A calculation method of field current of synchronous machines at sudden short‐circuit

The mutual leakage reactance between D‐axis damper and field windings is ignored in conventional D‐axis equivalent circuits. It has been pointed out, however, that the calculated value of the field current differs considerably from the measured value if this reactance is not taken into account. This is due to the difficulty of determining the physically correct damper winding impedance value. A method of determining the equivalent circuit constants using the mutual leakage reactance has been reported previously, where the D‐axis damper winding time constant is measured from the upper and lower envelopes of field current at sudden three‐phase short‐circuit. Yet there are machines for which the upper and lower envelopes of field current are not readily established, and in this case the method is unsatisfactory. The authors describe a method to accurately identify the equivalent circuit constants taking into account the mutual leakage reactance, using a standstill test with a small‐capacity DC power supply (DC decay testing method). The field current at sudden short‐circuit can be simulated accurately using these equivalent circuit constants. The validity of the proposed method is demonstrated by implementation results on two salient‐pole synchronous machines at the same specifications (one with damper winding, the other without). Furthermore, the dependent relation between the armature leakage reactance and mutual leakage reactance, as well as its influence on the calculation of field transient currents, are made clear. © 2005 Wiley Periodicals, Inc. Electr Eng Jpn, 151(3): 61–70, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.20113     

Calculation of equivalent circuit constants of synchronous machines considering field transient characteristics using DC decay testing method with open and shorted field windings

It has been reported that the calculated values of field transient behavior in a synchronous machine differ considerably from the measured values. This discrepancy is caused by the use of equivalent circuit constants in the standardized tests provided by JEC‐2130 and IEC‐60034‐4, in which the mutual leakage reactance between the damper and field windings is not accounted for. The authors have been studying a method for calculating equivalent circuit constants for the accurate simulation of transient behavior including the field winding side, by means of a standstill test with a small‐capacity DC power supply (DC decay testing method). The authors have previously presented a calculation method using operational impedances with the field windings opened, shorted, and shorted with an external resistance, obtained by the DC decay test. This paper presents a new method in which the external resistance used in our previous method is no longer needed. Instead, the field winding impedance is determined on the basis of its invariability against slip. The validity of the new method is demonstrated by comparing the calculated and measured values of the armature and field currents during a sudden three‐phase short‐circuit using 10 kVA/200 V/31.9 A/4 P/50 Hz test machines. © 2011 Wiley Periodicals, Inc. Electr Eng Jpn, 178(2): 39–46, 2012; Published online in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/eej.21207     

Determination of equivalent circuit constants of synchronous machines from the extended Dalton‐Cameron method

This paper presents a method of determining the equivalent circuit constants which accord with the physical construction of synchronous machines, using the dc decay testing method with the rotor in arbitrary position (proposed by the authors and called the extended Dalton–Cameron method). The conventional Dalton–Cameron method calculates the direct‐ and quadrature‐axis subtransient reactance from a standstill response test in any arbitrary rotor position using a single‐phase power supply. The extended Dalton–Cameron method determines the direct‐ and quadrature‐axis operational impedances for each slip from a standstill response test using a small‐capacity dc power supply. The direct‐ and quadrature‐axis operational impedance loci thus obtained synchronous machine constants (subtransient, transient, and synchronous reactances) are used to estimate the direct‐ and quadrature‐axis equivalent circuit constants which accord with the physical construction of synchronous machines. As an example, equivalent circuit constants are determined for a 10‐kW laminated salient‐pole‐type synchronous machine with damper winding. The validity of the equivalent circuit constants is confirmed by comparing the calculated resistance and leakage reactance of the field winding determined from the operational impedance when the terminals are short‐circuited, to those when the terminals are connected to an external resistance. © 2001 Scripta Technica, Electr Eng Jpn, 138(1): 56–67, 2002     

Small‐signal stability based on a synchronous generator model with field mutual‐leakage reactance

Power system small‐signal stability studies have been carried out using a synchronous machine model with a field mutual‐leakage reactance called the Canay reactance in the d‐axis equivalent circuit. The influence of the Canay reactance on the effectiveness of a power system stabilizer (PSS) was evaluated by the eigenvalue calculation method. The values of the Canay reactance reported in the literature were also investigated statistically, and an approximate expression applicable to power system stability studies was proposed. © 2005 Wiley Periodicals, Inc. Electr Eng Jpn, 154(2): 19–29, 2006; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.20163     

西门子隐极电机电抗和时间常数及突然短路电流

用额定电流时的主电抗和额定电压（突然短路饱和）时的电枢、励磁和阻尼绕组漏电抗、阻尼绕组谐波漏抗、励磁绕组对直轴阻尼绕组的漏抗,计算出隐极同步电机的超瞬变和瞬变电抗、时间常数以及突然短路电枢和励磁电流,与西门子（Siemens）公司提供的发电机超瞬变和瞬变电抗参数、时间常数、突然短路电流的计算机计算结果完全一致。     

水轮发电机瞬态电抗的数值计算

用直轴运算电抗的频率特性和二维正弦电磁场的有限元解法,求得了水轮发电机的直轴瞬态电抗。为计及励磁绕组的端部漏磁,用归算法把端部漏磁导并入了直线部分。为保证励磁绕组每匝的感应电流相等,对励磁绕组施加了串联约束。最后通过实例计算,比较了施加与不加串联约束对瞬态电抗值的影响。     

A method of predicting transient constants of synchronous machines

It is difficult to determine the subtransient (transient) reactance and subtransient (transient) short-circuit time constants of medium and large synchronous machines by the sudden three-phase short-circuit test because large-capacity equipment is required. This paper describes a new method of measuring these constants by means of a simple test using a small dc power supply. The key points of this method are as follows. (1) A dc voltage is applied to the armature winding (two terminals with the third one open) of a stationary synchronous machine through a resistance. When the two terminals are closed, the winding is short-circuited and the current in the armature winding decays. The whole process of decaying current is recorded. (2) The value of the transient phenomena of the winding calculated from circuit equations (armature, field winding and damper winding circuits) is compared with actual data, and the unknown equivalent circuit constants are identified by the least squares method. (3) Transient phenomena of the sudden three-phase short-circuit are calculated by the two-reaction theory using identified constants, and, hence, these constants are calculated. The transient constants of synchronous machines obtained by the new method agree closely with the observed values.     

Determination of Synchronous Reactance and No‐Load Saturation Curve of Synchronous Machines by dc Test Considering Magnetic Saturation Effect

dc Tests can accurately determine the unsaturated synchronous machine‐equivalent circuit constants by a simple standstill test. This paper presents two improved dc tests that account for the magnetic saturation of the stator iron core by the main flux. These tests are tentatively named Step Response Test (I) and Step Response Test (II). The former can predict the incremental d‐axis synchronous reactance by performing a Fourier transform of the voltage and current measured when a small step voltage is applied to the two armature terminals as a field current flows. The latter can determine the incremental d‐ and q‐axes synchronous reactances by the same Fourier transform of the voltage and current measured when a small step voltage is applied to the two armature terminals as an armature current flows. In addition, this paper introduces a new method to calculate not only the static d‐ and q‐axes synchronous reactances but also the no‐load saturation and short‐circuit characteristic curves. This new method does not require the results from any additional tests including the rotational driving tests and dimensional information, which can only be obtained from the manufacturer. To demonstrate the validity of the proposed method, results of an experiment using 10‐kVA laminated synchronous machines with damper winding are presented.     

同时带交流和整流负载的三相同步发电机系统的等效电路模型

同时带交流和整流负载的三相同步发电机系统是一个非线性系统 ,为了对此进行解析分析 ,将其中的三相同步发电机的d、q轴变量分解为低频分量和高频分量分别加以处理 ,忽略转子回路对高频电流的电阻和阻尼绕组对低频分量的作用 ,在d、q轴超瞬变电抗近似相等的条件下 ,分别建立了该系统的从整流负载侧和交流负载侧观察的等效电路模型。给出了模型中等效发电机的Park方程、稳态运行矢量图及相应稳态量的计算方法。该模型可用于系统稳态和似稳态过程的分析计算     

绕组不均布磁势的等效变换及漏电抗计算

当变压器绕组沿轴向分成若干段（或饼）时，其磁势沿轴向分布是不均匀的，因此将出现横向漏磁场，并使得漏电抗增大。本文研究了变压器一、二次绕组沿轴向分为若干段且沿径向呈“HV-LV-HV”排列的绕组的漏抗计算，给出了一种不均布磁势的等效变换方法，并分析了绕组段数（或线圈饼数）和段（或线饼）间气隙大小对漏电抗的影响。结果表明：当线圈饼数较少时，横向漏磁使得电抗值随气隙的增大而迅速增加，但当线饼数达到一定值以后，这种变化变得十分缓慢。文章最后在计算漏磁场分布的基础上，用有限元法求得电抗值验证了本方法。     

Study of asynchronizing phenomena using generator model with field mutual leakage reactance

This paper describes the effect of mutual leakage reactance in the rotor circuit on the analysis of generator transient characteristics. The authors derive a detailed equivalent circuit model for a 48P‐15,750‐kVA generator, analyze sudden short circuits and asynchronization phenomena of the generator by simulations with an electromagnetic transients program (ATP‐EMTP), and compare the results with experimental data. © 2005 Wiley Periodicals, Inc. Electr Eng Jpn, 153(3): 31–40, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.20147     

基于“场-路”耦合有限元分析法的变压器短路电抗仿真的研究

短路电抗法是检测电力变压器绕组变形的有效方法之一,开展变压器短路电抗的仿真计算研究,对于获取各种绕组变形故障时的特征信息具有重要意义。基于实验室中一台模型变压器的结构参数,分别建立了绕组正常及存在匝间短路故障时的有限元仿真模型,利用"磁-路"耦合的方法对变压器的漏磁场和漏感参数进行了计算,分析了绕组变形位置与变压器漏磁场之间的关系,并与在模型变压器上的实验结果进行了对比,结果表明:绕组内部发生匝间短路故障时,在径向中部的匝间短路对漏磁场的影响较大,而在轴向中层绕组的匝间短路对漏磁场的影响较小。研究成果对于指导短路电抗法的现场应用和绕组故障的检测提供了一定的理论依据。     

3 MW同步发电机阻尼绕组设计与超瞬态电抗性能验证

当一款发电机定转子主要尺寸定型后,转子的阻尼绕组性能是影响发电机超瞬态电抗的最主要因素。在不同的工况下,用户对发电机的超瞬态电抗的性能有不同的要求。通过阻尼绕组的调整基本可实现超瞬态电抗的调整。通过对1台3 MW无刷同步发电机转子阻尼绕组采用不同材质或不同的阻尼条数的设计方案,对超瞬态电抗值进行计算和分析,并通过低电压突然短路测试方式验证了不同方案对超瞬态电抗值的影响,以获得最佳的阻尼绕组设计方案。     

交交变频同步电机阻尼绕组损耗的分析与计算

本阐述了凸极同步电机中谐波增量磁场的作用及特点。给出了可计及包括端部影响的任意复杂转子回路的场路耦合计算格式。针对交交变颏同步电机阻尼绕组的计算问题，提出一种等效多端口网络的概念，并据此对两种阻尼绕组结构的损耗进行了分析比较。     

电力变压器内部短路故障对短路电抗的影响

根据电力变压器设计短路电抗的计算方法,研究了电力变压器内部各种短路故障对短路电抗的影响,指出了内部短路引起沿轴向安匝分布不均匀,从而增强了横向漏磁场分量。横向漏磁场对漏电感的作用是增加的。当内部短路发生在原边侧绕组时,虽然横向漏磁场分量增加了,但是原边绕组励磁总安匝数相对减少了,而且它引起漏电感减小的作用大于横向漏磁场分量增加引起漏电感增加的作用,所以短路电抗是减少的;当内部短路发生在线端短路的副边侧时,原边侧的短路电抗可能大于正常值。无论内部短路发生在何处,短路电抗均不等于额定值,其值之增加或减少随短路位置的变化是非线性的。     

用迭代最小二乘法辨识异步电动机漏抗

提出了迭代最小二乘寻优法辨识异步电动机漏抗的数学模型,采用ＭＡＴＬＡＢ语言编写了通用计算程序,估算鼠笼型异步电动机Ｔ型等效电路中的定、转子漏抗。该方法具有较高的计算精度、计算时间短及定、转子漏初值的变化对算法精度影响不大的特点。     

磁势不均布的变压器绕组漏电抗计算

研究了高压线圈饼式、低压线圈圆筒式且“HV- LV- HV”排列的变压器绕组的漏抗计算并给出了一种不均布磁势的等效变换方法。分析了线圈饼数和线饼间气隙对漏电抗影响的结果表明,线圈饼数较少时,横向漏磁使得电抗值随气隙的增大而迅速增加,但线饼数达到一定值以后趋势变缓。用有限元法计算漏磁场分布的基础上求得的电抗值验证了本方法。     

十五相感应电机对称缺相运行时的定子漏抗计算

定子参数计算是应用等值电路进行多相感应电机对称缺相运行性能分析的基础。通过引入关联矩阵反映所缺相数,分别对定子槽漏抗、谐波漏抗、端部漏抗进行计算,得到了十五相感应电机缺一个五相、两个五相绕组对称工况下的定子漏抗。计算结果表明,对于整距集中绕组的十五相感应电机,缺少五相或十相后,每相槽漏抗不变,谐波漏抗增大,而端部漏抗减小,故对称缺相运行工况下的定子漏抗参数与正常工况下并无明确倍数关系。在正常工况及缺十相对称运行工况下对十五相感应电机原理样机进行了堵转试验,试验测得的短路电抗与计算值相互吻合,间接验证了计算结果的正确性。     

六相同步发电机的稳态电磁参数

从Park方程的基本原理出发,建立了六相同步发电机的基本方程,得到了六相同步发电机的d轴等值电路和q轴等值电路。等值电路中的综合互感抗体现了六相同步发电机2个Y之间的磁耦作用,由电枢反应电抗和综合漏互感抗2部分组成。通过对六相同步发电机单Y运行(另一Y开路)和双Y运行的分析,得出双Y运行同步电抗为2倍的单Y运行同步电抗与单Y自漏抗之差。以空载短路试验的实例,测试了六相同步发电机特性曲线,以及d轴同步电抗、自漏抗和短路比。从电磁理论分析和实际运行特性2方面,验证了六相同步发电机的稳态电磁参数。     

非正弦供电十五相感应电机定子漏抗计算

为获得非正弦供电十五相感应电机基波和3次谐波等值电路中的定子漏抗参数,提出了基波和3次谐波定子槽漏抗、谐波漏抗和端部漏抗的分析方法并进行了计算。从槽比漏磁导公式出发求出了基波与3次谐波下的定子槽漏抗。考虑了十五相感应电机定子绕组基波电流与3次谐波电流产生磁势之不同特点,由各自谐波比漏磁导求出相应的谐波漏抗。通过引入气隙电流和镜像电流,用数值法计算线圈间端部电感作为求取基波和3次谐波端部漏抗的基础。分析计算表明,定子整距集中绕组的3次谐波槽漏抗为基波槽漏抗的3倍,但对谐波漏抗和端部漏抗无此比例关系成立。在基波电压下对十五相感应电机样机进行了堵转实验,短路电抗实测值与定转子漏抗计算值相互吻合,间接验证了该文所用计算方法的正确性。