Examination of the stability limit on the synchronous machine depending on the excitation current wave shape

The two-reaction theory of synchronous machines as developed by Blondel, Doherty, Nickle, Park and others is well known. The present paper attempts to develop the rotating-field theory of synchronous and induction machines as an important alternative to the two-reaction theory. The general analysis includes analysis of rotating machines under steady-state, transient-state and hunting conditions. Rotating reference frames are introduced. The new components, known as the forward and backward components, or f and b components, are then simply correlated to the direct and quadrature components, or d and q components. By use of the f and b components, it is shown that any external network and transmission line with lumped or distributed constants can be connected to a synchronous machine. This forms the basis of interconnection between synchronous and induction machines. A steady-state vector diagram of a salient-pole synchronous machine is given. Transient solution of short-circuit current and torque follows. An equivalent circuit for the same machine with direct- and quadrature-axis excitation is derived, and a 6-terminal network is developed for transient studies. The induction machine is similarly analysed with respect to its own rotor or with respect to a synchronously rotating reference frame. Interconnection of synchronous and induction machines is then possible for steady-state as well as transient studies. The hunting circuit involving one synchronous machine and a load is developed, based on Kron's uniformly rotating reference frame instead of the Blondel-Park reference frame. Hunting circuits for two rotating machines are developed, based on simple relations in absolute differential calculus. A number of instantaneous torque expressions are developed from the tensorial point of view. New expressions are given in terms of armature currents and flux linkages or their components.

Представлена нелінійна математична модель синхронного генератора як об'єкта регулювання напруги. Модель побудована на основі рівнянь Парка-Горєва для ідеалізованого синхронного генератора при припущенні, що перехідні процеси в колах якоря і демпферної обмотки протікають значно швидше, ніж в колі обмотки збудження. У моделі враховується вплив ступеня насичення магнітної системи на індуктивності синхронної машини, що дозволяє досліджувати роботу генератора в контурі регулювання напруги при значних змінах струму збудження і навантаження. Вихідними даними для отримання залежностей індуктивностей від струму збудження є експериментальні характеристики холостого ходу і короткого замикання. Модель синхронного генератора побудована в середовищі імітаційного моделювання MatLab/Simulink. В процесі моделювання порівнювалися моделі синхронного генератора без урахування насичення магнітної системи, з урахуванням впливу насичення тільки на індуктивність обмотки збудження і з повним урахуванням насичення. Отримані результати моделювання показують важливість урахування впливу струму збудження на індуктивності генератора при дослідженні процесів регулювання напруги. Запропонована модель може бути корисна при аналізі роботи системи автоматичного регулювання напруги синхронного генератора для отримання кривих перехідних процесів, наближених до реальних експериментальних даних.

Excitation system is one of the most important parts of synchronous generators, where the system functions to provide dc power to the field generator coil. Iin this study, a static excitation system consisting of transformers and connected thyristors in bridge configuration has been implemented in synchronous machines that operate as 206,1 mva capacity generators, 16,5 kv using the help of matlab simulink r2017b software. By adjusting the load given to the generator, variations in excitation currents can affect the amount of output voltage generated by the generator so that it can increase and decrease the induced voltage. In full load conditions, namely p = 175 mw, q = 100 mvar, the results of the study show that when the simulation is run at alpha 0 °, it is known that the average value of dc voltage is 496,4 v, excitation current is 1057 a and voltage generator output has increased beyond its nominal voltage of 16,72 kv. in this case, to maintain the terminal voltage, the excitation current must be reduced by increasing the angle of shooting of the thyristor to an alpha angle of 45 °, so that the average dc voltage can be reduced to 479,3 v, as well as the excitation current to 985,9 a. the generator output voltage at the alpha 45 ° angle is obtained according to its nominal value of 1,.5 kv.

Owing to several advantages like easy integration with renewable energy systems, requirement of less number of power conversion stages, better stability and inter-connectivity etc., dc grids are becoming popular. This paper presents an alternative generating systems for dc applications. A recently proposed brushless and permanent magnet-less synchronous generator is used for such purpose. The machine is basically a synchronous machine where an induction machine (that is embedded in the same machine structure) is used for providing controlled excitation to the synchronous machine. The synchronous and induction machines are wound for different number poles such that they remain magnetically decoupled. The field winding of the synchronous machine (SM) is fed by the rotor-induced-emf of the induction machine (IM) through a rotating diode rectifier. For any operating speed, the IM has the ability to operate in different modes simply by varying its stator frequency. In the present work, the synchronous generator (SG) is connected to a dc load through a diode bridge rectifier (DBR). A simple controller is proposed that maintains the load-side dc voltage under different loading conditions. The q-axis component of the stator current of IM is used to regulate the field-excitation of SM using rotor-flux-oriented-control technique. Extensive PLECS simulations are presented to demonstrate the working of the proposed controller. A sample experimental results from the prototype shows the usefulness of the developed generator for dc-grid application.

State of the art . The magnitude of winding EMF in a rotary electric machine depends on the rotational speed, which gives rise to an intuitive assumption that the current and torque amplitudes for an inductive synchronous electric machine (or voltage and torque amplitudes for a capacitive machine) will too. Research methods . This research uses mathematical modeling. Results . The following theorems hold true. Theorem 1. The current amplitude in the inductive load of an inductive synchronous electric machine does not depend on the rotational speed. Theorem 2. The torque amplitude for an inductive synchronous electric machine with an inductive load does not depend on the rotational speed. Theorem 3. The voltage amplitude for the capacitive load of a capacitive synchronous electric machine does not depend on the rotational speed. Theorem 4. The amplitude and torque for a capacitive synchronous electric machine with a capacitive load does not depend on the rotational speed. Conclusions . Contrary to a possible intuitive assumption, the current and torque amplitudes in an inductive synchronous electric machine with an inductive load do not depend on the rotational speed. With another load type, they do. For a capacitive synchronous electric machine with a capacitive load, the voltage and torque amplitude do not depend on the rotational speed.

The article discusses the results of a study of the static electromechanical characteristics of a synchronous machine (SM) when prototypes of induction resistances (IR) with improved parameters are included in its stator circuits.
 Widespread in practice, dynamic braking (DB) of synchronous machines provides for the dissipation of the kinetic energy of the rotor in the resistance boxes included in the stator winding. In the process of stopping, to maintain the constancy of the average braking torque of the SM, a bulky relay-contactor shunt circuit for stator resistances is used. At low speeds, regulation of the excitation current of the SM or its forcing can also be applied. However, it is not possible to eliminate significant fluctuations in the electromagnetic moment in this way.
 To optimize the SM DB process, instead of resistance boxes, it was proposed to include a three-phase induction resistance in the stator winding, the value of which automatically decreases along with the stator current frequency. This approach allows you to drastically reduce the number of contact equipment and ensure smooth braking of the machine with electromagnetic moment fluctuations within narrow limits. Known IR designs are designed for asynchronous motors with a phase rotor and satisfy the requirements of the given quality factor of their starting characteristics, but cannot ensure the constancy of the torque on the SM shaft in the DB mode.
 Therefore, the objective of the work is to improve the design of the IR and obtain the necessary inhibitory mechanical characteristics of the SM using experimental studies.
 The work provides a pilot plant diagram and a drawing explaining the design features of the IR.
 The studies were performed for a synchronous machine, type МСА-72 / 4А, equipped with a thyristor exciter and a speed sensor. In three phases of the SM stator, IRs connected by a "star" were turned on. The experiments were carried out in the direction of obtaining the necessary braking characteristics of the SM by varying the design of the internal elements of the IR.
 The figures show the mechanical characteristics of the SM obtained in the process of studying the effect on them of the thickness of the inner steel rings and massive ferromagnetic disks at three values of the fixed excitation current.
 The research results show that the desired form of the mentioned characteristics of the SM is achieved only when using massive internal elements in the design of the IR. A separate figure shows the curves of changes in some values of the SM load, which will facilitate the development of methods for calculating the DB mode of the machine for the optimal design of the IR.

Electric generating and distribution systems are capable of performing natural oscillations of frequency and of power, superposed upon the ordinary operation and sometimes disturbing the regular behavior of the system or its parts. These oscillations are due to the interlinked cooperation of the prime movers with their speed-governing mechanisms, the synchronous generators, the ramified network, and the numerous induction motors, and similar power consumers. Since most of the machines and network branches usually are different in size and in individual design, a multitude of natural oscillations will develop, the frequency spectrum of which can be divided into three groups. In perfect condition of the system, a single very low frequency develops, which is determined by the inherent properties of all speed governors and servomotors together, and by the inertias of the rotating masses of all the generators and motors together. This joint natural oscillation has a period around 10 to 20 seconds and causes an inphase movement of all mechanical parts of the system, which can be of considerable magnitude, while the electric power may oscillate in phase opposition within the various parts of the system. The next group of frequencies contains as many natural oscillations as there are different synchronous machines in the system and is defined by the faster electromechanical oscillations occurring between each synchronous generator and the entirety of all the other synchronous and induction machines.

The inertia control ability of photovoltaic power stations is weak. This leads to the problem that photovoltaic power stations cannot provide effective physical inertia support in the grid-connected system. In this paper, a photovoltaic power station controlled by a synchronous generator and virtual synchronous power generation is taken as the research object. A station-level dynamic inertia control model with synchronous machine and inverter control parameters coordinated is established. Firstly, the weakening of system inertia after a high-proportion photovoltaic grid connection is analyzed. Inertia compensation analysis based on an MW-level synchronous unit is carried out. According to the principle of virtual synchronous control of inverter, the virtual inertia control method and physical mechanism of a grid-connected inverter in a photovoltaic station are studied. Secondly, the inertia characteristics of the DC side of the grid-connected inverter are analyzed. The cooperative inertia control method of the photovoltaic grid-connected inverter and synchronous machine is established. Then, the influence of inertia on the system frequency is studied. The frequency optimization of the grid-connected parameter optimization of a photovoltaic station based on inertia control is carried out. Finally, aiming at the grid-connected control parameters, the inertia control parameter setting method of the photovoltaic station is carried out. The neural network predictive control model is established. At the same time, the grid-connected control model of the MW-level synchronous machine is embedded. The control system has the inertia characteristics of the synchronous generator and the fast-response dynamic characteristics of the power inverter.

There have been quite a few attempts to compute synchronous generator parameters based on voltage and current synchrophasors taken under power system transients. However, we have not seen any publications with thorough analysis as to how soon the phasor measurement unit reacts to disturbance conditions, which components of the transient are filtered out and which are passed through, as well as what the total vector error is. The goal of this research is to determine all of these characteristics of a phasor measurement unit when playing back transient oscillograms for a stator short circuit obtained through mathematical modeling. The transient oscillograms have been derived via both a full Park-Gorev system of flux linkage equations as well as the MATLAB/Simulink Synchronous Machine block. Physical modeling was then conducted via a real-time digital simulator (RTDS) along with a dedicated phasor measurement unit ENIP-2 (PMU), and the stator current phasors were recorded. Our analysis has shown that both RTDS and ENIP-2 (PMU) almost entirely filter out the exponentially decaying DC component of the fault current while closely following the periodical signal envelope. The total vector error has been estimated to become below 1–2 % after around 0,02–0,03 s into the fault when selecting the “P” class filters according to IEEE C37.118. We have come to a conclusion that synchrophasor measurements under power system disturbances could be utilized for estimating the synchronous, transient, and subtransient generator parameters. The selected synchronous machine model in the form of flux linkage equations is correct, as the obtained transient oscillograms are exactly the same as those produced by Simulink. “P” class phasor measurements can be recommended for representing transients in the stator circuit of a synchronous generator. The results of this investigation are meant to be employed for synchronous machine parameter estimation based on phasors sourced from RTDS and, hopefully, from phasor measurement units installed at power plants.

The paper deals with the stability, voltage control, and power limits of electric- power systems and machines?more particularly, large alternating-current systems. The subject is dealt with in the following sequence :? Definition of stability. Stability and power limits of simple circuits. Larger power lines. Artificial stability of power lines. Natural stability and power limits of alternators and synchronous machines. Short-circuits and transient stability of alternators. Internal reserve of excitation of synchronous machines. Artificial stability of alternators. Stability of exciters. Types of electric power supply systems. Feeders and transmission lines and their voltage control. The conclusions reached are that synchronous machines can be made sufficiently stable for all the usual purposes of power supply, and that the power limit and voltage regulation of transmission circuits depend principally on their series reactance.

The application of hybrid excited synchronous generator as a part of autonomous wind turbine is studied in a case of load and wind speed changes. The control system of autonomous wind turbine ensures maximum wind turbine power output at any given wind speed. Maximum power achieved by excitation current control in additional field winding. The excitation current and power control of generators is developed based on minimization of local functionals of instantaneous values of first order derivative of electromagnetic energy. It provides robustness to parametric and coordinate disturbances and high quality of control. On the example of an experimental sample of a synchronous generator with hybrid excitation the studies of maximum output power control of autonomous wind turbine were carried out. The study is carried out in a case of wind speed variation from 3 to 8 m/s and load increasing by 50%. The graphs of output power of wind turbine, speed and torque of generator, excitation and armature voltage sand currents are given.

A synchronous machine is an electro-mechanical converter consisting of a stator and a rotor. The stator is the stationary part of a synchronous machine that is made of phase-shifted armature windings in which voltage is generated and the rotor is the rotating part made using permanent magnets or electromagnets. The excitation current is a significant parameter of the synchronous machine, and it is of immense importance to continuously monitor possible value changes to ensure the smooth and high-quality operation of the synchronous machine itself. The purpose of this paper is to estimate the excitation current on a publicly available dataset, using the following input parameters: Iy: load current; PF: power factor; e: power factor error; and df: changing of excitation current of synchronous machine, using artificial intelligence algorithms. The algorithms used in this research were: k-nearest neighbors, linear, random forest, ridge, stochastic gradient descent, support vector regressor, multi-layer perceptron, and extreme gradient boost regressor, where the worst result was elasticnet, with R2 = −0.0001, MSE = 0.0297, and MAPE = 0.1442; the best results were provided by extreme boosting regressor, with R2¯ = 0.9963, MSE¯ = 0.0001, and MAPE¯ = 0.0057, respectively.

This paper describes a new brushless and magnet-less synchronous generator where an induction machine (IM) is embedded in a synchronous machine (SM) to provide the excitation. Hence, this machine is named as brushless induction excited synchronous generator (BINSYG). To avoid the magnetic interaction between both IM and SM, they are configured for different number of pole pairs. A rotating uncontrolled rectifier (mounted on the shaft) is proposed to be used to rectify the rotor voltage of the IM to provide the excitation to the SM. Thus, by controlling the IM from stator side, field current of the SM can be controlled smoothly. As an example, in this work, SM and IM are configured for two pole and six pole, respectively. Practical winding-design-challenges and mutual interaction between IM and SM fields are analyzed briefly for 2/6 (SM poles/IM poles) pole BINSYG. Extensive finite element simulations of the proposed machine have been conducted using Maxwell-2D and these simulated results are obeying the theoretical analysis. A 3 kVA laboratory prototype of 2/6 pole BINSYG has been developed to evaluate the performance when IM is operated in the plugging mode for definite advantages. While a brushless configuration is proposed, brushes and slip-rings are used for the experimental machine, such that, rotor side windings of SM and IM can be accessed for the better understanding of the performance. Experimental results from this prototype confirm the theoretical and finite element method predictions.

The capacitive power, which a properly regulated conventional synchronous machine can supply is severly limited at no load as well as at light loading. Such a machine, when operating at these loading conditions, cannot be fully utilized. In this paper, it will be shown that these limitations can be overcome by the dual-excitation of the synchronous machine. Such a dual-excited synchronous machine, when provided with appropriate schemes of excitation control, has extended dynamic stable region at any loading condition. Two modes of operation are found possible in this case. In the first, the two field windings are always equally excited, while in the second their excitation currents are adjusted so as to keep the rotor-angle fixed at a certain value independent of the loading condition. Although the first mode of operation is of advantage from the rotor heating point of view, it suffers from the drawback that the sign of the control signal for stable operation depends on the operating condition. To overcome this drawback, the second mode of operation is suggested. With this mode, the dynamic stability of the machine can be greatly improved over the whole loading range. However, since fixing the rotor-angle at a certain value necessitates unequal excitation currents in the two field windings, this mode of operation would result in unbalanced distribution of rotor heating.

Exact and precise parameter identification and modeling of synchronous machines have been of great concern to the power system analyzers as well as to the control experts. In last decades the standstill frequency response (SSFR) test for determining synchronous machines parameters has gained much more importance among other test methods because of its simplicity, reliability and its harmlessness to the machines which are going to be tested. In this research work the SSFT has been applied to the micro synchronous machine under different excitation currents in order to examine the effect of the magnetic saturation upon machine parameters. A new approach has been introduced to eliminate the armature resistance from the identification process and this assures the exactness of the data and avoids excessive errors. The three transfer functions concept is used to enhance the accuracy of estimation.