}\}">C</figure-callout>}}_d& 0& 0& -1/{\mathrm{<figure-callout\; id="0"\; label="C\; d"\; filenames="HDA0000036799760000031.png"\; state="\{\{state\}\}">C</figure-callout>}}_d& 0\\ 0& 0& 1/{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_2& 0& -1/{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_2\\ 0& 0& 0& 1/{\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">C</figure-callout>}}_2& 0\end{array}\right)\left(\begin{array}{c}{i}_{N1}\\ i_{N2}\\ u_d\\ i_2\\ {\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">u</figure-callout>}}_2\end{array}\right)+\left(\begin{array}{ccc}1/{\mathrm{<figure-callout\; id="1"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& 0\\ 0& 1/{\mathrm{<figure-callout\; id="2"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0\\ 0& 0& -1/{\mathrm{<figure-callout\; id="0"\; label="C\; d"\; filenames="HDA0000036799760000031.png"\; state="\{\{state\}\}">C</figure-callout>}}_d\\ 0& 0& 0\\ 0& 0& 0\end{array}\right)\left(\begin{array}{c}{u}_{N1}\\ u_{N2}\\ {\mathrm{<figure-callout\; id="8"\; label="i\; L\; Formula"\; filenames="HDA0000036799760000041.png,HDA0000036799760000051.png"\; state="\{\{state\}\}">i</figure-callout>}}_L& \\ \end{array},\right)$ Formula 8

(9) work as Us1=0, Us2=-Ud.

(a)A1＝1，B1＝1，

Or A1=-1, B1=-1,

Or A1=0, B1=1 and satisfy iN1＞0,

Or A1=-1, B1=0 and satisfy iN1＞0

Or A1=1, B1=0 and satisfy iN1＜0,

Or A1=0, B1=-1 and satisfy iN1＜0

(b)A2＝-1，B2＝1，

Or A2=0, B2=0 and satisfy iN2＜=0,

Or A2=-1, B2=0 and satisfy iN2＜=0,

Or A2=0, B2=1 and satisfy iN2＜=0,

When as (a) and (b) setting up simultaneously, state equation below being fit to:

$\left(\begin{array}{c}{\stackrel{\&CenterDot;}{i}}_{N1}\\ {\stackrel{\&CenterDot;}{i}}_{N2}\\ {\stackrel{\&CenterDot;}{u}}_d\\ {\stackrel{\&CenterDot;}{i}}_2\\ {\stackrel{\&CenterDot;}{u}}_2\end{array}\right)=\left(\begin{array}{ccccc}-{\mathrm{<figure-callout\; id="1"\; label="R\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">R</figure-callout>}}_N/{\mathrm{<figure-callout\; id="1"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& 0& 0& 0\\ 0& -{\mathrm{<figure-callout\; id="2"\; label="R\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">R</figure-callout>}}_N/{\mathrm{<figure-callout\; id="2"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 1/{\mathrm{<figure-callout\; id="2"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& 0\\ 0& -1/C_d& 0& -1/{\mathrm{<figure-callout\; id="0"\; label="C\; d"\; filenames="HDA0000036799760000031.png"\; state="\{\{state\}\}">C</figure-callout>}}_d& 0\\ 0& 0& 1/{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_2& 0& -1/{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_2\\ 0& 0& 0& 1/{\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">C</figure-callout>}}_2& 0\end{array}\right)\left(\begin{array}{c}{i}_{N1}\\ i_{N2}\\ u_d\\ i_2\\ {\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">u</figure-callout>}}_2\end{array}\right)+\left(\begin{array}{ccc}1/{\mathrm{<figure-callout\; id="1"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0& 0\\ 0& 1/{\mathrm{<figure-callout\; id="2"\; label="L\; N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_N& 0\\ 0& 0& -1/{\mathrm{<figure-callout\; id="0"\; label="C\; d"\; filenames="HDA0000036799760000031.png"\; state="\{\{state\}\}">C</figure-callout>}}_d\\ 0& 0& 0\\ 0& 0& 0\end{array}\right)\left(\begin{array}{c}{u}_{N1}\\ u_{N2}\\ {\mathrm{<figure-callout\; id="9"\; label="i\; L\; Formula"\; filenames="HDA0000036799760000032.png"\; state="\{\{state\}\}">i</figure-callout>}}_L& \\ \end{array},\right)$ Formula 9

The system state space output equation of situation (1)-(9):

$\left(\begin{array}{c}{u}_d\\ i_{N1}\\ i_{\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">N</figure-callout>}2}\end{array}\right)=\left(\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right)\left(\begin{array}{c}{u}_d\\ i_{N1}\\ i_{\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="HDA0000036799760000031.png,HDA0000036799760000032.png"\; state="\{\{state\}\}">N</figure-callout>}2}\end{array}\right)$ Formula 10

After obtaining state equation, the convergence when considering the rectifier input pulse entirely for zero condition adopts the adms method to find the solution the differential equation of dual four quadrant convertor model.

Step S402, make up dual four quadrant convertor realistic model according to state equation.

According to the mathematical model of dual FOUR-QUADRANT CONVERTER SYSTEM, make up the realistic model of dual FOUR-QUADRANT CONVERTER SYSTEM.Referring to Fig. 5, the simulink block diagram of the dual four quadrant convertor of the present invention is shown.This simulink block diagram comprises that mainly state equation judge module 41 and adams resolve module 42.Introducing each module below respectively constitutes and function.

At first introduce state equation judge module 41.

According to foregoing description, dual four quadrant convertor will have 9 kinds of different state equations under different pwm control signals, the situation that therefore needs to judge the conducting shutoff situation of dual power component and consider current on line side.Fig. 6 is state equation judge module 41 synoptic diagram, and input is the dual control signal of PWM, and dual electric current, is output as the matrix and the status signal of state equation.

State equation judge module 41 lower floors comprise two submodules, are respectively that control signal and electric current are judged submodule 411 (as Fig. 7) and logic determines and chooser module 412 (as Fig. 8).Judge that in control signal and electric current submodule 411 obtains the situation of control signal and electric current, the control signal situation mainly is meant to be defined A1, B1, A2, B2, the situation of electric current mainly is to judge it greater than minus situation, and the result who judges is delivered to logic determines and chooser module 412, and logic determines and chooser module 412 obtain state equation matrix and judge signal.Wherein, A1～A9 is 9 kinds of state equation matrix under the situation.

Referring to Fig. 9, be the logic determines submodule 4121 in logic determines and the chooser module 412, logic determines sub-module 4121 mainly is to judge that respectively control signal and electric current belong to any in three kinds of situations, and then, be used for judging and select the dual status signal that carries out logical operation acquisition judgement.

Introduce formation and function that adams resolves module 42 again.

After obtaining state equation, find the solution this differential equation group.Runge-Kutta method is the widely used numerical solution of finding the solution the differential equation of field of engineering technology, but when being applied to the state equation of this model, is at 0 o'clock at input pulse, and the result of calculation instability presents the trend of dispersing.Therefore, the convergence during in order to ensure zero condition adopts the Adms method to find the solution the differential equation of being set up.The Adms method is a kind of linear multi step solution at ordinary differential equation.The present invention sets up adams and resolves module 42, finds the solution the differential equation, as Figure 10.Be input as state equation matrix, judge signal and quantity of state, be output as the output of state equation.

Adopt the implicit expression adms formula of four step quadravalences:

$x_{n+1}=x_n+\frac{h}{24}(55f_{n+1}-59f_n+37f_{n-1}-9f_{n-2})$ Formula 11

Because exist algebraic loop can not be applied to real-time simulation in this algorithm, therefore need further conversion.According to

f _N+1=Ax _N+1+ BU _N+1, formula 12

Bring formula 11 into, can get

$x_{n+1}-\frac{h}{24}55{\mathrm{Ax}}_{n+1}=x_n+\frac{h}{24}(55{\mathrm{BU}}_{n+1}-59f_n+37f_{n-1}-9f_{n-2})$ Formula 13

Abbreviation is

$x_{n+1}={(I-\frac{h}{24}55A)}^{-1}(x_n+\frac{h}{24}(55{\mathrm{BU}}_{n+1}-59f_n+37f_{n-1}-9f_{n-2}))$ Formula 14

Go up according to this modular structure figure (as Figure 10) that analysis can get adms.

Go up according to this analysis and can get the concrete structure (as Figure 11) that adams resolves module 42.

Step S403, utilize dual four quadrant convertor realistic model to carry out simulation calculation.

The present invention is according to the different conducting situations of on-off element, and is positive and negative in conjunction with electric current, judges the affiliated situation of state equation, obtains the mathematical model of dual FOUR-QUADRANT CONVERTER SYSTEM, built the realistic model of this model by the Simulink module.This modeling method principle is directly perceived, easy to understand.Use the Simulink module to build, performing step is simple, and calculated amount is little in real time, helps the real-time of emulation.After building the realistic model of FOUR-QUADRANT CONVERTER SYSTEM state equation, convergence when considering the zero pulse state, adopt the adms method to find the solution the differential equation of dual four quadrant convertor model, utilize the adms method to resolve, emulation is more accurate, convergence when having guaranteed zero pulse fast, and effectively.

The above only is a preferred implementation of the present invention; should be understood that; for those skilled in the art; under the prerequisite that does not break away from the principle of the invention; can also make some improvements and modifications; also can above-mentioned embodiment make up, these technical schemes of improving, retouching and being combined to form also should be considered as protection scope of the present invention.

Claims (3)

1. dual four quadrant convertor emulation mode, described four quadrant convertor comprises current transformer and intermediate circuit, current transformer is made up of eight branch roads of parallel connection, the anode of the 11 on-off element (T11) connects output plus terminal in first branch road, negative electrode connects the anode that twelvemo is closed element (T12), and the negative electrode that twelvemo is closed element (T12) connects the output negative terminal; The negative electrode of the 11 diode (D11) connects output plus terminal in second branch road, and anode connects the negative electrode of the 12 diode (D12), and the anode of the 12 diode (D12) connects the output negative terminal; The anode of the 13 on-off element (T13) connects output plus terminal in the 3rd branch road, and negative electrode connects the anode of the 14 on-off element (T14), and the negative electrode of the 14 on-off element (T14) connects the output negative terminal; The negative electrode of the 13 diode (D13) connects output plus terminal in the 4th branch road, and anode connects the negative electrode of the 14 diode (D14), and the anode of the 14 diode (D14) connects the output negative terminal; The anode of the 21 on-off element (T21) connects output plus terminal in the 5th branch road, and negative electrode connects the anode that second twelvemo is closed element (T22), and the negative electrode that second twelvemo is closed element (T22) connects the output negative terminal; The negative electrode of the 21 diode (D21) connects output plus terminal in the 6th branch road, and anode connects the negative electrode of the 22 diode (D22), and the anode of the 22 diode (D22) connects the output negative terminal; The anode of the 23 on-off element (T23) connects output plus terminal in the 7th branch road, and negative electrode connects the anode of the 24 on-off element (T24), and the negative electrode of the 24 on-off element (T24) connects the output negative terminal; The negative electrode of the 23 diode (D23) connects output plus terminal in the 8th branch road, and anode connects the negative electrode of the 24 diode (D24), and the anode of the 24 diode (D24) connects the output negative terminal;

Transformer time limit circuit comprises the first AC power (U that is connected transformer time limit _N1), the first AC power (U _N1) the first inductance (L of an end through connecting _N1) and the first resistance (R _N1) after, be connected the common port that the 11 on-off element (T11) and twelvemo are closed element (T12), and the common port of the 11 diode (D11) and the 12 diode (D12); First AC power (the U _N1) other end is connected the common port of the 13 on-off element (T13) and the 14 on-off element (T14), and the common port of the 13 diode (D13) and the 14 diode (D14); Also comprise the second AC power (U that is connected transformer time limit _N2), AC power (U _N2) the second inductance (L of an end through connecting _N2) and the second resistance (R _N2) after, be connected the common port that the 21 on-off element (T21) and second twelvemo are closed element (T22), and the common port of the 21 diode (D21) and the 22 diode (D22); Second AC power (the U _N2) other end is connected the common port of the 23 on-off element (T23) and the 24 on-off element (T24), and the common port of the 23 diode (D23) and the 24 diode (D24);

Comprise the 3rd inductance (L that is connected on the positive and negative end of output in the intermediate circuit ₂) and the 3rd resistance (R ₂), and the first electric capacity (C that is connected with the positive and negative end of output _d); It is characterized in that this method comprises:

According to the different conducting states of each on-off element in the four quadrant convertor, make up corresponding state equation;

Adopt the Simulink module to build the state equation judge module of dual four quadrant convertor realistic model; Adopt the adams of the dual four quadrant convertor realistic model of Simulink module construction to resolve module;

Utilize dual four quadrant convertor realistic model to carry out simulation calculation.

2. the method for claim 1 is characterized in that, described state equation is specially:

Work as Us1=Us2=+Ud, state equation is:

$\left(\begin{array}{c}{\stackrel{\&CenterDot;}{i}}_{N1}\\ {\stackrel{\&CenterDot;}{i}}_{N2}\\ {\stackrel{\&CenterDot;}{u}}_d\\ {\stackrel{\&CenterDot;}{i}}_2\\ {\stackrel{\&CenterDot;}{u}}_2\end{array}\right)=\left(\begin{array}{ccccc}-R_{N1}/L_{N1}& 0& -1/L_{N1}& 0& 0\\ 0& -R_{N2}/L_{N2}& -1/L_{N2}& 0& 0\\ 1/C_d& 1/C_d& 0& -1/C_d& 0\\ 0& 0& 1/L_2& 0& -1/L_2\\ 0& 0& 0& 1/C_2& 0\end{array}\right)\left(\begin{array}{c}{i}_{N1}\\ i_{N2}\\ u_d\\ i_2\\ u_2\end{array}\right)+\left(\begin{array}{ccc}1/L_{N1}& 0& 0\\ 0& 1/L_{N2}& 0\\ 0& 0& -1/C_d\\ 0& 0& 0\\ 0& 0& 0\end{array}\right)\left(\begin{array}{c}{u}_{N1}\\ u_{N2}\\ i_L\end{array}\right)$

Work as Us1=Us2=-Ud, state equation is:

$\left(\begin{array}{c}{\stackrel{\&CenterDot;}{i}}_{N1}\\ {\stackrel{\&CenterDot;}{i}}_{N2}\\ {\stackrel{\&CenterDot;}{u}}_d\\ {\stackrel{\&CenterDot;}{i}}_2\\ {\stackrel{\&CenterDot;}{u}}_2\end{array}\right)=\left(\begin{array}{ccccc}-R_{N1}/L_{N1}& 0& 1/L_{N1}& 0& 0\\ 0& -R_{N2}/L_{N2}& 1/L_{N2}& 0& 0\\ -1/C_d& -1/C_d& 0& -1/C_d& 0\\ 0& 0& 1/L_2& 0& -1/L_2\\ 0& 0& 0& 1/C_2& 0\end{array}\right)\left(\begin{array}{c}{i}_{N1}\\ i_{N2}\\ u_d\\ i_2\\ u_2\end{array}\right)+\left(\begin{array}{ccc}1/L_{N1}& 0& 0\\ 0& 1/L_{N2}& 0\\ 0& 0& -1/C_d\\ 0& 0& 0\\ 0& 0& 0\end{array}\right)\left(\begin{array}{c}{u}_{N1}\\ u_{N2}\\ i_L\end{array}\right)$

Work as Us1=0, Us2=0, state equation is:

$\left(\begin{array}{c}{\stackrel{\&CenterDot;}{i}}_{N1}\\ {\stackrel{\&CenterDot;}{i}}_{N2}\\ {\stackrel{\&CenterDot;}{u}}_d\\ {\stackrel{\&CenterDot;}{i}}_2\\ {\stackrel{\&CenterDot;}{u}}_2\end{array}\right)=\left(\begin{array}{ccccc}-R_{N1}/L_{N1}& 0& 0& 0& 0\\ 0& -R_{N2}/L_{N2}& 0& 0& 0\\ 0& 0& 0& -1/C_d& 0\\ 0& 0& 1/L_2& 0& -1/L_2\\ 0& 0& 0& 1/C_2& 0\end{array}\right)\left(\begin{array}{c}{i}_{N1}\\ i_{N2}\\ u_d\\ i_2\\ u_2\end{array}\right)+\left(\begin{array}{ccc}1/L_{N1}& 0& 0\\ 0& 1/L_{N2}& 0\\ 0& 0& -1/C_d\\ 0& 0& 0\\ 0& 0& 0\end{array}\right)\left(\begin{array}{c}{u}_{N1}\\ u_{N2}\\ i_L\end{array}\right)$

Work as Us1=+Ud, Us2=-Ud, state equation is:

$\left(\begin{array}{c}{\stackrel{\&CenterDot;}{i}}_{N1}\\ {\stackrel{\&CenterDot;}{i}}_{N2}\\ {\stackrel{\&CenterDot;}{u}}_d\\ {\stackrel{\&CenterDot;}{i}}_2\\ {\stackrel{\&CenterDot;}{u}}_2\end{array}\right)=\left(\begin{array}{ccccc}-R_{N1}/L_{N1}& 0& -1/L_{N1}& 0& 0\\ 0& -R_{N2}/L_{N2}& 1/L_{N2}& 0& 0\\ 1/C_d& -1/C_d& 0& -1/C_d& 0\\ 0& 0& 1/L_2& 0& -1/L_2\\ 0& 0& 0& 1/C_2& 0\end{array}\right)\left(\begin{array}{c}{i}_{N1}\\ i_{N2}\\ u_d\\ i_2\\ u_2\end{array}\right)+\left(\begin{array}{ccc}1/L_{N1}& 0& 0\\ 0& 1/L_{N2}& 0\\ 0& 0& -1/C_d\\ 0& 0& 0\\ 0& 0& 0\end{array}\right)\left(\begin{array}{c}{u}_{N1}\\ u_{N2}\\ i_L\end{array}\right)$

Work as Us1=-Ud, Us2=+Ud, state equation is:

$\left(\begin{array}{c}{\stackrel{\&CenterDot;}{i}}_{N1}\\ {\stackrel{\&CenterDot;}{i}}_{N2}\\ {\stackrel{\&CenterDot;}{u}}_d\\ {\stackrel{\&CenterDot;}{i}}_2\\ {\stackrel{\&CenterDot;}{u}}_2\end{array}\right)=\left(\begin{array}{ccccc}-R_{N1}/L_{N1}& 0& 1/L_{N1}& 0& 0\\ 0& -R_{N2}/L_{N2}& -1/L_{N2}& 0& 0\\ -1/C_d& 1/C_d& 0& -1/C_d& 0\\ 0& 0& 1/L_2& 0& -1/L_2\\ 0& 0& 0& 1/C_2& 0\end{array}\right)\left(\begin{array}{c}{i}_{N1}\\ i_{N2}\\ u_d\\ i_2\\ u_2\end{array}\right)+\left(\begin{array}{ccc}1/L_{N1}& 0& 0\\ 0& 1/L_{N2}& 0\\ 0& 0& -1/C_d\\ 0& 0& 0\\ 0& 0& 0\end{array}\right)\left(\begin{array}{c}{u}_{N1}\\ u_{N2}\\ i_L\end{array}\right)$

Work as Us1=0, Us2=+Ud, state equation is:

$\left(\begin{array}{c}{\stackrel{\&CenterDot;}{i}}_{N1}\\ {\stackrel{\&CenterDot;}{i}}_{N2}\\ {\stackrel{\&CenterDot;}{u}}_d\\ {\stackrel{\&CenterDot;}{i}}_2\\ {\stackrel{\&CenterDot;}{u}}_2\end{array}\right)=\left(\begin{array}{ccccc}-R_{N1}/L_{N1}& 0& 0& 0& 0\\ 0& -R_{N2}/L_{N2}& -1/L_{N2}& 0& 0\\ 0& 1/C_d& 0& -1/C_d& 0\\ 0& 0& 1/L_2& 0& -1/L_2\\ 0& 0& 0& 1/C_2& 0\end{array}\right)\left(\begin{array}{c}{i}_{N1}\\ i_{N2}\\ u_d\\ i_2\\ u_2\end{array}\right)+\left(\begin{array}{ccc}1/L_{N1}& 0& 0\\ 0& 1/L_{N2}& 0\\ 0& 0& -1/C_d\\ 0& 0& 0\\ 0& 0& 0\end{array}\right)\left(\begin{array}{c}{u}_{N1}\\ u_{N2}\\ i_L\end{array}\right)$

Work as Us1=+Ud, Us2=0, state equation is:

$\left(\begin{array}{c}{\stackrel{\&CenterDot;}{i}}_{N1}\\ {\stackrel{\&CenterDot;}{i}}_{N2}\\ {\stackrel{\&CenterDot;}{u}}_d\\ {\stackrel{\&CenterDot;}{i}}_2\\ {\stackrel{\&CenterDot;}{u}}_2\end{array}\right)=\left(\begin{array}{ccccc}-R_{N1}/L_{N1}& 0& -1/L_{N1}& 0& 0\\ 0& -R_{N2}/L_{N2}& 0& 0& 0\\ 1/C_d& 0& 0& -1/C_d& 0\\ 0& 0& 1/L_2& 0& -1/L_2\\ 0& 0& 0& 1/C_2& 0\end{array}\right)\left(\begin{array}{c}{i}_{N1}\\ i_{N2}\\ u_d\\ i_2\\ u_2\end{array}\right)+\left(\begin{array}{ccc}1/L_{N1}& 0& 0\\ 0& 1/L_{N2}& 0\\ 0& 0& -1/C_d\\ 0& 0& 0\\ 0& 0& 0\end{array}\right)\left(\begin{array}{c}{u}_{N1}\\ u_{N2}\\ i_L\end{array}\right)$

Work as Us1=-Ud, Us2=0, state equation is:

$\left(\begin{array}{c}{\stackrel{\&CenterDot;}{i}}_{N1}\\ {\stackrel{\&CenterDot;}{i}}_{N2}\\ {\stackrel{\&CenterDot;}{u}}_d\\ {\stackrel{\&CenterDot;}{i}}_2\\ {\stackrel{\&CenterDot;}{u}}_2\end{array}\right)=\left(\begin{array}{ccccc}-R_{N1}/L_{N1}& 0& 1/L_{N1}& 0& 0\\ 0& -R_{N2}/L_{N2}& 0& 0& 0\\ -1/C_d& 0& 0& -1/C_d& 0\\ 0& 0& 1/L_2& 0& -1/L_2\\ 0& 0& 0& 1/C_2& 0\end{array}\right)\left(\begin{array}{c}{i}_{N1}\\ i_{N2}\\ u_d\\ i_2\\ u_2\end{array}\right)+\left(\begin{array}{ccc}1/L_{N1}& 0& 0\\ 0& 1/L_{N2}& 0\\ 0& 0& -1/C_d\\ 0& 0& 0\\ 0& 0& 0\end{array}\right)\left(\begin{array}{c}{u}_{N1}\\ u_{N2}\\ i_L\end{array}\right)$

Work as Us1=0, Us2=-Ud, state equation is:

$\left(\begin{array}{c}{\stackrel{\&CenterDot;}{i}}_{N1}\\ {\stackrel{\&CenterDot;}{i}}_{N2}\\ {\stackrel{\&CenterDot;}{u}}_d\\ {\stackrel{\&CenterDot;}{i}}_2\\ {\stackrel{\&CenterDot;}{u}}_2\end{array}\right)=\left(\begin{array}{ccccc}-R_{N1}/L_{N1}& 0& 0& 0& 0\\ 0& -R_{N2}/L_{N2}& 1/L_{N2}& 0& 0\\ 0& -1/C_d& 0& -1/C_d& 0\\ 0& 0& 1/L_2& 0& -1/L_2\\ 0& 0& 0& 1/C_2& 0\end{array}\right)\left(\begin{array}{c}{i}_{N1}\\ i_{N2}\\ u_d\\ i_2\\ u_2\end{array}\right)+\left(\begin{array}{ccc}1/L_{N1}& 0& 0\\ 0& 1/L_{N2}& 0\\ 0& 0& -1/C_d\\ 0& 0& 0\\ 0& 0& 0\end{array}\right)\left(\begin{array}{c}{u}_{N1}\\ u_{N2}\\ i_L\end{array}\right)$

3. the method for claim 1 is characterized in that, the adams of the dual four quadrant convertor realistic model of employing Simulink module construction resolves module and is specially;

Adopt the implicit expression adms formula of four step quadravalences:

$x_{n+1}=x_n+\frac{h}{24}(55f_{n+1}-59f_n+37f_{n-1}-9f_{n-2})$ Formula 11

Because exist algebraic loop can not be applied to real-time simulation in this algorithm, therefore need further conversion.According to

f _N+1=Ax _N+1+ BU _N+1, formula 12

Bring formula 11 into, can get

$x_{n+1}-\frac{h}{24}55{\mathrm{Ax}}_{n+1}=x_n+\frac{h}{24}(55{\mathrm{BU}}_{n+1}-59f_n+37f_{n-1}-9f_{n-2})$ Formula 13

Abbreviation is

$x_{n+1}={(I-\frac{h}{24}55A)}^{-1}(x_n+\frac{h}{24}(55{\mathrm{BU}}_{n+1}-59f_n+37f_{n-1}-9f_{n-2}))$ Formula 14

Utilize formula 14 to make up adams and resolve module.

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