The electrical loads in aircrafts are continuously increasing with the ongoing developments in avionics, upgrades in the sensor systems dealing with radars as well as the pilot interfaces. To go along with this there is an ongoing research development aimed at shifting towards the More Electric Aircrafts due to which the demand for electrical power on board an aircraft is likely to continue growing significantly over the coming years. As a result, there is a need for increase in the generating capacities of the existing electrical power systems on board the aircrafts. However, due to various constraints such as space availability, weight and aerodynamic implications, continuous increase in generator size is not a possible option and hence there is a need to improve the efficiency of the whole electrical system existing on board the aircraft.[1]
This research is a part of the project which aims to develop an integrated system of component models of aircraft which would allow optimum use of energy. The optimum use of energy in the electrical system would not only help in reducing the size and weight of the electrical generator but also in reduction of the fuel consumption by the generator to supply the electrical system of the aircraft during its flight. With the continuous rise in the fuel prices, reduction of fuel consumption is of great importance in the aircraft industry. A more efficient electrical system would also mean reduction in losses and hence a smaller and lighter cooling system. All these developments would result in the reduction of the load on the aircraft which would result in a better mileage of the aircraft and hence reduction in the fuel consumption by the aircraft as well.
In a more electric aircraft there are several electrical power systems such as the electrically driven environmental control system, all electric flight control system, electric fuel management and delivery system, electrically driven landing systems and electrically driven pneumatic systems for utility actuators. Each of these requires a number of motor drive systems. [2]
The aim of this research is to design and evaluate a dynamic model of an induction motor drive that would accommodate for the standard copper losses as well as the additional losses. The design of such a modified dynamic equivalent model would combine the advantages of the standard steady state model and the standard dynamic model of an induction motor drive.
The design of a dynamic model of an induction motor drive makes the control of the induction motor much simpler in comparison to the steady state equivalent circuit. However, the standard dynamic models of induction motor drives do not take into consideration the various additional losses taking place in the induction motor apart from the stator and rotor copper losses. These losses are generally calculated separately by modifying the standard steady state equivalent circuits using additional equivalent circuits dealing with the core losses, windage and frictional losses as well as the harmonic losses.
The various losses neglected in the standard dynamic model do have a small effect on the rotor current and rotor flux when the motor is running. As a result they also influence the output torque of the machine which will ultimately influence the accuracy of the prediction of the motor's behaviour characteristics. Therefore, to provide a more accurate simulation model, which is closer to the behaviour characteristics of the real concerned induction motor drive there is a need to include the neglected losses into the modified dynamic model of the induction motor drive. A more accurate simulation would give a better idea about the various other technical issues such as fuel storage capacity and ventilation within the aircraft.
Literature Review
Losses in Induction Motor
As per [1], the different types of losses in an induction motor are stator copper losses, rotor copper losses, friction and windage losses, core losses, stray load losses and brush contact losses.
Stator and Rotor Copper Losses
The stator and rotor copper losses take place because of the dissipation of power from the windings of the stator and rotor due to their resistance when the current flows through them.
In a three phase induction motor the stator copper loss is calculated as shown in equation (1).
where
I is the measured or calculated current per line terminal in Amperes.
R1 is the per phase dc resistance, in ohms.
However, it may be noted that the resistance of the stator windings varies with the temperature and hence the resistance value needs to be corrected to the operating temperature for the calculation of the stator copper loss.
The corrected Resistance can be calculated by using the equation(2).
where
Ra is the known value of winding resistance at temperature ta,
ta is the temperature in C, of winding when the resistance Ra was measured,
tb is the temperature in C, to which the resistance is corrected to,
Rb is the winding resistance, in ohms, corrected to the temperature tb,
k1 is a constant with value 234.5 for 100% IACS conductivity copper.
The rotor copper loss in an induction motor is calculated by using the relation as shown
Rotor Copper Loss = (Measured Stator Input Power - Stator Copper Loss - Core Loss) X Slip
The slip value can be calculated by using the equation (3) given below.
However, since slip is directly related to the rotor resistance, its value too needs to be corrected using the same basic relationship as for resistance and temperature. Hence, the corrected value of slip can be obtained by using the equation (4).
where
sa is the known value of winding resistance at temperature ta,
ta is the temperature in C, of winding when the resistance Ra was measured,
tb is the temperature in C, to which the resistance is corrected to,
sb is the winding resistance, in ohms, corrected to the temperature tb,
k1 is a constant with value 234.5 for 100% IACS conductivity copper.
However the measurement of stator and rotor copper losses explained above as per [1], does not take into consideration the skin effect and its influence on the total copper loss of the motor.
Stator and Rotor Core Losses
The iron losses consist of eddy currents and hysteresis losses in the laminations. They depend on flux density and frequency. Since the slip frequency in the rotor bars is very low, the core losses in the rotor are negligible in comparison to the stator core losses. The core losses are almost constant in the stator at a given voltage in case of constant frequency and constant overall flux [2].
However, in case of the induction motor drives, the frequency of the voltage supplied to the stator windings is not fixed even though an almost constant overall flux is maintained. Hence, the core losses vary in relation with the frequency.
The rated core losses when separated into the hysteresis and eddy current components take the form as shown in equation,
where Kh and Ke are constants which depend on the core type, rated flux density Br and the rated frequency fR. It can be observed from the core loss due to hysteresis is directly proportional to the rated frequency while the core loss due to eddy currents is directly proportional to the square of the rated frequency. Also assumed is that hysteresis loss is proportional to the square of mutual flux although in several studies it has been proposed that hysteresis loss is proportional to mutual flux raised to 1.6 or 1.7.
The circuit model typically used to predict the total core losses is as shown in figure1. The equivalent core loss resistance Rc is given as:
In a doubly fed induction motor where both the stator and the rotor are excited, the total core loss at any frequency can be expressed in terms of its rated value as,
Windage and Frictional Losses
Frictional and Windage losses are caused by friction in the bearings of the motor and aerodynamic losses due to various rotating parts of the motor. The friction and windage losses are essentially a function of motor speed and do not depend on the type of power supply. These losses can be expressed as []
Stator and Rotor Stray Load Losses
Stray load losses have not been completely understood or analysed correctly till now. These losses are generally defined as the losses that are not covered by the above mentioned types of losses. The stray losses are mainly attributed to the rotor current. However, since the measurement of rotor current is a difficult task, it is a common practice to express the stray losses as a function of the stator current. These losses are caused by the space harmonics of stator flux, rotor flux and the leakage flux near the end windings. However, they have been separated into the following components.
Flux pulsation losses in stator and rotor teeth in which the flux pulsation losses in the rotors are negligible. These pulsations are due to the change of reluctance of the magnetic path of teeth during the movement of the stator teeth against the rotor teeth and the fluctuation of ampere turns according to the distributed imbedding of the current carrying conductors in the slots.
Surface losses in the rotor due to space harmonics of the stator and surface losses in the stator caused by the space harmonics of the rotor. The losses in the stator being negligibly small.
Copper losses in the rotor cage due to rotor currents induced by the harmonics of the flux density.
Control Theories
Constant Volts/Hertz Control of Induction Motor Drives
Field Oriented Control of Induction Motor Drives
Direct Torque Control of Induction Motor Drives
Six Step VSI Induction Motor Drives
Space Vector PWM VSI Induction Motor Drives
Modelling of Induction Motor Drives
Steady State Loss Models of Induction Motor Drive
A simple per phase equivalent circuit model of an induction motor is a very important tool for analysis and performance prediction at steady state condition. The simple equivalent circuit shown in figure4 can be used to derive various power expressions to calculate the input power, stator copper losses, rotor copper losses, core losses, output torque and several other important power components. However, it may be noted that these calculations are valid only for a steady state condition and hence cannot be used to predict the performance of an induction motor drive. The simple equivalent circuit can not be used to predict the machine model performance in case of non-sinusoidal supplies unless the voltage waveform has been resolved into its time harmonics and a standard equivalent circuit is derived on the basis of each harmonic. Hence, there is a need for modifying the simple steady state equivalent circuit to accommodate for the variation in losses in the machine over its complete transient response.
Standard Dynamic Function Model of Induction Motor Drive
The standard dynamic function model of an induction motor drive can be derived from the standard steady state equivalent model through windings transformation. Although the standard dynamic function model is not useful in calculation of the various losses in the machine, it is mostly employed in circuit simulators such as Simulink, PSCAD, PSIM etc.
The standard dynamic model does not consider the impact of the various kinds of losses such as the core losses and stray load losses on the characteristic behaviour of the induction machine. Neglecting these additional losses results in inaccurate calculations of the various factors of the machine such as the rotor current and rotor flux and hence this would give an inaccurate prediction of the torque production. Such assumptions result in inaccurate prediction or simulation of the motor behaviour characteristic. For an accurate prediction of characteristic behaviour of a machine, a modified dynamic function model would be required that would consider all the different types of losses occurring in the machine so that the simulations would describe the real life machine characteristics much more accurately.
Methodology
3.1. Literature Search and Study
The aim of the dissertation project is to design a dynamic model of an induction motor drive that would include the various additional losses that are not considered in the standard dynamic model. To design such a model one would need to study the different kinds of losses taking place in an induction motor drive in great detail. To get detailed information on each type of losses associated to a motor drive, a thorough search needs to be done in the databases available. The various databases that are accessible include INSPEC, IEEE Explorer, Google Scholar and Web of Science to name a few. Through these databases various important journals and research papers dealing with topics related to the following can be accessed:
Induction motor losses
Steady state equivalent circuits of induction motors
Dynamic function models of induction motor drives
Control techniques in induction motor drives
Optimization techniques in induction motor drives
No Load and Locked Rotor tests of induction motors
Simulation and Modelling using Simulink
Once enough detailed information related to the above mentioned topics has been collected and sorted, the next step would be to perform an in-depth study of each of the topics mentioned above using the available sources such as the collected papers and journals as well as related books from the library if required.
3.2. Design of Modified Dynamic Model of Induction Motor Drive
The designing of the modified dynamic function model of an induction motor drive can be taken up only after a clear and in-depth understanding has been developed regarding the following topics:
induction motor losses
steady state equivalent circuits of induction motors
dynamic function models of induction motor drives
Before the dynamic model can be designed, a modified steady state equivalent model of the induction motor drive would need to be designed that would include all the additional losses such as core losses, stray load losses and windage and frictional losses if possible. The losses can be accounted for in the modified steady state model by adding a resistor in the model for each kind of loss. However, these resistors would not be constant and would vary with change in voltage, frequency, speed etc. depending on the relation that would be deduced from the in-depth study of the above mentioned topics. Once the modified steady state equivalent circuit has been designed it can be transformed to the dynamic function model by using the required transformation techniques.
3.3. Simulation & Modelling of the Dynamic Function Model of the Induction Motor Drive
To set up the simulation model of the design dynamic model of the induction drive, a simulating software SIMULINK would be used. The main advantage that SIMULINK holds over the various programming softwares is it does not require a compilation of a program code but instead the whole model can be set up using only basic function blocks. Using appropriate function blocks in SIMULINK, the various machine differential equations can be modelled.
3.4. No Load Test and Locked Rotor Test of an Induction Motor
To evaluate or analyze the performance of the designed modified dynamic model of induction motor drive, the various different losses such as stator and rotor copper losses, core losses, stray losses two specific tests will be needed to be performed i.e. No Load Test and the Locked Rotor Test.
The No Load Test is performed by running a motor at its rated voltage and rated frequency without connecting any load to it. Current, voltage and power are measure at the motor input. This test is used to calculate core losses, stator winding losses along with the windage and friction losses.
The Locked rotor test is performed while blocking the rotor by a mechanical mean to prevent its rotation. It can be used to calculate the rotor resistance and hence the rotor copper loss.
Project Planning
Literature search on various topics such as motor losses using various online databases such as INSPEC, IEEE Explore, Google Scholar and Web of Science.
Literature search on various topics such as 'steady state loss models'
Literature search on 'standard dynamic models of IM drives'
Inclusion of additional losses in modified dynamic models
Implementation of modified dynamic model on SIMULINK
Lab testing of IM to calculate various losses
Testing and Evaluation of the designed SIMULINK model
Comparison of losses obtained from Lab and Simulations
Consideration of possible alternate options
Simulation of various techniques employed at present and checking their results.
