Finite Element Method Based Design of a Liquid

Finite Element Method Based Design of a Liquid Rheostat Motor Starter Elshiekh K. Mohammedsaeed

Abdelrahman A. Karrar

EEE Department, Faculty of Engineering University of Khartoum Khartoum, Sudan [email protected]

College of Engineering and Computer Science University of Tennessee at Chattanooga Chattanooga, USA [email protected]

Abstract—This paper deals with a finite-element method based design of a liquid-rheostat reduced-voltage starter for three phase squirrel-cage induction motors which typically drive irrigation pump loads. A commercial software package named COMSOL Multiphysics 3.4, based on the computational concept of the finite element method was used to design the liquid rheostat, and to study the effect of the tank material on the starting resistance of a case study. The objective was to use the software package to calculate the required resistance of the electrolyte solution, analyze the effect of electrolyte tank material on the value of the starting resistance, and finally study the effect of the different shapes of the electrolyte tank and the electrodes. Keywords— Finite Element Method (FEM); Liquid Rheostat; Comsol; Motor Starter; conductivity; electrolyte.

I.

INTRODUCTION

When a large induction motor is started directly on line, there is a tendency of high current flow through the motor which may damage the winding permanently, and additionally may cause power quality problems to the upstream electrical network, in particular for low fault-level networks. This inrush current occurs because, at the instance of the starting, the impedance of the AC induction motor winding is very low. As the motor accelerates, the impedance increases and the current starts to diminish [1]. As an inexpensive solution for large induction motors with low starting torque requirements, stator liquid-resistance starting may be employed. Theoretical calculations for such resistors form a challenge, and the resistance is usually determined experimentally [2]. This paper deals with the finite element method based design of a Liquid Rheostat reduced voltage starter for three phase squirrel cage induction using Comsol Multiphysics Software. II.

being approximately proportional to the distance between them [2].

LIQUID RHEOSTAT BASIC DESIGN AND FEATURES

Basically, the liquid rheostat consists of metal electrodes in a tank of electrolyte as shown in Fig. 1. Usually the solution used is a few per cent of sodium carbonate by weight in clean water. The current flows between the electrodes through the electrolyte solution, the resulted resistance between electrodes

Fig. 1. Liquid Rheostat Main Parts

Knowledge is required of some of the characteristics of the electrolyte to be employed in a liquid rheostat during design. The value of the specific resistance of the usual liquids is especially important, as well as their variation with the degree of concentration and the changes of temperature. Different concentrations of Sodium carbonate (Soda Ash), Sodium chloride (common salt), or Sodium hydrate (caustic soda) are normally employed [3]. In actual practice, once the proper electrolyte concentration is reached smooth acceleration can be accomplished. Liquid rheostat can be also used with the external rotor circuit of the large wound rotor IM to control its speed. Smooth starting, adjustable resistance value (since the resistance is changeable with the density of electrolytic liquid), explosion proof (LRS is suitable for the explosive gas places such as mines), and low price (in case of higher than 1000 kW motor power rating, it is more economic than metal grid resistors) made liquid rheostat starters (LRS) remarkable in the industry.

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IV.

III. FINITE ELEMENT METHOD (FEM) The problem of calculating the exact resistance which will be required in the liquid rheostat becomes very challenging [4], and this work explores a finite element approach to accomplish this. In mathematics the finite element method (FEM) is a numerical technique for finding approximate solutions to boundary value problems. Analogues to the idea that connecting many tiny straight lines can approximate a larger circle, FEM encompasses all the methods for connecting many simple element equations over many small subdomains, named finite elements, to approximate a more complex equation over a larger domain [5]. In general, the FEM is simply described by the following equation: (1) {K} * {u} = {F} Where {K} is the property, {u} is the behavior, and {F} is the action. In electrical applications, {K} can represent the dielectric permittivity, {u} can represent the electric potential and {F} can represent the electric charge [6]. FEM is used to study the behavior of many electrical systems, by finding the solution of the upper equation with respect to the matrix {u}.

CASE STUDY

The following data was taken from an agricultural project that employs three-phase squirrel-cage induction motors (IM) to drive water pumps for irrigation purposes. The existing design suffered from tank cracks and the system failed after 3-4 months from starting service. Table I describes the IM specifications and the existing liquid rheostat, the single phase electrolyte tank design parameters and the electrodes design parameters. TABLE I

CASE STUDY DATA

IM Specifications

Liquid Rheostat specification

Type Rated kW

Three phase squirrel-cage 1250 kW

Tank Dimensions (m) Tank Material

Line voltage

11 kV

Frequency

50 Hz

Electrolyte concentration

No. of poles

8 pole

Efficiency

94%

cos θ

0.83

(P.F.) I LRC

348.98 A

Coupled Load

Water Pump

Electrolyte Conductivity Electrodes Dimensions (m) Electrodes Material Electrodes Electrical Conductivity

1.265×0.39×1.58 Fiberglass 1Kg of Sodium carbonate (Soda Ash) per 7 barrels of tap water. 0.3797 S/m (measured) 0.1×0.005×0.1 Copper 5.99×107 S/m

A. Laplace’s Equation in Conducting Medium Laplace equation is used to calculate the voltage distribution in a certain medium by using the voltage applied on the medium and its conductivity. For steady direct current, starting from differential relation [7], Laplace equation is (2) ∇ 2V = 0 The conductive medium equation used by Comsol software is (3) -∇ .(σ ∇ V - J e ) = Q j Since V is electric potential (V), σ is the conductivity of the medium (S.m -1 ) , J e is external current density (A.m -2 ) , and Q j is current source (A.m -3 ) [9]. B. The Boundary Conditions To determine specific distribution of the electric field, i.e., to determine uniquely the solution of the differential equation, the boundary conditions given at the boundary of the research region are needed [8]. In this paper, the boundary conditions are used to solve the differential Laplace’s equations to determine the electric potential distribution through the medium, and then integrate the electric potential to calculate the power dissipated (P). The resistance (R) can be calculated using the applied phase voltage (V P ) as in equation (4). R = VP 2 / P

(4)

Fig. 2. The existing single phase liquid rheostat design

CALCULATION OF THE REQUIRED PRIMARY RESISTANCE VALUE

V.

It is required to compare alternative designs of a liquidrheostat motor-starter for the squirrel cage induction motor with specifications mentioned in table II. The required primary resistance for starting can be calculated using the motor data in table II. Since the locked rotor current I LR C = 348.98 A The impedance of motor ( Z m ) during the full voltage starting Zm =

VP I LR C

Zm =

11*10 3 = 18.2 Ω 3 * 348.98

(5)

The resistance of LRS required to reduce the motor applied voltage to 70% during the starting period should be (6) R = Zm

R = 18.2 Ω VI.

THE LIQUID RHEOSTAT SIMULATION USING COMSOL MULTIPHYSICS

A. Comsol Multiphysics 3.4 Simulation Procedures The Simulation using Comsol Multiphysics 3.4 described by the following procedures: 1) Draw the model to be studied, apply correct subdomain settings and boundary conditions to the model. 2) Perform meshing the model and solve the Laplace equation for the system using FEM. 3) Obtain the voltage gradient around the plates and the electrolyte box boundary. 4) Calculate the dissipated power in the medium of the electrolyte box, and then obtain the LRS resistance. B. The Design of the Resistance Box and the Electrodes The idea is to design a model that simulates the resistor box as a vertical cube with cubic plate electrodes. The liquid resistance box is thought to be as a conductive medium. The electrolyte in the designed model is assumed to be uniform having a constant conductivity. The container of electrolyte is designed as a cubic (box) element with an opened top side. The two electrodes are identical in dimensions and in conductivity. The plate is designed as a cubic shaped element which is made of copper (conductivity of copper = 5.99 *1 0 7 (Ω . m ) -1 ). The fixed and moving electrodes are

subdomains it is also possible to specify initial condition and element types. Before the solution, the boundary conditions for each boundary of the model were selected. Table II shows the subdomain settings parameters, PDE coefficients as in equation (4), initial conditions, and the boundary conditions for each boundary. TABLE II SUBDOMAIN SETTINGS PARAMETERS, PDE COEFFICIENTS, INITIAL CONDITIONS, AND THE BOUNDARY CONDITIONS FOR EACH BOUNDARY. type

Je

Qj

Conductivity (S/m)

Initial voltage

Boundary condition

LRS box

0,0,0

0

0.3797

0

Electric Insulation

Fixed plate

0,0,0

0

5.99 * 10

7

0

Ground

Moving plate

0,0,0

0

5.99 * 10

7

0

Voltage

11 /

3 kV

C. The Solution of The Model Using Comsol Sofware After the model is drawn, its Laplace equation is solved. First step in solution process is Meshing the model. FEM is known with its unique Triangles. Initialize the Mesh allows the designer to see the triangles made by the COMSOL Multiphysics 3.4 solver as in Fig. 4.

identical in shape and made from the same material; the fixed electrode is located vertically inside the tank at 0.1 meter above the bottom center of the tank as is shown in Fig. 3. The moving one also is located vertically inside the box at the surface of the electrolyte. Fig. 4. Initialized Mesh Model

To obtain the specific distribution of the electric potential, i.e., to determine uniquely the solution of the differential equation, the model is solved by Comsol as shown in Fig. 5.

Fig. 3. The existing single phase liquid rheostat design

After drawing the LRS model with its dimensions, the subdomain settings were defined such as material properties, sources, and PDE coefficients on the subdomains. On the

Fig. 5. The solved model

The most important feature relevant to the topic is the calculation of the dissipated power inside the design using sub-domain integration of electric potential distribution through the medium as resistive heating; Fig. 6 shows the integration result. Finally using the resistive heating, the LRS resistance can be calculated using equation (4) since the applied phase voltage is known.

TABLE III SIMULATION RESULTS OF THE EXISTING LRS WITH DIFFERENT ELECTROLYTE TANK MATERIALS Tank material

Dissipated Power (MW)

Liquid resistance(Ω)

Figures

Fiber-glass

2.188674

18.43

Fig. 8(a)

Iron

3.657481

11.03

Fig. 8(b)

Epoxy coated iron

2.240741

18.00

Fig. 9(a)

Fiber-glass tank when the moving electrode on the half distance.

3.170582

12.72

Fig. 9(b)

Fig. 6. The results produced from Subdomain Integration.

Assuming that the electrolyte conductivity is constant (i.e. the concentration is constant and the liquid is homogenous), and using the previous simulation procedures, the existing system was simulated at first. Subsequently, different types of tank material and shapes were also simulated to analyze their effects on the liquid resistance. There are eight combinations of the tank shapes (box and cylinder with same volume and height) and electrodes shapes (box, cylinder, plate, and sphere with same volume as existing electrode shown in Fig. 7.). These combinations were simulated to find out which design offers the largest resistance.

Fig. 8. Potential distribution graphs, (a) fiberglass tank, (b) iron tank

Fig. 7. Different types of electrodes shapes, (a) box, (b) cylinder, (c) plate, (d) sphere.

VII.

RESULTS

A. Simulation results of The Existing LRS and different Electrolyte Tank Materials Using the existing LRS parameters, first a ( 11 / 3 ) kV (phase voltage) was applied to the moving (top) electrode at its initial position, while the fixed one was grounded. The simulation was then repeated with the tank material changed to different types as shown on table III.

Fig. 9. Potential distribution graphs, (a) epoxy coated iron tank, (b) fiberglass tank, when the moving electrode on the half of the initial distance.

B. Simulation Results of Different Designs Assuming that liquid conductivity is constant, different design combinations were simulated. The power dissipation and corresponding resistances are listed in table IV.

TABLE IV SIMULATION RESULTS OF DIFFERENT LRS DESIGNS

Type

Design Combinations Tank shape

Electrode shape

Power Dissipated (MW)

Liquid Resistance (Ω)

1

box

box

2.188674

18.43

2

Cylinder

1.753981

22.99

3

Plate

1.876235

21.50

4

Sphere

1.431331

28.18

box

2.089808

19.30

6

Cylinder

1.696506

23.77

7

Plate

1.650691

24.43

8

Sphere

1.401413

28.78

5

Cylinder

Fig. 13. Potential distribution graphs, (a) design type 7, (b) design type 8

VIII.

Fig. 10. Potential distribution graphs, (a) design type 1, (b) design type 2

DISCUSSION

A. The Existing and different Electrolyte Tank Materials As shown in Table III, the largest resistance value was introduced by the LRS that has the fiber glass tank, because fiber glass is a good insulation material in spite of its weak mechanical strength. On the other hand, the iron tank design has the smallest resistance, because of “leakage” current through the walls, since iron is a good conducting material. From this comparison it is concluded that that the liquid tank material has a significant effect on the value of LRS resistance during the starting process, because the resistance of the tank walls in effect partly parallels the liquid resistance. The epoxy coated iron tank design gives the best solution to the existing LRS, because it has the dual advantage of offering high resistance, and the ability better to resist the mechanical and thermal stress that leads to cracks in the electrolyte tank and causes system failure. When the position of moving electrode was changed to center of the displacement between the bottom and top of the fiberglass tank, the LRS resistance reduced from 18.43 ohm to 12.72 ohm. This means that the LRS resistance is roughly proportional to the distance between the bottoms of electrolyte tank and its top electrode.

Fig. 11. Potential distribution graphs, (a) design type 3, (b) design type 4

Fig. 14. Electrical circuit simple model of the effect of the tank material

Fig. 12. Potential distribution graphs, (a) design type 5, (b) design type 6

B. Different Designs The resistance of LRS is affected by both the electrolyte tank shape and the electrode shape, if their volume and the conductivity are constant.

The largest values of the LRS resistance among these different designs were observed in design type 4 and design type 8 as in table IV, because the sphere electrode has the smallest surface area. In these two types of design, the box electrolyte tank (type 8) has the highest resistance (28.78 ohm), because the walls of the cylinder tank have fixed distance (0.39628m) from the center of the electrode. In the design type 4, the distances from the electrode center along length and width of the box vary. IX.

CONCLUSION

The three phase squirrel cage induction motor is widely used in industry to drive different types of load. One of the cheapest starters of this motor is the liquid rheostat starters, because of its simple design and the inexpensive materials of which it is constructed compared to other types of starters. From the above results and discussion it was found that the finite element method is an effective tool to simulate and find suitable designs for the liquid rheostat, and to analyze effects of electrolyte tank material on the starter resistance. This will serve as an aid in selecting the proper material that optimizes both resistance and mechanical strength requirements. REFERENCES [1] [2]

[3] [4]

[5] [6] [7]

[8] [9]

Patrick J. Colleran, William E. Rogers, “Controlled starting of AC induction motors”, IEEE Transactions on Industry Applications, Vol. Ia-19, No. 6, November/December 1983. G. L. Mcfarl, W. Alvarez, “The liquid rheostat for speed control of wound rotor induction motors”, Paper 48-98, recommended by the AIEE industrial control committee and approved by the AIEE technical program commi1tteme for presentation at the AIEE winter general meeting, Pittsburgh, pa., January 26-30, 1948. W. Wilson, “Some notes on the design of liquid rheostats”, the Power Supply of the Central Mining-Rand Mines Group, Journal I.E.E., 1915, vol. 53, p. 609. Amoon H. Yuen, John D. Rittenhouse, Francis K. Fox, “Large woundrotor motor with liquid rheostat for refinery compressor drive”, Approved by the Petroleum Industry Committee for presentation at the IEEE Petroleum Industry Conf., San Francisco, Calif., August 24-26, 1964. IEEE Transactions On Industry And General Applications Wikipedia website [online], May 1, 2016. Olivier De Weck, Il Yong Kim, “Engineering design and rapid prototyping- finite element method”, Massachusetts Institute Of Technology, presentation, January 12, 2004. Chong Kiat Ng, “Simplified numerical based method for calculation of DC ground electrode resistance in multi-layered earth”, M.Sc. thesis, Univ. of Manitoba, Dept. Of Electrical and Computer Engineering, Manitoba, Canada, June 2000. Zhou Xixiang, Zhong Benshan, Brynjolfur Eyjolfsson, “Finite element resistivity modelling using specialized mesh structure”, The United Nations Univ., Geothermal Training Program, Iceland, April 1987. COMSOL Multiphysics 3.4 software package.