WO2021258810A1 - 一种基于交叉初始化的换流器参数化恒导纳建模方法 - Google Patents

一种基于交叉初始化的换流器参数化恒导纳建模方法 Download PDF

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WO2021258810A1
WO2021258810A1 PCT/CN2021/085704 CN2021085704W WO2021258810A1 WO 2021258810 A1 WO2021258810 A1 WO 2021258810A1 CN 2021085704 W CN2021085704 W CN 2021085704W WO 2021258810 A1 WO2021258810 A1 WO 2021258810A1
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model
converter
electromagnetic transient
simulation
equivalent
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French (fr)
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顾伟
曹阳
邹德虎
李珂
史坤
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东南大学
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR 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
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/18—Network design, e.g. design based on topological or interconnect aspects of utility systems, piping, heating ventilation air conditioning [HVAC] or cabling
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/24—Arrangements for preventing or reducing oscillations of power in networks
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/10—Numerical modelling
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2113/00—Details relating to the application field
    • G06F2113/04—Power grid distribution networks
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/06—Power analysis or power optimisation
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]

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  • the invention relates to the technical field of power system dynamic simulation and modeling, in particular to a converter parameterized constant admittance modeling method based on cross-initialization.
  • the high-frequency characteristics of power electronic devices have brought great difficulties to hardware-in-the-loop simulation.
  • converters which are widely used in new energy sources, have always been the key points of power system simulation analysis.
  • the processing of power electronic switches is related to the accuracy and efficiency of the entire network solution.
  • how to simulate the power electronic switch is the main difficulty in the simulation of this type of system.
  • the power electronic switch electromagnetic transient simulation model can be optimized from the aspects of average model, characteristic analysis modeling, integration method and interpolation algorithm.
  • the optimization of the electromagnetic transient model of the switching device can not only improve the simulation accuracy of the model, but also increase the maximum feasible step size of the simulation calculation to a certain extent.
  • the development of dynamic simulation has significant significance.
  • the parameterized constant admittance model of the converter based on cross-initialization can significantly improve the accuracy of electromagnetic transient simulation of new energy sources and the maximum feasible step size of the simulation. It can well solve the problem of virtual power loss and affect the electromagnetic transient of power electronic devices. Simulation modeling plays a guiding role and is of great significance in the electromagnetic transient analysis of modern power systems.
  • the technical problem to be solved by the present invention is to provide a converter parametric constant admittance modeling method based on cross-initialization.
  • the converter model has been optimized to improve the simulation accuracy of the model and the maximum feasible simulation step size, and well solve the virtual power loss problem, and further improve the simulation speed of the small-step electromagnetic transient simulation of the power electronic converter And precision.
  • the present invention provides a parametric constant admittance modeling method of a converter based on cross initialization, which includes the following steps:
  • the electromagnetic transient simulation model of the converter includes power electronic switches, inductors, capacitors, and control parts.
  • the specific relationships are as follows:
  • the DC side voltage U dc is provided by an external DC voltage source.
  • the DC side output current I dc and output power P dc pass through the parallel capacitors on the DC side and then pass into several groups of bridge arms composed of upper and lower switches, and then output to the AC power grid U In ac ; the grid feeds back active power P grid and reactive power Q gird to the outer loop controller, the outer loop controller outputs current reference values idref and iqref to the inner loop controller, and the inner loop controller sends the AC side dq axis current component id , Iq is compared with the reference value to generate the SPWM control signal of the inverter.
  • step (2) the cross-initialization correction method is specifically:
  • the injection current source of the action switch is calculated using the historical state quantities of the voltage and current of the other switch on the corresponding bridge arm, which can greatly reduce the error offset of the initial value at the switching time, assuming the commutation
  • the operating state of the converter is switched from S 1 off and S 2 on to S 1 on and S 2 off, and the initial value of the cross initialization is obtained:
  • step (3) the establishment of an electromagnetic transient simulation equivalent model of the inverter is specifically as follows:
  • ⁇ and ⁇ are the voltage coefficient and current coefficient of the equivalent injection current source, respectively.
  • the above formula is an algebraic equation containing unknown state quantity voltage u(t), current i(t) and known state quantity voltage u(t- ⁇ t) at the previous time and current i(t- ⁇ t) at the previous time.
  • step (4) the steps of establishing an electromagnetic transient simulation model according to the network topology and the expected control effect are as follows:
  • the parameter selection method of the present invention establishes an electromagnetic transient simulation model of a power electronic converter.
  • the advantage of parameter method modeling is to consider establishing a pure mathematical model on the basis of being able to break away from the limitations of actual physical objects.
  • the cross-initialization method is used for model state switching correction, which greatly reduces the transient error caused by state switching, thereby greatly reducing the voltage, current, and power ripples. It better solves the problem of virtual power loss; compared with the traditional constant admittance simulation model, the accuracy of the improved converter model is greatly increased, which will greatly improve the simulation results of the electromagnetic transient simulation of the power electronic converter.
  • it solves the problem of virtual power loss during state switching plays a guiding role in the electromagnetic transient modeling of new energy in the future, and is of great significance to the further development of electromagnetic transient simulation modeling.
  • Figure 1 is a schematic flow diagram of the method of the present invention.
  • Fig. 2 is a schematic diagram of the electromagnetic transient simulation model of the inverter of the present invention.
  • Figure 3 is a schematic diagram of the cross-initialization principle of the present invention.
  • Fig. 4 is a comparison diagram of the voltage waveforms of the A-phase upper arm switching of the Ron/Roff model, the LC model and the model of the present invention.
  • Figure 5 is a comparison diagram of the power loss waveforms of the A-phase upper arm switch of the Ron/Roff model, the LC model and the model of the present invention.
  • Fig. 6 is a comparison diagram of the simulated A-phase output active power of the Ron/Roff model, the LC model and the model of the present invention.
  • the present invention adopts a parameterization method to establish an electromagnetic transient model of the converter, analyzes the operating characteristics of the model to determine the optimal parameters, and uses a cross-initialization method to process state switching errors, and builds a constant admittance electromagnetic transient simulation parameterized model of the converter, thereby A new parametric constant admittance modeling method for converters based on cross-initialization is proposed.
  • Fig. 1 The parameterized constant admittance modeling method of converter based on cross initialization disclosed in the present invention is shown in Fig. 1, and includes the following steps:
  • Step (1) Perform electromagnetic transient simulation modeling for the power electronic converter, where the switch adopts the parameter historical current source constant admittance model, and the other components are established by the traditional electromagnetic transient simulation integral model, and the initial value and step of the system are given. long;
  • Step (2) Detect whether the operating state switch occurs, if the state switch occurs, perform cross-initialization correction, if it does not occur, do not deal with it;
  • Step (3) Calculate model parameters according to the network topology and expected control effect, establish the equivalent electromagnetic admittance matrix and historical current source of the whole network, and obtain the equivalent electromagnetic transient simulation model of the converter;
  • Step (5) Update the electromagnetic transient simulation equivalent admittance matrix and historical current source based on the current state of each node in the network for the next time solution, and return to step (2) until the simulation termination time is reached.
  • Step (11) The relationship between the internal links of the electromagnetic transient simulation model of the converter is as follows:
  • the DC side voltage U dc is provided by an external DC voltage source.
  • the DC side output current I dc and output power P dc pass through the parallel capacitors on the DC side and then pass into several groups of bridge arms composed of upper and lower switches, and then output to the AC power grid U In ac ; the grid feeds back active power P grid and reactive power Q gird to the outer loop controller, the outer loop controller outputs current reference values idref and iqref to the inner loop controller, and the inner loop controller sends the AC side dq axis current component id , Iq is compared with the reference value to generate the SPWM control signal of the inverter.
  • Step (21) The cross-initialization correction method is specifically as follows:
  • the injection current source of the action switch is calculated using the historical state quantities of the voltage and current of the other switch on the corresponding bridge arm, which can greatly reduce the error offset of the initial value at the switching time, assuming the commutation
  • the operating state of the converter is switched from S 1 off and S 2 on to S 1 on and S 2 off, and the initial value of the cross initialization is obtained:
  • Step (31) Establish an electromagnetic transient simulation equivalent model of the converter specifically as follows:
  • ⁇ and ⁇ are the voltage coefficient and current coefficient of the equivalent injection current source, respectively.
  • the above formula is an algebraic equation containing unknown state quantity voltage u(t), current i(t) and known state quantity voltage u(t- ⁇ t) at the previous time and current i(t- ⁇ t) at the previous time.
  • Step (41) Establish a parametric constant admittance model of the converter:
  • Step (42) Perform a complex frequency domain steady-state operation analysis on the switch model, and obtain the parameter expression of the switch model as:
  • Step (43) According to the network topology, the matrix equations about the midpoint voltage of the converter bridge arm and the switches in the off state are obtained. For example, the upper bridge arm switches are turned on and the lower bridge arms are turned off:
  • Step (44) analyzes the transient operating characteristics of the parameterized model, and obtains the corresponding parameters of the model in two different operating states as follows:
  • Step (46) Combine the interface parameters to solve the electromagnetic transient simulation equation of the converter, and obtain the current state of each node to update the electromagnetic transient equivalent admittance matrix and historical current source. Return to step (43) and continue the calculation until it reaches the Simulation termination time.
  • the following compares three different electromagnetic transient model simulation waveforms of power electronic converters to illustrate the technical advantages of the parametric constant admittance modeling method of the converter based on cross-initialization.
  • the simulation modeling of a three-phase bridge rectifier system is carried out, and the simulation step is 1 ⁇ s.
  • the relevant parameters of the inverter model are shown in Table 1.
  • the equivalent electromagnetic transient simulation model of the converter is shown in Figure 2.
  • the principle of cross-initialization is shown in Figure 3.
  • the simulation waveform comparison of Ron/Roff model, LC model and this modified model is shown in Fig. 4-6.
  • Fig. 4 is the voltage comparison of the A-phase upper arm switch S 1
  • Fig. 5 is the A-phase upper arm switch S 1 power. Loss comparison
  • Figure 6 is the comparison of A-phase output active power.
  • the waveform of the modified converter parameterized model (thin solid line) is closer to the Ron/Roff model (thick dashed line) than the waveform of the LC model (thick dotted line).
  • the paper mentioned in this paper is based on cross initialization
  • the parameterized model of the converter can improve the simulation convergence performance of the converter model, and the virtual power loss at the moment of state switching is greatly reduced.
  • the simulation results of the parameterized converter model based on cross-initialization and the Ron/Roff model are basically the same, which shows the effectiveness of the method proposed in this paper.

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Abstract

一种基于交叉初始化的换流器参数化恒导纳建模方法，包括如下步骤：步骤(1)对换流器进行参数化建模，开关采用参数历史电流源恒导纳模型，其他元件基于EMTP理论建立模型；步骤(2)检测是否发生状态切换，如果发生则进行交叉初始化修正；步骤(3)确定模型参数，建立全网等效导纳矩阵和注入电流源，得到电磁暂态仿真等效模型；步骤(4)根据基本求解方程I＝YU求解网络潮流，得到当前时刻换流器电磁暂态模型仿真结果；步骤(5)通过当前网络状态量计算下一时刻等效导纳矩阵和注入电流源，再回到步骤(2)，直至仿真终止。该方法优化了换流器模型，解决了虚拟功率损耗问题，进一步提高了换流器模型电磁暂态仿真的精度。

Description

一种基于交叉初始化的换流器参数化恒导纳建模方法 技术领域
本发明涉及电力***动态仿真与建模技术领域，特别是一种基于交叉初始化的换流器参数化恒导纳建模方法。
背景技术
自上世纪五十年代未第一只晶闸管问世以来，电力电子技术开始登上现代电气传动技术舞台，以此为基础开发的可控硅整流装置，是电气传动领域的一次革命，使电能的变换和控制从旋转变流机组和静止离子变流器进入由电力电子器件构成的变流器时代，这标志着电力电子的诞生。进入70年代晶闸管开始形成由低电压小电流到高电压大电流的系列产品，普通晶闸管不能自关断的半控型器件，被称为第一代电力电子器件。随着电力电子技术理论研究和制造工艺水平的不断提高，电力电子器件在容易和类型等方面得到了很大发展，是电力电子技术的又一次飞跃，先后研制出GTR、GTO、P-MOSFET等自关断全控型第二代电力电子器件。而以IGBT为代表的第三代电力电子器件，开始向大容易高频率、响应快、低损耗方向发展。而进入90年代电力电子器件正朝着复台化、标准模块化、智能化、功率集成的方向发展，以此为基础形成一条以电力电子技术理论研究，器件开发研制，应用渗透性，在国际上电力电子技术是竞争最激烈的高新技术领域。
随着大容量柔性直流输电、柔***流输电在我国电网中的进一步应用，以及电网中微网、可再生能源的大规模接入，现代电力***呈现电力电子化的趋势和复杂性日益增加的特征，对于可再生能源运行状态的仿真分析研究愈发重要。传统的数字机电暂态仿真已无法对其进行准确模拟，数字电磁暂态仿真逐渐成为精确模拟当今及未来电网的有效手段。然而，大量电力电子装置频繁的开关频率和复杂的控制策略，使得传统数字电磁暂态仿真效率极低，与当今电力***研究、生产、模拟等方面对仿真效率的需求极不相符。因此必须在兼顾准确性的前提下研究高效数字电磁暂态仿真技术。
电力电子器件的高频特性给硬件在环仿真带来了极大的困难，特别是在新能源中应用较广的换流器，一直是电力***仿真分析的关键点。电力电子开关的处理关系到整个网络求解的精度和效率。带有大量电力电子装置的***中，如HVDC、FACTS等，如何仿真其中的电力电子开关是该类***仿真的主要难点。为了兼顾其仿真精度和时间，可以从平均模型、特性分析建模、积分方法和插值算法等方面对电力电子开关电磁暂态 仿真模型进行优化。开关器件电磁暂态模型的优化，不仅可以提升模型的仿真精度，还能一定程度上提高仿真计算可行的最大步长，同时也可以加快其仿真时状态切换的误差收敛速度，对高精度电磁暂态仿真的发展有着显著意义。
我国电磁暂态仿真研究已经具备了一定的规模，逐渐推出了如ADPSS、DDRTS、CloudPSS等电磁暂态仿真平台，在电磁暂态仿真领域已经具备了一定的水平。但我国在电磁暂态仿真研究方面起步相对较晚，与日本、美国等仍然存在较大差距，对现代电力***中复杂的换流器模型的仿真是目前电磁暂态仿真研究的一大关键点，换流器模型的仿真效果直接影响现代电力***中新能源模型能否稳定控制与运行。
未来二三十年，将是我国能源生产消费方式和能源结构调整变革的关键时期，新能源技术将会迎来更加广阔的发展前景和发展机遇。基于交叉初始化的换流器参数化恒导纳模型，能明显提高新能源电磁暂态仿真的精度和仿真的最大可行步长，可以很好解决虚拟功率损耗问题，对电力电子器件的电磁暂态仿真建模起指导作用，在现代电力***电磁暂态分析中具有重要意义。
发明内容
本发明所要解决的技术问题在于，提供一种基于交叉初始化的换流器参数化恒导纳建模方法，在含有电力电子换流器模型电磁暂态仿真特别是小步长仿真中，对换流器模型进行了优化，提高了模型的仿真精度和可行最大仿真步长，并且很好的解决了虚拟功率损耗问题，进一步提高了电力电子换流器的小步长电磁暂态仿真的仿真速度和精度。
为解决上述技术问题，本发明提供一种基于交叉初始化的换流器参数化恒导纳建模方法，包括如下步骤：
(1)对电力电子换流器进行电磁暂态仿真建模，其中开关采用参数历史电流源恒导纳模型，其他元件采用传统电磁暂态仿真积分模型建立，并给定***初始值和步长；
(2)检测是否发生运行状态切换，如果发生状态切换则进行交叉初始化修正，如果未发生不做处理；
(3)根据网络拓扑结构和预期控制效果计算模型参数，建立全网等效电磁导纳矩阵和历史电流源，得到换流器电磁暂态仿真等效模型；
(4)根据电磁暂态基本求解方程I＝YU求解电磁暂态仿真等效模型建立的方程，获取当前时刻换流器电磁暂态模型仿真结果；
(5)根据当前时刻网络各节点状态量，更新电磁暂态仿真等效导纳阵和历史电流源用于下一时刻求解，回到步骤(2)，直至到达仿真终止时间。
优选的，步骤(1)中，换流器电磁暂态仿真模型包括电力电子开关、电感、电容和控制部分，具体关系如下：
直流侧电压U dc由外部直流电压源提供，直流侧输出电流I dc与输出功率P dc经过直流侧并联电容后传入若干组由上下两个开关组成的桥臂，再传出到交流电网U ac中；电网反馈有功功率P grid和无功功率Q gird给外环控制器，外环控制器输出电流参考值idref、iqref给内环控制器，内环控制器将交流侧dq轴电流分量id、iq与参考值大小进行比较产生逆变器的SPWM控制信号。
优选的，步骤(2)中，交叉初始化修正方法具体为：
在换流器运行状态切换时刻，动作开关的注入电流源使用对应桥臂上另一开关的电压和电流的历史状态量计算得到，可大大减小切换时刻初值的误差偏移，假设换流器运行状态由S 1关断、S 2导通切换至S 1导通、S 2关断，得到交叉初始化初值为：
Figure PCTCN2021085704-appb-000001
用上述状态量初值求解状态切换时刻注入电流源I inj,up(t),I inj,down(t)。
优选的，步骤(3)中，建立换流器电磁暂态仿真等效模型具体为：
对于给定电力电子开关，用以下方程来表述：
Figure PCTCN2021085704-appb-000002
其中，α、β分别为等效注入电流源的电压系数、电流系数。
对于电感、电容等元件，利用后向欧拉法求等效导纳和历史电流源：
Figure PCTCN2021085704-appb-000003
上式为含有未知状态量电压u(t)、电流i(t)和已知状态量前一时刻电压u(t-△t)、前一时刻电流i(t-△t)的代数方程，通过化简可得形如i＝G eq*u+I inj的形式，进而可得到电磁暂态仿真等效导纳矩阵G eq和等效注入电流源I inj，根据I＝YU求解该代数方程组。
优选的，步骤(4)中，根据网络拓扑结构和预期控制效果建立电磁暂态仿真模型的步骤如下：
(41)建立换流器参数化恒导纳模型：
Figure PCTCN2021085704-appb-000004
(42)对开关模型进行复频域稳态运行分析，得到开关模型参数表达式为：
Figure PCTCN2021085704-appb-000005
(43)根据网络拓扑结构求解得到关于换流器桥臂中点电压和关断状态下开关的矩阵方程，以上桥臂开关导通、下桥臂开关关断为例：
Figure PCTCN2021085704-appb-000006
(44)分析参数化模型暂态运行特性，得到两种不同运行状态下模型对应参数如下：
Figure PCTCN2021085704-appb-000007
时，
Figure PCTCN2021085704-appb-000008
Figure PCTCN2021085704-appb-000009
时，
Figure PCTCN2021085704-appb-000010
(45)建立换流器电磁暂态仿真***控制环节、网侧接口等模型，联立全网电磁暂态仿真***基本方程I＝YU；
(46)结合接口参数求解换流器电磁暂态仿真方程，得到当前时刻各节点状态量用于更新电磁暂态等效导纳矩阵和历史电流源，回到步骤(43)继续计算直到到达仿真终止时间。
本发明的有益效果为：本发明选择参数法建立了电力电子换流器电磁暂态仿真模型，参数法建模的优点是在能脱离实际物理对象的限制基础上考虑建立纯数学模型，以此来进一步保证换流器模型具备理想的运行特性；使用交叉初始化方法用于模型状态切换修正，极大降低状态切换带来的暂态误差，从而大幅减小了电压、电流、功率的纹波，较好的解决了虚拟功率损耗的问题；与传统恒导纳仿真模型相比，改进的换流器模型精度大幅上升，将极大改善电力电子换流器电磁暂态仿真的仿真结果，较大程度上解决了状态切换时产生的虚拟功率损耗问题，对未来新能源的电磁暂态建模起着指导作用，对电磁暂态仿真建模的进一步发展具有重要意义。
附图说明
图1为本发明的方法流程示意图。
图2为本发明的换流器电磁暂态仿真模型示意图。
图3为本发明的交叉初始化原理示意图。
图4为Ron/Roff模型、LC模型和本发明模型仿真A相上桥臂开关电压波形对比图。
图5为Ron/Roff模型、LC模型和本发明模型仿真A相上桥臂开关功率损耗波形对 比图。
图6为Ron/Roff模型、LC模型和本发明模型仿真A相输出有功功率对比图。
具体实施方式
下面结合附图对发明的技术方案进行详细说明。本发明采用参数化方法建立换流器电磁暂态模型，分析模型运行特性确定最优参数，同时采用交叉初始化方法处理状态切换误差，搭建换流器恒导纳电磁暂态仿真参数化模型，从而提出了一种新型的基于交叉初始化的换流器参数化恒导纳建模方法。
本发明公开的一种基于交叉初始化的换流器参数化恒导纳建模方法如图1所示，包括以下步骤：
步骤(1)对电力电子换流器进行电磁暂态仿真建模，其中开关采用参数历史电流源恒导纳模型，其他元件采用传统电磁暂态仿真积分模型建立，并给定***初始值和步长；
步骤(2)检测是否发生运行状态切换，如果发生状态切换则进行交叉初始化修正，如果未发生不做处理；
步骤(3)根据网络拓扑结构和预期控制效果计算模型参数，建立全网等效电磁导纳矩阵和历史电流源，得到换流器电磁暂态仿真等效模型；
步骤(4)根据电磁暂态基本求解方程I＝YU求解电磁暂态仿真等效模型建立的方程，获取当前时刻换流器电磁暂态模型仿真结果；
步骤(5)根据当前时刻网络各节点状态量，更新电磁暂态仿真等效导纳阵和历史电流源用于下一时刻求解，回到步骤(2)，直至到达仿真终止时间。
步骤(11)换流器电磁暂态仿真模型内部各环节关系如下：
直流侧电压U dc由外部直流电压源提供，直流侧输出电流I dc与输出功率P dc经过直流侧并联电容后传入若干组由上下两个开关组成的桥臂，再传出到交流电网U ac中；电网反馈有功功率P grid和无功功率Q gird给外环控制器，外环控制器输出电流参考值idref、iqref给内环控制器，内环控制器将交流侧dq轴电流分量id、iq与参考值大小进行比较产生逆变器的SPWM控制信号。
步骤(21)交叉初始化修正方法具体为：
在换流器运行状态切换时刻，动作开关的注入电流源使用对应桥臂上另一开关的电压和电流的历史状态量计算得到，可大大减小切换时刻初值的误差偏移，假设换流器运 行状态由S 1关断、S 2导通切换至S 1导通、S 2关断，得到交叉初始化初值为：
Figure PCTCN2021085704-appb-000011
用上述状态量初值求解状态切换时刻注入电流源I inj,up(t),I inj,down(t)。
步骤(31)建立换流器电磁暂态仿真等效模型具体为：
对于给定电力电子开关，用以下方程来表述：
Figure PCTCN2021085704-appb-000012
其中，α、β分别为等效注入电流源的电压系数、电流系数。
对于电感、电容等元件，利用后向欧拉法求等效导纳和历史电流源：
Figure PCTCN2021085704-appb-000013
上式为含有未知状态量电压u(t)、电流i(t)和已知状态量前一时刻电压u(t-△t)、前一时刻电流i(t-△t)的代数方程，通过化简可得形如i＝G eq*u+I inj的形式，进而可得到电磁暂态仿真等效导纳矩阵G eq和等效注入电流源I inj，根据I＝YU求解该代数方程组。
根据网络拓扑结构和预期控制效果建立电磁暂态仿真模型的具体过程为：
步骤(41)建立换流器参数化恒导纳模型：
Figure PCTCN2021085704-appb-000014
步骤(42)对开关模型进行复频域稳态运行分析，得到开关模型参数表达式为：
Figure PCTCN2021085704-appb-000015
步骤(43)根据网络拓扑结构求解得到关于换流器桥臂中点电压和关断状态下开关的矩阵方程，以上桥臂开关导通、下桥臂开关关断为例：
Figure PCTCN2021085704-appb-000016
步骤(44)分析参数化模型暂态运行特性，得到两种不同运行状态下模型对应参数如下：
Figure PCTCN2021085704-appb-000017
时，
Figure PCTCN2021085704-appb-000018
Figure PCTCN2021085704-appb-000019
时，
Figure PCTCN2021085704-appb-000020
步骤(45)建立换流器电磁暂态仿真***控制环节、网侧接口等模型，联立全网电磁暂态仿真***基本方程I＝YU；
步骤(46)结合接口参数求解换流器电磁暂态仿真方程，得到当前时刻各节点状态量用于更新电磁暂态等效导纳矩阵和历史电流源，回到步骤(43)继续计算直到到达仿真终止时间。
下面通过对比三种不同的电力电子换流器电磁暂态模型仿真波形以说明基于交叉初始化的换流器参数化恒导纳建模方法的技术优势。
针对于某一三相桥式整流***进行仿真建模，仿真步长为1μs。换流器模型相关参数如表1所示。换流器等效电磁暂态仿真模型如图2所示。交叉初始化原理如图3所示。Ron/Roff模型、LC模型和本修正模型的仿真波形比较如图4-6所示，其中图4为A相上桥臂开关S 1电压对比，图5为A相上桥臂开关S 1功率损耗对比，图6为A相输出有功功率对比。
表1换流器模型相关参数
换流器模型相关参数 参数大小
交流电压源线电压有效值U m(V) 380
交流电压源频率f ac(Hz) 50
直流侧负载R(Ω) 1
直流侧电容C(mF) 5
换流器内部等效杂散电阻R s(Ω) 0.1
换流器内部等效杂散电感L s(mH) 8
换流器开关等效导纳G eq(S) 1
有功功率额定值P(kW) 45
无功功率额定值Q(kvar) 0
载波频率f T(Hz) 5000
由图4-6可以看出，修正换流器参数化模型(细实线)的波形比LC模型(粗点线)的波形更加接近Ron/Roff模型(粗虚线)，本文所提基于交叉初始化的换流器参数化模型能够提高换流器模型仿真收敛性能，在状态切换时刻的虚拟功率损耗大大降低。同时由图4-6可以看出，基于交叉初始化的换流器参数化模型和Ron/Roff模型仿真结果基本一致，说明了本文所提方法的有效性。由图4-6可以看出，上述换流器***中，在不影响仿真速度的前提下，本文所提的基于交叉初始化的换流器参数化模型精度高，虚拟功率损耗极小，具有理想的稳态和暂态运行特性。

Claims (5)

  1. 一种基于交叉初始化的换流器参数化恒导纳建模方法，其特征在于，包括如下步骤：
    (1)对电力电子换流器进行电磁暂态仿真建模，其中开关采用参数历史电流源恒导纳模型，其他元件采用传统电磁暂态仿真积分模型建立，并给定***初始值和步长；
    (2)检测是否发生运行状态切换，如果发生状态切换则进行交叉初始化修正，如果未发生不做处理；
    (3)根据网络拓扑结构和预期控制效果计算模型参数，建立全网等效电磁导纳矩阵和历史电流源，得到换流器电磁暂态仿真等效模型；
    (4)根据电磁暂态基本求解方程I＝YU求解电磁暂态仿真等效模型建立的方程，获取当前时刻换流器电磁暂态模型仿真结果；
    (5)根据当前时刻网络各节点状态量，更新电磁暂态仿真等效导纳阵和历史电流源用于下一时刻求解，回到步骤(2)，直至到达仿真终止时间。
  2. 如权利要求1所述的一种基于交叉初始化的换流器参数化恒导纳建模方法，其特征在于，步骤(1)中，换流器电磁暂态仿真模型包括电力电子开关、电感、电容和控制部分，具体关系如下：
    直流侧电压U dc由外部直流电压源提供，直流侧输出电流I dc与输出功率P dc经过直流侧并联电容后传入若干组由上下两个开关组成的桥臂，再传出到交流电网U ac中；电网反馈有功功率P grid和无功功率Q gird给外环控制器，外环控制器输出电流参考值idref、iqref给内环控制器，内环控制器将交流侧dq轴电流分量id、iq与参考值大小进行比较产生逆变器的SPWM控制信号。
  3. 如权利要求1所述的一种基于交叉初始化的换流器参数化恒导纳建模方法，其特征在于，步骤(2)中，交叉初始化修正方法具体为：
    在换流器运行状态切换时刻，动作开关的注入电流源使用对应桥臂上另一开关的电压和电流的历史状态量计算得到，可大大减小切换时刻初值的误差偏移，假设换流器运行状态由S 1关断、S 2导通切换至S 1导通、S 2关断，得到交叉初始化初值为：
    Figure PCTCN2021085704-appb-100001
    用上述状态量初值求解状态切换时刻注入电流源I inj,up(t),I inj,down(t)。
  4. 如权利要求1所述的一种基于交叉初始化的换流器参数化恒导纳建模方法，其特征在于，步骤(3)中，建立换流器电磁暂态仿真等效模型具体为：
    对于给定电力电子开关，用以下方程来表述：
    Figure PCTCN2021085704-appb-100002
    其中，α、β分别为等效注入电流源的电压系数、电流系数；
    对于电感、电容等元件，利用后向欧拉法求等效导纳和历史电流源：
    Figure PCTCN2021085704-appb-100003
    上式为含有未知状态量电压u(t)、电流i(t)和已知状态量前一时刻电压u(t-△t)、前一时刻电流i(t-△t)的代数方程，通过化简可得形如i＝G eq*u+I inj的形式，进而可得到电磁暂态仿真等效导纳矩阵G eq和等效注入电流源I inj，根据I＝YU求解该代数方程组。
  5. 如权利要求1所述的一种基于交叉初始化的换流器参数化恒导纳建模方法，其特征在于，步骤(4)中，根据网络拓扑结构和预期控制效果建立电磁暂态仿真模型的步骤如下：
    (41)建立换流器参数化恒导纳模型：
    Figure PCTCN2021085704-appb-100004
    (42)对开关模型进行复频域稳态运行分析，得到开关模型参数表达式为：
    Figure PCTCN2021085704-appb-100005
    (43)根据网络拓扑结构求解得到关于换流器桥臂中点电压和关断状态下开关的矩阵方程，以上桥臂开关导通、下桥臂开关关断为例：
    Figure PCTCN2021085704-appb-100006
    (44)分析参数化模型暂态运行特性，得到两种不同运行状态下模型对应参数如下：
    Figure PCTCN2021085704-appb-100007
    时，
    Figure PCTCN2021085704-appb-100008
    Figure PCTCN2021085704-appb-100009
    时，
    Figure PCTCN2021085704-appb-100010
    (45)建立换流器电磁暂态仿真***控制环节、网侧接口等模型，联立全网电磁暂态仿真***基本方程I＝YU；
    (46)结合接口参数求解换流器电磁暂态仿真方程，得到当前时刻各节点状态量用于更新电磁暂态等效导纳矩阵和历史电流源，回到步骤(43)继续计算直到到达仿真终止时间。
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