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.     

A Simple Method to Determine Synchronous Machine Quantities Using Frequency Characteristics of Operational Impedances

This paper presents a simple method for determining synchronous machine quantities: d‐ and q‐axes time constants and reactances. This method determines them only by drawing additional lines in the frequency characteristics of operational impedances. A new systematic drawing strategy for determining transient/subtransient open‐circuit time constants and the d‐axis transient reactance is proposed. The frequency characteristics of operational impedances are obtained by the standstill dc test using a small dc power supply. Since the rotational test becomes unnecessary, the proposed method is suitable for tests in a factory. The validity of the proposed method was demonstrated with a numerical calculation example on a large‐capacity machine (800 MVA, 25 kV, two poles, 60 Hz) and an implementation test on a small‐capacity machine (10 kVA, 200 V, 31.9 A, four poles, 50 Hz).     

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.     

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     

A calculation method of equivalent circuit constants with mutual leakage reactance on synchronous machine with damper winding

The mutual leakage reactance between the d‐axis damper and field windings is ignored in the conventional d‐axis equivalent circuit. It has been pointed out that the calculated value of the field transient current differs considerably from the measured value when this reactance is not taken into account. A method to determine this reactance has been reported previously, but this method has problems concerning measurement precision. The authors have previously presented a calculation method for equivalent circuits, adapting a DC decay testing method, using two synchronous machines of the same specifications (one with damper winding, the other without). Yet, this method is not practical because of the use of two machines. This paper presents a calculation method for equivalent circuit constants taking into account the mutual leakage reactance to accurately represent the field transient current using a single machine. The proposed method determines equivalent circuit constants by calculating the physically correct d‐axis transient reactance from the operational impedances when the field winding is shorted and when the field winding is shorted with an external resistance. The validity of the proposed method is demonstrated by comparing the measured values with the calculated values of field and armature currents at sudden three‐phase short‐circuit. © 2009 Wiley Periodicals, Inc. Electr Eng Jpn, 167(2): 71–78, 2009; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.20891     

A method to determine direct‐ and quadrature‐axis inductances of permanent magnet synchronous motors

The equivalent circuit constants of permanent magnet synchronous motors are needed in the calculation of operation characteristics, construction of a control system, etc. These constants can be computed from the data on structural form and materials. However, measurements are necessary to obtain highly precise values. Methods for measurement of the d‐ and q‐axis inductances can be roughly divided into rotational and standstill methods. The standstill methods have the advantage that they are easy to carry out. However, it is difficult to consider magnetic saturation and distortion of the change in the armature winding inductance. The accuracy of the standstill method can be improved if these effects can be readily taken into account. This paper describes a standstill method for measuring accurate d‐ and q‐axis synchronous inductances of permanent magnet synchronous motors. By utilizing the fact that the EMF interference terms in the motor voltage equation considering the distortion of the inductance change are equal to zero when the rotor is in a specific position, the proposed method determines the inductances considering both magnetic saturation and inductance distortion effects from simple off‐line standstill testing. In addition, this method is capable of taking cross‐magnetic saturation into account when used with the necessary testing equipment. The proposed method was implemented on a 0.4‐kW interior permanent magnet synchronous motor with concentrated stator winding. The validity of the proposed method was demonstrated by comparing the measured and calculated results of the no‐load and on‐load characteristics. © 2010 Wiley Periodicals, Inc. Electr Eng Jpn, 171(3): 41–50, 2010; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.20969     

Prediction of starting performance of PM motors by DC decay testingmethod

This paper presents a method to predict the direct- and quadrature-axes operational impedances and starting performance of permanent-magnet (PM) motors by a simple standstill response testing method using a small-capacity DC power supply unit. In this method, not only the starting performance but also the direct- and quadrature-axes synchronous machine constants (synchronous, transient, and subtransient reactances) and equivalent circuit constants are calculated. This proposed strategy, tentatively named the DC decay testing method, is carried out on a 3.7-kW 200-V 22. A 100-Hz four-pole interior PM motor with a damper winding. The results measured by on-load tests and those predicted by the proposed method on starting performance demonstrate the validity and usefulness of the proposed method     

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 direct and quadrature axis inductances of synchronous reluctance motors with allowance for cross saturation

The d‐axis inductance of reluctance motor is affected by not only the d‐axis current but also the q‐axis current, because of cross magnetic saturation between the direct and quadrature axes. This situation is similar for the q‐axis inductance. The authors propose a method to determine the d‐axis inductance related to the d‐ and q‐axis currents and the q‐axis inductance related to the d‐ and q‐axis currents from a standstill test. This method involves the following four steps. First a rectangular‐wave voltage, alternated between plus and minus, is applied to the two armature winding terminals after breaking the rotor in the d‐axis position. Secondly, the voltage and current between the terminals are measured. Thirdly, the d‐axis inductance related with d‐axis current is calculated from the voltage and current. Finally, the process above is repeated when a DC current flows from the remaining armature terminal to neutral point terminal and the d‐inductance related to the d‐ and q‐axis currents is derived. A similar treatment applies when determining the q‐axis inductance related to the d‐ and q‐axis currents in the q‐axis rotor position. The method is implemented on a 1.1 kW–178 V–6.3 A‐4P–2200 min^?1 flux barrier type reluctance motor. Results of load performance on a vector controlled reluctance motor measured by on‐load tests and calculated from the d‐ and q‐axis inductances obtained by the proposed method clearly demonstrate the validity of the proposed method. © 2004 Wiley Periodicals, Inc. Electr Eng Jpn, 149(4): 52–59, 2004; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.10377     

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。     

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     

Steady-state performance of a line-start synchronous reluctance motor with capacitive assistance

This paper sets forth the steady-state performance analysis of a connection scheme that improves the power factor and torque with a lower magnetizing current for a line-start synchronous reluctance motor. The machine stator winding is split into two equal halves, one connected to the mains and the other connected to a balanced capacitor. Performance of the machine is improved if the capacitor value is such that the winding to which it connected operate at or very close to resonance in the d-axis. Current in both windings contributes positively to torque production and external control circuitry is not required. Steady-state equations arising from the d–q model gives a direct insight on the operating limits and how this capacitance aids the machines torque and power factor by boosting its direct axis reactance while the quadrature axis reactance remains fairly constant. An equivalent circuit is also deduced from the steady-state equations from which an explicit expression for input impedance of the new machine can be derived. Conditions for unity-power factor at varying load conditions are also examined. A comparison with conventional single-winding synchronous reluctance motor is given. Such comparison is fair because both machines have the same amount of copper and iron. Experimental results are provided to validate the analytical results.     

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。     

凸极同步电机小信号运算电感的计算

小信号运算电感数值计算中的问题有:增量磁导率的使用,转子绕组的处理等。本文采用场路耦合法处理转子的阻尼绕组和励磁绕组,既合理地反映了转子的复杂回路,又避免了端部漏磁引起的修正。通过对采用不同磁导率计算的比较,得到了一些具有实际意义的结果。     

A harmonic compensation brushless synchronous condenser using a cascade induction machine

In this paper, a new brushless synchronous condenser termed the BSC‐Filter is presented. It consists of two wound‐rotor induction machines connected in a cascade, and acts not only as a synchronous condenser but also as a passive filter with a capacitor connected to its stator field winding. An equivalent circuit model seen from the sixth harmonic in the field system is illustrated using the method of symmetrical coordinates. Based on this equivalent circuit model, a fundamental formula is derived to select the capacitor value properly. The validity of the theoretical analysis is verified through experiments, and basic characteristics of the BSC‐Filter are clarified. In addition to phase compensation, this new machine is capable of reducing low‐order fifth and seventh harmonics in power lines. © 2001 Scripta Technica, Electr Eng Jpn, 138(2): 71–78, 2002     

Acceleration tests to determine salient pole synchronous motorinrush currents and torques

Determining torque and current at locked rotor and various slips during the acceleration test on a synchronous machine is very tedious and time consuming. Induction and synchronous machines behave similarly during acceleration except that synchronous machine acceleration can include a pulsation torque. Because of the salient poles, conditions exist where the synchronous motor has minimum torque at quadrature axis and maximum torque at direct axis during locked rotor or stall. Since synchronous machines do not have large numbers of rotor bars in the amortisseur winding, like the induction motor has in the squirrel cage, their stall times tend to be shorter. Due to the shorter stall time and large starting torque, locked-rotor torque and current are generally determined from acceleration tests conducted at reduced voltage rather than by tests at stand-still. Data showing that saturation effects impact both torque and current are presented in this paper. The data shows that the voltage index that has to be applied to the torque and current measured at reduced voltage varies with speed and can be obtained from a series of acceleration tests     

Detection of Winding Faults in Wound Rotor Induction Motor Using Loci of Direct and Quadrature Axes of Rotor Currents

In this paper, loci of direct and quadrature axis of rotor currents are used for online detection of winding fault on stator side as well as rotor side in three-phase wound rotor induction motor. The proposed technique is used for detecting load on induction motor and open circuit fault condition on stator side as well as rotor side. Detection of winding fault is affected by unbalanced supply voltage. In order to overcome this problem, FFT of modulus of direct and quadrature axis is used. The experimental results of rotor current analysis are validated with stator current analysis. Research works reported in the literature are based on stator currents analysis. The proposed technique of detecting winding faults and distinguishing between stator winding faults and unbalanced supply voltage using rotor current is not reported in the literature.     

采用旋转因子法的同步电机模型

提出了一种新的适用于电力系统机网暂态过程数值仿真的有阻尼绕组同步电机模型。通过采用“旋转因子法”对同步电机的电压方程组进行差分化，成功地消除了因旋转电势引起的，存在于同步电机直轴电压方程和交轴电压方程之间的耦合，导出了相互解耦的直轴和交轴瞬态等值电路。文末的算例通过比较该模型与EMTP模型的仿真结果，证明这种新模型是正确的，其仿真算法比常用的EMTP算法更精确、更稳定。     

An expanded dalton-cameron method: DC decay testing method at an arbitrary rotor position

The Dalton-Cameron method is a well-known method for determining direct and quadrature axis subtransient reactance (x′_d and x′_q) by standstill response testing. This method entails calculating x′_d and x′_q from the voltage and current measured when a rated-frequency single-phase voltage is applied to each armature winding (U-V, V-W, and W-U) in turn. The authors have developed a new method to calculate x′_d, x′_q and the impedance loci by applying a dc voltage instead of a single-phase voltage. This method was named the expanded Dalton-Cameron method. The method is a small-capacity standstill test, and is carried out by using the following three steps. The first is to short-circuit the U and V terminals while a dc current flows between these terminals, to measure the voltage and current (V_DC and I_DC) when the dc current flows between these terminals and to record the dc decay current (i(t)) after these terminals are short-circuited. This same procedure is also performed for the V-W and W-U terminals in turn. The second step is to draw the impedance loci from the measured V_dc, I_dc and i(t) by means of Fourier transformation and to divide it into the direct-axis and quadrature-axis impedance loci (Z_d(js), Z_q(js)). The third step is to calculated the values of x′_d and x′_q from Z_d(js) and Z_q(js) and the starting performance on the basis of the two-reaction theory. Experimental and calculated results on starting performance, as well as a comparison with calculated results of x′_d and x′_q by the Dalton-Cameron method, clearly show that this method is very useful. © 1998 Scripta Technica, Electr Eng Jpn, 123(2): 53–60, 1998     

A Study of Converter-Fed Synchronous Machines by Means of Fourier Analysis

A new method for studying the steady-state operation of converter-fed synchronous machines based on Fourier expansion and the harmonic balance is presented. By means of the proposed method the real behavior of the noninstantaneous commutation or of the discontinuous operation, the current ripple in the dc side and in the field winding, can be predicted. An application of this method for a synchronous machine with direct and quadrature damper windings and salient poles connected to a midpoint converter is shown. This method is also useful for the study of other converter configurations and thyristor circuits.