WO2020124307A1 - 一种新颖的三相电压型变流器的逻辑切换建模方法 - Google Patents

一种新颖的三相电压型变流器的逻辑切换建模方法 Download PDF

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WO2020124307A1
WO2020124307A1 PCT/CN2018/121414 CN2018121414W WO2020124307A1 WO 2020124307 A1 WO2020124307 A1 WO 2020124307A1 CN 2018121414 W CN2018121414 W CN 2018121414W WO 2020124307 A1 WO2020124307 A1 WO 2020124307A1
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switching
logic
phase
phase voltage
voltage
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孙希明
孙涛
孙鹏飞
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Dalian University of Technology
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M7/00—Conversion of AC power input into DC power output; Conversion of DC power input into AC power output
    • H02M7/66—Conversion of AC power input into DC power output; Conversion of DC power input into AC power output with possibility of reversal
    • H02M7/68—Conversion of AC power input into DC power output; Conversion of DC power input into AC power output with possibility of reversal by static converters
    • H02M7/72—Conversion of AC power input into DC power output; Conversion of DC power input into AC power output with possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
    • H02M7/79—Conversion of AC power input into DC power output; Conversion of DC power input into AC power output with possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal
    • H02M7/797—Conversion of AC power input into DC power output; Conversion of DC power input into AC power output with possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/30—Circuit design
    • G06F30/36—Circuit design at the analogue level
    • G06F30/367—Design verification, e.g. using simulation, simulation program with integrated circuit emphasis [SPICE], direct methods or relaxation methods
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M1/00—Details of apparatus for conversion
    • H02M1/0003—Details of control, feedback or regulation circuits
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M7/00—Conversion of AC power input into DC power output; Conversion of DC power input into AC power output
    • H02M7/02—Conversion of AC power input into DC power output without possibility of reversal
    • H02M7/04—Conversion of AC power input into DC power output without possibility of reversal by static converters
    • H02M7/12—Conversion of AC power input into DC power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
    • H02M7/21—Conversion of AC power input into DC power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal
    • H02M7/217—Conversion of AC power input into DC power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only
    • H02M7/219—Conversion of AC power input into DC power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only in a bridge configuration
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M7/00—Conversion of AC power input into DC power output; Conversion of DC power input into AC power output
    • H02M7/42—Conversion of DC power input into AC power output without possibility of reversal
    • H02M7/44—Conversion of DC power input into AC power output without possibility of reversal by static converters
    • H02M7/48—Conversion of DC power input into AC power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
    • H02M7/53—Conversion of DC power input into AC power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal
    • H02M7/537—Conversion of DC power input into AC power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only, e.g. single switched pulse inverters
    • H02M7/5387—Conversion of DC power input into AC power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only, e.g. single switched pulse inverters in a bridge configuration
    • H02M7/53871—Conversion of DC power input into AC power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only, e.g. single switched pulse inverters in a bridge configuration with automatic control of output voltage or current

Definitions

  • the invention belongs to the technical field of electric power systems, and provides a novel logic switching modeling method of a three-phase voltage-type converter.
  • a converter is an electrical device that changes the voltage, frequency, number of phases, and other electrical quantities or characteristics of a power supply system.
  • some occasions need to change AC power to DC power, which is a rectifier circuit, while in other occasions need to change DC power to AC power, this reverse process corresponding to rectification is defined as Inverter circuit.
  • Inverter circuit a set of thyristor circuits can be used as both a rectifier circuit and an inverter circuit. This device is called a converter.
  • the classification of converters is based on many factors.
  • the main classification methods are the number of grid phases (single-phase, three-phase and multi-phase circuits), the form of energy storage on the DC side (voltage-type converters and current-type converters), Modulation level number (two-level, three-level and multi-level circuits) and PWM modulation method (hard switching and soft switching modulation) are divided, but it is still divided into voltage type and current type in the form of flow side energy storage
  • the most mainstream classification method The reason is that there is a coupling relationship between the two of them on the main circuit structure, and each has a corresponding control strategy. Among them, the most widely used are voltage-type and current-type converters with three-phase full-bridge topology.
  • a current-type converter requires a large inductance, and therefore has a large volume and a correspondingly large weight and loss.
  • the series connected diodes in order to prevent the current from flowing backwards also cause the main circuit to be more complicated and more lossy than the voltage type.
  • voltage-type converters have better performance in suppressing surge voltage and have a relatively simple structure and are easy to control, so they are the focus of research.
  • This application also discusses voltage-type converters as examples.
  • the analog control technology adopted by the three-phase converter of this patent is to model the three-phase voltage converter according to the rules with discrete logic switching as a logic switching system with hybrid evolution characteristics on the basis of voltage type, and Verify the stability of its system.
  • the state space averaging method is a small signal analysis method. This method is simple and easy to use, which is convenient for stability analysis and controller design. However, the small signal model is usually approximated by ignoring the higher order terms in the model, which is not suitable for the system. In the face of large disturbances, it is mostly used to model converters with only two different circuit states, which has great limitations.
  • the switch function description method improves on the above method and can reflect the continuous and discrete characteristics, but the obtained model is a time-varying, nonlinear high-order model, which is not conducive to the analysis and design of the subsystem, and ultimately needs to be adopted
  • Related improvement methods make the model linear, for example, using small signal linearization, synchronous coordinate transformation and Fourier transform to eliminate the time-varying model. Therefore, the conventional modeling methods of the converter are all from the perspective of a linear system, and the approximate linearized model of the system is obtained through averaging, coordinate transformation, or small signal linearization. In order to analyze and control the converter more accurately and meet the requirements of engineering performance indicators, it is very necessary to establish an accurate and unified mathematical model.
  • the present invention is directed to the limitation of the three-phase voltage-type converter approximate linearization modeling method in the traditional process, and provides a modeling method for the logic switching of the three-phase voltage-type converter, and the modeling is verified by simulation The stability and effectiveness of the method. Specifically, it is a modeling method with hybrid evolution characteristics based on the combination of discrete logic rules and continuous dynamic equations in a three-phase voltage converter. On this basis, the logic switching characteristics of three voltage-type converters under complex work are given, which ensures that the voltage can be output steadily in the case of switching in multiple working modes.
  • Three-phase voltage-type converter is a hybrid dynamic system with the coupling effect of discrete logical variables and continuous physical variables.
  • the hybrid dynamic system is generally considered to be a complex dynamic system formed by mixing and interacting with discrete event dynamic systems and continuous variable dynamic systems according to certain rules.
  • discrete events are generally logical variables or Boolean variables, and evolve according to the evolution of discrete event systems; continuous variables generally evolve according to the evolution of continuous dynamic systems, usually described by a set of physical differential equations.
  • a novel logic switching modeling method for three-phase voltage converters First, a switching signal of unipolar Boolean logic (binary logic) is defined. The switching signal is passed through a three-phase voltage converter. In the upper and lower bridge arms, the on and off are defined; secondly, Kirchhoff's voltage law and current law are used to establish the physical equations of each phase current and the physical equations of voltage in the three-phase voltage converter; then ,According to the defined unipolar Boolean logic (binary logic) switching signal, determine the eight dynamic systems of three-phase voltage converter with switching modes; Finally, according to the eight switching modes to design a A Boolean logic switching system that conforms to the three-phase voltage converter with discrete logic rules is obtained, so that a logic switching model with hybrid evolution characteristics of the three-phase voltage converter is obtained, and the stability analysis of the model is performed.
  • unipolar Boolean logic binary logic
  • the "upper arm is turned on and the lower arm is turned off” and “upper arm is turned off” for each phase of the three-phase voltage converter.
  • k a, b, c.
  • ⁇ (a), ⁇ (b), ⁇ (c) represent the working state of a, b, c related to the upper and lower bridge arms respectively.
  • the loop equation of the three-phase voltage converter in each phase is obtained based on Kirchhoff's voltage law, according to Kirchhoff's current law
  • the physical equation of the voltage change of the parallel large capacitor on the DC side is obtained. Therefore, the physical equation of the three-phase voltage converter is as follows:
  • L is the resistive inductive load on the three-phase AC side
  • i a , i b and i c are the a-phase current, b-phase current and c-phase current of the three-phase voltage converter respectively
  • R s and R l are three
  • the switching loss and load resistance of the phase converter e L is the DC voltage source voltage
  • R L is the internal resistance of the DC side voltage source
  • C is the large capacitor in parallel on the DC side
  • v dc is the voltage across the capacitor
  • i dc is the total current flowing into the inverter side.
  • v 0N is the voltage at points 0 and N.
  • the state variables x [i a , i b , i c , v dc ] T are selected to establish the state space equation of the three-phase voltage converter.
  • the fourth step is to obtain the dynamic system with the switching mode described for the unipolar Boolean logic switching function according to the various combinations of the Boolean logic switching function for the state space equation of the three-phase voltage converter described above, that is Boolean logic switching system of three-phase voltage converter with discrete logic rules:
  • Formula (7) represents the continuous-time switching dynamic model based on the logic switching signal:
  • q(k) ⁇ ⁇ 1, 2, 3, 4, 5, 6, 7, 8 ⁇ is a logic-based switching signal, it is a piecewise constant function, that is, at each time interval t ⁇ [t k ,t k+1 ), only one subsystem is activated, and the activation sequence of each subsystem follows certain logic rules;
  • a q(k) represents the 8 subsystems A 1 ⁇ A 8 of the dynamic system model, ie :
  • Formula (8) represents a discrete logic dynamic model based on logic switching signals.
  • the vector form is used to represent the discrete state of the system in the real field, that is, the i in the real field corresponds to the vector field as
  • q(k) is the discrete logic state of the logic system at time k
  • q(k+1) is the discrete logic state of the logic system at time k+1.
  • H is the structure matrix of the logical system model shown in formula (8), which is:
  • the switching system composed of eight subsystems of the three-phase voltage type converter established by the present invention finally realizes the cyclic action within the desired set under the action of the designed logic switching signal, and each The period of the second cycle can be different.
  • each state component of the system is a continuous function of time and as the logic cycle switching action progresses, it eventually converges to 0, indicating that the established system is in the designed logic switching signal It has asymptotic stability under the action, which is consistent with the previous analysis results.
  • Figure 1 is a block diagram of a voltage-type single closed-loop logic control; where: the logic signal controller generates the discrete logic switching sequence designed in this application.
  • u i is the input voltage
  • L f and C f are the inductance and capacitance of the LC filter
  • R is the external load resistance
  • u o is the output voltage.
  • Figure 2 is the topological structure diagram of the three-phase voltage SPWM inverter; where: L and R l are the three-phase AC side resistive load and load resistance; i a (t), i b (t) and i c (t) are the a-phase current, b-phase current and c-phase current of the three-phase voltage converter, which is a continuous function of time; S 1 ⁇ S 6 are fully controlled switching devices with freewheeling diodes connected in parallel, R s is the switching loss of the three-phase inverter; e L is the DC voltage source, R L is the internal resistance of the DC side voltage source, C is the large capacitor connected in parallel on the DC side, which is equivalent to the voltage source, and v dc represents the two Voltage at the terminal; i L is the power supply current on the DC side, and i dc is the total current flowing into the inverter side.
  • L and R l are the three-phase AC side resistive load and load resistance
  • Figure 3 is a switching diagram of discrete logic rules; among them: each subsystem runs sequentially under the logic switching rules designed in this description, and only one subsystem is activated at the same time.
  • Figure 5 is the change curve of state x 1 ; where: state x 1 represents the a-phase current on the AC side of the three-phase voltage converter.
  • Figure 6 is the change curve of state x 2 ; where: state x 2 represents the b-phase current on the AC side of the three-phase voltage converter.
  • Figure 7 is the change curve of state x 3 ; where: state x 3 represents the c-phase current on the AC side of the three-phase voltage converter.
  • Fig. 8 is the change curve of state x 4 ; where: state x 4 represents the voltage across the parallel capacitor on the DC side of the three-phase voltage converter.
  • a novel logic switching modeling method for three-phase voltage-type converters In this method: first, for the topology structure diagram of three-phase voltage-type converters, by defining a unipolar Boolean logic ⁇ (k) The switching function of the three-phase voltage converter represents the two working states of "upper arm on, lower arm off” and “upper arm off, lower arm on” in each phase. Secondly, according to the working state of each phase of the three-phase voltage converter, based on Kirchhoff's voltage law and Kirchhoff's current law, the physical equations of voltage and current changes of each phase are obtained.
  • the physical equations are uniformly converted into state space equations, and based on the Boolean logic switching function, the state space equations are converted into continuous switching dynamics with 8 seed modes under different working conditions. system. Finally, through these eight seed modes, it is designed as a discrete logic dynamic system, combined with a continuous switching dynamics model, and finally a logical switching dynamics model is proposed.
  • the logic switching system model of the three-phase voltage converter with hybrid evolution characteristics and the designed logic switching signal established by the above method are used to set the system model and simulate with Simulink module using the S function and LMI toolbox in MATLAB. Obtain its corresponding stability characteristics.
  • the specific steps of this method are as follows:
  • the first step is to represent the three-phase voltage-type converter by defining a switching function of a unipolar Boolean logic ⁇ (k) for the topological structure diagram of the three-phase voltage-type converter (see Figures 1 and 2).
  • ⁇ (k) a unipolar Boolean logic
  • the switching loss R s of the three-phase converter set is 1 ⁇
  • the resistive load L 8 mH
  • the DC side parallel capacitance C 10 mF
  • the DC side resistance R L 20 ⁇
  • DC voltage source voltage e L 0.
  • the fourth step is to obtain the dynamic system with the switching mode described for the unipolar Boolean logic switching function according to the various combinations of the Boolean logic switching function for the state space equation of the three-phase voltage converter described above, that is Boolean logic switching system of three-phase voltage converter with discrete logic rules:
  • H ⁇ 28 [(*) 1 ...,(254) 128 ,...,(248) 192 ,...,(255) 224 ,...,(128) 240 ,...,(252) 248 ,...,(224) 252 ,...,(240) 254 ,(128) 255 ,(*) 256 ];
  • n 8 namely A 1 -A 8 are shown in formulas (9)-(16).
  • the fifth step is to use the S-function and LMI toolbox in MATLAB to set up the system model and use Simulink according to the logic switching system model and the designed logic switching signal of the three-phase voltage converter with hybrid evolution characteristics established by the above method. Module for simulation. (See the attached figure for specific simulation)
  • the average cycle dwell time T * 0.0156s
  • the initial value of the discrete state is
  • the simulation time is set to 1s.

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Abstract

一种新颖的三相电压型变流器的逻辑切换建模方法，属于电力系统的技术领域。首先，定义单极性布尔逻辑的切换信号；其次，采用基尔霍夫电压定律与电流定律建立三相电压型变流器中各相电流及关于电压的物理方程；接着，根据切换信号，确定三相电压型变流器的8种具有切换模态的动力学系统；最后，根据这8种切换模态设计符合三相电压型变流器具有离散逻辑规则的布尔型逻辑切换系统，获得三相电压型变流器具有混杂演化特征的逻辑切换模型，对该模型进行稳定性分析。本发明解决了传统过程中三相电压型变流器近似线性化建模方法中的局限性问题，由8个子系统组成的切换系统在逻辑切换信号作用下，能够在期望集内进行循环动作，且每次循环的周期可不同。

Description

一种新颖的三相电压型变流器的逻辑切换建模方法 技术领域
本发明属于电力系统的技术领域，提供一种新颖的三相电压型变流器的逻辑切换建模方法。
背景技术
变流器是使电源系统的电压、频率、相数和其他电量或特性发生变化的电器设备。在实际的应用场合中，有些场合需要将交流电源变成直流电源，这就是整流电路，而在另外一些场合中则需要将直流电源变成交流电源，这种对应于整流的逆向过程，定义为逆变电路。在一定条件下，一套晶闸管电路既可以作整流电路又可作逆变电路，这种装置称为变流器。
目前，变流器的分类依据很多，主要的分类方式有以电网相数(单相、三相及多相电路)、直流侧储能形式(电压型变流器和电流型变流器)、调制电平数(两电平、三电平及多电平电路)及PWM调制方式(硬开关和软开关调制)划分，但以流侧储能形式将其划分为电压型和电流型仍是最主流的一种分类方式。原因在于它们两者有对耦的关系存在于主电路结构上，且各自有与之对应的控制策略。这其中应用最为广泛的则是以三相全桥为拓扑结构的电压型、电流型变流器。电流型变流器要达到稳定的电压输出，就需要较大的电感，因而体积大，重量和损耗也相应的比较大。与此同时，串联的二极管(为了防止电流反向流动)也造成主电路较之电压型更复杂、损耗更大。相比之下，电压型变流器在抑制浪涌电压能力方面有着更好的性能且结构相对简单，易于控制，所以是研究的重点，本申请也是以电压型变流器为例展开论述。本专利的三相变流器采用的模拟控制技术为在电压型的基础上，将三相电压型变流器按照具有离散的逻辑切换的规则建模为具有混杂演化特征的逻辑切换系统，并验证其系统的稳定性。
目前，传统的变流器建模方法有很多。状态空间平均法是一种小信号分析方法，这种方法简单易用，便于稳定性分析和控制器设计，但是小信号模型通常是通过忽略模型中的高次项而近似得到的，不适合系统面对大扰动的情形，多用于仅具有两种不同电路状态的变流器建模，有很大的局限性。而开关函数描述法对上述的方法有所改进，可以体现连续和离散的特征，但是所得到的模型为时变、非线性的高阶模型，不利于子系统的分析和设计，最终还需要采取相关改进方法使模型线性化，譬如用小信号线性化、同步坐标变换以及傅里叶变换等方法消除模型的时变性。因此，变流器常规的建模方法都是从线性系统的角度出发，通过平均化、坐标变换或小信号线性化等方法得到系统的近似线性化模型。为了更准确地分析和控制变流器，满足工程性能指标要求，建立精确统一的数学模型是十分必要的。兙俥
在对现有的技术文献与专利检索后发现，李琼林，刘会金在“电工技术学报，2009，24(11): 89-95”发表的“基于切换系统理论的三相变流器建模及其稳定性分析”一文。该文探讨了对三相变流器切换过程的稳定性进行了初步分析，但是由于系统模型是在等周期切换的这一特殊情况下建立的，并在稳定性分析过程中存在一定的局限性。因此，本文在此基础上进行改进，以离散的逻辑系统与连续的动力系统为基础，从三相电压型变流器的建模与稳定性分析两个方面分别进行设计。
发明内容
本发明针对传统过程中三相电压型变流器近似线性化建模方法的局限性问题，提供一种针对三相电压型变流器逻辑切换的建模方法，并通过仿真验证了该建模方法的稳定性及有效性。具体是通过基于三相电压型变流器中离散的逻辑规则与连续的动力学方程共同体现的具有混杂演化特征的建模方法。在此基础上，给出了三项电压型变流器在复杂工作下的逻辑切换特性，保证了其在多种工作模式切换的情况下电压能稳定的输出运行。
对于三相电压型变流器的工作原理，究其本质，三相电压型变流器是一种具有离散逻辑变量和连续物理变量二者相互耦合作用的混杂动力学系统。而一般认为的混杂动力学系统正是由离散事件动态系统和连续变量动态系统按照某种规则相互混合，相互作用而形成的一类复杂的动态系统。其中，离散事件一般为逻辑变量或者布尔变量，并按照离散事件系统的演化规律进行演化；连续变量一般按照连续动力学系统的演化规律进行演化，通常则由一组物理微分方程来进行描述。因此，正由于三相电压型变流器的工作特点，我们通过单极性布尔逻辑(二值逻辑)的切换信号与各相关于电流，电压的物理方程来设计一种符合该逆变器规律的逻辑切换系统来实现输出的电压或电流为标准的正弦波，以达到逆变电源的要求。俥
为实现上述的目的，本发明的技术方案如下：
一种新颖的三相电压型变流器的逻辑切换建模方法，首先，定义一种单极性布尔逻辑(二值逻辑)的切换信号，该切换信号是通过在三相电压型变流器中的上、下桥臂的导通与关闭进行定义；其次，采用基尔霍夫电压定律与电流定律建立三相电压型变流器中各相电流的物理方程以及关于电压的物理方程；接着，根据定义的单极性布尔逻辑(二值逻辑)的切换信号，确定三相电压型变流器的8种具有切换模态的动力学系统；最后，根据这8种切换模态设计一种符合三相电压型变流器具有离散逻辑规则的布尔型逻辑切换系统，从而获得三相电压型变流器具有混杂演化特征的逻辑切换模型，并对该模型进行稳定性的分析。
具体包括以下步骤：
第一步，针对三相电压型变流器的拓扑结构图，将三相电压型变流器每一相的“上桥臂导通，下桥臂关断”和“上桥臂关断，下桥臂导通”这两种状态分别用单极性布尔逻辑函数δ(k)＝1和δ(k)＝0来表示。即定义的单极性布尔逻辑(二值逻辑)δ(k)的切换函数为：
Figure PCTCN2018121414-appb-000001
其中：k＝a，b，c.δ(a)，δ(b)，δ(c)分别表示在a,b,c相关于上下桥臂的工作状态。兙俥第二步，在三相电压型变流器的拓扑结构图中，基于基尔霍夫电压定律获得三相电压型变流器在每一相的回路方程，根据基尔霍夫电流定律获得直流侧并联大电容电压变化的物理方程。因此，三相电压型变流器的物理方程如下：
Figure PCTCN2018121414-appb-000002
Figure PCTCN2018121414-appb-000003
Figure PCTCN2018121414-appb-000004
Figure PCTCN2018121414-appb-000005
Figure PCTCN2018121414-appb-000006
其中：L为三相交流侧的阻感负载，i a，i b和i c分别为三相电压型变流器的a相电流，b相电流和c相电流，R s与R l为三相变流器的开关损耗与和负载电阻；e L为直流电压源电压，R L为直流侧电压源的内部电阻，C为直流侧并联的大电容，v dc表示该电容两端的电压；i dc为流入逆变侧的总电流。v 0N是0点与N点的电压。
第三步，根据定义的布尔逻辑切换函数，选取状态变量x＝[i a,i b,i c,v dc] T，建立三相电压型变流器的状态空间方程。
Figure PCTCN2018121414-appb-000007
其中，x＝[i a，i b，i c，v dc] T,x(0)＝[20,20,20,20] T。
第四步，对于上述的三相电压型变流器的状态空间方程，根据布尔逻辑切换函数的各种组合，获得关于单极性布尔逻辑切换函数描述的具有切换模式的动力学系统,即得到三相电压型变流器关于离散逻辑规则的布尔型逻辑切换系统：
Figure PCTCN2018121414-appb-000008
q(k+1)＝Hq(k)      (8)
公式(7)表示基于逻辑切换信号的连续时间切换动态模型：x(t)＝[i a,i b,i c,v dc] T是系统在t时刻的连续状态变量，它是时间的连续函数；q(k)∈{1，2，3，4，5，6，7，8}是基于逻辑的切换信号，它是一个分段常值函数，即在每个时间间隔t∈[t k，t k+1)都只有一个子系统被激活，且各子系统的激活顺序遵循一定的逻辑规则；A q(k)表示本动力学系统模型的8个子系统A 1～A 8，即：
Figure PCTCN2018121414-appb-000009
Figure PCTCN2018121414-appb-000010
Figure PCTCN2018121414-appb-000011
Figure PCTCN2018121414-appb-000012
Figure PCTCN2018121414-appb-000013
Figure PCTCN2018121414-appb-000014
Figure PCTCN2018121414-appb-000015
Figure PCTCN2018121414-appb-000016
公式(8)表示基于逻辑切换信号的离散逻辑动态模型。在逻辑系统中，用向量形式表示实数域中系统的离散状态，即实数域中的i在向量域中对应表示为
Figure PCTCN2018121414-appb-000017
其中q(k)为逻辑系统在k时刻的离散逻辑状态，q(k+1)为逻辑系统的在k+1时刻的离散逻辑状态。H为公式(8)所示的逻辑系统模型的结构矩阵，为：
H＝σ 28[(*) 1…,(254) 128,…,(248) 192,…,(255) 224,…,(128) 240,…,(252) 248,…,(224) 252,…,(240) 254,(128) 255,(*) 256]；在本系统中，n＝8,即
Figure PCTCN2018121414-appb-000018
因此，公式(7)与公式(8)通过公共的离散逻辑状态q(k)进行耦合连接，进而连续的时间切换动态模型按照一定的离散逻辑动态模型的演化次序进行切换式的连续运行。
本发明的有益效果为：本发明建立的由三相电压型变流器的8个子系统组成的切换系统在所设计的逻辑切换信号作用下，最终实现了在期望集内进行循环动作，且每次循环的周期可以不同。此外，由各状态的仿真附图可以看出，系统各状态分量是时间的连续函数且随着逻辑循环切换动作的进行，其最终收敛于0，说明所建立的系统在所设计的逻辑切换信号作用下具有渐近稳定性，与之前的分析结果是吻合的。
附图说明
图1为电压型单闭环逻辑控制框图；其中：逻辑信号控制器产生本申请所设计的离散逻辑切换序列。u i为输入电压，L f和C f分别为LC滤波器的电感和电容，R为外加负载电阻，u o为输出电压。
图2为三相电压型SPWM逆变器的拓扑结构图；其中：L和R l分别为三相交流侧的阻感负载和负载电阻；i a(t)，i b(t)和i c(t)分别为三相电压型变流器的a相电流，b相电流和c相电流，它是时间的连续函数；S 1～S 6为并联有续流二极管的全控型开关器件，R s为三相逆变器的开关损耗；e L为直流电压源，R L为直流侧电压源的内部电阻，C为直流侧并联的大电容， 相当于电压源，v dc表示该电容两端的电压；i L为直流侧的电源电流，i dc为流入逆变侧的总电流。
图3为离散逻辑规则的切换图；其中：各子系统都是在本说明所设计的逻辑切换规则下依次运行，同一时刻只有一个子系统被激活。
图4为逻辑切换系统的基本结构示意图；其中：在本说明中，子系统个数为n＝8。
图5为状态x 1的变化曲线；其中：状态x 1表示三相电压型变流器的交流侧a相电流。
图6为状态x 2的变化曲线；其中：状态x 2表示三相电压型变流器的交流侧b相电流。
图7为状态x 3的变化曲线；其中：状态x 3表示三相电压型变流器的交流侧c相电流。
图8为状态x 4的变化曲线；其中：状态x 4表示三相电压型变流器的直流侧并联电容两端的电压。
图9为逻辑切换信号图；其中：切换信号在t＝0.03s时使系统进入了循环，我们称为期望集。
具体实施方式
以下结合具体实施例对本发明做进一步说明。
一种新颖的三相电压型变流器的逻辑切换建模方法，该方法中：首先，针对三相电压型变流器的拓扑结构图，通过定义一种单极性布尔逻辑δ(k)的切换函数来表示三相电压型变流器在每一相的“上桥臂导通，下桥臂关断”和“上桥臂关断，下桥臂导通”的两种工作状态。其次，根据三相电压型变流器每一相的工作状态，分别基于基尔霍夫电压定律与基尔霍夫电流定律获得了每一相电压与电流变化的物理方程。进一步的，利用状态空间描述的方法，将各物理方程统一的转化为状态空间方程，并基于布尔逻辑切换函数在不同的工作状态下，把状态空间方程转化为具有8种子模式的连续切换动力学系统。最后，通过这8种子模式，将它设计成一种离散的逻辑动态系统，并结合连续的切换动力学模型，最终提出了逻辑切换动力学模型。并对上述方法建立的具有混杂演化特征的三相电压型变流器的逻辑切换系统模型以及设计的逻辑切换信号，使用MATLAB中的S函数和LMI工具箱进行系统模型设置并用Simulink模块进行仿真，获得其相应的稳定性特征。该方法具体步骤如下：
第一步，针对三相电压型变流器的拓扑结构图(见附图1，2)，通过定义一种单极性布尔逻辑δ(k)的切换函数来表示三相电压型变流器在每一相的“上桥臂导通，下桥臂关断”或“上桥臂关断，下桥臂导通”的两种工作状态。
其中：对于子系统1：取δ(a)＝0，δ(b)＝0，δ(c)＝0。
对于子系统2：取δ(a)＝1，δ(b)＝0，δ(c)＝0。
对于子系统3：取δ(a)＝1，δ(b)＝1，δ(c)＝0。
对于子系统4：取δ(a)＝0，δ(b)＝1，δ(c)＝0。
对于子系统5：取δ(a)＝0，δ(b)＝1，δ(c)＝1。
对于子系统6：取δ(a)＝0，δ(b)＝0，δ(c)＝1。
对于子系统7：取δ(a)＝1，δ(b)＝0，δ(c)＝1。
对于子系统8：取δ(a)＝1，δ(b)＝1，δ(c)＝1。
兙俥第二步，在三相电压型变流器的拓扑结构图中，根据三相电压型变流器每一相的工作状态，我们基于基尔霍夫电压定律获得三相电压型变流器在每一相的回路方程，根据基尔霍夫电流定律获得直流侧并联大电容电压变化的物理方程。因此，获得三相电压型变流器的每一相电压与电流变化的物理方程，如公式(1)-(5)所示。
第三步，利用状态空间描述的方法，选取状态变量x＝[i a,i b,i c,v dc] T，将各物理方程统一的转化为状态空间方程，并基于布尔逻辑切换函数在不同的工作状态下，把状态空间方程转化为具有8种子模式的连续切换动力学系统，如公式(6)所示。
其中，设置的三相变流器的开关损耗R s＝1Ω，三相交流侧负载电阻为R l＝19Ω，阻感负载L＝8mH，直流侧并联电容C＝10mF，直流侧电阻R L＝20Ω，直流电压源电压e L＝0。
第四步，对于上述的三相电压型变流器的状态空间方程，根据布尔逻辑切换函数的各种组合，获得关于单极性布尔逻辑切换函数描述的具有切换模式的动力学系统,即得到三相电压型变流器关于离散逻辑规则的布尔型逻辑切换系统：
其中：q(k)∈Q＝{1，2，3，4，5，6，7，8}；
H＝σ 28[(*) 1…,(254) 128,…,(248) 192,…,(255) 224,…,(128) 240,…,(252) 248,…,(224) 252,…,(240) 254,(128) 255,(*) 256]；在本系统中，n＝8,即
Figure PCTCN2018121414-appb-000019
A 1-A 8如公式(9)-(16)所示。
第五步，根据使用上述方法建立的具有混杂演化特征的三相电压型变流器的逻辑切换系统模型以及设计的逻辑切换信号，使用MATLAB中的S函数和LMI工具箱进行系统模型设置并用Simulink模块进行仿真。(具体的仿真见附图说明)
其中：在极限环外的各子系统的驻留时间分别为τ 2＝0.006s，τ 3＝0.007s，τ 5＝ 0.004s，τ 6＝0.003s，τ 8＝0.01s，进入极限环后的平均循环驻留时间T *＝0.0156s，系统各连续状态的初始化取值为x＝[2 2 2 2] T,离散状态的初始化取值为
Figure PCTCN2018121414-appb-000020
仿真时间设置为1s。
实施结果
1)从仿真图5，图6和图7可以看出三相电压型变流器交流侧a，b，c三相回路中的电流是随时间变化的连续函数，且在没有达到稳定时其呈正弦型波动，在0.6秒左右以后，各状态都达到了稳定，体现了所构建的三相电压型变流器的逻辑切换系统模型的渐进稳定性以及说明所设计逻辑切换信号的有效性。
2)从仿真图8中可以看出直流侧并联电容两端的电压是随着时间连续且不断下降的，说明整体上它是一个放电的过程，而且该仿真曲线最终收敛到0，说明在本说明所设计的逻辑切换信号下，电容C两端的电压最终达到了稳定。
3)从仿真图9中可以看出本说明所设计的逻辑切换序列为2,5,6,3,8,1,7,4,1,7,4,…，也即所构建的三相电压型变流器的逻辑切换系统在期望集外各子系统的激活顺序依次为：子系统2，子系统5，子系统6，子系统3，子系统8，在期望集内的子系统激活顺序依次为：子系统1，子系统7，子系统4依次循环，且每次循环周期可以不同。
以上所述实施例仅表达本发明的实施方式，但并不能因此而理解为对本发明专利的范围的限制，应当指出，对于本领域的技术人员来说，在不脱离本发明构思的前提下，还可以做出若干变形和改进，这些均属于本发明的保护范围。

Claims (1)

  1. 一种新颖的三相电压型变流器的逻辑切换建模方法，其特征在于，该方法中：首先，定义一种单极性布尔逻辑的切换信号；其次，采用基尔霍夫电压定律与电流定律建立三相电压型变流器中各相电流的物理方程以及关于电压的物理方程；再次，根据定义的单极性布尔逻辑的切换信号，确定三相电压型变流器的8种具有切换模态的动力学系统；最后，根据8种切换模态设计一种符合三相电压型变流器具有离散逻辑规则的布尔型逻辑切换系统，获得三相电压型变流器具有混杂演化特征的逻辑切换模型；包括以下步骤：
    第一步，针对三相电压型变流器的拓扑结构图，将三相电压型变流器每一相的“上桥臂导通，下桥臂关断”和“上桥臂关断，下桥臂导通”这两种状态分别用单极性布尔逻辑函数δ(k)＝1和δ(k)＝0表示；定义的单极性布尔逻辑δ(k)的切换函数为：
    Figure PCTCN2018121414-appb-100001
    其中：k＝a，b，c.δ(a)，δ(b)，δ(c)分别表示在a,b,c相关于上下桥臂的工作状态；兙俥第二步，在三相电压型变流器的拓扑结构图中，基于基尔霍夫电压定律获得三相电压型变流器在每一相的回路方程，根据基尔霍夫电流定律获得直流侧并联大电容电压变化的物理方程；因此，三相电压型变流器的物理方程如下：
    Figure PCTCN2018121414-appb-100002
    Figure PCTCN2018121414-appb-100003
    Figure PCTCN2018121414-appb-100004
    Figure PCTCN2018121414-appb-100005
    Figure PCTCN2018121414-appb-100006
    其中：L为三相交流侧的阻感负载，i a，i b和i c分别为三相电压型变流器的a相电流，b相电流和c相电流，R s与R l为三相变流器的开关损耗与和负载电阻；e L为直流电压源电压，R L为直流侧电压源的内部电阻，C为直流侧并联的大电容，v dc表示该电容两端的电压；i dc为流入逆变侧的总电流；v 0N是0点与N点的电压；
    第三步，根据定义的布尔逻辑切换函数，选取状态变量x＝[i a,i b,i c,v dc] T，建立三相电压型变流器的状态空间方程；
    Figure PCTCN2018121414-appb-100007
    其中，x＝[i a，i b，i c，v dc] T,x(0)＝[20,20,20,20] T；
    第四步，对于上述的三相电压型变流器的状态空间方程，根据布尔逻辑切换函数的各种组合，获得关于单极性布尔逻辑切换函数描述的具有切换模式的动力学系统，得到三相电压型变流器关于离散逻辑规则的布尔型逻辑切换系统：
    Figure PCTCN2018121414-appb-100008
    q(k+1)＝Hq(k)    (8)
    公式(7)表示基于逻辑切换信号的连续时间切换动态模型：x(t)＝[i a,i b,i c,v dc] T是系统在t时刻的连续状态变量，是时间的连续函数；q(k)∈{1，2，3，4，5，6，7，8}是基于逻辑的切换信号，是一个分段常值函数，即在每个时间间隔t∈[t k，t k+1)都只有一个子系统被激活，且各子系统的激活顺序遵循逻辑规则；A q(k)表示本动力学系统模型的8个子系统A 1～A 8，即：
    Figure PCTCN2018121414-appb-100009
    Figure PCTCN2018121414-appb-100010
    Figure PCTCN2018121414-appb-100011
    Figure PCTCN2018121414-appb-100012
    Figure PCTCN2018121414-appb-100013
    Figure PCTCN2018121414-appb-100014
    Figure PCTCN2018121414-appb-100015
    Figure PCTCN2018121414-appb-100016
    公式(8)表示基于逻辑切换信号的离散逻辑动态模型；在逻辑系统中，用向量形式表示实数域中系统的离散状态，即实数域中的i在向量域中对应表示为
    Figure PCTCN2018121414-appb-100017
    其中q(k)为逻辑系统在k时刻的离散逻辑状态，q(k+1)为逻辑系统的在k+1时刻的离散逻辑状态；H为公式(8)所示的逻辑系统模型的结构矩阵，为：
    Figure PCTCN2018121414-appb-100018
    Figure PCTCN2018121414-appb-100019
    在本系统中，n＝8,即
    Figure PCTCN2018121414-appb-100020
    因此，公式(7)与公式(8)通过公共的离散逻辑状态q(k)进行耦合连接，连续的时间切换动态模型按照离散逻辑动态模型的演化次序进行切换式的连续运行。
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CN104834782A (zh) * 2015-05-08 2015-08-12 华北电力大学 基于载波相移的模块化多电平换流器的控制系统建模方法
CN107168100A (zh) * 2017-05-26 2017-09-15 华北电力大学 一种基于现场可编程门阵列的模块化多电平换流器实时仿真建模方法
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CN108365631A (zh) * 2018-03-21 2018-08-03 广东电网有限责任公司电力科学研究院 分布式并网变流器的无功电压控制电路仿真方法及系统

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CN104834782A (zh) * 2015-05-08 2015-08-12 华北电力大学 基于载波相移的模块化多电平换流器的控制系统建模方法
CN107168100A (zh) * 2017-05-26 2017-09-15 华北电力大学 一种基于现场可编程门阵列的模块化多电平换流器实时仿真建模方法
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