The aim of this project is to design a dynamic model of an induction motor drive with representative loss modelling of the additional losses such as the core losses, windage and friction losses as well as the stray load losses. This modified dynamic model would then be used to test the performance of the various proposed optimization strategies.
The completion of this project would require the following objectives to be achieved:
In-depth study and understanding of the various induction motor losses.
In-depth study and understanding of the steady state and dynamic models of induction motor drives.
Designing and Modelling of the modified dynamic model using SIMULINK.
Verification of the accuracy of the SIMULINK model by comparison with readings obtained from experiments on a given induction motor drive.
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. 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 project is part of a research programme aimed at developing an integrated suite of component models to allow energy use within an aircraft electrical system to be optimised. 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] Hence it would be of great importance to develop efficiency optimisation techniques for controlling the induction motor drives.
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 stray load losses.[3]
As an Induction motor drive’s parameters such as the supply voltage, supply frequency, speed and operating temperature vary, each type of loss varies in different magnitudes. Only after each type of the loss has been identified and its relation with the various motor parameters has been mathematically derived would it be possible to design a modified steady state equivalent model of the induction motor drive. Once the modified steady state equivalent model is designed, it could be transformed to derive the dynamic model.
A dynamic model of the induction motor drive which considers all the losses of an induction motor would be more accurate in predicting the behaviour characteristics of the given motor drive. At present numerous efficiency optimization strategies for controlling an induction motor drive have been proposed and by using the developed Simulink model the performance of the various proposed strategies can be analysed and compared with each other.
Literature Review
2.1. Losses in Induction Motor
As per the IEEE Standards[4], the different types of losses in an induction motor are stator and rotor copper losses stator and rotor core losses, friction and windage losses and stray load losses.
2.1.1. Stator and Rotor Copper Losses
The stator and rotor copper losses, also known as the winding 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).
(1)
where
I is the line current, in Amperes
R1 is the DC phase resistance, in Ohms
However, it may be noted that the resistance of the 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).
(2)
where
Ra is the resistance of the stator winding at temperature ta,
ta is temperature in C, at which resistance Ra of the stator winding was measured
tb is the operating temperature of the stator windings in C
Rb is the resistance of the stator winding at the operating 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
(3)
where
Pin is the measured stator input power
Ps,cu is the calculated stator copper loss
Pfe is the core or iron loss
S is the slip of the motor
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).
(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 the IEEE Standard Test Procedures [4], does not take into consideration the skin effect and its influence on the total copper loss of the motor. The influence of the skin effect on the stator windings and rotor bars has been deduced in an earlier study[5]. In stator windings, the skin effect is negligible but quite dominant in the rotor bars. The skin effect results in increase of the resistance of the rotor mainly due to the presence of harmonics in stator currents which create a dominant skin effect in the rotor. The rotor resistance at harmonic frequency fn is approximately given by:
(5)
where
Rrdc = DC Resistance of the rotor bars
C1 = Constant which accounts for the shape and material of the rotor bars
fn = nth harmonic frequency
d = bar depth [5]
Stator and Rotor Core Losses
The eddy current losses and hysteresis losses in the laminations make up the core losses in the induction motor. In cases where a constant frequency and constant overall flux is maintain, the core losses are considered to be constant. 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 stator and rotor core losses when separated into the hysteresis and eddy current components take the form as shown in equations (6),(7) respectively.
(6)
(7)
where Kh and Ke are the hysteresis and eddy current coefficients, ̉ۢ is the fundamental mutual flux and f is the fundamental frequency. It can be observed from the core loss equation that the losses due to hysteresis are directly proportional to the frequency while the losses due to eddy currents are directly proportional to the square of the frequency. Also assumed is that hysteresis losses and eddy current losses are proportional to the square of mutual flux. 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 equation:
(8)
where
Kc = ̉ۢf/Vm
Vm is mutual or airgap flux
s is the slip of the motor [5]
However in an earlier study it was proposed that the hysteresis loss is proportional to the mutual flux raised to 1.7 and this constant is known as the Steinmetz constant[6] while in another study the Steinmetz constant was proposed to be around 1.6 for metallic cores[7]. In a much recent study the total core loss was derived to be as shown in equation(9).
(9)
where (n+1) is the Steinmetz constant[8].
In this study separate equivalent rotor core loss resistance and equivalent stator core loss resistance were derived separately as given in equation(10)(11).
(10)
(11)
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.[5] These losses can be expressed as equation(12):
(12)
Stator and Rotor Stray Load Losses
Stray load losses are not very well defined as are grouped together as the losses that are not covered by other defined losses. These 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. These losses can be distributed into the following categories. [9]
Losses in the stator and rotor teeth due to flux pulsations 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.[10]
Surface losses in the rotor and stator due to their space harmonics. The surface losses in the stator are negligibly small.
Copper losses in the rotor cage due to the induced rotor currents created due to the flux density harmonics.
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 conditions. A simple equivalent circuit shown 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 behaviour characteristics of an induction motor drive. Although the steady state model is valid only in steady state conditions, motor losses are modelled in the steady-state models, using additional equivalent circuits with frequency-dependent parameters to calculate the various kinds of losses [3]
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 and PSIM. The dynamic model employs a time stepping approach that allows for variations in the input voltage, speed, torque etc while providing sufficient accuracy for greater time steps during extended transient phenomena and hence is the largely followed approach for dealing with the variable speed drives.[3]
The standard dynamic model does not consider the impact of the various additional losses such as the core losses and stray load losses on the characteristic behaviour of the induction machine. The need for including core losses in the dynamic model of an induction motor drive has been emphasized through recent research work. It has been concluded that the core loss is mainly present in the stator core. This iron loss does affect the rotor current and rotor flux during the operation of the induction motor. As a result, the iron loss also influences the torque produced. Hence, neglecting iron loss in the dynamic model would result in inaccuracy in the motor torque control.[11] In recent studies modifications have been proposed to the standard dynamic models to accommodate for losses due to harmonics.[12]
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.
Efficiency Optimization Strategies for Control of Induction Motor Drives
With the increasing of cost of electricity and fuel, the researches aimed at improving the efficiency of the induction motor drives have attained great importance. In various dynamic performance control strategies such as vector control and direct torque control which are the preferred strategies in industrial applications, a constant flux is usually maintained around a fixed rated value. As a result, when the motor is not at full load, the excessive energy which is stored in the coil inductances leads to decrease in the efficiency of the motor. In many of its applications, the induction motor drive is subjected to variable torque loads and hence does not operate at the rated value. Hence decreasing the flux during the low loads would result in optimizing the energy usage by the motor.[13]
Some of the proposed optimisation strategies suggest the usage of search controllers with the induction motor drives. In a recent study a proposed optimisation strategy employed loss model controller to determine the optimal airgap flux along with a search controller which measured the input power or stator current and searched for the optimal excitation value.[14] Another paper proposed a method which would not require the knowledge of the machine parameters but yield a true optimum efficiency at all the load torque and speed values. This method is based on adaptive flux level adjustment using a field oriented controller while directly measuring the input power to the motor drive system.[15] The efficiency of these and other proposed efficiency optimisation techniques can be verified by using a modified dynamic model of the induction motor drive.
Methodology
Literature Search and Study
Before the designing aspect of the project can be taken up, a thorough and detailed study of the topics related to the project is required. To access the required information on the necessary topics, a thorough search of literature could be performed through the numerous 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 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
Efficiency Optimization techniques in induction motor drives
No Load and Locked Rotor tests of induction motors
Simulation and Modelling using Simulink
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
The modified dynamic model will include the various additional losses in the circuit by adding equivalent resistances to represent each kind of loss. However, these equivalent resistances are not constant and would vary with change in voltage, frequency, speed etc. The variation in the losses can be determined by deriving an arithmetic relation for each kind of loss with the varying machine parameters. The design of the modified dynamic model would also require a clear understanding of the transformation techniques to derive the dynamic model from the modified steady state model of the induction motor drive.
Simulation & Modelling of the Dynamic 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 that 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 the appropriate function blocks available, the various machine differential equations can be modelled onto SIMULINK. For the simulation of the induction motor drive, an add-on blockset of SIMULINK, Piece-wise Linear Electrical Circuit Simulation (PLECS) could be used.
In PLECS blockset a functional block for an induction machine has already been provided. In the provided model all electric variables and parameters are viewed from the stator side. However, the provided model does not accommodate for the additional losses of the induction motor.[16] Hence the modified model for an induction motor can be developed by modifying the provided model or by building the whole of the modified model.
Lab Tests on an Induction Motor Drive
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.
Evaluation of the Modified Dynamic Model of Induction Motor Drive
Once the modified dynamic model of the induction drive has been set up on SIMULINK, its simulation could be used to collect readings of it behaviour characteristics as well as to calculate the various losses and their variation with the electrical variables and motor parameters. Most importantly, the efficiency of the simulated model could be calculated as well. These observed readings and calculated values from the simulation are to be compared with the readings obtained from the lab experiments to analyse the accuracy of the modified dynamic model.
