潮流计算-英文文献
潮流计算文献翻译(开题报告)
基于Matlab的电力系统潮流仿真计算（直角坐标）摘要：潮流计算是电力系统的一项重要分析功能，是进行故障计算，继电保护整定，安全分析的必要工具。
结合电力系统的特点，利用 MATLAB语言运行电力系统潮流计算，再结合牛顿—拉夫逊法潮流计算（直角坐标），主要特点是操作简单，软件运行稳定.计算准确，提高了计算速度。
关键词：电力系统潮流计算 MATLAB 牛顿—拉夫逊法潮流计算引言为了提高供电可靠性以及资源利用的综合经济性，把许多分散的各种形式的发电站，通过送电线路和变电所联系起来。
这种由发电机、升压和降压变电所，送电线路以及用电设备有机连接起来的整体，即称为电力系统。
电力系统运行方式管理中，潮流计算是确定电网运行方式的基本出发点；在规划领域，需要进行潮流计算分析验证规划方案的合理性；在实时运行环境，调度员潮流提供了电网在预想操作情况下电网的潮流分布以校验运行可靠性。
在电力系统调度运行的多个领域都涉及到电网潮流计算。
潮流计算是确定电力网络运行状态的基本因素，潮流计算问题是研究电力系统稳态问题的基础和前提。
利用MATLAB语言运行电力系统潮流计算，再结合牛顿—拉夫逊法潮流计算（直角坐标），是一种常规的算法。
1.潮流计算简介电力系统潮流计算也分为离线计算和在线计算两种，前者主要用于系统规划设计和安排系统的运行方式，后者则用于正在运行系统的经常监视及实时控制。
利用电子数字计算机进行电力系统潮流计算从50年代中期就已经开始。
潮流计算曾采用了各种不同的方法，这些方法的发展主要围绕着对潮流计算的一些基本要求进行的。
而牛顿—拉夫逊法潮流计算是最普遍的一种潮流计算法。
2.潮流计算的要求电力系统潮流计算问题在数学上是一组多元非线性方程式求解问题，其解法都离不开迭代。
对潮流计算的要求可以归纳为下面几点：（1）计算方法的可靠性或收敛性；（2）对计算机内存量的要求；（3）计算速度；（4）计算的方便性和灵活性。
由于电力系统结构及参数的一些特点，并且随着电力系统不断扩大，潮流计算的方程式阶数也越来越高，对这样的方程式并不是任何数学方法都能保证给出正确答案的。
潮流计算外文翻译
First, introduction an ideal electrical power system is by the sole constant frequency and the stipulation peak-to-peak value regulated voltage power supply. But in fact, as a result of the recent years along with science's and technology's unceasing development, the high efficiency traded the class equipment and the modulator use, high in the electrical power system presses the nonlinear element which the direct current transmission the application, the massive misalignment load's appearance as well as the power supply system itself existed and so on to cause in the system's voltage waveform distortion to be getting more and more serious, has caused the very big harm to the electrical power system, for example: Causes in the power supply system the part to lose increases, reduces current collector's service life, to disturb the communication system and so on. Serious when even can also cause equipment the damage, automatic control malfunction, relay protection misoperation, thus creates the power cut accident and so on and other questions. So-called " the friend knows other, is undefeated in many battles ", therefore, must realize to the electrical network overtone comprehensive program of public order, must make clear the overtone origin and the electrical network in under the each different movement way the overtone tidal current distributed situation, adopts the corresponding measure limit and the harmonic cancellation, thus changes the friendly power supply system power supply quality and guarantees system's security economy movement.Second, electrical power system overtone's origin in the electrical power system the overtone source is many and varied. Mainly has the following several kinds: in 1, system's each kind of misalignment current collector for example: Trades the class equipment, the modulator, the electrification railroad, the arc furnace, fluorescence the lamp, the domestic electric appliances as well as each kind of electronic energy conservation control device and so on is the electrical power system overtone important source. Even if these equipment supplies its ideal sine wave voltage, it uses the electric current is also non-linear, namely has the harmonic current existence. And these the equipment produces the harmonic current will also po ur into the electrical power system, will cause system each place voltage to have the harmonic component. These equipment's harmony the wave content decided that in its characteristic and the working condition, basically has nothing to do with the electrical power system parameter, may regard as overtone constant flow the source. 2, the power supply system itself exists the nonlinear element is overtone another origin. These nonlinear element mainly has the transformer to stir up the capacitor which, the reactor group the magnetism leg, the alternating and direct convertor station's silicon-controlled rectifier controlling element, the silicon-controlled rectifier control and so on.3rd, like the fluorescent lamp, the domestic electric appliances and so on single capacity is not big, but quantity and spreads very greatly in each place, electric power department with difficulty management current collector. If these equipment's current harmonics content is oversized, will then have the serious influence to the electrical power system, to this kind of equipment's current harmonics content, when manufacture namely should limit in certain quantity scope. 4, the generator send outovertone electric potential. The generator will send out the overtone electric potential at the same time also to have the overtone electric potential production, its overtone electricity the potential will be decided by generator's structure and the working condition, basically will have nothing to do with the external connection impedance. Therefore may regard as overtone constant pressure source , but its value is very small. the three, electrical power system overtone tidal current calculates the so-called electrical power system overtone tidal current computation, is through solution network equation In=YnUn (n=3,5,7 ...... n: Agrees wave number the number. In is the overtone source load pours into electrical network's n subharmonic electric current row vector. Yn is electrical network's n subharmonic conductance. Un is in the electrical network a various nodes bus bar n subharmonic voltage row vector). Obtains in the electrical network various nodes (bus bar) the harmonic voltage, enters to obtain in various legs' harmonic current.When in the electrical power system the existence has the overtone source, this time in the system the contact voltage and the branch current will have the higher harmonic. For the determination harmonic voltage and harmonic current's in power supply system distribution, needed to carry on to the overtone impedance constitution equivalent circuit the tidal current computation, when simultaneously in the rectifier unit power supply system possessed forbearance the part existed, but must act according to various legs overtone impedance the nature and the size, whether there is examined the resonant situation. carries on the overtone tidal current computation, must first determine the electrical network part's overtone impedance. (3.1), electrical network each kind of part's overtone impedance: (1), synchronous generator's overtone impedance the qualified generator's electric potential is the pure sine, does not include the higher harmonic, its generator electric potential only exists in the fundamental wave network. in higher harmonic network, because the generator overtone electric potential is very small, this time the visible generator overtone electric potential is zero. Therefore its and so on the value electric circuit is the junctor end and neutral point overtone reactance .And XGn=nXG1-------------(1) in the formula XG1 is when a fundamental wave generator's zero foreword, the positive sequence or the negative sequence reactance, has this subharmonic foreword characteristic to decide , if needs to take into account the network to lose, regarding the generator, may its impedance angle according to 85 degrees estimates, regarding the transmission line, part's and so on transformer and load equivalent generators, may its impedance angle according to 75 degrees estimates. . (2), transformer's overtone impedance the electrical power system overtone's peak-to-peak value often is elevates along with the frequency weakens, therefore in the fundamental wave tidal current computation high tension line , often neglects transformer's initiation leg and the capacitance between turns particularly. When calculates the harmonic current, only considers transformer's leakage reactance, and thought that recognizes the frequency with the harmonic order to be proportional. Generally, as soon as transformer's equivalent circuit simplifies for links to meet theoriginal vice-mid-side node overtone reactance **** *** is the transformer fundamental wave leakage reactance. under higher harmonic's function, the winding internal kelvin effect and approaches the effect to increase, by no w transformer's resistance harmonic order's square was proportional approximately with the , this time's transformer overtone impedance is: Zn=sqrt(n)RT1+jnXT1-------------------------------(3) And RT1 is the fundamental wave time-variable depressor's resistance. regarding the three-phase winding transformer, may use the star equivalent circuit, on its overtone impedance computation side Fathom. when the overtone source pours into when higher harmonic current three-phase not symmetry, then must figures out the three-phase overtone impedance according to transformer's wiring way and various forewords impedance meter . 3) reactor's overtone impedance , when only takes into account the reactor induction reactance, to the n subharmonic frequency is: XLn=Nxl*UN/sqrt(3)IN 4), transmission line's overtone impedance the transmission line has the uniform distribution parameter electric circuit, passes through the transmission line which change positionss completely to be possible to regard as is three-phase symmetrical. in tidal current computation, usually by lumped parameter PI equivalent circuit expression. Following chart: in takes into account in the distribution characteristic situation, then: ZLn=Znsh(rnl) Yln/2=(chrnl-1)/(Znshrnl) ZN and RN respectively be regarding in this subharmonic when line's wave impedance and propagation constant. Zn=sqrt(Z0n/Y0n) Rn=sqrt(Z0nYon) Z0N and Y0N respectively be this subharmonic when transmission line unit length impedance and conductance five), load overtone impedance .When overtone tidal current computation, the fundamental wave part may pour into power regarding according to the node, but regards as in the overtone network it is the constant impedance, may think that approximately the synthesis load is an equivalent electric motor. Its synthesis load's overtone equivalent resistance value is: ZN=SQRT (N) R1+JNX1 R1, X1 is the fundamental wave equivalent electric motor's negative sequence resistance, the reactance, its value may by this node fundamental wave voltage, power the value obtain after the conversion. the zero foreword electric current will not enter the load generally, thus in zero foreword's higher harmonic network, may neglect shoulders the leg. when after has determined in the electric circuit various electrical element's overtone impedance, may constitute an overtone function equivalent circuit, with the aim of carrying on the computation, under when plan overtone function equivalent circuit should pay attention to the following several characteristics: (1), the overtone function's equivalent circuit, should take the rectifier unit as a center, according to actual wiring constitution, therefore the rectification installs to set regards as the overtone source, but electrical power system's generator is not appears by the energy, but as overtone source loaded impedance part. (2), the circuit element impedance may use the famous value to carry on the computation, may also use the sign Yao value to carry on the computation. When uses famous value carries on the computation, the complete electric circuit should convert to some voltage reference, is advantageous for the analysis and theapplication. (3) in the general computation, part's all resistances may neglect, but when system some part occurs either close parallel or strings together the joint resonance, this time's resistance influence actually cannot neglect. (4), in harmonic current approximate calculation, what determined is the rectifier unit side total harmonic current, according to and so on overtone function the effect electric circuit, can determine various legs harmonic current and the voltage distribution. the 3.2nd, overtone tidal current calculates (3.2.1), not to allow the part network overtone tidal current to calculate (1), symmetrical system's overtone tidal current to calculate in the symmetrical system the three-phase situation to be the same, therefore may calculate according to a situation. when has determined the rectifier unit, no matter what after one side total harmonic current, the union overtone equivalent circuit, may determine in the system network, no matter what a leg's harmonic current distribution. Then again pours into the harmonic current according to the node harmonic voltage and the node relational I=YU (in its , Y is overtone conductance), might determine each place node harmonic voltage. Then may extract the tidal current power. It counts to calculate that the step is as follows: , the basis give the operating condition, by usual tidal current computational method solution fundamental wave tidal current. , according to the overtone source working condition, determined other related parameters and need to calculate harmonic order. , calculates various parts overtone parameter, forms various subharmonics node admittance matrix, and calculates the corresponding overtone net to pour into the electric current. , by type IN=YNUN determined that various nodes the harmonic voltage, and calculates various legs harmonic power. in which, should pay attention has the overtone injection current which the overtone instrumental measurement leaves, its phase angle is opposite in the fundamental current phase angle. Therefore after extracting the fundamental current, must carry on the overtone injection current phase angle the revision. Similarly, the system node's power is the fundamental wave power with agrees sum of the wave power, therefore the fundamental wave pours into the power also to carry on the revision. But the linear load's place fundamental wave pours into the power not to need to revise. (2), the symmetrical system overtone tidal current calculates in the symmetrical system, the three-phase situation is various, moreover mutual influence, must therefore simultaneously carry on three-phase system's idea to calculate. the symmetrical net tidal current's computation may divide into the network various subharmonics network, calculates the fundamental wave network first, after obtaining various nodes fundamental wave the voltage, calculates various overtones tidal current according to it each injection current, then presses this overtone injection current to resolve various subharmonics net to wind the equation, extracts various nodes various subharmonics voltage. (3.2.2), in the rectifier unit power supply system possesses forbearance the part has when the overtone tidal current to calculate , when in the rectifier unit power supply system possesses forbearance the part exists, the capacitor to rectifier unit's phase change process and voltage current wave the shape is influential. Generally under the base frequency, the induction reactance and thecapacitance leg's parameter differs really in a big way in the value, does not send produces the resonance effect, but a rectifier unit's non-sinusoidal return route, may regard as is several different frequencies and oscillation amplitude sine electric potential the comprehensive result which affects separately in the return route, because the induction reactance frequency characteristic and the capacitance frequency characteristic are just opposite, have the possibility subharmonic both value to be close in some under the , have the resonance effect. When besides carries on the normal overtone tidal current computation, but also wants to act according to various legs overtone impedance the nature and the size, whether there is examines the resonance. four, summarize in the electrical power system's overtone appearance, regarding the electrical power system movement is one kind " the pollution ". They reduced systemic voltage the unreliable profile quality, not only has affected electrical power system oneself seriously, moreover also harms the user and the periphery communications system. therefore to the electrical power system overtone's research regarding the improvement electrical energy quality, suppresses with the harmonic cancellation has vital significance .电力系统谐波成因分析及谐波潮流计算一、引言一个理想的电力系统是以单一恒定频率与规定幅值的稳定电压供电的。
电力系统潮流计算的计算机仿真-电气工程及其自动化毕业设计
电力系统潮流计算的计算机仿真-电气工程及其自动化毕业设计毕业设计（论文）材料之二（1）xxx工程大学本科毕业设计（论文）专业：电气工程及其自动化题目：电力系统潮流计算的计算机仿真作者姓名： xxx导师及职称： xxx（讲师）导师所在单位：电气工程学院2015年6 月2日xxx工程大学本科毕业设计（论文）任务书2015 届电气工程学院电气工程及其自动化专业学生姓名： xxxⅠ毕业设计（论文）题目中文：电力系统潮流计算的计算机仿真英文：Computer Analysis of Load Flow Calculation for Power SystemⅡ原始资料（也可以附参考文献）五节点等值电力网络如上图所示。
图中，节点1为平衡节点，其它节点都是PQ 节点，保持006.1.5j U +=为定值，给定各支路阻抗：18.006.02112j Z Z +==，18.006.03113j Z Z +==，12.004.04114j Z Z +==，06.002.05115j Z Z +==，03.001.03223j Z Z +==，24.008.05225j Z Z +==，24.008.04334j Z Z +==，也给定各节点输出功率：2.02.0~1j S --=，15.045.0~2j S +=，05.04.0~3j S +=，1.06.0~4j S +=。
试运用以极坐标表示的牛顿—拉夫逊法计算此五节点等值网络中的潮流分布。
计算精确度要求各节点不平衡量不大于510-。
Ⅲ 毕业设计（论文）任务内容1、课题研究的意义电力系统潮流计算是对复杂电力系统正常和故障条件下稳态运行状态的计算，又是研究电力系统的一项重要分析功能，同时也是进行故障计算、继电保护鉴定、安全分析的工具。
电力系统潮流计算是计算系统动态稳定和静态稳定的基础。
在电力系统规划设计和现有电力系统运行方式的研究中，都需要利用电力系统潮流计算来定量的比较供电方案或运行方式的合理性、可靠性和经济性。
潮流计算-英文文献
外文资料Summary of power flow calculationPower system is calculated on the trend of steady-state operation of the power system as a basis, it's running under the given conditions and determine the entire system wiring in various parts of the power system running: the voltage of the bus, all components of a mid-stream power, The power loss, and so on. Power system planning in the design and operation of the existing power system in the form of research, we need to calculate the trend of using quantitative analysis of comparative power programme or operation mode is reasonable. Reliability and economy. In addition, the power flow calculation is calculated static and dynamic stability of the foundation of stability. So the trend is calculated on the power system of a very important and very basis of calculation. Power flow calculation also divided into offline and online calculation of two terms, the former mainly used for system planning and design and organization of the operation mode, while the latter is running for the system of regular monitoring and real-time control. The use of electronic digital computer to calculate the trend of the power system from the mid-1950s has already begun. Power flow problems in mathematical calculation is a group of diverse non-linear equations to solve the problem, its solution can not be separated from iteration. Therefore, the flow calculation method, it requires first and foremost a reliable convergence, and give the correct answers. As the power system structure and parameters of some of the features, and with the continuous expansion of the power system, the trend of increasing order of the equation, so the formula is not any mathematical method can guarantee is given the correct answer. This calculation of the power system to become a staff continue to seek new and more reliable way of the important factors.Use of digital computers in the power flow problems at the beginning, the general adoption of a node admittance matrix-based successive into the law. The principle of this method is relatively simple to compare the volume of digital computer memory, to the 1950s computer manufacturing level and then the power system theoretical level. However, it is convergence of the poor, when the system large-scale change, the sharp rise in the number of iteration in the calculation of convergence are often not the case iteration. This forced the staff to the power system to calculate impedance matrix-based successive into the law. Impedance method to improve the flow of the convergence of computing, the solution of the admittance system can not solve some of the trend, in the 1960s, access to a wide range of applications, has the power system design. Operational and research has made great contribution. At present, there are stillsome in the power industry units impedance method to calculate the trend. Impedance of the main shortcomings of the occupation of the computer's memory, each iteration of the large amount of calculation. When the system continue to expand, the more prominent of these shortcomings. 16 K memory of a computer in the use of impedance method can only be calculated at 100 following the system, 32 K memory of the computer can only calculate 150 nodes under the system. In this way, many of the power system in order to use impedance method shall not be first on the trend of the system is the streamlining of work. In order to overcome resistance in memory and speed of the shortcomings of the mid-1960s to the development of the impedance matrix-based Block impedance. This approach to a large-scale system divided into several small regional system, the computer only need to store various parts of the system impedance matrix contact line between them and the resistance, not only substantial savings in memory capacity, but also improve the Computing speed.Overcome the shortcomings of the impedance of hungry is another way to use Newton - Raphson method. This is the mathematics of nonlinear equations to solve the typical method, a better convergence. In resolving the issue of power flow calculation, is admittance matrix-based, therefore, as long as we can in the iterative process as much as possible to maintain the formula coefficient matrix sparse, and can greatly improve Newton's Law trend of the efficiency of procedures . Since the mid-1960s, Newton's law in the use of the best order of elimination, the Newton in convergence. Memory requirements. Speed all over the impedance, as the late 1960s after the widespread adoption of the excellent way.Flow calculation flexibility and convenience of the request, the application of digital computers is also a very key issue. In the past for a long time, the power flow calculation relies on the Taiwan exchange. Taiwan simulates the exchange of power systems, computing platforms in the calculation of the trend of the exchange, calculated at any time surveillance systems can run different parts of the state to meet requirements, if they run certain parts of unreasonable, you can make adjustments immediately. In this way, the equivalent of the process on the computing staff lost operating system. Adjustment process is very intuitive, physical concept is very clear. When the use of digital computers to calculate the trend when it lost this visual. To make up for this shortcoming, the trend of the establishment of procedures to the extent possible, in terms of computer calculation in the process of strengthening the process of the computer monitor and control, and to facilitate a variety of modifications and adjustments. Power flow calculation is not a simple calculation, to run it as a form of adjustment may be more precise. In order to get a reasonable run, often need to keep in accordance with the results, modify the original data. In this sense, the trend in the preparation of our program, the ease of use and flexibility must be sufficient attention. Therefore, in addition to the requirements in various ways to modify as muchas possible. Adjustment, we must pay attention to input and output of convenience and flexibility, strengthening human-computer links, so that the calculation of staff to monitor timely and appropriate calculations to control the conduct of calculation .Power flow calculation is a power system analysis of the most basic terms, the complex power system under normal and failure conditions steady-state running the calculation. The trend is calculated to strike a target in the power system to be running the calculation. That is, voltage and power distribution node, to check whether the components of the system overload. Voltage meets all requirements of the distribution and allocation of power is reasonable and the power loss, and so on. Of the existing power system operations and expansion, the new power system planning and design of the power system for static and transient stability of the trend are calculated as the basis. If the trend of the results available on steady-state power system, or estimate the optimal security, such as the trend of the flow calculation method and the model has a direct impact. The actual power system that the main trend of technology adoption Newton - Raphson method.In the management of the operation mode, the trend of power grid operation mode is to determine the basic starting point in planning areas, the need for trend analysis verified the reasonableness of the plan in real-time operating environment, dispatchers, provided the trend of End-expected operating conditions in the power grid To check the trend of operational reliability. In the power system dispatching a number of areas related to the trend of grid computing. Electricity network is to determine the trend of running the basic factors, the trend is steady-state power system on the basis and prerequisite .外文原文翻译电力系统潮流计算综述电力系统潮流计算是研究电力系统稳态运行情况的一种计算，它根据给定的运行条件及系统接线情况确定整个电力系统各部分的运行状态：各母线的电压，各元件中流过的功率，系统的功率损耗等等。
潮流计算总结
潮流计算总结引言潮流计算是电力系统分析中的一项重要技术，用于确定电力系统各节点的电压幅值和相角。
随着电网规模的扩大和电力负荷的增加，潮流计算在电力系统的运行与规划中起到了至关重要的作用。
本文将对潮流计算相关的概念、方法和应用进行总结。
潮流计算的概念潮流计算，又称为电力网络潮流计算，是一种用于计算电力系统的电压幅值和相角的方法。
在潮流计算过程中，需要考虑各种电力设备的物理特性以及电力负荷的消耗。
潮流计算的目的是为了找到使得电网达到平衡和稳定的电压幅值和相角。
潮流计算的方法潮流计算可以通过不同的方法和算法进行，常用的方法包括牛顿-拉夫逊法（Newton-Raphson method）、高斯-赛德尔方法（Gauss-Seidel method）和快速潮流方法（Fast Decoupled Power Flow method）等。
牛顿-拉夫逊法牛顿-拉夫逊法是一种迭代的数学方法，用于求解非线性方程组。
在潮流计算中，通过将电力系统的节点电压幅值和相角作为未知数，建立电力系统的节点潮流方程，然后利用牛顿-拉夫逊法求解节点潮流方程的解。
该方法收敛速度较快，但对于特定的电力系统可能会出现发散的情况。
高斯-赛德尔方法高斯-赛德尔方法也是一种迭代的数学方法，通过不断更新节点电压幅值和相角的估计值，直至满足节点潮流方程的要求。
与牛顿-拉夫逊法相比，高斯-赛德尔方法的收敛速度较慢，但对于特定的电力系统往往能够保持稳定的收敛性。
快速潮流方法快速潮流方法是一种基于快速潮流方程的近似求解方法，该方法通过简化节点潮流方程，提高潮流计算的效率。
快速潮流方法在实际中广泛应用，能够满足大规模电力系统潮流计算的要求。
潮流计算的应用潮流计算在电力系统的运行与规划中具有广泛的应用价值。
网络规划和设计潮流计算可以用于电力系统的网络规划和设计，通过计算不同负荷条件下的电网潮流情况，为电网的扩建和优化提供科学依据。
电力系统运行与控制潮流计算可以用于电力系统的运行与控制，通过实时计算电网潮流情况，判断电力系统的稳定性和安全性，为运行人员提供决策支持。
电气工程外文文献原文与译文应用于独立运行微电网的潮流计算方法
毕业设计（论文）外文文献译文及原文Application of the Power Flow Calculation Method to Islanding Micro GridsY.H. Liu. Z.Q. Wu, S.J Lin, N. P. BrandonAbstract:Most existing power flow calculation methods use a swing bus as a reference node for the whole system Increasingly. new distributed generation resources (DGRs) are being added to the grid. Sometimes, local demand or failure of the grid can result in independent micro-grids forming, which are known as 'islanding' systems Howcver. current DGRs are often limited such that there is no single DGR which can balance the power demand and stabilize the frequency of the micro-grid, meaning that there is no swing bus from which the microgrid can bemanaged. According to existing research. a DGR coupled with a dcdicated cnergy storage .system and suitable control stratcgy (here termed a distributcd generation (DG system) has the ability to adjust its output. This means that a DG system can respond dynamically to grid events. This means that a DG .system can rcspond dynamically to grid events. In this paper. a new power flow calculation method (based on Newton-Raphson power flow solution) with good convergence is proposed that can accommodate the lack of a swing bus in an islanding system. This addresses power flow results and the frequency ofthe whole system. The method proposed is discussed in detail with cxamples of diffcrent DG systems with various adjustment coefficients and load models.The results arc compared with those of a traditional power flow calculation mcthod based around the use of a swing bus. In conclusion, this paper shows that the improved method is more apprpriate for islanding systems with mesh topology and for micro-grid management wihtno swing bus.Index Terms--Distributed Generation; Islanding; Micro Grid; Power Flow Calculation; Power SystemⅠ.NOMENCLATUREA. Indexesi,j numbef of node ;B. Constantsn number of nods of the system;m number of non-power-source nodes in the system;Ai percentage coefficient of constant impedance load in a compound load modeBi percentage coefficient ofconstant current load in a compound load model;Ci percentage coefficient of constant power load in a compound load model;错误！未找到引用源。
电力系统潮流计算不收敛的调整方法
电力系统潮流计算不收敛的调整方法洪峰【摘要】潮流调整是电力系统分析计算的重要内容,潮流计算不收敛调整技术是提高分析计算自动化水平的关键.针对电网由收敛到不收敛的动态过程进行分析,提出表征电网处在不收敛临界点的综合指标,基于该指标,提出潮流不收敛调整新算法.该方法考虑了发电机启停及出力约束条件,避免了调整过程中切除负荷的情况,EPRI 36节点系统和某实际系统算例分析验证了该算法的正确性和有效性.%The power flow adjustment is an important part of the analysis and calculation of power system, and the non-convergence adjustment technology is critical to improve the automation level of the analysis and calculation. The dynamic process of power flow calculation from convergence to non-convergence was analyzed, and the comprehensive index characterized the grid at the non-convergence critical point was put forward. On the basis, a novel adjustment method was proposed in this paper. The generator start-stop and output constraints were taken into account, which avoided the adjustment process to shed load. The simulation results of the EPRI36 node system and an actual power system verified the correctness and effectiveness of the proposed algorithm.【期刊名称】《电力科学与技术学报》【年(卷),期】2017(032)003【总页数】6页(P57-62)【关键词】电力系统;潮流计算;收敛临界点;潮流调整【作者】洪峰【作者单位】湖南省电力公司建设部,湖南长沙 410004【正文语种】中文【中图分类】TM74由于在实际工作中，出现潮流无解的问题，工作人员很难区分是病态潮流还是潮流无解。
基于MATLABGUIDE的电力系统潮流计算
1潮流计算1．1数学模型假设系统的节点个数为n ，其中第1，2，…，m 号节点为PQ 节点，第m＋1，m＋2，…，n－1号节点为PV 节点，第n 号节点为平衡节点。
在直角坐标下，节点电压V 觶i ＝e i ＋f i ，导纳矩阵Y ij ＝G ij ＋jB ij 。
对节点i 可列写方程：△P i ＝P is －e i nj ＝1Σ（G ij e j －B ij f j ）－f j nj ＝1Σ（G ij f j ＋B ij e j ）＝0i＝1，2，…，n－1△Q i ＝Q is －f i nj ＝1Σ（G ij e j －B ij f j ）－e j nj ＝1Σ（G ij f j ＋B ij e j ）＝0i＝1，2，…，m△V 2i ＝V 2is －V 2i ＝V 2is －（e 2i ＋f 2i ）＝0i＝m＋1，m＋2，…，n－1迭代过程的修正方程式：△W＝－J △V式中△W＝［△P 1，…，△P n－1，△Q 1，…，△Q m ，△V 2m＋1，…，△V 2n－1］T△V＝［△e 1，△e 2，…，△e n－1，△f 1，△f 2，…，△f n－1］TP e ＝鄣△P 1鄣△e 1…鄣△P 1鄣△e n－1………鄣△P n－11…鄣△P n－1n－1鄣鄣鄣鄣鄣鄣鄣鄣鄣鄣鄣P f ＝鄣△P 1鄣△f 1…鄣△P 1鄣△f n－1………鄣△P n－11…鄣△P n－1n－1鄣鄣鄣鄣鄣鄣鄣鄣鄣鄣鄣Q e ＝鄣△Q 1鄣△e 1…鄣△Q 1鄣△e n－1………鄣△Q m 1…鄣△Q m n－1鄣鄣鄣鄣鄣鄣鄣鄣鄣鄣鄣Q f ＝鄣△Q 1鄣△f 1…鄣△Q 1鄣△f n－1………鄣△Q m 1…鄣△Q m n－1鄣鄣鄣鄣鄣鄣鄣鄣鄣鄣鄣V e ＝鄣△V 2m＋1鄣△e 1…鄣△V 2m＋1鄣△e n－1………鄣△V 2n－1鄣△e 1…鄣△V 2n－1鄣△e n－1鄣鄣鄣鄣鄣鄣鄣鄣鄣鄣鄣鄣V f ＝鄣△V 2m＋1鄣△f 1…鄣△V 2m＋1鄣△f n－1………鄣△V 2n－1鄣△f 1…鄣△V 2n－1鄣△f n－1鄣鄣鄣鄣鄣鄣鄣鄣鄣鄣鄣鄣J＝P e P f Q e Q f V e V f 鄣鄣鄣鄣鄣鄣鄣鄣经过对雅可比矩阵改进重新分块，使之更适合于计算机编程。
潮流计算英语
潮流计算英语Title: The Trend of Computational EnglishComputational English, the fusion of computational linguistics and English language studies, has emerged as a burgeoning field in recent years, propelled by advancements in artificial intelligence and natural language processing. This interdisciplinary domain encompasses various aspects of language analysis, generation, and application, revolutionizing how we perceive and interact with English. In this essay, we delve into the key components and evolving trends within computational English, exploring its impact on linguistics, education, communication, and beyond.At its core, computational English leverages computational techniques to analyze, interpret, and generate English language data. Natural language processing (NLP) algorithms play a pivotal role in tasks such as textsummarization, sentiment analysis, and machine translation. These algorithms rely on linguistic principles to decipher the nuances of English syntax, semantics, and pragmatics, enabling machines to comprehend and produce human-like language output.One of the prominent trends in computational English is the development of intelligent tutoring systems (ITS)tailored for language learning. These systems employ NLP algorithms to provide personalized feedback, adaptive learning paths, and interactive exercises to enhancelearners' proficiency in English. By leveraging machine learning models, ITS can adapt to individual learning styles and track progress over time, offering a dynamic and immersive learning experience.Moreover, computational English intersects with sociolinguistics to analyze language variation and change in digital communication platforms. Social media, online forums,and messaging apps serve as rich sources of linguistic data, reflecting contemporary language usage, slang, and cultural trends. Computational linguists utilize techniques such as sentiment analysis and network analysis to uncover patterns in online discourse, shedding light on evolving linguistic norms and communicative strategies.The rise of computational creativity has also spurred innovation in English language generation. Generative models, such as recurrent neural networks (RNNs) and transformer architectures, can produce coherent and contextually relevant English text, ranging from poetry and storytelling to automated content generation. These models learn from vast corpora of text data, capturing the stylistic nuances and thematic patterns prevalent in English literature and discourse.Furthermore, computational English facilitates the development of assistive technologies for individuals withlanguage-related disabilities. Speech recognition systems, text-to-speech synthesis, and augmentative communication devices empower users to overcome communication barriers and access information in real-time. These assistive technologies leverage advanced NLP techniques to interpret spoken or written input and generate appropriate responses, fostering inclusivity and accessibility in diverse linguistic contexts.In the realm of academic research, computational English serves as a catalyst for interdisciplinary collaboration between linguists, computer scientists, psychologists, and educators. Cross-disciplinary initiatives explore innovative methodologies for corpus linguistics, discourse analysis, and psycholinguistic experiments, leveraging computational tools to address fundamental questions about language structure, acquisition, and usage.Looking ahead, the future of computational English holds immense promise and potential. Advancements in deep learning,cognitive computing, and human-computer interaction will continue to shape the landscape of linguistic research and technological innovation. As computational capabilities evolve, so too will our understanding of language dynamics and the ways in which technology can augment linguistic creativity, communication, and comprehension.In conclusion, computational English represents a convergence of computational methodologies and linguistic inquiry, redefining how we analyze, generate, and utilize English language data. From intelligent tutoring systems to assistive technologies and computational creativity, this interdisciplinary field permeates diverse domains, driving innovation and insights at the intersection of language and technology. As we navigate the complexities of linguistic diversity and digital communication, computational English remains at the forefront of transformative research and practical applications, shaping the future of language in the digital age.。
电力系统潮流计算毕业论文.doc
电力系统潮流计算毕业论文摘要潮流计算是在给定电力系统网络拓扑、元件参数和发电、负荷参量的条件下，计算有功功率、无功功率及电压在电力网中的分布。
本文以电力系统分析知识为基础，通过《电力系统分析综合程序》（PSASP）对已有实际电网进行潮流计算，大大缩短了计算时间，提高了计算精度；并通过PSASP 7.0版地理位置接线图宏观地显示电网的潮流分布，进行潮流仿真，为电网的电压调整以及静态和暂态稳定等计算提供必要的基础数据。
关键词：电力系统潮流计算；PSASP；收敛；电压调整ABSTRACTPower system flow calculation is given in power system network topology, components and power generation, load parameters, calculates active power, reactive power and voltage in the grid distribution. This paper is based on the knowledge of power system analysis for the foundation, and then uses the power system analysis sofeware package (PSASP) to have practical grid for flow calculation, greatly reducing the calculation time, improve the calculation accuracy; And through the PSASP version 7.0 geographic position wiring diagram to show the power distribution, the tide simulation, to provide the necessary basic data for grid voltage adjustment and static and transient stability calculation, etc.Keywords：Power flow calculation system; PSASP; Convergence; V oltage adjustment目录1 绪论 (1)1.1潮流计算简介 (1)1.2电力系统的结线方式和电压等级 (2)1.2.1 几种典型的结线方式及特点 (2)1.2.2 电力系统的电压等级 (3)1.3电力系统的潮流计算一般步骤 (3)1.4本设计的网络特点 (5)1.5本电网潮流计算与仿真的主要步骤 (5)2 电力网基本元件的数学模型 (6)2.1线路模型 (6)2.2变压器的模型 (7)2.2.1 双绕组变压器的参数和数学模型 (7)2.2.2 三绕组变压器的参数和数学模型 (9)2.3负荷模型 (10)2.4电力系统节点分类 (11)2.5小结 (12)3复杂电力系统潮流的计算机算法 (13)3.1节点电压方程 (13)3.2功率方程 (14)3.3牛顿—拉夫逊法迭代求解方程组 (14)3.4牛顿—拉夫逊法（直角坐标）潮流计算 (17)3.4.1 潮流计算时的修正方程式 (17)3.4.2 潮流计算的基本步骤 (19)3.5本章小结 (20)4 本电网的潮流计算与仿真 (21)4.1本电网的潮流计算 (21)4.1.1 建立基础元件数据库 (21)4.1.2 潮流计算作业的建立和计算 (24)4.1.3 结果输出 (26)4.2本电网潮流仿真 (27)5 PSASP潮流结果的处理 (29)5.1潮流结果的分析 (29)5.2电力系统的电压调整 (29)5.3本电网的电压调整后的潮流结果 (31)6 结论 (33)参考文献 (34)致谢 (35)1 绪论1.1 潮流计算简介（1）潮流计算电力系统潮流计算是研究电力系统稳态运行情况的一种基本电气计算。
潮流计算 文献综述
潮流计算文献综述英文回答：Edge Computing: A Literature Review.Edge computing is a distributed computing paradigm that brings computation and data storage resources closer to the edge of the network. This approach offers several advantages over traditional cloud computing, including:Reduced latency: By processing data closer to the source, edge computing can significantly reduce latency, which is critical for applications that require real-time response.Increased bandwidth: Edge computing can alleviate bandwidth constraints by distributing data processing and storage closer to end-users, reducing the need for long-distance data transfers.Improved security: By keeping data closer to the edge, edge computing can improve security by reducing the risk of data breaches and unauthorized access.In recent years, edge computing has gained significant traction in various industries, including:Industrial automation: Edge computing can enable real-time monitoring and control of industrial processes, improving efficiency and safety.Smart cities: Edge computing can support the deployment of smart city applications such as traffic management, environmental monitoring, and public safety.Healthcare: Edge computing can facilitate remote patient monitoring, enable real-time medical diagnostics, and improve access to healthcare services in remote areas.Numerous research studies have explored various aspects of edge computing, including:Architecture: Researchers have proposed different architectures for edge computing systems, considering factors such as network topology, resource allocation, and data management.Data processing: Edge computing introduces challenges in data processing due to limited resources. Researchers have investigated techniques for efficient data filtering, aggregation, and analysis.Security: Edge computing raises security concerns due to its distributed nature. Researchers have proposed security protocols and mechanisms to protect data and devices.Despite its advantages, edge computing also faces several challenges:Heterogeneity: Edge devices and networks can be highly heterogeneous, making it difficult to develop and deploy applications across different platforms.Resource constraints: Edge devices typically have limited computational resources and storage capacity, which can limit the capabilities of edge computing applications.Scalability: Scaling edge computing systems to support a large number of devices and applications can be challenging due to resource limitations and network constraints.中文回答：边缘计算，文献综述。
新型电力系统中不确定性潮流计算的研究
Operations Research and Fuzziology 运筹与模糊学, 2023, 13(4), 2601-2610 Published Online August 2023 in Hans. https:///journal/orf https:///10.12677/orf.2023.134259新型电力系统中不确定性潮流计算的研究廖泽伟贵州大学电气工程学院，贵州 贵阳收稿日期：2023年3月29日；录用日期：2023年7月21日；发布日期：2023年7月31日摘要潮流计算是电网工作人员进行电力系统规划和电力系统运行监测的一个基础环节，对电力系统稳定运行有着极为重要的意义。
近年来，“碳中和”概念的提出迫使电力行业实行能源转型，风力发电和光伏发电在电力系统中的渗透率逐渐提高。
但由于风光发电具有很强的随机性，因此新能源发电并网势必会导致电网随机波动增强，对电力系统安全和稳定的运行产生不利影响。
概率潮流分析可以解决含风光等不确定性因素的电力系统潮流计算准确性问题，有助于识别电力系统的薄弱环节和高风险工作方式，也可为网络规划和决策提供有价值的参考。
本文采用基于蒙特卡洛法和半不变量法的概率潮流计算方法，对含风光等不确定性因素的电力系统进行潮流分析，得到节点电压和支路功率的概率分布函数以及节点电压越限概率等信息，为电力系统规划和运行提供有价值的数据反馈。
关键词潮流计算，风力发电，光伏发电，概率潮流Research on Uncertain Power Flow Calculation in New Power SystemsZewei LiaoSchool of Electrical Engineering, Guizhou University, Guiyang GuizhouReceived: Mar. 29th, 2023; accepted: Jul. 21st, 2023; published: Jul. 31st, 2023AbstractPower flow calculation is a fundamental step for power system planning and operation monitoring by power grid personnel, and is of great significance for the stable operation of power systems. In recent years, the introduction of the concept of “carbon neutral” has forced the power industry to implement energy transformation, and the penetration of wind and photovoltaic power genera-tion in the power system has gradually increased. However, due to the strong randomness of wind廖泽伟 等power generation, the grid connection of new energy generation will inevitably lead to increased random fluctuations in the power grid, which will have a negative impact on the safe and stable operation of the power system. Probabilistic power flow analysis can solve the accuracy problem of power flow calculation in power systems with uncertain factors such as wind and rain, help identify weak links and high-risk working modes in power systems, and provide valuable refer-ence for network planning and decision-making. In this paper, a probabilistic power flow calcula-tion method based on the Monte Carlo method and the semi invariant method is used to perform power flow analysis for power systems with uncertainties such as wind and solar power. The probability distribution functions of node voltage and branch power, as well as the probability of node voltage exceeding limits, are obtained, providing valuable data feedback for power system planning and operation.KeywordsPower Flow Calculation, Wind Power Generation, Photovoltaic Power Generation, Probabilistic Power FlowCopyright © 2023 by author(s) and Hans Publishers Inc.This work is licensed under the Creative Commons Attribution International License (CC BY 4.0)./licenses/by/4.0/1. 引言1.1. 光伏发电的简介众所周知，太阳能是一种储量极为丰富的可再生能源，对太阳能的开发与利用是解决目前石油、煤等传统能源危机的一个重要途径，也是解决二氧化碳排放、全球变暖等环境问题的有利手段。
关于潮流计算外文文献原文.docx
Electrical Machines And Electrical Apparatus1 • Construction and Principles of Power TransformerTransformer is an indispensable component in many energy conversion systems. It makes possible electric generation at the most economical generator voltage, power transfer at the most economical transmission voltage, and power utilization at the most suitable voltage for the particular utilization device. The transformer is also widely used in low-power, low-current electronic and control circuits for performing such functions as matching the impedances of a source and its load for maximum power transfer, isolating one circuit from another, or isolating direct current while maintaining alternating current continuity between two circuits-Essentially, a transformer consists of two or more windings coupled by mutual magnetic flux. If one of these windings, the primary is connected to an alternating voltage source, an alternating flux will be produced whose amplitude will depend on the primary voltage, the frequency of the applied voltage, and the number of turns. The mutual flux will link the other winding, the secondary and will induce a voltage in it whose value will depend on the number of the secondary turns as well as the magnitude of the flux and the frequency. By properly proportioning the primary and the secondary turns, almost any desired voltage ratio, or ratio of transformation, can be obtained.The essence of transformer action requires only the existence of time-varying mutual flux linking two windings. Such action can occur for two windings coupled through air, but coupling between the windings can be made much more effectively using a core of iron or other ferromagnetic material, because most of the flux is then confined to a definite, high-permeability path linking the windings. Such a transformer is commonly called an iron-core transformer. Most transformers are of this type. The following discussion is concerned almost wholly with iron-core transforme匚In order to reduce the loss caused by eddy current in the core, the magnetic circuit usually consists of a stack of thin laminations. Two common types of construction are shown schematically in Fig. 1.1 • In the core type (Fig. 1.1a) the windings are wound around two legs of a rectangular magnetic core; in the shell type(Figl.lb) the windings are wound around the center leg of a three-legged core. Silicon -steel laminations 0-014 mm in thick are generally used for transformer used at frequencies below a few hundred Hz. Silicon steel has the desirable property of low cost, low core loss, and high permeability at high flux densities (1.0 to 1.5T). The cores of small transformer used in communication circuits at high frequenciesand low energy levels are sometimes made of compressed ferromagnetic alloys known as ferrites-Windings(a) (b)In each of these configurations, most of the flux is confined to the core and therefore links both windings. The winding also produce additional flux, known as leakage flux, which links one winding without linking the other. Although leakage flux is small fraction of the total flux, it plays an important role in determining the behavior of the transforme 匸In practical transformers, leakage is reduced by subdividing the windings into sections placed as close together as possible. In the core-type construction, each winding consists of two sections, one section on each of the two legs of the core, the primary and secondary windings being concentric coils. In the shell type construction, variations of the concentric-winding arrangement maybe used, or the windings may consist of a number of thin pancake coils assembled in a stack with primary and secondary coils interleaved.2. Advantages of Balanced Three-phase Versus Single-phase SystemsIn both transformers and rotating machines, a magnetic field is created by the combined action of the currents in the windings. In an iron-core transformer, most of this flux is confined to the core and links all the windings. This resultant mutual flux induces voltages in the windings proportional to their number of their turns and is responsible for the voltage-changing property of a transformer. In rotating machines, the situation is similar, although there is an air gap which separates the rotating and stationary components of the machine. Directly analogous to the manner in which transformer core flux links the various windings on a transformer core, the mutual flux in rotating machines crosses the air gap, linking the windings on the rotor and stator. As in a transformer, the mutual flux induces voltage in these winding proportional to the number of turns and time rate of change of the flux.A significant difference between transformers and rotating machines is that in rotating machines there is relative motion between the windings on the rotor and stator. This relative motion produces an additional component of the time rate of change of the various winding flux linkages. The resultantCore—Windingsvoltage component, known as the speed voltage, is characteristics of the process of electromechanical energy conversion. In a static transformer, however, the time variation of flux linkages is caused simply by the time variation of winding current; no mechanic motion is involved, and no electromechanical energy conversion takes place.The resultant core flux in a transformer induces a counter Electro-Motive Force(EMF) in the primary which, together with the primary resistance and leakage-reactance voltage drops, must balance the applied voltage. Since the resistance and leakage -reactance voltage drops usually are small, the counter EMF must approximately equal to the applied voltage and the core flux adjust itself accordingly. Exactly similar phenomena must take place in the armature windings of an AC motor. The resultant air-flux wave must adjust itself to generate a counter EMF approximately equal to the applied voltage. In both transformers and rotating machines, the Magneto-Motive Force (MMF) of all the currents must accordingly adjust itself to create the resultant flux required by this voltage balance. In any AC electromagnetic devices in which the resistance and leakage-reactance voltage drops are small, the resultant flux is very nearly determined by the applied voltage and frequency, and the cuiTents must adjust themselves accordingly to produce the MMF required to create this flux.In a transformer, the secondary current is determined by the voltage reduced by the secondary winding, the secondary leakage impedance, and the electric load. In an induction motor, the secondary(rotor) current is determined by the voltage induced in the secondary, the secondary leakage impedance, and mechanical load on its shaft. Essentially the same phenomena place in the primary winding of the transformer and in the armature (stator) windings of induction and synchronous motors. In all three, the primary, or armature, current must adjust itself so that the combined MMF of all currents creates the flux the required by the applied voltage.In addition to the useful mutual fluxes, in both transformers and rotating machines there are leakage fluxes which link individual windings without linking others. Although the detailed picture of the leakage fluxes in rotating machines is more complicated than that in transformers, their effects are essentially the same. In both, the leakage fluxes induce voltage in AC windings which are accounted for as leakage-reactance voltage drops. In both, the reluctances of the leakage-flux paths are dominated by that of a path through air, and hence the leakage fluxes arenearly linearly proportional to the current producing them・ The leakage-reactance therefore is often assumed to be constant, independent of the degree of saturation of the main magnetic circuit.Further examples of the basic similarities between transformer and rotating machines can be cited. Except for friction and windage, the losses in transformer and rotating machines are essentially the same. Tests for determining the losses and equivalent circuit parameters are similar: an open circuit, or no-load, test gives information regarding the excitation requirements and core losses(along with friction and windage losses in rotating machines), while a short-circuit test together with DC resistance measurements gives information regarding leakage reactance and winding resistances. 3. Elementary Knowledge of Rotating MachinesElectromagnetic energy conversion occurs when changes in the flux linkage result from mechanical motion. In rotating machines, voltage are generated in windings or groups of coils by rotating these windings mechanically through a magnetic field, by mechanically rotating a magnetic field past the winding, or by designing the circuit so that the reluctance varies with rotation of the motor. By any of these methods, the flux linking a specific coil is changed cyclically, and a time-varying is generated.A set of such coils connected together is typically referred to an armature winding. In general, the term armature winding is used to refer to a winding or a set of windings on a rotating machine which carry AC currents. In AC machines such as synchronous or induction machines, the armature winding is typically on the stationary portion of the motor refeiTed to as the stator, in which case these windings may also be referred to as stator windings.In a DC machine, the armature winding is found on the rotating member, referred to as the rotor. The armature winding of a DC machine consists of many coils connected together to form a closed loop. A rotating mechanical contact is used to supply current to the armature winding as the rotor rotates.Synchronous and DC machine typically include a second winding (or set of settings) which carry DC current and which are used to produce the main operating flux in the machine. Such a winding is typically refeiTed to as field winding. The field winding on a DC machine is found on the stator, while that on a synchronous machine is found on the rotor, in which case current must be supplied to the field winding via a rotating mechanical contact. As we have seen, permanent magnetic also produce DC magnetic flux and are used in the place of field windings in some machines.In most rotating machines, the stator and rotor are made of electrical steel, and the windings are installed in slots on these structures. The use of such high-permeability material maximizes the coupling between the coils and increase the magnetic energy density associated with the interaction.It also enables the machine designer to shape and distribute the magnetic fields according to the requirements of each particular machine design. The time varying flux present in the armature structures of these machines tends to induce cuiTents, known as eddy currents, in the electrical steeL Eddy currents can be a large source of loss in such machine and can significantly reduce machine performance. In order to minimize the effects of eddy currents, the armature structure is typically built from thin laminations of electrical steel with are insulated from each other.In some machines, such as reluctance machines and stepper motors, there are no windings on the roton Operation of these machines depends on the nonuniformity of air-gap reluctance associated with variations in rotor position in conjunction with time-varying currents applied to their stator windings. In such machines, both the stator and rotor structures are subjected to time-varying magnetic flux and, as a result, both may require lamination to reduce eddy-current losses.Rotating electric machines take many forms and are known by many names: DC, synchronous, permanent-magnet, induction, variable reluctance, hysteresis, brushless, and so on. Although these machines appear to be quite dissimilar, the physical principles governing their behavior are quite similar, and it is often helpful to think of them in the same physical picture.。
基于MALAB的牛顿拉夫逊法潮流计算毕业论文
基于MALAB的牛顿拉夫逊法潮流计算摘要本文，首先简单介绍了基于在MALAB中行潮流计算的原理、意义，然后用具体的实例，简单介绍了如何利用MALAB去进行电力系统中的潮流计算。
众所周知，电力系统潮流计算是研究电力系统稳态运行情况的一种计算，它根据给定的运行条件及系统接线情况确定整个电力系统各部分的运行状态：各线的电压、各元件中流过的功率、系统的功率损耗等等。
在电力系统规划的设计和现有电力系统运行方式的研究中，都需要利用潮流计算来定量地分析比较供电方案或运行方式的合理性、可靠性和经济性。
此外，在进行电力系统静态及暂态稳定计算时，要利用潮流计算的结果作为其计算的基础；一些故障分析以及优化计算也需要有相应的潮流计算作配合；潮流计算往往成为上述计算程序的一个重要组成部分。
以上这些，主要是在系统规划设计及运行方式安排中的应用，属于离线计算范畴。
牛顿－拉夫逊法在电力系统潮流计算的常用算法之一，它收敛性好，迭代次数少。
本文介绍了电力系统潮流计算机辅助分析的基本知识及潮流计算牛顿－拉夫逊法，最后介绍了利用MTALAB程序运行的结果。
关键词：电力系统潮流计算，牛顿－拉夫逊法，MATLABABSTRACTThis article first introduces the flow calculation based on the principle of MALAB Bank of China, meaning, and then use specific examples,a brief introduction, how to use MALAB to the flow calculation in power systems.As we all know, is the study of power flow calculation of power system steady-state operation of a calculation, which according to the given operating conditions and system wiring the entire power system to determine the operational status of each part: the bus voltage flowing through the components power, system power loss and so on. In power system planning power system design and operation mode of the current study, are required to quantitatively calculated using the trend analysis and comparison of the program or run mode power supply reasonable, reliability and economy. In addition, during the power system static and transient stability calculation, the results of calculation to take advantage of the trend as its basis of calculation; number of fault analysis and optimization alsorequires a corresponding flow calculation for cooperation; power flow calculation program often become the an important part. These, mainly in the way of system design and operation arrangements in the application areas are off-line calculation.Newton - Raphson power flow calculation in power system is one commonly used method, it is good convergence of the iteration number of small, introduce the trend of computer-aided power system analysis of the basic knowledge and power flow Newton - Raphson method, introduced by the last matlab run results.Keywords：power system flow calculation, Newton – Raphson method, matlab目录1 绪论 (1)1.1 课题背景 (1)1.2 电力系统潮流计算的意义 (2)1.3 电力系统潮流计算的发展 (2)1.4 潮流计算的发展趋势 (4)2 潮流计算的数学模型 (5)2.1 电力线路的数学模型及其应用 (5)2.2 等值双绕组变压器模型及其应用 (7)2.3 电力网络的数学模型 (10)2.4 节点导纳矩阵 (10)2.4.1 节点导纳矩阵的形成 (11)2.4.2 节点导纳矩阵的修改 (11)2.5 潮流计算节点的类型 (12)2.6 节点功率方程 (14)27 潮流计算的约束条件 (15)·3 牛顿－拉夫逊法潮流计算基本原理 (17)3.1 牛顿-拉夫逊法的基本原理 (17)3.2 牛顿-拉夫逊法潮流计算的修正方程 (20)3.3 潮流计算的基本特点 (23)3.4 节点功率方程 (25)4牛顿－拉夫逊法分解潮流程序 (26)1 牛顿－拉夫逊法分解潮流程序原理总框图 (26)4·4.2 形成节点导纳矩阵程序框图及代码 (28)4.2。
用matlab电力系统潮流计算
题目：潮流计算与matlab教学单位电气信息学院姓名学号年级专业电气工程及其自动化指导教师职称副教授摘要电力系统稳态分析包括潮流计算和静态安全分析。
本文主要运用的事潮流计算，潮流计算是电力网络设计与运行中最基本的运算，对电力网络的各种设计方案及各种运行方式进行潮流计算，可以得到各种电网各节点的电压，并求得网络的潮流及网络中的各元件的电力损耗，进而求得电能损耗。
本位就是运用潮流计算具体分析，并有MATLAB仿真。
关键词：电力系统潮流计算 MATLABAbstractElectric power system steady flow calculation and analysis of the static safety analysis. This paper, by means of the calculation, flow calculation is the trend of the power network design and operation of the most basic operations of electric power network, various design scheme and the operation ways to tide computation, can get all kinds of each node of the power grid voltage and seek the trend of the network and the network of the components of the power loss, and getting electric power. The standard is to use the power flow calculation and analysis, the specific have MATLAB simulation.Key words: Power system; Flow calculation; MATLAB simulation目录1 任务提出与方案论证 (2)2 总体设计 (3)2.1潮流计算等值电路 (3)2.2建立电力系统模型 (3)2.3模型的调试与运行 (3)3 详细设计 (4)3.1 计算前提 (4)3.2手工计算 (7)4设计图及源程序 (11)4.1MATLAB仿真 (11)4.2潮流计算源程序 (11)5 总结 (31)参考文献 (32)1 任务提出与方案论证潮流计算是在给定电力系统网络结构、参数和决定系统运行状态的边界条件的情况下确定系统稳态运行状态的一种基本方法,是电力系统规划和运营中不可缺少的一个重要组成部分。
基于Matpower的潮流计算方法
基于Matpower的潮流计算方法徐恒娇;王洪诚;胡江航;沈霞【摘要】介绍了Matpower软件的基本操作方法，并通过实际分析和计算，说明了Matpower软件在电力系统分析中的优越性，同时介绍了Matpower软件应用简易、计算精度高、准确快速和直观明了等特点。
%This paper introduces the basic operation method of the software Matpower, and based on the actual analysis and calculation, explains the superiority of the software Matpower. And at the same time the paper analyzes that Matpower has the characteristics of simple application, high accuracy, fast speed and intuitiveness.【期刊名称】《物联网技术》【年(卷),期】2013(000)001【总页数】3页(P43-45)【关键词】潮流计算;电力系统;Matpower;矩阵【作者】徐恒娇;王洪诚;胡江航;沈霞【作者单位】西南石油大学，四川成都 610500;西南石油大学，四川成都610500;中海油CACT作业者集团，广东深圳 518000;西南石油大学，四川成都610500【正文语种】中文【中图分类】TM7430 引言Matpower是基于Matlab M文件的组建包，主要用来解决电力潮流和优化潮流的问题[1]，是为研究人员提供的一种易于使用和可更新的仿真工具。
Matpower的设计理念是尽可能简单易懂，它可以执行电力常规潮流运算，如牛顿拉夫逊法，P-Q分解法等，也可以执行最优潮流程序。
本文主要对执行常规的潮流计算[2,3]进行分析。
外文翻译--基于优化的牛顿—拉夫逊法和牛顿法的潮流计算
外文翻译--基于优化的牛顿—拉夫逊法和牛顿法的潮流计算英文文献Power Flow Calculation by Combination of Newton-Raphson Method and Newton’s Method in Optimization.Andrey Pazderin, Sergey YuferevURAL STATE TECHNICAL UNIVERSITY ? UPIE-mail: pav@//0>., usv@//.Abstract--In this paper, the application of the Newton’s method in optimization for power flow calculation is considered. Convergence conditions of the suggested method using an example of a three-machine system are investigated. It is shown, that the method allows to calculate non-existent state points and automatically pulls them onto the boundary of power flow existence domain. A combined method which is composed of Newton-Raphson method and Newton’s method in optimization is presented in the paper.Index Terms?Newton method, Hessian matrix, convergence of numerical methods, steady state stabilityⅠ.INTRODUCTIONThe solution of the power flow problem is the basis on which otherproblems of managing the operation and development of electrical power systems EPS are solved. The complexity of the problem of power flow calculation is attributed to nonlinearity of steady-state equations system and its high dimensionality, which involves iterative methods. The basic problem of the power flow calculation is that of the solution feasibility and iterative process convergence [1].The desire to find a solution which would be on the boundary of the existence domain when the given nodal capacities are outside the existence domain of the solution, and it is required to pull the state point back onto the feasibility boundary, motivates to develop methods and algorithms for power flow calculation, providing reliable convergence to the solution.The algorithm for the power flow calculation based on the Newton's method in optimization allows to find a solution for the situation when initial data are outside the existence domain and to pull the operation point onto the feasibility boundary by an optimal path. Also it is possible to estimate a static stability margin by utilizing Newton's method in optimization.As the algorithm based on the Newton’s method in optimization has considerable computational cost and power control cannot be realized in all nodes, the algorithm based on the combination of the Newton-Raphson met hods and the Newton’s method in optimization is offered to be utilizedfor calculating speed, enhancing the power flow calculation.II. THEORETICAL BACKGROUNDA.Steady-state equationsThe system of steady-state equations, in general, can be expressed as follows: where is the vector of parameters given for power flow calculation. In power flow calculation, real and reactive powers are set in each bus except for the slack bus. Ingeneration buses, the modulus of voltage can be fixed. WX,Y is the nonlinear vector function of steady-state equations. Variables Y define the quasi-constant parameters associated with an equivalent circuit of an electrical network. X is a required state vector, it defines steady state of EPS. The dimension of the state vector coincides with the number of nonlinear equations of the system 1. There are various known forms of notation of the steady-state equations. Normally, they are nodal-voltage equations in the form of power balance or in the form of current balance. Complex quantities in these equations can be presented in polar or rectangular coordinates, which leads to a sufficiently large variety forms of the steady-state equations notation. There are variable methods of a nonlinear system of steady-state equations solution. They are united by the incremental vector of independent variables ΔX being searched and the condition of convergence being assessed at each iteration.B. The Newton's method in optimizationAnother way of solving the problem of power flow calculation is related to defining a zero minimum of objective function of squares sum of discrepancies of steady-stateequations:2?The function minimum 2 is reached at the point where derivatives on all required variables are equal to zero: 3It is necessary to solve a nonlinear set of equations 3 to find the solution for the problem. Calculating the power flow, which is made by the system of the linear equations with a Hessian matrix at each iteration, is referred to as the Newton'smethod in optimization [4]: 4The Hessian matrix contains two items: 5During the power flow calculation, the determinant of Hessian matrix is positive round zero and negative value of a determinant of Jacobian .This allows to find the state point during the power flow calculation, when initial point has been outside of the existence domain.The convergence domain of the solution of the Newton's optimization method is limited by a positive value of the Hessian matrix determinant. The iterative process even for a solvable operating point can converge to an incorrectsolution if initial approximation has been outside convergencedomain. This allows to estimate a static stability margin of the state and to find the most perilous path of its weighting.III. INVESTIGATIONS ON THE TEST SCHEMEConvergence of the Newton's method in optimization with a full Hessian matrix has been investigated. Calculations were made based on program MathCAD for a network comprising three buses the parameters of which are presented in Figure 1.Dependant variables were angles of vectors of bus voltage 1 and 2 ,independent variables were capacities in nodes 1 and 2, and absolute values of voltages of nodes 1, 2 and 3 were fixed.Fig. 1 ? The Test schemeIn Figure 2, the boundary of existence domain for a solution of the steady-state is presented in angular coordinates δ1-δ2. This boundary conforms to a positive value of the Jacobian determinant:As a result of the power flow calculation based on the Newton method in optimization, the angle values have been received, these values corresponding to the given capacities in Fig.2 generation is positive and loading is negative.For the state points which are inside the existence domain, the objective function 2 has been reduced to zero. For the state points which are on the boundary of the existence domain, objective function 2 has not been reduced to zero and the calculated values of capacities differed fromthe given capacities.Fig. 2 ? Domain of Existence for a SolutionFig.3 - Boundary of existence domain In Fig.3, the boundary of the existence domain is presented in coordinates of capacities P1-P2. State points occurring on the boundary of the existence domain 6 have been set by the capacities which were outside the existence domain. As a result of power flow calculation by minimization 2 based on the Newton's method in optimization, the iterative process converges to the nearest boundary point. It is due to the fact that surfaces of the equal level of objective function 2 in coordinates of nodal capacities are proper circles for threemachine system having the centre on the point defined by given values of nodal capacitiesThe graphic interpretation of surfaces of the equal level of objective function for operating point state with 13000 MW loading bus 1 and 15000 MW generating bus 2 is presented in Fig.3.Hessian matrix is remarkable in its being not singular on the boundary of existence domain. The determinant of a Hessian matrix 5 is positive around zero and a negative value of the Jacobian matrix determinant. This fact allows the power flow to be calculated even for the unstable points which are outside existence domain. The iterative process based on the system of the linear equations 4 solution has converged to the critical stability point within 3-5 iteration. Naturally,the iterative process based on Newton-Rapson method is divergent for such unsolvable operating points.The convergence domain of the method under consideration has been investigated. What is meant is that not all unsolvable operating points will be pulled onto theboundary of existence domain. A certain threshold having been exceeded the iterative process has begun to converge to the imaginary solution with angles exceeding 360It is necessary to note that to receive a critical stability operating point in case when initial nodal capacities are set outside the boundary of the existence domain, there is no necessity to make any additional terms as the iterative process converges naturally to the nearest boundary point.Pulling the operation point onto feasibility boundary is not always possible by the shortest and optimal path. There are a number of constraints, such as impossibility of load consumption increase at buses, constraints of generation shedding/gaining at stations. Load following capability of generator units is various, consequently for faster pulling the operation point onto the feasibility boundary it is necessary to carry out this pulling probably by longer, but faster path.The algorithm provides possibility of path correction of pulling. It is carried out by using of the weighting coefficients, which define degree of participation of eachnode in total control action. For this purpose diagonal matrix A of the weighting coefficients for each node is included into the objective function 2:All diagonal elements of the weighting coefficient matrix A should be greater-than zero:When initial approximation lies into the feasibility domain, coefficients are not influence on the computational process and on the result.In the figure 4 different paths of the pulling the same operation point onto feasibility boundary depending on the weighting coefficients are presented. Paths are presented for two different operating points.In tables I and II effect of weighting coefficients on the output computation is presented. In tables I and II k1 and k2 are weighting coefficient for buses 1 and 2, respectively.TABLE IWEIGHTING COEFFICIENT EFFECT ON OUTPUT COMPUTATION FOR INITIAL SET CAPACITIES P1 -13000 MW AND P2 15000 MWCoefficients ,MW ,MW ,deg ,deg1,1 -7800 9410 -45 555,1 -8600 8080 -69 250.005,1 -5700 10140 -1 93TABLE IIWEIGHTING COEFFICIENT EFFECT ON OUTPUT COMPUTATION FOR INITIAL SET CAPACITIES P1 -8000 MW AND P2 -5000 MWCoefficients ,MW ,MW ,deg ,deg1,1 -4360 -1680 -92 -800.01,1 -1050 -4920 -76 -941,0.35 5800 0 -99 -71Fig.4 - Paths of pulling the operation point onto the feasibility boundaryIV. COMBINATION OF METHODSIf to compare the Newton’s method in optimization for power flow calculation with newton-Raphson using a Jacobian matrix, the method computational costs on eachiteration will be several times greater as the property of Hessian matrix being filled up by nonzero elements 2.5-3 times greater than with Jacobian one. Each row of Jacobian matrix corresponding to any bus contains nonzero elements corresponding to all incident buses of the scheme. Each row of Hessian matrix contains nonzero elements in the matrix corresponding not only to the neighboring buses, but also their neighbors. However, it is possible to compensate this disadvantage through the combination Newton-Rap son method with Newton’s method in optimization. It means that the part of nodes can be calculated by conventional Newtonmethod, and the remaining buses will be computed by Newton’s method in optimization. The first group of passive nodes consists of buses in which it is not possible to changenodal capacity or it is not expedient. Hence, emergency control actions are possible only in a small group of buses supplying with telecontrol. Most of the nodes includingpurely transit buses are passive. Active nodes are generating buses in which operating actions are provided. Such approach allows to fix nodal capacity for all passive buses of the scheme which have been calculated by Newton-Rap son method. In active buses which have been calculated by Newton’s method in optimization, deviations from set values of nodal capacity are possible. These deviations can be considered as control action. The power flow calculation algorithm based on combination Newton ? Ra phson method and Newton’s method in optimization can be presented as follows:1.The linear equation system with Jacobian matrix is generated for all buses of the scheme.2. The solution process of the linear equation system with Jacobian is started by utilizing the Gauss method for all passive buses. Factorization of the linear equations system is terminated when all passive buses are eliminated. Factorizedequations are kept.3.The nodal admittance matrix is generated from not factorized the part of Jacobian matrix corresponding to active buses. This admittance matrix contains parameters of the equivalent network which contains only active buses.4.The linear equation system with Hessian matrix 4 is generated for the obtained equivalent by Newton’s method in optimization.5.The linear equation system with Hessian matrix is calculated and changes of independent variables are defined for active buses.6.Factorized equations of passive buses are calculated, and changes of independent variables are defined for passive buses.7.The vector of independent variables is updated using the changes of independent variables for all buses.8. New nodal capacities in all buses of the network are defined; constraints are checked; if it necessary, the list of active buses will be corrected.9. Convergence of the iterative process is checked. If changes of variables are significant, it is necessary to return to item 1.Taking into account the number of active buses in the network aren’t large, computationa l costs of such algorithm slightly exceed computational costs of the Newton-Rapson method.V. CONCLUSION1. The power flow calculation of an electric network by minimizingthe square sum of discrepancies of nodal capacities based on the Newton's method in optimizationmaterially increases the productivity of deriving a solution for heavy in terms of conditions of stability states and the unstable states outside the existence domain of the solution.2. During the power flow calculation, the determinant of Hessian matrix is positive around zero and negative value of the Jacobian matrix determinant. The iterative process naturally converges to the nearest marginal state point during the power flow calculation, when the initial operating point has been outside of the existence domain.3. There is a possibility of control action correction for the pulling operation point onto feasibility boundary by using matrix of weighting coefficients.4. Utilization of the combined method for power flow calculation all ows to use all advantages of Newton’s method in optimization and to provide high calculating speed.5. In case when the setting nodal powers are outside the existence domain, there are discrepancies in the active buses, which can be considered as control actions for pulling the state point onto the feasibility boundary. When the initial state point is inside the existence domain, the iterative process converges with zero discrepancies for both active and passive buses.中文翻译基于优化的牛顿??拉夫逊法和牛顿法的潮流计算摘要??在本文中,考虑到了优化的牛顿法在潮流计算中的应用。
潮流计算参考文献
潮流计算参考文献
以下是关于潮流计算的参考文献：
1. Glover, J. D., Sarma, M. S., & Overbye, T. J. (2011). Power System Analysis and Design. Cengage Learning.
该书是经典的电力系统分析教材，其中详细介绍了潮流计算的原理和算法。
2. Wood, A. J., & Wollenberg, B. F. (1996). Power Generation, Operation, and Control. John Wiley & Sons.
这本书对电力系统潮流计算的算法进行了深入讲解，并包括了数值计算技术和边际潮流分析。
3. 尚鲁班，姚国勇. (2006) 电力系统潮流计算[M]. 科学出版社. 这本书是在国内编写的一本介绍电力系统潮流计算的教材，包括了时间步长法、牛顿拉夫逊法等算法。
4. Bergen, A. R. and Vittal, V. (2000). Power Systems Analysis. Prentice Hall.
这本书主要涵盖了潮流计算的传统方法，以及分布式发电、大规模风力和太阳能的集成应用。
此外，还可以参考相关学术期刊和会议论文，如IEEE Transactions on Power Systems、IEEE Power Engineering Society General Meeting等。
电力系统潮流计算软件设计外文原文及中文翻译
电力系统潮流计算软件设计外文原文及中文翻译外文原文及中文翻译Modelling and Analysis of Electric Power SystemsPower Flow Analysis Fault AnalysisPower Systems Dynamics and StabilityPrefaceIn the lectures three main topics are covered,i.e.Power flow an analysisFault current calculationsPower systems dynamics and stabilityIn Part I of these notes the two first items are covered,while Part II givesAn introduction to dynamics and stability in power systems. In appendices brief overviews of phase-shifting transformers and power system protections are given.The notes start with a derivation and discussion of the models of the most common power system components to be used in the power flow analysis.A derivation of the power ?ow equations based on physical considerations is then given.The resulting non-linear equations are for realistic power systems of very large dimension and they have to be solved numerically.The most commonly used techniques for solving these equations are reviewed.The role of power flow analysis in power system planning,operation,and analysis is discussed.The next topic covered in these lecture notes is fault current calculations in power systems.A systematic approach to calculate fault currents in meshed,large power systems will be derived.The needed models will be given and the assumptions made when formulating these models discussed.It will be demonstrated thatalgebraic models can be used to calculate the dimensioning fault currents in a power system,and the mathematical analysis has similarities with the power ?ow analysis,soitis natural to put these two items in Part I of the notes.In Part II the dynamic behaviour of the power system during and after disturbances(faults) will be studied.The concept of power system stability isde?ned,and different types of pow er system in stabilities are discussed.While the phenomena in Part I could be studied by algebraic equations,the description of the power system dynamics requires models based on differential equations.These lecture notes provide only a basic introduction to the topics above.To facilitate for readers who want to get a deeper knowledge of and insight into these problems,bibliographies are given in the text.Part IStatic Analysis1 IntroductionThis chapter gives a motivation why an algebraic model can be used to de scribe the power system in steady state.It is also motivated why an algebraic approach can be used to calculate fault currents in a power system.A power system is predominantly in steady state operation or in a state that could with sufficient accuracy be regarded as steady state.In a power system there are always small load changes,switching actions,and other transients occurring so that in a strict mathematical sense most of the variables are varying with thetime.However,these variations are most of the time so small that an algebraic,i.e.not time varying model of the power systemis justified.A short circuit in a power system is clearly not a steady state condition.Such an event can start a variety of different dynamic phenomena in the system,and to study these dynamic models are needed.However,when it comes to calculate the fault current sin the system,steady state(static) model swith appropriate parameter values can be used.A fault current consists of two components,a transient part,and a steady state part,but since the transient part can be estimated from the steady state one,fault current analysis is commonly restricted to the calculation of the steady state fault currents.1.1 Power Flow AnalysisIt is of utmost importance to be able to calculate the voltages and currents that different parts of the power system are exposed to.This is essential not only in order to design the different power system components such asgenerators,lines,transformers,shunt elements,etc.so that these can withstand the stresses they are exposed to during steady state operation without any risk of damages.Furthermore,for an economical operation of the system the losses should be kept at a low value taking various constraint into account,and the risk that the system enters into unstable modes of operation must be supervised.In order to do this in a satisfactory way the state of the system,i.e.all(complex) voltages of all nodes in the system,must be known.With these known,all currents,and hence all active and reactive power flows can be calculated,and other relevant quantities can be calculated in the system.Generally the power ?ow,or load ?ow,problem is formulated as a nonlinear set of equationsf (x, u, p)=0(1.1)wheref is an n-dimensional(non-linear)functionx is an n-dimensional vector containing the state variables,or states,ascomponents.These are the unknown voltage magnitudes and voltage angles of nodes in the systemu is a vector with(known) control outputs,e.g.voltages at generators with voltage controlp is a vector with the parameters of the network components,e.g.line reactances and resistancesThe power flow problem consists in formulating the equations f in eq.(1.1) and then solving these with respect to x.This will be the subject dealt with in the first part of these lectures.A necessary condition for eq.(1.1) to have a physically meaningful solution is that f and x have the same dimension,i.e.that we have the same number of unknowns as equations.But in the general case there is no unique solution,and there are also cases when no solution exists.If the states x are known,all other system quantities of interest can be calculated from these and the known quantities,i.e. u and p.System quantities of interest are active and reactive power flows through lines and transformers,reactive power generation from synchronous machines,active and reactive power consumption by voltage dependent loads, etc.As mentioned above,the functions f are non-linear,which makes the equations harder to solve.For the solution of the equations,the linearizationy X Xf ?= (1.2)is quite often used and solved.These equations give also very useful information about the system.The Jacobian matrix Xf ?? whose elements are given by j iij X f X f ??=??）（(1.3)can be used form any useful computations,and it is an important indicator of the system conditions.This will also be elaborate on.1.2 Fault Current AnalysisIn the lectures Elektrische Energiesysteme it was studied how to calculate fault currents,e.g.short circuit currents,for simple systems.This analysis will now be extended to deal with realistic systems including several generators,lines,loads,and other system components.Generators(synchronous machines) are important system components when calculating fault currents and their model will be elaborated on and discussed.1.3 LiteratureThe material presented in these lectures constitutes only an introduction to thesubject.Further studies can be recommended in the following text books:1. Power Systems Analysis,second edition,by Artur R.Bergen and VijayVittal.(Prentice Hall Inc.,2000,ISBN0-13-691990-1,619pages)2. Computational Methods for Large Sparse Power Systems,An object oriented approach,by S.A.Soma,S.A.Khaparde,Shubba Pandit(Kluwer Academic Publishers, 2002, ISBN0-7923-7591-2, 333pages)2 Net work ModelsIn this chapter models of the most common net work elements suitable for power flow analysis are derived.These models will be used in the subsequent chapters when formulating the power flow problem.All analysis in the engineering sciences starts with the formulation of appropriate models.A model,and in power system analysis we almost invariably then mean a mathematical model,is a set of equations or relations,which appropriately describes the interactions between different quantities in the time frame studied and with the desired accuracy of a physical or engineered component or system.Hence,depending on the purpose of the analysis different models of the same physical system or components might be valid.It is recalled that the general model of a transmission line was given by the telegraph equation,which is a partial differential equation, and by assuming stationary sinusoidal conditions the long line equations, ordinary differential equations,were obtained.By solving these equations and restricting the interest to the conditions at the ends of the lines,the lumped-circuit line models (π-models) were obtained,which is an algebraic model.This gives us three different models each valid for different purposes.In principle,the complete telegraph equations could be used when studying the steady state conditions at the network nodes.The solution would then include the initial switching transients along the lines,and the steady state solution would then be the solution after the transients have decayed. However, such a solution would contain a lot more information than wanted and,furthermore,it would require a lot of computational effort.An algebraic formulation with the lumped-circuit line model would give the same result with a much simpler model ata lower computational cost.In the above example it is quite obvious which model is the appropriate one,but in many engineering studies these lection of the“correct”model is often the most difficult part of the study.It is good engineering practice to use as simple models as possible, but of course not too simple.If too complicated models are used, the analysis and computations would be unnecessarily cumbersome.Furthermore,generally more complicated models need more parameters for their definition,and to get reliable values of these requires often extensive work.i i+diu+du C ’dx G ’dxR ’dx L ’dx u dxFigure2.1. Equivalent circuit of a line element of length dx In the subsequent sections algebraic models of the most common power system components suitable for power flow calculations will be derived.If not explicitly stated,symmetrical three-phase conditions are assumed in the following.2.1 Lines and CablesThe equ ivalent π-model of a transmission line section was derived in the lectures Elektrische Energie System, 35-505.The general distributed model is characterized by the series parametersR′=series resistance/km per phase(?/km)X′=series reactance/km per phase(?/km)and the shunt parametersB′=shunt susceptance/km per phase(siemens/km)G′=shunt conductance/km per phase(siemens/km )As depicted in Figure2.1.The parameters above are specific for the line or cable configuration and are dependent onconductors and geometrical arrangements.From the circuit in Figure2.1the telegraph equation is derived,and from this the lumped-circuit line model for symmetrical steady state conditions,Figure2.2.This model is frequently referred to as the π-model,and it is characterized by the parameters）（Ω=+=impedance series jX R km km km Z ）（siemens admittance shuntjB G Y sh km sh km sh km =+= I mk Z km y sh km y sh mkI kmkmFigure2.2. Lumped-circuit model(π-model)of a transmission line betweennodes k and m.Note. In the following most analysis will be made in the p.u.system.Forimpedances and admittances,capital letters indicate that the quantity is expressed in ohms or siemens,and lower case letters that they are expressed in p.u.Note.In these lecture notes complex quantities are not explicitly marked asunder lined.This means that instead of writing km Z we will write km Z when this quantity is complex. However,it should be clear from the context if a quantity is real or complex.Furthermore,we will not always use specific type settings for vectors.Quite often vectors will be denoted by bold face type setting,but not always.It should also be clear from the context if a quantity is a vector or a scalar.When formulating the net work equations the nodeadmittance matrix will be used and the series admittance of the line model is neededkm km 1-km km jb g z y +== (2.1)With22km r g km km kmx r +=(2.2)and 22km x -b km km kmx r += (2.3)For actual transmission lines the series reactance km x and the series resistance km r are both positive,and consequently km g is positive and km b is negative.The shunt susceptance sh y km and the shunt conductance sh g km are both positive for real line sections.In many cases the value of sh g km is so small that it could be neglected.The complex currents km I and mk I in Figure2.2 can be expressed as functions of the complex voltages at the branch terminal nodes k and m:k sh km m k km km E y E E y I +-=)( (2.4)m k m mk )(E y E E y I sh km km +-=(2.5)Where the complex voltages arek j k k e θU E = (2.6)k j k k e θU E =(2.7) This can also be written in matrix form as））（（）（m k sh km km km km sh km km mk km E E y y y -y -y y I I ++=(2.8) As seen the matrix on the right hand side of eq.(2.8)is symmetric and thediagonal elements are equal.This reflects that the lines andcables are symmetrical elements.2.2 TransformersWe will start with a simplified model of a transformer where we neglect the magnetizing current and the no-load losses .In this case the transformer can be modelled by an ideal transformer with turns ratio km t in series with a series impedance km z which represents resistive(load-dependent)losses and the leakage reactance,see Figure2.3.Depending on if km t is real ornon-real(complex)the transformer is in-phase or phase-shifting.p k mU m ej θm I km I mkU kej θk U p e j θp Z km 1：t km p k mU m ej θm I km I mkU kej θk U p e j θp Z km t km ：1Figure2.3. Transformer model with complex ratio kmj km km e a t ?=（km -j 1-km km e a t ?=） mp k U m ej θm I km I mk U kej θk U p e j θp Z km a km ：1Figure2.4. In-phase transformer model 2.2.1In-Phase TransformersFigure2.4shows an in-phase transformer model indicating the voltage at the internal –non-physical –node p.In this model the ideal voltage magnitude ratio(turns ratio)iskm k p(2.9) Since θk = θp ,this is also the ratio between the complex voltages at nodes k and p, km j k j p k pa e U e U E E k p ==θθ(2.10)There are no power losses(neither active nor reactive)in the idealtransformer(the k-p part of the model),which yields0I E I E *mk p *km k =+(2.11) Then applying eqs.(2.9)and(2.10)giveskm mk km mk km -a I I -I I ==(2.12)A B Ck m I mk I kmFigure2.5. Equivalent π-model for in-phase transformerwhich means that the complex currents km I and mk I are out of phase by 180since km a ∈ R.Figure2.5 represents the equivalent π-model for thein-phase transformer in Figure2.4.Parameters A, B,and C of this model can be obtained by identifying the coefficients of the expressions for the complex currents km I and mk I associated with the models of Figures2.4 and 2.5.Figure2.4 givesm km km k km 2km p m km km km E y a E y a E -E y -a I ）（）（）（+==(2.13)m km k km km p m km mk E y E y a -E -E y I ）（）（）（+== (2.14)or in matrix form ））（（）（m k km km km km km km2km mk km E E y y a -y a -y a I I =As seen the matrix on the right hand side of eq.(2.15) is symmetric,but thediagonal elements are not equal when 1a 2km ≠.Figure2.5 provides now the following:m k km E A -E A -I ）（）（+=(2.16)m k mk E C A E A -I ）（）（++=(2.17)or in matrix form））（（）（m k mk km E E C A A -A -B A I I ++= (2.18)Identifying the matrix elements from the matrices in eqs.(2.15) and (2.18) yieldskm km y a A = (2.19)km km km y 1-a a B ）（= (2.20)km km )y a -(1C =(2.21) 2.2.2 Phase-Shifting TransformersPhase-shifting transformers,such as the one represented in Figure2.6,are used to control active power flows;the control variable is the phase angle and the controlled quantity can be,among other possibilities,the active power flow in the branch where the shifter is placed.In Appendix A the physical design of phase-shifting transformer is described. A phase-shifting transformer affects both the phase and magnitude of the complex voltages k E and p E ,without changing their ratio,i.e., km j km km k p e a t E E ?== (2.22)Thus, km k p ?θθ+=and k km p U a U =,using eqs. (2.11) and (2.22)km j -km *km mkkm e -a -t I I ?==I km m U m ej θm I mk pkU k ej θk Z km 1：a kme j φkmkm k p ?θθ+=k km p U a U = Figure2.6. Phase-shifting transformer with km j km km e a t ?=As with in-phase transformers,the complex currentskm I and mk I can be expressed in terms of complex voltages at the phase-shifting transformer terminals:m km *km k km 2km p m km *km km E y t -E y a E -E y -t I ）（）（）（+== (2.24)m km k km km p m km mk E y E y t -E -E y I ）（）（）（+==(2.25)Or in matrix form））（（）（m k km km km km *km km 2km mk km E E y y t -y t -y a I I =(2.26) As seen this matrix is not symmetric if km t is non-real,and the diagonal matrixelements are not equal if 1a 2km ≠.There is no way to determine parameters A, B,and Cof the equivalent π-model from these equations,since the coefficient km *km y t - ofEm in eq.(2.24)differs from km km y t -in eq.(2.25),as long as there is non zero phase shift,i.e. km t ?R.A phase-shifting transformer can thus not be represented by a π-model.2.2.3Unified Branch ModelThe expressions for the complex currents km I and mk I for both transformersand shifters derived above depend on the side where the tap is located;i.e., they are not symmetrical.It is how ever possible to develop unified complex expressions which can be used for lines,transformers,and phase-shifters, regardless of the side on which the tap is located(or even in the case when there are taps on both sides of thedevice).Consider initially the model in Figure2.8 in which shunt elements have beentemporarily ignored and km j km km e a t ?= and m k j mk mk e a t ?=。
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外文资料Summary of power flow calculationPower system is calculated on the trend of steady-state operation of the power system as a basis, it's running under the given conditions and determine the entire system wiring in various parts of the power system running: the voltage of the bus, all components of a mid-stream power, The power loss, and so on. Power system planning in the design and operation of the existing power system in the form of research, we need to calculate the trend of using quantitative analysis of comparative power programme or operation mode is reasonable. Reliability and economy. In addition, the power flow calculation is calculated static and dynamic stability of the foundation of stability. So the trend is calculated on the power system of a very important and very basis of calculation. Power flow calculation also divided into offline and online calculation of two terms, the former mainly used for system planning and design and organization of the operation mode, while the latter is running for the system of regular monitoring and real-time control. The use of electronic digital computer to calculate the trend of the power system from the mid-1950s has already begun. Power flow problems in mathematical calculation is a group of diverse non-linear equations to solve the problem, its solution can not be separated from iteration. Therefore, the flow calculation method, it requires first and foremost a reliable convergence, and give the correct answers. As the power system structure and parameters of some of the features, and with the continuous expansion of the power system, the trend of increasing order of the equation, so the formula is not any mathematical method can guarantee is given the correct answer. This calculation of the power system to become a staff continue to seek new and more reliable way of the important factors.Use of digital computers in the power flow problems at the beginning, the general adoption of a node admittance matrix-based successive into the law. The principle of this method is relatively simple to compare the volume of digital computer memory, to the 1950s computer manufacturing level and then the power system theoretical level. However, it is convergence of the poor, when the system large-scale change, the sharp rise in the number of iteration in the calculation of convergence are often not the case iteration. This forced the staff to the power system to calculate impedance matrix-based successive into the law. Impedance method to improve the flow of the convergence of computing, the solution of the admittance system can not solve some of the trend, in the 1960s, access to a wide range of applications, has the power system design. Operational and research has made great contribution. At present, there are stillsome in the power industry units impedance method to calculate the trend. Impedance of the main shortcomings of the occupation of the computer's memory, each iteration of the large amount of calculation. When the system continue to expand, the more prominent of these shortcomings. 16 K memory of a computer in the use of impedance method can only be calculated at 100 following the system, 32 K memory of the computer can only calculate 150 nodes under the system. In this way, many of the power system in order to use impedance method shall not be first on the trend of the system is the streamlining of work. In order to overcome resistance in memory and speed of the shortcomings of the mid-1960s to the development of the impedance matrix-based Block impedance. This approach to a large-scale system divided into several small regional system, the computer only need to store various parts of the system impedance matrix contact line between them and the resistance, not only substantial savings in memory capacity, but also improve the Computing speed.Overcome the shortcomings of the impedance of hungry is another way to use Newton - Raphson method. This is the mathematics of nonlinear equations to solve the typical method, a better convergence. In resolving the issue of power flow calculation, is admittance matrix-based, therefore, as long as we can in the iterative process as much as possible to maintain the formula coefficient matrix sparse, and can greatly improve Newton's Law trend of the efficiency of procedures . Since the mid-1960s, Newton's law in the use of the best order of elimination, the Newton in convergence. Memory requirements. Speed all over the impedance, as the late 1960s after the widespread adoption of the excellent way.Flow calculation flexibility and convenience of the request, the application of digital computers is also a very key issue. In the past for a long time, the power flow calculation relies on the Taiwan exchange. Taiwan simulates the exchange of power systems, computing platforms in the calculation of the trend of the exchange, calculated at any time surveillance systems can run different parts of the state to meet requirements, if they run certain parts of unreasonable, you can make adjustments immediately. In this way, the equivalent of the process on the computing staff lost operating system. Adjustment process is very intuitive, physical concept is very clear. When the use of digital computers to calculate the trend when it lost this visual. To make up for this shortcoming, the trend of the establishment of procedures to the extent possible, in terms of computer calculation in the process of strengthening the process of the computer monitor and control, and to facilitate a variety of modifications and adjustments. Power flow calculation is not a simple calculation, to run it as a form of adjustment may be more precise. In order to get a reasonable run, often need to keep in accordance with the results, modify the original data. In this sense, the trend in the preparation of our program, the ease of use and flexibility must be sufficient attention. Therefore, in addition to the requirements in various ways to modify as muchas possible. Adjustment, we must pay attention to input and output of convenience and flexibility, strengthening human-computer links, so that the calculation of staff to monitor timely and appropriate calculations to control the conduct of calculation .Power flow calculation is a power system analysis of the most basic terms, the complex power system under normal and failure conditions steady-state running the calculation. The trend is calculated to strike a target in the power system to be running the calculation. That is, voltage and power distribution node, to check whether the components of the system overload. Voltage meets all requirements of the distribution and allocation of power is reasonable and the power loss, and so on. Of the existing power system operations and expansion, the new power system planning and design of the power system for static and transient stability of the trend are calculated as the basis. If the trend of the results available on steady-state power system, or estimate the optimal security, such as the trend of the flow calculation method and the model has a direct impact. The actual power system that the main trend of technology adoption Newton - Raphson method.In the management of the operation mode, the trend of power grid operation mode is to determine the basic starting point in planning areas, the need for trend analysis verified the reasonableness of the plan in real-time operating environment, dispatchers, provided the trend of End-expected operating conditions in the power grid To check the trend of operational reliability. In the power system dispatching a number of areas related to the trend of grid computing. Electricity network is to determine the trend of running the basic factors, the trend is steady-state power system on the basis and prerequisite .外文原文翻译电力系统潮流计算综述电力系统潮流计算是研究电力系统稳态运行情况的一种计算，它根据给定的运行条件及系统接线情况确定整个电力系统各部分的运行状态：各母线的电压，各元件中流过的功率，系统的功率损耗等等。