Frequency Control Law Research Articles

Development of a Robust Scalar Control System for an Induction Squirrel-cage Motor Based on a Linearized Vector Model

The paper considers the problem of developing a digital system for an induction motor speed control which has a sensor and a speed regulator to increase accuracy of speed control. Speed control is carried out by a scalar method due to consistent change in the stator frequency and voltage. To obtain the uniformity of the motor overload capability in a given range the control mode is used associated with maintaining uniformity of flux linkage of the motor stator. Induction motor scalar models do not possess high accuracy and their parameters and their parameters can vary over a wide range, which complicates the controller design and achievement of robustness of the speed control system. To eliminate these disadvantages, it is proposed to use a vector model in a rotating coordinate system having subjected it to linearization at different points of the operating mode with the account of the adopted law of frequency control, to ensure robust absolute stability of the system on the basis of application of a graphical method for constructing a modified amplitude-phase characteristic.

State estimation and frequency stabilization of multi‐area power systems via fault‐alarm approach

AbstractThis work is mainly focused on designing hybrid memory state feedback load frequency control law for a class of multi‐area power systems against transmission delays, parameter uncertainties, actuator faults, and load disturbances via fault‐alarm approach. More specifically, the load disturbances are prompted by the incorporation of abundance amount of renewable energy resources, namely, photo voltaic and wind power. Additionally, the power system takes the effect of actuator faults into account, which is unavoidable and exists at any instant of time. Thus, to stabilize the addressed system, the fault‐alarm approach is exploited to develop the hybrid control law. Particularly, the state dynamics are well estimated by the aid of residual observer to detect the faulty condition of actuators. Also, by following the algorithm of fault detection, the spontaneous alert from the alarm is accomplished. Further, in consideration of appropriate Lyapunov–Krasovskii functional, the stability conditions having linear matrix inequality form are derived and which affirms the asymptotic stability of the power systems. Precisely, the controller gain matrices are obtained by solving the developed sufficient conditions. Eventually, the simulation results of two‐area interconnected power systems are presented to examine the applicability and advantage of the proposed theoretical result.

RESEARCH OF SCALAR CONTROL SYSTEM OF TWO TRACTION INDUCTION MOTORS FROM BY ONE INVERTER

Most adjustable-speed AC drive systems are constructed in such a way that one motor receives power from one inverter and uses vector control as the basic control principle. However, in some cases there is a need to power several motors in parallel from a single inverter, that minimizes the size, weight and cost of such a system. The most common examples of such systems are rail and urban electric vehicles, where two to four induction motors are connected to drive in parallel. Control of such a system is a difficult task, especially in conditions of unbalanced loads on the motors, that can occur in conditions of different adhesion of wheels with rails. The inability to provide individual control of the motor when powered by a single inverter can lead to a decrease in the safety level of such a vehicle due to the loss of stability when changing the current value of the adhesion coefficient of individual wheel pairs. Mechanical processes in the traction system are analyzed, in which each wheel pair is driven by a separate motor powered by a common inverter. It is shown that the identity of the values of the adhesion coefficients is an important condition for the stability of such a system, that cannot be guaranteed in the actual practice of the operation of the vehicle. Therefore, the development and research of control systems that are capable of operating the system in a variety of rail / road conditions is an important direction for the further development of such systems. The structure of mathematical model of traction electromechanical system consisting of two induction motors powered by one inverter is proposed. The adjustable-speed control is based on the scalar control system, that is the easiest to implement because it does not require the estimation of the state variables of the system components. Sinusoidal pulse width modulation is selected as the switch control signal method. Operation of traction electromechanical system with scalar frequency control law is investigated by mathematical modeling. It has been proven that changing the characteristics of a single wheel pair's adhesion can lead to a loss of stability by a system that is unacceptable in terms of providing a comfortable and safe operation of the vehicle. Keywords: traction electric drive, scalar control, adhesion, mathematical model, frequency control

COMPARATIVE ANALYSIS OF THE ENERGY INDICATORS OF SINGLE-MOTOR AND MULTIPLE-MOTOR ASYNCHRONOUS ELECTRIC DRIVE

The aim of the work is to conduct a comparative analysis of single-engine and multi-engine asynchronous traction electric drive based on energy based on the assessment of energy losses in traction asynchronous electric motors of different power using the proportional law of frequency control to control the speed of traction asynchronous electric motors in the first zone. The energy loss analysis in traction asynchronous electric motors was carried out for three values of the voltage frequency on the stator winding 50 Hz, 25 Hz and 12.5 Hz and for three values of the total load moment corresponding to the full, half full and empty bus on the asphalt road. In determining the total load moment, the rolling resistance of the bus and the air resistance were taken into account. As a result of the analysis, a formula was obtained that allows, based on the power of constant and variable losses in compared electric motors corresponding to the nominal load moment, to determine the number of low-power engines that make up the multi-motor drive, which will provide the energy effect from the use of multi-motor electric - the drive instead of the singlemotor electric drive. In addition, energy losses in the traction asynchronous electric motors included in the single-engine and multi-motor electric drive during acceleration of a full and empty bus to a maximum speed of 12.5 seconds were evaluated. To estimate the losses in the compared electric motors at voltage different from the nominal value, mathematical modeling was used in the MatLab package. It is shown that the use of a multi-motor asynchronous electric drive allows to reduce energy losses in traction asynchronous electric motors when the vehicle is moving at a constant speed and during acceleration with a different number of passengers. Moreover, to obtain the energy effect, the number of engines used in a multi-motor electricdrive should vary depending on the speed and acceleration of the bus, as well as on the total load moment of the multi-motor drive.

Properties, Characteristics and Parameters of Permanent Magnet Synchronous Motors under Vector and Scalar Frequency Control

In order to improve energy performance and simplify the system of frequency control of the speed of electric drives, the area of application of synchronous frequency-controlled electric drives with both dependent and independent frequency setting of the voltage supplying the engine is being expanded. This is due to the fact that, as compared with asynchronous variable frequency drives, synchronous ones undergo lower power losses and they have rigid mechanical characteristics without speed feedback. Also, the simplest law of frequency control, viz. a proportional one, which, however, provides the maximum electromagnetic torque of the engine unchanged at R1 = 0 at all frequencies due to the constant magnetic flux, is applicable to a synchronous frequency controlled motor. Characteristics and properties of permanent magnet synchronous motors (PMSM) with the dependent frequency setting of supplied voltage (under vector control of PMSM) have been discussed and reviewed in technical literature quite sufficiently. It cannot be said about the PMSM with independent frequency setting reference which work under scalar frequency control. In the present article a comparison of properties and characteristics of vector and scalar frequency controlled PMSM is presented. For a scalar frequency controlled PMSM a function of the relative voltage g on the relative frequency a (g = f(a)) taking into account the PMSM parameters has been defined. The derived function g = f(a) differs from a proportional law of frequency control g = a. It is found that the influence of the parameters on the law of frequency control is small, and it can be applied without adjustment in most cases, in contrast to the frequency control of the asynchronous motor. For scalar frequency control, a method for determining the parameters of synchronous motors has been proposed in accordance with the parameters of synchronous motors with permanent magnets, which are given for operation under vector control. According to the presented methodology the OMRON SGMH-50D engine parameters have been determined for scalar frequency control and the function of g = f(a) have been computed.

Design of observer-based non-fragile load frequency control for power systems with electric vehicles

This paper establishes an observer-based finite-time non-fragile load frequency control design using electric vehicles for power systems with modeling uncertainties and external disturbances. A state space representation of the addressed power systems together with dynamic interactions of electric vehicles is formulated. A full-order observer-based non-fragile controller is designed to ensure finite-time boundedness and satisfactory finite-time H∞ performance of the considered system. By constructing an augmented Lyapunov–Krasovskii functional and employing Wirtinger-based integral inequality, the required conditions are obtained in terms of linear matrix inequalities. The desired non-fragile load frequency control law is presented via the observer-based feedback approach. Simulations are given to show the effectiveness of the proposed control scheme.

Energetic Factors of a Frequency-Controlled Synchronous Electric Drive

As compared to asynchronous frequency-controlled electric drives, synchronous drives are characterized by lower power losses, rigid mechanical characteristics without speed feedback and by the simplest law of frequency control (when the voltage changes proportionally to the frequency). An analytical study of energy factors (power loss, efficiency, power factor) of frequencycontrolled synchronous motor with electromagnetic ignition and with excitation caused by permanent magnets has been fulfilled. The efficiency of the power converter, in this case (i. e. in the case of the frequency converter), depends on the structure of the converter (single-link or two-link), on the power semiconductor devices being used, on additional elements (i. e. chokes, capacitors, transformers, active resistance, etc.). The efficiency of a synchronous electric motor (which is a cofactor of general efficiency of a controlled synchronous electric drive) is of an interest in the scalar frequency control of the mentioned synchronous motor, since there are almost no publications on this subject. Therefore, the energy conversion efficiency of the synchronous motor, which receives energy from the frequency converter at different frequencies and converts to mechanical energy, has been considered. For the convenience of analytical research, we used the widely used concept of relative frequency as the ratio of the current value of the voltage frequency to the nominal one. It is demonstrated that the maximum efficiency is shifted in the direction of a lower load factor with a decrease in the relative frequency of the motor supply voltage. The method of calculating the energy performance of variable frequency synchronous motor that has been developed is illustrated by the graphs of efficiency and cosj for the engine of the SD3 13-34-6 type of the capacity of 500 kW and of a voltage of 6 kV and for a synchronous motor with permanent magnets of the YGT132S4 type of a capacity of 5.5 kW.

Influence of magnetic circuit saturation and skin effects on the adjustable induction motor characteristics

The aims of this work are to show the influence of saturation and the rotor skin effect current on the characteristics of an adjustable induction motor (AIM). The coefficient of the voltage increase is determined in order to realize the frequency control laws with constant flux. The regulation characteristics of the induction motor are obtained for developed control laws. Great advantages of a first proposed law of frequency control were revealed. The determination of the equivalent scheme parameters taking account the saturation of the magnetic circuit and the skin effect of the rotor current guarantee the accuracy of calculation of the adjustable induction motor energy indices.As a result of frequency control of the AIM research in a dynamic mode it is established, that while taking into account magnetic conductor saturation and skin effect current in a rotor winding faults while calculating current throws for a control mode U/f = const decreased about 6 compared with 13% without taking into account and, till 3 compared with 17% in a regulation law with a rotor constant flux linkage Ψ2 = const. Results of mathematical modeling in the course of which power indicators (efficiency and power factor) of the adjustable induction motor defined in transitional regimes at various laws of frequency regulation are experimentally confirmed.

On Higher Order Dynamics in the Fundamental Equation of Frequency in Islanded Microgrids

In islanded micro grids, the stability of the frequency has to be enhanced by the distributed producers. Moreover, distributed control schemes are highly appealing for evident robustness and flexibility reasons. This is generally achieved by using the fundamental frequency model in which the derivative of the grid frequency is proportional to the power unbalance in the grid. This paper discusses the relevance of this simple model when high gain closed-loop system is designed. In particular, the presence of higher order terms in the frequency dynamics that should be carefully taken into account in the distributed frequency control design is proved and appropriate frequency control law is proposed and validated.

THE STUDY OF TRANSIENT PROCESSES OF THE FREQUENCY-REGULATED SYNCHRONOUS ELECTRIC DRIVE

In order to improve the power indices and to simplify the system of frequency speed control the scope of application of synchronous variable-frequency electric drives with independent frequency setting is being expanded. The synchronous motors with electromagnetic excitation and permanent magnet excitation in various industrial settings, including load-lifting machines and mechanisms, are used. As compared with the asynchronous frequency-regulated electric drives the synchronous ones have lower power loss, harder mechanical characteristic without feedback for speed and the simplest law of frequency control, i. e., a proportional one that, however, provides the maximum electromagnetic torque of the motor constant at all frequencies, due to the constant magnetic flux. The article concerns an analytical study of transient processes of synchronous electric drive with consideration of the influence of damping winding when the motor supply voltage frequency varies linearly during the transient time. As a result of the analysis the formulas have been obtained that make it possible to calculate the angular velocity of the rotor and the electromagnetic torque of the motor at start-up, braking, and impingement and discharge of loads, evaluating the quality of the transition process and tracking the maximum value of the electromagnetic torque, that must not exceed the permissible value. Validation of the developed technique of calculation of transient processes of synchronous electric drive has been obtained by comparison of calculations according to the formulas with the simulation results of the electric drive on the basis of the synchronous motor of the SD3 13-34-6 type (power of 500 kW and voltage of 6 kV).

Application of the method of cluster analysis for formulation of the frequency-control law of an asynchronous motor

A simplified synthesis of energy-efficient scalar systems of frequency control of an asynchronous motor is considered. A method for formulating special frequency-control laws calculated for a certain range of loads is considered for provision of energy efficiency. Calculation of the frequency-control law of an asynchronous electric drive is carried out based on iteration optimization, in which the number of iterations may reach a thousand. It is resolved to find a simplified procedure for formulation of a law applicable to engineering calculations. The hypothesis is raised that there is a “similarity” of laws of control for motors with relatively similar parameters of the equivalent scheme. This assumes that the control law (which is quasi-optimal) obtained for one motor can be applied to other electric machines with similar parameters with some degree of error. It is suggested that motors with similar parameters be distinguished by means of clustering based on self-organizing artificial neural networks (a Kohonen map). The number of clusters is selected based on the dispersion of the desired motor parameters, which is determined from the deviation of optimization criteria from the extreme. Finally, a hexagonal Kohonen map with 49 clusters is obtained in which each cluster is assigned a set of quasi-optimal laws. Thus, it is sufficient to correlate a motor with some cluster (in other words, classify it) which automatically defines a quasi-optimal control law. Procedures of formation and training of the network and parameters of realization of optimized control laws are provided.

Decentralized Adaptive Load Frequency Control in a Multi-Area Power System

The emergence of competitive forces in the electricity market and the demand for lower electricity rates will inevitably reduce the degree of co-operation between interconnected utilities. Therefore, the power system centralized control strategy leaves space to a decentralized one. But the main problem is that a decentralized strategy has to guarantee the whole dynamic security without the need of exchanging information or of coordination among areas. The paper deals with the investigation on the design of a decentralized load frequency control law able to allow the independent operation of each area, assuring in the same time the whole power system stability. Utilizing a decomposition-aggregation technique it is possible to handle the multi-area power system as composed by n subsystems (areas) interconnected each other. In particular, the aggregation stage is performed by the use of an adaptive optimal decentralized control law. In the paper, it is demonstrated that, using the proposed approach, the independence of each area is allowed and, in the same time, the stability and a good performance of the power system are guaranteed.

Advanced Load Frequency Control

The problem of designing a load frequency control law which reduces transient frequency oscillations (swings) and reduces the number of control signals sent to power houses is investigated. A linear model of an area of an interconnected power system is developed, and a discrete time, linear-plus-deadband, feedback control law is designed. Feedback variables include cumulative inadvertent interchange, frequency deviation, integral of frequency deviation, real power absorbed by loads, and governor-turbine variables. This linear-plus-deadband control is an application of a special case of a more general set-theoretic class of control laws. A simulation of two areas with two hydro sources is presented. The dynamic response to a step load change is determined for the case of no load frequency control, load frequency control presently used by power companies, and load frequency control designed in this paper.