“ STATOR SIDE CONTROL OF THREE PHASE INDUCTION GENERATOR ”

A project report submitted in partial fulfilment of the Requirement for the degree of

BACHELOR OF ENGINEERING

In

ELECTRICAL AND ELECTRONICS ENGINEERING

Submitted by

BADE GOWTHAM (311126514008)

CHILLIMUNTHA.VARUN KUMAR (311126514016)

DASARI VAMSIDHAR (311126514021)

MATTAPARTHI MADHURI (311126514054)

MYSARLA RAMESH BABU (311126514064)

PAGOTI RAM VIKAS (311126514071)

Under the guidance of

Mr.S.HARISH , M.Tech

Assistant Professor

Department of Electrical and Electronics Engineering

ANIL NEERUKONDA INSTITUTE OF TECHNOLOGY AND SCIENCES

(Affiliated to Andhra University, Visakhapatnam, A.P.)

Sangivalasa, Bheemili, Visakhapatnam-531162.

ANIL NEERUKONDA INSTITUTE OF TECHNOLOGY AND SCIENCES

(Affiliated to Andhra University, Visakhapatnam, A.P.)

Sangivalasa, Bheemili, Visakhapatnam-531162.

CERTIFICATE

This is to certify that the project report entitled “STATOR SIDE CONTROL OF THREE PHASE

INDUCTION GENERATOR”, has been submitted by “BADE GOWTHAM,CH.VARUN

KUMAR,DASARI VAMSIDHAR,MATTAPARTHI MADHURI,MYSARLA RAMESH BABU,PAGOT

RAM VIKAS ” in partial fulfilment of the requirement for the award of “Bachelor of

Engineering” in Electrical and Electronics Engineering to Andhra University,

Visakhapatnam is a record of bonafide work carried out by them under my guidance and

supervision.

Project guide Head of the Department.

Mr.S. HARISH Prof.G.RAJA RAO

ACKNOWLEDGEMENTS

We express our deep sense of gratitude and respect to our beloved Head of the Department, “Prof. Dr. G. Raja Rao”, Department of Electrical and Electronics Engineering, Ail Neerukonda of Institute of Technologies and Sciences (ANITS), for his valuable guidance and co-operation throughout our project work.

We owe our gratitude to our project guide, “Mr.S. HARISH”, for his valuable guidance and encouragement in completion of our project work.

We are very thankful to the Principal and Management of ANITS, for their encouragement and co-operation to carry out this work.

We express our gratitude to all the teaching stall of Dept. Of EEE for providing a great assistance in accomplishment of our project.

Last but not the least, we thank one and all who supported us by all means in completing this project successfully.

BADE GOWTHAM (311126514008)

CH.VARUN KUMAR (311126514016)

DASARI VAMSIDHAR (311126514021)

MATTAPARTHI MADHURI (311126514054)

MYSARLA RAMESH BABU (311126514064)

PAGOTI RAM VIKAS (311126514071)

ABSTRACT

This thesis presents the need of Speed Control in Induction Motors. Out of the various methods

of controlling Induction motors, V/f Control has proven to be the most versatile. The overall

scheme of implementing V/f control has been presented. One of the basic requirements of this

scheme is the PWM Inverter. In this, PWM Inverters have been modelled and their outputs fed

to the Induction Motor drives. The uncontrolled transient and steady state response of the

Induction Motor has been obtained and analysed. A MATLAB code was developed to

successfully implement Open Loop V/f Control on a PWM-Inverter fed 3-phase Induction Motor,

and the Torque was found to be constant for various rotor speeds. This was followed by a

MATLAB model for Closed-Loop V/f Control on a PWM-Inverter fed 3-phase Induction Motor. It

was observed that using a Closed-Loop scheme with a Proportional Controller gave a very

superior way of controlling the speed of an Induction motor while maintaining a constant

maximum torque.

List of Figures:

Fig 1.1: Electrical and Mechanical system arrangement

Fig 1.2: Induction Machine fed from a storage battery and converter

Fig 1.3: Static VAR Compensator Scheme

Fig .1: Control Scheme of STATCON -Based voltage regulator

Fig 3.2: STATCOM Compensator Scheme

Fig 3.3: Energy Conversion System

Fig 3.4: Induction Machine excited by SVC in parallel with AC-LVR

Fig 2.5: Basic inverter circuit.

Fig 3.6: Regular sampled PWM comparator input voltages

Fig 3.7: Voltage control by varying ma

Fig 3.1: Conventional Per-phase Equivalent Circuit

Fig 3.9: D-axis equivalent circuit on a arbitrary frame

Fig 4.1: Q-axis equivalent circuit on a arbitrary frame

Fig 4.2: The graph on the left shows the Torque Vs Slip characteristics of an induction

Fig 4.1: Generation of triangular wave

Fig 4.4: Inverter model

Fig 4.5: Simulink Implementation of Flux linkage

Fig 5.1: Calculation of rotor speed.

Fig 5.2: Simulink Implementation of Flux linkages

Fig 5.3: Calculates magnetic flux linkages.

Contents

Chapter 1 Introduction

1.1 Electrical and mechanical system arrangement

1.2 Static VAR compensator scheme

1.3 Vector control methods

1.4 Sensor less vector control

1.5 Goal of the project

Chapter 2 PWM Inverters

2.1 Basic principles of inversion

2.2 Classification

2.2.1. Based on commutation

2.2.2. Based on source

2.2.3. Based on No. of phases of load

2.3 PWM Inverter

2.4 Design considerations

2.5 Digital Signal Processor Control of PWM Inverters

Chapter 3 Dynamic Model of Induction Motor

3.1 Introduction

3.2 D-Q Equivalent Circuit

3.3 Constant V/f Operation

Chapter 4 Simulink Using MATLAB/SIMULINK

4.1 Introduction

4.2 Using MATLAB

4.3 Modelling Of PWM Inverter

4.4 Implementation in MATLAB

4.5 Simulation Results

References

Chapter-1

INTRODUCTION

STATOR SIDE CONTROL OF THREE PHASE INDUCTION GENERATOR

Renewable energy has increased to cause a great interest in the development and use of alternative energy sources, such as wave, wind and micro-hydro. especially for supplying electric power in remote areas. The energies generated by non conventional sources have been practically utilized for pumping, lighting, or cooking to reduce firewood or fuels in the remote areas where higher power quality is not required. Traditionally, DC or synchronous generators have been used for stand-alone micro power systems they require a rotating wound and a field fed by an independent excitation system and brushes Out of these generators Squirrel-cage induction generator (IG) has several advantages for stand alone applications such as no need for an external power supply to produce the magnetic field, little maintenance, rugged and simple construction, and brushless rotor type [1-4]. The operation of an induction machine as a motor or generator is determined by the operating slip of the machine. A positive operational slip would indicate the operation of the machine as a motor, and a negative slip would indicate the generating mode of the machine. It is well known that an induction machine can be made to work as a self-excited generator, i.e. the generator can be excited by the (a) connection of three capacitors at the stator terminals of the machine (b) by using an inverter/rectifier system. In the case of the inverter/rectifier system, the dc side capacitor appears like three phase capacitors due to the switching signals of the inverter, and the single dc capacitor of the rectifier provides the required excitation for the induction generator. An extensive overview illustrating the vast amount of work done in different areas over the last 25 years such as self-excitation, voltage buildup modeling, steady state analysis of an induction machine. The system has been studied specifically for applications related to wind/wave energy, thereby studying the controller response for varying rotor speeds. Also the stability of an induction generator-rectifier under field orientation control and also highlighting the possible instability of an induction generator used in high speed applications. The varying load conditions as well as varying the rotor speed of the machine. The machine has been operated at a condition of minimum copper loss. The condition of minimum loss is achieved by regulating the command rotor flux using a loss minimization function. The steady state analysis deals with the operation of the self-excited generator under conditions of saturation. The induction machine has been studied for its output power capability and the effect of the parameters of the machine on the operation of the machine under different load conditions. The analysis highlighting the effect of the magnetizing flux on the excitation requirements of the system with the magnitude of the modulation signal as a measure of the required excitation. By fixing the magnetizing flux linkage the required modulation index for excitation of the machine can be determined. Along with the effect of saturation, the system has been studied under a condition of minimum copper loss [5]. Along with isolated Power Generation, research was focused on parallel operated induction generators on the autonomous or isolated operation. Which supplied static or dynamic loads One of the serious problems with the IG is its inherently poor voltage regulation.. These induction generators driven by individual prime movers employed balanced or unbalanced excitation capacitors to buildup desired voltage via self excited phenomena. The self-excited induction generator

(SEIG) was one of the earliest types of self-excited AC generators.The fundamental problem with the SEIG is its inability to control the terminal voltage and frequency under varying load conditions. Therefore, it becomes necessary to have an appropriate voltage regulation scheme. There are a number of techniques for achieving voltage buildup, voltage regulation; frequency control, reactive power compensation etc. are reviewed in this project/report.

These techniques are classified in two groups one is passive and other is active. The passive technique known as capacitive self-excitation eliminates the need for external reactive power provided by a capacitor connected across the machine terminals. The capacitive self-excitation seems to be the cheapest and simplest technique to implement an IG. Residual magnetism in the iron provides the initial excitation. Capacitive self-excitation has been recognized for many years, the utility of this mode of operation is limited because it does not provide a stiff output voltage- regulation under variable loads and/or variable speed operation and the machine can only achieve and maintain excitation under certain speed and load conditions and finally, the machine works in the saturation region, hence its efficiency can be low. The different types of active excitation like PWM inverters and field-oriented controllers to excite the IM by allowing a better efficiency and good voltage regulation. These methods regulate the generated voltage even though operating with variable speed and load by minimizing the inverter size. The IG voltage can be regulated controlling the IM magnetic flux. The electrical and mechanical connections of the induction generator system are given in fig.1.

Fig.1.1. Electrical and Mechanical system arrangement

The phenomenon of self-excitation in induction machines using an inverter/rectifier system and a single DC capacitor on the DC link side has been known since the 1970s [6-7].

However, self-excitation of three-phase induction generators using three capacitors connected at the stator terminals has been known since the 1930s [8-9]. The rotor speed of the induction generator driven by a wave turbine, or an unregulated prime mover, can vary at any time even if the generator is running unloaded. When the induction generator excited by external capacitors is loaded the magnitude of the generated voltage and frequency will vary with load whether the rotor speed is regulated or unregulated. The variation in generated voltage and frequency will be aggravated when the induction generator is driven by an unregulated prime mover where the speed will drop with loading. By varying the capacitance values of the excitation system the generated voltage can be compensated. However the generated frequency can only be compensated by varying the rotor speed of the induction generator. Since capacitance values are discrete it is difficult to produce a smooth voltage regulation [10]. The problems associated with AC capacitance excitation can be solved by applying vector control to an inverter/rectifier system with a single DC capacitor on the DC link side [6-7, 11-12]. All the excitation current required by the induction generator is provided by the single capacitor on the DC link side of the inverter. When the excitation comes from the DC side capacitor of the inverter, varying the current flowing to the generator, by controlling the switching of the IGBTs, varies the flux in the induction generator. Due to the switching of the inverter the single DC side capacitor acts like a three phase capacitor to the induction generator, which is on the AC side of the inverter. When the fundamental switching frequency of the inverter is varied, the reactive capacitance, due to the single DC capacitor on the DC link side of the inverter, will be varied as seen from the induction machine side and instead of three AC capacitors only single DC side capacitor provides all the reactive current or the VAR required by the induction generator for its excitation. However, for a system with a single DC capacitor, the voltage buildup can not start from the remnant flux in the core because of the switching losses in the inverter as well as power loss in the generator. Hence an initial voltage is required in the DC capacitor to start the control and to allow the voltage build up process. The initial voltage can be obtained from a previously charged DC capacitor or from a battery connected to the DC capacitor. The battery will be disconnected once the voltage build up process has started. For this two conversion topologies have been considered, using a diode bridge and chopper or a thyristor bridge, being equal the characteristics of the wind and of the machine from the design analysis, confirmed by the EM” simulations, one can conclude that the solution using a total controlled thyristor bridge allows a wider speed range and a higher battery recharging energy, with a lower number of capacitor benches. Other solution with Diode Bridge and chopper requires a smaller turbine and seems to exhibit problems for the control of the static converter is shown in Fig.2. In all theses refinement of the model for the design, sensitivity of the system to the parameter variation etc is studied [13]

Fig 1.2. Induction Machine fed from a storage battery and converter

Hence, the limitations of induction generator systems with capacitor self-excitation are poor voltage and frequency regulation. The poor voltage regulation of the machine results in under-utilization of the machine. In order to regulate its terminal voltage with the load and utilize the machine to its rated capacity, an external source of reactive current is required and also synchronous condenser for this purpose although the high added cost and maintenance requirement of the synchronous condenser override the advantages of the induction generator. The scheme based on switched capacitors used in limited application because it regulates the terminal voltage in discrete steps.

The static VAR compensator (SVC) uses a capacitor and inductor with thyristor switches. The application of Static Var Compensator is demonstrated by connecting an induction generator to an induction motor driving a pump. The Scheme is composed of a wind turbine which drives a generation unit (induction generator and static VAR compensator) as shown fig. 3 and a pumping unit (induction motor and centrifugal pump). The generator operates at variable speed and variable frequency, providing variable voltage, proportional to the speed, while its stator flux is kept approximately constant. The pumping unit drives a centrifugal pump. Since the motor is directly fed by the generator, its stator flux is approximately constant and proportional to the voltage over frequency (V/F ratio kept constant). For that can be used rotary converters (synchronous condenser) or static compensators (thyristor controlled reactor-fixed capacitor, TCR-FC) could be used and also a pulse width modulation (PWM) converter is used to control the instantaneous value of the magnetizing currents. A capacitor and a start up battery are connected to the DC link of the converter, allowing stand-alone operation of the system. Coupling inductors are used to limit current rates, smoothening compensator current waveforms and connecting it to the generation system. The power flow is done in such a way that the compensator controls the reactive power flow of the machines and the active power from the generator to the DC link capacitor to keep it charged at a determined voltage value. Since the capacitor voltage must be high enough to force the magnetizing currents into the AC bus and the generator voltage is approximately proportional to its speed, a control scheme is used to keep the capacitor DC voltage proportional to generator speed.[14]. This system operates at variable speed variable

frequency and in order to assess system operational range, efficiency, control effectiveness, performance and stability under transients, and overall behavior, steady state and dynamic operating conditions.

Fig. 1.3 Static VAR Compensator Scheme

This Static VAR Compensator method faces the problem of losses in the inductor. More over, the inductor switching also injects harmonics in the line current of the system. Control of current in the saturable core reactor is one of the methods used to regulate the generated voltage in the SEIG. This type of regulator involves a potentially large size and weight, due to the necessity of large inductor. The short/long shunt configurations of the SEIG proposed give better performance in terms of voltage regulation than their simple shunt counterpart. But the series capacitor used in these configurations causes the problem of sub synchronous resonance while supplying power to a inductive and/or dynamic load. The application of modern semiconductor devices, power converter circuits and control algorithms have resulted in a solid state var source with different operating characteristics than those obtained with SVCs. A solid state synchronous voltage source (SVS) employs a DC to AC inverter, which internally generates capacitive inductive and reactive power without the use of AC capacitors/reactors. This type of compensator has been proposed for large industrial applications and also described a comprehensive treatment of power flow control using SVS for shunt compensation, series compensation and phase angle control. Muljadi et al.have proposed a series compensation scheme of the SEIG, utilizing a PWM inverter and a source of power supply in for the purpose of control of excitation and real power flow. The SVS operated as a reactive shunt compensator exhibits V-I characteristics similar to the rotating synchronous condenser. So that this specific arrangement of SVS is called a static condenser (STATCON) shown in fig.4. The output voltage of the STATCON is generated by a DC to AC inverter operated from a DC capacitor. With the proper switching signals applied to the switching devices, it simply interconnects the three output terminals in such a way that the reactive output currents can flow freely among the phases and also circulation of reactive power exchange among the phases. Availability of reliable, fast solid state switches such as MOSFETs and IGBTs, and their decreasing cost, have led to an investigation of the use of solid state VAR sources in a SEIG system; it can then be made available option for power generation, while also competing with conventional synchronous

generators. STATCON for closed loop control of the terminal voltage of an SEIG at varying load conditions are explained. [15,28]

Fig. 1.4 Control Scheme of STATCON -Based voltage regulator

Recent advances in modern semiconductor switches, power converter circuits, and Digital Signal Processors (DSP) and control algorithms have opened a new perspective for designers in the field of Static Compensators (STATCOM). A STATCOM is basically a three-phase PWM AC/DC converter that controls the reactive power at its terminals by means of generating leading or lagging power factor with respect to its terminal voltages (fig.5). The on-line PWM control of the converter provides a fast dynamic response for the system.[16]

Fig. 1.5 STATCOM Compensator Scheme

By using Robust control techniques in non conventional power generation improves in prime-mover power extract and system operational flexibility increases. The robust controller design, using the LQG/LTR (Linear Quadratic Gaussian with Loop Transfer Recovery) methodology, with an integral action assures system stability, no steady-state errors, insensitivity to parameters variations. There are two types of AC-DC-AC link. The first is based in a current structure, formed by two controlled converters and a link reactor. In this topology, the power flux between generator and grid is controlled through current reactor. The second type is based in a voltage structure, constituted for two controlled converters and a link capacitor, as shown in fig.6. The power flux control is made through voltage capacitor. In this paper, a control system design based on LQG/LTR techniques is present for variable speed induction generator system using a voltage structure. With a discrete-time model of the system, a discrete-time LQG/LTR controller with an integral action is designed to control of power generation, machine excitation and power transfer between generator and grid by indirect control for slip and rotor flux.[17]

Fig. 1.6 Energy Conversion System

The SEIG driven by a constant-speed prime mover (CSPM) has been done by using the nodal admittance approach and the series impedance approaches with the assumptions i.e. negligible iron losses, constant resistances and reactance of the three-phase induction machine. Since the rate of change in the parameters and variables of the equivalent circuit is extremely small, so that the steady-state equivalent circuit can be used so far. Using the iterative technique, the steady-state analysis of the three-phase SEIG driven by a variable speed prime mover (VSPM) has been carried out in reference. All the parallel branches of the three phase SEIG approximate equivalent circuit are converted to its equivalent series branches. The terminal voltage of the three-phase SEIG with variable loads can be maintained constant by adjusting the value of the excitation capacitance or by controlling the prime mover speed since the adjustment of prime mover speed is not always possible, so, the adjustment of the capacitor value continuously may be preferred. The adjustable excitation capacitor value can be achieved by many control strategies using power electronic technology. Some of them are based on a shunt-connected PWM voltage source inverter, supplying constant frequency voltage, and some others supplying reactive current to the induction generator by a capacitor bank and an inverter simultaneously based on the instantaneous reactive power theory[18]. However, increasing the capacitance can compensate the generated voltage, but the stator current increases. So care should be taken not to exceed the stator rated current. The control system shown in fig.7, using power electronics, regulate the generated voltage for a dc load over a wide range of speed of the three phase SEIG driven by a variable-speed prime mover (VSPM) and a simple closed loop feedback control system using the PI compensator is designed for the load voltage regulation. The AC load voltage regulator (AC-LVR) is employed to control the load terminal voltage connected to the three-phase SEIG due to the DC load and the prime-mover, speed variations simultaneously. The three-phase SEIG is excited by the static VAR compensator (SVC) composed of the fixed excitation capacitor (FC) and to be thyristor switched capacitor (TSC) for increasing the system efficiency. A three-phase SEIG prototype setup was established for the low cost, reliable and simple control strategy. [19]

Fig. 1.7 Induction Machine excited by SVC in parallel with AC-LVR

Hybrid excitation unit, consisting of a capacitor bank and an active power filter (APF), is used for the IG loaded by a non-linear diode rectifier load and AC load. This unit enables the IG to supply the pure sinusoidal currents for both AC and non-linear DC loads with voltage regulators and very small rating of the APF. The advanced deadbeat current control strategy for a stand-alone IG, excited by the hybrid excitation unit is to reduce the system cost. To implement the Hybrid excitation scheme a phase locked loop (PLL) circuit and five sensors are necessary: one is used for detecting the DC-link voltage and four sensors are used to detect the AC-side currents of the APF and both the diode rectifier and AC loads, while obtaining a good voltage regulation in a transient state. A laboratory setup is built to validate the proposal scheme. Fig.8 shows a schematic configuration of a current control implementation for a three–phase IG with a three-phase voltage-source APF and a capacitor bank for supplying an AC load and a full bridge diode rectifier load as a small-scale AC and DC power generating system. At no-load, the operation of IG starts to generate its output voltage from a remnant magnetic flux in its core when the IG is driven by a prime mover and excited by a capacitor bank. Hall Effect current sensor detect the load current and the compensating current of the APF. The proposed deadbeat current controller controls the compensating current of the APF, which is equal to the current harmonics of the non-linear load, and the reactive current required for regulating the IG terminal voltage. A reference signal generator is designed and used for estimating the current reference value of two switching sampling time period ahead to achieve the robustness about the parameter uncertainties of the deadbeat current controlled APF system. A PI controller with proportional gain and integral gain is necessary to keep the capacitor voltage on the DC–link of the APF constant.

Fig.1.8. Hybrid Excitation unit

The dynamic performance responses of the three-phase IG, directly connected to a full-bridge diode rectifier with a DC-link filter for small-scale DC power applications shown in Fig.8. Changes in the DC load and the speed of the prime mover are applied to verify the model in stationary reference frame. A deadbeat current controller-based APF is proposed for a stand-alone IG scheme working with variable speed and supplying a different load types, DC and AC loads with voltage regulation and harmonic compensation. The significant features of this controller are using a designed PLL circuit and five sensors as well as the implementation of the controller neither needs a mechanical position nor a speed sensing system therefore is the low system cost promising. This scheme can operate within a wider speed range and the rated load with a significantly high voltage regulation performance.[20]

In order to reduce the size of the inverter in an instantaneous reactive power theory can be implemented i.e. the I G excitation is controlled simultaneously by a capacitor bank and an inverter. The inclusion of the capacitor bank supports minimizing the inverter current. This means a lower inverter size. It does not need any mechanical position sensor in the IM rotor. This increases the system reliability. These two features enable reduced costs and also maximum inverter current will be only 0.21 PU for the speed range between 1.0 PU – 1.2 PU shown in fig.9. An AC load can be directly connected to the IM stator and the controller is able to regulate the generated ac voltage, where as the frequency remains unregulated. And also connect a dc load to the inverter dc link and the dc-generated voltage can be regulated by controlling the inverter active current. Both the ac and dc loads can be simultaneously connected and their voltages regulated independently. Hence this method enables good voltage regulation, even when operating with variable speed and load. [21]

Fig1.9. Inverter reactive current versus rotor speed.

1.3 VECTOR CONTROL METHODS

The variable speed high performance generation system using SIEG is studied. The requirements of high dynamic performance is gained utilizing filed-oriented control (FOC)[22] in which the dynamic model of the induction generator is simplified and decoupled. The FOC strategy is being studied in the context developed by Hass and Blashke in Germany some thirty years ago. This technique improves the performance of the induction generator to a level comparable to that of the separately excited DC generator. Therefore, FOC of induction generator system bas permitted high performance dynamic response using the decoupled torque and flux control. The FOC strategy can he classified into two types, one is the direct filed orientation control (DFOC) and second is indirect filed orientation control (IFOC). The IFOC strategy is simpler than the DFOC. The orientation technique may be done for rotor or stator and/or air gap flux. The total stator flux of the induction generator is controlled by the d-axis stator current in the rotating or excitation reference frame. The q-axis stator current in the excitation reference frame controls the active output power generated by the induction generator. Hence the flux producing current and power producing currents can be independently controlled. The coupling between the d-axis and q-axis quantities during transient condition is removed by generating an appropriate decoupling term.

Fig.1.10. Block diagram of the Vector control

With the stator flux oriented vector control of an induction generator the total flux linkage is aligned to the d-axis of the stator flux linkage. In a similar way in a rotor flux oriented vector control the total flux linkage is aligned to the d-axis of the rotor flux linkage in the excitation reference frame [fig.10]. However, rotor flux oriented vector control is dependent more on the parameters of the induction generator. A decoupling signal is generated to cancel the effect of the q-axis current on the d-axis flux for the stator oriented vector control for the induction generator. The main advantage of stator flux oriented vector control [fig.11.] is that the error in the estimated flux depends only on the stator resistance. This method of flux linkage estimation is preferred because it requires only stator resistance. It can be easily obtained from measurement. If there is variation of stator resistance due to change in temperature it can be compensated for [23].The back emf is calculated from the stator terminal phase voltage and from stator phase current. When an integrator is implemented in a discrete form, like in a DSP controlled induction generator, an error can arise. An improved estimation of flux linkage is used that compensates for the integration error. [24]. any integration offset error is easily removed by offset adjustment. The DC bus voltage is maintained at constant value during open-circuit and loaded conditions. Since constant DC voltage is achieved, a DC load can use it directly, or, if required, it is a matter of having an inverter to produce a constant voltage and frequency AC output. This method has good application in wind powered electric generation because the characteristics of the output power and torque for a wind generator match with the slip characteristics of the induction generator. For high wind a dumping resistance can be added to absorb the extra power supplied by the wind turbine. [25]

Fig.1.11. Stator Oriented Vector Control of Induction Generator

In IDFO systems, studies were focused on issues related to a speed control loop built upon system with a current source inverter (CSI) is shown in fig.12. As the currents are not the control variables but are inputs, the analyses were not meant to reveal any current regulation instability and the conclusion of global stability of an IDFO system is misleading since it is valid only for the speed loop of a CSI type IDFO system. Hence, no proof of stability of the VSI type IDFO system itself has been provided and in stability analysis related to digitization or control loop time delay in a CSI type IDFO system. So that instability is related to digital implementation and should not be considered as fundamental to the IDFO control method. In fact, any other control methods will have similar instability problems if the control loop time delays or the discrimination errors are not controlled properly within a limit. To simplify the analysis of the inherently non-linear IDFO system, assumptions of constant speed and constant current command input are made to reduce the complex non-linear problem in to a series of simplified linear problems. The system poles for the linear problems are then examined for stability analysis. The effect of the input command is then taken into account and a new concept of system poles migration is then proposed to provide a complete view of system dynamics and stability under all possible conditions. A comparison of stability between the mirrored motoring and generating points is also included to reveal some fundamental differences in system dynamics between the motoring and generating modes. To keep the analysis straightforward, a d-q frame motor drive dynamics will be formulated using the notation of complex vector and also transfer function also derived for studying the stability of machine. [26]

Fig.1.12. Induction generator with an indirect field orientated control

1.4 SENSORLESS VECTOR CONTROL

That enables stiff voltage regulation and high efficiency and also draw back, the field orientation requires costly and unreliable mechanical position sensing systems as encoders or resolvers. There are other proposals that do not require position-sensing systems.The use of this encoder implies additional wiring, extra cost, extra space, and careful mounting which detracts from the inherent robustness of cage induction machines. So that a sensor less control structure based on a direct rotor flux-oriented (DRFO) vector-control system, for variable speed wind/wave energy applications. Speed estimation, obtained from a model reference adaptive system (MRAS) is used to control the electrical torque of the induction machine. A V/F control strategy is used in the low-speed region for starting and driving the WECS set into the speed operating range. In order to tune the MRAS system and compensate for the variation of the machine parameters, an estimation of the rotational speed is obtained from the rotor slot harmonics (RSH). The spectral analysis method used in this publication can track the rotational speed not only in steady state but also when the WECS is subjected to fast dynamic changes. Sensor less vector-control method, including tuning of the MRAS observer, for a WECS. The system proposed is shown in Fig. 13(a)-(b). An induction generator is driven from an emulated variable-speed wind turbine. A microprocessor-based system is used to implement the DRFO algorithms, the V/F control strategy, the MRAS

rotational speed observer, the spectral estimation algorithm, the control of the front-end converter, and the emulation of the wind turbine. The front-end converter supplies the electrical energy into the grid. This converter controls the dc link voltage of the back-to-back configuration using a fuzzy PI controller. The currents and voltages of the induction machine are referred to a reference frame aligned to the rotor flux. These currents take dc values in steady state. The rotor flux is calculated from the machine voltages and currents. The components of the flux are used to calculate the electrical angle for the vector rotators.

Fig. 1.13.(a). Control System for MRAS

Fig.1.13(b). Experimental setup for MRAS

In variable speed system, wind /wave turbine can be operated to produce its maximum power at every wind/wave speed by adjusting the shaft speed optimally. In order to achieve the maximum power point tracking (MPPT) control, some control schemes have been studied using DFOC and IFOC with stator flux orientation. In the proposed wind generation system, the IFOC with rotor flux orientation of SEIG is used. The current vector of the SEIG is suitably controlled according to the IG speed in order to optimize the wind turbine operation for various wind speeds. The IG is controlled by the stator current control with MPPT algorithm below the base speed. The IFOC of SEIG allows the control of the d-q stator currents. So, the output voltage of the PWM can be regulated and we can maximize the efficiency if required. Also studies the design and control of the grid connected PWM inverter with the MPPT algorithm and unity power factor. To verify the design of the controllers and wind/wave energy system performance, the whole systems starting by the turbine to the grid through the AC/DC/AC converter interference can be simulated using MAT LAB/SIMULINK. [29]

Chapter 2

PWM INVERTERS

PWM INVERTERS

Inverters are most widely used for motor control applications, Induction heating, uninterrupted power supplies.

Basic principles of Inversion:-

Is Ig1 Ig1

T1 D1 Ig2

vs /2 - Vo + V0

I0 T2 D2 vs /2

vs /2 -vs /2

Fig. 2.1 Basic inverter circuit. Fig. 2.2 waveforms.

A simple 1- φ half bridge inverter has been shown. For 0<t¿ T/2 thyristor T1

conducts & load is subjected to a voltage Vs/2 due to upper voltage source Vs/2. At

t=T/2 thyristor T2 is commutated & T2 is gated on. During the period T/2<t¿ T thyristor T2 conducts and the load is subjected to a voltage –Vs/2 due to the lower voltage source Vs/2. It is seen from fig that load voltage is an alternation voltage waveform of an amplitude Vs/2 and of frequency1/T HZ. The diodes are connected in anti parallel with thyristors will allow the current to flow when the main thyristors are turned off for non resistive loads.

Classification:-

(a) Based on commutation (i) Naturally commutated inverters(ii) Forced commutated inverters

Naturally commutated inverters:-

These make use of either source voltage or load voltage as commutation voltage. Output voltage of phase controlled line commutated inverters is Vdiα=Vdiocosα .With the variation of firing angle in the range 90 to 180○ the voltage reverses and varies from zero to negative maximum. Therefore power flow is from load to source if there is a de course of proper polarity. The commutating voltage is provided by the source. If RLC under damped network is connected as load current through load reversers when the set of thyristors T1, T2 stop conducting, the current is carried by diodes connected in anti parallel and voltage drop in

Load

these diodes appears as a reverse bias across T1,T2 . If the duration of reverse bias is more than SCR turn-off time tq. T1,T2 get commutated naturally and therefore no commutation will be needed. This method is called Load commutation.

Forced commutation:-

It solves many problems in conversion of electrical energy and speed control problems of ac motors. Inverters employing forced commutation have advantage that their output frequency can be carried in a reasonably wide range. When once a thyristor is brought to ON state the gate pulse has no effect on its conduction. For a thryistor to successfully turn off its current must fall below holding value and it must be maintained at this condition for time greater than turn off time. This is to accomplished energy storage elements like capacitors are used to provide a negative bias to outgoing thyristor. For successful commutation capacitor used in the circuit must be charged to required polarity. It can be done by

1) using the dc source voltage 2) using load current3) separate voltage source

(b)Based on source 1) Voltage source inverters

a) PWM inverters

b) Square wave inverters

c) 1- φ inverters with voltage cancellation.

In the former dc voltage is made available across the load alternatively by controlling conduction of thyristors.Current in the load is decided by the load impedance. In the latter dc line current is made to flow through the load alternative by controlling thyristors conduction. The load voltage depends upon the load impedance.

2) Current source inverter

(c)Based on No. of phases of load

1) 1- φ Type

2) 3- φ Type

3-φ Bridge Inverters:

A Basic 3-φ Inverter is a sin–step bridge inverter .It uses a minimum of sin thyristors.For one cycle of 360○ .each step would be of 60○ interval for a sin step inverter. This means that thyristors would be gated at regular intervals of 60○ in proper sequence, so that a 3-φ variable voltage is synthesized at the o/p terminals of sin-step inverter .these are 2 possible patterns of gating the thyristors.

180○ Mode of operation

120○ Mode of operation

3-φ 180○ mode VSI:-

In this each transistor conducts for 180○. Three transistors remain on at any instant of time.

It is seen that phase voltages have six steps per cycle and line voltages have one positive pulse and one negative pulse each of 120○ duration / cycle.

Vab= ∑

n=1,3,5

∞ 4 VsnΠ

cosnΠ6

sin n (wt+ Π6

)

Vao= ∑

n=6 R±1

∞ 2VsnΠ

sin n(wt ) , R=0, 1, 2, 3…………..

3-φ 120○ Mode VSI:-

In this type of controls, each transistor conducts for 120○ .Only two transistors remain on at any instant of time.

It is seen that phase voltages have one +ve pulse and one –ve pulse each of duration 120 ○.the line voltages have sin steps/cycle of output alternating voltage.

Va0= ∑n=1,3,5

∞ 2 VsnΠ

cosnΠ6

sin n( wt+ Π6

)

V ab= ∑

n=6 R±1

∞ 3VsnΠ

sin n(wt + Π3

) , where R=0, 1, 2, 3…………..

Advantages and Disadvantages of 120○ Mode over 180○ Mode:-

(1) In 180○ mode, When gate signal ig1 is cut off to turn off T1 at wt = 180○, gating signal ig2 is simultaneously applied to turn on ig2 in the same leg. In practice a communication interval must exit between removal of ig3 and application of ig2

because otherwise dc source mould experience a direct short circuit through T1 and T2.

(2) The potential of 3rd terminal pertaining to a particular leg in which neither device is conducting id not well defined.

Voltage Control of 3- Phase Inverters:-

(1) Signal pulse width Modulation

(2) Multiple pulse width modulation

(3) Sinusoidal PWM

(4) Modified Sinusoidal PWM

(5) Phase – Displacement control

In single pulse width modulation, there is only one pulse per half cycle and the width of the pulse is varied to control the inverter out put voltage. The harmonic content is high with this type of control.

The harmonic content can be reduced by using several pulses in each half cycle of out put voltage. This type of modulation is multiple pulse width modulation.

PWM INVERTER:-

PWM Inverters one gradually taking over other types of Inverters. In these forced commutation is essential. In pulse width modulation a control voltage control is compared with repetitive switching signals. Controlling the switch duty ratios in this way allowed the average dc voltage output to be controlled.

In order to produce sinusoidal output voltage waveform at desired frequency a sinusoidal controls signal at a desired frequency is compared with a carrier wave. The frequency of the carrier waveform establishes the inverter switching frequency and is kept constant along with its amplitude.

Amplitude Modulation Ratio (ma) =

V control

Vtri

Frequency Modulation Ratio (mf) = fs/f1.

The features of PWM inverter can be summarized as follows

The inverter has constant dc link voltage and it uses PWM principles for voltage control.

The output voltage waveform improves with respect to harmonic content Parallel operation of many inverters on the same dc system. Using a standby battery, uninterrupted operation is possible for long periods. Very good power factor on the ac side as an uncontrolled rectifier is used. Complicated control compared to square wave inverter. Four quadrant operations are possible. Single or multi motor operation is possible. Smooth change over of voltage and

frequency values at zero crossing for speed reversal with full torque capability at standstill.

Frequency limit is 150 Hz using thyristorised converters. By the use of transistors, this frequency limit can be increased.

A very wide speed range 1:∞ is possible. Drives of 450 kVA are available. Peak current capability of the inverter can be smaller compared to square wave

inverter. Filter size can be smaller compared to the filter used with square wave inverter. The voltage value is determined by switching frequency. Open loop operation is possible. The transient response is fast.

To obtain balanced 3-φ output-voltage in a 3-φ PWM inverter, the same triangular voltage waveform is compared with three sinusoidal control voltages that are 120○

out of phase. The carrier wave and reference waves are mixed in a comparator. When sinusoidal wave has magnitude higher than the triangular wave, the comparator output is high, otherwise it is low.

For generating PWM pulses DSP processor is used to generate sinusoidal voltage of desired magnitude and frequency. In this modulating signal is stepped wave. The stepped wave is not a sampled approximation to the sine wave. It is divided as shown in fig. this type of control gives low distortion, but higher fundamental output amplitude compared to that of normal PWM control. (Figures of waveforms)

Fig. 2.3 Regular sampled PWM comparator input voltages

Fig.2.4 Voltage control by varying ma

Linear modulation:

In the linear region (ma<1.0) fundamental frequency component in output voltage

varies linearly voltage varies with ma. V AN=ma

vd

2

Line to line rms voltage at fundamental frequency due to 120 ○ phase can be written as

displacement. V LL1=

√3√2

(V AN )1

= √32√2

ma .v d

=0.612 ma . v d

Over modulation:

In PWM over modulation, the peak of the control voltages is allowed to exceed the peak of the triangular wave form. Unlike the linear region, in this mode of the operation the fundamental frequency voltage magnitude does not increase proportionally with ma.In this region compared linear modulation region more sideband harmonics appear centered on frequencies of harmonics mf and for its multiples.

Square wave operation:

For sufficiently large values of ma the PWM degenerates into a square wave inverter waveform. This results in maximum values of VLL1 equal to 0.78Vd as

V LL1=

√3√2

× 4Π

×vd

2

=

√6Π

V d ¿0 .78V d

Switch utilization ratio:-

S.U.R =

V 01 I o max

qV T IT q = No. of switches in an Inverter.

=√3

V LL1

I o max

6×V d max . I 0 max √2

=

12√6

V LL1

V d max

Max. Switch utilization ratio =

12√6

× √32√2

ma

=

18

ma(ma≤1 .0)

Ripple in Inverter o/p:-

Vripple (t) = V0 −V01

iripple(t) =

1L∫0

t

vripple( t )dt+k

v AN=2

3v AN−1

3(v BN+vCN )

V AN 1=EA+ jw1 LI A

1

The voltage ripple (=VAN−VAN1) is the ripple in the phase to neutral voltage. For large values of mf, the current ripple in the PWM inverter will be significantly lower compared to a square wave inverter.

DC side current Id :-

I d=

3 V 0 I 0

V d

cos φ

Design considerations:-

Amplitude Modulation ratio:-

Though over modulation region compared to the region with ma<1.0, more sideband harmonics appear centered around the frequencies of harmonics mf and its multiples. It is preferred for motor control applications as higher voltages can be obtained.

Frequency Modulation Ratio:

(1) mf should be an odd integer:- choosing mf as an odd integer results in an odd symmetry [f(-t) = -f(t)]as well as half wave symmetry [f(t) = -f(t+Ts/2)] and

Hence all even harmonics disappear from waveform & only odd harmonics are present .Moreover only coefficients of sine series in the Fourier analysis are finite & those for cosine series are zero.

2) mf should be multiple of 3: Choosing mf value such that it is a multiple of 3 results in elimination of triple harmonics.

3) Mf should be an integer: choosing an mf value as an integer especially at low value of mf’s results in synchronous PWM which avoids production of sub harmonics.

For small values of mf (mf≤21)

(i) Synchronous PWM should be used.(ii) mf should be an odd integer.(iii) Slope of Vcontrol & Vmi should be of opposite polarity at the coincident zero

crossings. Hence by considering all the above facts mf is choosen as ‘15’:

Carrier frequency:-

Because of the reactive case in filtering harmonic voltages at high frequencies, it is desirable to use a high switching frequency as possible, but at the same time switching losses in the inverter increase proportionally with switching frequency. In most applications f s

is selected to be either less than 6 KHz or greater than 20 KHz to be above the audible range.

Hence it is chosen as 750Hz.

Synchronous & Asynchronous PWM:-

The triangular wave form signal control signal should be, synchronized to each other (synchronous PWM). Otherwise asynchronous PWM results in sub harmonics that are very undesirable in most applications. Synchronous pwm can be obtained by choosing integer values of mf.

Symmetric & Asymmetrical PWM:-

PWM signal is symmetric if the signal is symmetric around the period value. Symmetric PWM is generated if the carrier wave is triangular & asymmetric pwm generated if saw tooth wave is choosen as carrier wave. Generally symmetric PWM is used

Microprocessor Control of PWM Inverters

In recent years, there has been increasing emphasis on the use of digital and microprocessor based techniques for the generation of PWM waveforms. Sinusoidal PWM, employs a sine wave reference, or modulating, signal which is compared with an isosceles triangular carrier wave to determine the inverter switching instants. This technique, known as natural sampled PWM, has been widely adapted because of its ease of implementation using analog control circuitry. In a digital hardware implementation, the sine wave reference may be stored as a look-up table in read only memory (ROM), and sine values is accessed at a rate corresponding to the required fundamental frequency. A triangular carrier wave is generated by using an up/down counter, and the two waveforms are compared in a digital comparator. However, natural sampling is essentially an analog technique, and this form of digital implementation is not very effective.

In a microprocessor-controlled PWM inverter, it is difficult to calculate the pulse widths of the naturally sampled waveform because they cannot be defined the pulse widths of the naturally sampled waveform because they cannot be defined by an analytic expression. It is possible to simulate the process of natural sampling in software but, again, this is not an effective technique.

DIGITAL SIGNAL PROCESOR CONTROL OF PWM INVERTERS

For the generation of PWM signals for the control of inverter also adapt the principle which is quite similar to Regular sampling. In the DSP processor there is a particular in-built module called EVENT MANAGER Module which is mainly used to generate PWM signals. Complete explanation of this module is specified in next sections. The high frequency carrier wave is generated using up-down counter which is named as

GP TIMER. The timer starts counting up until it reaches the maximum value which is specified in the program and from then it starts counting down until it reaches zero from which it starts counting up again which results in a repetitive triangular wave. From the above explanation it is clear that the carrier wave frequency depends on frequency of the clock input to the counter and the maximum value of the counter specified in program. The angles at which intersection of the carrier wave and the modulating sine wave of desired frequency for one complete cycle of sine wave for the desired value of amplitude modulation ratios occur are predetermined. The sine values at which both waves match are loaded into the data memory as a look-up-table. These values are regularly read when triangular wave reaches maximum and minimum values and loaded into a register called Compare register. Transition in the pulse occurs when the counter value matches with the value in compare register. The size of the look-up-table depends on the frequency modulation ratio. As the triangular wave and sine wave matches two times in each cycle of triangular wave sine wave matches two times the ratio of triangular frequency to sine frequency in a complete cycle of sine wave. The Optimization techniques which have been adapted for Microprocessor control can also be applied for DSP control. The output wave of the PWM inverter is of the sine wave. The frequency of the sine wave can be changed either by keeping the frequency modulation ratio (mf) constant and by varying carrier frequency or by keeping carrier wave constant and by varying frequency modulation ratio (mf). Both the above mentioned techniques have been implemented in the project. The output voltage of the inverter is varied by varying the amplitude modulation ratio (ma). Both the frequency and voltage are simultaneously varied by keeping v/f ratio constant.

Chapter 3

Dynamic Model of Induction Motor

Dynamic Model of Induction Motor

3.1. Introduction

In developing the dynamic model of the induction motor, the following assumptions will be made without affecting the validity of the model.

The motor has symmetrical three phase windings. The mmf wave is sinusoidal distributed in space. The stator and rotor iron have infinite permeability. Skin effect and core losses are neglected. The motor is operating in the linear region of B-H characteristic.

In order to understand and analyze vector control, the dynamic model of the induction motor is necessary. It has been found that the dynamic model equations developed on a rotating reference frame is easier to describe the characteristics of induction motors. It is the objective of this chapter is to derive and explain induction motor model in relatively simple terms by using the concept of space vectors and d-q variables. It will be shown that when we choose a synchronous reference frame in which rotor flux lies on the d-axis, dynamic equations of the induction motor is simplified and analogous to a DC motor. Traditionally in analysis and design of induction motors, the “per-phase equivalent circuit” of induction motors shown in Fig. 3.1 has been widely used. In the circuit, Rs (Rr) is the stator (rotor) resistance and Lm is called the magnetizing inductance of the motor. Note that stator (rotor) inductance Ls (Lr) is defined by

Ls = Lls + Lm, Lr = Llr + Lm (3.1)

Where Lls (Lrs) is the stator (rotor) leakage inductance. Also note that in this equivalent circuit, all rotor parameters and variables are not actual quantities but are quantities referred to the stator. Parameters of the circuit are determined from no-load test and locked rotor test. It is also known that induction motors do not rotate synchronously to the excitation frequency. At rated load, the speed of induction motors is slightly (about 2 -7% slip in many cases) less than the synchronous speed. If the excitation frequency injected into the stator is

and the actual speed converted into electrical frequency unit is , slip s is defined by

s = ( – ) / = / (3.2)

and is called the slip frequency which is the frequency of the actual rotor current. In the steady-state AC circuit, current and voltage phasors are used and they are denoted by the underline. In Fig. 3.1, power consumption in the stator is interpreted as Is2Rs, while Ir2Rr/s represents both power consumption in the rotor and the mechanical output (torque). By subtracting rotor loss Ir2Rr from Ir2Rr/s, produced torque (mechanical power divided by the shaft speed) is given by

Te = ir2Rr (P/2) (1-s) / (swr) = ir

2Rr [P / (2we)], (3.3)

where P is the number of poles. Although the per-phase equivalent circuit is useful in analyzing and predicting steady-state performance, it is not applicable to explain dynamic performance of the induction motor.

Fig. 3.1 Conventional Per-phase Equivalent Circuit

3. 2. D-Q Equivalent Circuit

In many cases, analysis of induction motors with space vector model is complicated due to the the fact that we have to deal with variables of complex numbers. For any space vector Y, define two real quantities Sq and Sd as,

S = Sq + j Sd (3.24)

In other words, Sq = Re (S) and Sd = Im (S). Fig. 3.5 illustrates the relationship between d-q axis and complex plane on a rotating frame with respect to stationary a-b-c

frame. Note that d- and q-axes are defined on a rotating reference frame at the speed of ωa = pθa with respect to fixed a-b-c frame.

Fig 3.6 Definition of d-axis and q-axis on an arbitrary reference frame

With the above Eq. 3.22-3.23 can be written the following 4 equations of real variables

(3.25)

(3.26)

(3.27)

(3.28)

The above 4 equations are expressed in a matrix form as follows:

(3.29)

where 3.29a

For future reference, the above matrix equation simplified for popular reference frames in analysis and design of vector control will be introduced. For stationary reference frame, by substituting ωa = 0, the above equation is reduced to

(3.30)

Some implementation of vector control drive includes calculation in rotor reference frame (frame is attached to the rotor rotating at ωr ). In this case, we can substitute all ωa in Eq. (3.29) by ωr, which makes simplified rotor voltage equations. Moreover, for synchronous frame, we have

(3.31)

ird

vqsss

isd qrqs

Lm

drvds

As mentioned before, each variable (voltage, current or flux linkage) in the synchronous frame is stationary and fixed to a constant magnitude in steady-state. Based on Eq. 3.4, dynamic d-q equivalent circuit is shown in Fig. 3.2.

Fig. 3.2 D-axis equivalent circuit on a arbitrary frame

Fig. 3.3 Q-axis equivalent circuit on a arbitrary frame

vqs

Rs -a Ls Lr (a-m) Rriqs

vqr

irq

Expression for the Electromagnetic Torque

The electro magnetic torque Te can be expressed in terms of the stator, rotor or air gap flux linkages as follows:

(3.32)

(3.33)

(3.34)

3.3 CONSTANT V/f OPERATION:

If supply voltage and frequency are changed in such a manner so as to keep V/f a constant value, then the air-gap flux remains substantially constant. Speed control by means of frequency and voltage variations also allows the capability to operate the motor not only at speeds below the rated speed, but also above the rated speed. This capability is very attractive

in many applications, since the induction motors can be operated up to twice the rated speed without mechanical problems.

BELOW THE RATED SPEED—CONSTANT TORQUE REGION

In the region of speed below its rated value, where magnetizing flux kept constant by controlling V/f. if magnetizing flux is maintained constant, and the motor can deliver its rated torque by drawing its rated current at a constant F. hence this region is called as constant torque region .F is at its rated value in this region. At the constant rated torque, the power loss Pr=3RrIr

2 in the rotor resistances also constant, where Ir stays constant.

BEYOND THE RATED SPEED ----- CONSTANT POWER REGION

By increasing the stator frequency above its nominal value, it is possible to increase the motor speed beyond the rated speed .in most adjustable speed drive applications; the motor voltage is not exceeded beyond its rated value. There fore by keeping the Vs at its rated value, increasing the frequency F results in a reduced Vs/F and, hence by reduced magnetizing flux (øag). Hence this region P max = ωr Tmax can be held constant, called as constant power region. In practice, the motor can deliver higher than its rated power by noting that Im goes down as a result of decreased øag and therefore is equal to its rated value allows a higher value of Ir and, higher torque and power. Since Im is decreased, the core losses are reduced and better cooling at higher speeds.

HIGH SPEED OPERATION:

Depending on the motor design, beyond in range of 1.5 to2 times the rated speed, øag , is reduced so much that the motor approaches its pullout torque. At still higher speeds, motor can deliver only a fixed percentage of the pullout torques. Both the torque and the motor current decline with speed. Open-loop speed control is used when accuracy in speed response is not a concern such as in HVAC (heating, ventilation and air conditioning), fan or blower applications. In this case, the supply frequency is determined based on the desired speed and the assumption that the motor will roughly follow its synchronous speed. The error in speed resulted from slip of the motor is considered acceptable.

THE PRINCIPLE OF CONSTANT V/HZ :

Because, to avoid insulation break down, the stator voltage must assume the voltage applied to a three phase AC Induction motor is sinusoidal and neglect the voltage drop across the stator resistor. Then we have, at steady state,

V = jWØ i.e V=WØ => Ø =V/W= V/ (2* П *F)

Where V and Ø are phasors of stator voltage and stator flux, F is frequency

From which it follows that if the ratio V/f remains constant with the change of f, then Ø remains constant too and the torque is independent of the supply frequency. In actual implementation, the ratio between the magnitude and frequency of the stator voltage is usually based on the rated values of these variables, or motor ratings. However, when the frequency and hence also the voltage are low, the voltage drop across the stator resistance cannot be neglected and must be compensated. At frequencies higher than the rated value, the constant V/Hz principle also has to be violated not exceeds its rated value.

Although it has been superseded open loop Volt/Hertz control or Scalar Control as it is known, is still widely used in applications where don’t require precise speed control such as fans for Heating Ventilation and Air Condition (HVAC). This method is based on the torque speed curve for an induction motor.

Fig.3.4 the graph on the left shows the Torque Vs Slip characteristics of an induction

Traditionally variable speed electric machines were based on dc motors, but for 20 years, the inverter fed ac drives has largely taken over as the preferred solution for variable speed applications. For low performance application, open loop constant V/Hz control strategies are employed.

CHAPTER 4

SIMULATION USING MATLAB/SIMULINK

4.1 ABOUT MATLAB:

MATLAB is a high-performance language for technical computing. It integrates

Computation, visualization, and programming in an easy-to-use environment where problems

and solutions are expressed in familiar mathematical notation. Typical uses include Math and

computation Algorithm development Data acquisition Modeling, simulation, and prototyping

Data analysis, exploration, and visualization Scientific and engineering graphics Application

development, including graphical user interface building MATLAB is an interactive system

whose basic data element is an array that does not require dimensioning. This allows you to

solve many technical computing problems, especially those with matrix and vector

formulations, in a fraction of the time it would take to write a program in a scalar no

interactive language such as C or Fortran. The name MATLAB stands for matrix laboratory.

MATLAB was originally written to provide easy access to matrix software developed by the

LINPACK and EISPACK projects. Today, MATLAB engines incorporate the LAPACK and

BLAS libraries, embedding the state of the art in software for matrix computation. MATLAB

has evolved over a period of years with input from many users. In university environments, it

is the standard instructional tool for introductory and advanced courses in mathematics,

engineering, and science. In industry, MATLAB is the tool of choice for high-productivity

research, development, and analysis. MATLAB features a family of add-on application-

specific solutions called toolboxes. Very important to most users of MATLAB, toolboxes

allow you to learn and apply specialized technology. Toolboxes are comprehensive

collections of MATLAB functions (M-files) that extend the MATLAB environment to solve

particular classes of problems. Areas in which toolboxes are available include signal

processing, control systems, neural networks, fuzzy logic, wavelets, simulation, and many

others.

4.2 MODELING OF PWM INVERTER:

GENERATION OF TRIANGULAR WAVE:-

fig 4.1 generation of triangular wave

The frequency f is multiplied by the frequency modulation index mf and the product is multiplied by the gain (2П) which is further multiplied by the time t which gives the overall product as 2П mf t. This product is passed to a sine function sin (u). Later this function is passed to arcsine function block which produces triangular wave which can be seen in the oscilloscope

Inverter model:

Vao

Vbo

Vco

3

Vcn

2

Vbn

1

Van

-0.5

g8

0.5

g7

1/3

g6

1/3

g5

1/3

g4

2/3

g3

2/3

g2

2/3

g1

Switch3

Switch2

Switch1

4

Pul c

3

Pul b

2

Pul a

1

Vd

Fig.4.2 inverter model

The above figure shows modeling of three phase inverter.

In this a triangular wave is compared with a sine wave. When the amplitude of triangular

wave is greater than the amplitude of sine wave, the relay operates and produces the output

i.e, PWM signal. The triangular wave is compared with the sine wave in each phase and relay

in each phase operates accordingly to produce the pulse width modulated signals , which is

the output of the three phase inverter.

SIMULINK IMPLEMENTATION INDUCTION MACHINE MODEL

DESCRIPTION:-

The Asynchronous Machine block operates in either generating or motoring

mode. The mode of operation is dictated by the sign of the mechanical torque (positive for

motoring, negative for generating). The electrical part of the machine is represented by a

fourth-order state-space model and the mechanical part by a second-order system. All

electrical variables and parameters are referred to the stator. This is indicated by the prime

signs in the machine equations given below. All stator and rotor quantities are in the arbitrary

two-axis reference frame (dq frame). The subscripts used are defined as follows:

Subscript Definition s Stator quantity

d d axis quantity

q q axis quantity

r Rotor quantity

s Stator quantity

l Leakage inductance

m Magnetizing inductance

The induction machine modeling equations can be implemented in matlab/simulink

environment. In the process of simulink implementation the flux linkage equations are

implemented first. The simulink model of the equation (15) is given in Fig.2

Fig.4.3 Simulink Implementation of Flux linkage

The remaining equations (16),(17) and (18) are implemented in the same way..

Now the equation (19) becomes

Fig. 4.4 Calculation of rotor speed.

The complete simulink model of the flux linkages is shown in the Fig.4. Equations

(5) and (6) calculate q and d-axis magnetic flux linkages by using outputs of the simulink

model shown in Fig.5.

Fig.4.5 Simulink Implementation of Flux linkages

The simulink implementation of equations (5) and (6) becomes

Fig.4.6. calculates magnetic flux linkages.

Once the flux linkages are calculated the rest of the equations can be implemented

without any difficulty. The blocks solving the rest of the equations are also organized in

columns.

The blocks in column 2 solve equation (5) and (6).Equations (9) to (12) use the flux

linkages to solve for the stator and rotor d-q currents Fig. 6 shows the implementation

equation (9).

Fig.4.7 calculation of current

The remaining currents can be calculated in the similar manner.

The fourth and last column includes the electrical torque calculation from equation

(13) and speed calculation from equation (14). The implementation of which is shown in Fig

7. The rotor speed information is required for the calculation of the rotor flux linkages in

column 1. Therefore it is fed back to two blocks in the column.

The resulting model is modular and easy to follow. Any variable can be easily traced

using the simulink “scope” blocks.

The blocks in the first two columns calculate the flux linkages, which can be used in

vector control systems in a flux loop.

The blocks in column 3 calculate all the current variables, which can be used in the

current loops of any current control system and to calculate the three phase currents. The two

blocks column4, on the other hand, calculate the torque and speed of the induction machine,

which again can be used in torque control or speed control loops. These two variables can

also be used to calculate the output power the machine.

Fig.4.8

The inputs of a squirrel cage induction machine are the three- phase voltages, their

fundamental frequency, and the load torque .the outputs are the three phase currents,

electrical torque and rotor speed.

The d-q model requires that all the three phase variables have to be transformed to the

two-phase synchronously rotating frame. Consequently, the induction machine model will

have blocks transforming the three phase voltages to the d-q frame and the d-q currents back

to three phases.

4.3 IMPLEMENTATION IN MATLAB:

wr

120/(2*pi*4)

norm2

15

mf

iabc1

2*pi*60

We*

3*sqrt(3)*230/pi VdVabc1

230/(2*pi*60)

V/F

Step2

Step1

Step

Saturation

Vd

Pul a

Pul b

Pul c

Van

Vbn

Vcn

INVERTER

we Theta

INTEGRATOR With Reset

mf

V

theta

Pul a

Pul b

Pul c

CONTROL LOGICAND GATE DRIVE

Vas

Vbs

Vcs

TL

ias

ibs

ics

Te

wr

CAGE MOTOR MODEL

Fig.4.9. implementation of model with out closed loop

wr

120/(2*pi*4)

norm2

(2*pi*4)/120

norm1

27

mf

iabc1

1.654*460 Vd

Vabc2

Vabc1

460/(2*pi*60)

V/F

0

TL

Vas

Vbs

Vcs

TL

ias

ibs

ics

Te

wr

Subsystem

Saturation3

Saturation2

Saturation1

Saturation

Ramp1

Ramp

50

Proportional1

5

Proportional

1s

Integrator

Vd

Pul a

Pul b

Pul c

Van

Vbn

Vcn

INVERTER

we Theta

INTEGRATOR With Reset

mf

V

theta

Pul a

Pul b

Pul c

CONTROL LOGICAND GATE DRIVE

Fig.4.10. implementation of model with closed loop

The above figure shows the implementation of the proposed project

in matlab. The output of the three phase inverter i.e PWM signals are given to the three phase

slip ring induction motor. As the motor has to be runned under no load condition, torque

constant is given as zero. The output of the induction motor is given to a measurement block

which measures the required quantities. The graph of the corresponding quantity can be seen

in the corresponding oscilloscope.

Simulation results:

Dynamic Results:

0 0.5 1 1.5 2 2.5-200

-100

0

100

200

Time (sec)

Ia (

amps

)

Current in 3 - Phases

0 0.5 1 1.5 2 2.5-200

-100

0

100

200

Time (sec)

Ib (

amps

)

0 0.5 1 1.5 2 2.5-200

-100

0

100

200

Time (sec)

Ic (

amps

)

Fig 4.11 Variation of 3-Phase currents

0 0.5 1 1.5 2 2.5-100

-50

0

50

100

Time ( sec)

Spe

ed (

Rad

/sec

)

Variation of Speed

0 0.5 1 1.5 2 2.5-500

0

500

1000

1500

2000Reference Torque and Generated Torque

Time (sec)

Tor

que

(N-M

)

Fig4.12. Torque and Speed variation with open loop

0 0.5 1 1.5 2 2.5-400

-200

0

200

400

Time (sec)

Va

(vol

ts)

voltages in 3 - Phases

0 0.5 1 1.5 2 2.5-400

-200

0

200

400

Time (sec)

Vb

(vol

ts)

0 0.5 1 1.5 2 2.5-400

-200

0

200

400

Time (sec)

Vc

(vol

ts)

Fig.4.13 Variation of 3-Phase voltage with out closed loop

0 0.5 1 1.5 2 2.5-100

-50

0

50

100Current in 3 - Phases

Time (sec)

Ia (

amps

)

0 0.5 1 1.5 2 2.5-100

-50

0

50

100

Time (sec)

Ib (

amps

)

0 0.5 1 1.5 2 2.5-200

-100

0

100

Time (sec)

Ic (

amps

)

Fig. 4.14 Variation of 3-Phase currents with closed loop

0 0.5 1 1.5 2 2.5-2000

-1000

0

1000

2000

Time (sec)

Tor

que

(N-M

)

Reference torque and Generated torque

0 0.5 1 1.5 2 2.5-800

-600

-400

-200

0

200

400Variation of Speed

Time (sec)

Spe

ed (

rad/

sec)

Fig4.15. Torque and Speed variation with closed loop

0 0.5 1 1.5 2 2.5-1000

-500

0

500

1000

Time (sec)

Va

(vol

ts)

Voltage in 3 - Phases

0 0.5 1 1.5 2 2.5-1000

-500

0

500

1000

Time (sec)

Vb

(vol

ts)

0 0.5 1 1.5 2 2.5-1000

-500

0

500

1000

Time (sec)

Vc

(vol

ts)

Fig4.16 Variation of 3-Phase voltages with closed loop

REFERENCES

[1] C. Grantham, D. Sutanto and B. Mismail, “Steady-state and transient analysis of

self-excited induction generators”, IEE Proc. B, Vol. 136,No. 2, pp. 61-68,

March 1989

[2] D. Seyoum, C. Grantham and F. Rahman F., "The dynamic characteristics of an

isolated self-excited induction generator driven by awind turbine", Proc. IEEE

IAS 2002 Annual Meeting, Pittsburgh, USA,pp. 731-738.

[3] D. Seyoum, M. F. Rahman and C. Grantham, “Terminal voltage controlof a wind

turbine driven isolated induction generator using statororiented field control”,

Proc. IEEE- 2003 Applied Power ElectronicsConference and Exposition, Miami

Beach, Florida, USA, pp. 846 -852

[4] Marcos S. Miranda, Renato O. C. Lyra and Selenio R. Silva, ”An Alternative

Isolated Wind Electric Pumping System Using Induction Machines”, IEEE

Trans. on Energy Conversion, Vol.14, No.4 pp.1611- 1616, December, 1999.

[5] Jyoti Sastry, Olorunfemi Ojo and Zhiqiao Wu, “High Performance Control of a

Boost AC-DC PWM Rectifier-Induction Generator System,” IEEE Industrial

App.Conferance 14th IAS Annual Meeting Vol.2, pp: 1007-1014, 2-6 Oct. 2005.

[6] D.W.Navotny, D.J.Gritter and G.H. Studtmann, “ Self-Excitation in Inverter

Driven Induction Machines”, IEEE Trans. on Power Apparatus and Systems,

Vol.PAS-96, no.4, July/August 1977, pp.1117-1125.

[7] M.B. Brennen and A.Abbondanti,“StaticExciters for Induction Generators”, IEEE

Trans. on Industry Appli. vol. IAS-13, no.5,Sept./Oct. 1977,pp.422-428.

[8] E.D.Basset and F.M. Potter, “ Capacitive Excitation of Induction Generators”,

Trans. of the Amer.Inst.Electr.Eng. Vol. 54, no.5, May 1935,pp.540-545.