ISSN (Online) : 2454 -7190 ISSN (Print) 0973-8975 J.Mech.Cont.& Math. Sci., Vol.-13, No.-3, July-August (2018) Pages 159-172 Design approach to a wound towards optimization

1Pritish Kumar Ghosh, 2Pradip Kumar Sadhu, 3Amarnath Sanyal, *4DebabrataRoy, 5Biswajit Dutta 1,2Electrical Engineering, Indian Institute of Technology (Indian School of Mines), Dhanbad, 826004, India 3Ex Power Engineering, Jadavpur University, Kolkata,W.B.- 700032,India 4Electrical Engineering,Techno International Batanagar, South 24Parganas, W.B.- 700141,India 5ElectricalEngineering,Seacom Engineering College,Howrah,W.B.-711302,India

[email protected],[email protected],3ansanyal@yahoo. co.in,[email protected],[email protected],

*Corresponding author: Debabrata Roy,

Abstract

About 88% of the driving power is produced by 3-phase and single-phase induction motors. In most part it is by squirrel-cage motors, only a small fraction by the slip-ring or phase-wound type. It is because the cage-type motors are relatively inexpensive. But they suffer from low p.f. operation and low starting torque which cannot be manipulated by inserting resistance in the rotor circuit. Also, this type of induction motors is not easily speed-adjustable. Though a little more expensive, the slip-ring type induction motors do not have these disadvantages. Therefore, they are used as speed-adjustable drives and for drives where heavy duty starting is involved. The design of any kind of power equipment should be made cost-optimally in the present day competitive market. A new approach to reaching optimal solution has been shown in this paper by the method of sequential searching with respect to the chosen design variables. Also, another design has been made following a hybrid of analytical and synthetic approach. The design variables have been chosen from designers’ experience. In contrary to the popular belief that there is no need for going in for complexity of optimal design, the quasi-optimal solution may be obtained by the designer from his accumulated experience, we find that the idea is wrong. The optimal design approach saves a lot of money.

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J.Mech.Cont.& Math. Sci., Vol.-13, No.-3, July-August (2018) Pages 159-172 Keywords: Analytic design, synthetic design, hybrid design, optimal design, sequential searching, development of electrical engineering, Electrical applications. I. Introduction There are two types of induction motors in use- the squirrel cage and the phase-wound or slip-ring type. The squirrel cage type is cheaper, more robust and rugged and for these reasons it is used in almost all industrial applications. But the squirrel-cage type has torque limitations, they run at poor lagging power factor and are not easily speed-adjustable whereas torque, power factor etc. can be adjusted by various means in phase-wound types. Also the cage-type motors have poor starting torque and are unsuitable for heavy-duty starting. Hence, slip-ring types are used as adjustable drives and for high torque applications [I]. II. Constructional features and field of application In a wound-rotor induction motor, the rotor windings are connected to external resistances through slip rings.Adjustment of resistance allows control of the speed/torque characteristic of the motor. A low inrush current can start wound-rotor induction motors, by inserting high resistance into the rotor circuit; the resistance decreases as the motor accelerates. By employing slip-power recovery methods both speed and power factor can be adjusted. The rotor of a motor has more winding turns as compared to the squirrel- cage rotor. The induced voltage is higher and the current is lower, compared to a squirrel cage rotor. During the starting, a typical rotor has three terminals for the 3- phases connected to the slip rings. Each pole is wired in series with a variable power resistor. The rotor poles are switched to short circuit as soon as the motor reaches full speed.At the , the resistor reduces the field strength during start-up. Due to this, the inrush current reduces,higher starting torque provides another advantage over squirrel cage induction motor. In several forms of adjustable-speed drive, a wound-rotor motor is used. In certain types of variable-speed drives, wide speed range with high-energy efficiency is allowed, if the slip-frequency power is recovered from the rotor circuit and fed back to the supply.To supply external power to the rotor circuit in a doubly fed , the slip rings are used which in turn allows wide range speed control. Today speed control by use of slip ring motor is mostly superseded by induction motors with variable-frequency drives [I,V,XVII]. The schematic view of a slip-ring type motor is shown in fig. 1.

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J.Mech.Cont.& Math. Sci., Vol.-13, No.-3, July-August (2018) Pages 159-172 III. Optimization While computer programs are used for design calculations [XIII,XVII], the aim is always to reach an optimal solution through iterative procedure. Optimal solution is the best out of all feasible solutions with respect to a chosen objective function. The objective function may be maximum starting torque or maximum efficiency or minimum cost, subject to given constraints [IV,XV]. The cost of production of a slip-ring type motor depends on several design variables e.g. air-gap flux-density, current density in stator and rotor conductors, length/pole pitch ratio etc. The optimal solution subject to given constraints is sought by using mathematical programming techniques [IX]. Many designers have conducted extensive research on design optimization of induction motors. S.S. Sivaraju et al advanced a paper on novel design of induction motor enhancing the performance variables [XIX]. H.B. Ertran et al proceeded a new approach to optimal design of induction motors [VII]. R.N. Hasana emphasized on energy-saving through design optimization [VIII]. A large no. of authors used soft-computing techniques to reach the optimal design. R. Kannan et al [X] used PSO for optimization and V.P. Sakthivel et al applied the same [XVI] for economic design. C. Thanraj et al did the same with improved PSO [XX]. T. Tudorache et al used finite element methods [XXI], M. Cunkas et al, as well as A. Krishnamoorthy et al used genetic algorithm [III,XII] to reach the optimal solution. K. Ranjith Kumar et al worked on performance enhancement of slip-ring type induction motors [XIV]. F. Kentli advanced a paper on survey of design optimization through decades [XI] which gives a comprehensive study in this area. In this paper an attempt has been made to figure out the cost-optimal design under given constraints using classical techniques. Soft computing techniques have not been used as there is no ambiguity or uncertainty in the problem. However, a single mathematical expression for the objective function is very complex and is based on approximations. So the optimization has been sought through the design subroutine for slip-ring type motors, placed as a part of the multiple loop operation

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Figure1.Schematic view of a slip ring type induction motor IV. Bio gas through bio-methanation The over-all cost of production has been taken as the objective function. The key design variables [VI,XVII] are: ac = amp.conductor/m; Bav = average flux-density in the gap, height; width ratio of the slots, length: pole pitch ratio. The current density in the conductor is not separately treated as a variable as it depends on the choice of ac. In addition, there are some decision variables e.g. the choice for the conductor materials: copper or Aluminium, particularly for rotor, the choice of core materials etc. V. Theconstrains There is generally a no. of inequality constraints in a design problem that may be imposed by the customer or the authorities [IX,XV]. Limits are imposed on maximum temperature rise at full load, minimum efficiency and minimum power factor. Also there may be specifications demanding a certain minimum value of maximum torque/full load torque and starting torque/full load torque, maximum starting current/full load current etc. the design must conform to these constraints and at the same time be fabricated for minimum possible cost. Therefore, the design is a constrained non-linear optimization problem. VI. Design procedure Analytical method gives only a feasible solution, not the best out of them. In the synthetic approach, it may be possible to bring forth some changes so as to conform to the specs. However, it has got limitations and is unable to reach the optimal solution. To reach the optimal solution, some logically sound iterative procedure is to be followed, which in multiple steps converges to the optimal for

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J.Mech.Cont.& Math. Sci., Vol.-13, No.-3, July-August (2018) Pages 159-172 a given objective function. Every design variable has its bounds. If all of them are varied within their respective bounds at regular interval and an exhaustive search is made for the minimality of the cost function, it will be reached. However, this procedure takes longer computation time and larger memory. Therefore, mathematically more effective methods like gradient search etc. are normally used [IV,VII,XV]. By running the program, it has been found that the hypersurface of the cost function is concave. Taking advantage of this finding, we have made a sequential gradient search on the chosen design variables and we have been able to reach the minimal in much smaller no. of steps. Thus, the method has been found to be very effective in searching for the optimal.

VII. Case-study The case-study has been made on a 15 kW, 415 V, 3-phase, 50 Hz., delta- connected slip-ring type induction motor. Three variables have been chosen as design variables: the average flux-density in the gap, amp.conductor/m and the length/pole pitch ratio for which the bounds are given in standard test-books and handbooks [II,XVIII]. The design has to conform to the following specs: Efficiency: ; at full voltage without any series resistance in the rotor circuit, no load current ≤30%.Temperature rise ≤50°C. The first case-study has been made by hybrid approach (analytic + synthetic). Then, the 2nd. case-study has been made by running a specially constructed program to reach the optima. The following solutions have been reached: Specifications: K.W. Output = 15 kW; Line voltage = 415 V; Frequency = 50 Hz.; rated speed = 1430 R.P.M Constraints: both effy and p.f. at full load ≥0.85; no load current ≤ 30%; temp. rise of stator ≤ 50°C; max. torque/full load torque ≥ 2.5. Case study 1: Hybrid approach (Analytic + Synthetic) Chosen design variables (form designer’s experience): Amp. -Conductor/m = 32000; Average Flux-density = 0.460 Tesla; Length/Pole-pitch Ratio = 1.250 (to get best possible p.f.); Stator connection = DELTA (so that star-delta may be used);

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J.Mech.Cont.& Math. Sci., Vol.-13, No.-3, July-August (2018) Pages 159-172 Core material is Special Lohys; Conductor material: Copper (for both stator and rotor) Stator current density = 4.5 A/mm2; Rotor current density = 5 A/mm2 Assumed efficiency = 0.87; Assumed p.f.= 0.87 Computations: Input in KVA = 19.818;No. of Poles = 4; Synchronous R.P.S = 25 Output-coefficient = 153.82; D2L-Product = 0.00515 m3 Stator length = 170 mm; Stator bore diameter = 175 mm Net length of iron = 147 mm; No. of ducts = 1 Pole pitch =137 mm; Flux/pole = 0.01075 Waber No. of stator slots = 36; No. of stator slots/pole/phase = 3 Stator slot pitch = 15 mm; Stator slot angle = 20°; Stator connection: DELTA Pitch factor of stator = 0.9848; Breadth factor of stator = 0.9598; Winding factor of stator = 0.9452 No of stator conductors/slot = 30; Total no. of stator conductors = 1080 No of stator turns/phase = 180; Stator phase current = 37.10 A No of parallel conductors in stator = 2; SWG No. of stator conductors = 18½ Area of stator conductor = 0.9810 mm2; Diameter of stator conductor = 1.1176 mm Fine DCC insulation has been used. Diameter of stator conductor with insulation = 1.2976 mm; Total copper area/stator slot = 58.86 mm2 Parallel teeth & trapezoidal slots have been used for the stator. Width of stator teeth = 7mm; Stator wedge = 4 mm; Stator lip = 1 mm Width of stator slot over wedge = 8mm; Width of stator slot at bottom = 12 mm Depth of stator slot = 21 mm; Copper space factor in stator = 0.275 Area of stator core = 0.00448 m2; Depth of stator core = 30 mm; Outer diameter of stator = 278 mm

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J.Mech.Cont.& Math. Sci., Vol.-13, No.-3, July-August (2018) Pages 159-172 Gap contraction factor: Carter's coefficient for stator slot = 0.675; Carter’s coefficient for duct = 0.796 Carter's coefficient for rotor slot = 0.515; Gap contraction factor for stator slot = 1.124 Gap contraction factor for rotor slot = 1.023; Gap contraction factor for duct = 1.049 Equivalent gap contraction factor = 1.207; Full load slip = 0.04613 Full load operating speed = 1431 rpm; Air-gap length = 0.55 mm Rotor diameter = 173.9 mm; No. of rotor slots/pole/phase = 4 No. of rotor slots = 48; Full pitch bar winding is being used for the rotor; 3-phase. Rotor pitch factor = 1; Rotor breadth factor = 0.95766; Rotor winding factor = 0.95766 Rotor winding no. of turns/phase = 64; Rotor winding connection: STAR Rotor winding phase voltage = 146.245 V; Rotor length = 160.0 mm Rotor slot pitch = 11.4 mm; Depth of rotor core = 30.4 mm Inner diameter of rotor = 71.1 mm; Shaft diameter = 46 mm Flux-density at 1/3 rd. tooth height of rotor = 0.535 Tesla Min. width of rotor teeth = 2.322 mm Performance Analysis: Stator copper loss = 1114.7 W; Percent stator copper loss = 6.46 Rotor ohmic loss = 744.0 W; Percent slip at full load = 4.613; Speed at full load = 1431 R.P.M. Inner diameter of rotor = 71 mm; Diameter of shaft = 46 mm Magnetizing current: AT reqd. for airgap = 331; AT required for stator teeth = 74; AT required for rotor teeth =3 AT required for stator core = 19; AT required for rotor core = 6; Total AT required = 432 Magnetizing current = 4.34 A; Magnetizing current in % = 27.27 Rotational loss current = 0.27 A; Rotational loss current in % = 1.72 No Load current = 4.35 A; No load current in % = 27.33

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J.Mech.Cont.& Math. Sci., Vol.-13, No.-3, July-August (2018) Pages 159-172 Friction and windage loss = 330.0 W; Stator teeth Loss =114.1 W; Stator core Loss = 133.2 W Stator Iron Loss = 247.2 W; Percentage iron Loss = 1.43 Percentage efficiency = 86.03 Leakage reactance: Leakage reactance due to slotting = 0.69 Ω; Leakage Reactance due to overhang = 1.55 Ω Leakage reactance due to zigzag = 1.49 Ω; Leakage Reactance = 3.73 Ω Leakage reactance in percent = 14.74; Temperature rise of stator = 41.74°C Stator resistance = 1.466 Ω; Rotor resistance referred to stator = 0.431 Ω Equivalent resistance referred to stator = 1.897 Ω; Equivalent impedance referred to stator = 4.182 Ω Starting current = 96.3 A; Starting torque = 79.97 N-m Full load torque = 102.31 N-m; Full load current = 37.10 A Full load power factor = 0.9046; Starting/Full load current = 6.048 Starting/Full load torque = 0.782 (enough as starting torque will be increased by inserting resistance in the rotor circuit.); Maximum torque = 296.52 N-m Maximum/Full load torque = 2.898 (Overload capacity is enough) Cost Analysis: Specific cost in Indian market at present: Lohys core- Rs.125/- per Kg.; Copper- Rs. 580/- per Kg. Weight of iron = 35.23Kg; Cost of iron = Rs.4404/- Weight of copper = 7.18Kg; Cost of copper = Rs. 4163/- Cost of other materials taken as 80% = Rs. 6853/- Total cost of materials = Rs.15420/- Taking 20% as labour charge and 50 % as establishment charges including sales and distribution, the selling cost = Rs. 27756/-.

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J.Mech.Cont.& Math. Sci., Vol.-13, No.-3, July-August (2018) Pages 159-172 Case study 2: Optimal solution The optimal solution is reached by sequential searching against each variable. The specifications are same, as well as specific costs of material. Only slight variations have been made in the design variables. Chosen design variables (through program): Amp. -Conductor/m = 32500; Average flux-density = 0.465; Length/Pole-pitch Ratio = 1.2 Stator current density = 5.2 A/mm2; Rotor current density = 4 A/mm2 Computation Input in KVA = 19.818; Output-Coefficient = 157.93; No. of Poles= 4 Synchronous R.P.S = 25; D2L-Product = 0.00502 m3 Stator length = 165 mm; Stator bore diameter = 175 mm Net length of iron = 143 mm; No. of ducts = 1 Pole pitch =137 mm; Flux/pole = 0.01055 Waber No. of stator slots = 36; No. of stator slots/pole/phase = 3 Stator slot pitch = 15 mm; Stator slot angle = 20o Stator connection: DELTA Pitch factor of stator = 0.9848; Breadth factor of stator = 0.9598; Winding factor of stator = 0.9452 No of stator conductors/slot = 30; Total no. of stator conductors = 1080 No of stator turns/phase = 180; Stator phase current = 36.66 A No of parallel conductors in stator = 2; SWG No. of stator conductors = 19 Area of stator conductor = 0.8107 mm2; Diameter of stator conductor = 1.0160 mm Fine DCC insulation has been used Diameter of stator conductor with insulation = 1.196 mm; Total copper area/stator slot = 48.64 mm2 Parallel teeth and trapezoidal slots have been used for the stator.

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J.Mech.Cont.& Math. Sci., Vol.-13, No.-3, July-August (2018) Pages 159-172 Width of stator teeth= 7 mm; Stator wedge = 4 mm; Stator lip = 1 mm Width of stator slot over wedge = 8 mm; Width of stator slot at bottom = 12 mm Depth of slot = 21 mm; Copper space factor in stator = 0.228 Area of stator core = 0.00439 m2; Depth of stator core = 31 mm Outer diameter of stator = 279 mm Gap contraction factor: Carter's coeff. for stator slot = 0.675; Carter’s coeff. for duc t= 0.796; Carter's coeff. for rotor slot = 0.515 Gap contraction factor for stator slot = 1.124; Gap contraction factor for rotor slot = 1.023 Gap contraction factor for duct =1.051; Equivalent gap contraction factor = 1.209 Rotor winding: Airgap length = 0.55 mm; Rotordiameter = 173.9 mm No. of rotor slots/pole/phase = 4; No. of rotor slots = 48 Full pitch bar winding is being used for the rotor; 3-phase winding is being used. Rotor pitch factor = 1; Rotor breadth factor = 0.95766; Rotor winding factor = 0.95766 Rotor winding no. of turns/phase = 64; Rotor winding connection: STAR Rotor winding phase voltage = 143.49 V Rotor length = 155 mm; Rotor slot pitch = 11.4 mm Depth of rotor core = 30.8 mm; Inner diameter of rotor = 70.3 mm Shaft diameter = 46mm; Flux-density at 1/3 rd. tooth height of rotor = 0.542 Tesla Inner diam. of rotor = 70 mm; Min. width of rotor teeth = 2.387 mm Performance variables: Full load slip = 0.03813; Percent slip = 3.813

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J.Mech.Cont.& Math. Sci., Vol.-13, No.-3, July-August (2018) Pages 159-172 Full load operating speed = 1443 rpm Stator copper loss = 1331 W; Percent Stator copper loss = 7.72 Rotor ohmic loss = 606.6 W; Magnetizing current: AT reqd. for airgap = 335; AT reqd. for stator teeth = 74 AT reqd. for rotor teeth = 3; AT reqd. for stator core = 19 AT reqd. for rotor core = 6; Total AT reqd.= 436 Mag. current = 4.38 A; Mag. current in Percent = 27.53 Losses and efficiency: Rotational loss current = 0.27 A; Rotational loss in percent = 1.72 No load current = 4.39 A; No load current in percent = 27.58 Friction and windage loss = 330 W Stator teeth loss = 110.5 W; Stator core loss = 130.8 W; Stator iron Loss = 241.3 W Percentage iron loss = 1.40; Percentage efficiency = 85.67 Leakage reactance: Leakage Reactance due to slotting = 0.67Ω Leakage Reactance due to overhang = 1.55Ω Leakage Reactance due to zigzag = 1.48 Ω Leakage Reactance = 3.69 Ω Leakage Reactance in percent=14.60 Temperature rise of stator = 46.8°C Other performance criteria: Stator resistance = 1.751 Ω; Rotor resistance refd. to stator = 0.351 Ω; Eqv.resistance refd. to stator = 2.102 Ω; Eqv. impedance refd. to stator = 4.249 Ω

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J.Mech.Cont.& Math. Sci., Vol.-13, No.-3, July-August (2018) Pages 159-172 Starting Current = 94.7A; Starting torque = 62.64 N-m Full load torque =101.46 N-m; Full load current = 36.66 A; Full load power factor = 0.9065 lagging. Starting/Full load current = 5.952; Starting/Full load torque=0.617 Maximum Torque in N-m = 275.59; Maximum/Full Load Torque=2.716 Cost Analysis: Weight of iron = 34.502 kg.; Cost of iron = Rs. 4313/- Weight of copper = 5.85 Kg.; Cost of copper = Rs. 3395/- Cost of other materials taken as 80% = Rs. 6166/- Total cost of materials = Rs.13874/- Direct cost including 20% labour = Rs. 16649/- Selling cost including 50% overheads = Rs.24973/- Check against specs: Table .1 All Specifications

Item Speed, Efficienc p.f. at Temp. No load Max/f.l Selling rpm y at f.l., f.l., lag rise, °C current, torque cost, Rs. % %

Specified 1430 85 0.9 50 30 2.5 ------

Hybrid 1431 86.03 0.9046 41.74 27.33 2.892 27756/-

Optimal 1443 85.67 0.9065 46.8 27.53 2.716 24973/-

It may be noted that all the specs have been fulfilled in both the cases, but the overall cost is much lower in the optimal design approach.

VIII. Conclusion

It should be noted that the specifications have been fulfilled both for the hybrid and the optimal approach. However, there is a price differential which is quite large. In the hybrid approach, additional cost is Rs. 2783/- i.e. about 10% of the cost as compared to the optimal design. The temperature rise is a little higher but it is quite safe for the usual class B insulating material. There is little

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J.Mech.Cont.& Math. Sci., Vol.-13, No.-3, July-August (2018) Pages 159-172 difference in efficiency, no load current and the power factor. The slip is lower for the optimal case. From this study, it is evident that design of power electrical equipment should always be made on the basis of optimality in the present competitive market. The cost optimality can be changed or extended to optimality of chosen design variables e.g. maximum torque, efficiency or power factor by suitably modifying the objective function.

Reference

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