Estimation of synchronous machine parameters from performance relations

The parameters of synchronous machines are required in system analysis, fault calculations, sizing of cables, circuit breaker selection, power factor correction, and voltage drop calculations. One of the major stumbling blocks is the general lack of design and application data. The design information is generally restricted and not commonly available to all users. Furthermore, the parameters are difficult to obtain through field measurements. In this paper, a mathematical model is presented to estimate the parameters of a synchronous machine from name-plate details. The data used in the estimation include output kVA, voltage, current, speed, rated power factor, field voltage, field current, and short-circuit ratio. The equations are derived from a well-known performance model and solved using a spreadsheet program available on any personal computer. Two case studies are presented in this paper. There is reasonable agreement between the estimated and available parameter values. Finally, the usefulness of this procedure and some of the limitations are outlined.     

Improved lyapunov function for synchronous machine transient stability study

Contents The transient stability of a synchronous machine is analysed by utilizing Lyapunov's direct method. Lyapunov functions of Lur'e-type are developed, which include the effects of first and second-order speed governor. The used Lyapunov functions have been developed essentially by a systematic procedure based on the nonlinear control theory, Kalman's transformation and the second Lyapunov theorem. The paper evaluates the maximum region of asymptotic stability in the state-plane of a swinging synchronous machine while the computed critical clearing times are compared with those obtained by numerical integration. A numerical example is given.

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Verbesserte Lyapunovsche Funktion zur Untersuchung der transienten Stabilität von Synchronmaschienen

Übersicht Die transiente Stabilität einer Synchronmaschine wird mittels des Lyapunov'schen Direktverfahrens untersucht. Es werden Lyapunov'sche Funktionen Lur'scher Art entwickelt, die die Folgen des Geschwindigkeitsreglers erster und zweiter Ordnung beibehalten. Die benutzten Lyapunov'schen Funktionen sind im wesentlichen nach einer systematischen Prozedur auf der Grundlage der Theorie der nichtlinearen Kontrolle, der Kalman'schen Transformation und des zweiten Lyapunov'schen Ansatzes entwickelt worden. Es ist Ziel dieser Veröffentlichung, die Frage zu beantworten, was der größte Bereich der asymptotischen Stabilität auf der Zustandsebene einer schwingenden Synchronmaschine ist. Die berechneten kritischen Fehlerlöschzeiten werden mit denen verglichen, die durch numerische Integration erhalten werden. Es wird ein numerisches Beispiel angegeben.

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List of principal symbols E internal voltage of generator - E voltage of infinite bus - x _d transient reactance of generator - x _l reactance of each of the two transmission lines - ₀ 2f _o ,f _o=50 Hz - angle betweenE andE - ₀ , ₀ before and after-fault respectively steady-state value of - x _o x ₁₂+x _d - x ₁₂ total reactance between generator terminals and infinite bus - M inertia constant of generator - K _d mechanical damping coefficient - P _i instantaneous input power to generator - P _o post-fault steady-state input to generator - K _g the loop gain of the governing system - T _g equivalent time constant of governor - T _h time constant of the prime mover - V(x) Lyapunov function - V _mx critical maximum value ofV(x) - t _cl clearing time - t _er critical time     

Improvement of synchronous machine transient response by fast-acting phase-shift control

The transient response of a synchronous machine connected to a large system can be improved by the insertion of fast-acting phase shift. The concept is described in simple terms using the equal-area criterion and by computed results using a typical mathematical model. A strategy is then outlined to minimise the system disturbance.     

An extension of delta method to synchronous machine transient stability study

Contents The delta method is applied to solve the transient stability problem of a synchronous machine connected to an infinite bus. In the machine analysis emphasis is placed on the governor action or flux-decay effect. The swing equation of the machine is a third-order non linear differential equation. In the paper the delta method is extended to this third-order nonlinear swing equation. — The system trajectory and the critical clearing time of the system have been obtained. A numerical example is given.

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Anwendung der Delta Methode zur Untersuchung der transienten Stabilität einer Synchronmaschine

Übersicht Das Problem der transienten Stabilität einer Synchronmaschine, die an einem starren Netz angeschlossen ist, wird durch die Delta Methode untersucht. Besonders wird das Abklingen des magnetischen Durchflusses und der Einfluß der Reglertätigkeit untersucht. Die Schwingung der Maschine wird durch eine nichtlineare Differentialgleichung dritter Ordnung beschrieben. Die Delta Methode wird zur Anwendung dieser nichtlinearen Schwingungs-differentialgleichung dritter Ordnung erweitert. Die Systemtrajektoren und die kritische Abschaltzeit des Systems werden dadurch abgeleitet. Ein numerisches Beispiel folgt.

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List of principal symbols x _d direct-axis transient reactance - x _d, x_q direct-axis and quadrature-axis synchronous reactances - x _l reactance of each transmission line - x ₁₂ total reactance between generator terminals and infinite bus - measure of the distance of the fault from the machine terminals - rotor angle with respect to a synchronously rotating reference - E _q instantaneous voltage proportional to field flux linkage - E _ex exciter voltage refered to armature circuit - E voltage of infinite bus - M inertia constant of the machine - P _d damping coefficient - P _mx amplitude of power/angle curve - P _i mechanical input power - T _d equivalent time constant of the governor - T _d0 open-circuit transient-time constant of the generator - K _g loop gain of the governor system - - ₀ 2f ₀ - t _cl clearing time - t _cr critical clearing time - _s stable equilibrium rotor angle     

Estimation of synchronous machine parameters using new discrete time-filtering algorithm

This paper presents a new method for estimating synchronous machine parameters from frequency test using a discrete time-dynamic filter based on the least absolute value parameter estimation algorithm (see G.S. Christensen and S.A. Soliman, Automatica. 26 (2) (1990) 389–395). The proposed method uses a digital set of measurements for the direct axis impedance magnitude and phase as a function of the frequency for estimating the d-axis parameters, such as the direct reactance and the different direct axis time constants, as well as the q-axis parameters.A practical example from the literature is used (see F.B. De Mello and L.N. Hannet, IEEE Trans. Power Appar, Syst., PAS-102 (12) (1983) 3810–3815) to test the proposed algorithm, and results are obtained and compared with those obtained using other methods such as the least error squares algorithm (see S.A. Soliman, S.E. Emam and G.S. Christensen, Can. J. Electr. Comput. Eng., 14 (3) (1989) 98–102) and the Kalman filtering algorithm (see M. Mambo, T. Nishiwaki, Syokokawa and Y. Ueki, IEEE Trans Power Appar. Syst., PAS-100 (7) (1981) 3304–3311).     

基于虚拟同步机技术的储能机电暂态特性建模

虚拟同步机技术通过模拟传统同步发电机特性,使采用变流器的电源具有同步机组的惯量、阻尼、频率和电压调整等运行外特性,是解决新能源发电接入电网稳定运行的重要技术手段。提出一种用于机电暂态的虚拟同步机控制储能建模方法。该储能模型包括虚拟同步机控制、储能限制模块和模型接口模块,并考虑虚拟同步机定转子方程和储能充放电功率、荷电状态、运行效率、死区及逆变器限制特性。基于电力系统分析综合程序,采用用户自定义方式搭建模型。以IEEE 4机2区域和河南电网为例进行模型有效性验证,结果表明了所提建模技术相比于传统方法的优势。     

The effects of unbalanced networks on synchronous and asynchronous machine transient stability

Untransposed lines and feeders, together with single-phase loads, impose permanent unbalanced conditions on the rest of the power system. Unbalanced phase voltages at the terminals of a machine can be represented as balanced sets of positive-, negative- and zero-sequence voltages. The negative-sequence voltage gives rise to negative-sequence current which creates excessive heating, particularly in the rotor circuits. Much attention has been paid to the heating aspect, and protection provided against this, by limiting the levels of negative-sequence current; however, power system stability studies, in particular for multimachine systems, have until now ignored the imbalance and its effects upon the dynamic response of the rotor speed of each machine. This paper reconsiders the transient stability of a single synchronous generator connected to an infinite bus and evaluates the significance of the error incurred by representing the unbalanced line and shunt load by an equivalent balanced system. The paper also reconsiders the transient stability of a multimachine system containing a synchronous generator and an induction motor when subjected to different types and degrees of imbalance and finds that significant errors are incurred under certain conditions.     

带桥式交流器的凸极同步电机的稳态特性分析

本文给出了利用复数坐标变量系统解带桥式变流器的凸极同步电机稳态特性的计算方法,并对一台实际电机作了具体计算。计算波形和实验波形的一致性良好。文中还利用FFT对各电压及电流进行了诸波分析,并详细讨论了等效逆序电流的计算。最后,给出了计及谐波电流后的定子磁势。     

定转子电阻对同步电机瞬态时间常数影响

采用忽略部分定转子电阻影响的瞬态时间常数传统解析表达式计算同步电机瞬态特性时会产生一定的误差。为解决该问题,推导了计及定子电阻的直轴瞬态时间常数改进解析表达式和计及转子电阻的定子非周期瞬态时间常数改进解析表达式,通过7.5 kW模型机试验及时步有限元方法验证了该解析表达式的正确性。采用该解析表达式计算了瞬态时间常数随定转子电阻变化的规律,发现不同定转子电阻下,利用改进表达式计算瞬态时间常数的精度明显高于传统方法。     

Analogue computer simulation and phase space study of a synchronous machine with flux-decay effect transient stability

Contents The paper describes how a general-purpose electronic analogue computer and the phase space method may be used to solve the transient stability problem of a synchronous machine connected to an infinite bus. In the machine analysis emphasis is placed on the effects of the flux-decay, damping power and saliency during transient disturbances. The swing equation of the machine is a third-order nonlinear differential equation. In the paper the phase plane method is extended to this third-order nonlinear swing equation and the system trajectories, the boundary surface of asymptotic stability and the critical clearing time of the system have been obtained by the use of an analogue computer. A numerical example is given.

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Analogrechnersimulation und Phasenvariablenuntersuchung des Flußabfalleffekts im transienten Stabilitätsverhalten von Synchronmaschine

Übersicht Diese Arbeit beschreibt die Lösung des Problems der transienten Stabilität für Synchronmaschinen in starren Netzen mittels Simulation auf Analogrechnern und die Methode der Phasenvariablen. Besonders wird der Flußabfalleffekt, die Dämpfungsleistung und die Polausprägung bei transienten Störungen berücksichtigt. Eine nichtlineare Differentialgleichung dritter Ordnung beschreibt das dynamische Verhalten. Die Phasenvariablenmethode wird erweitert auf diese nichtlineare Differentialgleichung dritter Ordnung und es werden auf dem Analogrechner die Systemtrajektoren, die Grenzfläche der asymptotischen Stabilität und die kritische Löschzeit bestimmt. Ein numerisches Beispiel wird angegeben.

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List of principal symbols rotor angle with respect to a synchronously rotating reference - ₀, _s value of at the prefault and postfault stable-equilibrium point respectively - _u value of at the saddle point - M inertia constant of the machine - P _i mechanical input power - damping power - x _d ,x _q direct-axis and quadrature-axis synchronous reactances - x _d direct-axis transient reactance - x ₁₂ total reactance between generator terminals and infinite bus - x _l reactance of each transmission line - T _d0 open-circuit transient-time constant of the generator - E _q instantaneous voltage proportional to field flux linkage - E _ex exciter voltage referred to armature circuit - E voltage of infinite bus - t _c1 clearing time - t _cr critical clearing time - measure of the distance of the fault from the machine terminals     

Precise and reliable identification of the transient processes of a powerful synchronous machine by probabilistic statistical methods

Identification of the transient process (TP) obtained by probabilistic and statistical methods based on probability theory and mathematical statistics as well as on the graphical–analytical method (GAM) in accordance with State Standard GOST 10169–77 was considered according to the results of bench tests of an STM-800-2.6 kV synchronous machine (SM) at an 4512-V test voltage during a sudden symmetrical shortcircuit (SSC). Despite the high labor intensity and low precision and reliability of TP oscillograms due to the numerous graphic operations and transitions from analogue TP to the discrete form and back, the GAM is a basic one and is widely used. Oscillogram processing by the GAM aiming at TP transition from analogue to discrete form leads to deviation of peaks from their original location. For this reason, practically no electromagnetic parameters adequately correspond to the TP of SM. The method of minimization of the meansquare error of approximation of the transient component to the experimental data was proposed. This error is presented in the form of the surface in a 3D coordinate system, for which reason the procedure of optimization, modeling, and determining the error in each node sampling with account taken of the influence of different random factors allow to reveal the minimum error. The method of determining the surge current by one vertex without defining TP parameters during SSC experience was tested as well. Error analysis of identification results of the TP SM by GAM and PSM for all phases is presented.     

Identification of machine parameters of a synchronous motor

This paper presents a method for estimating the machine parameters of a synchronous motor. The presented method is equally applicable for a wound field synchronous motor, synchronous reluctance motor, or permanent magnet (PM) synchronous motor, both the interior and surface-mount types. The method works particularly well for machines having a significant amount of space harmonics, such as synchronous reluctance and interior PM (IPM) machines, where the harmonics are predominantly the slot harmonics. It is also well suited for surface PM machines operating under saturation, where the harmonics are saturation-induced. The presence of these harmonics makes the parameter identification difficult. Most of the methods presented so far in the literature have failed to properly identify machine parameters in the presence of space harmonics. In this paper, the machine parameters, identified by using a proposed algorithm, are compared with the finite element and the experimental results to demonstrate the effectiveness of the presented method. Both interior PM and surface PM machines are considered.     

Estimation of field current in vector-controlled synchronous machine variable-speed drives employing brushless asynchronous exciters

In wound-rotor synchronous machine variable-speed drives, accurate information about the field winding current is paramount to obtain high dynamic and steady-state performance, such as unity power factor. When brushless excitation is employed and no direct measurement of field winding current is available, it must be estimated. This is a topic which has not received much attention in the literature, despite its importance in high-power synchronous motor drives. This paper presents two different methods for field current estimation, applied in a vector-controlled voltage-source converter-fed drive. Experimental results illustrate the steady-state accuracy and dynamic performance.     

Adaptive control of a synchronous machine using the auto-searchingmethod

A novel adaptive control scheme is presented for the design of a power system stabilizer (PSS) and a static VAr (reactive volt-ampere) compensator (SVC). The developed adaptive proportional-integral (PI) controllers, whose gains are adjusted in real time using the online-measured system operating conditions and a look-up table stored in computer memory, can offer better damper effects for generator oscillations over a wide range of operating conditions than conventional PI controllers with fixed gain settings. The effects of the adaptive PSS and the adaptive SVC on generator damping and terminal voltage profile are examined by computer simulation of system dynamic responses to a major disturbance     

On-line measurement of synchronous machine parameters

The estimation of a synchronous machine's electrical parameters using an extended Kalman filter (EKF) is proposed. The estimation method is evaluated using digital computer simulations as well as practical measurements on a microalternator. The captured data are used, together with an initial set of machine parameters, as input to an EKF to estimate an improved set of parameters. Results indicate that the parameter estimation method is valid under certain conditions but that with high-order models, it is computationally intensive and that certain parameter estimates are noise sensitive     

A new identity dimensional D‐state observer for sensorless drive of permanent‐magnet synchronous motors

A new identity dimensionless D‐state observer whose state variables are the stator reaction flux and rotor flux is proposed for the sensorless drive of permanent‐magnet synchronous motors. Furthermore, sufficient conditions are newly and analytically derived for the observer gains that guarantee stable convergence of state variable estimates. Additionally, two new methods for designing observer gain are presented; these methods, the constant and speed‐dependent gain methods, satisfy the derived analytical conditions. The observer gain conditions used in the design methods are validated through extensive numerical experiments. In addition, typical design examples of the observer gains using the proposed design methods are presented. © 2012 Wiley Periodicals, Inc. Electr Eng Jpn, 181(1): 45–61, 2012; Published online in Wiley Online Library (wileyonlinelibrary.com). DOI 10.1002/eej.21200