Thermal Modelling of Induction Machine Using the Lumped Parameter Model
Chapter One
Purpose of Study
The objectives of this research work include:
To study the various parts or components of the induction machine;
To study the thermal behaviour or temperature limits of the induction machine and its components under various operating conditions;
To review the losses and methods of heat transfer in the induction machine;
To develop an accurate thermal model for an induction machine; To predict the temperature in different parts of the induction machine using the thermal model and software program and lastly, To investigate how the machine symmetry is affected by the nodal configuration.
CHAPTER TWO
LITERATURE REVIEW
An electrical machine is said to be well designed when it exhibits the required performance at high efficiency with operation within the range of the maximum allowed temperature. Several motors used in industrial applications rely on electromechanical or thermal devices for protection in the overload range [6] but thermal overheating and cycling degrade the winding insulation which results in the acceleration of thermal ageing. The consequence is insulation failure which eventually leads to motor failure. Presently, there is high reliability on thermal motor protection schemes using the thermal devices or the microprocessor embedded thermal models, all of which are based on the thermal heat transfer model of the induction machine.
The analysis of the heat transfer process is usually achieved by choosing an idealized machine geometry. It is then carefully divided into the fundamental elements and characterized by a node, thermal resistance, thermal capacitance and a heat source. In describing the fundamental elements, much about the machine construction cum the thermal properties of the materials used have to be known. A careful division of the machine into several parts gives a better result but poses a great deal of complexity in the computation task; this may have informed the suggestion of [7] that a compromise between a detailed model and an oversimplified one must be reached as the former can be very cumbersome to use both in computer simulation and software development.
In the market today, there exist many general purpose advanced computational fluid dynamic (CFD) packages. The CFD codes are designed using sophisticated and modern solution technology to enhance the handling of high demanding cases of thermal modelling of flow system whether external or internal. The electrical machine manufacturers have depended on this to a large extent especially in the cooling and ventilation modelling [8] and in the thermal management of alternating current electrical motors [9].
The thermal network models, (TNM) [10, 9] popularly called the lumped parameter model is one of the schemes adopted in studying thermal models for the determination of rise in temperature in electrical machines.
The finite-element method (FEM) is another scheme used in the determination of the temperature rise in electrical machines, and also in analyzing the thermal behavior of electrical machines. Many researchers [12, 13] have adopted this rather later method in one way or the other.
A number of thermal circuits of induction motors [14, 15], radial flux [16], stationary axial flux generators [17] and many others that have been proposed in the past were all studied using the lumped parameter model (LMP) approach and the results so obtained suggest a good agreement with the experimental data.
Here in, the thermal network model, that is, the lumped parameter model approach is adopted. The lumped parameters are derived entirely from the dimensional information, the thermal properties of the materials used in the design and the constant heat transfer coefficients. This translates to high level adaptability to various frame sizes.
The calculations of the parameter values arising from this lumped arrangement are comparatively complex and result in sets of thermal equations which mathematically describe the machine in full and which can be solved and adapted for online temperature monitoring for many applications including motor protection [11, 14, 18, 19].
The above approach is better in that it saves one the hurdles involved in the solution of heat conduction by Fourier analysis approach and that of convective heat transfer by use of Newtonian equations. The duo adopts the analytical models for the simulation of the temperature distribution within a generator [19, 21].
The thermal circuit method has been in vogue for the estimation of temperature rise in electrical machines through the aid of real resistance circuits but the calculation was enhanced by the introduction of computers in the early seventy’s. This computer time enabled the use of numerical methods such as the finite element and the finite difference analysis in the thermal modelling of electrical machines [22].
Among the early researchers is Soderberg who in [23] published work on thermal networks for electrical machines. He derived the equivalent thermal circuit for steady-state heat flows in stators and rotors having radial cooling ducts where he obtained good results for large turbine generators.
The adequacy of lumped parameter thermal network for any kind of component divided into arbitrary subparts having uniform heat generation was confirmed by Bates et al in [24]. They adopted an open circuit in the thermal model so that the heating of the cooling fluid was included in the calculations. It was reported in that within the same time, though after Kotnik’s work using equivalent circuit [25], Hak’s work on the calculation of temperature rise by thermal networks was published. He did not stop at that as he also published another work which looked at a model for the air-gap. The next were models for: axial heat transfer in electrical machines in 1957 and models for stator slot, tooth as well as yoke in 1960.
CHAPTER THREE
HEAT TRANSFER MECHANISMS IN ELECTRICAL MACHINES
HEATTRANSFER IN ELECTRICAL MACHINES
Heat is popularly defined as the form of energy that is transferred between two systems, usually a system and its surroundings by virtue of temperature difference [52, 53]. This gives thermal energy a clearer meaning in thermodynamics when we refer to adiabatic processes. Since from the first law of thermodynamics or the conservation of energy principle, energy cannot be created or destroyed [52], we have therefore, that the amount of heat transferred during a process between two states, say 1 and 2 is denoted by Q12 or simply Q . Hence, heat transfer per unit mass, m of a system is denoted by q which is obtained from
q =
(3.1)
Q KJKg-1………………………………………………………………………..
The amount of heat transferred per unit time to be simply called the rate of heat transfer is denoted by Q
where the over dot stands for the time derivative of Q . If Q varies with time, the amount of heat transfer during a process is obtained by integrating
Q over the time interval of the process as follows.
Q = t 2
t 1
Q dt
KJ (3.2)
If Q remains constant during a process the relation above reduces to Q = Q ∆t where ∆t = t2 – t1 is the time interval during which the process occurs.
In electrical machines as is represented in figure (4.1), page 28, heat is transferred from various parts to another. The transfer from the stator to the outside surrounding and that of the rotor to the stator plus many other transfers are not of the same mode. Hence we look at the various modes of heat transfer.
CHAPTER FOUR
THERMAL MODEL DEVELOPMENT AND PARAMETER COMPUTATION
CYLINDRICAL COMPONENT AND HEAT TRANSFERANALYSIS
The heat transfer processes is summarized in the simplified diagram of induction motor shown in figure (4.1) below. Conduction also occurs in the air-gap, between stator slots and stator iron and between rotor bars and rotor iron.
CHAPTER FIVE
LOSSES IN INDUCTION MACHINE
DETERMINATION OF LOSSES IN INDUCTION MOTORS
Power losses that occur during the transfer of power from the electrical supply to mechanical load give rise to the heating of the induction machines. Some of the loss components were described in [72] under iron losses, copper losses, harmonic losses, stray load losses and mechanical losses.
There are five main losses that occur in an induction machine and these are identified as follows:
- Stator copper losses that occur as a result of the current flowing in the
- Core losses linked to the magnetic flux in the machine, which is independent of the
- Stray load losses that vary with the driven
- Rotor copper
- Friction and windage (rotational) losses that occur in the bearings and ventilation
CHAPTER SIX
THERMAL MODELLING AND COMPUTER SIMULATION
THE HEAT BALANCE EQUATIONS
In the lumped parameter thermal circuit analysis, it is often assumed that the temperature gradient with certain parts of the machine is negligible. According to [60] this assumption can only be made if the internal resistance to the heat transfer is small compared with the external resistance. The Biot number
Bi , is usually used for determining the validity of this assumption. In the case where internal conduction resistance is compared with
exernal convective resistance,
Bi is defined as:
B = hc L ………………………………………………………………………………………………… ……
i
s
…(6.1)
where ks is the thermal conductivity of the solid material
L is the characteristic length of the solid body
hc is the convective heat transfer coefficient.
The criterion
Bi Ð0.1
ensures that the internal temperature will not
differ and in the words of [96], the assumption of uniform temperature is acceptable except for the early times of the step change in temperature and for such, the time for the change is localized in a thin ‘skin’ near the fluid or solid surface.
CHAPTER SEVEN
CONCLUSION AND RECOMMENDATIONS
CONCLUSION
In the work presented so far, the need for thermally modeling a system such as this machine is highlighted. The basics of the thermal modeling are introduced and the general equation for the implementation obtained. The calculation of thermal capacitances, thermal resistances and the consideration of losses all led to the determination of the thermal conditions of the core parts. For the full nodal configuration, the predicted temperature rise in degree centigrade for the core parts of the machine are as follows: frame (61.51), stator lamination (76.93), stator winding (79.94), end- windingR (80.85), rotor iron (68.55), rotor winding (68.25), end- ringR (63.86), end-ringL (63.86) and end-windingL (80.85) for SIM model and frame (61.13), stator lamination (76.40), stator winding (74.15), end-windingR (83.25), rotor iron (83.00), rotor winding (83.69), end-ringR (78.07), end-ringL (56.04), end-windingL (82.25), stator teeth (76.75), rotor teeth (82.92) for LIM model.
It is observed that contrary to the research results of some authors, the machine does not have a uniform increase in temperature in some of the core parts. The larger the machine, the more the difference in temperature meaning reduced asymmetry effect.
The transient and steady state models are analyzed. Tabular and graphical results from the steady and transient states simulation are presented leading to a clearer comparison of results obtained. Some discrepancies as may be noticed in this work are likely coming from the neglect of radiation effect cum errors due to assumptions and approximations.
In conclusion, this work can appropriately be employed to predict the temperature distribution in induction machine especially when used for wind energy generation. The results obtained here provide useful information in area of machine design and thermal characteristics of the induction machine.
RECOMMENDATION
The thermal lumped model that has been developed gives a good estimation of the machine temperature but there is more work that can be done to further improve the model, some of which are:
- Settingup an equivalent electrical model for loss The loss calculation for the lumped circuit model has been partly based on the estimated data. Setting up a separate electrical circuit for loss calculation based on geometrical data will give the free will of estimating the temperature on theoretical machine design with much ease.
- Accountingfor the Cooling The frame to ambient thermal resistance has been decided based on measured data, giving an empirical relation as the cooling characteristics were not available, future work needs to take the cooling characteristic into consideration so as to make the model functional for a realistic range of temperature condition.
- Calculation of the thermal losses in a FEM simulation program andvalidating the model through finite element method FEM calculations is likely to give a more sound
Generally, temperatures variations should be given considerable importance in the design and protection of our machines. A data base should be produced from several generated thermal results for predictive purposes. This will go a long way in the improvement of loadability schedules especially in wind energy generation schemes.
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